Conditional probability 3. Anya travels to work by car or by bicycle. The probability that she travels by car is 0.35 If she travels to work by car, the probability that she will be late is 0.12 If she travels to work by bicycle, the probability that she will be late is 0.25 a) Draw a probability tree diagram to show all the possible outcomes. b) Work out the probability that Anya will not be late.​

The length of the chord whose central angle is 80° in a circle with a radius of 4 centimeters is 5.14 cm using the law of cosines.

Given that,

Central angle of a chord = 80°

Radius of the circle = 4 centimeters

There will be a triangle formed by the chord and the two radius.

Let a be the length of the chord.

Using the law of cosines,

a² = 4² + 4² - (2 × 4 × 4) cos (80°)

a² = 16 + 16 - 32 cos (80°)

a² = 32 - 32 cos (80°)

a² = 26.4433

a = 5.14

Hence the length of the chord is 5.14 cm.

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Hence, the critical value for the 81% confidence interval is 1.311 occurs while comparing equations (1) and (2).

The cut-off scores used during confidence intervals, hypothesis testing, and other statistical techniques are known as the crucial values. They are used to establish the boundaries of confidence intervals in the case of confidence intervals.

Level of confidence c = 0.81

The degree of assurance c =  81%.

Now, the overall confidence level is shown as (1−α) , where α is the significance level.

= 1.0 - 0.81

= 0.19

Thus, the 81% confidence level suggests a significance level of 0.19.

Critical value Z(α/2) is:

P(Z >   Z(α/2)) =  (α/2)

                       = 0.19/2

P(Z >   Z(α/2)) = 0.095  ...eq 1

Using the z-table online, check the p-value for the z 0.095.

P(Z > 1.311) = 0.095  ...eq 2

Hence, the critical value for the 81% confidence interval is 1.311 occurs while comparing equations (1) and (2).

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Answer: Andre should buy Car 2. Brainliest?

Step-by-step explanation:

To compare the gas mileage of the two cars, we need to find out how many miles each car can travel per gallon of gas.

For Car 1: y = 25x

This means that for every gallon of gas used (x), the car can travel 25 times that amount in miles (y). So, the gas mileage for Car 1 is 25 miles per gallon (mpg).

For Car 2: we can calculate the miles per gallon by dividing the total miles traveled by the number of gallons of gas used:

For 2 gallons of gas, the car can travel 60 miles. So, the gas mileage is 30 mpg (60 miles ÷ 2 gallons).

For 5 gallons of gas, the car can travel 150 miles. So, the gas mileage is 30 mpg (150 miles ÷ 5 gallons).

For 7 gallons of gas, the car can travel 210 miles. So, the gas mileage is 30 mpg (210 miles ÷ 7 gallons).

For 8 gallons of gas, the car can travel 240 miles. So, the gas mileage is 30 mpg (240 miles ÷ 8 gallons).

For 11 gallons of gas, the car can travel 330 miles. So, the gas mileage is 30 mpg (330 miles ÷ 11 gallons).

Therefore, Car 2 has a consistent gas mileage of 30 mpg.

From the above calculations, we can see that Car 2 has a better gas mileage compared to Car 1. Car 2 can travel 30 miles on a gallon of gas, while Car 1 can only travel 25 miles on a gallon of gas.

Therefore, Andre should buy Car 2 if he wants to get the best gas mileage. Car 2 can travel 5 more miles per gallon than Car 1.

The final amount of money in the account after 7 years would be $8,790.56.

To calculate the final amount of money in an account, we can use the formula for compound interest:

A = [tex]P(1 + r/n)^{(nt)[/tex]

where A is the final amount of money, P is the initial amount of money, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, we have P = $7,300, r = 0.02 (since the interest rate is 2%), n = 2 (since the interest is compounded semi-annually), and t = 7 (since the money is left for 7 years). Plugging these values into the formula, we get:

A = $7,300(1 + 0.02/2)¹⁴

A = $7,300(1.01)¹⁴

A = $8,790.56

This means that the initial investment of $7,300 earned $1,490.56 in interest over the 7-year period due to the compounding effect of the semi-annual interest payments.

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Answer:

Step-by-step explanation:

(a) We know that the balance An in the nth month is given by:

An = k · An-1 - 400

where A0 = 14,000. Substituting n = 1, we get:

A1 = k · A0 - 400

A1 = k · 14,000 - 400

We also know that her uncle charges 0.9% interest per month on the balance. This means that the balance after one month should be:

A1' = A0 + 0.009 · A0 - 400

A1' = 14,000 + 0.009 · 14,000 - 400

A1' = 14,126

Setting A1 = A1', we can solve for k:

k · 14,000 - 400 = 14,126

k = 1.009

Therefore, k is approximately 1.009.

(b) To find her balance after two months, we can use the recursive formula with n = 2:

A2 = k · A1 - 400

A2 = 1.009 · 14,126 - 400

Using a calculator, we get:

A2 ≈ 14,272.34

Therefore, her balance after two months is approximately $14,272.34.

Answer: 5/64

Step-by-step explanation:

The probability of drawing a red marble on the first draw is 4/16 = 1/4 (since there are 4 red marbles out of 16 total marbles).

After replacing the first marble, the probability of drawing a yellow marble on the second draw is 5/16 (since there are 5 yellow marbles remaining out of 16 total marbles).

Therefore, the probability of drawing a red marble and then a yellow marble is (1/4) x (5/16) = 5/64

Answer:

Area = 20 [tex]units^{2}[/tex]

Perimeter  = 18 units

Step-by-step explanation:

Helping in the name of Jesus.

The value of the calculated area of the figure is 343.17 sq units

From the question, we have the following parameters that can be used in our computation:

Composite figure

The shapes in the composite figure are

This means that

Area = Semicircle + Rectangle

Using the area formulas on the dimensions of the individual figures, we have

Area = 12 * 18 + 1/2 * 3.14 * (18/2)^2

Evaluate the sum of products

Area = 343.17

Hence, the area of the figure is 343.17 sq units

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Okay, let's solve this step-by-step:

a)

Length = 30 in = 2.5 ft

Width = 15 in = 1.25 ft

Height = 18 in = 1.5 ft

Volume (cubic ft) = Length x Width x Height

= 2.5 x 1.25 x 1.5 = 3.75 cubic ft

Volume (cubic yards) = 3.75 / 27 = 0.14 cubic yards

b)

Since the box volume is 3.75 cubic ft and potting soil bags are 1.5 cubic ft,

you will need 3.75 / 1.5 = 2.5 bags of soil.

Each bag weighs 11.2 lbs, so 2.5 bags will weigh 2.5 * 11.2 = 28 lbs of soil.

c)

To paint the sides of the box, you need:

Length (2 sides) = 30 in x 2 = 60 in

Width (2 sides) = 15 in x 2 = 30 in

Height (4 sides) = 18 in x 4 = 72 in

Total inches of sides = 60 + 30 + 72 = 162 in

Conversion: 162 in / 12 in = 13.5 square ft

So you will need about 14 square feet of paint.

Let me know if you have any other questions!

The width of the rectangular field is 80 meters and the length is 120 meters for the given perimeter 400m.

Perimeter is a mathematical term that refers to the total distance around the outside of a closed two-dimensional shape. It is the sum of the lengths of all the sides of the shape.

According to the given information:

Let's break down the information given in the question:

Length of the rectangular field is 40m greater than the width.

The perimeter of the field is 400m.

Let's denote the width of the rectangular field as 'w' meters. According to the first information, the length of the field would be 'w + 40' meters, as it is 40m greater than the width.

Now, let's use the formula for the perimeter of a rectangle, which is given by:

Perimeter = 2 * (Length + Width)

Substituting the values we have:

Perimeter = 2 * (w + 40 + w)

Perimeter = 2 * (2w + 40)

Since the given perimeter is 400m, we can set up the equation:

400 = 2 * (2w + 40)

Now we can solve for 'w' by dividing both sides of the equation by 2:

400/2 = 2w + 40

200 = 2w + 40

Next, we subtract 40 from both sides of the equation to isolate the term with 'w':

200 - 40 = 2w

160 = 2w

Finally, we divide both sides of the equation by 2 to solve for 'w':

160/2 = w

80 = w

So, the width of the rectangular field is 80 meters. And since the length is 40 meters greater than the width, the length would be:

Length = Width + 40 = 80 + 40 = 120 meters.

So, the width of the rectangular field is 80 meters and the length is 120 meters.

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Ahem, here goes, my attempt at a minute-long rap in praise of the parallelogram:

Yo, listen up, the parallelogram is where it's at,

A shape so brilliant, the angles are sat.

Parallel sides that never converge,

Internal angles that never diverge.

Each side an equal length,

A geometry prodigy's dream length.

The diagonals intersect, another line through the middle they meet,

Creating symmetry so neat.

A rectangle it could be,

But it's oblong, not square, can't you see?

With depth and width in perfect balance we see,

A two-dimensional form of complexity.

While the square is simple, the parallelogram is hip,

A mathematical masterpiece, skip, skip, skip!

four right angles keep the shape so tight,

Parallel lines dominate left and right.

Rotated or reflected without a care,

Its structural integrity beyond compare.

triangles form at each corner you'll note,

Acute or obtuse, depends on the protractor's groove.

A versatile shape with reason and purpose galore,

The parallelogram, simply, carries the floor.

From geometry to art, its angles they intrigue,

As a basis for patterns, its potential we can truly plug.

A forgotten form that deserves more acclaim,

Put the parallelogram on geometry's game!

This shape so underrated, rarely appreciated it seems,

But with logic and virtue, strong foundations it gleams.

The parallelogram, the parallelogram, Hooray!

This is why the parallelogram is the best shape, I say!

Answer:

Whenever the base of an exponential function is less than 1 (5/7 < 1), the graph exhibits exponential decay and when the base is greater than 1, the graph exhibits exponential decay (7 > 1).

Final answer:  a base of 7 will cause the graph to increase as you go from left to right in both the x coordinates and the y coordinates.  

I provided a picture of a graph that shows both bases just in case you want to alter my answer slightly, but aren't sure how the graph would look

As per the given graph, the rational function that is graphed in the given image is option B: F(x) = x(x+3)(x-3) / (x-3)(x+3) as per the factors.

Based on the graph, we can see that the function has vertical asymptotes at x = -3 and x = 3.

Option A has only one factor of (x+3) and one factor of (x-3), so it would have only one vertical asymptote at x = 3 or x = -3, but not both.

Option B has two factors of (x-3) and two factors of (x+3), so it has two vertical asymptotes at x = 3 and x = -3, which matches the graph.

Option C has only one factor of (x-3) and no factor of (x+3), so it would have only one vertical asymptote at x = 3 or x = -3, but not both.

Option D has only one factor of (x+3) and no factor of (x-3), so it would have only one vertical asymptote at x = -3 or x = 3, but not both.

Therefore, the rational function that is graphed in the given image is option B: F(x) = x(x+3)(x-3) / (x-3)(x+3).

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(A) The gross profit is $20,150.

(B) The net income is $16,550

(A) To calculate the gross profit, we need to subtract the cost of goods sold from the total revenue generated by selling the printers.

Total revenue = 26 x $1,750 = $45,500

Cost of goods sold = 26 x $975 = $25,350

Gross profit = Total revenue - Cost of goods sold

Gross profit = $45,500 - $25,350

Gross profit = $20,150

Therefore, the gross profit is $20,150.

(B) To calculate the net income, we need to subtract all the operating expenses from the gross profit.

Gross profit = $20,150

Salary = $3,000

Advertising = $50

Office lease = $550

Total operating expenses = $3,600

Net income = Gross profit - Total operating expenses

Net income = $20,150 - $3,600

Net income = $16,550

Therefore, the net income is $16,550.

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81

72 + (12% of 72) = 80.64 and since you can't sell .64 computers, she needs to sell 81.

Answer:

79

Step-by-step explanation:

Let's start by writing out what we know:

A = 647 in base-n

A = 513 in base-(n+2)

To find A in base-10, we need to use the place value system and the definition of each base. Let's first convert A to base-10 using the given information.

In base-n, A is equal to:

A = 6n^2 + 4n + 7

In base-(n+2), A is equal to:

A = 5(n+2)^2 + 1(n+2) + 3

A = 5(n^2 + 4n + 4) + (n + 2) + 3

A = 5n^2 + 21n + 20

Now we have two expressions for A, so we can set them equal to each other and solve for n:

6n^2 + 4n + 7 = 5n^2 + 21n + 20

Simplifying and rearranging, we get:

n^2 + 8n + 13 = 0

Using the quadratic formula, we can solve for n:

n = (-8 ± sqrt(8^2 - 4(1)(13))) / (2(1))

n = (-8 ± 2) / 2

n = -3 or n = -5

Since n is a positive integer, we can disregard the negative solution and conclude that n = 3.

Now that we know n, we can substitute it back into the expression for A in base-n and solve for A in base-10:

A = 6n^2 + 4n + 7

A = 6(3^2) + 4(3) + 7

A = 79

Therefore, the number A written in base-10 is 79.

Hope this helps!

-1 +

2 -

3 +

4 -

5 +

6 -

...

-99 +

100

= -1 + 2 - 3 + 4 - 5 + 6 - ... - 99 + 100

= 1

The standard deviation for non-employed students is given as 0.524,

the margin of error is 0.083 and the 90% confidence interval for the mean GPAs of non-employed students is (3.147, 3.313).

Variables needed to solve the problem Sample size (n)

Sample mean, Sample standard deviation (s), Confidence level (CL)

Margin of error (E)

b. The standard deviation for non-employed students is given as 0.524.

c. Point estimate:

The point estimate for the mean GPA of non-employed students is the sample mean, which is given as 3.23.

Margin of error:

We can use the formula for the margin of error:

E = z(s/√n)

For a 90% confidence level, the critical value is 1.645.

E = 1.645(0.524/√114) = 0.083

Therefore, the margin of error is approximately 0.083.

d. Confidence interval:

The confidence interval is given by the formula:

(3.23 - 0.083, 3.23 + 0.083)

= (3.147, 3.313)

Therefore, the 90% confidence interval for the mean GPAs of non-employed students is (3.147, 3.313).

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Using the function y = √ (x-4) has the following:

Domain: x≥−4, Range: y≥0.

Correct answer is A.

A function is a relationship between each element of a non-empty set A and at least one element of another non-empty set B. A relation f between a set A (the function's domain) and a set B is how a function is defined in mathematics (its co-domain). Anytime an A and b B exist, f = (a,b)|

The domain of the function y=√ (x-4) is restricted by the square root of a non-negative number, which means that x-4 must be greater than or equal to zero. Thus, we have:

x-4 ≥ 0

x ≥ 4

Therefore, the domain of the function is x≥4.

The range of the function is determined by the output values of the function. Since the square root of any non-negative number is always non-negative, the output values of the function y=√x-4 will always be non-negative. Thus, the range of the function is y≥0.

Therefore, the correct answer is A. Domain: x≥−4, Range: y≥0.

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The above is an analysis of data related to income and expenditure. See the working below as well as the attached information.

R Calculation

Note that:

X: X Values

Y: Y Values

Mx: Mean of X Values

My: Mean of Y Values

X - Mx & Y - My: Deviation scores

(X - Mx)2 & (Y - My)2: Deviation Squared

(X - Mx)(Y - My): Product of Deviation Scores

X Values

∑ = 273195

Mean = 6829.875

∑(X - Mx)2 = SSx = 119242794.375

Y Values

∑ = 33625

Mean = 840.625

∑(Y - My)2 = SSy = 2396869.375

X and Y Combined

N = 40

∑(X - Mx)(Y - My) = 15978328.125

R Calculation

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = 15978328.125 / √((119242794.375)(2396869.375)) = 0.9451

Thus, the value of R is 0.9451.

4. This is a strong positive correlation, which means that high X variable scores go with high Y variable scores (and vice versa).

5) The value of R², the coefficient of determination, is 0.8932.

To drive this, just square the coefficient of determination. That is

R² = 0.9451² = 0.8932

5. To compute the standard errors of the estimate:

SE = √(SSE / (n-2))

where SSE is the sum of squared errors and n is the sample size.

From the regression output, we have SSE = 0.9326 and n = 40.

SE = √ (0.9326 / (40-2)) = 0.1570

Therefore, the standard error of estimate is 0.1570.

6) Yes, because the coefficient of determination is high (0.8932), indicating that 89.32 % of the variability i  n the amount spent can be explained by the linear relationship with monthly  income.

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Full Question:

Although part of your question is missing, you might be referring to this full question: See attached.

Answer:

$97.50

Step-by-step explanation:

To calculate the sale price of the skateboard, we need to apply a discount of 35% to the original cost of $150:

Discount amount = 35% x $150 = $52.50

The sale price is the original cost minus the discount amount:

Sale price = $150 - $52.50 = $97.50

Therefore, the sale price of the skateboard after a 35% discount is $97.5

The sale price of the skateboard is $97.50.

To calculate the sale price, we need to first determine the amount of the discount, and then subtract that discount from the original price.

The discount is 35% of the original price:

Discount = 0.35 x 150 = 52.50

So the sale price is the original price minus the discount:

Sale price = 150 - 52.50 = 97.50

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Answer:

584

Step-by-step explanation:

To find the herd population after 6 years, we need to evaluate P(6) using the given function:

P(6) = 205(1.13)^6

Using a calculator, we get:

P(6) ≈ 584

Rounding this to the nearest whole number, we get:

The herd population after 6 years ≈ 584.

The amount that Author saves in the same week is $32.

An equation which has a variable of unknown value is referred to as a simple equation. Thus, the value of the variable is to be determined.

From the given question, it can be deduced that;

Dejon saves $8 per week, while Author saves four times that of Dejon.

Thus, this implies that;

the amount that Author saves same week = 4 * $8

                                 = $32

Therefore, the amount that Author save in the same week is $32.

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Answer:

The correct answer is 16

Step-by-step explanation:

Answer:

C. 100

Step-by-step explanation:

Assuming that the proportion of tagged hogs in the population is the same as the proportion of tagged hogs in the sample that was later observed, we can set up a proportion to estimate the total population of wild hogs:

tagged hogs in population / total population = tagged hogs in sample / size of sample

We know that 20 wild hogs were tagged and released, and that 8 out of 40 hogs observed were tagged. So we can plug these numbers into the proportion and solve for the total population:

20 / total population = 8 / 40

Simplifying this equation, we get:

total population = (20 * 40) / 8 = 100

Therefore, the wildlife group can estimate that the total population of wild hogs in the area is 100. Answer choice C is correct.

Hope this helps!

I do not understand what do you mean

Answer: The length and width are 13 and 19

Step-by-step explanation:

This is because the factors of 247 are 1, 13, 19, and 247. 13 times 19 is 247, but if 13 and 19 are the sides, the perimeter would be 64 as well.

Answer:

D. y = (x - 3)(x - 6)

Step-by-step explanation:

The graph shows a parabola and the parabola intersects the x-axis at (-6, 0) and at (-3, 0).  When a function intersects the x-axis, the y value must automatically equal 0, since there is only horizontal movement on the x-axis.

(x-3)(x-6) is a binomial expression that will make a quadratic equation when expanded.  We refer to the coordinate where a parabola intersects the x-axis as roots, which are numbers that make the quadratic equation equal 0.

We know from the zero-product property, that when the product of two numbers is 0, at least on the numbers must be 0 (e.g., 4 * 0 = 0 or even 0 * 0 = 0).  Thus, we can solve any quadratic equation in the the x-intercept form (i.e., the form tha (x-3)(x-6) is currently in) by setting both expressions equal to 0 and solving for x.  This wil give an x-coordinate both times, but since you set the equations equal to 0, you know that your y-coordinate each time is 0:

Solution for x - 3 = 0:

x - 3 = 0

x = 3

Solving for x - 6 = 0

x - 6 = 0

x = 6

You can check by plugging in 3 for x and 6 for x and see if you get 0:

3 for x:

(3 - 3)(3 - 6) = 0

0 * -3 = 0

0 = 0

6 for x:

(6 - 3)(6 - 6) = 0

3 * 0 = 0

0 = 0