Solve the inequalities below. Write the solution set in interval notation and graph the solution.

8x−12>158x-12>15




Solution:

Interval notation for the solution:

Answer: 12 feet

Step-by-step explanation: If the length of the garden is 20 feet then that means 40 feet of fence was used to make both lengths of the garden. So we subtract 40 from 64 which leaves us with 24 feet and then we divide 24 by 2 to get 12 because there are 2 widths.

Hope this helps!

There are 4 zeros in the graph and the multiplicity is 5.

The zeros of a function are defined as the values of the variable of the function such that the function equals 0. Graphically, the zeros of a function are the points on the x-axis where the graph cuts the x-axis. In other words, we can say that the zeros of a function are the x-intercepts of its graph. The number of zeros of a polynomial function is equal to the degree of the polynomial.

In the given graph,

There are 4 turning points in the graph.

The 4 zeros from the graph are

(-3, 0), (-2, 0), (1, 0) and (1.5, 0)

The graph touches the x-axis and bounces off of the axis, it is a zero with  multiplicity is 5.

Therefore, there are 4 zeros in the graph and the multiplicity is 5.

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Answer:4/3

Step-by-step explanation: rise over run when finding slope, and the first point i can find (-3,-5) is 4 up and 3 right away from (0,-1)

The total number of cubic feet of grain or volume of the grain that the silo can hold is 28947.41 [tex]ft^3[/tex].

What is the volume of an object?

The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

Given that the top of a silo is a hemisphere

radius(r) = 12 ft.

Then,

the volume of a hemisphere = [tex]\frac{2}{3} \pi r^3[/tex] =  [tex]\frac{2}{3} * 3.14* 12^3 = 10851.84[/tex] [tex]ft^3[/tex]

And, the bottom of the silo is a cylinder with

height (h) = 40ft.

the volume of a cylinder =[tex]\pi r^{2} h = 3.14*12^2*40=18095.57 ft^3[/tex]

So, the total volume is

V = 10851.84 + 18095.57 = 28947.41 [tex]ft^3[/tex]

Then, total volume = total number of cubic feet of grain

Hence, the required answer is  28947.41 [tex]ft^3[/tex].

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Answer: The expected value for rolling a 1 or 6 is 50 points, and the expected value for rolling any other number is -5 points. The chance of rolling a 1 or 6 is 2/6, or 1/3. The chance of rolling any other number is 4/6, or 2/3. The expected value for rolling the die once is:

(1/3 * 50) + (2/3 * -5) = 16.67

So, if you rolled the die 100 times, you would expect to gain or lose:

100 * 16.67 = 1667 points

The answer is: a gain of about 1,667 points.

Step-by-step explanation:

A circle having radius 5 and centre at (0,0) has equation x² + y² = 25.

What is the equation of circle?

A circle is a closed curve that extends outward from a set point known as the centre, with each point on the curve being equally spaced from the centre. A circle with a (h, k) centre and a radius of r has the equation:

(x-h)² + (y-k)² = r²

Let (x,y) be any point on the circle.

Given that centre of the circle is origin (0,0).

Now, we know that the distance from any point on the circle to the centre is equal to the radius of the circle.

So, distance between point (x,y) and centre (0,0)  is equal to radius of the circle which is given 5 units.

Now, using the distance formula -

√[(x - 0)² + (y - 0)²] = 5

Squaring on both the sides of the equation -

(x - 0)² + (y - 0)² = 25

So, the equation of the circle with radius 5, centred at the origin is x² + y² = 25.

Therefore, the equation is x² + y² = 25.

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Answer:

-3550x - 12y + 20

Step-by-step explanation:

50x+ 20 - 60(1/5y+60x)

50x + 20 - 12y - 3600x

-3550x - 12y + 20

The number of 17 cars have clocks but no radios.

Subtraction is a mathematic operation. Which is used to remove terms or objects in the expression.

Given:

Out of 53 cars,41 had clocks,30 had radios and 6 had neither.

That means,

53-6 = 47 cars have either clocks or radios or both.

47 - 30 = 17 cars have no radio.

47 - 41 = 6 cars have no clocks.

Hence, 17 cars have clocks but no radios.

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The sum of the series b 2 b 4 b 6 b 8 b {10} is [tex]$\dfrac{180}{3}$[/tex] since it is a geometric series with a common ratio of [tex]$\dfrac{7}{4}$[/tex].

Since the given series [tex]$b 1 b 2 b 3 \cdots b {10}$[/tex] has a sum of 180, it can be deduced that the series is a geometric series with a common ratio of[tex]$\dfrac{7}{4}$[/tex]. This means that the ratio of any two consecutive terms in the series is a constant, [tex]$\dfrac{7}{4}$[/tex]. Therefore, the sum of the series b 2 b 4 b 6 b 8 b {10} can be calculated as follows:

[tex]$S = b2 + b4 + b6 + b8 + b_{10}$[/tex]

[tex]$= b2\left(\dfrac{7}{4}\right)^0 + b2\left(\dfrac{7}{4}\right)^2 + b2\left(\dfrac{7}{4}\right)^4 + b2\left(\dfrac{7}{4}\right)^6 + b2\left(\dfrac{7}{4}\right)^8$[/tex]

[tex]$= b2 \left[1 + \left(\dfrac{7}{4}\right)^2 + \left(\dfrac{7}{4}\right)^4 + \left(\dfrac{7}{4}\right)^6 + \left(\dfrac{7}{4}\right)^8\right]$[/tex]

[tex]$= b2 \left[\dfrac{1-\left(\dfrac{7}{4}\right)^{10}}{1-\left(\dfrac{7}{4}\right)^2}\right]$[/tex]

[tex]$= b2 \left[\dfrac{1-\left(\dfrac{7}{4}\right)^{10}}{\dfrac{3}{4}}\right]$[/tex]

[tex]$= \dfrac{4b2}{3} \left[1-\left(\dfrac{7}{4}\right)^{10}\right]$[/tex]

Since the sum of the series[tex]$b 1 b 2 b 3 \cdots b {10}$[/tex] is 180, we can substitute $b2$ with [tex]$\dfrac{180}{3}$[/tex]nd calculate the sum of the series $b 2 b 4 b 6 b 8 b {10}$:

[tex]$S = \dfrac{4\left(\dfrac{180}{3}\right)}{3} \left[1-\left(\dfrac{7}{4}\right)^{10}\right]$[/tex]

[tex]$= \dfrac{180}{3} \left[1-\left(\dfrac{7}{4}\right)^{10}\right]$[/tex]

Therefore, the sum of the series [tex]$b 2 b 4 b 6 b 8 b {10}$ is $\dfrac{180}{3}$[/tex].

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Answer:

Improper, proper, proper, improper

Step-by-step explanation:

Step-by-step explanation:

To be a proper fraction the numerator (top number) must be less the the denominator (bottom number). Let’s start at the top.

27/27

This would be an improper fraction because the numerator is equal to the denominator, not less.

6/17

Because 6 is less then 17 this would make it a proper fraction

8/9

Same case as the last one, this is a proper fraction because the numerator is less then the denominator

21/5

21 is definitely more the 5 making this a improper fraction.

Hope this helped :)

Answer:

Answer is in attached photo.

Step-by-step explanation:

The solution is in the attached photo, do take note to solve this question, we can assign 2 variables to the 2 conditions stated in the question, and solve them simultaenously.

Answer: The probability that a randomly selected individual is experiencing hypertension can be calculated by taking the ratio of the number of individuals with hypertension to the total number of individuals:

P(hypertension) = (21 + 36 + 30) / 180 = 87 / 180 = 0.4833

Given that a heavy smoker is selected at random, the probability that the person is experiencing hypertension can be calculated by taking the ratio of the number of heavy smokers with hypertension to the total number of heavy smokers:

P(hypertension | heavy smoker) = 30 / (30 + 19) = 30 / 49 = 0.6122

To determine if the events "hypertension" and "heavy smoker" are independent, we can compare the joint probability of both events happening to the product of their individual probabilities:

P(hypertension and heavy smoker) = 30 / 180 = 0.1667

P(hypertension) * P(heavy smoker) = 0.4833 * (30 / 180) = 0.1083

Since P(hypertension and heavy smoker) ≠ P(hypertension) * P(heavy smoker), we can conclude that the events "hypertension" and "heavy smoker" are not independent.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:The proportional relationship between x and y is;

x 7 14 28 35

y 1 2 4 5

The correct option is D.

Proportional relationships;

Proportional relationships between x and y satisfy the following equation;

Where k is some constant.

Rearranging the equation;

Then,

The proportional relationship between x and y is;

Hence, the proportional relationship between x and y is the correct option is D.

To find the derivative of a piecewise function, you need to take the derivative of each individual piece and then combine them into one piecewise function.

The derivative of each piece can be found using the usual rules of differentiation (such as the power rule, sum rule, product rule, etc.).

Once you have the derivatives of each piece, you can write the overall derivative as a piecewise function, where the expression for each piece is limited to a specific range of x-values. The limits of each piece are defined by the breakpoints in the original function.

For example, if the original function is given as:

f(x) = {x^2 for x < 0,

x for 0 <= x < 1,

2x for x >= 1}

Then the derivative of f(x) can be found as:

f'(x) = {2x for x < 0,

1 for 0 <= x < 1,

2 for x >= 1}

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The publisher nedds to produce 2414 books and sell so that production cost will equal the money from sales.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given:

A small publishing company is planning to publish a new book.

The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing).

The one-time fixed costs will amount to $27,160.

The variable costs will be $8.75 per book.

The publisher will sell the finished product to bookstores at a price of $20.00 per book.

Let x be the number of books.

Cost = 8.75x + 27160

Revenue = 20x

Revenue = cost

20x = 8.75x + 27160

11.25x = 27160

x = 2414.2

x ≈ 2414 books.

Therefore, the required number of books are 2414 books.

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The graph of the y+2x=6 is given in the attachment.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The standard equation of a line is expressed as y = mx + b, m is the slope

and b is the y-intercept.

Given the equation y = 2x - 2

If x = -2

y = 2(-2) - 2

y = -4-2

y = -6

If x  = 4

y = 2(4) - 2

y = 8-2

y = 6

The point (-2, -6) and (4, 6 )must be on the line graph.

Hence, the graph of the y+2x=6 is given in the attachment.

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Using the Chinese Remainder Theorem, the smallest positive integer solution is x1 = 62.

We can use the Chinese Remainder Theorem to find the smallest positive integer solution for this problem.

The Chinese Remainder Theorem states that if x ≡ a (mod m) and x ≡ b (mod n), then x is congruent to a unique value modulo mn. That is, there exists a unique solution x such that x is congruent to a modulo m and congruent to b modulo n, and the solution x is between 0 and mn - 1.

So, we want to find the smallest x such that:

x ≡ 6 (mod 8) and x ≡ 7 (mod 9)

We can start by finding a solution x1 such that x1 ≡ 6 (mod 8) and x1 ≡ 7 (mod 9). One such solution is:

x1 = 6 + 8k for some integer k

We can use the formula x1 = 6 + 8k to find a solution x1 that is also congruent to 7 (mod 9):

x1 = 6 + 8k = 7 + 9l (mod 9)

Expanding the right side of this equation, we get:

6 + 8k = 7 + 9l (mod 9)

6 - 7 = 9l - 8k (mod 9)

-1 = 9l - 8k (mod 9)

Since 9 and 8 are relatively prime, we can use the Extended Euclidean Algorithm to find integers r and s such that:

8r + 9s = gcd(8, 9) = 1

Using the Euclidean Algorithm, we can find r = -1 and s = 1. So,

-8 = 9(l - rk) (mod 9)

Since 9 is relatively prime to 8, l - rk is a multiple of 9. We can then rewrite the equation as:

-8 = 9j (mod 9)

Adding 9 to both sides of the equation, we get:

1 = 9j (mod 9)

So, j = 1.

Now, we have:

k = (1 - l) / r

Since r = -1, we can replace k with -l:

k = -l

So, we have:

x1 = 6 - 8l

And,

x1 = 7 + 9l (mod 9)

Combining these two equations, we get:

6 - 8l = 7 + 9l (mod 9)

Subtracting 9l from both sides, we get:

-2l = 13 (mod 9)

Dividing both sides by -2, we get:

l = -13 / -2 = 7 (mod 9)

So,

k = -l = -7 (mod 9)

And,

x1 = 6 - 8(-7) = 6 + 56 = 62 (mod 8)

So,

x1 = 62 (mod 8) and x1 = 7 (mod 9)

The smallest positive integer solution is x1 = 62

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Step-by-step explanation:

Median IJK = IM = PN + 2

Median PQR = PN

Therefore, IM = PN + 2

IM = PN + 2

PN = IM - 2

IM = (15 + 9 + PN)/2

PN = (15 + 9 + IM - 2)/2

15 + 9 + PN = 2IM

15 + 9 + IM - 2 = 2PN

25 + PN = 2IM

25 + IM - 2 = 2PN

PN = 2IM - 25

PN = 2PN - 25

3PN = 25

PN = 25/3

IM = PN + 2

IM = 25/3 + 2

IM = 29/3

Therefore, IM = 29/3 and PN = 25/3.

Answer:

Step-by-step explanation: 3

7

9

0

7

5

Answer:I.65

Step-by-step explanation:

The linear equation on the graph is:

y = x + 3

Here we have a linear equation.

Remember that the general one is y = a*x + b where b is the y-intercept, here we can see that the line intercepts the y-axis at y = 3

y = a*x + 3

And it passes through the point (-3, 0), replacing these values we get:

0 = a*-3 + 3

3a =  3

a = 3/3 = 1

The linear equation is:

y = x + 3

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Answer:

Below

Step-by-step explanation:

Start at -8... you have to go 8 units to reach 0

  then you have to go another 9 to reach 9     total = 8 + 9 = 17

Answer: Kaia is not correct

Step-by-step explanation: A function works as long as there is only one 'output' for every 'input', or for every x value, only one y value works. (There can be multiple x values for any y value). If you do the verticle line test on this graph, the line won't pass through two points at the same time anywhere. Therefore, Kaia is incorrect.

Answer:

  3.75%

Step-by-step explanation:

You want to know the semiannual interest rate if the annual rate is 7.5%.

The rate of interest for a period is the annual rate divided by the number of periods in a year.

Interest compounded semiannually is compounded 2 times per year. The semiannual rate is ...

  7.5%/2 = 3.75% . . . . semiannual rate

The animal listed in the table that weighs the most, eats the most,

and the animal that weighs the least, eats the least.

Molly's claim is correct.

The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.

A table is given below:

Animals     Weight of the animals,   The weight of food packages

Cat                  6 Kg                                    300 grams.

Dog                 12 Kg                                  900 grams.

From the table:

The animal listed in the table that weighs the most, eats the most,

and the animal that weighs the least, eats the least.

Therefore, Molly's claim is correct.

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In normal scientific notation, round off each integer to three significant digits:

a. 4.227 x 10⁻²

b. 7.125 x 10⁶

c. 4.452 x 10⁻⁴

d. 2.300 x 10⁻⁴

e. 9.722 x 10⁵

f. 4.855 x 10³

Scientific notation is a method of expressing numbers that are either too large or too little to be represented in decimal form. In the United Kingdom, it is known as scientific form, standard index form, or standard form. Scientific notation is a method of writing extremely big or extremely tiny integers. When a number between 1 and 10 is multiplied by a power of 10, it is expressed in scientific notation.

Here,

a. 422.65 times 10⁻³ = 4.227 x 10⁻²

b. 71.246 times 10⁵ = 7.125 x 10⁶

c. 0.00044515 = 4.452 x 10⁻⁴

d. 22.9987 times 10⁻⁵ = 2.300 x 10⁻⁴

e. 9.7222 times 10⁵ = 9.722 x 10⁵

f. 0.0048545 times 10⁵ = 4.855 x 10³

The following numbers in standard scientific notation, rounding off each to three significant digits:

a. 4.227 x 10⁻²

b. 7.125 x 10⁶

c. 4.452 x 10⁻⁴

d. 2.300 x 10⁻⁴

e. 9.722 x 10⁵

f. 4.855 x 10³

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At 0.05 alpha level, your claim is not significant.

In null-hypothesis significance testing, the p-value is the probability of obtaining test results at least as extreme as the result actually observed, under the assumption that the null hypothesis is correct.

Given is that a friend read online that 37% or less Americans have a gun in their household. I claim that the percent of Americans that have a gun in their household is actually greater than 37%. To test this claim, I survey 200 random Americans and find that 86 of them have a gun in their household. The alpha level is at .05.

We can write -

P{E} % = 86/200 x 100

P{E} % = 86/2

P{E} % = 43%

We can find the p - value using the formula -

[tex]$Z = \frac{\hat{p}-p 0}{\sqrt{\frac{p 0(1-p 0)}{n}}}[/tex]

where -

[tex]$\hat{p}=[/tex] Sample Proportion

[tex]$p_{o}[/tex] = Assumed population proportion in the null hypothesis.

It can be calculate to find that the p value is less than 0.05. So, we can conclude that the null hypothesis is rejected.

Therefore, at 0.05 alpha level, your claim is not significant.

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Answer:

6

Step-by-step explanation:

The growth in balance from year 20 to year 25 is $274.57.