What is an equation of the line that passes through the points (-3, -2)(−3,−2) and (3, 6)(3,6)? Put your answer in fully reduced form.

Answer:

21) 7(2x+3y)

22) 16(2x+3y)

The simplified expression is 2y² - 9.

To subtract the binomials (-3y^2 - 8) - (-5y^2 + 1), we need to distribute the negative sign to the terms inside the second set of parentheses:

(-3y^2 - 8) - (-5y^2 + 1) = -3y^2 - 8 + 5y^2 - 1

Next, we combine like terms by adding or subtracting the coefficients of the same degree:

-3y^2 + 5y^2 - 8 - 1 = (5y^2 - 3y^2) + (-8 - 1) = 2y^2 - 9

Therefore, the simplified expression is 2y² - 9.

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Answer:

2 pi

Step-by-step explanation:

The radius is 2

The area of a circle is

A = pi r^2

We have 1/2 of a circle so

1/2 A = 1/2 pi r^2

         =1/2 pi ( 2)^2

         =1/2 pi *4

      = 2 pi

For diameter 12 inches the would take approximately 904.78 cubic inches of air to inflate the soccer ball.

Diameter is a straight line segment that passes thrοugh the center οf a circle οr sphere, cοnnecting twο pοints οn the circumference. It is the lοngest chοrd οf the circle οr sphere and its length is twice the radius.

Tο find οut hοw much air is needed tο inflate the sοccer ball, we need tο first calculate the vοlume οf the ball. The fοrmula fοr the vοlume οf a sphere is:

V = (4/3)π\(r^3\)

where r is the radius of the sphere.

Since the diameter of the soccer ball is 12 inches, the radius is half of that, or 6 inches. We can substitute this value into the formula and simplify:

V = (4/3)π(\(6^3\)) = 904.78 cubic inches

This is the volume of the fully inflated soccer ball. If the ball is currently deflated, we need to add enough air to bring its volume up to 904.78 cubic inches.

The amount of air needed will depend on the pressure of the air being used to inflate the ball. If we assume that the pressure is constant, we can use the ideal gas law to calculate the volume of air needed:

PV = nRT

where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature.

Since we are assuming that the pressure and temperature are constant, we can simplify the formula to:

V = (n/R)P

where n/R is a constant for a given amount of gas, and P is the pressure.

Without knowing the pressure of the air being used, we cannot calculate the exact amount of air needed. However, we can assume a standard pressure of 14.7 pounds per square inch (psi) and use this to calculate the volume of air needed.

Assuming a pressure of 14.7 psi, we can calculate the volume of air needed as follows:

V = (n/R)P = (1/14.7)(14.7) = 1 cubic inch

Therefore, it would take approximately 904.78 cubic inches of air to inflate the soccer ball. However, the exact amount of air needed will depend on the pressure of the air being used.

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1. the mechanical advantage of the rake is 0.5. 2. the efficiency of the blade adjuster is approximately 92.73%.

1. The mechanical advantage of a simple machine is determined by the ratio of the output force to the input force. In this case, the woman applies an input force of 32 N to the rake, and the rake exerts an output force of 16 N.

The mechanical advantage (MA) can be calculated as MA = Output Force / Input Force.

Using the given values, we can substitute them into the formula:

MA = 16 N / 32 N = 0.5.

Therefore, the mechanical advantage of the rake is 0.5.

Explanation:

The mechanical advantage represents the amplification of force achieved by using a machine. In this case, the mechanical advantage of 0.5 means that the rake reduces the input force by half to produce the output force. It indicates that for every 1 unit of input force applied by the woman, the rake generates 0.5 units of output force.

2. Efficiency is a measure of how effectively a machine converts input work to output work. It is calculated as the ratio of output work to input work, expressed as a percentage.

The efficiency (η) can be calculated using the formula: Efficiency = (Output Work / Input Work) * 100%.

Given that the input work is 55 J and the output work is 51 J, we can substitute these values into the formula:

Efficiency = (51 J / 55 J) * 100% ≈ 92.73%.

Therefore, the efficiency of the blade adjuster is approximately 92.73%.

Explanation:

Efficiency quantifies the effectiveness of a machine in converting the input energy into useful output energy. In this case, the blade adjuster converts 51 J of input work into 51 J of output work. The efficiency of approximately 92.73% indicates that the blade adjuster is relatively efficient, as a high percentage of the input work is effectively converted into useful output work.

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Systematic risk is the type of risk for which you can be rewarded with a higher expected return.

So, the correct answer is A

Systematic risk, also known as market risk or non-diversifiable risk, affects the entire market and cannot be eliminated through diversification.

Investors are compensated for taking on systematic risk through higher expected returns as they bear the fluctuations and uncertainties associated with the overall market.

In contrast, firm-specific, diversifiable, and idiosyncratic risks are specific to individual companies or industries and can be mitigated through diversification in an investment portfolio, so investors don't get rewarded with higher expected returns for these types of risks

Hence, the answer of the question is A.

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\( \huge \purple{\tt{Answer:}} \)

\( \sf{sin~X} = \sf{\dfrac{opposite~side}{hypotenuse}} = \sf {\dfrac{18}{30}} = \sf {\dfrac{3}{5}} \)

quotient = the answer to a division problem

To divide by a fraction, multiply by the reciprocal of the fraction

reciprocal of a fraction = the numerator and denominator are reversed

First, convert "three and two thirds" into an improper fraction:

\(3\dfrac{2}{3}\)

⇒ Multiply the whole number by the denominator and add the numerator:

\(\dfrac{11}{3}\)

Now, we want to divide this number by three fifths:

\(\dfrac{11}{3}\div\dfrac{3}{5}\)

⇒ Dividing by a fraction is the same as multiplying by its reciprocal:

\(= \dfrac{11}{3}\times\dfrac{5}{3}\\\\=\dfrac{55}{9}\)

\(\dfrac{55}{9}\)

theannswer wold be 100 .33 .87

Based on the given information that t(26) = 3.13 and p < 0.05, the decision would be to reject the null hypothesis.

In hypothesis testing, the null hypothesis is typically a statement of no effect or no difference between groups, and rejecting the null hypothesis suggests that there is evidence of a significant effect or difference.

Since the p-value is less than 0.05, it means that the probability of obtaining the observed results by chance alone, assuming the null hypothesis is true, is less than 5%.

Therefore, the results are considered statistically significant at the 0.05 level.

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Step-by-step explanation:

Let's call the number of girls in the school "g". We know that there are 1000 boys, so the total number of students is 1000 + g.

The problem states that 48% of the total number of students were successful in the examination. Therefore, we can write an equation:

0.48(1000 + g) = 0.5(1000) + 0.4(g)

Simplifying and solving for g:

480 + 0.48g = 500 + 0.4g

0.08g = 20

g = 250

Therefore, the number of girls in the school is 250.

Answer:

250

Step-by-step explanation:

Hi dear,

Firstly, let the girls be G

1000 + G = Total number of students

50% of boy = 1000 × 0.5 = 500

40% of girls = G × 0.4 = 0.4G

0.48 • (1000 + G) = 480 + 0.48G

480 + 0.48G = 500 + 0.4G

Collect Like Terms

0.48G - 0.4G = 500 - 480

0.08G = 20

G = 20/0.08

G = 250

Therefore, the girls are 250( two hundred and fifty)in the school

Using trigonometric function the value of x is 51.3°.

What is trigonometric function?

The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.

Here Let us take the given right triangle as ABC.

∠A = x , ∠B = 90° and AB = 25 , AC= 40

Now using Cosine ratio then

Cos  A = \(\frac{adjacent}{hypotenuse}\)

=> cos x = \(\frac{25}{40}\)

=> cos x = \(\frac{5}{8}\)

=> x = \(cos^{-1}\frac{5}{8}\)

=> x = 51.3°

Hence the value of x is 51.3°.

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The total number of boxes required to cover the kitchen floor is 14.

The dimensions of the kitchen floor are 14' × 24'

⇒Length of the kitchen floor = 14 feet

⇒Width of the kitchen floor= 24 feet

The area of the kitchen floor= Length × Width

⇒ Area = 14 × 24

⇒ Area = 336 sq. ft.

Since, 4 boxes of flooring cover 100 sq. ft.

∴1 box will cover = 100/4 sq. ft.

⇒25 sq. ft.

Now, Number of boxes required to cover the floor of the kitchen will be,

⇒ Area of the floor / Area covered by 1 box of flooring

⇒336/25

⇒ 13.44

∴ The total number of boxes required to cover the kitchen floor is 14 (rounded up from 13.44).

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Answer:

-2

Step-by-step explanation:

Let's denote the lengths of the shorter and longer diagonals of the parallelogram as x and (x + 2) meters, respectively.

We know that the sum of the lengths of the diagonals is 18 m:

x + (x + 2) = 18

Simplifying the equation:

2x + 2 = 18

2x = 16

x = 8

So the shorter diagonal has a length of 8 meters, and the longer diagonal has a length of 10 meters.

The area of the parallelogram is given as 20 square meters:

Area = base * height

20 = 8 * height

height = 2.5 meters

Now, let's consider the changes in the diagonals. The shorter diagonal is increased by 10 cm, which is equivalent to 0.1 meters, and the longer diagonal is decreased by 15 cm, which is equivalent to 0.15 meters.

The new lengths of the diagonals are:

Shorter diagonal: 8 + 0.1 = 8.1 meters

Longer diagonal: 10 - 0.15 = 9.85 meters

The new area of the parallelogram can be calculated using the formula:

New Area = new base * new height

Let's denote the change in the acute angle between the diagonals as Δθ.

The change in area can be approximated using differentials:

ΔArea ≈ (∂A/∂x) * Δx + (∂A/∂θ) * Δθ

To ensure that the approximate change in area does not exceed 4 square meters, we can set up the inequality:

|ΔArea| ≤ 4

Substituting the values and differentials:

| (∂A/∂x) * Δx + (∂A/∂θ) * Δθ | ≤ 4

Solving for Δθ:

Δθ ≤ (4 - (∂A/∂x) * Δx) / (∂A/∂θ)

To calculate Δθ, we need to determine (∂A/∂x) and (∂A/∂θ).

The partial derivative of the area with respect to x (∂A/∂x) can be calculated as follows:

∂A/∂x = height = 2.5 meters

The partial derivative of the area with respect to θ (∂A/∂θ) can be calculated using the formula:

∂A/∂θ = (base * ∂height/∂θ) + (height * ∂base/∂θ)

Since the base and height are fixed, their derivatives with respect to θ are zero:

∂A/∂θ = (0 * ∂height/∂θ) + (height * 0) = 0

Now we can substitute the values into the formula for Δθ:

Δθ ≤ (4 - (∂A/∂x) * Δx) / (∂A/∂θ)

Δθ ≤ (4 - 2.5 * 0.1) / 0

Since (∂A/∂θ) is zero, the denominator is zero, and we have an undefined value for Δθ. This indicates that the change in the acute angle Δθ cannot be determined with the given information.

Therefore, we cannot approximate the increase or decrease in the acute angle between the diagonals based on the given data.

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Answer:

B. 7 1/2

Step-by-step explanation:

8x=12

x = 1.5

2y+10=22

2y = 12

y = 6

1.5 + 6 = 7.5

So, the sum of the solutions of the two equations is

B. 7 1/2

Answer:

Step-by-step explanation:

firstly we solve 8x=12 we divide both sides by 8 since 8 is the coefficient of x so we are trying to find x that is 8x divided by 8 which is x =12 divided by 8 which is 1.5 which means x=1.5 then we solve the second one 2y+10=22 we collect like terms which means 2y=22-10 as you should know the 10 changes to negative when crossed over to the other side so then 2y=12 is the answer then we divide both sides by the coefficient of y which is 2 so 2y divided by 2 =y 12 divided by 2 = 6 so y=6 then we add both of them together x=1.5+(y=6) so add 1.5 and 6 together answer is 7.5 or 7  1/2

The 99% confidence interval for the proportion of executives who want to strengthen innovation is: CI = (0.199, 0.261)

What is confidence interval?

A confidence interval is a statistical measure that provides a range of values within which the true population parameter, such as the mean or proportion, is estimated to lie with a specified level of confidence.

To find the confidence interval for a proportion, we need to use the formula:

CI = p ± z\(\sqrt{(pq/n)\)

where:

CI: confidence interval

p: sample proportion

q: 1 - p

z: z-score from the standard normal distribution for the desired confidence level (99% in this case)

n: sample size

From the problem statement, we know that p = 0.23, n = 1,379, and we want a 99% confidence interval. To find the z-score, we can use a standard normal distribution table or calculator, which gives us a value of 2.576.

Substituting the values into the formula, we get:

CI = 0.23 ± 2.576\(\sqrt{(0.230.77/1379)\)

CI = 0.23 ± 0.031

Therefore, the 99% confidence interval for the proportion of executives who want to strengthen innovation is:

CI = (0.199, 0.261)

This means we can be 99% confident that the true proportion of executives who want to strengthen innovation falls within this range.

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Answer:

True.

Step-by-step explanation:

We assume that the plane is flying at a constant height above the ground.

The angle of elevation is the angle made between the plane, you and the point on  the ground directly below the plane. As the plane approaches you the distance between you and the point on the ground decreases and therefore the angle of elevation increases.

Answer:

\d

Step-by-step explanation:

:)

Answer

55$

Step-by-step explanation:

The acceleration of the truck when it has a mass of 5000 kg and the truck driver presses on the brakes is 1.2m/s².

The rate of change of an object's velocity with respect to time is defined as acceleration. Vector quantities are accelerations.

The orientation of an object's acceleration is determined by the orientation of the net force acting on that object's acceleration, which is the rate at which velocity changes over time in terms of both speed and direction. A point or object moving in a straight line is accelerated if it accelerates or decelerates.

Acceleration will be:

= Force / mass

= 6000 / 5000

= 1.2 m/s²

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a) The cost of the stereo system is $4,760.

b) The total amount of interest paid is $1,760.

To find the cost of the stereo system, we need to calculate the sum of the down payment and the total of monthly payments over 4 years. The down payment is $400, and the monthly payment is $90 for 48 months (4 years). Thus, the total cost of the stereo system is $400 + ($90 × 48) = $4,760.

To calculate the total amount of interest paid, we need to subtract the initial principal amount (down payment) from the total cost of the stereo system. The initial principal amount is $400, and the total cost is $4,760. Therefore, the total interest paid is $4,760 - $400 = $1,760.

In summary, the cost of the stereo system is $4,760, and the total amount of interest paid is $1,760.

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The frequency shown in the given sinusoidal graph is:

f = 1/T (s⁻¹).

Frequency means the rate at which something occurs or is repeated over a particular period of time or in a given sample.

A sinusoidal function is a periodic function because the basic shape repeats indefinitely in both the positive and negative directions. The frequency of a sine wave is defined as the number of cycles it completes in a given interval and is the reciprocal of the period.

In a mathematical language, this is written as:

f = 1/T

Where,

f = frequency,

T = Period

To get the period, just subtract the x-coordinates of two consecutive peaks, so:

T = п - 0

T = п (s)

Therefore, the frequency is:

f = 1/T (s⁻¹).

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Answer:

x = -3/2

Step-by-step explanation:

7⁰ = 1 (anything to the power of 0 equals 1)

7²ˣ ⁺ ³ = 7⁰

Since the bases are the same, you 'forget' about the bases and then you solve for x.

2x + 3 = 0

2x = -3

x = -3/2

The interval of convergence is (-1, 3) and the radius of convergence is R = 1.

To determine the interval of convergence and radius of convergence for the given series \((-1)^n=1 * (x-2)^n,\) we need to use the ratio test.
The ratio test states that if we take the limit of the absolute value of the ratio of the n+1th term and the nth term as n approaches infinity, and the limit is less than 1, then the series converges absolutely. If the limit is greater than 1, the series diverges, and if the limit is equal to 1, then the test is inconclusive.
Applying the ratio test to the given series, we have:
\(|((-1)^n+1 * (x-2)^(n+1))/((-1)^n * (x-2)^n)|= |(-1)*(x-2)|= |x-2|\)
Taking the limit as n approaches infinity, we have:
lim (|x-2|) = |x-2|
Since the limit is less than 1 for |x-2| < 1, the series converges absolutely.
To find the radius of convergence, we need to find the value of x for which the limit is exactly 1.
lim (|x-2|) = 1
|x-2| = 1
x - 2 = 1 or x - 2 = -1
x = 3 or x = 1
Therefore, the interval of convergence is (-1, 3) and the radius of convergence is R = 1.

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Using the concept of linear equation in one variable, it is concluded that the total number of students who will go on the trip are 40.

An equation that contains only one variable and has its degree one is called a linear equation in one variable. The general form of linear equation in one variable is ax + b = 0, where a and b are real numbers and a ≠ 0.

Given that food and lodging charge per student = $ 60

Charge per student for bus = $ 40

And the amount paid for the cleaning fee for the bus = $ 30

Let the total number of students who are going on the trip = x

Now, the Total charge for food and lodging = $60x

The total charge for bus fare = $ 40x

Given that total cost paid = $ 4030

Hence, $60x + $40x + $30 = $4030

$100X = $4030 - $30

$100X = $4000

x = 40

Hence, the total number of students who will go on a trip is 40.

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Researchers use a finding's Effect size to measure magnitude and reliability.

a difference in significance does not always make a significant difference.

One reason is the arbitrary nature of the p<0.05 cutoff. We could get two very similar results, with p=0.04 and p=0.06, and mistakenly say they’re clearly different from each other simply because they fall on opposite sides of the cutoff.

The second reason is that p values are not measures of effect size, so similar p values do not always mean similar effects. Two results with identical statistical significance can nonetheless contradict each other.

Effect size refers to the measure of the magnitude of the experiment's effect. In other words, effect size measures how important is the relationship between two variables. The larger the effect size, the stronger this relationship is. Moreover, when the effect size is large, you are more likely to be dealing with a relationship that has practical significance.

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Nolan has to 18 hours work to have enough for the computer which costs 1,476.

We have been given that Nolan would like to buy a computer that costs 1,476. Working as a consultant, he bills his clients $82 per hour.

To determine the minimum number of hours he has to work to have enough for the computer.

The minimum number of hours he has to work is the ratio of the cost of a computer to his earnings per hour

The minimum number of hours = cost of computer /  his earnings per hour

The minimum number of hours = 1,476 / $82

Apply the division operation,

The minimum number of hours = 18

Therefore, Nolan has to 18 hours work to have enough for the computer which costs 1,476.

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