Find the equation of a line parallel to 3x+3y=6 that passes through the point (7,-1)

Dad's car's gas tank holds 14.8 gallons of the gas.

A mixed fraction is one generated by integrating a whole number as well as a fraction.

Changed the mixed fraction in decimal.

Total gas purchased = 37/2 = 18.5 gallons of gas.

Let x be the gallons of gas tank contains.

Then,

(1/2)x + (3/4)x = 18.5

Multiply both sides by 4,

2x + 3x = 74

5x = 74

x = 14.8 gallons

Thus, Dad's car's gas tank holds  14.8 gallons of the gas.

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(i) Relative growth rate, k = 48 million people/ year

(ii) Population in 2020 is given by 5920 million people.

Given that in 1950, the population of world was 2560 million.

In 1960, the population of world was 3040 million people.

Also it is mentioned that,  world population grows in constant relative proportion.

So, the difference between time = 1960 – 1950 = 10 years

The growth in population = 3040 mil – 2560 mil = 480 million

So the relative growth rate of population is = 480/10 = 48 million/year

Now N be the new population, k be the relative population growth rate, all figures in millions. And t be the time in years passes since 1950.

Then the mathematical model is,

N = 2560 + kt

So for 2020, t = 2020-1950 = 70

k = 48

So, N = 2560+48*70 = 5920

So the population in 2020 is 5920 million people.

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The probability that the sum of the numbers rolled on the dice is even =1/2.

For the given question,

A fair dice is rolled twice.

Six different results are available with a single roll of the dice (1,2,3,4,5,6)

Therefore, if two dice are rolled, there are a total of 36 possible results, or 6².

Sample space for the sum of even = [(1,1), (1,3), (1,5), (2,2), (2, 4),(2,6), (3, 1), (3,3),(3,5),(4,2),(4,4),(4,6), (5, 1), (5,3),(5,5),(6,2),(6,4),(6,6)]

Total sample space for sum of even = 18

For the probability that the sum of the numbers rolled is even is -

probability (sum is even) = 18 / 36 = 1/2

Thus, the probability that the sum of the numbers rolled is even is 1/2.

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Answer:

x = -1

Step-by-step explanation:

Now we have to,

→ find the required value of x.

The equation is,

→ -10 + x + 4 - 5 = 7x - 5

Then the value of x will be,

→ -10 + x + 4 - 5 = 7x - 5

→ -11 + x = 7x - 5

→ 7x - x = -11 + 5

→ 6x = -6

→ x = -6/6

→ [ x = -1 ]

Hence, the value of x is -1.

The required expression for the laundry service is y = 0.89x.

Given that,
The total cost for laundry service, in dollars, depends on the weight of the laundry, in pounds. This relationship is proportional, as it costs $22.25 for 25 pounds of laundry and $36.49 for 41 pounds of laundry.

proportionality is defined as between two or more sets of values, and how these values are related to each other in a sense are they directly proportional or inversely proportional to each other.

here
Let the pound of laundry be x and the charge corresponding to the pound of the laundry be y.
According to the question,
y ∝ x
y = kx
Put x = 25 and y = 22.25
22.25 = k 25
k = 0.89
Put back k in the proportional equation,
y = 0.89x

Thus, the required expression for the laundry service is y = 0.89x.

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Answer:

Step-by-step explanation:

The required expression for the laundry service is y = 0.89x.

Given that,

The total cost for laundry service, in dollars, depends on the weight of the laundry, in pounds. This relationship is proportional, as it costs $22.25 for 25 pounds of laundry and $36.49 for 41 pounds of laundry.

What is proportionality?

proportionality is defined as between two or more sets of values, and how these values are related to each other in a sense are they directly proportional or inversely proportional to each other.

here

Let the pound of laundry be x and the charge corresponding to the pound of the laundry be y.

According to the question,

y ∝ x

y = kx

Put x = 25 and y = 22.25

22.25 = k 25

k = 0.89

Put back k in the proportional equation,

y = 0.89x

Thus, the required expression for the laundry service is y = 0.89x.

The total 18 numbers such  that n<150 exist, if the sum of the numbers of factors of N and N^2 is 34

Let me give you an example. 12. Both 2- 2 times and 3- 1 times are factors of 12.

Factors in total (2+1)*(1+1)=6

It will have 2- 4 times and 3-2 times for 122.

15 total factors of 5*3

Situation 1: N = xy

attempting a reverse strategy for N*N Factors in 35=5*7 are x-4 times and y-6 times.

Regarding N-x-2 and Y-3 timings.

There are a total of (2+1)*(3+1)=12 factors.

Situation 2

Since N2 has 34 factors if N2 is raised to the power of 34, there are 17 factors for N.

Consequently, 17+1 = 18 factors in total.

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Answer:

The distance between [tex](-5,-6),(-9,-4)[/tex] is [tex]6 units[/tex].

Step-by-step explanation:

Distance Formula :

[tex]\sqrt{(x_{2}^{2} -x_{1}^{2}) +( y_{2}^{2} -y_{1}^{2})}[/tex]

Given,

The two points are

[tex](-5,-6),(-9,-4)[/tex]

To calculate the distance between two points, use the distance formula.

[tex]\sqrt{(x_{2}^{2} -x_{1}^{2}) +( y_{2}^{2} -y_{1}^{2})}[/tex]

Substitute the actual values of the points into the distance formula.

Distance[tex]=\sqrt{((-9)^{2} -(-5)^{2}) +( (-4)^{2} -(-6)^{2})}[/tex]

[tex]=\sqrt{(81-25)+(16-36)}[/tex]

[tex]=\sqrt{36}[/tex]

[tex]=6[/tex]

Answer:

16(2z-3) or GCF: 16

Step-by-step explanation:

32z-48 has a GFC of 16

16(2z-3)

Answer:

$16(2z-3)

Step-by-step explanation:

Prime factorization:

32: 2*2*2*2*2

48: 2*2*2*2*3

Notice any similarities:

2*2*2*2=16

$32z-$48 = $16(2z-3)

Answer: the square root of twenty-four would be plotted (A) between 4 and 5, but closer to 5 on a number line.

Step-by-step explanation:

Answer:

One number is 19 and the other is 6

Step-by-step explanation:

25 = x + (x- 13)

25 = x + x - 13

38 = 2x

19 = x

x = 19

25 - 19 = 6

Answer:

800

Step-by-step explanation:

we gotta go with the highest value to round since it’s only one sig fig

In order to round to 1 significance the remaining digit will marks as zero thus 837 to 1 significant figure will be 800.

To round up or down tens place then we need to look at the unit place if it is less than 5 then we need to keep it as it and if it is greater than 5 then we need to round up the tens digit.

In order to round to a hundred, we need to look at the tens digit if it is less than 5 then we keep as it is and if it is 5 or greater than 5 then we will round up.

In order to round to 1 significance the remaining digit will mark as zero

As per the given,

837 Here, 1 significant figure is 8.

The ramainging digit = 3 and 7

Put 0 instant of 3 and 7

837 → 800

Hence "In order to round to 1 significance the remaining digit will marks as zero thus 837 to 1 significant figure will be 800".

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The probability that a compact car's randomly chosen mpg would be higher than 30 is 0.797.

Given data;

A certain compact car's mpg (miles per gallon) has a mean of 31 and a standard deviation of 1.2 and is regularly distributed.

We need to get the probability that the mpg for a randomly selected compact car would be more than 30.

Therefore;

Mean = μ = 31

Standard deviation = σ = 1.2

Let;

P(X > 30) = P(X - 31/1.2 > 30 - 31/1.2)

               = P(Z > -0.833)

               = 0.797

Hence, the probability that the mpg for a randomly selected compact car would be more than 30 is 0.797.

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297 children like at most one kind of ice cream.

Total number of children = 397

Let C and P be the number of children like chocolate and pistachio ice cream respectively.

n(C) = 175

n(P) = 225

The number of student do not like chocolate or pistachio ice cream is,

n(P' and C') = 97

n(P or C)' = 97, by De Moivre's theorem

n(P or C) = 397-97 = 300

n(P) + n(C) - n(P and C) = 300

175 + 225 - n(P and C) = 300

400 - n(P and C) = 300

n(P and C) = 100

So the required number of children like at most one kind of ice cream = 397-n(P and C) = 397-100 = 297

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Andre takes 36 minutes to walk to the school.

Given, It take Jada 20 minutes to walks to school.

It takes Andre 80% a long to walk to school.

As, Andre takes 80% more to walk to school

So, the time Andre takes = 20×180/100

the time Andre takes = 2×18

the time Andre takes = 36 minutes

Hence, Andre takes 36 minutes to walk to the school.

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Pi([tex]\pi[/tex]) is the ratio of circumference to diameter for any circle.

Perimeter is the distance around a circle.

Circumference of circle [tex]C = \pi d[/tex].

Perimeter of circle [tex]= 2 \pi r[/tex]

What is circle ?

A circle is a spherical shape without boundaries or edges.

A circle is a closed, curved object with two dimensions in geometry.

Consider two small arcs AB and CD of two circles of radii x and y units, both of which make an angle of measure θ at the centers P and Q respectively.

For smaller values of θ, the arc length AB is almost equal to the length of the line segment [tex]\bar{AB}[/tex]. Similarly, arc CD ≅ [tex]\bar{CD}[/tex].

Using the SAS rule of triangle similarity, we can say that APB and CQD are similar triangles because their angles are the same and their ratios are AP: PB = CQ: QD = 1: 1. So, it stands to reason that AB: AP = CD: CQ.

Circumference = [tex]\pi \times[/tex] diameter or circumference = 2[tex]\pi \times[/tex] radius if this constant equals some value.

So it was proved.

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Answer: 50%

Step-by-step explanation:

Answer:

D. 75%

Step-by-step explanation:

There are 20 marbles, so each 1 has a chance of 5% If you were to choose randomly 75% of the time you will get either red or black and 25% you will get green or white

Answer:

A and D

Step-by-step explanation:

8(6) means 8x6 so that's 48

and 12(4) is the same as 4(12) so that should be simple enough

Answer:

15-p

Step-by-step explanation:

15-p

Answer:  [tex]\left(\text{x}, \text{y}\right) \to \left(-\text{y}, \text{x}\right)[/tex]

90 degree counter-clockwise rotation around the origin.

===================================================

Explanation:

Focus on A(-1,2) and A'(-2,-1)

The coordinates of point A have swapped to go from "-1,2" to "2,-1". Then we stick a negative in front of the new x coordinate to get "-2,-1"

In other words, we've gone from (x,y) to (y,x) to (-y,x)

Representing this with arrows looks like:

[tex]\left(\text{x}, \text{y}\right) \to \left(\text{y}, \text{x}\right) \to\left(-\text{y}, \text{x}\right)[/tex]

or in short

[tex]\left(\text{x}, \text{y}\right) \to \left(-\text{y}, \text{x}\right)[/tex]

which represents a 90 degree counter-clockwise rotation around the origin.

-----------------------------------

Let's see if this rule works with point B(2,5). We should rotate to B'(-5,2)

[tex]\left(\text{x}, \text{y}\right) \to \left(-\text{y}, \text{x}\right)\\\\\left(2,5\right) \to \left(-5, 2\right)[/tex]

Sure enough, it works for point B.

Lastly, let's check if it works for point C.

We should go from C(3,-4) to C'(4,3).

[tex]\left(\text{x}, \text{y}\right) \to \left(-\text{y}, \text{x}\right)\\\\\left(3,-4\right) \to \left(-(-4), 3\right)\\\\\left(3,-4\right) \to \left(4, 3\right)\\\\[/tex]

All points have been confirmed.

The equation of the straight lines are:

For m = 6 and (x1, y1) = (2, 8)  => y = 6x - 4

For m = 7 and (x1, y1) = (2, 10) => y = 7x - 4

We know that the equation of a line with gradient m and y-intercept is:

y = mx + c.

We need to find the equation of each of the straight lines, given its gradient and the coordinates of a point on the line.

We know the point-slope form of equation of line,

(y - y1) = m(x - x1)

For m = 6 and (x1, y1) = (2, 8)

(y - 8) = 6(x - 2)

y - 8 = 6x - 12

y = 6x - 4

For m = 7 and (x1, y1) = (2, 10)

(y - 10) = 7(x - 2)

y - 10 = 7x - 14

y = 7x - 4

Therefore,  the equation of the straight lines are:

For m = 6 and (x1, y1) = (2, 8)  => y = 6x - 4

For m = 7 and (x1, y1) = (2, 10) => y = 7x - 4

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Answer:

80

Step-by-step explanation:

The probability that the dart lands in centre is = √2-1.

acc to our question-,

hence,The probability that the dart lands in centre is = √2-1.

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m ∠5 and m ∠7 is  72 ° . All straight angles are 180 degrees, according to the straight angle theorem. A straight angle is formed when the angle's legs point precisely in the opposite directions. The symbol for a straight angle is 180 degrees, or  π (in radians).

An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

The names of basic angles are Acute angle, Obtuse angle, Right angle, Straight angle, reflex angle and full rotation. An angle is geometrical shape formed by joining two rays at their end-points. An angle is usually measured in degrees.

m ∠4 = 108°

m ∠5 = m ∠1

m ∠1 is in same line of m ∠4

So

m ∠1 = 180 - m ∠4

m ∠1 = 180 - 108

m ∠1 = 72 °

So m ∠5 = 72 °

m ∠7 is opposite to m ∠5 , opposite angles will be equal

Therefor m ∠7 = 72 °

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The probability of at least 15% of 100 Indianapolis residents supporting the patriots in gaint match Super Bowl XLVI is 0.293.

By using the normal distribution method, a mean u and standard deviation σ,

The ratio of people who wants the Giants to eat patriots is p = 0.90,

The assumed sample size denoted by n is 100,

and their distribution's mean is u = 0.90,

by using the standard deviation formula is

σ = √(p(1 - p) ÷ n),

σ = √(0.90(1 - 0.90) ÷ 100),

σ = 0.03,

we get that the standard deviation is σ = 0.03

Here the probability that at least 15% of 100 Indianapolis residents encouraged the Patriots in the gaint match  Super Bowl XLVI is

P(X > 0.15) = 1 - P((X - u) ÷ σ) > (0.90 - 0.15) ÷ 0.03))

The significant value of X,

X - u ÷ σ = Z

we get,

P(X > 0.75) = (Z<5)-1

P(X < 0.75) = 1.293 - 1

P(X < 0.75) = 0.293

By solving we get, The probability of at least 15% of 100 Indianapolis residents supporting the patriots in gaint match Super Bowl XLVI is 0.293.

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Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.

y = 180 -71 = 109

x = 360 - (81+100+71)

x = 360 -252

x = 108

answer is B

x = 108 and y = 109

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The value of X is 108 and the value of y is 109. The algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division.

Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.

y = 180 -71 = 109

x = 360 - (81+100+71)

x = 360 -252

x = 108

Therefore the value of x and y is x = 108 and y = 109

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If a baseball diamond is a square that measures 90ft on each side. The  expression for the distance from 2nd base to home plate in square root form isc =√ (90)² + (90)²   and the distance is 127ft.

Using the Pythagoreans theorem formula

c= √ a²+b²

Where:

c = length of hypotenuse

a and b =  length of the sides of the right triangle

Let plug in the formula

c =√ (90)² + (90)²

c =√ 8100 +8100

c =√16200

c = 127.3

c = 127 ft (Approximately)

Therefore the distance is 127ft.

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It a because i told the tese