An expression is shown below:

3(m + 5 + 9m)

Part A: Write two expressions that are equivalent to the given expression. (3 points)

Part B: Show that one of your expressions in Part A is equivalent to the given expression using algebraic properties. Explain which properties you used. (4 points)

Part C: Show that your other expression from Part A is equivalent to the given expression by substituting a number for m. (3 points)

Answer:

Step-by-step explanation:

20 milligrams

Answer:

x = 8

y = 6

Step-by-step explanation:

Recall that one of the properties of a parallelogram is that the diagonals bisect each other, which means they divide each other into equal segments.

Therefore,

LP = PN

x = y + 2 (eqn. 1)

PM = KP

2x - 8 = y + 10 (eqn. 2)

Substitute x = y + 2 into eqn. 2 to find y

Thus:

2(y + 2) = y + 10

2y + 4 = y + 10

Take like terms

2y - y = -4 + 10

y = 6

Substitute y = 6 into eqn. 1 to find x:

x = y + 2 (eqn. 1)

x = 6 + 2

x = 8

Answer:

x=-1

Step-by-step explanation:

the middlepoint is where its symetrical, and so you take the x part of the point. the point is (-1,4), and all we need is x, so you have x=-1

Answer: 100 inches

Step-by-step explanation:

From the question, we are given the information that Nia had a 20 inch by 30 inch enlargement made of a photograph and that she wanted to have it framed.

The number of inches of frame that she would use to enclose the photo will be gotten by calculating the perimeter of the shape and this will be:

= 2(length + width)

= 2(30 + 20)

= 2(50 inches)

= 100 inches

To enclose the photo, 100 inches of frame is needed.

Answer:

1.tenisha

2.1\5+1\3=1\×

3.n-12=1\3(n+2)

4.500×=120

Answer:

Y=x+3

Step-by-step explanation:

we have :

     x1= -7

     y1= -4

    m=1

as we know Y-y1=m(X-x1)

Y+4=(X+7)

Y+4=X+7

Y=X+7-4

Y=X+3

Answer:

3:7

Step-by-step explanation:

We know that there are 4 girls and 3 boys and 4+3=7.

Answer:

17degrees

Step-by-step explanation:

The sum of two supplementary angles is equation 180degrees. Hence:

5x+95 = 180

5x = 180-95

5x = 85

x = 85/5

x = 17

Hence the value of x is 17

Answer:

40% of policyholders are expected to have an accident next year

Step-by-step explanation:

Given the data in the question;

P( collision coverage ) = 60% = 0.6

P( comprehensive coverage ) = 70% = 0.7

Now, we make use of the Law of addition of probability, so

P( collision coverage and comprehensive coverage ) = P( collision coverage )  + P( comprehensive coverage ) - P( collision coverage or comprehensive coverage )

P( collision coverage and comprehensive coverage )  = 0.6 + 0.7 - 1

P( collision coverage and comprehensive coverage ) = 0.3

Now,

P( comprehensive coverage only ) = P( comprehensive coverage ) - P( collision coverage and comprehensive coverage )

P( comprehensive coverage only ) = 0.7 - 0.3

P( comprehensive coverage only ) = 0.4

And

P( collision coverage only) = P( collision coverage ) - P( collision coverage and comprehensive coverage )

P( collision coverage only) = 0.6 - 0.3 = 0.3

Next  we make use of the Law of total probability;

P( accident ) = [P( accident ║ collision coverage only) × P( collision coverage only)] + [P( accident ║ comprehensive coverage only) × P( comprehensive coverage only)] + [P( accident ║ collision coverage and comprehensive coverage only) × P( collision coverage and comprehensive coverage only)]

so we substitute in our values;

P( accident ) = [ 30% × 0.3 ] + [ 40% × 0.4 ] + [ 50% × 0.3 ]

P( accident ) = [ 0.3 × 0.3 ] + [ 0.4 × 0.4 ] + [ 0.5 × 0.3 ]

P( accident ) = 0.09 + 0.16 + 0.15

P( accident ) = 0.4 or 40%

Therefore,  40% of policyholders are expected to have an accident next year

Answer: y = 4/3x -8

Step-by-step explanation:

(6,0) (0,-8)

0-(-8)/6-0 = 8/6 = 4/3

y intercept is given already

Answer:

I guess it is the Answer C

Answer:

C

The distance around the edge of the circle

Answer:

3%

Step-by-step explanation:

Cost x sales tax rate =tax

370 x sales tax rate = 11.10

sales tax rate =11.10/370

sales tax rate=.03 or 3%

The sales tax rate is 3% if an item costs $370 before tax and the sales tax is $11.10.

The percentage is defined as a ratio expressed as a fraction of 100.

To determine the sales tax rate, we need to divide the amount of sales tax paid by the cost of the item before tax and then multiply the result by 100% to express it as a percentage.

As per the question, the amount of sales tax paid is $11.10, and the cost of the item before tax is $370. Therefore, the sales tax rate is:

sales tax rate = tax paid / (cost of the item before tax) x 100%

sales tax rate = $11.10 / $370 x 100%

Apply the division operation,

sales tax rate = $0.03 x 100%

Apply the multiplication operation,

sales tax rate = 3%

Therefore, the sales tax rate is 3%.

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Answer:

the answer would be log 2

Answer:

Mary's friend Larry is taller by 15cm.

Step-by-step explanation:

First look for the bigger number.

Then subtract the smaller number from the bigger number.

Explanation:

The sample space is simply the list of possible outcomes. We list all the hair colors possible in this class.

Answer:

if you becomes a.. what is this mean

Answer:

i have no idea

Step-by-step explanation:

i dont think turning into a virtual period will let me do anything. If you can clarify please let us know!

Step-by-step explanation:

the answer is in the above image

Answer:

Kindly check explanation

Step-by-step explanation:

H0 : quality does not vary among shift

H1 : quality varies among shift

The expected values :

(Row * column) / grand total

Given the data:

Observed values :

_________________total

_______467 191 42 __700

_______445 171 34 __650

_______254 129 17 _ 400

Total __ 1166 491 93 _ 1750

Expected value count using the formula :.

Expected Values:

466.4 ____196.4 ______37.2

433.086 _182.371___ 34.5429

266.514_ 112.229____ 21.2571

The Chisquare statistic (χ²) :

χ² = (observed - Expected)²/ observed

χ² = 5.76045

The degree of freedom = (row - 1) * (column - 1)

Degree of freedom = (3-1)*(3-1) = 2*2 = 4

Pvalue = 0.2178

Pvalue > α ; We foal to reject H0 ; Hence, we conclude that quality does not vary among shift

Answer:

Step-by-step explanation:

Use the formula P=MX+B

Answer:K=-2

Step-by-step explanation:

becuase you do the opposite of +9 which is -9 and you do 7-9 which is -2 so K=-2

Answer:

Balance will be £3.92

Step-by-step explanation:

Cost of  1 loaf = £1.52

Therefore, cost of 4 loaves = 4 x 1 . 52 = £6.08

So if you pay with £10 your balance will be = 10.00 - 6.08 =  £3.92

The solution is  £ 3.92

The amount of money after the purchase of 4 loaves of bread is given by the equation A = £ 3.92

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The total amount of money = £ 10

The cost of one loaf of bread = £ 1.52

Now , the number of loaves of bread = 4 loaves

So , the cost of 4 loaves of bread = 4 x cost of one loaf of bread

Substituting the values in the equation , we get

The cost of 4 loaves of bread = 4 x 1.52

The cost of 4 loaves of bread = £ 6.08

The amount of money after the purchase A = total amount of money - cost of 4 loaves of bread

Substituting the values in the equation , we get

The amount of money after the purchase A = £ 10 - £ 6.08

The amount of money after the purchase A = £ 3.92

Therefore , the value of A is £ 3.92

Hence , the amount is £ 3.92

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Step-by-step explanation:

if N= given Side then,

(20-2)180

18×180

3240° Answer

Answer:

n=20 side

sum=(n-2)180

=(20-2)180

=(18)180

=3240

Answer:

0.0721 = 7.21% probability that the mean height for the sample is greater than 65 inches.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 64.4 inches, standard deviation of 2.91

This means that [tex]\mu = 64.4, \sigma = 2.91[/tex]

Sample of 50 women

This means that [tex]n = 50, s = \frac{2.91}{\sqrt{50}}[/tex]

What is the probability that the mean height for the sample is greater than 65 inches?

This is 1 subtracted by the p-value of Z when X = 65. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{65 - 64.4}{\frac{2.91}{\sqrt{50}}}[/tex]

[tex]Z = 1.46[/tex]

[tex]Z = 1.46[/tex] has a p-value of 0.9279

1 - 0.9279 = 0.0721

0.0721 = 7.21% probability that the mean height for the sample is greater than 65 inches.

Answer:

Step-by-step explanation:

question no . 5

ratio of angle L

take angle as reference angle

using cos rule

cos L = base / hypotenuse

= 4/5

ratio of angle N

take angle N as reference angle

using sin rule

sin N = opposite / hypotenuse

= 4/5

for measure of angle L

cos L = 4/5

cos L = 0.8

L = [tex]cos^{-1}(0.8)[/tex]

L = 36.9

for meanure of angle N

sin N = 4/5

sin N = 0.8

N = [tex]sin^{-1}(0.8)[/tex]

N = 53.1

Answer:

See below

Step-by-step explanation:

Congruent means having the same size and shape.

If triangle A'B'C' is the image of triangle ABC after a dilation with a scale factor of 1/2 then the two triangles will not acquire the same size

This is because when a shape undergoes a dilation the dilated image is either larger or smaller and can therefore not maintain the same size as the pre image. Hence the triangles are not congruent.

Triangle ABC is not congruent to triangle A'B'C'

The triangles are given as:

Triangle ABC and A'B'C'

The other parameters are:

Scale factor, k = 1/2

Center = Point A

Since the scale factor is not 1, then the triangles would not be congruent; but they would be similar

Hence, triangle ABC is not congruent to triangle A'B'C'

Read more about dilation at:

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Answer:

[tex]x = 97[/tex]

Step-by-step explanation:

Given

[tex]t = 20[/tex] --- time (years)

[tex]A =1000[/tex] --- amount

[tex]r = 10\%[/tex] --- rate of interest

Required

The last 10 payments (x)

First, calculate the end of year 1 payment

[tex]y_1(end) = 10\% * 1000 * 150\%[/tex]

[tex]y_1(end) = 150[/tex]

Amount at end of year 1

[tex]A_1=A - y_1(end) - r * A[/tex]

[tex]A_1=1000 - (150 - 10\% * 1000)[/tex]

[tex]A_1 =1000 - (150- 100)[/tex]

[tex]A_1 =950[/tex]

Rewrite as:

[tex]A_1 = 0.95 * 1000^1[/tex]

Next, calculate the end of year 1 payment

[tex]y_2(end) = 10\% * 950 * 150\%[/tex]

[tex]y_2(end) = 142.5[/tex]

Amount at end of year 2

[tex]A_2=A_1 - (y_2(end) - r * A_1)[/tex]

[tex]A_2=950 - (142.5 - 10\%*950)[/tex]

[tex]A_2 = 902.5[/tex]

Rewrite as:

[tex]A_2 = 0.95 * 1000^2[/tex]

We have been able to create a pattern:

[tex]A_1 = 1000 * 0.95^1 = 950[/tex]

[tex]A_2 = 1000 * 0.95^2 = 902.5[/tex]

So, the payment till the end of the 10th year is:

[tex]A_{10} = 1000*0.95^{10}[/tex]

[tex]A_{10} = 598.74[/tex]

To calculate X (the last 10 payments), we make use of the following geometric series:

[tex]Amount = \sum\limits^{9}_{n=0} x * (1 + r)^n[/tex]

[tex]Amount = \sum\limits^{9}_{n=0} x * (1 + 10\%)^n[/tex]

[tex]Amount = \sum\limits^{9}_{n=0} x * (1 + 0.10)^n[/tex]

[tex]Amount = \sum\limits^{9}_{n=0} x * (1.10)^n[/tex]

The amount to be paid is:

[tex]Amount = A_{10}*(1 + r)^{10}[/tex] --- i.e. amount at the end of the 10th year * rate of 10 years

[tex]Amount = 1000 * 0.95^{10} * (1+r)^{10}[/tex]

So, we have:

[tex]Amount = \sum\limits^{9}_{n=0} x * (1.10)^n[/tex]

[tex]\sum\limits^{9}_{n=0} x * (1.10)^n = 1000 * 0.95^{10} * (1+r)^{10}[/tex]

[tex]\sum\limits^{9}_{n=0} x * (1.10)^n = 1000 * 0.95^{10} * (1+10\%)^{10}[/tex]

[tex]\sum\limits^{9}_{n=0} x * (1.10)^n = 1000 * 0.95^{10} * (1+0.10)^{10}[/tex]

[tex]\sum\limits^{9}_{n=0} x * (1.10)^n = 1000 * 0.95^{10} * (1.10)^{10}[/tex]

The geometric sum can be rewritten using the following formula:

[tex]S_n = \sum\limits^{9}_{n=0} x * (1.10)^n[/tex]

[tex]S_n =\frac{a(r^n - 1)}{r -1}[/tex]

In this case:

[tex]a = x[/tex]

[tex]r = 1.10[/tex]

[tex]n =10[/tex]

So, we have:

[tex]\frac{x(r^{10} - 1)}{r -1} = \sum\limits^{9}_{n=0} x * (1.10)^n[/tex]

[tex]\frac{x((1.10)^{10} - 1)}{1.10 -1} = \sum\limits^{9}_{n=0} x * (1.10)^n[/tex]

[tex]\frac{x((1.10)^{10} - 1)}{0.10} = \sum\limits^{9}_{n=0} x * (1.10)^n[/tex]

[tex]x * \frac{1.10^{10} - 1}{0.10} = \sum\limits^{9}_{n=0} x * (1.10)^n[/tex]

So, the equation becomes:

[tex]x * \frac{1.10^{10} - 1}{0.10} = 1000 * 0.95^{10} * (1.10)^{10}[/tex]

Solve for x

[tex]x = \frac{1000 * 0.95^{10} * 1.10^{10} * 0.10}{1.10^{10} - 1}[/tex]

[tex]x = 97.44[/tex]

Approximate

[tex]x = 97[/tex]

Answer:

73.0m

Step-by-step explanation:

see the attachment. Hope it helps.