Please help IXL problem

Answer:

x = - 5 , x = 7

Step-by-step explanation:

to find the zeros, let y = 0 , that is

x² - 2x - 35 = 0

consider the factors of the constant term (- 35) which sum to give the coefficient of the x- term (- 2)

the factors are - 7 and + 5 , since

- 7 × + 5 = - 35 and - 7 + 5 = - 2 , then

x² - 2x - 35 = (x - 7)(x + 5) = 0

equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5

x - 7 = 0 ⇒ x = 7

The Coalition for Airline Passengers Rights, Health, and Safety averages 400 calls a day to help stranded travelers deal with airlines. The hotline is staffed for 16 hours a day.

To calculate the average number of calls in different time intervals and the probability of different events related to these calls.

Part 1:

a. 60-minute interval average number of calls: 400/16 = 25 calls

30-minute interval average number of calls: 25/2 = 12.5 calls

15-minute interval average number of calls: 12.5/2 = 6.25 calls

Part 2:

b. To find the probability of exactly 6 calls in a 15-minute interval, we can use the Poisson distribution formula. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of exactly 6 calls in a 15-minute interval is:

P(6 calls) = (e^-6.25)*(6.25^6)/6! = 0.0686

c. To find the probability of no calls in a 15-minute interval, we can use the Poisson distribution formula. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of no calls in a 15-minute interval is:

P(0 calls) = e^-6.25 = 0.0047

d. To find the probability of at least two calls in a 15-minute interval, we can use the cumulative distribution function of the Poisson distribution. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of at least two calls in a 15-minute interval is:

P(X >= 2) = 1 - P(0 calls) - P(1 call) = 1 - 0.0047 - (e^-6.25)*(6.25^1)/1! = 0.9906

Thus, the average number of calls in a 60-minute interval is 25, in a 30-minute interval is 12.5, and in a 15-minute interval is 6.25. The probability of exactly 6 calls in a 15-minute interval is 0.0686, the probability of no calls in a 15-minute interval is 0.0047, and the probability of at least two calls in a 15-minute interval is 0.9906.

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Therefore, at least 49 street lights can be installed along one side of the street with equal distance between the lights.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The equals sign indicates that the two expressions are equal, and the goal of solving the equation is to find the value of x that makes this statement true. Equations can be solved using various algebraic techniques, such as simplifying and rearranging the expressions, applying operations to both sides of the equation, and factoring or expanding expressions. Solving an equation involves finding the values of the variables that make the equation true.

Here,

The distance between point A and B is AB, and the distance between point B and C is BC. Let's assume that the distance between each street light is "d".

Since there must be a street light at points A, B, and C, there will be a total of two gaps between these three street lights, which are AB and BC. Thus, the number of street lights required is equal to the sum of the lengths of AB and BC, divided by the distance "d" between the street lights, plus 1 for the street light at point B.

So, the total number of street lights required is

Number of street lights = (AB + BC) / d + 1

We know that AB = 1170 m and BC = 1625 m, and the distance between each street light should be equal. Therefore, we need to find the greatest common factor (GCF) of 1170 and 1625 to determine the distance between each street light.

1170 = 2 x 3 x 3 x 5 x 13

1625 = 5 x 5 x 13

The GCF of 1170 and 1625 is 65, which means the distance between each street light should be 65 meters.

Now we can calculate the total number of street lights required:

Number of street lights = (1170 + 1625) / 65 + 1

= 49

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Answer: \(g(-2)=2a\)

Step-by-step explanation:

\((f \cdot g)(-2)=f(-2)g(-2)\\\\\therefore a \cdot g(-2)=2a^2 \implies g(-2)=2a\)

The function g(-2) from the given functions is 2a.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given functions are f(-2)=a and (f·g)(-2)=2a².

Here, (f·g)(-2)=2a²

f(-2)·g(-2)=2a²

a·g(-2)=2a²

g(-2)=2a²/a

g(-2)=2a

Therefore, the function g(-2) is 2a.

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Answer:

A

Step-by-step explanation:

6/x* 5/(2x+1) = 30/ 2x^2+x

Okaayyy

Set B has the greater mode

x = 2y and x*$10 + y*8 = $84 are the required system of equations and when we solve it, we can observe that he spent 6 hours cleaning vehicles and 3 hours gardening.

A group of equations comprising one or more variables is known as a system of equations.

The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations.

We must first define the variables:

x is the amount of time spent cleaning autos.

x = the number of landscaping hours.

Since we know Alexander spent twice as much time cleaning vehicles as he did landscaping, we can say:

x = 2y

Additionally, we know that he made $84 in total, so:

x*$10 + y*8 = $84

The set of equations is thus:

x = 2y

x*$10 + y*8 = $84

We simply swap the first equation with the second one to answer it:

(2y)*$10 + y*8 = $84

y*$28 = $84

y = $84/$28 = 3

He thus spent three hours landscaping, and:
x = 2*y = 2*3 = 6

6 hours washing cars.

Therefore, x = 2y and x*$10 + y*8 = $84 are the required system of equations and when we solve it, we can observe that he spent 6 hours cleaning vehicles and 3 hours gardening.

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Answer:

870.1

Step-by-step explanation:

When you round it you get 870.1 but without rounding the answer is 970.056..

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The solution of measure of angle e is,

⇒ e = 58 degree

We have to given that,

Two lines are intersect each other.

Hence, By definition of linear pair angle, we get;

⇒ e + 122 = 180

Subtract 122 from both sides to isolate e.

This gives us,

⇒ e = 180 - 122

⇒ e = 58

Therefore, The solution of measure of angle e is,

⇒ e = 58 degree

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Answer:

The answer is C

Step-by-step explanation:

So in picture shows that it goes down so it's -1 and 2 to the left so it's -2. So if we check A P(0,-1) so as you can see the point doesn't stay on the same spot and it doesn't goes to the left side just 1 time so A is not it. B- doesn't goes down 2 times so is not B. D- doesn't go down 3 times. so it's C. :)

Answer:  The Answer Is Not Letter B or Letter C

A. P′ (0, −1)

Step-by-step explanation:

Math 370, Actuarial Problemsolving Problems on General Probability Rules

Problems on general probability rules, independence,

conditional probability

1. Assuming A, B, C are mutually independent, with P(A) = P(B) = P(C) = 0.1,

compute:

(a) P(A ∪ B) Solution: P(A) + P(B) − P(A)P(B) = 0.19

(b) P(A ∪ B ∪ C)

Solution: By formula the formula for P(A∪B∪C) and indep., P(A∪B∪C) =

3 · 0.1 − 3 · 0.1

2 + 0.1

3 = 0.271

(c) P(A \ (B ∪ C))

Solution: P(A) − P(A ∩ B) − P(A ∩ C) + P(A ∩ B ∩ C) = 0.081

2. Given that P(A) = 0.3, P(A|B) = 0.4, and P(B) = 0.5, compute:

(a) P(A ∩ B) Solution: P(A|B)P(B) = 0.4 · 0.5 = 0.2

(b) P(B|A) Solution: P(B ∩ A)/P(A) = 0.2/0.3 = 0.666

(c) P(A0

|B) Solution: P(A0 ∩ B)/P(B) = ((P(B) − P(A ∩ B))/P(B) = 0.6

(d) P(A|B0

) Solution: P(A∩B0

)/P(B0

) = (P(A)−P(A∩B))/(1−P(B)) = 0.2

3. Assume A and B are independent events with P(A) = 0.2 and P(B) = 0.3. Let C be

the event that at least one of A or B occurs, and let D be the event that exactly

one of A or B occurs.

(a) Find P(C).

Solution: The event C is just the union of A and B, so P(C) = P(A ∪ B) =

P(A) + P(B) − P(A)P(B) = 0.44

1

Math 370, Actuarial Problemsolving Problems on General Probability Rules

(b) Find P(D).

Solution: Drawing a Venn diagram, we see that D consists of the union of

A and B minus the overlap. Thus, P(D) = P(A ∪ B \ A ∩ B) = P(A ∪ B) −

P(A)P(B) = 0.38

(c) Find P(A|D) and P(D|A).

Solution: P(A|D) = P(A ∩ D)/P(D) = P(A \ A ∩ B)/P(D) = (0.2 − 0.2 ·

0.3)/0.38 = 7/19 . P(D|A) = P(A\A∩B)/P(A) = (0.2−0.2 · 0.5)/0.2 = 0.7 .

(d) Determine whether A and D are independent.

Solution: A and D are not independent since by the previous part, P(A|D) 6=

P(A).

Alternative solution: From above, P(A∩D) = 0.14, P(A)P(D) = 0.2·0.38 =

0.076, so P(A ∩ D) 6= P(A)P(D), and therefore A and D are not independent.

4. Given that P(A ∪ B) = 0.7 and P(A ∪ B0

) = 0.9, find P(A).

Solution: By De Morgan’s law, P(A0 ∩ B0

) = P((A ∪ B)

0

) = 1 − P(A ∪ B) =

1 − 0.7 = 0.3 and similarly P(A0 ∩ B) = 1 − P(A ∪ B0

) = 1 − 0.9 = 0.1. Thus,

P(A0

) = P(A0 ∩ B0

) + P(A0 ∩ B) = 0.3 + 0.1 = 0.4, so P(A) = 1 − 0.4 = 0.6 .

5. Given that A and B are independent with P(A) = 2P(B) and P(A ∩ B) = 0.15, find

P(A0 ∩ B0

).

Solution: By independence and the given data, 0.15 = P(A ∩ B) = P(A)P(B) =

2P(B)

2

, so P(B) = √

0.075 = 0.273, and P(A) = 2P(B) = 0.546. Hence P(A0∩B0

) =

P(A0

)P(B0

) = (1 − 0.546)(1 − 0.273) = 0.33 . (Note the use of the “independence of

complements” property here.)

6. Given that A and B are independent with P(A ∪ B) = 0.8 and P(B0

) = 0.3, find

P(A).

Solution: We have P(B) = 1 − 0.3 = 0.7 and 0.8 = P(A) + P(B) − P(A ∩

B) = P(A) + P(B) − P(A)P(B) = P(A)(1 − 0.7) + 0.7. Solving for P(A) gives

P(A) = (0.8 − 0.7)/0.3 = 0.33 .

2

Math 370, Actuarial Problemsolving Problems on General Probability Rules

7. Given that P(A) = 0.2, P(B) = 0.7, and P(A|B) = 0.15, find P(A0 ∩ B0

).

Solution: By De Morgan’s Law, P(A0 ∩ B0

) = P((A ∪ B)

0

) = 1 − P(A ∪ B) =

1−P(A)−P(B)+P(A∩B). Using the given values of P(A) and P(B) and P(A∩B) =

P(A|B)P(B) = 0.15 · 0.7 = 0.105 (the multiplication formula), we get P(A0 ∩ B0

) =

1 − 0.2 − 0.7 + 0.105 = 0.205 .

8. Given P(A) = 0.6, P(B) = 0.7, P(C) = 0.8, P(A ∩ B) = 0.3, P(A ∩ C) = 0.4,

P(B ∩ C) = 0.5, P(A ∩ B ∩ C) = 0.2, find P(A ∩ B0 ∩ C

0

).

Solution: If A, B0 and C

0 were independent, we could apply the product formula,

and the answer would be immediate, but we don’t know this (in fact, they are not).

However, from a Venn diagram we see that P(A∩B0∩C

0

) is equal to to P(A)−P(A∩

B)−P(A∩C)+P(A∩B∩C). Inserting the given values, we get 0.6−0.3−0.4+0.2 =

0.1 as answer.

Answer:

8m=10m

Step-by-step explanation:

The distance between the two points is

d = √( -2-x)² + (3 -y)² OR d = √ (x+2)² + (y-3)².

Distance between two points is the length of the line segment that connects the two points in a plane.

The distance between two points is expressed as;

d = √ (X-x )² + (Y-y)²

X = -2

x = x

Y = 3

y = y

Therefore the distance between the two points is

d = √( -2-x)² + (3 -y)²

or it can also be written in this form

d = √ x-(-2)² + (y-3)²

d = √ x+2)² + (y-3)²

therefore the model of the distance between the two points can be

d = √( -2-x)² + (3 -y)² OR d = √ (x+2)² + (y-3)².

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Answer:

no fred is not correct

Step-by-step explanation:

so u say

5/8×6/1

then u say 5×6=30

then u say 8×1=8

then u say 30÷8= 3.75

so yr answer is =3.75

hope u understand

Answer:

170, 171, 172

Step-by-step explanation:

x + x + 1 + x + 2 = 513

3x + 3 = 513

3x = 510

x = 170

x + 1 = 171

x + 2 = 172

Angie decorates 8 cupcakes after putting 4 sugar flowers on each cupcake.

To find the number of cupcakes c Angie decorates, we can use the equation:4c = 32where 'c' is the number of cupcakes Angie decorates.

4 represents the number of sugar flowers Angie puts on each cupcake, and 32 is the total number of sugar flowers Angie puts on the cupcakes.

To solve this equation for c, we need to isolate c on one side of the equation. We can do this by dividing both sides of the equation by 4. This gives us:c = 8

Therefore, Angie decorates 8 cupcakes.Here's how we get to this answer:4c = 32Divide both sides by 4 to isolate c:c/4 = 32/4c = 8

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Answer:

2.98

Step-by-step explanation:

First find 3% of 16.05 which is 0.48.

Then add 0.48 to 16.05 which is 16.53.

Then multiply .18 by 16.53 which gets you 2.98

Hope it helps

Answer:

To find the amount of the sales tax, we need to multiply the bill amount by the tax rate of 3% or 0.03:

Sales tax = 0.03 x $16.05 = $0.48

To find the total amount of the bill after the sales tax was added, we need to add the bill amount to the sales tax:

Total bill = $16.05 + $0.48 = $16.53

To find the amount of the tip, we need to calculate 18% of the total bill after the sales tax was added:

Tip = 0.18 x $16.53 = $2.98

Rounding to the nearest cent, Penelope left a tip of $2.98.

Step-by-step explanation:

Work Shown:

Complementary angles add to 90 degrees.

A+B = 90

(3x+18)+(2x+17) = 90

5x+35 = 90

5x = 90-35

5x = 55

x = 55/5

x = 11

Then we can determine each angle:

As a check: A+B = 51+39 = 90 to confirm the answer.

Answer:

-2

Step-by-step explanation:

Answer:

15.98 dollars

Step-by-step explanation:

its really easy

we need to subtract the total amount that she has spent from the total amount that she had in her purse

the total amount in Megan's purse=$45.12

total amount that Megan spent=$7.89+$21.25 =$29.14

now,

the exact amount that Megan has left = $45.12-$29.14=$15.98

Simplify the expression.

− 52

Answer:

Solution in photo

Step-by-step explanation:

Step-by-step explanation:

a) 11*5=55

15*5=75

8*5+5=45

b) No, because (55+75+45=175°) and the perimeter of a triangle is 180°

Answer:

21 years

Step-by-step explanation:

Given

\(Initial\ Height = 4\frac{1}{2}\)

\(Final\ Height = 40\)

\(Difference = 1\frac{3}{4}\)

Required

Determine the years it'll take to grow to the final height

This question depicts arithmetic progression and will be solved using

\(T_n = a + (n - 1)d\)

Where

\(T_n = 40\)

\(a = 4\frac{1}{2}\)

\(d = 1\frac{3}{4}\)

Substitute these values in the given formula;

\(40 = 4\frac{1}{2} + (n - 1)1\frac{3}{4}\)

Convert all fractions to decimal

\(40 = 4.5 + (n - 1) * 1.75\)

Open Brackets

\(40 = 4.5 + 1.75n - 1.75\)

Collect Like Terms

\(1.75n = 40 - 4.5 + 1.75\)

\(1.75n = 37.25\)

Divide both sides by 1.75

\(n = \frac{37.25}{1.75}\)

\(n = 21.2857142857\)

\(n = 21\) (Approximated)

The number of years it will take for the tree to have a height greater than 40 feet is 23 years

Given:

Height of the tree = 4 1/2 feet

Growth rate per year = 1 3/4 feet

Expected growth rate = 40 feet

Expected Number of years = y

The inequality:

4 1/2 + 1 3/4y > 40

Subtract 4 1/2 from both sides

1 3/4y > 40 - 4 1/2

7/4y > 40 - 9/2

7/4y > (80-9)/ 2

7/4y > 79/2

divide both sides by 7/4

y > 79/2 ÷ 7/4

y > 79/2 × 4/7

y > (79×4) ) (2×7)

y > (316) / 14

y > 22.57142857142857

Approximately,

y > 23 years

Therefore, number of years it will take for the tree to have a height greater than 40 feet is 23 years

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Based on the calculations that 300 is 40%, 375 is considered 50% or halfway.. in this case, we must multiply 375 by 2 and we will discover how many students were surveyed:

375 x 2 = 750

To solve this problem, we can use the formula for probability:

P(event) = number of favorable outcomes / total number of outcomes

First, let's find the total number of outcomes. We are selecting 4 balls from 11 without replacement, so the total number of outcomes is:

11C4 = (11!)/(4!(11-4)!) = 330

where nCr is the number of combinations of n things taken r at a time.

Now let's find the number of favorable outcomes for each part of the problem.

Part 1: Exactly two white balls and two red balls

To find the number of favorable outcomes for this part, we need to select 2 white balls out of 6 and 2 red balls out of 5. The number of ways to do this is:

6C2 * 5C2 = (6!)/(2!(6-2)!) * (5!)/(2!(5-2)!) = 15 * 10 = 150

So the probability of selecting exactly two white balls and two red balls is:

P(2W2R) = 150/330 = 0.45 (rounded to two decimal places)

Part 2: At least two white balls

To find the number of favorable outcomes for this part, we need to consider two cases: selecting 2 white balls and 2 red balls, or selecting 3 white balls and 1 red ball.

The number of ways to select 2 white balls and 2 red balls is the same as the number of favorable outcomes for Part 1, which is 150.

To find the number of ways to select 3 white balls and 1 red ball, we need to select 3 white balls out of 6 and 1 red ball out of 5. The number of ways to do this is:

6C3 * 5C1 = (6!)/(3!(6-3)!) * (5!)/(1!(5-1)!) = 20 * 5 = 100

So the total number of favorable outcomes for selecting at least two white balls is:

150 + 100 = 250

And the probability of selecting at least two white balls is:

P(at least 2W) = 250/330 = 0.76 (rounded to two decimal places)

Answer: Option A.

Step-by-step explanation:

Suppose you have a rectangle in the plane X-Y, such that one of the vertices of the rectangle is on the point (0,0) and the rectangle has sides parallel to both x-axis and y-axis.

Now, you rotate it around the y-axis. The created figure will be a cylinder with a radius and height depending on the measures of the original rectangle.

Now, if you cut it horizontally (this means that you have a cut parallel to the x-z plane) is equivalent to have a view of the cylinder from the top (as if you where on the positive y-axis), and this figure will be a circle, so the correct option is A:

According to the information, Hannah donated b/50 books in total.

First, we need to find the average number of books donated by each student. We can do this by dividing the total number of books donated by the number of students:

Hannah donated 3 times this amount, so we can multiply the average by 3 to find how many books she donated:

Simplifying this expression, we get:

Therefore, Hannah donated b/50 books in total.

Note: This question is in Spanish. Here is the question in English:

Hannah's school organized a book donation. There are 150 students in her school who donated a total of b books. Hannah donated 3 times the average number of books donated by each student. How many books did Hannah donate?

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