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spin [16.1K]
3 years ago
14

The sides of an isosceles triangle are 8, 8, and 3. The measure of the vertex angle to the nearest degree is _____°. 44 17 31 22

Mathematics
2 answers:
asambeis [7]3 years ago
6 0

Answer:

22 :)

Step-by-step explanation:

Doss [256]3 years ago
4 0
We may draw a vertical that bisects the vertex angle and the shorter side of the triangle, to form a right-triangle with the measurements:
hypotenuse = 8
length = 1.5

We may then apply:
sin(∅) = P / H
sin(∅) = 1.5 / 8
∅ = 10.8 ≈ 11°

This is half of the vertex angle, so the vertex angle is:
11 * 2 = 22°
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Leviafan [203]
Write in 0 and 0 at the top:  this indicates that if there are zero pennies, the height of the tower is 0.  This is the point (0,0).  Another point is (4, 28):  a tower of 28 pennies is 4 cm tall.

Find the slope of the line connecting (0,0) and (4,28).
            4cm - 0 cm
    m = ----------------- = (1/7) (cm/penny)
            28 - 0

The equation we need, relating # of pennies to height of tower, is 

       t = (1/7) (cm/penny)x, where x is the # of pennies.

Thus, if x = 1, then t=1/7 cm

And, if x =15, then t = 15/7 cm

And so on.
7 0
3 years ago
Randall wants to mix 50 lb of nuts worth $2 per lb with some nuts worth $7 per lb to make a mixture worth $6 per lb. How many po
defon

A = nuts of $2/lb

B = nuts of $7/lb


let's say we'll mix "x" lbs of B to get a mixture with A of "y" lbs, therefore


\bf \begin{array}{lcccl} &\stackrel{lbs}{quantity}&\stackrel{\textit{cost}}{per~lb}&\stackrel{\textit{cost}}{total}\\ \cline{2-4}&\\ A~ nuts&50&2&100\\ B~nuts&x&7&7x\\ \cline{2-4}&\\ mixture&y&6&6y \end{array} \\\\\\ \begin{cases} 50+x=\boxed{y}\\ 100+7x=6y \end{cases}\qquad \qquad \implies 100+7x=6\left( \boxed{50+x} \right) \\\\\\ 100+7x=300+6x\implies \blacktriangleright x=200 \blacktriangleleft

3 0
3 years ago
Directions for questions 4 & 5: We selected a random sample of 100 StatCrunchU students, 67 females and 33 males, and analyz
GaryK [48]

Answer:

The 95% confidence interval for the difference between means is (-2164.21, -299.13).

The lower limit on the confidence interval is -$2164.21.

The upper limit on the confidence interval is -$299.13.

Step-by-step explanation:

The sample data is:

Gender   Mean          Std. dev.     n

Female    2577.75      1916.29     67

Male        3809.42     2379.47     33

We have to calculate a 95% confidence interval for the difference between means, with a T-model.

The sample 1, of size n1=67 has a mean of 2577.75 and a standard deviation of 1916.29.

The sample 2, of size n2=33 has a mean of 3809.42 and a standard deviation of 2379.47.

The difference between sample means is Md=-1231.67.

M_d=M_1-M_2=2577.75-3809.42=-1231.67

The estimated standard error of the difference between means is computed using the formula:

s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{1916.29^2}{67}+\dfrac{2379.47^2}{33}}\\\\\\s_{M_d}=\sqrt{54808.468+171572.045}=\sqrt{226380.513}=475.795

The t-value for a 95% confidence interval is t=1.96.

The margin of error (MOE) can be calculated as:

MOE=t\cdot s_M=1.96 \cdot 475.795=932.54

Then, the lower and upper bounds of the confidence interval are:

LL=M_d-t \cdot s_{M_d} = -1231.67-932.54=-2164.21\\\\UL=M_d+t \cdot s_{M_d} = -1231.67+932.54=-299.13

The 95% confidence interval for the difference between means is (-2164.21, -299.13).

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