A rectangle has a perimeter of 48 inches. Each side is a whole number of inches. What is the difference between the greatest and least areas that the rectangle can have

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:

1,221,759.

Step-by-step explanation:

This is the number of combinations of 5 from 45.

This =   45! / 40! 5!

=  1,221,759.

Answer:

1,221,759

Step-by-step explanation:

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.

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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]

The values in the scatter diagram indicate;

a) The graph of the data showing the location of the car that costs £2600 and is 4 years of age created with MS Excel is attached

b) The value of the cars decreases as the age increases

c) £3687.9

To address the question, plot the new car data on a scatter diagram, describe the trend of decreasing value with increasing age, and estimate the value of a car based on its age by interpolating between data points.

The question requests steps on how to represent data on a scatter diagram as well as how to interpret and estimate values from it.

a. Add the new point to the scatter diagram for a car that's 4 years old and valued at £2600. This point (4, £2600) should be plotted on the graph along with the other data points.

b. Describe the relationship by observing how the value tends to change as the age of the cars increases. Generally, as cars age, their value decreases, which suggests a negative relationship between the age and the value of the cars.

c. For estimating the value of a car that is 3.5 years old can be found as follows; The equation of the trend line for the scatter diagram obtained usinfg MS Excel is; y = -1290.2·x + 8203.6, indicates that when x = 4, we get;

y = -1290.2 × 3.5 + 8203.6

-1290.2 × 3.5 + 8203.6 =

The estimated price of the car is £3687.9

The complete question found through search is presented as follows;

The scatter diagram shows information about 10 cars.

The 10 cars are of the same type and make

Another car is 4 years old and has been valued at £2,600

a) Show this information on the graph

b) Describe the relationship between the age and the values of the cars

A car of the same type and age is 3¹/₂ years old

c) Estimate the value of the car

q= -1/2

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

Answer:

  1. Is 8/15

Step-by-step explanation:

-3/2

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

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:

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:

4:3

Step-by-step explanation:

The ratio is 8:6, which simplifies to 4:3.

Answer:

16:9

Step-by-step explanation:

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.

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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.

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:

gfjhgfterjrjtryuyrt

Step-by-step explanation:

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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

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Answer:

2 mpm

Step-by-step explanation

The solution to this exercise has been attached below. The problem has been solved in this way:

________________

Answer:

Everything he said was correct!

Step-by-step explanation:

I hope this helps!

- sincerelynini

Answer:

See below.

Step-by-step explanation:

A rectangle has 4  * 90 degree angles and opposite sides are congruent and parallel.  A square also fits the bill.

Answer:

Area[tex]=70in^2[/tex]

Step-by-step explanation:

The given diagram is a tra-pezoid.

The area of a tra-pezoid is calculated using the formula;

Area[tex]=\frac{1}{2} (Sum\:of\:parallel\:sides)\times height[/tex]

This implies that;

Area[tex]=\frac{1}{2} (8+12)\times 7[/tex]

Area[tex]=\frac{1}{2} (20)\times 7[/tex]

Area[tex]=(10)\times 7[/tex]

Area[tex]=70in^2[/tex]

The last choice is correct.

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:

245.04

Step-by-step explanation:

The equation to a cylinder for area is A=2πrh+2πr^2

Fill in and solve.

A=2(3.14)(3)(10)+2(3.14)(3)^2

So using PEMDAS you get the answer 245.04

While taking @Jtakes700's answer and putting it into the form your asking, or putting into one of your options, you would get 78pi sq. in.

[tex]\bigtriangleup RSP \cong\bigtriangleup RQT\Rightarrow \frac{RS}{RQ}=\frac{RP}{RT}\Leftrightarrow RS=3 \\ \Rightarrow ST=RT-RS=5[/tex]

Answer:

5/6

Step-by-step explanation:

1/3 + 1/2 = 5/6

Answer:

18 cm

Step-by-step explanation:

Let the width of the rectangle be x cm, then the length of the rectangle is x+5 cm.

The area of the ractangle is

[tex]x\cdot (x+5)\ cm^2.[/tex]

The area of the square with side's length of x cm is

[tex]x^2\ cm^2.[/tex]

The area of the square with side's length of x+5 cm is

[tex](x+5)^2\ cm^2.[/tex]

The area of constructed figure is

[tex]x(x+5)+2x^2+2(x+5)^2\ cm^2.[/tex]

Since the  total area of the constructed figure is 120 cm², you have

[tex]x(x+5)+2x^2+2(x+5)^2=120.[/tex]

Solve this equation:

[tex]x^2+5x+2x^2+2x^2+20x+50=120,\\ \\5x^2+25x-70=0,\\ \\x^2+5x-14=0,\\ \\D=5^2-4\cdot (-14)=25+56=81,\\ \\x_{1,2}=\dfrac{-5\pm\sqrt{81}}{2}=-7,\ 2.[/tex]

The width of the rectangle cannot be negative, so x=2 cm and x+5=7 cm and the perimeter of the rectangle is

[tex]2x+2(x+5)=2\cdot 2+2\cdot 7=4+14=18\ cm.[/tex]

Answer:

Between 0 and 1

Step-by-step explanation:

The probability for each outcome in experimental probability must be a value between 0 and 1.  A probability of 0 means the event did not happen; the probability of 1 means it is certain.  We cannot have probabilities smaller than 0 or greater than 1.

All of the probabilities in an experiment must sum to 1 whole.

The probability assigned to each experimental outcome must be greater than 0 or less than 1 or lies in between 0 and 1.

The probability of extremely certain event is 1 and the probability of extremely uncertain event is 0. The sum of all the probabilities in an experiment is always equals to 1.

Hence the probability assigned to each experimental outcome must be greater than 0 or less than 1 or lies in between 0 and 1.

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Answer:

  ... you add the exponents

Step-by-step explanation:

An exponent is a way of showing repeated multiplication. For example, ...

  x^2 means x·x

and

  x^3 means x·x·x

If we multiply these two expressions together, we get ...

  (x^2)·(x^3) = (x·x)·(x·x·x) =  x·x·x·x·x

This is a product in which x appears as a factor 5 times, so we can write it using an exponent as ...

  x·x·x·x·x = x^5

___

That is, when we multiply the expressions, we add the numbers of times the factor appears in the product:

  2 + 3 = 5

  x^2 · x^3 = x^(2+3) = x^5

Answer: Add

Step-by-step explanation: When you multiply expression with the same base you ADD the exponents. The exponent tells you how many times you multiply the base by itself. This means the exponent corresponds to the amount of base replications. If you add the exponents you are adding the replications of the base. 

Fortnite Yee yee boi get them toes

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.

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%

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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.