Bill has $50 to spend on 2 birthday presents for his friends. If he spends $2.50 each for birthday cards, what is the range of money he can spend on each gift? Write and solve an inequality.

Answer:

Step-by-step explanation:

first use tan Ф = opp /adj      to find x         tan(30) = √3 / 3

then use sin Ф = opp / hyp   to find y         sin(30) = 1/2

       tan(30) = (√3) / 3  =  x / 48

                           x = (48√3) / 3

                          x = 16√3

        sin(30) = 1/2  = x / y

                        y  =  x / (1/2)

                        y  =  2x        x = 16√3

                        y  =  2[16√3]

                        y  =  32√3

check  using      a² + b²  = c²

             x² + 48² = y²

            (16√3)² + 48² = (32√3)²

           256 · 3  + 2304  =  1024 · 3

           768   +  2304   =   3072

                         3072  =  3072

Answer:

Step-by-step explanation:

tan(G) = 28.2/45.8

G = arctan(28.2/45.8) = 31.6°

Answer:

D. 7 1/2

Step-by-step explanation:

-3 divided by -2/5

-(-3(-5/2)

-(-3 x 5/2)

-15/2

7 1/2

Hope it helps

Answer:

w < 9

Step-by-step explanation:

w + 9 < 18

To solve this inequality, we MUST get the w by itself

Subtraction Property of Equality  w + 9 - 9 < 18 - 9

Answer w < 9

Answer:

Its A

Step-by-step explanation:

Answer:

H

Step-by-step explanation:

(5x-3) x (2x+7)

10x^2 + 35x - 6x - 21

10x^2 + 29x - 21

Answer:

r(t)= -3/t+6

r(t)= -3/6t=6

Answer: the answer is D

Step-by-step explanation:

Just did the assignment rn

Answer:

[tex]20[/tex]

Step-by-step explanation:

[tex]12[/tex]²[tex]+16[/tex]²[tex]=400.[/tex]

[tex]\sqrt{400}[/tex][tex]=20[/tex]

Answer:

15

Step-by-step explanation:

ΔRST ≈ ΔRDE

[tex]\frac{RS}{RT} =\frac{RD}{RE} \\\\\frac{35}{56} =\frac{x}{24} \\\\56x=840\\x=15[/tex]

RD = 15

Answer:

8.643, 8.639

Step-by-step explanation:

Step-by-step explanation:

What is the number 8.64 rounded to the nearest tenth? -

What is 2.098 rounded to two decimal places? ... You could also use round-to-odd, which is like round-to-even in its ability to remove bias, ...

A. [tex]3x-2x+0.5x=1.5x[/tex], so the expressions are equivalent.

B. [tex]3(x+4)-2(x+4)=x+4[/tex], so the expressions are not equivalent. To make the expressions equivalent, add 1 to expression B.

C. [tex]6(x+4)-2(x+5)=6x+24-2x-10=4x+14=2(2x+7)[/tex], so the expressions are equivalent.

D. [tex]3(x+4)-2(x+4)+0.5(x+4)=1.5(x+4)[/tex], so the expressions are not equivalent. To make the expressions equivalent, multiply expression B by (x+4).

Answer:

15: Yes, no, yes, yes, no; 16A: C = ($0.29)X + ($1.45)Y + ($2.50)Z; 16B: Yes

Step-by-step explanation:

For question 15: We need to multiply the widths and lengths given to see if they equal the area we are trying to achieve. Therefore, some of them work, and some do not.

For question 16:

Part A: We'll set a variable for the number of each supply she can buy. Pencils will be represented by X, pens by Y and Notebooks by Z, and we'll represent total cost by C. The total cost will therefore be represented by C = ($0.29)X + ($1.45)Y + ($2.50)Z.

Part B: We'll plug the numbers of items she wants to buy into our formula and see if it comes out to less than $20. So in this case C = ($0.29)(3) + ($1.45)(4) + ($2.50)(2). Therefore, C = $11.67, which is less than $20, so she can afford her school supplies.

Answer:

Step-by-step explanation:

1. Not a function

2. Not a Function

3. Function

Answer: 97

Step-by-step explanation:

2 and 3 form a supplementary angel, so the sum of the angles should equal 180

Answer:

bro its 10

Step-by-step explanation:

5 kilometers in 30mins and if he stayed at the same rate for an hour he would have ran 10 kilometers cause 5 x 2 = 10

Answer: The answer is C

Step-by-step explanation:

Answer:

B : 177

Step-by-step explanation:

hello :

put x=3.5 in the equation you have : y = 50(3.5)+2 =175+2=177

Answer:

x = 1/2

y = -1/3

Step-by-step explanation:

10x - 9y = 8    (Multiply by 3)

15x + 21y = 0.5 (Multiply by -2)

30x - 27y = 24

-30x - 42y = -1

-69y = 23

y = -1/3

10x - 9y = 8

10x - 9(-1/3) = 8

10x + 3 = 8

10x = 5

x = 1/2

Answer:

Your answer is 15/8

Answer:

X = 2 If the exponent 2 in the 2 does not have the x

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Answer:

the answer is 55m^2 I think

Answer:

55 is the Area

Step-by-step explanation:

4 x 10 = 40

5 x 3 = 15

15 ÷ 2 = 7.5

5 x 3 = 15

15 ÷ 2 = 7.5

7.5 + 7.5 = 15

40 + 15 = 55

Give Me Brainllest

Answer:

a) The mean for the total revenue he earns per game is of 13.2K while the standard deviation is of 3.63K.

b) 0.05 = 5% probability that he has four goals and two assists in one game

Step-by-step explanation:

In hockey, a point is counted for each goal or assist of the player.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval. The standard deviation is the square root of the mean.

(a) Find the mean and standard deviation for the total revenue he earns per game.

60% of six are goals, which means that 60% of the time he earned 3K.

40% of six are goals, which means that 40% of the time he earned 1K.

The mean is:

[tex]\mu = 6*0.6*3 + 6*0.4*1 = 13.2[/tex]

The standard deviation is:

[tex]\sigma = \sqrt{\mu} = \sqrt{13.2} = 3.63[/tex]

The mean for the total revenue he earns per game is of 13.2K while the standard deviation is of 3.63K.

(b) What is the probability that he has four goals and two assists in one game

Goals and assists are independent of each other, which means that we find the probability P(A) of scoring four goals, the probability P(B) of getting two assists, and multiply them.

Probability of four goals:

60% of 6 are goals, which means that:

[tex]\mu = 6*0.6 = 3.6[/tex]

The probability of scoring four goals is:

[tex]P(A) = P(X = 4) = \frac{e^{-3.6}*(3.6)^{4}}{(4)!} = 0.19122[/tex]

Probability of two assists:

40% of 2 are assists, which means that:

[tex]\mu = 6*0.4 = 2.4[/tex]

The probability of getting two assists is:

[tex]P(B) = P(X = 2) = \frac{e^{-2.4}*(2.4)^{2}}{(2)!} = 0.26127[/tex]

Probability of four goals and two assists:

[tex]P(A \cap B) = P(A)*P(B) = 0.19122*0.26127 = 0.05[/tex]

0.05 = 5% probability that he has four goals and two assists in one game

Answer:

0.0814 = 8.14% probability that at least one of the women has a Chlamydia infection

Step-by-step explanation:

For each women, there are only two possible outcomes. Either they have a Chlamydia infection, or they do not. The probability of a woman having the infection is independent of any other women. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The Centers for Disease Control and Prevention reports that the rate of Chlamydia infections among U.S. women ages 20 to 24 is 2791.5 per 100,000.

This means that:

[tex]p = \frac{2791.5}{100000} = 0.027915[/tex]

Take a random sample of three U.S. women in this age group.

This means that [tex]n = 3[/tex]

What is the probability that at least one of the women has a Chlamydia infection?

This is:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{3,0}.(0.027915)^{0}.(1-0.027915)^{3} = 0.9186[/tex]

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.9186 = 0.0814[/tex]

0.0814 = 8.14% probability that at least one of the women has a Chlamydia infection

Answer:

3

Step-by-step explanation:

[tex]72[/tex]÷[tex]24=3[/tex]

Answer:

x = 5

Step-by-step explanation:

x^2 * 5x = 5x^3

5x^3 = 625            Divide by 5

x^3 = 625/5

x^3 = 125               Take the cube root of 125

x = 5

Answer: More than 26.5 inches

Step-by-step explanation:

Solve this equation :

[tex]\frac{32+24+x}{3} \geq 27.5[/tex]

x>26.5