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quester [9]
3 years ago
10

A prism with a base area of 8 cm² and a height of 6 cm is dilated by a factor of 5/4 .

Mathematics
2 answers:
Andrei [34K]3 years ago
8 0
The volume of the original prism is calculated by multiplying the area of the base by the height,
                               volume = (8 cm²)(6 cm) = 48 cm³
By the word dilated we mean to say that the dimensions of the new prism is 5/4 times that of the original solid. If we let x be the volume of the new solid,
                           x / 48 cm³ = (5/4)³
The value of x from the equation above is equal to 93.75 cm³. 
hjlf3 years ago
5 0

Answer:

93.75 cm cubed

Step-by-step explanation:

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andrew-mc [135]

Answer:

B

Step-by-step explanation:

Multiply 13 into (10-6)= 13*4=52. Now find the number sentence that gives 52. This is B because 13*10 - 13*6 = 13*4 the original problem

3 0
3 years ago
The scale on a drawing is 1 cm = 4.5 meters. If the length of the drawing is 6.2 cm, what is the actual length in meters?
Nataly [62]

Answer:

I think the awnser is 27.9

Step-by-step explanation:

4.5*6.2=27.9

7 0
3 years ago
Which piece wise function is graphed below
AlekseyPX

Answer:

Option A

Step-by-step explanation:

Here is how to approach the problem:

We see that all our restrictions for all four answer choices are relatively the same with a couple of changes here and there.
One way to eliminate choices would be to look at which restrictions don't match the graph.

At x<-5, there is a linear function that does have a -2 slope and will intersect the x axis at -7. The line ends with an open circle, so any answer choice with a linear restriction of x less than or equal to -5 is wrong. This cancels out choices C and D.

Now we have two choices left.

For the quadratic in the middle, the vertex is at (-2,6) and the vertex is a maximum, meaning our graph needs to have a negative sign in front of the highest degree term. In our case, none of our quadratics left are in standard form, and instead are in vertex form.

Vertext form is f(x) = a(x-h)^2 + k.

h being the x-coordinate of the vertex and k being the y-coordinate.

We know that the opposite of h will be the actual x-coordinate of the vertex, so if our vertex is -2, we will see x+2 inside the parenthesis. This leaves option A as the only correct choice.

3 0
3 years ago
A grain of sand has a diameter that is 2 mm long. Under a magnifying glass, it looks 20 mm long. What magnification was used?​
nikklg [1K]

Answer:

Times 10 magnify

Step-by-step explanation:

4 0
2 years ago
A CBS News/New York Times opinion poll asked 1,190 adults whether they would prefer balancing the federal budget over cutting ta
nikklg [1K]

Using the <u>normal distribution and the central limit theorem</u>, it is found that there is a 0.0166 = 1.66% probability of a sample proportion of 0.59 or less.

In a normal distribution with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

  • It 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, which is the percentile of X.
  • By the Central Limit Theorem, the sampling distribution of sampling proportions of a proportion p in a sample of size n has mean \mu = p and standard error s = \sqrt{\frac{p(1 - p)}{n}}

In this problem:

  • 1,190 adults were asked, hence n = 1190
  • In fact 62% of all adults favor balancing the budget over cutting taxes, hence p = 0.62.

The mean and the standard error are given by:

\mu = p = 0.62

s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.62(0.38)}{1190}} = 0.0141

The probability of a sample proportion of 0.59 or less is the <u>p-value of Z when X = 0.59</u>, hence:

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{0.59 - 0.62}{0.0141}

Z = -2.13

Z = -2.13 has a p-value of 0.0166.

0.0166 = 1.66% probability of a sample proportion of 0.59 or less.

You can learn more about the <u>normal distribution and the central limit theorem</u> at brainly.com/question/24663213

7 0
2 years ago
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