e. A set of observations has a mean of 9.0 and standard deviation 4.0. Another set of 20 observations has a mean of 10.0. Given the standard deviation of the combined set of 35 observations is 3.0, find the variance of the second set.

A polynomial function f(x) of degree 3 with given zeros, 2, -3 , 5 and condition f(3)=6 is given by f(x) = -1/2 (x-2)(x+3)(x-5).

Degree of the polynomial function is equal to 3.

Zero's of the polynomial function is equal to 2, -3 , 5 .

And f(3) = 6

If 2, -3, and 5 are zeros of f(x), then we can write function as,

f(x) = a(x-2)(x+3)(x-5)

where a is some constant.

To determine the value of a, we can use the fact that f(3) = 6.

Substituting x = 3 into the equation above, we get,

f(3) = a(3-2)(3+3)(3-5)

     = -12a

Here we have,

f(3) = 6, so we can set these two expressions equal to each other and solve for a,

⇒ -12a = 6

⇒ a = -1/2

Now we can substitute this value of a back into the equation for f(x) that we found earlier,

⇒ f(x) = -1/2 (x-2)(x+3)(x-5)

Therefore, a polynomial function f(x) of degree 3 with zeros 2, -3, 5, and f(3) = 6 is equal to f(x) = -1/2 (x-2)(x+3)(x-5).

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The volume of a frustum of a pyramid with given dimensions is 6260 cubic units.

What is frustum of pyramid?

The top of a conventional pyramid is removed to create the frustum, which is a pyramid. It is known as a truncated pyramid for this reason. The height of a pyramid is represented by the letter h and is the distance from its base to its summit. Similar to it, it has two bases and a slant height indicated by the letter "s" (top and bottom).

We are given frustum of a pyramid with square base of side 22, square top of side 13 and height 20.

We know that volume of frustum of pyramid(V) = h(b^2 + a^2 + ab)/3

We are given b = 22, a = 13 and h = 20

From this, we get

⇒V = h(b^2 + a^2 + ab)/3

⇒V = 20(22^2 + 13^2 + 22*13)/3

⇒V = 20(484 + 169 + 286)/3

⇒V = 20(939)/3

⇒V = 20*313

⇒V = 6260 cubic units

Hence, the volume of a frustum of a pyramid with given dimensions is 6260 cubic units.

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Answer:

Step-by-step explanation:
The standard equation of a circle with center (a, b) and radius r is:

(x - a)^2 + (y - b)^2 = r^2

Using the given values, we have:

(x - (-3))^2 + (y - 5)^2 = 2^2

Simplifying:

(x + 3)^2 + (y - 5)^2 = 4

Therefore, the standard equation of the circle is (x + 3)^2 + (y - 5)^2 = 4.

Answer:

\( (x + 3)^2 + (y - 5)^2 = 4 \)

Step-by-step explanation:

\( (x - h)^2 + (y - k)^2 = r^2 \)

\( (x - (-3))^2 + (y - 5)^2 = 2^2 \)

\( (x + 3)^2 + (y - 5)^2 = 4 \)

Answer:

The nearest whole is 122.99 repeated

Step-by-step explanation:

Answer:

3

−

9

=

−

3

9

3

−

6

=

-21

Step-by-step explanation:

3x​−9y=−39, 3x−6y=−21 : x=5, y=6

Steps

[ ​3x−9y=−39 3x−6y=−21 ]

Show Steps

Isolate x for 3x−9y=−39: x=−13+3y

Substitute x=−13+3y

[ 3(−13+3y)−6y=−21 ]

Show Steps

Simplify

[ −39+3y=−21 ]

Show Steps

Isolate y for −39+3y=−21: y=6

For x=−13+3y

Substitute y=6

x=−13+3· 6

Simplify

x=5

The solutions to the system of equations are:

Answer:

no she needs $2.20 more

Step-by-step explanation:

2+ 1.10+.05= $3.15

$5.35 - $3.15 = the answer

Step-by-step explanation:

The definite integral of sin^5(x)dx from 0 to pi/2 can be evaluated using the method of substitution.

Let u = sin(x), then du = cos(x)dx

The integral becomes:

∫sin^5(x)dx = ∫u^5du from 0 to sin(π/2)

= (u^6)/6 evaluated at sin(π/2) and 0

= (sin^6(π/2))/6 - 0

= (1^6)/6

= 1/6

So, the definite integral of sin^5(x)dx from 0 to pi/2 is equal to 1/6.

Answer: 9.5 hours

In order to solve this, you must divide his total (80.75) by his hourly wage (8.50) When you do that, you get 9.5, so he worked 9.5 hours

Step-by-step explanation:

Answer:

j = 139.99 + 139.99 * 0.08625

Answer:

Step-by-step explanation:

Segments MS and QS are therefore congruent by the definition of bisector. Therefore, the correct answer option is: D. MS and QS.

In Mathematics and Geometry, a perpendicular bisector is a line, segment, or ray that bisects or divides a line segment exactly into two (2) equal halves and forms an angle that has a magnitude of 90 degrees at the point of intersection.

This ultimately implies that, a perpendicular bisector bisects a line segment exactly into two (2) equal halves, in order to form a right angle that has a magnitude of 90 degrees at the point of intersection.

Since line segment NS is a perpendicular bisector of isosceles triangle MNQ, we can logically deduce the following congruent relationships;

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Complete Question:

The proof that ΔMNS ≅ ΔQNS is shown. Given: ΔMNQ is isosceles with base MQ, and NR and MQ bisect each other at S. Prove: ΔMNS ≅ ΔQNS

We know that ΔMNQ is isosceles with base MQ. So, MN ≅ QN by the definition of isosceles triangle. The base angles of the isosceles triangle, ∠NMS and ∠NQS, are congruent by the isosceles triangle theorem. It is also given that NR and MQ bisect each other at S. Segments _____ are therefore congruent by the definition of bisector. Thus, ΔMNS ≅ ΔQNS by SAS.

NS and NS

NS and RS

MS and RS

MS and QS

Answer:

C

Step-by-step explanation:

If you use this calculation, you get:

\(q=\sqrt[3]{64}\)

q = 4

you can use this value in the other equation to check:

\(4^3=64\)

4 x 4 x 4 = 64

64 = 64

C is your answer

Hope this helps!

Answer:

The width w of the rectangular park = 1/2

Step-by-step explanation:

Given

The length of the rectangular park l = 2/3 miles

The area of the park A = 3/9 square miles

To determine

The width of the rectangular park w = ?

Using the formula of the Area of the rectangle

\(A\:=\:wl\)

\(w\:=\:\frac{A}{l}\)

    \(=\frac{\frac{3}{9}}{\frac{2}{3}}\)

    \(=\frac{3\cdot \:3}{9\cdot \:2}\)          ∵ Fraction rule:  \(\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot \:d}{b\cdot \:c}\)

    \(=\frac{9}{18}\)

    \(=\frac{1}{2}\)

Therefore, the width w of the rectangular park = 1/2

a_n=224(1/2)^n-1

Given:

The number of books is 7.

The arrangements of 7 books are,

It gives,

Answer: number of ways are 5040.

The slope of the line that is perpendicular to the tangent line at x=1 is, \(\frac{1}{4}\)

Option E is correct.

The derivative of given function with respect to x is known as slope of function.

Given function is, \(g(x)=-3x^{3}+5x-3\)

Now differentiate the above function.

     \(\frac{dg(x)}{dt}=-9x^{2} +5\)

 \(\frac{dg(x)}{dx}\) at \(x=1\) is,

        \(\frac{dg}{dt} =-9(1)^{2}+5 =-4\)

the slope of the line that is perpendicular to the tangent line at x=1 is,

       Slope\(=-\frac{1}{dg/dx}=\frac{1}{4}\)

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Answer:

x = 5 root 3

y = 30

z = 10

Step-by-step explanation:

The triangle has a right angle of 90° and a 60° angle.

The third angle must have measure 30° since 180° - 90° - 60° = 30°.

We have a 30-60-90 right triangle.

In a 30-60-90 the ratio of the lengths of the sides is:

short leg   :   long leg   : hypotenuse

   1            :     root 3     :      2

The long leg is root 3 times the short leg.

The hypotenuse is 2 times the short leg.

short leg: 5

long leg: 5 * root 3 = 5 root 3

long leg: 5 * 2 = 10

x = 5 root 3

y = 30

z = 10

The solution of the inequality 15n>8n-21 is given by, n<-3.

Inequality is a relation between two or more mathematical expression or quantities via unequal signs i.e. greater, less, greater or equal, less or equal, not equal.

Given that the inequality is 15n<8n-21

Solving the inequality we have,

15n<8n-21

15n-8n<8n-21-8n, subtracting from both sides

7n<-21

n<-3, dividing 7 from both sides

So the solution of the given inequality is, n<-3.

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The greatest common factor, GCF, of 8y, -12x, and 4xy is 4

From the question, we are to determine the greatest common factor of the given expressions.

The given expressions are 8y, -12x, and 4xy

To determine the greatest common factor, we will express each of the expressions as a product of their factors.

8y = 2 × 2 × 2 × y

-12x = 2 × 2 × 3 × -x

4xy = 2 × 2 × x × y

From above, we can observe that the greatest common factor is

2 × 2

= 4

Hence, the greatest common factor is 4

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Answer:

y= 0.05x + 50

Step-by-step explanation:

Slope intercept form: y= mx + b

The total monthly cost of the telephone plan is $50 plus a charge of $0.05 per minute.

The charge is dependent on the minutes used.

Whenever we see per, we automatically have our slope.

Slope: 0.05

And since 50 is the independent variable, 50 is our y-intercept.

y= 0.05x + 50

Hope it helps :D

By evaluating all the given values of the independent variable at x is equal to 6,x+4 and -x.

It is required to find the solution.

A function is defined as a relation between a set of inputs having one output each. function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.

Given:

The function f(x)= x^2 + 2x + 8

According to given question we have,

By put the value of x=6 in the function f(x) we get,

Evaluating the function f(6):

f(6) = (6)² + 2(6) + 8

f(6) = 36 + 12 + 8

f(6) = 56

By put the value of x=x+4 in the function f(x) we get,

Evaluating the function f(x+4):

f(x+4) = (x+4)² + 2(x+4) + 8

f(x+4) = x² + 8x + 16 + 2x + 8 + 8

f(x+4) = x² + 10x + 32

By put the value of x=-x in the function f(x) we get,

Evaluating the function f(-x):

f(-x) = (-x)² + 2(-x) + 8

f(-x) = x - 2x + 8

Therefore, by evaluating all the given values of the independent variable at x is equal to 6,x+4 and -x.

The probability that the two coins chosen together will be worth at least 35 cents is approximately 0.7222, or 13/18.

To solve this problem, let's consider the possible combinations of two coins that Reyna can choose. She has 5 coins worth 10 cents each and 4 coins worth 25 cents each.

1. Number of ways to choose two coins:

  Reyna can choose two coins from a total of 9 coins. The number of ways to choose two items from a set of n items is given by the combination formula: C(n, k) = n! / (k!(n-k)!), where n! denotes the factorial of n. In this case, n = 9 and k = 2.

  C(9, 2) = 9! / (2!(9-2)!) = 36

2. Number of ways to choose two coins worth at least 35 cents:

  Reyna can choose two coins worth at least 35 cents in two ways:

  - Choose two coins worth 25 cents each: There are 4 coins worth 25 cents each, so the number of ways to choose two of them is C(4, 2) = 6.

  - Choose one coin worth 25 cents and one coin worth 10 cents: There are 4 coins worth 25 cents each and 5 coins worth 10 cents each. The number of ways to choose one coin from each category is 4 * 5 = 20.

3. Probability calculation:

  The probability of an event occurring is given by the ratio of the number of favorable outcomes to the total number of possible outcomes.

  Probability = (Number of favorable outcomes) / (Total number of possible outcomes)

             = (6 + 20) / 36

             = 26 / 36

             = 13 / 18

             ≈ 0.7222

Therefore, the probability that the two coins chosen together will be worth at least 35 cents is approximately 0.7222, or 13/18.

The number 8 does not come into the equation for this particular problem. It seems to be unrelated to the given scenario.

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Answer:

The values of p = 0 < p ≤ 2/3

Step-by-step explanation:

First we write the probability of 6V flashlight working representing it as a binomial mass function of a binomial random variable

P ( 6v flashlight working  ) = P ( at least one 6V battery works )

                                           = P ( 1 6v battery work )  + P ( 2  6v battery work )

                                           = b( 2; 2, p ) + b( 1; 2, p )

write out a formula of  b( 2; 2, p ) + b( 1; 2, p )

P ( 6v flashlight working  )  = p^2 + 2p( 1 - p )

Next we write the probability of D flashlight working representing it as a binomial mass function of a binomial random variable

P ( D flashlight works ) = p ( at least two D batteries works )

                                     = b( 4; 4, p ) + b(3;4, p ) + b(2; 4, p )

write out a formula of  b( 4; 4, p ) + b(3;4, p ) + b(2; 4, p )

P ( D flashlight works ) = \(P^4 + 4p^3 ( 1- p ) + 6p^2 ( 1- p)^2\)

attached below is the remaining solution

Answer: 3/2, 2/3, 1/3

Step-by-step explanation:

the actual length of the cement truck is 165cm. To determine the actual length of the cement truck, we can use the scale factor provided.

If the toy cement truck is 11cm long and the scale factor used is 1cm : 15cm, then we can write the following proportion:

1cm / 15cm = 11cm / x

Solving for x, we can cross-multiply and get:

x = (15cm * 11cm) / 1cm

x = 165cm

Therefore, the actual length of the cement truck is 165cm.

This answer makes sense in a real-life context. Scale models are often used in industries such as architecture, engineering, and construction to represent buildings, machines, and other structures before they are built in full-scale. The scale factor allows designers and builders to create models that are smaller in size but still represent the same proportions and features of the actual structure.

In the case of a toy cement truck, the scale factor used allows manufacturers to create a smaller, more affordable version of the real truck while still maintaining the same proportions and features. This can make the toy more accessible to children and collectors alike. Additionally, understanding the scale factor used to create a toy can provide insights into the actual size and features of the real-life object, making it easier to visualize and understand.

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Answer:

y= (0, .7)

x= (-1.2, 0)

Step-by-step explanation:

r u taking a test?

Answer:I have the same quastion too

Step-by-step explanation:

Answer:

5(5x-3)

Step-by-step explanation:

The common factor in this expression is 5 so divide 5 to all the values

25/5=5

-15/5= -3

Put these values into parenthesis and leave the 5 on the left side and out of the parenthesis

5(5x-3)

Answer:

5(5x - 3)

Step-by-step explanation:

The greatest common factor here is 5. Divide each term by 5 and simplify.

25x/5 = 5x

15/5 = 3

Therefore, the answer is 5(5x - 3).

The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 16,80, 400,... Find the 6th term.​

we have

a1=16

a2=80

a3=400

so

a2/a1=80/16=5

a3/a2=400/80=5

In this problem we have a geometric sequence

where the common ratio is equal to r=5

the equation for the geometric sequence is equal to

substitute the give values

Find the 6th term

For n=6

substitute

therefore

Answer:

Step-by-step explanation:

Hello!

To see if driving heavy equipment on wet soil compresses it causing harm to future crops, the penetrability of two types of soil were measured:

Sample 1: Compressed soil

X₁: penetrability of a plot with compressed soil.

n₁= 20 plots

X[bar]₁= 2.90

S₁= 0.14

Sample 2: Intermediate soil

X₂: penetrability of a plot with intermediate soil.

n₂= 20 (with outlier) n₂= 19 plots (without outlier)

X[bar]₂= 3.34 (with outlier) X[bar]₂= 2.29 (without outlier)

S₂= 0.32 (with outlier) S₂= 0.24 (without outlier)

Outlier: 4.26

Assuming all conditions are met and ignoring the outlier in the second sample, you have to construct a 99% CI for the difference between the average penetration in the compressed soil and the intermediate soil. To do so, you have to use a t-statistic for two independent samples:

Parámeter of interest: μ₁-μ₂

Interval:

[(X[bar]₁-X[bar]₂)±\(t_{n_1+n_2-2;1-\alpha/2}\)*Sa\(\sqrt{\frac{1}{n_1} +\frac{1}{n_2} }\)]

\(t_{n_1+n_2-2;1-\alpha/2}= t_{20+19-2;1-(0.01/2)}= t_{37; 0.995}= 2.715\)

\(Sa= \sqrt{\frac{(n_1-1)S_1^2+(n_2-1)S_2^2}{n_1+n_2-2} } = \sqrt{\frac{19*0.0196+18*0.0576}{20+19-2} }= 0.195= 0.20\)

[(2.90-2.29)±2.715*0.20\(\sqrt{\frac{1}{20} +\frac{1}{19} }\)]

[0.436; 0.784]

I hope this helps!

Using the t-distribution, it is found that the 99% confidence interval for the decrease in penetrability of compressed soil relative to intermediate soil is (-0.418, 1.182).

Using a calculator, we find that for the compressed soil, the mean and the standard deviation are given by:

\(\mu_C = 2.9075, s_C = 0.1427\)

For the intermediate soil, omitting the high outlier of 4.26, we have that:

\(\mu_I = 3.2895, s_I = 0.2385\)

The distribution of the decrease has mean and standard deviation given by:

\(\overline{x} = \mu_I - \mu_C = 3.2895 - 2.9075 = 0.382\)

\(s = \sqrt{s_C^2 + s_I^2} = \sqrt{0.1427^2 + 0.2385^2} = 0.2779\)

The interval is given by:

\(\overline{x} \pm ts\)

By the conservative method, the amount of degrees of freedom is one less than the smaller sample size, which in this case is 19, for the intermediate soil.

Then:

\(\overline{x} - ts = 0.382 - 2.8784(0.2779) = -0.418\)

\(\overline{x} + ts = 0.382 + 2.8784(0.2779) = 1.182\)

The 99% confidence interval for the decrease in penetrability of compressed soil relative to intermediate soil is (-0.418, 1.182).

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