The intensity of sound is I=7.943 × 10⁻¹¹ Wm⁻²
Step-by-step explanation:
The intensity level in dB of a sound of intensity I is given as
(10dB)log₁₀ (I/I₀), where I₀ is the intensity of threshold of hearing
The intensity of threshold of hearing I₀= 1×10⁻¹² Wm⁻²
In this question;
I=?
I₀=1×10⁻¹² Wm⁻²
Sound intensity in dB = 19 dB
Substitute values in the equation
(10dB)log₁₀ (I/I₀)= 19
(10)log₁₀ (I/1×10⁻¹²)=19
log₁₀ (I/1×10⁻¹²) =19/10
log₁₀ (I/1×10⁻¹²) =1.9
(I/1×10⁻¹²)=10^1.9
(I/1×10⁻¹²)=79.43
(I/1×10⁻¹²)=79.43
I=79.43 * 10⁻¹²
I=7.943 *10⁻¹¹ Wm⁻²
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A solid oblique pyramid has a square base with edges measuring x cm. The height of the pyramid is (x + 2) cm. A solid oblique pyramid has a square base with edges measuring x centimeters. The height is (x + 2) centimeters. Which expression represents the volume of the pyramid?
The expression to represent the volume of solid oblique pyramid is (x³+2x²)/3.
What is the volume?Volume is the measure of the capacity that an object holds.
Formula to find the volume of the object is Volume = Area of a base × Height.
Given that, a solid oblique pyramid has a square base with edges measuring x cm. The height of the pyramid is (x+2) cm.
We know that, the volume of square base pyramid is a²h/3
Now, x²(x+2)/3
= (x³+2x²)/3
Therefore, the volume of solid oblique pyramid is (x³+2x²)/3.
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The volume of the given solid oblique pyramid with a square base of edge length x cm and height (x+2) cm can be calculated using the formula for the volume of a pyramid, 1/3 * (base area) * (height). The volume can thus be represented by the expression 1/3 * x^3 + 2/3 * x^2 cm^3.
Explanation:The question refers to a solid oblique pyramid with a square base, where the edge length of the base is x, and the height is (x+2) cm. To calculate the volume of the pyramid, you can use the formula for the volume of a pyramid: 1/3 * (base area) * (height). For the given pyramid, the base is a square with side length x, so the area of the base is x*x or x^2. Because the height of the pyramid is (x + 2), we substitute into the formula to get: 1/3 * x^2 * (x + 2). Multiplying it out, the expression representing the volume of the pyramid is: 1/3 * x^3 + 2/3 * x^2 cm^3.
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You have 100 dollars, and there is a dollar bill behind each door. You roll a 100 sided die 100 times, and you take the dollar behind the door on the die roll if the bill has not been taken already (e.g. you roll 16, then you take the dollar behind door 16 if you haven’t already taken it). What is your expected payoff?
Answer:
63.21.
Step-by-step explanation:
You have 100 dollars, and there is a dollar bill behind each door. You roll a 100 sided die 100 times, and you take the dollar behind the door on the die roll if the bill has not been taken already (e.g. you roll 16, then you take the dollar behind door 16 if you haven’t already taken it). What is your expected payoff?
X=Σ100i=1 1Ai
where Ai is the event that door i is opened at least once, and 1Ai is the indicator function for event Ai.
Thus the expected payoff is:
E[X]=Σ100 as i=1 Pr[Ai].
to calculate Pr[Ai].
Ai∁ is the probability of the event that after 100 rolls, door i is not chosen, which is:
Pr[Ai∁]=(99/100)^100
Thus:
Pr[Ai]=1−Pr[Ai∁]=1−(99/100)^100.
E[X]=Σ100i=1Pr[Ai]=100×(1−(99/100)^100).
Also based on the following approximation for large n's:
(1−1n)n≈1e
we have:
(99/100)^100=(1−1/100)^100≈1/e.
The expected pay off is
E[X]=100×(1−(99/100)^100)≈100×(1−1/e)≈63.21.
In the scenario where you roll a 100-sided die 100 times to collect a dollar behind each numbered door, the expected payoff is $100, since each number has an equal likelihood of being rolled once.
Explanation:The question you're asking involves probability and expected value, a concept from mathematics specifically relevant in understanding outcomes in scenarios involving randomness and repetition, like the one described with 100-sided dice and dollars behind doors. When rolling a 100-sided die 100 times for dollars behind 100 doors, your expected payoff is relatively straightforward to calculate. Since each roll has an equal chance to land on any number between 1 and 100 and no number will be chosen more than once, the expected outcome is that you will roll each number once.
Thus, on average, you are expected to open each door exactly once, so the expected payoff would be neatly the sum of all the dollars behind every door. As there are 100 doors, each with a dollar behind it, your expected payoff is simply $100.
Rewrite with only sin x and cos x.
sin 2x - cos x
2 sin x cos2x
sin x
cos x (2 sin x - 1)
2 sin x
Answer:
cos x (2 sin x − 1)
Step-by-step explanation:
sin(2x) − cos x
Use double angle formula.
2 sin x cos x − cos x
Factor.
cos x (2 sin x − 1)
Final answer:
The expression sin 2x - cos x can be rewritten as cos x (2 sin x - 1).
Explanation:
Given the expression sin 2x - cos x, we can rewrite it using only sin x and cos x. Using the trigonometric identity sin 2x = 2 sin x cos x, we can substitute it into the expression:
sin 2x - cos x = 2 sin x cos x - cos x
Factoring out the common factor cos x, we get:
sin 2x - cos x = cos x (2 sin x - 1)
So, the expression sin 2x - cos x can be rewritten as cos x (2 sin x - 1).
8. When starting your credit history, a low-credit-limit, high-interest-rate credit card should be paid ____.
in full, on time, every time
in even payments each time
at least the minimum due
as much as you can when due
9. APY means ____.
annual percentage yield
annual percentage yearly
apportioned percentage yield
applied percentage yield
Answer:
8. When starting your credit history, a low-credit-limit, high-interest-rate credit card should be paid in full, on time, every time.
9. APY means annual percentage yield.
Explanation:
8. A person's credit history tells about the ability of a person to pay and repay his debts. This is very important especially when you want to avail of a credit card from a company because it reflects on how responsible you are when it comes to repaying your debts. However, when you are just starting your credit history, it is important to give a good impression, so you'd have an easier approval in the future.
Usually, for starters with low salary, a low-credit-limit with a high-interest-rate credit card is common. It is very important to pay your debts in full, on time and every time in order to avoid incurring a balance that you will be carrying from one month to the other. If you do this, you will be ending up paying lots of interest charge.
Paying in full, on time and every time will also give you the chance to have an increased credit limit in the future.
9. APY is also known as "Annual Percentage Yield." This is the actual amount (rate of return) that a person could earn while his money is being deposited in the bank in one year. Other than the deposited money, investment that earns a rate of return could also refer to bonds and stock share. APY considers the compounding interest in its computation. This means that the higher your balance, the higher the APY. The value of the asset also increases.
Tyler ordered a pizza to eat while he watches a movie. Before the movie began, he ate 1/4 of the pizza. During the movie, he ate another 3/8 Before storing the remaining pizza, he ate a final 1/16 of the pizza. How much leftover pizza does Tyler have.
Answer:
Tyler has [tex]\frac{5}{16}[/tex] Left over Pizza.
Step-by-step explanation:
Given:
Total pizza = 1
Pizza ate at First time = [tex]\frac{1}{4}[/tex]
Pizza ate at Second time = [tex]\frac{3}{8}[/tex]
Pizza ate at Final time = [tex]\frac{1}{16}[/tex]
We need to find find the amount of pizza left.
Now to find the Amount of Pizza left is equal to Total Pizza minus Pizza ate at First time minus Pizza ate at second time minus Pizza ate at Final time.
Framing in the equation form we get;
Amount of Pizza left = [tex]1- \frac{1}{4} -\frac{3}{8} -\frac{1}{16}[/tex]
Now Taking the LCM we get;
Amount of Pizza left = [tex]\frac{1\times16}{16}- \frac{1\times4}{4\times 4} -\frac{3\times2}{8\times2} -\frac{1\times1}{16\times1}= \frac{16}{16}- \frac{4}{16} -\frac{6}{16} -\frac{1}{16}= \frac{16-4-6-1}{16}= \frac{5}{16}[/tex]
Hence Tyler has [tex]\frac{5}{16}[/tex] Left over Pizza.
Suppose that x is normally distributed with a mean of 30 and a standard deviation of 3.What is P?
a) 0.469b) 0.956c) 0.493d) 0.490e) 0.466f) none of the above
Answer:
If we assume that the deviation is [tex]\sigma=3[/tex] then the solution is:
[tex]P(2.55<X<64.95)=P(-9.15<z<11.65)=P(z<11.65)-P(z<-9.15)[/tex]
f) None of the above
If we assume that the deviation is [tex]\sigma=15[/tex] then the solution is:
[tex]P(2.55<X<64.95)=P(-1.83<z<2.33)=0.956[/tex]
b) 0.956
Step-by-step explanation:
1) Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
2) Solution to the problem
Let X the random variable that represent the variable of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(30,3)[/tex]
Where [tex]\mu=30[/tex] and [tex]\sigma=3[/tex]
We are interested on this probability
[tex]P(2.55<X<64.95)[/tex]
And the best way to solve this problem is using the normal standard distribution and the z score given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
If we apply this formula to our probability we got this:
[tex]P(2.55<X<64.95)=P(\frac{2.55-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{64.95-\mu}{\sigma})=P(\frac{2.55-30}{3}<Z<\frac{64.95-30}{3})=P(-9.15<Z<11.65)[/tex]
And we can find this probability on this way:
[tex]P(-9.15<z<11.65)=P(z<11.65)-P(z<-9.15)[/tex]
And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.
[tex]P(-9.15<z<11.65)=0.99999[/tex]
If we assume that the deviation is [tex]\sigma=15[/tex] then the solution is:
[tex]P(2.55<X<64.95)=P(\frac{2.55-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{64.95-\mu}{\sigma})=P(\frac{2.55-30}{15}<Z<\frac{64.95-30}{15})=P(-1.83<Z<2.33)[/tex]
And we can find this probability on this way:
[tex]P(-1.83<z<2.33)=P(z<2.33)-P(z<-1.83)[/tex]
And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.
[tex]P(-1.83<z<2.33)=0.956[/tex]
Two percent of the jazz records sold in April were from a new label. About how many records were from the new label?
Approximately, 2% of the jazz records sold in April were from the new label.To find this, multiply the percentage (2%) by the total jazz records sold, expressing the percentage as a decimal (0.02). The formula is[tex]\( N = 0.02 \times J \),[/tex] where [tex]\( N \)[/tex] is the number of records from the new label, and [tex]\( J \)[/tex]is the total number of jazz records sold.
Explanation:In order to determine the number of jazz records sold from the new label in April, you need to multiply the percentage by the total number of jazz records sold. Let's denote the total number of jazz records as J. The formula for calculating the number of records from the new label (N) is given by:
[tex]\[ N = (2/100) \times J \][/tex]
This is based on the fact that 2% is equivalent to 0.02 when expressed as a decimal. Therefore, the number of records from the new label is obtained by multiplying 0.02 by the total number of jazz records (J). This calculation provides the direct answer to the question.
Understanding percentages is essential in various fields, and in this scenario, it helps determine the specific quantity of records from the new label in relation to the total jazz records sold. This mathematical approach allows for a precise estimation, providing insights into the market share or performance of the new label within the jazz genre for the specified period, in this case, the month of April.
A student bought a juice pouch forn$2.50 and 3 bags of chips. The total cost was $5.05.Write and solve an equation to determine the cost of a bag of chips,c
Answer:
The cost of a bag of chips is [tex]c=\$0.85[/tex]
Step-by-step explanation:
Let
c ----> the cost of a bag of chips
we know that
The cost of a juice pouch ($2.50) plus the cost of 3 bags of chips must be equal to $5.05
The cost of 3 bags of chips is equal to multiply 3 by its cost c
so
The linear equation that represent this situation is
[tex]2.50+3c=5.05[/tex]
solve for c
Subtract 2.50 both sides
[tex]3c=5.05-2.50[/tex]
[tex]3c=2.55[/tex]
Divide by 3 both sides
[tex]c=2.55/3[/tex]
[tex]c=\$0.85[/tex]
A triangle is formed from the points L(-3, 6), N(3, 2) and P(1, -8). Find the equation of the following lines:
the median from N
the right bisector of LP
the altitude from N
Answer:
Part A) [tex]y=\frac{3}{4}x-\frac{1}{4}[/tex]
Part B) [tex]y=\frac{2}{7}x-\frac{5}{7}[/tex]
Part C) [tex]y=\frac{2}{7}x+\frac{8}{7}[/tex]
see the attached figure to better understand the problem
Step-by-step explanation:
we have
points L(-3, 6), N(3, 2) and P(1, -8)
Part A) Find the equation of the median from N
we Know that
The median passes through point N to midpoint segment LP
step 1
Find the midpoint segment LP
The formula to calculate the midpoint between two points is equal to
[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
we have
L(-3, 6) and P(1, -8)
substitute the values
[tex]M(\frac{-3+1}{2},\frac{6-8}{2})[/tex]
[tex]M(-1,-1)[/tex]
step 2
Find the slope of the segment NM
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
N(3, 2) and M(-1,-1)
substitute the values
[tex]m=\frac{-1-2}{-1-3}[/tex]
[tex]m=\frac{-3}{-4}[/tex]
[tex]m=\frac{3}{4}[/tex]
step 3
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{3}{4}[/tex]
[tex]point\ N(3, 2)[/tex]
substitute
[tex]y-2=\frac{3}{4}(x-3)[/tex]
step 4
Convert to slope intercept form
Isolate the variable y
[tex]y-2=\frac{3}{4}x-\frac{9}{4}[/tex]
[tex]y=\frac{3}{4}x-\frac{9}{4}+2[/tex]
[tex]y=\frac{3}{4}x-\frac{1}{4}[/tex]
Part B) Find the equation of the right bisector of LP
we Know that
The right bisector is perpendicular to LP and passes through midpoint segment LP
step 1
Find the midpoint segment LP
The formula to calculate the midpoint between two points is equal to
[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
we have
L(-3, 6) and P(1, -8)
substitute the values
[tex]M(\frac{-3+1}{2},\frac{6-8}{2})[/tex]
[tex]M(-1,-1)[/tex]
step 2
Find the slope of the segment LP
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
L(-3, 6) and P(1, -8)
substitute the values
[tex]m=\frac{-8-6}{1+3}[/tex]
[tex]m=\frac{-14}{4}[/tex]
[tex]m=-\frac{14}{4}[/tex]
[tex]m=-\frac{7}{2}[/tex]
step 3
Find the slope of the perpendicular line to segment LP
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
[tex]m_1*m_2=-1[/tex]
we have
[tex]m_1=-\frac{7}{2}[/tex]
so
[tex]m_2=\frac{2}{7}[/tex]
step 4
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{2}{7}[/tex]
[tex]point\ M(-1,-1)[/tex] ----> midpoint LP
substitute
[tex]y+1=\frac{2}{7}(x+1)[/tex]
step 5
Convert to slope intercept form
Isolate the variable y
[tex]y+1=\frac{2}{7}x+\frac{2}{7}[/tex]
[tex]y=\frac{2}{7}x+\frac{2}{7}-1[/tex]
[tex]y=\frac{2}{7}x-\frac{5}{7}[/tex]
Part C) Find the equation of the altitude from N
we Know that
The altitude is perpendicular to LP and passes through point N
step 1
Find the slope of the segment LP
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
L(-3, 6) and P(1, -8)
substitute the values
[tex]m=\frac{-8-6}{1+3}[/tex]
[tex]m=\frac{-14}{4}[/tex]
[tex]m=-\frac{14}{4}[/tex]
[tex]m=-\frac{7}{2}[/tex]
step 2
Find the slope of the perpendicular line to segment LP
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
[tex]m_1*m_2=-1[/tex]
we have
[tex]m_1=-\frac{7}{2}[/tex]
so
[tex]m_2=\frac{2}{7}[/tex]
step 3
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{2}{7}[/tex]
[tex]point\ N(3,2)[/tex]
substitute
[tex]y-2=\frac{2}{7}(x-3)[/tex]
step 4
Convert to slope intercept form
Isolate the variable y
[tex]y-2=\frac{2}{7}x-\frac{6}{7}[/tex]
[tex]y=\frac{2}{7}x-\frac{6}{7}+2[/tex]
[tex]y=\frac{2}{7}x+\frac{8}{7}[/tex]
In June, Susie buys a dozen of cans of Dog's Dinner dog food at $1.89 per can. She also buys two bags of 'Dem Bones dental chews that each cost $12.69, and a new toy for $10.25. She pays sales tax at a rate of 7.25%. What is her total cost for the month of June?
Answer:
$62.54
Step-by-step explanation:
12 cans dog food = 12 × 1.89 = $22.68
2 bags dental chews = 2 × 12.69 = 25.38
1 toy = 10.25
Subtotal = 58.31
Sales tax = 0.0725 × 58.31 = 4.23
TOTAL = $62.54
Suzie's total cost for June was $62.54.
In order to raise revenue, the federal government planned a tax amnesty program that allows tax delinquents to pay all owed tax without added financial penalty. However, economists projected that the federal government would collect a far lower percentage of total tax owed by delinquents than did state governments implementing similar programs.
Answer:
The correct option is E: "Unlike most federal tax delinquents, most state tax delinquents fail to pay state tax because of an oversight rather than a decision not to pay."
Step-by-step explanation:
Option A is not the correct answer because it is out of context
Option B is also out of context because what we are looking for is a connection between defaulters at state and federal level
Option C is also wrong because it would lead to the direct opposite of the projection by economists.
Option D is also wrong because once again it is out of context.
Option E is correct
Kevin, Dustin, and Mike collect baseball cards. Together Dustin and Kevin have 81 cards. If Dustin and Mike combined their cards, they would total 96. The sum of Kevin's and Mike's cards is 93. How many baseball cards do they each have? Show all of your mathematical thinking below.
Answer: Kelvin has 39 cards
Dustin has 42 cards
Mike has 54 cards
Step-by-step explanation: please see attachment for explanation
A gas station sells 4820 gallons of regular unleaded gasoline in a day when they charge $1.35 per gallon, whereas they sell 3902 gallons on a day that they charge $1.40 per gallon. Find a linear function that expresses gallons sold as a function of price. (Hint: express the given information as two ordered pairs, and then find the equation of the line that goes through the two points.) Use this function to predict the number of gallons sold at a price of $1.22 per gallon.
Answer:
The linear function that expresses gallons sold as a function of price is [tex]y=-18360x+29606[/tex].
The number of gallons sold at a price of $1.22 per gallon is 7206.8
Step-by-step explanation:
Consider the provided information.
A gas station sells 4820 gallons of regular unleaded gasoline in a day when they charge $1.35 per gallon,
They sell 3902 gallons on a day that they charge $1.40 per gallon.
Let x represents the price per gallon and y represents the number of gallons sold.
Thus the ordered pairs are (1.35,4820) and (1.40,3902)
Now find the slope of line using the formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{3902-4820}{1.40-1.35}[/tex]
[tex]m=\frac{-918}{0.05}[/tex]
[tex]m=-18360[/tex]
Now find the slope intercept as shown:
[tex](y-y_1)=m(x-x_1)[/tex]
[tex](y-4820)=-18360(x-1.35)[/tex]
[tex]y=-18360x+24786+4820[/tex]
[tex]y=-18360x+29606[/tex]
Hence, the linear function that expresses gallons sold as a function of price is [tex]y=-18360x+29606[/tex].
The number of gallons sold at a price of $1.22 per gallon.
Substitute x=1.22 in above equation.
[tex]y=-18360(1.22)+29606[/tex]
[tex]y=-22399.2+29606[/tex]
[tex]y=7206.8[/tex]
Hence, the number of gallons sold at a price of $1.22 per gallon is 7206.8
give the equation of the circle whose center is (5 -3) and goes through (2 5)
Answer:
Step-by-step explanation:
The standard form for the equation of a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]
From the info given, we have the center, (h, k) as (5, -3) and the x and y coordinates of (2, 5). We will use these to solve for r-squared, then plug back in what we need to write the equation.
[tex](2-5)^2+(5-(-3))^2=r^2[/tex] which simplifies to
[tex](-3)^2+(8)^2=r^2[/tex] and
[tex]9+64=r^2[/tex] so
[tex]r^2=73[/tex]
Filling in the equation:
[tex](x-5)^2+(y+3)^2=73[/tex]
Katherine owns a food truck that sells tacos and burritos. She only has enough supplies to make 106 tacos or burritos. She sells each taco for $3.50 and each burrito for $6.50. Katherine must sell a minimum of $470 worth of tacos and burritos each day. If 79 tacos were sold, determine all possible values for the number of burritos that Katherine must sell in order to meet the requirements. Your answer should be a comma separated list of values. If there are no possible solutions, submit an empty answer.
Answer:
No possible solutionsStep-by-step explanation:
She has the option for supplying the total of 106 items. This 106 items can be either tacos or burritos or both with a total of 106 items.
If 79 tacos are sold, then it gives [tex]79 \times 3.50 = 276.5[/tex]
She needs to make $470 in total.
She needs to make $(470 - 276.5) = $193.5 more till now.
After selling 79 tacos, she has an option to sell maximum (106 - 79) = 27 burritos.
If she wants to make $193.5, she needs to sell [tex]\frac{193.5}{6.5} = 29.7[/tex] that is 30 burritos.
As she can sell 27 burritos in maximum, so there is no possible solutions.
If AB is the diameter of the circle with center X and C is a point on the circle such that AC = AX = 3, what is the perimeter of triangle ABC ?
Answer:
Step-by-step explanation:
The perimeter of a shape or plane figure is the distance round the shape. The diagram of the circle and the triangle ABC formed is shown in the attached photo.
To determine the length of AC, we would apply the Pythagoras theorem which is expressed as follows
Hypotenuse^2 = opposite ^2 + adjacent ^2
AC = hypotenuse
Opposite = 3
Adjacent = 3
AC^2 = 3^2 + 3^2 = 9 + 9 = 18
AC = √18 = 4.24
BX = AX = 3(they are both radii)
BC = AC = 4.24
The perimeter of triangle ABC would be
3 + 3 + 4.24 + 4.24 = 14.48
A store buys a video game for the wholesale price of $39.99. The markup on the game is 70%. If sales tax is 8% then how much money would you need to buy the game?
Answer:The amount of money that you would need to buy the game is $73.324
Step-by-step explanation:
The store buys a video game for the wholesale price of $39.99. There was a markup of 70% on the price of the game. The value of the markup would be
70/100× 39.99 = 0.7×39.99 = $27.993
Cost of the game plus 70% markup would be
39.99 + 27.993 = $67.893
There is sales tax of 8% on the game. This means that the value of the tax would be
8/100 × 67.893 = 0.08 × 67.893 = $5.431
The amount of money that you would need to buy the game would be
67.893 + 5.431 = $73.324
In a certain high school, the probability that a student drops out is 0.07 , and the probability that a dropout gets a high-school equivalency diploma (GED) is 0.25 . What is the probability that a randomly selected student gets a GED?
Using probability concepts and the information given, it is found that there is a 0.0175 = 1.75% probability that a randomly selected student gets a GED.
The percentages given are:
7% of the students drop out, and of those, 25% get a GED.100 - 7 = 93% of the students do not drop hence, meaning of those, 0%, that is, none need to get a GED, as they will have the graduation diploma.Hence:
[tex]p = 0.07(0.25) + 0.93(0) = 0.0175[/tex]
There is a 0.0175 = 1.75% probability that a randomly selected student gets a GED.
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The probability that a randomly selected student gets a GED is 0.0175, or 1.75%.
Explanation:To find the probability that a randomly selected student gets a GED, we need to multiply the probability of a student dropping out (0.07) by the probability of a dropout getting a GED (0.25). This can be calculated using the formula:
Probability of getting a GED = Probability of dropping out * Probability of getting a GED if dropped out = 0.07 * 0.25 = 0.0175
Therefore, the probability that a randomly selected student gets a GED is 0.0175, or 1.75%.
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A woman is purchasing fruit for some pies she is making for a party she wants to purchase at least 10 pounds of strawberries and blueberries.Strawberries are sold for $2 per pound and blueberries are sold for $3 per pound she does no want to spend more that $25 total for the fruit
The system of inequalities to represent the situation is x + y ≥ 10 and
2x + 3y ≤ 25.
What is inequality?The relation between two unequal expressions is defined as inequality.
Given that, Strawberries are sold for $2 per pound, and blueberries are sold for $3 per pound.
Let the woman purchase x pounds of strawberries and y pounds of blueberries.
Given that, the woman wants to purchase at least 10 pounds of strawberries and blueberries, therefore,
x + y ≥ 10
The total cost of purchasing x pounds of strawberries and y pounds of blueberries is:
2x + 3y
Since the woman doesn't want to spend more than $25, it follows:
2x + 3y ≤ 25
Hence, the system of inequalities to represent the situation is x + y ≥ 10 and 2x + 3y ≤ 25.
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To calculate the total cost of the fruit, use the equation 2x + 3y ≤ 25, where x represents the pounds of strawberries and y represents the pounds of blueberries. Graph the inequalities to find the feasible region and determine the affordable combinations of strawberries and blueberries.
Explanation:To calculate the total cost of the fruit, we need to consider the cost of strawberries and blueberries separately. Let's assume the woman purchases x pounds of strawberries and y pounds of blueberries. The cost of strawberries is $2 per pound, so the cost of strawberries will be 2x dollars. Similarly, the cost of blueberries is $3 per pound, so the cost of blueberries will be 3y dollars. The total cost will be the sum of the cost of strawberries and blueberries, which should not exceed $25. Therefore, the equation becomes: 2x + 3y ≤ 25.
Since the woman wants to purchase at least 10 pounds of strawberries, we have another condition x ≥ 10. We can graph these inequalities on a coordinate plane and find the feasible region where both conditions are satisfied. From the graph, we can determine the possible combinations of strawberries and blueberries that meet the woman's requirements.
Once we find the feasible region, we can choose a few points within that region and calculate the total cost for each point. By comparing the total cost to $25, we can determine which combinations of strawberries and blueberries are affordable for the woman.
Hank has a board 1.75 meters long. He used 0.8 meter to build the walls of a birdhouse. He used 0.4 of what is left for the floor. He needs 0.6 meter for the roof. Dies he have enough wood for the roof? Explain
Answer:No, he doesn't have enough wood for the roof.
Step-by-step explanation:
Total length of Hank's board is 1.75 meters. He used 0.8 meter to build the walls of a birdhouse. This means that the length of the board left would be
1.75 - 0.8 = 0.95 meters
He used 0.4 of what is left for the floor. This means that the length of the board left would be
0.95 - 0.4 = 0.55 meters
He needs 0.6 meter for the roof. Since he has only 0.55 meters left, then, he doesn't have enough wood for the roof.
A landscaping company charges customers for lawn care based on the area of their yards. Mr. Jones was charged $52 for his yard, which is 40 feet by 65 feet. If a neighbor's yard is 50 feet by 80 feet, what would the neighbor be charged based on how much Mr. Jones was charged?
Answer: The neighbor would be charged $80
Step-by-step explanation:
The dimensions of Mr Jones's yard are 40 feet by 65 feet. This means that the shape of Mr Jones's yard is rectangular. The formula for determining the area of a rectangle is length × width. The area of the yard would be
40 × 65 = 2600 square feet
Mr. Jones was charged $52 for his yard. This means that the amount that he was charged per square foot would be 52/2600 = $0.02
If a neighbor's yard is 50 feet by 80 feet, it means that the area of his yard would be 50 × 80 = 4000 square feet. The amount that the neighbor would be charged is
4000 × 0.02 = $80
The company charges $0.02 per square foot. With the neighbor's yard having an area of 4000 square feet, the total cost would be $80.
Explanation:To determine how much the neighbor would be charged, we need to find out the price per square foot the landscaping company charges. We start with Mr. Jones's yard. His yard area is 40 feet by 65 feet; multiplying these gives an area of 2600 square feet. Now, the cost for his yard is $52; by dividing this by the area, we get a cost of about $0.02 per square foot. For the neighbor's yard, which is 50 feet by 80 feet, we multiply these values to get an area of 4000 square feet. At a rate of $0.02 per square foot, the total cost for the neighbor's yard would be 4000 square feet * $0.02/square foot = $80.
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Which of the equations below represents a line parallel to the y-axis? A. x = 4 B. x = -y C. x = y D. x = 4y
Answer:
b
Step-by-step explanation:
The number 2^1993 + 3^1993 is a multiple of 5. What is the units digit of the quotient (2^1993 + 3^1993)/5?
The units digit of the quotient (2^1993 + 3^1993)/5 is 9.
Explanation:The units digit of the sum of two numbers is determined by the units digit of each number. To find the units digit of 2^1993, we can observe the pattern of its units digits: the units digit of 2 repeats every four powers. Therefore, 2^1993 has the same units digit as 2^1, which is 2. Similarly, the units digit of 3^1993 is the same as the units digit of 3^3, which is 7.
Now, we can calculate the units digit of the sum: 2 + 7 = 9. Since the sum is divisible by 5, and the units digit is 9, the quotient (2^1993 + 3^1993)/5 has a units digit of 9 as well.
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A store sells hardcover books for $8 and paperback books for $5. You buy 7 books, represented by the equation x+y=7, where is the number of hardcover books and y is the number of paperback books. The equation 8x+5y=41 represents the total cost. How many of each type of book did you buy?
Answer:
Total number of Hardcover books is TWO while the number of Paperback books is FIVE
Step-by-step explanation:
No. of hardcover book = x
No. of paperback book = y
Cost of one hardcover book = $8
Cost of one paperback book = $5
We are given that:
x+y=7 (Equation 1)
8x+5y=41 (Equation 2)
We can find out value of x and y by solving both equations simultaneously.
[tex]Multiplying Equation 1 by 5:\\5x+5y=35\\8x+5y=41\\Subtracting both equations\\-3x=-6\\x=2\\\\According to Equation 1:\\x+y=7\\Putting value of x=2\\2+y=7\\y=5[/tex]
Hence, Total number of Hardcover books is TWO while the number of Paperback books is FIVE
Write in simple radical form:
(1 +[tex]\frac{1}{\sqrt{3} }[/tex]) / (1 - [tex]\frac{1}{\sqrt{3} }[/tex])
show steps.
Answer:
The answer to your question is [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Here, there is a difference of squares, so just solve it and simplify
[tex]( 1 + \frac{1}{\sqrt{3} } ) (1 - \frac{1}{\sqrt{3} } )[/tex]
Multiply the binomials
= 1 - [tex]\frac{1}{3}[/tex]
Simplify
= [tex]\frac{3 - 1}{3}[/tex]
= [tex]\frac{2}{3}[/tex]
A boy thinks he has discovered a way to drink extra orange juice without alerting his parents. For every cup of orange juice he takes from a container of orange juice, he pours one cup of water back into the container. If he completes this process three times on the same container of juice, the resulting mixture will be exactly 50% water and 50% juice. How many cups of orange juice were originally in the container. (P.S ITS NOT 6)
Answer:
4.847 cups
Step-by-step explanation:
Let's say x is number of cups of orange juice originally in the container.
The boy takes 1 cup of orange juice out, so there is x−1 cups left out of a total volume of x cups. So the new concentration in the container is:
(x − 1) / x
Next, he takes another cup out, but this time, it isn't 100% orange juice any more. So the number of cups of orange juice left in the container is x − 1 − (x − 1) / x. The total volume is still x cups, so the new concentration is:
[x − 1 − (x − 1) / x] / x
Repeating this logic, after he replaces the third cup with water, the final concentration is:
{x − 1 − (x − 1) / x − [x − 1 − (x − 1) / x] / x} / x
This final concentration is equal to 1/2.
1/2 = {x − 1 − (x − 1) / x − [x − 1 − (x − 1) / x] / x} / x
1/2 x = x − 1 − (x − 1) / x − [x − 1 − (x − 1) / x] / x
1/2 x² = x (x − 1) − (x − 1) − [x − 1 − (x − 1) / x]
1/2 x² = x (x − 1) − (x − 1) − (x − 1) + (x − 1) / x
1/2 x² = x (x − 1) − 2 (x − 1) + (x − 1) / x
1/2 x³ = x² (x − 1) − 2x (x − 1) + (x − 1)
1/2 x³ = x³ − x² − 2x² + 2x + x − 1
0 = 1/2 x³ − 3x² + 3x − 1
0 = x³ − 6x² + 6x − 2
Using a calculator to solve this:
x = 4.847
There are originally 4.847 cups in the container.
A rectangle has an area of 96cm2. The width is four less than the length. What is the perimeter?
Answer:
Step-by-step explanation:
Let L represent the length of the rectangle.
Let W represent the width of the rectangle.
The formula for determining the area of a rectangle is expressed
LW^2
The rectangle has an area of 96cm2. This means that
LW = 96 - - - - - - - - - - 1
The width is four less than the length. This means that
L = W + 4
Substituting L = W + 4 into equation 1, it becomes
W(W + 4)= 96
W^2 + 4W = 96
W^2 + 4W - 96 = 0
W^2 + 12W - 8W - 96 = 0
W(W + 12) - 8(W + 12) = 0
(W + 12)(W - 8) = 0
W = 8 or W = -12
Since the width cannot be negative, the W = 8cm
L = W + 4 = 8 + 4 = 12 cm
The formula for determining the perimeter of a rectangle is
Perimeter = 2(L + W)
Perimeter = 2(8 + 12) =2×20
Perimeter of rectangle = 40 cm
.
Final answer:
Perimeter is 40cm.
Explanation:
To find the perimeter of a rectangle with an area of 96 cm2 where the width is four less than the length, we first need to set up equations for the area and the relationship between the sides.
Let the length be represented by L and the width by W.
We know:
Area (A) = Length (L) × Width (W) = 96 cm2Width (W) = Length (L) - 4 cmWe can substitute the second equation into the first to find the length:
A = L × (L - 4 cm) = 96 cm2
L^2 - 4L - 96 = 0
(L - 12)(L + 8) = 0
L = 12
The perimeter (P) of a rectangle is given by 2 × Length + 2 × Width or P = 2L + 2W.
Substituting the values of L and W into this formula will yield the perimeter of the rectangle.
For example, if L = 12 cm (which is a possible solution to the above problem), then W = L - 4 cm = 8 cm.
Therefore, the perimeter would be:
P = 2L + 2W = 2(12 cm) + 2(8 cm) = 40 cm
In the United Kingdom,Alzheimer's disease is said to affect one in fifty people over 65 years of age.If approximately 250,000 people over 65 are affected in the UK, how many people over 65 are there in total? Answer total people over 65
Total people over 65 are :12,500,000
Step-by-step explanation:
Given that the disease affects 1/50 people over 65 years of age and it is approximated that 250,000 people over 65 years are affected then;
Form an expression for total number of people over 65 of age;
Let x be the total number of people over 65 of age
Then 1/50 *x = 250,000
x=250,000 *50 =12,500,000 people are over 65 years of age
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Keywords : disease, people, age, total
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Bankruptcy is a process when a lender tries to obtain money from an individual's employer to pay an unpaid debt.
Answer:
false
Step-by-step explanation:
Answer:
False!!!!!
Step-by-step explanation:
it is Garnishment, not Bankruptcy! Hope this helps yall.
The nth harmonic number is defined non-recursively as: 1 1/2 1/3 1/4 ... 1/n. Come up with a recursive definition and use it to guide you to write a method definition for a double-valued method named harmonic that accepts an int parameters n and recursively calculates and returns the nth harmonic number.
Answer:
57
Step-by-step explanation: