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3 years ago

1/5 ÷ 2. simple for a couple of points lol

Mathematics

2 answers:

Sergio039 [100]3 years ago

8 0

0.1

Have a amazing day!!

Darina [25.2K]3 years ago

8 0

Answer:

1/10 and in decimal form, it would be 0.1

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Have you ever been frustrated because you could not get a container of some sort to release the last bit of its contents? The ar

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

4 years ago

Can someone please help me

SashulF [63]

Answer:

1. $\dfrac{44}{13}=3\dfrac{5}{13}$

2. 9.6

3. 0

Step-by-step explanation:

Thales’ Theorem: If arms of an angle are cut by parallel straight lines, then the ratio of the lengths of the line segments obtained on one arm are equal to the corresponding segments obtained on the second arm.

1. By Thales's theorem,

$\dfrac{9}{4}=\dfrac{11-x}{x}\\ \\9x=4(11-x)\ [\text{Cross multiply}]\\ \\9x=44-4x\\ \\9x+4x=44\\ \\13x=44\\ \\x=\dfrac{44}{13}$

2. By Thales's theorem,

$\dfrac{8}{12}=\dfrac{x}{24-x}\\ \\12x=8(24-x)\ [\text{Cross multiply}]\\ \\12x=192-8x\\ \\12x+8x=192\\ \\20x=192\\ \\x=9.6$

3. By Thales's theorem,

$\dfrac{4x}{5x}=\dfrac{4x-8}{6x-10}\\ \\\dfrac{4}{5}=\dfrac{4x-8}{6x-10}\\ \\5(4x-8)=4(6x-10)\ [\text{Cross multiply}]\\ \\20x-40=24x-40\\ \\20x=24x\\ \\4x=0\\ \\x=0$