Lolly wrote a total of 10 pages over 5 hours. How many hours will Lolly have to spend writing this week in order to have written a total of 20 pages?

By solving the linear equations we get the final values of x = 4 & y = 4.

What is the linear equation?

A linear equation is an algebraic equation of the form y=mx + b, where m is the slope and b is the y-intercept, and only a constant and a first-order  term are included.

We have,

               2x + 7y = -20           ----------(i)

                x - 3y = 16               ----------(ii)

By multiplying equation (ii) with 2 we get,

               2x + 7y = -20 ---------(III)

               2x - 6y = 32 -----------(IV)

taking subtraction of equations (III) and (IV), we get

               y = 4

by putting value of y in equation (ii) we get,

               x = 4

Hence by solving the linear equations we get the values of x = 4 & y = 4.  

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The time it takes for a rocket following the path h(x)= -4x² + 16x to hit the ground is 4 seconds.

How to find the time for a rocket to hit the ground?

The given path equation is a function of x which is a time variable here. When the rocket hits ground, height of the rocket gets zero.

Hence equating the equation of height to zero and solving for x will give the time required for the rocket to hit the ground.

According to the given question:

We are given equation for height as

h(x) = -4x² + 16x

where x is the time in seconds

When object hits the ground the height becomes 0

So, we can set h(x) = 0 and then we can solve for x

-4x² + 16x = 0

Dividing by -4x from both sides

x - 4 = 0

x = 4 sec

So, the time it takes for a rocket  to hit the ground is 4 seconds.

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The difference in average speed between two cars is  4 kilometers per hour . Average speed of cars are 32 kilometers per hour and 28 kilometers per hour. The average speed is the total distance traveled by the object in a particular time interval.

The overall distance the object covers in a given amount of time is its average speed. A scalar value represents the average speed. It has no direction and is indicated by the magnitude.

Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is travelling along a path.

Both can be measured and quantified since they are physical quantities. Both phrases refer to moving bodies alone; they do not refer to static bodies.

Average speed of first car = total distance / total time

                                            =  160/ 5 = 32

Average speed of second car = total distance / total time  

                                                   = 140/ 5 = 28

The difference in average speed between two cars = 32 -28= 4

4 kilometers per hour is the  difference

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The inequality for this graph is:

x<2

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The final expression of (-2/9)x² - (1/9)x² is (-1/3)x².

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

(-2/9)x² - (1/9)x²

Taking out the common.

(-1/9) (2x² + x²)

Adding the like terms.

(-1/9)3x²

-1/9 x (3x²)

(-1/3)x²

Thus,

The final expression of (-2/9)x² - (1/9)x² is (-1/3)x².

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The equation of the straight line, in point-slope form, is  

          [tex]y +3 = \frac{1}{4} ( x + 4)[/tex]

we have , the required line is perpendicular to the given line.

Also let us take any two coordinates of the given line , like  (-1 , 1 ) and  

( 0 , -3) . So the slope (m₁) of given line = [tex]\frac{y2 -y1}{x2 - x1 }[/tex]

                                      m₁ = -4

as the required line is perpendicular to the given line so , we know

for two perpendicular lines

                                   m₁  m₂ =  -1

therefore ,                 m₂ = 1/4

Now the required line passes through (-4,-3)

and the equation of straight line in point slope form is given by

                                               [tex](y_{} - y_{1}) = m (x - x_{1} )[/tex]

here m = 1/4

y₁ = -3

x₁  = -4

therefore the required equation  in point-slope form is

         y + 3 = 1/4 ( x +4 )

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1) The speed of a horsefly in feet per second is; 0.63 beats per minute

2) The number of times that the dragonfly's wing beats per minute is; 3 ft/s

3) The number of times that a bumble bee travels in one minute is; 0.11 miles per minute

Dimensional analysis is defined as the study of the relationship that exists between physical quantities with the help of dimensions and units of measurement.

Dimensional Analysis is also defined as a method of problem solving that takes into consideration the identity property of multiplication whereby the product of a number and 1 will always give the same number, that is 1 × n = n whereby the value "n" remains the same after the multiplication.

1) We are given from the table that the speed of a horsefly in miles per hour = 4.4 miles per hour. We want to know the speed expressed in feet per second.

From conversions, we know that;

1 mile per hour = 1/1.467 ft/s

Thus; 4.4 miles per hour = 4.4 * 1/1.467 = 3 ft/s

2) We are given from the table that the dragonfly's wing beat per second = 38 beats per second. We want to know the dragonfly's in wing beat per minute

From conversions, we know that;

1 beat per second = 1/60 beat per minute

Thus; 38 beats per second = 38 * 1/60 = 0.63 beats per minute

3) We are given from the table that the speed of a bumble bee in miles per hour = 6.4 miles per hour. We want to know the speed expressed in miles per minute

From conversions, we know that;

1 mile per hour = 1/60 miles per minute

Thus;

6.4 miles per hour = 6.4 * 1/60 = 0.11 miles per minute

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The slope of the line passing through the point (2,1) and (7,8) is 7/5

What is a slope?

Slope is the inclination of the line with x-axis. measure of how steep a curve or line is. There are various way to calculate the slope of a line. One of the basic way is from coordinates. It is the ratio of difference of y coordinate to the corresponding x- coordinate. it is also known as slope formula

We are given the coordinates as

(2, 1) and (7, 8).

We use the slope formula to find the slope

Slope = (8-1)/(7-2)

Slope = 7/5

Hence the slope of the passing through the given point is 7/5

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Answer:

[tex]\lim_{x \to -\infty} f(x) = \infty[/tex] and [tex]\lim_{x \to \infty} f(x) = \infty[/tex]

Hope this helps!

Step-by-step explanation:

The number of students that went on the field trip is 137.

Let s represent the number of seventh grade students that went on the field trip.

Total number of participants = number of students + number of teachers

a + 19

Number of participants that rode the larger bus : 2/3 x (a + 19) = 104

In order to determine the value of a, take the following steps:

Multiply both sides of the fraction by 3 / 2

a + 19 = 104 x 3 / 2

a + 19 = 156

Subtract 19 from both sides of the equation:

a = 156 - 19

a = 137

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D

Step-by-step explanation:

The domain is the X-values in your function

as you can see, the X values continue to increase as the lines continue, infinitely

The height of the rectangular vessel into which the volume of water that completely fills the cylindrical bucket is poured is approximately 25 centimeters

What is the relation between height and volume of a cylinder?

The volume of a cylinder is the product of the base area of the cylinder and the height of the cylinder.

Height of the cylindrical bucket, h = 50 cm

Radius of the bucket, r = 21 cm

The level of water in the cylindrical container = The container is filled completely with water

The shape of the vessel into which the water is poured = Rectangular vessel

Length of the rectangular vessel into which the water in the cylinder is poured, L = 63 cm

Breadth of the rectangular  vessel, B = 44 cm

Level to which the water fills the rectangular vessel = The rectangular vessel is completely filled with the water poured in from the cylinder

Volume of water in the cylinder, V = Volume of the cylinder = π·r²×h

Therefore;

V = π × 21² × 50 = 22050·π

The volume of water transferred from the cylinder = 22050·π cm³

Volume of the rectangular vessel, [tex]V_s[/tex] = L × B × H

[tex]V_s[/tex] = V = 22050·π cm³

Therefore;

The height of the rectangular vessel, H = [tex]V_s[/tex]/(L × B)

H = 22050·π/(63 × 44) = 24.9899415626 ≈ 25

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Answer:

the answer is 1.4N/kg

The sentence which represents the equation [tex]8\frac{3}{4} = 17-x[/tex] is  First Option (i.e.  [tex]8\frac{3}{4}[/tex] is the same as the 17 decreased by a number).

What is a number sentence?

A mathematical statement made up of numbers and symbols is called a number sentence. The sentences illustrate many mathematical operations, including addition, subtraction, multiplication, and division.

Given, [tex]8\frac{3}{4} = 17-x[/tex]

where, [tex]x[/tex] is a number and ([tex]17-x[/tex]) represents [tex]17[/tex] is decreased by a number [tex]x[/tex]

And, [tex]8\frac{3}{4}[/tex]  will be equal to the [tex]17[/tex] is decreased by a number [tex]x[/tex].

Therefore, the required answer choice will be the first option i.e. [tex]8\frac{3}{4}[/tex] is the same as [tex]17[/tex] decreased by a number.

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The slope of the line parallel to the line that has an equation of 2x + 4y = 56  is -2

The line equation is given as

2x + 4y = 56

Subtract 2x from both sides

This gives

4y = -2x - 56

Divide through the equation by 4

So, we have

y = -0.5x - 14

A linear equation is represented as

y = mx + c

Where m represents the slope

This means that

m = -0.5

Parallel lines have the same slope

This means that the slope of the line parallel to the line is -0.5

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Answer:

A. [tex]y=-3x+16[/tex]

B. [tex]y=3x+5[/tex]

C. [tex]y=\frac{1}{3}x+1[/tex]

Step-by-step explanation:

A.

[tex]y-10=-3(x-2)[/tex]

[tex]y-10=-3x+6[/tex]

[tex]y=-3x+16[/tex]

B.

[tex]y-2=3(x+1)[/tex]

[tex]y-2=3x+3[/tex]

[tex]y=3x+5[/tex]

C.

[tex]y-2=\frac{1}{3}(x-3)[/tex]

[tex]y-2=\frac{1}{3}x-1[/tex]

[tex]y=\frac{1}{3}x+1[/tex]

Out of the next 5 visitors, 2 will be asked to attempt the survey. (A) yes, because 2 out of 5 is equal to 40%.

It is given the probability that the randomly selected person is asked to participate in an online survey is 0.4

This means that there is a 40% chance of a visitor being asked to join the survey.

Probability of an event = no. of favorable outcomes / total no of outcomes

P(E) = n(E) / n

Therefore, if the number of visitors to the website is 5,

n = 5

P(E) = 0.4

Hence,

n(E) / 5 = 0.4

or, n(E) = 0.4  X  5

or, n(E) = 2

Therefore, out of the next 5 visitors, 2 will be asked to participate in the survey.

Correct Question

The probability that a randomly selected visitor to a certain website will be asked to participate in an online survey is 0.40. Avery claims that for the next 5 visitors to the site, 2 will be asked to participate in the survey. is Avery interpreting the probability correctly?

(A) yes, because 2 out of 5 is equal to 40%.

(B) yes, because participants in the survey are selected at random.

(C) no, because there could be voluntary response bias.

(D) no, because only 40% of all people will visit the site.

(E) no, because 0.40 represents probability in the long run over many visits to the site.

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not sure how much she bought, but all you’d have to do is multiply the cost of salmon fillets ($8.30) times the amount she bought.

Example: if Mrs. Patrolia bought 3 pounds it would be $8.30 x 3.

Answer:

6cm square

Step-by-step explanation:

Answer:

34 inches

Step-by-step explanation:

[tex]c = \sqrt{ {16}^{2} + {30}^{2} } [/tex]

[tex]c = \sqrt{256 + 900} [/tex]

[tex]c = \sqrt{1156} = 34[/tex]

Answer:

34 inches...................

Answer:

Step-by-step explanation:

5) f(1)= 2x^3-3x^2-2x+a=-4

     2^3- 3^2-2+a= -4

      a=-1

6)b= 42

(Excuse me if this doesn't make sense).

Your formula would be (4,1)

Your zero is (0,0)

To graph it:

If your y is 1, your x is 4

If your y is 2, your x is 8.

There's a video for this if my explanation and photo doesn't help

Answer:

167 miles without the cost of the rental

Step-by-step explanation:

Daniela needs to rent a car while on vacation. The rental company charges $19.95, plus 18 cents for each mile driven. If Daniela only has $50 to spend on the car rental, what is the maximum number of miles she can drive? Round your answer to the nearest mile.

equation: where m = miles driven

50 = 0.18m + 19.95

subtract 19.95 from both sides:

50 - 19.95= 0.18m + 19.95 - 19.95

30.05 = 0.18m

divide both sides by 0.18:

30.05/0.18 = 0.18m/0.18

m = 166.9444

rounded: 167 miles without the cost of the rental

Answer:

167 :)

Step-by-step explanation:

it's math :)

Answer:

4x

Step-by-step explanation:

the quotient of x and 2 is [tex]\frac{x}{2}[/tex] , then

8 × [tex]\frac{x}{2}[/tex] ( cancel 8 and 2 by 2 )

= 4 × x

= 4x

The manufacturer needs to adjust the equipment to meet the standard with the margin of error of 2.34.

The calculated number known as the margin of error is added to and removed from the mean value to get the resulting confidence interval. The confidence interval expands as the margin of error does.

Calculate the 95% confidence interval's margin of error based on the aforementioned data.

α = 0.05

n = 20

s = 5

The following is the formula to determine the margin of error:

E = T(n-1) ×s/√n

The t-distribution table is used to determine the value of tn-1 at 19 degrees of freedom.

Replace the values in the formula above.

E = 2.093 ×5/√20

Thus, its margin of error is 2.34 as a result.

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The probability that the married couple will have adjacent desks is 0.2857and the probability that the married couple will have non-adjacent desks is 0.7143.

Probability is synonymous with potential. It is a branch of mathematics that studies the occurrence of a random event. The number ranges from 0 to 1. In mathematics, probability has been introduced to predict how likely events are to occur.

Given that

Of 7 new employees, 2 employees are married to each other; these 7 employees are to be assigned 7 desks that are lined up in a row.

If the assignment of the employees to the desks is made randomly, we have to find the probability that the married couple will have adjacent desks and will have non-adjacent desks.

Now, the event that the couple has non-adjacent desks is the complement of the event that they have adjacent desks.

Now, first, let us determine in how many ways can the couple have adjacent desks.

Let us consider the married couple as a single entity, that always stays together.

Then, in total, there are 6 entities; 5 non-related employees and 1 married couple.

Now, these 6 can be arranged among themselves in 6! number of ways.

The married couple can have adjacent desks in 2! ways.

So, the favorable number of cases, in which the couple has adjacent desks, is 6!*2!.

Again, 7 employees can be assigned desks in 7! number of possible ways.

That is, the number of all possible cases is 7!.

This means that

P(The couple has adjacent desks)

=6!*2!/7!

=0.2857.

Now,

P(The couple will have non-adjacent desks)

=1-P(The couple will have adjacent desks)

=1-0.2857

=0.7143

Therefore the probability that the married couple will have adjacent desks is 0.2857and the probability that the married couple will have non-adjacent desks is 0.7143.

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The equation in the given question is answered in main body.

What is equation?

In arithmetic , an equation may be a formula that expresses the equality of 2 expressions, by connecting them with the sign =

Main body:

according to question :

A) equation for Saturday sale = 84c +157d = 2640

equation for Sunday sale = 67c +134d = 2211

when subtracted we will get, 17c +23d = 429

This equation shows the difference in sales of these 2 days in terms of ticket sold and collection.

B) According to second part solution are c= 9 , d= 12.

equation given : 17c+23d = 429

now substituting value of c and d.

⇒17(9) + 23(12)

⇒153+276

⇒429 = R.H.S

Hence equation satisfies.

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The number of batches of muffins Ms. Kirkland can bake with 7 ½ pounds of flour is 5 batches.

Given that, Ms. Kirkland is baking muffins. Each batch of muffins uses 1 ½ pounds of flour.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Here, [tex]1\frac{1}{2} = \frac{3}{2}[/tex] and [tex]7\frac{1}{2} = \frac{15}{2}[/tex]

The number of batches of muffins can she bake

= 15/2 ÷ 3/2

= 15/2 × 2/3

= 5 batches

Hence, the number of batches of muffins Ms. Kirkland can bake with 7 ½ pounds of flour is 5 batches.

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Answer: The answer is 5

Step-by-step explanation: I have my ways ;>

A graph of the given system of linear equations is shown in the image attached below.

In Mathematics, a graph can be defined as a type of chart that is commonly used to graphically represent data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate.

Next, we would rewrite the first equation in standard form as follows:

y - 2x = 0

Adding 2x to both sides of the equation, we have the following:

y - 2x + 2x = 0 + 2x

y = 0 + 2x

y = 2x

By critically observing the graph (see attachment), a solution to the given system of linear equations are 2.5 and 5.

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The value of the experimental probability of rolling a 6 is found as 1/5.

For the given question-

Thus, by the definition of the probability-

Probability (getting 6) = number of occurred outcomes/ Total outcomes

Probability (getting 6) = 18/90

Probability (getting 6) = 1/5

Thus, the value of the experimental probability of rolling a 6 is found as 1/5.

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