1. construct a stem-and-leaf plot of the data
45, 50, 54, 56, 57, 57, 64,65,66,71, 75, 76,83,83,83,
84,84,85,86,86,86,89,89,89,91,96,99

Answer:

C.) 75

Step-by-step explanation:

Answer:

1400 cm/ 2.54 cm per inch = 551 inches. Step-by-step explanation: There are 39.3701 inches in 1 meter, so all you have to do is multiply. :) 551 inches.Step-by-step explanation:

Answer:

3/5

can also be written as 3:5

Step-by-step explanation:

Use:

squares/circles

Fill in the given info.

6/10

simplify (reduce the fraction)

6/10 = 3/5

3/5 is the ratio in simplest form.

For this case

P = 10 000

i=0.055

t=120

After you compute the formula you would get

A = 6 170 141

The range of milk production that 95% of the cows will fall within is option B: 4.8 gallons to 7.6 gallons.

To find the range of daily milk production that 95% of the cows will fall within, we can use the empirical rule, which states that for a normal distribution:

About 68% of the observations fall within one standard deviation of the mean.

About 95% of the observations fall within two standard deviations of the mean.

About 99.7% of the observations fall within three standard deviations of the mean.

Since we are looking for the range of milk production that 95% of the cows will fall within, we need to find the range that is within two standard deviations of the mean. That range is:

Mean ± 2SD

= 6.2 ± 20.7

= 6.2 ± 1.4

= [4.8, 7.6]

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Answer:

B=28

Step-by-step explanation:

The maximum price Matthew can pay for the car, considering his repayment capability and the loan terms, is approximately $126,318.29.

To determine the maximum price Matthew can pay for the car, we need to consider his repayment capability and the terms of the loan.

Matthew can make annual repayments of $35,000. Since the loan term is six years, the total amount he can repay over the loan period is $35,000 multiplied by six, which equals $210,000.

To calculate the maximum price of the car, we need to account for the interest rate of 9.25%. The interest rate represents the cost of borrowing and is applied to the loan amount.

Let's assume the loan amount is denoted by P.

The formula to calculate the future value of a loan with interest is:

FV = P(1 + r)^n

Where:

FV = Future value (total amount repaid)

P = Principal amount (maximum price of the car)

r = Interest rate per period (9.25% or 0.0925)

n = Number of periods (six years)

Since Matthew can repay a total of $210,000 over the loan period, we can set up the equation:

$210,000 = P(1 + 0.0925)^6

Now we can solve for P:

P = $210,000 / (1 + 0.0925)^6

Evaluating this expression, we find:

P ≈ $126,318.29

Therefore, the maximum price Matthew can pay for the car, considering his repayment capability and the loan terms, is approximately $126,318.29.

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Answer:

33/12 or 2.75

Step-by-step explanation:

6 1⁄6 - 3 5⁄12

37/6 - 41/12

74/12 - 41/12

33/12 or 2.75

Answer:

D is the correct option

Step-by-step explanation:

this implies that Engels will grade the examination paper within a maximum time of 20 * 12 minutes, but if she adds comments then the time will exceed 20 * 12 minutes

The option that shows the relationship between the squares that he shaded yellow and green would be = 0.4 which is less than 0.6. That is 0.4< 0.6 option A.

The figure that Raul has is made up of = 100 congruent squares.

This means the all the squares in the figure are the same in size.

The fraction of the figure that is painted yellow = 40/100 = 0.4.

The fraction of the square that is painted green = 60/100 = 0.6.

From the image attached, the relationship between the portion shaded yellow and the portion shaded green is that 0.4 is less than 0.6.

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Hey there! I'm happy to help!

NUMBER 1

This is a trick to solve any proportion.

Multiply the diagonal numbers.

5(16)=80

Divide by the number that isn't the one you want to find.

90/8=10

And you are left with the number you haven't touched. We haven't touched x, so x=10.

NUMBER 2

Cross multiply.

45(-50)=-2250

Divide.

-2250/3=-750

So x=-750.

QUESTION 3

4(27)=108

108/12=9

So x+3=9, subtract 3 from both sides x=6.

Have a wonderful day! :D

The given function is strictly decreasing in interval (−∞, 4) & trictly increasing in interval  (4, −∞).

What is an increasing and decreasing functions?

For a given function, y = F(x), the function is known as an increasing function if the value of y increases as the value of x increases, and the function is known as a decreasing function if the value of y decreases as the value of x increases.

We have,

\(\frac{5}{512}\left(x-4\right)^2\left(x-8\right)\left(x-10\right)\left(x^2+16\right)\)

\(\frac{d}{dx}\left(\frac{5}{512}\left(x-4\right)^2\left(x-8\right)\left(x-10\right)\left(x^2+16\right)\right)\)

\(=\frac{5}{512}\frac{d}{dx}\left(\left(x-4\right)^2\left(x-8\right)\left(x-10\right)\left(x^2+16\right)\right)\)

\(f'(x)=\left(x-4\right)^2,\:g=\left(x-8\right)\left(x-10\right)\left(x^2+16\right)\)

\(=\frac{5}{512}\left(\frac{d}{dx}\left(\left(x-4\right)^2\right)\left(x-8\right)\left(x-10\right)\left(x^2+16\right)+\frac{d}{dx}\left(\left(x-8\right)\left(x-10\right)\left(x^2+16\right)\right)\left(x-4\right)^2\right)\)\(=\frac{5}{512}\left(2\left(x-4\right)\left(x-8\right)\left(x-10\right)\left(x^2+16\right)+\left(4x^3-54x^2+192x-288\right)\left(x-4\right)^2\right)\)

\(f'(x)=\frac{5\left(x-4\right)\left(3x^4-53x^3+300x^2-816x+1856\right)}{256}\)

The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace y with 0 and solve for x.

x = 4, 4i, −4i, 10, 8

∴ f′(x) = 0  

   x = 4,

Now, the point 4 divides the real line into two disjoint intervals i.e., (−∞, 4) and (4, −∞)

In interval (−∞, 4),  f′(x) < 0

Hence, the given function (f) is strictly decreasing in interval (−∞, 4)

​

In interval (4, −∞),  f′(x) > 0

Hence, the given function (f) is strictly increasing in interval  (4, −∞)

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​

Fix(2.5) is equal to 1. The expected value of X (E(X)) is equal to 13/36. P(X > 0.3 and X < 0.6) is equal to 0.432.

A continuous random variable X has a probability density function (pdf) given by:

fix (x) = {x² + 4/3 x if 0 < x < 1

0 otherwise. Let's solve the questions step-by-step: To find the cumulative distribution function (CDF) Fix(t) of X, we integrate the pdf from 0 to t. To find Fix(-3), we integrate the pdf from 0 to -3, which is not possible since -3 is outside the valid range of x (0 < x < 1). Therefore, Fix(-3) does not exist. To find Fix(0.6), we integrate the pdf from 0 to 0.6:

∫(0 to 0.6) (x² + 4/3 x) dx = [1/3 x³ + 2/3 x²] (0 to 0.6)

= (1/3 × 0.6³ + 2/3 × 0.6²)

= 0.432.

Therefore, Fix(0.6) is equal to 0.432. To find Fix(2.5), we integrate the pdf from 0 to 1 (since the valid range of x is 0 < x < 1):

∫(0 to 1) (x² + 4/3 x) dx = [1/3 x³ + 2/3 x²] (0 to 1)

(1/3 × 1³ + 2/3 × 1²) = 1.

Therefore, Fix(2.5) is equal to 1. To find the expected value of X (E(X)), we need to integrate x times the pdf from 0 to 1:

E(X) = ∫(0 to 1) x × (x² + 4/3 x) dx.

Simplifying the integral:

E(X) = ∫(0 to 1) (x³ + 4/3 xv) dx

= [1/4 x⁴ + 4/9 x³] (0 to 1)

= (1/4 × 1³ + 4/9 × 1³)

= 13/36.

Therefore, the expected value of X (E(X)) is equal to 13/36. To find P(X > 0.3 and X < 0.6), we need to use the definition of conditional probability:

P(X > 0.3 and X < 0.6) = P(X < 0.6) - P(X < 0.3).

Using the CDF we obtained earlier, we have:

P(X > 0.3 and X < 0.6) = Fix(0.6) - Fix(0.3)

= 0.432 - 0

= 0.432.

Therefore, P(X > 0.3 and X < 0.6) is equal to 0.432.

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\(y=-\frac{5}{4}x -5\)Answer:



Step-by-step explanation:

As Franklin is purchasing replacement, the Nerf football cost an amount of $9.48.

To get the cost of the Nerf football, we will subtract the cost of the playground balls and the package of jump ropes from the total order cost.

The cost of 4 playground balls is:

= 4 * $17.25

= $69.00

The cost of package of 10 jump ropes = $18.75

So, the total cost of playground balls and jump ropes will be:

= $69.00 + $18.75

= $87.75

Cost of Nerf football = Total order cost - Total cost of playground balls and jump ropes

Cost of Nerf football = $97.23 - $87.75

Cost of Nerf football = $9.48

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The conditions that must be met to use the normal approximation for the confidence level are np>5 and n(1-p)>5

Sampling Distribution: A sampling distribution is a probability distribution of a statistic that is obtained through repeated sampling of a specific population. It describes a range of possible outcomes for a statistic, such as the mean or mode of some variable, of a population.

Given that the sampling distribution of the population proportion is based on a binomial distribution.

The conditions that must be met to use the normal approximation for the confidence level are np>5 and n(1-p)>5

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The least number of packs of nails Jess needs to buy is 1.

To find the least number of packs of nails Jess needs to buy, we need to find the lowest common multiple (LCM) of the pack sizes of hammers and nails.
Step 1: Identify the numbers
Hammers come in packs of 3, and nails come in packs of 6.
Step 2: Find the LCM of 3 and 6
List the multiples of each number:
Multiples of 3: 3, 6, 9, 12, ...
Multiples of 6: 6, 12, 18, 24, ...
The lowest common multiple of 3 and 6 is 6.
Step 3: Determine the number of packs of nails.

Since the LCM is 6 and nails come in packs of 6, Jess needs to buy 1 pack of nails to have the same number of each item.

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The expected net payoff E(m) is equal to m + 10.5 and the optimal value of m is 20.

To calculate the expected net payoff, we need to determine the probabilities of stopping at each value from 1 to 20 and calculate the corresponding payoff for each case.

Let's denote the expected net payoff as E(m), where m is the threshold value at which the gambler decides to stop.

(a) To calculate the expected net payoff E(m), we sum the probabilities of stopping at each value multiplied by the payoff for that value.

E(m) = (1/20) * m + (1/20) * (m + 1) + (1/20) * (m + 2) + ... + (1/20) * 20

Simplifying the equation:

E(m) = (1/20) * (m + (m + 1) + (m + 2) + ... + 20)

E(m) = (1/20) * (20 * m + (1 + 2 + ... + 20))

E(m) = (1/20) * (20 * m + (20 * (20 + 1)) / 2)

E(m) = (1/20) * (20 * m + 210)

E(m) = m + 10.5

Therefore, the expected net payoff E(m) is equal to m + 10.5.

(b) To find the optimal value of m, we need to maximize the expected net payoff E(m).

Since E(m) = m + 10.5, we can see that the expected net payoff is linearly increasing with m.

Therefore, the optimal value of m would be the maximum possible value, which is 20.

Hence, the optimal value of m is 20.

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Answer:

he is using at least 1,237 minutes a month

Step-by-step explanation:

15+0.06m ≥ 89.22

m ≥ 1,237

Answer:

Step-by-step explanation:

The experimental probability of the cube landing on three is 1/10.

The required dimensions of the given prism are 3/2, 3/2, 2 centimeter.

Prism  is a three-dimensional strong item where the two closures are indistinguishable. It is the mix of the level countenances, indistinguishable bases and equivalent cross-segments. The essences of the crystal are parallelograms or square shapes without the bases.

We have,

Side of the cube is 1/2 centimeter.

Length has 3 cubes,

Length = 3(1/2) = 3/2 = 3/2 centimeter

And

Width has 3 cubes,

Width = 3(1/2) = 3/2 centimeter.

Similarly,

Height has 4 cubes,

Height = 4/2 = 2 centimeter.

Thus, dimensions of the cuboid are 3/2, 3/2, 2 centimeter.

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The conversion method from milimeter to nanometer is Quantity in nanometer = quantity in milimeter × 10⁶.

In the question, the two short forms mm and nm are representative of milimeter and nanometer. As per the known information, the milimeter represents 1/10³ meters and nanometer represents 1/10⁹ meters. So, we see that the difference between the exponents of 10 is 6 (as 9 - 3 = 6).

Therefore, the conversion of milimeter to nanometer will be through the mentioned formula -

Quantity in nanometer = quantity in milimeter × 10⁶

For instance, the quantity 3 mili meters in nanometer will be calculated as follows.

Quantity in nanometer = 3 × 10⁶ nanometer

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The probability that the bolt will be inserted in 19 minutes or less is 0.8413.

It should be noted that the probability will be illustrated as:

P(X < x) = P[z < (x - u/sd)]

where

x = number

u = mean

SD = standard deviation

Therefore given the numbers, this will be:

P(x < 19) = P(z < (19 - 15)/4)

= P(z < 4/4) = P(z < 1)

= 0.8413

Therefore, the probability that the bolt will be inserted in 19 minutes or less is 0.8413.

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The mean time it takes for workers at a factory to insert a delicate bolt into an engine is 15 minutes. The standard deviation of time to insert the bolt is 4.0 minutes and the distribution of time is approximately Normally distributed. For a randomly selected worker, what is the approximate probability the bolt will be inserted in 19 minutes or less?

Answer:

cant read it at all

Step-by-step explanation:

Answer:

Step-by-step explanation:

take 45 degree as reference angle

using cos rule

cos 45=adjacent/hypotenuse

1/\(\sqrt{2}\)=x/4(do cross multiplication)

x\(\sqrt{2\)=4

x=4/\(\sqrt{2}\)

x=2\(\sqrt{2}\)

The width of each class interval from the given grouped frequency distribution table is 9.

In a frequency distribution, the numerical width of a class is referred to as the class interval. Data is organised into classes in a grouped frequency distribution. The class interval is determined by the difference between the upper and lower class limits.

The give class intervals are 20-29, 30-39, 40-49 and 50-59.

The size, or width, of a class interval is the difference between the lower and upper class boundaries and is also referred to as the class width, class size, or class length.

So, class width = Upper class - Lower class

29-20=9

39-30=9

Therefore, the width of each class interval is 9.

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Answer:

1/17 + 4i/17

Step-by-step explanation:

Answer:

Step 1: 8x - 12 = 1; Step 2: 8x = 13

Step-by-step explanation:

Given equation:

4(2x - 3) = 1

Step 1: open the parenthesis

4(2x - 3) = 1

8x - 12 = 1

Step 2: collect like terms

8x - 12 = 1

8x = 1 + 12

8x = 13

step 3: divide both sides by the coefficient of x

8x = 13

x = 13/8

The correct steps to solve the equation:

Step 1: 8x - 12 = 1; Step 2: 8x = 13