potential rational roots of f(x) = x4 – 2x3 + 5x2 – 7x + 9

The answer is A, A is the answer

The sampling interval would be 20, the correct option is B.

It is a type of sampling technique in which each sample has an equal probability of being chosen.

The total number of residents in the building is 80.

Random sampling is done and the residents are interviewed.

The percentage of the residents that are being interviewed is 25%.

The sampling interval has to be calculated.

The sampling interval is given by = 25 % of 80

= 25 * 80 / 100

= 20

The number of residents that were interviewed is 20.

The sampling interval is 20 people.

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Answer:

[tex]3 ^{1}/_{6}[/tex]

Step-by-step explanation:

6 goes into 19 3 times with a remainder of 1.

So your base number is going to be 3 with your remainder of 1 going into your numerator over the denominator of six.

ANSWER

[tex]3 \frac{1}{6} [/tex]

EXPLANATION

The given expression is :

[tex] \frac{19}{6} [/tex]

This is an improper fraction because the numerator is greater than the denominator.

To express this as a mixed number find the number of times the denominator will divide the numerator exactly and express the remainder over the denominator in simplest form.

[tex] \frac{19}{6} = 3 \frac{1}{6} [/tex]

Answer:

A.

C.

D.

Step-by-step explanation:

Answer:

the first, third, and the 4th

Step-by-step explanation:

The answer is a. If the graphs of the equations were parallel lines then they would have no solutions.

Hope this helps!

If this helps you please make it brainliest.

The statement is NOT true will the graphs of the equations are parallel lines because the system has no solution. Then the correct option is A.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

This system of equations d = 5t + 2 and 2d = 4 + 10t has infinitely many solutions.

The statement is NOT true will the graphs of the equations are parallel lines because the system has no solution. Then the correct option is A.

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Answer:

12

Step-by-step explanation:

Mary worked for 30 hours. This is calculated by first determining how many lamps Mia assembled, then subtracting this from the total to find out how many lamps Mary assembled. Finally, we divide the number of lamps assembled by Mary by her rate to find out how many hours she worked.

The question requires us to find out how many hours Mary worked if we know that together, Mary and Mia assembled 600 lamps, Mary assembles 10 lamps per hour, Mia assembles 12 lamps per hour, and Mia worked for 25 hours.

First, we can determine how many lamps Mia assembled by multiplying her working hours by her rate, resulting in 300 lamps (12 lamps per hour * 25 hours).

Next, we subtract the number of lamps assembled by Mia from the total to find how many lamps Mary assembled, resulting in 300 lamps (600 lamps total - 300 lamps assembled by Mia).

Finally, we can calculate how many hours Mary worked by dividing the number of lamps she assembled by her rate, resulting in 30 hours (300 lamps / 10 lamps per hour).

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Answer:

The mass of the rubber ball is 169.5 g

Step-by-step explanation:

we know that

The density is equal to the ratio of the mass by the volume

D=m/V

Solve for m

m=D*V

In this problem we have

V=113 cm³

D=1.5 g/cm³

substitute

m=1.5*113=169.5 g

Answer:

For example, the function [tex]y=x^{2}[/tex] does not have a y-intercept of (0, 1). To prove this, let's make x=0, and if the value of 'y' is different from 1, then, the graph does nt have a y-intercept of (0,1):

[tex]y=x^{2}[/tex] ⇒ [tex]y=(0)^{2}[/tex] ⇒ [tex]y=0[/tex]

Therefore, the y-intercept is at (0, 0) not (0, 1).

Answer:

The center of the circle is point (8 , 6)

Step-by-step explanation:

* At first lets revise how to find the mid-point between two points

- If (x1 , y1) and (x2 , y2) are the end point of a segment

- If (x , y) is the mid-point of this segment

- To find  x add x1 and x2, then divide the answer by 2

∴ x = (x1 + x2)/2

- Similar to find y add y1 and y2, then divide the answer by 2

∴ y = (y1 + y2)/2

∴ The mid-point (x , y) = [(x1 + x2)/2 , (y1 + y2)/2]

* Now lets solve the problem

- The center of the circle is the mid-point of the diameter

- Consider the center of the circle is (x , y)

- (x , y) is the mid-point of the diameter of the circle with endpoints

 (4 , 9) and (12 , 3)

- Let (4 , 9) is (x1 , y1) and (12 , 3) is (x2 , y2)

∵ x1 = 4

∵ x2 = 12

∵ x = (x1 + x2)/2

∴ x = (4 + 12)/2 = 16/2 = 8

* Similar

∵ y1 = 9

∵ y2 = 3

∵ y = (y1 + y2)/2

∴ y = (9 + 3)/2 = 12/2 = 6

∴ (x , y) = (8 , 6)

* The center of the circle is point (8 , 6)

Answer:

The center is (8,6) and radius is 5 units of the wheel

Step-by-step explanation:

On the design of the new car the steering wheel has a diameter with endpoints at (4 9) and (12,3)

End point of diameter is (4 9) and (12,3)

As we know mid point of diameter is center of circle.

Mid point formula:

[tex](x,y)\rightarrow (\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})[/tex]

Mid point of  (4 9) and (12,3)

[tex]Centre: (\dfrac{4+12}{2},\dfrac{9+3}{2}[/tex]

Center: (8,6)

Radius is distance between center and any one end point of diameter.

Distance formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]

[tex]R=\sqrt{(8-4)^2+(6-9)^2[/tex]

[tex]R=\sqrt{16+9}=\sqrt{25}[/tex]

Radius = 5

Hence, The center is (8,6) and radius is 5 units of the wheel

Answer:

The Answer is B

Step-by-step explanation:

+7 at the end means up 7

The - 4 in the middle represents right 4

These are found using basic rules of translating equations

For this case we have to define function transformation that:

Let k> 0:

To graph [tex]y = f (x) + k,[/tex] the graph is displayed k units up.

To graph[tex]y = f (x) -k[/tex], the graph is displayed k units units down.

Let h> 0:

To graph[tex]y = f (x-h)[/tex], the graph moves units to the right.

To graph [tex]y = f (x + h)[/tex], the graph moves h units to the left.

We have [tex]y = - \sqrt [3] {x}[/tex]

It moves 7 units up and 4 to the right.

So we have to:

[tex]h = 4\\k = 7[/tex]

The shifted graphic is:

[tex]y = - \sqrt [3] {x-4} +7[/tex]

ANswer:

[tex]y = - \sqrt [3] {x-4} +7[/tex]

Answer: The Electronic Funds Transfer Act is a federal law that protects consumers engaged in the transfer of funds through electronic methods. This includes the use of debit cards, automated teller machines and automatic withdrawals from a bank account.

Step-by-step explanation:

Answer: It limits liability if their debit card is stolen and used

Answer:

In 9 years, the account will be worth $1699.48

Step-by-step explanation:

Compound interest is interest calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan. Ian invested $1.315 in savings account which earns 2.86% interest compunded quaterly.

The ammount of money the account will be worth is given by the formula:

[tex]A = P(1 + \frac{[\frac{r}{4}}{100} )^4n[/tex]

where r: Rate of annual interest = 2.86%

n: the number of years = 9

P= Principal ammount = $1315

Then A= $1699.48

Since only 12 balls are small, each color has 25, 22 red balls are large - that leaves 3 red balls that are small. 12 small balls total less the 3 red small balls - that leaves 9 green small balls.

Answer:

0.87

Step-by-step explanation:

3 - 0.39 = 2.61

2.61 : 3 = 0.87

To find the cost of one bag of crisps, subtract the change from the amount paid for the biscuits to find the cost of the biscuits in pence, then divide by three since three bags of crisps cost the same as one pack of biscuits. The cost of one bag of crisps is 87 pence.

The student is asking for the cost of one bag of crisps in pence, given that three bags cost the same as one pack of biscuits. Tom paid the shopkeeper £3 for a pack of biscuits and received 39p as change.

First, we calculate the actual cost of the biscuits:

£3 paid - £0.39 change = £2.61 or 261p (since 1 pound equals 100 pence)

Next, we know that this cost is equal to three bags of crisps, so:

261p / 3 bags = 87p per bag

Therefore, the cost of one bag of crisps is 87 pence.

Answer:

1/5

Step-by-step explanation:

2/10 chance that a pug would be selected

2/10 is simplified to 1/5

The probability that a randomly selected dog is a pug is 1/5.

Given:

There are 10 dogs at the dog park.

2 dogs are pugs.

We have to find the probability that a randomly selected dog is a pug.

We know, probability is given by:

⇒ Probability = Total number of dogs which are pug / Total number of dogs at the park

⇒ Total number of dogs which are pug = 2

⇒ Total number of dogs at the park = 10

⇒ P(pug) = 2/10

⇒ P(pug) = 1/5

Therefore, the probability that a randomly selected dog is a pug is 1/5.

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The correct answer is C. -3/2

Answer: [tex]8.66in^3[/tex]

Step-by-step explanation:

The oy rocket shown is formed by a rectangular prism and a regular pyramid whose base is a square.

The volume of the rectangular prism can be calculated with:

[tex]V_{rp}=l*w*h[/tex]

Where "l" is the length, "w" is the width and "h" is the height.

You can observe that:

[tex]l=8in\\w=1in\\h=1in[/tex]

Then, you can substitute values:

[tex]V_{rp}=(8in)(1in)(1in)=8in^3[/tex]

The volume of the regular square pyramid can be calculated with:

[tex]V_p=\frac{s^2*h}{3}[/tex]

Where "s" is the lenght of a side of the base and "h" is the height of the pyramid.

You can observe in the figure that:

[tex]s=1in\\h=2in[/tex]

Substitute into the formula. Then:

[tex]V_p=\frac{(1in)^2(2in)}{3}=\frac{2}{3}in^3[/tex]

The volume of the toy rocket is the sum of the volume of the rectangular prism and the volume of the regular square pyramid. Then:

[tex]V_{toy}=8in^3+\frac{2}{3}in^3=8.66in^3[/tex]

Answer: 226200 ft

Step-by-step explanation:

Length=100 ft

Width=58 ft

Height=78 ft

(78x58x100)/2=226200 ft

I know it sounds crazy, but I'm pretty sure that's the answer.

Answer:

[tex]\large\boxed{V=226,200\ ft^3}[/tex]

Step-by-step explanation:

The formula of a volume of a prism:

[tex]V=BH[/tex]

B - area of a base

H - height

We have the triangle in the Base. The fomula of an area of a triangle:

[tex]A_\triangle=\dfrac{bh}{2}[/tex]

b - base

h - height

We have b = 58ft and h = 78ft. Substitute:

[tex]B=\dfrac{(58)(78)}{2}=(29)(78)=2,262\ ft^2[/tex]

The volume:

B = 2,262 ft², H = 100 ft. Substitute:

[tex]V=(2,262)(100)=226,200\ ft^3[/tex]

Answer:

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Answer:

h = 15 feet

Step-by-step explanation:

A right triangle is formed by the slant height, the radius of the base and h, with the slant height being the hypotenuse.

Using Pythagoras' theorem in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

Since base diameter = 16 then radius = 8

h² + 8² = 17²

h² + 64 = 289 ( subtract 64 from both sides )

h² = 225 ( take the square root of both sides )

h = [tex]\sqrt{225}[/tex] = 15

The height of the given cone will be 15 feet.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. The theorem can be used to determine how steep mountains or slopes are. To calculate the distance between an observer and a location on the ground when the observer is looking down from a tower or structure. It is mostly utilized in the construction industry.

Given, A right cone has a slant height of 17 feet, and the diameter of the base is 16 feet.

Since slant height and radius of the base makes a right-angle triangle with the base of radius and hypotenuse of the slant.

Thus, from the Pythagorean theorem:

hypotenuse² = height² + base²

In our case,

Hypotenuse = slant height = 17 feet

Base = radius of base of the cone = 16/2 = 8

Thus,

17² = height² + 8²

height² = 17² - 8²

height² = 225

height = 15 feet

Therefore, the height of the given cone will be 15 feet.

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Answer:

The number of paper clips that Crystal has is 3 and the number of paper clips that Gayle has is 14

Step-by-step explanation:

Let

x----> the number of paper clips that Crystal has

y --->   the number of paper clips that Gayle has

we know that

[tex]y=x+11[/tex] ----> equation A

[tex]x=42/y[/tex] ----> equation B

substitute equation A in equation B

[tex]x=\frac{42}{x+11} \\ \\x^{2} +11x=42\\ \\x^{2} +11x-42=0[/tex]

Solve the quadratic equation by graphing

The solution is [tex]x=3\ paper\ clips[/tex]

see the attached figure

Find the value of y

[tex]y=3+11=14\ paper\ clips[/tex]

therefore

The number of paper clips that Crystal has is 3

The number of paper clips that Gayle has is 14

Are you asking what the 8 equal parts are ? If so 100/8=12.5

Dividing 100% into 8 equal parts means each part is 12.5% of the whole, showcasing a basic division of percentages.

The question "100% with 8 equal parts" involves dividing a whole into equal portions, which is a fundamental concept in mathematics. When we talk about 100% as being the whole, dividing it into 8 equal parts means we are essentially finding what 1/8th of this whole is, percentage-wise.

To calculate, we understand that 100% divided by 8 equals 12.5%. Therefore, each part of the 8 equal divisions of the whole is 12.5% of that whole. This is a simple percentage division problem and is relevant in understanding fractions, percentages, and their practical implications in everyday scenarios.

Answer:

Option a

Step-by-step explanation:

A function is a relationship between two sets called domain and co domain  where there is one output for every input. If you have more than one output for a particular input, i.e. if the mapping of elements of A to B are not unique,  then the quantities represent a relation. A graph of a relationship can be shown to be a function using the vertical line test, which says that at any point if a vertical line makes two intercepts of the curve, the curve cannot be a function.

Given are two sets with {1,2,3,4,5,6} and {2,3,4,5,6,7} where there is a mapping.

We find that while 1,3 have unique mappings 2 does not have an image at all while 4 and 5 have the same image.

Since there is an element in the I set which does not have an image, this cannot be a function.

Option a

I would personally choose B.

Answer:

15

Step-by-step explanation:

The angle in total is 90* because its a right angle.

The equation is 4x+30=90

subtract 30 from both sides

4x=60

divide 4 from both sides

x=15

hope this helped!

Answer:

15

Step-by-step explanation: 90-30=60   60÷4=15

[tex] \frac{15}{2} g - 7 = \frac{3}{5} \\ \\ \\ 1. \: \frac{15g}{2} - 7 = \frac{3}{5} \\ 2. \: \frac{15g}{2} = \frac{3}{5} + 7 \\ 3. \: \frac{15g}{2} = \frac{38}{5} \\ 4. \: 15g = \frac{38}{5} \times 2 \\ 5. \: 15g = \frac{76}{5} \\ 6. \: g = \frac{ \frac{76}{5} }{15} \\ 7. \: g = \frac{76}{5 \times 15} \\ 8. \: g = \frac{76}{75} [/tex]

Answer:

(7, -2.4). (3,8,1) = 9

The vectors are not perpendicular

Step-by-step explanation:

The  inner product between two vectors A = {a, b, c} and B = {d, e, h} is:

[tex]A * B = a * d + b * e + c * h[/tex]

In this case the vectors are (7, -2,4) and (3,8,1). Then the product point is:

[tex](7, -2,4). (3,8,1) = 7 * 3 + (- 2) * 8 + 4 * 1\\\\(7, -2.4). (3,8,1) = 9[/tex]

The dot product between two vectors is equal to zero only if the vectors are perpendicular to each other.

In this case the dot product is nonzero, therefore the vectors are not perpendicular

Answer:

[tex]\large\boxed{8425095_{10}=808E87_{16}}[/tex]

Step-by-step explanation:

You divide the given number by 16. Write the result underneath, and the rest of the division on the right.

The number in the hexadecimal system is wrote from the bottom.

10 = A, 11 = B, 12 = C, 13 = D, 14 = E, 15 = F

[tex]\begin{array}{c|c}8425095&7\\526568&8\\32910&14=E\\2056&8\\128&0\\8&8\\0\end{array}\\\\8425095_{10}=808E87_{16}[/tex]

I minimized the steps in the second part. Hope you understand

[tex]\(e^3\)=2.71828[/tex]

In [tex]\(e^3\)[/tex], "e" represents Euler's number, an irrational mathematical constant approximately equal to 2.71828. When raised to the power of 3, [tex]\(e^3\)[/tex] signifies the exponential growth of "e" compounded three times. This can be interpreted as the result of continuously compounding interest or growth at a rate of "e" over three time periods. The expression [tex]\(e^3\)[/tex] calculates the value after three such compounding intervals, showcasing the inherent rapid and self-reinforcing nature of exponential growth. In practical terms, [tex]\(e^3\)[/tex] can represent scenarios where a quantity increases or decreases exponentially, such as population growth, financial investments, or decay processes. Understanding [tex]\(e^3\)[/tex] involves recognizing the profound impact of continuous compounding, making it a fundamental concept in various scientific and mathematical applications.

Answer:

9

Step-by-step explanation:

shorter leg = x

longer leg = x + 3

Hypotenuse = x + 6

x² + (x + 3)² = (x + 6)²

x² + x² + 6x + 9 = x² + 12x + 36

2x² + 6x + 9 = x² + 12x + 36

x²  - 6x  - 27 = 0

(x - 9) ( x + 3) = 0

x = 9 or x = -3 (rejected)

The length of the shorter leg of the right angles triangle is 9.

What is a right-angle triangle?

A triangle is said to be right-angled if one of its inner angles is 90 degrees, or if any one of its angles is a right angle. The right triangle or 90-degree triangle is another name for this triangle.

A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse

The right triangle's three sides are interconnected. The Pythagorean Theorem explains this connection. This theorem states that in a right triangle,  [tex]h^{2} = x^{2} + y^{2}[/tex];

where, h = hypotenuse; x = perpendicular side; y = base side;

Given that:

shorter leg = x

longer leg = x + 3

Hypotenuse = x + 6

⇒x² + (x + 3)² = (x + 6)²

⇒x² + x² + 6x + 9 = x² + 12x + 36

⇒2x² + 6x + 9 = x² + 12x + 36

⇒x²  - 6x  - 27 = 0

⇒(x - 9) ( x + 3) = 0

⇒x = 9 or x = -3.

x=-3 is not possible;

Hence, The length of the shorter leg = 9.

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Answer: 48.6 degrees

Step-by-step explanation:

Here we use the sin(-1) which is opp/ hypt. We get the ratio of 3/4 and put in our calculator .75 sin(-1) and get the output 48.59, which is rounded to 48.6.