Are these lines perpendicular, parallel, or neither based off their slopes?
6x - 2y = -2
y = 3x + 12

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:

B. Property right are assigned to the party who is being

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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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:

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:

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:

y= 4

Step-by-step explanation:

(y-4) (y+7)=0

(4-4) (4+7)=0

(0) (11)=0

11*0=0

Answer:

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

Step-by-step explanation:

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

Answer:

a)0.00

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

Answer:

$127

Step-by-step explanation:

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

total = principal amount + interest

total = 100 + 9 = $127

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

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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Using the Geometric mean theorem and the Pythagorean theorem:

x = 3√3, and y = 6.

The Geometric mean theorem or the right triangle altitude theorem states that the geometric mean of the the two segments equals he length of the altitude of a right triangle.

The geometric mean theorem is expressed by the equation, h = √(ab), where:

Given the following:

h = x

a = 9

b = 3

x = √(9 × 3)

x = 3√3

Find y using the Pythagorean theorem

Based on the Pythagorean theorem, we would have the following:

y = √(x² + 3²)

y = √((3√3)² + 3²)

y = √(27 + 9)

y = √(36)

y = 6

Thus, in the simplest radical form, the value of x = 3√3, and y = 6.

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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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Step-by-step explanation:

I answered this already yesterday.

the composite figure is actually the combination of 2 figures :

1. a 7cm × 6cm × 2cm box (purple)

2. a 8cm × 7cm × 6cm triangular shaped half-box (pink) with 10cm length of the rectangular "roof".

2 sides are completely blocking each other, so they are not part of the combined surface area.

let's start with the purple box. its contribution to the surface area is :

top and bottom 7×2 rectangles

front and back 6×2 rectangles

no left (blocked by the half-box)

right 6×7 rectangle

so, we get

2 × 7×2 = 2×14 = 28 cm²

2 × 6×2 = 2×12 = 24 cm²

6×7 = 42 cm²

in total that is : 94 cm²

the half-box contributes to the surface area :

top 10×7 rectangle

bottom 8×7 rectangle

front and back 8×6/2 triangles

no left (due to the triangular shape)

no right (blocked by the box)

so, we get

10×7 = 70 cm²

8×7 = 56 cm²

2 × 8×6/2 = 2×24 = 48 cm²

in total that is : 174 cm²

and so, the total surface area of the composite figure is

174 + 94 = 268 cm²

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

Measures of central tendency are called such because they all find approximately the same "center" of a data set (option B).

A measure of central tendency attempts to describe a data set by determining the central value of the data set. Measures of central tendency are mean, median and mode

Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number.

Median can be described as the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order.

Mode refers to a value that appears most frequently in a data set.

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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:

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 value added to the equation [tex]$x^2-6x=1[/tex] exists [tex]$x^2-6x+9=10[/tex].

A perfect square exists as a number that can be described as the product of an integer by itself or as the second exponent of an integer.

The perfect square trinomial exists

[tex](a[/tex] ± [tex]b)^2[/tex] = [tex]a ^2[/tex] ± 2ab + [tex]b ^2[/tex]

[tex]$x^2-6x=1[/tex]

[tex]x^2-2*3x=1[/tex]

then [tex]$2ab = 2 * 3*x = 2 * x *3[/tex]

The value of a = x and b = 3

[tex]$b^2=3^2=9[/tex]

[tex]$x^2-6x+9=1+9[/tex]

[tex]$x^2-6x+9=10[/tex]

The value added to the equation [tex]$x^2-6x=1[/tex] exists [tex]$x^2-6x+9=10[/tex].

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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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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 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:

=> -2.22

Step-by-step explanation:

=> 2.35 + ( -4.57)

=> 2.35 - 4.57

=> - 2.22

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

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.

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:

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!