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2 years ago

If the measures of two complimentary angles are 7x and 11x , then find x

Mathematics

2 answers:

JulsSmile [24]2 years ago

7 0

Answer:

x = 5

Step-by-step explanation:

Complementary angles are two angles whose sum is 90º

So, if we have two complementary angles 7x and 11x we know that their sum is 90

We are going to write the equation and solve for x:

$7x+11x=90\\18x=90\\x=90/18\\x= 5$

Therefore, x would be 5. And the angles would be 7(5) = 35º and 11(5) = 55º

Irina18 [472]2 years ago

3 0

As you know that sum of complementary angles equal 90°

so,

7x + 11x = 90
18x = 90
x = 90/18
x =5

so,
option A is the correct one.

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snow_tiger [21]

Answer:

Yes. There is enough evidence to support the claim that the remaining toothpaste is significantly is less than 10% of the advertised net content.

Step-by-step explanation:

The sample of the remaining toothpaste is: [.53, .65, .46, .50, .37].

This sample has a size n=5, a mean M=0.502 and standard deviation s=0.102.

$M=\dfrac{1}{5}\sum_{i=1}^{5}(0.53+0.65+0.46+0.5+0.37)\\\\\\ M=\dfrac{2.51}{5}=0.502$

$s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{5}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{4}\cdot [(0.53-(0.502))^2+...+(0.37-(0.502))^2]}\\\\\\s=\sqrt{\dfrac{1}{4}\cdot [(0.001)+(0.022)+(0.002)+(0)+(0.017)]}\\\\\\ s=\sqrt{\dfrac{0.04188}{4}}=\sqrt{0.01047}\\\\\\s=0.102$

The 10% of the advertised content is:

$0.10\cdot 6.0\;oz=0.6\:oz$

Hypothesis test for the population mean:

The claim is that the remaining toothpaste is significantly is less than 10% of the advertised net content.

Then, the null and alternative hypothesis are:

$H_0: \mu=0.6\\\\H_a:\mu< 0.6$

The significance level is 0.05.

The estimated standard error of the mean is computed using the formula:

$s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.102}{\sqrt{5}}=0.046$

Then, we can calculate the t-statistic as:

$t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{0.502-0.6}{0.046}=\dfrac{-0.098}{0.046}=-2.148$

The degrees of freedom for this sample size are:

$df=n-1=5-1=4$

This test is a left-tailed test, with 4 degrees of freedom and t=-2.148, so the P-value for this test is calculated as (using a t-table):

$P-value=P(t$

As the P-value (0.049) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the remaining toothpaste is significantly is less than 10% of the advertised net content.

7 0

2 years ago

Find the midpoint between each pair of points.<br> (-1,-5) and (-5,9)

Paul [167]

Answer:

work is pictured and shown

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2 years ago

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Dmitrij [34]

Answer:

There is not sufficient evidence to warrant the rejection of the claim that the mean weight of cereal is atleast 14 oz

Step-by-step explanation:

The hypothesis for the test above will be stated as follows :

The claim to be tested is the alternative hypothesis, which is the negation of the Null hypothesis

H0 : μ < 14

H1 : μ ≥ 14

If the Null is rejected, then it means that the company's claim that the mean weight of its cereal being atleast 14 is valid ;

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1 year ago

What percent of 137.4 is 96?

Neporo4naja [7]

X = 96

100 137.4

137.4x=(100)(96)

137.4x=9600

137.4x/137.4=9600/137.4

x=70%

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2 years ago

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Answer:

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Step-by-step explanation:

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