The speeds on the interstate are normally distributed with a mean of 70 mph and a standard deviation of 5 mph. Approximately what percent of speeds fall between 60 mph and 80 mph?

Answers

Answer 1

Answer: $\mathbb P(60<X<80)=\mathbb P\left(\frac{60-70}5<\frac{X-70}5<\frac{80-70}5\right)=\mathbb P(-2<Z<2)$

The empirical rule asserts that approximately 95% of a distribution falls within two standard deviations of the mean.

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A cherry blossom tree grows 2 inches per year. A cherry blossom tree is 28 currently inches. How tall, in inches, will the cherry blossom tree be in 13 years?
Which of the following shows that polynomials are closed under subtraction when polynomial 5x − 6 is subtracted from 3x2 − 6x + 2?answers: 3x2 − 11x + 8 may or may not be a polynomial 3x2 − 11x + 8 will be a polynomial 3x2 − x + 4 may or may not be a polynomial 3x2 − x + 4 will be a polynomial
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If bc = 8.3 cd = 6.7 and ad = 11.6 find ab to the nearest tenth
Express 14.69 as a mixed number

Megan draws a triangle on coordinate axes. She reflects the triangle across the y-axis and then translates it 5 units to the right. Which statement is true about the triangle formed from these transformations?A. It will be larger than the original triangle
B. It will be smaller than the original triangle
C. It will be congruent to the original triangle
D. It will be a different shape then the original triangle

Answers

Answer C: It will be congruent to the original triangle. Reflections and translations do not affect the size of a shape, only it’s position and the way it is viewed.

Final answer:

The triangle formed from reflecting the original triangle across the y-axis and then translating it 5 units to the right will be congruent to the original triangle.

Explanation:

The triangle formed from reflecting the original triangle across the y-axis and then translating it 5 units to the right will be congruent to the original triangle.

When a figure is reflected across the y-axis, its shape remains the same, but its orientation is flipped. Then, by translating the reflected triangle 5 units to the right, we are simply shifting it horizontally without changing its size or shape.

Therefore, the statement that is true about the triangle formed from these transformations is C. It will be congruent to the original triangle.

Learn more about Transformations here:

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Solve this in an equality 8z+3-2z <51

Answers

Answer: x < 8

8z+3-2z<51

Collect like terms.

6z+3<51

Move constant to the right side and change its sign.

6z<51-3

Subtract the numbers.

6z<48

Divide both sides of the inequality by 6.

z < 8

If the price of an object dropped 65% down to $99.99, what was the original price?

Answers

If the price of an object dropped 65% down it means that 35% is $99.99, well,
then we make a proportion and solve 99.99 multiply by 100 and divide by 35,
then we get the original price $285,7

maybe I have a mistake)

The answer is 153.83. Because if you multiply 99.99 by .65, thats the answer

The design of a digital box camera maximizes the volume while keeping the sum of the dimensions at 6 inches. If the length must be 1.5 time the height, what should each dimension be?

Answers

$v=1.5l*l*w$
$w=6-l-1.5l$
$v=1.5l*l*(6-l-1.5l)$
which simplifies to
$v=9l^2-3.75l^3$
and so we take the derivative of that function in terms of l
$(d)/(dx)v=18l-11.25l^2$
then we set that to 0
$-11.25l^2+18l=0$
using the quadratic formula
$(-b+or- √(b^2-4ac))/(2a)$
$(-18+or- √(18^2-4*11.25*0))/(2*-11.25)$
simplifying..
$(-18+or- √(324))/(-22.5)$
$(-18+√(324))/(-22.5)=0$
$(-18-√(324))/(-22.5)=1.6$

at this point i noticed an error, i used l instead of h... but thats ok

pluggin 0 and 1.6 for h, lets check answers
1.6: h=1.6 l=2.4 w=2
0: h=0 l=0 w=6

so the answer is h=1.6 l=2.4 w=2, which gives the greatest volume of 7.68

What is the scale factor from ABC to DEF?

Answers

Answer:

Step-by-step explanation:

The scale factor is the ratio of corresponding sides, image to original, so

scale factor = $(EF)/(BC)$ = $(11)/(66)$ = $(1)/(6)$ → C

The quotient of twice a number t and 12

Answers

2t/12 would be your expression.

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