Describe the set 3 ≤ x ≤ 10
using interval notation.
B. [3,10]
D. (3,10]
A. (3,10)
C. [3,10)

Answer:

Part 1: (n÷2)-7 = -12

Part 2: n = -10

Step-by-step explanation:

Part 1:

Let's first write "the quotient of a number and 2" using numbers and variables. Let "n" represent "a number". The key word that we see here is quotient, meaning we have to divide something by something else. "The quotient of a number and 2 means that "a number" is the dividend (number that is divided) and "2" is the divisor (number that divides the dividend). Therefore we obtain:

n÷2

The first part says "seven less than the quotient of a number and 2". The keyword here is less, meaning we have to use subtraction. Therefore:

(n÷2)-7

The last part says "is equal to -12". Therefore the whole expression we just wrote is equivalent to -12:

(n÷2)-7 = -12

Part 2

Remember the Order of Operations:

Parentheses

Exponents

M/D: Multiplication/Division (whichever comes first in the equation)

A/S: Addition/Subtraction (whichever comes first in the equation)

Start by adding 7 to both sides

(n÷2) = -5

Then, multiply both sides by 2

[tex]\frac{n}{2}=-5\\n=-10[/tex]

Note: I used a fraction to display the division because it is easier to see why we have to multiply both sides by 2; to cancel out the denominator.

The number of years the amount has been in the venture account with 12% interest per year is 4.

Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.

A sum of $2,500 was deposited in a venture account, which pays 12% compounded per year and it accumulated to $3,950.

Then the number of the years will be

We know the compound interest formula

[tex]\rm A = P(1+r)^t[/tex]

where

A = Accumulated amount

P = Deposited value

r = rate of interest

t = time

Then we have

[tex]3950 = 2500 (1.12)^t\\\\1.58\ =1.12^t[/tex]

Taking log both sides, then we have

[tex]\rm \ln 1.58 = t \times \ln 1.12\\\\or \ \ \ \ t = 4.036 \approx 4 \ years[/tex]

Then the number of the years is 4.

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The zeros of the polynomial are -3, -2, 4 and 6 and the graph of the polynomial is graph (a)

The polynomial is given as:

P(x) = x^4 - 5x^3 - 20x^2 + 60x + 144

Expand the polynomial function

P(x) = x^4 - 10x^3 + 5x^3 + 24x^2 - 50x^2 + 6x^2 + 120x - 60x + 144

Rewrite the function as:

P(x) = x^4 - 10x^3 + 24x^2 + 5x^3 - 50x^2 + 120x + 6x^2 - 60x + 144

Factorize the function

P(x) = x^2(x^2 - 10x + 24) + 5x(x^2 - 10x + 24) + 6(x^2 - 10x + 24)

Factor out x^2 - 10x + 24

P(x) = (x^2 + 5x + 6)(x^2 - 10x + 24)

Expand each bracket

P(x) = (x^2 + 3x + 2x + 6)(x^2 - 4x - 6x + 24)

Factorize each bracket

P(x) = [x(x + 3) + 2(x + 3)][x(x - 6) - 4(x - 6)]

Factor out x + 3 and x - 6

P(x) = (x + 3)(x + 2)(x - 4)(x - 6)

Set to 0

(x + 3)(x + 2)(x - 4)(x - 6) = 0

Solve for x

x =-3, -2, 4 and 6

Hence, the zeros of the polynomial are -3, -2, 4 and 6 and the graph of the polynomial is graph (a)

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Answer:

x = 1

Step-by-step explanation:

Question: 4x - 4 = 8

•shifting the -4 to the right side:

⇒4x = 8 - 4

⇒4x = 4

•shifting the 4 to the right side:

⇒x = 4/4

•by cross cancellation we get:

⇒x = 1 Answer...

hope that helps...

Answer:

$30.21

Step-by-step explanation:

Answer:

1/2=2/4

Step-by-step explanation:

1/4=4/8 - no, if you multiply 1/4 x 4 to get numerator match = 4/32

1/2=2/4 - YES , 1/2 x 2  = 2/4

3/5=5/10 = no if you multiply 3/5 x 2 to get denominator match = 6/10

2/3=3/6 = no if you multiply 2/3 x 2 to get denominator match = 4/6

Using proportions, it is found that Levi should put 2.8125 gallons of water in the tank.

A proportion is a fraction of a total amount.

Considering the improper fraction, the total amount of water that the tank holds is given by:

T = 3 4/8 = 3 + (4/8) = 3.5 gallons.

He wants the tank to be 75% full, hence, applying the proportion, the amount of water that he should put on the tank is of:

A = 0.75 x 3.5 = 2.8125 gallons.

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Answer:

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A z-table is also known as the standard normal distribution table. The percentage of the population that would fall in the 10 to 22 mm Hg range is 0.9386.

A z-table also known as the standard normal distribution table, helps us to know the percentage of values that are below (or to the left of the Distribution) a z-score in the standard normal distribution.

Given the mean and the standard deviation are 16mmHg and 3.2 mmHg, therefore, the percentage of the population whose blood pressure will fall in the range of 10 to 22 mm Hg are,

[tex]P(10 < x < 22) = P(\dfrac{10-16}{3.2} < Z < \dfrac{22-16}{3.2})[/tex]

[tex]= P(-1.875 < Z < 1.875)\\\\=P(Z < 1.875)-P(Z < -1.875)\\\\= 0.9693-0.0307\\\\= 0.9386[/tex]

Hence, the percentage of the population that would fall in the 10 to 22 mm Hg range is 0.9386.

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Answer:

2,012 is greater than 30

Step-by-step explanation:

The correct solution for the inequality is k > -9.

Given is an inequality -2k + 12 < 30, we need to solve for k,

To solve the inequality -2k + 12 < 30 for k, follow these steps:

Subtract 12 from both sides of the inequality to isolate the term with 'k':

-2k + 12 - 12 < 30 - 12

-2k < 18

Divide both sides by -2, but remember that when you divide an inequality by a negative number, the direction of the inequality sign flips:

(-2k)/(-2) > 18/(-2)

k > -9

So, the correct solution for the inequality is k > -9.

Among the options you provided, the correct answer is: k > -9.

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69.12ft

11x2 = 22

C= pi x d

= pi x 22

= 22pi

Or

69.11503838

Hope this helps!

Step-by-step explanation:

To get the perimeter, add up all of the sides.

So, the playground is a rectangle.

It has two sides measuring 58m, and two measuring 91m.

58+58+91+91=298

For the area, length x width

58x90=5278

Answer:

25. -7/5 [tex]\leq[/tex] x [tex]\leq[/tex] 1

Step-by-step explanation:

18:

[tex]5-|x|\leq 2\\-|x| \leq -3\\|x|\leq 3\\x\geq -3[/tex]or       [tex]x\leq 3[/tex]

25:

[tex]3|5x+1|-6\geq 12\\3|5x+1|\geq 18\\|5x+1|\geq 6\\x\leq -7/5[/tex]or               [tex]x\geq 1[/tex]

[tex]-7/5\leq x\leq 1[/tex]

I don't think I explained this well let me know if you need more explanation.

Using it's concept, it is found that the prevalence of frequent multivitamin use is of 0.4523 = 45.23%.

The prevalence of a sample is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, 588 out of 1300 women reported taking a multivitamin at least 4 times a week during the month before pregnant, hence the prevalence is given by:

p = 588/1300 = 0.4523 = 45.23%.

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Answer:

-2

Step-by-step explanation:

The slope of the function can also be described as its gradient.

To find the gradient of the function you can use:

[tex] \frac{change \: in \: y}{change \: in \: x} [/tex]

This gives us

[tex] \frac{ (- 10) - 10}{8 - ( - 2)} [/tex]

Which equals -2

The elements that are in A and B in the Venn diagram that represents the pizza topping preferences are (Maria, Zack, Bo).

A venn diagram represents information in a set using circles. The intersection of both circles represents those that like both pepperoni and olives. This is element A and B.

The names at the intersection of both circles are (Maria, Zack, Bo).

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Answer:

A

Step-by-step explanation:

because that's the answer

The correct graph that includes a function, its inverse, and a dashed line that verifies the relationship is shown in option 1.

Used the concept of function that states,

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable and another variable.

Ask about the function, its inverse, and a dashed line that verifies the relationship.

Now from the first graph;

The dashed line is y = x.

And the graph shows the functions and their inverse as both graphs are opposite to each other.

Therefore, option 1 is true.

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Your correct answer is 3.

Sure hope this helps you and pls mark me brainiest :)

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Answer:

[tex]55.555...\ (\%)[/tex]

Step-by-step explanation:

What percent of values is between the first and third quartiles

[tex]\text{Quartile 1} =\frac{75+100}{2} =87.5[/tex]

[tex]\text{Quartile 2} =\frac{200+225}{2} =212.5[/tex]

50 < 75 < 87.5 < 100 < 125 < 150 < 175 < 200 < 212.5 < 225 < 250

Then we have 5 values between the first and third quartiles which are :

100, 125, 150, 175, 200

Therefore,

The percent of values between the first and third quartiles is :

[tex]\frac{5}{9} \times 100=55.555...[/tex]

Answer:

500(-1/5)^(n-1)

Step-by-step explanation:

Each term after the first is obtained by multiplying by -1/5.

This is a geometric series.

The nth term = a1 r^n-1)

= 500(-1/5)^(n-1)

Answer:

Step-by-step explanation:

Answer:

The area enclosed by the given curves is  square units.

Step-by-step explanation:

The given equations are

Draw the graph of the given equations.

From the below graph it is clear that both curves intersect each other at (2,12) and (4,24).

The area of the region enclosed by curves is

Therefore the area enclosed by the given curves is square units.

The spinner game is an illustration of probability, and the spinner game that is fair is (b) If you spin a number greater than 10, you win.

The number of sections in the spinner is given as:

n = 20

There are 10 numbers greater than 10 i.e. 11 to 2.

So, the probability that a number greater than 10 is spun is:

P = 10/20

P = 0.5

The probability that a number that is not greater than 10 is spun is calculated using the following complement rule

q = 1 - p

This gives

q = 1 - 0.5

Evaluate

q = 0.5

Notice that both probabilities are the equal

Hence, the spinner game that is fair is (b) If you spin a number greater than 10, you win.

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Answer:

t = 14 years

Step-by-step explanation:

r = R/100

r = 9/100

r = 0.09 per year,

Then, solve the equation for t

t = ln(A/P) / n[ln(1 + r/n)]

t = ln(9,589.78/2,733.00) / ( 12 × [ln(1 + 0.09/12)] )

t = ln(9,589.78/2,733.00) / ( 12 × [ln(1 + 0.0075)] )

t = 14 years

Summary:

The time required to get a total amount of $9,589.78 with compoundeded interest on a principal of $2,733.00 at an interest rate of 9% per year and compounded 12 times per year is 14 years.

Answer:

Answer is [tex]\frac{4}{3}[/tex]

Step-by-step explanation:

To find the interval of x. Use our equations to equal each other.

[tex]-x^2+2x=y,y=0[/tex]

[tex]-x^2+2x=0\\-x(x-2)=0\\-x=0 , (x-2)=0\\x=0 ,2[/tex]

[tex]\int\limits^2_0 {-x^2+2x} \, dx[/tex]

Integrate.

[tex]\frac{-x^3}{3}+x^2\\(\frac{-2^3}{3}+2^2)-[\frac{-0^3}{3}+0^2]\\-\frac{8}{3} +4-0\\-\frac{8}{3}+\frac{12}{3} =4/3[/tex]

Using Desmos I have Graphs of both of the equations you have provided. The problem asks us to find the shaded region between those curves/equations.

Proof Check your interval of x.

Answer:

A) R24.10
B) R25.90

((ASSUMING THERES NO TAXES WITH THE PAYMENT))

Step-by-step explanation:
A)

first add up the costs of each item to get the ttal cost with addition as follows...

9.50 + 0.50 + 2.75 + 11.35 ((Adding like terms by adding 0.50 to 9.50 equaling 10.00))

10.00 + 2.75 + 11.35 ((adding the more simple options togeter since .75 is a more common fraction at 3/4))

12.75 + 11.35 ((finnishing off the system by adding the last two numbers together equaling to 24.10))

therefore Thabo spent a total of 24.10

B)
to find out the change, all we need to do is subtract the total cost from the total amount Thabo used to pay as shown below

50.00 - 24.10

in conclusion, Thabo would have R25.90 in change from the transaction ((assuming theres no tax))

Answer:

$0.68

Step-by-step explanation:

you have to do:

9.95 x .068

or

9.95 x 6.8 ÷ 100

and you would get 0.6766 but rounded to the nearest hundredth would be $0.68

Answer:

3 for City A and 6 for City B.

Step-by-step explanation:

All you have to do is look where it stands bye.

Hope this helps!