What is the surface area

Answer:

143°

Step-by-step explanation:

We know that the two lines are parallel, which means that since ∠A and ∠B are same-side angles, they are equal. That means we can set the expressions equal:

7x + 24 = 3x + 92

4x = 68

x = 17

Plug this into the expression for A:

∠A = 7x + 24 = 7 * 17 + 24 = 143

The answer is 143°.

Since both lines are parallel, both equations are equal.

7x + 24 = 3x + 92

Solve for x.

~Subtract 24 to both sides

7x + 24 - 24 = 3x + 92 - 24

~Simplify

7x = 3x + 68

~Subtract 3x to both sides

7x - 3x = 3x - 3x + 68

~Simplify

4x = 68

~Divide 4 to both sides

4x/4 = 68/4

~Simplify

x = 17

Substitute 17 with x in ∠A

∠A = 7x + 24

∠A = 7(17) + 24

∠A = 119 + 24

∠A = 143

Best of Luck!

Answer:

Check the explanation

Step-by-step explanation:

First define the below events

Delayt : Traffic delay in current period

Delayt-1 : Traffic delay in preceding period

No-Delayt : No traffic delay in current period

No-Delayt-1 : No traffic delay in preceding period

Based on above definitions, define below given probabilities

P(No-Delayt/No-Delayt-1) = Probability of "no delay" in current period given that "no delay" in preceding period

= 0.85

P(Delayt/Delayt-1) = Probability of "delay" in current period given that "delay" in preceding period

= 0.75

and given that one period = 30 minutes

a) Given that motorist already knows that there is a traffic delay, probability of delay in next 60 minutes will be possible if both the consecutive periods is in "delay" state.

Period A Period B

---------------- -----------------

Delay -------> Delay ------> Delay

Since both the delay events should occur together(consecutive) to get the required probability, hence

Probability that next 60 minutes(two consecutive periods) will be in delay state

= P(Delayt/Delayt-1) * P(Delayt/Delayt-1)

= 0.75 * 0.75

= 0.5625 [ANSWER]

b) probability that in the long run the traffic will not be in the delay state is equivalent to proability that all the time in No-delay state.

First calculate the probability of currren period in delay state given that preceding period in No-delay state

 P(Delayt/No-Delayt-1) = 1 - P(No-Delayt/No-Delayt-1)

= 1 - 0.85

= 0.15

Now the required probability,

  P(All the time No-Delay state) = 1 - P( one period in delay state)

= 1 - ( P(Delayt/Delayt-1) + P(Delayt/No-Delayt-1) )

= 1 - (0.75 + 0.15)

= 0.10 [ANSWER]

c) Yes. Because this assumption assumes that for the 30 minutes traffic will be in delay state and just after 30 minutes, there will be No-delay state which is a hypothetical situation. In general scenario, traffic doesn't behave like this. To make the model more realistic, the probabilities might have been modeled as a function of time, instead of being constant for 30 minutes.

Answer:

Paul is the youngest at 17 years old. Fiona is 20 years old, Sara is 23 years old

Step-by-step explanation:

Assign variables to the ages.

S = sara's age

F = Fiona's age

P = Paul's age.

S + F + P = 60

S = 3 + F

P = F - 3

(3 + F) + F + (F - 3) = 60

3 + 3F - 3 = 60

3F = 60

F = 20

S = 23

P = 17

Answer:

Red-5-0.1

Blue-0.26

White-10

Green-22

Step-by-step explanation:

In the experiment, Alexis drew colored balls and you need to organize the results in a frequency table. The numbers given represent frequency counts for each color. Keep in mind that the total draws were 50, so no frequency count should exceed this number.

The question is about Alexis' experiment involving drawing colored balls from a box. The results of the 50 trials are recorded in a frequency table. As the student, you are expected to correctly assign certain numbers to their respective places in this table. These numbers represent the total counts per color across the 50 trials.

To accomplish this, you must first understand what a frequency table is. A frequency table is a method of organizing raw data in a compact form by displaying a series of data values in ascending order, along with their corresponding frequencies.

In this scenario, the frequencies are the number of times Alexis drew a ball of a specific color. For example, if she drew a red ball 15 times, we would put 'Red' in the color column and '15' in the frequency column.

Please note that not all the provided numbers will be used, and there should be no number in the table higher than 50 since that was the maximum number of trials Alexis performed.

For more such questions on frequency table, click on:

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Answer:

Step-by-step explanation:

34

Answer:

121

Step-by-step explanation:

Answer:

if the 1/4 is supposed to be small and above the 12, the answer should be 12

Step-by-step explanation:

test

Answer:

1) The most common salary is $460.

2) The salary that half of the employees surpassed is $475

3) The percentage of employees with salaries below $485 is 75%

4) 75% of the employees have a salary above $450.

5) The salary that stands 3 standard deviations below the mean is $380

6) 33% of the employees have a salary above $483.

7) The salary that stands 2 standard deviations above the mean is $530

Step-by-step explanation:

Hello!

1. What is the most common salary?______________

The measure that allows you to know which one is the most common value (i.e. the most frequent/observed number) in a data set is the mode. According to the given statistics, the most common salary is $460.

2. What salary did half the employees surpass?_________________

The measure that divides the sample in exactly a half (bottom 50% from the top 50%) is the median. In this example the salary that half of the employees surpassed is $475.

3. About what percent of employee's salaries is below $485?__________________

As you can see in the descriptive statistics, the third quartile (Q₃) is $485.

The Q₃ is the value that divides the bottom 75% of the sample from the top 25%. So the percentage of employees with salaries below $485 is 75%

4. What percent of the employees are above $450?___________________

The first quartile (Q₁) is the value that separates the bottom 25% of the sample from the top 75%. In this case Q₁= $450, which means that 75% of the employees have a salary above $450.

5. What salary is 3 standard deviations below the mean?____________________

The mean is $ 470 and the standard deviation is $30, the salary that stands 3 standard deviations below the mean is

X[bar]-3S= $470-3*$30= $380

6. About what percent of employee's salaries is above $483?__________________

P₆₇= $483, this value is the 67th percentile and means that 67% of the employees have a salary below $483.

If 67% are below $483, then 100 - 67= 33% of the employees have a salary above $483.

7. What salary is 2 standard deviations above the mean?______________________

The mean is $ 470 and the standard deviation is $30, the salary that stands 2 standard deviations above the mean is

X[bar]+2S= $470+2*$30= $530

I hope you have a SUPER day!

Answer:

36x² - 9y²

Step-by-step explanation:

We see that the given expression (6x + 3y)(6x - 3y) looks just like the expression (a + b)(a - b). When multiplied out, this is a difference of squares identity that I highly recommend you memorise:

(a + b)(a - b) = a² - b²

Here, a = 6x and b = 3y, so plug these in:

(6x + 3y)(6x - 3y) = (6x)² - (3y)² = 36x² - 9y²

Answer:

36x² - 9y²

Step-by-step explanation:

(6x + 3y)(6x − 3y)

(6x)² - (3y)²

36x² - 9y²

Answer:

475  milliliters  of oil

Step-by-step explanation:

1 liter =1000 milliliters

1 deciliter =100 milliliters

To make it easier, we convert all our units to milliliters.

Volume of the water bottle =0.6 liter

=0.6 X 1000 =600 milliliters

Volume of colored water = 1.25 deciliters

=1.25 X 100 =125 milliliters

Therefore:

Volume of oil needed to fill the bottle = 600-125

=475  milliliters

Sam will need to add 475 milliliters of oil to the 0.6-liter bottle after adding 1.25 deciliters of colored water to create his homemade lava lamp.

The question involves calculating the volume of oil needed to fill the remainder of a 0.6-liter bottle after adding some colored water. To solve this, we need to convert the measurements into the same units and perform subtraction. In this case, we convert deciliters to milliliters, as we know that 1 deciliter is equivalent to 100 milliliters. The student has filled the bottle with 1.25 deciliters of colored water, which is 1.25 × 100 milliliters = 125 milliliters of water.

Since the bottle can hold 0.6 liters, which is equal to 600 milliliters, the amount of oil required will be the total bottle capacity minus the volume of colored water already added. Thus, we calculate 600 milliliters (bottle capacity) – 125 milliliters (water added) to find the volume of oil needed.

So, Sam will need 600 mL – 125 mL = 475 milliliters of oil to fill the rest of his homemade lava lamp.

Answer:

Jenny = 23 | Nancy = 11

Step-by-step explanation:

Cutting off one corner of a rectangular prism creates a bicapped trigonal prismatic shape.

When you cut off one of the corners of a rectangular prism, you would get a shape known as a bicapped trigonal prismatic. This shape is formed by twisting one face of a cube relative to another, folding opposing faces towards one another, and distorting the original rectangular prism.

Answer:

a) The price that maximizes profit is p =$43.

b) The utility shouldn't pass all this increase on the consumers because this would mean a decrease in the profits. They should pass only $7 to consumers price.

Step-by-step explanation:

We have an electric utility company which has a demand function defined by:

[tex]p=59-10^{-5}x[/tex]

where p is the price and x is the the energy in thousands of kWh.

The cost of the company is defined as:

[tex]C(x)=3\cdot 10^6+27x[/tex]

We have to calculate the price that maximizes the utility's profit R(x).

We can define the profit as:

[tex]R(x)=p\cdot x-C=(59-10^{-5}x)\cdot x-(3\cdot 10^6+27x)\\\\R(x)=-10^{-5}x^2+(59-27)x-3\cdot10^6\\\\R(x)=-10^{-5}x^2+32x-3\cdot10^6[/tex].

To maximize R, we have to derive it and equal to zero

[tex]\dfrac{dR}{dx}=0\\\\\\\dfrac{dR}{dx}=-2\cdot10^{-5}x+32=0\\\\\\x=(32/2)\cdot 10^5=16\cdot 10^5=1.6\cdot 10^6[/tex]

The price that maximizes the profit is then:

[tex]p=59-10^{-5}x=59-10^{-5}(16\cdot 10^5)=59-16=43[/tex]

b) When the unit cost rise from $27 to $41, the utility profit function changes.

We have to calculate the new price that maximizes profit, and then we will know if the rise in cost was transferred to price completely.

The new profit function is:

[tex]R(x)=p\cdot x-C=(59-10^{-5}x)\cdot x-(3\cdot 10^6+41x)\\\\R(x)=-10^{-5}x^2+(59-41)x-3\cdot10^6\\\\R(x)=-10^{-5}x^2+18x-3\cdot10^6[/tex]

To maximize R, we have to derive it and equal to zero

[tex]\dfrac{dR}{dx}=0\\\\\\\dfrac{dR}{dx}=-2\cdot10^{-5}x+18=0\\\\\\x=(18/2)\cdot 10^5=9\cdot 10^5[/tex]

We calculate the new price as:

[tex]p=59-10^{-5}x=59-10^{-5}(9\cdot 10^5)=59-9=50[/tex]

The new price is $7 dollars above the previous maximizing price, so the rise in unit cost is only transferred 50% to the price.

The utility shouldn't pass all this increase on the consumers because this would mean a decrease in the profits. They should pass only $7 to consumers price.

Answer:120

Step-by-step explanation:

Volume=length x width x height

volume of box=4x2.5x1.5

Volume of box=15

Length of side of cube=1/2=0.5

Volume of cube=0.5x0.5x0.5

Volume of cube=0.125

Number of cube that can pack inside there box=15 ➗ 0.125=120

Answer:

17 inches

Step-by-step explanation:

Answer:

Given:

Face ____________Count

1_________________14

4_________________15

2_________________5

5_________________14

3_________________11

6_________________1

a) I rolled the die 60 times and my values are recorded.

Assuming the die is fair, each face is expected to show 10 times.

[tex] 60* \frac{1}{6} = 10 [/tex]

b) To check if my results are unusual hypothesis test is used to address this. In this case the test is called goodness of fit.

c) For the null and alternative hypothesis :

The null hypothesis states , the die is fair (the number of times each face appear is equal)

The alternative hypothesis states the die is not fair.

H0 : p = 0.6

H1 : p ≠ 0.6

d)

The number of times the die is rolled is recorded.

The number of times the die is rolled is independent because the outcomes are independent.

Here the expected value of observation is more than five because the null hypothesis expects each die roll to be 10. Thus, the condition is satisfied.

e) Number of degrees of freedom for this test is n-1.

n = 6 (total faces in a die)

Therefore, degrees of freedom =

6-1 = 5

Answer:

  B.  4 bags

Step-by-step explanation:

The number of bags that will have the same quantities of the different gifts is the Greatest Common Divisor of the numbers of gifts.

  GCD(24, 32, 44) = 4

Mrs. Dupree can make at most 4 identical bags.

___

How to find the GCD

The GCD can be found by looking at factors:

4 is the largest common factor of these numbers.

__

The GCD can also be found using Euclid's algorithm. In that algorithm, the larger number is divided by the smaller, with the remainder replacing the larger number after each step. If the remainder is zero, the smaller number is the GCD.

The GCD of several numbers can be found by finding the GCD of a pair, then of that value and the next number:

  GCD(24, 32, 44) = GCD(GCD(24, 32), 44) = GCD(8, 44) = 4

_

  32/24 = 1 r 8 . . . . first step in Euclid's algorithm for GCD(24, 32)

  24/8 = 3 r 0   ⇒   GCD(24, 32) = 8

Then

  44/8 = 5 r 4

  8/4 = 2 r 0   ⇒   GCD(8, 44) = 4 = GCD(24, 32, 44)

Answer:

[tex]3.3\leq x\leq 3.5[/tex]

Step-by-step explanation:

The 95% confidence interval can be calculated as:

[tex]x'-z_{\alpha/2}\frac{s}{\sqrt{n}} \leq x\leq x'+z_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]

Where [tex]x[/tex] is the mean consumption of milk, [tex]x'[/tex] is the sample mean, [tex]s[/tex] is the population standard deviation, [tex]n[/tex] is the size of the sample, [tex]\alpha[/tex] is 5%  and [tex]z_{\alpha /2}[/tex] is the z-value that let a probability of [tex]\alpha /2[/tex] on the right tail.

So, replacing [tex]x'[/tex] by 3.4 liters, [tex]s[/tex] by 1.3 liters, n by 650 and [tex]z_{\alpha /2}[/tex] by 1.96, we get that the 95% confidence interval is equal to:

[tex]3.4-(1.96*\frac{1.3}{\sqrt{650}})\leq x\leq 3.4+(1.96*\frac{1.3}{\sqrt{650}}) \\3.4-0.1\leq x\leq 3.4+0.1\\3.3\leq x\leq 3.5[/tex]

Answer:

Step-by-step explanation:

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean.

Since the sample size is large and the population standard deviation is known, we would use the following formula and determine the z score from the normal distribution table.

Margin of error = z × σ/√n

Where

σ = population standard Deviation

n = number of samples

From the information given

x = 3.4

σ = 1.3

n = 650

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.025 = 0.975

The z score corresponding to the area on the z table is 1.96. Thus, confidence level of 95% is 1.96

Margin of error = 1.96 × 1.3/√650 = 0.1

Confidence interval = 3.4 ± 0.1

The lower end of the confidence interval is

3.4 - 0.1 = 3.3 litres

The upper end of the confidence interval is

3.4 + 0.1 = 3.5 litres

Answer:

x250+y525=7200 the answer is no

Step-by-step explanation:

Answer:

Step-by-step explanation:

The growth factor is 1 added to the growth rate of 1.5%, so is 1.015. This factor is applied each year. So the number of students will be the original number multiplied by this factor as many times as there are years (after 2002).

Repeated multiplication is signified using an exponent. The function can be written as ...

  n(t) = 972×1.015^t

In 12 years after 2002, the number of students is modeled as ...

  n(12) = 972×1.015^12 ≈ 1162 . . . students in 2014

__

When the change is described as "increased by ...", it means the function is modeling growth. If the population were to decrease, it would be considered decay. That is, the "growth factor" is greater than 1 for growth, and less than 1 for decay. 1.015 is greater than 1, so this is considered growth.

Answer:36

Step-by-step explanation:u

6^7/6^5

6^(7-5)

6^2

6x6=36

Answer:

The answer is A

Step-by-step explanation:

When doing an equation you always have to follow this order: exponents, parentheses, multiply/divide, then addtion/subtraction

Answer:

See Explanation

Step-by-step explanation:

The W-2 form is a form which an employer must send to an employee and the Internal Revenue Service (IRS) at the end of each year.  Every January, the employee should receive a Form W-2 Wage and Tax Statement from his/her employer. The contents of this form are the amount of money made by the employee during the previous year and how much was paid as tax.

When a citizen gets their W-2 form for the previous year, they can use it to decide if they qualify for a tax refund which could be in cash or used towards the next years' tax.

Finally,

Answer:

1. refund

2. w-2

3. online

Answer:

P(H/A) = 0.6716

Step-by-step explanation:

Let's call H the event that Joe flipped heads, T the event that Joe flipped tails and A the event that Joe wear one read and one black sock.

So, the probability that he flipped heads given that Joe wears one read and one black sock is calculated as:

P(H/A) = P(H∩A)/P(A)

Where P(A) = P(H∩A) + P(T∩A)

On the other hand, nCx gives the number of combinations in which we can select x elements from a group of n elements. nCx is calculated as:

[tex]nCx=\frac{n!}{x!(n-x)!}[/tex]

So, the probability that Joe wear one red and one black sock given that he picks the socks from the first drawer is:

[tex]\frac{6C1*4C1*2C0}{12C2}=0.3636[/tex]

Because he need to choose one red sock from the 6 that are in the first drawer, one black sock from the 4 that are in the first drawer and 0 white socks. Additionally there are 12C2 ways to choose a pair of socks.

Therefore the probability P(H∩A) that that Joe flipped heads and Joe wear one read and one black sock is:

P(H∩A) = 0.5*0.3636 = 0.1818

Because there is a probability of 0.5 to flipped heads and the probability that Joe wear one red and one black sock given that he flipped heads is 0.3636.

At the same way, the probability that Joe wear one red and one black sock given that he picks the socks from the second drawer is:

[tex]\frac{4C1*2C1*4C0}{10C2}=0.1778[/tex]

Therefore the probability P(T∩A) that that Joe flipped tails and Joe wear one read and one black sock is:

P(T∩A) = 0.5 * 0.1778 = 0.0889

Finally, P(A) and P(H/A) is equal to:

P(A) = 0.1818 + 0.0889 = 0.2707

P(H/A) = 0.1818/0.2707 = 0.6716

The domain and range of each function y = 3.52 is All real numbers and {3.52}.

The domain of a function is defined as the set of all the possible input values that are valid for the given function.

The range of a function is defined as the set of all the possible output values that are valid for the given function.

We are given that;

The function y=3.52

Now,

For the function y = 3.52, the output (y-value) is always the same, regardless of the input (x-value). Therefore, the domain of this function is all real numbers, and the range of this function is the single value 3.52.

Therefore, the domain and range will be All real numbers and {3.52}

Learn more about the domain and range of the function:

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The value of θ in radians when sin(θ) = 1 is π/2, approximately equal to 1.57 rounded to the nearest hundredth.

To find the value of θ in radians when sin(θ) = 1, we know that sine is the ratio of the length of the opposite side to the length of the hypotenuse in a right triangle.

Since the sine of an acute angle cannot exceed 1, and sin(θ) = 1, this indicates that θ must be a 90-degree angle, or π/2 radians.

In radians, π represents the ratio of the circumference of a circle to its diameter, and π/2 corresponds to one-fourth of the circumference, which equals a right angle.

Therefore, the value of θ in radians is π/2, or approximately 1.57 rounded to the nearest hundredth.

Answer:

A) Since all of the students had an opportunity to respond, this is evidence that a majority of all the students supports major changes.

Step-by-step explanation:

Since all the students were given equal opportunity then the response suggest that a major change is required by the students.

Answer: d

Step-by-step explanation: the responses were from voluntary response sample, so the cafeteria staff should not use the results to draw any conclusions

Answer:

Brent

Step-by-step explanation:

More numbers = More combinations

Answer:

Brent’s club has more possible team combinations because there are more members to choose from.

Step-by-step explanation:

I completed it on edg 2020

Answer:

The volume of the hemisphere is 496741.6 m³

Step-by-step explanation:

The volume of an sphere is given by:

[tex]V_{s} = \frac{4\pi r^{3}}{3}[/tex]

In which [tex]\pi = 3.14[/tex] and r is the radius.

An hemisphere is half of an sphere, so it's volume is half the sphere's volume. So

[tex]V_{h} = \frac{V_{s}}{2} = \frac{2\pi r^{3}}{3}[/tex]

In this question:

[tex]r = 61.9[/tex]. So

[tex]V_{h} = \frac{2\pi (61.9)^{3}}{3} = 496741.6[/tex]

The volume of the hemisphere is 496741.6 m³

Answer:

The volume of the hemisphere = 496741.6 m³

Step-by-step explanation:

Volume of a sphere is= (4/3) × π × r³

r is the radius

π is 22/7

hemisphere is half of an sphere,

so the volume of henisphere is  (2/3) × π × r³

Given that ;

r = 61.9 m

[tex]V = \frac{2\pi (61.9)^{3}}{3} = 496741.6[/tex]

therefore, the volume of the hemisphere is 496741.6 m³

Answer:

13824 cubic inches

Step-by-step explanation:

So all we need to do is:

1) Find the volume of 1 cube of the 8

2) Multiply that by 8, because 8 of them make the prism.

SO 1)

the volume of cube = side * side * side = 12*12*12 = 1728

SO 2)

the volume of prism = vol(cube) * 8 = 1728 * 8 = 13824

ANSWER: 13824 cubic inches ;)

Answer:

2.50 per two bottles of sprite

Step-by-step explanation: