Answer:
(3/4)(√3)r²
Step-by-step explanation:
The largest such triangle is an equilateral triangle. It will have a side length of r√3. The area can be found a number of ways, one of which is to use the formula for the area of an equilateral triangle of side length s:
A = s²·(√3)/4
Using s=r√3, we get ...
A = (3/4)(√3)r²
Which statements are true about reflections? Check all that apply.
An image created by a reflection will always be congruent to its pre-image.
An image and its pre-image are always the same distance from the line of reflection
If a point on the pre-image lies on the line of reflection, the image of that point is the same as the pre-image.
The line of reflection is perpendicular to the line segments connecting corresponding vertices.
The line segments connecting corresponding vertices are all congruent to each other.
The line segments connecting corresponding vertices are all parallel to each other.
Answer:1 2 34 6
Step-by-step explanation:
Just answered it
Answer:
1,2,3,4,6
Step-by-step explanation:
Edge 2021
Factor the expression below.
x^2-10x+25
A.
(x - 5)(x - 5)
B.
5(x2 - x + 5)
C.
(x + 5)(x + 5)
D.
(x - 5)(x + 5)
Answer:
A. [tex]\displaystyle (x - 5)^2[/tex]
Step-by-step explanation:
Find two quantities that when added to −10, they are also multiplied to 25, and that number is a double −5.
I am joyous to assist you anytime.
Final answer:
The expression x^2-10x+25 can be factored as (x - 5)(x - 5).
Explanation:
The expression x^2-10x+25 can be factored as (x - 5)(x - 5). To factor the expression x^2-10x+25, we need to find two numbers that when multiplied together give us 25 (the constant term), and when added together give us -10 (the coefficient of the x term). In this case, the two numbers are -5 and -5. Therefore, the factored form of the expression is (x - 5)(x - 5), which is the same as option A.
The entire school of students were surveyed, a total of 950 students. 75% or students said they preferred chocolate ice cream to vanilla. How many students prefer chocolate ice cream?
Answer:
Number of students who prefer chocolate ice cream is approximately 713.
Step-by-step explanation:
Given,
Total number of students = 950
Students who prefer chocolate ice cream = 75%
We have to find out number of students who prefer chocolate ice cream.
For calculating number of students who prefer chocolate ice cream, we have to multiply total number of students with given percentile of students.
Now framing the above sentence in equation form, we get;
Number of students who prefer chocolate ice cream = [tex]950\times75\%[/tex]
Now we have to remove the percentile.
For this we have to divide 75 by 100, we get;
Number of students who prefer chocolate ice cream =[tex]950\times\frac{75}{100}=\frac{71250}{100}=712.50\approx713[/tex]
Hence Number of students who prefer chocolate ice cream is approximately 713.
Susan is celebrating her birthday by going out to eat at five guy's for burgers. If the bill in $40 and she wants to leave a tip if 15%, how much will the tip be?
Answer:
$6
Step-by-step explanation:
Susan can easily figure the tip by the following procedure. 10% of the bill is the amount with the decimal point moved one place to the left, so is $4.00. 5% of the bill is half that, or $2.00.
15% of the bill is 10% + 5%, so is $4.00 +2.00 = $6.00. The tip will be $6.00.
Cindy goes to the market and spends $15 on 2 lbs of apples and 3 lbs of grapes. The grapes cost $2.45 per pd.
How much is one pound of apples?
Answer:
The apples cost $3.82 per pounds.
Step-by-step explanation:
We are given the following in the question:
Cost of grapes = $2.45 per pd
Total money spent = $15
Total purchasing = 2 lbs of apples and 3 lbs of grapes
Total cost of grapes =
[tex]=\text{Cost of grapes}\times \text{Amount of grapes}\\= 2.45\times 3 = 7.35\$[/tex]
Total cost of apples =
[tex]\text{Total cost} - \text{Total cost of grapes}\\= 15 - 7.35 = 7.65\$[/tex]
Cost of apple =
[tex]= \dfrac{\text{Total cost of apple}}{\text{Amount of apple}}\\\\= \dfrac{7.65}{2} = 3.825\$\text{ per pound}[/tex]
Thus, the apples cost $3.82 per pounds.
Answer: one pound of apple costs $3.825
Step-by-step explanation:
Let x represent the cost of one pound of apple.
Total amount spent on 2 lbs of apple and 3 lbs of grapes is $15
The grapes cost $2.45 per pound. This means that the total cost of 3 lbs of grapes would be
2.45 × 3 = $7.35
Since Cindy spent a total of $15, it means that
2x + 7.35 = 15
Subtracting 7.35 from both sides of the equation, it becomes
2x + 7.35 - 7.35 = 15 - 7.35
2x = 7.65
x = 7.65/2 = $3.825
A 15 ft. Ladder is placed against a building so that the distance from the top of the ladder to the ground is 10 ft. Find the distance (to the nearest tenth) from the bottom of the ladder to the building
Answer:
11.2 ft
Step-by-step explanation:
Assuming the building meets the ground at right angles, the right triangle formed has side length 10 ft and hypotenuse 15 ft. Then the other side length (d) is given by the Pythagorean theorem as ...
d² + 10² = 15²
d² = 225 -100 = 125
d = √125 = 5√5 ≈ 11.2 . . . feet
The bottom of the ladder is about 11.2 feet from the building
Which rule describes a linear relation?
A) Double x and subtract five to get y.
B) Multiply x and y to get 20.
C) Multiply x times itself and add five to get y.
D) Divide 40 by x to get y.
A linear relation is described by an equation of the form y = mx + b, where m is the slope and b is the y-intercept. None of the options provided describe a linear relation.
Explanation:A linear relation is described by a linear equation of the form y = mx + b, where m is the slope and b is the y-intercept. Option A, "Double x and subtract five to get y," does not fit this form. Options B, C, and D do not fit this form either. Therefore, none of the given options describe a linear relation. The correct answer is none of the above.
If the instructions for a problem ask you to use the smallest possible domain to completely graph two periods of y = 5 + 3 cos 2(x - pi / three ), what should be used for Xmin and Xmax? Explain your answer.
please try to keep the ans short yet easy to understand >
Answer:
Xmin = π/3 and Xmax = 7π/3
Step-by-step explanation:
I assume that the function is:
y = 5 + 3 cos² (x − π/3)
cos² x has a period of π, so to graph two periods, you need a domain that is 2π wide, so:
Xmax − Xmin = 2π
You can choose any values you want for Xmax and Xmin, so long as they are 2π units apart. To make it easy to graph, you'll probably want to choose Xmin = π/3 and Xmax = 7π/3.
Graph:
desmos.com/calculator/9w3pptakde
At a summer camp there is one counselor for every 6 campers. Write a direct variation equation for the number of campers, y, that there are for x counselors. Then graph.
Answer:
The direct variation equation can be given as:
[tex]y=6x[/tex]
Step-by-step explanation:
Given:
At a summer camp there are 6 campers under one counselor.
To find the direct variation equation for the number of campers in terms of number of counselor.
Solution:
[tex]y\rightarrow[/tex] Number of campers
[tex]x\rightarrow[/tex] Number of counselors
We have [tex]y[/tex] ∝ [tex]x[/tex]
The direct variation equation can be written as:
[tex]y=kx[/tex]
where [tex]k[/tex] is the direct variation constant.
There are 6 campers under one counselor. Using this statement we can find value of [tex]k[/tex]
Given: when [tex]x=1[/tex] then [tex]y=6[/tex]
We have,
[tex]6=k(1)[/tex]
∴ [tex]k=6[/tex]
Thus, the direct variation equation can be given as:
[tex]y=6x[/tex]
We can find the points using the equation to plot.
[tex]x[/tex] [tex]y=6x[/tex]
0 0
1 6
2 12
The graph is sown below.
Spends a total of $38.75 on 5 drinks and 2 bags of popcorn. Noah spends a total of $37.25 on 3 drinks and 4 bags of popcorn. Write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn.
Answer:
3d + 4p = $37.25
5d + 2p = $38.75
Actual Answer:
Bag of popcorn is $5
A drink is $5.75
Step-by-step explanation:
Let drinks = d
Let popcorn = p
Noah: 3d + 4p = $37.25
Other: 5d + 2p = $38.75
Choose a variable to eliminate (We'll choose p)
3d + 4p = $37.25
(5d + 2p = $38.75) -2
Distribute
-10d - 4p = -77.5
The -4p cancels out the 4p, then we combine
-7d = -40.25
Divide both sides by -7
-7d/-7 = -40.25/-7
d = 5.75
Back to 3d + 4p = $37.25
Substitute d with 5.75
3(5.75) + 4p = $37.25
17.25 + 4p = 37.25
Move the constant to the other side
17.25 + 4p = 37.25
-17.25 -17.25
4p = 20
Divide both sides by 4
4p/4 = 20/4
p = 5
Strawberries are $2.50 A pound and cantaloupes are $2.25 at the local supermarket. Sally bought 7 pounds of the two kinds of fruit for a family breakfast. If she spent exactly $16.75 and bought at least 1 pound of each fruit how many pounds of fruit did she buy there is no sales tax
Answer:
Sally bought 4 pounds of Strawberries and 3 pounds of Cantaloupes.
Step-by-step explanation:
Let the number of pounds of Strawberries bought by Sally = x
Let the number of pounds of Cantaloupes bought by Sally = y
[tex]\[x + y = 7\][/tex] ---------------------------------(1)
Moreover,
[tex]\[2.5 x + 2.25 y = 16.75\][/tex] ---------------(2)
Solving (1) and (2) by substitution:
[tex]\[x = 7 - y\][/tex]
=> [tex]\[2.5 *(7-y) + 2.25 y = 16.75\][/tex]
=> [tex]\[17.5 - 2.5y + 2.25 y = 16.75\][/tex]
=> [tex]\[0.25y = 0.75\][/tex]
=> [tex]\[y = 3\][/tex]
From (1), x = 7-3 = 4
A café owner wanted to compare how much revenue he gained from lattes across different months of the year. What type of variable is ‘month’?
Final answer:
The 'month' variable referenced by the café owner is a categorical variable used to group revenue data across different time periods within a year.
Explanation:
In the context of the café owner's situation, the type of variable that 'month' represents is a categorical variable. A categorical variable is one that has two or more category values and can be used to group or label individuals or items in a dataset. In this case, 'month' is used as a means to categorize the revenue data collected over different time periods within a year, allowing the café owner to compare the performance of latte sales across these distinct categories.
A figura a seguir representa a planta de um apartamento . O dono desse apartamento deseja colocar carpete na sala e no dormitório .Sabendo que o metro quadrado colocado do carpete escolhido custa 48reais quanto o dono do apartamento deverá gastar?
Answer:
O dono deverá gastar 1764 reais
Step-by-step explanation:
Oi!
Em anexo, você encontrará a figura do apartamento que encontrei na web.
Para encontrar a superfície do tapete que o proprietário precisa comprar, precisamos encontrar a superfície do dormitório e da sala.
Superfície do dormitório:
A superfície do dormitório é calculada multiplicando a base pela altura do retângulo.
Da figura:
base = 3,5 m
altura = 3 m
Superfície do tapete do dormitório = 3,5 m · 3 m = 10,5 m²
A superfície da sala de estar é a superfície do retângulo composto pela sala e pelo banheiro menos a superfície do banheiro:
superfície da sala de estar = superfície do retângulo sala / banheiro - superfície do banheiro
Superfície do banheiro:
Conhecemos um lado do banheiro: 2 m
O outro lado será:
lado do banheiro = 9 m - 3,5 m - 3,5 m = 2 m
Então, a superfície do banheiro será:
Superfície do banheiro = 2 m · 2 m = 4 m²
Superfície da sala / banheiro
A altura do retângulo é (3 m + 2,5 m) 5,5 m
A base do retângulo é (9 m - 3,5 m) 5,5 m
Então, a superfície da sala / banheiro é (5,5 m) ² = 30,25 m²
Superfície da sala
A superfície da sala será igual à superfície da sala / banheiro menos a superfície do banheiro:
Superficie da sala = 30,25 m² - 4 m² = 26,25 m²
A superfície do tapete será (26,25 m² + 10,5 m²) 36,75 m²
Como cada metro quadrado custa $ 48, o proprietário terá que gastar
(48 reais / m² · 36,75 m²) 1764 reais.
Tenha um bom dia!
June and Stella can each create six floral arrangements in one hour. If they take in 372 Valentineâs Day orders, how many hours will they need to fulfill them?
Answer:
31 hours
Step-by-step explanation:
June and Stella can create 6 floral arrangements in one hour.
They take in 372 Valentine's Day order
No of hours = orders / (June's rate + Stella's rate)
June's rate = 6 arrangements / hour
Stella's rate = 6 arrangements / hour
June's rate + Stella's rate = 2(6 arrangements /hour)
= 12 arrangements / hour
No of hours = 372 arrangements / 12 arrangements / hour
= 31 hours
June and Stella have 31 hours to fulfill the 372 Valentine's Day order
Which point satisfies the equation 2x+3y=8
A) (1,4)
B) (2,2)
C) (-1,3)
D) (-2,4)
The subject property is a four-bedroom, two-bath, two-car-garage home in a new subdivision. Comp A is a three-bedroom, two-bath home with a screened-in porch that sold for $365,500. The appraiser values the porch at $12,500 and estimates the bedroom adjustment at $22,000. What is A's adjusted sale price?
Answer: $375,000
Step-by-step explanation:
Given : The subject property is a four-bedroom, two-bath, two-car-garage home in a new subdivision.
Comp A is a three-bedroom, two-bath home with a screened-in porch that sold for $365,500.
I.e. It has one less bedroom and one extra porch .
i.e. It requires to add one bedroom and remove screened-in porch .
Since ,The appraiser values the porch at $12,500 and estimates the bedroom adjustment at $22,000.
So , the A's adjusted sale price would become
Selling price of Comp A + Value of bedroom - Value of porch
= $365,500 + $22,000- $12,500
= $375,000
Hence, A's adjusted sale price= $375,000
Suppose that in the maintenance of a large medical-records file for insurance purposes the probability of an error in processing is 0.0010, the probability of an in filing is 0.0009, the probability of an error in retrieving is 0.0012, the probability of an error in processing as well as filing is 0.0002, the probability of an error in processing as well as retrieving is 0.0003, and the probability of an error in processing and filing as well as retrieving is 0.0001. What is the probability of making at least one of these errors? (P(R intersection F)=0.0002) Be sure to draw a Venn diagram.
Answer:
The probability of making at least one of these errors is 0.0025
Step-by-step explanation:
Consider the provided information.
Let P represents the error in processing.
Let F represents the error in filling.
Let R represents the error in retrieving.
The probability of an error in processing is 0.0010: P(P) = 0.0010
The probability of an in filing is 0.0009: P(F) = 0.0009
The probability of an error in retrieving is 0.0012: P(R) = 0.0012,
The probability of an error in processing as well as filing is 0.0002:
P(P∩F) = 0.0002
The probability of an error in processing as well as retrieving is 0.0003,
P(P∩R) = 0.0003
The probability of an error in processing and filing as well as retrieving is 0.0001.
P(P∩F∩R)=0.0001
P(R∩F)=0.0002
The probability of at least one is:
P(P∪F∪R)=P(P)+P(R)+P(F)-P(P∩F)-P(P∩R)-P(R∩F)+P(P∩F∩R)
P(P∪F∪R)=0.0010+0.0009+0.0012-0.0002-0.0002-0.0003+0.0001
P(P∪F∪R)=0.0025
Hence, the probability of making at least one of these errors is 0.0025
The required diagram is shown below.
The Rockwell hardness index for steel is determined by pressing a diamond point into the steel and measuring the depth of penetration. For 50 specimens of a certain type of steel, the Rockwell hardness index averaged 62 with a standard deviation of 8. The manufacturer claims that this steel has an average hardness index of at least 64. Test this claim at the 1% significance level?
Answer:
We conclude that the steel has an average hardness index of at least 64.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 64
Sample mean, [tex]\bar{x}[/tex] = 62
Sample size, n = 50
Alpha, α = 0.051
Sample standard deviation, s = 8
First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu = 64\\H_A: \mu < 64[/tex]
We use one-tailed(left) z test to perform this hypothesis.
Formula:
[tex]z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }[/tex]
Putting all the values, we have
[tex]z_{stat} = \displaystyle\frac{62 - 64}{\frac{8}{\sqrt{50}} } = -1.767[/tex]
Now, [tex]z_{critical} \text{ at 0.05 level of significance } = -2.33[/tex]
Since,
[tex]z_{stat} > z_{critical}[/tex]
We fail to reject the null hypothesis and accept the null hypothesis. Thus, we conclude that the steel has an average hardness index of at least 64.
This means that there is not enough evidence to support the claim that the average hardness index is less than 64.
To test the manufacturer's claim, we can conduct a one-sample z-test. The null hypothesis is that the average hardness index is 64, and the alternative hypothesis is that the average hardness index is less than 64.
Given:
Sample size (n) = 50 Sample mean [tex](\(\bar{x}\))[/tex] = 62Population standard deviation = 8 Population mean under the null hypothesis= 64First, we calculate the standard error (SE) of the mean:
[tex]\[ SE = \frac{\sigma}{\sqrt{n}} = \frac{8}{\sqrt{50}} \approx 1.1314 \][/tex]
Next, we calculate the test statistic (z):
[tex]\[ z = \frac{\bar{x} - \mu_0}{SE} = \frac{62 - 64}{1.1314} \approx -1.7679 \][/tex]
Now, we need to find the critical z-value for a one-tailed test at the 1% significance level.
From the standard normal distribution table, the critical z-value for the 99th percentile is approximately 2.326.
Since the calculated z-value (-1.7679) is greater than the critical z-value (-2.326), we fail to reject the null hypothesis.
This means that there is not enough evidence to support the claim that the average hardness index is less than 64.
A triangle is drawn on the coordinate plane. It is translated 4 units right and 3 units down. Which rule describes the
translation?
(x, y) - (x + 3, y - 4)
(x, y) - (x +3, y + 4)
(x, y) - (x + 4, y-3)
(x, y) - (x + 4, y + 3)
Answer:
[tex](x,y) - (x + 4, y-3)[/tex]
Step-by-step explanation:
Given:
A triangle is drawn on the coordinate plane. It is translated 4 units right and 3 units down.
It is translated 4 units right and 3 units down.
We need to find the rule of translation.
Solution:
Now to the right of the axis which is positive of X axis and 4 units to the right means 4 units are added to X co-ordinate.
Also to the Down of the axis which is negative of Y axis and 3 units to the down means 3 units are Subtracted to Y co-ordinate.
Hence The co-ordinates at which triangle is drawn is [tex](x + 4, y-3)[/tex]
The number of E.coli bacteria cells in a pond of stagnant water can be represented by the function below, where A represents the number of E.coli bacteria cells per 100 mL of water and t represents the time, in years, that has elapsed.
A(t)=136(1.123)^4t
Based on the model, by approximately what percent does the number of E.coli bacteria cells increase each year?
A.
60%
B.
59%
C.
41%
D.
40%
Answer:
Option B. 59%Explanation:
The function that represents the number of E.coli bacteria cells per 100 mL of water as the time t years elapses is:
[tex]A(t)=136(1.123)^{4t}[/tex]The base, 1.123, represents the multiplicative constant rate of change of the function, so you just must substitute 1 for t in the power part of the function:
[tex]rate=(1.123)^{4t}=(1.123)^4=1.590[/tex]Then, the multiplicative rate of change is 1.590, which means that every year the number of E.coli bacteria cells per 100 mL of water increases by a factor of 1.590, and that is 1.59 - 1 = 0.590 or 59% increase.
John sells tickets to a school concert. Adult tickets cost $6.50 and children's tickets cost $4.50. John collects a total of 157.50 from the ticket sales and he sells twice as many adult tickets as children's tickets. How many tickets does he sell all together?
Answer: The total number of tickets that John sold is 27
Step-by-step explanation:
Let x represent the number of adult tickets that John sold at the concert.
Let y represent the number of children's tickets that John sold at the concert.
Adult tickets cost $6.50 and children's tickets cost $4.50. John collects a total of 157.50 from the ticket sales it means that
6.5x + 4.5y = 157.5 - - - - - - - - - -1
John sells twice as many adult tickets as children's tickets. This means that
x = 2y
Substituting x = 2y into equation 1, it becomes
6.5 × 2y + 4.5y = 157.5
13y + 4.5x = 157.5
17.5y = 157.5
y = 157.5/17.5 = 9
x = 2×9 = 18
The total number of tickets that John sold is 9 + 18 = 27
A train tunnel is modeled by the quadratic function h ( x ) = − 0.18 ^ 2 + 25 , where x is the distance, in feet, from the center of the tracks and h ( x ) is the height of the tunnel, also in feet. Assume that the high point of the tunnel is directly in line with the center of the train tracks.
Round your answers to the nearest tenth as needed.
a) What is the maximum height of the tunnel? feet.
b) How wide is the base of the tunnel? feet.
Answer:
a) 25 feet
b) Base width 23.57 feet
Step-by-step explanation: The expression:
h(x) = -0,18*x² + 25
is a quadratic function ( a parable). as a < 1 open down
The vertex of the parable is V(x,y)
a) V(x) = - b/2a = 0/2a V(x) = 0 to find V(y) we make use of the original equation and plugging x = 0
y = - 0.18*x² + 25 ⇒ y = 0 + 25 ⇒ y = 25
The Vertex is V ( 0 , 25 )
Now vertex in this case is the maximum height.
h(max) = 25 feet
b) To find how wide is the base of the tunnel. We have to consider that for h = 0 we are at ground level therefore the two roots of the quadratic equation will give the wide of the base of the tunnel
Then
h (x) = -018*x² +25 ⇒ 0 = -018*x² +25 ⇒ x² = 25/0.18
x² = 138.89
x = ± 11.79 ft
So we found interception with x axis and wide of the base is
2 * 11.79 = 23.57 feet
How many positive multiples of 7 that are less than 1000 end with the digit 3?
Answer:
14
Step-by-step explanation:
Ordinarily, a quick multiplication of 7 by other integers up to 10 indicates that only 7*9 yields 63, i.e ends with 3 as required.
Thus the set of possible multiples of the integer 7 ending with the digit 3 will form the arithmetic series with the first term being Ao = 63 and the common difference being d= 7*10= 70. That is we can see the series in details....
the nth term could be evaluated from the formular
An=Ao+(n-1)d (1)
The series could be explicitly depicted as follows:
9*7=63= 63+70*0
(10+9)*7=133 = 63+70*1
(20+9)*7=203=63+70*2
(30+9)*7=273=63+70*3
.................................
(130+9)*7=973=63+70*13
The last 'n' corresponding to the problem statement could be evaluated from equation (1), assuming An=1000:
1000=63+(n-1)*70
1000-63=70(n-1)
937/70=13.38=n-1
n=14.38
Thus the number of possible multiples of 7 less than 1000 ending with digit 3 will be 14.
Check: 7 times 142 is 994, so there are exactly 142 positive multiples of 7 less than 1000.
One tenth of these, ignoring the decimal fraction, end with a digit of 3.
A rectangular area is to be enclosed by a wall on one side and fencing on the other three sides. If 18 meters of fencing is are used, what is the maximum area that can be enclosed?
A: 9/2 m^2
B:81/4 m^2
C: 27 m^2
D: 40 m ^2
E: 81/2 m^2
Explanation:
Let L be the length and W be the width.
We have only 2 sides are fenced
Fencing = 2L + W
Fencing = 18 m
2L + W = 18
W = 18 - 2L
We need to find what is the largest area that can be enclosed.
Area = Length x Width
A = LW
A = L x (18-2L) = 18 L - 2L²
For maximum area differential is zero
So we have
dA = 0
18 - 4 L = 0
L = 4.5 m
W = 18 - 2 x 4.5 = 9 m
Area = 9 x 4.5 = 40.5 m² = 81/2 m²
Option E is the correct answer.
Terry earns a salary of $36,000 per year. He is paid once per month. He receives a 2.5% pay raise.
How much more money is Terry earning each month?
$25
$75
$90
Answer: $75
Step-by-step explanation:
Since Terry is paid once a month and earns $36000 in a year,
a year = 12 months
To get the amount he is paid in a month we simply divide the $36000 by 12
$36000 / 12 = $3000
In a month he is paid $3000
Now to get the pay raise;
since the pay raise is 2.5 %, we will find 2.5% of $3000
2.5/100 × $3000 = 2.5 × $30 =$75
There Terry receive an increase of $75 in a month
Two identical rubber balls are dropped from different heights. Ball 1 is dropped from a height of 115 feet, and ball 2 is dropped from a height of 269 feet. Use the function f(t)= -16t^2 + h to determine the current height, f(t), of a ball dropped from a height h, over the given time t.
Write a?function for the height of ball 2
h_2(t)= ____
Answer:
[tex]h_2(t)=-16t^2+269[/tex]
Step-by-step explanation:
Put the initial height of ball 2 into the given formula. The problem statement tells you "h" stands for the initial height, and that height is 269 feet.
[tex]h_2(t)=-16t^2+269[/tex]
At the end of the day, February 14th, a florist had 120 roses left in his shop, all of which were red, white or pink in color and either long or short-stemmed. A third of the roses were short-stemmed, 20 of which were white and 15 of which were pink. The percentage of pink roses that were short-stemmed equaled the percentage of red roses that were short-stemmed. If none of the long-stemmed roses were white, what percentage of the long-stemmed roses were red?
Answer:
25%.
Step-by-step explanation:
We have been given that at the end of the day, February 14th, a florist had 120 roses left in his shop, all of which were red, white or pink in color and either long or short-stemmed.
We are also told that 1/3 of the roses were short-stemmed.
[tex]\text{Short-stemmed roses}=120\times \frac{1}{3}=40[/tex]
Since 20 of those were white and 15 of which were pink, so short stemmed red roses would be [tex]40-(20+15)=40-35=5[/tex].
Now, we will find number of long-stemmed roses by subtracting number of short-stemmed roses from total roses as:
[tex]\text{Long-stemmed roses}=120-40=80[/tex]
We are also told that none of the long-stemmed roses were white, so total number of white roses would be [tex]20+0=20[/tex].
Let p represent the number of total pink roses.
Now, total number of red roses would be total roses (120) minus total pink roses (p) minus total white roses (20).
[tex]\text{Total red roses}=120-p-20[/tex]
[tex]\text{Total red roses}=100-p[/tex]
We have been given that the percentage of pink roses that were short-stemmed equaled the percentage of red roses that were short-stemmed. We can represent this information in an equation as:
[tex]\frac{\text{Short-stemmed pink roses}}{\text{Total pink roses}}=\frac{\text{Short-stemmed red roses}}{\text{Total red roses}}[/tex]
[tex]\frac{15}{p}=\frac{5}{100-p}[/tex]
Let us solve for p by cross-multiplication:
[tex]1500-15p=5p[/tex]
[tex]1500-15p+15p=5p+15p[/tex]
[tex]1500=20p[/tex]
[tex]20p=1500[/tex]
[tex]\frac{20p}{20}=\frac{1500}{20}[/tex]
[tex]p=75[/tex]
Since total number of pink roses is 75, so total number of red roses would be [tex]100-75=25[/tex].
We already figured it out that 5 roses are short-stemmed, so long-stemmed roses would be [tex]25-5=20[/tex].
Now, we have long stemmed roses is equal to 20 and total long-stemmed roses is equal to 80.
Let us find 20 is what percent of 80.
[tex]\text{Percentage of the long-stemmed roses that were red}=\frac{20}{80}\times 100[/tex]
[tex]\text{Percentage of the long-stemmed roses that were red}=\frac{1}{4}\times 100[/tex]
[tex]\text{Percentage of the long-stemmed roses that were red}=25[/tex]
Therefore, 25% of the long-stemmed roses were red.
Patricia has 6 less than three times the number of CDs in her collection than Monique has x CDs, write an expression to represent the number of CDs in Patricia's collection.
Answer:
The Expression representing Number of CDs in Patricia collection [tex]3x-6[/tex]
Step-by-step explanation:
Given:
Let the Number of CDs Monique has be represented as 'x'
Now Given:
Patricia has 6 less than three times the number of CDs in her collection than Monique has.
It means Number of CDs Patricia has is equal to 3 multiplied by number of CDs Monique has and then Subtracting by 6.
Framing in equation form we get;
Number of CD' Patricia has = [tex]3x-6[/tex]
Hence The Expression representing Number of CDs in Patricia collection [tex]3x-6[/tex]
Ali simplifies the expression 9y+y to 9y2. Use the drop-down menus to complete the statements below to explain why Ali's solution is correct or incorrect.
Answer:
ali's solution is incorrect
9y+y is the same as 9y+1y
9y^2 is the same as 9y x y
9y+y simplifies to 10y.
Step-by-step explanation:
Answer:
The Middle One which says 9Y2 is the same as 9y . 2y
Step-by-step explanation:
A consumer claims that the mean lifetime of a brand of fluorescent bulbs is less than1500 hours. She selects 25 bulbs and finds the mean lifetime to be 1480 hours with the standard deviation of 80 hours. If you were to test the consumer's claimat the 0.05 significance level, what would you conclude?
Answer:
We conclude that the mean lifetime of a brand of fluorescent bulbs is equal to 1500 hours.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 1500 hours
Sample mean, [tex]\bar{x}[/tex] = 1480 hours
Sample size, n = 25
Alpha, α = 0.05
Sample standard deviation, s = 80 hours
First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu = 1500\text{ hours}\\H_A: \mu < 1500\text{ hours}[/tex]
We use one-tailed(left) t test to perform this hypothesis.
Formula:
[tex]t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }[/tex]
Putting all the values, we have
[tex]t_{stat} = \displaystyle\frac{1480-1500}{\frac{80}{\sqrt{25}}}= -1.25[/tex]
Now,
[tex]t_{critical} \text{ at 0.05 level of significance, 24 degree of freedom } = -1.71[/tex]
Since,
[tex]t_{stat} > t_{critical}[/tex]
We fail to reject the null hypothesis and accept the null hypothesis.
We conclude that the mean lifetime of a brand of fluorescent bulbs is equal to 1500 hours.
After performing a one-sample t-test, the calculated t value of -1.25 does not exceed the critical value of -1.711 at the 0.05 significance level. Therefore, we do not have sufficient evidence to support the claim that the mean lifetime of the bulbs is less than 1500 hours.
Explanation:The question asks to test the claim that the mean lifetime of a certain brand of fluorescent bulbs is less than 1500 hours. To test this at the 0.05 significance level, we would perform a one-sample t-test since the sample size is less than 30, and we do not know the population standard deviation.
First, we formulate our null hypothesis (H0) as the mean lifetime of the bulbs being 1500 hours or more, and the alternative hypothesis (Ha) being the mean lifetime less than 1500 hours.
Next, we calculate the test statistic using the sample mean, population mean, standard deviation, and sample size:
[tex]t = (Sample Mean - Population Mean) / (Standard Deviation / \sqrt(Sample Size))[/tex]
[tex]= (1480 - 1500) / (80 / \sqrt(25))[/tex]
= -20 / (80 / 5)
= -20 / 16
= -1.25
Then, we check this t value against the t-distribution table for 24 degrees of freedom (df = n - 1) at the 0.05 significance level. The critical value for a one-tailed test with df = 24 at alpha = 0.05 is approximately -1.711. Since our calculated t value of -1.25 is not less than -1.711, we do not reject the null hypothesis.
Conclusion: At the 0.05 significance level, we do not have sufficient evidence to support the consumer's claim that the mean lifetime of the bulbs is less than 1500 hours.