Carla earns $564 for 30 hours of work. Which represents the unit rate?

a) $30 per hour
b) $168 per hour
c) $18.80 per hour
d) $5.30 per hour ​

Answer:

X = 5

Step-by-step explanation:

If 4x = 20

And we are asked to find the solution.

It simply means looking for the value of x

So

4x = 20

X = 20/4

X = 5

X is simply the solution

X = 5

Answer:

D 2.16

Step-by-step explanation:

a p e x just use log

Answer:

Option B

Step-by-step explanation:

The number that had never been married will vary in each sample due to the random selection of adults.

This number will vary in each sample to the random selection process but they might or might not be as close as possible to one another after sampling.

Answer:

[tex] 167.47 \: {cm}^{3} [/tex]

Step-by-step explanation:

[tex]V_{cone} = \frac{1}{ 3} \pi {r}^{2}h \\ \\ = \frac{1}{ 3} \pi \times {4}^{2} \times 10 \\ \\ = \frac{1}{ 3} \times 3.14 \times 16 \times 10 \\ \\ = \frac{1}{ 3} \times \: 502.4 \\ \\ = 167.466667 \\ \\ = 167.47 \: {cm}^{3} [/tex]

Step-by-step explanation:

can u give image PlZzzzz ....

Answer:

Hey!

Your answer should be Y=2x+4

Step-by-step explanation:

Hope this helps!

Step-by-step explanation:

y=7x-10

Answer:

[tex]\huge \boxed{y=7x-10}[/tex]

Step-by-step explanation:

[tex]-7x+y=-10[/tex]

[tex]\sf Add \ 7x \ on \ both \ sides.[/tex]

[tex]-7x+y+7x=-10+7x[/tex]

[tex]y=7x-10[/tex]

Answer:

-45/2 - 12/2 = -57/2

Step-by-step explanation:

Substitute 15 for x in the given equation:  y = (-3/2)x - 6 becomes

y = (-3/2)(15) - 6 = -45/2  -  6 when x = 15.  This is equivalent to -57/2

Answer:

see below

Step-by-step explanation:

You can remove one or more of the other color marbles to increase the probability of drawing a green marble

or

You can add  one or more green marbles to have more green marbles in the bag

Answer:

a. 0.4772 = 47.72 %

b. 0.7605 = 76.05 %

Step-by-step explanation:

What we must do is calculate the z value for each value and thus find what percentage each represents and the subtraction would be the percentage between those two values.

We have that z is equal to:

z = (x - m) / (sd)

x is the value to evaluate, m the mean, sd the standard deviation

a. ind the least proportion of data falls between 70 and 80 If the histogram is bell shaped:

So for 70 copies we have:

z = (70 - 70) / (5)

z = 0

and this value represents 0.5

So for 80 copies we have:

z = (80 - 70) / (5)

z = 2

and this value represents 0.9772

p (70 > x > 80) = 0.9772 - 0.5

p (70 > x > 80) = 0.4772 = 47.72 %

b.  Find the proportion of data between 65 and 77

So for 65 copies we have:

z = (65 - 70) / (5)

z = -1

and this value represents 0.1587

So for 77 copies we have:

z = (77 - 70) / (5)

z = 1.4

and this value represents 0.9192

p (65 > x > 77) = 0.9192 - 0.1587

p (65 > x > 77)  = 0.7605 = 76.05 %

Answer:

9672 per year

Step-by-step explanation:

Take the amount he earns per week times the number of weeks he works

186* 52

9672 per year

Answer:

$9672

Step-by-step explanation:

Jack earns $186 in 1 week.

In 52 weeks,

186 × 52 = 9672

He earns $9672.

The missing part in the question;

and the payoff is $2.20 won for every dollar bet. (As the player’s probability of winning in this case is [tex]\dfrac{1}{4}[/tex]........

Also:

For such a bet, the casino pays off as shown in the following table.

The table can be shown as:

Keno Payoffs in 10 Number bets

Number of matches        Dollars won for each $1 bet

0  -   4                                        -1

5                                                  1

6                                                  17

7                                                  179

8                                                 1299

9                                                 2599

10                                               24999

Answer:

Step-by-step explanation:

Given that:

Twenty numbers are selected at random by the casino from the set of numbers 1 through 80

A player can select from 1 to 15 numbers; a win occurs if some fraction of the player’s chosen subset matches any of the 20 numbers drawn by the house

Let assume X to represent the numbers of player chooses which are in the Casino-selected-set of 20.

Let assume the random variable X has a hypergeometric distribution with parameters  N= 80 and m =20.

Then, the probability mass function of a hypergeometric distribution can be defined as:

[tex]P(X=k)=\dfrac{(^m_k)(^{N-m}_{n-k})}{(^N_n)}, k =1,2,3 ... n[/tex]

Now; the probability that i out of  n numbers chosen by the player among 20  can be expressed as:

[tex]P(X=k)=\dfrac{(^{20}_k)(^{60}_{n-k})}{(^{80}_n)}, k =1,2,3 ... n[/tex]

Also; given that ; When the player selects 2 numbers, a payoff (of odds) of $12 won for every $1 bet is made when both numbers are among the 20

So; n= 2; k= 2

Then :

Probability P ( Both number in the set 20)  [tex]=\dfrac{(^{20}_2)(^{60}_{2-2})}{(^{80}_2)}[/tex]

Probability P ( Both number in the set 20) [tex]= \dfrac{20*19}{80*79}[/tex]

Probability P ( Both number in the set 20) [tex]=\dfrac{19}{316}[/tex]

Probability P ( Both number in the set 20) [tex]=\dfrac{1}{16.63}[/tex]

Thus; the payoff odd for [tex]=\dfrac{1}{16.63}[/tex] is 16.63:1 ,as such fair payoff in this case is $16.63

Again;

Let assume X to represent the numbers of player chooses which are in the Casino-selected-set of 20.

Let assume the random variable X has a hypergeometric distribution with parameters  N= 80 and m =20.

The probability mass function of the hypergeometric distribution can be defined as :

[tex]P(X=k)=\dfrac{(^m_k)(^{N-m}_{n-k})}{(^N_n)}, k =1,2,3 ... n[/tex]

Now; the probability that i out of  n numbers chosen by the player among 20  can be expressed as:

[tex]P(n,k)=\dfrac{(^{20}_k)(^{60}_{n-k})}{(^{80}_n)}, k =1,2,3 ... n[/tex]

From the table able ; the expected payoff can be computed as shown in the attached diagram below. Thanks.

Answer:x>-1

Step-by-step explanation:

Step 1: Subtract 3 from both sides.

-3x+3-3<6-3

-3x<3

Step 2: Divide both sides by -3.

-3x/-3<3/3

X>-1

Answer:

a. p=0.562

b. E = 0.0253

c. The 90% confidence interval for the population proportion is (0.537, 0.587).

d. We have 90% confidence that the interval (0.537, 0.587) contains the true value of the population proportion.

Step-by-step explanation:

We have to calculate a 90% confidence interval for the proportion.

The sample proportion is p=0.562.

[tex]p=X/n=583/1038=0.562[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.562*0.438}{1038}}\\\\\\ \sigma_p=\sqrt{0.000237}=0.0154[/tex]

The critical z-value for a 90% confidence interval is z=1.645.

The margin of error (MOE) can be calculated as:

[tex]MOE=z\cdot \sigma_p=1.645 \cdot 0.0154=0.0253[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=p-z \cdot \sigma_p = 0.562-0.0253=0.537\\\\UL=p+z \cdot \sigma_p = 0.562+0.0253=0.587[/tex]

The 90% confidence interval for the population proportion is (0.537, 0.587).

We have 90% confidence that the interval contains the true value of the population proportion.

Answer:

See the answers below.

Step-by-step explanation:

[tex]a.\:\frac{f\left(x\right)-f\left(a\right)}{x-a}=\frac{2x^2-x-5-\left(2a^2-a-5\right)}{x-a}\\\\=\frac{2x^2-x+a-2a^2}{x-a}\\\\=\frac{2\left(x+a\right)\left(x-a\right)-1\left(x-a\right)}{x-a}\\\\=\frac{\left(x-a\right)\left[2\left(x+a\right)-1\right]}{x-a}\\\\=2x+2a-1\\\\\\b.\:\frac{f\left(x+h\right)-f\left(x\right)}{h}=\frac{2\left(x+h\right)^2-\left(x+h\right)-5-\left(2x^2-x-5\right)}{h}\\\\=\frac{2\left(x^2+2xh+h^2\right)-\left(x+h\right)-5-\left(2x^2-x-5\right)}{h}\\[/tex]

Expand and simplify to get:

[tex]=\frac{2h^2+4xh-h}{h}\\\\=\frac{h\left(2h+4x-1\right)}{h}\\\\=2h+4x-1[/tex]

Best Regards!

Answer:

first you need to multiply -6 and 3

Answer:

-6 and 3

Step-by-step explanation:

sorry it was an late answer I'm just tryna gain points :D

Answer:

a) The volume of the wooden block is 240 cm^3.

b) The density of the wooden block is 0.7 g/cm^3.

Step-by-step explanation:

The volume of the rectangular wooden block can be calculated as the multiplication of the length in each dimension: length, wide and height.

With dimensions 10 cm x 3 cm x 8 cm, the volume is:

[tex]V=L\cdot W\cdot H = 10\cdot 3\cdot 8=240[/tex]

The volume of the wooden block is 240 cm^3.

If we know that the mass of the wooden block is 168 g, we can calculate the density as:

[tex]\rho = \dfrac{M}{V}=\dfrac{168}{240}=0.7[/tex]

The density of the wooden block is 0.7 g/cm^3.

Answer:

3m + 4c

Step-by-step explanation:

Whenever a word problem says the word earn that means the slope, also known as the rate of change, will be positive. Knowing this you can determine that both the caramel and milk chocolate slopes will be positive. After figuring all that out the only thing left to do is to make the equation. You know you have two slopes, and each slope needs a variable, so you will have to look back at the question. It is given that m represents the milk chocolate and c represents the caramel. Now all you have to do is make the slope the coefficient to the corresponding variable. The milk chocolates are 3 dollars, so the 3 goes in front of the m and the caramel chocolates are 4 dollars, so teh 4 goes in front of the 4. Since both slopes are positive no negatives or minus signs will be used in the equation. Knowing all this information you can now create the expression 3m + 4c.

Answer:

D

Step-by-step explanation:

3m + 4c

Answer:

a = T - 4

Step-by-step explanation:

Simply just subtract 4 on both sides to get the answer!

Answer:

a=T-4

Step-by-step explanation:

subtract 4

Answer: 41 candles

Step-by-step explanation:

Multiply the dimensions of the candle first.

V = l*w*h

7 * 2 = 14

14 * 10 = 140

Now, divide the total amount of wax used by the amount of wax used for one candle.

5,740 / 140 = 41

Answer:

The probability that at exactly one of them does exactly two language classes is 0.32.

Step-by-step explanation:

We can model this variable as a binomial random variable with sample size n=2.

The probability of success, meaning the probability that a student is in exactly two language classes can be calculated as the division between the number of students that are taking exactly two classes and the total number of students.

The number of students that are taking exactly two classes is equal to the sum of the number of students that are taking two classes, minus the number of students that are taking the three classes:

[tex]N_2=F\&S+S\&G+F\&G-F\&S\&G=12+4+6-2=20[/tex]

Then, the probabilty of success p is:

[tex]p=20/100=0.2[/tex]

The probability that k students are in exactly two classes can be calcualted as:

[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{2}{k} 0.2^{k} 0.8^{2-k}\\\\\\[/tex]

Then, the probability that at exactly one of them does exactly two language classes is:

[tex]P(x=1) = \dbinom{2}{1} p^{1}(1-p)^{1}=2*0.2*0.8=0.32\\\\\\[/tex]

Answer:

36=2×3×3×3

Answer

[tex]36 = 2 \times 2 \times 3 \times 3 \\ \: \: \: \: \: \: \: \: = {2}^{2} \times {3}^{2} [/tex]

Step-by-step explanation:

First write the prime factors of 36 that you can see here

[tex]2 \: \: \: 2 \: \: \: 3 \: \: \: 3[/tex]

Now write 36 as a product of its prime factors.

[tex]36 = 2 \times 2 \times 3 \times 3 \\ \: \: \: \: \: \: \: \: = {2}^{2} \times {3}^{2} [/tex]

Answer:

[tex]\boxed{\df\ \dfrac{-19}{2}}[/tex]

Step-by-step explanation:

Hi,

x=-2

it gives

9*(-2)-4y=20

<=> -18-4y=20

<=> 18-18-4y=20+18=38

<=> -4y=38

<=> y = -38/4=-19/2

hope this helps

Answer:

Considering the audience helps a writer identify the types of details and language needed in the writing. Considering the audience helps the writer identify what is important to him or her. Considering the audience allows the writer to write about what he or she wants. Knowing the audience for a particular essay is important because it determines the content that will appear in the writing. If you are arguing for a change to occur, identifying the level at which you want this change to occur and/or the people you want to persuade to help create this change (audience) is important step by step

Answer:

The probability that none of the households are tuned to 50 Minutes is 0.04398.

Step-by-step explanation:

We are given that the television show 50 Minutes has been successful for many years. That show recently had a share of 20, meaning that among the TV sets in use, 20% were tuned to 50 Minutes.

A pilot survey begins with 14 households have TV sets in use at the time of a 50 Minutes broadcast.

The above situation can be represented through binomial distribution;

[tex]P(X = r)= \binom{n}{r} \times p^{r} \times (1-p)^{n-r} ;x = 0,1,2,3,.........[/tex]

where, n = number of samples (trials) taken = 14 households

r = number of success = none of the households are tuned to 50 min

p = probability of success which in our question is probability that households were tuned to 50 Minutes, i.e. p = 20%

Let X = Number of households that are tuned to 50 Minutes

So, X ~ Binom(n = 14, p = 0.20)

Now, the probability that none of the households are tuned to 50 Minutes is given by = P(X = 0)

               P(X = 0)  =  [tex]\binom{14}{0} \times 0.20^{0} \times (1-0.20)^{14-0}[/tex]

                              =  [tex]1 \times 1 \times 0.80^{14}[/tex]

                              =  0.04398

Answer:

55.82 cm

Step-by-step explanation:

d1= 8.72 cm

a= 15.6 cm

A rhombus= 1/2*d1*d2 = A square

A square= 15.6²= 243.36 cm²

d2= 2A/d1= 2*243.36/8.72 ≈55.82 cm

Answer:

The formula is 1/2h(a+b)

h stands for the perpendicular height

a and b stand for the two horizontal lengths which are parallel to each other

Answer:

x= -3 +√2 ≈ -0.1716,  and x = - 3 -2√2 ≈ -5.8284

Step-by-step explanation:

y= -1/2(x+3)² +4

For x -intercept, y = 0.

0 = - 1/2(x+3)² + 4 /*(-2)

0 = (x+3)² - 8

(x+3)² = 8

√(x+3)² = +/-√8

x+3 = +/-√8

x = - 3+/- 2√2

x= -3 +√2 ≈ -0.1716,  and x = - 3-2√2 ≈ -5.8284

Answer:

Step-by-step explanation:

The question is incomplete and lacks the required diagram. Find the diagram attached. Here is also the complete question.

"The formula for the area of a parallelogram is A = bh, where b is the base and h is the height. Which simplified expression represents the area of the parallelogram? –4x3 + 14x – 24 square centimeters 2x3 – 6x2 – 14x + 24 square centimeters –4x3 – 14x + 24 square centimeters 2x3 + 6x2 + 14x + 24 square centimeters"

Area of a parallelogram = Base * Height.

Given the height of the parallelogram = (x-4)cm

Base = (2x² + 2x-6) cm

Area of the parallelogram =  (x-4)cm *  (2x² + 2x-6) cm

Area of the parallelogram = (x-4)(2x²+2x-6)

Area of the parallelogram = 2x³+2x²-6x-8x²-8x+24

= 2x³+2x²-8x²-6x-8x+24

=  (2x³-6x²-14x+24)cm²

Answer:

The answer is A) -9.7 > -18.2

Step-by-step explanation:

This is because, when you are thinking about negative numbers, the closer they are to 0, the greater they are. So, it is warmer in Minnesota.

Answer:

A and A

Step-by-step explanation:

Step-by-step explanation:

solve f(x) by supposing it has y and and then interchange it with x .

hope this is helpful

Answer:

a) The probability that a student will do homework regularly and also pass the course = P(H n P) = 0.57

b) The probability that a student will neither do homework regularly nor will pass the course = P(H' n P') = 0.12

c) The two events, pass the course and do homework regularly, aren't mutually exclusive. Check Explanation for reasons why.

d) The two events, pass the course and do homework regularly, aren't independent. Check Explanation for reasons why.

Step-by-step explanation:

Let the event that a student does homework regularly be H.

The event that a student passes the course be P.

- 60% of her students do homework regularly

P(H) = 60% = 0.60

- 95% of the students who do their homework regularly generally pass the course

P(P|H) = 95% = 0.95

- She also knows that 85% of her students pass the course.

P(P) = 85% = 0.85

a) The probability that a student will do homework regularly and also pass the course = P(H n P)

The conditional probability of A occurring given that B has occurred, P(A|B), is given as

P(A|B) = P(A n B) ÷ P(B)

And we can write that

P(A n B) = P(A|B) × P(B)

Hence,

P(H n P) = P(P n H) = P(P|H) × P(H) = 0.95 × 0.60 = 0.57

b) The probability that a student will neither do homework regularly nor will pass the course = P(H' n P')

From Sets Theory,

P(H n P') + P(H' n P) + P(H n P) + P(H' n P') = 1

P(H n P) = 0.57 (from (a))

Note also that

P(H) = P(H n P') + P(H n P) (since the events P and P' are mutually exclusive)

0.60 = P(H n P') + 0.57

P(H n P') = 0.60 - 0.57

Also

P(P) = P(H' n P) + P(H n P) (since the events H and H' are mutually exclusive)

0.85 = P(H' n P) + 0.57

P(H' n P) = 0.85 - 0.57 = 0.28

So,

P(H n P') + P(H' n P) + P(H n P) + P(H' n P') = 1

Becomes

0.03 + 0.28 + 0.57 + P(H' n P') = 1

P(H' n P') = 1 - 0.03 - 0.57 - 0.28 = 0.12

c) Are the events "pass the course" and "do homework regularly" mutually exclusive? Explain.

Two events are said to be mutually exclusive if the two events cannot take place at the same time. The mathematical statement used to confirm the mutual exclusivity of two events A and B is that if A and B are mutually exclusive,

P(A n B) = 0.

But, P(H n P) has been calculated to be 0.57, P(H n P) = 0.57 ≠ 0.

Hence, the two events aren't mutually exclusive.

d. Are the events "pass the course" and "do homework regularly" independent? Explain

Two events are said to be independent of the probabilty of one occurring dowant depend on the probability of the other one occurring. It sis proven mathematically that two events A and B are independent when

P(A|B) = P(A)

P(B|A) = P(B)

P(A n B) = P(A) × P(B)

To check if the events pass the course and do homework regularly are mutually exclusive now.

P(P|H) = 0.95

P(P) = 0.85

P(H|P) = P(P n H) ÷ P(P) = 0.57 ÷ 0.85 = 0.671

P(H) = 0.60

P(H n P) = P(P n H)

P(P|H) = 0.95 ≠ 0.85 = P(P)

P(H|P) = 0.671 ≠ 0.60 = P(H)

P(P)×P(H) = 0.85 × 0.60 = 0.51 ≠ 0.57 = P(P n H)

None of the conditions is satisfied, hence, we can conclude that the two events are not independent.

Hope this Helps!!!