Hello my daughter needs help on her homework Thi is her question
Can you work out the diameter of these new planets using the clues below?
Vesta is 10 times bigger than Athena.
Athena has half the diameter of Vulcan.
Juno is 10 times bigger than Athena.
Ceres is 100 times bigger than Vulcan.
Vulcan is 20 530km in diameter.
Apollo is 100 times bigger than Athena
I hope you all can help my daughter as me and her father is confused as well

Answer:

Step-by-step explanation:

Considering story 1,

The weight of each book is x pounds. The weight of 5 books would be 5x pounds. Since the weight of the empty bag is 3 pounds and the weight of the bag and the books is 17 pounds, then the equation is

5x + 3 = 17

Considering story 2

x represents the increase in length of each rectangle. The new length of each rectangle would be x + 5. Since the three identical triangles has a total length of 17 feet, the equation would be

3(x + 5) = 17

Considering story 3,

x represents the cost of each bookmark. The cost of a $3 book and 5 booksmarks is 5x + 3. Since the amount spent is $17, the equation is

5x + 3 = 17

Considering story 4,

x represents the weight of each packet of paper. The weight of each bag is x + 3. Since the weight of 5 bags is 17 pounds, the equation is

5(x + 3) = 17

Considering story 5,

x represents the number of pencils that Noah has. The number of pencils that Andre has is 3x. Since he has 17 pens and pencils altogether, the equation would be

3x + 5 = 17

Answer:

Step-by-step explanation: first you take x and multiply it by z and u start taking the guys p and start blowing. if u dont know how 2 pls look it up<33 then ur answer should end up at 69

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Answer:

Bicycle : $117

Tricycle : $87

Unicycle : $183

Step-by-step explanation:

Write a system of equations:

x + 3y + z = 561

7x + y = 906

2x + 7y + 5z = 1758

Where:

x = price of bicycle

y = price of tricycle

z = price of unicycle

Solve for x, y, and z.

Step-by-step explanation:

Random: stated

a) Conditions met Random: stated

Normal: [tex]n_{1} p_{1}=333>10[/tex]

[tex]n_{1}\left(1-p_{1}\right)=2122[/tex]

[tex]n_{2} p_{2}=499>10[/tex]

[tex]n_{2}\left(1-p_{2}\right)=1953[/tex]

Independent: Sample is less than of population.

b) (0.047,0.089) Use 2 -prop interval function of graphing utility

[tex]x_{1}: 333[/tex]

[tex]n_{1}: 2455[/tex]

[tex]x_{2}: 499[/tex]

[tex]n_{2}: 2452[/tex]

[tex]C-[/tex]Level : 0.95

c) The vaccine appears to be effective because we are 95% confident that the proportion of infants without the vaccine who got ear infections was 4.7% to 8.9% more than infants who are vaccinated.

Answer:

Option C is correct.

Step-by-step explanation:

The area of 1 side of the divider is approximately 8 x 3 = 24 < 25  

Hope this helps!

:)

Answer:

B. Jazz and opra

Step-by-step explanation:

40 percent of 55 is 22. Find whatever is equal to 22

B) Jazz & Opera music combo were chosen by 40% of people surveyed

Given : Total respondents = 55

So, 40% of total respondents = 40% of 55 = 22

County & Opera are chosen by 15 + 10 = total 25 respondents, ie not equal to 40%

Jazz & Opera are chosen by 12 + 10 = total 22 respondents, ie equal to 40%

Jazz, Opera, Rock & Country, Jazz, Rock are totally more respondents.

To learn more about Percentage Respondents, refer https://brainly.com/question/8191920?referrer=searchResults

Answer:

And for this case we can begin completing the square like this:

[tex] f(x) = x^2 +10x + (10/2)^2 +21 -(10/2)^2[/tex]

And after aggrupate the terms we got:

[tex] f(x) = (x+5)^2 +21 -25 [/tex]

And finally we have:

[tex] f(X)= (x+5)^2 -4[/tex]

And for this case our vertex would be:

[tex] (h,k) = (-5,-4) [/tex]

Step-by-step explanation:

For this case we have the following equation given:

[tex] f(x) = x^2 +10x +21[/tex]

And we want to find a formula in terms in the vertex form given by:

[tex] f(x) = a(x-h)^2 +k[/tex]

And for this case we can begin completing the square like this:

[tex] f(x) = x^2 +10x + (10/2)^2 +21 -(10/2)^2[/tex]

And after aggrupate the terms we got:

[tex] f(x) = (x+5)^2 +21 -25 [/tex]

And finally we have:

[tex] f(X)= (x+5)^2 -4[/tex]

And for this case our vertex would be:

[tex] (h,k) = (-5,-4) [/tex]

Answer:

E[X]= [tex]2 + 3 e^{(-2/3)[/tex]

Step-by-step explanation:

The objective of this question is to determine E[X].

T is defined (0,infinity)

X=max(c,T)

where; c=constant

E[X]=c+function (c,infinity) Sf(t)dt

E[X] =[tex]e^{-t/3[/tex]

E[X]=2+function (2,infinity)[tex]e^{-t/3[/tex]dt

E[X] =[tex](2+e^{-t/3})/(1/3)[/tex] function (2,infinity)

E[X]= [tex]2 + 3 e^{(-2/3)[/tex]

If X = T   if T ≥ 2 and X = 2    if 0 ≤ T < 2,

So Since T is  exponentially distributed with mean 3,  the density function of T is  [tex]f(t) = (1/3)e^{(-t/3)[/tex]

Answer:

d.

Step-by-step explanation:

x^2 because their is no other x^2

2x because their is no more x.

-7+1 equals -6

Answer:

D

Step-by-step explanation:

(f + g)(x) means that you add the two functions together, which results in (f + g)(x) = 2x + 1 + x² - 7 = D) x² + 2x - 6. Hope this helps!

Answer:

Step-by-step explanation:

Hi Sorry this took so long!

1. True

A=hbb /2 or Half of Base times Height.

2.False it would be 63

A= b * h

3.True

A=a+b/2 * h

Hope this helps!

Answer:

g(x) = 4x - 1

Step-by-step explanation:

We have that:

[tex]g(x) = ax + b[/tex]

So

[tex]g(2t) = a*(2t) + b[/tex]

Equaling both sides:

[tex]g(2t) = 8t - 1[/tex]

[tex]a*(2t) + b = 8t - 1[/tex]

b = -1.

And

[tex]2a = 8[/tex]

[tex]a = \frac{8}{2}[/tex]

[tex]a = 4[/tex]

Then

g(x) = 4x - 1

Answer:

I'm pretty sure it would be B; go 2 units to the right and 12 units up.

Step-by-step explanation:

the question is asking for the percentage that got it right not the number of letters in the word, and 9 is the number of letters, and 12 is the number that got it right.

The correct data for 2 in coordinate grid will be from the origin, go 9units to the right and 12units up.

How to locate a point on graph?

To locate a point having coordinate (x,y) in graph, we have to go x direction right or left depending on the sign of x-coordinate(for right +,for left -), then we have to go y direction up or down depending on the sign of y-coordinate(for up +,for down -).

The graph is done by taking Number of letters in the word in x axis and Percentage of students who spelled the word correctly in y axis.

According to the table, it is clear that for data 2 Number of letters in the word is 9. so x=9

And Percentage of students who spelled the word correctly is 12

so y=12

So the coordinate of the point for data 2 is (9,12)

To locate the point (9,12) in coordinate grid we have to go 9units to the right in x axis and then we have to go 12units up in y axis direction.

Therefore The correct data for 2 in coordinate grid will be from the origin, go 9units to the right and 12units up.

Learn more about the location of point in graph

here: https://brainly.com/question/26865

#SPJ2

Answer:

X = 9

Step-by-step explanation:

1. Subtract 72 from both sides.

24x = 216

2. Divide 24 on both sides

x = 9

Answer:

X = 9

Step-by-step explanation:

We have to separate the like terms

72 + 24x = 288

24x = 288 - 72

24x = 216

We then divide both sides by 24

X = 9

Step-by-step explanation:

4x - 12 < 16 + 8x

Bringing like terms on one side

-12 - 16 < 8x - 4x

-28 < 4x

-28/4 < x

-7 < x

Answer:

The minimum number of widgets for the company to earn more than 50 dollars = 104 widgets.

Step-by-step explanation:

Complete Question

Inequality

Imagine the polynomial function shown represents the profits, in y dollars, earned by the production of x widgets.

y = -0.04x² + 40x - 3600

What is the minimum number of widgets for the company to earn more than 50 dollars?

Solution

For the profit to be more than 50

y > 50

-0.04x² + 40x - 3600 > 50

-0.04x² + 40x - 3650 > 0

0.04x² - 40x + 3650 < 0

(x - 898.4) (x - 101.6) < 0

Using the inequality table to obtain the required solution to this inequality

Eqn | x < 101.6 | 101.6 < x < 898.4 | x > 898.4

(x - 898.4) | -ve | - ve | + ve

(x - 101.6) | -ve | + ve | + ve

(x-898.4)(x-101.6) | +ve | - ve | +ve

Hence, the inequality that satisfies the equation of (x - 898.4) (x - 101.6) < 0, that is, negative, is 101.6 < x < 898.4.

And from this range, the minimum number of widgets for the company to earn more than 50 dollars = 102 widgets.

But 102 widgets give a profit of 13 dollars, 103 widgets give a profit of 47 dollars and it is until 104 widgets that the profits exceed 50 dollars truly.

Hope this Helps!!!

Answer:4

Step-by-step explanation:

Answer:

a = 4

Step-by-step explanation:

Multiply by 2 on each side

6a = 24

a = 4

Answer:

All parallelograms are squares

Step-by-step explanation:

Reasoning:

You can have a parallelogram with side lengths, i dont know, 5 and 3, right? That isn't a square :)

Answer:

-399

Step-by-step explanation:

21=b/-19

b=21 x -19

b=-399

Answer:

-399

explanation

b=21×-19

b=-399

Answer:

The test statistic Z = 1.844 < 1.96 at 0.05 level of significance

Null hypothesis is accepted

Yes he is right

The manager claims that at least 95 % probability that the plant is operating properly

Step-by-step explanation:

Explanation:-

Given data Population mean

                                           μ     = 885 tons /day

Given random sample size

                                          n = 60

mean of the sample

                                        x⁻  = 875 tons/day

The standard deviation of the Population

                                      σ = 42 tons/day

Null hypothesis:- H₀: The manager claims that at least 95 % probability that the plant is operating properly

Alternative Hypothesis :H₁: The manager do not claims that at least 95 % probability that the plant is operating properly

Level of significance =  0.05

The test statistic

 [tex]Z = \frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }[/tex]

[tex]Z = \frac{875 -885}{\frac{42}{\sqrt{60} } }[/tex]

[tex]Z = \frac{-10}{5.422} = -1.844[/tex]

|Z| = |-1.844| = 1.844

The tabulated value

                         [tex]Z_{\frac{0.05}{2} } = Z_{0.025} = 1.96[/tex]

The calculated value Z = 1.844 < 1.96 at 0.05 level of significance

Null hypothesis is accepted

Conclusion:-

The manager claims that at least 95 % probability that the plant is operating properly

Answer:

0.136m

This is because if you draw a diagram, and label all the sides of the triangle (opp, hyp, adj), the adjacent angle is 3m. You can now use the sine rule to find the hypotenuse (length of ladder) by doing: cos 20= 3/h. You divide cos(20) by 3 and you get the answer of 0.13602m

Answer:

Step-by-step explanation:

Given:-

- The following system of equations is given:

                       [tex]6x_1 - 6x_2 -4x_3 = 0\\\\x_1 - 7x_2 -6x_3 = 0\\\\x_1 - 5x_2 -nx_3 = 0\\[/tex]

Solution:-

- The matrix equation consists of coefficient matrix "A" and a variable matrix " x ". These two matrices undergo multiplication to yield a solution column vector "b".

- The matrix A, is a symmetrical square matrix with its elements representing the coefficients of each variable as follows:

            [tex]A = \left[\begin{array}{ccc}a_1_1&a_1_2&a_1_3\\a_2_1&a_2_2&a_2_3\\a_3_1&a_3_2&a_3_3\end{array}\right][/tex]

- Where the elements first subscript denotes the equation number and second subscript denotes the variable number.

             [tex]A = \left[\begin{array}{ccc}6&-6&-4\\1&-7&-6\\1&5&n\end{array}\right][/tex]

- Similarly, the variable matrix " X " is a column vector that lists all the variables in the the system of equations in a ascending order.

             [tex]X = \left[\begin{array}{c}x_1&x_2&x_3\end{array}\right][/tex]

- The solution vector " b " is the corresponding solution or any number written on the right hand side of the equals to sign " = " :

              [tex]b = \left[\begin{array}{c}0&2&-2\end{array}\right][/tex]

- Now, we can express the given system in the asked format:

            [tex]A*X = b\\\\\left[\begin{array}{ccc}6&-6&-4\\1&-7&-6\\1&5&n\end{array}\right]*\left[\begin{array}{c}x_1&x_2&x_3\end{array}\right] = \left[\begin{array}{c}0&2&-2\end{array}\right][/tex]

- The augmented matrix is a matrix that combines the coefficient matrix " A " and the solution vector " b ". A solution vector "b" as an extra column to the coefficient matrix:

            [tex][ A | b ]\\\\ \left[\begin{array}{ccccc}6&-6&-4&|&0\\1&-7&-6&|&2\\1&5&n&|&-2\end{array}\right][/tex]

- Now we will perform row reduction operation such that the system is consistent and has infinite number of solution.

- Row operation: R3 - R2 & R1/6

            [tex]\left[\begin{array}{ccccc}1&-1&-\frac{2}{3} &|&0\\1&-7&-6&|&2\\0&12&n+6&|&-4\end{array}\right][/tex]  

- Row operation: R2 - R1 & R3 / 12

            [tex]\left[\begin{array}{ccccc}1&-1&-\frac{2}{3} &|&0\\0&-6&-\frac{16}{3} &|&2\\0&1&\frac{n+6}{12} &|&-\frac{1}{3}\end{array}\right][/tex]

- Row operation: R2 / 6

           [tex]\left[\begin{array}{ccccc}1&-1&-\frac{2}{3} &|&0\\0&-1&-\frac{8}{9} &|&\frac{1}{3} \\0&1&\frac{n+6}{12} &|&-\frac{1}{3}\end{array}\right][/tex]

For the above system to be consistent and have infinite many solution then the coefficient of " x3 " for the 2nd and 3rd row must be equal:

           [tex]-x_2 - ( \frac{n+6}{12})*x_3 = \frac{1}{3}[/tex]

           [tex]-x_2 - ( \frac{8}{9})*x_3 = \frac{1}{3}[/tex]

The coefficient of " x_3 " must be equal:

           [tex]( \frac{n+6}{12}) = \frac{8}{9} \\\\\\\n = \frac{14}{3}[/tex]

- The augmented matrix in reduced form becomes:

           [tex]\left[\begin{array}{ccccc}1&-1&-\frac{2}{3} &|&0\\0&1&\frac{8}{9} &|&-\frac{1}{3} \\0&0&0 &|&0\end{array}\right][/tex]

Answer: Rank = Number of non-zero rows = 2

- The number of linearly independent rows are equal to the rank of the augmented matrix.

Hence,

Answer: Number of linearly independent rows = 2

Row operation: R1 + R2

             [tex]\left[\begin{array}{ccccc}1&0&\frac{2}{9} &|&-\frac{1}{3} \\0&1&\frac{8}{9} &|&-\frac{1}{3} \\0&0&0 &|&0\end{array}\right][/tex]

- The variable "x_3" will take any arbitrary value for which the solution holds infinitely many solutions.

           [tex]x_2 + \frac{8}{9}*x_3 = -\frac{1}{3} \\\\x_2 = - ( \frac{8}{9}*x_3 + \frac{1}{3} )\\\\x_1 + \frac{2}{9}*x_3 = -\frac{1}{3} \\\\x_1 = - ( \frac{2}{9}*x_3 + \frac{1}{3} )\\[/tex]

- Taking x_3 = α:

Answers:

           [tex]x_1 = -\frac{1}{3} + \frac{2}{9} \alpha \\\\x_2 = -\frac{1}{3} + \frac{8}{9} \alpha[/tex]

Answer:

7719

Step-by-step explanation:

2,573*3=7719

Answer:

[tex] \boxed{C. \: 7,719} [/tex]

Step-by-step explanation:

Amount saved by Kate's family last year = 2,573 pennies

Amount saved by Zoe's family last year = 3 × Amount saved by Kate's family last year

= 3 × 2,573

= 7,719 pennies

Answer:

26.39

Step-by-step explanation:

sin B = 4/9

B = inverse sin 4/9 = 26.387

Answer:

La ecuación química necesita ser equilibrada para que siga la ley de conservación de la masa.

Step-by-step explanation:

The above questions answer is 8 and 14

Answer:

r = sqrt of 5 or 2.2

Step-by-step explanation:

(1)²+(2)²=r²

5 = r²

r = sqrt of 5 or 2.2

Answer:

The 95% confidence interval for the standard deviation of the diameter is (0.0014; 0.0036).

Step-by-step explanation:

We have to calculate a confidence interval for the standard deviation.

The confidence level is 95%.

The size of the sample is n=10.

The sample standard deviation is s=0.002.

The lower limit is calculated as:

[tex]LL=s\sqrt{\dfrac{n-1}{\chi_{(1-\alpha)/2;n-1}}}\\\\\\LL=0.002\sqrt{\dfrac{10-1}{19.02}}=0.002\sqrt{0.473}=0.002*0.688=0.0014[/tex]

[tex]UL=s\sqrt{\dfrac{n-1}{\chi_{\alpha/2;n-1}}}\\\\\\UL=0.002\sqrt{\dfrac{9}{2.7}}=0.002\sqrt{3.33}=0.002*1.826=0.0036[/tex]

The 95% confidence interval for the standard deviation of the diameter is (0.0014; 0.0036).

Answer:

a) 0.0065 = 0.65% probability of receiving no emails during an hour.

b) 0.1212 = 12.12% probability of receiving at least three emails during an hour

c) The expected number of emails received during 15 minutes is 1.2604.

d) 0.2835 = 28.35% probability that no emails are received during 15 minutes

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given time interval.

In this question.

121 emails per day.

A day has 24 hours, so per hour, 121/24 = 5.0417, which means that [tex]\mu = 5.0417n[/tex], in which n is the number of hours.

A. What is the probability of receiving no emails during an hour?

n = 1, so [tex]\mu = 5.0417[/tex]

This is P(X = 0).

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-5.0417}*(5.0417)^{0}}{(0)!} = 0.0065[/tex]

0.0065 = 0.65% probability of receiving no emails during an hour

B. What is the probability of receiving at least three emails during an hour?

Either you receive less than three emails during an hour, or you receive at least 3. The sum of the probabilities of these events is decimal 1. So

[tex]P(X < 3) + P(X \geq 3) = 1[/tex]

We want [tex]P(X \geq 3)[/tex]

Then

[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]

In which

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-5.0417}*(5.0417)^{0}}{(0)!} = 0.0065[/tex]

[tex]P(X = 1) = \frac{e^{-5.0417}*(5.0417)^{1}}{(1)!} = 0.0326[/tex]

[tex]P(X = 2) = \frac{e^{-5.0417}*(5.0417)^{2}}{(2)!} = 0.0821[/tex]

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0065 + 0.0326 + 0.0821 = 0.1212[/tex]

0.1212 = 12.12% probability of receiving at least three emails during an hour

C. What is the expected number of emails received during 15 minutes?

15 minutes is a fourth of an hour, so n = 1/4 and [tex]\mu = \frac{5.0417}{4} = 1.2604[/tex]

The expected number of emails received during 15 minutes is 1.2604.

D. What is the probability that no emails are received during 15 minutes?

[tex]P(X = 0) = \frac{e^{-1.2604}*(1.2604)^{0}}{(0)!} = 0.2835[/tex]

0.2835 = 28.35% probability that no emails are received during 15 minutes