18. a population has a mean of 300 and a standard deviation of 12. a sample of 64 observations will be taken. the probability that the sample mean will be between 295 to 305 is

Answer:

Step-by-step explanation:

To perform a dilation with a center at the origin and a scale factor of 2, we multiply each coordinate by 2.

For point X(-3, 1):

x-coordinate: -3 * 2 = -6

y-coordinate: 1 * 2 = 2

So the image of point X after the dilation is X'(-6, 2).

For point Y(-1, 2):

x-coordinate: -1 * 2 = -2

y-coordinate: 2 * 2 = 4

So the image of point Y after the dilation is Y'(-2, 4).

For point Z(2, 1):

x-coordinate: 2 * 2 = 4

y-coordinate: 1 * 2 = 2

So the image of point Z after the dilation is Z'(4, 2).

Graph of the original triangle XYZ:

   Y(0, 2)

     /\

    /  \

   /____\

X(0, 0)  Z(3, 0)

Graph of the triangle after dilation

   Y'(-2, 4)

      /\

     /  \

    /____\

X'(-6, 0)  Z'(4, 0)

its hard

The number of bacteria that were present when the antibiotic was first introduced is 14

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

The graph (see attachment)

The number of bacteria that were present when the antibiotic was first introduced is when the graph intersects with the y-axis

In this case, the graph intersects with the y-axis at

y = 14

Hence, the number of bacteria that were present when the antibiotic was first introduced is 14

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Complete question

Biologists introduced a population of bacteria to a test environment. The function f models the population size (in thousands) as a function of time (in days) after introduction.

The graph shows a bacteria population (see attacment)

How many bacteria were present when the antibiotic was first introduced?

The calculated area of the middle shape is 18 square units

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

The figures

From the figure, we have the middle shape to be a rectangle

The width of the rectangle is

Width = 6

The length of the rectangle is calculated as follows

15 = 3 * 5

27 = 3 * 3 * 3

The common factor is 3

So, we have

Length = 3

The area of the rectangle is calculated as

Area = Length * Width

So, we have

Area = 3 * 6

Evaluate

Area = 18

Hence, the area of the middle shape is 18 square units

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The amount of fluid in container B is 9.5 ounces.

to separate into two or more parts or pieces. : to separate into classes or categories. : cleave entry 2, part.

To determine the amount of fluid in container B, we can divide the amount of fluid in container A by the given ratio of 8. Since container A contains 76 ounces, we divide 76 by 8 to find that each unit of the ratio represents 9.5 ounces. Therefore, container B would contain 9.5 ounces of fluid.

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Answer:

0.714

Step-by-step explanation:

5/7

(5X100) / 7 = 500/7.

50/7 = 7 remainder 1. carry that one over and place it before last zero in 500.

10/7 = 1 remainder 3.

we have 71 remainder 3.

3/7: 300/7 = 42.83

we now have answer of 0.714282

= 0.714 to nearest thousandth

You have 48 different choices for your schedule if you need to select one math, one English, one science, and one history course. It's important to note that this calculation assumes that there are no restrictions or prerequisites for the courses, and that all options are available to all students.

When selecting your schedule in school, you have to choose one math course from the three options, one English course from the four options, one science course from the two options, and one history course from the two options. To find out how many different schedule options you have, you need to multiply the number of options for each subject. So, you have:
3 options for math x 4 options for English x 2 options for science x 2 options for history = 48 possible schedule combinations.
Therefore, you have 48 different choices for your schedule if you need to select one math, one English, one science, and one history course. It's important to note that this calculation assumes that there are no restrictions or prerequisites for the courses, and that all options are available to all students.
To determine the number of possible schedules, you need to multiply the number of choices for each subject together. You have three math courses, four English courses, two science courses, and two history courses. The formula for calculating the total number of choices is:
Total choices = (Math choices) x (English choices) x (Science choices) x (History choices)
Total choices = (3) x (4) x (2) x (2) = 48
So, you have 48 different possible schedules when selecting one math, one English, one science, and one history course.

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These measurements are based on the Original ratio of 1 pouch of tuna to 26 oz (737g) of mayonnaise. If you prefer a different ratio of tuna to mayonnaise, the amounts needed for a double batch may be different.

If one pouch of tuna is mixed with 26 oz (737g) of mayonnaise to make a full batch, then to make a double batch of tuna, we need to double the amounts of both the tuna and the mayonnaise.

we simply need to multiply the amount of tuna in a single batch by 2:

1 pouch of tuna x 2 = 2 pouches of tuna

So, we need 2 pouches of tuna for a double batch.

26 oz (737g) of mayonnaise x 2 = 52 oz (1474g) of mayonnaise

So, we need 52 oz (1474g) of mayonnaise for a double batch.

Therefore, to make a double batch of tuna, we would need 2 pouches of tuna and 52 oz (1474g) of mayonnaise. It's important to note that these measurements are based on the original ratio of 1 pouch of tuna to 26 oz (737g) of mayonnaise. If you prefer a different ratio of tuna to mayonnaise, the amounts needed for a double batch may be different.

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It is possible that the question or problem described could be investigated using a mathematical population model. A population model is a mathematical representation of a population, which can be used to make predictions about the population’s behavior and characteristics.

The usefulness of such a model would depend on the specific question or problem at hand. If the question involves understanding how a population will grow or change over time, a mathematical model could be very helpful. However, if the question is more complex and involves multiple factors or variables, a mathematical model may not be sufficient on its own.

For example, if the question is about predicting the spread of a disease in a population, a mathematical model that takes into account the size of the population, the infectiousness of the disease, and the effectiveness of various interventions could be very useful. On the other hand, if the question is about understanding the motivations and behavior of individuals within a population, a mathematical model may not be the best approach. In this case, other methods such as surveys or interviews may be more appropriate.

In summary, whether or not a mathematical population model is appropriate for investigating a question or problem depends on the specific details of that question or problem. In some cases, a population model can provide valuable insights and predictions, while in other cases it may not be sufficient on its own.

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The annual interest rate, r, is 0.1 or 10%. A 10% annual interest rate resulted in the investment growing from $5,000 to $6,050 in 2 years.

To find the annual interest rate, r, we can rearrange the compound interest formula A = P(1 + r) and solve for r.

Given that an investment of $5,000 grows to $6,050 in 2 years, we can substitute these values into the formula:

$6,050 = $5,000

[tex] {1 + r}^{2}[/tex]

Dividing both sides by $5,000, we have:

1.21 =

[tex](1 + r)^2[/tex]

Taking the square root of both sides, we get:

√1.21 = 1 + r

Simplifying, we have:

1.1 - 1 = r

0.1 = r

This means that the investment grew by 10% annually over the 2-year period. Compound interest is calculated by adding the interest earned to the initial amount, and as time passes, the interest is earned on both the initial amount and the accumulated interest from previous periods. In this case, a 10% annual interest rate resulted in the investment growing from $5,000 to $6,050 in 2 years.

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The probability of selecting exactly two mid-sized cars and four compact cars out of a total of six cars is approximately 11.56%.

The answer to this question involves using the formula for combinations and multiplying the probabilities of each selected car.

Calculate the number of ways to select two mid-sized cars and four compact cars.
- Choose 2 mid-sized cars from 10: C(10, 2) = 10! / (2! * (10 - 2)!) = 45 ways
- Choose 4 compact cars from 15: C(15, 4) = 15! / (4! * (15 - 4)!) = 1365 ways

There are a total of 25 cars to choose from and we need to select 2 mid-sized cars from the 10 available and 4 compact cars from the 15 available. Using the formula for combinations, we get:

C(10,2) * C(15,4) = 45 * 1365 = 61,425

This represents the number of ways we can select exactly 2 mid-sized cars and 4 compact cars. To find the probability, we divide this number by the total number of possible selections:

C(25,6) = 53,130

So the probability of selecting exactly 2 mid-sized cars and 4 compact cars is:

61,425 / 53,130 ≈ 0.1156 or 11.56%

In conclusion, the probability of selecting exactly two mid-sized cars and four compact cars out of a total of six cars is approximately 11.56%.

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False. The formula PV - FV(1 + n) does not determine the present value of $1.

But rather it is a formula used to calculate the present value of a future cash flow or investment. PV stands for present value, FV stands for future value, and n represents the number of periods for which the investment will be held. The formula states that the present value of an investment or cash flow is equal to the future value of that investment or cash flow, discounted at a specified rate of return over a specific period of time.

In other words, the formula is used to determine the value today of a future cash flow or investment based on the time value of money. By discounting the future value of the cash flow or investment at a specified rate, the formula calculates the present value that would be equivalent to receiving that cash flow or investment at a future date.

Therefore, the correct statement would be: The formula PV - FV(1 + n) is used to determine the present value of a future cash flow or investment.

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The product of [tex]\sqrt{30}[/tex] and [tex]\sqrt{10}[/tex] is 10[tex]\sqrt{3}[/tex].

The correct answer would be 10[tex]\sqrt{3}[/tex].

To find the product of [tex]\sqrt{30}[/tex] and [tex]\sqrt{10\\}[/tex], we can simplify it by multiplying the square roots and simplifying the result.

[tex]\sqrt{30 * 10 = (30 * 10) = 300}[/tex]

Now, let's simplify [tex]\sqrt{300}[/tex]. To do this, we can find the prime factorization of 300:

[tex]300 = 2 * 2 * 3 * 5 * 5 = 2^2 * 3 * 5^2[/tex]

Taking the square root of 300:

[tex]\sqrt{300}[/tex] = ([tex]\sqrt{(2^2 * 3 * 5^2)}[/tex]

Using the properties of square roots, we can split the square root into separate square roots:

[tex]\sqrt{300}[/tex] = [tex]\sqrt{2^2}[/tex] * [tex]\sqrt{3}[/tex] * [tex]\sqrt{5^2 }[/tex]

Simplifying each square root separately:

[tex]\sqrt{2^2}[/tex] = 2

[tex]\sqrt{3[/tex] = [tex]\sqrt{3[/tex]

[tex]\sqrt{5^2 }[/tex]= 5

Combining the simplified square roots:

[tex]\sqrt{300}[/tex] = 2[tex]\sqrt{3}[/tex] * 5 = 10[tex]\sqrt{3}[/tex]

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The solution of the system of equations 5x-4y=34 and -x+8y=22 is x = -6 and y = 4, or (x, y) = (-6, 4).

Given the system of equation in the question;

5x - 4y = 34 _____1

-x + 8y = 22 _____2

To solve the system of equation, first solve for x in equation 2 and plug it  into equation 1.

-x + 8y = 22

x = 8y - 22 _____ 3

Plug equation 3 into equation 1

5x - 4y = 34

Plug in x = 8y - 22

5( 8y - 22 ) - 4y = 34

Solve for y

40y - 110 - 4y = 34

40y - 4y = 34 + 110

36y = 144

y = 144/36

y = 4

Plug y = 4 into equation 3

x = 8( 4 ) - 22

x = 32 - 22

x = 10

Therefore, the solution is x = 10 and y = 4.

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Answer:

a = 157

b = 23

c = 157

Step-by-step explanation:

Angle b is a vertical angle to the angle measuring 23 so they are equal.

b = 23

Angle c  and the angle measuring 23 forms a straight line so they add to 180.

c+23 =180

c = 180-23

c = 157

Angle c and a are vertical angles so they are equal.

c = a = 157

Answer:

a = 157°

c = 157°

b = 23°

Step-by-step explanation:

We know that vertically opposite angles are equal.

∴ b = 23°

We know that angles in a straight line are added up to 180°.

∴ b + c = 180

23 + c = 180

c = 180 - 23

c = 157°

a = 157° ( vertically opposite angles ⇒ c = a )

Therefore, the value of derivatives dy/dx = -3 tan t/2 and d2y/dx2 = -3(1 - cos t)/(2(1+cos t)^2).

To find dy/dx and d2y/dx2, we need to first express y in terms of x:

x = 2 sin t --> sin t = x/2 --> cos t = ±sqrt(1 - sin^2 t) = ±sqrt(1 - x^2/4)

y = 3 cos t = ±3sqrt(1 - x^2/4)

Since 0 < t < 2π, we can determine the sign of cos t by looking at the quadrant that x lies in. Since x = 2 sin t, we have x > 0 when 0 < t < π and x < 0 when π < t < 2π. Therefore, when 0 < t < π, we have:

cos t = sqrt(1 - sin^2 t) = sqrt(1 - x^2/4)

y = 3 sqrt(1 - x^2/4)

dy/dx = -3x/2 sqrt(1 - x^2/4)^(-1)

Taking the derivative of dy/dx with respect to x, we get:

d2y/dx2 = -3/2 [sqrt(1 - x^2/4)^(-1) - 3x^2/8 (1 - x^2/4)^(-3/2)]

Plugging in x = 2 sin t and simplifying, we get:

dy/dx = -3 sin t / sqrt(4 - 4 sin^2 t) = -3 sin t / 2 cos t = -3 tan t/2

d2y/dx2 = -3/4 (sec^2 t/2 - 3 tan^2 t/2) = -3/4 [(2/(1+cos t) - 3 tan^2 t/2)]

Using the identity cos^2(t/2) = (1+cos t)/2 and simplifying, we get:

d2y/dx2 = -3/4 [(4/(1+cos t) - 3) / (1+cos t)] = -3(1 - cos t)/(2(1+cos t)^2)

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The curved surface area of the cone is 148.19 square cm

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

Radius, r = 5 cm

Height, h = 8 cm

The slant  height l of the cone is calculated as

l² = 8² + 5²

So, we have

l² = 89

This gives

l = √89

The curved surface area of the cone is then calculaed as

Area = πrl

So, we have

Area = π * 5 * √89

Evaluate

Area = 148.19

Hence, the curved surface area of the cone is 148.19 square cm

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Answer:

Ava lives 8/5 or 1 3/5 miles further from the school compared to Jayna.

Step-by-step explanation:

Answer:

The correct answer is D. ƒ(x) = x – 3.

The function rule for a table is a mathematical expression that relates the input values to the output values. In this case, the input values are the numbers in the first column of the table, and the output values are the numbers in the second column of the table.

To find the function rule, we can look for a pattern in the table. We can see that each output value is 3 less than the corresponding input value. For example, when the input value is 1, the output value is -2. When the input value is 2, the output value is -1.

This pattern can be expressed mathematically as ƒ(x) = x – 3. This function rule tells us that the output value is equal to the input value minus 3.

Step-by-step explanation:

The calculated value of the exponential decay factor is 1/5

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

The table of values

From the table of values, we can see that

x            f(x)

1             625

2             125

3             25

This show that as x increases by 1, the function f(x) values decreases by a constant factor

This means that

The function is a decay function and the rate of decay is calculated as

Rate = 125/625

Evaluate

Rate = 1/5

Hence, the exponential decay factor is 1/5

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The value of number of columns in which they can march is, 8

According to the problem ,

Members in army contingent = 1000

And, Members in army band = 56

Hence, To find maximum number of columns to march behind army band in the same number of columns,

we have to find HCF of 1000 and 56

1000 = 56 × 17 + 48

56 = 48 × 1 + 8

48 = 8 × 6 + 0

Here, Remainder has become zero.

Since, the divisor in this is, 8 .

HCF ( 1000 , 56 ) = 8

Thus, Required columns = HCF ( 1000 , 56 ) = 8

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The values of the third side that would make this a right triangle are C. √ 73 m.

The value that should make the shape a right triangle would be the value that obeys the Pythagorean Function which is:

Longest side ² = Side A  ² + Side B ²

Picking √ 73, we have a value of :

= 8. 544 m

Plugging into the formula, we have:

8. 544 ² = 3 ² + 8 ²

72. 99 = 9 + 64

73 = 73

This shows that the value would be 8. 544 or any value that is around 8. 5 m as this can be rounded off.

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The area of the triangle with base 2x and height (x - 7) in simplified form is x² - 7x

Area of a triangle = ½ × base × height

Base = 2x

Height = (x - 7)

Area of a triangle = ½ × base × height

= ½ × 2x × (x - 7)

= (2x² - 14x) / 2

= x² - 7x

Hence, the triangle given the dimensions has an area of x² - 7x

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Saying you will destroy someone in a race could be positive or negative depending on the context of the situation.

Using the word "destroy" to describe beating someone in a race can be viewed as negative or positive, depending on the context and the relationship between the individuals.

In some situations, it may be seen as a playful or friendly challenge, indicating a competitive but good-natured spirit. However, in other cases, it may come across as aggressive or intimidating, potentially damaging the relationship between the participants.

It is important to consider the tone and the relationship when using language that could be interpreted as confrontational or threatening.

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To find a value of c such that P(z ≥ c) = 0.55, we need to use a standard normal distribution table or calculator.From the standard normal distribution table, we find that the z-score corresponding to a right-tailed area of 0.55 is approximately 0.126.

Therefore, we have:

P(z ≥ c) = 0.55

P(z ≤ c) = 1 - P(z ≥ c) = 1 - 0.55 = 0.45

Using the standard normal distribution table, we find that the z-score corresponding to a left-tailed area of 0.45 is approximately -0.126.

So, c = -0.126.

Therefore, the value of c that satisfies P(z ≥ c) = 0.55 is approximately -0.126.

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The triangle similar to ΔABC is ΔSTU, in which m∠S = 87° and m∠U = 70°. Option C

We have,

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

In ΔABC, we know that m∠A = 87° and m∠B = 23°.

The angle m∠C must therefore be 70°,

since the sum of the angles in a triangle is always 180°.

now, we have,

In ΔSTU, we are given that m∠S = 87°, which corresponds to ∠A in ΔABC.

We are also given that m∠U = 70°, which corresponds to ∠C in ΔABC.

so, we get,

as, This is because two triangles are similar if their corresponding angles are congruent.

Therefore, ΔSTU is similar to ΔABC.

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The above answer is in response to the full question below

In Δ ABC, m∠A = 87° and m∠B = 23°.

Select the triangle that is similar to ΔABC.

A. ΔXYZ, in which m∠X= 87° and m∠z = 50°

B. ΔLMN, in which m∠M=20° and m∠N=87°

C. ΔSTU, in which m∠s = 87° and m∠U=70°

D. ΔPQR, in which m∠P= 110° and m∠R = 23°

We can conclude that mZADB = mZBDC = 90° (statement 7) because a right angle is defined as an angle that measures 90° (statement 9). Thus, ZADB and ZBDC are both right angles (statement 9).

1. Given reasons
2. Linear Pair Theorem
3. Angle Addition Postulate
4. Definition of congruence
5. Substitution
6. Division Property of Equality
7. Simplification
8. Simplification
9. Definition of a right angle
Proof:
We are given that ZADB and ZBDC form a linear pair and that their measures are congruent. By the Linear Pair Theorem, we know that the measures of these two angles add up to 180° (statement 2). Let mZADB = x and mZBDC = x, then we can use the Angle Addition Postulate to write mZADB + mBDC = mZBDC (statement 3).

By substituting x for mZADB and mBDC, we get 2x = x + x, which simplifies to 2x = 2x. Using the Division Property of Equality (statement 6), we get x = x, which simplifies to 1 = 1. Therefore, we can conclude that mZADB = mZBDC = 90° (statement 7) because a right angle is defined as an angle that measures 90° (statement 9). Thus, ZADB and ZBDC are both right angles (statement 9).

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Answer: they all have the same amount of squares but are placed differently in each example.

Step-by-step explanation:

there are 6 yellow squares and 10 blue squares for each of the 4 examples. The only difference is how they’re arranged.

It will take all three pumps, Working together, 1.56 minutes to fill the pool.

The given information, we can write three equations as follows:

1) (1/A + 1/B)*35 = C  ---(Equation 1)

2) (1/B + 1/C)*40 = C  ---(Equation 2)

3) (1/A + 1/C)*56 = C  ---(Equation 3)

We want  how many minutes it will take all three pumps, working together, to fill the pool, so let's represent the time taken by all three pumps working together as "t".

When all three pumps work together, they can fill the pool in one minute, so their combined rate is 1/C.

Using the rate formula, we can write the following equation:

1/A + 1/B + 1/C = 1/t   ---(Equation 4)

We have four unknowns (A, B, C, and t), so we need to solve for one of them to get the answer. Let's solve for "t".

First, we can simplify Equations 1, 2, and 3 as follows:

1) 1/A + 1/B = C/35

2) 1/B + 1/C = C/40

3) 1/A + 1/C = C/56

Next, we can substitute these equations into Equation 4 to get:

(C/35) + (C/40) + (C/56) = 1/t

Now, we can simplify and solve for "t":

LCD = 39200

1120C + 980C + 700C = 39200

2800C = 39200

C = 14

Substituting this value of "C" into any of the simplified equations, we can solve for "A" and "B". Let's use Equation 1:

1/A + 1/B = 14/35

5(A+B) = 98

A+B = 19.6

Now we can use A+B+C = 1/t to solve for "t":

t = 1 / (A+B+C) = 1 / (19.6 + 14) = 0.026 hours = 1.56 minutes

Therefore, it will take all three pumps, working together, 1.56 minutes to fill the pool.

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Answer:

x=6

Step-by-step explanation:

VZ=UZ

3x+5=23

3x=18

x=6

The probability of drawing 2 green balls simultaneously from a bag containing 2 yellow and 4 green balls can be determined using the following method:

First, calculate the total number of balls in the bag. There are 2 yellow balls and 4 green balls, so the total is 6 balls.

Now, let's find the probability of drawing 2 green balls. To do this, consider the number of green balls (4) and the total number of balls (6). When drawing the first green ball, there are 4 green balls out of 6 total balls. Therefore, the probability of drawing one green ball is 4/6.

Since the balls are drawn simultaneously, there's no change in the number of balls for the second draw. So, the probability of drawing a second green ball remains 4/6.

Now, we can calculate the probability of both events occurring simultaneously by multiplying the probabilities:

(4/6) * (4/6) = 16/36

To simplify the fraction, divide both numerator and denominator by their greatest common divisor (4):

16/36 = 4/9

So, the probability of drawing 2 green balls simultaneously is 4/9.

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