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2 years ago

In ΔXYZ, ∠Y=90° and ∠X=24°. ∠ZWY=81° and XW=7.1. Find the length of WY to the nearest 10th.

Mathematics

1 answer:

Brums [2.3K]2 years ago

4 0

Answer:

0.5

Step-by-step explanation:

delta math

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How many positive integers can be expressed ad a product of two or more of the prime numbers 5,7,11,and 13 if no one product is

sertanlavr [38]

Answer:

11 positive integers can be expressed.

Step-by-step explanation:

Consider the provided information.

The number of possible prime numbers are 5,7,11,and 13.

There are 4 possible prime numbers.

How many positive integers can be expressed as a product of two or more of the prime numbers, that means there can be product of two numbers, three number or four numbers.

The formula to calculate combinations is: $^nC_r=\frac{n!}{r!(n-r)!}$

The number of ways are:

$^4C_2+^4C_3+^4C_4=\frac{4!}{2!(4-2)!}+\frac{4!}{3!(4-3)!}+\frac{4!}{4!}$

$^4C_2+^4C_3+^4C_4=\frac{4!}{2!2!}+\frac{4!}{3!}+1$

$^4C_2+^4C_3+^4C_4=6+4+1$

$^4C_2+^4C_3+^4C_4=11$

Hence, 11 positive integers can be expressed.

8 0

2 years ago

Hi, I have a Q, how do I use it?

anygoal [31]

Answer:

use what

Step-by-step explanation:

3 0

1 year ago

A rectangular box is to have a square base and a volume of 12 ft3. If the material for the base costs $0.17/ft2, the material fo

katen-ka-za [31]

Answer:

(a)Length =2 feet

(b)Width =2 feet

(c)Height=3 feet

Step-by-step explanation:

Let the dimensions of the box be x, y and z

The rectangular box has a square base.

Therefore, Volume of the box $V=x^2z$

Volume of the box $=12 ft^3\\$

$Therefore, x^2z=12\\z=\frac{12}{x^2}$

The material for the base costs $\$0.17/ft^2$ , the material for the sides costs $\$0.10/ft^2$ , and the material for the top costs $\$0.13/ft^2$ .

Area of the base $=x^2$

Cost of the Base $=\$0.17x^2$

Area of the sides $=4xz$

Cost of the sides= $=\$0.10(4xz)$

Area of the Top $=x^2$

Cost of the Base $=\$0.13x^2$

Total Cost, $C(x,z) =0.17x^2+0.13x^2+0.10(4xz)$

Substituting $z=\frac{12}{x^2}$

$C(x) =0.17x^2+0.13x^2+0.10(4x)(\frac{12}{x^2})\\C(x)=0.3x^2+\frac{4.8}{x} \\C(x)=\dfrac{0.3x^3+4.8}{x}$

To minimize C(x), we solve for the derivative and obtain its critical point

$C'(x)=\dfrac{0.6x^3-4.8}{x^2}\\Setting \:C'(x)=0\\0.6x^3-4.8=0\\0.6x^3=4.8\\x^3=4.8\div 0.6\\x^3=8\\x=\sqrt[3]{8}=2$

Recall: $z=\frac{12}{x^2}=\frac{12}{2^2}=3\\$

Therefore, the dimensions that minimizes the cost of the box are:

(a)Length =2 feet

(b)Width =2 feet

(c)Height=3 feet

7 0

2 years ago

What is the value of x?

vitfil [10]

Answer:

x = 27

Step-by-step explanation:

Based on the angle bisector theorem, we would have the following:

(x + 8)/10 = (2x - 5)/14

Cross multiply

14(x + 8) = 10(2x - 5)

14x + 112 = 20x - 50

Collect like terms

14x - 20x = -112 - 50

-6x = -162

Divide both sides by -6

-6x/-6 = -162/-6

x = 27

8 0

2 years ago

At a sale, suits were sold for $116 each. This price was 58% of a suit's original price. How much did a suit originally cost?

Fudgin [204]

To find the original price first put the % into decimal form.

58% is 0.58.

Then divide the discounted price ($116) by the % in decimal form:

116 / 0.58

Original price is $200.00

4 0

2 years ago