In Dale's cooler there are 9 bottles of soda and 6 bottles of water.
Dale is going to choose 8 bottles at random from the cooler to give to his friends.

What is the probability that he will choose 5 sodas and 3 waters? Round your answer to three decimal places.

Answer:

The radius of the circle is 12.006 m.

Step-by-step explanation:

Let us assume the radius of the circle = r

Circumference  = 75.4 m

Now, CIRCUMFERENCE OF A CIRCLE = 2 π r

⇒ 75 .4 m = 2 π r

Now, putting  π = 3.14, we get:

75 .4 m = 2 (3.14)  r

⇒ 75.4 = 6. 28 r

or, r = 75.4/6.28 =  12.006

or, r  = 12.006 m

Hence, the radius of the circle with circumference 75.4 m is 12.006 m.

Answer:

1.  45/482 of the students are in grade 4.

2.  5/9 of the students of the grade 4 are boys.

3. 7/15 of the grade 4 students are in Ms. Ashley's class

4. 3/4 of the students in Mr. Ben's class do not have siblings in the same school.

5. There are 14 students with glasses and 7 without glasses.

Step-by-step explanation:

1. Let's review the information given to us for solving the questions:

Number of students in the school = 482

Ms. Ashley's Grade 4 class = 21 students

Ms. Ashley's Grade 4 class boys = 15 students

Ms. Ashley's Grade 4 class girls = 6 students

Ms. Ashley's Grade 4 class with glasses = 2/3 * 21 = 42/3 = 14 students

Mr. Ben's Grade 4 class = 24 students

Mr. Ben's Grade 4 class boys = 10 students

Mr. Ben's Grade 4 class girls = 14 students

Mr. Ben's Grade 4 class with siblings in the school = 1/4 * 24 = 24/4 = 6 students

2. Let's answer all the questions:

1. What fraction of the students in the school are in grade 4?

(Ms. Ashley's Grade 4 class + Mr. Ben's Grade 4 class)/ Number of students in the school

21 + 24 / 482 = 45/482

2. What fraction of the grade 4 students are boys?

(Ms. Ashley's Grade 4 boys + Mr. Ben's Grade 4 boys)/ (Ms. Ashley's Grade 4 class + Mr. Ben's Grade 4 class)

15 + 10 / 21 + 24

25 / 45 = 5/9

3. What fraction of the grade 4 students are in Ms. Ashley's class?

Ms. Ashley's Grade 4 class / (Ms. Ashley's Grade 4 class + Mr. Ben's Grade 4 class)

21 / 21 + 24

21 / 45 = 7/15

4. What fraction of the students in Mr. Ben's class that do not have siblings in the same school?

(Mr. Ben's Grade 4 class - Mr. Ben's Grade 4 class with siblings in the school)/ Mr. Ben's Grade 4 class

24 - 6 / 24

18 / 24 = 3/4

5. In Ms. Ashley's class, are there more students that wear glasses or do not wear glasses?

There are 14 students with glasses and 7 without glasses.

Note: Same answer to question 14038475, answered by me.

Answer:

2x-5

Step-by-step explanation:

(4x-7)-(2x-2)=4x-2x-7-(-2)=2x-7+2=2x-5

Answer:

2x-5

Step-by-step explanation:

For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cut-off point with the y axis

We have two points that belong to the AB line:

[tex](x_ {1}, y_ {1}) :( 2,1)\\(x_ {2}, y_ {2}): (- 1, -8)[/tex]

We can find the slope:

[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-8-1} {- 1-2} = \frac {-9} {- 3} = 3[/tex]

By definition, if two lines are parallel then their slopes are equal. Thus, a line parallel to AB will have slope [tex]m = 3[/tex], then the equation will be of the form:

[tex]y = 3x + b[/tex]

We substitute the given point and find b:

[tex](x, y) :( 0,2)\\2 = 3 (0) + b\\2 = b[/tex]

Finally, the equation is:

[tex]y = 3x + 2[/tex]

Answer:

[tex]y = 3x + 2[/tex]

Answer:

0.2

Step-by-step explanation:

Absolute values are positive version of any number. So the absolute value of both 0.2 and -0.2 would be 0.2

The product of 3 factorial is 6.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

We have to find the value of 3 factorial.

By the definition of factorial, factorial of any natural number can be defined as,

a factorial = 1 × 2 × ....... × (a - 1) × a

Here we have to find 3 factorial.

3 factorial can be written as,

3 factorial = 3 × 2 × 1 = 6 × 1 = 6

Hence the required product of 3 factorial is 6.

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Answer:

-3

Step-by-step explanation:

2(x+-3)=1/2x

2x+6=1/2x

6=-1/2x

x=-3

Answer:

-3 is the write answer

Step-by-step explanation:

2(x+3)=1/2x

2x+6=1/2x

6=-1/2x

x=-3

Answer:

The relationship between number of animals owned and the number of vet bills is an example positive correlation.

Step-by-step explanation:

Correlation:

Now, as the number of animals increase the number of vet bills will increase. Thus, it could be said that increase in one variable leads to increase in another variable.

Thus, the given relationship is an example of positive relationship or a positive correlation.

5/7 x 7/3

Multiply the numerators together and the denominators:

(5 x 7) / (7 x 3)

35/21 reduces to 5/3 = 1 2/3

Answer:

Tanya's average speed was [tex]\frac{1}{2}[/tex] laps per minutes.

Step-by-step explanation:

Tanya walked 15 laps on an indoor track in 30 minutes.

Therefore, the average speed of Tanya is [tex]\frac{15}{30} = \frac{1}{2}[/tex] laps per minutes.

Calculation:

The average speed formula is given by [tex] V = \frac{\textrm {Distance covered}}{\textrm {Number of munutes spent}}[/tex]

The distance is 15 laps.

The time is 30 minutes.

Therefore, [tex]V = \frac{15}{30}[/tex] laps per minute.

After simplification, [tex]V = \frac{1}{2}[/tex] laps per mins.

Therefore, Tanya's average speed was [tex]\frac{1}{2}[/tex] laps per minute. (Answer)

Final answer:

To find the radius of the circular trampoline, we can use the formula for the area of a circle and rearrange it to solve for the radius. The radius of the trampoline is approximately 6.5 ft (rounded to the nearest tenth).

Explanation:

To find the radius of the circular trampoline, we can use the formula for the area of a circle, which is A = πr². In this case, the area is given as 132.2 ft². We can rearrange the formula to solve for the radius:

r² = A/π

r² = 132.2/π

r ≈ √(132.2/π)

r ≈ √(42)

r ≈ 6.5 ft (rounded to the nearest tenth)

Final answer:

To find the radius of the trampoline, we use the formula for the area of a circle and rearrange it to solve for the radius. After substituting the given area and approximating π as 3.14, we find that the radius is approximately 6.5 ft when rounded to the nearest tenth.

Explanation:

The area of a circle is given by the formula A = πr², where A is the area and r is the radius of the circle. Given the area of the trampoline as 132.2 ft², we can solve for the radius using the area formula. We rearrange the formula to solve for the radius: r = √(A/π).

Substituting the given area and the approximate value for π (3.14), we get r = √(132.2/3.14). This simplifies to r = √(42.085...), which is approximately r = 6.487 ft. Rounding to the nearest tenth gives us a radius of 6.5 ft.

Answer:

[tex]\large\boxed{\dfrac{3x+6}{x-4}\div\dfrac{2x^2+9x+10}{x^2+4x}=\dfrac{3x(x+4)}{(x-4)(2x+5)}}[/tex]

Step-by-step explanation:

Just like that

[tex]\dfrac{3x+6}{x-4}\div\dfrac{2x^2+9x+10}{x^2+4x}=\dfrac{3x+6}{x-4}\cdot\dfrac{x^2+4x}{2x^2+9x+10}\\\\=\dfrac{3(x+2)}{(x-4)}\cdot\dfrac{x(x+4)}{2x^2+4x+5x+10}=\dfrac{3(x+2)}{(x-4)}\cdot\dfrac{x(x+4)}{2x(x+2)+5(x+2)}\\\\=\dfrac{3(x+2)}{(x-4)}\cdot\dfrac{x(x+4)}{(x+2)(2x+5)}\qquad\text{cancel}\ (x+2)\\\\=\dfrac{3x(x+4)}{(x-4)(2x+5)}[/tex]

A point B is (1 , -9)

Step-by-step explanation:

The formula of the slope of a line is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

where [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] are two points

lie on the line

We need to find a point B that makes that true

Assume that point B is (x , y)

∵ Point A = (5 , 3)

∵ Point B = (x , y)

∴ [tex]x_{1}=5[/tex] and [tex]x_{2}=x[/tex]

∴ [tex]y_{1}=3[/tex] and [tex]y_{2}=y[/tex]

- Substitute these values in the formula of m

∴ [tex]m=\frac{y-3}{x-5}[/tex]

∵ m(A , B) = 3

- Equate the formula of the slope by 3

∴ [tex]\frac{y-3}{x-5}=3[/tex]

- By using cross multiplication

∴ y - 3 = 3(x - 5)

- Simplify the right hand side

∴ y - 3 = 3x - 15

- Add 3 for both sides

∴ y = 3x - 12

To find point B chose any value for x and substitute it in the

equation to find y

∵ x = 1

∴ y = 3(1) - 12 = 3 - 12

∴ y = 9

∴ Point B = (1 , -9)

V.I.N: You can find many values of point B by chose different values of x and find the corresponding values of y

A point B is (1 , -9)

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Answer:

The corresponding answers to the questions are  9.625 cm² , 459, 304.5m², 1 : 3 , 3:4 , 10,000 pounds , 36 inches.

Step-by-step explanation:

1.

Area of triangle = 0.5 x base length x height

Here base length = 5.5cm and height = 3.5cm

So area will be 0.5 x 5.5 x 3.5 cm² = 9.625 cm²

2.

919/2 rounding off to nearest whole

We know that the value of 919/2 = 459.5 .

So the nearest whole number value to which it can be rounded off is 459.

3.

We know that area of parallelogram is base length x height

Here, base length =14.5m and height = 21m

So area = 14.5 x 21 m² = 304.5m²

4.

No. of grilled cheese sandwiches sold = 200

No. of tacos sold                                     = 100

No. of grilled chicken salads sold          = 150

Total lunches sold                                   = 200 + 100 + 150 = 450

So, ratio of chicken salads to lunches sold is 150 : 450 = 1 : 3

5.

Given number : 7,208,631

Odd digits here - 7,3,1 - 3 digits

Even digits here - 2,0,8,6 - 4 digits

So, ratio of odd digits to even digits is 3:4

6.

One ton = 2000 pounds

So 5 tons = 5 x ( 1 ton) = 5 x 2000 pounds = 10,000 pounds

7.

Table length = 3 feet

We know that 1 foot = 12 inches

So table length = 3 foot = 3 X 12 inches = 36 inches

Answer: 729

Step-by-step explanation: 1st term X common ratio(desired term-1)

The 7th term in the sequence is -2187.

To find the 7th term in the sequence 1, -3, 9, -27, ..., we can observe that each term is obtained by multiplying the previous term by -3. Therefore, to find the 7th term, we start with the first term 1 and repeatedly multiply by -3:

So, the 7th term in the sequence is -2187.

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Answer:

D. pyramid (not including the vertex)

E. prism

Step-by-step explanation:

D and E are the answers to this question.

D. pyramid (not including the vertex)

E. prism

Answer:

199.8°

Step-by-step explanation:

The circle has radius r = 7 ft.

Now, the circumference of the circle is given by the formula C = 2πr

So, [tex]C = 2 \times \frac{22}{7} \times 7 = 44[/tex] ft.

Now, 44 ft arc length is equivalent to 360°  

Hence, 24.42 ft arc length is equivalent to [tex]\frac{360}{44} \times 24.42 = 199.8[/tex] degree.

Therefore, the central angle is 199.8° (Answer)

Answer:

80cents per pound

Step-by-step explanation:

24 divided by 30 is .8

Answer:

 2[tex]\frac{1}{2}[/tex] cups

Step-by-step explanation:

Given, a recipe uses 8[tex]\frac{3}{4}[/tex] cups of milk for every 3[tex]\frac{1}{2}[/tex] cups of oatmeal.

So, For each 8.75 cups of milk ,3.5 cups of oatmeal is required.

Or,

we can say 3.5 cups of oatmeal require 8.75 cups of milk.

Thus,

1 Cup of oatmeal will require  [tex]\frac{8.75}{3.5}[/tex] cups of milk.

                                              =   2.5 cups of milk .

Thus answer is 2.5 cups, Which we can write 2 + 0.5 cups

                                                                      =  2[tex]\frac{1}{2}[/tex] cups (In mixed form)

Answer:13 hours

Step-by-step explanation:

So you would divide 737 (miles) by 11 (hours) in order to find how far he traveled in 1 hour. You should get 67. So he travels at 67 miles in 1 hour. Then you would divide 871(total miles) by 67(distance traveled in 1 hour) to find out how many hours it took to travel 871. You should get 13(hours).

Hoped it helped.

Answer:

$9.40

Step-by-step explanation:

well since you work 37.5 hours and you earn $352.50 you divide them to get your hourly wage

352.5 ÷ 37.5 = 9.4

so your hourly wage is $9.40

Final answer:

To calculate the hourly wage, the total earnings of $352.50 should be divided by the total work hours of 37.5. The hourly wage comes out to be $9.40.

Explanation:

To find out your hourly wage, you need to divide your total earnings by the number of work hours. In this instance, you worked 37.5 hours (since 1/2 an hour is equivalent to 0.5 hours) and earned $352.50. So, your hourly wage would be calculated as follows:

Hourly Wage = Total Earnings ÷ Number of Work Hours

Hourly Wage = $352.50 ÷ 37.5 hours

Hourly Wage = $9.40 per hour

Therefore, your hourly wage is $9.40.

Answer:

75% decrease

Step-by-step explanation:

Answer:

75%

Step-by-step explanation:

Answer:

Speed = 39.3 miles/hr

Time = 6.5 hrs.

Distance = Speed x time

= 39.3 x 6.5

= 245.45 miles (approx.)

Hope this helps!

Answer:

Speed = 39.3 miles/hr

Time = 6.5 hrs.

Distance = Speed x time

= 39.3 x 6.5

= 255.45 miles (approx.)

Step-by-step Explanation:

Answer:

  (-1/4)(2x +5y)

Step-by-step explanation:

Multiply and divide by -1/4:

  [tex]-\frac{1}{2}x-\frac{5}{4}y=\dfrac{(-\frac{1}{4})(-\frac{1}{2}x-\frac{5}{4}y)}{-\frac{1}{4}}=\left(-\dfrac{1}{4}\right)(-4)\left(-\dfrac{1}{2}x-\dfrac{5}{4}y\right)\\\\=\left(-\dfrac{1}{4}\right)\left(2x+5y)[/tex]

Answer:

[tex]log_{b}(b^{x r}) [/tex]

Step-by-step explanation:

A picture of the question is shown in the figure attached. There we can see that the step corresponding to Properties of exponents is the option:

[tex]log_{b}(b^{x r}) [/tex]

which is equivalent to

[tex]log_{b}((b^{x})^{r}) [/tex]

This question is based on the property of exponents.Therefore, the correct option is (c), [tex]\bold{log _a(b^{x r})}[/tex].

Given that :

[tex]\bold{log_a(M^r)}[/tex]

In this question, we have choose appropriate correct option for for given expression.

According to the question,

It is given that,

[tex]\bold{log_a(M^r)}[/tex]                                                                                            ...(1)

Now, substitute the value of M = [tex]\bold{b^{x}}[/tex]. We get,

Thus, [tex]\bold{log_a(M^r)} = \bold{log _a((b^{x})^r)}[/tex]                                                            ...(2)

As we know that, by using the property of exponents,

[tex]\bold{(x^{m})^n = x ^{mn}}[/tex]

Now, applying this property in expression (2).

We get,

[tex]\bold{log _a((b^{x})^r)} = \bold{log _a(b^{x r})}[/tex]

Therefore, the correct option is (c), [tex]\bold{log _a(b^{x r})}[/tex].

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Answer:

6

Step-by-step explanation:

Because you have to added than reverse the question than it will give you your answer backwards

Answer:

15

Step-by-step explanation:

Answer:

3*5

Step-by-step explanation:

GCF of 45 and 75 = 15

15: 1,3,5,15

3 and 5 are prime numbers so: 3*5=15

Answer:

The answer is 19 feet or B.

Step-by-step explanation:

First you should know that a square has equal sides.

Then it tells you to add 5 feet on the original field. So you add 5 to 19 and you get 24. After that, you multiply the 24 by itself to get 576 feet.

Step-by-step explanation:

[tex](6i)^3\qquad\text{use}\ (ab)^n=a^nb^n\\\\=6^3i^3\\\\\text{If}\ i=\sqrt{-1},\ \text{then}\\\\6^3i^3=216(-i)=-216i\\\\\text{else}\\\\6^3i^3=216i^3[/tex]

Final answer:

The expression equivalent to (6i)^3 is -216i, achieved by cubing the digit 6 to get 216 and remembering that i^3 is -i.

Explanation:

To find an expression equivalent to (6i)^3, we follow the rules of exponentiation and imaginary numbers. First, we cube the digit part, which is 6, to get 6^3 = 216. Next, we cube the imaginary unit i. Recall that i is the imaginary unit where i^2 = -1. Thus, i^3 is the same as i^2 multiplied by i, which equals to -i.

Combining these, we obtain (6i)^3 = 6^3 * i^3 = 216 * (-i) = -216i. This is the simplified form of the original expression.