y=-1/2x +7

Line k is perpendicular to the line defined by the equation
above and passes through the point (4,0). Which of the
following points also lies on line k?
A) (0,8)
B) (2,-4)

C) (2,-2)
D) (2,8)

Answer:

For a give event with outcomes:

{x₁, x₂, ..., xₙ}

Each with probabilities:

{p₁, p₂, ..., pₙ}

The expected value is:

Ev = x₁*p₁ + ... + xₙ*pₙ

Here we have the outcomes and probabilities:

win $1, with a probability 20%/100% = 0.2

win $2, with a probability 25%/100% = 0.25

win $5, with a probability of 35%/100% = 0.35

do not win, with a probability of 20%/100% = 0.2

Then the expected value of the game is:

Ev = $1*0.2 + $2*0.25 + $5*0.35 + $0*0.2 = $2.45

And if we know that the game costs $2, then the expected value is:

Ev = $2.45 - $2 = $0.45

The expected value is  $0.45

Answer:

C

Step-by-step explanation:

We see that the y-intercept is 3. So it is either A of B.

Plug in the point that is on the line (1, -2), we see that the point works for C.

The missing statement is linear pair postulate of intersecting lines

Two straight lines that intersect at the same location are said to be intersecting lines. The junction point is the place where two intersecting lines meet. Four angles are created when two lines cross. The four angles added together always equal 360 degrees.

Perpendicular lines are two straight lines that intersect and form right angles. When two perpendicular lines intersect, they form four right angles.

When lines intersect, two angle relationships are formed:

Opposite angles are congruent

Adjacent angles are supplementary

Given data ,

Let the lines be represented as l and m

where AB intersects DE at point C

Now , from the figure ,

∠BCA + ∠ECA = 180° ( angles on the straight line = 180° )

Therefore , ∠BCA + ∠ECA = supplementary and the postulate is linear pair

Hence , ∠BCA is supplementary to ∠ECA

To learn more about intersection of 2 lines click :

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Answer:

700 apples

Step-by-step explanation:

Let

x = Total number of apples in the cart

Percentage of apples sold = 40%

Number of apples sold = Percentage of apples sold * Total number of apples in the cart

= 40% * x

= 0.4 * x

= 0.4x

Number of apples left in the cart = 420

Total number of apples in the cart = Number of apples sold + Number of apples left in the cart

x = 0.4x + 420

x - 0.4x = 420

0.6x = 420

x = 420/0.6

x = 700

x = Total number of apples in the cart = 700

Lawrence started with 700 apples

Answer:

D. [tex] \frac{15}{8} [/tex]

Step-by-step explanation:

Recall: SOH CAH TOA

Thus,

Tan A = Opposite/Adjacent

Reference angle (θ) = A

Length of side Opposite to <A = 15

Length of Adjacent side = 8

Plug in the known values

[tex] Tan(A) = \frac{15}{8} [/tex]

Given:

Adam's locker has a password that consists of 4 non-repeated letters from A - Z.

To find:

The number of different passwords.

Solution:

Total number of letters from A - Z is 26.

So, the number of selecting a letter for first place is 26.

The passwords consists non-repeated letters. So, the remaining numbers is [tex]26-1=25[/tex].

The number of selecting a letter for second place is 25.

Similarly,

The number of selecting a letter for third place is 24.

The number of selecting a letter for fourth place is 23.

The total number of possible different passwords is:

[tex]26\times 25\times 24\times 23=358800[/tex]

Therefore, the total number of different passwords is 358800.

Answer:

20 degrees

Step-by-step explanation:

we can consider 33 to be the radius of a circle.

31 would then be the cos of the angle in that circle.

the regular cos function is defined for the standard circle with radius 1. so, that would be multiplied by 33 for this circle here.

31 = cos(?) × 33

cos(?) = 31/33 = 0.9393...

? = 20.05 ≈ 20 degrees

Answer:

5/3

Step-by-step explanation:

3^5 = 27 ^x

Rewrite 27 and 3^3

3^5 = 3^3^x

We know that a^b^c = a^(b*c)

3^5 = 3^(3x)

The bases are the same so the exponents are the same

5 = 3x

Divide by 3

5/3 =x

Answer:

x = [tex]\frac{5}{3}[/tex]

Step-by-step explanation:

[tex]3^{5} = 27^{x}[/tex]

These problems are getting you ready to work with exponential functions,

and ultimately with logarithms. The point here is that with variable exponents (notice the exponent is an x (on the right one) and not a number. Variable exponents can not be solved with regular algebra "rules" you need new ones.

The new ones will be Logs....

For now (until you learn logs) , you have to use some "tricks"

the "trick" in this problem is that you have to realize that 27 = [tex]3^{3}[/tex]...

with "common bases" this problem becomes trivial

[tex]3^{5} =(3^{3} ) ^{x}[/tex]

so now the bases are the same and the equals sign suggests that

3x = 5

thus x = [tex]\frac{5}{3}[/tex]

Answer:

[tex]\frac{13}{5}=2\frac{3}{5}[/tex]

Step-by-step explanation:

Given fraction is [tex]\frac{13}{5}[/tex].

To convert this fraction into a mixed number, divide the numerator 13 by the denominator 5.

5) 13 (2

  10

    3

Here, quotient = 2

Remainder = 3

Divisor = 5

Therefore, given fraction can be written as,

[tex]2\frac{3}{5}[/tex]

Answer:

Number of cups of dough needed = 15 cups

Step-by-step explanation:

Cup of dough needed for each dumpling = 4/5 cup of dough

Total dumplings = 12

how many cups of dough does Aubrey need to make 12 dumplings?

Number of cups of dough needed = Total dumplings / Cup of dough needed for each dumpling

= 12 ÷ 4/5

= 12 × 5/4

= 60/4

= 15

Number of cups of dough needed = 15 cups

Answer:

63

Step-by-step explanation:

a=9

7a

7(9)

63

Answer:

BD = 3 units

Step-by-step explanation:

Since, AD is an angle bisector of ∠BAC,

m∠BAD = m∠CAD = 20°

CD = 3 units

In ΔACD and ΔABD,

m∠BAD = m∠CAD = 20° (Given)

AD ≅ AD [Reflexive property]

Therefore, by H-A property of congruence both the triangles will be congruent.

And by CPCTC,

CD ≅ BD = 3 units

Answer:

The height above sea level at B is approximately 1,604.25 m

Step-by-step explanation:

The given length of the mountain railway, AB = 864 m

The angle at which the railway rises to the horizontal, θ = 120°

The elevation of the train above sea level at A, h₁ = 856 m

The height above sea level of the train when it reaches B, h₂, is found as follows;

Change in height across the railway, Δh = AB × sin(θ)

∴ Δh = 864 m × sin(120°) ≈ 748.25 m

Δh = h₂ - h₁

h₂ = Δh + h₁

∴ h₂ ≈ 856 m + 748.25 m = 1,604.25 m

The height above sea level of the train when it reaches B ≈ 1,604.25 m

7.7cm

the rest is vastly (a and d) off or just enough off (can't be less then 5.2, because that's already the shortest side), to solve this by looking at it

Answer:

1) -7929

2) -2401

3)-5414

4) -7592

5) 12888

6)-237726

7) 7287

8)-4588

9)-394495

10) 891856

Answer:

4 + x =5

Step-by-step explanation:

By adding a variable you can set up an addition sentence

Answer:

25.

Step-by-step explanation:

Let the number of pupils be x, then:

there are 0.6x girls and 0.4x boys.

From the given information:

0.6x - 0.4x = 5

0.2x = 5

x = 5/0.2

= 50/2

= 25.

Answer:

Triangle ISK

Step-by-step explanation:

Answer:

Triangle ISK

Step-by-step explanation:

if the angles and sides of one triangle are equal to the corresponding sides and angles of the other triangle, they are congruent.

∠Q = ∠I

∠R = ∠S

∠S = ∠K

hope this helps! feel free to clarify if unsure

Answer:

QXV=WXV

Step-by-step explanation:

Answer:

-0.301

Step-by-step explanation:

Correct Question :-

If log 2 = 0.301 , find log 0.5

Solution :-

We are here given that the value of log 5 is 0.699 . Here the base of log is 10 .

[tex]\rm\implies log_{10}2= 0.301 [/tex]

And we are supposed to find out the value of log 0.5 . We can write it as ,

[tex]\rm\implies log_{10}(0.5) = log _{10}\bigg( \dfrac{5}{10}\bigg)[/tex]

Simplify ,

[tex]\rm\implies log _{10}\bigg( \dfrac{1}{2}\bigg)[/tex]

This can be written as ,

[tex]\rm\implies log_{10} ( 2^{-1})[/tex]

Use property of log ,

[tex]\rm\implies -1 \times log_{10}2 [/tex]

Put the value of log 2 ,

[tex]\rm\implies -1 \times 0.301 =\boxed{\blue{-0.301}} [/tex]

Hence the value of log (0.5) is -0.301 .

*Note -

Here here there was no use of log 5 in the calculation .

Answer:

[tex]\sqrt{89}[/tex] = 9.83

Step-by-step explanation:

[tex]\sqrt{89}[/tex]

[tex]\sqrt{25 + 64} \\\sqrt{5^2 + 8^2}[/tex]

Answer: 89

Step-by-step explanation:

Answer:

a) 272 used at least one prescription​ medication.

b) The 90% confidence interval estimate of the percentage of adults aged 57 through 85 years who use at least one prescription medication is (85.6%, 87.6%).

Step-by-step explanation:

Question a:

86.6% out of 3149, so:

0.866*3149 = 2727.

272 used at least one prescription​ medication.

Question b:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 3149, \pi = 0.866[/tex]

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].  

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.866 - 1.645\sqrt{\frac{0.866*0.134}{3149}} = 0.856[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.866 + 1.645\sqrt{\frac{0.866*0.134}{3149}} = 0.876[/tex]

For the percentage:

0.856*100% = 85.6%

0.876*100% = 87.6%.

The 90% confidence interval estimate of the percentage of adults aged 57 through 85 years who use at least one prescription medication is (85.6%, 87.6%).

The number of subjects in the study who used at least one prescription medication is 2727 approx. The needed 90% confidence interval is:  [0.8560, 0.8758] or in percentage as: 85.6% to 87.58%

Suppose that we have:

Then, we get:

[tex]CI = \hat{p} \pm Z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]

where [tex]Z_{\alpha/2}[/tex] is the critical value of Z at specified level of significance and is obtainable from its critical value table(available online or in some books)

For this case, we have:

Part (a):

The number of subjects used at least one prescription​ medication is:

[tex]\dfrac{3149}{100} \times 86.6 \approx 2727[/tex]

Thus, the sample proportion we get is:

[tex]\hat{p} = \dfrac{2727}{3149} \approx 0.8659[/tex]

For level of significance 0.10, we get: [tex]Z_{\alpha/2} = 1.645[/tex]

Thus, the confidence interval needed is:

[tex]CI = \hat{p} \pm Z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\CI \approx 0.8659\pm 1.645 \times \sqrt{\dfrac{0.8659(1-0.8659)}{3149}}\\\\\\CI \approx 0.8659 \pm 0.0099[/tex]

Thus, CI is [0.8659 - 0.0099, 0.8659 + 0.0099] = [0.8560, 0.8758]

Thus, the number of subjects in the study who used at least one prescription medication is 2727 approx. The needed 90% confidence interval is:  [0.8560, 0.8758] or in percentage as: 85.6% to 87.58%

Learn more about population proportion here:

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Answer:

54.94954839

Step-by-step explanation:

tan(70) = x/20

tan(70) times 20 = x

Step-by-step explanation:

First sentence

Let the number be X

second sentence

X-5

Third sentence

X-5=14

X=19

The number is 19

Hi there!  

»»————-　★　————-««

I believe your answer is:

19

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\text{"I am thinking of a number. l take away 5. The result is 14."}\\\\\text{5 taken away from 'said number' would be 14.}\\\\\boxed{n-5=14}\\\\\\\boxed{\text{Solving for 'n'...}} \\\\\rightarrow n - 5 + 5 = 14 + 5\\\\\rightarrow \boxed{n = 19}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

c

Step-by-step explanation:

w=3   x=15

Answer:

me and you have the same questions

Answer:

1. -2, 3

2. 4, -1

3. 0, -2

4. -3, -1

5. 2/3, 0

6. 5/2, 4

Step-by-step explanation:

Answer:

[tex]2x = \frac{1}{2} \times 20 = 10 \\ = > x = 5[/tex]