At the beginning of the school year, each student's height was measured Ryans's height was measured 48.2 inches his friend Sara was 2.05 inches shorter than their friend Joel had measured 3 inches taller than Sara. what were the heights of Sara and Joel?


FIRST 3 PEOPLE WHO ANSWER GETS BRAINLESS........

Answer: A

Step-by-step explanation: 256 times 2.5% is 256 times 0.025 which equals 6.4. Add 6.4 to 256

ఊhe directional derivative of f at the point (1, 2, 2) in the direction of the vector v = (1/5√2)i + (1/5√2)j is 2√2.

To find the directional derivative of the function f(x, y, z) = 2z^2x + y^3 at the point (1, 2, 2) in the direction of the vector v = (1/5√2)i + (1/5√2)j, we can use the formula for the directional derivative:

D_v(f) = ∇f · v

where ∇f is the gradient of f.

Taking the partial derivatives of f with respect to each variable, we have:

∂f/∂x = 2z^2

∂f/∂y = 3y^2

∂f/∂z = 4xz

Evaluating these partial derivatives at the point (1, 2, 2), we get:

∂f/∂x = 2(2)^2 = 8

∂f/∂y = 3(2)^2 = 12

∂f/∂z = 4(1)(2) = 8

Therefore, the gradient ∇f at (1, 2, 2) is given by ∇f = 8i + 12j + 8k.

Substituting the values into the directional derivative formula, we have:

D_v(f) = ∇f · v = (8i + 12j + 8k) · (1/5√2)i + (1/5√2)j

= 8(1/5√2) + 12(1/5√2) + 8(0)

= (8/5√2) + (12/5√2)

= (8 + 12)/(5√2)

= 20/(5√2)

= 4/√2

= 4√2/2

= 2√2

Hence, the directional derivative of f at the point (1, 2, 2) in the direction of the vector v = (1/5√2)i + (1/5√2)j is 2√2.

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Answer:

8

Step-by-step explanation:

count up from where s is (-7) to where v is (1) there are 8 numbers in between them. making that he length

Answer:

S= -7 to V= 1 so your answer is 8

The balloon payment at the end of 7 years would be $173,819.97, which is option A.

A 7/23 balloon mortgage means that April will make payments on the loan as if it were a 23-year mortgage, but the remaining balance of the loan will be due in full after 7 years.

To find the balloon payment at the end of 7 years, we can first calculate the monthly payment using the loan amount, interest rate, and loan term:

n = 23 * 12 = 276 (total number of payments)

r = 4.15% / 12 = 0.003458 (monthly interest rate)

P = (r * PV) / (1 - (1 + r)^(-n))

where

PV = $197,000

P = (0.003458 * $197,000) / (1 - (1 + 0.003458)^(-276)) = $1,007.14 (monthly payment)

Now we can calculate the remaining balance on the loan after 7 years. Since April is making payments as if it were a 23-year mortgage, she will have made 7 * 12 = 84 payments by the end of the 7th year.

Using the formula for the remaining balance of a loan after t payments:

B = PV * (1 + r)^t - (P / r) * ((1 + r)^t - 1)

Where

t = 84 (number of payments made)

B = $197,000 * (1 + 0.003458)^84 - ($1,007.14 / 0.003458) * ((1 + 0.003458)^84 - 1)

B = $173,819.97

Therefore, the balloon payment at the end of 7 years would be $173,819.97, which is option A.

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The number of possible combinations of main course and desert are { PF, PT, PM, BF, BT, BM, CF, CT, CM} .

The different ways in which items from a set may be chosen, usually without replacement, to construct subsets, are called permutations and combinations. When the order of the selection is a consideration, this selection of subsets is referred to as a permutation; when it is not, it is referred to as a combination.

The possible choices for deserts are 3 and that for main course is 3. So the total combinations possible are:

3 * 3 = 9 combinations.

Hence the combinations can be as follows:

{ PF, PT, PM, BF, BT, BM, CF, CT, CM}

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In this problem 0.7 is the standard deviation of the contents.

It is a statistic that gauges a dataset's dispersion from its mean, and it is calculated as the variance's square root. By calculating the deviation of each data point from the mean, the standard deviation may be determined as the square root of variance. The standard deviation reveals the degree of data skewedness. It gauges how far away from the mean each observed value is. Approximately 95% of values in any distribution will be within two standard deviations of the mean. A dataset's dispersion from its mean is measured by standard deviation. It is determined as the variance's square root. In the financial industry, standard deviation is frequently employed as a gauge of an asset's relative riskiness.

Given,

A random sample of 196 bottles of cologne showed an average content of 4 ounces. it is known that the standard deviation of the contents (i.e., of the population) is 0.7 ounces.

In this problem 0.7 is the standard deviation of the contents.

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The value of x is x=7.

A triangle is a polygon with 3 sides.

Given, the measures of the interior angles of the triangle are 60°, 70°, and 6x+8.

Since the sum of the measures of the interior angles of a triangle is 180°, it follows:

60+ 70+ 6x+8 = 180

138 + 6x =180

6x = 180-138

6x = 42

x = 42/6

x = 7

Hence, the value of x is x=7.

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Step-by-step explanation:

look in the comments I'll put the answers as I go along x

Answer:

#11 21

Step-by-step explanation:

You have the right steps for question 10, let me work #11 n/3 -5 = 2

So following your steps: move the -5 so n/3 = 2+5 so n/3 = 7, now

multiply both sides by 3 so n = 21

Answer:

4xy

Step-by-step explanation:

(x+y) (x+y) - (x-y) (x-y)​

(x² + xy + xy + y²) - (x² - xy - xy + y²)

(x² + 2xy + y²) - (x² - 2xy + y²)

x² + 2xy + y² - x² + 2xy - y²

x² - x² + 2xy + 2xy + y² - y²

4xy

Answer:

that could literally be anything, as long as the first sum is greater then the second.

example;

(2+4) (3+5) - (6+1) (5+2)

(or, 6+8 = 14, 7+7 = 14, 14 - 14 = 0)

hope this helped :)

Answer:

Width=7

Length=21

Step-by-step explanation:

Width=x

length=3x

x+x+3x+3x=56

8x=56

x=7

width = x = 7

length = 3x = 21

Answer:

Length = 21 and Width = 7

Step-by-step explanation:

Length (L)= 3x width (W)

L = 3W

Perimeter (P) = 56

Perimeter = 2L + 2W

56 = 2(3W) + 2W

56 = 6W + 2W

56 = 8W

W = 56/8

W = 7

L = 3W

L = 3(7)

L = 21

therefore Length = 21 and Width = 7

Answer:

10/20 because then it's still a 50 50 chance so the answer it 10

The discounted price of the suit is $168.

Explanation: To calculate the discounted price, we need to subtract the discount percentage from 100% and then multiply it by the original price. In this case, the original price of the suit is $280, and it was discounted by 40%.

First, we calculate the discount amount:

Discount amount = Original price * (Discount percentage / 100)

Discount amount = $280 * (40 / 100)

Discount amount = $280 * 0.4

Discount amount = $112

Next, we will subtract the discount amount from the original price to find the discount price:

Discounted price = Original price - Discount amount.

Discounted price = $280 - $112

Discounted price = $168

Therefore, the discounted price of the suit is $168 after applying a 40% discount to the original price of $280.

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Answer:

3/2, 1/2

Step-by-step explanation:

hope it helps and hope is what u asking for

For the given problem, the integral of \(\frac{1}{\sqrt{a^2-x^2}}\)  is  \($\sin^{-1}\frac{x}{a} + C$.\)

A mathematical notion that depicts the area under a curve or the accumulation of a quantity over an interval is known as an integral. Integrals are used in calculus to calculate the total amount of a quantity given its rate of change.

The process of locating an integral is known as integration. Finding an antiderivative (also known as an indefinite integral) of a function, which is a function whose derivative is the original function, is what integration is all about. The antiderivative of a function is not unique since it might differ by an integration constant.

For given problem,

\($\int \frac{1}{\sqrt{a^2-x^2}} dx$\)

Let \($x = a \sin\theta$\) , then \($dx = a \cos\theta d\theta$\)

\($= \int \frac{1}{\sqrt{a^2-a^2\sin^2\theta}} a\cos\theta d\theta$\)

\($= \int \frac{1}{\sqrt{a^2\cos^2\theta}} a\cos\theta d\theta$\)

\($= \int d\theta$\)

\($= \theta + C$\)

Substituting back for\($x = a\sin\theta$:\)

\($= \sin^{-1}\frac{x}{a} + C$\)

Therefore, the integral of \(\frac{1}{\sqrt{a^2-x^2}}\) is \($\sin^{-1}\frac{x}{a} + C$.\)

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Answer:

C=6π=18.84 ( if π=3.14)

Step-by-step explanation:

distance around the edge of the pond means the circumference of the circle=

C=2πr

C=2π(3)

C=6π=18.84 ( if π=3.14)

The approximate distance around the edge of the pond is 18.84 feet.

Given that, a circular pond has a radius of 3 feet.

The circumference of a circle is the perimeter of the circle. It is the total length of the boundary of the circle. The circumference of a circle is the product of the constant π and the diameter of the circle.

We know that, the circumference of a circle is 2πr.

Now, 2×3.14×3

= 18.84 feet

Hence, the approximate distance around the edge of the pond is 18.84 feet.

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Step-by-step explanation:

you start a 8 on the y axis on the graph, then you go down one and 3 to the right.

Answer:

It should be 4 or (0,4)

Step-by-step explanation:

The y-intercept is just where one of the lines of the graph crosses the y-axis, which in the picture shows it crosses at (0,4)

The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.

The slope of the tangent line to the graph of the function y = x^4 - 10x^2 + 9 at x = 1 can be found by taking the derivative of the function and evaluating it at x = 1. The equation of the tangent line can then be determined using the point-slope form.

Taking the derivative of the function y = x^4 - 10x^2 + 9 with respect to x, we get:

dy/dx = 4x^3 - 20x

To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative:

dy/dx (at x = 1) = 4(1)^3 - 20(1) = 4 - 20 = -16

Therefore, the slope of the tangent line is -16.

To find the equation of the tangent line, we use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Given that the point of tangency is (1, y(1)), we substitute x1 = 1 and y1 = y(1) into the equation:

y - y(1) = -16(x - 1)

Expanding the equation and simplifying, we have:

y - y(1) = -16x + 16

Rearranging the equation, we obtain the equation of the tangent line:

y = -16x + (y(1) + 16)

To find the slope of the tangent line, we first need to find the derivative of the given function. The derivative represents the rate of change of the function at any point on its graph. By evaluating the derivative at the specific value of x, we can determine the slope of the tangent line at that point.

In this case, the given function is y = x^4 - 10x^2 + 9. Taking its derivative with respect to x gives us dy/dx = 4x^3 - 20x. To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative equation, resulting in dy/dx = -16.

The slope of the tangent line is -16. This indicates that for every unit increase in x, the corresponding y-value decreases by 16 units.

To determine the equation of the tangent line, we use the point-slope form of a linear equation, which is y - y1 = m(x - x1). We know the point of tangency is (1, y(1)), where x1 = 1 and y(1) is the value of the function at x = 1.

Substituting these values into the point-slope form, we get y - y(1) = -16(x - 1). Expanding the equation and rearranging it yields the equation of the tangent line, y = -16x + (y(1) + 16).

The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.

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Answer:

Step-by-step explanation:

First, outside, inside, last.

w*w

6*w

9*w

9*6

\(w^2+15w+54\)

Answer: w^2 + 15w + 54

Step-by-step explanation:

FOIL = first, outside, inside, last.

First —> multiply first numbers of each parentheses.

Outside —> multiple the OUTSIDE numbers in each parentheses (first number in the first parentheses, second number in the second parentheses.

Inside —> multiply the INSIDE numbers in each parentheses (the second number in the first parentheses, first number in the second parentheses).

Last —> multiply second number of each parentheses.

(W + 9)(w + 6)

F = w^2

O = 6w

I = 9w

L = 54

W^2 + 6w + 9w + 54

W^2 +15w + 54

Answer:

800

Step-by-step explanation:

2 times 4 is 8, 20 has one zero and 40 has one zero. Just add both zeros to 8, if you know the answer to 2x4.

The correct option is D

(x + 2) is a binomial expression.

A binomial expression is an expression that contains two terms (from the word "bi") and are connected by either addition or subtraction.

From the options, the binomial expression is: x + 2

EXPLANATION

Given the function

f(x) = sqrt(x-1) -3

The minimum value on the interval 2≤x≤10 is -3.

We can get this by sketching different points as follows:

x y=sqrt(x-1) -3

0 undefined

1 -3

2 -2

5 -1

10 0

Answer:

14.6

Step-by-step explanation:

In the example

x =kh

k is the constant of proportionality

We will have a Deficit balance of $30 at the end of the month.

"Unilateral transfer" is the term used to describe the balance of payments deficit's most obvious cause. For instance, Americans who contribute money to another country in the form of foreign aid do not receive anything in return (economically speaking). Few economists would argue that foreign aid-related balance of payment deficits are a "bad thing."

Weekly net income = $380

Monthly net income = $380 * 4 weeks = $1520.

Monthly expenses = $1550

Balance = Monthly income - monthly expenses = $-30.

The negative sign shows a deficit of $30 monthly

Therefore, We will have a Deficit balance of $30 at the end of the month.

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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.