The regular price of a baseball cleats is $80. If the cleats are on sale for 45% off. then: (how to solve this two questions?) a) What is the value of the discount, in dollars? b) What is the final selling price of the cleats, before tax?​

Answer

X= 64.8 gives the minimum average cost

Explanation:

The question can be interpreted as

C(x)= 5x^3 -40^2 + 21000x

To find the minimum total cost, we will need to find the minimum of

this function, then Analyze the derivatives.

CHECK THE ATTACHMENT FOR DETAILED EXPLANATION

Answer:

Step-by-step explanation:

Since there are  2 red and 5 white balls in the box, the total number of balls in the bag = 2+5 = 7balls.

Probability that at least 1 ball was​ red, given that the first ball was replaced before the second can be calculated as shown;

Since at least 1 ball picked at random, was red, this means the selection can either be a red ball first then a white ball or two red balls.

Probability of selecting a red ball first then a white ball with replacement = (2/7*5/7) = 10/49

Probability of selecting two red balls with replacement = 2/7*2/7 = 4/49

The probability that at least 1 ball was​ red given that the first ball was replaced before the second draw= 10/49+4/49 = 14/49

If the balls were not replaced before the second draw

Probability of selecting a red ball first then a white ball without replacement = (2/7*5/6) = 10/42 = 5/21

Probability of selecting two red balls without replacement = 2/7*2/6 = 4/42 = 2/21

The probability that at least 1 ball was​ red given that the first ball was not replaced before the second draw = 5/21+4/21 = 9/21 = 3/7

The probability that at least 1 ball was red, given that the first ball was replaced before the second draw is 28.5%; and the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw is 22.5%.

Since two balls are drawn in succession out of a box containing 2 red and 5 white balls, to find the probability that at least 1 ball was red, given that the first ball was A) replaced before the second draw; and B) not replaced before the second draw; the following calculations must be performed:

Therefore, the probability that at least 1 ball was red, given that the first ball was replaced before the second draw is 28.5%; and the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw is 22.5%.

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Answer:

Option A

Step-by-step explanation:

Equation of the given quadratic function is,

y = 2x² + 8x + 3

y = 2(x² + 4x) + 3

  = 2(x² + 4x + 4 - 4) + 3

  = 2(x + 2)² - 8 + 3

  = 2(x + 2)² - 5

By comparing this equation with the equation of a quadratic function in vertex form,

y = a(x - h)² + k

Here (h, k) is the vertex of the parabola

Vertex of the given equation will be (-2, -5) and coefficient 'a' is positive (a > 0)

Therefore, vertex will lie in the 3rd quadrant and the parabola will open upwards.

Option (A). Graph A will be the answer.

Answer:

x < 11.5

Step-by-step explanation:

2x + 9 < 32

(2x + 9) - 9  < 32 - 9

2x < 23

2x/2 < 23/2

x < 11.5

Answer:

x < 11 1/2

Step-by-step explanation:

2x+9<32

Subtract 9 from each side

2x+9-9 < 32-9

2x<23

Divide by 2

2x/2 <23/2

x < 11 1/2

X is any number less than 11 1/2

Answer:

[tex]\displaystyle y=-\frac{1}{3}x+3[/tex]

Step-by-step explanation:

First, notice that since the graph of the function is a line, we have a linear function.

To find the equations for linear functions, we need the slope and the y-intercept. Recall the slope-intercept form:

[tex]y=mx+b[/tex]

Where m is the slope and b is the y-intercept.

We are given the point (0,3) which is the y-intercept. Thus, b = 3.

To find the slope, we can use the slope formula:

[tex]\displaystyle m=\frac{\Delta y}{\Delta x} =\frac{2-3}{3-0}=-1/3[/tex]

Therefore, our equation is:

[tex]\displaystyle y=-\frac{1}{3}x+3[/tex]

Step-by-step explanation:

the average change H = Δy/ Δx

so H = ( f(4) - f(2) )/ (4 -2) = ( 0 -1 ) / 2 = -1/2

Answer:

14.  C   41

15. k = 72

Step-by-step explanation:

14.

For parallel lines, alternate exterior angles must be congruent.

3x - 43 = 80

3x = 123

x = 41

15.

The sum of the measures of the angles of a triangle is 180 deg.

k + 33 + 75 = 180

k + 108 = 180

k = 72

Answer:

1. 32

2. 41

3. 72

Step-by-step explanation:

Step-by-step explanation:

given,

base( b) = 6cm

height (h)= 11cm

now, area of parallelogram (a)= b×h

or, a = 6cm ×11cm

therefore the area of parallelogram (p) is 66cm^2.

hope it helps...

Answer:

d.  a = 39

Step-by-step explanation:

Question:

for which value of "a" will the trinomial be factorizable.

x^2+ax-40

For the expression to have integer factors, a = sum of the pairs of factors of -40.

-40 has following pairs of factors

{(1,-40), (2,-20, (4,-10), (5,-8), (8, -5), (10,-4), (20,-2), (40,-1) }

meaning that the possible values of a are

+/- 39, +/- 18, +/- 6, +/- 3

out of which only +39 appears on answer d.  a=39

Answer:

99% confidence interval for the mean of college students

A) 112.48 < μ < 117.52

Step-by-step explanation:

step(i):-

Given sample size 'n' =150

mean of the sample = 115

Standard deviation of the sample = 10

99% confidence interval for the mean of college students are determined by

[tex](x^{-} -t_{0.01} \frac{S}{\sqrt{n} } , x^{-} + t_{0.01} \frac{S}{\sqrt{n} } )[/tex]

Step(ii):-

Degrees of freedom

ν = n-1 = 150-1 =149

t₁₄₉,₀.₀₁ =  2.8494

99% confidence interval for the mean of college students are determined by

[tex](115 -2.8494 \frac{10}{\sqrt{150} } , 115 + 2.8494\frac{10}{\sqrt{150} } )[/tex]

on calculation , we get

(115 - 2.326 , 115 +2.326 )

(112.67 , 117.326)  

The set of numbers that can represent the lengths of the sides of a triangle are 3,5,7. That is option B.

Triangle is defined as a type of polygon that has three sides in which the sum of both sides is greater than the third side.

That is to say, 3+5 = 8 is greater than the third side which is 7.

Therefore, the set of numbers the would represent a triangle are 3,5,7.

Learn more about triangle here:

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Step-by-step explanation:

With the packaging of 8

48 cookies = 48 ÷ 8 = 6 boxes

With the packaging of 24

48 cookies = 48 ÷ 24 = 2 boxes

Answer:

0.07

Step-by-step explanation:

The number of sophmores is 2+25+3 = 30.

Of these sophmores, 2 drive to school.

So the probability that a student drives to school, given that they are a sophmore, is 2/30, or approximately 0.07.

Answer:

[tex]\large \boxed{0.07}[/tex]

Step-by-step explanation:

The usual question is, "What is the probability of A, given B?"

They are asking, "What is the probability that you are driving to school if you are a sophomore (rather than taking the bus or walking)?"

We must first complete your frequency table by calculating the totals for each row and column.

The table shows that there are 30 students, two of whom drive to school.

[tex]P = \dfrac{2}{30}= \mathbf{0.07}\\\\\text{The conditional probability is $\large \boxed{\mathbf{0.07}}$}[/tex]

Answer:

OD. 45,45,90

Step-by-step explanation:

Answer:

7 + 5(x - 3) = 22

5(x - 3) = 15

x - 3 = 3

x = 6

Answer:

x = 6

Step-by-step explanation:

Step 1: Distribute 5

7 + 5x - 15 = 22

Step 2: Combine like terms

5x - 8 = 22

Step 3: Add 8 to both sides

5x = 30

Step 4: Divide both sides by 5

x = 6

Answer:

The answer is below

Step-by-step explanation:

We have the following information:

Number of songs you like = 2

Total number of songs = 12

a) P(you like both of them) = 2/12 x 1/11 = 0.015

This is unusual because the probability of the event is less than 0.05

b) P(you like neither of them) = 10/12 x 9/11  = 0.68

c) P(you like exactly one of them) = 2 x 2/12 x 10/11 = 0.30

d) If  a song can be replayed before all 12,

P(you like both of them) = 2/12 x 2/12  =0.027

This is unusual because the probability of the event is less than 0.05

P(you like neither of them) = 9/12 x 9/12  = 0.5625

P(you like exactly one of them) = 2 x 2/12 x 9/12 = 0.25

Answer:

3/20

Step-by-step explanation:

15%

15/100

/5  /5

3/20

Answer:

a) k=2.08 1/hour

b) The exponential growth model can be written as:

[tex]P(t)=Ce^{kt}[/tex]

c) 977,435,644 cells

d) 2.033 billions cells per hour.

e) 2.81 hours.

Step-by-step explanation:

We have a model of exponential growth.

We know that the population duplicates every 20 minutes (t=0.33).

The initial population is P(t=0)=58.

The exponential growth model can be written as:

[tex]P(t)=Ce^{kt}[/tex]

For t=0, we have:

[tex]P(0)=Ce^0=C=58[/tex]

If we use the duplication time, we have:

[tex]P(t+0.33)=2P(t)\\\\58e^{k(t+0.33)}=2\cdot58e^{kt}\\\\e^{0.33k}=2\\\\0.33k=ln(2)\\\\k=ln(2)/0.33=2.08[/tex]

Then, we have the model as:

[tex]P(t)=58e^{2.08t}[/tex]

The relative growth rate (RGR) is defined, if P is the population and t the time, as:

[tex]RGR=\dfrac{1}{P}\dfrac{dP}{dt}=k[/tex]

In this case, the RGR is k=2.08 1/h.

After 8 hours, we will have:

[tex]P(8)=58e^{2.08\cdot8}=58e^{16.64}=58\cdot 16,852,338= 977,435,644[/tex]

The rate of growth can be calculated as dP/dt and is:

[tex]dP/dt=58[2.08\cdot e^{2.08t}]=120.64e^2.08t=2.08P(t)[/tex]

For t=8, the rate of growth is:

[tex]dP/dt(8)=2.08P(8)=2.08\cdot 977,435,644 = 2,033,066,140[/tex]

(2.033 billions cells per hour).

We can calculate when the population will reach 20,000 cells as:

[tex]P(t)=20,000\\\\58e^{2.08t}=20,000\\\\e^{2.08t}=20,000/58\approx344.827\\\\2.08t=ln(344.827)\approx5.843\\\\t=5.843/2.08\approx2.81[/tex]

Answer:

(a) Yes, there are 10 independent trials, each with exactly two possible outcomes, and a constant probability associated with each possible outcome.

(b) The probability that exactly 6 out of 10 randomly sampled 18- 20-year-olds consumed an alcoholic drink is 0.203.

(c) The probability that exactly 4 out of 10 randomly sampled 18- 20-year-olds have not consumed an alcoholic drink is 0.203.

(d) The probability that at most 2 out of 5 randomly sampled 18-20-year-olds have consumed alcoholic beverages is 0.167.

Step-by-step explanation:

We are given that data collected by the Substance Abuse and Mental Health Services Administration (SAMSHA) suggests that 69.7% of 18-20-year-olds consumed alcoholic beverages in 2008.

(a) The conditions required for any variable to be considered as a random variable is given by;

So, in our question; all these conditions are satisfied which means the use of the binomial distribution is appropriate for calculating the probability that exactly six consumed alcoholic beverages.

Yes, there are 10 independent trials, each with exactly two possible outcomes, and a constant probability associated with each possible outcome.

(b) Let X = Number of 18- 20-year-olds people who consumed an alcoholic drink

The above situation can be represented through binomial distribution;

[tex]P(X = r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r}; x = 0,1,2,......[/tex]

where, n = number of trials (samples) taken = 10 people

            r = number of success = exactly 6

            p = probability of success which in our question is % 18-20

                  year-olds consumed alcoholic beverages in 2008, i.e; 69.7%.

So, X ~ Binom(n = 10, p = 0.697)

Now, the probability that exactly 6 out of 10 randomly sampled 18- 20-year-olds consumed an alcoholic drink is given by = P(X = 6)

           P(X = 3) =  [tex]\binom{10}{6}\times 0.697^{6} \times (1-0.697)^{10-6}[/tex]

                         =  [tex]210\times 0.697^{6} \times 0.303^{4}[/tex]

                         =  0.203

(c) The probability that exactly 4 out of 10 randomly sampled 18- 20-year-olds have not consumed an alcoholic drink is given by = P(X = 4)

Here p = 1 - 0.697 = 0.303 because here our success is that people who have not consumed an alcoholic drink.

           P(X = 4) =  [tex]\binom{10}{4}\times 0.303^{4} \times (1-0.303)^{10-4}[/tex]

                         =  [tex]210\times 0.303^{4} \times 0.697^{6}[/tex]

                         =  0.203

(d) Let X = Number of 18- 20-year-olds people who consumed an alcoholic drink

The above situation can be represented through binomial distribution;

[tex]P(X = r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r}; x = 0,1,2,......[/tex]

where, n = number of trials (samples) taken = 5 people

            r = number of success = at most 2

            p = probability of success which in our question is % 18-20

                  year-olds consumed alcoholic beverages in 2008, i.e; 69.7%.

So, X ~ Binom(n = 5, p = 0.697)

Now, the probability that at most 2 out of 5 randomly sampled 18-20-year-olds have consumed alcoholic beverages is given by = P(X [tex]\leq[/tex] 2)

        P(X [tex]\leq[/tex] 2) = P(X = 0) + P(X = 1) + P(X = 3)

= [tex]\binom{5}{0}\times 0.697^{0} \times (1-0.697)^{5-0}+\binom{5}{1}\times 0.697^{1} \times (1-0.697)^{5-1}+\binom{5}{2}\times 0.697^{2} \times (1-0.697)^{5-2}[/tex]

=  [tex]1\times 1\times 0.303^{5}+5 \times 0.697^{1} \times 0.303^{4}+10\times 0.697^{2} \times 0.303^{3}[/tex]

=  0.167

Answer:

Side 1: 40 feet

Side 2: 20 feet

Side 3: 22 feet

Step-by-step explanation:

Side 1 is twice the length of side 2 and side 2 is 20 feet, which means side 1 is 40 feet. Side 3 is the the length of the second side plus 2, which means it has a length of 22 feet.

Answer:

40%

Step-by-step explanation:

We can find what percent 48 is of 120 by dividing:

48/120 = 0.4 or 40%

So, she saved 40% from the original price.

Answer:

[tex]\dfrac{dx}{dt}=-1.3846$ sales per day[/tex]

Step-by-step explanation:

The price​ p, in​ dollars, and the number of​ sales, x, of a certain item follow the equation: 6p+3x+2px=69

Taking the derivative of the equation with respect to time, we obtain:

[tex]6\dfrac{dp}{dt} +3\dfrac{dx}{dt}+2p\dfrac{dx}{dt}+2x\dfrac{dp}{dt}=0\\$Rearranging$\\6\dfrac{dp}{dt}+2x\dfrac{dp}{dt}+3\dfrac{dx}{dt}+2p\dfrac{dx}{dt}=0\\\\(6+2x)\dfrac{dp}{dt}+(3+2p)\dfrac{dx}{dt}=0[/tex]

When x=3, p=5 and [tex]\dfrac{dp}{dt}=1.5[/tex]

[tex](6+2(3))(1.5)+(3+2(5))\dfrac{dx}{dt}=0\\(6+6)(1.5)+(3+10)\dfrac{dx}{dt}=0\\18+13\dfrac{dx}{dt}=0\\13\dfrac{dx}{dt}=-18\\\dfrac{dx}{dt}=-\dfrac{18}{13}\\\\\dfrac{dx}{dt}=-1.3846$ sales per day[/tex]

The number of sales, x is decreasing at a rate of 1.3846 sales per day.

Answer:

The series of numbers that correspond to the general rule of  [tex]X_n=2n+1[/tex] is {3, 5, 7, 9}.

Step-by-step explanation:

We are given with the following series options below;

a. 3, 5, 7, 9

b. 2, 4, 5, 8

c. 4, 6, 8,10

d. 2, 3, 4, 5

And we have to identify what number series has a general rule as [tex]X_n=2n+1[/tex].

For this, we will put the values of n in the above expression and then will see which series is obtained as a result.

So, the given expression is ; [tex]X_n=2n+1[/tex]

If we put n = 1, then;

[tex]X_1=(2\times 1)+1[/tex]

[tex]X_1 = 2+1 = 3[/tex]

If we put n = 2, then;

[tex]X_2=(2\times 2)+1[/tex]

[tex]X_2 = 4+1 = 5[/tex]

If we put n = 3, then;

[tex]X_3=(2\times 3)+1[/tex]

[tex]X_3 = 6+1 = 7[/tex]

If we put n = 4, then;

[tex]X_4=(2\times 4)+1[/tex]

[tex]X_4 = 8+1 = 9[/tex]

Hence, the series of numbers that correspond to the general rule of  [tex]X_n=2n+1[/tex] is {3, 5, 7, 9}.

16, think of 4 plus 4 plus 4 plus 4.

Answer:

[tex]3\frac{4}{5}[/tex]

Step-by-step explanation:

You first need to make the denominators the same and the LCM (least Common Multiple of this equation is 10.

10/10-->1

1/2--> 5/10

2--> 20/10

3/10, the denominator is already 10, so don't need to change.

10/10+5/10+20/10+3/10=38/10=[tex]3\frac{8}{10}[/tex]=[tex]3\frac{4}{5}[/tex]

Answer:

3 4/5

Step-by-step explanation:

hopefully this helped :3

Answer:

C

Step-by-step explanation:

write an equation for the costs:

if x is the number of sodas

and y is the number of waters

2.75x + 2y <= 15

(<= is less than or equal to)

if we substitute 3 for y

we get 2.75x + 2(3) <= 15

2.75x + 6 <= 15

2.75x <= 9

9 / 2.75 = 3.2727

however, you cannot buy part of a soda

so, round to 3

you also cannot buy negative sodas

so, the answer is C

Answer:

See below.

Step-by-step explanation:

There are 3 edges and 3 faces  projecting out from a vertex of a cube.

So the polygon produced would be a triangle.

Answer:

A triangle.

Step-by-step explanation:

As shown above, the plane which slices a corner intersects the polyhedron in [tex] n [/tex] faces which depend on the particular polyhedron.

Here it is a cube, and it intersects three faces. Since the intersection of two planes is a line and there are three planes to intersect with, there are three sides of the polygon.

Hence the polygon is a triangle.

Answer:

Yes, he can buy 8 donuts and 4 energy drinks.

Step-by-step explanation:

If Tension is able to buy 8 donuts and 4 energy drinks, then both inequalities would be valid when we use these numbers as inputs. Let's check each expression at a time:

[tex]0.75*d + 2*e \leq 25\\0.75*8 + 2*4 \leq 25\\6 + 8 \leq 25\\14 \leq 25[/tex]

The first one is valid, since 14 is less than 25. Let's check the second one.

[tex]360*d + 110*e \geq 1000\\360*8 + 110*4 \geq 1000\\2880 + 440 \geq 1000\\3320 \geq 1000[/tex]

The second one is also valid.

Since both expressions are valid, Tension can buy 8 donuts and 4 energy drinks and achieve his goal of having a caloric surplus of at least 1000 cal.

Answer:

Step-by-step explanation:

Given the confidence interval of the heights of american heights given as (65.3,73.7);

Lower confidence interval L = 65.3 and Upper confidence interval U = 73.7

Sample mean will be the average of both confidence interval . This is expressed mathematically as [tex]\overline x = \frac{L+U}{2}[/tex]

[tex]\overline x = \frac{65.3+73.7}{2}\\\overline x = \frac{139}{2}\\\overline x = 69.5[/tex]

Hence, the sample mean is 69.5