One angle of a triangle is equal to the sum of the remaining angles. If the ratio of measures of the ren
is 2:1, find the measures of the three angles of the triangle.

9514 1404 393

Answer:

  B. neither perpendicular nor parallel

Step-by-step explanation:

If the lines were perpendicular, the coefficients would be swapped and one negated. (You would have 8x -y = c, or 9x +2y = c in the system.)

If the lines were parallel, the coefficients in the two equations would only differ by a common factor. (Both equations would reduce to 2x -9y = c, or x +8y = c.)

The lines are not the same line (coefficients are different).

So, the only reasonable description is ...

  neither perpendicular nor parallel

Answer:

-8 and 3

Step-by-step explanation:

The slope of the line will be - 8, the equation is y=-8x+3

Answer:

3043 (base 6)

Step-by-step explanation:

216      36    6    1

3           0      4  3

216* 3 = 648

6*4 = 24

1*3 = 3

648+24+3 = 675

Answer:

A. Periodic deposit:

The goal is to make $130,000 by depositing a set amount every year.

This set amount is an annuity. The $130,000 is therefore the future value of the annuity after 18 years.

Future value of annuity = Annuity * Future value of annuity factor, 7%, 18 years

130,000 = Annuity * 33.9990

Annuity = 130,000 / 33.9990

= $3,823.64

B. Sources of the financial goal.

Money from deposits = Periodic deposit * no. of years

= 3,823.64 * 18

= $68,825.52

Money from interest:

= Financial goal - Money from deposits

= 130,000 - 68,825.52

= $61,174.48

Answer:

2nd option,

The function is negative for all read values of x where -6<x<-2

The function f(x) = (x + 2)(x + 6) is a quadratic function, and the function is negative for all real values of x where –6 < x < –2.

Quadratic functions are functions that have an exponent or degree of 2

The function is given as:

f(x) = (x + 2)(x + 6)

From the graph of the function, the vertex is at (-4,-4) and the x-intercepts are at x = -6 and x = -2

Since the vertex is minimum, then the function is negative for all real values of x where –6 < x < –2.

Read more about x-intercepts at:

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Answer:

The height is 20 meters

Step-by-step explanation:

First set up the equation (Area)80=bh/2 then set up another equation, (height) h=4+2b (base). After this you can substitute h in the equation to end up with 80=(b(2b+4))/2 simplify it to get 80=b^2+2b then solve. The base is 8 meters, plug into the formula that we made before and you find the height is 20 meters.

Answer:

I don't know the answer it is to hard.

Answer:

The last one

Step-by-step explanation:

What we know:

We have a total of 16 coins

The 16 coins consist of dimes and quarters

The value of the coins is 3.10

The value of a dime is .10

The value of a quarter is .25

Using this information we can create a system of linear equations

First off we know that we have a total of 16 coins which consist of dimes and quarters

The number of Quarters can be represented by q and then number of dimes can be represented by d.

If we have a total of 16 coins then q + d must equal 16

So equation 1 is q + d = 16

Now we need to create a second equation

We know that the total value of the coins is 3.10 and we know that the coins consist of dimes and quarters

As you may know a quarter has a value of .25 cents and a dime has a value of 10 cents

If the total value of the coins is 3.10 the the number of dimes (d) times .10 + the number of Quarters times .25 must equal 3.10

This can also be written as

.25q + .10d = 3.10

So the two equations are

q + d = 16 and .25q + .10d = 3.10

These equations are shown in the last answer choice

Note: b is very similar to d

However the the value of the coins are incorrect in B

In B the value of the dime is represented by 10 which is not correct because the value of a dime is .10 not 10

Answer:

the 3rd, 4th, and 5th one

Step-by-step explanation:

Answer:

Step-by-step explanation:

:)

Answer:

$3 profit

Step-by-step explanation:

Since you got a profit of $9 on Saturday and a loss of $6 on Sunday, you have to subtract 9 and 6, which is 3.

Answer:

50/60 = .8333=  83.33%

Step-by-step explanation:

The probability that the call arrived when the switchboard was not fully busy is 0.75.

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.

Given:

Here X follows uniform distribution with parameter a and b.

Where,

a = 0 and b = 1.

Then,

The density function of Y is given by:

P( 15 < Y ≤ 60)

or, P( 0.25 < Y ≤ 1)

So,  P( 0.25 < Y ≤ 1) = [tex]\int\limits^{1}_{0.25}{f(y) \, dy[/tex]

                                = [tex][y]^1 _ {0.25}[/tex]

                                = (1- 0.25)

                                = 0.75

Hence, The probability that the call arrived when the switchboard was not fully busy is 0.75.

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Answer:

Step-by-step explanation:

4

Answer:

Missing length = 12

Step-by-step explanation:

Let x represent the missing length.

Since the triangles are similar, ∆KLM ~ ∆KRS, therefore, the ratio of their corresponding side lengths would be the same. This implies that:

KL/KR = KM/KS

KL = 65

KR = 65 - 52

KR = 13

KM = 60

KS = x

Plug in the values

65/13 = 60/x

Cross multiply

65*x = 60*13

65x = 780

Divide both sides by 65

65x/65 = 780/65

x = 12

Answer:

1 hour and 40 minutes

Step-by-step explanation:

→ Convert 3 hr and 25 minutes to minutes

( 3 × 60 ) + 25 = 205 minutes

→ Convert 1 hr and 45 minutes to minutes

( 1 × 60 ) + 45 = 105 minutes

→ Minus the answers from each other

205 - 105 = 100 minutes

→ Convert 100 minutes to hours and minutes

1 hour and 40 minutes

Recall the angle sum identity for cosine:

cos(x + y) = cos(x) cos(y) - sin(x) sin(y)

cos(x - y) = cos(x) cos(y) + sin(x) sin(y)

==>   sin(x) sin(y) = 1/2 (cos(x - y) - cos(x + y))

Then rewrite the equation as

sin(4x) sin(5x) + sin(4x) sin(3x) - sin(2x) sin(x) = 0

1/2 (cos(-x) - cos(9x)) + 1/2 (cos(x) - cos(7x)) - 1/2 (cos(x) - cos(3x)) = 0

1/2 (cos(9x) - cos(x)) + 1/2 (cos(7x) - cos(3x)) = 0

sin(5x) sin(-4x) + sin(5x) sin(-2x) = 0

-sin(5x) (sin(4x) + sin(2x)) = 0

sin(5x) (sin(4x) + sin(2x)) = 0

Recall the double angle identity for sine:

sin(2x) = 2 sin(x) cos(x)

Rewrite the equation again as

sin(5x) (2 sin(2x) cos(2x) + sin(2x)) = 0

sin(5x) sin(2x) (2 cos(2x) + 1) = 0

sin(5x) = 0   or   sin(2x) = 0   or   2 cos(2x) + 1 = 0

sin(5x) = 0   or   sin(2x) = 0   or   cos(2x) = -1/2

sin(5x) = 0   ==>   5x = arcsin(0) + 2nπ   or   5x = arcsin(0) + π + 2nπ

… … … … …   ==>   5x = 2nπ   or   5x = (2n + 1)π

… … … … …   ==>   x = 2nπ/5   or   x = (2n + 1)π/5

sin(2x) = 0   ==>   2x = arcsin(0) + 2nπ   or   2x = arcsin(0) + π + 2nπ

… … … … …   ==>   2x = 2nπ   or   2x = (2n + 1)π

… … … … …   ==>   x = nπ   or   x = (2n + 1)π/2

cos(2x) = -1/2   ==>   2x = arccos(-1/2) + 2nπ   or   2x = -arccos(-1/2) + 2nπ

… … … … … …    ==>   2x = 2π/3 + 2nπ   or   2x = -2π/3 + 2nπ

… … … … … …    ==>   x = π/3 + nπ   or   x = -π/3 + nπ

(where n is any integer)

9514 1404 393

Answer:

  2.64 gallons

Step-by-step explanation:

Each gallon costs $3.79, so the number of gallons that can be bought with $10 is ...

  $10/($3.79/gal) = (10/3.79) gal ≈ 2.6385 gal ≈ 2.64 gallons

Explanation:

Stratified sampling involves breaking a population of people into separate groups, where there isn't any overlap.

An example would be having a high school with freshmen, sophomores, juniors and seniors. A person can only belong to one group (so we can't have someone whos a freshman and a sophomore at the same time for instance). In that example, each group or strata is a different grade level.

As for this particular problem, each strata is a different ethnicity, and there are 6 strata total.

The researcher is using stratified sampling. The correct option is C.

A method of sampling from a population that can be divided into subpopulations is known as stratified sampling in statistics. When subpopulations within a larger population differ, it may be desirable to sample each subpopulation separately in statistical surveys.

Stratified sampling involves breaking a population of people into separate groups, where there isn't any overlap.

An example would be having a high school with freshmen, sophomores, juniors, and seniors. A person can only belong to one group (so we can't have someone whos a freshman and a sophomore at the same time for instance). In that example, each group or strata is a different grade level.

As for this particular problem, each stratum is different ethnicity, and there is 6 strata total.

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Answer:

Hence The probability that she is taking a night​ class given that Jane has a​ part-time teacher = P(jane has a part-time teacher and she is taking night class )/P(jane has a part-time teacher)    = 0.6999.

Step-by-step explanation:  

Probability(full-time teacher/ day ) = 0.85  

Probability(part-time teacher/ day ) = 1- 0.85 = 0.15  

Probability(full-time teacher/ night) = 0.30  

Probability(part-time teacher/ night) = 1 - 0.30 = 0.70  

total no of section = 4+2 = 6  

P(jane has part time teacher) = P(jane is from day section)*Probability(part-time teacher/ day )+P(jane is from night section)*Probability(part-time teacher/ night)  

= (4/6)(0.15)+(2/6)(0.70) = 0.33  

P(jane has part time teacher and she is taking night class ) = P(jane is from night section)*Probability(part-time teacher/ night) = (2/6)(0.70) = 0.23  

According to Bayes theorem :    

The probability that she is taking a night​ class given that Jane has a​ part-time teacher = P(jane has a part-time teacher and she is taking night class )/P(jane has a part-time teacher)  

= 0.23/0.33  

= 0.6999

Answer:

The correct answer is "Test 20%, Service 10%".

Step-by-step explanation:

As we know,

The coefficient of variation (CV) is:

⇒ [tex]CV=\frac{Standard \ deviation}{Mean}\times 100[/tex]

Now,

CV of test will be:

= [tex]\frac{40}{200}\times 100[/tex]

= [tex]20[/tex] (%)

CV of service will be:

= [tex]\frac{2}{20}\times 100[/tex]

= [tex]10[/tex] (%)

Answer:

11 red + 24 blue = 35 marbles

If 1 blue is withdrawn

11 red + 23 blue = 34 marbles

P = 23 / 34 = .38   probability of drawing blue marble

9514 1404 393

Answer:

  B(8, 4)

Step-by-step explanation:

Reflection across the origin negates both coordinate values.

  (x, y) ⇒ (-x, -y) . . . . . reflection across the origin

  A(-8, -4) ⇒ B(8, 4)

Answer:

x = 6; y = -6

Step-by-step explanation:

-4x - 2y = -12

4x + 8y = -24

Add the two equations, so x is eliminated:

6y = -36

6y/6 = -36/6

y = -6

Plug in y, to solve for x

-4x - 2y = -12

-4x - 2(-6) = -12

-4x +12 = -12

-4x = -12 -12

-4x = -24

-4x/-4 = -24/-4

x = 6

Answer from Gauthmath

Answer:

The p-value of the test is 0.4414, higher than the standard significance level of 0.05, which means that there is not a a significant difference in the proportion of apartment dwellers and home owners who own artificial Christmas trees.

Step-by-step explanation:

Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.

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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Apartment:

38 out of 78, so:

[tex]p_A = \frac{38}{78} = 0.4872[/tex]

[tex]s_A = \sqrt{\frac{0.4872*0.5128}{78}} = 0.0566[/tex]

Home:

46 out of 84, so:

[tex]p_H = \frac{46}{84} = 0.5476[/tex]

[tex]s_H = \sqrt{\frac{0.5476*0.4524}{84}} = 0.0543[/tex]

Test if the there a significant difference in the proportion of apartment dwellers and home owners who own artificial Christmas trees:

At the null hypothesis, we test if there is no difference, that is, the subtraction of the proportions is equal to 0, so:

[tex]H_0: p_A - p_H = 0[/tex]

At the alternative hypothesis, we test if there is a difference, that is, the subtraction of the proportions is different of 0, so:

[tex]H_1: p_A - p_H \neq 0[/tex]

The test statistic is:

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

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.

0 is tested at the null hypothesis:

This means that [tex]\mu = 0[/tex]

From the samples:

[tex]X = p_A - p_H = 0.4872 - 0.5476 = -0.0604[/tex]

[tex]s = \sqrt{s_A^2 + s_H^2} = \sqrt{0.0566^2 + 0.0543^2} = 0.0784[/tex]

Value of the test statistic:

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

[tex]z = \frac{-0.0604 - 0}{0.0784}[/tex]

[tex]z = -0.77[/tex]

P-value of the test and decision:

The p-value of the test is the probability of the difference being of at least 0.0604, to either side, plus or minus, which is P(|z| > 0.77), given by 2 multiplied by the p-value of z = -0.77.

Looking at the z-table, z = -0.77 has a p-value of 0.2207.

2*0.2207 = 0.4414

The p-value of the test is 0.4414, higher than the standard significance level of 0.05, which means that there is not a a significant difference in the proportion of apartment dwellers and home owners who own artificial Christmas trees.

Answer:

9000

Step-by-step explanation:

20 x 18 x 25

20 options for one member

18 options for another member

25 members for the last member

Answer:

Sixteen million, one hundred and seven thousand, three hundred twenty

Step-by-step explanation:

Answer:

2[tex]\sqrt{2}[/tex]

Step-by-step explanation:

See the photo for the steps. :)

Answer:

A

Step-by-step explanation:

260 pairs

Step-by-step explanation:

220-100= 120

(29200+2000)÷120= 260

Answer:

Can you select multiple answers to this question? then option A, B and C all three applies, if only one the go for option C, since that's the major change happens to the parent function

Answer:

Option (A)

Step-by-step explanation:

Solution of two functions represented by the graph are the common points or point of intersection of the graphs.

From the graph attached,

Parabola and ellipse are intersecting each other at four points.

Therefore, solutions of the given non linear functions will be FOUR.

Option (A) will be the correct option.