If angle a measures 67 degrees ,how much does angle b measure ?

Final answer:

When Mai turns 65, the value of her individual Retirement Account will be $61,917.28.

Explanation:

To calculate the future value of an investment with compound interest, we can use the formula:

FV = P(1+r)^n

Where FV is the future value, P is the principal amount (initial investment), r is the interest rate (as a decimal), and n is the number of compounding periods.

In this case, Mai invested $2000 and the interest rate is 10% compounded annually.

So, when Mai turns 65, the number of compounding periods would be 65 - 21 = 44 years.

Plugging in the values into the formula:

FV = $2000(1+0.10)^44 = $61,917.28

Therefore, the value of Mai's individual Retirement Account when she turns 65 will be $61,917.28.

Answer:

50

Step-by-step explanation:

An angle that measures 50° Turns through 50 1° angles because 50 *1 = 50

1 degree * 50 turns = 50 degrees

Answer:

x=15.08 cm

y=7.54 cm

Step-by-step explanation:

We are given that

Volume of box=1715 cubic cm

Side length of base=x

l=b=x

Height of box=h=y

Volume of box=lbh=x^2y

[tex]1715=x^2y[/tex]

[tex]y=\frac{1715}{x^2}[/tex]

Surface area of box=Area of bottom+area of four faces=[tex]x^2+4xy[/tex]

[tex]S=x^2+4x(\frac{1715}{x^2}=x^2+\frac{6860}{x}[/tex]

Differentiate w.r.t x

[tex]S'(x)=2x-\frac{6860}{x^2}[/tex]

[tex]S'(x)=0[/tex]

[tex]2x-\frac{6860}{x^2}=0[/tex]

[tex]2x=\frac{6860}{x^2}[/tex]

[tex]x^3=\frac{6860}{2}=3430[/tex]

[tex]x=(3430)^{\frac{1}{3})=15.08[/tex]

Again differentiate w.r.t x

[tex]S''(x)=2+\frac{13720}{x^3}[/tex]

Substitute x=15.08

[tex]S''(x)=2+\frac{13720}{(15.08)^3}>0[/tex]

Hence, the surface area is minimum at x=15.08 cm

[tex]y=\frac{1715}{(15.08)^2}=7.54 cm[/tex]

The dimensions of the bin that will minimize the surface area are:

Base side (x): 7.5cm

Height (y): 36.13cm

Let's express the surface area and volume of the box in terms of x and y:

Surface area (A):

A = 2x^2 + 4xy

Volume (V)V = x^2y

We are given that the volume of the box must be 1715cm3:

1715cm3 = x^2y

Solving for y, we get:

y = 1715/x^2

Now, we want to minimize the surface area (A) subject to the constraint that the volume (V) is 1715cm3. We can use Lagrange multipliers to solve this optimization problem.

L(x, y, λ) = A - λ(V - 1715)

L(x, y, λ) = 2x^2 + 4xy - λ(x^2y - 1715)

Taking partial derivatives of L with respect to x, y, and λ, we get:

∂L/∂x = 4x + 4y - 2λxy = 0

∂L/∂y = 4x - λx^2 = 0

∂L/∂λ = -x^2y + 1715 = 0

Substituting V = x^2y into the third partial derivative, we get:

∂L/∂λ = -V + 1715 = 0

Solving these equations simultaneously, we get:

x = 7.5

y = 36.13

Answer:

Step-by-step explanation:

%17 because you take %78 of %22

(the second part is more tricky...

17% were first time takers who past.

%60  of %78 = %46.8 = percentage of people who were first time takers who failed.

so total percentage of first time takers = 46.8 +17 = %63.8.

Then 17/63.8 X %100 = percent of first time takers who passed.

=26.6 percent therefore %27 is correct.

Answer:

The GCF is 6n^3

Step-by-step explanation:

The function [tex]k(x) = 2x^2[/tex] is which the average rate of change over the interval 1 < x < 5 greater than the average rate of change of g(x).

Given data:

The function is represented as [tex]g(x)=1.8x^2[/tex].

Now, the average rate of change of the function is S.

The value of [tex]S=\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}}[/tex].

The interval of the function is from 1 < x < 5.

So, for g(x), [tex]S=\frac{f(5)-f(1)}{5-1}[/tex].

The value of S = 10.8

For the function [tex]k(x) = 2x^2[/tex], the rate of change is:

[tex]S=\frac{k(5)-k(1)}{4}[/tex]

[tex]S=\frac{50-2}{4}[/tex]

So, the value of S = 12 and is greater than 10.8

Hence, the function is [tex]k(x) = 2x^2[/tex].

To learn more about rate of change of function, refer:

https://brainly.com/question/29548786

#SPJ4

The complete question is attached below:

For which function is the average rate of change over the interval 1 < x < 5 greater than the average rate of change over the same interval for the function g(x) = 1.8x^2?
A.=f(x) = x^2

B.=g(x) = 1.2x^2

C.=h(x) = 1.5x^2

D.=k(x) = 2x^2

Answer:

30 years old now

Step-by-step explanation:

Add the years to her age then to determine her age now

11+19 = 30

She is 30 years old now

Answer:

37 students

Step-by-step explanation:

Final answer:

To determine the number of students on the trip, multiply the number of adults by their ticket cost, subtract this from the total cost, and then divide the remainder by the student ticket cost to find that 37 students went on the trip.

Explanation:

The question involves a group pricing problem where the wildlife club spent $350 on zoo admission, adults tickets cost $7.50 each, and student tickets cost $5 each. If there were 22 adults on the trip, we need to calculate the number of students who attended.

To solve this, we first calculate the total cost for adult admissions by multiplying the number of adults by the cost per adult ticket: 22 adults × $7.50/adult = $165. Then, we subtract this amount from the total cost to determine the amount spent on student tickets: $350 total - $165 for adults = $185 for students.

Finally, we divide the remaining amount by the cost per student ticket to find the number of student tickets: $185 ÷ $5/student = 37 students. Therefore, 37 students went on the trip.

Answer:

120 m

Step-by-step explanation:

Let the length of the pole be a and the shadow be b at 58° and b+90 at 36°.

Then, as the pole and its shadow form a right triangle, we have:

As,

The equations change to:

Comparing the two equations:

Then

Answer:

Step-by-step explanation:

We take all the blues and all the reds and  1 green and divide it at the total number of bages.

14/20

The probability of Carol pulling a green chip from the bag is 7 out of 20. This is calculated by dividing the number of green chips by the total number of chips.

The subject of this question is Probability which falls under Mathematics. In this particular question, Carol has a total of 20 chips: 3 red, 10 blue, and 7 green.

Probability is calculated as 'the number of ways an event can occur' divided by 'the total number of outcomes'. Here, the event is pulling out a green chip. There are 7 green chips, and 20 total chips. So, the probability would be calculated as:

Number of green chips (Favorable outcomes) / Total chips (Total outcomes)

Which translates to: 7/20

That means, the probability of pulling out a green chip from the bag is 7 out of 20 times, if we repeat this experiment infinite times under the same conditions.

https://brainly.com/question/22962752

#SPJ3

Answer:

answer 1

Step-by-step explanation:

Answer:A

Step-by-step explanation:

The standard error of the mean pertains to the variability of the mean between different samples, rather than the variability of individual measurements. Therefore, the correct interpretation is D. The typical distance between means of samples of size 25 and the population mean foot length is approximately 0.8 cm.

The most accurate interpretation for the standard error of the mean in the context of the given problem is: D. "The typical distance between means of samples of size 25 and the population mean foot length is approximately 0.8 cm".

The standard error of the mean (SEM) demonstrates the standard deviation of the sampling distribution of the means. It measures how far the sample mean of the data is likely to be from the true population mean. SEM gives us an estimate of the precision of our sample mean in relation to the true population mean. It's important to recognize that SEM is not about the dispersion of individual measurements, but rather about the dispersion of sample means.

https://brainly.com/question/14524236

#SPJ6

Answer:4

Step-by-step explanation: Odd 5/4 and 10/8 are both equal

Answer:

Your answer should be 4...

Step-by-step explanation:

In the first time you planted, you planted 10 total bulbs, and 8 of them bloomed. That means that 80% of the bulbs that you planted bloomed. So if you plant 5 more bulbs, theoretically your answer should be 4, since 80% of 5 is 4.

I'm sorry if this answer isn't a lot of help, there isn't a lot of information to go off of.

Answer:

Refer below.

Step-by-step explanation:

True statements for Approximately 25 men in the sample weigh are:

More than 150 lbs.

More than 162 lbs.

Between 150 and 155 lbs.

Between 155 and 162 lbs.

Based on the experimental data, approximately 25 men in this sample weigh:

A boxplot simply refers to a type of chart that can be used for the graphical representation of the five-number summary of any data set, especially based on skewness, locality, and spread.

Additionally, the five-number summary of a data comprises the following:

In this scenario, the true statement is that approximately 25 men in this sample would weigh:

Read more on boxplots here: https://brainly.com/question/14277132

#SPJ5

Answer:

Anonymous simulation would be used to determine a game of darts.

The simulation which can be used to determine the game of darts is anonymous simulation.

Dart game is a game which is played in real by throwing darts over the dart boards which has to be pointed at a fixed places which gives the points.

Simulation games are the games which aims in designing the game as a context of various real life activities.

It aims in helping the real world to train, analyze and predict things in a way of entertainment.

The simulator which can be used to determine the game of darts is anonymous simulator.

Hence the description of the simulator which can be used to determine a game of darts is anonymous simulator.

To learn more about Simulators, click on the link given below :

https://brainly.com/question/17545219

#SPJ3

Answer 2 dollars a ride.

Step-by-step explanation:

26=50-12x

x=2

x

Answer:

(a)The percentage of hatchbacks that run on gasoline.=78%

(b) The percentage of diesel vehicles that are hatchbacks.=21%

(c)The percentage of SUVs that run on gasoline=30%

(d)The percentage of gasoline vehicles that are sedans=42%

(e)The percentage of sedans that run on diesel =44%

(f)The percentage of gasoline vehicles that SUVs.=8%

Step-by-step explanation:

This table gives information about vehicles sold at a dealership in a month.

------------------Gasoline-------Diesel

Hatchback------18---------------5

Sedan------------15---------------12

SUV----------------3----------------7

(a)The percentage of hatchbacks that run on gasoline.

Total Number of Hatchbacks=23

Number that run on Gasoline=18

Percentage that run on gasoline=(17/23)X100=78%

(b) The percentage of diesel vehicles that are hatchbacks.

Total Number of Diesel Vehicles=5+12+7=24

Number of Diesel Hatchbacks=5

Percentage of diesel vehicles that are hatchbacks=(5÷24)X100=21%

(c)The percentage of SUVs that run on gasoline

Total Number of SUVs=10

Number of Gasoline SUVs=3

Percentage of SUVs that run on gasoline=(3÷10)X100=30%

(d)The percentage of gasoline vehicles that are sedans.

Total Number of Gasoline Vehicles=18+15+3=36

Number of Gasoline sedans=15

Percentage of Sedans that run on gasoline=(15÷36)X100=42%

(e)The percentage of sedans that run on diesel

Total Number of Sedans=15+12=27

Number of Diesel Sedans=12

Percentage of sedan that run on diesel=(12÷27)X100=44%

(f)The percentage of gasoline vehicles that SUVs.

Total Number of Gasoline Vehicles=18+15+3=36

Number of Gasoline SUVs=3

Percentage of SUVs that run on gasoline=(3÷36)X100=8%

Answer:

(a)The percentage of hatchbacks that run on gasoline.=78%

(b) The percentage of diesel vehicles that are hatchbacks.=21%

(c)The percentage of SUVs that run on gasoline=30%

(d)The percentage of gasoline vehicles that are sedans=42%

(e)The percentage of sedans that run on diesel =44%

(f)The percentage of gasoline vehicles that SUVs.=8%

Step-by-step explanation:

hope that helps

Answer:

y=6x-2

Step-by-step explanation:

Answer:

y is 6

Step-by-step explanation:

they are very similar in alot of ways but im not sure how to discribe im good at putting them onto a graph

Final answer:

The concentrations of Solution A, Solution B, and the final alcohol mixture are needed to determine how many milliliters of Solution B to mix with Solution A. Without these specifics, we provide a general approach using the method of allegations and unit conversion.

Explanation:

The student's question pertains to the mixing of two solutions with different concentrations of alcohol to achieve a specific concentration in the resulting mixture. We cannot provide a direct answer to the question as stated because the concentrations of Solution A, Solution B, and the resulting mixtures are not specified. To calculate the amount of Solution B needed, we must know the concentration (percentage by volume or molarity) of alcohol in Solution A and Solution B, as well as the desired concentration of the final mixture.

For instance, if we were given a situation where Solution A is 60% alcohol and we need to mix it with Solution B, which is 40% alcohol, to make a resulting mixture that is 50% alcohol, we could use the method of allegations to find the correct proportions. Using the formula:

Solution A concentration + Solution B concentration = Total concentration of mixture

We can then solve for the unknown by inputting the given values and applying algebraic methods to find the volume of Solution B.

Assuming we use mL for milliliters and L for liters, to accurately measure and mix the solutions, we may also need to convert units between mL and L, taking into account that there are 1,000 milliliters in 1 liter.

Noticing that there is a pattern of repetition in the question (the numbers are repeated twice), we are assuming that the mean number of words per minute is 88, the standard deviation is of 14 WPM, as well as the number of sixth graders is 137, and that there is a need to estimate the probability that the sample mean would be greater than 89.87.

Answer:

"The probability that the sample mean would be greater than 89.87 WPM" is about [tex] \\ P(z>1.56) = 0.0594[/tex].

Step-by-step explanation:

This is a problem of the distribution of sample means. Roughly speaking, we have the probability distribution of samples obtained from the same population. Each sample mean is an estimation of the population mean, and we know that this distribution behaves normally for samples sizes equal or greater than 30 [tex] \\ n \geq 30[/tex]. Mathematically

[tex] \\ \overline{X} \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex] [1]

In words, the latter distribution has a mean that equals the population mean, and a standard deviation that also equals the population standard deviation divided by the square root of the sample size.

Moreover, we know that the variable Z follows a normal standard distribution, i.e., a normal distribution that has a population mean [tex] \\ \mu = 0[/tex] and a population standard deviation [tex] \\ \sigma = 1[/tex].

[tex] \\ Z = \frac{\overline{X} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex] [2]

From the question, we know that

We also know the size of the sample for this case: [tex] \\ n = 137[/tex] sixth graders.

We need to estimate the probability that a sample mean being greater than [tex] \\ \overline{X} = 89.87[/tex] WPM in the distribution of sample means. We can use the formula [2] to find this question.

The probability that the sample mean would be greater than 89.87 WPM

[tex] \\ Z = \frac{\overline{X} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex] \\ Z = \frac{89.87 - 88}{\frac{14}{\sqrt{137}}}[/tex]

[tex] \\ Z = \frac{1.87}{\frac{14}{\sqrt{137}}}[/tex]

[tex] \\ Z = 1.5634 \approx 1.56[/tex]

This is a standardized value and it tells us that the sample with mean 89.87 is 1.56 standard deviations above the mean of the sampling distribution.

We can consult the probability of P(z<1.56) in any cumulative standard normal table available in Statistics books or on the Internet. Of course, this probability is the same that [tex] \\ P(\overline{X} < 89.87)[/tex]. Then

[tex] \\ P(z<1.56) = 0.94062 \approx 0.9406[/tex]

However, we are looking for P(z>1.56), which is the complement probability of the previous probability. Therefore

[tex] \\ P(z>1.56) = 1 - P(z<1.56) = 1 - 0.9406[/tex]

[tex] \\ P(z>1.56) = P(\overline{X}>89.87) = 0.0594[/tex]

Thus, "The probability that the sample mean would be greater than 89.87 WPM" is about [tex] \\ P(z>1.56) = 0.0594[/tex].

Answer: 18.1 inches

Step-by-step explanation: A volleyball is spherical in shape, and the surface area of a sphere is giving by the formula

from the data giving, the surface area was calculated to be 227 square inches. from the above formula, we define the radius, r to be the subject of formula, we arrive at

if we substitute for the surface area, we arrive at

Hence the radius of the volleyball will be 18.1 inches  

Hope this helps

Answer:

73.8 degrees because 96.5-22.7=73.8

Step-by-step explanation:

Answer:

It makes the solution of the equation easier

Step-by-step explanation:

Here we have the formula relating Celsius and Fahrenheit given as follows;

[tex]C = \frac{5\times (F - 32)}{9}[/tex]

From the above Celsius to Fahrenheit equation, we have that to solve for F we rearrange the formula as follows

[tex]C =\frac{5F}{9} - \frac{32\times 5}{9}[/tex]

Which is the same as

[tex]C =\frac{5F}{9} - 17\frac{7}{9}[/tex]

It is then seen that rearranging the equation between Celsius and Fahrenheit makes it easier to solve for either °C or °F.

Answer:

It’s easier to find the solution to a variable when that variable is by itself on one side of the equal sign. Rearranging formulas before substituting values for each variable makes calculations more straightforward. With this approach, we only need to perform operations such as multiplication, division, addition, and subtraction on one side of the equal sign, and we simplify instead of solving by using the properties of equality.

Step-by-step explanation:

The amount of cement is needed to create the walkway around the rectangular pool will be 176 square yards . Then the correct option is A.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

The area is the combination of two rectangles of 12 by 4, and four triangles of 4 by 4, and two rectangles of 6 by 4.

Then the area will be

A = 2(12 x 4) + 4(1/2 x 4 x 4) + 2(6 x 4)

A = 96 + 32 + 48

A = 176 square yards

Then the correct option is A.

More about the geometry link is given below.

https://brainly.com/question/7558603

#SPJ5

Answer:

The answer is A.

Step-by-step explanation:

(Only if your question "Amos’s solution is (2, –14). What did he do wrong? ")

Trust me, I got it right

Answer:

103.62

Step-by-step explanation:

[tex]C = \pi d\\3.14 * 33 =103.62[/tex]

Answer:

The sample size required is 102.

Step-by-step explanation:

The (1 - α)% confidence interval for population mean μ is:

[tex]CI=\bar x\pm z_{\alpha/2}\times\frac{\sigma}{\sqrt{n}}[/tex]

The margin of error for this interval is:

[tex]MOE= z_{\alpha/2}\times\frac{\sigma}{\sqrt{n}}[/tex]

Given:

σ = 9.2

(1 - α)% = 90%

MOE = 1.5

The critical value of z for 90% confidence level is:

[tex]z_{0.10/2}=1.645[/tex]

*Use a z-table.

Compute the value of n as follows:

[tex]MOE= z_{\alpha/2}\times\frac{\sigma}{\sqrt{n}}[/tex]

      [tex]n=[\frac{z_{\alpha/2}\times \sigma}{MOE}]^{2}[/tex]

         [tex]=[\frac{1.645\times 9.2}{1.5}]^{2}\\=101.795\\\approx102[/tex]

Thus, the sample size required is 102.

To calculate the sample size for a 90% confidence interval with a 1.5 margin of error using a known standard deviation of 9.2, you would need a sample size of approximately 101.

90% Confidence Interval Sample Size Calculation

To determine the required sample size for a 90% confidence interval with a maximum margin of error of 1.5, and a known population standard deviation of 9.2, you can use the following formula:

n = (Z*σ/E)^2

Here, 'n' is the sample size, 'Z' is the Z-score corresponding to the desired confidence level, 'σ' is the population standard deviation, and 'E' is the maximum margin of error. For a 90% confidence level, the Z-score is approximately 1.645 (since 5% is in each tail of the normal distribution). Plugging in the values we have:

n = (1.645 * 9.2 / 1.5)^2

The calculation yields:

n = (15.074 / 1.5)^2

n = (10.049)^2

n = 101.0

Therefore, you would need a sample size of approximately 101 to ensure the sample mean does not deviate from the population mean by more than 1.5 with a 90% confidence interval.

Answer:

The answer to your question is the letter C. 13248 square units

Step-by-step explanation:

Data

Right triangle                      Rectangle

short leg = 69                     base = x + 100

hypotenuse = 115

Process

1.- Calculate the long leg of the right triangle.

       c² = a² + b²

       b² = c² - a²

       b² = 115² - 69²

       b² = 13225 - 4761

       b² = 8464

       b = 92

2.- Calculate the length of the base of the rectangle

       base = 92 + 100

       base = 192

3.- calculate the area of the rectangle

       Area = 192 x 69

                = 13248 square units