6. How much would it cost to buy 3 medium sodas and 2 hot dogs?

Answer:

That

Step-by-step explanation:

Answer:

x = 111°

x° = 111°

(x-42)° = 69°

Step-by-step explanation:

Any polygon with *n* number of sides has an interior angle sum of (n-2) × 180°.

Therefore this right trapezoid must have an interior angle sum of 360° because

a trapezoid has 4 sides → n = 4 →

(n-2) × 180° = (4-2) × 180° = 2 × 180° = 360°

Because we are given a 90 degree angle with a set of parallel sides, the angle above that must also be a right angles well so these will total 180°.

The last two angles are given by the two expressions x°, and (x-42)°. Because we know the sum of these angles which are 360° we can create the following equation from these angles and solve!

180° + 2x - 42° = 360°

(Group the constants / numbers without a variable ; associative property of addition)

180° - 42° + 2x = 360°

(Find the total value of the constants)

138° + 2x = 360°

(subtract 138° from both sides to isolate 2x on the left side ; subtraction property of equality)

138° - 138° + 2x = 360° - 138°

(Work out the value of the constants again)

2x = 222°

(divide by 2 on both sides to cancel out the coefficient of 2 in 2x to get x by itself ; division property of equality)

2x / 2 = 222° / 2

(Simplify the two expressions)

x = 111°

_____________________

To find the measure of the x expressions, just substitute x = 111° into the expressions and simplify to find the measure!

So:

x = 111° → x° = 111°

x = 111° → (x-42)° → (111 - 42)° = (69)° →

(x-42)° = 69°

Answer:

Quantitative: i) The number of students in the school vis - a - vis the number of classes in the school. In order words, simply number of students per class

ii) The rate of graduation of students.

Categorical:i) Courses being taken by students

ii) Region of country of students.

Step-by-step explanation:

To answer this question effectively, it's important for us to know that a quantitative variable usually has numerical values, and also have units of measure as well while categorical variables simply places each student into a specific category.

Now, the two quantitative variables we will consider are;

i) The number of students in the school vis - a - vis the number of classes in the school. In order words, number of students per class

ii) The rate of graduation of students.

Also, the two categorical variables we will consider are;

i) Courses being taken by students

ii) Region of country of students

The equation, which is used to find any corresponding length and width that fit the pattern in the provided table is,

\(I=\dfrac{k}{w}\)

Area of a rectangle is the product of the length of the rectangle and the width of the rectangle. It can be given as,

\(A=a\times b\)

Here, (a)is the length of rectangle and (b) is the width of the rectangle.

A rectangle with constant area has possible lengths and widths as shown in the table below.

Width vs. Length of a rectangle

In the above table, the length of a rectangle is decreasing with increasing the width of a rectangle.

For such relation, the value of w should be inversely proportional to the length of it. The first option given as,

\(I=\dfrac{k}{w}\)

Here l is the length, w is the width, and k is a constant (w not-equals 0).

In this expression, the length of the rectangle is inversely proportional to the width of the rectangle.

Thus, the equation, which is used to find any corresponding length and width that fit the pattern in the provided table is,

\(I=\dfrac{k}{w}\)

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Answer:

a

Step-by-step explanation:

Answer:

y=3/5x+3

Step-by-step explanation:

Use the equation for slope-intercept y=mx+b. First we will find the slope of this function (m) by taking two points. For this equation, I took (0,3) and (5,6). Using the equation (y2-y1)/(x2-x1), we get
(6-3)/(5-0), or a slope of 3/5.
All that's left is to find the y-intercept, or b. This is easy, since we can see that the function intercepts at (0,3).
Leaving us with a function y=3/5x+3

The score a student would need to have a 30th percentile score on the SAT is approximately 1345. Option B is correct.

To find the score that corresponds to the 30th percentile, we need to use a z-table to determine the z-score that corresponds to a cumulative probability of 0.30.

Using the formula for converting a raw score to a z-score:

z = (x - μ) / σ

where x is the raw score, μ is the mean, and the σ is the standard deviation.

Rearranging this formula to solve for x:

x = z × σ + μ

To find the z-score for a 30th percentile, we can look up the corresponding value in a z-table or use a calculator with a built-in normal distribution function. The z-score corresponding to a cumulative probability of 0.30 is approximately -0.52.

Substituting the known values into the formula above:

x = -0.52 × 312 + 1509

Simplifying:

x ≈ 1345

Hence, B. 1345 is the correct answer.

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To find the value of cos(B) given the side lengths of a triangle, we can use the Law of Cosines. With AC = 15 cm, AB = 17 cm, and BC = 8 cm, we can apply the formula to determine cos(B)=0.882.

The Law of Cosines states that in a triangle with sides a, b, and c, and angle C opposite side c, the following equation holds: c² = a² + b² - 2ab*cos(C).

In this case, we have side AC = 15 cm, side AB = 17 cm, and side BC = 8 cm. Let's denote angle B as angle C in the formula. We can plug in the values into the Law of Cosines:

BC² = AC² + AB² - 2ACAB*cos(B)

Substituting the given side lengths:

8² = 15² + 17² - 21517*cos(B)

64 = 225 + 289 - 510*cos(B)

Simplifying:

64 = 514 - 510*cos(B)

510*cos(B) = 514 - 64

510*cos(B) = 450

cos(B) = 450/510

cos(B) ≈ 0.882

Therefore, cos(B) is approximately 0.882.

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The number of rows of seats needed to seat the greatest possible number of participants in each row is 5

The highest common factor is the highest number that divides the numbers given.

On the basis of given data

Total number of children = 26

Total number of adults = 39

The highest common factor of both the number is 13 ,

Therefore the highest possible number of people that can sit in one row so that the number is in constant in all the rows.

So 2 rows of children of 13 each and

3 rows of adult of 13 each

Which makes the total number of rows = 5

Therefore the number of rows of seats needed to seat the greatest possible number of participants in each row is 5

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Answer:

Perimeter = 22.809836694575                              

Step-by-step explanation:

A(-2, 2)  ;  B(6,2)  ;  C(0, 8)

\(AB=\sqrt{\left( 6--2\right)^{2} +\left(2-2 \right)^{2} } =\sqrt{64} =8\)

\(AC=\sqrt{\left( 0--2\right)^{2} +\left(8-2 \right)^{2} } =\sqrt{40} =2\sqrt{10}\)

\(BC=\sqrt{\left( 0-6\right)^{2} +\left(8-2 \right)^{2} } =\sqrt{72} =6\sqrt{2}\)

Then

The perimeter of ΔABC = AB + BC + AC

                                       \(=8+6\sqrt{2} +2\sqrt{10}\)

                                       = 22.809836694575

Answer:

C) 170 centimeters

Step-by-step explanation:

The missing graph-diagram to the question is attached in the image below.

Using the line of best fit, the predicted height for someone with a first metacarpal bone that has a length of 4.45 centimeters can be determined as follows:

The length of 4.5 centimeters appears on the horizontal x-axis; This implies that 4.45 is a half distance between the undotted 4.4 centimeters and the dotted 4.5 centimeters. Similarly, on the vertical y-axis, 170 is directly equivalent to the dotted point of 4.5 centimeters. Thus, the predicted height with a 4.45 centimeters length is approximately 170 centimeters by using the line of best fit.

The supply of loanable funds in the country is equal to national saving, government expenditures, domestic investment and net capital outflow added up and is 140 billion.

The supply of loanable funds in a country is the total amount of money available for lending. This is calculated by adding National Saving, Government Expenditures, Domestic Investment and subtracting Net Capital Outflow. In this case, National Saving is $80 billion, Government Expenditures are $40 billion, Domestic Investment is $50 billion and Net Capital Outflow is $30 billion. Thus, the Supply of Loanable Funds is equal to $140 billion. National Saving refers to the amount of income that is not spent by the people of a country and is saved instead. Government Expenditures are all the money that the government spends. Domestic Investment is the amount of money that is invested within a country. Finally, Net Capital Outflow is the difference between total capital inflows and total capital outflows from a country. Therefore, by adding National Saving, Government Expenditures, Domestic Investment and subtracting Net Capital Outflow, the Supply of Loanable Funds is equal to $140 billion.

Supply of loanable funds = National Saving + Government Expenditures + Domestic Investment - Net Capital Outflow

= 80 + 40 + 50 - 30

= 140 billion

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We are 98% confident that the mean of the true population y lies between 10.8 and 13.4.

To construct the confidence interval, we first need to calculate the critical value of t using the given values of C and n. Since C = 0.98, we can find the level of significance as α = 1 - C = 0.02.

Using a t-table or calculator, the critical value of t for a two-tailed test with 14 degrees of freedom and

\(\frac{\alpha}{2} = 0.01\) is approximately 2.977.

Next, we can calculate the sample standard deviation as s = σ/√n = \(\frac{0.95}{\sqrt{15}}= 0.245\).

Then, we can use the formula for a confidence interval for the population mean using the t-distribution:
(y ± t)×\(\frac{s}{\sqrt{n}}\)

Substituting the given values, we get:

(12.1 ± 2.977)×\(\frac{0.245}{\sqrt{15}}\)

Simplifying and rounding to one decimal place, we get the confidence interval: (10.8, 13.4)

Therefore, we are 98% confident that the true population mean y lies between 10.8 and 13.4.

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Answer:

the answer is 59.5375 ant there is all details there

The average speed of the car up to one decimal place will be 54.2 miles per hour.

The distance covered by the particle or the body in an hour is called the average speed. It is a scalar quantity. It is the ratio of the total distance to the total time.

We know that the average speed formula is given as,

Average speed = Total distance / Total time

A car travels a distance of 230 miles in 4 hours and 15 minutes.

Convert the minutes into hours. Then we have

⇒ 4 + 15 / 60

⇒ 4 + 0.25

⇒ 4.25 hours

The average speed of the car, in miles per hour, will be given as,

Average speed = 230 / 4.25

Average speed = 54.2 miles per hour

The average speed of the car up to one decimal place will be 54.2 miles per hour.

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P.9 the probability that the helicopter cannot fly with five persons aboard is essentially 0.

P.10 the probability that n trials are performed until k successes occur is given by the negative binomial distribution formula above.

P.9 Let's assume X represents the total weight of the five individuals seeking a helicopter ride. X follows a normal distribution with a mean of 180 lb and a standard deviation of 5 lb.

To find the probability that X exceeds 1000 lb, we need to calculate the area under the normal distribution curve to the right of 1000 lb. However, since the normal distribution is continuous and extends from negative infinity to positive infinity, the probability of exceeding 1000 lb is extremely small.

In this case, it is reasonable to approximate the distribution of the total weight as a normal distribution. We can use a continuity correction factor to account for the approximation. Since we are dealing with weights, which are continuous variables, we can apply the continuity correction by subtracting 0.5 from the upper limit before calculating the probability.

Let Z be the standardized value of X:

Z = (1000 - 180) / 5 = 164

Using a standard normal distribution table or a statistical calculator, we can find the probability corresponding to Z = 164. However, the probability of such an extreme value is extremely close to 0

P.10 The negative binomial distribution represents the number of trials required to achieve a fixed number of successes (k) in a sequence of independent Bernoulli trials, each with a probability of success (p).

The probability mass function of the negative binomial distribution is given by:

P(X = n) = C(n - 1, k - 1) * p^k * (1 - p)^(n - k)

Where:

X represents the number of trials required to achieve k successes,

n is the total number of trials,

k is the number of successes required,

p is the probability of success in each trial, and

C(n - 1, k - 1) is the number of combinations (n - 1) choose (k - 1), which is equal to (n - 1)! / [(k - 1)! * (n - k)!].

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Answer:

Step-by-step explanation:

use the distributive property to multiply 4 by 2x and 4 by -5. the answer will be 8x - 20

Answer:

45 in.

Step-by-step explanation:

Step 1:

Length × Width = Area           How to find Area

Step 2:

5 in. × 9 in.       Equation

Answer:

45 in.       Multiply

Hope This Helps :)

Question: In a sale, the price of a book is reduced by 25%. The price of the book in the sale is £12. Work out the original price of the book

Answer: £16

Step-by-step explanation:

To determine the original price of the book, we can use the fact that the sale price is 75% (100% - 25%) of the original price. Let's denote the original price as x.

75% of x = £12

To solve for x, we can set up the equation:

0.75x = £12

To isolate x, we divide both sides of the equation by 0.75:

x = £12 / 0.75

x = £16

Therefore, the original price of the book was £16.

Answer:

a.) x=10

Step-by-step explanation:

3(10)+28= 30+28

58

5(10)+52= 50+52

102

2(10)-10= 20-10

10

58+102+10= 180

Answer:

add all of the angles which equals to 180 degree

being

3x + 28 + 5x + 52 + 2x + 10=180°

which is

10x + 90 = 180

x = 180-90/10

x=11

Step-by-step explanation:

then find the value of x for each angle

second picture unclear.

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have a great day

Answer:

x=5 is the answers for the question

Step-by-step explanation:

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Answer:

5

Step-by-step explanation:

Solve the equation for X step by step.

16 = 4x - 4

add 4 to each side

16 + 4 = 4x - 4 + 4    which simplifies to  20 = 4x

divide each side by 4

20/4 = 4x/4  which then simplifies to 5 = x

Answer:

B. x= -2

Step-by-step explanation:

To calculate the 90% confidence interval for the average EPS of all industrials listed on the DJIA, we will use the formula:

Confidence interval = sample mean ± (critical value * standard deviation / √sample size)

Step 1: Find the critical value.
Since we want a 90% confidence interval, the corresponding critical value can be obtained from the z-table. The critical value for a 90% confidence level is 1.645.

Step 2: Calculate the margin of error.
The margin of error is given by (critical value * standard deviation / √sample size).
Substituting the values, we get: 1.645 * 0.395 / √9 = 0.29175.

Step 3: Calculate the confidence interval.
The confidence interval is given by the sample mean ± margin of error.
Substituting the values, we get: 1.85 ± 0.29175.

The 90% confidence interval for the average EPS of all industrials listed on the DJIA is (1.55825, 2.14175).

We can be 90% confident that the true average EPS of all industrials listed on the DJIA falls within the range of 1.55825 to 2.14175.

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Answer:

Step-by-step explanation: so

l*w*h
7.5ft*4ft*8ft

that would be 240ft^3

Then 2.5^3

would be 15.625^3

So then u would do

240ft^3/15.625ft^3 = 15.36 boxes of paper

So u could fit abt 15 boxes of paper in the back of his truck

Answer:

3 and -4

Step-by-step explanation:

this is simple but difficult

let the number be x and second number be y

3x + 2y=1

x-y/2=5

from the 2nd equation

x-y/2=5

x=5+y/2

substitute value for x into equation 1

3x + 2y=1

3(5+y/2) + 2y= 1

15 +3y/2 +2y=1

15 + 7y/2=1

7y/2= 1 - 15

7y/2=-14

cross multiply

7y= -28

y= -28/7

y= -4

therefore second number is -4

substitute value for y into 1st equation

3x + 2y=1

3x + 2(-4) = 1

3x - 8= 1

3x= 1+8

3x= 9

x= 9/3

x= 3

therefore first number is 3

therefore two numbers are;

3 and -4

We cannot simplify this further because 3 and 5 have no factors in common, other than 1. So we just leave it as is.

To find the value of the function f(x) = \(2x^3 - 5x + 7\) at x = -4, we substitute -4 into the function and simplify. The value of the function at

x = -4 is -101.

To calculate the value of the function \(f(x) = 2x^3 - 5x + 7\)at x = -4, we substitute -4 for x in the equation:

\(f(-4) = 2(-4)^3 - 5(-4) + 7\)

Simplifying the expression, we have:

f(-4) = 2(-64) + 20 + 7

f(-4) = -128 + 20 + 7

f(-4) = -101

Therefore, when x = -4, the value of the function \(f(x) = 2x^3 - 5x + 7\)is -101. This means that if we substitute -4 into the function, we get a result of -101.

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Answer:28

Step-by-step explanation:hope it helps :)

The equation that relates c, the number of crates, and b, the number of boxes is: b = 16c

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. For example, 3x + 5 = 15.

The equation that relates c, the number of crates, and b, the number of boxes is:

b = 8c × 2

Simplifying this expression, we get:

b = 16c

Therefore, the number that completes the equation is 16.

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Step-by-step explanation:

that's wrong .....wait ...........

The total weight of the 14 packages that Melissa weighed is gotten as; Total weight = 42 pounds

We are given;

Mean weight = 3

Now,formula for mean is;

Mean = total/sample size

We are given;

Sample size = 14

Thus;

3 = total/14

Total = 3 * 14

Total weight = 42 pounds

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