All categories

3 years ago

Help pls pls pls pls

Mathematics

1 answer:

Nana76 [90]3 years ago

5 0

Step-by-step explanation:

as with any division of a multiplication of various factors, we can always simplify by reducing the factors in the top and the bottom of the same base.

in the same way we can for example do

36×2⁶×3⁴×5² / 4×2⁵×3³×5²

and deal with every exponent base individually creating

9×2¹×3¹×5⁰ = 9×2×3

we can do with variable based exponents.

24a⁸b⁸c⁶ / 8a⁷b³c³ =

= 3a¹b⁵c³

you know, when we divide, we simply subtract exponents.

8-7, 8-3, 6-3

and the constants are simply divided 24/8 = 3

You might be interested in

Toby wants to find the volume of a solid toy soldier.

mr Goodwill [35]

Answer:

Toby wants to find the volume of a solid toy soldier.He fills a rectangular container 8 cm long, 6 cm wide,and 10 cm high with water to a depth of 4 cm. Toby totally submerges the toy soldier in the water. The height of the water with the submerged toy soldier is 6.6 cm. Which of the following is closest to the volume, in cubic centimeters, of the toy soldier?

A. 125 B. 156 C. 192 D. 208 E.317

The volume of the toy is 125 cubic cm ,option A is the closest answer.

Step-by-step explanation:

Given:

A rectangular container .

Length of the container =8 cm

Width of the container = 6 cm

Height of the container when water is filled = $(h_1)$ = 4 cm

Height of the container when the toy is submerged = $(h_2)$ =6.6 cm

Volume of the toy = Volume of the container with the toy - Volume of the container (with water)

Volume of the toy = $(l\times b\times h_2) - (l\times b\times h_1)$

= $(l\times b\times)(h_2-h1)$

= $(6\times 8)(6.6-4)$

= $48\times 2.6$

= $124.8$ cubic centimeters.

So,the closest value to the volume of the toy is 125 cubic centimeters.

6 0

3 years ago

A math professor notices that scores from a recent exam are normally distributed with a mean of 61 and a standard deviation of 8

Alexeev081 [22]

Answer:

a) 25% of the students exam scores fall below 55.6.

b) The minimum score for an A is 84.68.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 61 and a standard deviation of 8.

This means that $\mu = 61, \sigma = 8$

(a) What score do 25% of the students exam scores fall below?

Below the 25th percentile, which is X when Z has a p-value of 0.25, that is, X when Z = -0.675.

$Z = \frac{X - \mu}{\sigma}$

$-0.675 = \frac{X - 61}{8}$

$X - 61 = -0.675*8$

$X = 55.6$

25% of the students exam scores fall below 55.6.

(b) Suppose the professor decides to grade on a curve. If the professor wants 0.15% of the students to get an A, what is the minimum score for an A?

This is the 100 - 0.15 = 99.85th percentile, which is X when Z has a p-value of 0.9985. So X when Z = 2.96.

$Z = \frac{X - \mu}{\sigma}$

$2.96 = \frac{X - 61}{8}$

$X - 61 = 2.96*8$

$X = 84.68$

The minimum score for an A is 84.68.

8 0

3 years ago

Sven participates in his employer’s 401k plan. His annual salary is $52,000. Sven contributes 7.5% of his annual salary. His emp

IgorLugansk [536]

Answer:

$ 6,500

Step-by-step explanation:

(52,000)(0.075)+(52,000)(0.05) = 3,900 + 2,600

= 6,500

5 0

2 years ago

A company is designing a new cylindrical water bottle. The volume of the bottle will be 179 cmcubed. The height of the water bot

tresset_1 [31]

Answer:

The radius of the water bottle is 2.72cm

Step-by-step explanation:

In this question, we are concerned with calculating what the radius of the cylindrical water bottle is given its volume and height.

Mathematically, the volume of a cylinder is V = pi * r^2 * h

From the question, we know that V = 179 cm^3. , h = 7.7cm while r = ?

we substitute these values into the volume equation.

179 = pi * r^2 * 7.7

179 = 3.14 * r^2 * 7.7

179 = 24.178 * r^2

r^2 = 179/24.178

r^2 = 7.403

r = square root 7.403

r = 2.72 cm

7 0

3 years ago

The coordinate m is 2.5 and mn=4. What are the possible coordinates for n

steposvetlana [31]

Refer to the figure shown below.

The coordinates of point m are (2,5).
Let (x,y) = the coordinates of pont n.

Because mn = 4, use the Pythagorean theorem to obtain
(x - 2)² + (y - 5)² = 4²

This represents a circle with center at (2,5) and radus = 4.

Answer:
Possible coordinates for n lie on the circle (x-2)² + (y-5)² = 16.

7 0

3 years ago