Order this set of numbers from LEAST to GREATEST
5, -13/4, -3, 16/5

A- 16/5, 5, -13/4, -3
B- 5, 16/5, -13/4, -3
C- -13/4, -3, 16/5, 5
D- -3, 13/14, 16/5, 5​

We need to know about test statistic to solve the problem. The formula we will need to calculate test statistic is  (sample mean- population mean)/(standard deviation/\(\sqrt{size of sample}\))

Test statistic is a number calculated by a statistical test. It describes how far the observed data is from the null hypothesis of no relationship between variables or no difference among sample groups. The test statistic can be calculated using the sample mean, the population mean and population standard deviation.

test statistic= (sample mean- population mean)/(standard deviation/\(\sqrt{size of sample}\))

Therefore the formula to calculate the test statistic will be (sample mean- population mean)/(standard deviation/\(\sqrt{size of sample}\))

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Answer:

x = 12

y = 9

z = 11

Step-by-step explanation:

so, let's just do all the calculations in there :

(3×5)⁴ = 3⁴×5⁴

(2×3)⁵ = 2⁵×3⁵

(2×5)⁷ = 2⁷×5⁷

multiplying all 3 terms is then

3⁴×5⁴×2⁵×3⁵×2⁷×5⁷

more let's "group" and combine these terms based on the bases of the power operations, as we need to get an expression showing 2, 3 and 5 with their powers.

so, for the base of 2 we have

2⁵×2⁷ = 2¹²

for the base of 3 we have

3⁴×3⁵ = 3⁹

fire the base of 5 we have

5⁴×5⁷ = 5¹¹

so we get

2¹² × 3⁹ × 5¹¹

=>

x=12

y=9

z=11

Answer:

A.) 4991/157216

B.) 2401/1336336

C.) 16399/314432

Step-by-step explanation:

Given the following :

Granny Smith = 23

Honey crisp = 14

Red delicious = 31

Probability = (number of required outcome / number of possible outcomes)

Number of possible outcomes = 23 + 14 + 31 = 68

With replacement :

A.) one of each :

P(granny Smith) × P(Honey crisp) × P(Red delicious)

P(granny Smith) = 23/68

P(Honey crisp) = 14/68 = 7/34

P(red delicious) = 31/68

(23/68 × 7/34 × 31/68) = 4991/157216

B) 4 honey crisp:

P(4 Honey crisp) = P(honey crisp) × P(honey crisp) × P(honey crisp) × P(honey crisp)

7/34 × 7/34 × 7/34 × 7/34 = 2401/1336336

C.) 2 granny Smith and 1 red delicious

P(granny Smith) × P(granny Smith) × P(red delicious)

23/68 × 23/68 × 31/68 = 16399/314432

Answer:

a.  The car sweeps out 0.799 radians per second.

b. f(t) = 8 cos (0.799t)

Step-by-step explanation:

Given that:

The radius r = 8 feet

a.

The time t it takes to complete one full lap = 7.854 seconds

Recall that:

Angular velocity ω = 2π / t

So if in 7.854 seconds, the car sweeps = 2π radian

∴

per second, the car will sweep ω  = 2π/ 7.854

ω = 0.799 rad/sec

Thus, the car sweeps out 0.799 radians per second.

b.

Since, r = 8 feet.

Suppose the car travels an angle θ in time (t),

Then the general equation for the horizontal component is:

f(t) = rcos( ωt)

f(t) = 8 cos (0.799t)

The true statements are:

The given parameters are:

To do this, we simply calculate the angular velocity as follows:

\(\omega = \frac{2\pi}{T}\)

Substitute 7.854 for T

\(\omega = \frac{2\pi}{7.854}\)

Simplify

\(\omega = 0.255 \pi\)

Hence, the car swept out \(0.255 \pi\) radians per seconds

To do this, we simply make use of the general equation for the horizontal component as follows:

\(f(t) = r\cos( \omega t)\)

Substitute 8 for r

\(f(t) = 8\cos( \omega t)\)

Substitute \(\omega = 0.255 \pi\)

\(f(t) = 8\cos( 0.255\pi t)\)

Hence, the function f that determines the car's distance at time t is: \(f(t) = 8\cos( 0.255\pi t)\)

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Answer:

Circle

Step-by-step explanation:

56/120

Step-by-step explanation:

The body masses of the two children in terms of their father's body mass, x, are:

First child's body mass = 5x/6 kg

Second child's body mass = 4x/5 kg

To express the body mass of the man's two children in terms of their father's body mass, we can use the given ratios.

Let the body mass of the man be x kg.

The first child's body mass is five-sixths of their father's body mass:

Body mass of the first child = (5/6) * x

= 5x/6 kg.

The second child's body mass is four-fifths of their father's body mass:

Body mass of the second child = (4/5) * x

= 4x/5 kg.

Therefore, the body masses of the two children in terms of their father's body mass, x, are:

First child's body mass = 5x/6 kg

Second child's body mass = 4x/5 kg

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Answer:

= 16m2o−8mno

Step-by-step explanation:

The collection of sample averages, known as the sampling distribution, would have an average that is equal to the average height of the entire population.

When measuring the height of each team and calculating their average, we are essentially taking samples from the population of all teams. The sampling distribution is created by repeating this process multiple times and calculating the average for each sample. According to the central limit theorem, as the sample size increases, the sampling distribution approaches a normal distribution regardless of the shape of the population distribution.

Therefore, the average of the sampling distribution, which represents the average height of all teams, would be equal to the average height of the entire population. The sampling distribution allows us to make inferences about the population based on the collected samples and provides a measure of the variability of the sample averages.

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40. A vector w that is perpendicular to the plane containing the given points A,B, and C is  (9,-4,-6)

41. A vector w that is perpendicular to the plane containing the given points A,B, and C is  (1,1,3)

40. To find a vector that is perpendicular to the plane containing A, B, and C, we can find the cross product of two vectors that lie in the plane. For example, we can use the vectors AB and AC:

AB = (2-(-1), 1-1, -1-2) = (3,0,-3)

AC = (0-(-1), -2-1, 4-2) = (1,-3,2)

Taking the cross product of these vectors, we get:

AB x AC = (0-(-9), -2-(-2), -3-(-3)) = (9,-4,-6)

So the vector w = (9,-4,-6) is perpendicular to the plane containing A, B, and C.

41. Again, to find a vector that is perpendicular to the plane containing A, B, and C, we can find the cross product of two vectors that lie in the plane. For example, we can use the vectors AB and AC:

AB = (0-1, 1-0, 0-0) = (-1,1,0)

AC = (2-1, 3-0, 1-0) = (1,3,1)

Taking the cross product of these vectors, we get:

AB x AC = (1,1,3)

So the vector w = (1,1,3) is perpendicular to the plane containing A, B, and C.

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The solution is,  -3 4/5 when converted to a decimal is -3.5.

We know that,

A decimal is a number that consists of a whole and a fractional part. Decimal numbers lie between integers and represent numerical value for quantities that are whole plus some part of a whole.

here, we have,

given number is:

-3 4/5

= - (3 + 4/5)

= - 17/5

= -3.5

Hence,  -3 4/5 when converted to a decimal is -3.5.

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Answer:

Step-by-step explanation:

100 : number of trials

49/100: experimental probability

1oo represents the number of trials in the experiment.

49/100 represents the probability of heads in the experiment.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

The number of times the coin was flipped = 100.

Number of heads that land up = 49

Number of tails that land up = 51

Now,

Number of trials = 100

The probability of getting a head.

= 49/100

The probability of getting a tail.

= 51/100

Thus,

100 is the number of trials.

49/100 and 51/100 are experimental probabilities.

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Answer:

(12,-1)

Step-by-step explanation:

Plug in the x and y values into the equation to see if it gives you 14 and 9.

Option 1:

(1) - 2(12)

1 - 24 = -23 Not it

Option 2:

(-1)-2(-12)

-1 + 24 = 23 Not it

Option 3:

(12) - 2(-1)

12 +2 = 14 Yes, but make sure with the second equation

12 +3(-1)

12 - 3 . Works

Answer is (12,-1)

Answer:

its c, i took the test

If z is a standard normal variable, the probability that z lies between -0.55 and 0.55 is D. 0.4176.

The probability that z lies between -0.55 and 0.55 can be found by using the standard normal distribution table or a calculator with a built-in normal distribution function.

Using a standard normal distribution table, we can find the area under the curve between -0.55 and 0.55, which is equivalent to the probability we are trying to find.

The table gives us the area to the left of a z-score, so we need to subtract the area to the left of -0.55 from the area to the left of 0.55.

Looking at the table, we can find that the area to the left of -0.55 is 0.2912, and the area to the left of 0.55 is 0.7088.

Therefore, the area between -0.55 and 0.55 is:
0.7088 - 0.2912 = 0.4176

So the answer is D. 0.4176.

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The probability of finding 0 contaminated pieces in  225 g of chocolate is 5.57 X 10⁻⁷.

Here the number of contaminated fragments follows a Poisson process. Hence, let the distribution for the same be X.

Hence we get X ~ Poi(λt)

where λ is the mean no. of contaminated pieces and t is the no. of bars consumed.

For P(X = x) we get [(λt)ˣ  e^(-λt)]/x!

Here λ = 14.4 and t = 1 Hence we will get

P(X = x) = [(14.4)ˣ e⁻¹⁴°⁴]/x!

Here we need to find the probability of the no. of contaminated pieces = 0

Therefore

P(X = 0) = [(14.4)⁰ e⁻¹⁴°⁴]/0!

Hence the probability of finding 0 contaminated pieces in a bar of chocolate is

P(X = 0) =  e⁻¹⁴°⁴

= 5.57 X 10⁻⁷

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On solving the provided question, by properties of parallel lines we got to know that -  1 - A  2 - C  3 - B  4 - D

When two or more lines cross the intersection line, alternate exterior angles result. These angles are created on a number of sides outside the transverse lines. Any two parallel lines that cross one another create two angles with the horizontal line. In the area between the parallel lines, interior angles are formed, while alternate exterior angles are formed in the area outside the parallel lines.

Matches are -

1 - A

2 - C

3 - B

4 - D

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the rate at which water is being pumped into the tank in cubic centimeters per minute. is 1508527.582 cm³/min

The net rate of flow dV/dt = flow rate in - flow rate out

Let flow rate in = k. Since flow rate out = 8900 cm³/min,

dV/dt = k - 8900

Now, the volume of a cone V = πr²h/3 where r = radius of cone and h = height of cone

dV/dt = d(πr²h/3)/dt = (πr²dh/dt)/3 + 2πrhdr/dt (since dr/dt is not given we assume it is zero)

So, dV/dt = (πr²dh/dt)/3

Let h = height of tank = 11 m, r = radius of tank = diameter/2 = 3/2 = 1.5 m, h' = height when water level is rising at a rate of 21 cm/min = 3.5 m and r' = radius when water level is rising at a rate of 21 cm/min

Now, by similar triangles, h/r = h'/r'

r' = h'r/h = 3.5 m × 1.5 m/12 m = 5.25 m²/12 m = 2.625 m = 262.5 cm

Since the rate at which the water level is rising is dh/dt = 21 cm/min, and the radius at that point is r' = 262.5 cm.

The net rate of increase of water is dV/dt = (πr'²dh/dt)/3

dV/dt = (π(262.5 cm)² × 21 cm/min)/3

dV/dt = (π(68906.25 cm²) × 21 cm/min)/3

dV/dt = 1447031.25π/3 cm³

dV/dt = 4545982.745/3 cm³

dV/dt = 1515327.582 cm³/min

Since dV/dt = k - 6800 cm³/min

k = dV/dt - 6800 cm³/min

k = 1515327.582 cm³/min - 6800 cm³/min

k = 1508527.582 cm³/min

So, the rate at which water is pumped in is 1508527.582 cm³/min

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Answer: their bank balance would be

- 64.49

Step-by-step explanation:

They have 100 in savings and 121.50 in their bank account. It means that the total amount that they have to buy the freezer is

100 + 121.5 = 221.5

The cost of the freezer is 285.99. If they buy the freezer, the amount that would be left in their bank account or the bank balance would be

221.5 - 285.99 = - 64.49

The negative value is due to the face that they the cost of the freezer is higher than what they have in total.

Given:

1 chocolate chip cookie recipe = 12 cup of chocolate chips per batch.

Alonzo wants to make 3 12 batches.

Lets's find the number of chocolate chips he will need.

Number of batches he wants to make is = 3 x 12 = 36 batches

SInce 1 chocolate chip cookie recipe calls for 12 cup of chocolate chips per batch, we have:

The maximum purchase price per unit of the component that Ms. Alexander should negotiate with her supplier is $19.00, which is equal to the variable cost per unit to manufacture the part in-house.

In this scenario, Ms. Alexander needs to determine the maximum price per unit that she should be willing to pay the supplier for the component. She conducted a cost analysis and found that manufacturing the part in-house would require $450,000 in capital equipment and have a variable cost of $19.00 per unit.

Since there is no fixed cost associated with purchasing the component from the supplier, the maximum purchase price per unit should not exceed the variable cost per unit of manufacturing in-house. This ensures that the company does not incur additional costs by outsourcing the component.

Therefore, Ms. Alexander should negotiate a price with the supplier that is equal to or lower than the variable cost per unit, which is $19.00. By doing so, the company can avoid the initial capital investment and ongoing variable costs associated with in-house production, making it more cost-effective to purchase the component from the supplier.

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Offer A will provide a greater total income after 5 years.

Given that an applicant receives a job offer from two different companies, and Offer A is a starting salary of $ 55,000 and a 5% increase for 5 years while Offer B is a starting salary of $ 56,000 and an increase of $ 2,000 per year, to determine which offer will provide a greater total income after 5 years, the following calculation must be performed:

Therefore, Offer A will provide a greater total income after 5 years.

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Answer:

first one

Step-by-step explanation:

Tracey bought 10 movies

some cost 13 and the others 16

Let x be the movies that cost 13 and y ones that cost 16

we can state that

since Tracey both ten

since the total price is 139

so the system is :

\(\left \{ {{13x+16y=139} \atop {x+y=10}} \right.\)

A frustum is one of two pieces of a double cone divided at the vertex. A double cone is a three-dimensional shape that is created by connecting two cones with their vertices touching.

When the double cone is cut through the vertex, it creates two pieces known as frustums. A frustum has a circular base and a smaller circular top, which are parallel to each other. The height of the frustum is the distance between the two circular bases.

The volume of a frustum can be calculated using the formula V = (1/3)h(a^2 + ab + b^2), where h is the height, a is the radius of the larger base, and b is the radius of the smaller top. Frustums are commonly found in architecture and engineering, such as in the design of buildings and bridges.

A "napped cone" is one of two pieces of a double cone divided at the vertex. When a double cone is bisected through its vertex, it results in two identical, mirror-image napped cones. These geometric shapes have various applications in mathematics, engineering, and design due to their unique properties.

Napped cones share some characteristics with regular cones, such as having a circular base, but their pointed vertex is replaced by a flat plane where the double cone was divided. This creates a shape that is both symmetrical and easy to manipulate for various purposes.

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Answer:

7

Step-by-step explanation:

Answer: lol pretty sure its 7

Step-by-step explanation: i divided 35 and 5

Answer:

a) The number of CDs Ahmed has

Hope it helps...

The margin of error should be calculated using a critical value of tα/2 in this scenario.

When calculating a margin of error, the choice of critical value depends on the sample size, the known population standard deviation, and the shape of the population distribution. In this case, the sample size is 200, which is relatively large. With a large sample size, the Central Limit Theorem allows us to approximate the sampling distribution of the mean as approximately normal, even if the population is skewed.

Since the population appears to be skewed and the population standard deviation is known, we should calculate the margin of error using a critical value of tα/2. This is because the t-distribution is more appropriate for skewed populations when the population standard deviation is known. The critical value of tα/2 will be used to determine the margin of error, which will help estimate the true population mean.

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Hey there! I'm happy to help!

Since we are using graphs, we will do not need to algebraically solve this system of equations.

When you graph a system of equations, the solution is always the point at which the two lines intersect.

Here is our system of equations graphed. We see that the lines intersect at about (1 1/3, 2 1/3). Therefore, the correct answer is C. x=1 1/3, y=2 1/3

Have a wonderful day! :D

The hypotheses for the test are H₀: σ₁² = σ₂² and H₁: σ₁² ≠ σ₂². This is a two-tailed test to assess if there is a difference in the standard deviations of sound levels between the areas designated as "casualty doors" and operating theaters. The claim being investigated is whether or not there is a difference in the standard deviations.

The hypotheses for the test are:

H₀: σ₁² = σ₂² (There is no difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

H₁: σ₁² ≠ σ₂² (There is a difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

This hypothesis test is a two-tailed test because the alternative hypothesis is not specifying a direction of difference.

To substantiate the claim that there is a difference in the standard deviations, we will conduct a two-sample F-test at a significance level of 0.10, comparing the variances of the two groups.

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The distance between two raisins will increase by a factor of the square root of 2.

As the bread dough rises and doubles in size, each linear dimension of the dough, including the distance between the raisins, will also double. This means that the distance between two raisins will increase by a factor of 2.

However, since the change in distance is related to a change in the linear dimension, and not the area, the increase in distance is proportional to the square root of 2, not 2. This means that the distance between the two raisins will increase by a factor of the square root of 2, or approximately 1.41.

This increase in distance between the raisins is a result of the increase in the volume of the dough, as the yeast ferments the sugars in the dough, producing carbon dioxide and causing the dough to rise. The increase in volume causes the dough to stretch, resulting in the increased distance between the raisins.

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The perimeter of the new rectangle is given by the expression 2l + 4b - 40 cm.

Given that a rectangle is of length l​ cm and breadth b​ cm.

The length of the rectangle is decreased by 10​ cm, therefore the new length of the rectangle = l - 10 cm.

The breadth is doubled, therefore the new breadth of the rectangle = 2b cm.

The perimeter of the rectangle is given by;

Perimeter = 2(l+b)

Let's substitute l - 10 for the new length and 2b for the new breadth to get;

Perimeter = 2(l-10+2b)

Perimeter = 2(l+2b-20)

Perimeter = 2l+4b-40

Therefore the perimeter of the new rectangle is 2l + 4b - 40.

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