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MAVERICK [17]
3 years ago
13

The grades on the last history exam had a mean of 80%. Assume the population of grades on history exams is known to be distribut

ed normally, with a standard deviation of 5%. Approximately what percent of students earn a score between 70% and 80%?
A. 2.2%
B. 10%
C. 47.7%
D. 50%
E. 52.5%
Mathematics
1 answer:
Trava [24]3 years ago
4 0

Answer:

I got C because A and B are too small for the standard division to be a mean of 80% and the number also cannot be 50% or higher because it could bring the median lower and or higher

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In isosceles △ABC the segment BD (with D∈ AC ) is the median to the base AC . Find BD, if the perimeter of △ABC is 50m, and the
Morgarella [4.7K]

Let the equal sides of the isosceles Δ ABC be x.

Given that the perimeter of Δ ABC = 50m.

Therefore, 2x + AC = 50 --- (1)

It is also given that the perimeter of Δ ABD = 40m.

Therefore, x + BD + AD = 40

BD is the median of the Δ ABC. Therefore, D is the midpoint of AC.

So AD = CD.

Or, AD = \frac{1}{2} AC

Therefore, x + BD + \frac{1}{2} AC = 40

Multiply both sides by 2.

2x + 2BD + AC = 80

From (1), 2x + AC = 50.

Therefore, 2BD + 50 = 80

2BD = 80 - 50

2BD = 30

BD = 15m.

6 0
3 years ago
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Bryce has $28. He spends $15. Then, his mom gives him $5 more. Which equation shows how Bryce can correctly find his total amoun
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Answer:

28 - 15 + 5 = 18. Add and subtract will get you ,your answer. Bryce has $18

Step-by-step explanation:

Simple math hope this helped

7 0
2 years ago
A commonly used unit of mass in the English system is the pound-mass, abbreviated lbm, where 1 lbm = 0.454 kg. What is the densi
Rashid [163]
<h2>Density of ethyl alcohol is 56.25 lbm/ft³ </h2>

Step-by-step explanation:

We have 1 lbm = 0.454 kg

1 kg = 2.203 lbm

1 m = 3.28 ft

Density of ethyl alcohol = 9.01 x 10² kg/m³

\texttt{Density = }\frac{9.01\times 10^2\times 2.203}{3.28^3}=56.25lbm/ft^3

So

Density of ethyl alcohol = 56.25 lbm/ft³

3 0
3 years ago
Use Cramer Rule to solve the following system: 8x−5y=70 and 9x+7y=3
nlexa [21]

Answer:

(x,y) = (5,-6)

Step-by-step explanation:

\underline{\textbf{Determinant of a matrix.}}\\\\\text{For a}~ 2 \times 2 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2\\b_1&b_2 \end{vmatrix} = a_1b_2 - a_2b_1\\\\\\\text{For a}~ 3 \times 3 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2&a_3\\ b_1&b_2&b_3\\ c_1&c_2&c_3 \end{vmatrix} = a_1\begin{vmatrix} b_2&b_3\\c_2&c_3 \end{vmatrix} - a_2 \begin{vmatrix} b_1&b_3\\c_1&c_3 \end{vmatrix}+ a_3 \begin{vmatrix} b_1&b_2\\c_1&c_2 \end{vmatrix}\\\\\\

                     ~~~~~~~~~~~~~~~~~~=a_1(b_2c_3-b_3c_2) -a_2(b_1c_3-b_3c_1) +a_3(b_1c_2-b_2c_1)

\underline{\textbf{Cramer's Rule to solve a system of two equations.}}\\\\\text{Consider the system of two equations:}\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_1x + b_1 y= c_1\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_2x +b_2 y = c_2\\\\\text{Here,}\\\\x = \dfrac{D_x}{D}= \dfrac{\begin{vmatrix} c_1&b_1\\c_2&b_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\\\ y= \dfrac{D_y}{D}= \dfrac{\begin{vmatrix} a_1&c_1\\a_2&c_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\

\underline{\textbf{Solution:}}\\\\~~~~~~~~~~~~~~~~~~~~~~~8x-5y = 70~~~~~~...(i)\\\\~~~~~~~~~~~~~~~~~~~~~~~9x +7y = 3~~~~~~~...(ii)\\\\\text{Applying Cramer's rule:}\\\\x = \dfrac{D_x}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 70& -5 \\3&7 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{70(7) -(-5)(3)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{490+15}{56+45}\\\\\\~~=\dfrac{505}{101}\\\\\\~~=5

y = \dfrac{D_y}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 8& 70 \\9&3 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{(8)(3) -(70)(9)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{24-630}{56+45}\\\\\\~~=-\dfrac{606}{101}\\\\\\~~=-6

\textbf{Hence, the solution to the system of equation is}~ (x,y) = (5,-6)

7 0
2 years ago
PLEASE HELP ME!! PLEASE DON'T ANSWER IF YOU ARE NOT PSOTIVE ON WHAT THE ANSWER IS!!!
Talja [164]

Answer:

its A

Step-by-step explanation:

im not gonna step by step it becuase i dont have time but its A

5 0
3 years ago
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