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3 years ago

Find the missing measurement of AC

Mathematics

1 answer:

IgorLugansk [536]3 years ago

8 0

Answer:

AC = 78

Step-by-step explanation:

Since all the angles are equal (60°), this is an equiangular triangle (meaning all angles re equal). Equiangular triangles are also equilateral meaning that all sides are equal)

We are given then one side is 11x-32 and another side is 5x+28

These two sides must be equal so we can set them equal to each other and solve for x

11x - 32 = 5x + 28

6x - 32 = 28

6x = 60

x = 10

If x = 10, then we can substitute x into either of the two equations to find the length of all three sides (since all sides have equal length)

11(10)-32 = 110 - 32 = 78

AB = BC = AC = 78

AC = 78

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#27.
First cross multiply
2 (2a-3) = 3 (a-1)
next use the distribute property on both sides
4a - 6 = 3a - 3
combine like terms, subtract 3a from both sides and add 6 to both sides
a = 3

#28
cross multiply
3x = 4, then divide both sides by 3
x = 4/3

#30
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3 years ago

A farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. no fencing is needed along the bar

jeyben [28]

Hi,

Let assume a the west side,

b the length of the north wall (i suppose the answer is smaller then the barn.

Cost of the fence= a*6+a*12+b*12=3000 $.

So 3a+2b=500==>b=(500-3a)/2

Area =a*b=a(500-3a)/2= 250a-3/2a²

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3 years ago

A Web music store offers two versions of a popular song. The size of the standard version is

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3 years ago

A theory predicts that the mean age of stars within a particular type of star cluster is 3.3 billion years, with a standard devi

Luden [163]

Answer:

Null hypothesis: $\mu \leq 3.3$

Alternative hypothesis: $\mu > 3.3$

$z=\frac{3.4-3.3}{\frac{0.4}{\sqrt{50}}}=1.768$

Since is a one right tailed test the p value would be:

$p_v =P(z>1.768)=0.039$

Step-by-step explanation:

Data given and notation

$\bar X=3.4$ represent the sample mean

$\sigma=0.4$ represent the population deviation for the sample

$n=50$ sample size

$\mu_o =3.3$ represent the value that we want to test

$\alpha$ 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 to be tested

We need to conduct a hypothesis in order to determine if the mean is higher than 3.3, the system of hypothesis would be:

Null hypothesis: $\mu \leq 3.3$

Alternative hypothesis: $\mu > 3.3$

Compute the test statistic

We know the population deviation, so for this case is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-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".

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

$z=\frac{3.4-3.3}{\frac{0.4}{\sqrt{50}}}=1.768$

P value

Since is a one right tailed test the p value would be:

$p_v =P(z>1.768)=0.039$

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Marina86 [1]

Answer:

um The picture is not clear send it again please

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3 years ago

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