• Nabeel's sand box is 7 feet wide, 5 feet long and 2 feet deep
What is the volume of the sand box?

Answers

Answer 1
The volume is 70.

When measuring volume you do
“Hight • Width • Length”

Related Questions

Math write your answer step by step

Answers

Find the length of the shaded bits

Help with math problems

Answers

The graph that shows the solution of the inequality 7 ≥ n + 5 is the graph of option D.

What is the solution to the inequality 7 ≥ n + 5?

The solution to the inequality 7 ≥ n + 5 is as follows:

7 ≥ n + 5

7 - 5 ≥ n

2 ≥ n

n ≤ 2

2, Let p be the number of pages Eduardo wrote before today. Then, the inequality that represents the situation is:

p + 16 > 50

To solve for p, first subtract 16 from both sides of the inequality:

p + 16 - 16 > 50 - 16

p > 34

Therefore, Eduardo wrote at least 34 pages before today.

Let r be the number of rows of seeds the farmer needs to plant. Then, the equation that represents the situation is:

6.5r ≥ 52

divide both sides of the equation by 6.5:

r ≥ 8

Therefore, the farmer needs to plant at least 8 rows of seeds to harvest at least 52 bushels of tomatoes.

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The figure below is a square pyramid.
What is the surface area of the figure?
51 square meters
96 square meters
120 square meters
180 square meters
5 m
A
6 m

Answers

The surface area of the square pyramid with a side length of 6 and a slant height of 5 is 96 square units.

How to find surface area?

To calculate the surface area of a square pyramid, we need to find the area of the square base and the area of each triangular face.

The formula for the surface area of a square pyramid is:

[tex]S = (a^2) + 2as[/tex]

where a is the length of one side of the square base and s is the slant height.

Plugging in the given values, we get:

[tex]S = (6^2) + 2(6)(5)[/tex]

[tex]S = 36 + 60[/tex]

[tex]S = 96[/tex]

Therefore, the surface area of the square pyramid with a side length of 6 and a slant height of 5 is 96 square units.

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Solve the systems by graphing.

Y=1/2 x-5
y=-X+4

Answers

Answer:  (6, -2)

Step-by-step explanation:

         First, we will graph these equations. See attached. One has a y-intercept of -5 and then moves 2 units right for every unit up (we get this from the slope of 1/2). The other has a y-intercept of 4, and moves right one unit for every unit down (we get this from the slope of -1).

         The point of intersection is the solution, this is the point at which both graphed lines cross each other. Our solution is:

                         (6, -2)     x = 6, y = -2

I NEED HELP WITH Assessment: Plot Twists

Answers

Note that the line plot or number line for the data above is given as attached.

What is the explanation for the above response?

1) To create an inequality for a line plot using the given data set, we can use the minimum and maximum distances as the endpoints of the inequality.

The minimum distance is 1 3/8, which is equivalent to 1.375 miles. The maximum distance is 3 1/4, which is equivalent to 3.25 miles.

Therefore, the inequality can be written as:

1.375 ≤ x ≤ 3.25

where x represents the distance of a ski trail in miles.

This inequality states that any value of x (distance of a ski trail) that is between 1.375 and 3.25, inclusive, is a valid value for the data set.


2. The total number of ski trails is 12.

3. The difference in length between the longest ski trail (3 1/4) and the shortest ski trail (1 3/8) is: 3 1/4 - 1 3/8 = 1 7/8

4. The total length of the ski trails that are 2 7/8 is:

2 7/8 + 2 7/8 + 2 7/8 = 8 1/4

5. The sum of the lengths of the shortest (1 3/8) and the longest (3 1/4) ski trails is:

1 3/8 + 3 1/4 = 4 5/8

6. Sam is correct. The longest ski trail is 3 1/4 miles and the shortest ski trail is 1 3/8 miles, so:

3 1/4 > 3 * 1 3/8

10 1/4 > 4 1/8

2.5 > 1

Therefore, the longest ski trail is indeed more than three times the length of the shortest ski trail.

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What is the solution to the system of equations below? x + 3 y = 15 and 4 x + 2 y = 30 (4, 10) (3, 6) (6, 3) (10, 4)

Answers

Answer:

x=15-3y

in second equation,

4x+2y=30

2(2x+y)=30

2x+y=15

Now,putting the value of x from above

2×(15-3y)+y=15

30-6y+y=15

30-15=5y

y=3

Then,

x=15-3×3

x=6

#(6,3) is ans

Answer:

(6,3)

Step-by-step explanation:

Question 10
Clarke is buying clothes for school.
• He buys 2 pairs of pants for $25.50 each and 2 shirts for $16 each.
The shirts are on sale for 25% off.
• He also has a coupon for 20% off the entire purchase.
How much will Clarke pay for the clothes before adding taxes?

Answers

Answer:

$60

Step-by-step explanation:

2*25.50=51

25% of 16=4

16-4=12

12*2=24

51+24=75

20% of 75=15

75-15 =

60

The coordinates at the end of
the diameter of a circle are
(3,0) and (-5,-4). Find the
equation of the circle.

Answers

Answer:

[tex](x+1)^{2} +(y+2)^{2} =20[/tex]

Step-by-step explanation:

Using the mid point formula to find the center of the circle:

midpoint = [tex](\frac{x_{1} +x_{2} }{2} ,\frac{y_{1} +y_{2} }{2} )[/tex]

Midpoint = [tex](\frac{3+-5}{2} ,\frac{0+-4}{2} )[/tex]

Midpoint = [tex](-1,-2)[/tex]

The midpoint is the same as the centre of the circle


Find the distance(the diameter of the circle) between those two points to find the radius:

Distance formula = [tex]\sqrt{(y_{2}-y_{1} )^{2} +(x_{2} -x_{1} ) ^{2} }[/tex]

Distance formula = [tex]\sqrt{(-4-0)^{2} +(-5-3)^{2} }[/tex]

Distance formula = [tex]\sqrt{16+64}[/tex]

Distance formula = [tex]\sqrt{80}[/tex]

So,the diameter is [tex]\sqrt{80}[/tex] and to find the radius we need to divide the diameter by two

Radius = [tex]\frac{\sqrt{80} }{2}[/tex]

Radius = [tex]2\sqrt{5}[/tex]


the equation of circle:

Radius = [tex]2\sqrt{5}[/tex]

Center = (-1,-2)

[tex](x-h)^{2} +(y-k)^{2} =r^{2}[/tex]

[tex](x- -1)^{2} +(y- - 2)^{2} =(2\sqrt{5} )^{2}[/tex]

[tex](x+1)^{2} +(y+2)^{2} =20[/tex]

Suppose you model a game of chance with a discrete probability distribution. Let X be the net amount of money won or lost by the player. Let P ( X ) be the probability of the corresponding outcome. The three events are as follows: There is a 23% chance the player wins 5 dollars. There is a 29% chance the player breaks even. There is a 48% chance the player loses 3 dollars. Complete the table below to model the scenario

Answers

Mathematicians have used probability to determine how likely certain events are to occur. The possible values of  X will be 10, 0, -5 with following probabilities:

P(X = 10 ) = 0.23

P(X = 0 ) = 0.48

P(X = -5) = 0.29

What in mathematics is probability?

Probability is the ability to happen. . From 0 to 1 is used to express the value. Whenever we are unsure of how an event will turn out, we can talk about the probabilities of various outcomes, or how likely they are. The study of probability-based events is often known as statistics. The amount of favorable outcomes and the overall number of outcomes thus affect how likely an event is to occur. The probability is typically expressed as a ratio between the number of positive outcomes and all of the outcomes in the sample space.

Given:

The probability distribution of X can be represented as:

X      P(X=x)

-5      0.29

0       0.48

10      0.23

The outcomes is attached as table below.

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The complete question is:

The table below to model the scenario is attached below:

present age of father is four times the age of his son when the son will be as old as his father is now the sum of there is will be 99. find their present age

Answers

Let the present age of the son be x.
Then, the present age of the father is 4x.

We know that when the son will be as old as his father is now, the sum of their ages will be 99. Let y be the number of years until this happens. Then, the son's age will be x+y and the father's age will be 4x+y.

According to the given condition:

x+y + (4x+y) = 99

Simplifying the above equation, we get:

5x + 2y = 99

We also know that y = 4x - x = 3x (since the father is currently three times as old as the son)

Substituting y = 3x in the above equation, we get:

5x + 2(3x) = 99

11x = 99

x = 9

Therefore, the present age of the son is x = 9 years and the present age of the father is 4x = 36 years.

Question 5 Among various ethnic groups, the standard deviation of heights is known to be approximately three inches. We wish to construct a 95% confidence interval for the mean height of male Swedes. Forty- eight male Swedes are surveyed. The sample mean is 72 inches. Round answers to 3 decimal places. a. Find the following: i. I = ii. σ = iii. n = b. Construct a 95% confidence interval for the population mean height of male Swedes. i. State the confidence interval. CI: ii. Calculate the error bound. EBM: c. What will happen to the size of the confidence interval if 1,000 male Swedes are surveyed instead of 48? The confidence interval will Select an answer Question Help: VIDEO Submit Question​

Answers

As a result, the range of the population's mean height for male Swedes is between 70.331 and 73.669 inches.

what is range ?

The range of a function or relation in mathematics is the collection of all feasible output values (also known as the dependent variable). It is the collection of all possible values that such a function can have. For instance, since its function can output anything non-negative real integer, f(x) = x2 would have a range of all non-negative real numbers. The range is frequently stated as a collection of numbers or as a circle, and it may be either finite or infinite.

given

For the population mean height of male Swedes, the following formula provides a 95% confidence interval:

where n is the sample size, x is the sample mean, y is the standard deviation of height, n* is the z-score corresponding to a 95% confidence level, which is 1.96, and z* is the z-score.

By entering the specified values, we obtain:

CI = 72 ± 1.96 * (3/√48)

CI = (70.331, 73.669) (70.331, 73.669)

As a result, the range of the population's mean height for male Swedes is between 70.331 and 73.669 inches.

By multiplying the critical value (1.96), by the standard error, one may determine the error bound:

EBM = 1.96 * (3/√48) ≈ 1.382

The error bound is therefore roughly 1.382 inches.

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perform the operations and simply so there are no quotients

sin theta/ 1+ sin theta - sin theta/1-sin theta

Answers

Answer: We can simplify the expression as follows:

sin theta / (1 + sin theta) - sin theta / (1 - sin theta)

= [(sin theta)(1 - sin theta) - (sin theta)(1 + sin theta)] / [(1 + sin theta)(1 - sin theta)]

= [(sin theta - sin^2 theta) - (sin theta + sin^2 theta)] / [1 - sin^2 theta]

= -2 sin theta / cos^2 theta

= -2 tan theta

So the simplified expression is -2 tan theta, with no quotients.

Step-by-step explanation:

Who was Leonhard Euler?
What was one of the significant contributions he made to the field of mathematics that we explored in this module (sequences and series)?
Give a mathematical example and explain.

Answers

Answer:

Leonhard Euler was a Swiss mathematician who lived from 1707-1783. He made significant contributions to many areas of mathematics, including number theory, calculus, and geometry.

One of Euler's significant contributions to the field of sequences and series is his work on the summation of infinite series. In particular, he developed a method for finding the sum of an infinite geometric series, which has the form:

a + ar + ar^2 + ar^3 + ...

where a is the first term, r is the common ratio, and the series continues infinitely.

Euler's method for finding the sum of this series is as follows:

If |r| < 1, then the sum of the series is:

a / (1 - r)

For example, let's consider the infinite geometric series:

2 + 4 + 8 + 16 + ...

In this series, a = 2 and r = 2. Since |r| < 1, we can use Euler's formula to find the sum:

sum = a / (1 - r)

= 2 / (1 - 2)

= -2

Therefore, the sum of the infinite geometric series 2 + 4 + 8 + 16 + ... is -2.

Euler's formula is just one example of his many contributions to mathematics. His work on sequences and series laid the foundation for many important concepts in calculus, and his ideas continue to influence the field of mathematics today.

The answer to this question

Answers

So, the corresponding point for g(x) on the graph of f(x) is (-3/2, F (-3/2)).

What is function?

In mathematics, a function is a relation between a set of inputs (the function's domain) and a set of possible outputs (the function's range) with the property that each input is associated with exactly one output.

Functions are often described using a formula or an equation, such as [tex]f(x) = x^2,[/tex] where "f" is the name of the function, "x" is the input variable, and "[tex]x^2[/tex]" is the output. The value of the function for a specific input value of "x" can be found by substituting that value into the equation.

Functions are used in many areas of mathematics, science, engineering, and economics to model real-world phenomena, analyze data, and solve problems. They are also important in computer science, where they are used to write algorithms and design software.

if we know the point (x, y) on the graph of a function f(x), we can find the corresponding point for the function g(x) = F(-1/2x) by substituting -1/2x for x in the expression for f(x) and simplifying. That is, we can find the point (u, v) on the graph of g(x) such that u = -1/2x and v = F(-1/2x), where (x, y) is a point on the graph of f(x).

For example, if f(x) = x^2 and the point (3, 9) is on the graph of f(x), then we can find the corresponding point for g(x) = F(-1/2x) by substituting -1/2x for x in the expression for f(x) and simplifying:

[tex]u = -1/2x = -1/2(3) = -3/2\\v = F(-1/2x) = F(-1/2(3)) = F(-3/2)[/tex]

So, the corresponding point for g(x) on the graph of f(x) is (-3/2, F(-3/2)). However, without knowing the specific definition of fix,

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Mary has $20 .she wants to buy a book that is marked do 30% from it's original price of $28. It the sales tax is 2.5%,does Mary have enough money to buy the book

Answers

Answer:

she does not have enough!

Step-by-step explanation:

thirty percent of $28 is $8.4, so you would subtract the two leaving you with $19.6

2.5 sales tax of $19.6 is $0.49

Adding those two the total comes to $20.09 which is just over the budget!

Answer:  She does not have enough money.

She needs 9 cents (aka $0.09)

========================================================

Explanation:

A discount of 30% means Mary would pay the remaining 70% (because 100-30 = 70)

The decimal form of 70% is 0.70

Let A = 0.70 since we'll use it later.

An increase of 2.5% means we will also have the multiplier 1.025; which you can think of it like saying 100% + 2.5% = 1 + 0.025 = 1.025

Let B = 1.025 since we'll use it later

Multiply the values of A and B to get: 0.70*1.025 = 0.7175

This is the net multiplier when combining the 30% discount and 2.5% tax.

The original price $28 then becomes 0.7175*28 = 20.09 which is 9 cents (aka $0.09) over the goal of $20

Therefore, Mary does not have enough money to buy the book. She'll need that remaining 9 cents.

Apply the formula d=r⋅t to answer the following questions.

Part A

Tom drove a total of 150 miles in 3 hours. Assuming he drove at a constant speed, what speed was Tom driving?
______ miles per hour
Question 2
Part B

Zac drove for 2.5 hours at a constant speed of 40 miles per hour. How many miles did he drive?
______ miles
Question 3
Part C

Dan drove 130 miles at a constant speed of 65 miles per hour. How many hours did he drive?
_____ hours

Answers

Using the formula d = rt we have: Part A: Tom was driving at a speed of 50 miles per hour. Part B: Zac drove 100 miles. Part C: Dan drove for 2 hours.

What is distance formula?

The link between distance, rate, and time is demonstrated by the equation d = r*t. The product of the rate (r) and the time (t) yields the distance (d) (t). In other words, the velocity of motion and the amount of time spent travelling affect the distance covered. Assuming that the time spent travelling is constant, increasing the rate of movement will result in an increase in the amount of distance travelled in a given amount of time. According to this, as journey duration increases, so does the distance travelled.

The given formula is d = r(t).

Part A:

Tom drove a total of 150 miles in 3 hours, so:

150 miles = r * 3 hours

r = 50 miles per hour

Part B:

constant speed of 40 miles per hour for 2.5 hours, so:

d = 40 miles per hour * 2.5 hours

d = 100 miles

Part C:

constant speed of 40 miles per hour for 2.5 hours, so:

130 miles = 65 miles per hour * t

t = 130 miles / 65 miles per hour

t = 2 hours

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Mar 30, 11:25:22 PM
Omar owns a small business selling bagels. He knows that in the last week 91
customers paid cash, 8 customers used a debit card, and 27 customers used a
credit card.
If next week, he is expecting 1900 customers, about how many would you
expect to pay with a credit card? Round your answer to the nearest whole
number.

Answers

Rounding this to the nearest whole number, we can estimate that about 407 customers would pay with a credit card next week.

How to estimate number of customers?

To estimate the number of customers who would pay with a credit card next week, we can use the proportion of customers who paid with a credit card in the last week as a guide.

First, we need to find the total number of customers who visited Omar's business in the last week:

Total customers = Cash customers + Debit card customers + Credit card customers

Total customers = 91 + 8 + 27

Total customers = 126

Next, we can find the proportion of customers who paid with a credit card:

Proportion of credit card customers = Credit card customers / Total customers

Proportion of credit card customers = 27 / 126

Proportion of credit card customers = 0.2143

Now, we can estimate the number of customers who would pay with a credit card next week by multiplying the total number of expected customers by the proportion of credit card customers from the last week:

Expected credit card customers = Total expected customers x Proportion of credit card customers

Expected credit card customers = 1900 x 0.2143

Expected credit card customers = 407.17

Rounding this to the nearest whole number, we can estimate that about 407 customers would pay with a credit card next week.

However, it is important to note that this estimate is based on the assumption that the proportion of customers paying with a credit card remains the same next week. Factors such as changes in consumer behavior or market conditions may affect this proportion, and hence, the accuracy of the estimate.

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Writing & Solving Equations


1. Sofia paid a total of $365 for her accommodation in Bali, Indonesia. Sofia will be
spending 5 nights at the hotel. The cost per night is $59 US Dollars.


a) Write an equation to help Sofia figure out how much money was charged in fees.


b) Determine the amount of money charged for fees. Show all your work to justify
your answer.
1

Answers

After answering the presented question, we can conclude that variable

a) equation to help Sofia figure out how much money was charged in fees is 365 = 59 × 5 + f

b) the amount of money charged for fees is $70.

What is a Variable?

A variable is something that can be altered in the context of a mathematical notion or experiment. Variables are frequently denoted by a single symbol. The characters x, y, and z are frequently used as generic variables symbols. Variables are qualities with a wide range of values that can be investigated. Size, age, money, where you were born, academic position, and type of housing are just a few examples. Variables can be classified into two major groups using both numerical and categorical methods.

a) Total cost = Cost per night × Number of nights + Fees

365 = 59 × 5 + f

b) Solving for f, we get:

f = 365 - 295

f = 70

Therefore, the amount of money charged for fees is $70.

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A skeleton was found at an archaeological dig. A technique used for estimating age indicated that the skeleton was 60 centuries old,
plus or minus 0.8 centuries. According to this estimate, what is the greatest possible age of the skeleton?
The greatest possible age of the skeleton is centuries.

Answers

To find the greatest possible age of the skeleton, we need to add the error to the estimate:

60 centuries + 0.8 centuries = 60.8 centuries

Therefore, the greatest possible age of the skeleton is 60.8 centuries.

HELP PLEASEEEE QUICK!! THANK YOU SM♥️

Select numbers to complete the
three expressions so that each is
equivalent to 24x + 36y.

1. 12 (— x+—y) 2. —(4x+—y) 3.—(—x+12y)
0. 0. 0
1. 1. 1
2. 2. 2
3. 3. 3
4. 4. 4
5. 5. 5
6. 6. 6
7. 7. 7
8. 8. 8
9. 9. 9.

Answers

After answering the presented question, we can conclude that As a equation result, for any x and y values, these expressions will be identical to 24x + 36y.

What is expression?

Expressions can be used to represent numerical or algebraic quantities, and can be used to perform calculations. For example, the expression "2 + 3" represents the sum of the numbers 2 and 3, which is 5. Similarly, the expression "x + 5" represents the sum of the variable x and the number 5, and can be evaluated to a specific value depending on the value of x.

[tex]12(2x-y)[/tex]

[tex]-6(4x-3y)[/tex]

[tex]3(x+12y)[/tex][tex]12(2x-y)=24x-12y[/tex]

So,[tex]24x-12y+24=24x+36y-6(4x-3y)=-24x+18y[/tex]

So,[tex]-24x+18y+42x+18y=24x+36y[/tex]

[tex]3(x+12y)=3x+36y[/tex]

So,[tex]3x+36y+21x-24y=24x+36y[/tex]

As a result, for any x and y values, these expressions will be identical to 24x + 36y.

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Use rounding to estimate the product of 5555 and 4444. Round both numbers to the nearest thousand to find your answer.

Answers

6000, and 4000. when it comes to rounding, anything with the number 5 or above rounds up. while anything with the number 4 or below, rounds down. hope this helps ! :)

Answer: 6666 and 3333

Step-by-step explanation: 5 or above give it a shove, 4 or below let it go.

A poster storage tube in the shape of a cylinder has a diameter of 3.5 inches and a volume of 122.5 pie cubic inches.

What is the height of the poster storage tube in inches?

Answers

The height of the poster storage tube is approximately 40 inches.

What is Volume?

Vοlume is the amοunt οf space that a three-dimensiοnal οbject οccupies. It is measured in cubic units such as cubic meters, cubic feet, οr cubic inches. The fοrmula fοr calculating the vοlume οf a sοlid οbject depends οn its shape. Fοr example, the vοlume οf a cube can be calculated using the fοrmula V = s³, where s is the length οf a side, while the vοlume οf a cylinder can be calculated using the fοrmula V = πr²h, where r is the radius οf the base and h is the height.

The formula for the volume of a cylinder is V = πr²h, where r is the radius of the base and h is the height of the cylinder.

Since the diameter of the cylinder is given as 3.5 inches, the radius is half of that or 1.75 inches. Also, the volume is given as 122.5π cubic inches.

Therefore, we can use the formula to solve for the height:

V = π[tex]r^{2}[/tex]h

122.5π = π(1.75)(1.75)h

122.5 = 3.0625h

h = 122.5/3.0625

h ≈ 40

Therefore, the height of the poster storage tube is approximately 40 inches.

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Find the area of the shaded region of circle W below. Round your answer to the nearest tenth if necessary. ​

Answers

The area of the shaded region is = area of the sector - the area of the right angle triangle. so the area is [tex]9\pi /4 -9/2[/tex]

What do you know about area of circle?

Area of circle formula = [tex]\pi r^{2}[/tex]. The area of a circle is [tex]\pi[/tex] multiplied by the square of the radius. The area of a circle when the radius 'r' is given is [tex]\pi r^{2}[/tex]

The area of a circle when the diameter 'd' is known is [tex]\pi d\frac{2}{4}[/tex]. π is approx. [tex]3.14 or \frac{22}7}[/tex]. Area(A) could also be found using the formulas A = [tex](\frac{\pi}{4} )*d^{2}[/tex], where 'd' is the radius and A= [tex]\frac{c^{2} }{4\pi }[/tex], where 'C' is the given circumference.

According to the given information

The area of the shaded region is = area of the sector - the area of the right angle triangle.

A = [tex]9\pi /4 -9/2[/tex]

Therefore the area of the shaded region is = area of the sector - the area of the right angle triangle. so the area is [tex]9\pi /4 -9/2[/tex]

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3. When Ahmad goes to work, he has to pass through two sets of traffic lights, P and Q. The
7
probability that he has to stop at P is
The probability that he has to stop at Q, given that he has
20
to stop at Pis
stop at P is
2
5
7
The probability that he does not have to stop at Q, given that he does not have to
10
(a) Construct a tree diagram to represent the above information..
(b) Find the probability that he has to stop at both P and Q.
(c) Find the probability that he has to stop at least once.
(d) If he has to stop at Q, what is the probability that he would have stopped at P.
[3 marks]
[2 marks]
[2 marks]
[3 marks]

Answers

P(stop at P|stop at Q) = P(stop at P and stop at Q) / P(stop at Q) is 28/47

How to solve questions?

(a) Tree diagram:

                 | P stop 7/20

                 |

          -------|-------

         |              |

   Q stop|  P stop 2/5  | P not stop 3/5

         |              |

    ------|-------      |    

         |              |

  Q not stop| P stop 1/10 | P not stop 9/10

         |              |

          -------|-------

                 |

                 | P not stop 13/20

                 

(b) The probability that he has to stop at both P and Q is:

P(stop at P) * P(stop at Q|stop at P) = (7/20) * (2/5) = 7/50

(c) The probability that he has to stop at least once is:

P(stop at P and/or stop at Q) = 1 - P(not stop at P) * P(not stop at Q|not stop at P)

                             = 1 - (13/20) * (9/10) = 11/20

(d) If he has to stop at Q, the probability that he would have stopped at P is:

P(stop at P|stop at Q) = P(stop at P and stop at Q) / P(stop at Q)

                       = (7/50) / (13/20 * 2/5 + 7/50)

                       =28/47

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In a random sample of eight people, the mean driving distance to work was 18.5 miles and the standard deviation
was 7.9 miles. Assume the population is normally distributed and use the t-distribution to find the margin of error and
construct a 90% confidence interval for the population mean μ. Interpret the results.
Identify the margin of error.
(Round to one decimal place as needed.)
Construct a 90% confidence interval for the population mean.
(Round to one decimal place as needed.)
Interpret the results. Select the correct choice below and fill in the answer box to complete your choice.
(Type an integer or a decimal. Do not round.)

Answers

Answer: To find the margin of error and construct a 90% confidence interval for the population mean, we can use the following formula:

Margin of error = t-value x (standard deviation / square root of sample size)

where t-value is the value obtained from the t-distribution table with n-1 degrees of freedom and a confidence level of 90%.

For a sample size of 8 and a confidence level of 90%, the degrees of freedom is 7 and the t-value is 1.895 (obtained from a t-distribution table).

Using the given values, we can calculate the margin of error as:

Margin of error = 1.895 x (7.9 / sqrt(8)) ≈ 5.69 (rounded to one decimal place)

So the margin of error is approximately 5.69 miles.

To construct a 90% confidence interval for the population mean, we can use the formula:

Confidence interval = sample mean ± margin of error

Substituting the values, we get:

Confidence interval = 18.5 ± 5.69

So the 90% confidence interval for the population mean is (12.81, 24.19).

Interpretation:

We are 90% confident that the true mean driving distance to work for the population lies between 12.81 and 24.19 miles. This means that if we were to take many samples of 8 people and calculate the confidence interval for each sample, 90% of those intervals would contain the true population mean. The margin of error is the amount by which the sample mean may differ from the true population mean.

Step-by-step explanation:

Find the missing side lengths. Leave your answers as radicals in simplest form

Answers

Answer:

a = b = 32

Step-by-step explanation:

Use trigonometry:

[tex] \sin(45°) = \frac{a}{6} [/tex]

Cross-multiply to find a:

[tex]a = 6 \times \sin(45°) = 6 \times \frac{ \sqrt{2} }{2} = \frac{6 \sqrt{2} }{2} = 3 \sqrt{2} [/tex]

Use the Pythagorean theorem to find b:

[tex] {b}^{2} = {6}^{2} - {a}^{2} [/tex]

[tex] {b}^{2} = {6}^{2} - ( {3 \sqrt{2}) }^{2} = 36 - 9 \times 2 = 36 - 18 = 18[/tex]

[tex]b > 0[/tex]

[tex]b = \sqrt{18} = 3 \sqrt{2} [/tex]

find the interest rate if £9000 has a final value of £13102 in 5 years. give your answer to 1.d.p

Answers

The rate of interest is 7.7 %  if £9000 has a final value of £13102 in 5 years

When interest is compounding, it indicates that the balance as a whole, rather than just the principal, is taken into account when the following interest period begins.

For instance, after a year, a $100 loan with 5% annual compound interest will have a debt of $105 due. The interest will be applied to the entire $105, creating a new amount of $110.25 the next year, rather than being taken as 5% of $100.

The interest will be added to that $110.25 the following year, and so on throughout the loan.

This is distinct from simple interest, which is a periodic payment to the loan holder of a fixed sum of money derived from a percentage of the principal

We have given that the final amount is 13102 and the principal amount is 9000 and time n is 5 years we have to find the rate

We have the formula

[tex]A=p(1-\frac{r}{100})^n[/tex]

A= 13102

P=9000

n=5

r = ?

[tex]13102=9000(1-\frac{r}{100})^5\\\\1.455=(1-\frac{r}{100})^5\\\\1.077=1-\frac{r}{100}\\\\r=7.7[/tex]

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Let x represent one number and let y represent the other number. Use the following conditions to write a system of nonlinear equations. Solve the system and find the numbers. The sum of two numbers is 7 and the product of the two numbers is 12

the two numbers are:

Answers

By answering the presented question, we may conclude that Therefore, equation the two numbers are either 3 and 4, or 4 and 3.

What is equation?

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the number "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

the system of equations:

[tex]x + y = 7\\x * y = 12 \\y = 7 - x\\x * (7 - x) = 12\\7x - x^2 = 12\\x^2 - 7x + 12 = 0\\(x - 3)(x - 4) = 0\\If x = 3, then y = 4\\If x = 4, then y = 3\\[/tex]

Therefore, the two numbers are either 3 and 4, or 4 and 3.

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Marcus drew a scale drawing of the rectangular park in his neighborhood. on his drawing, the length of the park is 8 inches and the width of the park is 6 inches. the key on his drawing shows 1 inch=20 feet. what is the actual area of the park?

Answers

the actual area of the park is 19,200 square feet.

Marcus drew a scale drawing of the rectangular park in his neighborhood. He drew the length of the park as 8 inches and the width of the park as 6 inches. The key on his drawing shows 1 inch=20 feet. To find the actual area of the park, we need to convert the measurements in Marcus's drawing to the actual measurements in feet.

Since 1 inch on Marcus's drawing represents 20 feet in actuality, we can use a scale factor of 1 inch : 20 feet to convert the measurements. We can then multiply the actual length and width of the park in feet to find the actual area of the park in square feet.

To convert the length of 8 inches to feet, we multiply it by the scale factor:

8 inches × (20 feet/1 inch) = 160 feet

Similarly, we can convert the width of 6 inches to feet:

6 inches × (20 feet/1 inch) = 120 feet

So the actual length of the park is 160 feet and the actual width of the park is 120 feet.

To find the actual area of the park, we multiply the actual length by the actual width:

160 feet × 120 feet = 19,200 square feet

Therefore, the actual area of the park is 19,200 square feet.

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find the area of triangle if the angles are 3 cm 4 cm and 5 cm​

Answers

Answer:3x4x5 = 60
but how r angles Cm did u mean sides or lxhxw

Step-by-step explanation:

Answer:

It's not possible to determine the area of a triangle based on the given information about the angles.

To find the area of a triangle, we need to know at least one side length in addition to the angles. The formula for the area of a triangle is:

Area = (1/2) * base * height

where the base is any side of the triangle, and the height is the perpendicular distance from that side to the opposite vertex.

Without knowing any side lengths, we cannot calculate the height and therefore cannot find the area of the triangle.

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