f(x) = 4x2 + 7x - 18
Find f(-9)

Answer:

381

Step-by-step explanation:

Let n be the number

When 125 is subtracted from one third of a number the result is 2

1/3n - 125 = 2

Add 125 to each side

1/3n -125+125 = 2+125

1/3n = 127

Multiply each side by 3

1/3n *3 = 127*3

n =381

Given:

The diameter of the sphere = 42 cm

To find the volume of the given sphere.

Formula:

The volume of a sphere is given by [tex]V=\frac{4}{3} \pi r^3[/tex]

The radius is given by [tex]r=\frac{d}{2}=\frac{42}{2}=21[/tex]

Volume of the sphere:

The volume of the sphere is given by

[tex]V=\frac{4}{3} (3.14)(21)^3[/tex]

Simplifying, we get;

[tex]V=\frac{4}{3}(3.14)(9261)[/tex]

Multiplying the terms, we have;

[tex]V=\frac{116318.16}{3}[/tex]

Dividing, we get;

[tex]V=38772.7[/tex]

Thus, the volume of the sphere is 38772.7 cubic cm.

Answer:

The length of ladder is 17 feet .

Step-by-step explanation:

Refer the attached figure .

Let the length of ladder AC be h

We are given that the distance from the ground to the top of the ladder is 9 feet less than the length of the ladder.

So ,Perpendicular = AB = h-9

Distance from the bottom of the ladder to the building= BC = Base =15 feet.

Using Pythagoras theorem

[tex]Hypotenuse^2=Perpendicular^2+Base^2\\h^2=(h-9)^2+15^2\\h^2=h^2+81-18h+225\\18h=306\\h=\frac{306}{18}\\h=17[/tex]

Hence The length of ladder is 17 feet .

Answer:

20

Step-by-step explanation:

the answer is 20 for sure

Answer:

14.3€

Step-by-step explanation:

Let:

[tex]C=Price\hspace{3}of\hspace{3}the\hspace{3}shirt\\P=Price\hspace{3}of\hspace{3}the\hspace{3}pants\\T=Total\hspace{3}cost[/tex]

Now, let's write the data provided by the problem, using algebraic notation.

The total cost of the clothes is 20€, so:

[tex]P+C=T\\\\P+C=20[/tex]

The price of the shirt is :

[tex]C=\frac{2}{5} P[/tex]

Replacing this value into the first equation:

[tex]P+\frac{2}{5} P=20[/tex]

Solving for P:

[tex]\frac{7}{5} P=20\\\\P=\frac{100}{7} \approx 14.3[/tex]

So, the price of the pants is 14.3€ and the price of the shirt is:

[tex]C+14.3=20\\\\C=20-14.3=5.7[/tex]

Translation:

Deja que:

[tex]C=Precio\hspace{3}de\hspace{3}la\hspace{3}camisa\\P=Precio\hspace{3}del\hspace{3}pantalon\\T=Costo\hspace{3}total[/tex]

Ahora, escribamos los datos proporcionados por el problema, usando notación algebraica.

El costo total de la ropa es de 20 €, entonces:

[tex]P+C=T\\\\P+C=20[/tex]

El precio de la camisa es:

[tex]C=\frac{2}{5} P[/tex]

Reemplazando este valor en la primera ecuación:

[tex]P+\frac{2}{5} P=20[/tex]

Resolviendo para P:

[tex]\frac{7}{5} P=20\\\\P=\frac{100}{7} \approx 14.3[/tex]

Entonces, el precio del pantalón es de 14.3 € y el precio de la camisa es:

[tex]C+14.3=20\\\\C=20-14.3=5.7[/tex]

The price of the pants is 14.3€ and the price of the shirt is: [tex]C+14.3=20\n\nC=20-14.3=5.7[/tex].

Let:

[tex]C=Price\hspace{3}of\hspace{3}the\hspace{3}shirt\nP=Price\hspace{3}of\hspace{3}the\hspace{3}pants\nT=Total\hspace{3}cost[/tex]

Now, let's write the data provided by the problem, using algebraic notation.

The total cost of the clothes is 20€, so:

P+C=T\n\nP+C=20

The price of the shirt is :

C=(2)/(5) P

Replacing this value into the first equation:

P+(2)/(5) P=20

Solving for P:

[tex](7)/(5) P=20\n\nP=(100)/(7) \approx 14.3[/tex]

So, the price of the pants is 14.3€ and the price of the shirt is:

[tex]C+14.3=20\n\nC=20-14.3=5.7[/tex].

Complete question :-

Vicente spends 20 euros on a pair of pants and a shirt. He doesn't know the price of each item, but he does know that the shirt costs two-fifths of what the pants cost. How much do the pants cost?

Answer:

The sample size n= 2500

A survey with 2500 left-handed people guarantees  the given margin error is 2%

Step-by-step explanation:

Explanation:-

The margin of error = [tex]\frac{2 S.D}{\sqrt{n} }[/tex]

here for proportions , the standard deviation (σ) = [tex]\sqrt{p(1-p)} \leq \frac{1}{2}[/tex]

[tex]Margin of error = \frac{2 S.D}{\sqrt{n} } \leq \frac{2(\frac{1}{2}) }{\sqrt{n} }[/tex]

[tex]Margin of error = \frac{1}{\sqrt{n} }[/tex]

now The necessary sample size is

[tex]n= \frac{1}{(M.E)^{2} }[/tex]

Given data the survey in order to get a margin of error of 2%

M.E = 0.02

[tex]n= \frac{1}{(0.02)^{2} } = 2500[/tex]

Conclusion:-

The sample size n= 2500

A survey with 2500 left-handed people guarantees the given margin error is 2%

Answer:

Overconfidence

Step-by-step explanation:

In this question we have a company that is offering a certain higher discount when a customer purchases its wares at bulk rather than in bits, we want to know what exactly the customer wants its company to experience.

The correct answer to this is overconfidence. The company wants its customers to experience overconfidence by going for the second option which shows a massive reduction in value of what they should pay

Answer:

x + 52 + 78 = 180

Step-by-step explanation:

By angle sum property of a triangle:

[tex]x + 52 + 78 = 180[/tex]

Answer: the top one x+52+78=180

Answer:

√3·5x

Step-by-step explanation:

√(75x²) = √75·√x²

or          =√3√25√x²     Recognize that both 25 and x² are perfect squares.

or           =√3·5x

Answer:

a. It is flawed because it is a voluntary response sample

Step-by-step explanation:

Sampling method:

The process of selecting the samples from the population to conduct investigation is called sampling method. The sampling method must not be biased, meaning that the samples must be selected randomly.

In the given problem, 540 ​subjects were chosen for this survey. These subjects were internet users who responded to a question that was posted on a news website. This suggests that the subjects volunteered for the survey so that means their selection was not random at all, therefore, the sampling method is flawed because it is a voluntary response sample.

Note: A voluntary response sample is a sample where subjects decide themselves whether to be a participate in the survey or not.

The sampling method is flawed because it is a voluntary response sample, potentially leading to bias as it relies on self-selected internet users. The correct option is a.

The sampling method described in the survey appears to be flawed because it is a voluntary response sample, making option (a) the correct choice.

In this survey, the participants are self-selecting internet users who chose to respond to a question on a news website. This type of sampling is known as a voluntary response sample. It is flawed because it introduces bias into the data. Those who voluntarily respond may not represent the broader population accurately. People who eat bananas regularly or have strong opinions about bananas may be more likely to respond, leading to an overrepresentation of certain groups and potentially skewing the results.

Statistical significance (option c) and being a census (option d) are not the primary issues in this case. Statistical significance depends on the sample size and how well it represents the population, and a census surveys the entire population, which is not the case here.

In summary, the sampling method used in this survey is flawed because it relies on voluntary responses and may not provide a representative view of the population's banana-eating habits.

The correct option is a. It is flawed because it is a voluntary response sample.

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Complete question below :

What is the soundness of the sampling method used in the survey described below?

In a survey of 540 subjects, each was asked how often he or she ate bananas. The survey subjects were internet users who responded to a question that was posted on a news website.

a. It is flawed because it is a voluntary response sample.

b. It appears to be sound because the data are not biased in any way.

c. It is flawed because it is not statistically significant.

d. It is flawed because it is a census.

Answer: therefore A= 0.1 and B=0.85

Step-by-step explanation:

The values of 'a' and 'b' in the frequency table are 0.1 and 0.1

We have,

To complete the conditional relative frequency table, we need to find the values of the letters 'a' and 'b'.

We know that the total for each row and column should add up to 1.

So, we can use this information to set up two equations and solve for the values of 'a' and 'b'.

Equation 1:

0.9 + b = 0.88

This equation represents the total percentage of students aged 16 years who finish homework before 10 pm.

We subtract 0.9 and 0.88 from both sides to get:

b = 0.88 - 0.9

b = -0.02

This means that the value of 'b' is negative, which doesn't make sense.

So, we made an error in setting up the equation.

We can check the table to find the correct value of 'b'.

We know that the total for the column "Before 10 pm" should be 1.

This means that the sum of the percentages 0.9 and 'b' should be equal to 1.

So,

Equation 2:

0.9 + b = 1

Solving for 'b', we get:

b = 1 - 0.9

b = 0.1

Now, we can use Equation 2 to solve for 'a':

0.15 + a = 0.12

Subtracting 0.15 from both sides, we get:

a = 0.12 - 0.15

a = -0.03

Again, we get a negative value for 'a', which doesn't make sense.

So, we need to check our work again.

We know that the total for the row "16 years" should be 1.

This means that the sum of the percentages 0.9 and 'a' should be equal to 1.

So,

0.9 + a = 1

Solving for 'a', we get:

a = 1 - 0.9

a = 0.1

Therefore,

The values of 'a' and 'b' in the frequency table are 0.1 and 0.1

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Answer: The diagonal length of the suitcase is 30 inches. Assuming that the length and height of the suitcase form a right angle (90 degree angle), you can use the Pythagorean Theorem ( a2+b2 = c2) to solve this problem. The diagonal length is equal to the square root of the sum of the length squared and the height squared.

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

if you think about a rectangle cut by its diagonal then yoou can see that its just 2 right triangles and youre looking for the long end

Using pythagorean theorem you put in the numbers

[tex]24^{2} + 18^2 = c^2[/tex]

solving gives you

[tex]900 = c^2[/tex]

[tex]\sqrt{900} = c[/tex]

30 = c

Answer:

[tex]k = \frac{1}{3}[/tex]

Step-by-step explanation:

The coeficcient of dillation is:

[tex](6,3)[/tex]

[tex](3\cdot 2, 3\cdot 1)[/tex]

[tex]3\cdot (2,1)[/tex]

The constant of dilation is [tex]k = \frac{1}{3}[/tex].

Final answer:

To find the constant of dilation for a point A (6,3) mapping onto A\'(2,1) under dilation with respect to the origin, the coordinates are compared resulting in a constant of dilation of 1/3.

Explanation:

The question involves finding the constant of dilation when a point A (6,3) maps onto A\'(2,1) under a dilation with respect to the origin.

The constant of dilation can be found by comparing the coordinates of A with those of A\'.

For point A with coordinates (x,y) mapping to A\' with coordinates (x\',y\'), the dilation factor (k) is found by the formula k = x\'/x = y\'/y when the dilation is centered at the origin (0,0).

In this case, for the x-coordinates: k = 2/6 = 1/3, and for the y-coordinates: k = 1/3 which confirms our calculation, as the dilation factor must be consistent across both coordinates.

Therefore, the constant of dilation is 1/3.

Answer:

The margin of error for the survey is 0.016

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 1024

Sample proportion:

[tex]\hat{p} = 89\% = 0.89[/tex]

We have to find the margin of error associated with a 90% Confidence interval.

Formula for margin of error:

[tex]z_{stat}\times \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]

[tex]z_{critical}\text{ at}~\alpha_{0.10} = 1.64[/tex]

Putting the values, we get:

[tex]M.E = 1.64\times (\sqrt{\dfrac{0.89(1-0.89)}{1024}})\\\\M.E=0.016[/tex]

Thus, the margin of error for the survey is 0.016

The margin of error for the given survey, when wanting a 90% confidence level, is approximately 1.58%. This means that the true proportion of American adults who approve of cloning endangered animals is likely to be within 1.58% above or below the survey's result of 89%.

The subject matter of this question is in the field of statistics, specifically exploring concepts of confidence intervals and margin of error. A 90% confidence interval implies that we are 90% certain that the true population proportion lies within the calculated range, whereas the margin of error gives us the range that this estimate might deviate from the actual value.

In your scenario, you have a sample size of 1024 adults with 89% approving cloning of endangered animals. To compute the margin of error in this case, we first need to find the standard error. The standard error (SE) for a proportion is calculated as √[P(1 - P) / n] where P is the sample proportion and n is the total sample size. Let's compute this:

For a 90% confidence interval, the critical value from the z-table is 1.645 ((double-tail distribution). Therefore, the margin of error (E) is calculated as:

To interpret this value, you could say that with 90% confidence, the true proportion of American adults in favor of cloning endangered animals is within the range of 1.58% above or below 89%.

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Answer:

y=2x-2 I hope this helps

Step-by-step explanation:

Slope intercept form, y=mx+b

Answer:

A) 7(c + d)

Step-by-step explanation:

5(c + d) + 2(c + d)

5c + 5d + 2c + 2d

7c + 7d

7(c + d)

Answer:

A

Step-by-step explanation:

Distribute the 5

5(c + d) + 2(c + d)

5*c+5*d  +2(c + d)

5c+5d +2(c + d)

Distribute the 2

5c+5d+ 2*c+2*d

5c+5d+2c+2d

Combine like terms (combine the ds and the cs)

5c+2c +5d+2d

7c+7d

A is equivalent to this answer

7(c + d)

Distribute the 7

7*c+7*d

7c+7d

So, A is the answer

Answer:

It is one

Step-by-step explanation:

Answer:

V = 220 feet³

Step-by-step explanation:

Formula: V = LWH

(8ft) (5ft) (5.5ft) = 220 ft^3

Answer:

B 2x-31 = -2x-31

Step-by-step explanation:

A is exactly the same on the left side as the right so it has infinite solutions

B 2x-31 = -2x-31

 Add 2x on each side

2x+2x-31 = -2x+2x-31

4x -31 = 31

Add 31

4x =62

This has one solution

C 2x+31 = 2x-31

Subtract 2x from each side

31 = -31

This is never true so it has no solutions

D 2x-2 = 2x-31

Subtract 2x from each side

-2 = -31

This is never true so it has no solutions

Answer:

B)

Step-by-step explanation:

2x - 31 = -2x - 31

4x = 0

x = 0

x = 0 is the only solution

Answer:

The probability that there will be repair exactly 3 toaster is 0.0574.

Step-by-step explanation:

Binomial Distribution:

A discrete random variable X having the set {0,1,2,3......,n} as the spectrum, is said have a binomial distribution with parameter n= number of trials and p=probability of number of success on an individual trial, if the p.m.f (probability mass function) of X given by,

[tex]P(X=x)=C(n,x)p^x(1-p)^{n-x}[/tex]    x=0,1,2,......,n

               =0                                   elsewhere

where 0<p<1 and n is a positive integer.

Total number of toaster in cartons(n) = 10.

Probability of number of success on an individual trial p= 10% = 0.10

[tex]\therefore P(X=3)= C(10,3)(0.10)^3(1-0.10)^{10-3}[/tex]

                    [tex]=\frac{10!}{3!(10-3)!}(0.10)^3)(0.90)^7[/tex]

                    =0.0574

The probability that there will be repair exactly 3 toaster is 0.0574.

Answer:

4+35=39, 23+43-23+46-34-34+6=27. So it is a no solution question.

Step-by-step explanation:

Both of the equations do not equal

Answer:

69

Step-by-step explanation:

I love the number 69, and tbh it's the answer to everything

Answer:

Length of the rope = 15.6 ft.

Step-by-step explanation:

Given:

Height of the pole from the ground = 12 ft

Adjacent distance from the pole = 10 ft

We have to find the length of the rope attached by Scott to secure the pole.

According to the question :

In forma  right angled triangle as shown in the figure.

We have to find the measure of the hypotenuse.

Length of rope = Hypotenuse measure

Let the length of the rope = "h" ft

Using Pythagoras formula.

⇒ [tex](hypotenuse)=\sqrt{opposite^2+ adjacent^2}[/tex]

⇒ Plugging the values.

⇒ [tex]h=\sqrt{12^2 + 10^2}[/tex]

⇒ [tex]h=\sqrt{144 + 100}[/tex]

⇒ [tex]h=\sqrt{244}[/tex]

⇒ [tex]h=15.62[/tex] ft

The length of the rope, rounded to the nearest tenth is 15.6 ft.

Answer:

27

Step-by-step explanation

14 is the radius so multiply by pi to get 87.96

then turn 200 fee into in which is 2400in

and divide 2400 by 87.96

Answer:

56x^7

Step-by-step explanation:

48x^7-(-8x^7) = 48x^7 + 8x^7 = 56x^7

Answer:

c

Step-by-step explanation:

The error was to include the number -14 in the inequality.

An inequality is a statement that is formed when two expressions are joined using an inequality operator.

The inequality that represents the statement is

x  > -14

Bryan wrote the inequality as x ≥ -14 , which is wrong as there is an open circle at -14 on the number line.

An open circle depicts that the number is not included.

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On a timeline, a milestone 11 years in the future will be to the left of a milestone 20 years in the future and to the right of a milestone 25 years in the future, considering events are arranged from left (earlier) to right (later).

On a Timeline a milestone 11 years in the future will be to the left of a milestone 20 years in the future and to the right of a milestone 25 years in the future. This question revolves around understanding the sequential order of events plotted on a timeline, which is a graphical representation of events placed in a chronological sequence. A timeline is typically read from left to right, with events placed according to their date from earliest to latest. Therefore, if we are talking about the future, 11 years from now is sooner than 20 years from now, so it would be placed to the left. Similarly, it is later than 25 years from now, hence it would be to the right of the 25-year milestone.

Answer: 8.8%

Convert the fraction to a decimal, then multiply by  100

8.77192982  rounded to the nearest 10 is 8.8%

8.8% is the answer

Answer:

18pi or 56.52 units²

Step-by-step explanation:

Radius² = (-3-0)² + (2-5)²

= 18

Area = pi × r²

3.14 × 18

56.52

The area of the circle is 57.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

To find the area of the circle, we need to know the radius.

The radius can be determined using the distance formula between the center of the circle (2, -3) and the point on the circle (5, 0).

The distance formula is given by:

d =√(5 - 2)² + (0 - (-3))²

= √3²+ 3²

=√9 + 9

=√18

The radius is the distance between the center and a point on the circle, which is the square root of 18.

Now, we can calculate the area of the circle using the formula:

Area = π × radius²

Area = π ×√18²

= 18π

= 56.52

Hence, the area of the circle is 57.

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Answer:A terminating decimal is a decimal that ends. It's a decimal with a finite number of digits

Step-by-step explanation:

Answer: A terminating decimal is a decimal that ends. It's a decimal with a fixed number of digits.

Explanation: A decimal numeral (also often just decimal or, less correctly, decimal number), refers generally to the notation of a number in the decimal numeral system. Decimals may sometimes be identified by a decimal separator (usually "." or "," as in 25.9703 or 3,1415). Decimal may also refer specifically to the digits after the decimal separator, such as in "3.14 is the approximation of π to two decimals". Zero-digits after a decimal separator serve the purpose of signifying the precision of a value.

The numbers that may be represented in the decimal system are the decimal fractions. That is, fractions of the form a/10n, where a is an integer, and n is a non-negative integer.