In total, Amy and Jack had $1377. Amy spent 0.8 of her money and Jack spent 1/3 of his. They spent the same amount of money.
A) What was the ratio of Amy's money to Jack's money?
B) How much did Jack have at first? ​

Answer:

a=11

Step-by-step explanation:

So, the line that (9a+6) and 75 are sharing is straight, meaning that it is 180 degrees. Also, (9a+6) and 75 are sharing the line. Even though we don't know there exact measurements, when know that by adding them together we will get 180 degrees.

1. (9a+6) + 75 = 180

2. 9a + 81 = 180

3. 9a = 99

4. a = 11

Hope this helped!

Answer:

The answer is 81.85%

Step-by-step explanation:

The z score is used to determine by how many standard deviations the raw score is above or below the mean.

The z score is given by:

z = x - μ/σ

where,

For x = 88

z = 88 - 116/14

z = (-2)

For x = 130

z = 130 - 116/14

z = (1)

Thus,

P(88 < x < 130) = P(-2 < z < 1)

= P(z < 1) - P(z < -2)

= 0.8413 - 0.0228 = 81.85%

Thus, 81.85% of the population would be between 88 and 130.

Answer: The correct answer is 29 units

Step-by-step explanation: Can i Get the brainliest answer?

The distance between points (8, 3) and (3, 1) on the coordinate plane is √29 units.

Given that, the distance between points (8, 3) and (3, 1) on the coordinate plane.

The distance formula which is used to find the distance between two points in a two-dimensional plane is also known as the Euclidean distance formula. On 2D plane the distance between two points (x1, y1) and (x2, y2) is Distance = √[(x2-x1)²+(y2-y1)²].

Now,

Put, (x1, y1)=(8,3) and (x2, y2)=(3,1) in distance formula, that is

Distance = √[(1-3)²+(3-8)²]

= √(4+25)

= √29 units

Therefore, the distance between points (8, 3) and (3, 1) on the coordinate plane is √29 units.

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Answer:

x=9

Step-by-step explanation:

plug in the number 9

-2(9)= -18

-18+3= -15

Answer:

9w2x.

Step-by-step explanation:

8w2x + w2x

= 9w2x.

Answer:

Answer -$ 12.9

Step-by-step explanation:

Answer:

12.90

Step-by-step explanation:

Answer:

0.4589

Step-by-step explanation:

We solve using z score formula

The z score formula for a random number of samples is:

z = (x-μ)/σ/√n, where x is the raw score, μ is the population mean, and σ is the population standard deviation

Hence:

z = 246.7 - 245.3/96/√50

z = 0.10312

Probability value from Z-Table:

P(x<246.7) = 0.54107

P(x>246.7) = 1 - P(x<246.7) = 0.45893

Approximately to 4 decimal places = 0.4589

The probability that a single randomly selected value is greater than 246.7 is 0.4589

The photo along with the mat will be something like this:

So, new side length = 3 + 2x

new height = 5 + 2x

Hence,

Rectangle Area (A) = length * height

Thus,

Answer:

9 burgers

Step-by-step explanation:

total amount of beef = 6 lbs

amount of beef in each patty = 2/3 lb

number of burgers = total amount of beef ÷ amount of beef in each patty

= 6  ÷ 2/3

= 6 x 3/2

= 9

All of 4x+8 is under a cube root sign.

=====================================================

Work Shown:

To find the inverse, we swap x and y, then solve for y.

\(y = \frac{1}{4}x^3 - 2\\\\x = \frac{1}{4}y^3 - 2\\\\x+2 = \frac{1}{4}y^3\\\\4(x+2) = y^3\\\\4x+8 = y^3\\\\y^3 = 4x+8\\\\y = \sqrt[3]{4x+8}\\\\\)

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

Side note:

If \(f(x) = \frac{1}{4}x^3 - 2\) and \(g(x) = \sqrt[3]{4x+8}\), then \(f(g(x)) = x\) and \(g(f(x)) = x\)for all x values in the domain. Effectively, you use function composition to confirm that we have the correct inverse equation.

Answer:

5x=45

Step-by-step explanation:

Solve: 4+x=12

~ Subtract 4

~ x = 8

~ (not nine)

-----

Solve: 2x=20

- Divide by 2 (isolate x)

- x = 10

- (not nine)

-----

Solve: x+7=26

~ Subtract 7

~ x = 19

~ (not nine)

-----

Solve: 5x=45

- Divide by 5 (isolate x)

- x = 9

- (Nine! Our answer)

X is next to the number 10, so x would be the number of dinner tickets sold.

Rewrite x + y = 100 to x = 100-y

Now replace that in the 2nd equation:

10(100-y) + 6y = 900

Simplify:

1000 -10y + 6y = 900

Combine like terms:

1000 -4y = 900

Subtract 1000 from both sides

-4y = -100

Divide both sides by-4

Y = 25

Replace y in the first equation and solve for x

X + 25 = 100

X = 75

A) 75 dinner tickets were sold

B) 25 dessert tickets were sold

C) 75 x 10 = $750

D) 25 x 6 = $150

The correct model demonstrating the use of base ten blocks for the problem 5 + 7 = ? will show one ten block and two unit blocks, which represents the sum, 12.

To determine which model correctly demonstrates the use of the base ten blocks for the problem 5 + 7 = ?, follow these steps:

Represent the first number, 5, with base ten blocks. Since 5 is less than 10, you will use five unit blocks (each representing one).

Represent the second number, 7, with base ten blocks. Again, since 7 is less than 10, you will use seven unit blocks.

Combine the base ten blocks representing both numbers. In this case, you will have a total of 12 unit blocks (five from the first number and seven from the second number).

Check if any groupings of 10 can be made. Since 12 is greater than 10, you can create a group of 10 unit blocks and have two unit blocks left over.

Represent the combined number using base ten blocks. In this case, you will have one ten block (representing 10) and two unit blocks (representing 2).

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Answer: c

Step-by-step explanation:

Answer:

It is A ( read below )

Step-by-step explanation:

There are two VERY similar looking ap3x questions, this one is A but if you look closely on the rightside triangle the angle may say 24 not 25. This is why!

The corresponding angles of the triangles ΔABC and ΔDEF will be the same. Thus, the correct option is A.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The corresponding angles of the triangles ΔABC and ΔDEF will be the same.

And the ratio is calculated as,

6/8 = 7.5/10

3/4 = 3/4

Thus, the correct option is A.

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Answer:

b. 1.97

Step-by-step explanation:

1cm≈0.032feet

60/0.032≈1.97feet

The condition that must be true in order for a confidence interval based on de Moivre's equation to be valid is:

d. The underlying distribution of the data must be normally distributed.

A confidence interval is an interval estimate of a population parameter that specifies a range of values within which the parameter is likely to lie with a certain level of confidence. In other words, it represents the degree of uncertainty associated with the estimate.

De Moivre's equation is a formula for approximating the probability of a specific number of successes in a series of independent Bernoulli trials. This formula is only relevant if the sample size is large enough such that the normal approximation to the binomial distribution is valid. Thus, this formula can be used to calculate confidence intervals for binomial proportions when the sample size is large enough to apply the normal approximation.

Answers to other options:

a. We must be forming a confidence interval for a coefficient in a multiple regression model - This statement is incorrect. De Moivre's equation is not related to multiple regression models.

b. All of these answers are correct - This statement is incorrect because not all of the options are correct. Only one option is correct.

c. We must be forming a confidence interval for a population mean based on a sample mean - This statement is incorrect. De Moivre's equation is not relevant for calculating confidence intervals for population means. The Central Limit Theorem is used instead.

Hence, option "d" only is true.

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Baking cupcakes for the time suggested for baking a cake may result in overbaked and dry cupcakes.

This is because cupcakes are smaller and have less volume than cakes, so they require less baking time to cook through. Overbaking can also cause cupcakes to lose their moisture and become tough. It is important to follow the suggested baking time for cupcakes to achieve the desired texture and flavor.

To ensure that cupcakes are baked correctly, it is recommended to test them for doneness using a toothpick or cake tester. Insert the toothpick in the center of the cupcake, and if it comes out clean, the cupcakes are done.

If the toothpick has batter on it, the cupcakes need more time to bake. Adjust the baking time accordingly, and continue checking until the toothpick comes out clean.

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The area of a square is given by A = x², and its area is given by dA/dt = 2x(dx/dt). The square's sides increase at 4 m/s, so dx/dt = 4. Substituting dx/dt = 4 and A = 16m², we get dA/dt = 8x, which equals 32 m²/s.

Let x be the length of the square, then its area, A can be given by:A = x²Differentiating the above expression with respect to t, we have:

dA/dt = 2x(dx/dt)Given that the sides of the square is increasing at a rate of 4 m/s.

Therefore, we can say that dx/dt = 4.Substituting dx/dt = 4 and A = 16m² into the expression

dA/dt = 2x(dx/dt), we have:

dA/dt = 2x(dx/dt)

= 2x(4)

= 8x

= √A (since A = x²)

Therefore, x = √16 = 4m

Substituting this value of x into the expression dA/dt = 2x(dx/dt),

we have: dA/dt

= 8x

= 8(4)

= 32 m²/s

Therefore, the rate of change of the area of the square is 32 m²/s when the area of the square is 16m².

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Answer:

65

Step-by-step explanation:

First let's multiply both the numerator and denominator by 100 so that the decimal number becomes a whole number.

15.6 * 100 / 0.24 * 100

= 1560 / 24

= 65

The recurrence relation for the total amount of money in the savings account at the end of n months can be expressed using a recursive formula that takes into account the monthly deposits and the compounded interest. Let A_n be the total amount of money in the account at the end of the nth month. Then, we have:

A_n = A_{n-1} + 100 + (0.06/12)*A_{n-1}

Here, A_{n-1} represents the total amount of money in the account at the end of the (n-1)th month, which includes the deposits made in the previous months and the accumulated interest. The term 100 represents the deposit made at the beginning of the nth month.

The term (0.06/12)*A_{n-1} represents the interest earned on the balance in the account at the end of the (n-1)th month, assuming a monthly interest rate of 0.06/12.

Using this recursive formula, we can calculate the total amount of money in the account at the end of each month, starting from the initial balance of $0. For example, we can calculate A_1 = 100 + (0.06/12)*0 = $100, which represents the balance at the end of the first month.

Similarly, we can calculate A_2 = A_1 + 100 + (0.06/12)*A_1 = $206, which represents the balance at the end of the second month. We can continue this process to calculate the balances at the end of each month up to the nth month.

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Answer:

Step-by-step explanation:

Answer: 1

Step-by-step explanation: 1.27 is 27 hundredths from 1, but 73 hundredths from 2. Therefore it's nearest whole number is 1.00 = 1.

Answer:

1.) x = 150

2.) x = 8.5

Step-by-step explanation:

1.)

\(\frac{x}{5}+10=40\\\\\frac{x}{5}=30\\\\x=150\)

2.)

\(4x-36=-2\\\\4x=34\\\\x=8.5\)

Answer:

1. x = 150

2. x = 8.5

Step-by-step explanation:

1. x/5 + 10 = 40

Get x by itself and then solve for x.

First, subtract 10 from both sides

x/5 + 10 - 10 = 40 - 10

x/5 = 30

Then, multiply by 5 to get x by itself.

x/5 = 30

x/5 * 5 = 30 * 5

x = 150

2. 4x - 36 = -2

Get x by itself and then solve for x.

First, add 36 to both sides

4x - 36 + 36 = -2 + 36

4x = 34

Then, Divide each side by 4

4x/4 = 34/4

x = 8.5

The volume of the solid formed by rotating the region inside the first quadrant enclosed by the curves y = x and y = 5x about the x-axis is (250π/7) cubic units. When finding the volume of a solid of revolution, we use the method of cylindrical shells.

To calculate the volume, we integrate the area of each cylindrical shell formed by rotating an infinitesimally small strip about the x-axis. The height of each shell is the difference between the y-values of the two curves, which is (5x - x²). The circumference of each shell is given by 2πx, and the thickness is dx. Therefore, the volume of each shell is 2πx(5x - x²)dx.

To find the total volume, we integrate this expression over the interval where the two curves intersect. Setting\(y = x^2\)and y = 5x equal to each other, we get x² = 5x. Solving this equation, we find two intersection points: x = 0 and x = 5. Thus, the limits of integration are from 0 to 5.

Integrating the expression \(2\pi x(5x - x^2)dx\) from 0 to 5 gives us the volume of the solid formed by rotating the region inside the first quadrant. Evaluating this integral, we find the volume to be (250π/7) cubic units.

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The term that best represents the intersection of two pages of an open book is point.

A third item made up of everything that is simultaneously contained in all of the other things is called an intersection of two or more objects in mathematics. In Euclidean geometry, for instance, the intersection of two lines in a plane that are not parallel is where they come together. More broadly, the set of elements that are a part of all of the sets is what is meant by the intersection of sets in set theory. The items being considered do not need to be in a shared space, unlike the Euclidean concept.

A point is the most frequent shape for an intersection in plane geometry, while there are other shapes that can be used as well. An intersection is an item of lesser dimension that is incident to each in incidence geometry, which is typically applied to flats.

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The cosine of θ is the ratio of the length of the adjacent side to the length of the hypotenuse

The cosine of an angle is a trigonometric function that relates the length of the adjacent side of a right triangle to the length of the hypotenuse. Specifically, it is defined as the ratio of the length of the adjacent side to the length of the hypotenuse.

In mathematical terms, if we have a right triangle where one of the angles is labeled as theta (θ), then the cosine of theta is given by the formula:

cos(θ) = adjacent side / hypotenuse

1) Cos R =30/34 =15/17

Cos S = 16/34 = 8/17

2) Cos R = 24/26 = 12/13

Cos S = 10/26 = 5/13

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The answer is B.

To obtain A'B'C'D' from ABCD, we can clearly see that it has been shifted 2 units right and 3 units down.

The sampling variance of Spencer's estimator can be calculated using the formula for the variance of the sum or difference of two random variables.

In this case, Spencer's estimator is the average weight of the first and last apple, denoted as (X1 + Xn)/2.

The variance of the sum or difference of two independent random variables is the sum of their individual variances. Since the weights of the apples are independently distributed with mean µ and variance σ^2, the variance of each apple weight is σ^2.

To find the sampling variance of Spencer's estimator, we need to find the variance of (X1 + Xn)/2. Using the formula for variance, we can simplify the calculation as follows:

Var[(X1 + Xn)/2] = (1/4) * Var(X1 + Xn)

Since X1 and Xn are independent, the variance of their sum is the sum of their individual variances:

Var(X1 + Xn) = Var(X1) + Var(Xn) = 2σ^2

Plugging this back into the previous equation, we get:

Var[(X1 + Xn)/2] = (1/4) * 2σ^2 = σ^2/2

Therefore, the sampling variance of Spencer's estimator is σ^2/2.

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