3. Corbett’s sold 3 more footballs than basketballs on Saturday. In total, they sold 27 balls. How many of each kind were sold?

4. A hamburger has twice as many calories as a bowl of soup. Together they have 738 calories. How many calories are in each?

5. Carmen’s golf score was 6 strokes less than Lisa’s. Their two scores totalled 168. What was each girl’s score?

6. The sum of two consecutive numbers is 191. What are the two numbers?

Therefore, the distance between opposite corners of the bed is 85 inches.

A triangle is a three-sided polygon that is formed by connecting three non-collinear points. It is a simple closed figure with three sides and three angles. Triangles are classified according to the relative lengths of their sides and the measure of their angles. There are several types of triangles, including equilateral triangles, isosceles triangles, scalene triangles, acute triangles, obtuse triangles, and right triangles.

Here,

The distance between opposite corners of a rectangle can be found using the Pythagorean theorem, which states that for a right triangle with legs of length a and b and hypotenuse of length c, c² = a² + b².

In this case, the length and width of the bed form the legs of a right triangle, and the distance between opposite corners is the length of the hypotenuse.

Using the Pythagorean theorem, we can find the length of the hypotenuse:

c² = 40² + 75²

c² = 1600 + 5625

c² = 7225

c = √(7225)

c = 85

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Answer:

8

Step-by-step explanation:

edge 2020

Answer:

yes it is 8

Step-by-step explanation:

Domain: the smallest possible x-value to the largest possible x-value

In the case of this graph, we see the parabola starts at x = -3, and continues on forever.

Domain: [-3, infinity)

Range: the smallest possible y-value to the largest possible y-value

In the case of this graph, the parabola will continue to expand forever.

Range: (-infinity, infinity)

Therefore, while the domain has a restriction, the range does not and is all real numbers.

Hope this helps!

Answer:

2.7n=8.1^n-7

thank you for the lovely question

Answer:

First, use the distributive property and distribute 8 to the \((x,2)\) in the first part of the equation to get \(8x + 16\).

Next, also use the distributive property to distribute the 4 to the \((2x+9)\) in the second part of the equation to get \(8x+36\).

The simplified equation looks like this: \(8x+16=8x+36\).

Answer:

Certificate of Deposit

Step-by-step explanation:

A product offered by banks and credit unions that provides an interest rate premium in exchange for the customer agreeing to leave a lump-sum deposit untouched for a predetermined period of time.

Answer:

A CD in the financial sense is short for certificate of deposit.

Answer:

5/2.5

Step-by-step explanation:

Answer: -3/4 < -1/2 < 1/2 < 3/4

Step-by-step explanation:

The standard form equation of an ellipse with center at the origin, vertex (0,√29), and co-vertex (-5,0) can be written as:

x^2/a^2 + y^2/b^2 = 1

where a is the length of the semi-major axis (distance from the center to the vertex), and b is the length of the semi-minor axis (distance from the center to the co-vertex).

Since the vertex is (0,√29), we know that a = √29. And since the co-vertex is (-5,0), we know that b = 5. Substituting these values into the equation, we get:

x^2/29 + y^2/25 = 1

So, the equation of the ellipse in standard form with center at the origin, vertex (0,√29), and co-vertex (-5,0) is x^2/29 + y^2/25 = 1.

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By applying the Laplace transform to the given differential equation and initial conditions, we obtained Y(s) = 0. Taking the inverse Laplace transform of Y(s), we found y(t) = 0 as the solution to the initial value problem.

To solve the given initial value problem (IVP) using the Laplace transform, we start by taking the Laplace transform of the given differential equation and the initial conditions. Let's go through the steps:

Applying the Laplace transform to the differential equation y' + 254 – 7ebt, we get:

sY(s) - y(0) + 254Y(s) - 7eY(s)/(s-b) = 0.

Substituting the initial conditions y(0) = 0 and y'(0) = 0:

sY(s) + 254Y(s) - 7eY(s)/(s-b) = 0.

Next, we can solve this equation for Y(s):

sY(s) + 254Y(s) - 7eY(s)/(s-b) = 0.

sY(s) + 254Y(s) - 7eY(s)/(s-b) = 0.

sY(s) + 254Y(s) - (7eY(s)/(s-b)) = 0.

Rearranging the equation:

Y(s)(s + 254 - 7e/(s-b)) = 0.

Y(s) = 0.

Now, to find y(t), we need to take the inverse Laplace transform of Y(s) = 0. The inverse Laplace transform of 0 is simply the zero function:

y(t) = 0.

Therefore, the solution to the initial value problem is y(t) = 0.

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The face value of the non-interest-bearing note for the woman's loan should be approximately $500.26. The face value of the non-interest-bearing note for the man's loan should be approximately $2417.91.

To find the face value of a non-interest-bearing note, we can use the formula:

Face Value = Proceeds / (1 - Discount Rate * (Days to Maturity / 360))

1. Calculation for the woman's loan:

Proceeds = $485

Discount Rate = 13.22%

Days to Maturity = 80 (from April 10 to June 29)

Face Value = $485 / (1 - 0.1322 * (80 / 360))

Face Value = $485 / (1 - 0.1322 * 0.2222)

Face Value = $485 / (1 - 0.0294)

Face Value = $485 / 0.9706

Face Value = $500.26 (approximately)

Therefore, the face value of the non-interest-bearing note for the woman's loan should be approximately $500.26.

2. Calculation for the man's loan:

Amount needed = $2350

Discount Rate = 14.4%

Days to Maturity = 70 (from July 10 to September 18)

Face Value = $2350 / (1 - 0.144 * (70 / 360))

Face Value = $2350 / (1 - 0.144 * 0.1944)

Face Value = $2350 / (1 - 0.0279)

Face Value = $2350 / 0.9721

Face Value = $2417.91 (approximately)

Therefore, the face value of the non-interest-bearing note for the man's loan should be approximately $2417.91.

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Answer:

what's the question

Step-by-step explanation:

5+b or b+5. It can be written either way. Some teachers are strict about how you write it but who cares?

hope it helps!

Answer:

x=2,-4

Step-by-step explanation:

The average rate of change of the graphed function on the interval [3,6] is given as follows:

r = 4/3.

The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function. Hence we must identify the change in the output, the change in the input, and then divide then to obtain the average rate of change.

The numeric values of the function at x = 3 and x = 6 are given as follows:

Hence the average rate of change on the interval is given as follows:

r = (5 - 1)/(6 - 3)

r = 4/3.

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Answer:

Say you take a pizza and cut it perfectly down the middle so there are two slices. Each slice is a half or 1/2 of the pizza.

The number of ways to arrange the letters is 423360.

We have,

COMBINATORICS

There are 13 letters in total, including 5 vowels (O, I, A) and 8 consonants (C, M, B, N, T, R, S).

Now,

Take out the vowels from the word.

We get,

_C_M_B_N_T_R_C_S_

We see that,

There are 7 spaces where we can put the vowels.

And there are 8 consonants.

So,

= \(^7C_5\) / 2! x 8!

We divide the combination by 2! because there are two vowels with repetition.

Now,

= \(^7C_5\) / 2! x 8!

= ((7 x 6)/2 x 2)x 8 x 7 x 6 x 5 x 4 x 3 x 2

= 7 x 3 x 4 x 7 x 6 x 5 x 4 x 3 x 2

= 423360

Thus,

The number of ways to arrange the letters is 423360.

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Answer:

Step-by-step explanation:

Kaitlin: y = 60x + 750

y = 60(19) + 750

     1140 + 750 = $1890 total

Answer:

x=5

Step-by-step explanation:

     May I have brainiest I'm trying to level up!

                 </3 PureBeauty

Answer:

x=5

Step-by-step explanation:

6x-3 = 3x +12

+3            +3

6x = 3x +15

-3x   -3x

3x = 15

divided both sides by 3 to get your answer

Answer:

1,4, 2,8, and 3,12 are all equivalent

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The value of cos(x) for |x| ≤ 1/12 accurate to 12 decimal places (rounded), we need at least 5 terms in the series of cos(x). We will use Taylor's theorem to derive this result.

Taylor's theorem, also known as the Taylor series theorem, is a mathematical formula used to represent functions as a sum of infinitely many derivatives in order to approximate them over a certain interval.

This formula allows us to derive the value of a function at a point using information about its derivatives at that point.

In essence, Taylor's theorem is a tool used in calculus to model complex functions that cannot be easily solved.

Using Taylor's theorem to solve the question:

We know that the Taylor series expansion of cos(x) is given by the formula:

cos(x) = 1 - x²/2! + x⁴/4! - x⁶/6! + ...

To get an accurate value of cos(x), we need to keep adding terms in the series until the absolute value of the next term is less than our required accuracy.

Using |x| ≤ 1/12 and rounding to 12 decimal places, we have an error tolerance of 0.000000000001.

Therefore, we need to find the smallest value of n such that \(|x^(n+1)/(n+1)!| ≤ 0.000000000001,\)

where x = 1/12.

Substituting x = 1/12,

we have |(1/12)^(n+1)/(n+1)!| ≤ 0.000000000001

Using a calculator, we can find that n = 4 satisfies this inequality.

Therefore, we need at least 5 terms in the series of cos(x) to compute the value of cos(x) for |x| ≤ 1/12 accurate to 12 decimal places (rounded).

Conclusion:

To calculate the value of cos(x) for |x| ≤ 1/12 accurate to 12 decimal places (rounded), we need at least 5 terms in the series of cos(x). We used Taylor's theorem to derive this result.

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Answer: A. 33

Step-by-step explanation:

Answer:

1 more.

Step-by-step explanation:

A regular octagon has 4 pairs.

A regular hexagon has 3 pairs.

Hope this helped.    :)

Answer:

Divide both side by 9

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

Given

6x - 5y = 14 ← substitute y = 2 into the equation

6x - 5(2) = 14

6x - 10 = 14 ( add 10 to both sides )

6x = 24 ( divide both sides by 6 )

x = 4

Answer:

\(\huge\boxed{\sf x = 4}\)

Step-by-step explanation:

\(\sf 6x-5y = 14\\\\Put \ y = 2\\\\6x - 5(2) = 14\\\\6x - 10 = 14\\\\ Adding \ 10 \ to \ both \ sides\\\\6x = 14+10\\\\6x = 24\\\\Dividing \ both \ sides \ by \ 6\\\\x = 24 / 6\\\\x = 4\\\\\rule[225]{225}{2}\)

Hope this helped!

The statement 'The distribution of the sample​ mean, x overbar, will be normally distributed if the sample is obtained from a population that is normally​ distributed, regardless of the sample size.'  is True

In this question we have been given a statement 'The distribution of the sample​ mean, x overbar, will be normally distributed if the sample is obtained from a population that is normally​ distributed, regardless of the sample size.'

We need to state whether the statement is True or False.

We know that the sampling distribution of the sample mean is the probability distribution of all possible values of the random variable x that are computed from a sample of size n.

Also if a random variable X is normally​ distributed, the distribution of the sample​ mean, x overbarx​, is normally distributed.

Therefore, given statement is True.

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The width of the runway is approximately 28.3 feet. The length of the runway in feet is Length = 3.75 miles * 5,280 feet/mile

The new runway being constructed on the east side of the estate, which extends to the ranch house, is 3.75 miles long and covers a total area of 5.6 acres. To determine the width of the runway in feet, we can use the following information:

1 acre = 43,560 square feet

First, let's convert the length of the runway from miles to feet:

1 mile = 5,280 feet

Therefore, the length of the runway in feet is:

Length = 3.75 miles * 5,280 feet/mile

Next, let's calculate the width of the runway using the area and length:

Area = Length * Width

Since we are given the area in acres, we need to convert it to square feet:

Area = 5.6 acres * 43,560 square feet/acre

Now, we can solve for the width:

Width = Area / Length

Substituting the values we have:

Width = (5.6 acres * 43,560 square feet/acre) / (3.75 miles * 5,280 feet/mile)

Simplifying the expression:

Width = (5.6 * 43,560) / (3.75 * 5,280) feet

Calculating the value:

Width ≈ 560,784 / 19,800 feet

Width ≈ 28.3 feet

Therefore, the width of the runway is approximately **28.3 feet**.

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There is an infinite number of solutions to the inequality equation 3x - y > 4. The graph is shown below.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The system of inequality is given below.

y < 3x - 4

The inequality can be written as

3x - y > 4

The graph of the equation is given below.

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The solution set of the example inequality, 2•x + 3 ≤ -3, is the option;

A possible inequality that can be used to get one of the options, (the inequality is not included in the question) is as follows;

Solving the above inequality, we have;

2•x + 3 ≤ -3

2•x ≤ -3 - 3 = -6

2•x ≤ -6

Therefore;

x ≤ -6 ÷ 2 = -3

x ≤ -3

Which gives;

-∞ < x ≤ -3 in interval notation is (-∞, -3]

The solution set of the inequality, 2•x + 3 ≤ -3, is therefore the option;

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The length of diagonal of the checkerboard is \(40\sqrt{2} cm\).

The Pythagoras theorem can be applied to a right angle triangle. It states that the square of hypotenuse is equal to sum of square length of base and height of the triangle. Mathematically: Hypotenuse² = Perpendicular² + Base². The diagonal of a square divides the square in two right triangles.

The each side of a checkerboard measures 40 cm, that means checkerboard is a square. So, applying the Pythagoras theorem in the triangle formed by diagonal and two sides of square,

\(D^2=S^2+S^2\\D^2=40^2+40^2\\D=40\sqrt{2} cm\)

Where D is the length of diagonal and S is the length of side of checkerboard.

Therefore, the length of the diagonal of checkerboard is \(40\sqrt{2} cm\).

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Answer

root 354

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

(√19 -√7)(√19 +√7)

( a +b)( a -b) = a²-b²

(√19)² -(√7)² = 19 -7 = 12