Fill in the Venn Diagram and Answer the Questions.

The point of intersection of the equations C = 100t + 5000 and C = 75t + 7000 represents the  the point in time where the cost of installing either will be the same.

Linear equations are equations where the right hand side and left hand side involves expressions with one or more variables for which the highest degree of the variable being 1.

We have two linear equations given,

C = 100t + 5000 and C = 75t + 7000.

The point of intersection of these linear equations will be when both the equations are equal.

100t + 5000 = 75t + 7000

100t - 75t = 7000 - 5000

25t = 2000

t = 2000/25

t = 80

This is the point in time where the cost of installing either will be the same, that is after 80 months.

Cost of installing = (100 × 80 ) + 5000 = 13,000

Or                         = (75 × 80) + 7000 = 13000

Hence the point of intersection of these equations represent the point in time where the cost of installing either will be the same.

To learn more about Linear Equations, click :

https://brainly.com/question/12412488

#SPJ1

Answer:20.5 miles

Step-by-step explanation:

the formula for distance, rate (speed), and time is

Distance=rate×time

D=40 (this is the speed he was going for the first customer) × [tex]\frac{12}{60}[/tex] (time)

the time is 12/60 because we the speed was in miles per HOUR and the time was in miles per MINUTE. To convert minutes to hours, we divide by 60.

D=40× [tex]\frac{12}{60}[/tex]

D=48/6

D=8 miles

Second trip:

D= 50×[tex]\frac{15}{60}[/tex]

D=50×[tex]\frac{1}{4}[/tex] (15/60 simplified is 1/4)

D= 12.5 miles

ANSWER: 8 miles + 12.5 miles = 20.5 miles

Answer: y=6x

Step-by-step explanation: You have to find the relationship between x and y. For this, 1 (x) times 6 = 6 (y). 2 (x) times 6 = 12 (y). This pattern will repeat in this table for eternity, so the relationship is y=6x.

A 90% confidence interval places the true mean normal body temperature between 98.14269 and 98.35577.

library(UsingR)

attach(normtemp)

print(normtemp)

hist(normtemp$temperature)

shapiro.test(normtemp$temperature)

qqnorm(normtemp$temperature)

qqline(normtemp$temperature)

We can observe that the data follows a normal distribution from the histogram and q plot.

The points in the q plot fall on a straight line and correspond to a normal distribution.

P-value = 0.2332, P>0.05, from the Shapiro test

hence, we fail to reject null htpothesis.

On accepting the null hypothesis we get to know that the data follows normal distribution.

The output for the given code will be ,

data: normtemp$temperature

t = 1527.9, df = 129, p-value < 2.2e-16

alternative hypothesis: true mean ≠0

90 percent confidence interval:

98.14269 98.35577

sample estimates:

mean of x

98.24923

Therefore , we can conclude that ,

The true mean normal body temperature is believed to be between 98.14269 and 98.35577 with a 90% confidence interval.

98.6 is not included in the 90% confidence interval.

To learn more about  confidence interval

brainly.com/question/27630001

#SPJ4

The development made to the Judaism is mentioned below;

Action as Leader;

Abraham;

Abraham's care for others is one of his leadership strengths. Abraham expressed his sorrow for Sodom and Gomorrah when the Lord informed him that they would be destroyed. He "stick his neck out for his people," as one who cares for others. He pleaded with God on their behalf.

Moses;

Early on, Moses realized he didn't have to handle everything by himself. He eventually succeeded as a leader by using delegation.

David;

As a man of God, David had learned to wait on the Lord, but he also had to learn how to be patient with those around him.

Solomon;

His name in Hebrew means peace and he used his wisdom to bring about peace in the world through deeds rather than conquest.

Contribution to Judaism

Abraham;

Before Abraham, people believed in multiple gods; Abraham was the first to preach that there is only one God. Ironically, Terach, Abraham's father, had made a fortune by selling idols of several deities.

Moses;

The Jews were delivered from slavery in Egypt by Moses, who also guided them to the Holy Land that God had promised.

David;

Many of the Old Testament Psalms are attributed to him; they were probably penned on his renowned lyre, upon which he was reputed to be a master.

Solomon;

As the Israelite monarch who constructed the first Temple in Jerusalem, Solomon is well-known. He was also the second and final king of a united Israel, which was at the height of its power during his rule (after his father, David).

Learn more about development of Judaism here;

https://brainly.com/question/13960265

#SPJ4

Answer: Fred will be 3(x-5) years old in 8 years, which is 3x-15 years old.

We know that x-1=3x-15, so x=16.

Fred is 16 years old now.

Step-by-step explanation:

Fred's age four years ago was (x - 5), Fred will be (x+7) years old in 8 years. Fred is currently eight years old.    

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Given that Fred is (x-1) years old

i) Fred age 4 years ago

Subtract 4 years from the present age

x -1  - 4

x - 5

So, Fred's age 4 years ago is  (x - 5)  

ii) Add 8 years to the present age  

(x-1) + 8

(x+7)

So, Fred's age after 8 years from now is (x+7) years      

iii) By the given statement

⇒ (x+7)  = 4 [ x - 5 ]

We can then solve for x by expanding the right side of the equation:

⇒ x + 7 = 4x - 20

Then, we can combine like terms to get:

⇒ 4x - x = 20 + 7

⇒ 3x = 27

⇒  x = 9

Fred's present age = (x-1) = 9 - 1 = 8 years

Thus, Fred's current age is 8 years.  

Learn more about the equations here:

brainly.com/question/10413253

#SPJ2

The question seems to be incomplete the correct question would be:

Fred is (x-1) years old now How old: (1) was he 4 years ago. (ii) will he be 8 years from now? (ii) is he now, if his age in 8 years time will be three times his age 4 years ago?​

Step 1: We need to test the given hypothesis.

We can take x1- x2 to represent the difference between the jumping and relaxed times.

[tex]H0: u1 = u2\\H1: u1 \neq u2[/tex]

Step 2: Simplification

We need to find the mean and standard deviation of both samples.

[tex]u1 = 32.375, s1 = 9.620477\\u2 = 30.625, s2 = 8.331309[/tex]

The differences between the jumping and relaxed times are calculated:

[tex]5, 7, 2, 1, -2, 2, 2, -3[/tex]

The number of differences is ∑(8, i-1) = [tex](d_{i} - \alpha ) ^{2}[/tex] = 75.5

Standard deviation differences are:

[tex]\sqrt{\frac{75.5}{7} }[/tex] = 3.284

The standard error is SE = 1.161

Using this, we can find the value of the test statistic t:

[tex]t = \frac{u1 - u2}{SE}[/tex] = 1.507

Using this and the graph, we get that the p value is 0.17554.

Therefore, since p-value is greater than α = 0.05, we cannot reject the hypothesis H0, and we can conclude that it is insufficient evidence to conclude that the average difference is not zero.

Since p-value is greater than α = 0.05, we cannot reject the hypothesis H0, and we can conclude that it is insufficient evidence to conclude that the average difference is not zero.

To learn more about hypothesis testing,

brainly.com/question/29996729

#SPJ4

I expect to land right side up using probability is 2.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The likelihood that an event will occur increases with its probability.

Probability theory, which is widely employed in disciplines including statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, game theory, and philosophy, has given these ideas an axiomatic mathematical formalization.

I expect to land right side up using probability is 10(0.2)

so that the answer is 2.

to learn more about probability visit:

brainly.com/question/11234923

#SPJ4

As per the given distribution, the mean of the sampling distribution is Pa - Pb

The term mean in distribution refers adding all numbers in the data set and then dividing by the number of values in the set.

Here we have given that the proportions of flowers that are blue are papa and pbpb , respectively.

And we need to find the mean of the sampling distribution

While we looking into the given question the mean of a sampling distribution is the population mean from which values are sampled.

Here for a population of mean µ, then the mean of the sampling distribution is μx

=> μα = μ

Here from the given parameters, let us consider that then independent random samples of 50 species-a flowers and 100 species-b flowers are selected

Then it can be written as Pa refers sample proportion of blue specie - a and Pb refers sample proportion of blue specie - b

Therefore, the resulting mean is Pa - Pb

To know more about mean here.

https://brainly.com/question/22871228

#SPJ4

let z be standard normal random variable. let v be chi-squared random variable with d degrees of freedom. let x and v be independent random variables. [tex]$= \frac{1}{\sqrt{2\pi}}\int_{0}^{\in[/tex]

Let [tex]$X$[/tex]and [tex]$V$[/tex] be independent random variables.

[tex]$X \sim N(0,1)$[/tex] , [tex]$V \sim \chi^2(d)$[/tex]

We know that for a standard normal random variable [tex]$X$[/tex] and a [tex]$\chi^2$[/tex] random variable [tex]$V$[/tex] with [tex]$d$[/tex] degrees of freedom, the random variable [tex]$T$[/tex] given by:

[tex]$T = \frac{X}{\sqrt{\frac{V}{d}}}$[/tex]

has a student t-distribution with d degrees of freedom.

This can be seen by the following calculation:

[tex]$f_T(t) = \int_{-\infty}^{\infty} f_X(xt)\frac{1}{\sqrt{2\pi v}}e^{-\frac{v}{2}}\frac{v^{d/2}}{\Gamma(d/2)}\frac{1}{v^{d/2}}e^{-\frac{v}{2d}t^2}dv$[/tex]

[tex]$= \frac{1}{\sqrt{2\pi}}\int_{0}^{\in[/tex]

Learn more about independent variable here

https://brainly.com/question/29430246

#SPJ4

a) The variables are;

d = the number of hours walking his neighbor's dog.

c = the number of hours washing cars

b) The system of inequalities are;

6c + 7.5d ≥ 75

d + c ≤ 15

c) The two possible combinations are; (5, 10) and (10, 5)

d) Yes it will be sufficient

We are told that;

Tom is going to walk his neighbors dog for $6 an hour. Thus;

Money from walking neighbor's dog = $6 per hour

Money from car wash = $7.5 per hour

Total Number of hours of work not more than 15 hours

a) Let d represent the number of hours walking his neighbor's dog.

Let c represent the number of hours washing cars

b) Thus, money from walking neighbor's dog = 6c

Money from car wash = 7.5d

Therefore;

Total money saved = 6c + 7.5d

Since total number of hours of work is not more than 15 hours, then we have the inequality;

d + c ≤ 15

Tom needs to make at least $75 to cover prom expenses and so we have the inequality as;

6c + 7.5d ≥ 75

The system of inequalities represents this solution are;

6c + 7.5d ≥ 75

d + c ≤ 15

From the graph, the shaded part in between both lines provides the possible number of hours which we have as possibly; (5, 10) and (10, 5)

If he works 10 hours washing neighbors dogs and 3 hours on the cars, he will earn;

6(3) + 7.5(10) = $84

This is sufficient.

Read more about system of equations at; https://brainly.com/question/13729904

#SPJ1

The total amount paid for the used car plus expenses will be $6,914.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Zaida purchased a used car for $6,500.

State tax was 4%, 100 point inspection was $72, $45 for license plate, and $37 for state emissions testing.

Now,

Since, Zaida purchased a used car for $6,500. State tax was 4%, 100 point inspection was $72, $45 for license plate, and $37 for state emissions testing.

Hence, The total amount paid for the used car plus expenses is,

⇒ $6500 + 4% of 6500 + $72 + $45 + $37

⇒ $6500 + $260 + $154

⇒ $6,914

Thus, The total amount paid for the used car plus expenses = $6,914

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

Answer:

both of them are incorrect so the answer is no

Step-by-step explanation:

If the value of y grater than 6 or equal to 6 it should be 6 or above but in (6,2) the value of y is 2 and x=6 so the value of y is less than 6

and in (-2,5) the value of x is -2 and y=5 , again the value of y is not above 6 so the answer is no for both.

As per the constant of proportionality, the electric held at the point 7 as a result of a point charge at the origin is К.

What is meant by constant of proportionality?

In math, constant of proportionality refers the ratio that relates two given values in what is known as a proportional relationship.

Here we have given that electric  charge produces a vector field called the electric field, which represents the force on a unit positive charge placed at the point. Two positive or two negative charges repel one another, whereas two charges of opposite sign attract one another. The divergence of Ē is proportional to the density of the electric charge.

Here we need to find the positive constant of proportionality The electric held at the point.

As per the definition of the constant of proportionality, we have identified the following values from the given question,

Here we know that the two positive or two negative charges repel one another, whereas two charges of opposite sign attract one another.

And the divergence of Ē is proportional to the density of the electric charge.

So, based on these details, the point 7 as a result of a point charge at the origin is К.

To know more about Constant of proportionality here,

https://brainly.com/question/29126727

#SPJ4

Answer:

<=> (8+9y)x=-y+9

<=> 8x+9yx+y=9

<=> y(9x+1)=9-8x

<=> y=(9-8x)/(9x+1)

domain: 9x+1 [tex]\geq[/tex] 0 <=> x [tex]\geq[/tex] -1/9 => R / {-1/9}

range: R/{-8/9} (horizontal asymptot)

unit D must be the youngest rock unit and the order of formation must be A, B, C, D

The Law of Cross Cutting Relations states that any feature (such as a fault or a like) that cuts across a rock unit must be younger than the rock unit.

In the picture, the dark colored rock (unit D) cuts across all of the other rock units (A, B, and C).

Therefore, unit D must be the youngest rock unit and the order of formation must be A, B, C, D.

Therefore, the order of formation is A, B, C, D.

Learn more about unit here

https://brainly.com/question/19866321

#SPJ4

y = -1/4x + 34/4 is the equation of the line which is perpendicular to the line  y = -4x - 3

Given,

The line, y = -4x - 3

Point, (x₁, y₁) = (10, 6)

We have to find the equation of line that is perpendicular to the given line;

Here,

Slope of the line, m = -1/4 (Because the line is perpendicular)

We have to find the equation line by using the formula;

y - y₁ = m(x - x₁)

Here,

y - 6 = -1/4(x - 10)

y - 6 = -1/4x + 10/4

y = -1/4x + 10/4 + 6

y = -1/4x + 34/4

That is,

The equation of the line perpendicular to the given line is y = -1/4x + 34/4

Learn more about equation of line here;

https://brainly.com/question/12642593

#SPJ4

Answer:

h - (3/h)

Step-by-step explanation:

The expression for the sequence of operations described is h - (3/h).

To evaluate this expression, we would first need to divide 3 by h to find the quotient, and then subtract that quotient from h. This would give us the final result of the sequence of operations.

For example, if h = 10, we would first divide 3 by 10 to get 0.3. We would then subtract 0.3 from 10 to get 9.7. This would be the final result of the sequence of operations.

In general, the expression h - (3/h) can be used to represent any sequence of operations that involves subtracting the quotient of 3 from h. The value of h can be any number, and the final result of the sequence of operations will depend on the specific value of h that is used.

Answer:

55 degrees

Step-by-step explanation:

Sum of ALL three angles of a triangle ALWAYS equal 180

rule is 6x+5 will equal the sum of the 2 known angles because of this

6x+5=3x+x+45

6x+5=4x+45

-4x.    -4x

2x+5=45

    -5. -5

2x=40

/2. /2

x=20

6(20)+5

120+5

125

180-125

55

hopes this helps please mark brainliest

Answer:

n = 6

Step-by-step explanation:

(5 x [tex]10^{5}[/tex]) ( 3 x [tex]10^{n}[/tex]) = 1.5[tex]10^{12}[/tex]

(5x3) ([tex]10^{5+n}[/tex]) = 1.5 x[tex]10^{12}[/tex]

15 x ([tex]10^{5+n}[/tex]) = 1.5 x [tex]10^{12}[/tex]

1.5 x [tex]10^{1}[/tex] ([tex]10^{5+n}[/tex]) = 1.5 X [tex]10^{12}[/tex]

1.5 X [tex]10^{1}[/tex] X  [tex]10^{5+N}[/tex] = 1.5 X [tex]10^{12}[/tex]

1.5 X [tex]10^{1+5+N}[/tex] = 1.5 X [tex]10^{12}[/tex]

1.5  X [tex]10^{6 + 6}[/tex] = 1.5 X [tex]10^{12}[/tex]

1.5 X [tex]10^{12}[/tex] = 1.5 X [tex]10^{12}[/tex]

The percentage of students who owns either a television or stereo is given by the set formula P ( A ∪ B ) = 23 %

What is Set Theory Formula?

The set formula is given in general as n(A∪B) = n(A) + n(B) - n(A⋂B), where A and B are two sets and n(A∪B) shows the number of elements present in either A or B and n(A⋂B) shows the number of elements present in both A and B.

The union of two sets is a new set that contains all of the elements that are in at least one of the two sets

The intersection of two sets is a new set that contains all of the elements that are in both sets

The equation is n(A∪B) = n(A) + n(B) - n(A⋂B)

Given data ,

Percentage of college students who owns a television or stereo be represented as = P ( A ∪ B )

Percentage of college students who owns a television is P ( A ) = 15 %

Percentage of college students who owns a stereo is P ( B ) = 10 %

Let the percentage of college students who owns a television and stereo  is P ( A ∩ B ) = 2 %

So , the value of P ( A ∪ B ) is calculated as

P (A∪B) = P ( A ) + P ( B ) - P ( A ⋂ B )

Substituting the values in the equation , we get

P (A∪B) = 15 + 10 - 2

On simplifying the equation , we get

P (A∪B) = 25 - 2

P (A∪B) = 23 %

Therefore , the value of P (A∪B) is 23 %

Hence , the percentage of students is 23 %

To learn more about set theory click :

https://brainly.com/question/26397859

#SPJ1

The value of x and y for the given linear equations are as follows.

For question8: x=4,y=-1

For question9 :x=-1.2, y=-(111/37)

An equation in which is  the highest power of to the  variables 1 is knowns as the  linear equation. Mathematically: it is an  algebraic equations that can be also  written in the form of  ax + b = 0 or ax + by + c = 0, where a, b and c are definitely real numbers and x and y are variables with the highest power one.

Question 8

5x+4y=16------- eq1

-2x-4y=-4-------ea 2

5x=16-4y

X=(16-4y)/5

X=4(4-y)/5

Now substitute the value of x in equations 2

-2x-4y=-4

-2(4(4-y)/5)-4y=-4

-2(16-4y)/5-4y=-4

(-32+8y)/5-4y=-4

-32+8y-20y=-20

8y-20y= -20+32

-12y=12

y=-1

Now substitue the value of y in following equation

5x+4y=16

5x+4(-1)=16

5x-4=16

5x=4+16

x=20/5

x=4

Question 9

-5x+y=3-------------eq 1

3x-8y=24-------------eq2

-5x=-3-y

-5x= -(3+y)

x=(3+y)/5

Now substitute the value of x in equation 2

3(3+y)/5-8y=24

(9+3y)/5-8y=24

9+3y-40y=24

3y-40y=120-9

y=-(111/37)

Now substitue the value of y in following equation

-5x+y=3

-5x+(-111/37)=3

-185x-111=111

-185x=222

x= -222/185

x= -1.2

To know more about linear equations click-

https://brainly.com/question/2030026

#SPJ1

The system of the equation is written as

xx + yy ≥ 16

$4.25xx + $0.75yy ≤ $30

the graph is attached and the solution from the graph is (5.1, 10.9)

The problem is a simultaneous equation of two unknowns with two equations.

The equations are formed as follows

If xx represents the number of cupcakes purchased

yy represents the number of cookies purchased

cupcakes for $4.25 each and cookies for $0.75 each. Myesha has $30

$4.25xx + $0.75yy = $30

buy at least ( ≥ ) 16 cupcakes and cookies altogether

xx + yy ≥ 16

The simultaneous equation

xx + yy ≥ 16

$4.25xx + $0.75yy = $30

One solution from the graph is (5, 11)

Learn more about simultaneous equation here:

https://brainly.com/question/29327287#answer-25010047

#SPJ1

Balinese metallophones have thicker metal keys than Javanese ones so   they produce a brighter sound. therefore correct answer is B.

A metallophone is any musical instrument in which the sound- producing body is a piece of metal( other than a substance string), conforming of tuned essence bars, tubes, rods, coliseums, or plates. ultimate repeatedly the metal body is struck to produce sound, generally with a mallet, but may likewise be triggered by discordance, keyboard action, or other means.

Metallophones have been used in music in Asia for thousands of spells. There are several different types used in Balinese and Javanese gamelan ensembles, containing the gender, gangsa and saron. These devices have a single row of bars, tuned to the distinctive pelog or slendro scales, or a subset of them.

To  learn more about Balinese,

https://brainly.com/question/29114170

Answer: -26=2(3p-5) is false

Step-by-step explanation:

The solution is 4

Substitute in 4 in place of the variables to prove whether its false or true

1/4(4)+17=18

18=18 true

5=4(4)-11

5=16-11

5=5 true

-26=2(3(4)-5)

-26=2(7)

-26[tex]\neq[/tex]14

3(4+4)=24

3(8)=24

24=24 true

-26=2(3p-5) is false

Answer:

The third option is false, because when you plug in 4 for p, you get 14, and 14 is not equal to -26.

Hope this helps! :D

Step-by-step explanation:

The range of projectile =21556.122 m

The maximum height of the projectile will be = 5280.03 m

The speed at which the projectile hits will be 650 m/s.

Initial speed [tex]v_0=650 \:m/s[/tex]

Angle of elevation [tex]\theta=30^{\circ}[/tex]

Acceleration due to gravity [tex]=9.8 m/s^2[/tex]

i) Range of the Projectile:

[tex]$$\begin{aligned}& R=\frac{v_0^2 \sin (2 \theta)}{g}=\frac{(650)^2 \sin (30)}{9.8} \\& R=21556.122 m\end{aligned}$$[/tex]

ii) Maximum Height of the projectile.

[tex]$$\begin{aligned}& H=\frac{v_0{ }^2 \sin ^2 \theta}{2 g}=\frac{(650)^2 \sin ^2(30)}{2 \times 9.8} \\& H=5389.03 m\end{aligned}$$[/tex]

iii) The speed at which the projectile hits the ground is the same as the initial speed.

i.e. speed [tex]$=650 \mathrm{~m} / \mathrm{s}$[/tex]

For more such questions on Projectile:

https://brainly.com/question/24949996

#SPJ4

Answer: 3(x+y)+4=8

simplified:  3x+3y=4

Step-by-step explanation:

three times x (the first number) & y (the second number) & 4. Which means +4. is 8. which means =8

3(x+y)+4=8

The correlation coefficient is,

This is the interpretation of the correlation coefficient,

To read more about Correlation coefficient

https://brainly.com/question/4219149

#SPJ4