Mason had 30 dollars to spend on 3 gifts. He spent 10 1/4
dollars on gift A and 3 4/5
dollars on gift B. How much money did he have left for gift C?

Neil is growing sugar crystals for his science fair experiment. He wants to find out if the amount of sugar affects the size of the crystal. Neil adds 18 tablespoons of sugar to his first bowl of water. He plans to add less sugar to the second bowl.

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Answer:

y=7

Step-by-step explanation:

x=3

Let the unkown be x. the given proportion would be

20/3 = x/6

By crossmultiplying, it becomes

x * 3 = 20 * 6

3x = 120

x = 120/3

x = 40

The correct option is C

Rotating EF 90° clockwise would produce the same image as rotating CD

270° counterclockwise

There are different ways of transformations such as:

Rotation

Dilation

Translation

Reflection

Now, the coordinates are given as:

EF = E(4, -5) and F(3, -2)

Now, rotation by 90° clockwise would produce:

E'(-5, -4) and F(-2, -3)

This is a rotation rule of (x, y) → (y, -x)

Thus, if CD has the coordinates C(-4, 5) and D(-3, 2), then the rotation by 270° counterclockwise would produce:

C'(5, 4) and D(2, 3)

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J = (3,0)

K = (3,negative two)

L = [ 0, negative two]

I apologise for the way this is set out, half of the keys on my laptop do not work

Answer:

J- (3,0)

K- (3,-2)

L- (1,-2)

Reasoning- Just move the points to where it's asking.

Th length of the enclosed area of the scale model in inches is 32 inches.

Joseph and Raquel are building a scale model of the Alamo Mission for their Texas history project using a scale in which 2 inches represents 30 feet.

The enclosed area of the Alamo Mission was 480 feet long and 160 feet wide.

The length of the enclosed area of the scale model in inches can be calculated as follows:

30 feet = 2 inches

480 feet = ?

cross multiply

length of the enclosed area = 480 × 2 / 30

length of  the enclosed area = 960 / 30

length of the enclosed area = 32 inches

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Answer: C. 324 cm∧3

Just took quiz.

Based on the calculations, the volume of this pyramid is equal to: D. 324 cm³.

Given the following data:

Mathematically, the volume of a pyramid can be calculated by using this formula:

Volume = 1/3 × base area × height

Next, we would find the height of this pyramid from the right-angled triangle ABC by applying Tan trigonometry formula:

Tanθ = Opp/Adj = BC/AC

Tan60 = height/6

√3 = height/6

Height = 6√3 cm.

Now, we can calculate the volume of this pyramid:

Volume = 1/3 × base area × height

Volume = 1/3 × 54√3 × 6√3

Volume = 1/3 × 972

Volume = 324 cm³.

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Part 1:

To find the distance between two points, we can use the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Substituting the values into the formula, we get:

d = sqrt((7 - 3)^2 + (3 - 6)^2)

Simplifying, we get:

d = sqrt(4^2 + (-3)^2)

d = sqrt(16 + 9)

d = sqrt(25)

d = 5

Therefore, the distance between the points (3, 6) and (7, 3) is 5 units.

PART 2:

d = sqrt(64 + 36)

d = sqrt(100)

d = 10

Therefore, the distance between the points (1, 7) and (9, 1) is 10 units.

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The measures of the corresponding inscribed angles, and then add those angles together to find the measure of angle L. Therefore, the measure of angle L is 64 degrees.

The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc. In other words, if we have an angle whose vertex is on the circumference of a circle, and whose sides intersect two points on the circumference, then the measure of the angle is half the measure of the arc between those two points.

In this problem, we are given the measures of two arcs, DR and SV, and we want to find the measure of angle L. We can start by using the Inscribed Angle Theorem to find the measures of the corresponding inscribed angles. Let's call these angles A and B, where A is the inscribed angle that intercepts arc DR, and B is the inscribed angle that intercepts arc SV.

Using the Inscribed Angle Theorem, we can find that m∠A=12m⌢DR=12(34∘)=17∘m∠B=12m⌢SV=12(94∘)=47∘

To find the measure of angle L, we simply add angles A and B together: m∠L=m∠A+m∠B=17∘+47∘=64∘

Therefore, the measure of angle L is 64 degrees.

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Divide the number satisfied by total people surveyed then multiply by 100 for the percent.

960/2400 = 0.4

0.4 x 100 = 40%

The answer is 40%

There is a significant relationship between the number of cats she owns and the number of times an old widow was married (r = +0.91, p < 0.05, r² = 0.82).

Given, the Pearson correlation coefficient of +0.91,

There appears to be a strong +ve correlation between the number of cats she owns and the number of times an old widow was married.

It suggests that the more times a widow was married,the more cats she tends to own.

Approximately 82% of the variance in the number of cats owned can be explained by the number of times a widow was married is indicated by the coefficient of determination (r²).

Hence, we can say that there is a significant relationship between the number of cats she owns and the number of times an old widow was married (r = +0.91, p < 0.05, r² = 0.82).

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-6 + 10i

Step-by-step explanation:

Greetings !

Write the expression in product form

\(2i \times (5 + 3i)\)

Apply distributive law a(b+c)=ab+ac

\(2i5 + 2i3i\)

Multiply the numbers

Multiply the numbers

Apply exponent rule aa=a²

\(ii = i {}^{2} \\ = 6i {}^{2} \)

Apply imaginary number rule i²=-1

=6(-1)=-6

\( = 10i - 6\)

Rewrite in standard complex form:

\( - 6 + 10i\)

Hope it helps!

The equations are x² = y + 16 & 4y - 1 = 7x and the solution is (5, 9)

From the question, we have the following parameters that can be used in our computation:

x = first number

y = second number

Given that

The square of the first number is 16 more than the second number

This means that

x² = y + 16

Also, we have the difference expression to be

4y - 1 = 7x

When these equations are solved graphicaly, we have

(x, y) = (5, 9)

Hence, the equations are x² = y + 16 & 4y - 1 = 7x and the solution is (5, 9)

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Answer: 12 cups

Step-by-step explanation:

Answer:

12 cups

Step-by-step explanation:

1 pint = 2 cups

6 pints = 6 × 2 cups = 12 cups

To determine if a matrix is a linear combination of other matrices, we need to check if it can be written as a weighted sum of those matrices where the weights are scalar values (numbers).

If a matrix can be expressed in this way, it is said to be a linear combination of the other matrices.

For example if we have matrices: A, B & C and we can write matrix D as follows:

Then D is a linear combination of matrices A, B and C. This concept is important in linear algebra as it allows us to express one matrix in terms of others. Making it easier to manipulate & analyze the matrices. A matrix is a linear combination of other matrices if it can be expressed as a weighted sum of those matrices where the weights are scalar values.

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The equation 7^(x+3) = 2log2^(x+3) has no exact solution. Therefore, the correct choice is B. There is no solution.

To solve the equation 7^(x+3) = 2log2^(x+3), we need to isolate the variable x. However, we notice that the equation involves both exponential and logarithmic terms, which makes it challenging to find an exact solution algebraically.

Taking the logarithm of both sides can help simplify the equation:

log(7^(x+3)) = log(2log2^(x+3))

Using the properties of logarithms, we can rewrite the equation as:

(x+3)log(7) = log(2)(log2^(x+3))

However, we still have logarithmic terms with different bases, making it difficult to find an exact solution algebraically.

To approximate the solution, we can use numerical methods such as graphing or iterative methods like the Newton-Raphson method. Using these methods, we find that the equation does not have a real-valued solution. Therefore, the correct choice is B. There is no solution.

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Answer:

I believe the answer is function

Step-by-step explanation:

A similarity statement is a statement used in geometry to prove exactly why two shapes have the same shape and are in proportion.

Answer:

\((fog)(x) = - {x}^{2} + x + 9\)

Step-by-step explanation:

\((fog)(x) = f(g(x)) \\ = - ( {x}^{2} - x - 4) + 5 \\ = - {x}^{2} + x + 4 + 5 \\ = - {x}^{2} + x + 9\)

I hope I helped you^_^

(a) Using induction: n^7 ≤ 2^n for n ≥ 37. (b) Using leaping induction: n^7 ≤ 2^n for n ≥ 37.(a) Using induction, we can prove that n^7 ≤ 2^n for n ≥ 37.

Base Case: For n = 37, we have 37^7 = 69,343, while 2^37 ≈ 137,438,953,472. Since 69,343 ≤ 137,438,953,472, the base case holds.

Inductive Step: Assume that for some k ≥ 37, k^7 ≤ 2^k. We need to show that (k + 1)^7 ≤ 2^(k + 1).

Expanding (k + 1)^7 using the binomial theorem, we have:

(k + 1)^7 = C(7, 0)k^7 + C(7, 1)k^6 + C(7, 2)k^5 + C(7, 3)k^4 + C(7, 4)k^3 + C(7, 5)k^2 + C(7, 6)k + C(7, 7)

Since k ≥ 37, each term in the expansion is multiplied by a positive coefficient. Thus, we can rewrite the inequality as:

(k + 1)^7 ≤ 2k^7 + 2k^6 + 2k^5 + 2k^4 + 2k^3 + 2k^2 + 2k + 2

By the induction hypothesis, k^7 ≤ 2^k, so we can substitute this in the inequality:

(k + 1)^7 ≤ 2^k + 2k^6 + 2k^5 + 2k^4 + 2k^3 + 2k^2 + 2k + 2

Now, we need to prove that 2^k + 2k^6 + 2k^5 + 2k^4 + 2k^3 + 2k^2 + 2k + 2 ≤ 2^(k + 1).

Dividing both sides by 2, we have:

2^k + k^6 + k^5 + k^4 + k^3 + k^2 + k + 1 ≤ 2^k

Since k ≥ 37, each term on the left-hand side is positive, and the inequality holds.

Therefore, we have shown that if k^7 ≤ 2^k for some k ≥ 37, then (k + 1)^7 ≤ 2^(k + 1).

By the principle of mathematical induction, we can conclude that n^7 ≤ 2^n for n ≥ 37.

Keywords: induction, n^7, 2^n, base case, inductive step, binomial theorem, induction hypothesis.

(b) Using leaping induction, we can prove that n^7 ≤ 2^n for n ≥ 37.

For this approach, we'll use a different base case and an alternative inductive step.

Base Case: For n = 37, we have 37^7 = 69,343, while 2^37 ≈ 137,438,953,472. Since 69,343 ≤ 137,438,953,472, the base case holds.

Inductive Step: Instead of considering (k + 1), we'll consider (k + 7) in each step.

Assume that for some k ≥ 37, k^7 ≤ 2^k. We need to show that (k + 7)^7 ≤ 2^(k + 7).

Expanding (k + 7)^7 using the bin

omial theorem, we have:

(k + 7)^7 = C(7, 0)k^7 + C(7, 1)k^6(7) + C(7, 2)k^5(7^2) + ... + C(7, 6)k(7^6) + C(7, 7)(7^7)

Now, we can observe that each term in the expansion contains a factor of 7 raised to some power, while k^7 ≤ 2^k. Thus, we can rewrite the inequality as:

(k + 7)^7 ≤ 2^k + 7^1(7^6) + 7^2(7^5) + ... + 7^6(7^1) + 7^7

Simplifying further, we have:

(k + 7)^7 ≤ 2^k + 7^7(1 + 7 + 7^2 + ... + 7^5 + 7^6)

Since k ≥ 37, we know that k ≤ 7k. Therefore, we can rewrite the inequality as:

(k + 7)^7 ≤ 2^k + 7^7(1 + 7 + 7^2 + ... + 7^5 + 7^6) ≤ 2^k + 7^7(7^6 + 7^6 + ... + 7^6 + 7^6) = 2^k + 7^7(7^6 × 6)

By the induction hypothesis, k^7 ≤ 2^k, so we can substitute this in the inequality:

(k + 7)^7 ≤ 2^k + 7^7(7^6 × 6) ≤ 2^k + 7^7(2^k × 6)

Combining the terms, we have:

(k + 7)^7 ≤ (2^k + 7^7(2^k × 6)) = 2^k(1 + 7^7 × 6)

Since 1 + 7^7 × 6 is a constant, we can denote it as C. Therefore, we have:

(k + 7)^7 ≤ 2^k × C = 2^(k + 7)

Hence, we have shown that if k^7 ≤ 2^k for some k ≥ 37, then (k + 7)^7 ≤ 2^(k + 7).

By the principle of leaping induction, we can conclude that n^7 ≤ 2^n for n ≥ 37.

Keywords: leaping induction, n^7, 2^n, base case, inductive step, binomial theorem, induction hypothesis.

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Answer:  Let's assume that the base of the rectangle is "x", and the height of the rectangle is "y". Let's also assume that the side length of the equilateral triangle is "t".

Then, we can write the perimeter of the window as:

p = x + 2y + 3t

We want to find the value of "x" that maximizes the area of the window. The area of the window can be expressed as:

A = xy + (1/2) * t * sqrt(3) * t

where the first term represents the area of the rectangle and the second term represents the area of the equilateral triangle.

To simplify the expression, we can use the perimeter equation to eliminate "y" and "t". Solving for "y", we get:

y = (1/2) * (p - x - 3t)

Solving for "t", we get:

t = (1/3) * (p - x - 2y)

Substituting these expressions into the area equation, we get:

A = x/2 * (p - x - 2y) + (1/6) * (p - x - 2y)^2 * sqrt(3)

Expanding this expression and simplifying, we get:

A = (1/12) * (p^2 - 2px + 3x^2) * sqrt(3) + (1/2) * px - (1/2) * x^2

To find the value of "x" that maximizes this expression, we can take the derivative of "A" with respect to "x" and set it equal to zero:

dA/dx = (1/12) * (6x - 2p) * sqrt(3) + (1/2) * p - x = 0

Simplifying this expression, we get:

x = (1/33) * (6 + sqrt(3)) * p

Therefore, in order to obtain a window of maximum area, the base of the rectangle should be equal to (1/33) * (6 + sqrt(3)) times the perimeter of the window.

This took a while brainliest would be appreciated (:

A) 500

B) 54 minutes

C) 68cents and 60 cents

D)

E) $40.95

A proportion is a statement that says that two ratios are equal. They can be used in many everyday situations like comparing sizes, cooking, calculating percentages, and more.

Proportions can be written as equivalent fractions or as equal ratios.

A) 42% = 210

100% = (210 x 100)/42

= 500 people

B) 135 berries = 15 minutes

    486 berries = ??minutes

= (486 x 15)/135

= 54 minutes

C) unit price = $6.75/10 = 0.675cents or 68cents

    ii) unit price = $7.25/12 = 0.604cents or 60cents

D) Inconclusive question.

E) 40% of 65 = $26

65 - 26 = $39

Tax = 5% = $1.95

Total = $39 + 1.95

Final Price of jacket = $40.95

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Answer:

hi my name is chelsea and i wiuld like ti thank yiu fir the points

Answer:

180 deg rotation

Step-by-step explanation:

You can't simply translate the original figure into its image. You'd need a reflection or a rotation. For example, if you reflected triangle HTY over the x-axis, and then reflected it over the y-axis, you'd get triangle H'T'Y. The problem does not allow for reflections, so this cannot be used. That means you must use a rotation.

Use the origin as the center of rotation.

Rotate triangle HTY 180 degrees clockwise or counterclockwise.

You end up with the image.

Answer: 180 deg rotation

Answer: They are congruent

Step-by-step explanation:

All angles are the same, meaning all sides must be in scale to each other, aka they are congruent!

Answer:

answer is non of above.

Step-by-step explanation:

i. they are similar triangles cause all their angles are same.

ii. they can't be congruent; for being congruent they must show ASA, SSS, SAS axioms(which they don't)

iii. they don't have same sizes(implies they can't have same area)

If triangle ABC is a right triangle and

A half circle has 180 degrees, so the sum of \(\begin{gathered} 90\text{ + (}x\text{-12)}+x\text{ = 180 } \\ x\text{ - 12 + x = 180 - 90 } \\ 2x\text{ - 12 = 90} \\ 2x\text{ = 90 + 12} \\ 2x\text{ = 102} \\ x=\text{ 102/2 } \\ x=\text{ 51º} \end{gathered}\)So, if x= 51º, then m

Answer: The input values for this function are the number of hours traveled, represented by the variable h. Therefore, appropriate input values for this function would be any positive number representing a number of hours traveled.

For example, some appropriate input values could be:

h = 1: This represents 1 hour of travel, or a total distance of 140 miles.

h = 2: This represents 2 hours of travel, or a total distance of 280 miles.

h = 3.5: This represents 3.5 hours of travel, or a total distance of 490 miles.

Note that the input values do not have to be whole numbers, they can be any positive number representing a number of hours traveled.

Step-by-step explanation:

Answer:

slope = \(\frac{2}{5}\)

Step-by-step explanation:

calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 2, 2 ) and (x₂, y₂ ) = (3, 4 )

m = \(\frac{4-2}{3-(-2)}\) = \(\frac{2}{3+2}\) = \(\frac{2}{5}\)

Answer:

1/16

Step-by-step explanation:

plug in -4 instead of the x.

if the exponent is negative it can be written as 1/2^4

so the answer is 1/16