Which shapes have the same volume as the given rectangular prism?

base area = 50 cm^2​

Answer:

c) Both receive the same push

Step-by-step explanation:

The buoyancy force is equal to the weight of the displaced fluid:

B = ρVg

where ρ is the density of the water, V is the volume of displaced water, and g is the acceleration due to gravity.

Since both spheres displace the same amount of water, they have equal buoyancy forces.

Answer:

12

Step-by-step explanation:

Given:

Let the number be x.

According to the question,

8(x-6)= 4 x

8 x-48=4 x

8 x-4 x= 48

4 x=48

x=48/4

x=12

Thank you!

Step-by-step explanation:

firstly suppose f(X) as y and later interchange it with x and solve it to get inverse function of x.

The inverse of the given function is [tex]f^{-1}(x)=\dfrac{x+4}{2}[/tex].

Important information:

We need to find the inverse of the given function.

Substitute [tex]f(x)=y[/tex].

[tex]y=2x-4[/tex]

Interchange [tex]x[/tex] and [tex]y[/tex].

[tex]x=2y-4[/tex]

Isolate [tex]y[/tex].

[tex]x+4=2y[/tex]

[tex]\dfrac{x+4}{2}=y[/tex]

Substitute [tex]y=f^{-1}(x)[/tex].

[tex]\dfrac{x+4}{2}=f^{-1}(x)[/tex]

Thus, the inverse of the given function is [tex]f^{-1}(x)=\dfrac{x+4}{2}[/tex].

Find out more about 'Inverse of a function' here:

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Answer:

we approach the issue by taking note of that a 2 x 2 matrix can either have 1 0r 2 pivot columns. If the matrix has no pivot columns then every entry in the matrix must be zero.

-> if our matrix has two pivot columns then : [tex]\left(\begin{array}{rr}-&*&0&-\end{array}\right)[/tex]

-> if our matrix has one pivot column then we have a choice to make. If the first column is pivot column then: [tex]\left(\begin{array}{rr}-&*&0&0\end{array}\right)[/tex]

->otherwise, if the pivot column is the second column then: [tex]\left(\begin{array}{rr}0&-&0&0\end{array}\right)[/tex]

Answer: 585 miles

Step-by-step explanation: 60 x 7 for the first 7 hours = 420 miles, then 3 x 55 for the last 3 hours = 165 add them together, 420+265 you get= 585

60 miles per hour x 7 hours = 420 miles

55 miles per hour x 3 hours = 165 miles

Total miles = 420 + 165 = 585 miles

Answer:

[tex]-\frac{10}{3}ft/s[/tex]

Step-by-step explanation:

We are given that

Height of man=5 foot

[tex]\frac{dy}{dt}=-10ft/s[/tex]

Height of street light=20ft

We have to find the rate of change of the length of his shadow when he is 25 ft form the street light.

ABE and CDE are similar triangle because all right triangles are similar.

[tex]\frac{20}{5}=\frac{x+y}{x}[/tex]

[tex]4=\frac{x+y}{x}[/tex]

[tex]4x=x+y[/tex]

[tex]4x-x=y[/tex]

[tex]3x=y[/tex]

[tex]3\frac{dx}{dt}=\frac{dy}{dt}[/tex]

[tex]\frac{dx}{dt}=\frac{1}{3}(-10)=-\frac{10}{3}ft/s=-\frac{10}{3}ft/s[/tex]

Hence, the rate of change of the length of his shadow when he is 25 ft from the street light=[tex]-\frac{10}{3}ft/s[/tex]

Answer:

(x+4) or (x-1)

Step-by-step explanation:

Do this by factoring out your equation. To do this, think about which two numbers multiply to be -4 but also add up to be 3 (the -4 came from multiplying the first value (the 1 that is attached to the [tex]x^{2}[/tex]) and the last value, which is -4. The 3 came from the middle term).

The two numbers you should have gotten are 4 and -1. Therefore, (x+4) and (x-1) are both of the binomials that could be your answer

Answer:

k = -21

Step-by-step explanation:

9/ (2k-3) = 4/(k+1)

Using cross products

9 * (k+1) = 4(2k-3)

Distribute

9k+9 = 8k -12

Subtract 8k from each side

9k-8k +9 = 8k-8k-12

k+9 = -12

Subtract 9 from each side

k+9-9 = -12-9

k = -21

Answer:

[tex]\huge\boxed{k=21}[/tex]

Step-by-step explanation:

[tex]\dfrac{9}{2k-3}=\dfrac{4}{k+1}[/tex]

First step:

Find domain.

We know: the denominator must be different than 0.

Therefore we have:

[tex]2k-3\neq0\ \wedge\ k+1[/tex]

[tex]2k-3\neq0\qquad\text{add 3 to both sides}\\2k\neq3\qquad\text{divide both sides by 2}\\\boxed{k\neq1.5}\\\\k+1\neq0\qquad\text{subtract 1 from both sides}\\\boxed{k\neq-1}\\\\\text{Domain:}\ x\in\mathbb{R}\backslash\{-1;\ 1.5\}[/tex]

Second step:

Solve for k.

[tex]\dfrac{9}{2k-3}=\dfrac{4}{k+1}\qquad\text{cross multiply}\\\\9(k+1)=4(2k-3)\qquad\text{use the distributive property}:\ a(b+c)=ab+ac\\\\(9)(k)+(9)(1)=(4)(2k)-(4)(3)\\\\9k+9=8k-12\qquad\text{subtract 9 from both sides}\\\\9k=8k-21\qquad\text{subtract}\ 8k\ \text{from both sides}\\\\\boxed{k=21}\in\text{Domain}[/tex]

Answer:

never intersect

Step-by-step explanation

parallel lines do not intersect and neither do parallel planes

Answer:

9/14

Step-by-step explanation:

3/7 + 50%×3/7 =

= 3/7 + 1/2×3/7

= 3/7 + 3/14

= 6/14 + 3/14

= 9/14

The required fraction which 50% grater than 3/7 is 9/14.

Fraction to determine that 50% grater than 3/7.

Fraction of the values is number represent in form of Numerator and denominator.

Here, fraction = 50% grater than 3/7
                     = 1.5 x 3/7
                    = 4.5/7
                     =  45/70
                     = 9/14

Thus, The required fraction which 50% grater than 3/7 is 9/14.

Learn more about fraction here:
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Answer:

Step-by-step explanation:

Cos θ = u*v    

             IuI *IvI

u * v = 7*(-1) + (-2)*2

       = -7 - 4

      = -11

IuI = [tex]\sqrt{7^{2}+(-2)^{2}}\\[/tex]

    = [tex]\sqrt{49+4}\\\\[/tex]

    = [tex]\sqrt{53}[/tex]

I vI = [tex]\sqrt{(-1)^{2}+2^{2}}\\[/tex]

     = [tex]\sqrt{1+4}\\\\[/tex]

      = [tex]\sqrt{5}\\[/tex]

Cos θ = [tex]\frac{-11}{\sqrt{53}*\sqrt{5} } \\\\[/tex]

          = [tex]\frac{-11}{16.28}\\\\[/tex]

   Cos θ = -0.68

θ = 132.5°

Answer:

b. 9

Just use PEMDAS

Answer:

0.3811 = 38.11% probability that he weighs between 170 and 220 pounds.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 200, \sigma = 50[/tex]

Find the probability that he weighs between 170 and 220 pounds.

This is the pvalue of Z when X = 220 subtracted by the pvalue of Z when X = 170.

X = 220

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{220 - 200}{50}[/tex]

[tex]Z = 0.4[/tex]

[tex]Z = 0.4[/tex] has a pvalue of 0.6554

X = 170

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{170 - 200}{50}[/tex]

[tex]Z = -0.6[/tex]

[tex]Z = -0.6[/tex] has a pvalue of 0.2743

0.6554 - 0.2743 = 0.3811

0.3811 = 38.11% probability that he weighs between 170 and 220 pounds.

Answer:

1.3 in

Step-by-step explanation:

If 0.75 is 0.55 less than the average amount, the answer must be 0.75 + 0.55 = 1.3 inches.

Answer:

1.3 in

Step-by-step explanation:

Answer:

x = 45 degrees

Step-by-step explanation:

The measure of exterior angles is equal to the sum of non-adjacent interior angles

=> 2x = x+45

=> 2x-x = 45

=> x = 45 degrees

Answer:

45 degrees.

Step-by-step explanation:

The exterior angle = sum of the 2 opposite interior angles.

2x =  x + 45

2x - x = 45

x = 45.

Answer:

top left

Step-by-step explanation:

Consider finding points on the graph using the equation.

x = 0 : f(0) = [tex]0.5^{0}[/tex] + 4 = 1 + 4 = 5 ← y- intercept

Since y- intercept is 5, this excludes the lower 2 graphs, which have y- intercepts of 1

x = 1 : f(1) = [tex]0.5^{1}[/tex] + 4 = 0.5 + 4 = 4.5 ⇒ (1, 4.5 )

x = - 1 : f(- 1) = [tex]0.5^{-1}[/tex] + 4 = [tex]\frac{1}{0.5}[/tex] + 4 = 2 + 4 = 6 ⇒ (1, 6 )

These points lie on the top left graph

Answer:

Step-by-step explanation:

First, we need to divide the amount into 2 equal parts:

$819/2 = $414.50

Now, because they spent $183 more on textbooks, we add half of that to $414.50.

$414.50 + $91.50 = $506

$414.50 - $91.50 = $323

To make sure that the amount spent on textbooks is $183 more than the amount spent on course materials and computers, we need to add $183 to $323. If we get $506, our answer is correct.

$323 + $183 = $506 ✅

Answer:

4x-3y

Step-by-step explanation:

Answer:

s-7<3

in order to find the value adding 7 on both sides

s-7+7<3+7

s<10

Step-by-step explanation:

i hope this will help you :)

Answer:

s-7<3

in order to find the value adding 7 on both sides

s-7+7<3+7

s<10

Step-by-step explanation:

Answer:

12 m

Step-by-step explanation:

Given that the design, ABCD, was dilated to get a photocopy, EFGH, a scale factor or ratio was multiplied by the original lengths of the design to get the new measurement of the photocopy.

Thus, we are given the ratio, CD:GH = 2:3.

This means, any of the corresponding lengths of both figures would be in that same ratio.

Using the ratio of the design to the photocopy, 2:3, we can find the length of side EH of the photocopy.

The corresponding side of EH in the design is AD = 8m. Thus, AD to EH = ⅔

[tex] \frac{AD}{EH} = \frac{2}{3} [/tex]

[tex] \frac{8}{EH} = \frac{2}{3} [/tex]

Cross multiply

[tex] 3*8 = 2*EH [/tex]

[tex] 24 = 2*EH [/tex]

Divide both sides by 2 to make EH the subject of formula

[tex] \frac{24}{2} = \frac{2*EH}{2} [/tex]

[tex] 12 = EH [/tex]

The length of side EH = 12 m

Answer:

Laura tiene 15 años mientras que su madre tiene 35 años.

Step-by-step explanation:

Deje que la edad de Laura sea L.

Deje que la edad de su madre sea m.

Tiene 3/7 de la edad de su madre:

L = 3 m / 7

En 5 años, la edad de su madre será el doble de su edad:

(m + 5) = 2 (L + 5)

m + 5 = 2L + 10

m - 2L = 5

Pon el valor de L:

m - 2 (3 m / 7) = 5

m - 6 m / 7 = 5

Multiplica por 7:

7m - 6m = 35

m = 35 años

=> L = 3 * 35/7 = 15 años

Laura tiene 15 años mientras que su madre tiene 35 años.

Answer:

Step-by-step explanation:

Hello,

[tex]x = (fof^{-1})(x)=f(f^{-1}(x))=\dfrac{-2}{f^{-1}(x)}-1\\\\<=>f^{-1}(x)(x+1)=-2\\\\<=> f^{-1}(x)=\dfrac{-2}{x+1}[/tex]

and this is g(x)

so they are inverses

Hope this helps

Answer:

when a number is divisible by 9, then the number is divisible by 3.

Step-by-step explanation:

They tell us "When a number is divisible by 9, the number is divisible by 3" we could change it by:

when a number is divisible by 9, then the number is divisible by 3.

Which makes sense because the number 9 is a multiple of the number 3, which means that the 9 can be divided by 3, therefore, if the number can be divided by 9, in the same way it can be divided by 3 .

Answer:

a

Step-by-step explanation:

Answer: a) 503.2m

b) 621.6m

Step-by-step explanation:

The diagram representing the scenario is shown in the attached photo.

A represents her starting point.

CD = x = how far east she is from her starting point

BC = y = how far south she is from her starting point

Angle BAC = 180 - 129 = 51°

Angle ACD = angle BAC = 51° because they are alternate angles

To determine x, we would apply the cosine trigonometric ratio

Cos 51 = x /800

x = 800Cos51 = 800 × 0.629 = 503.2m

To determine y, we would apply the sine trigonometric ratio

Sin 51 = y /800

y = 800Sin51 = 800 × 0.777 = 621.6m

Answer:

3/2

Step-by-step explanation:

We can find the slope of this line by using two points

(1,-3) and (3,0)

m = (y2-y1)/(x2-x1)

    = (0- -3)/(3 -1)

    = (0+3)/(3-1)

    = 3/2

Answer:

$11,450

Step-by-step explanation:

thats the median price according to Google

Answer:

9,000 inches^3

Step-by-step explanation:

The first part is 20 x 20 x 20, which equals 8,000

The second part is 10 x 10 x 10, which is 1,000

1,000 + 8,000 = 9,000

Answer:

6

Step-by-step explanation:

nerd physics

Answer:

(a) [tex]\frac{1}{13}[/tex]

(b) [tex]\frac{3}{13}[/tex]

(c) [tex]\frac{10}{13}[/tex]

Step-by-step explanation:

The probability of an event B occurring is given by;

P(B) =  [tex]\frac{n(E)}{n(S)}[/tex]

Where;

P(B) = probability of the event B

n(E) = number of favourable outcomes

n(S) = total number of events in the sampled space.

From the question, the card is drawn randomly from a standard 52-card deck. The probability of

(a) drawing a "king" card is analyzed as follows.

Let the event of drawing the "king" card be B.

In a standard 52-card deck, the number of cards that are of type king is 4. i.e 1 from the diamond pack, 1 from the spade pack, 1 from the heart pack and 1 from the club pack.

Therefore, the number of favourable outcomes is 4, while the total number of events in the sampled space is 52.

The probability of drawing a "king" card, P(B) is;

P(B) = [tex]\frac{4}{52}[/tex]

P(B) = [tex]\frac{1}{13}[/tex]

(b) drawing a "face" card is analyzed as follows.

Let the event of drawing the "face" card be B.

In a standard 52-card deck, a face card can either be a Jack, Queen or a King. There are 4 Jack cards, 4 Queen cards and 4 King cards in the deck.  The number of cards that are of type face is 12.

Therefore, the number of favourable outcomes is 12, while the total number of events in the sampled space is 52.

The probability of drawing a "face" card, P(B) is;

P(B) = [tex]\frac{12}{52}[/tex]

P(B) = [tex]\frac{3}{13}[/tex]

(c) drawing a card that is not a "face" is analyzed as follows;

The sum of the probability of drawing a face card and the probability of not drawing a face card is always 1.

Let the event of drawing a "face" card be B and the event of not drawing a "face" card be C.

P(B) + P(C) = 1

P(C) = 1 - P(B)

From (b) above, the P(B) = [tex]\frac{3}{13}[/tex]

Therefore,

P(C) = 1 - [tex]\frac{3}{13}[/tex]

P(C) = [tex]\frac{10}{13}[/tex]