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Answer:

Rock D.

Step-by-step explanation:

We can assume that the force that the catapult does is always the same.

So, here we need to remember Newton's second law:

F = m*a

force equals mass times acceleration.

Where acceleration is the rate of change of the velocity.

So, if we want the rock to hit closer to the catapult, the rock must be less accelerated than rock B.

So, we can rewrite:

a = F/m

So, as larger is the mass of the rock, smaller will be the acceleration of the rock after it leaves the catapult (because the mass is in the denominator). So if we want to have a smaller acceleration, we need to choose a rock with a larger mass than rock B.

Assuming that the mass depends on the size, the only one that has a mass larger than rock B is rock D.

So we can assume that rock D is the correct option.

Answer:

AC = 28

Step-by-step explanation:

Ok, we know that:

Points A, B, and C are collinear.

Point B is between A and C.

We want to find the length AC (distance between A and C), if we know that:

AB = 16

BC = 12

Ok, knowing that B is between the other points, we know that:

AB + BC

defines the total length of the segment that connects the 3 points.

Thus, if we define this segment as a length, we only use the endpoints, A and C.

Then we have that:

AB + BC = AC

now we can solve this:

16 + 12 = AC

28 = AC

Answer:

8,-9,9

Step-by-step explanation:

9514 1404 393

Answer:

  10

Step-by-step explanation:

Possible tower heights using 3 blocks are ...

  {9, 10, 11, 12, 14, 15, 16, 19, 20, 24}

There are 10 different heights possible.

_____

Each block can be used 1, 2, or 3 times.

Using a 3 in block as the smallest, we have ...

  3+3+3 = 9

  3+3+4 = 10

  3+3+8 = 14

  3+4+4 = 11

  3+4+8 = 15

  3+8+8 = 19

Using a 4-in block as the smallest, we have ...

  4+4+4 =12

  4+4+8 = 16

  4+8+8 = 20

And ...

  8+8+8 = 24

Answer:

[tex]n = (\frac{1.96\sqrt{\pi(1-\pi)}}{M})^2[/tex]

The sample size needed is n(if a decimal number, round up to the next integer), considering the estimate of the proportion [tex]\pi[/tex](if no previous estimate use 0.5) and M is the desired margin of error.

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 z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is of:

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

95% confidence level

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

Needed sample size:

The needed sample size is n. We have that:

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

[tex]M = 1.96\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]\sqrt{n}M = 1.96\sqrt{\pi(1-\pi)}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{\pi(1-\pi)}}{M}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96\sqrt{\pi(1-\pi)}}{M})^2[/tex]

[tex]n = (\frac{1.96\sqrt{\pi(1-\pi)}}{M})^2[/tex]

The sample size needed is n(if a decimal number, round up to the next integer), considering the estimate of the proportion [tex]\pi[/tex](if no previous estimate use 0.5) and M is the desired margin of error.

Answer:

b. x^4 varies directly as y.

Step-by-step explanation:

x^4 = 7×y

x^4 is proportional to y.

Answer:

70910 not sure

Step-by-step explanation:

70.91 x 10 = 709.1 70.91 x 100 = 7,091 70.91 x 1,000 =

Answer:

Step-by-step explanation:

We see the data is not uniform. One of the prices is very high compared to the others. Since there is an outlier, the median is the best measure of central tendency.

This is the second option.

Answer:

3,872.316

Step-by-step explanation:

Answer:

to nearest hundreds it would be: 3,900

Step-by-step explanation:

872 it closer to 900 than 800

Answer:

5

Step-by-step explanation:

(5/6) / (1/6) = 5

Answer:

5 batches

Step-by-step explanation:

Divide yesterday's batches by the usual.

(5/6)/(1/6) = 5

Since it only takes 1/6 to make a batch and they used 5x that we know they made 5 batches.

Answer:

22 kg

Step-by-step explanation:

1297 cans * (17 grams)/(1 can) * (1 kg)/(1000 g) = 22.049 kg

Answer: 22 kg

Answer:

the answer is B

Step-by-step explanation:

Answer:

The answer is below

Step-by-step explanation:

12 inches = 1 ft.

6 inches = 6 inches * (1 ft./12 inches) = 0.5 ft.

Therefore the diameter of the cast iron (D) = 6 inches = 0.5 ft.

The area of cast iron (A) = πD²/4 = π(0.5)²/4 = 0.196 ft²

The velocity (V) = 6 ft./s, the acceleration due to gravity (g) = 32.2 ft./s²

ε/D = 0.0004 ft./ 0.5 ft. = 0.0008

Using the moody chart, find the line ε/D = 0.0008 and determine the point of intersection with the vertical line R = 2.7 * 10⁵. Hence we get f = 0.02.

The head loss (h) is:

[tex]h_f=f*\frac{L}{d}* \frac{V^2}{2g}=0.02*\frac{200\ ft}{0.5\ ft} *\frac{(6\ ft/s)^2}{2*32.2\ ft/s^2}=4.5\ ft[/tex]

The pressure drop (Δp) is:

Δp = ρg[tex]h_f[/tex] = [tex](62.4\ lbf/ft^3)(4.5\ ft)= 280\ lbf/ft^2[/tex]

Answer:

x = 14

Step-by-step explanation:

Please note, the word trapezium is a synonym for the word trapezoid.

This problem gives one the area of the trapezoid, a well as one of the measurements of a base and the height of the figure. One is asked to find the length of the other base. This can be done by using the formula to find the area of a trapezoid. This formula is the following,

[tex]A=(h)(\frac{b_1+b_2}{2})[/tex]

Where (A) represents the area of a trapezoid, ([tex]b_1[/tex]) and ([tex]b_2[/tex]) represents the bases and (h) represents the height. Substitute in the given values and solve for the unknown base.

[tex]b_1=7\\h=6\\A=84[/tex]

[tex]A=(h)(\frac{b_1+b_2}{2})\\[/tex]

Substitute,

[tex]84=6(\frac{7+b_2}{2})\\[/tex]

Inverse operations,

[tex]84=6(\frac{7+b_2}{2})[/tex]

[tex]14=\frac{7+b_2}{2}[/tex]

[tex]28=7+b_2[/tex]

[tex]14=b_2[/tex]

9514 1404 393

Answer:

  64.6

Step-by-step explanation:

One standard deviation is 4.3. Then +2 standard deviations is ...

  (+2)(4.3) = +8.6

This amount added to the mean gives ...

  56 +8.6 = 64.6 . . . . +2σ from the mean

Question 1

Question 2

Question 3

Answer:

-9

Step-by-step explanation:

Two-thirds of a number is negative six. The number is -9. Let the number is x, 2/3x =-6, x=-6x3/2=-9.

Answer:

Step-by-step explanation:

128.1

Answer:

la conclave Tu pa I ya me tiene dcado esta ndjfjejcuejfn

Step-by-step explanation:

jdjfiifw rjfje djfje fjdjje fjejrj cjdjrn d djdjjff jddjd bdbdjrjrbd. dbebdb d d dbrbdbd. d dd rjrj I'd. drbdbdb. ffbdjjdjdb. d f. bdjdbd bdjdjdjd d dbdhn

Answer: 13

Step-by-step explanation:

Given

The number is 2925

The prime factorization of 2925 is

[tex]\Rightarrow 2925=3\times 3\times 5\times 5\times 13\\\Rightarrow 2925=3^2\times 5^2\times 13[/tex]

To make 2925 a perfect square, we have to eliminate 13 from it, so divide 2925 by 13 to make it a perfect square

The perfect Sqaure becomes [tex](3\times 5)^2=225[/tex]

Answer:

4.5 hours.

= 4 hours and 30 minutes.

Step-by-step explanation:

Distance = Rate x Time

in this case, D = 459 miles

because each driver will drive for the same length of time, we can use their average rate

so, D = average rate x Time

459 miles = (53mph + 49mph)/2 x Time

459 miles / 51mph = 9 hours

Since the total time is 9 hours, each driver will drive for 4 hours 30mins.

Proof: 53mph x 4.5h + 49mph x 4.5h

= 238.5m + 220.5m = 459 miles

Answer:

10

Step-by-step explanation:

10+3 = 13

13 x 7 = 91

Answer:

7(3x)=91

21x=91

x=91/21

Answer:

x = 11.

Step-by-step explanation:

√(x - 2) + 8 = x

√(x - 2) = x - 8

Square both sides:

x - 2 = x^2 - 16x + 64

x^2 - 17x + 66 = 0

(x - 6)(x - 11) = 0

x = 6, 11.

Test for an extraneous solution:

x = 6:

Left side = √(6-2) + 8 = 10

Right side = 6

x = 11:

Left side = √9 + 8 = 11

Right side =  11

So x = 6 is extraneous.

Answer:

AnD = {8,10}

Step-by-step explanation:

A = {2, 4, 6, 8 ,10 ...}

B = {1, 3, 5, 7 ,9 ...}

C = {,2 ,3 ,4 ,5 ...}

D = { 8, 9 ,10 ,11 ...}

AnD = {8, 10}

Answer:

33

1/2(83-50)=25

83-x=50

x=33