Given the function g(x) = -5x + 2 and h(x) = x2 – 1. Find h(3)

Answer: So there is only 1 possible outcome when choosing 8 candidates out of a pool of 8, which is simply selecting all 8 candidates.

Step-by-step explanation: Assuming that the order of the candidates does not matter, the number of possible outcomes can be calculated by finding the number of ways to choose a group of 8 candidates out of a total of 8.

This can be represented by the combination formula:

nCr = n! / (r! * (n-r)!)

where n is the total number of candidates and r is the number of candidates to be chosen.

In this case, we have:

n = 8 (total number of candidates)

r = 8 (number of candidates to be chosen)

Therefore, the number of possible outcomes is:

8C8 = 8! / (8! * (8-8)!) = 1

So there is only 1 possible outcome when choosing 8 candidates out of a pool of 8, which is simply selecting all 8 candidates.

A company CEO says that 85% of their customers are repeat customers. A sample of 200 customers was taken, and it was found that 162 of them were repeat customers. We want to know if this sample supports the CEO's claim, or if it suggests that less than 85% of the company's customers are repeat customers. We performed a statistical test and found that the sample provides evidence at a significance level of 5% that less than 85% of customers are repeat customers. The conditions for this test are met because the sample was taken randomly, and the sample size is small enough compared to the overall population size.

The solution is, the total costs for year 1 will be $2,240, for year 2 they will be $2,040, and for year 3 they will be $2,120.

Here, we have,

Given that one of your company's salesmen estimates he will drive 20,000 miles this year and each of the next two years, and as the service manager for the company's fleet of six-cylinder compact automobiles, you are asked to determine the total costs for each of the three years, to determine said cost, the following calculation must be made:

Year 1:

20000 x 0.112 = X

2,240 = X

Year 2:

20000 x 0.102 = X

2,040 = X

Year 3:

20000 x 0.106 = X

2,120 = X

Therefore, the total costs for year 1 will be $2,240, for year 2 they will be $2,040, and for year 3 they will be $2,120.

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Answer:

Step-by-step explanation:

Graph crosses x-axis when y=0 (that is f(x)=0).

   [tex](x+3)(x+2)(x-1)=0 \text{ when:}[/tex]

           [tex]x+3=0\text{ or }x+2=0\text{ or }x-1=0[/tex]

           [tex]\text{So }x=-3,-2,1[/tex]

SOLUTION:  Graph crosses x-axis at [tex]x=-3,-2,1[/tex].

Step-by-step explanation:

You want to find the equation for a line that passes through the point (4,21) and has a slope of 01.

First of all, remember what the equation of a line is:

y = mx+b

Where: m is the slope, and b is the y-intercept

To start, you know what m is; it's just the slope, which you said was 01. So you can right away fill in the equation for a line somewhat to read:

y=01x+b.

Now, what about b, the y-intercept?

To find b, think about what your (x,y) point means:

(4,21). When x of the line is 4, y of the line must be 21.

Because you said the line passes through this point, right?

Now, look at our line's equation so far: . b is what we want, the 1 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the the point (4,21).

Answer:

1) 13

2) 29

3) 61

4) 151

Step-by-step explanation:

1:

Vertical angles are congruent.  Angle A is equal to Angle C

3x - 10 = 29  Add 10 to both sides

3x - 10 + 10 = 29 + 10

3X = 39  Divide both sides by 3

x = 13

2:

29
Vertical angles have the same measurement.

3:

A straight angle (straight line) is 180. The square in the angle means that angle measures 90.

180 - 90 - 29 = 61

4:

180 - 29 = 151

Helping in the name of Jesus.

The graph of the piecewise function is the one at B.

Here we want to identify which one of the given graphs is the one of the given picewise function.

If you look at the domains, you can see that these are:

x ≤ -2

-2 < x < 0

0 < x

So, we need to have:

The only option that has these is the middleone, so the correct option is B.

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The option that describes the weight of the contents that Carly can

pack in her bag is: C at most 43.8 pounds

Some of the inequality signs are:

Greater than

Less than

Greater than or equal to

Less than or equal to

Now, we are told that Passenger Bags Can Weigh No More than 50 Pounds.

Since her bag weighs 6.2 pounds empty, then we can say that the maximum weight of the contents that Carly can pack in her bag is:

50 - 6.2 = 43.8 pounds

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Answer:

No, Pete's results are not likely to be representative of the population he is trying to analyze. The sample he selected is not random and is biased towards customers who have purchased the largest number of items. This may not be representative of the general population of customers who have purchased a smaller number of items, and their opinions may differ from those of the selected customers. Additionally, the sample size of 5 is small, which may not provide sufficient statistical power to draw accurate conclusions about the entire population. To obtain a representative sample, a larger sample size should be chosen randomly from the population to reduce the likelihood of bias and increase the precision of the estimates.

I hope you pass class if you need more help on other feel free to ask.

Step-by-step explanation:

Step-by-step explanation:

4 ⅓ feet = 51.95999 inch ~ 52 inches.

hope this helps.

Answer:

x = 82°

Step-by-step explanation:

From inspection of the given diagram:

The tangent of a circle is always perpendicular to the radius.

Therefore, m∠BAP = m∠BCP = 90°.

Since the sum of the interior angles in a quadrilateral is 360°, then:

⇒ m∠BAP + m∠APC + m∠BCP + m∠ABC = 360°

⇒ 90° + 98° + 90° + x = 360°

⇒ 278° + x = 360°

⇒ 278° + x - 278° = 360° - 278°

⇒ x = 82°

Therefore, the value of x is 82°.

Answer:

3w+18

Step-by-step explanation:

3 x w = 3w

3 x 6 = 18

The factorization of 7x^2 -6x is x(7x - 6).

It should be noted that to factorize 7x^2 -6x, we need to find two numbers that can multiply to give 7 times the coefficient of x^2 (which is 7), and add to give the coefficient of x (which is -6).

The first step is to factor out the greatest common factor (GCF) of the two terms, which is x:

7x^2 - 6x = x(7x - 6)

Now we can see that the two numbers we need are 7 and -6, since 7 times -6 is -42 and 7 + (-6) is 1. So we can rewrite the expression as:

7x^2 - 6x = x(7x - 6) = x(7x + (-6)) = x(7x - 6)

Therefore, the factorization of 7x^2 -6x is x(7x - 6).

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Factorize 7x^2 -6x

The radius of the circle that has an area of 380 square inches is calculated as: 11 inches.

The radius of a circle is half of the diameter. It connects from the center of the circle to any point on the circumference on the circle.

We are given the following information about a circle:

Area of the circle = 380 square inches

To find the radius of the circle, recall the formula of the area of a circle which is:

area = πr², where r is the radius, π = 3.14

Therefore:

380 = πr²

380 = 3.14 * r²

380/3.14 = r²

r² = 121.01

r = √121.01

r = 11 inches.

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Answer:

A. 11x

B. 3x² +6x

Step-by-step explanation:

If you think math is boring, you're wrong. Math can be very funny, especially when you know some good jokes. Here's one for you:

Q: How do you know that the correct answer is A. 11x and B. 3x² +6x?

A: Because they are both polynomials, and polynomials are always right!

What are polynomials, you ask? Well, they are expressions that consist of one or more terms of non-negative integer powers of a variable. For example, 11x is a polynomial with one term, and 3x² +6x is a polynomial with two terms.

But what about C. 2x²-√x and D. 1-5x²/x? Are they polynomials too? No, they are not, because they contain terms with negative or fractional powers of x. For example, √x is the same as x^(1/2), which is a fractional power of x.

Polynomials are fun, aren't they? They can help you do all kinds of things, like shopping, engineering, and driving a taxi. But did you know that polynomials can also make you laugh? Here are some jokes about polynomials that will tickle your funny bone.

- What do you call a polynomial that is always happy? A jolly-nomial.

- How do you make a polynomial sad? You take away its degree.

- What do you get when you cross a polynomial with a rabbit? A poly-hop-nomial.

- Why did the polynomial go to the dentist? Because it had a root canal.

- How do you know if a polynomial is lying? You check its coefficients.

- What do you call a polynomial that likes to party? A disco-nomial.

- What do you say when you see a polynomial with no terms? Oh, the zero-nomy!

- How do you divide a polynomial by another polynomial? You don't. That's a rational expression.

- What do you call a polynomial that is always angry? A cross-nomial.

- What do you call a polynomial that is afraid of everything? A chicken-nomial.

So, remember: polynomials are always right, and non-polynomials are always wrong. And if you don't believe me, just ask them yourself. They'll tell you the same thing!

✧☆*: .｡. That's all folks, have fun with math! (✧ω✧) .｡.:*☆✧

Answer:

638.45

Step-by-step explanation:

The interest on the couch will be:

0.13 * $565 = $73.45

So the total amount Sharon paid for the couch with interest is:

$565 + $73.45 = $638.45

so we'd want to find all "t" when the ball was 9 meters up in the air, or namely what's "t" when h(t) = 9, well, let's simply set h(t) = 9

[tex]\stackrel{h(t)}{9}=2+13t-5t^2\implies 0=-5t^2+13t-7 \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~~~~~~~\textit{quadratic formula} \\\\ 0=\stackrel{\stackrel{a}{\downarrow }}{-5}t^2\stackrel{\stackrel{b}{\downarrow }}{+13}t\stackrel{\stackrel{c}{\downarrow }}{-7} \qquad \qquad t= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}[/tex]

[tex]t= \cfrac{ - (13) \pm \sqrt { (13)^2 -4(-5)(-7)}}{2(-5)} \implies t = \cfrac{ -13 \pm \sqrt { 169 -140}}{ -10 } \\\\\\ t= \cfrac{ -13 \pm \sqrt { 29 }}{ -10 }\implies t= \begin{cases} \frac{ -13 + \sqrt { 29 }}{ -10 }\\\\ \frac{ -13 - \sqrt { 29 }}{ -10 } \end{cases}\implies t\approx \begin{cases} 0.76\\\\ 1.84 \end{cases} ~~ \textit{\LARGE seconds}[/tex]

there are two values, Check the picture below, that's about the parabolic path for the object, and it hits 9 meters high twice, once on the way up, and again on the way down.

Answer:

X=0.8

Step-by-step explanation:

X/Y=3/15

=> X=(3/15)*Y

=> X=(3/15)*4=0.8

a. The amount that remains to be refinanced is $175,000

b. The new monthly payment will be $1166.67

c. The gain is $35,000

Simple interest is an interest charge that borrowers pay lenders for a loan. Simple interest is expressed as:

S.I = P× R×T/100

the rate for first 5 years is 5%

SI = 140000 × 5 × 5/100

SI = $35000

Amount after five years = 140000+35000

= $175000

The amount that remains to be refinanced is $175000

For the remaining 10years

SI =[175000× 2× 10/100

= 35000

amount = 175000+35000

= $210,000

The total amount with this package = $210000

The number of months = 15 ×12 = 180

amount that will be paid monthly = 210000/180 = $1166.67

The gain = total amount without package - amount with package

SI = 140000×5×15/100

= $105,000

amount = 140,000+105,000 = $245,000

gain = 245000-210,000

= $35000

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Answer:

37.5

Step-by-step explanation:

To find the interquartile range (IQR) for a data set, we need to find the difference between the upper quartile (Q3) and the lower quartile (Q1).

To find Q1 and Q3, we first need to order the data set from lowest to highest:

25, 49, 50, 60, 60, 70, 70, 74, 81, 85, 89, 100

There are 12 data points in this set, so the median is the average of the sixth and seventh numbers:

median = (70 + 70)/2 = 70

To find Q1, we take the median of the first half of the data set (the numbers to the left of the median). There are six numbers in the first half, so the median is the average of the third and fourth numbers:

Q1 = (49 + 50)/2 = 49.5

To find Q3, we take the median of the second half of the data set (the numbers to the right of the median). Again, there are six numbers in the second half, so the median is the average of the ninth and tenth numbers:

Q3 = (85 + 89)/2 = 87

Now we can find the IQR by subtracting Q1 from Q3:

IQR = Q3 - Q1 = 87 - 49.5 = 37.5

Therefore, the interquartile range for the given data set is 37.5.

a) The complete form of the table is given below

b) The mean estimate of the mean waiting time is 2.56

From the question, we are to complete the table and calculate the estimate of the mean

The complete form of the given table is

Waiting Time          Midpoint (x)           Number of customers(f)             fx

       0-                            0.5                                    5                               2.5

       1-                             1.5                                     28                             42

       2-                            2.5                                    32                             80

       3-                            3.5                                    26                              91

      4 - 5                         4.5                                     9                               40.5

                                                                               100                              256

b)

Mean is given by the formula,

Mean = ∑(fx) / ∑f

Thus,

Mean = 256 / 100

Mean = 2.56

Hence, the mean estimate is 2.56

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Using it's critical points, it is found that the least possible degree of the polynomial graphed above is 4.

The critical points of a function are the values of x for which:

f'(x) = 0

At these critical points, the behavior of the function changes from increasing to decreasing or vice versa.

If a function has n critical points, the least possible degree is of n + 1.

From the changes in behavior of the graph, the function has critical points at:

x ≈ -3.5

x ≈ -1.5

x ≈ 0.25

The function has 3 critical points, hence the least possible degree of the polynomial graphed above is 4.

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Answer:

24 = 31.4n + (-8.4) is the correct equation.

Answer: 1 just like my answer dawg

Step-by-step explanation:

The probability of event A given the event B is 0.35 or 7/20.

It is given that A and B are two events.

Given probabilities are as follows:

Probability of A and B is = P(A and B) = 0.14

Probability of B = P(B) = 0.4

We know that the conditional probability of event A given B is given by,

P(A | B)

= P(A and B)/P(B)

= 0.14/0.4 [Substituting the value which are given]

= 14/40

= 7/20 [Eliminating the similar values from numerator and denominator]

= 0.35

Hence the probability of event A given the event B is 0.35 or 7/20.

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The following sets of side dimensions could be combined to create a right triangle 6, 8, 13 is √3, √13, 4.

In the triangle, there are three angles: two acute angles and one 90-degree angle. The hypotenuse, perpendicular, and base are the terms used to describe the sides of a right-angled triangle.

The next choice shows the triangle's side length:

The point is,

The hypotenuse square of a right-angled triangle is equal to the sum of its squares on its other two sides, according to Pythagoras' Theorem.

Using Pythagoras' Theorem.

Use the formula:

a² + b² = c²

For 4, 8, 11

4, 8, 11

4² + 8² = 16 + 64 = 80

11² = 121

80 is not equal to 121 it cann ot form a right triangle

For 6, 8, 13

6² + 8² = 36 + 64 = 100

13² = 169

100 is equal to 169 - 69 can form a right triangle

For √3, √5, 8

(√3)² + (√5)² = 3 + 5 = 8

8² = 64

8 is equal to 64 cannot form a right triangle

For √3, √13, 4

(√3)² + (√13)² = 3 + 13 = 16

4² = 16

16 is equal to 16 can form a right triangle

In order to create a right triangle, one may utilise the following set of side measurements √3, √13 and 4 form a triangle.

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Maraging (18% Ni) steel has a better tolerance to defects and fracture toughness compared to Medium strength steel.

The tolerance to defects and fracture toughness of a material can be evaluated using its fracture toughness parameter, Kic. The higher the Kic value, the better the material's tolerance to defects and fracture toughness.

To compare the two materials, we can use the concept of critical stress intensity factor (Kic) and factor of safety (FoS). The critical stress intensity factor is the maximum value of stress intensity factor (K) that a material can withstand without fracturing. The factor of safety is the ratio of the maximum allowable stress to the design stress, and it is used to ensure a safety margin in the design.

Assuming that the two materials have the same defect to tolerance ratio, we can calculate the maximum allowable stress for each material using the following formula:

σmax = FoS * Kic / (π * a)

where σmax is the maximum allowable stress, FoS is the factor of safety (assumed to be 2), Kic is the fracture toughness parameter, and a is the size of the defect.

Let's assume a defect size of 1 mm for both materials. Using the values given in the question, we get:

For Maraging (18% Ni) steel:

σmax = 2 * 82 * 10^6 / (π * 1 * 10^-3) = 52.1 GPa

For Medium strength steel:

σmax = 2 * 50 * 10^6 / (π * 1 * 10^-3) = 31.8 GPa

Therefore, Maraging steel has a higher maximum allowable stress, which indicates that it has a better tolerance to defects compared to medium strength steel.

To compare the fracture toughness of the two materials, we can use their respective Kic values. The higher Kic value indicates a better tolerance to defects and fracture toughness.

Comparing the given values, we can see that Maraging (18% Ni) steel has a higher fracture toughness parameter (Kic= 82 MNm-3/2) compared to Medium strength steel (Kic= 50 MNm-3/2).

Therefore, Maraging (18% Ni) steel has a better tolerance to defects and fracture toughness compared to Medium strength steel.

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√2 is an irrational number

Irrational number, any real number that cannot be expressed as the quotient of two integers—that is, p/q, where p and q are both integers. For example, there isn't number among integers and fractions that equals Square root of 5.

Also √2 doesn't have numbers among integers and fraction that can be equal to it. Other examples of irrational numbers are √3, √11 e.t.c.

Therefore since we don't have any integer or fractions that equals square root of 2 or √2, then √2 is an irrational number not a real number.

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The requried shorter base is 4 centimeters and the longer base is 3 times that, or 12 centimeters.

Let's call the shorter base of the trapezoid "b" and the longer base "3b" (since one base is 3 times the length of the other). We know the height is 6 centimeters, and the area is 48 square centimeters. The formula for the area of a trapezoid is:

Area = (b₁ + b₂) * h / 2

where b₁ and b₂ are the lengths of the two parallel bases and h is the height.

Plugging in the values given in the problem, we get:

48 = (b + 3b) * 6 / 2

48 = 2b * 6

4 = b

Therefore, the shorter base is 4 centimeters and the longer base is 3 times that, or 12 centimeters.

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Step-by-step explanation:

the volume of a regular shape is always

ground area × height

9.

so, the ground area is 12 cm².

the whole volume is 288 cm³.

therefore,

288 = 12 × height

height = 288/12 = 24 cm.

10.

we do this almost exactly the same way.

but here we have no regular shape (uniform from the bottom to the top). we have a pyramid.

the volume for a pyramid is

ground area × height / 3.

the ground area is 300 cm².

the volume is 2,050 cm³.

2,050 = 300 × height / 3.

6,150 = 300 × height.

height = 6150/300 = 20.5 cm