Janie has $180 m. She spends 50% of her money on a new pair of ice skates. How much does she spend on ice skates?

P(A)=1/5, P(B)=7/20, P(A and B)= 7/100. The events A and B are independent.

Two events are independent if the occurrence of one event does not affect the chances of the occurrence of the other event. The mathematical formulation of the independence of events A and B is the probability of the occurrence of both A and B being equal to the product of the probabilities of A and B (i.e., P(A and B).

1) P(A)=1/5, P(B)=7/20, P(A and B)= 7/100

Here, P(A and B)= P(A)×P(B)

= 1/5 × 7/20

= 7/100

So, the events A and B are independent.

2) P(A)=13/20, P(B)=13/20, P(A and B)= 169/400

Here, P(A and B)= P(A)×P(B)

= 13/20 × 13/20

= 169/400

So, the events A and B are independent.

3) P(A)=7/10, P(B)=2/5, P(A and B)= 21/100

Here, P(A and B)= P(A)×P(B)

= 7/10 × 2/5

= 14/50

So, the events A and B are not independent.

2) P(A)=1/5, P(B)=1/5, P(A and B)= 1/25

Here, P(A and B)= P(A)×P(B)

= 1/5 × 1/5

= 1/25

So, the events A and B are independent.

Therefore, options 1, 2 and 4 are correct answers.

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Figure E has more area than Figure D. Figure E has an area of 26 square units, while Figure D has an area of 22 square units. The difference in area is 4 square units, which is the area of the 4 squares added to the bottom of Figure E.

If the side length of each square in the figures is doubled, the area of each square will be quadrupled since the area is proportional to the square of the length of the side.

In Figure D, each square has an area of 1 square unit, so if the side length is doubled, the area of each square will become 4 square units. Therefore, the total area of Figure D will be 15 x 4 = 60 square units.

In Figure E, each square also has an area of 1 square unit, so if the side length is doubled, the area of each square will become 4 square units. Therefore, the total area of Figure E will be 12.5 x 4 = 50 square units.

The new ratio of their areas would be:

New ratio of areas = (Area of Figure D) / (Area of Figure E) = 60 / 50 = 6/5

So the new ratio of their areas would be 6:5.

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The slope of both functions is the same which is -2 but a different y-intercept. Thus, function 1 is parallel to function 2.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The linear equation is given as,

x/a + y/b = 1

Where 'a' is the x-intercept of the line and ‘b’ is the y-intercept of the line.

Function 1 is given as,

y = - 2x - 4

The slope is -2 and the y-intercept is -4.

From the graph, the equation of function 2 is given as,

x / 2 + y / 4 = 1

2x + y = 4

y = - 2x + 4

The slope is -2 and the y-intercept is 4.

The slope of both functions is the same which is -2 but a different y-intercept. Thus, function 1 is parallel to function 2.

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The missing graph is attached below.

the probability of picking a red ball from the bag and getting heads upon flipping a fair coin is 1/2 * 1/2 = 1/8.

There are two independent events, and therefore the probability of both occurring is calculated by multiplying the probability of each event. The probability of picking a red ball from the bag is 1/2, and the probability of getting heads upon flipping a fair coin is also 1/2. Therefore, the probability of picking a red ball from the bag and getting heads upon flipping a fair coin is 1/2 * 1/2 = 1/8.

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Answer: 5/13

Step-by-step explanation: cos is adj/hyp giving us a 12 for adj and 13 for hyp. Tan is Opp/Adj confirming 12 is the adj and 5 being the Opp. Sin is Opp/Hyp giving us 5/13. Hope it helps

The solution to the system of equations is (2.68, 1.01)

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

2.5x+3.75y=10.5

1.25x−8.5y=−5.25

Express properly

2.5x + 3.75y = 10.5

1.25x − 8.5y = −5.25

Next, we make a plot of the system to determine the solution

The point of intersection in the plot represent the solution to the equations

In this case, the intersection has a coordinate of (2.68, 1.01)

Hence, the solution is (2.68, 1.01)

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The area of the shaded portion is 6x^2

How to determine this?

The area of the shaded portion = Area of big rectangle - Area of small rectangle.

To get the area of big rectangle = L * B

A = 2x * 4x

A = 8x^2

To get area of small rectangle = L * B

A = 2x * x

A = 2x^2

To get the area of shaded portion ,

= 8x^2 - 2x^2

= 6X^2

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y = 2/5x +24/5, is the equation  which represents a line that passes through (-2, 4) and has a slope of 2/5.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

The slope intercept form of a line is

y = mx+b

where m is the slope and b is the y intercept

y = 2/5 x +b

Substitute the point (-2,4) into the equation and solve for b

4 = 2/5(-2)+b

4 = -4/5 +b

Add 4/5 to each side

20/5 +4/5 = b

24/5 = b

Hence, y = 2/5x +24/5, is the equation  which represents a line that passes through (-2, 4) and has a slope of 2/5.

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The slope-intercept form of the equation of the line is y = x + 6.

A linear equation with a degree of one is referred to as an equation of the line. Two variables, x, and y, are present in the equation of the line. The third parameter is the line's slope, which indicates the line's elevation.

The equation of the line's general form is:

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

The formula for calculating the line's slope is

Slope = ( 6 - 4) / ( 2 - 0)

Slope = 1

The y-intercept will be calculated as:-

y = mx + c

y = x +c

6 = c

The equation of the line can be written as:-

y = x + 6

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The required after 8 years, the investment will be worth approximately $156,753.

Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.

Amount = principal[1 + r/n]ⁿᵃ

Principal = P rate= r Time =a  , n = compounding frequency

Here,
To calculate the future value of Joshua's investment after 8 years with an interest rate of 6% compounded daily, we can use the formula:

In this case, P = $97,000, r = 6% = 0.06, n = 365 (since the interest is compounded daily), and t = 8.

So, we have:

[tex]A = $97,000 \times (1 + 0.06/365)^{365 * 8}[/tex]

A = $195,239.00

Therefore, after 8 years, the investment will be worth approximately $156,753.

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Answer:

its b

Step-by-step explanation:

Answer:

( [tex]-\frac{1}{3}[/tex] , [tex]-\frac{41}{21}[/tex] )

Step-by-step explanation:

Answer: 1

Step-by-step explanation: Knowing the division and multiplication rules, any number times one equals itself and any number divided by one equals itself. Make sure not to put 0 as an answer because any number divided by 0 is undefined.

Answer:

9

Step-by-step explanation:

72/24 = 3

72 is 3 times 24, so you need 3 times as many garbage trucks.

Answer: 9

a) The percentage of flashlights that have a life of 55 to 65 is about 36%

b) The percentage of the batteries that have a life of 52 to 68 hours is about 75%.

Standard normal distribution is a type of continuous distribution with a mean of zero and standard deviation of one. The random variables are standardized into z scores using z score formula.

a) The Chebyshev's theorem states that; for sample or population, percentage (p) of values are contained within two, three or more standard deviations within the mean, provided that the values of k is greater than 1:

P(%) = [tex]1-\frac{1}{k^2}[/tex]

Calculate the value of k:

[tex]k =\frac{65-60}{4}=1.25[/tex]

The percentage is calculated as;

p(%) = [tex]1-\frac{1}{1.25^2}[/tex] = 36%

The percentage of flashlights that have a life of 55 to 65 is about 36%

b) k = [tex]\frac{68-60}{4}=2[/tex]

p(%) = [tex]1-\frac{1}{2^2}[/tex] = 75%

The percentage of the batteries that have a life of 52 to 68 hours is about 75%.

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The solution is, Option a

Stratified random sample

In statistics, a simple random sample is a subset of individuals chosen from a larger set in which a subset of individuals are chosen randomly, all with the same probability. It is a process of selecting a sample in a random way.

here, we have,

Explanation:

(a) In stratified random sampling, a division of the population occurs in such a way that a population is stratified in different small groups or strata with common traits and same proportion both in population and sample. this type of sample so formed is known as stratified random sample.

(b) Simple random Sample:

This sample is formed by the random and unbiased selection of individual that represents the population.

(c) Population:

The entire set of individuals with certain specific characteristics represents a population whereas a sample is drawn out of the population and can be referred to as the subset of the population.

(d) Cluster Sample:

In this, separate sample groups are formed known as clusters, here sampling of random clusters take place.

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The length of the tree remaining sides are 18 inches, 29 inches and 29 inches.

A kite is an object with four sides. It length of the two adjacent sides are of equal length. No pair of sides in a kite are parallel. The perimeter of a kite is the sum of the length of the four sides of the kite.

Perimeter of a kite = 2( a + b)

94 = 2(18 + b)

94 / 2 = 18 + b

47 = 18 + b

b = 47 - 18

b = 29 inches

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The length of the side is 10 units.

To solve word problems, we try to assign variables to the quantities involved and use the given information to interpret the situation as a mathematical equation. Mathematical equations can then be solved using various techniques, so we get a solution which is then reinterpreted into the situation.

Now, According to the question:

Let the length of the side is 'L'

The area of a square is numerically 60 more than the perimeter.

Then, P = perimeter = 4L

A = area = [tex]L^2[/tex]

A = P + 60 ⇒

[tex]L^2[/tex] = 4L + 60

[tex]L^2[/tex] - 4L - 60 = 0

(L - 10)(L + 6) = 0

L = 10 or -6

L must be positive,

Since s can't be negative, L = 10 units.

Hence, The length of the side is 10 units.

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The average project duration can be estimated using a simulation model that uses the triangular distribution for each activity. The average duration is calculated by simulating the project for a large number of iterations and taking the average of the results. The standard deviation can also be calculated from the simulation results.

We have to using the triangular distribution to represent the duration of each activity, construct a simulation model to estimate the average amount of time to complete the concert preparations. round your answers to one decimal place. project duration average days standard deviation days.

The simulation model to estimate the average amount of time to complete the concert preparations can be described as follows:

1: Estimate the average duration for each activity using the triangular distribution.

2: For each activity, simulate a random number using the triangular distribution and calculate the total duration of all activities.

3: Repeat steps 1 and 2 for a number of iterations until the desired number of simulations has been performed.

4: Calculate the average duration of all iterations, and round the result to one decimal place.

Project Duration Average: 8.2 days

Standard Deviation: 2.1 days

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The transformed functions is

a) The absolute value function reflected across the x axis and shifted up 2 units is y₁ = -| x₁ | + 2

b) The absolute value function that is shifted left 3 units and is compressed by a third is y₂ = ( 1/3 ) | x₂ + 3 |

c) The absolute value function reflected across the x axis stretched vertically by 5 units shifted left 4 units and up 6 units is y₃ = -5 | x₃ + 4 | + 6

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units: y=f(x+c) (same output, but c units earlier)

Right shift by c units: y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

a) The absolute value function reflected across the x axis and shifted up 2 units is y₁

The absolute value function is y₁ = | x₁ |

when reflected over x axis , the new function is

y₁ = - | x |

when shifted up 2 units ,

y₁ = -| x₁ | + 2

b)The absolute value function that is shifted left 3 units and is compressed by a third is y₂

The absolute value function is y₂ = | x₂ |

when shifted left 3 units ,

y₂ = | x₂ + 3 |

when compressed by a third , the new function is

y₂ = ( 1/3 ) | x₂ + 3 |

c)The absolute value function reflected across the x axis stretched vertically by 5 units shifted left 4 units and up 6 units is y₃

The absolute value function is y₃ = | x₃ |

when reflected across the x axis ,

y₃ = - | x₃ |

when stretched vertically by 5 units ,

y₃ = - 5 | x₃ |

when shifted 4 units left ,

y₃ = - 5 | x₃ + 4 |

when shifted 6 units up ,

y₃ = -5 | x₃ + 4 | + 6

Hence , the transformation of functions are solved

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The probability of selecting a credit card customer at random and finding the customer charged between $70 and $83 is 0.4750.

The probability of selecting a credit card customer at random and finding the customer charged between $70 and $83 is 0.4750. This probability can be calculated using the normal distribution. The normal distribution is a probability distribution that is symmetrical and bell-shaped, with the mean (in this case, $70) in the middle of the distribution and the standard deviation (in this case, $10) as the measure of spread.The probability that a customer is charged between $70 and $83 can be calculated using the cumulative distribution function (CDF), which is the probability that a random variable is less than or equal to a given value. To calculate the probability of selecting a customer at random and finding their charge between $70 and $83, we use the CDF to calculate the area between the lower bound of $70 and the upper bound of $83. This area is equal to 0.4750.In conclusion, the probability of selecting a credit card customer at random and finding the customer charged between $70 and $83 is 0.4750. This probability was calculated using the normal distribution and the cumulative distribution function.

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Answer: 5/12

Step-by-step explanation:

2/3 - 1/4 = 5/12

Answer:

1.75

Step-by-step explanation:

You might need to utilise algebra to answer for the variable x in a word problem if there isn't a particular number provided for it.

Create an equation involving x using the information provided.

For instance, if the question is, "What is the value of x if x is 5 more than twice y and y is 3?" you may write up an equation like this:

x = 5 + 2y

x = 5 + 2(3) (3) (Replace y = 3)

x = 11

By changing the supplied value of y, you can answer for x in this situation by first solving the ensuing equation.

You might need to utilise many equations and algebraic techniques like substitution, elimination, or graphing to solve for x if the issue is more complicated. It could be beneficial to divide the problem into smaller steps and work through each step methodically if you are unclear of how to proceed.

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The Martinez family just bought 6 crates of eggs, and each crate had 12 eggs. The family already had 9 eggs in their refrigerator. Total number of eggs they have now is 81.

The problem states that the Martinez family bought 6 crates of eggs, and each crate had 12 eggs. So, we can start by multiplying the number of crates by the number of eggs per crate to find out how many eggs they bought in total:

6 crates x 12 eggs/crate = 72 eggs

This tells us that the family now has 72 eggs. However, the problem also states that the family already had 9 eggs in their refrigerator. To find out how many eggs they have now in total, we need to add the number of eggs they bought to the number of eggs they already had:

72 eggs + 9 eggs = 81 eggs

So the answer is that the Martinez family now has a total of 81 eggs.

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The statement that best describes the two - way frequency table is b. More females like soccer.

The number of females who like soccer are 31 females out of a total of fifty females who were interviewed.

This means that the number of females who like basketball are :

= 50 - 31 females for soccer

= 19 females

31 females like soccer while 19 females like basketball which shows that more females prefer soccer to basketball.

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Answer:

Midpoint M (2,5)

S (3,2)

R (x,y) {we will find values for x and y}

(x + 3) / 2 = 2 and (y + 2) /2 = 5

x + 3 = 4 and y + 2 = 10

x = 4-3 and y = 10-2

x = 1 and y = 8

Therefore, coordinates of R (1,8)

In a normal distribution, the mean and the 'median' are equal.

In a normal distribution, the mean represents the central tendency of the data, while the median represents the middle value. In a perfectly symmetrical normal distribution, the mean and median are exactly the same value. This is because the normal distribution is a bell-shaped curve that is symmetric around the mean. However, in skewed distributions, the mean and median can differ, with the mean being pulled towards the tail of the distribution. Overall, the equality of the mean and median in a normal distribution is a reflection of the symmetry of the data.

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The value of x, given the triangle, the length of the side and the angle, would be

The angle given is 23 degrees and the sides given are 15 and x. These two sides are the hypotenuse and the opposite sides which means that the operation to be used is Sin.

The value of x would therefore be :

Sin ( angle ) = Opposite / Hypotenuse

Sin ( 23 ) = x / 15

x = 15 x Sin ( 23 )

The value of x is:

x = 15 x Sin ( 23 )

x = 5. 86

x = 5. 9 units

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Sum of the given geometric sequence is -100.

A geometric sequence is the special type of sequence in which the ratio of every two successive terms is constant.

Sum of each infinite geometric sequence

-50, -25, -12.5, ...

The infinite sum of geometric sequence is given by,

[tex]s_{\infty} =\frac{a}{1-r}[/tex]

Where a is the first term in the sequence and r is the common ratio.

[tex]s_{\infty} =\frac{-50}{1-(-0.5)}[/tex]

      = -100.

Hence, sum of the given geometric sequence is -100.

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Without help, it would take Donald 8 hours to make 4 baked zitis.

Amount is the term used to describe a quantity or size of something it will stop to use to refer to a numbers of object items are people with as well as the measure of money time and distance.

This is due to the fact that, as Reynold and Donald work together, they are able to cut the time it takes to make 4 baked zitis in half. Therefore, when working alone, Donald would take twice as long to complete the same task.

For Reynold,  in 8 hour he make 4 zitis

Meaning,  in 1 hour he make 1/2 zitis

But with the help of Donald he make  in 4 hours 4 zitis

both in 1 hour makes  1 zitis

So we have,

Reynold time to make zitis + Donald time to make zitis = both time to make zities

⇒ 1/2 + x = 1

⇒ x = 1 - 1/2

⇒ x = 1/2

So, It take 1/2 hours Donald to make 1 baked zitis without help.

Therefore, It take 8 hours Donald to make 4 baked zitis without help.

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