Given ƒ(x) = 2x2 − 3x + 7, find ƒ(2.5)

We want to graph the given function for the given domain.

The graph can be seen at the end of the answer.

The given function is:

y = 2*x

The given domain is D: {-2, 0, 2, 4}

To graph this, we need to evaluate the function in the given values of the domain, we will get four points.

y = 2*(-2) = -4

Then we have the point (-2, -4)

y = 2*0 = 0

Then we have the point (0, 0)

y = 2*2 = 4

Then we have the point (2, 4)

y = 2*4 = 8

Then we have the point (4, 8)

Then we need to graph these four points, the graph can be seen below:

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Answer:

Step-by-step explanation:

We have the length of AC which is opposite angle B; we also have the length of the hypotenuse.  We will use trig here to solve for angle B.  The sin ratio is the one that fits.

sin(B) = side opposite / hypotenuse:

[tex]sin(B)= \frac{ 4.8}{ 5.1}[/tex] so

sin(B) = .9411764706

Now we will use the 2nd button on our calculators.  This will give us the missing angle value.  Press 2nd then sin and you will see on your screen:

[tex]sin^{-1 ([/tex]

Enter that decimal after the open parenthesis and hit "enter" to get

B = 70.25 or 70°

Answer:

75 miles/hour

Step-by-step explanation:

Given information: d=337.5 miles and t=4.5 hours.

The given formula is

[tex]r=\frac{d}{t}[/tex]

where d is the distance in miles, r is the rate, and t is the time in hours.

We need to find the rate for d=337.5 miles and t=4.5 hours.

Substitute d=337.5 and t=4.5 in the above formula.

[tex]r=\frac{337.5}{4.5}[/tex]

[tex]r=75[/tex]

The value of r is 75, therefore we need to travel at the rate of 75 miles per hours to cover 337.5 miles in 4.5 hours.

Answer with explanation:

Number of People Surveyed (S)= 45

Confidence Level = 99%

Percentage of population who believe that food court needs to be remodeled =24 %

→So, 24% of 45

[tex]=\frac{24}{100}\times 45=10.80[/tex]

= 11 people

Probability of population who thinks that food court needs to be remodeled(P)

        [tex]=\frac{11}{45}[/tex]  

[tex]Z_{99 percent}= 2.58[/tex]

Confidence level for a population is given by

  [tex]=P \pm Z\sqrt{\frac{P*(1-P)}{S}}[/tex]

Substituting the values, of Z, P and S in above equation

    [tex]=0.25\pm 2.58\sqrt{\frac{0.25*0.75}{45}}\\\\=0.25 \pm 2.58*0.064549\\\\=0.25 \pm 0.17\\\\= 0.25 - 0.17 , 0.25+0.17\\\\=0.08 , 0.42[/tex]

→→0.08 ≤proportion of shoppers who believe the food court needs to be remodeled≤0.42

→→8%≤proportion of shoppers who believe the food court needs to be remodeled≤42%

Another way is to note that there are (104)(104) (“10 choose 4”) ways to select 4 balls from a collection of 10. If 4 of those 10 balls are “special” in some way (in this case, “special” = “red”), then the number of ways to choose 4 special balls is (44)(44). (The factor of (60)(60) is included to convey that, after choosing 4 special balls, we choose none of the 6 non-special balls.) This line of reasoning gives the second expression.

Answer:

The required answer is $2839.25.

Step-by-step explanation:

[tex]112\times12=1344[/tex] dollars

Plus down payment = [tex]1344+275=1619[/tex] dollars

Now, compound interest is found as:

[tex]A=p(1+\frac{r}{n})^{nt}[/tex]

p = 3592

r = 21.80% or 0.2180

n = 12

t = 1

Substituting the values in formula:

[tex]A=3592(1+\frac{0.2180}{12})^{12}[/tex]

=> [tex]A=3592(1.018167)^{12}[/tex]

A = $4458.25

So, Balance = [tex]4458.25-1619=2839.25[/tex] dollars

Therefore, the required answer is $2839.25.

Answer:

a). m∠4 = 143°

b). m∠2 = 37°

c). ∠4 ≅ ∠8

d). ∠3 + ∠5 ≅ 180°

Step-by-step explanation:

a). Given m∠7 = 37°

Since m∠7 ≅ m∠6 [Vertically opposite angles]

and m∠6 + m∠4 = 180° [Sum of interior angles formed by parallel lines l, m and transverse.]

Therefore, 37°+ m∠4 = 180°

m∠4 = 180 - 37

        = 143°

b). Since m∠6 ≅ m∠2  [Corresponding angles]

and m∠6 ≅ m∠7 [Vertically opposite angles]

Therefore, m∠2 ≅ m∠6 ≅ m∠7 ≅ 37°

c). ∠4 ≅ ∠8 [Corresponding angles]

d). ∠3 + ∠5 ≅ 180° [Interior angles of parallel lines m, l and a transverse].

The next number in the pattern -0.8, -3.2, -12.8, -51.2 is -204.8.

A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in the other expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.

Given:

The numbers are -0.8, -3.2, -12.8, -51.2.

To find the pattern:

Divide the number to find the proportionate rate,

-3.2/-0.8 = 4

-12.8/-3.2 = 4

-51.2 /-3.2 = 4

So, the proportionality relationship is,

number = 4 x previous number.

So, the next number,

-51.2 x 4

= -204.8

Therefore, the number is -204.8.

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Answer:

B. 150 children

Step-by-step explanation:

Let, number of children  = x and number of adults = y.

Since, total number of people attended the fair are 350.

So, x + y = 350.

Moreover, charges per child is $2 and adult is $3.

As, total sales are given to be $900.

So, 2x + 3y = 900

Thus, we get the system of equations,

2x + 3y = 900

x + y = 350

We will now solve the equations,

x + y = 350 ⇒ y = 350 - x

So, 2x + 3y = 900 ⇒ 2x + 3(350 -x) = 900 ⇒ 2x + 1050 - 3x = 900 ⇒ -x = -150 ⇒ x = 150.

Then, y = 350 - x ⇒ y = 350 - 150 ⇒ y = 200.

Hence, number of children and adults that attended the fair are 150 and 200 respectively.

To cook a 12 3/4 pounds ham which requires 2/5 of an hour for each pound, it will take approximately 5.1 hours. If dinner is at 4:45 pm, you should start cooking around 11:39 am.

The subject of your question is Mathematics. To solve this problem, let's understand first that the cooking time for a ham is 2/5 of an hour for each pound. This means that for each pound of ham, it should be cooked for 2/5 hour.

A.) To find how long you should cook a ham that weighs 12 3/4 pounds, you need to multiply that weight by 2/5. (12 3/4) * (2/5) ≈ 5.1 hours. So, you would need to cook the ham for approximately 5.1 hours.

B.) If dinner time is at 4:45 pm, and you know that the ham takes about 5.1 hours to cook, simply subtract 5.1 hours from the dinner time to find out when you should start cooking. 4:45pm - 5.1 hours ≈ 11:39am. Hence, you should begin cooking at around 11:39am to have the ham ready by 4:45pm.

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The value of k in the expression is 12.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

To simplify the given expression, we first need to expand the second term using the distributive property:

(x + 8)(x - 4) = x² - 4x + 8x - 32 = x² + 4x - 32

Now we can substitute this expression into the original expression:

x² + 16x + 64 - (x² + 4x - 32)

Simplifying further, we can combine like terms:

12x + 96

Now we can see that the expression can be rewritten as:

12(x + 8)

So the value of k is 12.

Thus,

The value of k is 12.

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To find the relative frequency of applicants whose score X is less than 500 on the quantitative GRE, calculate the Z-score for 500 and find the corresponding area under the standard normal curve.

To find the relative frequency of applicants whose score X is less than 500, we need to calculate the Z-score for 500. The formula for calculating the Z-score is: Z = (X - mean) / standard deviation. Plugging in the values, we get Z = (500 - 544) / 103 = -0.427.

Next, we need to find the corresponding area under the standard normal curve for the Z-score of -0.427. Using a calculator or a standard normal table, we find that the area to the left of -0.427 is approximately 0.3356.

Therefore, the relative frequency of applicants whose score is less than 500 is 0.3356, or 33.56%.

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Answer:

[tex]7\cdot g-3 = 42[/tex]

Step-by-step explanation:

As the first three guest are three and each aditional guest costs $ 7 dollars. The formula is presented as follows:

[tex]7\cdot (g-3) = 42[/tex]

Or:

[tex]7\cdot g = 63[/tex]

Or:

[tex]g = 9[/tex]

The wrong equation is:

[tex]7\cdot g-3 = 42[/tex]

The x and y intercept of the given line is required,

The x intercept is [tex](6.2,0)[/tex]

The y intercept is [tex](0,3.1)[/tex]

The given line is [tex]2x+4y=12.4[/tex]

x intercept [tex]y=0[/tex]

[tex]2x+4\times 0=12.4\\\Rightarrow x=\dfrac{12.4}{2}\\\Rightarrow x=6.2[/tex]

The x intercept is [tex](6.2,0)[/tex]

y intercept [tex]x=0[/tex]

[tex]2\times 0+4y=12.4\\\Rightarrow y=\dfrac{12.4}{4}\\\Rightarrow y=3.1[/tex]

The y intercept is [tex](0,3.1)[/tex]

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Answer:  The required area of the room that is NOT covered by the carpet is 192 ft².

Step-by-step explanation:  Given that the Smith wants to buy a 9 ft. by 12 ft. carpet and center it in a 15 ft. by 20 ft. room.

We are to find the area of the room that is NOT covered by the carpet.

We know that the area of a rectangle is given by the product of its length and breadth.

So, the area of the carpet bought by Smith is

[tex]A_c=9\times12=108~\textup{ft}^2,[/tex]

and the are of the room is

[tex]A_r=15\times 20=300~\textup{ft}^2.[/tex]

Therefore, area of the room that is NOT covered by the carpet will be

[tex]A=A_r-A_c=300-108=192~\textup{ft}^2.[/tex]

Thus, the required area of the room that is NOT covered by the carpet is 192 ft².