What's the area
5.1 5.1 5.1 ?

Answer:

B. y + z = x

Step-by-step explanation:

x is an exterior angle of the triangle.

y and z are the opposite angles opposite the exterior angle.

The exterior angle theorem of a triangle states that the measure of an exterior angle equals the measure of the sum of the two angles opposite the exterior angle.

Thus:

y + z = x

Answer:

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Step-by-step explanation:

Quantitative data is supported by the empirical value in the form of counts or numbers, where each data set is attached with a particular numerical value.  Qualitative data describes and can be expressed as the number of the subject.

For the class:

For the Time:

Learn more:

brainly.com/question/555216

D. 63

2a+5b+3c

2(12)+5(6)+3(3)

24+30+9=63

Hope this helps! :)

Answer:

ans: 4

Step-by-step explanation:

corresponding sides are proportional since given triangle are similar triangle, I.e

(4/5.5) = { (2x+8)/(6x-2)}

8/11 = ( x+ 4 ) / ( 3x - 1 )

8( 3x - 1 )= 11( x + 4 )

24x - 8 = 11x + 44

13x = 52

x = 4

Answer:

x =42

Step-by-step explanation:

x and 138 are same side interior angles.  Same side interior angles are supplementary when the lines are parallel

x+138 = 180

x = 180-138

x =42

Answer:

42°

Step-by-step explanation:

138° + x = 180°

180° - 138° = 42°

9514 1404 393

Answer:

  B, E

Step-by-step explanation:

The table tells you that f(0) = 3/2. (0 is found in the x-column; 3/2 is found in the f(x) column.)

__

You can find f(4) by evaluating the formula.

  f(4) = 1/2·4 +3/2 = 4/2 +3/2

  f(4) = 7/2 . . . . agrees with last answer choice

Answer:

A ,B and E ;)

Step-by-step explanation:

Answer:

b. x=22

Step-by-step explanation:

3x-23=43

3x=43+23

3x=66

x=22

Answer:

C. 3/8

Step-by-step explanation:

[tex] - 3x + 8y = 12 \\ \therefore 8y =3x + 12 \\ \therefore \: y = \frac{3}{8} x + 12 \\ equating \: it \: with \\ y = mx + b \: we \: find: \\ m = \frac{3}{8} \\ \therefore \: slope = \frac{3}{8} [/tex]

The answer above is wrong I took the test. It's in the picture below!

Answer:

Kindly check explanation

Step-by-step explanation:

Given :

Interest amount paid on loan = $90

Principal value, amount borrowed = $500

Period, t = 16 days

The equivalent annual interest :

Using the simple interest formula :

simple interest = principal * rate * time

Using, days of year = 365

Plugging in the values into the formula :

90 = 500 * rate * (16/365)

90 = 500 * rate * 0.0438356

90 = 21.917808 * rate

Rate = 90 / 21.917808

Rate = 4.10 = 4.10 * 100% = 410%

If days of year = 360 is used :

90 = 500 * rate * (16/360)

Rate = 90 / 22.222

Rate = 4.05 = 4.105 * 100% = 405%:

-10369

too lazy but that's the exact value

Answer:

Step-by-step explanation:

(-2)³ *(-4)² * 3⁴ = (-8) * 16 * 81

                      = -10368

Answer:

x = 84 , y = 168

Step-by-step explanation:

[tex]Sin 60 = \frac{opposite side}{hypotenuse}\\\\ \frac{\sqrt{3}}{2}= \frac{AB}{BC}\\\\ \frac{\sqrt{3}}{2} = \frac{84\sqrt{3}}{y}\\\\Cross\ multiply ,\\\\y*\sqrt{3} =2*84 \sqrt{3}\\\\y= \frac{2*84*\sqrt{3}}{\sqrt{3}}\\\\y=168[/tex]

[tex]Cos\60 = \frac{adjacent}{hypotenuse}\\\\ \frac{1}{2}= \frac{AC}{BC}\\\\ \frac{1}{2}= \frac{x}{168}\\\\ \frac{1}{2}*168=x\\\\x= 84[/tex]

Complete question :

Complete the expressions Write each answer as a number, a variable, or the product of a number and a variable 7(9r + 2) = 7 . 9r + 7 . ___ = ___ +

Answer:

2 ; 63r ; 14

Step-by-step explanation:

Given :

7(9r + 2)

Opening the bracket :

7*9r + 7*2 - - - - (1)

Taking the product

63r + 14 - - - - (2)

Now filling the blanks :

First blank corresponds to 2 (from (1))

Second blank corresponds to 63r (from (2))

Third blank should be 14

Answer:

yes...

Step-by-step explanation:

its a congrate triangle

Answer:

Reason 5

Step-by-step explanation:

Reason 1 and 2 are Given

Reason 3 is Reflexive

Reason 4 is Side-Side-Side congruency

Answer:

Reason 5

Step-by-step explanation:

It helps to know what CPCTC means and how it's used.

CPCTC means "corresponding parts of congruent triangles are congruent."

To use it, you must first either prove two triangles to be congruent or be given that two triangles are congruent.

Once you have the congruent triangles, then you state that two corresponding parts of those triangles are congruent, and you use CPCTC as the reason.

In step 4, the triangles are proven congruent by SSS.

Then CPCTC can be used as reason 5 for stating that the corresponding angles A and C are congruent.

Step-by-step explanation:

(a) 3pq / 4r² × 2rs / 6q²......first start by expanding the expression

It will be ;

3 × p × q / 4 × r × r X 2 × r × s / 6 × q × q

so now ,cancel out like terms. The q on top can cancel out with the q down same thing happens to r

so you'll get something like ;

3 × q / 4 × r X 2 × s / 6 × q ......so now divide , like 3 into 6 and 2 into 4 ,then you'll get something like;

qs / 4q

that's the answer

(b)15 ab² / 8 c²d ÷ 3ab / 4cd.......start by changing the sign from ÷ to × and then 3ab and 4cd will switch places

15ab² / 8c² d × 4cd / 3ab.....expand the expression

15 ×a×b×b / 8×c×c×d X 4×c×d / 3×a×b

then cancel like terms and you'll get;

15b / 8c X 4/3.....then divide 3 into 15 and 4 into 8

5b / 2c

hope this helps

Step-by-step explanation:

12) ASA - we need the second angle.

13) We need the side and second angle.

14) We need second side. First side we know is equal since both triangles share it.

The little lines theu each section are telling you all those sections are identical, which mean they are the same length.

You are told one section is 10, which means x is also 10

X = 10

Both figures r similar (given )

[tex] \frac{5}{2.5} = \frac{3}{1.5} = \frac{2}{1} = \frac{4}{x} \\ \frac{2}{1} = \frac{4}{x} \\ \frac{ \cancel{2}}{1} = \frac{ \cancel{4}^ { \tiny{2}}}{x} \\ x = 2 \: \: ans[/tex]

Answer:

(a) There is a significant relationship between y and [tex]x_1, x_2, x_3, x_4[/tex]

(b) [tex]SSE_{(x_1 ,x_2 ,x_3 ,x_4) }= 45[/tex]

(c) [tex]SSE_{(x_2,x_3)} = 100[/tex]

(d) [tex]x_1[/tex] and [tex]x_4[/tex] are significant

Step-by-step explanation:

Given

[tex]y = 17.6+3.8x_1 - 2.3x_2 +7.6x_3 +2.7x_4[/tex] --- estimated regression equation

[tex]n = 30[/tex]

[tex]p = 4[/tex] --- independent variables i.e. x1 to x4

[tex]SSR = 1760[/tex]

[tex]SST = 1805[/tex]

[tex]\alpha = 0.05[/tex]

Solving (a): Test of significance

We have:

[tex]H_o :[/tex] There is no significant relationship between y and [tex]x_1, x_2, x_3, x_4[/tex]

[tex]H_a :[/tex] There is a significant relationship between y and [tex]x_1, x_2, x_3, x_4[/tex]

First, we calculate the t-score using:

[tex]t = \frac{SSR}{p} \div \frac{SST - SSR}{n - p - 1}[/tex]

[tex]t = \frac{1760}{4} \div \frac{1805- 1760}{30 - 4 - 1}[/tex]

[tex]t = 440 \div \frac{45}{25}[/tex]

[tex]t = 440 \div 1.8[/tex]

[tex]t = 244.44[/tex]

Next, we calculate the p value from the t score

Where:

[tex]df = n - p - 1[/tex]

[tex]df = 30 -4 - 1=25[/tex]

The p value when [tex]t = 244.44[/tex] and [tex]df = 25[/tex] is:

[tex]p =0[/tex]

So:

[tex]p < \alpha[/tex] i.e. [tex]0 < 0.05[/tex]

Solving (b): [tex]SSE(x_1 ,x_2 ,x_3 ,x_4)[/tex]

To calculate SSE, we use:

[tex]SSE = SST - SSR[/tex]

Given that:

[tex]SSR = 1760[/tex] ----------- [tex](x_1 ,x_2 ,x_3 ,x_4)[/tex]

[tex]SST = 1805[/tex]

So:

[tex]SSE_{(x_1 ,x_2 ,x_3 ,x_4)} = 1805 - 1760[/tex]

[tex]SSE_{(x_1 ,x_2 ,x_3 ,x_4) }= 45[/tex]

Solving (c): [tex]SSE(x_2 ,x_3)[/tex]

To calculate SSE, we use:

[tex]SSE = SST - SSR[/tex]

Given that:

[tex]SSR = 1705[/tex] ----------- [tex](x_2 ,x_3)[/tex]

[tex]SST = 1805[/tex]

So:

[tex]SSE_{(x_2,x_3)} = 1805 - 1705[/tex]

[tex]SSE_{(x_2,x_3)} = 100[/tex]

Solving (d): F test of significance

The null and alternate hypothesis are:

We have:

[tex]H_o :[/tex] [tex]x_1[/tex] and [tex]x_4[/tex] are not significant

[tex]H_a :[/tex] [tex]x_1[/tex] and [tex]x_4[/tex] are significant

For this model:

[tex]y =11.1 -3.6x_2+8.1x_3[/tex]

[tex]SSE_{(x_2,x_3)} = 100[/tex]

[tex]SST = 1805[/tex]

[tex]SSR_{(x_2 ,x_3)} = 1705[/tex]

[tex]SSE_{(x_1 ,x_2 ,x_3 ,x_4) }= 45[/tex]

[tex]p_{(x_2,x_3)} = 2[/tex]

[tex]\alpha = 0.05[/tex]

Calculate the t-score

[tex]t = \frac{SSE_{(x_2,x_3)}-SSE_{(x_1,x_2,x_3,x_4)}}{p_{(x_2,x_3)}} \div \frac{SSE_{(x_1,x_2,x_3,x_4)}}{n - p - 1}[/tex]

[tex]t = \frac{100-45}{2} \div \frac{45}{30 - 4 - 1}[/tex]

[tex]t = \frac{55}{2} \div \frac{45}{25}[/tex]

[tex]t = 27.5 \div 1.8[/tex]

[tex]t = 15.28[/tex]

Next, we calculate the p value from the t score

Where:

[tex]df = n - p - 1[/tex]

[tex]df = 30 -4 - 1=25[/tex]

The p value when [tex]t = 15.28[/tex] and [tex]df = 25[/tex] is:

[tex]p =0[/tex]

So:

[tex]p < \alpha[/tex] i.e. [tex]0 < 0.05[/tex]

Hence, we reject the null hypothesis

Answer:

25/30

5/8

Step-by-step explanation:

Which fraction is it out of all of these 6/14,5/8,25/30,or 3/6?

to determine which fractions are greater than 1/2, convert the fractions to decimals

to convert to decimals, divide the numerator by the denominator

1/2 = 0.5  less than half

6/14 = 0.43 less than half

5/8 = 0.625 greater than half

25 / 30 = 0.83 greater than half

3 / 6 = 0.5 equal to half

Answer:

Following are the solution to the given question:

Step-by-step explanation:

Please find the attached file.

For question 1:

Forecast for December:

[tex]\to \frac{(77+75+83)}{3} \\\\ \to 78.33[/tex]

For question 2:

Forecast for December:

[tex]\to (77 \times .5+75 \times 3+83 \times .2) \\\\\to 79.40[/tex]

For question 3:

Forecast for December:

[tex]\to 72.22+(83-72.22)\times 0.2 \\\\\to 74.37[/tex]

For question 4:

So, the 3-month weighted moving average (3.58)

Answer:

A.2b2(x2-x-3)

B.x2+2x+2x+4

=x(x+2)+2(x+2)

=(x+2)(x+2)

C.x2-2^2

=(x+2)(x+2)

Answer:

24

Step-by-step explanation:

First: 12*10=120

Then: 12*12=144

=> Ms. Xu's old: 144-120=24

Answer:

a) 0.0304 = 3.04% probability a randomly chosen apple exceeds 100 g in weight.

b) The weight that 80% of the apples exceed is of 78.28g.

Step-by-step explanation:

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.

Weights of apples are normally distributed with a mean of 85 grams and a standard deviation of 8 grams.

This means that [tex]\mu = 85, \sigma = 8[/tex]

a. Find the probability a randomly chosen apple exceeds 100 g in weight.

This is 1 subtracted by the p-value of Z when X = 100. So

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

[tex]Z = \frac{100 - 85}{8}[/tex]

[tex]Z = 1.875[/tex]

[tex]Z = 1.875[/tex] has a p-value of 0.9697

1 - 0.9696 = 0.0304

0.0304 = 3.04% probability a randomly chosen apple exceeds 100 g in weight.

b. What weight do 80% of the apples exceed?

This is the 100 - 80 = 20th percentile, which is X when Z has a p-value of 0.2, so X when Z = -0.84.

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

[tex]-0.84 = \frac{X- 85}{8}[/tex]

[tex]X - 85 = -0.84*8[/tex]

[tex]X = 78.28[/tex]

The weight that 80% of the apples exceed is of 78.28g.

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Answer:

The answer is C

Step-by-step explanation:

You need to find a common denominator and in this case its 20. SO you change 3/4ths to 15/20 and 4/5ths to 16/20ths and 19/20 stays the same. Then you cancel out the 20 because its all the same number (I think) and you have your answer.

Answer:

A trinomial is a perfect trinomial if the first and last terms are positive, perfect squares and the middle term is twice the product of their square roots.

Therefore, if you mean perfect as in positive, the answer is True.

Answer:

Follows are the response to the given question:

Step-by-step explanation:

The volume of the box:

[tex]V = x\times x \times h = 256000 \ cm^3\\\\\to x^2 \times h = 256000\\\\\to h = \frac{256000}{x^2}[/tex]  

The surface area of the open box is:

[tex]A(x) = x \times x + 2 \times (x \times h +x \times h)\\\\A(x) = x^2 + 4 \times x \times h\\\\A(x) = x^2 + \frac{1024000}{x}\\\\\frac{d(x^n)}{dx} = n \times x^{(n - 1)}\\\\[/tex]

Use above formula

[tex]A'(x) = 2 \times x - \frac{1024000}{x^2}\\\\[/tex]

[tex]A'(x) = 0\\\\2\times x - \frac{1024000}{x^2} = 0\\\\2x = \frac{1024000}{x^2}\\\\x^3 = 512000\\\\x = (512000)^{(\frac{1}{3})} = 80\ cm\\\\[/tex]

Now

[tex]A''(x) = 2\times 1 + 2\times \frac{1024000}{x^3}\\\\A''(x) = 2 + \frac{2048000}{x^3}\\\\x = 80 \ cm\\\\A''(80) = 2 + \frac{2048000}{80^3} = 6\\\\[/tex]

therefore [tex]A"(x) > 0,[/tex] x amount of material used in minimum.

[tex]h = \frac{256000}{80^2} = 40\ cm[/tex]

Step-by-step explanation:

(2x-y+3)(2x-y-3)=

4x²-2xy-6x-2xy+y²+3y+6x-3y-9=

4x²-4xy+y²-9=

(2x-y)²-9