4.
a) Name the highlighted arc and determine if it is a major arc, minor arc, or semicircle.
b) Find the measure of the highlighted arc.

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached image for the step by step explanation of the answer to the question

Step-by-step explanation:

25.2 + 800 - 427.43 x 2.4 ÷ 13

825.2 - 1025.832 ÷ 13

200.632 ÷ 13

= 15.44

Final answer:

The equation representing the total monthly cost of the A Fee and Fee plan based on the number of minutes used is y = 0.20x + 29, where y is the total monthly cost and x is the number of minutes.

Explanation:

To find an equation in the form y = mx + b, where x is the number of monthly minutes used and y is the total monthly cost of the A Fee and Fee plan, we first need to determine the slope (m) and the y-intercept (b).

We have two points based on the information given: (290, 87) and (980, 225). The slope (m) is calculated by the difference in cost divided by the difference in minutes:

m = (225 - 87) / (980 - 290)

m = 138 / 690

m = 0.20

Now that we have the slope, we can use one of the points to find b, the y-intercept.

Using the point (290, 87) and the slope 0.20:

87 = 0.20(290) + b

b = 87 - 58

b = 29

The equation representing the total monthly cost (y) based on the number of minutes used (x) is therefore:

y = 0.20x + 29

Answer:[tex]h=\dfrac{kL^2}{8mg}[/tex]

Step-by-step explanation:

Given

Mass of ball is M  is dropped from a height h

spring constant is k

Here we can use conservation of energy

Mass has a Potential energy of E=mgh

and when it falls on the spring then it compresses it a length of 0.5 L

Now potential energy is converted into Elastic potential energy and then spring unleashes this energy to the mass and again provide kinetic energy to mass to move upward .

In this way energy is conserved. So, mass must move to an initial  height h

[tex]mgh=\frac{1}{2}k(\frac{L}{2})^2[/tex]

[tex]h=\dfrac{kL^2}{8mg}[/tex]

considering [tex]h >> 0.5L[/tex]

The toxicity level of the lake water is calculated by dividing the current level of toxins (0.86 mg per liter) by the maximum safe level (1.04 mg per liter) and then converting to a percentage, which results in approximately 83%.

To determine the toxicity level of lake water, we need to divide the amount of dissolved toxins per liter by the maximum safe amount and convert it to a percentage.

Given that the lake currently has 0.86 milligrams of dissolved toxins per liter of water and the maximum safe level is 1.04 milligrams per liter, we calculate the toxicity level using the following steps:

Therefore, the correct answer is C. 83%.

Answer:

Standard deviation = 7.76

Step-by-step explanation:

The formula for determining standard deviation when dealing with population proportion is expressed as

Standard deviation = √npq

Where

n represents the number of samples from the population.

p represents the probability of success.

q represents the probability of failure.

From the information given,

n = 500 policyholders

p = 14% = 14/100 = 0.14

q = 1 - 0.14 = 0.86

Standard deviation = √500 × 0.14 × 0.86 = 7.76

Answer: std dev = 0.01552

Step-by-step explanation:

we will solve this by taking a step by step analysis of the problem.

i hope at the end of this section, you will feel confident  to try out other questions.

given that the size of the sample (n) = 500

The Insurance company records indicate that 14% of its policyholders file claims involving theft or robbery of personal property from their homes.

hence sample proportion of policyholders filing claims involving theft or robbery from their homes (p) = 14% =0.14

let Z be the number of policyholders files involving theft or robbery of personal property from their homes.

so Z~Bin(500,0.14) and p=Z/500

we know from basic mathematics that standard deviation = √(variance)

so variance is  given thus;

V[Z] = 500*0.14*(1-0.14)

or V[p] = V[Z/500] = 500*0.14*0.86/500² = 0.14*0.86/500

so standard deviation is;

sqrt[V[p]]=sqrt(0.14*0.86/500) = sqrt(0.0002408) = 0.01552

∴ the standard deviation = 0.01552

cheers i hope this helps!!!!

Answer:

5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Answer:

Option B could be used to find c, the number of cups ofvinegar that Brian should use with 12 cups of water

Step-by-step explanation:

Brian makes a cleaning solution using a ratio of 4 cups of water to 1 cup of vinegar.

Let c be the number of cups of vinegar that Brian should use with 12 cups of water.

1 cup of vinegar uses cup of water = 4

c cups of vinegar uses cup of water = 4c

We are c, the number of cups ofvinegar that Brian should use with 12 cups of water

So, 4c=12

[tex]4=\frac{12}{c}[/tex]

So, equation =[tex]\frac{4}{1}=\frac{12}{c}[/tex]

So, Option B could be used to find c, the number of cups ofvinegar that Brian should use with 12 cups of water

Answer:

Deepwater Horizon

good movie too btw

-Hops

Answer:

48 000 gallons / 2 days = 24 000 gallons per day

24 000 gallons / 24 hours = 1 000 gallons per hour

1 000 gallons / 60 minutes = 16.(6) gallons per minute

I had the same question on a quizz, the question was:In two days, 48,000 gallons of oil gushed out of a well. At what rate did the oil flow from the well?

Hope that was helpful.Thank you!!!

Answer:

39 children and 13 adults

Step-by-step explanation:

3children = 1 adult

52 = x * (3children + 1adult)

52= x * 4

13 = x

x = 13

total children = 3x

3x = 39

The problem poses a system of linear equations where the number of attendees 'a + c = 52' and 'c = 3a'. Resolving these equations gives 'a = 13' adults and 'c = 39' children.

This is a problem about creating and solving a system of linear equations. Let's denote the number of adults who attended the ball game as 'a' and the children who attended the game as 'c'. According to the problem, we have two parts of information that can be written as equations:

You can substitute the equation for 'c' in the first equation: a + (3a) = 52. Solving this, you find that 'a' equates to 13. Substitute 'a = 13' into the second equation, you will find that 'c = 39'. This indicates that there were 13 adults and 39 children who attended the game.

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Answer:

(1)Base Area= 81 square yards.

(2)

(3)Height=12 Units

Step-by-step explanation:

Question 1

Volume of the rectangular prism=2,592 cubic yards.

Height of the rectangular prism=32 yards

Volume of a rectangular prism =lbh (where lb is the Base Area)

Therefore:

lbh=2592

32lb=2592

lb=2592/32=81

Base Area= 81 square yards.

Question 2

Volume of the rectangular prism=432 cubic feet.

Height of the rectangular prism=9 feet

Volume of a rectangular prism =lbh (where lb is the Base Area)

Therefore:

lbh=432

9lb=432

lb=432/9=48

Base Area= 48 square yards.

Any dimension whose product is 48 is a possible choice.

They are:

Question 3

Volume of the rectangular prism=960 cubic units.

Base Area of the rectangular prism, lb=80 Square Units

Volume of a rectangular prism =lbh (where lb is the Base Area)

Therefore:

lbh=960

80h=960

h=960/80=12

Height= 12 units.

Answer:

81 square yards.

Step-by-step explanation:

what the other guy said just less words

Answer: 30

Step-by-step explanation:

By dividing 15 miles by 0.5 miles, we find that there are 30 segments. Since Nella and Lydia do not rest at the start, they take one rest less than the number of segments, resulting in 29 rests during their hike.

The student is trying to determine the number of times Nella and Lydia will rest during a 15 mile hike if they stop after every 0.5 mile. The calculation involves dividing the total distance (15 miles) by the distance between rests (0.5 miles).

To find the number of rests, we perform the following calculation:

However, we need to consider that they do not rest at the start, only after each 0.5 mile. Hence, the total number of rests would be one less than the total number of segments.

30 segments - 1 = 29 rests.

Therefore, Nella and Lydia will rest 29 times during their hike.

Answer:

[tex]1450-2.0\frac{30}{\sqrt{25}}=1450-12[/tex]    

[tex]1450+2.0\frac{30}{\sqrt{25}}=1450+12[/tex]    

And the best option would be:

c. 1450 +/- 12

Step-by-step explanation:

Information provided

[tex]\bar X=1450[/tex] represent the sample mean for the SAT scores

[tex]\mu[/tex] population mean (variable of interest)

[tex]s^2 = 900[/tex] represent the sample variance given

n=25 represent the sample size  

Solution

The confidence interval for the true mean is given by :

[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]   (1)

The sample deviation would be [tex]s=\sqrt{900}= 30[/tex]

The degrees of freedom are given by:

[tex]df=n-1=2-25=24[/tex]

The Confidence is 0.954 or 95.4%, the value of [tex]\alpha=0.046[/tex] and [tex]\alpha/2 =0.023[/tex], assuming that we can use the normal distribution in order to find the quantile the critical value would be [tex]z_{\alpha/2} \approx 2.0[/tex]

The confidence interval would be

[tex]1450-2.0\frac{30}{\sqrt{25}}=1450-12[/tex]    

[tex]1450+2.0\frac{30}{\sqrt{25}}=1450+12[/tex]    

And the best option would be:

c. 1450 +/- 12

To calculate the difference between the expected reimbursements of insurance policies G and H for a given month, we need to find the expected reimbursement for each policy and then take the difference of the two values.

To calculate the difference between the expected reimbursements of insurance policies G and H for a given month, we need to find the expected reimbursement for each policy and then take the difference of the two values.

For policy G, there is a 45% chance of no claims, in which case the reimbursement is 0. If a claim is made, the loss amount follows an exponential distribution with a mean of 5. We need to find the expected value of the reimbursement in this case. Let X be a random variable representing the loss amount. The expected reimbursement for policy G is then given by:

Expected Reimbursement for Policy G = 0.45(0) + 0.55(0.8)(E(X) - 2)

Similarly, for policy H, there is a 35% chance of no claims and a 65% chance of a claim with a loss amount following an exponential distribution with a mean of 9. Let Y be a random variable representing the loss amount. The expected reimbursement for policy H is:

Expected Reimbursement for Policy H = 0.35(0) + 0.65(0.8)(E(Y) - 2)

To find the difference between the expected reimbursements, we subtract the expected reimbursement for policy H from the expected reimbursement for policy G:

Difference = Expected Reimbursement for Policy G - Expected Reimbursement for Policy H

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Answer:

The average yearly change in samanthas height was of 3.3 inches.

Step-by-step explanation:

She mesured 40 1/2 = 40.5 inches.

In 5 1/2 years = 5.5 years, she grew to 57 inches.

During the 5 1/2 years, what was the average yearly change in samanthas height?

The total change was of 57-40.5 = 16.5 inches

16.5/5 = 3.3

The average yearly change in samanthas height was of 3.3 inches.

Answer:

D.) [tex]y+1=-3(x-10)[/tex]

Step-by-step explanation:

The original point slope form equation is as follows:

[tex]y - y_1 = m(x-x_1)[/tex]

When you input a negative or positive value into the equation, the sign may or may not change. In this case, we input a negative y value -- this caused the sign to change to '+1' rather than stay at '-1'

Answer:

There are 22 chickens and 8 rabbits

Step-by-step explanation:

1 chicken = 2 legs

1 rabbit = 4 legs

we need to do 2 equations to solve this problem

c + r = 30

c*2 + r*4 = 76

we clear c in the first equation

c + r = 30

c = 30 - r

we replace c with (30 - r) in the second equation

(30 - r) * 2 + r * 4 = 76

60 - 2r + 4r = 76

-2r + 4r = 76 - 60

2r = 16

r = 16/2

r = 8

now we replace r in the first equation

c = 30 - r

c = 30 - 8

c = 22

There are 22 chickens and 8 rabbits

Do  you know that you have the correct solution because you can verify it by multiplying

22 * 2 + 8 * 4 =

44 + 32 = 76

The systematic sampling method that would result in the smallest sample size is A. Surveying each 50,000th number.

The sample size that is given will depend on the number that the systematic sampling model uses. The higher the number, the smaller the sample size.

If each 50,000th number is being surveyed then the sample size would be:

= 500,0000 / 50,000

= 10 users

This is the smallest sample size that can be acquired here.

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Answer:

-9 21/50

Step-by-step explanation:

Answer:

divide 252 by 7 and you get 36

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The absolute value parent function is [tex]\mid x \mid[/tex], or answer choice D. Hope this helps!

Answer:

Probability that the sample average time taken is less than 11 minutes for Day 1 is 0.86864.

Probability that the sample average time taken is less than 11 minutes for Day 2 is 0.88877.

Step-by-step explanation:

We are given that the time taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal probability distribution with average time 10 minutes and a standard deviation of 2 minutes.

Also, five individuals fill out the form on Day 1 and six individuals fill out the form on Day 2.

(a) Let [tex]\bar X[/tex] = sample average time taken

The z score probability distribution for sample mean is given by;

                                Z  =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)

where, [tex]\mu[/tex] = population mean time = 10 minutes

            [tex]\sigma[/tex] = standard deviation = 2 minutes

            n = sample of individuals fill out form on Day 1 = 5

Now, the probability that the sample average time taken is less than 11 minutes for Day 1 is given by = P([tex]\bar X[/tex] < 11 minutes)

         P([tex]\bar X[/tex] < 11 minutes) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{11-10}{\frac{2}{\sqrt{5} } }[/tex] ) = P(Z < 1.12) = 0.86864

The above probability is calculated by looking at the value of x = 1.12 in the z table which has an area of 0.86864.

(b) Let [tex]\bar X[/tex] = sample average time taken

The z score probability distribution for sample mean is given by;

                                Z  =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)

where, [tex]\mu[/tex] = population mean time = 10 minutes

            [tex]\sigma[/tex] = standard deviation = 2 minutes

            n = sample of individuals fill out form on Day 2 = 6

Now, the probability that the sample average time taken is less than 11 minutes for Day 2 is given by = P([tex]\bar X[/tex] < 11 minutes)

         P([tex]\bar X[/tex] < 11 minutes) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{11-10}{\frac{2}{\sqrt{6} } }[/tex] ) = P(Z < 1.22) = 0.88877

The above probability is calculated by looking at the value of x = 1.22 in the z table which has an area of 0.88877.

An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. Of particular interest was whether higher income would result in shoppers spending more on groceries. A random sample of shoppers at a local supermarket was obtained. A questionnaire was administered asking about the weekly income of each shopper's family and their grocery bill for that week. The explanatory variable is:

A. weekly income.

B. weekly expenditure.

C. gender.

D. None of the answer options is correct

Answer:

A. weekly income.

Step-by-step explanation:

Explanatory variables are variables that shows the difference in response variables, the explanatory variable influences the response variable. It is an independent variable that can be manipulated. The independent variable helps explain the response variable.

In this case, the explanatory variable is the weeky income because the respose variable (weekly expenditure) variation depends on it. The economist wants to use the weekly income of each shoppers family to determine how much they will spend on groceries. So, the weekly income is the explanatory variable.

The distance the lifeguard should run along the shore before jumping into the water, can be determined by minimizing the function of time, that is, the time it takes for the lifeguard to reach the child. This problem can be solved either by using calculus or the graphical method with a graphing tool.

This problem can be solved using optimization of functions, which is a part of calculus. We would let 'x' be the distance along the shore that the lifeguard runs before jumping into the water. Then the total time taken to reach the child is given by the formula T = x/4 + sqrt((60-x)² + 40²)/1.1. We are looking for the minimum of T as a function of x. However, it would require knowledge of calculus to solve this problem. As an alternative, one can also use a graphing calculator or similar tool to graph the time function and then determine the minimum on the graph.

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Final answer:

To save the child, you should run along the shore for approximately 15 seconds before jumping into the water.

Explanation:

To determine how far along the shore you should run before jumping into the water to save the child, you need to find the time it takes to run along the shore and then swim directly to the child.

First, calculate the time taken to run along the shore using the formula: time = distance / speed. In this case, the distance is 60 meters and the speed is 4 meters per second. So, the time taken to run along the shore is 60 / 4 = 15 seconds.

Next, calculate the time taken to swim directly to the child using the formula: time = distance / speed. In this case, the distance is 40 meters and the speed is 1.1 meters per second.

So, the time taken to swim directly to the child is 40 / 1.1 ≈ 36.364 seconds.

Therefore, the total time taken to save the child is the sum of the time taken to run along the shore and the time taken to swim directly to the child.

So, in order to save the child, you should run along the shore for approximately 15 seconds before jumping into the water.

Yes, a square can be considered as a rhombus and a rectangle both.

The square is a quadrilateral with all sides equal and all angles equals to 90° and having equal diagonals.

Square being a rhombus and a rectangle :-

Rhombus :-

It has it's all sides equal having their diagonals equal and intersect at right angle rhombus is a parallelogram so a square, all the properties that a rhombus holds are also the properties of a square, so we can say a square can be considered as a rhombus.

Rectangle :-

A square is always a rectangle because, it has all the properties of a rectangle, such as parallel and equal opposite sides, vertex angles being a right angle, diagonals being equal.

Hence, a square can be considered as a rhombus and a rectangle both.

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Final answer:

A square is both a rhombus and a rectangle because it has four equal sides and four right angles, fulfilling the criteria for both shapes.

Explanation:

A square indeed has all the properties of a rhombus, which is a parallelogram with four equal sides, and it also has the properties of a rectangle, which is a quadrilateral with four right angles. Since a square has four equal sides and four right angles, it satisfies the criteria to be called both a rhombus and a rectangle. Therefore, the answer is yes; a square is both a rhombus and a rectangle.

Answer:

±5sqrt(2) = x

Step-by-step explanation:

50 - x^2 = 0

Add x^2 to each side

50 - x^2 +x^2= 0+x^2

50 = x^2

Take the square root of each side

±sqrt(50) = sqrt(x^2)

±sqrt(25*2)) = x

±sqrt(25) sqrt(2) = x

±5sqrt(2) = x

Answer: C

Step-by-step explanation: It divides the original segment into two equal pieces

The properties that do not apply for the perpendicular bisector should be option c. that it divides the original segment to two equal pieces.

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Answer:

reflection over the y- axis is x=0

so x will be negative.

(4,-6) will be (-4,-6)

Answer:

93.18 feet

Step-by-step explanation:

Given:

Length of backyard pool = 31.74 feet

Height of backyard pool = 14.85 feet

To find: Length of fencing bought by Mirele

Solution:

To find the length of fencing bought by Mirele, use the formula for the perimeter of a rectangular pool.

Length of fencing bought by Mirele = 2 ( length + height ) = 2 ( 31.74 + 14.85 ) = 2 ( 46.59 ) = 93.18 feet

Answer:

93.18 feet

Step-by-step explanation:

Answer:

$12 per foot

Step-by-step explanation:

$72.00 divided by 6 is $12

Answer:

The cost per foot of the sandwich is $12.

Step-by-step explanation:

You need to use division for this problem.

Pretend you are cutting the 6-foot sanwhich into 1-foot pieces. You will have 6 pieces. You have to give each piece an equal amount of money. Think about your 6-times tables. What times 6 = 72?

__ x 6 =72

or

72/6 = __