Use factoring and the zero-product property to solve the following problems.

Answer:

x + 3 - 2/ (x + 2).

Step-by-step explanation:

The length of the other side = area / length of the known side

= (x^2 + 5x + 4) / (x + 2)

Do the long division:

x + 2 ( x^2 + 5x + 4 ( x + 3 < - quotient

          x^2 + 2x

         ------------

                    3x + 4

                     3x + 6

                    ----------

                           - 2 <--- remainder.

The  answer is   x + 3 - 2/ (x + 2).

Answer:

  1. Is 8/15

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let g represent the green fee each person pays. Then the cost of the two club rentals and four green fees is ...

  2·6 + 4g = 76 . . . . . . the equation for total cost

  4g = 64 . . . . . . . . . . . subtract 12

  g = 16 . . . . . . . . . . . . divide by 4

The cost of the green fees was $16 per person.

Answer:

Final answer is approx x=4.26.

Step-by-step explanation:

Given equation is [tex]1.8^{-x+7} = 5[/tex]

Now we need to solve equation [tex]1.8^{-x+7} = 5[/tex] and round to the nearest hundredth.

[tex]1.8^{-x+7} = 5[/tex]

[tex]\log(1.8^{-x+7}) = \log(5)[/tex]

[tex](-x+7)\log(1.8) = \log(5)[/tex]

[tex](-x+7) = \frac{\log(5)}{\log(1.8)}[/tex]

[tex](-x+7) = \frac{0.698970004336}{0.255272505103}[/tex]

[tex]-x+7 = 2.73813274192[/tex]

[tex]-x = 2.73813274192-7[/tex]

[tex]-x =−4.26186725808[/tex]

[tex]x =4.26186725808[/tex]

Round to the nearest hundredth.

Hence final answer is approx x=4.26.

Answer:

  a.

Step-by-step explanation:

A catenary looks a lot like a parabola. Only graph "a" has that appearance.

___

A graphing calculator can help you choose, or you can recognize the nature of the terms of the sum.

e^x looks like graph D; e^-x looks like graph B. Their sum will always be positive, so cannot create graph C. At x=0, the average of the two graphs B and D will be 1, corresponding to the minimum of graph A.

Use the distance formula to find the length of each side.

AB = √((5+1)^2 + (-1-1)^2) = √(6^2+-2^2) = √40 = 2√10 = 6.3

BC = √((0+1)^2 +(-3-1)^2) = √(1^2 + -4^2) = √17 = 4.1

AC = √((0-5)^2 +(-3+1)^2) = √(5^2 + -2^2) = √29 = 5.4

Perimeter = 6.3 + 4.1 + 5.4 = 15.8

6.3 + 4.1 + 5.4 = 15.8 is your answer.

Answer:

55 people is the minimum sample size

Step-by-step explanation:

The formula for minimum sample size is  for µ is:  n = [(z*σ)/E]²

We are given z = 1.95996, σ = 15 and E = 4

E is 4 because they said they want the interval no wider than 8, so that means 4 lower and 4 higher than the mean, so E is 4

Calculate:  n = [(1.95996*15)/4]² = 54.02, we always round up when talking about people.  Since 54.02 is the score, we need more than 54 people, since we can't have parts of a person, we need to round up to 55

To estimate the mean IQ score of all people who have successfully passed a college statistics course with a 95% confidence interval and a total width not exceeding 8 points, we require a sample size of 137, using the given standard deviation.

In mathematics, specifically in statistics, the required sample size to estimate a population mean with a given level of confidence and margin of error can be obtained by using many formulas, but when we have an estimate of the population standard deviation (σ), the formula to calculate the sample size (n) is: n = ((Z × σ) / E)^2, where E is the desired margin of error, Z is the z-score related to the desired level of confidence.

Here, we are given the standard deviation (σ) as 15 (even though we believe the true standard deviation for the subpopulation in question is probably less), the desired margin of error (E) as 4 (since we want the total width of the confidence interval to be 8, the margin of error will be half of this), and the z-score (Z) for a 95% confidence interval is approximately 1.96 (as given in the question).

Plugging these values into the formula, we get: n = ((1.96 × 15) / 4)^2 which is approximately 136.09. As we can't have a fraction of a person, we round this up to the nearest whole number, so the required sample size is 137.

https://brainly.com/question/31538429

#SPJ3

Answer:

Find a line which also has 3/4 as the slope or 3x - 4y in standard form.

Step-by-step explanation:

If the line is 3x - 4y = 1 then the line which is parallel will have the same coefficients of x and y. Parallel lines never cross and to ensure this have the same slope. The slope is a ratio which can be solved for in an equation using the coefficients of x and y. Here the slope is:

3x - 4y = 1

-4y = -3x + 1

y = 3/4x - 1/4.

Find a line which also has 3/4 as the slope or 3x - 4y in standard form.

Answer: y= 3/4x +5

Step-by-step explanation: just did it

Answer:

we cant see what the lines look like soooo

Step-by-step explanation:

Answer:

parabola

Step-by-step explanation:

That would be a parabola.  The "single point" is the "focus" of the parabola, and the "given line" is the "directrix."

Answer:

Step-by-step explanation:

total students = 200

95% of students arrived on time

5% of students were late.

95% x 200 = 190 students (on time)

 5% x 200 = 10 students (late)

               -------------------------------------

                      200 students

Answer:

[tex](2,3)[/tex]

Step-by-step explanation:

The first equation is  [tex]x+y=5[/tex]

The second equation is [tex]y=\frac{1}{2}x+2[/tex]

When we graph these two equations, they will meet at a point which represent the solution of the two equations.

We can solve the two equations simultaneously to determine their point of intersection.

Let us substitute the second equation into the first equation to get;

[tex]x+\frac{1}{2}x+2=5[/tex]

Multiply through by 2 to get;

[tex]2x+x+4=10[/tex]

Group similar terms to obtain;

[tex]2x+x=10-4[/tex]

Simplify;

[tex]3x=6[/tex]

Divide both sides by 3;

[tex]\Rightarrow x=2[/tex]

Put [tex]x=2[/tex] into the second equation;

[tex]y=\frac{1}{2}(2)+2[/tex]

[tex]\Rightarrow y=1+2[/tex]

[tex]\Rightarrow y=3[/tex]

Therefore the graphs of the two functions intersect at (2,3)

See graph in attachment.

each bag weighs 0.625 ounces

The cost of each bag of popcorn will be 0.625 ounces.

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

Division = divide any two numbers or variables called division.

As per the given,

Weight of empty bag  = 5 ounce

Weight of full bag = 35 ounce

Weight of popcorns bag = 3 5 - 5 = 30 ounce

Number of bags = 48

Per bag weight = 30/48 = 0.625 ounce

Hence "The cost of each bag of popcorn will be 0.625 ounces".

To learn more about the arithmetic operators,

brainly.com/question/25834626

#SPJ5

Fortnite Yee yee boi get them toes

The approximate effective interest rate of the loan is 330%.

The cost of borrowing money or the fee you charge to lend it is known as interest. The most common way to represent interest is as a yearly percentage of the loan amount. The interest rate on the loan is known as this percentage.

Given:

The amount owed increases by $75 in two weeks.

n= 52/2 = 26 periods

If the loan applied with same interest rate, then the total amount owed

=[tex](1375/1300)^{26}[/tex]  x $1300

Now, If we subtract the original principle $1300, then the compounding interest as a percentage of that principle is

= [[tex](1375/1300)^{26}[/tex]  x $1300  - $1300] / $1300

= 5,493.8 - 1300 / 1300

= 330%

Learn more about interest here:

https://brainly.com/question/3610860

#SPJ2

Final answer:

To find the effective interest rate of Josh's payday loan, you divide the interest ($75) by the principal ($1300) and multiply by 100 to get a two-week rate. Then you annualize it by multiplying by the number of two-week periods in a year (26), resulting in an approximate annual interest rate of 150%. The options provided in the question appear to be incorrect considering this calculation.

Explanation:

To calculate the effective interest rate of Josh's payday loan, we first need to determine the interest he's paying compared to the principal. The fee associated with the loan can be considered the interest, which in this case is $75. Since the loan is for $1300, we can calculate the interest rate for the two-week period by dividing the interest by the principal and then multiplying by 100 to get a percentage:

Interest Rate for 2 Weeks = ($75 ÷ $1300) × 100

Then, to annualize this rate, since there are 26 two-week periods in a year, we multiply the result by 26:

Annualized Interest Rate = Interest Rate for 2 Weeks × 26

Performing the calculations gives us:

Interest Rate for 2 Weeks = (75 ÷ 1300) × 100 ≈ 5.769%

Annualized Interest Rate = 5.769% × 26 ≈ 150%

However, the options given in the question do not match this calculation. It seems there might be a mistake with the options provided. The effective interest rate calculated here is approximately 150%, which is much lower than the options given. It is crucial to double-check the information or the methodology if this seems inconsistent with expected results. Note that payday loans typically have extremely high-interest rates, so a very high annual percentage rate (APR) is possible, but it may be calculated in a different manner.

Answer:

Step-by-step explanation:

We know that the sum of the measures of angles on one side of the parallelogram is 180°.

We have the equation:

(6x - 12) + (132 - x) = 180

6x - 12 + 132 - x = 180               combine like terms

(6x - x) + (-12 + 132) = 180

5x + 120 = 180              subtract 120 from both sides

5x = 60          divide both sides by 5

x = 12

Opposite angles in the parallelogram are congruent.

Therefore:

6y + 18 = 6x - 12

Put the value of x to the equation and solve it for y:

6y + 18 = 6(12) - 12

6y + 18 = 72 - 12

6y + 18 = 60           subtract 18 from both sides

6y = 42          divide both sides by 6

y = 7

Answer:

Option b

Step-by-step explanation:

According to the property of sum of logarithms we know that

[tex]log(ab) = log(a) + log(b)[/tex].

In this case we have the equation:

[tex]log(2x) = 3[/tex]

Using the property of sum of logarithms:

[tex]log(2) + log(x) = 3[/tex]

[tex]log(x) = 3 - log(2)[/tex]

We also know that:

[tex]10 ^{(logx)} = x[/tex]     -------- Inverse logarithm

So:

[tex]x = 10 ^{3-log(2)}[/tex]

[tex]x = 500[/tex]

Another easiest way to solve it is the following:

Make [tex]w = 2x[/tex].

Then:

[tex]log(2x) = log(w)[/tex]

[tex]log(w) = 3[/tex]

[tex]w = 10^3[/tex]  -------- Inverse logarithm property

[tex]w = 1000[/tex]  

but [tex]w= 2x[/tex]. Then:

[tex]2x = 1000\\\\x = 500[/tex]

Answer: 9/25

Step-by-step explanation: .36 equals 36/100 in decimal form.

Reducing it into its simplest form:

Both numbers are divisible by 4-

36/100 = 9/25 - which is the simplest form.

Answer:

D : One Real Root

Step-by-step explanation:

Isolate "4x" by subtracting 7 from both sides.

So we get

4x = -7

Then we divide each side by 4 to get -7/4

x = -7/4 so there is only one real root.

Final answer:

The equation 4x+7=0 is a linear equation with only one real root, which is -1.75. Therefore, the correct option is d. 1 real root.

Explanation:

The given equation 4x+7=0 is a linear equation, not a quadratic equation. To find the roots, we only have one variable raised to the first power, which means this equation will only have one solution. We can solve this by isolating the variable x:

4x = -7

x = -7 / 4

x = -1.75

Therefore, the correct answer is d. 1 real root, as the equation has exactly one real solution and no imaginary roots.

-3/2

perpendicular slopes are those that are opposite sign and reciprocal of the original given slope

Answer:

gfjhgfterjrjtryuyrt

Step-by-step explanation:

hgfdjjrfdsfdjuytitdfgfdsuygeryauvfudsgygwerauyerwaguyfdsguyagsuydzgfuygewsabfuyguyeravcuyeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraerajhbfcds

4.97 is 1 standard deviation below the mean, since 5.00 - 0.03 = 4.97. Similarly, 5.03 is 1 standard deviation above the mean. The 68-95-99.7 rule (sometimes called "empirical rule") says that approximately 68% of any normally distributed population lies within 1 standard deviation of the mean, so

[tex]P(4.97<X<5.03)\approx0.68[/tex]

So out of 120 nails, we can expect [tex]0.68\cdot120=81.6\approx82[/tex] nails to be within the prescribed length.

The number of nails in a bag of 120 that are between 4.97 and 5.03 in. Long will be 82.

A normal distribution is a symmetrical continuous probability distribution in which values are usually clustered around the mean.

4.97 is 1 standard deviation below the mean, since 5.00 - 0.03 = 4.97.

Similarly, 5.03 is 1 standard deviation above the mean.

The 68-95-99.7 rule (sometimes called "empirical rule") says that approximately 68% of any normally distributed population lies within 1 standard deviation of the mean, so

P(4.97<X<5.03)068

So out of 120 nails, we can expect  0.68 x120= 81.57=82 nails to be within the prescribed length.

Hence the number of nails in a bag of 120 that are between 4.97 and 5.03 in. Long will be 82.

To know more about normal distribution follow

https://brainly.com/question/4079902

#SPJ2

change 7 5/6 to an improper fraction

= 47/6

change 6 1/2 to an improper fraction

13/2

rewrite

Q - 47/6 = 13/2

add 47/6 on both sides

Q = 13/2 + 47/6

times 13/2 by 3 to get a common denominator of 6

Q = 39/6 + 47/6

Q = 86/6

change to mixed number

14 2/6

simplify

= 14 1/3

Answer:

A

Step-by-step explanation:

We can write this as Sinx by "flipping" the [tex]-\sqrt{2}[/tex].

So we will have:  [tex]Sin(x)=-\frac{1}{\sqrt{2} }[/tex]

From basic trigonometry, we know the value of  [tex]\frac{1}{\sqrt{2}}[/tex]  of sine is of the angle [tex]\frac{\pi}{4}[/tex]

But when is sine negative? Either in 3rd or 4th quadrant. But the answer has to be between 0 and  [tex]\frac{3\pi}{2}[/tex], so we disregard 4th quadrant.

To get the angle in 3rd quadrant, we add π to the acute angle of the first quadrant (which is π/4 in our case). Thus we have:

[tex]\frac{\pi}{4}+\pi\\=\frac{\pi +4\pi}{4}\\=\frac{5\pi}{4}[/tex]

A is the right answer.

Answer:

The measure of angle BEH is 55°

Step-by-step explanation:

we know that

m<DEB=45° -----> by corresponding angles

m<GEH=80° -----> by corresponding angles

m<DEB+m<BEH+m<GEH=180° ------> line DG

substitute the values and solve for m<BEH

45°+m<BEH+80°=180°

m<BEH=180°-125°=55°

Answer:

e) The mean of the sampling distribution of sample mean is always the same as that of X, the distribution from which the sample is taken.

Step-by-step explanation:

The central limit theorem states that

"Given a population with a finite mean μ and a finite non-zero variance σ2, the sampling distribution of the mean approaches a normal distribution with a mean of μ and a variance of σ2/N as N, the sample size, increases."

This means that as the sample size increases, the sample mean of the sampling distribution of means approaches the population mean.  This does not state that the sample mean will always be the same as the population mean.

correct answer is option (c)

The Statement: The sampling distribution of the sample mean is always reasonably like the distribution of X, the distribution from which the sample is taken. is not True.

What is Standard deviation?

The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean. By calculating the departure of each data point from the mean, the standard deviation may be determined as the square root of variance.

How Standard deviation is calculated?

Standard deviation is calculated by taking the square root of a value derived from comparing data points to a collective mean of a population. The formula is:

[tex]\begin{aligned} &\text{Standard Deviation} = \sqrt{ \frac{\sum_{i=1}^{n}\left(x_i - \overline{x}\right)^2} {n-1} }\\ &\textbf{where:}\\ &x_i = \text{Value of the } i^{th} \text{ point in the data set}\\ &\overline{x}= \text{The mean value of the data set}\\ &n = \text{The number of data points in the data set} \end{aligned}[/tex]

So, In the given options,

The Statement: The sampling distribution of the sample mean is always reasonably like the distribution of X, the distribution from which the sample is taken is False, because according Central limit theorem,

regardless of the shape of the population(X): If the sample size is greater than 30. The Sample distribution will be Normal Distribution.

Hence,

The Statement: The sampling distribution of the sample mean is always reasonably like the distribution of X, the distribution from which the sample is taken. is not True.

To know more about the Standard deviation refer to the below link:

https://brainly.com/question/475676

#SPJ2

Answer:

[tex]k=\frac{9}{2}[/tex]

Step-by-step explanation:

The  given sequence is

[tex]5,2k,13[/tex]

For the sequence to be arithmetic, then

[tex]2k-5=13-2k[/tex]

We group similar terms to get;

[tex]2k+2k=13+5[/tex]

[tex]4k=18[/tex]

Divide both sides by 4;

[tex]k=\frac{18}{4}[/tex]

Simplify;

[tex]k=\frac{9}{2}[/tex]

Answer:

The correct answer is 3rd option 9/2

Step-by-step explanation:

From the given sequence, 5, 2k, 13

Which are in AP.

We can consider a₁ = 5 , a₂ = 2k and a₃ = 13

To find the value of k

We have,

a₂ = (a₁ + a₃)/2

Here,

2k = (5 + 13)/2 = 18/2 = 9/2

Therefore the correct answer is option 3

9/2

Answer:

[tex]tanY = \frac{4}{5}[/tex] and [tex]tanZ=\frac{5}{4}[/tex]

Explanation:

The tan of an angle in a triangle is equal to [tex]\frac{opposite}{adjacent}[/tex] for the side lengths. Opposite side is the one found directly across the triangle and the adjacent is the side touching the angle that is not the hypotenuse. This means the tan for Y is 4 over 5 and the tan for Z is 5 over 4.

The tangent ratios are:

tan(Y) = 5/4

tan(Z) = √41/4

In a right triangle with sides labeled X, Y, and Z, and angles labeled x, y, and z, you can use the trigonometric ratios to find the tangent ratios for angles Y and Z.

The tangent ratio is defined as:

For angle Y (opposite to side XY): tan(Y) = opposite / adjacent = XY / ZX

For angle Z (opposite to side ZY): tan(Z) = opposite / adjacent = ZY / XZ

Given the following values:

ZX = 4

XY = 5

ZY = √41

Let's calculate the tangent ratios:

For angle Y (opposite to XY):

tan(Y) = XY / ZX = 5 / 4

For angle Z (opposite to ZY):

tan(Z) = ZY / XZ = √41 / 4

So, the tangent ratios are:

tan(Y) = 5/4

tan(Z) = √41/4

for such more question on tangent ratios

https://brainly.com/question/13583559

#SPJ3

Answer:

so ans is C.)yes;3.5x

Step-by-step explanation:

x | y

8 |28

16 |56

20|70

8*3.5=28

16*3.5=56

20*3.5=70

so ans is C.)yes;3.5x

The y varies directly with x and the proportional relation is y = 3.5x option (C) yes;3.5x is correct.

It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.

We have data in the table:

x | y

8 |28

16 |56

20|70

y ∝ x

y = kx

Plug x = 8 y = 28

28 = 8k

k = 3.5

y = 3.5x

Thus, the y varies directly with x and the proportional relation is y = 3.5x option (C) yes;3.5x is correct.

Learn more about the proportional here:

brainly.com/question/14263719

#SPJ2