2) Jenny has a water tank that needs to be
filled up. The water tank can hold 500 gallons
of water. She adds 20 gallons of water every
hour. How many hours does it take for Jenny
to be able to fill up the tank?

First we can find value of x and. When x=0 then y=-1  and x=1 then y= 3

A linear equation is an algebraic equation of the form y=mx+b involving only a constant and a first-order (linear) term where m is the slope and b is the y-intercept.So the above given equation is called a "linear equation of two variables," where y and x are the variables.

Finding the y value is easy if you know the slope of the line and the x coordinate. Review the equation for the slope of a line. The equation for finding the slope is: m = [y1 - y2] / [x1 - x2]. If you know x, you can solve for y to find the y value for the slope of the line.

Now we have y= 4x-1

lets x=0   then y= -1

     x=1      then y=3

     x=2     then y=7

To find slope

y=mx+c

y= 4x-1

so by comparing we can find m=4

Then we can evaluate given equation y=4x-1

To learn more about linear equation visit;

https://brainly.com/question/11897796

#SPJ1

The speed of Ana is in miles per hour 7.5mph

By dividing the distance Ana covered by the amount of time she spent running, one may calculate her speed in miles per hour. Since the question asks for the speed to be calculated in miles per hour, an hour rather than a minute would be utilized as the unit of time.

Speed = distance ÷ time

Distance =  3/4

Time =  1/10

Speed = 3/4  ÷  1/10

Speed =  3/4   x 10 = 15/2 miles per hour

or, 7.5mph

Divide the distance Ana covered by the time she ran to get her speed.

Know more about Speed

https://brainly.com/question/4931057

#SPJ4

The question is incomplete

Ana runs 3/4 mile in 6 minutes or 1/10 hour. Assuming she runs at a constant rate, what is her speed, in miles per hour

The probability that the first card is a heart and the second card is a 10 is 1/51.

Probability with Replacement is used for questions where the outcomes are returned to the sample space again. This means that once the item is selected, it is replaced in the sample space, so the number of elements of the sample space remains unchanged.

The following combinations are possible:

When we choose first card, total no. of card is 52 and card of heart is 13

so the probability of the first card to be heart is

P(1)= 13/52

= 1/4

When we choose second card, total no. of card is 51 and card of 10 is 4

so the probability of the first card to be 10 is

p(2)= 4/51

So the final probability is

= P(1)* P(2)

= 1/4 * 4/51

= 1/51

To learn more about probability replacement to refer:

brainly.com/question/14020129

#SPJ4

Using the provided values and the conditions, The inequality equations required are : [tex]x+y \leq 20[/tex] and [tex]450x+200y \geq 4800[/tex].

An equation is a mathematical statement in which two expressions are set equal to each other. It is typically written using an "=" sign, with the expressions on either side of the sign representing equivalent values. For example, the equation 2 + 2 = 4 states that the value of 2 plus 2 is equal to the value of 4. Equations can be used to express relationships and to solve problems.

An inequality is a mathematical statement that compares two values or expressions. It is similar to an equation, but instead of using the "=" sign to indicate that the two sides are equal, it uses one of the following symbols: ">", "<", "≥", "≤" to indicate that the two sides are not equal. For example, the inequality 2 + 2 > 4 states that the value of 2 plus 2 is greater than 4. Similarly, the inequality 2 + 2 < 4 states that the value of 2 plus 2 is less than 4. Inequalities can be used to express constraints in a problem or to define a range of solutions. They can also be represented graphically by using a number line.

x= number of tables sold

y= number of chair sold

max furniture in a day = 20

so, [tex]x+y \leq 20[/tex].

least selling amount = 4800

so, [tex]450x+200y \geq 4800[/tex]

To learn more about inequalities visit:

https://brainly.com/question/28823603

#SPJ4

Answer:

b:  5x-4y+31=0

Step-by-step explanation:

Let's look for an equation of the form y=mx+b, where m is the slope and b the y-intercept (the value of y when x=0).

We are given the slope, m, as (5/4), so we can write:  y = (5/4)x+b.

To find b, just enter the given point, (-3,4), into the above equation and solve for b:

 y=(5/4)x + b

 4=(5/4)(-3) + b   for (-3,4)

 4 = -(15/4)+b

 4 + (15/4) = b

 4 + (3 3/4) = b

b = 7 3/4

The equation becomes y = (5/4)x + 7 3/4

Also written as:  y = (5/4)x + (31/4)

To match this with one of the options, let's multiply by 4 to remove the two fractions:

   y = (5/4)x + (31/4)

   4y = (5)x + (31)

Rearrange so that the expression is = 0:

4y-5x-31 = 0

Now multiply by -1:   -4y+5x+31=0

Rearrange and this will match option b:  5x-4y+31=0

f(x) =2(3ˣ) is an exponential function which has an initial value of 2.

Another word for "involving an exponent" in mathematics is exponential. For instance, an exponential rise in a number occurs when you raise it to the tenth power.

A mathematical function with the formula f(x) = aˣ is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently seen. A variable is used as the exponent in exponential functions.

The exponential function that has an initial value of 2 is f(x) = 2ˣ.

f(x) = 2(3ˣ) can be written as f(x) = 2 × 3ˣ, so it starts at 2 × 3⁰ = 2 × 1 = 2.

f(x) = 3(2ˣ) can be written as f(x) = 3 × 2ˣ, so it starts at 3 × 2⁰ = 3 × 1 = 3

To know more about exponential function refer to:

https://brainly.com/question/2456547

#SPJ1

Answer:

SAA

Step-by-step explanation:

The difference between the areas is 481 square miles.

Given information:

Alaska is 873 sq miles in size, as well as Rhode Island, is 392 sq miles in total.

To determine the difference between the areas in square miles, the following calculation must be performed: subtract Alaska from Rhode Island square miles then we get:

Let X be the total difference:

873 - 392 = X

481 = X

Therefore, the difference in the areas in square miles is 481.

To know more about differences:

https://brainly.com/question/21877748

#SPJ4

The ratio for cos (cosine) of angle θ is: cos(θ) =  adjacent side of θ / hypotenuse

We know that in right triangle the cosine of an angle is nothing but the ratio of the side adjacent of  given angle to the hypotenuse.

In right tirnagle for an angle θ, the ratio for cosine of angle θ would be:

cos(θ) =  adjacent side of θ / hypotenuse

Consider following right triangle PQR with angle PQR = 90 degrees

Here, PR is the hypotenuse.

Assume that angle QPR measure α degrees and angle PRQ measures θ degrees.

By definition of cosine of angle θ,

cos(θ) =  adjacent side of θ / hypotenuse

cos(θ) =  QR / PR

And by definition of cosine of angle α,

cos(α) =  adjacent side of α / hypotenuse

cos(α) = PQ / PR

Learn more about the ratio here:

https://brainly.com/question/29774220

#SPJ4

Answer: The ship is going to another planet.

Step-by-step explanation:

I hate i-ready,

Your welcome mate

Therefore, the inequality problem solution is even if Guliskhan runs for 60 seconds and cycles for 90 seconds, she will not be able to travel the required distance.

Both formulae and inequalities are mathematical phrases created by connecting two expressions. The equal sign (=) in an equation denotes that the two expressions are regarded as equal. In contrast, an inequality indicates that the two phrases are not always equal by using the symbols >,≥,≤, or.<

Here,

R should stand for Guliskhan's running seconds, and B should stand for her bicycling seconds.

Guliskhan is said to bike at a pace of 7 meters per second, hence the distance (in meters) that he covers in B seconds will be 7B.

An inequity of 3R + 7B 1000 has been handed to us.

We can observe that 7B reflects the cycling distance covered by Gulkishan in meters in B seconds.

Guliskhan covers a distance of 3R meters in the number of seconds she runs for, where R is the number of seconds she runs for.

Guliskhan moves at a steady pace of 3 meters per second because of this.

B. Since Gulkiskhan 3R plus 7B has traveled a total distance greater than or equal to 1000 meters, her minimum intended distance is 1000 meters.

C. Let's replace R=60 and B=90 in our inequality to see if Guliskhan is capable of traveling this minimum distance.

=>3*60 + 7*90 ≥ 1000

=>180 + 630 ≥ 1000

=>810 ≠> 1000

Therefore, even if Guliskhan runs for 60 seconds and cycles for 90 seconds, she will not be able to travel the required distance.

To know more about inequality , visit

brainly.com/question/28823603

#SPJ4

Therefore , the solution to the given problem of trigonometry comes out to be tanθ = - √35 .

Trigonometry is the discipline of mathematics that studies correlations between angles and sides of triangles. Trigonometry is present in all of geometry because every straight-sided shape may be reduced to a set of triangles. Remarkably intricate connections exist between trigonometry and other areas of mathematics, particularly calculus, real or complicated, exponentials, logarithms, and infinite series.

Here.

Given : Cosθ = -1/6

To find : Tanθ

Since cosθ is in second quadrant

Thus,

Cosθ = B/H

According to pythagoras theorem,

H²= B²+ P²

=> 6² = 1² + P²

=> 36-1 =P²

=>P= √35

So ,

value of Tanθ comes out to be

=> tanθ = - √35 /1

=>tanθ = - √35

Therefore , the solution to the given problem of trigonometry comes out to be tanθ = - √35 .

To know more about trigonometry , visit

brainly.com/question/12068045

#SPJ1

A figure made by two intersecting lines or two rays extending from the same point is called an angle.

What is an angle?

Two lines intersect at a location, creating an angle. An "angle" is the term used to describe the width of the "opening" between these two rays.  Angles are used in the design of buildings, roadways, and sports venues by engineers and architects.

A figure made by two intersecting lines or two rays extending from the same point is called an angle.The character ∠ is used to represent it. Angles are frequently expressed in degrees and radians, a unit of circularity or rotation. We encounter angles frequently in life.

To learn more about the angle from the given link

https://brainly.com/question/25215131

#SPJ4

The percent of fans that are between 18 and 27 years old is 16.80%.

From the information, the average age of a group of fans at a hockey game is 34 years with a standard deviation of 8 years and we want to calculate the percent of fans are between 18 and 27 years old.

It should be noted that this will be Illustrated through the normal curve.

The probability will be:

P(18 ≤ X ≤ 27)

= P(18 - 34/8) ≤ Z ≤ (27 - 34 / 8

= P(-2.0 ≤ Z ≤ -0.875)

= 0.1908 - 0.02275 (From the standard normal calculator)

= 16.80%

The percentage is 16.80%.

Learn more about percentages on:

brainly.com/question/24877689

#SPJ1

Answer:

He scored an average of 4.8 points per minute.

In given right triangle ACB, the ratios for sin A and cos A :

sin(A) = 48/50

cos(A) = 14/50

Consider the following diagram.

In a right triangle ACB, the angle ACB = 90 degrees.

We know that in right triangle for an angle θ, the trigonmetric ratios are:

sin(θ) = opposite side of θ/ hypotenuse

cos(θ) = adjacent side of θ / hypotenuse

Here, side AC = 14 units, side CB = 48 units and the hypotenuse AB = 50 units

We need to find the ratios for sin A and cos A

In right triangle ACB for angle A,

sin(A) = opposite side of angle A/ hypotenuse

sin(A) = CB/AB

sin(A) = 48/50

And cos(A) = adjacent side of A / hypotenuse

cos(A) = AC/AB

cos(A) = 14/50

Learn more about the ratio here:

https://brainly.com/question/29774220

#SPJ4

Answer:

  -2

Step-by-step explanation:

You want to know the dilation scale factor that gives triangle A'B'C from triangle ABC.

We notice that point A' is 4 units down and 2 units right of C, whereas A is 2 units up and 1 unit left of C. The ratio of these distances is the scale factor.

If up and right are positive, then ...

  k = (A' -C)/(A -C) = (2, -4)/(-1, 2) = -2

The dilation scale factor is -2.

Answer: 347

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the number be x then:.

According to the question:

6 * (x + 25) = 30

therefore,

x + 25 = 30 / 6

x + 25 = 5

x = 5 - 25 = -20

Answer:

Yes

Step-by-step explanation:

there are 16 cups in a gallon. if he uses 1/2 a cup to make 1 pitcher, there would be 32 pitchers made. 19+9 is 28 so the answer is yes.

^^mark brainliest pls:D

The scale factor of the dilation is 2. An expansion happens when the scaling factor's absolute value exceeds one.

The scale factor is defined as the proportion of the new image's size to that of the previous image. A fixed location in the plane serves as the center of dilatation. The scale factor and the center of dilation are used to determine the dilation transformation. The image stretches if the scaling factor is greater than 1.

As per the rule of scale factor

Q'U'/QU = SF

SF= Scale factor

=    (5+5)/5= Scale factor

=      10/5= 2

To know more about scaling factor's  visit:-

brainly.com/question/29464385

#SPJ4

There are 29.8 students in the running club overall.

The quotient is the number we get when we divide two numbers. For instance, in the case of 8 4 = 2, where the division result is 2, it is the quotient. The divisor is 4, and the dividend is 8.

The remnant is the amount that does not wholly enter the divisor, whereas the quotient is the number of times a division is completed to the fullest extent possible. By way of illustration, 42 is the quotient and 1 is the remainder when 127 is divided by 3 to provide 42 R 1.

Given,

30+9-46 (2/3) % × 30

Multiply

30 + 9 - (46 × 30) × 0.00666666666666667

Calculate quotient,

30 + 9 - 1380 × 0.00666666666666667

Simplifying quotient,

30 + 9 - 9.2

Then we get,

39 - 9.2

Then 29.8

get the result: 29.8

The complete question is:

Thirty 8 th  graders signed up for running club, however nine dropped out before the first practice. If 46 (2/3)  of the club are 8 th graders, how many total students are in the running club?

To learn more about quotient, refer to:

https://brainly.com/question/11995925

#SPJ4

The value of d when F = 0.7 Newton's by solving with inverse variation is 0.61 meters to 2 D.P

Let

F = k/ d²

Where k = constant of proportionality

If F = 0.045 Newtons and d = 2.4 metres

F = k/ d²

0.045 = k / 2.4²

cross product

k = 0.045 × 2.4²

k = 0.2592

Find d when F = 0.7 Newton's

F = k/ d²

0.7 = 0.2592 / d²

cross product

0.7 × d² = 0.2592

0.7d² = 0.2592

divide both sides by 0.7

d² = 0.2592 / 0.7

d² = 0.370285714285714

find the square root of both sides

d = √0.370285714285714

d = 0.6085110634045

d = 0.61 to 2 decimal place.

Therefore, d is equal to 0.61 meters to 2 decimal place if F is 0.7 Newton's.

Read more on inverse variation:

https://brainly.com/question/13998680

#SPJ1

The equation 1.6: n = 0.16 can be written as: [tex]1.6 = 2.511^n[/tex]

And we know that this is correct because we can check that it is the equivalent by multiplying [tex]2.511^n[/tex] by itself n times which results in 1.6.

What is an exponent?

An exponent is a mathematical operation that represents the number of times a value is multiplied by itself. It is usually written as a small number raised to the power of a larger number, such as 2^3, which means 2 multiplied by itself 3 times, or 2 * 2 * 2 = 8.

To write the equation 1.6: n=0.16 using an exponent, we can divide both sides of the equation by 1.6 to get: n = 0.16/1.6 = 0.1

And then we can raise the base 10 to the power of n: [tex]10^n = 10^{0.1} = 2.511[/tex]

Hence, the equation 1.6: n = 0.16 can be written as: [tex]1.6 = 2.511^n[/tex]

And we know that this is correct because we can check that it is the equivalent by multiplying [tex]2.511^n[/tex] by itself n times which results in 1.6.

To learn more about the exponent, visit:

https://brainly.com/question/13669161

#SPJ4

The equation 1.6: n = 0.16 can be written as: 1.6 = [tex]2.511^n[/tex]

And we know that this is correct because we can check that it is the equivalent by multiplying [tex]2.511^n[/tex] by itself n times which results in 1.6.

What is an exponent?

An exponent is a mathematical operation that represents the number of times a value is multiplied by itself. It is usually written as a small number raised to the power of a larger number, such as 2^3, which means 2 multiplied by itself 3 times, or 2 * 2 * 2 = 8.

To write the equation 1.6: n=0.16 using an exponent, we can divide both sides of the equation by 1.6 to get: n = 0.16/1.6 = 0.1

And then we can raise the base 10 to the power of n: [tex]10^n=10^{0.1}=2.511[/tex]

Hence, the equation 1.6: n = 0.16 can be written as: 1.6 = [tex]2.511^n[/tex]

And we know that this is correct because we can check that it is the equivalent by multiplying [tex]2.511^n[/tex] by itself n times which results in 1.6.

To learn more about the exponent, visit:

brainly.com/question/13669161

#SPJ4

Answer:

19.95 + .71 × x = 125.74

x = 141.053

x is the answer

Answer:

d ≥ 50

Step-by-step explanation:

To receive the discount, you must spend at least $50, which can be represented by the inequality d ≥ 50. This inequality means that the amount you must spend (d) is greater than or equal to $50. If you spend more than $50, you will receive the discount. If you spend less than $50, you will not receive the discount.

The width of the arch at its base can be found by setting ƒ(x) = 0 and solving for x. This gives  x=12 feet.

Horizontal distance is the length of a straight line between two points, measured only in the horizontal direction. It is typically measured in units such as kilometres, meters, miles, or yards.

No, the box truck will not fit under the arch. The height of the arch at a horizontal distance of 8 feet is ƒ(8) = -0. 5(8)2 + 6(8) = 4 feet, which is less than the height of the truck (13. 5 feet).
The maximum height a truck that is 8 feet wide and is passing under the bridge can be is ƒ(8) = 4 feet.

To learn more about horizontal distance
https://brainly.com/question/16411732
#SPJ4

Answer:

6 1/4 pounds

Step-by-step explanation:

There are 7 1/2 pounds of potatoes, which is equivalent to 7 1/2 = 7.516=120

120 ounces of potatoes.

If 1/6 of the potatoes are rotten, then 1/6*120 = 20

20 ounces of potatoes are rotten.

Thus, the weight of the good potatoes is 120-20 = 100

100 ounces.

Converting this back to pounds, we get

100/16 = 6 1/4

6 1/4 pounds.

It is assumed the given figure is a parallelogram.

Use properties of a parallelogram:

Find the missing values:

The Avogadro's number of every element remains is the same. The number of atoms of 1 mole in every element is Avogadro's number. One mole of an element is 6.02214076×10²³ atoms.

What is an atom?

Each atom is made up of a nucleus and one or more electrons that are linked to it. One or more protons and a significant number of neutrons make up the nucleus. Only the most prevalent type of hydrogen is neutron-free. Atoms that are neutral or ionized make up every solid, liquid, gas, and form of plasma.

The proportionality factor that connects the number of constituent particles (often molecules, atoms, or ions) in a sample with the amount of material in that sample is called the Avogadro constant, also known as NA or L. It has a precise value of  6.02214076 × 10²³ reciprocal moles and serves as a SI defining constant.

The number of atoms of one mole substance is 6.02214076 × 10²³ which is Avogadro's number.

To learn more about Avogadro's number, click on the below link:

https://brainly.com/question/20970268

#SPJ4