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2 years ago

A square-based pyramid has a base side length of 2 cm and a slant height of 3 cm.

Mathematics

1 answer:

Aleksandr-060686 [28]2 years ago

7 0

Answer:

What is the questions here? if you want area the answer is 3.

Step-by-step explanation:

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In ΔDEF, the measure of ∠F=90°, the measure of ∠D=20°, and EF = 92 feet. Find the length of FD to the nearest tenth of a foot.

Mashutka [201]

Answer:

FD ≈ 252.8 feet

Step-by-step explanation:

By applying tangent rule in the given right triangle,

tan(20°) =

0.36397 =

FD =

FD = 252.77

FD ≈ 252.8 feet

3 0

2 years ago

Zander is in charge of filling goodie bags for the upcoming school party.He plans to order prizes from an online party store.The

VladimirAG [237]

2 gross finger puppets; 2 gross bookmarks; 4 gross assorted pencils; 2 gross animal erasers; 2 gross foam craft kits; 2 gross glow in the dark stickers.

This gives 14 gross prizes; 14*144 = 2016.
Expecting 225 guests, with 8 prizes per bag = 225*8 = 1800

This gives enough extra for 27 more bags, in case more people than expected show up.

3 0

2 years ago

Sarah claims that the thickness of the spearmint gum she produces is 7.5 one-hundredths of an inch. A quality control specialist

satela [25.4K]

Answer:

$t=\frac{7.55-7.5}{\frac{0.103}{\sqrt{10}}}=1.539$

$p_v =2*P(t_{(9)}>1.539)=0.158$

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis.

Step-by-step explanation:

Data given and notation

Data: 7.65, 7.60, 7.65, 7.7, 7.55, 7.55, 7.4, 7.4, 7.5, 7.5

We can begin calculating the sample mean given by:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

And the sample deviation given by:

$s=\sart{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

And we got:

$\bar X=7.55$ represent the sample mean

$s=0.103$ represent the sample standard deviation

$n=10$ sample size

$\mu_o =7.5$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is equal to 7.5 or no, the system of hypothesis would be:

Null hypothesis: $\mu = 7.5$

Alternative hypothesis: $\mu \neq 7.5$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{7.55-7.5}{\frac{0.103}{\sqrt{10}}}=1.539$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=10-1=9$

Since is a two sided test the p value would be:

$p_v =2*P(t_{(9)}>1.539)=0.158$

Conclusion

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis.

3 0

3 years ago

Find all solutions to the equation.<br><br> 7 sin2x - 14 sin x + 2 = -5

cestrela7 [59]

$\bf 7sin^2(x)-14sin(x)+2=-5\implies 7sin^2(x)-14sin(x)+7=0 \\\\\\ \stackrel{\textit{notice, this is just }ax^2+bx+c}{\stackrel{\stackrel{ax^2}{\downarrow }}{sin^2(x)}\stackrel{\stackrel{bx}{\downarrow }}{-2sin(x)}\stackrel{\stackrel{c}{\downarrow }}{+1}}=0\implies [sin(x)-1][sin(x)-1]=0 \\\\\\ sin(x)-1=0\implies sin(x)=1\implies \measuredangle x=sin^{-1}(1)\implies \measuredangle x=\cfrac{\pi }{2} \\\\\\ ~~~~~~~~~~~~~~\stackrel{\textit{and for all solutions using }n \in \mathbb{Z}}{\cfrac{\pi }{2}+2\pi n}$

7 0

3 years ago

Read 2 more answers

8(x-2) = 64

Amiraneli [1.4K]

Answer:

I think d

Step-by-step explanation:

.....................

5 0

2 years ago