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3 years ago

No freeze antifreeze mixture contains 30% alcohol.how many alcohol is there in 15 quarts of no freeze?

1 answer:

8 0

$\bf \begin{array}{|c|ll}
\cline{1-1}
\textit{a\% of b}\\
\cline{1-1}
\\
\left( \cfrac{a}{100} \right)\cdot b
\\\\
\cline{1-1}
\end{array}~\hspace{5em}\stackrel{\textit{30\% of 15}}{\left( \cfrac{30}{100} \right)15}\implies 4.5$

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A certain standardized test's math scores have a bell-shaped distribution with a mean of 530 and a standard deviation of 119. Co

kumpel [21]

Answer:

a) 68.2%

b) 31.8%

c) 2.3%

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 530

Standard Deviation, σ = 119

We are given that the distribution of math scores is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P(test scores is between 411 and 649)

$P(411 \leq x \leq 649)\\\\= P(\displaystyle\frac{411 - 530}{119} \leq z \leq \displaystyle\frac{649-530}{119})\\\\= P(-1 \leq z \leq 1)\\\\= P(z \leq 1) - P(z < -1)\\= 0.841 - 0.159 = 0.682 = 68.2\%$

b) P(scores is less than 411 or greater than 649)

$P(x < 411 < x, x > 649)\\=1 = P(411 \leq x \leq 649)\\=1 - 0.682\\=0.318 = 31.8\%$

c) P(score greater than 768)

P(x > 768)

$P( x > 768) = P( z > \displaystyle\frac{768 - 530}{119}) = P(z > 2)$

$= 1 - P(z \leq 2)$

Calculation the value from standard normal z table, we have,

$P(x > 768) = 1 -0.977 = 0.023 = 2.3\%$

5 0

4 years ago

Which function has a vertex at (2, –9)? f(x) = –(x – 3)2 f(x) = (x + 8)2 f(x) = (x – 5)(x + 1) f(x) = –(x – 1)(x – 5

Tanzania [10]

The answer is C. f(x) = (x -5)(x +1)

3 0

3 years ago

Read 2 more answers

The measures of the obtuse angles in the isosceles trapezoid are five more than four times the measures of the acute angles. Wri

emmainna [20.7K]

Answer:

a. i. x + y = 180 (1) and x - 4y = 5 (2)

ii. The two acute angles are 35° each and the two obtuse angles are 145° each.

Step-by-step explanation:

a. The measures of the obtuse angles in the isosceles trapezoid are five more than four times the measures of the acute angles. Write and solve a system of equations to find the measures of all the angles.

i. Write a system of equations to find the measures of all the angles.

Let x be the obtuse angles and y be the acute angles.

Since we have two obtuse angles at the top of the isosceles trapezoid and two acute angles at the bottom of the isosceles trapezoid, and also, since the sum of angles in a quadrilateral is 360, we have

2x + 2y = 360

x + y = 180 (1)

Its is also given that the measures of the obtuse angles in the isosceles trapezoid are five more than four times the measures of the acute angles.

So, x = 4y + 5 (2)

x - 4y = 5 (2)

So, our system of equations are

x + y = 180 (1) and x - 4y = 5 (2)

ii. Solve a system of equations to find the measures of all the angles.

Since

x + y = 180 (1) and x - 4y = 5 (2)

Subtracting (2) from (1), we have

x + y = 180 (1)

x - 4y = 5 (2)

5y = 175

dividing both sides by 5, we have

y = 175/5

y = 35°

From (1), x = 180° - y = 180° - 35° = 145°

So, the two acute angles are 35° each and the two obtuse angles are 145° each.

4 0

3 years ago

1. A system of linear equations that has one solution has slopes that are__________

algol13

Answer:

different

Step-by-step explanation:

different slopes gives one solution

same slopes with different constant has no solution

same slopes and constants has many solutions

3 0

3 years ago

Find a linear equation whose graph is the straight line with the given property.

Triss [41]

Answer:

Step-by-step explanation:

-5.25+2.25 - 3

1-0.5 = 0.5

=-6 =m

y=-6x

5 0

3 years ago