How many 4-letter words with at least one vowel can be constructed from the
letters A, B, C, D, and E? (Note that A and E are vowels.)

The values of x for each equation is given below:

To find the value(s) of x, you will need to solve each equation for x.

1. -1/2 - 4x/5 = 1/2 - 2x

Add 1/2 to both sides:

-1/2 - 4x/5 + 1/2 = 1/2 - 2x + 1/2

Combine like terms on the left side:

0 - 4x/5 = 1 - 2x

Multiply both sides by 5:

0 - 4x = 5 - 10x

Add 4x and 10x to both sides:

4x + 10x = 5

Combine like terms:

14x = 5

Divide both sides by 14:

x = 5/14

2. 2x - 3x/2 = -x + 1/3

Multiply both sides by 2:

4x - 3x = -2x + 2/3

Combine like terms:

x = 2/3

3. 5/3 - x/5 = -1

Add x/5 to both sides:

5/3 - x/5 + x/5 = -1 + x/5

Combine like terms on the left side:

5/3 = -1 + x/5

Add 1 to both sides:

5/3 + 1 = -1 + x/5 + 1

Combine like terms:

6/3 = x/5

Multiply both sides by 5:

30/3 = x

Divide both sides by 3:

10 = x

4. -2x - 4 = -1/5 + 3x/4

Add 2x to both sides:

-4 = 2x - 1/5 + 3x/4

Add 1/5 to both sides:

-4 + 1/5 = 2x + 3x/4 + 1/5

Combine like terms:

-39/5 = 5x/4

Multiply both sides by 4/5:

-39/5 * 4/5 = 5x/4 * 4/5

Combine like terms:

-39/5 = 5x/4

Multiply both sides by 4:

-39 = 20x/4

Divide both sides by 20:

-39/20 = x

5. -6x + 1 = x - 1

Add 6x to both sides:

-6x + 6x + 1 = x - 1 + 6x

Combine like terms:

0 = 7x

Divide both sides by 7:

0/7 = 7x/7

Combine like terms:

0 = x

The values of x are: 5/14, 2/3, 10, -39/20, and 0.

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plug in 20 = x for function f(x)

1.2(1.11)^20 = ?

Answer:

$19

Step-by-step explanation:

calculate 94-18/4 = 19

Answer:

No solutions

Step-by-step explanation:

[tex]-8(v+1)=2(1-4v)-9\\-8v-8=2-8v-9\\8=-7\\8\neq-7[/tex]

Hence, there are no solutions to make both sides of the equation true.

The new position of minute hand if it starts from 1 and turns 210°  will be at the 40 minutes mark on the clock face.

The minute hand of a clock completes a full rotation every 60 minutes, or 360°. This means that each minute on the clock face corresponds to an angle of 6 degrees. (360 divided by 60 minutes). If the minute hand starts from the 1 and turns 210 degrees, we can calculate the number of minutes it has moved by dividing 210 by 6, which gives us 35. Therefore, the new position of the minute hand will be 35 minute mark on the clock face. However, since the minute hand started at the 1, we need to add 5 minutes in the final answer.

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The solution of the function - 6x + 14 = - 2ˣ + 6 is 2. The required graphs are given below.  

We can solve the given function by adding or subtracting the same integer on both sides. Here adding or subtracting the same number on both sides doesn't change the condition of the function. In end-use trial and error mothed to find the value of the variable 'x'

Here we have

f(x) = - 6x + 14  and g(x) = - 2ˣ + 6  

The solution of - 6x + 14 = - 2ˣ + 6 can be calculated as follows

=> - 6x + 14 =  - 2ˣ + 6    

=> - 6x + 8 = - 2ˣ    

=> - 6x + 8 = - 2ˣ

=> - 6x + 2ˣ = - 8          

By using the trial and error method

At x = 2

=> - 6(2) + 2² = -8

=> - 12 + 4 = -8

Therefore,

The solution of the function - 6x + 14 = - 2ˣ + 6 is 2. The required graphs are given below.  

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Answer:

w = 25 / 4 feet wide.

Step-by-step explanation:

Let's call the width of the walkway "w."

The area of the rectangular pool is 13 * 27 = 351 ft^2.

The area of the walkway can be calculated by adding up the area of four rectangles, one around each side of the pool:

2 * (13 + w) * w + 2 * (27 + w) * w = 384

Expanding the equation:

2 * 13w + 2w^2 + 2 * 27w + 2w^2 = 384

Combining like terms:

2w^2 + 40w = 384

Solving for w^2:

2w^2 + 40w - 384 = 0

Using the quadratic formula:

w = (-40 ± √(40^2 - 4 * 2 * -384)) / (2 * 2)

Simplifying:

w = (-40 ± √(1600 + 3072)) / 4

w = (-40 ± √4272) / 4

w = (-40 ± 65) / 4

w = (25 / 4) or (-105 / 4)

Since w must be a positive value, w = 25 / 4 feet wide.

Answer:look it up frfr

Step-by-step explanation:

Length of the segments are 11 units and 10 units and measures of the angles are 54° and 126°.

Parallelogram is a type of polygon with four sides, four angles and four vertices. It is a type of Quadrilateral.

Opposite sides are parallel, and the opposite sides and opposite angles are equal.

Since, CDEF is a parallelogram, opposite angles are equal.

(9y)° = (7y + 28)°

9y - 7y = 28

2y = 28

y = 14

∠C = ∠E = 9y = 126°

Sum of the angles of a quadrilateral is 360°.

∠D = ∠F = (360° - (126°×2)) / 2 = 54°

Opposite sides are also equal for a parallelogram.

2x = x + 5

2x - x = 5

x = 5

CF = DE = 2x = 10 units

CD = FE = 3x - 4 = 11 units

Hence opposite sides are equal with lengths 10 units and 11 units and opposite angles are equal with measures 54° and 126°.

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Perceived lack of anonymity is the source of bias that is most relevant to the given situation.

The data collected in the study, which is Mood on a Happy/OK/Sad scale, is qualitative or categorical data.

This describes an observational study.

What is Statistics?

Statistics is a field of study that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves the use of mathematical and statistical methods to extract meaningful insights from data and to draw conclusions or make decisions based on the findings.

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a)

63 cans in 7 boxes.

b)

11 boxes are needed for 99 cans.

It is a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

36 cans in 4 boxes.

This means,

1 box = 36/4 cans

1 box = 9 cans

Multiply 7 on both sides.

7 box = 63 cans ______(1)

1 box = 9 cans

Multiply 11 on both sides.

11 box = 99 cans ______(2)

Now,

From (1) and (2)

a)

63 cans in 7 boxes.

b)

11 boxes are needed for 99 cans.

Thus,

63 cans in 7 boxes.

11 boxes are needed for 99 cans.

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The expected value of the sample mean amount of money spent on books is equal to the population mean, which is $400.

This is a property of the sampling distribution of the sample mean, which states that the mean of all possible sample means is equal to the population mean.

In other words, if we take all possible random samples of size 100 from the population of undergraduate students, and calculate the mean amount of money spent on books for each sample, then the average of all these sample means will be $400.

The expected value of the sample mean amount of money spent on books can be calculated using the formula:

E(X) = μ

where X is the sample mean, and μ is the population mean.

In this case, the population mean is given as $400. Therefore, the expected value of the sample mean amount of money spent on books is also $400.

However, we can also calculate the standard error of the mean (SE) to get a measure of the variability of the sample mean. The formula for SE is:

[tex]SE = σ / sqrt(n)[/tex]

where σ is the population standard deviation, and n is the sample size.

Substituting the values, we get:

[tex]SE = 80 / sqrt(100) = 8[/tex]

This property is true regardless of the sample size, as long as the sample is randomly selected and independent. However, as the sample size increases, the sampling distribution of the sample mean becomes more normal and the standard error of the mean decreases, making the sample mean a more precise estimate of the population mean.

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First, use the equation for a hemisphere. Since a sphere's equation is [tex]\frac{4}{3}\pi r^{3}[/tex], and a hemisphere is half a sphere, we can use the equation [tex]\frac{2}{3}\pi r^{3}[/tex]. We know the radius is 6 inches, and we can approximate pi as 3.14, so now let's plug in our values:

[tex]\frac{2}{3}\ (3.14) 6^{3}=\frac{2}{3} \ (3.14)(216)= \frac{2}{3}(678.16)= 452.16[/tex]

The volume of the hemisphere is about [tex]452.16 in^{3}[/tex].

The formula for the volume of a cone is [tex]\pi r^{2}\frac{h}{3}[/tex]. Again, let's plug in our values:

[tex](3.14)(36)\frac{6}{3} =(3.14)(36)(2)=(3.14)(72)=226.08[/tex]

The volume of the cone is about [tex]226.08 in^{3}[/tex].

Subtract 226.08 from 452.16 and you get 226.08.

The volume of the remaining solid will be [tex]226.08 in^{3}[/tex].

The length of the segment AE is 10 units.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.

The two triangles triangle ABE and triangle CDE are similar triangles.

We know that, the ratio of segments of similar triangle are equal thus:

10 / 8 = 2x + 6 / x+ 6

10(x + 6) = 8(2x + 6)

10x + 60 = 16x + 48

60 - 48 = 16x - 10x

12 = 6x

x = 2

Substitute the value of 2 in 2x + 6:

2(2) + 6 = 10 units.

Hence, the length of the segment AE is 10 units.

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Answer:

b) octogon

c) irregular pentagon

d) irregular hexagon

Step-by-step explanation:

The answers are:

To calculate the interest and maturity value, we need to use the formula:

Interest = Principal x Rate x Time

Maturity Value = Principal + Interest

Where:

For the given information, we have:

Drum Set:

Principal = $900.00

Rate = 4% = 0.04

Time = 10/365 = 0.0274 years (assuming an exact interest calculation based on days)

Interest = $900.00 x 0.04 x 0.0274 = $0.98

Maturity Value = $900.00 + $0.98 = $900.98

Used Car:

Principal = $1,960.00

Rate = 6% = 0.06

Time = 9/365 = 0.0247 years (assuming an exact interest calculation based on days)

Interest = $1,960.00 x 0.06 x 0.0247 = $2.88

Maturity Value = $1,960.00 + $2.88 = $1,962.88

Used Dirt Bike:

Principal = $4,800.00

Rate = 4% = 0.04

Time = 10/365 = 0.0274 years (assuming an exact interest calculation based on days)

Interest = $4,800.00 x 0.04 x 0.0274 = $5.23

Maturity Value = $4,800.00 + $5.23 = $4,805.23

School Tuition for Twins:

Principal = $9,675.00

Rate = 6% = 0.06

Time = not specified

We don't have the time period for this investment, so we can't calculate the interest or maturity value without that information.

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The equation is [tex]y=-87(x-1)^{2} (x-3)^{3}[/tex].

What is meant by zeroes of polynomials?

All the x-values that bring a polynomial, p(x), to zero are referred to as its zeros. They are intriguing to us for a variety of reasons, one of which is that they provide information on the graph's x-intercepts for the polynomial.

It is given that degree of the equation is 5. so the highest power is 5 and there will be 5 zeroes.

It is given that 2 zeroes at x=1 and 3 zeroes at x= 3.

So, the equation is [tex]y=a(x-1)^{2} (x-3)^{3}[/tex].

We will substitute x=2 and y= 87 in the above equation.

[tex]87=a(2-3)^{3} \\a=-87[/tex]

Therefore now the equation will be:

[tex]y=-87(x-1)^{2} (x-3)^{3}[/tex].

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Answer: £122.45

Step-by-step explanation: 7.90*15.5

Answer: 109?

Step-by-step explanation:

Answer:

y=-2 over 1x+18

Step-by-step explanation:

Because angles 1 and 2 are adjacent, we will see that the measure of angle 2 is 77°.

Here we know that m∠1 = 103°, and we want to find the measure of angle 2, which is an angle adjacent to angle 1.

That means that if we add their measures, then we will get a plane angle, this means that:

m∠1 + m∠2 = 180°

Then we can write:

103° + m∠2 = 180°

m∠2 = 180° - 103° = 77°

That is the measure of angle 2.

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Answer:

-5/3.

Step-by-step explanation:

To find the slope of a line perpendicular to another line, we need to remember that the slopes of two perpendicular lines are negative reciprocals of each other. To find the slope of the line perpendicular to 3x - 5y = 45, we need to first convert it to slope-intercept form, which is y = mx + b, where m is the slope of the line.

First, isolate the y-term:

3x - 5y = 45

5y = -3x + 45

y = -(3/5)x + 9

So the slope of the original line is -3/5. The slope of the line perpendicular to it would be the negative reciprocal of this slope, which is -5/3.

Therefore, the slope of a line perpendicular to 3x - 5y = 45 is -5/3.

Answer:

3/5

Step-by-step explanation:

The probability that the student is from other majors is 0.40, the probability that the student majors only math is 0.13, and the probability that the student does not major engineering is 0.73.

a) Probability of a student being from other majors = (150-90) / 150 = 0.40

b) Probability of a student majoring only math = (30 - 20) / 150 = 0.13

c) Probability of a student not majoring engineering = (150 - 40 - 20) / 150 = 0.73

Probability = Number of Favorable Outcomes / Total Number of Outcomes

For part a)

Number of Favorable Outcomes = 150-90 = 60

Total Number of Outcomes = 150

Therefore, Probability = 60 / 150 = 0.40

For part b)

Number of Favorable Outcomes = 30-20 = 10

Total Number of Outcomes = 150

Therefore, Probability = 10 / 150 = 0.13

For part c)

Number of Favorable Outcomes = 150-40-20 = 90

Total Number of Outcomes = 150

Therefore, Probability = 90 / 150 = 0.73

The probability that the student is from other majors is 0.40, the probability that the student majors only math is 0.13, and the probability that the student does not major engineering is 0.73.

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Answer:

12

Step-by-step explanation:

6 with 9 figers

Answer:

Let x be 6 and y be 9.

x + y = 6 + 9 = 15.

However, x + y does not equal 15. Hence, we can deduce that:

x + y = 15 [tex]\neq[/tex] 15.

15 does not equal 15, so if 15 is 15 and not equal to 15, we can prove that since 6 does not equal 9, 6 is 9. We can therefore conclude that we need to solve for x + x. Since we proved that something is something by not being something, 2x ix 2x but not 2x.

2x isn't 2x but is 2x, so the answer isn't the answer but is still the answer. Therefore, this question isn't a question when it is a question.

:) I am teaching you Maths in Ohio.

After dilation, the coordinates of image will be (-1,3).

What exactly is dilation?

Dilation is the process of modifying the size of an item or form by reducing or expanding its dimensions according to specific scaling variables. A circle of radius 10 unit, for example, is reduced to a circle with radius 5 unit. This approach is utilised in photography, arts and crafts, and the creation of logos, among other things. There are four primary types of transformations in geometry. They are as follows:

Dilation Properties

Some characteristics of forms that stay constant during dilation changes are:

Now,

As given dilation factor= -3

that means the image will be small and x coordinate will displace from its current value - 3 that is -1.

and y coordinate will be same that is 3

Hence,

          After dilation, the coordinates of image will be (-1,3).

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The difference between the investment below and one with the same principal at the same rate compounded yearly is $18123.29.

The Payback Period is the most straightforward metric to use when contrasting investment options. Simply defined, this is the minimal amount required for you to recoup your initial investment.

compound interest, which is referred to as

[tex]A = P(1+r/n)^n×t[/tex]

Where

A = amount at the end of t years

r = interest rate.

n = periodic interval

P = principal amount deposited

Considering  investment compounded annually

P = 7000

r = 3% = 3/100 = 0.03

n = 1

t = 17 years

[tex]A = 7000(1 + 0.03/1)^1× 12A = 7000(1.03)^12[/tex]

A = $9980.32

For the second investment,

n = 6

[tex]A = 7000(1 + 0.08/6)^6 × 12A = 7000(1 + 0.0133)^72A = 7000(1.0133)^72A = $18123.29[/tex]

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The transformation that maps △UVW to △EFG is (d) (x, y) = (-2x, -2y)

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

The figure

From the figure, we can see that

Triangle EFG is twice the triangle UVW in side lengths

This means that

(x, y) = (2x, 2y)

The orientations are 180 degrees apart

So, we have

(x, y) = (-2x, -2y)

Hence, the transformation is (d) (x, y) = (-2x, -2y)

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Answer:

x=4.5  

Step-by-step explanation:

2 [x-3]-5=7

2x - 3 - 5 =7

2x - -2 =7

7+2=9

9/2=4.5

i may be wrong <3

The mean absolute deviation, mad, of the given data, 21, 25, 16, 8, 16, 10, is 4.83

From the question, we are to calculate the mean absolute deviation, mad, of the given data

First, we will calculate the mean of the data

21, 25, 16, 8, 16, 10

Mean = (21 + 25 + 16 + 8 + 16 + 10)/6

Mean = 96/6

Mean = 16

Now, we will determine the positive differences of each number from the mean

         Positive differences

21        5

25       10

16        0

8         8

16        0

10        6

Now, we will find the mean of the positive differences

Mean absolute deviation =(5 + 10 + 0 + 8 + 0 + 6)/6

Mean absolute deviation = 29/6

Mean absolute deviation = 4.83

Hence, the mad is 4.83

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Since angle S is 65°, angle Y will also be 65°

Similar shapes are shapes that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

Since quadrilateral QRST is similar to quadrilateral WXYZ, then angle Q = angle W , angle R = angle X and angle S = angle Y and angle T = angle Z.

Since angle S is 65° from the diagram shown, angle will be measured as 65°.

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We can say that  by equation 12 metres below the ocean's surface, a fish may be found. 28 metres above the ocean's surface, a sea bird may be seen and distance between them is 40 meters.

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

We require knowledge about an object's elevation to tackle such issues.

12 metres below the ocean's surface, a fish may be found.

28 metres above the ocean's surface, a sea bird may be seen.

A fish is 12 metres below the ocean's surface.

The fish's elevation is negative since it is below sea level. Consequently, the fish's elevation is -12 metres.

B.) A marine bird flies 28 metres above the water's surface.

given that the seabird is above the water. The sea bird is 28 metres above sea level.

If the bird soars straight over the fish, (C),

If the fish and the bird are immediately above one another,

Distance between fish and bird = |(elevation of the fish)| + |(elevation of the sea bird)|

= |-12| + |28|

= 12 + 28

= 40 meters

distance between them is 40 meters.

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