If y varies inversely as x, and y = 32 when x = 3, find y when x = 15.

Answer:

x = 2

y = - 1

Step-by-step explanation:

5x/6 + y/3 = 4/3

2x/3 - y/2 = 11/6

Multiply the above equation by 6 to express in linear form

6 × (5x/6 + y/3 = 4/3)

5x + 2y = 8.... (1)

6 × (2x/3 - y/2 = 11/6)

4x - 3y = 11.... (2)

Thus, the equation are:

5x + 2y = 8.... (1)

4x - 3y = 11.... (2)

Next, multiply equation (1) by 3 and equation (2) by 2. This is illustrated below:

3 × (5x + 2y = 8)

15x + 6y = 24 ..... (3)

2 × (4x - 3y = 11)

8x - 6y = 22 ... (4)

Next, add equation 3 and 4 together. This is illustrated below:

.. 15x + 6y = 24... (3)

+ 8x - 6y = 22 .... (4)

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

23x = 46

Divide both side by 23

x = 46/23

x = 2

Next, substitute the value of x into any of the equation. Here, we shall substitute the value of x into equation (3). This is illustrated below:

15x + 6y = 24... (3)

x = 2

15(2) + 6y = 24

30 + 6y = 24

Collect like terms

6y = 24 - 30

6y = - 6

Divide both side by 6

y = - 6/6

y = - 1

Therefore, the value of x and y is

x = 2

y = - 1

Answer:

$17.33

Step-by-step explanation:

3.5×4.95

=17.325

= $17.33

Answer:

Oof

Step-by-step explanation:

Answer:

get a fast metabloism

Step-by-step explanation:

Answer:

D.40

Step-by-step explanation:

2(5)squared -10

2(25)-10

50-10=40

Answer:

   give brainliest --- \(\sqrt{247}\)

Step-by-step explanation:

the height, radius, and circumference of the cone form a right triangle. So we use pythagorean theorem:

3^2+h^2=16^2

simplify

9+h^2=256

h^2=247

h = \(\sqrt{247}\)

PLS GIB BRAINLIEST

Answer:

15.7cm

Step-by-step explanation:

use Pythagoras theorem

16^2-3^2=a

a=15.7cm(1d.p.)

and thats the height

please mark as brainliest

Answer:

Pic is not working sorry. :(

Step-by-step explanation:

The probability that a truck drives between 122 and 127 miles in a day is 0.0165, rounded to four decimal places.

To find the probability that a truck drives between 122 and 127 miles in a day, we'll use the z-score formula and standard normal distribution table. Follow these steps:

Step 1: Calculate the z-scores for 122 and 127 miles.
z = (X - μ) / σ

For 122 miles:
z1 = (122 - 90) / 18
z1 = 32 / 18
z1 ≈ 1.78

For 127 miles:
z2 = (127 - 90) / 18
z2 = 37 / 18
z2 ≈ 2.06

Step 2: Use the standard normal distribution table to find the probabilities for z1 and z2.
P(z1) ≈ 0.9625
P(z2) ≈ 0.9803

Step 3: Calculate the probability of a truck driving between 122 and 127 miles.
P(122 ≤ X ≤ 127) = P(z2) - P(z1)
P(122 ≤ X ≤ 127) = 0.9803 - 0.9625
P(122 ≤ X ≤ 127) ≈ 0.0178

So, the probability that a truck drives between 122 and 127 miles in a day is approximately 0.0178 or 1.78%.

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Answer:

a) subtracting '8' on both sides, we get

                                      - 5 x² + 8-8 = 133-8

                                        - 5 x²  = 125

b) The solution is x = 5 i

Step-by-step explanation:

Explanation:-

Step (i):-

Given quadratic equation  - 5 x² + 8 = 133

subtracting '8' on both sides, we get

                                      - 5 x² + 8-8 = 133-8

                                       - 5 x²  = 125

Step(ii):-

dividing '-5' on both sides, we get

          \(\frac{-5 x^2}{-5} = \frac{125}{-5}\)

            x²  = -25

            \(x = \sqrt{-25}\)

            x = 5 i

Answer:

its b

Step-by-step explanation:

Combine liked terms

5v + 2v = 7v

2 + 7v = -12

Subtract 2

7v = -14, v = -2

Solution: v = -2

Answer: V = -2

Step-by-step explanation:

Answer:

Sarah's fish tank

Step-by-step explanation:

Nick needs area - the space covering a flat surface

Min needs perimeter - the distance around something

Sarah needs volume - the space inside something

Answer:

true im not sure tho but trust me

Step-by-step explanation:

True. the interpretation of the slope is different in a multiple linear regression model as compared to a simple linear regression model.

The slope and intercept of a line reveal the steepness of the line and the location in which it intersects an axis. The slope and intercept of the logistic relationship of the two variables can be utilized to get the average change rate. The ratio of a change in the variable y to the rise in the x component is known as the the line's slope.

Y = a + bX, where X seems to be the mediating variable and Y is the response variable, is the equation of a linear regression line. A is the intersection (the result of y for x = 0), and b is the line's slope.

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Answer: 10, 12, 14 are the next numbers

Explanation:

Answer:

b

Step-by-step explanation:

Answer:

54.1 inches (round to 1 dp)

Step-by-step explanation:

the formula to calculate the diagonal or a rectangle is

\(\sqrt{(w^{2} +l^{2})}\)

30^2+45^2 is 2925

and \(\sqrt{2925}\)

and the answer to that is 54.1 inches (to 1 dp)

Part A: To find the total surface area of the rectangular prism, we need to calculate the areas of all six faces and then add them together.

Given dimensions:

Length = 7 feet

Width = 3 feet

Height = 4.8 feet

Surface Area of each face:

Front and back faces: Length * Height

= 7 feet * 4.8 feet

= 33.6 square feet

Top and bottom faces: Width * Length

= 3 feet * 7 feet

= 21 square feet

Side faces: Width * Height

= 3 feet * 4.8 feet

= 14.4 square feet

Total Surface Area:

2 * (Front and back faces) + 2 * (Top and bottom faces) + 2 * (Side faces)

= 2 * 33.6 square feet + 2 * 21 square feet + 2 * 14.4 square feet

= 67.2 square feet + 42 square feet + 28.8 square feet

= 137 square feet

Therefore, the total surface area of the bench is 137 square feet.

Part B: To calculate the cost of covering the bench with ceramic tiles, we need to multiply the total surface area by the cost per square foot.

Cost per square foot = $0.89

Total Surface Area = 137 square feet

Total cost to cover the bench:

= Cost per square foot * Total Surface Area

= $0.89 * 137 square feet

= $121.93

Therefore, it will cost $121.93 to cover the bench with ceramic tiles.

Answer:

17 < h = 42

Step-by-step explanation:

Hoped this helped! :)

we cannot have a negative number for x (its against the laws of math), so the domain would be all non-negative numbers

Answer:

h - 17 = 42

Step-by-step explanation:

I know this because it was the answer on quizziz

The solution to the equation \((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\) is 10.3891

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

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\)

Using the following trigonometry ratio

sin²(x) + cos²(x) = 1

We have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = (\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + 1 + e^2\)

The sum to infinity of a geometric series is

S = a/(1 - r)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = \frac{1/2}{1 - 1/2} + \frac{9/10}{1 - 1/10} + 1 + e^2\)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 1 + 1 + 1 + e^2\)

Evaluate the sum

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 3 + e^2\)

This gives

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 10.3891\)

Hence, the solution to the equation is 10.3891

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Answer:

Subtraction.

to solve the equation you would subtract 24 from both sides.

The result of m is 32

-

To solve this equation, let's just:

\( \\ \large \sf 24 + m = 56\)

\(\large \sf m = 56 - 24\)

\( \purple{ \boxed{\large \sf m = 32}}\)

So, the answer will be 32

(a) The number 72% is a D. statistic.

(b) The unknown true percentage of American citizens who like ''real TV'' is a C. parameter.

It is related to statistics and parameters.

(a) The number 72% is a statistic because it represents a summary measure of the sample of individuals who participated in the phone-in poll.

A statistic is a numerical value calculated from a sample of data, and it is used to make inferences about the population from which the sample was drawn.

(b) The unknown true percentage of American citizens who like ''real TV'' is a parameter.

A parameter is a numerical characteristic of a population, such as a mean, proportion, or standard deviation, and it is typically unknown and estimated from sample data.

In this case, the percentage of all American citizens who like ''real TV'' is unknown and cannot be directly observed, so it is considered a parameter.

The phone-in poll only represents a sample of individuals who called in to the newspaper and cannot be used to estimate the parameter for the entire population.

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To find the slant asymptote of the function y = x^2 + 4x + 4, we need to perform polynomial long division. In this case, we will divide the function by y = x.


1. Divide the function y = x^2 + 4x + 4 by y = x using polynomial long division.
2. x goes into x^2 x times. Write x on top.
3. Multiply x by x, which is x^2. Write x^2 under x^2 in the dividend and subtract it.
4. Bring down 4x from the dividend.
5. x goes into 4x, 4 times. Write 4 next to x on top.
6. Multiply 4 by x, which is 4x. Write 4x under 4x in the dividend and subtract it.
7. Bring down the constant term 4 from the dividend.
8. Since the degree of the remaining dividend (constant term) is lower than the divisor's degree (x), we stop dividing.


After performing polynomial long division, we get the quotient y = x + 4, which is the equation of the slant asymptote for the given function.

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Answer:

If you mean the name of the angle then it's a reflex angle

Answer: 81.2

Step-by-step explanation:

a. the factors of equation is \(f(x)=(x-1)(x-10)(2x-3)\)

b. the factors of equation is \(f(x)=(x-1)(x^2+x+4)\)

A polynomial is an expression consisting of variables and coefficients that involves only the operations of addition, subtraction, and multiplication, with non-negative integer exponents.

a. Given function,

\(f(x)=2x^3 -25x^2 + 53x - 30\)

By using trial and error method, put values of x =1, x= 10, and x= 3/2 are satisfied values for above function,

\(f(x)=(x-1)(x-10)(2x-3)\)

therefore, the factors of equation is (x-1) (x-10) (2x-3)

b. Given function,

\(f(x)=x^3 +3x - 4\)

Similarly using trial and error method,

\(f(x)=(x-1)(x^2+x+4)\)

therefore, the factors of equation is (x-1) (x² + x + 4)

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Factor of given polynomials are a. (x-1)(x-10)(2x-3), b. (x-1)(x² + x + 4) .

In mathematics, a polynomial is an expression that consists of variables and coefficients, combined using the operations of addition, subtraction, and multiplication, but not division by a variable. The variables in a polynomial can only have non-negative integer exponents.

Polynomials can have different degrees, which is the highest power of the variable in the expression. For example, the polynomial 3x² - 5x + 2 is a quadratic polynomial, since its highest power of x is 2. If the degree of a polynomial is n, then it has at most n roots, which are the values of x that make the polynomial equal to zero.

Polynomials are used in many areas of mathematics and science, including algebra, calculus, physics, and engineering. They are used to model and analyze many different types of phenomena, such as motion, population growth, and electrical circuits.

Polynomials can also be added, subtracted, and multiplied together to form new polynomials. Additionally, polynomials can be factored, which involves breaking them down into simpler polynomials that multiply together to give the original polynomial.

a) f(x)= 2x³ - 25x² + 53x - 30
⇒(x-1)(x-10)(2x-3)

b) f(x)= x³ + 3x - 4
⇒(x-1)(x² + x + 4)

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The complete question is:

Answer:

\(Mean = 0.36\)

\(SD = 0.5817\)

\(P(x=3) = 0.003588\)

Step-by-step explanation:

Given

Let

A = Event of being a universal donor.

So:

\(P(A) = 0.06\)

\(n = 6\)

Solving (a): Mean and Standard deviation.

The mean is:

\(Mean = np\)

\(Mean = 6 * 0.06\)

\(Mean = 0.36\)

The standard deviation is:

\(SD = \sqrt{np(1-p)}\)

\(SD = \sqrt{6*0.06*(1-0.06)}\)

\(SD = \sqrt{0.3384}\)

\(SD = 0.5817\)

Solving (b): P(x = 3)

The event is a binomial event an dthe probability is calculated as:

\(P(x) = ^nC_x * p^x * (1-p)^{n-x}\)

So, we have:

\(P(x=3) = ^6C_3 * 0.06^3 * (1-0.06)^{6-3}\)

\(P(x=3) = ^6C_3 * 0.06^3 * (1-0.06)^3\)

\(P(x=3) = 20 * 0.06^3 * (1-0.06)^3\)

\(P(x=3) = 0.003588\)

Answer:

- 1210

Step-by-step explanation:

According to BODMAS / PEMDAS rule, we will do multiplication first and then subtraction . So -23 * 56 = -1288 and then the subtraction , 78 + (-1288) =78-1288= -1210

The fraction should be -1210 / 1

Answer:

actaully its 1/4

Step-by-step explanation:

The cost of ordering shirts for a club is 268 units.

Define Function.

A function, according to a technical definition, is a relationship between a set of inputs and a set of possible outputs, where each input is connected to precisely one output.

 This means that a function f will map an object x exactly to one object f(x) in the set of possible outputs if the object x is in the set of inputs (called the codomain).

The statement that f is a function from X to Y using the function notation f: X→Y

The function that represents the cost of the shirts(x) is f(x) = 8x+12

Now, for x = 32

 f(x) = 8x+12

f(32) = 8(32) + 12

        = 256 +12

f(32) = 268 units

.

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Answer:

91 hundreths, (1*1)+(9*1/10), .19

<3 love from maddie

Answer:

(1*1)+(9*1/10) then 91 hundreths and last 0.19

Hope it helps!