Factor the expression. 6x^2 + 31x + 28

A.) (x + 4)(6x + 7)
B.) (x + 2)(6x + 14)
C.) (3x + 7)(3x + 4)
D.) (x + 14)(6x + 2)

The domain of all three functions is all real numbers. The range of f(x) and h(x) is all real numbers, but the range of g(x) is all real numbers except 0.

The statements that accurately compare the domain and range of the functions are:

For the functions f(x) = 3x^2, g(x) = 1/3x, and h(x) = 3x:

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Answer:c and d

Step-by-step explanation:

i got it right

The p-value is 0.0768. Since the p-value is less than the significance level of 0.05, we reject the null hypothesis.

- Decision regarding H0: Reject H0

- p-value: 0.0768.

The null hypothesis (H0) states that the mean waiting time is 3 minutes or more, while the alternate hypothesis (H1) states that the mean waiting time is less than 3 minutes.

- Null hypothesis (H0): μ ≥ 3

- Alternate hypothesis (H1): μ < 3

The decision rule is to reject H0 if the test statistic (z-score) is less than -1.645.

To compute the test statistic (z-score), we use the formula:

[tex]\[ z = \frac{{\bar{x} - \mu}}{{\frac{\sigma}{\sqrt{n}}}} \][/tex]

Where:

- [tex]\(\bar{x}\)[/tex] is the sample mean waiting time (2.75 minutes)

- [tex]\(\mu\)[/tex] is the population mean waiting time (3 minutes)

- [tex]\(\sigma\)[/tex] is the population standard deviation (1 minute)

- [tex]\(n\)[/tex] is the sample size (50)

Substituting the given values:

[tex]\[ z = \frac{{2.75 - 3}}{{\frac{1}{\sqrt{50}}}} \][/tex]

[tex]\[ z = \frac{{-0.25}}{{0.1414}} \][/tex]

[tex]\[ z ≈ -1.768 \][/tex]

Since -1.768 is less than -1.645, we reject the null hypothesis.

To find the p-value, we look up the z-score (-1.768) in the standard normal distribution table. The corresponding area to the left of -1.768 is approximately 0.0384. Since this is a one-tailed test, we multiply by 2 to get the total probability of both tails:

[tex]\[ p-value ≈ 2 \times 0.0384 = 0.0768 \][/tex]

Thus, the p-value is 0.0768. Since the p-value is less than the significance level of 0.05, we reject the null hypothesis.

Complete questions:

The waiting time for customers at MacBurger Restaurants follows a normal distribution with a population standard deviation of 1 minute. At the Warren Road MacBurger, the quality-assurance department sampled 50 customers and found that the mean waiting time was 2.75 minutes. At the 0.05 significance level, can we conclude that the mean waiting time is less than 3 minutes? State the null hypothesis and the alternate hypothesis. State whether the decision rule is true or false: Reject H0 if z < −1.645. True False Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) What is your decision regarding H0? Reject H0 Do not reject H0 What is the p-value? (Round your answer to 4 decimal places.)

Answer:

y = 2x+3

Step-by-step explanation:

The slope is "what happens to the graph when you move one unit to the right in x-direction". As you can check, if you move 1 to the right, the y value increases by 2. Therefore the slope is 2.

The intercept is the graph's y value when x=0, ie., when it passes the y axis. This is at y=3.

Now we have our two ingredients, so y = slope * x + intercept, so 2x+3

Answer:

x = 52/9

Step-by-step explanation:

The exterior angle is half the difference of the intercepted arcs, so we have ...

9x -5 = (158 -64)/2

9x = 52 . . . . . . . . . . . add 5

x = 52/9 = 5 7/9

Answer:

B) 34.1 cm

Step-by-step explanation:

The longer diagonal is longer than either side, but shorter than their sum. The only answer choice in the range of 24–39 cm is choice B.

_____

You are given sufficient information to use the Law of Cosines to find the diagonal length. If we call it "c", then the angle opposite that diagonal is the larger of the angles in the parallelogram: 120°. The law of cosines tells you ...

c^2 = a^2 +b^2 -2ab·cos(C)

Here, we have a=24, b=15, C=120°, so ...

c^2 = 24^2 +15^2 -2·24·15·cos(120°) = 576 +225 +360 = 1161

c = √1161 ≈ 34.073 . . . . cm

Rounded to tenths, the diagonal length is 34.1 cm.

Answer:

No. Anna is incorrect.

Step-by-step explanation:

In order to find if the answer is right, just find the diagonals using the pythogorean theorem.

a² + b² = c²

For the rectangle, the base is 14 and the height is 7. We will have to find the hypotenuse.

14² + 7² = c²

196 + 49 = c²

245 = c²

c = √245

c = √49 × √5

c = 7√5

For the square, the base is 7 and the height is 7. We will have to find the hypotenuse.

7² + 7² = c²

49 + 49 = c²

98 = c²

c = √98

c = √49 × √2

c = 7√2

Now compare :

7√5 and 7√2

Clearly, 7√5 is not the double of 7√2

Answer: Third Option

[tex]f(x) +3[/tex]

Step-by-step explanation:

The function [tex]y=log_2(x)[/tex] passes through point (2, 1) because the exponential function [tex]2 ^ x = 2[/tex] when [tex]x = 1[/tex].

Then, if the transformed function passes through point (2, 4) then this means that the graph of [tex]y=log_2(x)[/tex] was moved vertically 3 units up.

The transformation that vertically displaces the graph of a function k units upwards is:

[tex]y = f (x) + k[/tex]

Where k is a positive number. In this case [tex]k = 3[/tex]

Then the transformation is:

[tex]f(x) +3[/tex]

and the transformed function is:

[tex]y = log_2 (x) +3[/tex]

Find the points of Midtown and Downtown then use the midpoint formula.

Midtown = (6,12)

Downtown = (12,4)

Midpoint = X2+X1 /2 , Y2+Y1 /2

Midpoint = 12+6 /2 , 4+12 /2

Midpoint = 18/2 , 16,2

Midpoint = (9,8)

Answer:

68

Step-by-step explanation:

∠DPG and ∠EPF are vertical angles, so they are equal.

7x = 4x + 48

3x = 48

x = 16

So ∠DPG is:

∠DPG = 7x

∠DPG = 112

∠DPE and ∠DPG are supplementary, so they add up to 180:

∠DPE + ∠DPG = 180

∠DPE + 112 = 180

∠DPE = 68

Answer:

Last option

−1 • f(x)

Step-by-step explanation:

The function [tex]f(x) = (0.5) ^ x[/tex] passes through point (-1, 2) because:

[tex]f(-1) = (0.5) ^ {-1}= \frac{1}{(0.5)} = 2[/tex]

and also goes through the point (0, 1)

Because:

[tex]f(0) = (0.5)^0 = 1[/tex]

Then, if the transformed function passes through the point (0, -1) and passes through the point (-1, -2) then this means that the graph of [tex]f(x) = (0.5) ^ x[/tex] reflected on the axis x. This means that if the point [tex](x_0, y_0)[/tex] belongs to f(x), then the point [tex](x_0, -y_0)[/tex] belongs to the transformed function

The transformation that reflects the graph of a function on the x-axis is.

[tex]y = cf(x)[/tex]

Where c is a negative number. In this case [tex]c = -1[/tex]

Then the transformation is:

[tex]y = -1*f(x)[/tex]

and the transformed function is:

[tex]f (x) = - (0.5) ^ x[/tex]

Answer:

f(x) -2 is the correct answer.

Step-by-step explanation:

Just took the test!

The area of shaded regions can be found using geometric principles or methods of integration depending on the actual shape and context. In most cases, area is proportional to the square of the distances. Integration techniques would be used if the shaded region is under a curve on a graph.

To find the area of the shaded regions, depending upon the shape and complexity of the region, you'd typically use geometric principles and calculations, potentially including those related to rectangles, triangles, circles, and/or other shapes. In some cases, these calculations might include figuring out the area of a larger shape and then subtracting the area of a smaller, non-shaded shape. For example, the area of a disc could be found by using the equation А = лr², and placing limits of integration from r = 0 to r = R in case the shaded area is comprised of thin rings of different radii. In other cases, you might be using principles of integration if the shaded region is under a curve on a graph, integrating the function f(x) from a certain lower limit x₁ to upper limit x₂. Also, keep in mind that the area is usually proportional to the square of the distances in a certain set-up.

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Answer:

Step-by-step explanation:

So we need to balance two things here.  The overall volume, and the amount of hydrochloric acid.

Let's say x is the volume of the 12% solution and y is the volume of the 6% solution.

The sum of the volumes equals the total volume:

x + y = 24

And the sum of the amounts is the total amount:

0.12 x + 0.06 y = 0.09 (24)

We now have two equations and two variables.  We can solve this system of equations with either substitution or elimination.  Using substitution:

x = 24 - y

0.12 (24 - y) + 0.06 y = 0.09 (24)

2.88 - 0.12 y + 0.06 y = 2.16

0.72 = 0.06 y

y = 12

x = 24 - 12 = 12

So she needs to mix 12 ounces of 12% solution with 12 ounces of 6% solution to get 24 ounces of 9% solution.

The amount of 12% solution and the amount of 6% solution Doreen Schmidt should mix to obtain 9% hydrochloric acid solution is 12 ounces each.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the amount of 12% solution needed to be mixed be represented by x, while the amount of 6% solution needed to be mixed be represented by y.

Now, since the total amount of solution needed to be made is 24 ounces, therefore, an equation can be formed as,

x+y=24

Solve the equation of x,

x=24 - y

Also, the total concentration of the combined should be 9%, therefore, we can write,

(12% of x) + (6% of y) = 9% of 24

0.12x + 0.06y = (0.09×24)

Substitute the value of x,

0.12(24-y) + 0.06y = 2.16

2.88 - 0.12y + 0.06y = 2.16

y = 12 ounces

substitute the value of y in the equation of x,

x = 24 - y

x = 24 - 12

x = 12

Hence, the amount of 12% solution and the amount of 6% solution Doreen Schmidt should mix to obtain 9% hydrochloric acid solution is 12 ounces each.

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Answer:

Sally; Sally

Step-by-step explanation:

For the free throws... let's see the stats:

Sally: 10 free throws

Jesse: 8 free throws.

Advantage?: Sally

For the three-points baskets:

Sally: 3

Jesse: 1

Advantage: Sally

Sally dominates in both categories, sorry Jesse.

Answer:

sally sally

Step-by-step explanation:

the numbers are just greater for both stats for her

Find the total of male students:

4 + 6 + 2 + 2 = 14 total males.

There are 2 male juniors.

The probability of a male being a junior is 2/14 = 1/7 = 0.143 = 14.3 = 14%

Find the total of male students:

4 + 6 + 2 + 2 = 14 total males.

There are 2 male juniors.

The probability of a male being a junior is 2/14 = 1/7 = 0.143 = 14.3 = 14%

Answer:

Option C and D are correct.

Step-by-step explanation:

Area of rectangle = 144 cm^2

Width of rectangle = 9 cm

Length of rectangle = ?

We know,

Area of rectangle = Length * Width

144 = Length * 9

144/9 = Length

=> length = 16 cm

Option A is incorrect as 3 times width = 3* 9 = 27 but our length = 16 cm

Option B is incorrect as length = 16 cm and not 63 cm

Option C is correct as Length < 2(Width)

=> 16 < 2(9) => 16 < 18 which is true.

Option D is correct.

Perimeter = 2(Length + Width)

Perimeter = 2(16+9)

Perimeter = 50 cm

Option E is incorrect as Length ≠ Width

Answer:

C. The length is less than 2 times the width.

D. The perimeter is 50 centimeters.

Step-by-step explanation:

The area of the rectangle is given as 144 square centimeters and its width is 9 centimeters. The formula for the area of a rectangle is given as;

Area = length*width

144 = length*9

length = 144/9

length = 16 centimeters

A. The length is 3 times the width.

3 times the width; 3*9 = 27 cm which is not equal to 16. Hence this statement is false.

B.The length is 63 centimeters.

This statement is also false since the length is 16 cm

C.The length is less than 2 times the width.

ANSWER

[tex]y = 2x -4[/tex]

EXPLANATION

Part a)

Eliminating the parameter:

The parametric equation is

[tex]x = 5 + ln(t) [/tex]

[tex]y = {t}^{2} + 5[/tex]

From the first equation we make t the subject to get;

[tex]x - 5 = ln(t) [/tex]

[tex]t = {e}^{x - 5} [/tex]

We put it into the second equation.

[tex]y = { ({e}^{x - 5}) }^{2} + 5[/tex]

[tex]y = { ({e}^{2(x - 5)}) } + 5[/tex]

We differentiate to get;

[tex] \frac{dy}{dx} = 2 {e}^{2(x - 5)} [/tex]

At x=5,

[tex] \frac{dy}{dx} = 2 {e}^{2(5 - 5)} [/tex]

[tex]\frac{dy}{dx} = 2 {e}^{0} = 2[/tex]

The slope of the tangent is 2.

The equation of the tangent through

(5,6) is given by

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y - 6 = 2(x - 5)[/tex]

[tex]y = 2x - 10 + 6[/tex]

[tex]y = 2x -4[/tex]

Without eliminating the parameter,

[tex] \frac{dy}{dx} = \frac{ \frac{dy}{dt} }{ \frac{dx}{dt} } [/tex]

[tex]\frac{dy}{dx} = \frac{ 2t}{ \frac{1}{t} } [/tex]

[tex]\frac{dy}{dx} = 2 {t}^{2} [/tex]

At x=5,

[tex]5 = 5 + ln(t) [/tex]

[tex] ln(t) = 0[/tex]

[tex]t = {e}^{0} = 1[/tex]

This implies that,

[tex]\frac{dy}{dx} = 2 {(1)}^{2} = 2[/tex]

The slope of the tangent is 2.

The equation of the tangent through

(5,6) is given by

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y - 6 = 2(x - 5) =[/tex]

[tex]y = 2x -4[/tex]

The equation of the tangent to the curve at the point (5,6) is [tex]\(y = 2x - 4\)[/tex].

To find the equation of the tangent to the curve given by the parametric equations [tex]\(x = 5 + \ln(t)\)[/tex] and [tex]\(y = t^2 + 5\)[/tex] at the point (5,6), we can approach this problem in two ways: by eliminating the parameter \(t\) and without eliminating the parameter.

Method 1: Eliminating the Parameter

Step 1: Express (t) in terms of (x)

[tex]\[ x = 5 + \ln(t) \implies \ln(t) = x - 5 \implies t = e^{x-5} \][/tex]

Step 2: Substitute (t) into (y)

[tex]\[ y = t^2 + 5 \implies y = (e^{x-5})^2 + 5 \implies y = e^{2(x-5)} + 5 \][/tex]

Step 3: Find [tex]\(\frac{dy}{dx}\)[/tex]

[tex]\[ y = e^{2(x-5)} + 5 \][/tex]

[tex]\[ \frac{dy}{dx} = 2e^{2(x-5)} \][/tex]

Step 4: Evaluate [tex]\(\frac{dy}{dx}\)[/tex] at (x = 5)

[tex]\[ \frac{dy}{dx}\bigg|_{x=5} = 2e^{2(5-5)} = 2e^0 = 2 \][/tex]

Step 5: Equation of the tangent line

The slope (m = 2). The tangent line at (5,6) is:

[tex]\[ y - 6 = 2(x - 5) \][/tex]

[tex]\[ y = 2x - 10 + 6 \][/tex]

[tex]\[ y = 2x - 4 \][/tex]

Method 2: Without Eliminating the Parameter

Step 1: Find [tex]\(\frac{dx}{dt}\)[/tex] and [tex]\(\frac{dy}{dt}\)[/tex]

[tex]\[ x = 5 + \ln(t) \implies \frac{dx}{dt} = \frac{1}{t} \][/tex]

[tex]\[ y = t^2 + 5 \implies \frac{dy}{dt} = 2t \][/tex]

Step 2: Find [tex]\(\frac{dy}{dx}\)[/tex]

[tex]\[ \frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}} = \frac{2t}{\frac{1}{t}} = 2t^2 \][/tex]

Step 3: Find (t) at the point (5,6)

From [tex]\(x = 5 + \ln(t)\)[/tex]:

[tex]\[ 5 = 5 + \ln(t) \implies \ln(t) = 0 \implies t = e^0 = 1 \][/tex]

Step 4: Evaluate [tex]\(\frac{dy}{dx}\)[/tex] at (t = 1)

[tex]\[ \frac{dy}{dx}\bigg|_{t=1} = 2(1)^2 = 2 \][/tex]

Step 5: Equation of the tangent line

The slope (m = 2). The tangent line at (5,6) is:

[tex]\[ y - 6 = 2(x - 5) \][/tex]

[tex]\[ y = 2x - 10 + 6 \][/tex]

[tex]\[ y = 2x - 4 \][/tex]

Thus, using both methods, the equation of the tangent to the curve at the point (5,6) is [tex]\(y = 2x - 4\)[/tex].

Answer:

c. {(4, -12)}

Step-by-step explanation:

It is convenient to rearrange the equation to standard form:

5x +y = 8

Then check the offered points.

(6, -11): 5·6 -11 = 19 ≠ 8

(4, -12): 5·4 -12 = 8 . . . . . . this is in the solution set

(5, -9): 5·5 -9 = 16 ≠ 8

(3, -14): 5·3 -14 = 1 ≠ 8

To find the solution set, substitute the x and y values into the equation and check if it is true.

To find the solution set for the equation, we need to check which coordinates from the replacement set satisfy the equation y = -5x + 8.

The solution set for the equation, given the replacement set, is {(3, -14)}.

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1 Simplify \frac{14}{30}

​30

​

​14

​​  to \frac{7}{15}

​15

​

​7

​​ .

\frac{7}{15}\div 14.00

​15

​

​7

​​ ÷14.00

2 Use this rule: a\div \frac{b}{c}=a\times \frac{c}{b}a÷

​c

​

​b

​​ =a×

​b

​

​c

​​ .

\frac{7}{15}\times \frac{1}{14.00}

​15

​

​7

​​ ×

​14.00

​

​1

​​  

3 Use this rule: \frac{a}{b}\times \frac{c}{d}=\frac{ac}{bd}

​b

​

​a

​​ ×

​d

​

​c

​​ =

​bd

​

​ac

​​ .

\frac{7\times 1}{15\times 14.00}

​15×14.00

​

​7×1

​​  

4 Simplify 7\times 17×1 to 77.

\frac{7}{15\times 14.00}

​15×14.00

​

​7

​​  

5 Simplify 15\times 14.0015×14.00 to 210210.

\frac{7}{210}

​210

​

​7

​​  

6 Simplify.

1/30

ANSWER

The volume of the dilated cone is

[tex]40 {m}^{3}[/tex]

EXPLANATION

The volume of the given cone is

[tex]5000 {m}^{3} [/tex]

When this cone is dilated with a scale factor of 1/5, the volume of the dilated cone becomes,

[tex] ({ \frac{1}{5} })^{3} \times 5000 {m}^{3} [/tex]

We simplify to obtain:

[tex] { \frac{1}{125} }\times 5000 {m}^{3} [/tex]

This gives us:

[tex]40 {m}^{3} [/tex]

Final answer:

When a cone is scaled down by a factor of 1/5, its new volume is 40 m³, calculated by cubing the scale factor and multiplying it by the original volume.

Explanation:

When a cone is dilated by a scale factor, its volume changes according to the cube of that scale factor.

Since the original volume of the cone is 5000 m³ and the scale factor is 1/5, we use the proportionality principle which states that the volume of a shape is proportional to the cube of its linear dimensions (V ∝ L3).

Therefore, if we dilate the cone by a scale factor of 1/5, the new volume (V1) would be:

V1 = V-original × (scale factor)³
= 5000 m³ × (1/5)³
= 5000 m³ × 1/125
= 40 m³

This calculation shows that, as a result of applying the scale factor, the volume of the cone has been reduced significantly.

Answer:

  3y - 5 + 2y = 7

Step-by-step explanation:

Subtracting 5 from the second equation gives ...

  x = 3y -5

Using the expression on the right for x in the first equation gives ...

  x + 2y = 7 . . . . . . . . first equation

  (3y -5) +2y = 7 . . . . with expression substituted for x

  3y - 5 + 2y = 7 . . . . with parentheses removed

Answer:

x = 0

Step-by-step explanation:

Since the product is not equal zero, we need to multiply both parenthesis first:

[tex](x-3)(x+9) =-27[/tex]

[tex]x*x+x*9+(-3)*x+(-3)*9=27[/tex]

[tex]x^2+9x-3x-27=27[/tex]

[tex]x^2+6x-27=27[/tex]

Add 27 from both sides:

[tex]x^2+6x-27+27=-27+27[/tex]

[tex]x^2-6x=0[/tex]

Factor [tex]x[/tex] out:

[tex]x(x+6)=0[/tex]

Apply the zero product:

[tex]x=0,x+6=0[/tex]

[tex]x=0,x=-6[/tex]

The solutions of the equation are [tex]x=0[/tex] and [tex]x=-6[/tex].

We can conclude that the correct answer is x = 0.

Answer:

C: x = 0

There is no solution.

Answer:

Nickola swam for 4 hours and ran for 5.5 hours

Step-by-step explanation:

To solve this, we can use a system of equations.

First we can set up a system of equations like this

[tex]2s+15r=90.5[/tex] and

[tex]s+r=9.5[/tex]

Next we will use substitution to solve for one of the values. We can solve the second equation such that

[tex]s=9.5-r[/tex]

Now we can substitute this into the first equation for s

[tex]2(9.5-r)+15r=90.5[/tex]

Now we can solve for r

[tex]19-2r+15r=90.5[/tex]

[tex]19+13r=90.5[/tex]

[tex]13r=71.5[/tex]

[tex]r=5.5[/tex]

Now we can plug this value into the second equation to get the value for s

[tex]s+5.5=9.5[/tex]

[tex]s=4[/tex]

Now we can plug these values into the first equation to make sure we have the right values

[tex]2(4)+15(5.5)=90.5[/tex]

[tex]90.5=90.5[/tex]

Answer:

9

Step-by-step explanation:

If n is the number of tablets, the maximum value it can have is given by ...

0.25n = 2.25

Dividing by the coefficient of n gives ...

n = 2.25/0.25 = 9

The patient can take a total of 9 tablets through the day.

Answer:

The answer is 2:9

Step-by-step explanation:

On plato

The point estimates for the mean and standard deviation of the given data set is respectively; 68 and 17.6.

What is a point Estimate?

A) In order to find the point estimate of the mean, we will add up the data and divide it by the number of values.

Here,

∑x = 57 + 61 + 86 + 74 + 72 + 73 + 20 + 57 + 80 + 79 + 83 + 74

    = 816

n = 12 numbers

Thus;

Mean = ∑x/n

         = 816/12

Mean = 68

B) In order to find the estimate of the standard deviation, we have the formula;

s = √[(n*(∑x²) - (∑x)²)/n(n - 1)]

∑x² = 57² + 61² + 86² + ... + 74²

     = 59,010

s = √[ (12*(59,010) - (816)²)/(12)(11)]

s = 17.6

Hence, The point estimates for the mean and standard deviation of the given data set is respectively; 68 and 17.6.

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Answer:

D.

Step-by-step explanation:

I also haven't learned this yet but i could tell that in the second image if A.F = 1/2AC and DE = A.F, therefore DE = 1/2AC. The problem is that i don't know if it is B or D.

Sorry .-.

Answer:

5/12 or 41.66%

Step-by-step explanation:

When throwing two six-sided dice, you have 36 possible outcomes:

{1,1} {1,2} {1,3} {1,4} {1,5} {1,6} {2,1} {2,2} {2,3} {2,4} {2,5} {2,6} {3,1} {3,2} {3,3} {3,4} {3,5} {3,6} {4,1} {4,2} {4,3} {4,4} {4,5} {4,6} {5,1} {5,2} {5,3} {5,4} {5,5} {5,6} {6,1} {6,2} {6,3} {6,4} {6,5} {6,6}

To find what is the probability the second player will win, we need to see how many of those 36 possibilities have a combined total of 8 or more (to beat the 7 of the first player):

These 15 combinations have a total of 8 or more:

{2,6} {3,5} {3,6} {4,4} {4,5} {4,6} {5,3} {5,4} {5,5} {5,6} {6,2} {6,3} {6,4} {6,5} {6,6}

So, the probability the second player gets 8 or more and wins is:

15/36 or 5/12 or 41.66%

Expand:

[tex]n(n-1)-(n+3)(n+2)=(n^2-n)-(n^2+5n+6)=-6n-6[/tex]

Then we can write

[tex]n(n-1)-(n+3)(n+2)=6\boxed{(-n-1)}[/tex]

which means [tex]6\mid n(n-1)-(n+3)(n+2)[/tex] as required.

Answer:

P(cream and sugar) = 0.4

Step-by-step explanation:

* Lets study the meaning of or , and on probability

- The use of the word or means that you are calculating the probability

 that either event A or event B happened

-  Both events do not have to happen

- The use the word and, means that both event A and B have to happen

* The addition rules are:

# P(A or B) = P(A) + P(B) ⇒ mutually exclusive (events cannot happen

 at the same time)

# P(A or B) = P(A) + P(B) - P(A and B) ⇒ non-mutually exclusive (if they

 have at least one outcome in common)

- The union is written as A∪B or “A or B”.

- The intersection is written as A∩B or “A and B”

* Lets solve the question

∵ P(cream) = 0.5

∵ P(sugar) = 0.6

∵ P(cream or sugar) = 0.7

- To find P(cream and sugar) lets use the rule of non-mutually exclusive

∵ P(A or B) = P(A) + P(B) - P(A and B)

∴ P(cream or sugar) = P(cream) + P(sugar) - P(cream and sugar)

- Lets substitute the values of P(cream) , P(sugar) , P(cream or sugar)

 in the rule

∵ 0.7 = 0.5 + 0.6 - P(cream and sugar) ⇒ add the like terms

∴ 0.7 = 1.1 - P(cream and sugar) ⇒ subtract 1.1 from both sides

∴ 0.7 - 1.1 = - P(cream and sugar)

∴ - 0.4 = - P(cream and sugar) ⇒ multiply both sides by -1

∴ 0.4 = P(cream and sugar)

* P(cream and sugar) = 0.4

Answer:

0.4

Step-by-step explanation:

Answer:

a) starting height: 5.5 ft

b) hang time: 5.562 seconds

c) maximum height: 126.5 ft

d) time to maximum height: 2.75 seconds

Step-by-step explanation:

a) The starting height is the height at t=0.

h(0) = -16·0 +88·0 +5.5

h(0) = 5.5

The starting height is 5.5 feet.

__

b) The ball is in the air between t=0 and the non-zero time when h(t) = 0. We can find the latter by solving ...

-16t^2 + 8t +5.5 = 0

t^2 -(11/2)t = 5.5/16 . . . . . subtract 5.5, then divide by -16

t^2 -(11/2)t +(11/4)^2 = (5.5/16) +(11/4)^2 . . . . complete the square

(t -11/4)^2 = 126.5/16 . . . . . . . . . . . . . . . . . . . . call this [eq1] for later use

t -11/4 = √7.90625

t = 2.75 +√7.90625 ≈ 5.562

The ball will be in the air about 5.562 seconds.

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c) If we multiply [eq1] above by -16 and add the constant on the right, we get the vertex form of the height equation:

h(t) = -16(t -11/4) +126.5

The vertex at (2.75, 126.5) tells us ...

The maximum height of the ball is 126.5 feet.

__

d) That same vertex point tells us ...

The maximum height will be reached at t = 2.75 seconds.

_____

If you really need answers fast, a graphing calculator can give them to you in very short order (less than a minute).

Answer:

b

Step-by-step explanation: