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3 years ago

What is the value of a in the diagram below?

Mathematics

1 answer:

adell [148]3 years ago

7 0

Answer:

a=8

Step-by-step explanation:

We can use ratios of similar triangles to solve

The smaller triangle has sides a and 12 and the larger triangle has sides a+a+4 and 12+18 which combine to 2a+4 and 30

a 2a +4

--------- = -----------

12 30

Using cross products

30a = 12(2a+4)

30a = 24a +48

Subtract 24a from each side

30a -24a = 24a-24a +48

6a = 48

Divide each sdie by 6

6a/6 =48/6

a =8

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Mr majors ordered six hot dogs and a bucket of popcorn at the concession stand. If the popcorn was 3.20 and the total was 18.20

maw [93]

The answer is $2.50 per hot dog

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3 years ago

Suppose that in a random selection of 100 colored candies, 28% of them are blue. The candy company claims that the percentage

Zigmanuir [339]

Answer:

We conclude that the percentage of blue candies is equal to 29%.

Step-by-step explanation:

We are given that in a random selection of 100 colored candies, 28% of them are blue. The candy company claims that the percentage of blue candies is equal to 29%.

Let p = population percentage of blue candies

So, Null Hypothesis, $H_0$ : p = 29% {means that the percentage of blue candies is equal to 29%}

Alternate Hypothesis, $H_A$ : p $\neq$ 29% {means that the percentage of blue candies is different from 29%}

The test statistics that will be used here is One-sample z-test for proportions;

T.S. = $\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of blue coloured candies = 28%

n = sample of colored candies = 100

So, the test statistics = $\frac{0.28-0.29}{\sqrt{\frac{0.29(1-0.29)}{100} } }$

= -0.22

The value of the z-test statistics is -0.22.

Also, the P-value of the test statistics is given by;

P-value = P(Z < -0.22) = 1 - P(Z $\leq$ 0.22)

= 1 - 0.5871 = 0.4129

Now, at a 0.10 level of significance, the z table gives a critical value of -1.645 and 1.645 for the two-tailed test.

Since the value of our test statistics lies within the range of critical values of z, so we insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that the percentage of blue candies is equal to 29%.

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3 years ago

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Katarina [22]

I'm pretty sure the answer is education

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3 years ago

Read 2 more answers

Software to detect fraud in consumer phone cards tracks the number of metropolitan areas where calls originate each day. It is f

almond37 [142]

Answer:

The probability is 0.001812

Step-by-step explanation:

Let's call: F the event in which a user is fraudulent, L the event in which a user is legitimate and A the event in which the user calls from two or more metropolitan areas.

So, the probability that the user is fraudulent given that the user call from two or more metropolitan areas is calculated as:

P(F/A) = P(F∩A)/P(A)

Where P(A) = P(F∩A) + P(L∩A)

So, P(F∩A) is the probability that the user is fraudulent and the user calls from two or more metropolitan areas. it is calculated as:

P(F∩A) = 0.0121% * 30% = 0.00363%

Because 0.0121% is the proportion of fraudulent users and 30% is the percentage of the fraudulent users that call from two or more metropolitan areas in a single day.

At the same way, P(L∩A) is the probability that a user is legitimate and the users calls from two or more metropolitan areas. It is calculated as:

P(L∩A) = (100%-0.0121%) * 2% = 1.999758%

Because (100%-0.0121%) is the proportion of legitimate users and 2% is the percentage of the legitimate users that call from two or more metropolitan areas in a single day.

Then, P(A) is calculated as:

P(A) = 0.00363% + 1.999758%

P(A) = 2.003388%

Finally, If the same user originates calls from two or more metropolitan areas in a single day, the probability that the user is fraudulent, P(F/A), is equal to:

P(F/A) = 0.00363 / 2.003388

P(F/A) = 0.001812

5 0

2 years ago

Which is the general form of the equation of the circle shown ?

Evgen [1.6K]

Answer:

there is no circle

Step-by-step explanation:

or equation...

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3 years ago

What is the value of a in the diagram below?​

What is the value of a in the diagram below?