Q3:
A company sells bikes for $120 each. They pay a monthly rent of $1,800 for their store and each bike costs them $60 in materials. Write the revenue and cost functions and find the break-even point by graphing.

Answer:

Ans 1. [tex]x= 7[/tex]

Ans 2.a.

[tex]\overline {AC} \cong \overline {JL} \\\textrm{is the additional information required to prove the triangles are congruent by SAS postulate}[/tex]

Ans.2.b.

[tex]\overline {BC} \cong \overline {KL} \\\textrm{is the additional information required to prove the triangles are congruent by the HL theorem}[/tex]

Step-by-step explanation:

Solution:

1.

Vertically opposite angles are equal.

[tex]\therefore (x+16) = (4x-5)\\\therefore (4x-x) = (16+5)\\\therefore (3x) = (21)\\\therefore x = 7[/tex]

2.a.

proof for Δ BAC ≅ ΔKJL by SAS postulate.

InΔ BAC and Δ KJL

BA ≅  KJ               Given

∠ BAC ≅ ∠ KJL   {measure each angle is 90}

[tex]\overline{AC} \cong \overline{JL}\ \textrm{additional information require to prove the tangles are congruent by SAS postulate}\\\therefore \triangle BAC \cong \triangle KJL\ \textrm{By Side-Angle-Side postulate...PROVED}[/tex]

2.b.

proof for Δ BAC ≅ ΔKJL by HL theorem.

InΔ BAC and Δ KJL

BA ≅  KJ               Given

∠ BAC ≅ ∠ KJL   {measure each angle is 90}

[tex]\overline{BC} \cong \overline{KL}\ \textrm{additional information require to prove the tangles are congruent by HL theorem}\\\therefore \triangle BAC \cong \triangle KJL\ \textrm{By Hypotenuse Leg Theorem......PROVED}[/tex]

Answer:

A. 20%

Step-by-step explanation:

These events are independent, because if David eats a healthy breakfast cannot influence on would be rain or not.

"And" for probabilities  of independent events means "x" (times).

80% = 0.8

25% = 0.25

0.8*0.25 = 0.2 = 20%

Answer:

Step-by-step explanation:

The function goes up to the right until it gets to the vertex at x=0. Then it goes down to the right. That is, it is ...

  increasing from -∞ to 0 (not including 0)

  decreasing from 0 to +∞ (not including 0)

_____

At x=0, the function is neither increasing nor decreasing, so x=0 is not part of either interval.

Answer:  54 mph

Step-by-step explanation:

Speed x Time = Distance

So, Speed = Distance/Time

Speed = 324 miles/6hrs = 54 mph

Answer: P = 0.156

Step-by-step explanation:

Initially in the jar, we have 9 red and 13 blue marbles, so we have a total of 22 marbles in the jar.

If we want to take a red ball for the jar, the probability of getting one is equal to the number of red balls divided by the total number of balls, so:

P1 = 9/22 .

Now, suppose you already took one red ball, we want to take the second one; the probability is calculated in the same way, but now we already took a red ball, so we have 8 red balls and 21 balls in total; so:

P2 = 8/21

Now the probability of both events to happen is equal to the product of their probabilities:

P = P1*P2 = (9/22)*(8/21) = 0.1558

Now we want to round it to the nearest thousandth.

The thousandth is the second number after the decimal point, and the number that comes after is an 8, so we need to round it up; then we get:

P = 0.156, or 15.6% in percentage form.

Final answer:

There are 371 students who have taken a course in either calculus or discrete mathematics, 157 students have taken calculus but not discrete mathematics, and 24 students have taken discrete mathematics but not calculus.

Explanation:

To determine how many students have taken a course in either calculus or discrete mathematics, we use the principle of inclusion and exclusion. The formula for two sets A (calculus students) and B (discrete mathematics students) is: |A∪B| = |A| + |B| - |A∩B|.

A. Using the provided numbers: |A∪B| = 347 (calculus students) + 214 (discrete mathematics students) - 190 (students in both) = 371 students have taken a course in either calculus or discrete mathematics.

B. The number of students who have taken calculus but not discrete mathematics is found by subtracting the number of students who have taken both from the total number of calculus students: 347 - 190 = 157 students.

C. Similarly, the number of students who have taken discrete mathematics but not calculus is found by subtracting the number of students who have taken both from the total number of discrete mathematics students: 214 - 190 = 24 students.

Answer:

120 calories and 9 grams of fiber.

Step-by-step explanation:

We are told that 1/3 cup serving contains 80 calories and 6 grams of fiber.

Let's multiply everything by 3. So,

1 cup serving has 3*80 = 240 calories and 3*6 = 18 grams of fiber.  

But, we want to really know about 1/2 cup. So, now we multiply everything by 1/2.  

1/2 cup has (1/2) (240) = 40 calories and (1/2) (18 grams) = 9 grams of fiber.

Answer:

240 calories and 9 grams of fiber

Step-by-step explanation:

Answer:

Area = 2500 square feet is the largest area enclosed

Step-by-step explanation:

A rectangular piece of land borders a wall. The land is to be enclosed and to be into divided 3 equal plots with 200 feet of fencing

Let x be the length of each box and y be the width of the box

Perimeter of the box= 3(length ) + 4(width)

[tex]200=3x+4y[/tex]

solve for y

[tex]200=3x+4y[/tex]

[tex]200-3x=4y[/tex]

divide both sides by 4

[tex]y=50-\frac{3x}{4}[/tex]

Area of the rectangle = length times width

[tex]Area = 3x \cdot y[/tex]

[tex]Area = 3x \cdot (50-\frac{3x}{4})[/tex]

[tex]A=150x-\frac{9x^2}{4}[/tex]

Now take derivative

[tex]A'=150-\frac{9x}{2}[/tex]

Set it =0 and solve for x

[tex]0=150-\frac{9x}{2}[/tex]

[tex]150=\frac{9x}{2}[/tex]

multiply both sides by 2/9

[tex]x=\frac{100}{3}[/tex]

[tex]A''=-\frac{9}{2}[/tex]

For any value of x, second derivative is negative

So maximum at x= 100/3

 [tex]A=150x-\frac{9x^2}{4}[/tex] , replace the value of x

[tex]A=150(\frac{100}{3})-\frac{9(\frac{100}{3})^2}{4})[/tex]

Area = 2500 square feet is the largest area enclosed

Final answer:

To find the largest enclosed area with 200 feet of fencing divided into 3 plots, solve the equation 2l + 4w = 200 and substitute the value of l into the area formula.

Explanation:

To find the largest area that can be enclosed with 200 feet of fencing and divided into 3 equal plots, we can first find the length of each side of the rectangular piece of land. Let's assume the length of the land is 'l' and the width is 'w'.

Since the land is divided into 3 equal plots, each plot will have a length of l/3 and a width of w.

From the information given, we can form the equation 2l + 4w = 200 (each length side is counted twice and each width side is counted once). We can solve this equation for l and substitute it back into the area formula (A = l * w) to find the largest possible area.

Answer:

She have $1133.33 in account which pays  5% annual interest and he have $1933.33 in account which pays 10% annual interest

Step-by-step explanation:

Let x be the amount she invested at 5% annual interest

She invested $800 more in 10%

So, she invested x+800 at 10% annual interest

Case 1:

Principal = x

Time = 1 year

Rate of interest = 5%

[tex]Si =\frac{P \times R \times T}{100}[/tex]

[tex]SI=\frac{x \times 5 \times 1}{100}[/tex]

[tex]SI=\frac{5}{100}x[/tex]

Case 2:

Principal = x+800

Time = 1 year

Rate of interest = 10%

[tex]Si =\frac{P \times R \times T}{100}[/tex]

[tex]SI=\frac{(x+800) \times 10 \times 1}{100}[/tex]

[tex]SI=\frac{10}{100}(x+800)[/tex]

Interest = Amount - principal = 880+1.1x-x=880+0.1x

Her total interest for a year is $250

So, [tex]\frac{5}{100}x+\frac{10}{100}(x+800)=250[/tex]

[tex]\frac{5}{100}x+\frac{10}{100}(x+800)=250[/tex]

[tex]\frac{5}{100}x+\frac{10}{100}x+80=250[/tex]

[tex]\frac{15}{100}x+80=250[/tex]

[tex]\frac{15}{100}x=250-80[/tex]

[tex]x=170 \times \frac{100}{15}[/tex]

[tex]x=1133.33[/tex]

So the amount she invested at 5% annual interest is $1133.33

She invested at 10% annual interest=x+800=1133.33+800=1933.33

Hence she have $1133.33 in account which pays  5% annual interest and he have $1933.33 in account which pays 10% annual interest

The amount she has in the account that an annual interest of 5% is $3400.

The amount she has in the account that an annual interest of 10% is  $4,200.

x - y = $800 equation 1

0.1x + 0.05y = $250 equation 2

Where:

Multiply equation 1 by 0.1

0.1x - 0.1y = 80 equation 3

Subtract equation 3 from equation 2

0.05y = 170

Divide both sides by 0.05

y = $3,400

Substitute for y in equation 1

x - 3400 = 800

x = 3400 + 800

x = $4,200

To learn more about simultaneous equations, please check: https://brainly.com/question/25875552

To calculate the conditional probability of at most 3 men entering the drugstore given that 10 women entered using Poisson Distribution. The gender doesn't influence the probability, therefore the events are treated as independent. Assumption made is that occurrences are independent and happen at a known average rate.

To compute the conditional probability that at most 3 men entered the drugstore, given that 10 women entered in that hour, we would apply Poisson Distribution. Poisson Distribution is used to find the probability of a number of events in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event.

However, in this case, the number of men entering is independent of the number of women entering. Therefore, the fact that we know 10 women entered does not affect the probability regarding the number of men. The gender of the individuals entering the drugstore is irrelevant, and we can consider them as independent events. The result is the same if we simply asked: What is the probability that at most 3 people entered the drugstore?

To calculate this, we would use the formula for Poisson Distribution, summing up the probabilities of 0, 1, 2 and 3 events happening. The assumption made here is that the occurrences are independent of each other and occur with a known average rate, λ, which is 10 in this question.

https://brainly.com/question/33722848

#SPJ3

Answer:

5^20

Step-by-step explanation:

For each comic book, there are five different choices for which kid will receive that comic book. 20 decisions are made, one for each comic book with five different possibilities for each choice. The number of ways to distribute the comic books to the five kids is 5^20.

Final answer:

The formula for distributing 20 comic books among five kids with no restrictions is C(24, 5) = 42,504 ways.

Explanation:

To distribute the 20 comic books to five kids with no restrictions on how many each kid receives, we can use the concept of distributing identical items among distinct groups.

The number of ways to distribute the comic books in this scenario is represented by the formula: C(n+r-1, r) where n is the number of items (in this case, 20 comic books) and r is the number of groups (5 kids).

Therefore, the number of ways to distribute the comic books to the five kids is: C(20+5-1, 5) = C(24, 5) = 42,504 ways.

To calculate the area between the birth rate and death rate curves for a given time interval, find the net growth rate function by subtracting the death rate from the birth rate, and then integrate this function over the time interval. The result reflects the population surge due to the rates of births and deaths.

The student's question involves calculating the area between two exponential growth curves, birth rate and death rate, over a given time interval. To find the area between the curves b(t) = 2300e0.024t and d(t) = 1450e0.019t from t = 0 to t = 10, we need to integrate the difference between them with respect to time over the given interval.Step-by-step Solution:

Subtract the death rate from the birth rate to get the net growth rate function: g(t) = b(t) - d(t) = 2300e0.024t - 1450e0.019t.

Integrate the net growth rate function with respect to t from 0 to 10 to find the total area.

Use a calculator or computer software to perform the integration and round the final answer to the nearest integer.

This computation will give the total number of people added to the population over the 10-year period, which reflects the population surge resulting from the different rates of increase in births and deaths.

https://brainly.com/question/33152886

#SPJ3

Answer:

Sample 2

Step-by-step explanation:

Correlation  is a technique that show strongly pairs of variables.

For example height and width .There are several different correlation techniques .Correlation is determined by dividing  product of two variables. standard deviation.Standard deviation is a dispersion of  data. Co relation between two variable could be positive or negative or both.

Correlation between two sample is computed. if test statistic is larger in sample 1 then sample 2 will have the larger value of correlation coefficient.

Answer:

[tex]y=Ae^{-2x}[/tex]

Step-by-step explanation:

Given that the functions f(x) that have the property that the tangent lines to the graphs of f(x)pass through the point (x+2,0).

Let (x,y) be any arbitrary point of contract

The tangent line passes through two points (x,y) and (x+2,0)

Slope of tangent line = f'(x) = change in y/change in x= [tex]\frac{-y}{2}[/tex]

i.e. we have

[tex]\frac{dy}{dx} =\frac{-y}{2}[/tex]

Separate the variables

[tex]\frac{dy}{y} =-2x\\lny =-2x+c[/tex]

Raise to power e

[tex]y=Ae^{-2x}[/tex]

Thus the functions would have the above form for various values of A

Answer:

c. probably understates the percent of people who favor a system of national health insurance.

Answer:

Step-by-step explanation:

There are at least a couple of ways you could go at this. Here, we'll use an area formula to find m∠A, then use the law of cosines to find BC. Using BC, we can use the law of sines to find another angle.

  Area = (1/2)·AB·AC·sin(∠A)

  65·2/(12·17) = sin(∠A) ≈ 65/102

  ∠A = arccos(65/102) ≈ 39.587°

From the law of cosines, ...

  BC² = AB² +AC² -2·AB·AC·cos(∠A)

  BC² = 12² +17² -2·12·17·cos(39.587°) ≈ 118.5735

  BC ≈ √118.5735 ≈ 10.889

Then ∠C can be found from the law of sines:

  sin(∠C)/AB = sin(∠A)/BC

  ∠C = arcsin(AB/BC·sin(∠A)) ≈ 44.609°

The measure of ∠B will be the angle that makes the total be 180°:

  39.587° +∠B +44.609° = 180°

  ∠B = 95.804°

_____

There is actually another solution, in which ∠A is obtuse. We thought the diagram showed an acute triangle, so we didn't investigate the other alternative. The above calculations show the triangle is obtuse in any event.

See the second attachment for the other solution.

Answer:

21.10 m

Step-by-step explanation:

Given:

Height of the temple above ground is, [tex]H=24\ m[/tex]

Total number of steps is, [tex]N=91[/tex]

Let us assume that each step is of same height, then the height of each step is given as:

[tex]\textrm{Each step height}=\frac{Total\ Height}{Total\ steps}=\frac{H}{N}=\frac{24}{91}\ m[/tex]

Now, height corresponding to 1 step = [tex]\frac{24}{91}\ m[/tex]

∴ Height corresponding to 80 steps = [tex]\frac{24}{91}\times 80=\frac{24\times 80}{91}=21.10\ m[/tex]

So, I would be at a height of 21.10 m above the ground at the [tex]80^{th}[/tex] step.

Answer:

Step-by-step explanation:

Phil is going to store to buy a hat and a coat.

Let $x represent the cost of the cos of the hat. The coat cost 3 times as much as the hat. It means that the cost of the coat will be 3×x = $3x

His mom tells him that he cannot spend more than $120. Assuming he spends exactly $120. It means that

3x + x = 120

4x = 120

x = 120/ 4 = 30

The hat costs $30

The coat costs 30×3 = $90

The most he can spend on a coat is $90 since he cannot spend more than $120

Answer:

x − 1

x + 2

Step-by-step explanation:

f(x) = 2x³ + 5x² − x − 6

Plug in the zero of each binomial.  If that zero is also a zero of f(x), then the binomial is a factor of f(x).

f(1) = 0

f(-1) = -2

f(2) = 28

f(-2) = 0

The correct options are option A and option D that is the factors of given binomial expressions are x  - 1 and x + 2.

What is binomial factor ?

Binomial factors are polynomial factors that have exactly two terms. Factoring a polynomial is the first step to finding its roots.

The given binomial expression is equal to :

2x³ + 5x² - x - 6

We know that factor theorem states that if [tex]x_{1}[/tex] , [tex]x_{2}[/tex], --- --- --- --- , [tex]x_{n}[/tex] are roots of a function , them (x - [tex]x_{1}[/tex]) , (x - [tex]x_{2}[/tex]) , --- --- --- --- , ( x - [tex]x_{n}[/tex]) are the factors of given binomial expression.

In the given question :

f(x) = 2x³ + 5x² - x - 6

If we put x = 1 , then we get f(x) = 0 . This implies the binomial factor will be (x - 1).

So ,

(ax² + bx + c ) ( x - 1) = 2x³ + 5x² - x - 6

ax³ + (b-a) x² + (c - b) x - c = 2x³ + 5x² - x - 6

If we compare both sides we get :

a  = 2 , b - a  = 5 , c - b  = 1 and c = 6

So , b = 7

We know that general form is given by :

ax² + bx + c

or

2x² + 7x + 6

Then :

Δ = 7² - 4 × 2 × 6 = 1

and other roots of solutions are :

x1 = [tex]\frac{-7 + \sqrt{1} }{4}[/tex] = [tex]\frac{-3}{2}[/tex]

x2 = [tex]\frac{-7 - \sqrt{1} }{4}[/tex] = -2

So , the other factors will be x + [tex]\frac{3}{2}[/tex] and x + 2.

Therefore , the correct options are option A and option D that is the factors of given binomial expressions are x  - 1 and x + 2.

Learn more about binomial factors here :

https://brainly.com/question/13692780

#SPJ2

Answer:

The mean and standard deviation of Y are, 94 and 0.28 respectively.

Step-by-step explanation:

Let the random variable , 'Test grades on the last statistics exam' be X.

Then according to the question,

E(X) = 78 ------------(1)

and

[tex]\sigma_{X}[/tex] = 0.14------------(2)

Now, according to the question,

Y = 2(X - 31)

⇒E(Y) = 2(E(X) - 31)

          = [tex]2 \times (78 - 31)[/tex]

          = 94  ----------------(4)

and

V(Y) = 4V(X)

⇒[tex]\sigma_{Y} = 2 \times \sigma_{X}[/tex]

⇒[tex]\sigma_{Y} = 2 \times 0.14[/tex] = 0.28

So, the mean and standard deviation of Y are, 94 and 0.28 respectively.

He has a 26% of getting a strike, which means he has a 74% chance of not getting a strike ( 100% - 26% = 74%).

Multiply the chance of not getting a strike by the number of attempts:

0.74 x 0.74 x 0.74 x 0.74 x 0.74 = 0.22

The answer is B) 0.22

The probability of making a free throw is 77%, the probability of not making one would be 23% ( 100% - 77% = 23%).

Add the probability of making the first one ( 0.77) by the probability of making the second one multiplied by the probability of missing the second one ( 0.77x 0.23)

0.77 + (0.77 x 0.23)

0.77 + 0.18 = 0.95

The answer is D) 95%

Final answer:

To find the probability that Keyshawn doesn't get a strike until after his first five attempts, we need to find the probability of him not getting a strike on each individual attempt. The probability that Keyshawn doesn't get a strike until after his first five attempts is 0.19. To find the probability that Coram makes his first free throw within his first two shots, we need to find the probability of him making a free throw on the first or the second shot. The probability that Coram makes his first free throw within his first two shots is 95%.

Explanation:

To find the probability that Keyshawn doesn't get a strike until after his first five attempts, we need to find the probability of him not getting a strike on each individual attempt. Since each attempt is independent, we can multiply the probabilities together.

The probability of him not getting a strike on each attempt is 1 - 0.26 (the probability of getting a strike). So the probability of not getting a strike on the first five attempts is (1 - 0.26) * (1 - 0.26) * (1 - 0.26) * (1 - 0.26) * (1 - 0.26).

Calculating this expression, we get:

(0.74) * (0.74) * (0.74) * (0.74) * (0.74) = 0.192.

So the probability that Keyshawn doesn't get a strike until after his first five attempts is approximately 0.192.

Therefore, the correct answer is A) 0.19.

To find the probability that Coram makes his first free throw within his first two shots, we need to find the probability of him making a free throw on the first or the second shot. These events are mutually exclusive, so we can add the probabilities together.

The probability of him making a free throw on the first shot is 0.77, and the probability of him missing the first shot and making a free throw on the second shot is (1 - 0.77) * 0.77. So the total probability is 0.77 + (1 - 0.77) * 0.77.

Calculating this expression, we get:

0.77 + 0.23 * 0.77 = 0.77 + 0.1771 = 0.9471.

So the probability that Coram makes his first free throw within his first two shots is approximately 0.9471.

Therefore, the correct answer is D) 95%.

Ground: y = 0

- 16t² + 128t + 50 = 0

Apply quadratic equation.

t = 0, 8 (rounded to the nearest second)

8 seconds

The time it will take for the object to hit the ground is approximately 4 seconds (rounded to the nearest second).

The given function a(t) = -16t^2 + 128t + 50 represents the approximate altitude, in feet, of an object released from the top of a building t seconds after it is released. To find the time it will take for the object to hit the ground, we need to find the value of t when the altitude is 0.

Setting a(t) = 0, we get:

-16t^2 + 128t + 50 = 0

Using the quadratic formula, we can solve for t.

t = (-b ± √(b^2 - 4ac)) / (2a)

Substituting the values a = -16, b = 128, and c = 50, we get t = 0.54 s or t = 3.79 s. Since the object is already at a height of 0 at t = 0 (the time of release), the time it will take for the object to hit the ground is approximately 4 seconds (rounded to the nearest second).

https://brainly.com/question/29545516

#SPJ3

Answer:

1 : -1

2:2

3:-5

4: 1/2

5: -3

6: -3/2

7: 1/2

8: -1/2

9: 1

10: 1/3

Step-by-step explanation:

well all u have to do is do rise over run, rise/run. find 2 points and go up according to how much it goes up and go left or right based on the graph. AND sometimes the slope will be negative like number 1.

The plot is missing. I have written the stem-leaf plot below.

Answer:

(a) 35 participants

(b) 22 participants traveled more than 14 km.

Step-by-step explanation:

Given:

(a)

The stem-leaf plot is given as:

12| 3  3  6 7 9 9

13| 1 1 4 5 5

14| 0 0 2 3 3 8 8 9

15| 2 2 2 2 2 3 5 5 7

16| 4 5 5 9 9

17| 3 5

The total number of numbers on the leaf side gives the total number of participants.

So, the number of participants is equal to the total number of elements on the leaf part. The total number of elements on the leaf part is 35.

Therefore, the total number of participants is 35.

(b)

Given:

12| 3  3   6 7 9 9

13| 1 1 4 5 5

14| 0 0 2 3 3 8 8 9

15| 2 2 2 2 2 3 5 5 7

16| 4 5 5 9 9

17| 3 5

One element of the stem part and one part of leaf part is represented as:

12 | 3 means 12.3 km

So, the number of walkers traveling more than 14.0 km is the list of all numbers greater than 14.0 km. Let us write all the numbers which are greater than 14.0 km. The numbers are:

14 | 2 3 3 8 8 9 = 6 participants

15 | 2 2 2 2 2 3 5 5 7 = 9 participants

16 | 4 5 5 9 9 = 5 participants

17 | 3 5 = 2 participants

Therefore, the total number is the sum of all the above which is equal to:

= 6 + 9 + 5 + 2 = 22 participants

Answer:

Step-by-step explanation:

She uses all the food to feed the dogs in 6 days. She feeds the with an equal amount of food in 6 days. This means that whatever amount of food she buys, the least amount she would feed the dogs with is 1/6 of that amount.

There are 31 cups of dog food. This means that the amount she would feed them with each day is

1/6 × 31 = 5.1 cups

So the least amount is 5 cups

Therefore,

The number of cups she feeds her dogs with would be between 5 and 6 cups.

Answer: 2432 visitors

Step-by-step explanation:

An employee of a museum surveyed a random sample of 350 visitors that came to the museum. Of the visitors that were surveyed, 266 stopped at the gift shop.

Since 266 out of 350 stopped at the gist shop, we find the fraction or decimal of people who stopped at the gift shop. This will give 266/350 = 19/25 or 0.76.

If 3200 visitors come to the museum, the expected number of people to stop at the gift shop are:

= 0.76 × 3200

= 2432

2432 visitors are expected to stop at the gift shop out of 3200 visitors.

Answer:

I will forward the challenge to the ISCAP.

Step-by-step explanation:

If the classifying agency does not provide a full response within 120 days, then as per my responsibility, I will forward the challenge to the ISCAP.

ISCAP is the Inter agency security classification appeals panel.

ISCAP is a deciding panel that decides on certain classification or declassification issues to its users, with a forum for further review.

Answer:

$25 each ticket!

Step-by-step explanation:

6*4=24

124-24=100

100/4=25

Answer:

x=4

Step-by-step explanation:

EF is half of the top and bottom lines comined so you would make an equation:

5x+8/2=2x+6

5x+8=4x+12

x=4