Which correctly describes how to determine the measure of angle 1? 2 parallel lines are crossed by a transversal to form 8 angles. Clockwise from top left, the angles are 1, 2, blank, blank; blank 81 degrees, blank, blank. The 81° angle and angle 2 are corresponding angles so angle 2 must measure 81°. Angles 1 and 2 are supplementary angles so angle 1 must measure 99°. The 81° angle and angle 2 are alternate interior angles so angle 2 must measure 81°. Angles 1 and 2 are supplementary angles so angle 1 must measure 99°. The 81° angle and angle 2 are corresponding angles so angle 2 must measure 99°. Angles 1 and 2 are supplementary angles so angle 1 must measure 81°. The 81° angle and angle 2 are alternate interior angles so angle 2 must measure 99°. Angles 1 and 2 are supplementary angles so angle 1 must measure 81°.

Answer:

simple really

Step-by-step explanation:

10 gigabytes of data on my computer, x gigabytes are movies and the rest is music.

so it will have to be 10-X= remaining gigabites of music

Answer:

Movies: x gig

pictures: x/2 gig

music:  10 - x - x/2 = 10 - (3/2)x

Answer:

  $4,457,391.19

Step-by-step explanation:

The sum of n terms of a geometric sequence with common ratio r and initial value "a" is ...

  S = a(r^n -1)/(r -1)

Here, your growth factor is r = 1 +6% = 1.06. So, the sum of expenses over 35 years will be ...

  S = $40,000(1.06^35 -1)/(1.06 -1) = $4,457,391.19

Answer:

This question is about:

sin(A/2) and cos(A/2)

First, how we know when we need to use the positive or negative signs?

Ok, this part is kinda intuitive:

First, you need to know the negative/positve regions for the sine and cosine function.

Cos(x) is positive between 270 and 90, and negative between 90 and 270.

sin(x) is positive between  0 and 180, and negative between 180 and 360.

Then we need to see at the half-angle and see in which region it lies.

If the half-angle is larger than 360°, then you subtract 360° enough times such that the angle lies in the range between (0° and 360°)

and: Tan(A/2) = Sin(A/2)/Cos(A/2)

So using that you can infer the sign of the Tan(A/2)

Now, why these relationships use the two signs?

Well... this is because of the square root in the construction of the relationships.

This happens because:

(-√x)*(-√x) = (-1)*(-1)*(√x*√x) = (√x*√x)

For any value of x.

so both -√x and √x are possible solutions of these type of equations, but for the periodic nature of the sine and cosine functions, we can only select one of them.

So we should include the two possible signs, and we select the correct one based on the reasoning above.

Answer:

C

Step-by-step explanation:

102.35-20-33.33-52.80+25+24.75

45.97

Answer:

2/10 for Rebecka and either 2/9 or 1/9 for Aaron depending on if Rebecka selects a poodle or not.

Step-by-step explanation:

do some math

Answer:

A 95% confidence interval for the population mean score for all bowlers in this league is [86.64, 94.48].

Step-by-step explanation:

Since in the question only 9 random scores are given, so I am performing the calculation using 9 random scores.

We are given that the scores of bowlers in particular league follow a normal distribution such that the standard deviation of the population is 6.

The accompanying data set of 9 random scores in ascending order is given as; 75, 86, 86, 88, 89, 93, 93, 98, 107

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                             P.Q.  =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\bar X[/tex] = sample mean score = [tex]\frac{\sum X}{n}[/tex] = [tex]\frac{815}{9}[/tex] = 90.56

            [tex]\sigma[/tex] = population standard deviation = 6

            n = sample of random scores = 9

            [tex]\mu[/tex] = population mean score for all bowlers

Here for constructing a 95% confidence interval we have used a One-sample z-test statistics because we know about population standard deviation.

So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5% level

                                                   of significance are -1.96 & 1.96}  

P(-1.96 < [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < 1.96) = 0.95

P( [tex]-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\bar X-\mu}[/tex] < [tex]1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.95

P( [tex]\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.95

95% confidence interval for [tex]\mu[/tex] =  [ [tex]\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] , [tex]\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ]

                                          = [ [tex]90.56-1.96 \times {\frac{6}{\sqrt{9} } }[/tex] , [tex]90.56+1.96 \times {\frac{6}{\sqrt{9} } }[/tex] ]

                                          = [86.64 , 94.48]

Therefore, a 95% confidence interval for the population mean score for all bowlers in this league is [86.64, 94.48].

Answer:

1 year

Step-by-step explanation:

1. Convert 10% into a z-score, using a calculator or whateva

2. Z = -1.281551 ( you can find this by doing the following equation: (x - mean) / (standard deviation)

3. Hence -1.281551 = (x - 4) / 2 or, x = 1.436898, ( rounded to the nearest year ) = 1 year

Answer:

D. Two-sample chi-square

Step-by-step explanation:

A chi-square test is a test used to compare the data that is observed, from the data that is expected.

In a two-sample chi-square test the observed data should be similar to the expected data if the two data samples are from the same distribution.

The hypotheses of the two-sample chi-square test is given as:

H0: The two samples come from a common distribution.

Ha: The two samples do not come from a common distribution

Therefore, in this case, the best statistical test to utilize is the two-sample chi-square test.

Answer:

[tex] P(X \geq 3)= 1- P(X<3)= 1-P(X \leq 2)= 1- [P(X=0) +P(X=1) +P(X=2)][/tex]

And we can find the individual probabilites using the probability mass function and we got:

[tex] P(X=0) = (15C0) (0.08)^{0} (1-0.08)^{15-0}=0.286 [/tex]

[tex] P(X=1) = (15C1) (0.08)^{1} (1-0.08)^{15-1}=0.373 [/tex]

[tex] P(X=2) = (15C2) (0.08)^{2} (1-0.08)^{15-2}=0.227 [/tex]

And replacing we got:

[tex] P(X\geq 3) = 1-[0.286+0.373+0.227 ]= 0.114[/tex]

Step-by-step explanation:

For this case we can assume that the variable of interest is "drivers were involved in a car accident last year" and for this case we can model this variable with this distribution:

[tex] X \sim Bin (n =15, p =0.08)[/tex]

And for this case we want to find this probability;

[tex] P(X \geq 3)[/tex]

and we can use the complement rule and we got:

[tex] P(X \geq 3)= 1- P(X<3)= 1-P(X \leq 2)= 1- [P(X=0) +P(X=1) +P(X=2)][/tex]

And we can find the individual probabilites using the probability mass function and we got:

[tex] P(X=0) = (15C0) (0.08)^{0} (1-0.08)^{15-0}=0.286 [/tex]

[tex] P(X=1) = (15C1) (0.08)^{1} (1-0.08)^{15-1}=0.373 [/tex]

[tex] P(X=2) = (15C2) (0.08)^{2} (1-0.08)^{15-2}=0.227 [/tex]

And replacing we got:

[tex] P(X\geq 3) = 1-[0.286+0.373+0.227 ]= 0.114[/tex]

Answer:

A. 3

Step-by-step explanation:

[tex] log_{4}(64) = y \\ 64 = {4}^{y}(\because if \: log_a b = x \implies b = a^x) \\ {4}^{3} = {4}^{y} \\3 = y..(equal \: bases \: have \: equal \: exponents ) \\ \huge \purple { \boxed{y = 3}}[/tex]

Answer:

-2w - 4

Step-by-step explanation:

What is the simplest form of this expression

2(w - 1) + (-2)(2w + 1) =

= 2w - 2 - 4w - 2

= -2w - 4

Answer: -2w-4

Step-by-step explanation:

subtract 4w of 2w

2w-2-4w-2

subtract 2 of -2

-2w-2-2

final answer

-2w-4

Answer:

the probability that the mean student loan debt for these people is between $31000 and $33000 is 0.1331

Step-by-step explanation:

Given that:

Mean = 30000

Standard deviation = 9000

sample size = 100

The probability that the mean student loan debt for these people is between $31000 and $33000 can be computed as:

[tex]P(31000 < X < 33000) = P( X \leq 33000) - P (X \leq 31000)[/tex]

[tex]P(31000 < X < 33000) = P( \dfrac{X - 30000}{\dfrac{\sigma}{\sqrt{n}}} \leq \dfrac{33000 - 30000}{\dfrac{9000}{\sqrt{100}}} )- P( \dfrac{X - 30000}{\dfrac{\sigma}{\sqrt{n}}} \leq \dfrac{31000 - 30000}{\dfrac{9000}{\sqrt{100}}} )[/tex]

[tex]P(31000 < X < 33000) = P( Z \leq \dfrac{33000 - 30000}{\dfrac{9000}{\sqrt{100}}} )- P(Z \leq \dfrac{31000 - 30000}{\dfrac{9000}{\sqrt{100}}} )[/tex]

[tex]P(31000 < X < 33000) = P( Z \leq \dfrac{3000}{\dfrac{9000}{10}}}) -P(Z \leq \dfrac{1000}{\dfrac{9000}{10}}})[/tex]

[tex]P(31000 < X < 33000) = P( Z \leq 3.33)-P(Z \leq 1.11})[/tex]

From Z tables:

[tex]P(31000 < X <33000) = 0.9996 -0.8665[/tex]

[tex]P(31000 < X <33000) = 0.1331[/tex]

Therefore; the probability that the mean student loan debt for these people is between $31000 and $33000 is 0.1331

Answer:

144

Step-by-step explanation:

Find: Length of segment BC

CD+DB=BC

3x+8+4x+10=BC

7x+18=BC

BC also equals 8x (given on the screen shot)

7x+18= 8x

x=18

18 times 8 = 144

Check:

3( 18) + 8 + 4(18) + 10

54+8 + 72+10

64+ 80= 144  TRUE

Question:

A silver coin is dropped from the top of a building that is 64 feet tall. the position function of the coin at time t seconds is represented by

s(t) = -16t² + v₀t + s₀

Determine the position and velocity functions for the coin.

Answer:

position function: s(t) = (-16t² + 64) ft

velocity function: v(t) = (-32t) ft/s

Step-by-step explanation:

Given position equation;

s(t) = -16t² + v₀t + s₀                ---------(i)

v₀ and s₀ are the initial values of the velocity and position of the coin respectively.

(a) Since the coin is dropped, the initial velocity, v₀, of the coin is 0 at t = 0. i.e

v₀ = 0.  

Also since the drop is from the top of a building that is 64 feet tall, this implies that the initial position, s₀, of the coin is 64 ft at t=0. i.e

s₀ = 64ft

Substitute the values of v₀ = 0 and s₀ = 64 into equation (i) as follows;

s(t) = -16t² + (0)t + 64    

s(t) = -16t² + 64

Therefore, the position function of the coin is;

s(t) = (-16t² + 64) ft

(b) To get the velocity function, v(t), the position function, s(t), calculated above is differentiated with respect to t as follows;

v(t) = [tex]\frac{ds(t)}{dt}[/tex]

v(t) = [tex]\frac{d(-16t^2 + 64)}{dt}[/tex]

v(t) = -32t + 0

v(t) = -32t

Therefore, the velocity function of the coin is;

v(t) = (-32t) ft/s

Answer:

-$3576

Step-by-step explanation:

Depreciation using double declining method=100%/useful life*2

Depreciation using double declining method=100%/10*2=20%

2017 depreciation=$60,000*20%=$12000

2018 depreciation=($60,000-$12000)*20%=$9600

2019 depreciation=($60,000-$12000-$9600 )*20%=$7680

2020 depreciation=($60,000-$12000-$9600-$7680 )*20%=$6144

carrying value in 2021=$60000-$12000-$9600 -$7680-$6144 =$24576

Loss on disposal of machine=$21,000-$24576  =-$3576

Answer:

7

Step-by-step explanation:

2x-3=11

Move the -3 to the right side by adding 3 to both sides of the equation

2x=14

Divide both sides by 2 to get x by itself

x=7

Answer:

  7

Step-by-step explanation:

2x -3 = 11

2x = 14 . . . . add 3

x = 7 . . . . . . divide by 2

The number 7 makes the equation true when substituted for x.

Answer:

0.3174

Step-by-step explanation:

Z-score:

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 area under the normal curve to the left of Z. Subtracting 1 by the pvalue, we find the area under the normal curve to the right of Z.

Left of z = -1

z = -1 has a pvalue of 0.1587

So the area under the standard normal curve to the left of z = -1 is 0.1587

Right of z = 1

z = 1 has a pvalue of 0.8413

1 - 0.8413 = 0.1587

So the area under the standard normal curve to the right of z = 1 is 0.1587

Left of z = -1 or right of z = 1

0.1587 + 0.1587 = 0.3174

The area is 0.3174

Answer:

1000

Step-by-step explanation:

=> [tex]\frac{1}{10^{-3}}[/tex]

According to the law of exponents, [tex]\frac{1}{a^{-m}} = a^{m}[/tex]

So, it becomes

=> [tex]10^{3}[/tex]

=> 1000

Answer:

B. Multiply 6 by 3

Step-by-step explanation:

Do the opposite order of what Hannah did. The last step that she did was divide by 3, so you would multiply the result (6) with 3:

B. Multiply 6 by 3

Your step by step for getting the number Hannah started with:

First, multiply 6 with 3:

6 x 3 = 18

Next, subtract 4:

18 - 4 = 14

Next, divide by 2:

14/2 = 7

Hannah started with the number 7.

~

Answer: Hannah started with 7.

B. Multiply 6 by 3

Explanation:

Let the number be y

2 × y = 2y

(2y + 4)/3 = 6

2y + 4 = 6×3 = 18

2y + 4 = 18

2y = 18 - 4 = 14

y = 14/2 = 7

To solve the problem backward, the first step is to multiply 6 by 3.

Answer:

The probability that a truck drives between 86 and 125 miles in a day.

P(86≤ X≤125) = 0.5890 miles

Step-by-step explanation:

Step(i):-

Given mean of the Population = 100 miles per day

Given standard deviation of the Population = 23 miles per day

Let 'X' be the normal distribution

Let x₁ = 86

[tex]Z_{1} = \frac{x_{1} -mean}{S.D} = \frac{86-100}{23} =-0.61[/tex]

Let x₂= 86

[tex]Z_{2} = \frac{x_{2} -mean}{S.D} = \frac{125-100}{23} = 1.086[/tex]

Step(ii):-

The probability that a truck drives between 86 and 125 miles in a day.

P(86≤ X≤125) = P(-0.61 ≤ Z≤ 1.08)

                      = P(Z≤ 1.08) - P(Z≤ -0.61)

                      = 0.5 +A(1.08) - ( 0.5 - A(-0.61))    

                      = A(1.08) + A(0.61)             ( A(-Z)=  A(Z)

                      = 0.3599 + 0.2291

                     = 0.5890

Conclusion:-

The probability that a truck drives between 86 and 125 miles in a day.

P(86≤ X≤125) = 0.5890  miles per day

Answer:

(-2 ,3)

Step-by-step explanation:

Step 1: Rewrite first equation

x = 4 - 2y

-2x + y = 7

Step 2: Substitution

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

Step 3: Solve y

-8 + 4y + y = 7

-8 + 5y = 7

5y = 15

y = 3

Step 3: Plug in y to find x

x + 2(3) = 4

x + 6 = 4

x = -2

The probability of picking greens on both occasions will be 5/18.

The probability of picking greens cards will be:

= 5/9 × 4/8

= 5/18

The probability of picking at least one green will be:

= 1 - P(both aren't green)

= 1 - (4/9 × 3/8)

= 1 - 1/6.

= 5/6

From the tree diagram, the probability as a fraction of P(G2 | G1) will be:

= 4/8 = 1/2

Learn more about probability on:

brainly.com/question/24756209

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The correct answer is The line will be less steep because the rate will be slower

Explanation:

The rate of the graph is defined by the number of gallons filled vs the time; this relation is shown through the horizontal axis (time) and the vertical axis (gallons). Additionally, there is a constant rate because each hour 2,500 gallons are filled, which creates a steep constant line.

However, if the rate decreases, fewer gallons would be filled every hour, and the line will be less steep, this is because the number of gallons will not increase as fast as with the original rate. For example, if the rate is 1,250 gallons per hour (half the original rate), after 8 hours the total of gallons would be 1000 gallons (half the amount of gallons); and this would make the line to be less steep or more horizontal.

Answer:

true

Step-by-step explanation:

The test for divisibility by 9 is to add all the digits of the number. If that sum is divisible by 9, then the number is divisible by 9.

Answer:

A

Step-by-step explanation:

Since we are given BC is congruent to DC and angle b and d are 90. We can prove that <C is congruent to itself by reflexive  property of congruence. We can also you use linear pair theorem to prove <CDA is congruent to <CBE. Since they are right angles, we can prove that they are congruent by rt <s thm. Thus, we cna prove they are congruent by ASA. Hope it helps

Answer:

50%

Step-by-step explanation:

Cost of 3 bananas= Rs. 5 ⇒ cost of 1 banana= Rs. 5/3

Selling price of 2 bananas= Rs. 5 ⇒ selling price of 1 banana= Rs. 5/2

Gain= Rs. (5/2- 5/3)= Rs. (15/6- 10/6)= Rs. 5/6

Gain %= 5/6÷5/3 × 100%= 50%

Answer:

B. 120 m²

Step-by-step explanation:

To find the surface area of the composite solid, we would need to calculate the area of each solid (square pyramid and square prism), then subtract the areas of the sides that are not included as surface area. The sides not included as surface area is the side the pyramid and the prism is joint together.

Step 1: find the surface area of the pyramid:

Surface area of pyramid with equal base sides = Base Area (B) + ½ × Perimeter (P) × Slant height (l)

Base area = 4² = 16 m

Perimeter = 4(4) = 16 m

Slant height = 3 m

Total surface area of pyramid = 16 + ½ × 16 × 3

= 16 + 8 × 3 = 16 + 24

= 40 m²

Step 2: find the area of the prism

Area = 2(wl + hl + hw)

Area = 2[(4*4) + (5*4) + (5*4)]

Area = 2[16 + 20 + 20]

Area of prism =  2[56] = 112 m²

Step 3: Find the area of the sides not included

Area of the sides not included = 2 × area of the square base where both solids are joint

Area = 2 × (4²)

Area excluded = 2(16) = 32 m²

Step 4: find the surface area of the composite shape

Surface area of the composite shape = (area of pyramid + area of prism) - excluded areas

= (40m²+112m²) - 32m²

= 152 - 32

Surface area of composite solid = 120 m²

Answer:

3x / 2 + 9 = 5

3x / 2 = -4

3x = -8

x = -8/3

(2 + v) / 3 = 9

2 + v = 27

v = 25

32 / (d - 2) = 10

32 = 10 * (d - 2)

3.2 = d - 2

d = 5.2

2p - 4 = 3p / 2

2 * (2p - 4) = 3p

4p - 8 = 3p

p - 8 = 0

p = 8

3b / 2 = 12

3b = 24

b = 8

Answer:

Subtract 2 and two-thirds from both sides of the equation

8 minus 2 and two-thirds = 5 and one-third

Substitute the value for r to check the solution.

Step-by-step explanation:

2 2/3  + r   = 8

Subtract 2 2/3 from each side

2 2/3  + r  - 2 2/3   = 8 - 2 2/3

r = 5 1/3

Check the solution

2 2/3 +5 1/3 =8

8 =8

Answer:

1, 3, 5

Step-by-step explanation:

edge