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3 years ago

Find the value of x to the nearest tenth

Mathematics

2 answers:

Salsk061 [2.6K]3 years ago

5 0

Answer:

x = 41.2

Step-by-step explanation:

Assuming the dotted line at the top is parallel to the segment with length x, it follows from the alternate interior angles theorem that the interior angle of the triangle (marked in diagram) is also 27º.

Using SOH-CAH-TOA, we get that tan(27º) = 21/x, so x = 21/tan(27º), which is approximately equal to 41.2.

NemiM [27]3 years ago

3 0

41.2 I think that is right

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A manufacturer produces light bulbs that have a mean life of at least 500 hours when the production process is working properly.

denpristay [2]

Answer:

We conclude that the population mean light bulb life is at least 500 hours at the significance level of 0.01.

Step-by-step explanation:

We are given that a manufacturer produces light bulbs that have a mean life of at least 500 hours when the production process is working properly. The population standard deviation is 50 hours and the light bulb life is normally distributed.

You select a sample of 100 light bulbs and find mean bulb life is 490 hours.

Let $\mu$ = population mean light bulb life.

So, Null Hypothesis, $H_0$ : $\mu \geq$ 500 hours {means that the population mean light bulb life is at least 500 hours}

Alternate Hypothesis, $H_A$ : $\mu$ < 500 hours {means that the population mean light bulb life is below 500 hours}

The test statistics that would be used here One-sample z test statistics as we know about the population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean bulb life = 490 hours

σ = population standard deviation = 50 hours

n = sample of light bulbs = 100

So, the test statistics = $\frac{490-500}{\frac{50}{\sqrt{100} } }$

= -2

The value of z test statistics is -2.

Now, at 0.01 significance level the z table gives critical value of -2.33 for left-tailed test.

Since our test statistic is higher than the critical value of z as -2 > -2.33, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the population mean light bulb life is at least 500 hours.

7 0

3 years ago

Health insurers are beginning to offer telemedicine services online that replace the common office visit. A company provides a v

Veronika [31]

Answer:

$\text {CI} = (60.54, \: 81.46)\\\\$

Therefore, we are 95% confident that actual mean savings for a televisit to the doctor is within the interval of ($60.54 to $81.46)

Step-by-step explanation:

Let us find out the mean savings for a televisit to the doctor from the given data.

Using Excel,

=AVERAGE(number1, number2,....)

The mean is found to be

$\bar{x} = \$71$

Let us find out the standard deviation of savings for a televisit to the doctor from the given data.

Using Excel,

=STDEV(number1, number2,....)

The standard deviation is found to be

$s = \$ 22.35$

The confidence interval is given by

$\text {confidence interval} = \bar{x} \pm MoE\\\\$

Where the margin of error is given by

$$ MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $ \\\\$

Where n is the sample of 20 online doctor visits, s is the sample standard deviation and $t_{\alpha/2}$ is the t-score corresponding to a 95% confidence level.

The t-score is given by is

Significance level = α = 1 - 0.95 = 0.05/2 = 0.025

Degree of freedom = n - 1 = 20 - 1 = 19

From the t-table at α = 0.025 and DoF = 19

t-score = 2.093

So, the margin of error is

$MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 2.093\cdot \frac{22.35}{\sqrt{20} } \\\\MoE = 2.093\cdot 4.997\\\\MoE = 10.46\\\\$

So the required 95% confidence interval is

$\text {CI} = \bar{x} \pm MoE\\\\\text {CI} = 71 \pm 10.46\\\\\text {CI} = 71 - 10.46, \: 71 + 10.46\\\\\text {CI} = (60.54, \: 81.46)\\\\$

Therefore, we are 95% confident that actual mean savings for a televisit to the doctor is within the interval of ($60.54 to $81.46)

7 0

3 years ago

Sandy has 27 roses, 9 daisies, and 18 tulips. She wants to arrange all the flowers in bouquets. Each bouquet has the same number

AlekseyPX

Answer:

The greatest number of flowers that could be in a bouquet is 9 flowers

Step-by-step explanation:

We solve the above question using Greatest Common Factor method. We find the factors of 27, 9 and 18. The greatest factor common to the 3 number is our answer.

The factors of 9 are: 1, 3, 9

The factors of 18 are: 1, 2, 3, 6, 9, 18

The factors of 27 are: 1, 3, 9, 27

Then the greatest common factor is 9.

The greatest number of flowers that could be in a bouquet is 9 flowers

5 0

3 years ago

Part F

Rina8888 [55]

Answer:

my last answer is correct

Step-by-step explanation:

7 0

2 years ago

Simplify polynomial

Kay [80]

Answer:

j² - 5j²k - 2

Step-by-step explanation:

3j² - j²k - 6 - 4j²k - 2j² + 4

To simplify this polynomial, we can collect like terms. A term is number(s) or variable(s) that are grouped together by multiplication. Like terms have the same variable and exponent.

We have three groups of like terms:

The j-squares (j²), the j-squared k (j²k) and the constants (no variable).

Remember to include the negatives!

The j-squares are: 3j² ; -2j²

The j-squares k are: - j²k ; - 4j²k

The constants are: - 6 ; 4

Simplify:

3j² - j²k - 6 - 4j²k - 2j² + 4

Rearrange the polynomial by like terms

= (- j²k - 4j²k) + (3j² - 2j²) + (- 6 + 4)

Add or subtract the like terms

= (-5j²k) + (j²) + (-2)

Remove brackets and rearrange so the negative is not first

= j² + - 5j²k + - 2

Simplify where two signs are together. Adding a negative is subtraction.

= j² - 5j²k - 2 Simplified

8 0

3 years ago