2. Factor 12³ + 60x² + 75x.​

The approximate population variance is 937.85.

To approximate the population variance, we need to calculate the sample variance first and then use the following formula to approximate the population variance:

Population variance ≈ (sample variance) × [(n)/(n-1)], where n is the sample size.

To calculate the sample variance, we need to first calculate the sample mean:

Sample mean = (Σ (midpoint of class interval × frequency))/n

= [(9.5 × 15) + (29.5 × 13) + (49.5 × 8) + (69.5 × 10) + (84.5 × 10)]/56

= 44.375

Next, we can use the formula for calculating the sample variance:

Sample variance = [(Σ(frequency × (midpoint of class interval - sample mean)^2))/(n-1)]

= [(15 × (9.5-44.375)^2) + (13 × (29.5-44.375)^2) + (8 × (49.5-44.375)^2) + (10 × (69.5-44.375)^2) + (10 × (84.5-44.375)^2)]/55

= 918.75

Finally, we can use the formula to approximate the population variance:

Population variance ≈ (sample variance) × [(n)/(n-1)]

= 918.75 × [(56)/(55)]

≈ 937.85

Therefore, the approximate population variance is 937.85.

To learn more about calculate visit:

https://brainly.com/question/30151794

#SPJ11

The price that Maura sell each scarf would be =$33. Maura sells each scarf for $33. That is option A.

To calculate the amount of money that Maura spends on each scarf the following is carried out.

The amount of money that she spends on the scarf material = $5.50

The percentage selling price of each scarf = 600% of $5.50

That is ;

= 600/100 × 5.50/1

= 3300/100

= $33.

Therefore, each price that is sold by Maura would probably cost a total of $33.

Learn more about cost price here:

https://brainly.com/question/26008313

#SPJ1

We need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit which is compounded semi-annually.

To solve this problem, we can use the formula for the future value of an annuity:

\(FV = P * ((1 + r)^n - 1) / r\)

Where:

FV is the future value of the annuity

P is the periodic payment or deposit amount

r is the interest rate per period

n is the number of periods

In this case, the deposit amount is $726.56, the interest rate is 6.45% compounded semi-annually, and the future value is $31,300. We need to find the number of deposits (n).

We can rearrange the formula and solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Substituting the given values:

n = log((31,300 * 0.03225) / (726.56 * 0.03225 + 31,300)) / log(1 + 0.03225)

Using a calculator or software, we find that n ≈ 9.989.

Therefore, we need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit.

To know more about annual rate click here

brainly.com/question/6026546

#SPJ4

Answer:

x=-4

Step-by-step explanation:

Answer:

x = -4

Step-by-step explanation:

10x + 2 = 8x - 6

10x - 8x = - 6 - 2

2x = - 8

x = -4

Answer:

  1414 kL

Step-by-step explanation:

The volume of the donut-shaped moat is the product of its surface area and depth. The area is the product of its centerline length and its width.

The diameter of the centerline of the moat is (50 m -5 m) = 45 m. The length of that centerline is ...

  C = πd = π(45 m) = 45π m

The area is this length times the width of the moat:

  moat area = (45π m)(5 m) = 225π m²

The volume is the product of the area and the depth of the moat:

  V = Ah = (225π m²)(2 m) = 450π m³ ≈ 1413.72 m³

1 cubic meter is 1000 liters, 1 kiloliter.

The volume of the moat is about 1414 kL.

Answer:

             \(\bold{a_{16}=78}\)

Step-by-step explanation:

\(a_1=3,\ a_2=3+5=8,\ a_3=8+5=13,\ a_4=13+5=18\ \implies\ d=5\\\\a_n=a_1+(n-1)d\\\\a_n=3+(n-1)(5)\\\\a_n=3+5n-5\\\\a_n=5n-2\\\\ a_n=78\quad\implies\quad n=\,??\\\\78=5n-2\\\\78+2=5n\\\\5n=80\\\\n=16\)

Z- test statistics should be used when computing a confidence interval given only the number in a sample, the population standard deviation and the sample mean.

A z-test can be used to assess whether or not the means of two populations differ if the data has a normal distribution. For this reason, it is essential to set up the null hypothesis, and the alternative hypothesis, and determine the z-test statistic's value. The choice criterion is founded on the z critical value.

The z-test formula compares the z statistic with the z critical value to see if there is a difference between the means of the two populations. In hypothesis testing, the z critical value delineates the acceptance and rejection regions of the distribution graph. If the test statistic falls within the rejection region, the null hypothesis can be rejected; otherwise, it cannot.

To know more about the z-test, visit:

https://brainly.com/question/14269947

#SPJ4

Answer:

27.2368421053

Step-by-step explanation:

Answer:

$7.6 ;

No, you will not be able to buy 3 more CDs

$9.5

$28.5

Step-by-step explanation:

Given that :

Cost of 4 CDs = $30.40

Cost per CD is equal

Sale price = 80% of original price

Price p per CD:

Cost of 4 CDs / number of CDs

$30.40 / 4

= $7.6

2)

No, you will not be able to buy 3 more CDs

If x = original price

80% of x = 7.6

0.8x = 7.6

x = 7.6 / 0.8

x = $9.5

$9.5 * 3 =$28. 5

Hence, $25 can't buy 3 CDs the next day (28.5 > $25)

Answer:

There is evidence to said that the proportion of all shoppers who currently prefer to buy generic instead of name-brand products is higher than 0.18

Step-by-step explanation:

First, we need to define the null and alternative hypothesis as:

H0: p = 0.18

H1: p > 0.18

Where p is the proportion of shoppers that said that they prefer to buy generic instead of name-brand products.

Then, we can calculated the test statistic using the following equation:

\(z=\frac{p'-p}{\sqrt{\frac{p(1-p)}{n} } }\)

Where p' is the proportion of the sample and n is the size of the sample.

Replacing p by 0.18, p' by 0.21 (315/1500 = 0.21) and n by 1500, we get:

\(z=\frac{0.21-0.18}{\sqrt{\frac{0.18(1-0.18)}{1500} } }=3.02\)

So, using the standard normal table, the p-value is calculated as:

p-value = P(z>3.02) = 0.0013

Additionally, At a 5% significance level, the critical value is the z value that let 5% on the right tail, so it is calculated as:

P(Z>z) = 0.05

Critical Value = 1.64

Finally, taking into account that the 5% significance level is higher than the p-value and the critical value is higher than the test statistic, we reject the null hypothesis and there is evidence to said that the proportion of all shoppers who currently prefer to buy generic instead of name-brand products is higher than 0.18

Answer: 25

Step-by-step explanation:

28+97=125

125/4= 31.25

25/4=6.25

31.25-6.25=25

The simplified expression is \(\frac{70-7\sqrt{3}-10\sqrt{7}+\sqrt{21}}{97}\).

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression.

The given statement is "7-radical 7 over10+radical 3".

Write the statement in mathematical form and simplify:
\(\frac{7 - \sqrt{7}}{10 + \sqrt{3}}\\\\\frac{7 - \sqrt{7}}{10 + \sqrt{3}}\times\frac{10 - \sqrt{3}}{10 -\sqrt{3}}\\\\\frac{(7 - \sqrt{7})(10-\sqrt{3})}{100-3}\\\\\frac{70-7\sqrt{3}-10\sqrt{7}+\sqrt{21}}{100-3}\\\\\frac{70-7\sqrt{3}-10\sqrt{7}+\sqrt{21}}{97}\)

Hence, the simplified expression is \(\frac{70-7\sqrt{3}-10\sqrt{7}+\sqrt{21}}{97}\).

Learn more about algebraic expressions here:

https://brainly.com/question/953809

#SPJ1

Answer:

y=5$

Step-by-step explanation:

Determining a single pair of congruent corresponding sides are congruent would prove triangle 1 is similar to triangle 2.

The correct option is (b).

Given,

Consider the two triangles:

From the figure,

To find the which statement is true?

We have to prove the two triangles are congruent by SSS criteria

SSS Criteria says that:

If the two triangles are unequal sides then ;

The two triangles can be proved similar by the SSS similarity theorem if their corresponding sides are proportional.

Now, According to the question:

The true statement is the:

Hence, Determining a single pair of congruent corresponding sides are congruent would prove triangle 1 is similar to triangle 2.

The correct option is (b).

Learn more about Triangles at:

https://brainly.com/question/24163065

#SPJ1

Answer:

hey! this is your answer:

Step-by-step explanation:

function =

f(n)= 2.5n + 15

It takes 4 years for it to grow to 25 ft.

becuase,

25= 2.5(4) + 15

the equation equals itself out when 4 is put in.

The unit tangent vector t(1) at t = 1 is:

t(1) = (4 i + 6 j + 3 k) /\(\sqrt{(61)}\)

To find the unit tangent vector,

we need to calculate the derivative of the position vector r(t) with respect to the parameter t, and then normalize the resulting vector.

Given the position vector r(t) = 4t i + 3t^2 j + 3t k,

we can find the derivative:

r'(t) = d(r(t))/dt

     = 4 i + 6t j + 3 k

Now, we can evaluate r'(t) at t = 1:

r'(1) = 4 i + 6(1) j + 3 k

      = 4 i + 6 j + 3 k

To obtain the unit tangent vector,

we need to normalize r'(1):

t(1) = r'(1) / ||r'(1)||

where ||r'(1)|| represents the magnitude or length of r'(1).

The magnitude of r'(1) is given by:

||r'(1)|| = \(\sqrt{((4^2) + (6^2) + (3^2))}\)

       = \(\sqrt{61}\))

This is the normalized vector representing the direction of the tangent to the curve at the point where t = 1.

Learn more about Vectors here:

https://brainly.com/question/31900604

#SPJ11

Answer:

The innings pitched last season is 225.

Step-by-step explanation:

Given that,

Earned run average = 2.80

Allowed earned run = 70

The given equation is

\(E=\dfrac{9R}{I}\)

We need to calculate the innings pitched last season

Using given equation

\(E=\dfrac{9R}{I}\)

\(I=\dfrac{9R}{E}\)

Where, E = earned run

R = allowed earned run

I = innings pitch

Put the value into the formula

\(I=\dfrac{9\times70}{2.80}\)

\(I=225\)

Hence, The innings pitched last season is 225.

Step-by-step explanation:

h o g   =   6 ( x^2 + x - 2)   + 1

             = 6x^2 + 6x -12 + 1

             = 6x^2 + 6x -11              put in -7 for 'x'

                  6 (-7^2) + 6 (-7) - 11

               = 241

* * * edited * * *

Answer: This is so confusing.... like i think you broke my brain XD

Step-by-step explanation:

The term is called an identity element. In multiplication, the identity element is one because any number multiplied by one results in the same number. In addition, the identity element is zero because any number added to zero results in the same number.

The term in mathematics for the operation or number that leaves others unchanged when combined with them is called the identity element.

It is also known by the name of neutral element.

In multiplication, the identity element is one (1) because when you multiply a number by one the result remains the same as the original number. For any number a,

a1=1a=a.

While in addition, the identity element is zero (0) because when you add zero to a number, the result remains the same as the original number. For any number a,

a+0=0+a=a.

There is no identity element for subtraction, and division only has an identity element for certain sets.

Know more about identity element here:

https://brainly.com/question/31372727

#SPJ11

\( {\qquad\qquad\huge\underline{{\sf Answer}}} \)

The given graph doesn't represent a function, as it has two values of y for a single value of x ( that is : for x = 3 it has two solutions, -3 and -6 )

therefore it can't be considered as a function ~

A correct option is an option (d)

The given expression is,

\((\sqrt{6x^2}+4\sqrt{8x^3})(\sqrt{9x}-x\sqrt{5x^5} )\)

Now, simplifying the given expression as,

\((\sqrt{6x^2}+4\sqrt{8x^3})(\sqrt{9x}-x\sqrt{5x^5} )=(x\sqrt{6}-8\sqrt{2}x\sqrt{x} )(3\sqrt{x} -x\sqrt{5x^5}) \\ = (x\sqrt{6}+8x\sqrt{2x} )(3\sqrt{x} -x^3\sqrt{5x} )\\=3x\sqrt{6x} -x^4\sqrt{30x}+24x^2\sqrt{2x} -8x^5\sqrt{10x}\)

So, the correct option is an option (d).

Learn More:https://brainly.com/question/2548064

We have `f(a) = (a+7)/a`, `f(a+h) = (a+h+7)/(a+h)`, and the difference quotient is `(h(a+7))/(ah+h^2)`.

Given a function `f(x)` is defined by `f(x) = (x+7)/x`.

We need to find `f(a)`, `f(a+h)`, and the difference quotient `(f(a+h)-f(a))/h` where `h≠0`.

Solution:

`f(x) = (x+7)/x`

At `x=a`, we have

`f(a) = (a+7)/a`.

At `x = a + h`,

we have `

f(a+h) = [(a+h)+7]/(a+h)`.

So,

`f(a+h) = (a+h+7)/(a+h)`.

Now,

`f(a+h)−f(a)` is `[(a+h)+7]/(a+h) − (a+7)/a`.

LCM of `(a+h)` and `a` is `a(a+h)`.

So, we get `f(a+h)−f(a)` as `(a+h)(a+7)−a(a+h+7)/a(a+h)`.

On simplification, we have `f(a+h)−f(a)` as `(ah+7h)/(a(a+h))`.

Now, `(f(a+h)−f(a))/h` is `(ah+7h)/(ah+h^2)`.

On simplification, we have `(f(a+h)−f(a))/h` as `(h(a+7))/(ah+h^2)`.

Hence, `f(a) = (a+7)/a`, `f(a+h) = (a+h+7)/(a+h)`, and the difference quotient is `(h(a+7))/(ah+h^2)`.

Given a function `f(x)` is defined by `f(x) = (x+7)/x`. We have found `f(a)`, `f(a+h)`, and the difference quotient `(f(a+h)-f(a))/h` where `h≠0`. Thus, we have `f(a) = (a+7)/a`, `f(a+h) = (a+h+7)/(a+h)`, and the difference quotient is `(h(a+7))/(ah+h^2)`.

To know more about the difference quotient, visit:

brainly.com/question/6200731

#SPJ11

Answer:

17

Step-by-step explanation:

You already owe 5 dollars and if you borrow 12 more, you have to pay that back later. You just add 5 and 12 and get 17.

The total debt is $17.

Combining items and counting them as a single, large group is done through addition.

Given that, the debt amount is $5.

Now, you borrowed $12 more, therefore, the total debt is:

5 + 12

= 17

Hence, the total debt is $17.

Learn more about the addition:
https://brainly.com/question/29560851

#SPJ2

The 90-degree angle is also known as a right angle, it is one of the most prevalent angles used in architecture. The 90-degree angle, constructed by two lines that are perpendicular to each other, is a basic geometric concept.

Geometric shapes like squares, and rectangles use right angles exclusively. There are different ways to create a 90-degree angle or get whether an angle is 90 degrees, depending on the application, the tools, and the information at hand.

The three angles of a triangle always total 180 degrees, if the sum of the other two angles is 90, then it is a right triangle with a 90-degree angle. exactly, the four angles of a quadrilateral (a shape with four sides) always total 360.

yet, if adding the other three angles yields 270, then the angle in question is a right angle.

Calculate whether an angle is 90 degrees or not using the Pythagorean Theorem.

This well-known theorem is also known as "A squared plus B squared equals C squared," which says that the sum of the squares of lengths of the next to sides of a right triangle is equal to the square of the length of the hypotenuse side.

To know more about Angle:

https://brainly.com/question/7116550

#SPJ4

Answer:

x = -45

Step-by-step explanation:

0.5x = 0.3x - 9

Subtract 0.3x to both sides

0.2x = -9

Divide 0.2 to both sides

x = -45

Best of Luck!

Answer:

y = 410

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

y = 23x - 4

x = 18

Step 2: Evaluate

Answer:

y = 410

Step-by-step explanation:

y = 23x - 4    If x = 18

y = (23*18) - 4

y = 414 - 4

y = 410

There are 6 pairwise comparisons that need to be made in order to gain a complete understanding of which treatment effects differ significantly from others.

In order to determine which treatment effects differ significantly from others, we need to make pairwise comparisons between all possible pairs of treatment groups. Let's consider an example with four treatment groups labeled A, B, C, and D.

To determine which treatment effects differ significantly from others, we need to compare the mean scores of each treatment group with the mean scores of every other treatment group. This means we need to make the following pairwise comparisons:

A vs B

A vs C

A vs D

B vs C

B vs D

C vs D

Therefore, there are 6 pairwise comparisons that need to be made in order to gain a complete understanding of which treatment effects differ significantly from others.

It's worth noting that when making multiple pairwise comparisons, there is an increased risk of making a Type I error (i.e., rejecting the null hypothesis when it is actually true) due to the multiple testing problem. To control for this, researchers may choose to adjust the significance level or use methods such as the Bonferroni correction to adjust the p-values of the individual tests.

Learn more about "pairwise comparisons" : https://brainly.com/question/13012475

#SPJ11

Answer:

z ≥ −15

Step-by-step explanation:

5z ≥ −75

Divide each side by 5

5z/5 ≥ −75/5

z ≥ −15

Maximum 8A/144 people are allowed to entire the park.

The entire space taken up by the surface of the park is called area.

If the park is rectangular shaped, then the area is the product of length and breadth. If it is square shaped, area can be determined by the square of the side length.

Given, length of unused space = 12 foot

    breadth of unused space = 12 foot

Area of unused space = 12 x 12 = 144 square feet

Maximum 8 people is allowed for every 144 squares feet space

Let, area of the entire park is A square feet

Now maximum number of people allowed = (8 × A)/ 144

hence, 8A/144 people is allowed.

To know more about area visit:

https://brainly.com/question/19477740

#SPJ4