The length of a rectangle is 4 less than twice the width. If the perimeter of the rectangle is 130, find the length of the rectangle.

Answer: 2.5 inches

Step-by-step explanation: 3*5/6= 2.5

Answer:

  b)  -3

Step-by-step explanation:

You want the value of 'a' when the quadratic y = –3x² – 15x – 11 is written in the form y = a(x – h)² + k.

The leading coefficient in either form is the coefficient of x². It is the same in both forms: -3.

Answer: x > 5.

Step-by-step explanation:

The information given in the question can be expressed in an equation as:

Let the cost of each book be x

Cost of mug + Cost of books > 24

9 + (3 × x) > 24

9 + 3x > 24

3x > 24 - 9

3x > 15

x > 5.

Therefore, each book cost more than $5.

The complete statements are:

To do this, we evaluate each equation

So, we have

Equation 1

x + c = 0

Make x the subject

x = -c

The above implies that x and c are additive inverses

Hence, as c increases, the value of x decreases

Equation 2

-xc = -c

Divide both sides by -c

So, we have

x = 1

The above implies that c does not have any effect on the value of a

Hence, as c increases, the value of x stay the same

Equation 3

x/c = 1

Make x the subject

x = c

The above implies that x and c have the same value

Hence, as c increases, the value of x increases

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The p-value is 0.01, which means that it is very rare to observe a test statistic that is equal to or more extreme than the one that was actually observed. SO the option a is correct.

In the given question, in a hypothesis test for population proportion, we calculated the p-value is 0.01 for the test statistic, we have to find which statement of the p-value is correct.

The p-value is the probability of obtaining results as extreme as, or more extreme than, the observed results of a statistical hypothesis test, assuming that the null hypothesis is true. A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.

A large p-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis.

If the null hypothesis is correct, the p-value is the likelihood that a test statistic will be equal to or more extreme than the one that was actually observed. Given that the null hypothesis is correct in this situation, the p-value of 0.01 indicates that it is extremely unusual to see a test statistic as dramatic as the one that was actually seen. This shows that the alternative hypothesis is more likely to be correct and that the null hypothesis is probably not true.

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Assuming that the events of each executive receiving a pay raise are independent, we can use the multiplication rule for independent events to find the probability that all four received a raise.

Let's denote the event that an executive receives a raise by "R". Then, the probability that an executive receives a raise is P(R) = 0.78, and the probability that an executive does not receive a raise is P(not R) = 1 - P(R) = 0.22.

The probability that all four executives receive a raise is:

P(R and R and R and R) = P(R) x P(R) x P(R) x P(R)

= 0.78 x 0.78 x 0.78 x 0.78

= 0.37 or 0.0037 (rounded to 4 decimal places)

Therefore, the probability that all four executives received a raise when they asked for one is approximately 0.0037 or 0.37%.

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In order to calculate the time it will take for Andrew to settle the loan, we can use the formula for compound interest. So, it will take Andrew approximately 5.22 years to settle the loan.

The formula is given as A = P(1 + r/n)^(nt), Where: A = the final amount, P = the principal (initial amount borrowed), R = the annual interest rate, N = the number of times the interest is compounded in a year, T = the time in years.

We know that Andrew borrowed R200 000 from a bank at an annual interest rate of 5.25% compounded quarterly and that he will make repayments of R6 000 at the end of every 3 months.

Since the first repayment will be made 3 months from now, we can consider that the initial loan repayment is made at time t = 0. This means that we need to calculate the value of t when the total amount repaid is equal to the initial amount borrowed.

Using the formula for compound interest: A = P(1 + r/n)^(nt), We can calculate the quarterly interest rate:r = (5.25/100)/4 = 0.013125We also know that the quarterly repayment amount is R6 000, so the amount borrowed minus the first repayment is the present value of the loan: P = R200 000 - R6 000 = R194 000

We can now substitute these values into the formula and solve for t: R194 000(1 + 0.013125/4)^(4t) = R200 000(1 + 0.013125/4)^(4t-1) + R6 000(1 + 0.013125/4)^(4t-2) + R6 000(1 + 0.013125/4)^(4t-3) + R6 000(1 + 0.013125/4)^(4t)

Rearranging the terms gives us: R194 000(1 + 0.013125/4)^(4t) - R6 000(1 + 0.013125/4)^(4t-1) - R6 000(1 + 0.013125/4)^(4t-2) - R6 000(1 + 0.013125/4)^(4t-3) - R200 000(1 + 0.013125/4)^(4t) = 0

Using trial and error, we can solve this equation to find that t = 5.22 years (rounded to 2 decimal places). Therefore, it will take Andrew approximately 5.22 years to settle the loan.

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Answer: 48

Step-by-step explanation:

We need to find the least common multiple of 12 and 16.

Finding the prime factorizations of 12 and 16,

\(12=2^{2} \times 3\\\\16=2^{4}\)

Thus, the least common multiple is \(2^{4} \times 3=\boxed{48}\)

Answer: undefined

Step-by-step explanation:

(0+5)/(0+0)

Answer:

2x+5=21

2x+5-5=21-5

2x=16

2x/2=16/2

2x+2=18

2x+2-2=18-2

2x=16

2x/2=16/2

Step-by-step explanation:

To determine if the triangles are congruent we are going to use the SAS theorem of similarity.

SAS stands for "side, angle, side" and means that we have two triangles where:

• the ratio between two sides is the same as the ratio between another two sides

• and we we also know the included angles are equal.

Notice that the ratio between sides QW and SW is the same as the ratio between RW and ZW:

hence the first condition of the theorem is fullfil.

We also notice that angle W is the same for triangle SZW and QRW, therefore the second condition for the theorem is alsso fullfilled.

Therefore we concldue that the triangles are similar.

The equation of the  given model is y = 13.16x + 251.05

First choose two point

The first point = (44, 830)

The second point = (63, 1080)

The slope of the line m = \(\frac{y_2-y_1}{x_2-x_1}\)

Substitute the values in the equation

The  slope of the line = (1080-830) / (63 - 44)

= 250 / 19

Consider the point (44, 830)

The point slope form is

\(y-y_1=m(x-x_1)\)

Where m is the slope of the line

y - 830 = 250/19(x - 44)

y - 830 = (250/19)x - 11000/19

y = (250/19)x - 11000/19 + 830

y = 250/19 x + 4770/19

y = 13.16x + 251.05

Hence, the equation of the  given model is y = 13.16x + 251.05

The complete question is

The table shows the fat content and calories for the burgers at a fast food chain.

Fat (g) 25 44 63 32 37 20 11 52

Calories 590 830 1080 680 750 420 310 820

Write the best fit line that models the impact of fat content on calories. Explain how you got your answer.

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Answer:

D. 1500 π

Step-by-step explanation:

V=πr²h

r=10

h = 15

10²=100

100 x 15 = 1500

1500π

Answer:

option D is a correct answer...

Answer:

119 is the value of x when y = 7

Step-by-step explanation:

Since y varies inversely with x, we can use the following equation to model this:

y = k/x, where

Step 1:  Find k by plugging in values:

Before we can find the value of x when y = k, we'll first need to find k, the constant of proportionality.  We can find k by plugging in 49 for y and 17 for x:

Plugging in the values in the inverse variation equation gives us:

49 = k/17

Solve for k by multiplying both sides by 17:

(49 = k / 17) * 17

833 = k

Thus, the constant of proportionality (k) is 833.

Step 2:  Find x when y = k by plugging in 7 for y and 833 for k in the inverse variation equation:

Plugging in the values in the inverse variation gives us:

7 = 833/x

Multiplying both sides by x gives us:

(7 = 833/x) * x

7x = 833

Dividing both sides by 7 gives us:

(7x = 833) / 7

x = 119

Thus, 119 is the value of x when y = 7.

Answer:

\copy n paste your answer and it should be there

Step-by-step explanation:

The speed of the moving body that is being referred to here is 80 kilometer per hour.

The given problem is a straightforward one based on the idea of the universal law of motion. According to the universal law of motion, any uniformly traveling body's distance traveled is determined by the product of its speed and the time elapsed. Distance is calculated as speed * time. Therefore the body is going at a speed of 80 kilometers per hour, according to the same relation as above, assuming that it is moving at a constant speed.

                                \(Distance = speed * time\)

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Answer: x= 6

Step-by-step explanation:

Since the shape is a parallelogram, the angles will either be equal to each other or add up to 180.  

You can see they do not look the same so they add up to equal 180

12x + 3 +105 = 180

12x + 108 = 180

12x = 72

x = 6

Answer:

13

Step-by-step explanation:

Use the distance formula and plug in both points

Answer:

its either 11 or 13 im not sure

Step-by-step explanation:

There are many different types of trees that can be found in wood or forested areas, and the specific types of trees will depend on the region and climate. However, some common types of trees that can be found in woods include: oak trees, maple trees, pine trees, birch trees, cedar trees, cherry trees, and walnut trees.

These are just a few examples of the types of trees that can be found in wood or forested areas, and there are many more depending on the region and climate.

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\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 30000\\ P=\textit{original amount deposited}\dotfill & \$20000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ t=years \end{cases} \\\\\\ 30000 = 20000[1+(0.09)(t)] \implies \cfrac{30000}{20000}=1+0.09t\implies \cfrac{3}{2}=1+0.09t \\\\\\ \cfrac{3}{2}-1=0.09t\implies \cfrac{1}{2}=0.09t\implies \cfrac{1}{2(0.09)}=t\implies 5.6\approx t\)

Answer:

c in a proportion you need it to be written so that the proportions are above each other like 2.5 cups over 5 servings

Answer:

x=14

Step-by-step explanation:

3x-15=27 (add 15 to both sides)

3x=42 (divide both sides by three)

x=14

The required number is -4.

A linear equation only has one or two variables. No variables in a linear equation is raised to power greater than 1 or used as denominator of a fraction.

Now it is given that, 15 is subtracted from three times a certain number,

the result is 27.

Now let x be the number.

Three times the number = 3x

Therefore, 15 is subtracted from three times a certain number = 15 - 3x

Therefore, the equation for 15 is subtracted from three times a certain number, the result is 27 is,

15 - 3x = 27

Subtracting 15 both the side we get,

15 - 3x - 15 = 27 - 15

⇒ -3x = 12

or, x = -12/3

⇒ x = -4

which is the required number.

Thus, the required number is -4.

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The coordinates of the point at 3/4 of the distance from A to B from A is (-3.5, 1.25)

The coordinates of point A = (-5, -4),

The coordinates of the point B = (-3, 3)

Let the point at the distance 3/4 from A to B = P

The coordinates of point 3/4 from A to B = P

At the x-coordinate, the distance from B to A is =  -3-(-5) = 2 units.

At the y-coordinate, the distance from B to A is = 3-(-4) = 7 units.

Hence, the coordinates of P = (-5 + (3/4×(x-coordinate), -4 + 3/4×(y-coordinate)

                                            P = (-5 + (3/4×(2), -4 + 3/4×(7))

                                            P = (-3.5, 1.25)

Hence, the coordinates of the point at 3/4 of the distance from A to B from A is (-3.5, 1.25).

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The complete question is -

What are the coordinates of the point 3/4 of the way from A to B?

Answer:

i like it is 1/2 can you make smaller hope this help

Step-by-step explanation:

The side EC is 6 units.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given that Point B lies on line AC, as shown on the coordinate grid below.

AD = 2 units,

DB = 3 units, and

BE = 4 units

We need to find EC.

As we observe the triangle ADB is similar to BEC.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

AD is corresponding side of BE and DB is corresponding side of EC.

As the sides are proportional

2/3=4/x

2x=12

x=6

Hence, the side EC is 6 units.

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Answer:

225 pages in 75 days. hope this helped!

Step-by-step explanation:

Answer:

75*3 or 225

Step-by-step explanation:

3 pages per day the 75 days it's 75*3 which is 225

Hope this helps plz mark brainliest if correct :D

Answer:

x = 5/2

Step-by-step explanation:

Answer:

x=2.5

Step-by-step explanation:

15x + 9x = 33 + 27

24x = 60

x = 60 ÷ 24

x = 5/2 = 2.5

The difference quotient evaluated in x = 2 gives:

[ f(2 + h) - f(2)]/h = h + 9

So the last option is the correct one.

Here we know the function:

f(x) = x^2 + 5x + 6

And we want to find the difference quotient:

[ f(2 + h) - f(2)]/h

Let's evaluate the function:

f(2 + h) = (2 + h)^2 + 5*(2 + h) + 6

            = 2^2 + h^2 + 4h + 10 + 5h + 6

            = h^2 + 9h + 20

f(2) = 2^2 + 5*2 + 6

f(2) = 4 + 10 +  6 = 20

Then we have:

[ f(2 + h) - f(2)]/h

[h^2 + 9h + 20 - 20]/h

[h^2 + 9h ]/h

Taking the quotient we get:

[h^2 + 9h ]/h = h + 9

So the correct option is the last one.

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Answer:

#1

Well lets solve the polynomial first.

(4p +3) ^2

That is basically

(4p + 3) (4p + 3)

And we’re trying to find the error in the “equal” solution.

16p^2 + 8p + 9.

So let’s solve the polynomial first

Following F.O.I.L

F- First

O- Outter

I- Inner

L- Last

So doing the equation in order.

4p * 4p = 16p^2

4p * 3 = 12p

3 * 4p = 12p

3* 3 = 9

Added it all up.

16p^2 + 12p + 12p + 9

Simplify.

16p^2 +24p +9
We can see that in this case the 8p is wrong.

So we replace 8p with 24p

In this case the last option.

Factoring #2

So we’re factoring

9x^2 -6x - 3

So how are we gonna do this.

So I’m just gonna go over the simple method.

The standard form of a quadratic is

Ax^2 + bx + c = 0

We don’t have to worry about the equal 0 part here for now.

ax^2 + bx + c

A being the number next to x^2

B is the number being next to x

C is the number that is next to nothing, jsut a plain whole number (sometimes whole number)

So let’s plug it in.

(It’s already plugged in so we can solve)

9x^2 - 6x - 3

Multiply a and c in ths case being, 9 and -3.

You’d get -27

We need two numbers that multiply to -27 and add up to -6

From here it’s guessing and checking.

Here’s my process.

trial 1

Since the sum is negative, it has to be negative + negative or positive + negative greater then the positive. Or vice versa but positive is less then negative.

But the product has to be -27,negative * negtaive is positive, so it has to be positive * negative and positive + negative.

I look at -27 and think of two numbers that would give the lowest.

-9 * 3

-9 * 3 = -27

-9 + 3 = -6

It looks like I got it already on the first try.

The numbers are -9 and 3

end of trial 1

So now I know that the numbers are -9 and 3.

Using that information I just plug it into the quadratic but replace it with b.

9x^2 -9x + 3x - 3

Now you can simplify this

In the end you’d get

3 (3x+1)(x-1)

You’d have the third option open to you

Figure out the second one using these strategies

Answer:

  $5

Step-by-step explanation:

The graph shows the green cab costs $5 even if you don't go anywhere (miles = 0).

The cost to get into a green cab is $5.

Answer:

15

Step-by-step explanation:

because it's the where the green lines cross the graph.