Write an expression equivalent to the following problems using the fewest number of terms. 2x + 10) + (−3x + 15)

The ages of Lute,  Maya and Aran are respectively; 24, 8 and 6 years old.

Let Lute's age be x

Thus;

Maya's age = ¹/₃x

Aran's age = ¹/₄x

We are told the sum of their ages is 38. Thus;

x + ¹/₃x + ¹/₄x = 38

Multiply through by 12 to get;

12x + 4x + 3x = 456

19x = 456

x = 456/19

x = 24

Maya's age =  ¹/₃ * 24 = 8 years

Aran's age = ¹/₄ * 24 = 6 years

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The sample size required is 1725.

(A) Sample size calculation

p=0.15

For 98%, z=2.326

d=0.02

Sample size = (z^2*p*(1-p))/d^2

= (2.326^2*0.15*0.85)/0.02^2

=1724.5

The sample size required= 1725

(B) Sample size calculation

p=0.5

For 98%, z=2.326

d=0.02

Sample size = (z^2*p*(1-p))/d^2

= (2.326^2*0.5*0.5)/0.02^2

= 3381.4

The sample size required= 3382

In records, the pattern size is the degree of the variety of character samples utilized in a test. For example, if we're testing 50 samples of folks that watch television in a town, then the pattern length is 50.

Sample size willpower is the act of selecting the range of observations or replicates to consist of in a statistical pattern. The sample size is a crucial function of any empirical look at in which the intention is to make inferences about a populace from a sample.

Your question is incomplete. Please find the complete question below.

A researcher for the U.S. Department of the Treasury wishes to estimate the percentage of Americans who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within 2 percentage points with98% confidence if

(a) Does he use a 2006 estimate of 15% obtained from a Coinstar National Currency Poll?

(b) he does not use any prior estimate?

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Answer:

Option A

Step-by-step explanation:

   [tex]\sf Slope=\dfrac{Change \ in \ y}{Change \ in \ x}=\dfrac{rise}{run}[/tex]

We can find the equation of line, by comparing the slope of line segment AC and slope of AE.

Slope of AC = Slope of AE

           [tex]\sf \dfrac{4}{3}=\dfrac{y +2}{x}[/tex]

Cross multiply

4*x = 3*(y +2)

4x   = 3y + 3*2

4x  = 3y + 6

Equation of the line in  standard form:

         4x - 3y - 6= 0

Answer:

-14

Step-by-step explanation:

Given -x+5y=7

Now we substitute x+5y into -2(-x+5y)

-2(-x+5y) = (-2)(7)

= - 14

Based on the inscribed quadrilateral conjecture: trapezoid QPRS can be inscribed in a circle because its opposite angles are supplementary.

The inscribed quadrilateral conjecture states that the opposite angle of any inscribed quadrilateral are supplementary to each other. That is, they have a sum of 180 degrees.

From the diagram given, the opposite angles in the trapezoid, 115 + 65 = 180 degrees.

Therefore, we can conclude that: trapezoid QPRS can be inscribed in a circle because its opposite angles are supplementary.

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The maximum error in the calculated surface area is 24.19cm² and the relative error is 0.0132.

Given that the circumference of a sphere is 76cm and error is 0.5cm.

The formula of the surface area of a sphere is A=4πr².

Differentiate both sides with respect to r and get

dA÷dr=2×4πr

dA÷dr=8πr

dA=8πr×dr

The circumference of a sphere is C=2πr.

From above the find the value of r is

r=C÷(2π)

By using the error in circumference relation to error in radius by:

Differentiate both sides with respect to r as

dr÷dr=dC÷(2πdr)

1=dC÷(2πdr)

dr=dC÷(2π)

The maximum error in surface area is simplified as:

Substitute the value of dr in dA as

dA=8πr×(dC÷(2π))

Cancel π from both numerator and denominator and simplify it

dA=4rdC

Substitute the value of r=C÷(2π) in above and get

dA=4dC×(C÷2π)

dA=(2CdC)÷π

Here, C=76cm and dC=0.5cm.

Substitute this in above as

dA=(2×76×0.5)÷π

dA=76÷π

dA=24.19cm².

Find relative error as the relative error is between the value of the Area and the maximum error, therefore:

[tex]\begin{aligned}\frac{dA}{A}&=\frac{8\pi rdr}{4\pi r^2}\\ \frac{dA}{A}&=\frac{2dr}{r}\end[/tex]

As above its found that r=C÷(2π) and r=dC÷(2π).

Substitute this in the above

[tex]\begin{aligned}\frac{dA}{A}&=\frac{\frac{2dC}{2\pi}}{\frac{C}{2\pi}}\\ &=\frac{2dC}{C}\\ &=\frac{2\times 0.5}{76}\\ &=0.0132\end[/tex]

Hence, the maximum error in the calculated surface area with the circumference of a sphere was measured to be 76 cm with a possible error of 0.5 cm is 24.19cm² and the relative error is 0.0132.

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Answer:

45units^2

Step-by-step explanation:

Break the polygon into two shapes. A rectangle and a triangle.

The area formula for a rectangle is A=L•W or

Area = Length x Width. Counting the units for length and width is 9 x 2. Which would equal 18units.

Now for the triangle, the formula is A=1/2 (b•h)

The base is 9 and Height is 6.

9 • 6 = 54

Since a triangle is half the area of a rectangle you divide 54 by 2. Area for triangle is 27.

Now add the rectangle area and triangle area.

18+27=45

Area=45 units ^2

Answer: 6.8

Step-by-step explanation:

By the Law of Cosines,

[tex]c^2 = 5^2 + 9^2 - 2(5)(9)\cos 48^{\circ}\\\\c=\sqrt{5^2 + 9^2 - 2(5)(9)\cos 48^{\circ}}\\\\c \approx 6.8[/tex]

The rule of reflection in the image shown is: (x, -y).

Reflection is a transformation which creates a new image by flipping over a line of reflection. The new image is congruent to the original image after reflection. The rule of reflection over an x-axis is given as, (x, -y).

In the image given we can see that rotating triangle LMN over the x-axis gave us:

M(-5, 4) → M'(-5, -4)

L(-4, 2) → L'(-4, -2)

N(-2, 3) → N'(-2, -3)

Therefore, the rule of reflection is: (x, -y).

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Okay so a 24hr clock is very simple. We usually turn to "PM" when its 12:00 (day time).
In the 24hr clock we do not, we don't use PM or AM but its crucial to know when converting a standard clock time to military time (aka. 24hr).

9:30 PM in 24hr clock is 12:00 + 9:30 because 9:30 is past that first 12 hours.

So in 24hr clock time it is 21:30. You can also count backwards from midnight to figure it out, for example 12:00 AM (midnight), minus 9:30 is 2:30. Therefore 24:00-2:30=21:30.

Hopefully it helps, heart will help me alot too!

Answer:

21:30

Step-by-step explanation:

The 24hour clock uses 0:00 for midnite. 1am through noon are just 1:00 - 12:00. But the pm hours continue counting up, 13 - 23.

For example, 1pm is 13:00 and 2pm is 14:00.

To change to 24 hour clock, for pm hours, ADD 12.

So for your problem, 9:30 is:

9:30 + 12

= 21:30

Answer:

4(2x+7) which is equal to 8x+28

Look at the multiples of lcm(3, 8) = 24, each of which are divisible by both 3 and 8. Naturally, the number we're looking for must have at least two digits.

The last/ones digit of a number [tex]n[/tex] can be computed by evaluating [tex]n \pmod{10}[/tex]. Suppose the ones digit is 1. Then

[tex]n \equiv 24k \equiv 20k + 4k  \equiv 4k \equiv 1 \pmod{10}[/tex]

but this has no solution since no multiple of 4 ends in 1. So our number ends with a 2.

If our number has two digits, then in order for it to be divisible by 3, the first digit must be 1, since 1 + 2 = 3. But 12 is not divisible by 24.

If our number has three digits, then it's either 111 (with digital sum 1 + 1 + 1 = 3) or 222 (digital sum 2 + 2 + 2 = 6), since no other triplet of 1s and 2s sums to a multiple of 3. But 111 = 3×37 and 222 = 2×111, so neither are divisible by 24.

Now suppose [tex]n[/tex] has four digits. Also suppose that the tens digit is 2. Then our number must be 1122 to uphold divisibility by 3, but 1122 = 2×3×11×17 is not divisible by 8. So the tens digit must be 1. This in turn leaves two remaining candidates, 1212 and 2112. We have 1212 = 12×(100 + 1) not divisible by 8, so our number must be [tex]\boxed{n=2112}[/tex]. And it is, since 2112 = 24×88.

A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. The area of a rectangle with side lengths of 6/8 meter and 4/10 meter is 0.3 meters².

A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.

The area of a rectangle with side lengths of 6/8 meter and 4/10 meter is,

Area of rectangle = 6/8 meter × 4/10 meter

                              = 24 / 80 meters²

                              = 6 /20 meters²

                              = 0.3 meters²

Hence, The area of a rectangle with side lengths of 6/8 meter and 4/10 meter is 0.3 meters².

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3 roots are exist, since the polynomial is of third degree.

According to statement

This follows immediately from the zero product property: if ab=0, then either a=0 or b=0. We have3 roots are exist, since the polynomial is of third degree.

(9x+ 7)(4x +1)(3x+ 4) = 0

from which it follows that each of which admits only one solution.

AND

using the fundamental theorem of algebra, expanding we have a polynomial that is of third degree:

(9x+ 7)(4x +1)(3x+ 4) = 0

108x^3 + 255 x^2 +169x + 28 =0

The theorem states that a polynomial will have up to n distinct roots. In this case, it follows that there are exactly 3, since the solutions to the system above are all distinct.

So, 3 roots are exist, since the polynomial is of third degree.

DISCLAIMER : The question was incomplete. Please find the full content below.

QUESTION

According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function? (9x + 7)(4x + 1)(3x + 4) = 0 1 root 3 roots 4 roots 9 roots

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[tex]in \: pounds \\ 12 \times 288 = 3456 \: pounds[/tex]

[tex]1 \: kilo = 2.2046 \: pounds[/tex]

[tex]x \: kilos = 3456 \: pounds[/tex]

[tex]x = \frac{3456}{2.2046} = 1567.61 \: kilos[/tex]

The probability that a two-digit number selected at random has a tens digit less than its units digit is 0.2667 (4/15).

[tex]A=24B=90\\\\P=A/B\\\\P=24/90\\p=4/15[/tex]

There are 90 two-digit numbers (99-9). Of these, six numbers are divisible by 15 (15, 30, 45, 60, 75, 90). This is also divisible by 5. Therefore, the preferred case is 30-6 = 24. Therefore, the required probability is 24/90 = 4/15.

The probability of an event can be calculated by simply dividing the number of favorable results by the total number of possible results using a probabilistic expression. Whenever you are uncertain about the outcome of an event, you can talk about the probability of a particular outcome, that is, its potential.

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Answer:

12 and 14

Step-by-step explanation:

The first number can be assigned x, the second will be assigned x+2 so that it will be even.

3(x)+5(x+2) = 106

3x+5x+10 = 106

8x = 96

x = 12

x+2 = 14

The two consecutive even numbers such that the sum of three times the smaller and five times the larger is 106 are 12 and 14, computed using the linear equation in one variable 3x + 5(x + 2) = 106.

We are given two consecutive even numbers, thus the larger number will be two more than the smaller one, as consecutive even numbers differ by two.

We assume the smaller number to be x.

Thus, the larger number = x + 2.

We have been given that three times the smaller number summed with five times the larger number results in 106.

This can be shown by the linear equation in one variable:

3x + 5(x + 2) = 106.

To find the numbers, we need to solve this linear equation in one variable as follows:

3x + 5(x + 2) = 106,

or 3x + 5x + 10 = 106 {Simplifying},

or, 8x + 10 = 106 {Simplifying},

or, 8x + 10 - 10 = 106 - 10 {Subtracting 10 from both sides of the equation},

or, 8x = 96 {Simplifying},

or, 8x/8 = 96/8 {Dividing both sides of the equation by 8},

or, x = 12 {Simplifying}.

Thus the smaller number, x = 12.

The larger number, x + 2 = 12 + 2 = 14.

Thus, the two consecutive even numbers such that the sum of three times the smaller and five times the larger is 106 are 12 and 14, computed using the linear equation in one variable 3x + 5(x + 2) = 106.

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The lines YZ and WZ are equivalent because the diagonal bisects the parallelogram into two parts of which are equal.

Properties of a parallelogram include;

From the figure, we have that lines YZ and WZ are equivalent because the diagonal bisects the parallelogram to two four of which they are of equal lengths.

Thus, the lines YZ and WZ are equivalent because the diagonal bisects the parallelogram into two parts of which are equal.

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A number in a fraction implies the part of a number in another given number. While percentage relates a given number to 100%. Thus the answers to the given question are:

a. a fraction of penalty shots that the team missed = [tex]\frac{81}{100}[/tex]

b. percentage of penalty shots missed =  [tex]\frac{81}{100}[/tex] x 100%

                                                           = 81%

A fraction is a part of a given number stated in a quotient form. Generally, all numbers can be expressed in form of fractions, even whole numbers.

The percentage is an expression that shows the part of a number in a given number with respect to 100%. An example is 10%([tex]\frac{10}{100}[/tex]).

From the given question, let;

n, number of penalty shots made = 19

T, the total number of penalties taken = 100

Thus, the number of penalties missed = T - n

                                               = 100 - 19

                                               = 81

Thus,

i. a fraction of penalty shots that the team missed = [tex]\frac{81}{100}[/tex]

ii. percentage of penalty shots missed =  [tex]\frac{81}{100}[/tex] x 100%

                                                           = 81%

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The appropriate hypothesis which is used to test the dropout rate are [tex]H_{0}:p > =0.081\\[/tex] and [tex]H_{1}: p < 0.081[/tex].

Given Drop out rate through 24 year old who are not enrolled is 8.1%, sample size=1000 and we have to find the hypothesis to test the drop out rate of the school.

The variable which needs to be studied is X=Number of individuals with age between 16 and 24 years old that are high school dropouts.

The parameter of interest is the proportion to high school drop outs is p.

Sample proportion=[tex]p^{1}[/tex]=0.065

The hypothesis can be formed as under:

[tex]H_{0}:p > =0.081[/tex]  (null hypothesis)

[tex]H_{1}:p < 0.081[/tex]      ( alternate hypothesis)

Null hypothesis is a hypothesis which is tested for its validity and alternate hypothesis is hypothesis which is opposite of null hypothesis means if null hypothesis is rejected then the alternate hypothesis will be true.

[tex]Z_{H_{0} }=(p^{1}-p)/\sqrt{p*(1-p)/n}[/tex]

=[tex]0.065-0.081/\sqrt{(0.081*0.0919)/1000}[/tex]

=-1.85

Hence the appropriate hypothesis  are [tex]H_{0}:p > =0.081[/tex] and [tex]H_{1}:p < 0.081[/tex].

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Answer:

Angle Q is acute.

Step-by-step explanation:

In an obtuse triangle, there is one obtuse angle and the other two angles are acute.

The daughter's age in 6 years time is 20

Let their current age be x and y

So, we have:

x = 3y

7 years ago, we have:

x - 7 : y - 7 = 5 : 1

Express as fraction

[tex]\frac{x - 7}{y - 7} = \frac 51[/tex]

Cross multiply

x - 7 = 5y - 35

This gives

x = 5y - 28

Substitute x = 3y in x = 5y - 28

3y = 5y - 28

Evaluate the like terms

2y = 28

Divide by 2

y = 14

In 6 years time, we have:

y + 6 = 20

Hence, the daughter's age in 6 years time is 20

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Transformation is a process that involves either increasing, or decreasing the size of a given object, or changing its orientation to produce an image.

The required transformations are:

i. For graph a - translation.

ii. For graph b - dilation.

Rigid transformation involves a change in the orientation of a given object or resizing of a given object to produce an image. The types of transformation are reflection, translation, rotation, and dilation.

i. Reflection is a type of transformation that requires flipping a given object about a reference point or line.

ii. Translation is a type of transformation that involves moving an object in a particular direction without a change in its size and orientation.

iii. Rotation is a type of transformation that involves turning an object at a given angle about a reference point.

iv. Dilation is a type of transformation that require increasing or decreasing the size of the object using a given factor.

Therefore the necessary transformation to transform the blue graph of f(x) into the red graph of g(x) is:

a. For graph a is translation.

b. For graph b is dilaton.

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The value of x from the given expression is 5/6

Given the expression to expand expressed as:

15 = 3/5(6x + 20)

We are to determine the value of x

15(5) = 3(6x + 20)

Expand

75 = 18x +60

Collect like terms

18x = 75 - 60

18x = 15

x = 15/18

x = 5/6

Hence the value of x from the given expression is 5/6

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:x = -3 [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: CD + DE = CE[/tex]

[tex]\qquad \tt \rightarrow \: x + 10 + x + 4 = 8[/tex]

[tex]\qquad \tt \rightarrow \: 2x + 14 = 8[/tex]

[tex]\qquad \tt \rightarrow \: 2x =8 - 14[/tex]

[tex]\qquad \tt \rightarrow \: 2x = - 6[/tex]

[tex]\qquad \tt \rightarrow \: x = - 3[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

[tex]\huge \boxed{\sf x=-3}\\\\\\\displaystyle \sf CD+DE=8 \\\\x+10+x+4=8\\\\2x+14=8\\\\Subtracting\ 14\ from\ each\ side\\\\ 2x+14-14=8-14\\\\2x=-6\\\\ Dividing\ each\ side\ by\ 2 \\\\ \frac{2x}{2} =\frac{-6}{2} \\\\x=-3[/tex]

Answer:

[tex]\frac{\sqrt{61} }{\sqrt{97} }[/tex]

Step-by-step explanation:

Sin(y) = opposite over hypotenuse

opposite side is [tex]\sqrt{61}[/tex]

hypotenuse is [tex]\sqrt{97}[/tex]

The system of inequalities is:

v + h ≤ 8

v < 2

h ≥ 1.5

Let's define the variables:

The maximum time that you can spend on both activities is 8 hours, then:

v + h ≤ 8

You want to spend less than 2 hours on video games, so:

v < 2

You want to spend at least, 1.5 hours on homework, so:

h ≥ 1.5

Then the system of inequalities is:

v + h ≤ 8

v < 2

h ≥ 1.5

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Answer:

36 total students in the class

Step-by-step explanation:

There are 24 boys in the class.

Since they sit in pairs, and exactly 1/4 of the boys sit with a girl, then one-quarter of the 24 boys sits with a girl.

1/4 * 24 = 6, so 6 of the boys sit with a girl.  Reflexively, 6 girls sit with a boy.

Since the problem states that exactly half of the girls sit with a boy, then half of the total number of girls is 6 (since we know that exactly 6 girls were sitting with a boy).

1/2 * x = 6

Multiplying both sides by 2...

x=12

So there are 12 girls total in the class, half (6) of whom sit with a boy.  

There are 24 boys total in the class, one-quarter (6) of whom sit with a girl.  The rest of the boys (18) sit in pairs with another boy (9 pairs), and the rest of the girls (6) sit with another girl (3 pairs).

Since there are 12 girls total and 24 boys total in the class, the total number of students is the sum of 12 and 24

12+24 =36 total students in the class

The correct answer would be option(C) opposite angles of a parallelogram are congruent.

A parallelogram defined as a special type of quadrilateral which has both pairs of opposite sides parallel and equal.

Given that PQRS is a parallelogram.

PQ ≅ RS

QR ≅ PS

By the SSS criterion, ΔPQR ≅ ΔRSP and ΔPQS ≅ ΔRSQ.

Therefore, ∠QPS ≅ ∠SRQ and ∠PQR ≅ ∠RSP since corresponding angles of congruent triangles are congruent.

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Answer:

"B"

Step-by-step explanation: