In figure #4, identify all of the vertical pairs of angles,

If for the first 150 miles of a trip, an car drives at v mph, for the next 200 miles, the car drives at (v+25) mph and the average speed of the whole trip is 35 mph, then the value of v will be 20mph (A).

Given Information:

Average speed = 35 mph

Total distance = 150 + 200 = 350 miles

For the first 150 miles of a trip, an car drives at v mph speed

⇒ Time, t1 = 150/v hrs

For the next 200 miles, the car drives at (v+25) mph speed

⇒ Time, t1 = 200 / (v+25) hrs

Now, the formula for average speed is given as,

Total distance / Total time

= [tex]\frac{350}{\frac{150}{v}+\frac{200}{(v+25)} }[/tex]

⇒ [tex]\frac{350}{\frac{150}{v}+\frac{200}{(v+25)} }[/tex] = 35 mph

[tex]\frac{350 v (v+25)}{150(v+25) + 200v}[/tex] = 35

[tex]\frac{350v^{2} + 8750v}{150v +3750 + 200v}[/tex] = 35

350v² + 8750v = 35 (350v + 3750)

v² + 25v = 35v + 375

v² - 10v = 375

v² - 10v - 375 = 0

Now, the above equation for speed can be written as,

v² - 20v + 15v - 375 = 0

v(v-20) + 15(v-20) = 0

(v-20) (v+15) = 0

v = 20

or v = -15

Since, speed is a scalar quantity, it can't be negative. Thus, v = 20 mph

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Answer:

35%

Step-by-step explanation:

All the prime numbers from 1 to 20 are:

2 3 5 7 11 13 17 19

7 / 20 = 35 / 100 = 35%

The effective annual yield is 3.04%

What is effective annual yield?

Effective annual yield is the rate of return that considers the frequency of compounding, in other words, the number of times in a year that interest on the balance is compounded.

The easiest way to determine the effective annual yield in this case is to compare the end of the year balance with the initial balance at the start of the year

effective annual yield=(ending balance/initial balance)-1

ending balance=$4,121.66

initial balance=$4000

effective annual yield=($4,121.66/$4000)-1

effective annual yield=3.04%

Another way to determine the effective annual yield is use the below formula which considers that interest rate is 3% compounded monthly, in other words, n, the frequency of compounding is 12

EAR=(1+r/n)^n-1

r=3%

n=12

EAR=(1+3%/12)^12-1

EAR=3.04%

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Answer:

a)0.00

b)13year,8month,2weeks and 6day

Answer:

First we write y and its derivatives as power series:

y=∑n=0∞anxn⟹y′=∑n=1∞nanxn−1⟹y′′=∑n=2∞n(n−1)anxn−2

Next, plug into differential equation:

(x+2)y′′+xy′−y=0

(x+2)∑n=2∞n(n−1)anxn−2+x∑n=1∞nanxn−1−∑n=0∞anxn=0

x∑n=2∞n(n−1)anxn−2+2∑n=2∞n(n−1)anxn−2+x∑n=1∞nanxn−1−∑n=0∞anxn=0

Move constants inside of summations:

∑n=2∞x⋅n(n−1)anxn−2+∑n=2∞2⋅n(n−1)anxn−2+∑n=1∞x⋅nanxn−1−∑n=0∞anxn=0

∑n=2∞n(n−1)anxn−1+∑n=2∞2n(n−1)anxn−2+∑n=1∞nanxn−∑n=0∞anxn=0

Change limits so that the exponents for  x  are the same in each summation:

∑n=1∞(n+1)nan+1xn+∑n=0∞2(n+2)(n+1)an+2xn+∑n=1∞nanxn−∑n=0∞anxn=0

Pull out any terms from sums, so that each sum starts at same lower limit  (n=1)

∑n=1∞(n+1)nan+1xn+4a2+∑n=1∞2(n+2)(n+1)an+2xn+∑n=1∞nanxn−a0−∑n=1∞anxn=0

Combine all sums into a single sum:

4a2−a0+∑n=1∞(2(n+2)(n+1)an+2+(n+1)nan+1+(n−1)an)xn=0

Now we must set each coefficient, including constant term  =0 :

4a2−a0=0⟹4a2=a0

2(n+2)(n+1)an+2+(n+1)nan+1+(n−1)an=0

We would usually let  a0  and  a1  be arbitrary constants. Then all other constants can be expressed in terms of these two constants, giving us two linearly independent solutions. However, since  a0=4a2 , I’ll choose  a1  and  a2  as the two arbitrary constants. We can still express all other constants in terms of  a1  and/or  a2 .

an+2=−(n+1)nan+1+(n−1)an2(n+2)(n+1)

a3=−(2⋅1)a2+0a12(3⋅2)=−16a2=−13!a2

a4=−(3⋅2)a3+1a22(4⋅3)=0=04!a2

a5=−(4⋅3)a4+2a32(5⋅4)=15!a2

a6=−(5⋅4)a5+3a42(6⋅5)=−26!a2

We see a pattern emerging here:

an=(−1)(n+1)n−4n!a2

This can be proven by mathematical induction. In fact, this is true for all  n≥0 , except for  n=1 , since  a1  is an arbitrary constant independent of  a0  (and therefore independent of  a2 ).

Plugging back into original power series for  y , we get:

y=a0+a1x+a2x2+a3x3+a4x4+a5x5+⋯

y=4a2+a1x+a2x2−13!a2x3+04!a2x4+15!a2x5−⋯

y=a1x+a2(4+x2−13!x3+04!x4+15!x5−⋯)

Notice that the expression following constant  a2  is  =4+  a power series (starting at  n=2 ). However, if we had the appropriate  x -term, we would have a power series starting at  n=0 . Since the other independent solution is simply  y1=x,  then we can let  a1=c1−3c2,   a2=c2 , and we get:

y=(c1−3c2)x+c2(4+x2−13!x3+04!x4+15!x5−⋯)

y=c1x+c2(4−3x+x2−13!x3+04!x4+15!x5−⋯)

y=c1x+c2(−0−40!+0−31!x−2−42!x2+3−43!x3−4−44!x4+5−45!x5−⋯)

y=c1x+c2∑n=0∞(−1)n+1n−4n!xn

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Answer:

20 and 35 dollars.

Step-by-step explanation:

x + x + 15 = 55

2x + 15 = 55

2x = 55 - 15

2x = 40

x = 40/2

x = 20

One of the brothers has saved 20 dollars, while the other has 35 dollars.

Answer:

A) -6

Step-by-step explanation:

its just by substituting 3 in place of x

3(3-4)+2(3)-(3)²

3(-1)+6-9

-3+(-3)= -6

pls gimme brailiest if it helped :)

Answer:

A. -6

Step-by-step explanation:

3(x-4) + 2x - x²

Evaluate

Let x =3

Substitute into the expression

3( 3-4) +2(3) - 3^2

Parentheses first

3( -1) +2(3) - 3^2

Exponents next

3( -1) +2(3) - 9

Multiply

-3 +6 -9

Add and subtract

-6

Y receives $30000 less than if the profit were divided in proportion to how much they invested.  

In a proportional tax system, everyone is compelled to pay the same amount of taxes as a percentage of their income.

Profit will Divide into 4 equal parts.

The total Profit for the month is  = $120,000

The party will receive a sum of = $30,000

This shows that Y also receive the same amount

Y = $30,000 (Profit received)

Now

If the Profits were divided in proportion to the investments made .

The proportion on investment made by Y.

The total investment made = $12000+$6000+$25000+$7000

                                            = $50000

Out of this the Amount invested by Y = $25000

The Proportional Profit of Y.

=  (25000/ 50000) x 120000                      

= $60,000

So Y receives 60000 - 30000

                       = 30000

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The five number summary and interquartile range for the data-set is given by:

The five number summary is composed by the minimum and maximum value, and the first quartile, median and third quartile. As for each of these data, they are explained below.

In this problem, we have that:

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Answer:

=> -2.22

Step-by-step explanation:

=> 2.35 + ( -4.57)

=> 2.35 - 4.57

=> - 2.22

The assumption that is necessary before conducting a test of hypothesis is that there is a significant amount of complaints for use of e-tickets.

The assumption is that there is a significant amount of complaints for use of e-tickets.

H0: there is a significant amount of complaints for use of e-tickets.

H1: Number of complaints for use of e-tickets is not significant.

H1: parameter > value

Notice the inequality points to the right

Decision Rule: Reject H0 if test statistic > critical value

Decision Rule: Reject H0 if p -value = 0.05

The hypothetical mean is 15.00 and The actual mean is 13.50

The difference between these two values is -1.50.

The sample size is 20

Mean 13.50

SD 1.50

The test statistic will be -4.459.

Lastly z it's important to reject the null hypothesis since the test statistic is greater than the critical value of 1.7291.

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Answer:

$127

Step-by-step explanation:

interest = (100)(0.09)(3) = $27

total = principal amount + interest

total = 100 + 9 = $127

The arrangement of the fractions given from the lowest to the highest is illustrated

a. 1/2, 3/4, 5/10, 9/20.

We can change this to percentages.

1/2 = 1/2 × 100 = 50%

3/4 = 3/4 × 100 = 75%

5/10 = 5/10 × 100 = 50%

9/20 = 9/20 × 100 = 45%

Therefore, the arrangement will be 9/20, 5/10, 1/2, and 3/4.

b. 3/8, 1/15, 3/20, 9/10

3/8 = 37.5%

1/15 = 6.67%

3/20 = 15%

9/10 = 90%

The arrangement will be 1/15, 3/20, 3/8, and 9/10.

c. 7/9, 1/3, 5/6, 3/4

7/9 = 77.7%

1/3 = 33.3%

5/6 = 82%

3/4 = 75%

The arrangement will be 1/3, 3/4, 7/9, and 5/6.

d.3/12, 1/5 7/15 1/20

3/12 = 25%

1/5 = 20%

7/15 = 48%

1/20 = 5%

The arrangement will be 1/20, 1/5, 3/12, and 7/15.

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We know

In a function

x represents the input and y represents output

So

x is time

So

f(30) represents distance traveled in 30mins

A number line ranges from minus 5 to 5 with increment of 1 unit. Left, Point F is plotted on the number line at minus 3. Right, point G is plotted on the number line at 1.50, then the distance between F and G is 4.50.

Calculating the Distance between F and G:

It is given that, on a number line,

Point F is located at -3

Point G is at 1.50

Since, 1.5 > (-3) and each number is at a 1 unit difference form the adjacent number on the number line,

The difference between F and G = 1.50 - ( -3 )

This implies that the distance between F and G = 1.50 + 3

= 4.50 units

The numbers lying between the points F and G on the number line are: -2, -1, 0, and 1

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Answer: 4 1/2

Step-by-step explanation:

Got it right

IfIf a free kick is given in a soccer game where the player taking the kick is 14 yards from the left post. How far is the kicker from the right post, to the nearest yard is: A. 23 yards.

Using sine theorem

Let Left triangle=3/sinx=14/sin∝

Let Right triangle=5/sinx=y/sin(180°-∝°)

Let Sin∝°=sin(180°-∝°)  sinx=sinx

Let y represent how far is the kicker

Hence:

3/5=14/y

y=5×14/3

y=70/3

y=23.3333

y=23 yards (Approximately)

Therefore If a free kick is given in a soccer game where the player taking the kick is 14 yards from the left post. How far is the kicker from the right post, to the nearest yard is: A. 23 yards.

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Answer:

C

Step-by-step explanation:

for AB to be parallel to CD then the slopes of both segments must be equal

using the slope formula to find the slopes , then

A (x₁, y₁ ) and B (x₂, y₂ )

[tex]m_{AB}[/tex] = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

C (x₃, y₃ ) and D (x₄, y₄ )

[tex]m_{CD}[/tex] = [tex]\frac{y_{4}-y_{3} }{x_{4}-x_{3} }[/tex]

then

[tex]m_{CD}[/tex] = [tex]m_{AB}[/tex]

[tex]\frac{y_{4}-y_{3} }{x_{4}-x_{3} }[/tex] = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex] → C

Answer:

Sum of 374 and 25 = 374+25 = 399

now subtract 9 from the sum, i.e. 399 = 399 - 9 = 390 is your answer

Answer:

Step-by-step explanation:

374+25

=399

Now, subtracting the sum from 9

9-399

=   -390

Answer:

g(2) = 16; g(-2) = 4; g(a) = 3a + 10; 3(a+2) = 3a + 16

Step-by-step explanation:

We want to substitute the value in the parentheses on the left-hand side for the value of x on the right-hand side

Thus, g(2) = 3(2) + 10 = 6 + 10 = 16

g(-2) = 3(-2) + 10 = -6 + 10 = 4

g(a) = 3(a) + 10 = 3a + 10

g(a + 2) = 3(a + 2) + 10 = 3a + 6 + 10 = 3a + 16

Answer:

Step-by-step explanation:

overall the answer is wrong i say it is the first one  

Answer:

The first one is theost plausible because root 16 is 4, 30 + 4 is 34, the actual answer is 25.38

Answer:

10

Step-by-step explanation:

Every number with exponent zero is equal to 1

(7³×8)⁰ = 1

5⁰ = 1

then:

(3² + 5⁰) / (7³×8)⁰

= (3² + 1) / 1

= (9+1) / 1

= 10

3^2 = 9

3^2 = 95^0 =1

(7^3 x 8)^0 is 1

(anything to power of zero is one)

9 + 1 / 1 gives us the fraction 10/1

10/1 + 1/3 => make denominator the same, so I'll multiply 10/1 by 3

We get : 30/3 + 1/3 => 31/3

Thus answer is 31/3

Hope this helps!

Answer:

ummation of n=1 to n=7 (-2)^n

Step-by-step explanation:

summation of n=1 to n=7 (-2)^n

Based on the type I error, if a hypothesis test leads to the probability of a type I error decreasing, then the a. probability of incorrectly accepting the null hypothesis decreases.

A type I error refers to when we are are engaged in a hypothesis test and end up rejecting the Null hypothesis even though it is true.

If we are in hypothesis tests and the probability of a type 1 error decreases, then it means that the probability of us correctly rejecting the null hypothesis when it is false increases.

It also means that the probability of us correctly accepting the null hypothesis when it is true increases as well.

This can further be said as the probability of us accepting the null hypothsis when it is false, decreases. There are therefore less chances of us incorrectly accepting the null hypothesis.

Options for this question include:

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Last one

Because if we simplify

Verified

Answer:

D is the correct Answer.

Step-by-step explanation:

4x^3+-6xy^3

      2xy

When dividing exponents you will subtract. Leaving you with 2x^3-3y^2.

Therefore your answer is D.

The probability that the number of heads is equal to the number showing on the die is [tex]\frac{21}{128}[/tex] .

According to the question

we roll one fair six-sided die, and flip six coins

i.e

The Total Outcomes is the product of the sample spaces for the dice and the coins.  

sample spaces for the dice = 6

sample spaces for the coins = 2⁶

S = 6.2⁶

S = 384

Now, The  probability is

Therefore, the Favorable Outcomes

Consider the number of ways to get each total of heads from 1 to 6.

= 2⁶-1 (as TTT is excluded )

= 63

The probability that the number of heads is equal to the number showing on the die

As

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

Probability(Event) = Favorable Outcomes/Total Outcomes

By substituting the values in the formula

Probability(Event) = [tex]\frac{63}{384}[/tex]

Probability(Event) = [tex]\frac{21}{128}[/tex]

Hence, the probability that the number of heads is equal to the number showing on the die is [tex]\frac{21}{128}[/tex]

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Answer:

it helps you control your spending, track your expenses, and save more money.

Answer:

given,

final interest = Prt

p = 7500

r = 15%

t= 8 yrs

Fi= 7500 x 0.15 x 8

= 1125 x 8

=9000

total savings = 9000 + 7500 = 16500

Answer:

28 DVDs

Step-by-step explanation:

Given information from the question, we can deduce:

2 weeks = 4 DVDs

1 week =

[tex] \frac{4}{2} \\ = 2[/tex]

2 DVDs on average.

Which means,

14 weeks = 2 × 14 = 28 DVDs

Therefore, Katy will buy 28 DVDs in 14 weeks.

Answer: 12 square units

Step-by-step explanation: first you must count hom many units there are between points A and B, which is 4, and then count the points between B and C, which is 6.

Now that we have the units we do 6 x 4 = 24, however, you may be asking why we do not do 24 then, well if you were to be doing 6 x 4, you would be getting the area of a rectangle, and half of a rectangle is a triangle, so we have to do 24/2 which equals 12.