The radii of Earth and Pluto are 6,371 kilometers and 1,161 kilometers, respectively.
URGENT
Approximately how many spheres the size of Pluto does it take to have the same volume as Earth?
A.121
B. 154
C. 165
D.176
E.189

Answer:

2. x = 11

3. x = 19

4. x = 23

5. x = 6

6. x = 10

Step-by-step explanation:

2. x + 12 =23

x = 23 - 12

x = 11

3. x - 6 = 13

x = 13 + 6

x = 19

4. x - 9 = 14

x = 14 + 9

x = 23

5. 2x = 12

x = 12/2

x = 6

6. 3x = 30

x = 30/3

x = 10

Answer:

5.6

Step-by-step explanation:

We want to find the value of x, which is part of the segment that includes the length 10.

We need to use Power of Points, one property of which essentially says that if we have two intersecting chords such that they are each cut into two parts to make a and b, and c and d, then ab = cd (see attachment).

Here, we can say that a = 10, b = x, c = 7, and d = 8. Plug these in:

ab = cd

10 * x = 7 * 8

10x = 56

x = 56/10 = 5.6

The answer is 5.6.

Each diagonal has two parts (a, b, c, and d).

The formula is ab = cd

We have the values:

a = 10

b = x

c = 8

d = 7

Put these in the formula:

10x = (8)(7)

Solve for x.

10x = (8)(7)

10x = 56

10x/10 = 56/10

x = 5.6

Therefore, the answer is x = 5.6

Best of Luck!

Answer:

Step-by-step explanation:

Answer:

14000

Step-by-step explanation:

A year he contributes :10/100 × 80000= 8000

Then his employer pays 0.75 × 8000= 6000

The total money contributed to is

401k is = 8000 + 6000 = 14000

Answer:

Step-by-step explanation:

If we let c and p represent the cups of cheese and plates of nachos, we have ...

  c = 2/3p . . . . . each plate of nachos requires 2/3 cups of cheese

Solving for p, we find ...

  (3/2)c = p . . . . . multiply by 3/2

Then for 5 cups of cheese, we have ...

  (3/2)(5) = p = 15/2 = 7 1/2 . . . . plates of nachos

5 cups of cheese will make 7 full plates of nachos.

__

For 9 plates of nachos, we need ...

  c = 2/3(9) = 6 . . . . . . cups of cheese

Since we have 5 cups of cheese, we need 1 more cup of cheese to make 9 plates of nachos.

Answer:

slope intercept form y = m x +C

                                [tex]y = \frac{4x}{3} -\frac{40}{3}[/tex]

Step-by-step explanation:

step(i):-

Given two points are A  (7,-4) and B(-1,2)

Slope of two lines formula

 [tex]m= \frac{y_{2} -y_{1} }{x_{2} -x_{1} } = \frac{-1-7}{2-(-4)} =\frac{-8}{6} = \frac{4}{3}[/tex]

Step(ii):-

The equation of the straight line passing through the two points

                                      y-y₁ = m(x-x₁)

Let (x₁ , y₁) = (7,-4)

                                    y - (-4) =[tex]\frac{4}{3}[/tex] (x-7)

On cross multiplication , we get

                                    3(y+4) = 4(x-7)

                                    3 y +12 = 4 x -28

subtract '12' on both sides , we get

                                    3 y = 4 x -28 -12

                                     3 y = 4 x - 40

Dividing '3' on both sides, we get

Now slope intercept form y = m x +C

                                      [tex]y = \frac{4x}{3} -\frac{40}{3}[/tex]

Final answer:-

slope intercept form y = m x +C

                                [tex]y = \frac{4x}{3} -\frac{40}{3}[/tex]

Answer:

29 miles were used per gallon

Step-by-step explanation:

257 / 9 = 28.555..

We can round 28.555 to about 29.

So John got 29 miles per gallon.

Answer:

-3n+31

Step-by-step explanation:

ok

The nth term of the sequence 28, 25 ,22, 19, 16 is aₙ=31-3n.

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

The given sequence is 28, 25 ,22, 19, 16

Twenty eight comma twenty five comma twenty two comma nineteen comma sixteen.

The sequence is an arithmetic sequence as there is a common difference between consecutive terms.

The first term is a=28

Common difference =25-28=-3

aₙ=28+(n-1)(-3)

aₙ=28-(n-1)(3)

aₙ=28-3n+3

aₙ=31-3n

Hence the nth term of the sequence 28, 25 ,22, 19, 16 is aₙ=31-3n.

To learn more on Sequence click:

https://brainly.com/question/21961097

#SPJ2

Answer:

The 95% confidence interval for the overall noncompliance proportion is (0.0387, 0.1169).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 180, \pi = \frac{14}{180} = 0.0778[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.0778 - 1.96\sqrt{\frac{0.0778*0.9222}{180}} = 0.0387[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.0778 + 1.96\sqrt{\frac{0.0778*0.9222}{180}} = 0.1169[/tex]

The 95% confidence interval for the overall noncompliance proportion is (0.0387, 0.1169).

Answer:

the number is 65.

Step-by-step explanation:

n-16=49

n=65

Therefore, the number is 65.

Answer:

[tex] 75= 119 -1.96 \sigma[/tex]

[tex] \sigma = \frac{75-119}{-1.96}= 22.45[/tex]

And tha's equivalent to use this formula:

[tex] 163= 119 +1.96 \sigma[/tex]

[tex] \sigma = \frac{163-119}{1.96}= 22.45[/tex]

Step-by-step explanation:

For this case the 95%of the values are between the following two values:

(75 , 163)

And for this case we know that the variable of interest X "length of a movie" follows a normal distribution:

[tex] X \sim N( \mu, \sigma)[/tex]

We can estimate the true mean with the following formula:

[tex]\mu = \frac{75+163}{2}= 119[/tex]

Now we know that in the normal standard distribution we know that we have 95% of the values between 1.96 deviations from the mean. We can find the value of the deviation with this formula:

[tex] 75= 119 -1.96 \sigma[/tex]

[tex] \sigma = \frac{75-119}{-1.96}= 22.45[/tex]

And tha's equivalent to use this formula:

[tex] 163= 119 +1.96 \sigma[/tex]

[tex] \sigma = \frac{163-119}{1.96}= 22.45[/tex]

Answer:

Base price: $13.

Surcharge: $2 per additional pound.

Step-by-step explanation:

The base price can be considered a constant, while the surcharge is a function of the additional weight of the package, over 1 pound.

Then, we can model this as a linear function, with additional weight as the independent variable.

[tex]f(x)=b+sx[/tex]

being b: base price, and s: surcharge for each additional pound.

The 7-pound package cost $25. The additional weigth in this case is 7-1=6 pounds.

The 22-pound package cost $55. The additional weigth is 21 pounds.

So we have the first point (6, 25):

[tex]f(6)=b+s(6)=25\\\\b=25-6s[/tex]

Then, for the second point (21, 55) we have:

[tex]b=25-6s\\\\f(21)=(25-6s)+s(21)=55\\\\25+(21-6)s=55\\\\15s=55-25=30\\\\s=30/15=2\\\\\\b=25-6(2)=25-12=13[/tex]

Then, the prices are:

Base price: $13.

Surcharge: $2 per additional pound.

[tex]\dfrac{y+1}{y+2}+\dfrac{y+8}{y+9}=\dfrac{y+2}{y+3}+\dfrac{y+7}{y+8}[/tex]

Write all fractions in terms of a common denominator:

[tex]\dfrac{y+1}{y+2}=\dfrac{(y+1)(y+9)(y+3)(y+8)}{(y+2)(y+9)(y+3)(y+8)}[/tex]

[tex]\dfrac{y+8}{y+9}=\dfrac{(y+8)^2(y+2)(y+3)}{(y+2)(y+9)(y+3)(y+8)}[/tex]

[tex]\dfrac{y+2}{y+3}=\dfrac{(y+2)^2(y+9)(y+8)}{(y+2)(y+9)(y+3)(y+8)}[/tex]

[tex]\dfrac{y+7}{y+8}=\dfrac{(y+7)(y+2)(y+9)(y+3)}{(y+2)(y+9)(y+3)(y+8)}[/tex]

Then move all fractions to one side and simplify the numerator:

[tex]\dfrac{(y+1)(y+9)(y+3)(y+8)+(y+8)^2(y+2)(y+3)-(y+2)^2(y+9)(y+8)-(y+7)(y+2)(y+9)(y+3)}{(y+2)(y+9)(y+3)(y+8)}=0[/tex]

The numerator dictates when the fraction reduces to 0. The denominator can never be 0, so we know that y cannot take any of the values -2, -9, -3, nor -8.

So the equation reduces to

[tex](y+1)(y+9)(y+3)(y+8)+(y+8)^2(y+2)(y+3)-(y+2)^2(y+9)(y+8)-(y+7)(y+2)(y+9)(y+3)=0[/tex]

Expand the left side; you would end up with

[tex]-6(2y+11)=0[/tex]

[tex]2y+11=0[/tex]

[tex]2y=-11[/tex]

[tex]\implies\boxed{y=-\dfrac{11}2}[/tex]

Answer:

[tex] P=12000, r= 0.04, t=3[/tex]

And n=4 since the rate is compounded quarterly, so then replacing this info we got:

[tex] A = 12000 (1+ \frac{0.04}{4})^{4*3} = 13521.9[/tex]

So then Mario will have about $13521.9 after the 3 years with the rate of interest used.

Step-by-step explanation:

For this case we can use the formula for future value based on a compound interest given by:

[tex] A= P (1+ \frac{r}{n})^{nt}[/tex]

Where A represent the future value, P the present value or the inversion r is the rate of interest on fraction, n the number of times that the rate of interest is compounded in a year and t the number of years.

For this case we know this:

[tex] P=12000, r= 0.04, t=3[/tex]

And n=4 since the rate is compounded quarterly, so then replacing this info we got:

[tex] A = 12000 (1+ \frac{0.04}{4})^{4*3} = 13521.9[/tex]

So then Mario will have about $13521.9 after the 3 years with the rate of interest used.

Answer:

5.5

Step-by-step explanation:

5x-2.5+6x-3=_____(2x-1)

11x-5.5=5.5(2x-1)

11x-5.5=11x-5.5

Answer:

5.5

Step-by-step explanation:

Answer: log1= 1

not sure about Mk

Answer:

k*log_10M

Step-by-step explanation:

take the k and put it in front of the equation and it cannot be further simplified.

Answer:

It is

Step-by-step explanation:

Using Pythagoras 51^2 = 50^2 + b^2

b=10.0499  

Answer:

1.05 radians

Step-by-step explanation:

Given that Vanessa is skiing along a circular ski trail that has a radius of 2.5 km. She starts at the 3-o'clock position and travels in the Counter Clockwise direction.

She stops skiing when she is 1.244 km to the right and 2.169 km above the center of the ski trail.

This can be represented as (1.244, 2.169) on a circle of radius 2.5 km.

From the coordinate point (1.244, 2.169) derived, x=1.244 and y=2.169.

By the definition of tangent,

[tex]\tan \theta =\frac{y}{x} \\\\\tan \theta =\dfrac{2.169}{1.244}\\\\ \theta=\arctan \dfrac{2.169}{1.244}\\\\\\ \theta=1.05006[/tex]

Vanessa swept out approximately 1.05 radians since she started skiing.

Answer:

21/50

Step-by-step explanation:

Given that Jackson's sweets from last Halloween from last year was 42% chocolate, we can assume he had a total of 100 sweets.

Out of 100 sweets, 42 pieces are chocolate, so:

42/100

When simplifying this fraction into its simplest form, the most you can do is divide the numerator(top) and denominator(bottom) by 2.

Your result would be 21/50

Hope this helps!

Answer:

[tex]2\frac{4}{10}=\frac{24}{10}=\frac{12}{5}[/tex]

Step-by-step explanation:

Here we have a number in the ones place, 2, and a number in the tenths place, 4.

Here our whole number is 2, the numerator is 4, and it is in the tenths place, so our denominator will be 10

Our fraction becomes [tex]2\frac{4}{10}[/tex] which then turns into the improper fraction [tex]\frac{24}{10}[/tex] and then simplifying if needed becomes [tex]\frac{12}{5}[/tex] after dividing the fraction by 2

Answer:

126

Step-by-step explanation:

this is because you have 3 angles so its a triangle you have 360 degrees so 360 - 108 = 252 you need to divide it by 2 as there are 3 angles so you get 126 i hope it helps

Answer:

option A is your answer in my opinion.

Sry i am not sure

Answer:

Rewrite in standard form to find the center (h,k) and radius r.

Center: (−1,−2)

Radius: √6

Rewrite in standard form to find the center (h,k) and radius r.

Center: (3/2,6)

Radius: 11/2

Rewrite in standard form to find the center (h,k) and radius r.

Center: (3,−7)

Radius: 8

Rewrite in standard form to find the center (h,k) and radius r.

Center: (0,10)

Radius: 9

Rewrite in standard form to find the center (h,k) and radius r.

Center: (−4,−4)

Radius: 4√2

Answer:

146

Step-by-step explanation:

j=3 13 = 39

g=5 13 = 65

a=4 13 = 42

Answer:

156 sweets

Step-by-step explanation:

3+4+5=12

12/12 x 39 x 12/3=156 sweets

Answer:

Step-by-step explanation:

Given the equation model 4x+(-4) = -2x+8

To find the value of x, the following steps must be followed

[tex]4x+(-4) = -2x+8\\4x-4 = -2x+8\\subtracting\ 8\ from\ both\ sides\\4x-4-8=-2x+8-8\\4x-12=-2x\\4x+2x=12\\6x=12\\x=\frac{12}{6}\\ x = 2[/tex]

The value of x is 2

Question:

The model below represents 4x + (-4) = -2x + 8.

4 long green tiles and 4 square red tiles = 2 long red tiles and 8 square green tiles.

What is the value of x when solving the equation 4x + (-4) = -2x + 8 using the algebra tiles?

x = -4

x = -2

x = 2

x = 4

Answer:

x = 2

Step-by-step explanation:

Given

4x + (-4) = -2x + 8 which represents a model of coloured tiles of various lengths (shapes)

Required

Find x

To find x, we'll solve the expression 4x + (-4) = -2x + 8 using the knowledge of algebra.

4x + (-4) = -2x + 8

Open bracket

4x - 4 = -2x + 8

Collect like terms

4x + 2x = 4 + 8

Perform addition arithmetic operation on both sides of the equation

6x = 12

Multiply both sides by ⅙

⅙ * 6x = ⅙ * 12

x = 2

Hence, the value of x that satisfies the expression 4x + (-4) = -2x + 8 is 2

Answer:

[tex]\bar v = 60\,mph[/tex]

Step-by-step explanation:

The distance travelled by Lisa in the first four hours of her trip is:

[tex]\Delta s = \left(50\,mph)\cdot (4\,h)[/tex]

[tex]\Delta s = 200\,mi[/tex]

The distance remaining and her average speed are, respectively:

[tex]\Delta s_{R} = 440\,mi - 200\,mi[/tex]

[tex]\Delta s_{R} = 240\,mi[/tex]

[tex]\bar v = \frac{240\,mi}{4\,h}[/tex]

[tex]\bar v = 60\,mph[/tex]

Answer: 6.6

Step-by-step explanation:

We have two triangles. Find the hypothenuse of the first triangle to make it easier to solve the second triangle.

First triangle:

a = 6

b = 8

c = ?

Use pythagorean's theorem

[tex]c^2=a^2+b^2\\c=\sqrt{a^2+b^2}[/tex]

[tex]c=\sqrt{(6)^2+(8)^2}\\ c=\sqrt{36+64}\\ c=\sqrt{100}\\ c=10[/tex]

This hypothenuse is valid for both triangles. Having said this, we already have 2 sides of the second triangle; c and a. We need to find b.

[tex]c^2=a^2+b^2\\b^2=c^2-a^2\\b=\sqrt{c^2-a^2}[/tex]

[tex]b=\sqrt{(12)^2-(10)^2}\\ b=\sqrt{144-100}\\ b=\sqrt{44}\\ b=6.6[/tex]

Answer:

1/20 and 0.05 :)

Step-by-step explanation:

Answer:

[tex]5cm ^{3} [/tex]

Step-by-step explanation:

[tex]v = whl \\ = \frac{5}{2} \times \frac{4}{1} \times \frac{1}{2} \\ = \frac{20}{4} \\ = 5 {cm}^{3} [/tex]

Answer:

Option 4.

Step-by-step explanation:

The information is that the points G and H are the midpoints of ED and EF.

For example G will be  (5 + (-2))/ 2 , (4 - 0) / 2 which is  (1.5, 2).

If we calculate H it is (6.5, -3).

The answer is option 4.