Algebra Review

Write an algebraic expression for each verbal expression.

1. the sum of one-third of a number and 27

2. the product of a number squared and 4

3. Write a verbal expression for 5n^3 +9.

Answer:

The answer is below

Step-by-step explanation:

The question is not complete, let me solve a question that is exactly like this one.

A certain car model has a mean gas mileage of 34 miles per gallon (mpg) with a standard deviation 5 mpg. A pizza delivery company buys 43 of these cars. What is the probability that the average mileage of the fleet is greater than 33.5 mpg?

Answer:

Given that the mean (μ) is 34 miles per gallon (mpg) with a standard deviation (σ) 5 mpg. The sample (n) is 43.

The z score is used in statistics to determine by how much the raw score is above or below the mean. It is given by:

[tex]z=\frac{x-\mu}{\sigma} \\for\ a \ sample\ size:\\z=\frac{x-\mu}{\sigma/\sqrt{n} }[/tex]

For the average mileage of the fleet is greater than 33.5 mpg (x > 33.5):

[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }\\z=\frac{33.5-34}{5/\sqrt{43} } =-0.66[/tex]

From the normal distribution table, The probability that the average mileage of the fleet is greater than 33.5 mpg = P(x > 33.5) = P(z > -0.66) = 1 - P(z < -0.66) = 1 - 0.2546 = 0.7454 = 74.54%

Answer:

-5

Step-by-step explanation:

Answer:

The Perimeter is 24 inches

Step-by-step explanation:

Perimeter is all the sides of something added up. All sides on a square are equal so each side is 6 inches

6+6+6+6=24

Answer:

Each gardner will get  1/16 of a pile of pine needles.

Step-by-step explanation:

1/2 ÷ 8

*Switch the division to multiplication and flip the 8 (or 8/1) upside-down.

= 1/2 · 1/8

= 1/16

9514 1404 393

Answer:

  20,971,520

Step-by-step explanation:

The population is doubling every hour, so after 17 hours it will be the initial population (160) multiplied by 2^17 = 131,072.

After 17 hours, he can expect to find 160×131072 = 20,971,520 bacteria.

Answer:

Step-by-step explanation:

probabilty distribution= interval of x/total area of the distribution

OR  P(x)= frequency of x/total frequency(N)*the interval of x(w)

x                   f                   probabilty f/N*w

16                 10                  0.2

17                  16                  0.32

18                  20                  0.4

19                    4                   0.08

w is the width of the bar( interval) 17-16=1

N=10+16+20+4=50

( only need to draw histogram)

[tex]\\ \sf\longmapsto 0.9(7x+14)=1.5-(x+2)[/tex]

[tex]\\ \sf\longmapsto 6.3x+12.6=1.5-x-2[/tex]

[tex]\\ \sf\longmapsto 63x+12.6=-x-0.5[/tex]

[tex]\\ \sf\longmapsto 63x+x=-0.5-12.6[/tex]

[tex]\\ \sf\longmapsto 64x=-13.1[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{-13.1}{64}[/tex]

[tex]\\ \sf\longmapsto x=0.2[/tex]

Step-by-step explanation:

Hey, there!!

It's so simple,

Given,

length (l)= 2/3cm

Breadth (b) = 1/4cm

and height (h)=5/6cm

now, we use the formula for volume of rectangular prism is,

v = l× b× h

or, v= (2/3 × 1/4 × 5/6)^3

By simplifying it we get,

The volume is 5/36cm^3.

Hope it helps...

Answer:

see explanation

Step-by-step explanation:

(43)

3[tex]x^{5}[/tex] - 75x³ ← factor out 3x³ from each term

= 3x³(x² - 25) ← this is a difference of squares and factors in general as

a² - b² = (a - b)(a + b) , thus

x² - 25 = x² - 5² = (x - 5)(x + 5)

Thus

3[tex]x^{5}[/tex] - 75x³ = 3x³(x - 5)(x + 5)

(44)

81c² + 72c + 16 ← is a perfect square of the form

(ac + b)² = a²c² + 2abc + b²

Compare coefficients of like terms

a² = 81 ⇒ a = [tex]\sqrt{81}[/tex] = 9

b² = 16 ⇒ b = [tex]\sqrt{16}[/tex] = 4

and 2ab = 2 × 9 × 4 = 72

Thus

81c² + 72c + 16 = (9c + 4)²

1. 3x^5 -75x³

=3x³(x²-25)

=3x³(x²-5²)

=3x³(x-5)(x+5)

2. 81c²+72c+16

=81c²+36c+36c+16

=9c(9c+4)+4(9c+4)

=(9c+4)(9c+4)

=(9c+4)²

Answer:

Step-by-step explanation:

a) Putting 6 into the first (left) machine will give an output of ...

  y = √(6 -5) = √1 = 1

Putting 1 into the second (right) machine will give an output of ...

  y = 1² -6 = -5

This answers the second question, but not the first question.

__

If we put 6 into the right machine first, we get an output of ...

  y = 6² -6 = 30

Putting 30 into the left machine, we get an output of ...

  y = √(30 -5) = √25 = 5 . . . . . the desired output.

The input must go into the right machine first, then its output goes into the left machine to get a final output of 5 from an input of 6.

__

b) The left machine cannot produce negative outputs, so achieving an output of -5 with the arrangement used in part A is not possible. (green curves in the attached graph)

However, as we have shown above, inputting 6 to the left machine first, following that by processing with the right machine, can produce an output of -5. (purple curve in the attached graph)

Answer:

6/50

Step-by-step explanation:

There are 50 tiles

6 purple

18 pink

26 orange

P( purple) = purple/ total

                = 6/50

Answer:

b ≈ 9.5, c ≈ 14.7

Step-by-step explanation:

Using the Sine rule in Δ ABC, that is

[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] , substitute values

[tex]\frac{7}{sin23}[/tex] = [tex]\frac{b}{sin32}[/tex] ( cross- multiply )

b × sin23° = 7 × sin32° ( divide both sides by sin23° )

b = [tex]\frac{7sin32}{sin23}[/tex] ≈ 9.5 ( to the nearest tenth )

Also

[tex]\frac{a}{sinA}[/tex] = [tex]\frac{c}{sinC}[/tex]

[tex]\frac{7}{sin23}[/tex] = [tex]\frac{c}{sin125}[/tex] ( cross- multiply )

c × sin23° = 7 × sin125° ( divide both sides by sin23° )

c = [tex]\frac{7sin125}{sin23}[/tex] ≈ 14.7 ( to the nearest tenth )

Answer:

B

Step-by-step explanation:

11q + 5 ≤ 49

Subtract 5 from each side

11q + 5-5 ≤ 49-5

11q ≤44

Divide each side by 11

q ≤44/11

q≤4

There is a close circle at 4 because of the equals sign and the lines goes to the left

Answer:

B

Step 1:

To solve this, we need to isolate the variable q. To do so, we will subtract 5 from both sides of the inequality.

[tex]11q+5(-5)\leq 49(-5)\\11q\leq 44[/tex]

Step 2:

We divide both sides by 11 to get our q.

[tex]\frac{11q}{11}\leq \frac{44}{11} \\q\leq 4[/tex]

q ≤ 4

Step 3:

To find the correct graph, we need to know that a close circle means a ≤ or ≥ and an open one means a < or >. Here, we are using a ≤ so C and D are not our answers. Also remember that if the "arrow" is pointing left (<), then the arrow on the graph should be facing the left side. If the arrow is facing the right side, then that means we are using > or ≥. Here, we are using ≤ (left), so that means the arrow on the graph should be on a 4, facing left, with a closed circle.

Our answer is B.

Answer: 0.0476

Step-by-step explanation:

Given : Two friends and 5 other people compete with each other for first and second chair in an orchestra.

Total people in this competition= 2+5=7

By permutation , Number of ways to arrange 7 people= 7!

Also, number of ways for two friends end up as first and second chair together= 2 × 5!   [ 2 ways to arrange friends on first and second chair and 5! ways to arrange others]

I.e. Required probability = [tex]\dfrac{2\times5!}{7!}[/tex]

[tex]=\dfrac{2!\times5!}{7\times6\times5!}\\\\=\dfrac{1}{7\times3}\\\\=\dfrac{1}{21}\\\\=0.0476[/tex]

Hence, the probability that the two friends end up as first and second chair together = 0.0476

Answer:

This list of all the outcome of  [tex]E^c[/tex] is  [tex]E^c = \{ 1,2,9,10,11,12,\}[/tex]

 [tex]P(E^c ) = 0.5[/tex]

Step-by-step explanation:

From the question we are told that

      The sample sample space is  [tex]S = \{ 1,2,3,4,5,6,7,8,9,10,11,12 \}[/tex]

       The number of elements in the sample space is [tex]n = 12[/tex]

        The event is  [tex]E = \{ 3,4,5,6,7,8 \}[/tex]

        The  number of outcomes in the Event is  [tex]n_e = 6[/tex]

The objective in to obtain [tex]P(E^c)[/tex]

 Now  [tex]E^c[/tex]  is the compliment of  E  and number of elements in [tex]E^c[/tex] ican be mathematically evaluated as

            [tex]nE^c = n - n_e[/tex]

substituting values

            [tex]E^c = 12-6[/tex]

             [tex]E^c = 6[/tex]

This list of all the outcomes of [tex]E^c[/tex] is

        [tex]E^c = \{ 1,2,9,10,11,12,\}[/tex]

Generally  [tex]P(E^c )[/tex]  which is the probability of  [tex]E^c[/tex] is mathematically evaluated  as

      [tex]P(E^c ) = \frac{nE^c}{n}[/tex]

substituting values

         [tex]P(E^c ) = \frac{6}{12}[/tex]

         [tex]P(E^c ) = 0.5[/tex]

Answer:

8

Step-by-step explanation:

The given is a special right triangle with angle measures

90-60-30 and side lengths represented by

2a-a[tex]\sqrt{3}[/tex]-a

x is the side length that sees angle measure 90 degrees so it's represented by 2a

and 4[tex]\sqrt{3}[/tex] is the side length that sees angle measure that sees 60 degrees so the value of a is 4

therefore x = 2*4 = 8

Split up the interval [1, 9] into n subintervals of equal length (9 - 1)/n = 8/n :

[1, 1 + 8/n], [1 + 8/n, 1 + 16/n], [1 + 16/n, 1 + 24/n], …, [1 + 8 (n - 1)/n, 9]

It should be clear that the left endpoint of each subinterval make up an arithmetic sequence, so that the i-th subinterval has left endpoint

1 + 8/n (i - 1)

Then we approximate the definite integral by the sum of the areas of n rectangles with length 8/n and height [tex]f(x_i)[/tex] :

[tex]\displaystyle \int_1^9 (x^2-4x+6) \,\mathrm dx \approx \sum_{i=1}^n \frac8n\left(\left(1+\frac8n(i-1)\right)^2-4\left(1+\frac8n(i-1)\right)+6\right)[/tex]

Take the limit as n approaches infinity and the approximation becomes exact. So we have

[tex]\displaystyle \int_1^9 (x^2-4x+6) \,\mathrm dx = \lim_{n\to\infty} \sum_{i=1}^n \frac8n\left(\left(1+\frac8n(i-1)\right)^2-4\left(1+\frac8n(i-1)\right)+6\right) \\\\ = \lim_{n\to\infty} \frac8n \sum_{i=1}^n \left(1+\frac{16}n(i-1)+\frac{64}{n^2}(i-1)^2-4-\frac{32}n(i-1)+6\right) \\\\= \lim_{n\to\infty} \frac8{n^3} \sum_{i=1}^n \left(64(i-1)^2-16n(i-1)+3n^2\right) \\\\= \lim_{n\to\infty} \frac8{n^3} \sum_{i=0}^{n-1} \left(64i^2-16ni+3n^2\right) \\\\= \lim_{n\to\infty} \frac8{n^3} \left(64\sum_{i=0}^{n-1}i^2 - 16n\sum_{i=0}^{n-1}i + 3n^2\sum{i=0}^{n-1}1\right) \\\\= \lim_{n\to\infty} \frac8{n^3} \left(\frac{64(2n-1)n(n-1)}{6} - \frac{16n^2(n-1)}{2} + 3n^3\right) \\\\= \lim_{n\to\infty} \frac8{n^3} \left(\frac{49n^3}3-24n^2+\frac{32n}3\right) \\\\= \lim_{n\to\infty} \frac{8\left(49n^2-72n+32\right)}{3n^2} = \boxed{\frac{392}3}[/tex]

Answer:

Step-by-step explanation:

Answer:

22,2

Step-by-step explanation:

average also known as mean

so you find it by adding all the numbers together and dividing them by how many there are

so 21,8 + 24,2 + 20.6 = 66,6 divided by 3 equals 22,2

volume of a cone

.

.

.

volume of sphere

.

.

number of spheres that can be made......

.

.

hence a hemisphere can be formed

Answer:

[tex] y = \dfrac{1}{20}x + 35 [/tex]

Step-by-step explanation:

Let y = cost.

Let x = number of miles.

We have two (x, y) points: (100, 40) and (220, 46).

Now we find the equation of the line that passes through those two points using the two-point form of the equation of a line.

[tex] y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1) [/tex]

[tex] y - 40 = \dfrac{46 - 40}{220 - 100}(x - 100) [/tex]

[tex] y - 40 = \dfrac{6}{120}(x - 100) [/tex]

[tex] y - 40 = \dfrac{1}{20}(x - 100) [/tex]

[tex] y - 40 = \dfrac{1}{20}x - 5 [/tex]

[tex] y = \dfrac{1}{20}x + 35 [/tex]

Step-by-step explanation:

Consuelo Butler

08/07

Homework: Practice

Exam 3

Question 1, 12.1.13

HW Score: 10%, 3 of 30 points

Score: 1 of 1

A professor had students keep track of their social interactions for a week. The

number of social interactions over the week is shown in the following grouped

frequency distribution. How many students had at least 60 social interactions for

the week?

12

Number of Social

Interactions

30-34

35-39

40-44

45-49

50-54

55-59

60-64

65-69

70-74

75-79

Frequency

9

14

11

15

16

8

7

By calculating the greater than cumulative frequency using the given frequency table, 12 students had at least 60 social interactions for the week.

The greater than cumulative frequency is also known as the more than type cumulative frequency. Here, the greater than cumulative frequency distribution is obtained by determining the cumulative total frequencies starting from the highest class to the lowest class.

Class interval     Frequency     Cumulative frequency

30-34                9                   85

35-39                14                   76

40-44                11                   62

45-49                15                   51

50-54                16                   36

55-59                 8                   20

60-64                 7                   12

65-69                 3                    5

70-74                  1                    2

75-79                  1                     1

[We read the cumulative frequencies with respect to the corresponding lower class limits. For example, 85 students had 'more than 30' social interactions, 76 students had 'more than 35 social interactions and so on.]

By reading the greater than cumulative frequency, we find that 12 students had at least 60 social interactions for the week.

Learn more about greater than cumulative frequency here

https://brainly.com/question/5102661

#SPJ2

Answer:

144 = c - 379

Step-by-step explanation:

"144 is the same as 379 less than c"

144 = c - 379

Answer and Step-by-step explanation:

This can be written in an equation like this:

144 = c - 379

The question is saying that 144 is the same answer as the result of 379 less than c (or c minus 379). This is why we equal 144 to the result of c minus 379.

#teamtrees #PAW (Plant And Water)

Answer:

3 weeks

Step-by-step explanation:

6 quarts = 12 pints

12 divided by 3 = 4

Step-by-step explanation:

1 quart = 2 pints

6 quarts = 2 x 6 = 12 pints

12 ÷ 4 = 3

He can have 3 weeks

Answer:

[tex] \alpha = 7[/tex]

Step-by-step explanation:

[tex]a(vector) = 4i - 2j[/tex]

[tex]b(vector) = \alpha i + 2j[/tex]

[tex]ab(vector) = ( \alpha - 4)i \: + 4j[/tex]

Now,

Let K * ab (unit vector) = ab (vector)

Solving further :

[tex] \alpha = 7[/tex]

Answer:

Hello,

Answer 26.9

Step-by-step explanation:

[tex]z=\dfrac{x-m}{\sigma} \\m=20.8\\\sigma=5.2\\\\p(z>?)\geq 0.12\ \longrightarrow 1-p(z\leq ?)=(1-0.12))\\\\Using\ table\ of\ normal\ reduce\ with\ 4 \decimals : ?=1.175\\\\x=1.175*5.2+20.8=26.91\approx{26.9}[/tex]

The geometric mean of the numbers is 5.38

Given the values a, b, c and d

The geometric mean of the values will be expressed as:

[tex]GM = (abcd)^{1/4}[/tex]

Given the values 4, 5, 6, and 7, the geometric mean will be expressed as:

[tex]GM = (4\times5\times6\times7)^{1/4}\\[/tex]

[tex]GM = (840)^{1/4}\\GM=\sqrt[4]{840} \\GM = 5.38[/tex]

Hence the geometric mean of the numbers is 5.38.

Learn more: https://brainly.com/question/23875011

Answer:

A. 340 grams

Step-by-step explanation:

My brain