Enter the correct answer in the box by replacing the values of a and b. f(x) = a(b)^x

Answer:

Step-by-step explanation:

Hello, because of the end behaviour it means that the leading coefficient is negative so we can construct such polynomial function as below.

[tex]\large \boxed{\sf \bf \ \ -(x+7)(x-6) \ \ }[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

The polynomial function will be f ( x ) = - x² - x + 42

What is Quadratic Equation?

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+ bx + c = 0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

Given data ,

The polynomial function is of second degree with zeros of -7 and 6

So , x = -7 and x = 6

Let the function be f ( x ) where f ( x ) = ( x + 7 ) ( x - 6 )

Now , as x tends to infinity , the negative makes no such difference on the zeros of the function f ( x ) ,

And , f ( x ) = - ( x + 7 ) ( x - 6 )

Therefore , to find the polynomial function , f ( x ) = - ( x + 7 ) ( x - 6 )

f ( x ) = - [ x² - 6 x + 7 x - 42 ]

        = - [ x² + x - 42 ]

        = - x ² - x + 42

Hence , the polynomial function f ( x ) = - x ² - x + 42

To learn more about polynomial function click :

https://brainly.com/question/25097844

#SPJ2

Answer:

the answer is A) h=3V/(Pi*r^2)

Step-by-step explanation:

This question is asking to solve for h, the equation is allready solved for V.

to solve for h means to get h by itself on one side of the equation.

1) V=(1/3)*pi*r^2*h. Divide 1/3*pi*r^2 to the other side of the equation

2) V/(1/3)*pi*r^2=h. 1/3 on the bottom denominator means we can multiply the reciprocal to the bottom and the top and get an equivalent answer. In short, move the 3 from the 1/3 onto the top.

3) (3*V)/(pi*r^2)=h. Simplify.

4) 3V/(Pi*r^2)=h.

Answer:

C

Step-by-step explanation:

Firstly, we set up the null and alternative hypothesis as follows;

The null hypothesis is;

H0: μ ≥ 12

The alternative hypothesis is;

Ha : μ < 12

Next step is to calculate the test statistic z

Mathematically;

z = (x - μ )/ σ /√n

= (11.58 - 12) /1.93/√(80

Test statistic z = -1.92

Now we proceed to find the probability value that is equal to the value of the test statistic. We can find this by using the standard normal table or NORMSTD function on excel

P(z < -1.92) = 0.0274

P-value = 0.0274

alpha = 0.05

From the above, we can see that

P-value < alpha

And because of this, we are going to reject the null hypothesis and therefore accept the alternative.

We then conclude that there is sufficient evidence to conclude that "The average battery life (between charges) of this model of tablet is at least 12 hours."

Answer:

x +0y+0z = 400

-x +y+0z = 150

-8x +0y +z = 250

Step-by-step explanation:

The last column is the solution

The rest of the columns are the coefficients of the variables

x +0y+0z = 400

-x +y+0z = 150

-8x +0y +z = 250

Answer:

B. 323 square centimeters

Step-by-step explanation:

multiply the inches by the conversion number

50 x 6.45 = 322.5

Answer:

[tex]\boxed{Option \ B}[/tex]

Step-by-step explanation:

[tex]1 \ inch^2 = 6.45 \ cm^2[/tex]

Multiplying both sides by 50

[tex]1 * 50 \ inch^2 = 6.45 * 50 \ cm^2\\[/tex]

[tex]50 \ inch^2 = 323 \ cm^2[/tex]

Answer:

√96

Step-by-step explanation:

PQ is tangent to both lines, so PQ is perpendicular to PO and QO'.

The radius of the smaller circle is 3, and the radius of the larger circle is 8.

If we draw a line from O to O', and another line from point O to line QO' that is parallel to PQ, we get a right triangle where OO' is the hypotenuse, the short leg is 8−3=5, and the long leg is the same length as PQ.

Using Pythagorean theorem:

x² + 5² = 11²

x = √96

Answer:

[tex]D(21) = 1.612\ ft[/tex]

Step-by-step explanation:

The question has missing details;

[tex]D(t) = \frac{5.4}{1+2.9e^{-0.01t}}[/tex]

Given that t = 21

Solve for Diameter, D

To do this, we simply substitute 21 for t in the above function

[tex]D(t) = \frac{5.4}{1+2.9e^{-0.01t}}[/tex] becomes

[tex]D(21) = \frac{5.4}{1+2.9e^{-0.01 * 21}}[/tex]

[tex]D(21) = \frac{5.4}{1+2.9e^{-0.21 }}[/tex]

Solve for [tex]e^{-0.21}[/tex]

[tex]D(21) = \frac{5.4}{1+2.9* 0.81058424597}[/tex]

Simplify the denominator

[tex]D(21) = \frac{5.4}{1+2.35069431331}[/tex]

[tex]D(21) = \frac{5.4}{3.35069431331}[/tex]

[tex]D(21) = 1.61160628069[/tex]

[tex]D(21) = 1.612\ ft[/tex] (Approximated)

Hence, the diameter of the 21 year old tree is 1.612 feet

Answer:

$50.

Step-by-step explanation:

The formula for the stocks is...

Par value of preferred stock = (Number of issued shares) * (par value per share)

So, we can say that...

Par value per share = par value of preferred stock / number of issued shares.

The par value of the Buzz Tool Company is $50,000. There are 1,000 issued shares. So, each stock would be $50,000 / 1,000 = $50 / 1 = $50.

Hope this helps!

Answer: par value is $50.00

Step-by-step explanation:

$50,000.00 ÷ 1,000

= $50.00

Answer:

9 x^2

Step-by-step explanation:

( 3x) ^2

We are multiplying 3x * 3x

9 x^2

Answer:

$13.62

Step-by-step explanation:

By working backward we can see that before she cleaned the windows she had $6.81.

We know that she spent half her allowance on the arcade and the $6.81 she had before cleaning the windows is the other half.

So, if you multiply by 2 you get that here weekly allowance is $13.62.

Answer:

$13.62

Step-by-step explanation:there

Question:

Diners frequently add a​ 15% tip when charging a meal to a credit card. What is the price of the meal without the tip if the amount charged is ​$20.70? How much was the​ tip?

Answer:

Price of meal = $18

Tip price = $2.70

Step-by-step explanation:

Let the price of the meal be y;

Let the tip be t

From the question;

15% of y is the tip charge (t). i.e

t = 15%y

=> t = 0.15y          --------(i)

The total amount charged is $20.70  (This means that the sum of the price of the meal and the tip is $20.70)

=> y + t = 20.70            [substitute the value of t=0.15y from equation (i)]

=> y + 0.15y = 20.70

=> 1.15y = 20.70

=> y = [tex]\frac{20.70}{1.15}[/tex]

=> y = $18

Therefore the price of the meal, y, is $18.

From equation (i),

t = 0.15y           [substitute the value of y = $18]

t = 0.15(18)

t = $2.70

Therefore the tip was $2.70

Answer:

We can assume that the decline in the population is an exponential decay.

An exponential decay can be written as:

P(t) = A*b^t

Where A is the initial population, b is the base and t is the variable, in this case, number of hours.

We know that: A = 800,000.

P(t) = 800,000*b^t

And we know that after 6 hours, the popuation was 500,000:

p(6h) = 500,000 = 800,000*b^6

then we have that:

b^6 = 500,000/800,000 = 5/8

b = (5/8)^(1/6) = 0.925

Then our equation is:

P(t) = 800,000*0.925^t

Now, the population after 24 hours will be:

P(24) = 800,000*0.925^24 = 123,166

Answer:

122,070 bacteria.

Step-by-step explanation:AA0ktA=500,000=800,000=?=6hours=A0ekt

Substitute the values in the formula.

500,000=800,000ek⋅6

Solve for k. Divide each side by 800,000.

58=e6k

Take the natural log of each side.

ln58=lne6k

Use the power property.

ln58=6klne

Simplify.

ln58=6k

Divide each side by 6.

ln586=k

Approximate the answer.

k≈−0.078

We use this rate of growth to predict the number of bacteria there will be in 24 hours.

AA0ktA=?=800,000=ln586=24hours=A0ekt

Substitute in the values.

A=800,000eln586⋅24

Evaluate.

A≈122,070.31

At this rate of decay, researchers can expect 122,070 bacteria.

Answer:

We conclude that the true average weight loss for the vegan diet exceeds that for the control diet by more than 1 kg.

Step-by-step explanation:

We are given that an article reported on the results of an experiment in which half of the individuals in a group of 66 postmenopausal overweight women were randomly assigned to a particular vegan diet, and the other half received a diet based on National Cholesterol Education Program guidelines.

The sample mean decrease in body weight for those on the vegan diet was 6 kg, and the sample SD was 3.2, whereas, for those on the control diet, the sample mean weight loss and standard deviation were 3.8 and 2.4, respectively.

Let = true average weight loss for the vegan diet.

[tex]\mu_2[/tex] = true average weight loss for the control diet.

So, Null Hypothesis, : 1 kg      {means that the true average weight loss for the vegan diet exceeds that for the control diet by less than or equal to 1 kg}

Alternate Hypothesis, : > 1 kg      {means that the true average weight loss for the vegan diet exceeds that for the control diet by more than 1 kg}

The test statistics that will be used here is Two-sample t-test statistics because we don't know about population standard deviations;

                            T.S.  =  [tex]\frac{(\bar X_1-\barX_2)-(\mu_1-\mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex]   ~    [tex]t__n_1_+_n_2_-_2[/tex]

where, = sample mean weight loss for the vegan diet = 6 kg

 = sample mean weight loss for the control diet = 3.8 kg

 = sample standard deviation weight loss for the vegan diet = 3.2 kg

 = sample standard deviation weight loss for the control diet = 2.4 kg

[tex]n_1[/tex]  = sample of vegan diet women = 33

[tex]n_2[/tex] = sample of control diet women = 33

Also, [tex]s_p=\sqrt{\frac{(n_1-1)\times s_1^{2}+(n_2-1)\times s_2^{2} }{n_1+n_2-2} }[/tex]  = [tex]\sqrt{\frac{(33-1)\times 3.2^{2}+(33-1)\times 2.4^{2} }{33+33-2} }[/tex] = 2.83

So, the test statistics =  [tex]\frac{(6-3.8)-(1)}{2.83 \times \sqrt{\frac{1}{33}+\frac{1}{33} } }[/tex]  ~  [tex]t_6_4[/tex]

                                    =  1.722  

The value of t-test statistics is 1.722.

Also, the P-value of the test statistics is given by;

               P-value = P([tex]t_6_4[/tex] > 1.722) = 0.0461 or 4.61%

Since the P-value of our test statistics is less than the level of significance as 0.0461 < 0.05, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the true average weight loss for the vegan diet exceeds that for the control diet by more than 1 kg.

Answer:

y = 2666.67

Step-by-step explanation:

Well to solve this we can make a system of equations.

x = cost of car alone

y = cost of accesories,

[tex]\left \{ {{x+y=24000} \atop {x=8y}} \right.[/tex]

So now we plug in 8y for x in x + y = 24000.

(8y) + y = 24000

9y = 24000

Divide both sides by 9

y = 2666.666666

or 2666.67 rounded to the nearest hundredth.

Now that we have y we can plug that in for y in x=8y.

x = 8(2.666.67)

x = 21,333.33 rounded to the nearest hundredth.

Thus,

accessories "y" cost around 2666.67.

Hope this helps :)

Answer:

C. 15 centimeters

Step-by-step explanation:

The Triangle Midsegment Theorem

segment LM = 1/2 of AC

LM = 1/2 * 30

LM = 15 cm

Answer:

Step-by-step explanation:

a. A conclusion with regards to the null hypothesis is this:

Since the p value observed which is 0.0433 is less than the alpha level of significant 0.05, we can reject the null hypothesis.

b. A final conclusion that addresses the original claim is this:

Since we rejected the null hypothesis, it means it means there was enough statistical evidence to support the claim that more than 47​% of adults would erase all of their personal information online if they could.

Answer:

a = 37

Step-by-step explanation:

the sum of any triangle angles is 180

then 62 + 81 + a = 180

a = 37

.. ..

Answer:

a = 37 degrees

Step-by-step explanation:

81+62 = 143

We know that all angles of a triangle = 180 degrees

180-143= 37 degrees

a = 37 degrees

Answer:i explained it

Step-by-step explanation:

The total cost of the fence will be 30(2L + 2W) + 2*25 W <= 9000

60L + 110W <= 9000

60 L <= 9000 - 110W

L <= 150 - 11/6 W

For a given width, the maximum area will correspond to the maximum length, so we can just go ahead and say L = 150 - 11/6 W

A = LW = (150 - 11/6 W) W

A = 150 W - 11/6 W2

A' = 150 - 11/3 W = 0

150 = 11/3 W

W = 450/11

Answer:

A=1,728

Step-by-step explanation:

To find the area of a prism, you must find the area of one side, then multiply it by so it would be Width*Hight*Depth, W*H*D.

The width is 12, the hight is 12, and the depth is 12 so you can write

A=12*12*12

Multiply 12 by 12

A=144*12

Multiply 12 by 144 to get your final total area

A=1,728

Hope this helps, feel free to ask follow-up questions if confused.

Have a good day! :)

Answer:

y = -1/2x - 3

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Step 1: Determine known variables

Slope = -1/2 (m = -1/2)

y-intercept - (0, -3), so b = -3

Step 2: Write in known variables

y = -1/2x - 3

Answer:

y = -1/2 - 3

Step-by-step explanation:

Well slope intercept is y = ax + b

ax is the slope which is given,

b is the y intercept which is -3 because the point (0,-3)

doesn’t have a x coordinate meaning if the line goes through that point it touches the y intercept at -3.

Thus,

the equation in slope-intercept is y = -1/2 - 3.

Hope this helps :)

Answer:

Step-by-step explanation:

Let x represent the number of pounds of chocolate in the mix. Then the total price of 10 pounds of mix is ...

  10x +5(10 -x) = 80

  5x +50 = 80

  5x = 30

  x = 6 . . . . . . . . pounds of chocolate

  10 -x = 4 . . . . . pounds of jelly candy

6 pounds of chocolate and 4 pounds of jelly should be used to make the mixture.

Answer:

$54,000

Step-by-step explanation:

Assuming that her salary does not change. Note that annual means "a year", which would mean 12 months.

First, find how much Linda makes per month. Divide the total earned in 3 months with 3 months:

13,500/3 = 4,500

Next, multiply 4,500 (the amount made per month) with 12 to get your annual salary:

4,500 x 12 = 54,000

Linda makes $54,000 annually.

Answer:

Hey there!

The slope is rise over run, or 1/-4.

This gives us the slope, which is -1/4.

Hope this helps :)

Answer:

1/4

Step-by-step explanation:

( i mean i think it is - 1/4 but that isn't an answer choice- )

Slope (m) =

ΔY overΔX= -1 over 4  = -0.25

subtract x^1 and x^2 also y^1 and y^2

and put the answer of y' s over the answer of x 's

divide and you got your answer!

Answer:

no tiene mas informaion?

Step-by-step explanation:

Answer:

20b^3+12b^2

Step-by-step explanation:

v=(2b)^2 (5b+3) = 4b^2 (5b+3) = 20b3+12b^2

Answer:

1,-1,3,4

1,6,-2,-4

-4,6,-6,6

Step-by-step explanation:

I believe you just put in the values into the box. Watch the video to see how they did it to make sure it looks like how I did it.

Answer:

It will take 18,569.2 years for carbon–14 to decay to 10 percent of its original amount

Step-by-step explanation:

The amount of Carbon-14 after t years is given by the following equation:

[tex]A(t) = A(0)e^{-rt}[/tex]

In which A(0) is the initial amount and r is the decay rate, as a decimal.

Carbon–14 is a radioactive isotope that decays exponentially at a rate of 0.0124 percent a year.

This means that [tex]r = \frac{0.0124}{100} = 0.000124[/tex]

How many years will it take for carbon–14 to decay to 10 percent of its original amount?

This is t for which:

[tex]A(t) = 0.1A(0)[/tex]

So

[tex]A(t) = A(0)e^{-rt}[/tex]

[tex]0.1A(0) = A(0)e^{-0.000124t}[/tex]

[tex]e^{-0.000124t} = 0.1[/tex]

[tex]\ln{e^{-0.000124t}} = \ln{0.1}[/tex]

[tex]-0.000124t = \ln{0.1}[/tex]

[tex]t = -\frac{\ln{0.1}}{0.000124}[/tex]

[tex]t = 18569.2[/tex]

It will take 18,569.2 years for carbon–14 to decay to 10 percent of its original amount

Answer:

D

Step-by-step explanation:

100/5=20

20*7=140

Question

Combine like terms to create an equivalent expression.

-3.6-1.9t+1.2+5.1t

Answer:

3.2t - 2.4

Step-by-step explanation:

Given;

-3.6 - 1.9t + 1.2 + 5.1t

Combining like terms means bringing terms that have "t" together and separately, those that don't have "t" together. i.e

=> − 1.9t + 5.1t - 3.6 + 1.2

=> 3.2t - 2.4

Therefore, the equivalent expression is;

3.2t - 2.4

Answer:

3.2t - 2.4

Step-by-step explanation:

right on khan

Vamos lá.....

Duas maneiras praticas:

1 - Multiplicar a fraçao pelo total, vai informar quanto a fracao representa (o que é questionado na questao)

2 - Regra de 3.

1:

72 × (3/8)

216/8

27

Ele acertou 27 questoes

(pergunta mais que interessante: qntas questoes havia na prova??? 72)