Solve the system of equations using substitution. + 4y = -7
3x +2y = -21
A. (-7,0)
B. (-7, -1)
c. (6,1)
D. (0,7)
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a) The probability that an apple from the tree has a weight greater than 90 grams is of: 0.2514 = 25.14%.

b) i) The p-value of the test is of: 0.0045.

b) ii) The conclusion of the test is given as follows: There is enough evidence to conclude that the mean weight of apples from tree A is greater than the mean weight of apples from tree B, as the p-value of the test is less than the significance level.

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The mean and the standard deviation of the weight of the apples are given as follows:

\(\mu = 85, \sigma = 7.5\)

The probability that an apple from the tree has a weight greater than 90 grams is one subtracted by the p-value of Z when X = 90, hence:

Z = (90 - 85)/7.5

Z = 0.67

Z = 0.67 has a p-value of 0.7486.

1 - 0.7486 = 0.2514 = 25.14%.

For each sample, the mean and the standard error are given as follows:

Hence, for the distribution of differences, the mean and the standard error are given as follows:

The test statistic is given by the division of the mean by the standard error of the distribution of differences, hence:

z = 4.2/1.61 = 2.61.

Using the z-table, with z = 2.61, the p-value is of:

0.0045.

As the p-value is less than the significance level, there is enough evidence to conclude that the mean weight of apples from tree A is greater than the mean weight of apples from tree B.

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Extra people required is 50.

Each of the five workers should increase their efficiency to a rate of 15 sandwiches per 10 hour shift.

Proportions are defined as the concept where two or more ratios are set to be equal to each other.

Question 1 :

Number of associates = 30

Number of direct workers = 30 - 2 = 28

You work 8 hours a day and 5 days a week with two 15 minutes break or 30 minutes break per day.

Direct rate = 150 units per hour

Number of working hours in a week with break = 8 × 5 = 40 hours per week Number of working hours in a week = 7.5 hours per day × 5 days a week

                                                            = 37.5 hours per week

Units that department produce in a 40 hour week = 37.5 × 150 = 5625 units

28 people produce 5625 units in a week

Let x people produce 10,000 + 5625 = 15,625 units in a week

Using proportion,

28 : 5625 = x : 15,625

28 / 5625 = x / 15,625

x = (28 × 15,625) / 5625 = 77.78 ≈ 78

Extra people required = 78 - 28 = 50

Question 2 :

Number of sandwiches made in 10 minutes = 1

Number of sandwiches made in 10 hours = 60

5 workers are there. one worker makes 60/5 = 12 sandwiches

But Deli want number of sandwiches in 10 hours = 75

One worker should make 75/5 = 15 sandwiches instead of 12.

Number of sandwiches made in 8 minutes should be 1.

So the working efficiency on each worker should be increased and produce each one should produce 15 sandwiches in a 10 hour shift.

Hence extra people required in question 1 is 50 and efficiency of each worker in question 2 should be increased to 15 sandwiches in 10 hours shift.

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\( \sf \: 1. \bigg[ \frac{4 + ( - 5)}{ - 2 - 3} \bigg]\bigg[ \frac{14 + ( - 21)}{ 2 - 8} \bigg] \\ \)

\( \sf \longrightarrow \: \bigg[ \frac{4 + ( - 5)}{ - 2 - 3} \bigg]\bigg[ \frac{14 + ( - 21)}{ 2 - 8} \bigg] \\ \)

\( \sf \longrightarrow \: \bigg[ \frac{4 - 5}{ - 2 - 3} \bigg]\bigg[ \frac{14 - 21}{ 2 - 8} \bigg] \\ \)

\( \sf \longrightarrow \: \bigg[ \frac{ - 1}{ - 5} \bigg]\bigg[ \frac{ - 7}{ - 6} \bigg] \\ \)

\( \sf \longrightarrow \: \frac{1}{ 5} \times \frac{ 7}{ 6} \\ \)

\( \sf \longrightarrow \: \frac{7}{30} \\ \)

C) 7/30 ✅

________________________________

\( \sf \: 2. \bigg[ \frac{7+ ( - 6)}{ - 4 - 9} \bigg]\bigg[ \frac{20 + ( - 45)}{ 8 - 2} \bigg] \\ \)

\( \sf \longrightarrow\bigg[ \frac{7 + ( - 6)}{ - 4 - 9} \bigg]\bigg[ \frac{20 + ( - 45)}{ 8 - 2} \bigg] \\ \)

\( \sf \longrightarrow\bigg[ \frac{7 - 6}{ - 4 - 9} \bigg]\bigg[ \frac{20 - 45}{ 8 - 2} \bigg] \\ \)

\( \sf \longrightarrow\bigg[ \frac{1}{ - 4 - 9} \bigg]\bigg[ \frac{ - 25}{ 8 - 2} \bigg] \\ \)

\( \sf \longrightarrow\bigg[ \frac{1}{ - 13} \bigg]\bigg[ \frac{ -25}{ 6} \bigg] \\ \)

\( \sf \longrightarrow \: \frac{ - 25}{ - 78} \\ \)

\( \sf \longrightarrow \: \frac{ 25}{ 78} \\ \)

A] 25 / 78 ✅

________________________________

\( \sf \: 3. \bigg[ \frac{4+ ( - 5)}{ - 2 - 4} \bigg]\bigg[ \frac{18 + ( - 36)}{ 7 - 3} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{4+ ( - 5)}{ - 2 - 4} \bigg]\bigg[ \frac{18 + ( - 36)}{ 7 - 3} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{4 - 5}{ - 2 - 4} \bigg]\bigg[ \frac{18 - 36}{ 7 - 3} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{-1}{ - 6} \bigg]\bigg[ \frac{18 - 36}{ 7 - 3} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{-1}{ - 6} \bigg]\bigg[ \frac{-18}{ 4} \bigg] \\ \)

\( \sf \longrightarrow \frac{18}{ - 24} \\ \)

\( \sf \longrightarrow -\frac{6}{ 8} \\ \)

\( \sf \longrightarrow -\frac{3}{ 4} \\ \)

C] -3/4 ✅

________________________________

\( \sf \: 4. \bigg[ \frac{7+ ( - 3)}{ - 6 - 2} \bigg]\bigg[ \frac{18 + ( - 6)}{ 6- 7} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{7+ ( - 3)}{ - 6 - 2} \bigg]\bigg[ \frac{18 + ( - 6)}{ 6- 7} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{7- 3}{ - 6 - 2} \bigg]\bigg[ \frac{18 - 6}{ 6- 7} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{4}{ - 6 - 2} \bigg]\bigg[ \frac{12}{ 6- 7} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{4}{ - 8} \bigg]\bigg[ \frac{12}{ -1} \bigg] \\ \)

\( \sf \longrightarrow \frac{48}{ 8} \\ \)

\( \sf \longrightarrow \frac{6}{ 1} \\ \)

\( \sf \longrightarrow 6 \\ \)

D] 6 ✅

________________________________

\( \sf \: 5. \bigg[ \frac{8+ ( - 2)}{ - 5- 6} \bigg]\bigg[ \frac{40 + ( - 48)}{ 9 - 8} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{8+ ( - 2)}{ - 5- 6} \bigg]\bigg[ \frac{40 + ( - 48)}{ 9 - 8} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{8 - 2}{ - 5- 6} \bigg]\bigg[ \frac{40 - 48}{ 9 - 8} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{6}{ - 5- 6} \bigg]\bigg[ \frac{-8}{ 9 - 8} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{6}{ - 11} \bigg]\bigg[ \frac{-8}{ 1} \bigg] \\ \)

\( \sf \longrightarrow \frac{-48}{ - 11} \\ \)

\( \sf \longrightarrow \frac{48}{ 11} \\ \)

B] 48/11 ✅

________________________________

Answer:

0.15 = 3/20. 0.369= 369/1000.

Answer:

r = 112

Hope This Helps! If you need a step-by-step let me know!

The Ti-84 Plus calculator can be used to find the z-scores that bound the middle 96% of the area under the standard normal curve. The z-scores should be entered in ascending order and rounded to two decimal places.

To calculate the z-scores, we need to find the boundaries that enclose the middle 96% of the area under the standard normal curve. Since the standard normal curve has a total area of 1, the remaining 4% is divided equally into two tails, each containing 2%. To find the z-scores corresponding to these boundaries, we can use the inverse normal distribution function on the Ti-84 Plus calculator.

Using the inverse normal distribution function, we can find the z-score that corresponds to a cumulative probability of 0.02 (2% on one tail). This z-score represents the lower boundary. Similarly, we can find the z-score corresponding to a cumulative probability of 0.98 (2% on the other tail), which represents the upper boundary.

By entering these z-scores in ascending order and rounding them to two decimal places, we can determine the z-scores that bound the middle 96% of the area under the standard normal curve using the Ti-84 Plus calculator.

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On January 31st, the money invested would have amounted to $10,737,418.

What is meant by investment?

An asset or object acquired with the intention of creating income or recognition is referred to as an investment. The purchase of products that are not consumed right away but will be utilised to create wealth down the road is referred to as an investment in an economic outlook. An investment in finance is a financial asset that is purchased with the expectation that it will either continue to generate income or be sold at a profit at a later date.

Given,

 A penny is invested on January 1.

It doubles each day.

We should find the amount on January 31.

First day = 1

Second day = 2

Third day = 4

Fourth day = 8

So basically if it is the xth day of January, then the amount on that day is 2ˣ⁻¹

Therefore on the January 31st, the money invested would have amounted to

2³¹⁻¹ = 2³⁰ = 1,073,741,824 pennies = $10,737,418.24 = $10,737,418

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Answer:

1:6 and 8:48

Step-by-step explanation:

Answer: delation

Step-by-step explanation:

The three sorts of unbending changes are interpretation, revolution, and reflection. Each of these changes can be utilized to demonstrate that two triangles are compatible, as long as the comparing sides and points are compatible after the change.

Be that as it may, there's one change that cannot be utilized to demonstrate coinciding between two triangles, which may be a enlargement. A expansion may be a change that changes the estimate of an protest, but does not protect separations or points. Subsequently, in case we expand one triangle, we cannot ensure that the comparing sides and points of the two triangles will be compatible.

Answer:

it is 6

Step-by-step explanation:

The age of Jeremy could be less than 22 years

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

Jeremy = Rachel - 2

Let Jeremy = x and Rachel = y

So, we have

y = y - 2

Their ages added together is less than 46

So, we have

x + y < 46

This gives

x + x + 2 < 46

So, we have

2x < 44

Divide

x < 22

Hence, Jeremy could be less than 22 years

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Question

Jeremy is two years older than Rachel. The sum of the ages of Jeremy and Rachel is less than 46

How old could Jeremy be?

Answer 315 people.

Step-by-step explanation:

Answer:

315

Step-by-step explanation:

45% is part of the 700 people who vote for a political party at the upcoming election.

Step 1. Use \(\frac{part}{whole} =\frac{part}{whole}\) where 45% is part of the 700 people

Answer: \(\frac{45}{100} =\frac{?}{700}\)

Step 2. Divide 45 by 100

Answer: 0.45

Step 3. Multiply it by 700

Answer: 315

so 315 people were planning to vote for a political party

a. The parameter values that describe the distribution of the length of the cylinders are a mean (μ) of 3.25 inches and a standard deviation (σ) of 0.003 inches.

b. The probability density function (PDF) for the length of the cylinders is given by f(x) = (1 / (0.003 * √(2π))) * exp(-(x - 3.25)^2 / (2 * 0.003^2)). This formula represents the likelihood of observing a specific length (x) of the cylinders, assuming a symmetrical, Normally distributed data with a mean of 3.25 inches and a standard deviation of 0.003 inches.

a. The parameter values that describe the distribution of the length of the cylinders are:

Mean (μ): 3.25 inches

Standard deviation (σ): 0.003 inches

b. The probability density function (PDF) of a Normally distributed random variable with a mean of μ and a standard deviation of σ is given by:

f(x) = (1 / (σ * √(2π))) * exp(-(x - μ)^2 / (2σ^2))

In this case, for the length of the cylinders, the PDF would be:

f(x) = (1 / (0.003 * √(2π))) * exp(-(x - 3.25)^2 / (2 * 0.003^2))

This formula represents the probability density function that describes the likelihood of observing a specific length (x) of the cylinders, given the mean and standard deviation of the distribution.

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Usando conceptos de probabilidad, se encuentra que hay una probabilidad de 1/12 de de obtener 5 y sol.

---------------------------------

\(P(A \cap B) = P(A)P(B)\)

---------------------------------

Entonces, la probabilidad deseada viene dada por

\(P(A \cap B) = P(A)P(B) = \frac{1}{6} \times \frac{1}{2} = \frac{1}{12}\)

Probabilidad de 1/12 de de obtener 5 y sol.

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Answer:

a.

Step-by-step explanation:

The volume of cube 4x².

Volume is a three-dimensional measurement that's used to gauge a solid shape's capacity. It implies that the volume of a closed form determines how much space it can occupy in three dimensions.

We have,

Edges of cube as = 4 , x and x.

So, volume of cube

= 4 x (x . x)

= 4 . x²

= 4x²

Thus, the volume of cube 4x².

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Answer:

A. 6+6+6+6=24

Hope this helps!

Answer:

its a

Step-by-step explanation:

⇒ because if you add 6 four types it equals = 24 inches hope this helped

1. Set of states in the United States whose names start with a C: {Connecticut, California, Colorado} (Set-builder notation: {x | x is a state in the United States and the name of the state starts with a C})

2. Set of students in the class who have at least one brother: {Alice, Bob, Charlie, Emma, Jack} (Set-builder notation: {x | x is a student in the class and x has at least one brother})

Set of states in the United States whose names start with a C:

By listing: {Connecticut, California, Colorado}

Set-builder notation: {x | x is a state in the United States and the name of the state starts with a C}

Set of students in the class who have at least one brother:

By listing: {Alice, Bob, Charlie, Emma, Jack}

Set-builder notation: {x | x is a student in the class and x has at least one brother}

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Answer:

Answer is B

Step-by-step explanation:

y = -1

tan(41π/36) can be written in terms of the tangent of a positive acute angle as (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

To express tan(41π/36) in terms of the tangent of a positive acute angle, we need to find an angle within the range of 0 to π/2 that has the same tangent value.

First, let's simplify 41π/36 to its equivalent angle within one full revolution (2π):

41π/36 = 40π/36 + π/36 = (10/9)π + (1/36)π

Now, we can rewrite the angle as:

tan(41π/36) = tan((10/9)π + (1/36)π)

Next, we'll use the tangent addition formula, which states that:

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))

In this case, A = (10/9)π and B = (1/36)π.

tan(41π/36) = tan((10/9)π + (1/36)π) = (tan((10/9)π) + tan((1/36)π)) / (1 - tan((10/9)π)tan((1/36)π))

Now, we need to find the tangent values of (10/9)π and (1/36)π. Since tangent has a periodicity of π, we can subtract or add multiples of π to get equivalent angles within the range of 0 to π/2.

For (10/9)π, we can subtract π to get an equivalent angle within the range:

(10/9)π - π = (1/9)π

Similarly, for (1/36)π, we can add π to get an equivalent angle:

(1/36)π + π = (37/36)π

Now, we can rewrite the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Since we are looking for an angle within the range of 0 to π/2, we can further simplify the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Therefore, tan(41π/36) can be written in terms of the tangent of a positive acute angle as the expression given above.

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Step-by-step explanation:

solution

here, let

b= 16

p= 12

h=x=?

now, we know that,

h=√p^2+ b^2

= √12^2+ 16^2

= √144+ 256

= √400

=20 in Ans

therefore, x= 20 in

hope i helped

From the information given, it can be deduced that the actual distance from Terre Haute to Indianapolis to Bloomington is 150km.

From the complete information, we are told that on the map of Indiana, 1cm = 50km.

Therefore, since Terre Haute to Indianapolis to Bloomington measures 3 cm on the map, the actual distance will be:

= 3 × 50 = 150km

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Answer:

if you are from connexus 8th grd 02051 pre-algebra A unit 5 lesson 6

then here are the correct answers

Step-by-step explanation:

1. B. 150 km

2. A. 300 km

3. D. 7.5 cm

4. B. 30 yd ^ 2

5. A. 90 x 45

i hope this helps please coment if you can! = ) <3

Answer:

I think it is 4 white and 3 blue

Step-by-step explanation:

Because they have 3 cups of white then 6 cups of white so i think they multiplied it. Then they have 4 cups of blue then 8 cups of blue. So if you multiply it, it will give you the answer. I hope this is right and it helped and can you mark me brainliest!!!!!!!!

Answer:

1. <2, <7

2. 58

3. 78

4. a and b

h5. <2 and <7 ( i think this is the same question as the first one)

Step-by-step explanation:

2. 2x + 7 = 123 (you have to make them equal to each other because they are consecutive interior angles)

2x + 7 = 123, subtract 7

2x = 116, divide 2 for both sides to make x by itself

x = 58

3. 78 because of consecutive interior angles

Standard deviation is the square root of variance .

So,

It is used in measuring any deviation or shift from the calculated mean.  

From a data set, the mean of the data can be determined with which the standard deviation can be measure.

Therefore, Standard deviation is use to measure variation that exist in an individual data set. There are different type of data set from which variation is measured.

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The ordered functions from least to greatest average rate of change from x = 0 to x = 1 is given as follows:

g(x), f(x), h(x).

The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function. Hence we must identify the change in the output, the change in the input, and then divide then to obtain the average rate of change.

From x = 0 to x = 1, the input changes by one, hence we must simply obtain the change in the output for each function:

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Answer:

f=1.5⋅d or equivalent. The bag will last 140 days since 210÷1.5=140.

Step-by-step explanation:

Therefore, the rank of matrix 'a' in this case would be 5.

To find the rank of a matrix, we need to perform row reduction to obtain its row echelon form (REF) or reduced row echelon form (RREF). However, since the matrix 'a' is not provided, I cannot perform the calculations or determine its rank.

The rank of a matrix is equal to the number of non-zero rows in its row echelon form or reduced row echelon form. If the system of equations 'ax = 0' has a two-dimensional solution space, it means that the rank of matrix 'a' is less than the number of columns (6) but greater than 4 (since the solution space is two-dimensional).

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Answer:

f(-1) = 3

Step-by-step explanation:

This line has function f(x) = 2x - 1, so

f(-1) = 3.

Answer:

f(-1) = 3

Step-by-step explanation:

See attached.  For some reason Brainly thinks my explanation has links or swear words.  It does not.  

The surface area of the given cylinder is 602.88 square centimeters.

The surface area of the cylinder is: A = 2πr(r+h)

where 'r' is the radius of the base (circle) of the cylinder

'h' is the height of the cylinder

The cylinder with a height of 10 cm and a radius of 6 cm.

⇒ A = 2πr(r+h)

Here h = 10 cm and r = 6 cm

Substitute the known values in the above formula,

⇒ A = 2(3.14)(6)(6+10)

⇒ A = (12.56)(6)(16)

Apply the multiplication operation, and we get

⇒ A = 602.88

Therefore, the surface area of the given cylinder is 602.88 cm².

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