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corresponding angles are equal

The angles are corresponding same side interior angles so they must be equal

\(\\ \tt{:}\longrightarrow 2x+5=135\)

\(\\ \tt{:}\longrightarrow 2x=130\)

\(\\ \tt{:}\longrightarrow x=65\)

The percentage as a fraction is 29/100 and 0.29 as decimal

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

Number = 29%

Multiply the expression by 1

So, we have the following representation

Number = 29% * 1

Express 1 as 100/100

Number = 29% * 100/100

So, we have

Number = 29 * 1/100

This gives

Number = 29/100

Divide the expression

Decimal = 0.29

Hence, the fraction is 29/100

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Answer:

d.72 cups

Step-by-step explanation:

Since you know that she mixed 3 cups of cereal and 2 cups of trial mix you can set up the equation 3*2 . You will use this to help you figure out the answer.Next you multiply trail mix*cereal. this will give you 3*24 which is 72

The single payment 2 years from now will be of $13,287.26

Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.

Given that money earns 7.74% compounded quarterly, a payment of $2,070 due 2 years ago, but not paid, and $300 today.

To calculate investments or debts with compound interests.

Where:

V(n) is the value of the debt after n years,

R is the annual interest rate,

t is the number of times the debt is going to be compounded annually,

n is the number of years the debt is going to be compounded,

P is the principal amount being owed.

we know that the debt will be cancelled in 2 years from now. Therefore we have that n = 2 for both debts, because after the 2rd year the debts.

Then you have that t = 4, because the debt is compounded quarterly.

We can add up the two principals $2,070 + $300 = $2,370 to make it our value P, so P = 9000.

And finally we have that R = 7.74.

Then, solve the equation for P

P = A / (1 + r/n)^nt

P = 2,370 / (1 + 7.74/365)(365)^(2)

P = $13,287.26

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Answer:

The greatest common factor (GCF) of these two monomials is \(16\, a\).

Step-by-step explanation:

Rewrite \(32\, a\) and \(48\, a\) as the products of the variable \(a\) and and prime number factors:

Write an expression for the GCF of these two monomials in terms of these factors (\(2\)'s, \(3\), and \(a\).) Try to include as many of each factor as possible, as long as the resulting product is present in both monomials.

For example, there are five factor \(2\)'s in the first monomial but only four in the second monomial. Therefore, include the factor \(2\!\) in the GCF for only four times.

The factor \(a\) appeared once in both monomials. Hence, include \(a\!\) for one in the expression for the GCF.

On the other hand, the factor \(3\) is found in the second monomial but not in the first. Therefore, this factor should not be included in the expression for the GCF.

Therefore, the expression for the GCF would be:

\(2 \times 2\times 2\times 2 \times a = 16\, a\).

Answer:

3/6

Step-by-step explanation:

Answer:

0.31 if you get exactly 3 heads or 0.66 probability if you get at least 3 heads, or 50%

Step-by-step explanation:

0.31 is the probability of getting exactly 3 Heads in 6 tossed

0.66 is the probability of getting at least 3 heads

The 90% , 99% confidence interval for the population mean is 32.145 < \(\rm \mu\) < 35.855 and 31.093 <  \(\rm \mu\) < 36.907

Probability is the study of likeliness of an event to happen.

It is given that

Total Population = 50

Mean = 35

The confidence interval is given by

\(\rm CI = \mu + z \dfrac{s}{\sqrt n}\)

\(\rm \mu\) is the mean

z is the confidence level value

s is the standard deviation

n is the population width

(a) The 90% confidence interval for the population mean

90% \(\rm \alpha / 2\)  = 0.05

Z = 1.64

34 \(\rm \pm\) 1.64 * 8 / √50

34 \(\rm \pm\)  1.855

32.145 < \(\rm \mu\) < 35.855

(b)  The 99% confidence interval for the population mean

99% \(\rm \alpha / 2\)  = 0.005

Z=2.57

34  \(\rm \pm\) 2.57 * 8 / √50

34 \(\rm \pm\)  2.907

31.093 <  \(\rm \mu\) < 36.907

Therefore the confidence interval for population mean has been determined.

The complete question is

A simple random sample of 50 items from a population width =7  resulted in a sample mean of 35. If required, round your answers to two decimal places.

a. Provide a 90% confidence interval for the population mean

b. Provide a 99% confidence interval for the population mean

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Answer:

Its the first choice. Width:9 Length:13

Step-by-step explanation:

If the length is 4 meter more than the width than that means whatever the width is you must add 4 to it, in this case the width is 9 so add 4 to it which equals 13. If the length matches your answer it is the correct choice.

The area of a rectangle is the product of its dimensions. The dimension of the rectangle is: \(Length = 13m\) and \(Width = 9m\)

Given that:

\(L =4 + W\)

\(Area = 117\)

The area of a rectangle is:

\(Area = L \times W\)

So, we have:

\(L \times W= 117\)

Substitute \(L =4 + W\)

\((4 + W) \times W = 117\)

Expand

\(4W + W^2 = 117\)

Rewrite as:

\(W^2 + 4W- 117 = 0\)

Expand

\(W^2 + 13W - 9W - 117 = 0\)

Factorize

\(W(W + 13) - 9(W + 13) = 0\)

Factor out W + 13

\((W - 9)(W + 13) = 0\)

Solve for W

\(W = 9\) or \(W = -13\)

The dimension cannot be negative.

So:

\(W = 9\)

Recall that:

\(L =4 + W\)

\(L = 4 + 9\)

\(L = 13\)

So, the dimension of the rectangle is:

\(Length = 13m\)

\(Width = 9m\)

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Answer:

first u find a common denominator for all of them and then add them all together

Step-by-step explanation:

I really do hope this helps!!!

Answer:

35.61

Step-by-step explanation:

Add 10 +2+16+5= 33

Then add 5/8+7/8= 1.5

Then add 8/9+2/9= 1.1

Then add 33+1.5+1.1= 35.61

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To write the equation of a circle centered at (h, k) with a diameter of d, we can use the standard form of the equation:

(x - h)^2 + (y - k)^2 = r^2

where (h, k) represents the center of the circle and r represents the radius.

In this case, the center of the circle is (-4, 4), and the diameter is 14. The radius is half of the diameter, so the radius would be 14 / 2 = 7.

Substituting the values into the equation, we have:

(x - (-4))^2 + (y - 4)^2 = 7^2

Simplifying further:

(x + 4)^2 + (y - 4)^2 = 49

Therefore, the equation of the circle centered at (-4, 4) with a diameter of 14 is:

(x + 4)^2 + (y - 4)^2 = 49

Answer:

-3.786×10^7

Step-by-step explanation:

Answer:

the answer is -3.786×10^7

Answer:

The vendor sold 212 sodas and 34 hot dogs.

Step-by-step explanation:

Subtract 34 from 246 for the number of sodas sold.

Factors are the numbers that divide the supplied number exactly and are multiplied by another number to get specific numbers.

A prime factor is any semi natural integer that is able to divided only by itself and by 1. Actually, a few of the initial number theory are 2, 3, 5, 7, 11, and so forth. a sum that has multiplied to yield a new sum. For illustrate, if we divide 15 by 3 and 5, we get 3 5 = 15. components: All prime but non-composite components are referred to here as prime factors. 2, 3, and 5 are a some of the major determinants of 30. It is essential to list 2 twice as 2 2 3 (or 22 3) in order to factorise 12 since only 2 and 3 represent prime factors of 12. 2 + 3 can really be added to make 12.

given

As contrast to multiples, which are multiplied by another number to produce particular numbers, factors are the numbers that split the supplied number exactly.

Factors are the objects that numbers can be multiplied by one another to produce another number (e.g., 1, 2, 3, and 6 are factors of 6). When you multiply a number by an integer, you obtain multiples (e.g., 20 is a multiple of 4).

e.g., 1, 2, 3, and 6 are factors of 6

e.g., 20 is a multiple of 4

Factors are the numbers that divide the supplied number exactly and are multiplied by another number to get specific numbers.

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Answer:

1385 square feet

Step-by-step explanation:

42ft÷2=21ft to get the radius

21^2=441ft

441×π=441π

441π=1385.44236

=1385 to the nearest whole number

The number of different frames you can create, if There are 4 different styles, each available in 5 different colors, there are 3 different shades of blue to choose from, is 12.

A combination is a choice of items from a group of different items, where the order of the choices is irrelevant.

Given:

There are 4 different styles, each available in 5 different colors, there are 3 different shades of blue to choose from,

Calculate the total number of frames, we can create as shown below,

The number of frames = different styles available for blue color × shades of blue

The number of frames = 4 × 3

The number of frames = 12

Thus, the number of frames you can create is 12.

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Answer:

-2

Step-by-step explanation:

Answer:

Y= -2

Step-by-step explanation

The equation for the relationship between the total fee and vertical distance is: y = 100 + x/3000.

Vertical distance is the measurement of the straight line distance between two points in a vertical plane. It is the difference between the higher and lower altitudes of two points and is measured in a straight line from the highest point to the lowest point.

This equation can be explained as follows. The total fee for a trip to climb Mount Kilimanjaro is split into two parts. The first part is the initial fee of $100, which is a fixed cost independent of the distance climbed. The second part is the cost per vertical meter, which is calculated by dividing the vertical distance climbed (x) by 3000 (the constant fee for each vertical meter climbed) and then multiplying the result by the constant fee. Therefore, the equation for the relationship between the total fee and vertical distance is y = 100 + x/3000.

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Answer:

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K

Now we know PR∥QX , according to construction with transversal line TX.

∠PTS=∠QXS (Alternate angle)

In △PTS and △QSX

∠PTS=∠QXS (Alternate angle)

∠PST=∠QSX(vertically opposite angles)

PS=SQ(S is mid point of PQ)

△PTS≅△QSX(AAS rule)

So, TP=QX(CPCT)

As we know, TP=TR (T is midpoint)

Hence, TR=QX

Now, in quadrilateral TSQR

TS∥QR

Hence proved.

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Answer:

Option 2: -¾

Step-by-step explanation:

First identify 2 points on the line.

(0, 1), (4, -2)

Substitute the coordinates into the gradient formula below:

\(\boxed{gradient = \frac{y1 - y2}{x1 - x2} }\)

☆ (x₁, y₁) is the 1st coordinate and (x₂, y₂) is the 2nd coordinate.

Slope of the line

\( = \frac{1 - ( - 2)}{0 - 4} \)

\( = \frac{1 + 2}{ - 4} \)

\( = - \frac{3}{4} \)

☆ Since the line is sloping downwards looking from the left to right, the line must have a negative slope.

Step-by-step explanation:

2. The number of ways to choose 2 people from a group of 4 (where the order doesn't matter) is ₄C₂.

The number of ways to choose 2 people from a group of 3 (not including Jason) is ₃C₂.

So the probability is ₃C₂ / ₄C₂ = 3/6 = 1/2.

3. If Damian has already been selected, then the probability that J.T. will be selected from the remaining 8 is 1/8.

4. This question is oddly worded.  The sales and marketing teams will be equally represented on average.  If many pairs are selected and replaced, sales will be selected 4/9 of the time, and marketing will be selected 5/9 of the time.  However, for any particular pair, the representation will not be proportional.

Answer:

n=8

Step-by-step explanation:

Add 8 to both sides of the equals sign, then bring down -8n, add -72+8, You'll get -64, lastly you divide -64 and -8, and you'll get your answer

The average rate of change (AROC) of a function f(x) on an interval [a, b] is equal to the slope of the secant line to the graph of f(x) that passes through (a, f(a)) and (b, f(b)), a.k.a. the difference quotient given by

\(f_{\mathrm{AROC}[a,b]} = \dfrac{f(b)-f(a)}{b-a}\)

So for f(x) = x² on [1, 5], the AROC of f is

\(f_{\mathrm{AROC}[1,5]} = \dfrac{5^2-1^2}{5-1} = \dfrac{24}4 = \boxed{6}\)

The ratio of w to y from the given numbers is 8:9 .

The given ratios are w:z = 4:3 and y:z = 3:2 and from z to x is 1: 6.

Now we have to find the ratio w : y .

w:z = 4:3

this can be written as w/z = 4/3 ,

therefore  w = 4z / 3

Again  y : z = 3 : 2

therefore y = 3z / 2

Now we have to find the ratio w : y

Therefore :

w : y =  4z / 3 ÷ 3z / 2 = 8 / 9

An ordered pair containing integers, a fraction with the first number as the numerator and the second largely in the denominator, and even the value represented by this fraction can all be thought of as ratios.

Rational numbers, and occasionally natural numbers as well, are ratios of counts stated in terms of (non-zero) natural numbers. When two numbers are measured with the same unit, which happens frequently, their ratio is a single parameter.

Therefore the ratio of w to y is 8:9 .

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Answer:

19/20 , 1 1/4 , 1 4/5

Step-by-step explanation:

1.8 = 1 4/5 (fraction)

1.8 converts to 18/10. This can be simplified twice, firstly by making it 9/5 since both 18 and 10 are divisible by two, but can be simplified further to 1 4/5

1.25 = 1 1/4 (fraction)

1.25 converts to 125/100. This can be simplified to 5/4 or 1 1/4

0.95 = 19/20 (fraction)

0.95 converts to 95/100. This can be simplified to 19/20

Ascending Order (smallest to largest)

smallest - 19/20

middle - 1 1/4

largest - 1 4/5

I believe this is the right answer, but haven't done fractions in a while so may want to double check to make sure

Answer:

x = 16°

Step-by-step explanation:

What we know:

∠JML = 47°

∠JKL = (7x + 21)°

∠JML is an inscribed angle

∠JKL is an inscribed angle

Inscribed angles are half of the value of their intercepted arc

So if m∠JML = 47° then mArc JL is double that or 94°

And ∠JKL is intercepted by Arc JML which is the rest of the circle not intercepted by ∠JML so

mArc JL + Arc JML = 360°

94 + Arc JML = 360

Subtract 94 from both sides to isolate Arc JML

Arc JML = 266°

So if Arc JML = 266° then it's intercepted inscribed angle is half of that.

Arc JML ÷ 2 = ∠JKL

266 ÷ 2 = ∠JKL

133 °= ∠JKL

Now we can use this value and set it equal to the expression to find the value of x

(7x + 21) = 133

Subtract 21 from both sides to isolate the x

7x = 112

Divide both sides by 7

x = 16

Answer:

Step-by-step explanation:

For the product to be zero one of the picks needs to be zero. It is easier to find the probability of NOT selecting a zero and subtract that from one.

P(0)=1-P(!0)

P(0)=1-(5/6)(4/5)

P(0)=1-4/6

P(0)=(6-4)/6

P(0)=1/3