In a recent poll, 32% of the referees who were surveyed said that ejecting angry coaches was their favorite thing to do. If 152 referees gave this response, how many were surveyed in total?

Answers

Answer 1

Answer:

Answer: 475 referees were surveyed in total.

Step-by-step explanation:

Let x represent the number of referees that were surveyed.

In a recent poll, 32% of the referees who were surveyed said that ejecting angry coaches was their favorite thing to do. This means that the number of referees that gave this response is

32/100 × x = 0.32 × x = 0.32x

If 152 referees gave this response, then the total number of referees that were surveyed would be

0.32x = 152

x = 152/0.32 = 475

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Write the explicit formula for the geometric sequence. Then find the fifth term in the sequence. a1 = –4, a2 = 8, a3 = –16

83. Use properties of exponents to rewrite each expression with only positive, rational exponents. Then find the numerical value of each expression when x = 9, y= 8, and z= 16. In each case, the expression evaluates to a rational number.b. 11√y2z4

Answers

Answer:

$2^{(18)/(11)}$

Step-by-step explanation:

The given expression is

$\sqrt[11]{y^2z^4}$

The exponent property $\sqrt[n]{x^ay^b}=x^(a/n)y^(b/n)$

Applying this exponent property, we have

$\sqrt[11]{y^2z^4}\n\n=y^(2/11)z^(4/11)$

Now, the given numeric values are x = 9, y= 8, and z= 16

On substituting these values in the simplified expression, we get

$(2)^(2/11)(16)^(4/11)$

This can be further simplified by writing $16=2^4$

$(2)^(2/11)(2^4)^(4/11)\n\n(2)^(2/11)(2)^(16/11)$

Now, applying the product rule of exponent: $x^a\cdot x^b=x^(a+b)$

$(2)^(2/11+16/11)\n\n=2^{(18)/(11)}$

make a sequence of integers that starts with 43. each new term is the sum of the squares of the digits of the previous term. the sequence would be a₁= 43, a₂= 4²+3² =25, and so on. keep going until you find the first integer that appears twice in the sequence

Answers

a₁ = 43
a₂ = 4² + 3² = 16 + 9 = 25
a₃ = 2² + 5² = 4 + 25 = 29
a₄ = 2² + 9² = 4 + 81 = 85
a₅ = 8² + 5² = 64 + 25 = 89
a₆ = 8² + 9² = 64 + 81 = 145
a₇ = 1² + 4² + 5² = 1 + 16 + 25 = 42
a₈ = 4² + 2² = 16 + 4 = 20
a₉ = 2² + 0² = 4 + 0 = 4
a₁₀ = 4² = 16
a₁₁ = 1² + 6² = 1 + 36 = 37
a₁₂ = 3² + 7² = 9 + 49 = 58
a₁₃ = 5² + 8² = 25 + 64 = 89

As we can see, the first integer that appears twice in the sequence is 89.

To form a right triangle, Emil put together three square tiles with side lengths of 12 centimeters, 15 centimeters, and x centimeters. Which statement is true about the area A of the smallest tile?

Answers

Answer: A= 15^2 - 12^2

Step-by-step explanation:

Answer:

yes,because it passes the vertical line test

Step-by-step explanation:

How you solve b-9+6b=30

Answers

b - 9 + 6b = 30

b+ 6b - 9 = 30

7b - 9 = 30

7b = 39

b = $(39)/(7)$

Nice days...........

associative property is moving a+b=b+a
add like terms
1b+6b-9=30
7b-9=30
add 9 to both sides
7b=39
divide both sides by 7
b=39/7
39/7=5 and 4/7

Solve for x: −3|2x + 6| = −12 A.) x = 1 and x = 5
B.) x = −1 and x = −5
C.) x = −9 and x = 3
D.) No solution

Answers

Since this is an equation involving an absolute value, let 2x + 6 be positive first such that,

-3(2x + 6) = -12
2x + 6 = 4
2x = -2, x = -1
Then, let 2x + 6 be negative,
-3(-2x - 6) = -12
-2x - 6 = 4
-2x = 10 ; x = -5
Thus, the answer to this item is letter B.

$-3|2x + 6| = -12 \n|2x+6|=4\n2|x+3|=4\n|x+3|=2\nx+3 =-2 \vee x+3=2\nx=-5 \vee x=-1$