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2 years ago

WILL MARK BRAINLIEST

Mathematics

1 answer:

ValentinkaMS [17]2 years ago

8 0

Answer:

The answer to your question is:

x = 13

x + 10 = 23

5x - 42 = 23

Step-by-step explanation:

Data

angle 1 = x + 10

angle 2 = 5x - 42

They are vertical angles so, they measure the same.

x + 10 = 5x -42

x - 5x = -42 - 10

- 4x = -52

x = -52/-4

x = 13

angle 1 = x + 10 = 13 + 10 = 23

angle 2 = 5x - 42 = 5(13) -42 = 65 -42 = 23

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A coffee shop sold 7 cups,3 pints, and 9 quarts of coffee. Express the number of cups of coffee sold in base 2

sweet-ann [11.9K]

Answer:

The total number of cups of coffee sold are 51 which can be expressed in base $2$ as $110011$ .

Step-by-step explanation:

Considering the following information

$1$ cup = $1$ cup

$7$ pints = $14$ cups ∵ $1$ pint = $2$ cups
$9$ quarts = $36$ cups ∵ $1$ quart = $4$ cups

So, total number of cups will be = $51$ cups

Converting $51$ to the base $2$

Divide $51$ by $2$ by repeatedly and observe remainder

$\frac{51}{2}=25\quad \mathrm{Remainder}\quad \:1$

$\frac{25}{2}=12\quad \mathrm{Remainder}\quad \:1$

$\frac{12}{2}=6\quad \mathrm{Remainder}\quad \:0$

$\frac{6}{2}=3\quad \mathrm{Remainder}\quad \:0$

$\frac{3}{2}=1\quad \mathrm{Remainder}\quad \:1$

$\frac{1}{2}=0\quad \mathrm{Remainder}\quad \:1$

Read and observe the remainder from top to bottom would yield $110011$ .

Therefore, the total number of cups of coffee sold are 51 which can be expressed in base $2$ as $110011$ .

Keywords: base 2, number

Learn more about number bases from brainly.com/question/13725148

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2 years ago

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Dvinal [7]

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2 years ago

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A matched pairs experiment compares the taste of instant versus fresh-brewed coffee. Each subject tastes two unmarked cups of co

Bogdan [553]

Answer:

We conclude that the majority of people prefer the taste of fresh-brewed coffee.

Step-by-step explanation:

We are given that of the 50 subjects who participate in the study, 16 prefer the instant coffee.

We have to test the claim that a majority of people prefer the taste of fresh-brewed coffee.

Let p = proportion of the population who prefer fresh-brewed coffee

So, Null Hypothesis, $H_0$ : p $\leq$ 50% {means that the majority of people does not prefer the taste of fresh-brewed coffee}

Alternate Hypothesis, $H_A$ : p > 50% {means that the majority of people prefer the taste of fresh-brewed coffee}

The test statistics that would be used here One-sample z proportion statistics;

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

where, $\hat p$ = sample proportion who prefer fresh-brewed coffee = $\frac{34}{50}$ = 0.68

n = sample of subjects = 50

So, test statistics = $\frac{0.68-0.50}{\sqrt{\frac{0.68(1-0.68)}{50} } }$

= 2.73

The value of z test statistics is 2.73.

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

P-value = P(Z > 2.73) = 1 - P(Z $\leq$ 2.73)

= 1 - 0.99683 = 0.0032

Since, in the question we are not given with the level of significance so we assume it to be 5%. Now, at 5% significance level the z table gives critical values of 1.645 for right-tailed test.

Since our test statistics is more than the critical value of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the majority of people prefer the taste of fresh-brewed coffee.

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2 years ago

Aaron is 6 years old, Beth is 9 years old and Charlie is 15 years old. They are going to share £5940 in the same ratio as their

Andre45 [30]

Answer:

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