Answer:
Simple interest is calculated using initial principle while compound interest is calculated considering the interest also .
Step-by-step explanation:
Interest is the cost of borrowing money, where the borrower pays a fee to the lender for using his money. The interest, typically expressed as a percentage, can either be compounded or simple .
Simple interest is based on the principal amount , while compound interest is based on the principal amount and the interest that adds onto it in every period and the final principle is used for calculating the interest.
Simple interest is calculated on the principal amount of a loan and it's easier to find out than compound interest.
Diane is a software saleswoman. Let y represent her total pay (in dollars). Let x represent the number of copies of English is Fun she sells. Suppose that x and y are related by the equation =+160090xy. Answer the questions below. Note that a change can be an increase or a decrease. For an increase, use a positive number. For a decrease, use a negative number.
1.What is the change in Mary's total pay for each copy of English is Fun she sells?
2.What is Mary's total pay if she doesn't sell any copies of English is Fun? ?
There is an error in the equation provided. Looking at other similar question such as this, I think the equation related to x and y should be 90x + 1600 = y
Answer:
a) 90
b) 1600
Step-by-step explanation:
The equation 90x + 1600 = y is an equation of a straight line in the form y = mc + c
Adjusting the equation to the general form we get
y = 90x + 1600
m = 90
c = 1600
a) the change in Mary's total pay for each copy she sells in this case is referring to the change of y to the change of x.
In other word, it is the slope of the function.
m = 90
b) if Mary didn't sell any copies, the value of x will be 0.
In graph of a straight line, the value when x= 0 is at the value of y-intercept,
c = 1600
How tall is a tree which is 15 feet shorter than a pole that is 3 times as tall as the tree?
Step-by-step explanation:
Let t be the height of pole.
Given that the tree is 5 feet shorter than a pole.
Height of pole = t + 15
Also given that the pole is 3 times as tall as the tree.
Height of pole = 3t
So we have
t + 15 = 3t
2t = 15
t = 7.5 feet
Height of tree = 7.5 feet
The question asks how tall a tree is if it is 15 feet shorter than a pole which is three times its height. The height of the tree can be found by setting up an equation to represent the problem and then solving for the height of the tree, which is 7.5 feet.
Explanation:The subject of this question is a mathematical problem dealing with a tree and a pole with their heights related to one another. In the problem, we know that the pole is 15 feet taller than a tree and the pole is also 3 times as tall as the tree. We can set that up as an equation and solve for the height of the tree.
Let's call the height of the tree as 'T' and then, because the pole is three times the height of the tree, we can call the pole's height as '3T'. The problem tells us that the pole is also 15 feet taller than the tree, so we can express the pole's height as 'T + 15' as well.
Now we have two ways to express the pole's height: '3T' and 'T + 15'. We can set those equal to each other and solve for 'T'.
3T = T + 15
Subtract 'T' from both sides to get:
2T = 15
Then divide both sides by 2 and you get T = 7.5. Therefore, the tree is 7.5 feet tall.
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After she creates the budget above, Zoe moves in with a roommate so she can save money for a car. Her rent is now 25 percent of her salary. Which of these should she do to buy a car quickly? Increase savings to 15 percent and increase entertainment to 20 percent Increase savings to 15 percent and increase gas to 15 percent Increase savings to 25 percent and decrease clothing to 10 percent Increase savings to 30 percent?
Answer:
Increase savings to 25 percent and decrease clothing to 10 percent
Step-by-step explanation:
i got it right
Zoe should increase her savings to 25% of her income and reduce non-essential expenses like clothing to save for a car more quickly.
Explanation:To assist Zoe in saving money for a car quickly after moving in with a roommate and having her rent reduced to 25% of her salary, she should adjust her budget to allocate more towards savings.
The most effective strategy for this goal would be to:
Increase savings to a higher percentage of her income.Reduce or maintain other expense categories at a lower percentage to compensate for the increased savings.Specifically, increasing savings to 25% of her income and decreasing clothing expenses to 10% is an advisable option.
She should avoid increasing expenses in non-essential categories like entertainment or gasoline if her goal is to save for a car as quickly as possible.
One of the lightest smartphones on the market today weighs 113 g. To protect your phone, you may want to use a screen protector, which weighs 27.2 g, and a heavy duty phone case, which weighs 114 g. What is the total weight of the phone, screen protector, and case?
Answer:
154.2g
Step-by-step explanation:
This is quite straightforward, what we need to add the masses together.
113g + 114g + 27.2g = 154.2g
The total weight of the smartphone, screen protector, and heavy duty phone case is 254.2 grams.
Explanation:Given that the smartphone weighs 113 g, the screen protector weighs 27.2 g, and the heavy duty phone case weighs 114 g, the total weight (in gram) of the phone, screen protector, and case would simply be the sum of these weights. In this case, we take 113 g + 27.2 g + 114 g which results in 254.2 g as the total weight. Therefore, if you use both a screen protector and a heavy duty case to protect your phone, the total weight would be 254.2 g.
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In a January 2017 Washington Post-ABC News poll, respondents were asked "There is a proposal to offer nearly 140 billion dollars in tax cuts for private companies if they pay to build new roads, bridges and transportation projects. The companies then could charge tolls for people to use these roads, bridges and transportation. Do you support or oppose this proposal?" Of the 1005 people polled, 66 percent of those surveyed said they oppose the above proposal. An objective of this study is to
Answer:
estimate a population proportion
Step-by-step explanation:
The choices are missing in the question, correct question is:
In a January 2017 Washington Post-ABC News poll, respondents were asked “There is a proposal to offer nearly 140 billion dollars in tax cuts for private companies if they pay to build new roads, bridges and transportation projects. The companies then could charge tolls for people to use these roads, bridges and transportation. Do you support or oppose this proposal?” Of the 1005 people polled, 66 percent of those surveyed said they oppose the above proposal. An objective of this study is to ________ .
a. test a claim about a population mean
b. estimate a population mean
c. test a claim about a population proportion
d. estimate a population proportion
Population proportion estimate will give the percentage of people who support or oppose the proposal of 140 billion dollars in tax cuts for private companies so that they build charge tolled new roads, bridges and transportation projects.
People are asked "Do you support or oppose this proposal?", this shows that the purpose of the study is to estimate a population proportion.
The Washington Post-ABC News poll aimed to calculate public opinion on a policy proposal regarding tax cuts and infrastructural developments paid by private companies. The majority of respondents opposed the proposal signifying its unpopularity among the surveyed population. However, results from this single poll may not represent wider public sentiment.
Explanation:The question pertains to a public policy proposal. In a Washington Post-ABC News poll from January 2017, participants were asked to indicate their support or opposition to a proposition concerning tax cuts and infrastructure development funded by private companies. The question revolves around an actual policy proposal that could have impacts on the economy and society. The study's objective in this case is to gauge public opinion on the proposal, which could be used to inform policy decisions or strategies by politicians, businesses, or advocacy groups.
The fact that 66 percent of the 1005 people polled opposed the proposal suggests a majority of the respondents were not in favor of the plan. In recognizing such data and understanding its implications, it is important to remember that this is just one poll and may not necessarily represent the broader public's views.
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Choose the correct graph of the given system of equations.
y + 2x = −1
3y − x = 4
A.) graph of two lines that intersect at the point negative 1, 1, with text on graph that reads One Solution negative 1, 1
B.) graph of two lines that intersect at the point 1, 1, with text on graph that reads One Solution 1, 1
C.) graph of two parallel lines with positive slopes with text on the graph that reads No Solution
D.) graph of two lines on top of each other with text on graph that reads Infinitely Many Solutions
A.) graph of two lines that intersect at the point negative 1, 1, with text on graph that reads One Solution negative 1, 1
Step-by-step explanation:
The two simultaneous equation given are;
y+2x= -1
3y-x=4
multiply the first equation by 1 and the second equation by 2 to make the terms with x equal
y+2x = -1
6y-2x=8
-------------- ---add the terms with x to eliminate x
7y=7 -------divide both sides by 7 to remain with y
7y/7 =7/7
y= 1 -----use the value of y in the first equation
y+2x= -1
1+2x= -1
2x= -2
2x/2= -2/2
x= -1
The solution is (-1,1)
You can plot the equations on a graph tool as shown below to visualize the solution where the two linear equations intersect
See attached graph
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graph of two lines that intersect at the point negative 1, 1, with text on graph that reads One Solution negative 1, 1
Jim places $10,000 in a bank account that pays 9.8% compounded continuously. After 2 years, will he have enough money to buy a car that costs $12 comma 160? If another bank will pay Jim 10% compounded semiannually, is this a better deal?
Final answer:
Jim will not have enough money to buy the car after 2 years with a bank account that pays 9.8% interest compounded continuously. The other bank offering 10% interest compounded semiannually is a better deal as Jim will have enough money to buy the car.
Explanation:
To determine if Jim will have enough money to buy a car that costs $12,160 after 2 years with a bank account that pays 9.8% interest compounded continuously, we can use the formula for compound interest:
A = P * e^(rt)
where A is the ending amount, P is the principal (initial amount), e is Euler's number (approximately 2.71828), r is the interest rate, and t is the number of years. Plugging in the values, we have:
A = $10,000 * e^(0.098*2) = $10,000 * e^0.196 ≈ $11,961.34
Therefore, Jim will not have enough money to buy the car.
To determine if the other bank offering 10% interest compounded semiannually is a better deal, we can use the same formula:
A = P * (1 + r/n)^(nt)
where n is the number of times interest is compounded per year. Plugging in the values, we have:
A = $10,000 * (1 + 0.10/2)^(2*2) = $10,000 * (1 + 0.05)^4 = $10,000 * 1.05^4 ≈ $12,265.63
Therefore, the other bank is a better deal as Jim will have enough money to buy the car.
You have to decide between two different companies that sell dirt. Company A sells dirt for $137.5 for 50 square feet and has a delivery fee of $100 dollars. Company B sells dirt for $15 for 5 square feet and offers free delivery. How much dirt do you need to buy for both companies to charge the same.
You need to buy 400 square feet of dirt for both companies to charge the same
Solution:
Given that,
Company A sells dirt for $137.5 for 50 square feet and has a delivery fee of $100 dollars
Dirt sold for $137.5 for 50 square feet
Let us find dirt sold for 1 square feet:
50 square feet = $ 137.5
1 square feet = [tex]\frac{137.5}{50} = 2.75[/tex]
Thus dirt sold for $2.75 for 1 square feet
Company A has a delivery fee of $ 100 dollars
Amount Charged by company A:
Let "x" be the amount of dirt bought for 1 square feet
A = 2.75(x) + 100
A = 2.75x + 100 --- eqn 1
Company B sells dirt for $15 for 5 square feet and offers free delivery
Dirt sold for $ 15 for 5 square feet
5 square feet = $ 15
1 square feet = [tex]\frac{15}{5} = 3[/tex]
Thus dirt sold for $ 3 for 1 square feet
Company B offers free delivery
Amount Charged by company B:
A = 3x ---- eqn 2
Let us equate eqn 1 and eqn 2 to find the dirt you need to buy for both companies to charge the same
2.75x + 100 = 3x
3x - 2.75x = 100
0.25x = 100
x = 400
Thus you need to buy 400 square feet of dirt for both companies to charge the same
Exhibit 5-3 The probability distribution for the number of goals the Lions soccer team makes per game is given below. Number of Goals Probability 0 .05 1 .15 2 .35 3 .30 4 .15 Refer to Exhibit 5-3. What is the probability that in a given game the Lions will score less than 3 goals?
Answer:
0.55 is the probability that Lions will score less than 3 goals.
Step-by-step explanation:
We are given the following in the question:
Number of goals(x): 0 1 2 3 4
Probability: 0.05 0.15 0.35 0.30 0.25
We have to find the probability that Lions will score less than 3 goals.
[tex]P(X<x) = \displaystyle\sum_{X=0}^{X=x-1}P(x_i)\\\\P(x<3)=P(x=0)+P(x=1)+P(x=2)\\P(x<3)=0.05 + 0.15 + 0.35=0.55[/tex]
0.55 is the probability that Lions will score less than 3 goals.
Final answer:
The probability that the Lions soccer team will score less than 3 goals in a game is 0.55 or 55%.
Explanation:
To find the probability that the Lions soccer team scores less than 3 goals in a game, we need to add up the probabilities of scoring 0, 1, and 2 goals. From Exhibit 5-3, the probability of scoring 0 goals is 0.05, 1 goal is 0.15, and 2 goals is 0.35.
The total probability of scoring less than 3 goals is the sum of these probabilities:
P(0 goals) = 0.05
P(1 goal) = 0.15
P(2 goals) = 0.35
Thus, P(score < 3 goals) = P(0 goals) + P(1 goal) + P(2 goals) = 0.05 + 0.15 + 0.35 = 0.55.
Therefore, the probability that the Lions will score less than 3 goals in a given game is 0.55 or 55%.
From the point on the ground 500 ft from the base of a building, it is observed that the angle of elevation to the top of the building is 24 degrees and the angle of tlevation to top top of a flagpole atop the building is 27 degress. Find the height of the building and the length of the flagpole.
Answer:
building: 222.61 ftflagpole: 32.15 ftStep-by-step explanation:
The tangent function of an angle in a right triangle is the ratio of the opposite side to the adjacent side. Here, the adjacent side is 500 ft, so we have ...
tan(24°) = (building height)/(500 ft)
building height = (500 ft)tan(24°) ≈ 222.61 ft
__
Similarly, the height to the top of the flagpole is ...
total height = (500 ft)tan(27°) ≈ 254.76 ft
The length of the flagpole is the difference of these heights:
flagpole length = 254.76 ft -222.61 ft = 32.15 ft
The height of the building is 222.61 ft; the length of the flagpole is 32.15 ft.
The height of the building is approximately 250.4 feet, and the length of the flagpole is approximately 24.4 feet, according to the principle of trigonometry using tangent function.
Explanation:The question deals with a mathematical concept called trigonometry. Specifically, we will use the tangent function. Tangent of an angle in a right triangle is the ratio of the side opposite to the angle over the side adjacent to the angle.
Let's denote H as the height of the building and F as the length of the flagpole. We know that Tan(24°) = H / 500 and Tan(27°) = (H+F) / 500. Now we can solve these two equations to find H and F.
First, calculate H. Using the first equation, H = Tan(24°) * 500 ≈ 250.37 feet.
Next, calculate H+F. Using the second equation, H+F = Tan(27°) * 500 ≈ 274.73 feet.
Then, calculate F by subtracting H from the second result. So F = 274.73 - 250.37 = 24.36 feet.
Therefore, the height of the building is approximately 250.4 feet, and the length of the flagpole is approximately 24.4 feet.
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A group of 444 friends is playing cards. The deck has 707070 cards. To start the game, the dealer makes a pile of 151515 cards in the center. Then she deals the remaining cards one at a time to each player until all the cards are gone. What is the greatest number of cards any player will have after all the cards are dealt?
Answer:
The correct answer is 14 not 17 or 7
Step-by-step explanation:
Find the regression equation, letting the first variable be the
predictor (x) variable.
Using the listed duration and interval after times, find the best predicted "interval after" time for an eruption with a duration of 253 seconds. How does it compare to an actual eruption with a duration of 253 seconds and an interval after time of 83 minutes?
Duration - 242 - 255 - 227 - 251 - 262 - 207 - 140
Interval After - 81 - 81 - 92 - 102 - 94 - 91
Answer:
[tex]y=0.00673(253) +90.190=91.894[/tex]
And the difference is given by:
[tex]r_i =91.894-83=8.894[/tex]
Step-by-step explanation
We assume that th data is this one:
x: 242-255 -227-251-262-207-140
y: 91- 81 -91 - 92 - 102 - 94 - 91
Find the least-squares line appropriate for this data.
For this case we need to calculate the slope with the following formula:
[tex]m=\frac{S_{xy}}{S_{xx}}[/tex]
Where:
[tex]S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}[/tex]
[tex]S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}[/tex]
So we can find the sums like this:
[tex]\sum_{i=1}^n x_i =242+255+227+251+262+207+140=1584[/tex]
[tex]\sum_{i=1}^n y_i =91+ 81 +91 + 92 + 102 + 94 + 91=642[/tex]
[tex]\sum_{i=1}^n x^2_i =242^2 +255 ^2 +227^2 +251^2 +262^2 +207^2 +140^2=369212[/tex]
[tex]\sum_{i=1}^n y^2_i =91^2 + 81 ^2 +91 ^2 + 92 ^2 + 102 ^2 + 94 ^2 + 91^2=59108[/tex]
[tex]\sum_{i=1}^n x_i y_i =242*91 +255*81 +227*91 +251*92 +262*102 +207*94 +140*91=145348[/tex]
With these we can find the sums:
[tex]S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=369212-\frac{1584^2}{7}=10775.429[/tex]
[tex]S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=145348-\frac{1584*642}{7}=72.571[/tex]
And the slope would be:
[tex]m=\frac{72.571}{10775.429}=0.00673[/tex]
Now we can find the means for x and y like this:
[tex]\bar x= \frac{\sum x_i}{n}=\frac{1584}{7}=226.286[/tex]
[tex]\bar y= \frac{\sum y_i}{n}=\frac{642}{7}=91.714[/tex]
And we can find the intercept using this:
[tex]b=\bar y -m \bar x=91.714-(0.00673*226.286)=90.190[/tex]
So the line would be given by:
[tex]y=0.00673 x +90.190[/tex]
The prediction for 253 seconds is:
[tex]y=0.00673(253) +90.190=91.894[/tex]
And the difference is given by:
[tex]r_i =91.894-83=8.894[/tex]
Arianna claims that the rectangles shown below are similar, while Miguel claims that they are not similar.
Whose claim is correct and why?
A
Miguel is correct because the two rectangles are not oriented in the same direction.
B
Arianna is correct because the four angles of the smaller rectangle are the same as the four angles of the larger rectangle.
C
Arianna is correct because the smaller rectangle has side lengths that are half the size of the side lengths of the larger rectangle.
D
Miguel is correct because the measures of the sides of the smaller rectangle are not proportional to the measures of the sides of the larger rectangle.
Answer:
D
Step-by-step explanation:
.
Which of the following is NOT an arithmetic sequence?
A) 4, 7, 10, 13, 16
B) 1, 2, 3, 4, 5
C) 15, 9, 3, -3, -9
D) 2, 4, 8, 16, 32
Answer:
D) 2, 4, 8, 16, 32
Step-by-step explanation:
We have given four sets of sequence.
And we have to find out which sequence is not an arithmetic sequence.
For this the given sequences should satisfy the value of common difference(d) and Arithmetic Progression formula.
A.P. Formula,
[tex]T_n=a+(n-1)d[/tex]
Where [tex]T_n[/tex] = nth term of an A.P.
a = first term of an A.P.
n = number of terms.
d = common difference.
'd' is calculated by subtracting fist term from second term.
[tex]d = second\ term-first\ term[/tex]
A) 4, 7, 10, 13, 16
[tex]d = 7-4=3[/tex]
[tex]d = 10-7=3[/tex]
Here d=3 and 5th term is 16.
So we find out the 5th term by using the formula of A.P. To check whether the sequence is in A.P. or not.
[tex]T_5=4+(5-1)3=4+4\times\ 3=4+12=16[/tex]
Here the given sequence fulfills the condition of being in A.P.
Hence the given sequence is an arithmetic sequence.
B) 1, 2, 3, 4, 5
[tex]d =2-1=1[/tex]
[tex]d =3-2=1[/tex]
Here d=1 and 5th term is 5.
[tex]T_5=1+(5-1)1=1+4=5[/tex]
Here the given sequence fulfills the condition of being in A.P.
Hence the given sequence is an arithmetic sequence.
C) 15, 9, 3, -3, -9
[tex]d =9-15=-6[/tex]
[tex]d =3-9=-6[/tex]
Here d=-6 and 5th term is -9.
[tex]T_5=15+(5-1)-6=15+4\times -6=15+(-24)=-9[/tex]
Here the given sequence fulfills the condition of being in A.P.
Hence the given sequence is an arithmetic sequence.
D) 2, 4, 8, 16, 32
[tex]d_1=4-2=2[/tex]
[tex]d_2=8-4=4[/tex]
Here [tex]d_1=2\ But\ d_2=4[/tex]
The common difference between the terms is not same.
In case of [tex]d_1[/tex].
[tex]T_5=2+(5-1)2=2+4\times 2=2+8=10[/tex]
In case of [tex]d_2[/tex].
[tex]T_5=2+(5-1)4=2+4\times 4=2+16=18[/tex]
Here the given sequence does not fulfills the condition of being in A.P.
Hence the given sequence is not an arithmetic sequence.
Hence the correct option is D) 2, 4, 8, 16, 32.
You are riding your bicycle. It takes you 9 minutes to go 2.5 miles. If you continue traveling at the same rate, how long will it take you to go 9 miles.
A survey has a margin of error of +/- 4%. In the survey, 67 of the 110 people interviewed said they would vote for candidate A. If there are 9570 people in the district, what is the range of the number of people who will vote for candidate A?
A. 5956 to 6260 people
B. 5596 to 6062 people
C. 5695 to 6620 people
D. 5569 to 6026 people
Answer:
option B
Step-by-step explanation:
given,
sample of person interviewed 110
people voted for A = 67
percentage of the person voted for A = [tex]\dfrac{67}{110}[/tex]
= 0.609
now, for all the people
= 0.609 x 9570
= 5829 people
now compensating the error
+ 4 % = 1.04 x 5829 = 6062 people
- 4 % = 0.96 x 5829 = 5596 people
so, the range of people voted for candidate A is
5596 to 6062 People
Hence, the correct answer is option B
The area of the bottom of a shoebox can be written as a(x) = 2x2 - 4 and the height of the shoebox can be written as h(x) = 3x + 2. write an expression to represent the volume v(x) of the shoebox.
a.v(x) = 6x3 - 8
Answer:V(x) = 6x³ + 4x² - 12x - 8
Step-by-step explanation:
The shoe box can either be cube shaped or cubiod shaped. The volume of the box is length × breadth × height
Since Area = Length × Breadth
Volume = Area × Height
V(x) = A(x) × H(x)
A(x) = 2x² - 4
H(x) = 3x + 2
V(x) = (2x² - 4)(3x + 2)
V(x) = 6x³ + 4x² - 12x - 8
Jane had 27 stickers two weeks ago. She was buying stickers each day for those two weeks. She bought 3 stickers two weeks ago, and on each day she bought two more stickers than she bought on the previous day. How many stickers does she have now?
Answer:
At Present Jane has Total Stickers = 251
Step-by-step explanation:
Stickers Initially = 27
Jane bought stickers on 1st day = 3
Remaining days = 13
Each next day she bought 2 more stickers than the previous day, so:
Stickers bought in the last 2 weeks (14 days) = n+(n+2)+(n+2+2)+(n+2+2+2)+.............+(n+2(13))
here n =3
So:
Stickers bought in the last 2 weeks (14 days) = 3+5+7+9+11+13+15+17+19+21+23+25+27+29
Stickers bought in the last 2 weeks (14 days) = 224
At Present Jane has Total Stickers = Stickers Initially+ Stickers bought in the last 2 weeks (14 days)
At Present Jane has Total Stickers = 27+224
At Present Jane has Total Stickers = 251
Which choice could be the equation of a line parallel to the line represented by this equation?
3x− 2y = 6
a. 2x− 3y = 6
b. y=3/2x+4
c. 5x− y = −2
d. y=2/3x-8
A necklace at Jared is originally $99. It is on sale for 10% off. If there is a 3% tax on the DISCOUNTED PRICE, what is the total price of the necklace? Round to the nearest cent!
Answer: the total price of the necklace is $91.8
Step-by-step explanation:
The original Price of the necklace at Jared is is $99. It is on sale for 10% off. This means that there is a discount on the original price. The discount is 10/100 × 99 = $9.9
The new price of the necklace at Jared is the original price - the discount. It becomes
99 - 9.9 = $89.1
If there is a 3% tax on the discounted price, the amount of tax would be 3/100×89.1 = $2.673
The total cost of the necklace will be new cost + the amount of tax. It becomes
89.1 + 2.673 = $91.8
I really need help ASAP
Answer choices: 101,19,50,60,79
A=
B=
C=
D=
E=
Answer:
Step-by-step explanation:
1) The sum of the angles on a straight line is 180 degrees. This means that
51 + b + 110 = 180
161 + b = 180
b = 180 - 161 = 19 degrees
2) Angle a = 60 degrees. This is so because they are vertically opposite angles.
3)The sum of angles in a triangle is 180 degrees. Therefore
angle a + angle b + angle c
60 + 19 + c = 180
79 + c = 180
c = 180 - 79 = 101 degrees
4) d + c = 180(sum of the angles on a straight line is 180 degrees). Therefore
d + 101 = 180
d = 180 - 101 = 79 degrees.
5) e + 51 + b + a = 180( sum of the angles in a triangle is 180 degrees). Therefore
e + 51 + 60 + 19 = 180
e + 130 = 180
e = 180 - 130 = 50 degrees
The formula s = StartRoot StartFraction S A Over 6 EndFraction EndRoot gives the length of the side, s, of a cube with a surface area, SA. How much longer is the side of a cube with a surface area of 1,200 square inches than a cube with the surface area of 768 square inches?
Answer:
[tex]2\sqrt{2}\ ft\ longer[/tex]
Step-by-step explanation:
Area Of A Cube
Suppose a cube with side length s, the area of one side is
[tex]A_s=s^2[/tex]
Since the cube has 6 sides, the total area is
[tex]A=6A_s=6s^2[/tex]
But if we have the area, we can solve the above formula for s to get
[tex]A=6s^2[/tex]
[tex]\displaystyle s=\sqrt{\frac{A}{6}}[/tex]
We have two different cubes with areas 1,200 square inches and 768 square inches. Let's compute their side lengths
[tex]\displaystyle s_1=\sqrt{\frac{1,200}{6}}=\sqrt{200}[/tex]
[tex]\displaystyle s_1=10\sqrt{2}\ ft[/tex]
[tex]\displaystyle s_2=\sqrt{\frac{768}{6}}=\sqrt{128}[/tex]
[tex]\displaystyle s_2=8\sqrt{2} ft[/tex]
The difference between them is
[tex]10\sqrt{2}\ ft-8\sqrt{2}\ ft=2\sqrt{2}\ ft\approx 2.83\ ft[/tex]
The side of the cube with area 1,200 square inches is [tex]2\sqrt{2}\ ft[/tex] longer then the side of the cube with area 768 square inches
Answer:
Its B
Step-by-step explanation:
Edge 2021
Asking for help in the following question #1 and #2 are based of algebra 2.
≅
⇒⇒⇒⇒⇒⇒
Answer:
Step-by-step explanation:
For the first one, revenue - cost = profit. We have equations for revenue and profit, so filling in:
[tex]-.3x^2+150x-cost=-.5x^2+250x-300[/tex]
Let's add cost to both sides to make it positive and bring everything on the right over to the left and combine like terms:
[tex].2x^2-100x+300=cost[/tex]
For the second one:
P(x)*T(x) = [tex](x^2-3x-7)(3x)[/tex]
Distribute the 3x into everything inside the parenthesis to get
[tex]3x^3-9x^2-21x[/tex]
For the second part of that problem, C(x)*P(x) = [tex](x-4)(x^2-3x-7)[/tex]
Distribute the x into everything first to get:
[tex]x^3-3x^2-7x[/tex]
The distribute the -4 into everything to get:
[tex]-4x^2+12x+28[/tex]
Combine the like terms and put everything together to get
[tex]x^3-7x^2+5x+28[/tex]
A journalist is interested in whether there is a significant difference in the salary offered to electrical engineering and chemical engineering graduates at the University of Texas at Austin. She reviews the statistics for starting annual salaries for 2013-2014 and finds the following:
The test statistic is t = 2.4693, with a p-value of 0.0142. Which of the following is an appropriate conclusion?
The samples provide evidence that there is a statistically significant difference between the starting salary of chemical engineering and electrical engineering graduates at the University of Texas at Austin for 2013-2014.
The samples do not provide statistically significant evidence that there is a difference in starting salaries of chemical engineering and electrical engineering graduates at the University of Texas at Austin for 2013-2014.
We cannot use the t-test in this case because the variables (starting salary of engineering graduates) may not be normally distributed.
Answer:
the appropriate conclusion is that
The samples provide evidence that there is a statistically significant difference between the starting salary of chemical engineering and electrical engineering graduates at the University of Texas at Austin for 2013-2014.
Step-by-step explanation:
Since the p-value is small, it indicates statistically significant results. This means that there is a statistically significant difference between the starting salary of chemical engineering and electrical engineering graduates at the University of Texas at Austin for 2013-2014.
The samples provide evidence of a statistically significant difference in the starting salaries between chemical engineering and electrical engineering graduates at the University of Texas at Austin for 2013-2014, as indicated by the p-value of 0.0142, which is below the 0.05 significance level.
Detailed explanation:
The journalist's question concerns whether there is a significant difference in the starting salaries of chemical engineering and electrical engineering graduates at the University of Texas at Austin for the academic year 2013-2014. The test statistic is t = 2.4693 with a p-value of 0.0142.
The samples provide evidence that there is a statistically significant difference between the starting salary of chemical engineering and electrical engineering graduates at the University of Texas at Austin for 2013-2014. This conclusion is reached because the p-value is less than the common significance level of 0.05, thus we reject the null hypothesis, which states that there is no difference in starting salaries between the two groups.
Hence the final answer is that there is a statistically significant difference between the starting salary of chemical engineering and electrical engineering graduates at the University of Texas at Austin for 2013-2014
Hence the first option is correct
Statistics show that ________ of homeless adults living in shelters experience mental illness.
Answer:
26%
Step-by-step explanation:
For similar questions check the following link for flash cards:
https://quizlet.com/207660833/chapter-16l23-25-flash-cards/
The question is about the incidence of mental illness among homeless adults in shelters. The specific percentage is not provided, but the rate is recognized as high, indicating the need for mental health resources to effectively address homelessness.
Explanation:The question you've asked is related to the prevalence of mental illness among homeless adults residing in shelters. A specific percentage is not given, but it is commonly understood that a significant percentage of the homeless population does struggle with mental illness. However, it is essential to note that the exact percentage can vary due to different factors, such as location, available resources, and demographics. Hence, this information accentuates the need for mental health resources in addressing and alleviating homelessness.
Learn more about Mental Illness here:https://brainly.com/question/33861241
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A civics teacher asked her students to indicate whether they believed each of two headlines. One headline was false and the other was true, but the students did not know this. The probability that a student selected at random believed the true headline was 90% and the probability that the student believed the false headline was 82%. She found that 75% of the students believed both headlines. In this sample, are the events "believed the false headline" and "believed the true headline" mutually exclusive?
Answer:
Not mutually exclusive
Step-by-step explanation:
In the rule of probability, for two events to be mutually exclusive, the probability of them occuring at the same time must be 0.
In this case P(true and false) = 0 to be mutually exclusive.
In the term of Vann diagram 'true and false' in this case represent the intersection of two events 'true' and 'false'. And if it is shown in Vann diagram, both group will be apart from each other or the value inside the Vann diagram is 0.
Therefore,
We know from statistics that
P(A and B) = P(A) + P(B) - P(A or B)
Translating into this case
P(true or false) = P(true) + P(false) - P(true and false)
= 0.9 + 0.82 - 0.75 = 0.97
Therefore, this event is not mutually exclusive.
Answer:
no and 0.97
Step-by-step explanation:
Mrs. Allan's car uses 8 gallons of gas for a 224-mile trip. Mrs. Owen's car uses 6 gallons of gas for a 210-mile trip. How many gallons of gas would each car use if both cars traveled 560 miles?
Answer:
Mrs. Allan's Car will use 20 gallons of gas for 560 miles trip.
Mrs. Owen's Car will use 16 gallons of gas for 560 miles trip.
Step-by-step explanation:
Given:
Number of Miles for Mrs Allan car = 224 miles
Number of gallons of gas required = 8
We need to find the number of gallons of gas required for 560 miles for Mrs. Allan's car.
First we will find, in 1 gallons how many miles does Mrs Allan's Car drives.
For 8 gallons = 224 miles
So for 1 gallons = Number of miles in 1 gallon of gas
By using Unitary method we get;
Number of miles in 1 gallon of gas = [tex]\frac{224}{8}= 28\ miles[/tex]
Now we know that;
for 28 miles = 1 gallon of gas is required.
So for 560 miles = Number of gallon of gas required in 560 miles.
Again by using Unitary method we get;
Number of gallon of gas required in 560 miles = [tex]\frac{560}{28}= 20\ gallons[/tex]
Hence Mrs. Allan's Car will use 20 gallons of gas for 560 miles trip.
Also Given:
Number of Miles for Mrs Owen's car = 210 miles
Number of gallons of gas required = 6
We need to find the number of gallons of gas required for 560 miles for Mrs. Owen's car.
First we will find, in 1 gallons how many miles does Mrs Owen's Car drives.
For 6 gallons = 210 miles
So for 1 gallons = Number of miles in 1 gallon of gas
By using Unitary method we get;
Number of miles in 1 gallon of gas = [tex]\frac{210}{6}= 35\ miles[/tex]
Now we know that;
for 35 miles = 1 gallon of gas is required.
So for 560 miles = Number of gallon of gas required in 560 miles.
Again by using Unitary method we get;
Number of gallon of gas required in 560 miles = [tex]\frac{560}{35}= 16\ gallons[/tex]
Hence Mrs. Owen's Car will use 16 gallons of gas for 560 miles trip.
A group of 40 children attend a baseball game. Each child received either a hotdog or a bag of popcorn. Hotdogs were $2.25 and popcorn was $1.75. If the total bill was $83.50, how many hotdogs and bags of popcorn were purchased
Answer:
27 hot dogs13 bags of popcornStep-by-step explanation:
Had all received popcorn, the bill would have been 40×$1.75 = $70. The bill was $13.50 more than that. Each hot dog purchased in place of popcorn adds $0.50 to the bill, so the number of hot dogs must be ...
$13.50/$0.50 = 27
Of course, the remainder of the 40 items were popcorn, so 13 bags of popcorn.
27 hot dogs and 13 bags of popcorn were purchased.
If f is a continuous function such that the integral from 1 to 4 of f of x, dx equals 10, evaluate the integral from 2 to 8 of 2 times f of 2 times x, dx.
Answer: 10
Step-by-step explanation:
Since integral from 1 to 4 of f(x) =10
To evaluate integral from 2 to 8 of 2 times f(2x), using substitution method
Let U = 2x, dU = 2dx, dx = dU/2
Evaluate the limit, upper limit gives dU = 2*4 = 8, lower limit gives dU = 2*1 = 2.
Since this limit are the same as the limit for the question,
Therefore, F(4) - F(1) = F(8) - F(2) = 10
Substituting dx=dU/2
Gives,
Integral from 2 to 8 of 2 times f(2x)= (1/2)(2)(F(8)-F(2)) = 10
Answer
Step-by-step explanation:
answer c
Cans of regular Coke are labeled as containing 12 oz12 oz. Statistics students weighed the contents of 88 randomly chosen cans, and found the mean weight to be 12.0912.09 ounces. Assume that cans of Coke are filled so that the actual amounts are normally distributed with a mean of 12.00 oz12.00 oz and a standard deviation of 0.1 oz0.1 oz. Find the probability that a sample of 88 cans will have a mean amount of at least 12.09 oz12.09 oz.
Answer: 0.0055
Step-by-step explanation:
Let [tex]\overline{x}[/tex] denotes the sample mean amount that can has.
We assume that cans of Coke are filled so that the actual amounts are normally distributed with a mean of 12.00 oz and a standard deviation of 0.1 oz.
i.e. [tex]\mu=12[/tex] and [tex]\sigma=0.1[/tex]
sample size : n= 8
Then, the probability that a sample of 88 cans will have a mean amount of at least 12.09:
[tex]P(\overline{x}\geq12.09)=1-P(\overline{x}<12.09)\\\\=1-P(\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}<\dfrac{12.09-12}{\dfrac{0.1}{\sqrt{8}}})\\\\=1-P(z<2.5456)\ \ [\because z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=1-0.9945\ \ [\text{By z-table}]\\\\=0.0055[/tex]
Hence, the required sample size = 0.0055