23. For the data in the table, does y vary directly with x? If it does, write an equation for the direct (1 point) variation.
yes; y=2 x
yes; y=5 x
yes; y=7 x
no; y does not vary directly with x.

Answer:

Step-by-step explanation:

You want the payroll costs for a 224-hour project completed by 4 men, both without and with overtime pay.

The payroll cost for a 224-hour project with workers paid $7.50 per hour will be ...

  ($7.50/h) × (224 h) = $1680

The total amount paid to the men will be $1680.

From 9 am to 6 pm is 9 hours. Deducting an hour for lunch leaves 8 straight-time hours per day. 4 men working 4 days will put in ...

  (4 men) × (8 h/day/man) × (4 days) = 128 hours . . . . straight time

Completion of the 224-hour project in that time will require ...

  224 -128 = 96 . . . . . hours of overtime

The overtime hours get paid at a 50% premium, so effectively require pay for additional hours of ...

  (96 h) × 50% = 48 h . . . . . added payroll cost

The payroll for 4 men for working 224 hours in 4 days will be ...

  (224 h +48 h) × $7.50 = $2040

The total paid to the men for completion in 4 days will be $2040.

__

Additional comment

The expression for the pay with overtime could be written ...

  men × days × pay per man-day

  4 × 4 × (8 × $7.50 + (224/16 -8) × 1.5 × $7.50)

Using the commutative and associative and distributive properties of arithmetic, this can be evaluated many different ways.

We have rearranged it to ...

  $7.50 × (16×8 + 224 -16×8 + 0.5(224 -16×8)) = $7.50(224 +0.5(96))

We have interpreted "750$" to mean $7.50. If each man actually gets paid a rate of $750 per hour, then the totals get multiplied by 100:

  $168,000 for no overtime

  $204,000 for overtime

This may be the case after a few years' inflation. We know some professionals get paid perhaps $400 per hour, so it is not too much of a stretch to imagine $750 per hour for some highly specialized tasks.

\(-1 \frac{3}{5}+1\frac{1}{2}=-\frac{1}{10}\)

Answer:

In the equation y = 2 cos(5x + 3) - 6, we can ignore the coefficients 2 and -6 for the purposes of calculating the period because they do not change the period. They only change the amplitude (2) and vertical shift (-6) of the function.

The coefficient 5 in front of x inside the cosine function affects the period of the function. It is a horizontal compression/stretch of the graph of the function.

The period of the basic cosine function, y = cos(x), is 2π. When there is a coefficient (let's call it b) in front of x, such as y = cos(bx), the period becomes 2π/b.

So, in your case, b = 5, so the period T of the function y = 2 cos(5x + 3) - 6 is:

T = 2π / 5

This is the simplest form for the period of the given function.

Answer:

4:3

Step-by-step explanation:

Answer:

The total weight of the purchased cherries is \(11\frac{1}{4}\) pounds.

Step-by-step explanation:

Multiply \(2\frac{1}{4}\) by 5.

\(2\frac{1}{4} * 5 = 11 \frac{1}{4}\)

Answer:

11.25 or 45/4

Step-by-step explanation:

2 1/4 times 5

With the Application of Integral calculus the volume of  solid generated is π.

what is integral calculus?

We study integrals and their characteristics in the calculus area known as integral calculus. A crucial idea is integration, which is the opposite of difference. The fundamental theorem of calculus establishes a connection between integral and differential calculus.

v = 2π∫0√π/2xcosx2dx

  = π·sinx20√π/2

v = π

Hence the volume of  solid generated when the region enclosed by the given curves is revolved about the y-axis is π

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The simple interest is $420 and the maturity value is $$6,720

Using this formula to find the simple interest

Simple interest = Principal  × Interest rate × Time

Where:

Principal = $6300

Interest rate =4% or 0.04

Time = 20 month = 20/12 = 1.6666666

Let plug in the formula

Simple interest = $6,300 × 0.04 × 1.6666666

Simple interest = $420

Using this formula to find the maturity value

Maturity value = Principal + Interest

Maturity value = $6,300 + $420

Maturity value = $6,720

Therefore the interest is $420.

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To test penalties' effect on a team's wins, analyze the data and calculate the correlation coefficient. Penalties and wins may be correlated, but one does not necessarily cause the other.

Other factors like team skill and strategy may influence penalties and wins.

The new questions using mathematics are

Is there a relationship between the gravity of penalties assessed against a football team (penalty yards) and their total points scored in a season?

Does the number of fouls committed by a basketball team in a season influence their shooting percentage?

By  using the available data, one can conduct a statistical analysis to establish a potential correlation between the total number of penalties a team has accumulated throughout a season and their overall number of wins.

Although there is a correlation between fines and victories, it does not imply that one is the direct cause of the other. It is possible that there are other contributing elements, such as team abilities, tactics, etc.

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Answer:

x=7

Step-by-step explanation:

6(x-5)=12

We will use the distributive property to get the answer of 6(x-5)

6(x-5)=12

6x-30=12

6x=12+30

6x=42

6x/6=42/6

x=7

Proof:

6(x-5)=12

6(7-5)=12

42-30=12

12=12 or

6(7-5)=12

6(2)=12

12=12

Hope this helps ;) ❤❤❤

Answer:

x = 19

Step-by-step explanation:

So cos and sin are closely related, but they are not equal. In order for these two to be equal to each other, the angles (in the parenthesis by the cos and by the sin) have to be complementary. That is, they have to add up to 90°

Use this idea to set up an equation.

x + 16 + 3x - 2 = 90

Combine like terms.

4x + 14 = 90

Subtract 14.

4x = 76

Divide by 4.

x = 19

x = 19

If you are kooking for the angles:

x + 16

= 19 + 16

= 35

and

3x - 2

= 3(19) - 2

= 57 - 2

= 55

Check: 35 + 55=90

Also,

cos35 = sin55

Answer: 5/7

Step-by-step explanation:

Answer:

The value of a₅ is 1875.

Step-by-step explanation:

Given:

a₁ = 3

aₙ = 5aₙ₋₁

To find the value of a₅, we can apply the recursive formula to compute each term successively:

Step 1: Compute a₂

a₂ = 5a₁ = 5(3) = 15

Step 2: Compute a₃

a₃ = 5a₂ = 5(15) = 75

Step 3: Compute a₄

a₄ = 5a₃ = 5(75) = 375

Step 4: Compute a₅

a₅ = 5a₄ = 5(375) = 1875

Slope of line is 1/2.

What is slope?

In arithmetic, the slope or gradient of a line is a range that describes each the direction and therefore the gradient of the road.

Main body:

to find the slope from a graph , we need to fix two co-ordinates at slope for axis

let point at x be = (40,40)

let point y = (80,60)

Formula for slope ,

m = y₂-y₁/x₂-x₁

m = 60-40/80-40

m = 20/40

m = 1/2

hence , slope of line is 1/2.

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Answer:

10,13,14,20,30.............

The cosine of angle B is: cos(B) = AC / AB = 20/29

The Pythagorean Theorem, a well-known geometric theorem that states that the sum of the squares of the legs of a right-angled triangle is equal to the square of the hypotenuse (the opposite side of the right angle) - that is, in familiar algebraic notation. , a2 + b2 = c2 .

In a right triangle, the cosine of an angle is defined as the ratio of the adjacent side to its hypotenuse. In this case, angle B is the angle we are interested in, and the adjacent side is side AC. Using the Pythagorean theorem, we find the length of side AC:

AC² = AB²+ BC²

AC² = 29² - 21²

AC² = 400

AC = 20

Therefore, the cosine of angle B is:

cos(B) = AC / AB = 20/29

Other trigonometric ratios of angle B can be found using the following formulas:

sin(B) = BC / AB = 21/29

tan(B) = BC / AC = 21/20

csc(B) = AB / BC = 29 / 21

sec(B) = AB / AC = 29/20

bed (B) = AC / BC = 20 / 21  

Thus, the trigonometric ratios of angle B are:

sin(B) = 21/29

cos(B) = 20/29

tan(B) = 21/20

csc(B) = 29/21

sec(B) = 29/20

crib(B) = 20/21

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Answer:

B. a=10

an=an-1-4

this is the answer

Answer:

The current area of the circle is 81π in².

They want to " 'decrease' " the radius to 9 in.

First, find the current radius for the current circle.

Areas of circle = πr²,

81π = πr²

First, divide π from both sides of the equation:

(81π)/π = (πr²)/π

r² = 81

Isolate the variable, r. Root both sides of the equation:

√(r²) = √(81)

r = √( 9 * 9) = 9

The radius currently is 9 in.

The NBA is not making any changes at all, therefore the question will be void. (Note that the other answer choice is -9, however, you cannot have a negative measurement, therefore, the answer is voided).

~

The fundamental idea behind probability sampling is that a sample of individuals must contain essentially the same variations that exist in the population.

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Answer:

Step-by-step explanation:

\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^4\\\\=4[cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^3\; \frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)] --- eq(1)\)

Lets look at the derivative part:

\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)] \\\\= \frac{d}{dx}[cos(3x^2) \sqrt[3]{5x^3 -1} ] + \frac{d}{dx}[sin(4x^3)]\\\\=cos(3x^2) \frac{d}{dx}[ \sqrt[3]{5x^3 -1} ] + \sqrt[3]{5x^3 -1}\frac{d}{dx}[ cos(3x^2) ] + cos(4x^3) \frac{d}{dx}[4x^3]\\\\=cos(3x^2) \frac{1}{3} (5x^3 -1)^{\frac{1}{3} -1} \frac{d}{dx}[5x^3 -1] + \sqrt[3]{5x^3 -1} (-sin(3x^2))\frac{d}{dx}[ 3x^2] + cos(4x^3)[(4)(3)x^2]\)

\(=\frac{cos(3x^2) 5(3)x^2}{3(5x^3 - 1)^{\frac{2}{3} }} -\sqrt[3]{5x^3 -1}\; sin(3x^2) (3)(2)x + 12x^2 cos(4x^3)\\\\=\frac{5x^2cos(3x^2) }{(5x^3 - 1)^{\frac{2}{3} }} -6x\sqrt[3]{5x^3 -1}\; sin(3x^2) + 12x^2 cos(4x^3)\)

Substituting in eq(1), we have:

\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^4\\\\=4[cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^3\; [\frac{5x^2cos(3x^2) }{(5x^3 - 1)^{\frac{2}{3} }} -6x\sqrt[3]{5x^3 -1}\; sin(3x^2) + 12x^2 cos(4x^3)]\)

Answer:

the method of exact differential equations:

We need to check if this differential equation is exact. To do that, we check if the partial derivative of the first term with respect to y is equal to the partial derivative of the second term with respect to x:

∂/∂y(x(x-y)) = x(-1) = -x

∂/∂x(y^2) = 0

Since these partial derivatives are not equal, the differential equation is not exact. We can try to make it exact by multiplying the entire equation by a suitable integrating factor.

Let's find the integrating factor (IF) by taking the partial derivative of the IF with respect to y and equating it to the partial derivative of the second term with respect to x:

∂/∂y(IF) = -y^2/(x(x-y)^2)

∂/∂x(y^2) = 0

From the first equation, we can see that an integrating factor of IF = x(x-y)^2 should make the equation exact. Multiplying the entire equation by this integrating factor, we get:

x(x-y)^2dy + y^2x(x-y)dx = 0

Now, we just need to find a function φ(x,y) such that:

∂φ/∂x = x(x-y)^2dy

∂φ/∂y = y^2x(x-y)dx

Integrating the first equation with respect to x, we get:

φ(x,y) = ∫x(x-y)^2dy + f(x)

φ(x,y) = -1/3(x-y)^3x + f(x)

Now, we differentiate this equation with respect to x and equate it to the second equation:

∂φ/∂x = -(x-y)^3 + f'(x)

∂φ/∂y = y^2(x-y)^3

Comparing the two, we can see that f'(x) = 0, which means that f(x) is a constant. We can choose this constant to be zero without loss of generality.

Therefore, the solution to the differential equation is given by:

-1/3(x-y)^3x + C = 0

where C is an arbitrary constant.

Answer:1.325

Step-by-step explanation:

The vertex of point A' in the dilated triangle A'B'C' is (6, 4.5).

1. Start by calculating the distance between the vertices of the original triangle ABC:

  - Distance between A(4, 3) and B(3, -2):

    Δx = 3 - 4 = -1

    Δy = -2 - 3 = -5

    Distance = √((-\(1)^2\) + (-\(5)^2\)) = √26

  - Distance between B(3, -2) and C(-3, 1):

    Δx = -3 - 3 = -6

    Δy = 1 - (-2) = 3

    Distance = √((-6)² + 3²) = √45 = 3√5

  - Distance between C(-3, 1) and A(4, 3):

    Δx = 4 - (-3) = 7

    Δy = 3 - 1 = 2

    Distance = √(7² + 2²) = √53

2. Apply the scale factor of 1.5 to the distances calculated above:

  - Distance between A' and B' = 1.5 * √26

  - Distance between B' and C' = 1.5 * 3√5

  - Distance between C' and A' = 1.5 * √53

3. Determine the coordinates of A' by using the distance formula and the given coordinates of A(4, 3):

  - A' is located Δx units horizontally and Δy units vertically from A.

  - Δx = 1.5 * (-1) = -1.5

  - Δy = 1.5 * (-5) = -7.5

  - Coordinates of A':

    x-coordinate: 4 + (-1.5) = 2.5

    y-coordinate: 3 + (-7.5) = -4.5

4. Thus, the vertex of point A' in the dilated triangle A'B'C' is (2.5, -4.5).

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The values of functions are

(a) f(0) = -3.                           (b) f(4) = 77.

(c) f(-4) = 45.                         (d) -f(x) = -4x² - 4x + 3.

(e) f(x+1) =  4x² + 12x + 1.       (f) f(-x) =  4x² - 4x - 3.

(g) f(3x) =  36x² + 12x - 3.

(h) f(x+h) =  4x² + 8xh + 4h² + 4x + 4h - 3.

The concept used in this question is evaluating a polynomial function for different values of the input variable. To do this, we substitute the given value into the function in place of the input variable and simplify the resulting expression.

Here we have

The function f(x) = 4x² + 4x-3.

To find the values of functions can be done by replacing x

(a) f(0) = 4(0)² + 4(0) - 3 = 0 + 0 - 3 = -3

(b) f(4) = 4(4)² + 4(4) - 3 = 64 + 16 - 3 = 77

(c) f(-4) = 4(-4)² + 4(-4) - 3 = 64 - 16 - 3 = 45

(d) -f(x) = -[4x² + 4x - 3] = -4x² - 4x + 3.

(e) f(x+1) = 4(x+1)² + 4(x+1) - 3 = 4(x² + 2x + 1) + 4x + 4 - 3 = 4x² + 12x + 1.

(f) f(-x) = 4(-x)² + 4(-x) - 3 = 4x² - 4x - 3.

(g) f(3x) = 4(3x)² + 4(3x) - 3 = 36x² + 12x - 3.

(h) f(x+h) = 4(x+h)² + 4(x+h) - 3 = 4(x² + 2xh + h²) + 4x + 4h - 3

= 4x² + 8xh + 4h² + 4x + 4h - 3.

Hence,

The values of functions are

(a) f(0) = -3.                           (b) f(4) = 77.

(c) f(-4) = 45.                         (d) -f(x) = -4x² - 4x + 3.

(e) f(x+1) =  4x² + 12x + 1.       (f) f(-x) =  4x² - 4x - 3.

(g) f(3x) =  36x² + 12x - 3.

(h) f(x+h) =  4x² + 8xh + 4h² + 4x + 4h - 3.

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The element of A n B is { 7, 8}

A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind.

For example, if the element of P is even numbers from 1 to 20 and element of Q is factor of 6 from 1 to 20 then we can say that set Q is a subset of set P.

The sign 'n' means intersection and this means what is common to two or more set.

If set A = { 1,2,5,7,8}

set B = { 6,7,8,9}

then we can see that 7 and 8 are common to both sides, then

A n B = { 7,8}

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Answer:

replace the x with -3

Step-by-step explanation:

if you ever have f(x) = 'insert equation' and then it says find f('insert number'), you replace what ever variable is after the first 'f' with the number after the second 'f'. hope this helped!

Answer:

-9

Step-by-step explanation:

The city of Brussels will be the warmest. The difference in temperature between Oslo and London is -9°C and the temperature at 6:00 pm in Paris will be -2°C.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

(a)

A city which has the lowest temperature will be warmest since -1°C is the lowest so Brussels will have the warmest city.

(b)

The difference in temperature between Oslo and London will be as,

-12 °C - (-3 °C) = -9 °C.

(c)

At 6.:00 pm the temperature will be -5 °C + 3 °C = -2 °C.

Hence "The city of Brussels will be the warmest. The difference in temperature between Oslo and London is -9°C and the temperature at 6:00 pm in Paris will be -2°C".

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Answer:

A

Step-by-step explanation:

Use the above 3 points, base = 1, height = 1, so area is 1/2

The term is tn=-3n+11

From the question, we have

The sequence is 8, 5, 2, –1, –4, ...

d = 5-8 = -3

t1 = 8

tn = t1+(n-1)d

tn=8+(n-1)(-3)

tn=8-3n+3

tn=-3n+11

Addition:

The phrase "the addition" refers to combining two or more numbers. Adding two numbers is indicated by the plus sign (+), therefore adding three is written as three plus three. Additionally, the number of times the plus symbol (+) is used is up to you. For example, 3 + 3 + 3 + 3. Mathematical addition is a crucial component of the learning curriculum for kids. In primary school, students learn simple addition sums such as one-digit facts,

Math addition sums, and double-digit Math addition sums. One of the most fundamental and interesting

Math concepts for elementary school children is addition sums. Math is a fascinating subject, and children first learn basic mathematical concepts like adding numbers in their early years.

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