Given the functions f(x) = 6x + 11 and g(x) = x^2 + 6, which of the following functions represents f[g(x)] correctly?

Answer:

4

Step-by-step explanation:

Answer:

The value of b is 19.

Step-by-step explanation:

With what the problem states, we have that:

[tex]\frac{4b + 19}{6b + 11} = 0.76[/tex]

Doing cross multiplication

[tex]4b + 19 = 0.76(6b + 11)[/tex]

[tex]4b + 19 = 4.56b + 8.36[/tex]

[tex]4.56b - 4n = 19 - 8.36[/tex]

[tex]0.56b = 10.64[/tex]

[tex]b = \frac{10.64}{0.56}[/tex]

[tex]b = 19[/tex]

The value of b is 19.

Answer:

4x+1

Step-by-step explanation:

f(x)=x-4 and g(x)=3x+5,

(f+g) (x) = x-4 +3x+5

Combine like terms

           = 4x+1

Answer:

Step-by-step explanation:

The height is 6 units.

The radius is 8 units.

The volume is 128 π cubic units.

Answer:

B the mean increases by 6.8

Answer:

The sales level that has only a 3% chance of being exceeded next year is $3.67 million.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

In millions of dollars,

[tex]\mu = 3.2, \sigma = 0.25[/tex]

Determine the sales level that has only a 3% chance of being exceeded next year.

This is the 100 - 3 = 97th percentile, which is X when Z has a pvalue of 0.97. So X when Z = 1.88.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.88 = \frac{X - 3.2}{0.25}[/tex]

[tex]X - 3.2 = 0.25*1.88[/tex]

[tex]X = 3.67[/tex]

The sales level that has only a 3% chance of being exceeded next year is $3.67 million.

Answer: $3,670,198

Step-by-step explanation:

Here, the mean, μ, is 3.2 million =3,200,000 and the standard deviation, σ, is 250,000. Let x be sales for next year. To determine the sales level that has only a 3% chance of being exceeded next year, the area to the right of x is 0.03. So the area to the left of x is 1−0.03=0.97.

Open Excel. Click on an empty cell. Type =NORM.INV(0.97,3200000,250000) and press ENTER.

Round the answer to the nearest dollar, is x≈3,670,198. Thus, the sales level that has only a 3% chance of being exceeded next year is $3,670,198.

Answer:

23 sides

Step-by-step explanation:

The sum S of the interior angles of an n sided polygon is given as

S = (n - 2)180°

Where S is the sum of the interior angles and n is the number of sides.

Given that the sum of the interior angles is 3780° then

3780° = (n - 2)180

Divide both sides of the equation by 180

21 = n - 2

n = 21 + 2

= 23

The polygon has 23 sides

Answer:

Step-by-step explana[tex]f(x) = (x^{2} - 6x + 36) . (x^{2} + 2x + 4)\\f (x) = (x^{4} + 2x^{3} + 4x^{2} - 6x^{3} - 12x^{2} - 24x + 36x^{2} + 72x + 144)\\f(x) = (x^{4} - 4x^{3} + 28x^{2} + 48x + 144)[/tex]

x=6 and x=-2 are the roots of the equation f(x)= (x - 6)²(x + 2)².

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

We need to find the roots of f(x) = (x - 6)²(x + 2)²

f(x)= (x - 6)²(x + 2)²

f of x equal to x minus six whole power six into x plus two whole square

=(x²+36-12x)(x²+4+4x)

Apply distributive law.

=x⁴+4x²+4x³+36x²+144+144x-12x³-48x-48x²

=x⁴-8x³-8x²+96x+144

Hence, x=6 and x=-2 are the roots of the equation f(x)= (x - 6)²(x + 2)².

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Answer:

1. We can't see any boat on the river at this scale.

2. 0.025 inches. We won't be able to see it

Step-by-step explanation:

the beginning of the question states that; according to this map, the driving distance is 3 miles, we're most interested in the graphics at the bottom left, which indicates that 1 inches on the map corresponds to 2,000 ft in real life.

If 1 inches = 2000 ft,

x inches = 50 ft

we cross multiply to give

2000x ft = 50 ft-inches

x = 50/2000 = 0.025 inches

Answer: they deleted my answer but here is how to do it If that helps some

Step-by-step explanation:

way to solve a linear system algebraically is to use the substitution method. The substitution method functions by substituting the one y-value with the other. We're going to explain this by using an example.

y=2x+4

3x+y=9

We can substitute y in the second equation with the first equation since y = y.

3x+y=9

3x+(2x+4)=9

5x+4=9

5x=5

x=1

This value of x can then be used to find y by substituting 1 with x e.g. in the first equation

y=2x+4

y=2⋅1+4

y=6

The solution of the linear system is (1, 6).

You can use the substitution method even if both equations of the linear system are in standard form. Just begin by solving one of the equations for one of its variables.

Answer:

There is enough evidence to support the claim that  the proportion of women working the graveyard shift is less than the proportion of men working the graveyard shift (z=-2.44).

Critical value (α=0.01) zc=-2.33.

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the proportion of women (subindex 1) working the graveyard shift is less than the proportion of men (subindex 2) working the graveyard shift.  

Then, the null and alternative hypothesis are:

[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0[/tex]

The significance level is 0.05.

The sample 1, of size n1=343 has a proportion of p1=0.0437.

[tex]p_1=X_1/n_1=15/343=0.0437[/tex]

The sample 2, of size n2=294 has a proportion of p2=0.0918.

[tex]p_2=X_2/n_2=27/294=0.0918[/tex]

The difference between proportions is (p1-p2)=-0.0481.

[tex]p_d=p_1-p_2=0.0437-0.0918=-0.0481[/tex]

The pooled proportion, needed to calculate the standard error, is:

[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{15+27}{343+294}=\dfrac{42}{637}=0.0659[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.0659*0.9341}{343}+\dfrac{0.0659*0.9341}{294}}\\\\\\s_{p1-p2}=\sqrt{0.0002+0.0002}=\sqrt{0.0004}=0.0197[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.0481-0}{0.0197}=\dfrac{-0.0481}{0.0197}=-2.44[/tex]

For a significance level of 0.01 and a left-tailed test, the critical value of z is zc=-2.326.

If the test statistic is smaller than the critical value, the null hypothesis is rejected.

The test statistic z=-2.44 is smaller than the critical value zc=-2.326, so the null hypothesis is rejected.

There is enough evidence to support the claim that  the proportion of women working the graveyard shift is less than the proportion of men working the graveyard shift.

Answer:

The fourth term of the expansion is -220 * x^9 * y^3

Step-by-step explanation:

Question:

Find the fourth term in (x-y)^12

Solution:

Notation: "n choose k", or combination of k objects from n objects,

C(n,k) = n! / ( k! (n-k)! )

For example, C(12,4) = 12! / (4! 8!) = 495

Using the binomial expansion formula

(a+b)^n

= C(n,0)a^n + C(n,1)a^(n-1)b + C(n,2)a^(n-2)b^2 + C(n,3)a^(n-3)b^3 + C(n,4)a^(n-4)b^4 +....+C(n,n)b^n

For (x-y)^12, n=12, k=3, a=x, b=-y, and the fourth term is

C(n,3)a^(n-3)b^3

=C(12,3) * x^(12-3) * (-y)^(3)

= 220*x^9*(-y)^3

= -220 * x^9 * y^3

The fourth term in the binomial expansion of ( x - y )¹² is given by the equation A₄ = -220 x⁹y³

The general term of the binomial expansion is Tr+1 = nCr x^n-r y^r . Here the coefficient values are found from the pascals triangle or using the combinations formula, and the sum of the exponents of both the terms in the general term is equal to n.

( x + y )ⁿ = ⁿCₐ ( x )ⁿ⁻ᵃ ( y )ᵃ

Given data ,

Let the binomial expansion be represented as A

Now , the value of A is

A = ( x - y )¹²   be equation (1)

On simplifying the equation , we get

The fourth term of the binomial expansion is calculated by

A₄ = ⁿC₃ a⁽ⁿ⁻³⁾ b³

Substituting the values in the equation , we get

A₄ = ¹²C₃ x⁽¹²⁻³⁾ ( -y )³

On further simplification , we get

A₄ = ( 12 )! / ( 9 )! 3! x⁹ ( -y )³

A₄ = 12 x 11 x 10 / 2 x 3 x⁹ ( -y) ³

A₄ =  -220 x⁹y³

Hence , the fourth term of binomial expansion is  -220 x⁹y³

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Answer:

[tex]3\sqrt{5}[/tex]

Step-by-step explanation:

Use the distance formula:

[tex]\sqrt{(8-5)^2+(-4-2)^2}=\sqrt{9+36}=3\sqrt{5}[/tex]

Answer: [tex]\sqrt{45} =3\sqrt{5}[/tex]

Step-by-step explanation:

To find the distance between 2 points use this formula:

[tex]\sqrt{(x1-x2) ^{2} +(y1-y2)^{2} }[/tex]

rad[(2+4)^2+(5-8)^2)]

=rad[36+9]

=rad45

=3rad5

Answer:

No, it is not less expensive to keep the old car as the price calculation is higher then the New Car

Purchasing new car is less expensive

Step-by-step explanation:

NEW CAR EXPENSES= $21,240

OLD CAR EXPENSES= $25,800

NB: Kindly check attached picture for calculations

Answer:

its D on ed

Step-by-step explanation:

3 sqrt x^9 * x

The expression is [tex]x^{10/3}[/tex]

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

∛[tex]x^{10}[/tex]

This can be written as,

= [tex]x^{10/3}[/tex]

Thus,

The expression is [tex]x^{10/3}[/tex]

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Answer:

x-intercept: 4    y-intercept: - 6

Step-by-step explanation:

To find the y-intercept, we must first solve for y.

Isolate variable y on the left side of the equation by subtracting 3x from both sides.

- 2y = - 3x + 12

Now divide both sides by - 2 to find y.

y = 3/2x - 6

The y-intercept is - 6.   (remember formula y = mx + b, where b is the y-intercept)

To find the x-intercept, we must solve for x.

Isolate variable x on the left side of the equation by adding 2y to both sides.

3x = 2y + 12

Now divide both sides by 3 to find x.

x = 2/3y + 4

The x-intercept is 4.    (remember formula x = my + b, where b is the x-intercept)

Answer:

4 and - 6

Step-by-step explanation:

3x-2y=12

Answer:

the answer is 26

Step-by-step explanation:

The ratio of students who cheer to those who participate in a sport is 13/82.

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Total students participated in sports

= 35 + 27 + 43 + 33 + 26

= 164

and, students who cheered = 26

So, the ratio of students who cheer to those who participate in a sport

= 26 / 164

= 13 / 82

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Answer:

1: 2.5, 2: 5.0 , 3:7.5 , 4:10 , 5: 12.5

Step-by-step explanation:

asumming it is proportional, you divide 7.5 by 3 which will give you the cost per pound which is $2.5, then you multiply this number by the amount of pounds you want

Answer:

1: 2.5 , 2: 5.0 , 3:7.5 , 4:10 , 5: 12.5

Step-by-step explanation:

Answer:

• The base is 8 and the height is 6

Step-by-step explanation:

A rectangle has two dimensions:

The base, which is the distance between the points who have the same value of y.

The height, which is the distance between the points who have the same value of x.

Distance between 2 points:

Points (a,b) and (c,d).

[tex]D = \sqrt{(c-a)^{2} + (d-b)^{2}}[/tex]

I suppose there was a small typing mistake, as these points do not make a rectangle.

I will say that we have these following points:

L(0,6), M(8,6), N(8,0), O(0,0).

Base:

Same value of y.

L(0,6), M(8,6), or N(8,0) and O(0,0).

They will have the same result, will use the second.

[tex]D = \sqrt{(8-0)^{2} + (0-0)^{2}} = \sqrt{64} = 8[/tex]

The base is 8.

Height:

Same value of x.

L(0,6), O(0,0) or M(8,6) and N(8,0).

[tex]D = \sqrt{(8-8)^{2} + (6-0)^{2}} = \sqrt{36} = 6[/tex]

The height is 6.

So the correct answer is:

• The base is 8 and the height is 6

The median is the middle number in the data set when

the data set is written from least to greatest.

So let's write our data set from least to greatest.

4, 9, 15, 16, 18, 21, 25, 27, 30, 31, 33

Now, we identify the middle number.

4, 9, 15, 16, 18, 21, 25, 27, 30, 31, 33

Notice that 21 appears in the middle.

So the median of the data set is 21.

Answer:

Median: 21

Step-by-step explanation:

arrange all the numbers from least to greatest:

4, 9, 15, 16, 18, 21, 25, 27, 30, 31, 33

median = is the middle number in the data set/listed numbers.

Since there are eleven numbers in the set of data, we divide it equally, to find the median.

{4, 9, 15, 16, 18} 21 {25, 27, 30, 31, 33}

Answer:

[tex]\dfrac{dA}{dt}+ \dfrac{A}{100}=0[/tex]

A(0) = 70  (i.e the pounds of salt dissolved into the tank)

Step-by-step explanation:

Given that:

a large mixing tank initially holds 400 gallons of water  in which 70 pounds of salt have been dissolved.

The rate at which pure water is pumped into the tank is 4 gal/min

After stirring; the pure water is then pumped out at the same rate.

The objective is to determine the differential equation  for the amount of salt A(t) in the tank at time t > 0. What is A(0)

Taking the differential of:

[tex]\dfrac{dA}{dt}=R_{in}-R_{out}[/tex]     ---- (1)

where ;

[tex]R_{in[/tex] = 0

[tex]R_{out} =\dfrac{A(t)}{400}*4[/tex]

[tex]R_{out} =\dfrac{A}{100}[/tex]

replacing them into (1) ; we have:

[tex]\dfrac{dA}{dt}=0 - \dfrac{A}{100}[/tex]

[tex]\dfrac{dA}{dt}=- \dfrac{A}{100}[/tex]

[tex]\dfrac{dA}{dt}+ \dfrac{A}{100}=0[/tex]

A(0) = 70 (i.e the pounds of salt dissolved into the tank)

The differential equation for the amount of salt A(t) in the tank at time t > 0 is [tex]\frac{dA}{dt} + \frac{A}{100} = 0[/tex]

A (0)= 70

Given that,

[tex]dA\div dt=R_{in}-R_{out}[/tex]

Rin=0

[tex]R_{out}=A(t)\div 400 \times (4)\\\\ =A\div 100[/tex]

so,

[tex]dA\div dt=R_{in}-R_{out}\\\\dA\div dt=0- A\div 100[/tex]

So,

[tex]dA\div dt +A\div 100=0[/tex]

A(0)=70

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Answer:

Step-by-step explanation:

Volume of a rectangular prism=length x width x height

450=43*12*x

x=0.87209cm

Answer:

[900, 1300]

Step-by-step explanation:

According to the empirical rule, 95% is within ±2 standard deviations.

1100 − 2(100) = 900

1100 + 2(100) = 1300

Answer:

Step-by-step explanation:

The question is incomplete. The complete question is

Coaching companies claim that their courses can raise the SAT scores of high school students. But students who retake the SAT without paying for coaching also usually raise their scores. A random sample of students who took the SAT twice found 427 who were coached and 2733 who were uncoached. Starting with their verbal scores on the first and second tries, we have these summary statistics:

Try 1 Try 2 Gain

n x s x s x s

Coached 427 500 92 529 97 29 59

Uncoached 2733 506 101 527 101 21 52

Use Table C to estimate a 90% confidence interval for the mean gain of all students who are coached.

at 90% confidence.

Now test the hypothesis that the score gain for coached students is greater than the score gain for uncoached students. Let μ1 be the score gain for all coached students. Let μ2 be the score gain for uncoached students.

(a) Give the alternative hypothesis:

μ1 - μ2.

(b) Give the t test statistic:

(c) Give the appropriate critical value for \alpha =5%:

Solution:

The formula for determining the confidence interval for the difference of two population means is expressed as

Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)

Where

x1 = sample mean score gain for all coached students

x2 = sample mean score gain for all uncoached students

s1 = sample standard deviation score gain of coached students

s2 = sample standard deviation score gain of uncoached students

For a 90% confidence interval, the z score is 1.645

From the information given,

x1 = 29

s1 = 59

n1 = 427

x2 = 21

s2 = 52

n2 = 2733

x1 - x2 = 29 - 21 = 8

z√(s1²/n1 + s2²/n2) = 1.645√(59²/427 + 52²/2733) = 4.97

90% Confidence interval = 8 ± 4.97

a) The population standard deviations are not known. it is a two-tailed test. The random variable is μ1 - μ2 = difference in the score gain for coached and uncoached students.

We would set up the hypothesis.

The null hypothesis is

H0 : μ1 = μ2 H0 : μ1 - μ2 = 0

The alternative hypothesis is

H1 : μ1 > μ2 H1 : μ1 - μ2 > 0

This is a right tailed test.

b) Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(x1 - x2)/√(s1²/n1 + s2²/n2)

t = (29 - 21)/√(59²/427 + 52²/2733)

t = 2.65

The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [59²/427 + 52²/2733]²/[(1/427 - 1)(59²/427)² + (1/2733 - 1)(52²/2733)²] = 9.14/0.1564

df = 58

c) from the t distribution table, the critical value is 1.67

In order to reject the null hypothesis, the test statistic must be smaller than - 1.67 or greater than 1.67

Since - 2.65 < - 1.67 and 2.65 < 1.67, we would reject the null hypothesis.

Therefore, at 5% significance level, we can conclude that the score gain for coached students is greater than the score gain for uncoached students.

Here is the complete question.

A one-tailed hypothesis test with the t statistic Antisocial personality disorder (ASPD) is characterized by deceitfulness, reckless disregard for the well-being of others, a diminished capacity for remorse, superficial charm, thrill seeking, and poor behavioral control. ASPD is not normally diagnosed in children or adolescents, but antisocial tendencies can sometimes be recognized in childhood or early adolescence. James Blair and his colleagues have studied the ability of children with antisocial tendencies to recognize facial expressions that depict sadness, happiness, anger, disgust, fear, and surprise. They have found that children with antisocial tendencies have selective impairments, with significantly more difficulty recognizing fearful and sad expressions. Suppose you have a sample of 40 16-year-old children with antisocial tendencies and you are particularly interested in the emotion of fear. The average 16-year-old has a score on the emotion recognition scale of 11.80. (The higher the score on this scale, the more strongly an emotion has to be displayed to be correctly identified. Therefore, higher scores indicate greater difficulty recognizing the emotion). Assume that scores on the emotion recognition scale are normally distributed. You believe that children with antisocial tendencies will have a harder time recognizing the emotion of fear in other words, they will have higher scores on the emotion recognition test).

What is your null hypothesis stated using symbols?

What is your alternative hypothesis stated using symbols?

This is a               tailed test. Given what you know, you will evaluate this hypothesis using a               statistic.

Answer:

Step-by-step explanation:

Given that :

the population mean = 11.80

Thus;

The null hypothesis stated using symbols is :

[tex]\mathbf{H_o = \mu = 11.80}[/tex]

The alternative hypothesis stated using symbols is:

[tex]\mathbf{H_i = \mu > 11.80}[/tex]

However, Since the alternative hypothesis looks somewhat greater than the null hypothesis, then the test is based one right - tailed test

Thus;

This is a     one   tailed test and the hypothesis uses a    t   statistic

Answer:

y=2/5 - 1/5

explanation:

Answer:

Dr. Kora will pay an interest of $6,000

Step-by-step explanation:

Simple interest = P × R × T

Where:

P = Principal = $8000

R = Rate = 7.5% = 0.075

T = Time = 10 years

∴ Simple interest = 8000 × 0.075 × 10 = $6,000

Therefore Dr. Kora will pay an interest of $6,000

Answer:

1) This is because some has their own shape and the commonly used loop is the clothoid loop, e.t.c.

2) This is because researchers found out that it helps ease the passage of the kidney stones.

Step-by-step explanation:

Hope it helps

Thanks.

Answer:

1) Roller coaster loops are never circular...why do you think that is?:

This force is called the Centripetal Force.

Newton's first Law of Motion of motion tells us that, without this force, the coaster would like to travel in a straight line and at constant speed. The centripetal force is pushing the coaster around in a circle. It is your body's (equal and opposite) reaction to this force, often referred to as the Centrifugal Force, that explains the feeling you get .There is a force (provided by the rails), that is pushing the trucks of the coaster towards the centre of the loop. t of being squashed into your seat (Newton's third Law of Motion)

2. Riding Big Thunder Mountain Railroad at Disney World could help dislodge kidney stones....why do you think that is?:

Riding the Big Thunder Mountain Railroad roller coaster at Disney World could help ease the passage of small kidney stones.  Kidney stones are hard masses of minerals that form in the kidneys. They can range in size, from a tiny grain of sand to, in extreme cases, the size of a golf ball. Patients with kidney stones don't always need treatment, because the stones can pass out of the body on their own, but the process of passing them can be quite painful. Riding the Big Thunder Mountain Railroad roller coaster at Disney World could help ease the passage of small kidney stones, according to the new study because of 'The intense ride helps get rid of them'.

Answer: use google calculator It’s reliable

Step-by-step explanation:

Answer: a=1, b=2, c=below x

Step-by-step explanation:

Answer:

[tex] ME = 1.64 \sqrt{\frac{0.32 (1-0.32)}{150}}= 0.0625[/tex]

Step-by-step explanation:

For this case we have the following info given:

[tex] n = 150[/tex] represent the sampel size selected

[tex] X = 48[/tex] represent the number of households who relied strictly on cell phones for their service

The estimated proportion of households who relied strictly on cell phones for their service is given by:

[tex] \hat p =\frac{X}{n}= \frac{48}{150}= 0.32[/tex]

And the margin of error would be given by:

[tex] ME = z_{\alpha/2} \sqrt{\hat p(1-\hat p)}{n}[/tex]

The confidence is 90% so then the significance is [tex]\alpha=1-0.9=0.1[/tex] and [tex] \alpha/2 =0.05[/tex] the critical value for this case from the normal standard distribution is:

[tex] z_{\alpha/2}= 1.64[/tex]

And the margin of error would be:

[tex] ME = 1.64 \sqrt{\frac{0.32 (1-0.32)}{150}}= 0.0625[/tex]