Yesterday, You Typed 8 Pages In 48 Minutes. Today, You Typed 20 Pages In 2 Hours. Plot The Two Points (2024)

Answer:

Given that RS bisects MO at N, we know that:

RN = RO (by definition of a bisector)

MN + NO = MO (by the angle bisector theorem)

Given that MN = 5x + 8 and NO = 10 + 3x, we can substitute these values into the second equation to find the value of x.

MN + NO = MO

(5x + 8) + (10 + 3x) = MO

8x + 18 = MO

Now we can use the first equation to find the value of x.

RN = RO

5x + 8 = 10 + 3x

3x = 2

x = 2/3

Therefore, the value of x is 2/3.

For the problem , (a) The cost to park in a mall garage is $50 entry fee plus $10 per four , the function is y = 50 + 10x , the domain is (0,∞) and range is also (0,∞) .

and (b) A swimming pool in a hotel is draining at a rate of 3 feet per minute , the function is y = -3t , domain is (0,∞) and range is (0,∞) .

Part(a) ;

The cost to park in a mall garage is $50 entry fee plus $10 per four ;

the the number of hours be = "x" ;

the fixed entry fees for the mall garage is = $50 ;

the per hour charge for the garage is = $10 ;

it can be represented as : y = 50 + 10x ;

the function is : y = 50 + 10x ;

The domain of this function is (0,∞) , as the input hours can't be negative and

the range of function is (0,∞) as the charge cannot be negative

since the parking hours will be non negative .

Part(b) ,

A swimming pool is draining at the rate of 3 feet per minute.

Rate of draining is represented as "y = -3t" where t is number of minutes and

the negative sign in the function denotes the water is draining .

The domain and Range of this function is (0,∞) , as the input hours can't be negative .

The given question is incomplete , the complete question is

Find the Function , Domain and Range for the following problems :

(a) The cost to park in a mall garage is $50 entry fee plus $10 per four.

(b) A swimming pool in a hotel is draining at a rate of 3 feet per minute.

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The equations that enable us to compute x are tanx=3/4 and x=tan⁻¹(3/4)

What are trigonometric functions?

In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.

Given here: length of the pole=3m and distance of the stake from the pole=4m and the angle that the rope makes with the pole is x

We know Arctan function is the inverse of the tangent function. It is usually denoted as arctan x or tan⁻¹x. The basic formula to determine the value of arctan is θ = tan-1(Perpendicular / Base).

Thus we have the value of x as

x=tan⁻(perpendicular/Base)

=tan⁻¹(3/4)

=36.87°

Thus the two possible ways to compute the angle x are:

tanx=3/4 and x=tan⁻¹(3/4)

Hence, The equations that enable us to compute x are tanx=3/4 and x=tan⁻¹(3/4)

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The best statistical test to be used is multiple linear regression analysis.

Multiple linear regression is a statistical method that allows you to examine the relationship between two or more independent variables (in this case, level of education, gender, and annual income of the student's parents) and one dependent variable (annual income and student loan debt).

It will help you determine how much of the variation in the dependent variable is explained by the independent variables, and the strength and direction of the relationships between the variables.

In this case, this test will allow us to determine the impact of a student's level of education, gender, and the annual income of their parents on their annual income and student loan debt while accounting for the possible confounding effect of the annual income of their parents on these variables.

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The incenter is where a triangle's angle bisectors meet. Since C is the incenter, segment BC should be the angle bisector. So, there is an error in line 3; segment AB and BC are congruent.

Any triangle with any 2 sides that are the same length is defined as an isosceles triangle. An isosceles triangle has two equal-sized angles that are opposite from one other and have equal sides.

If all three angles of the three triangles are acute, the circumcenter of an isosceles triangle sits inside the triangle. The circumcircle's chords are the sides of the triangle. In this case, the circumcenter is outside of the triangle since one of the angles is 90 degrees.

The circumcenter of a triangle ABC is the location where the perpendicular bisectors of its sides cross.

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The complete question is given below:

The statements that are true about quadrilaterals are:

A: All squares are rhombuses, but not all rhombuses are squares.C.Opposite angles in a parallelograms are congruent.The diagonals of a parallelogram bisect eachother.

What are the features of the parallelogram ?

Parallelograms lack right angles, not all of them can be rectangles. There must be right angles for a parallelogram to be considered a rectangle.

Not every parallelogram has a rectangular component. A rhombus is not a square since its angles are not 90 degrees, yet a square is a rhombus. In a parallelogram, the opposing angles are equal (or congruent) The complementary angles to each other are consecutive angles (that means they add up to 180 degrees).A parallelogram's diagonals cut each other in half.

Therefore, option A,C and F are correct.

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The smallest integer that satisfies the inequality is 110

How to find the smallest integer to satisfy the inequality

The least number is calculated by first generation g the inequality equation

The statement "A number increased by 15 is greater than 124" is written in an equation form, assuming the number is x

x + 15 > 124

Solving for x with the generated expression

x + 15 > 124

isolating x

x + 15 - 15 > 124 - 15

x > 124 - 15

x > 109

since x is greater than 109 the least integer greater than 109 is 110

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The number of laps swum by Rita: L

The number of laps swum by John: 3L

The number of laps swum by Rodell: 3L + 25

What is algebra? Algebra is the branch of mathematics that studies the use of symbols, variables, and other mathematical objects to represent and analyze relationships between quantities. Algebra is used to solve many practical problems, such as how much a car costs after taxes, how much gas is needed to travel a certain distance, and how many items must be purchased to stay within a certain budget. Algebraic equations and inequalities can be solved through various techniques, such as substitution, elimination, and graphing. Algebraic equations can also be used to solve problems involving functions, which are equations that represent relationships between two or more variables. Algebraic functions can be used to predict future behavior of a system or to determine the best solution to a given problem.

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The scale factors of the shapes are 1.25, 1.25. 5 and 2, respectively

How to determine the scale factors

To do this, we divide the side length of the larger shape with the corresponding side of the small shape

using the above as a guide, we have the following scale factors calculations

figure 7 = 15/12 = 1.25

figure 8 = 25/20 = 1.25

figure 9 = 40/8 = 5

figure 10 = 10/5 = 2

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The increase in the minimum wage from $8.10 to $15, indicates that the percentage increase in the minimum wage is 85.[tex]\overline{185}[/tex]%

What does a percentage of an amount represent?

A percentage represent the number, amount, proportion or ratio of an item to another (possibly larger) item per hundred (100) units of the comparison or larger item.

Percentages, quantitatively describes the idea of the amount of a substance. It is a measure of the amount or occurrence of an item.

The specified original minimum wage at Ben's Burger = $8.10

The new amount to which the minimum wage is increased = $15

The percentage increase can be obtained using the formula;

[tex]\% \ increase = \frac{New - Original}{Original} \times 100[/tex]

The percentage increase is therefore; ((15 - 8.10)/8.1) × 100 = 85.[tex]\overline{185}[/tex] %

The percentage increase in the minimum wage paid per hour at Ben's Bar is 85.[tex]\overline{185}[/tex]%

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For making of 60 biscuits the quantity and packs of butter required by Helen is :

a. The exact amount of butter is 480 grams to make 60 biscuits.

b. Number of packs of butter Helen needs to buy is 2 packs.

Amount of sugar need to make 15 biscuits = 60 grams

Flour is three time of sugar to make 15 biscuits = 60 × 3

= 180 grams

Amount of flour to make 60 biscuits = 180 × 4

= 720 grams

Butter is two times as sugar to make 15 biscuits= 60 × 2

= 120grams

a. Exact amount of butter to make 60 biscuits is:

Butter required to make 60 biscuits = 120 × 4

= 480 grams

b. One pack is of 250 grams

Number of packs of butter she need to buy = 480 / 250

= 1,92

≈ 2packs

Therefore, the quantity of butter and number of packs of butter is given by :

a. The exact amount of butter required to make 60 biscuits is 480 grams.

b. The number of packs she needs to purchase is 2 packs.

The above question is incomplete, the complete question is :

Helen has to buy all the butter she needs to make 60 biscuits. She buys the butter in 250g packs.

(i) What is the exact amount of butter she needs?

(ii) How many packs of butter will she have to buy?

Figure is attached.

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The next time they will flash together will be at 4:00 AM.If they flash together at 1:00 AM.

According to the given information we are trying to find the smallest time interval at which both the lighthouses will flash together.The first lighthouse flashes every 15 minutes, and the second lighthouse flashes every 18 minutes.

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a. Function
b. Function
c. Not a function
d. Function

It’s easy to tell if a graph or a data table is a function or not. For a graph, use the vertical line test. Simple draw or imagine a vertical line straight down from the top to the bottom of the graph. The vertical line can only touch the line on the graph once, anything more than once will fail it as a function. So like circles will fail the vertical line test, and therefore, is not a function. You also have to go through the whole graph, left to right, with the vertical line test.
For data tables, look out for x values. In one table, the same x value cannot happen more than once. If you see two same x values, it is not a function, if not, it is. So as you see in the third one, there are duplicates of -100, -25, and -4. Whereas in others, there are no duplicate x values.

Answer: 22

Step-by-step explanation:

25+ [14 - {8+ (13-4)}]​

= 25 + [14 - {8 + 9 }]​

= 25 + [14 - 17]

= 25 - 3

= 22

7x-21=11x-73

-21=4x-73

52=4x

X=13

Answer:

[tex]7x - 21 = 11x - 73 \\ \dashrightarrow \: 11x - 7x = 73 - 21 \\ \dashrightarrow \: 4x = 52 \\ \ \: \: \: \: dividing \: both \: sides \: by \: 4 \\ \dashrightarrow \: \cancel \frac{4x}{4} = \cancel \frac{52}{4} \\ \\ \dashrightarrow \: \: \boxed{ x = 13}[/tex]

hope helpful :)

On average, a player can expect to lose $0.50 for every ticket they play in the Daily 3 lottery. Therefore, the Daily 3 lottery game is not a good investment, as the expected value is negative, and players are likely to lose money in the long run.

How to find the expected value?

To find the expected value of the Daily 3 lottery game, we need to calculate the probability of winning and the expected payout for winning.

The probability of winning the Daily 3 game with a single ticket is 1/1000, since there are 1000 possible 3-digit number combinations and only one of them is the winning combination.

The expected payout for winning is $500, since this is the prize for matching the winning digits in the correct order.

To calculate the expected value, we can use the formula:

Expected Value = (Probability of Winning) x (Payout for Winning) - (Cost of Playing)

Plugging in the values we found, we get:

Expected Value = (1/1000) x ($500) - ($1)

= $0.50 - $1

= -$0.50

This means that, on average, a player can expect to lose $0.50 for every ticket they play in the Daily 3 lottery. Therefore, the Daily 3 lottery game is not a good investment, as the expected value is negative, and players are likely to lose money in the long run.

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The equation of the circle into the standard form will be (x + 7)² + (y + 15)² = 1.

What is the equation of a circle?

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

Let r be the radius of the circle and the location of the center of the circle be (h, k). Then the equation of the circle is given as,

(x - h)² + (y - k)² = r²

The area of the circle is 9π. Then the radius of the circle is given as,

A = π

πr² = π

r² = 1

The center of the circle is at (-7, -15). Then the equation of the circle is given as,

(x + 7)² + (y + 15)² = 1

The equation of the circle into the standard form will be (x + 7)² + (y + 15)² = 1.

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Answer:

20

Step-by-step explanation:

=12÷3[-15-5{6-8+2}]

=12÷3[-15-5{6-10}]

=12÷3[-15-5-4]

=12÷3[20-4]

=12÷3+16

=4+16

=20

Answer:

$327.73

Step-by-step explanation:

$25,800 - $8,000 = $17,800

The car loan is a total of 60 months (so at 60 her payment will be $0) and the interest rate is 3.99%

Growth formula: A = P(1+r)^t

We're asking for what value at x = 60 would make P(1+r)^60 = 0?

As such, $327.73

For the given quadratic function, the coefficient b is equal to 12.

What is a Quadratic Function?

The quadratic function can represent a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function, the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.

The question gives some points of the quadratic function, see below.

x f(x)

−10 24

−9 17

−8 12

−7 9

−6 8

−5 9

−4 12

From the given data you can find the coefficients by solving the system linear equation.

You can write a system linear equation using the points: (-10,24) ,(-9,17) and (-8,12) for example. Then, you have three equations:

100a-10b+c=24 (1)

81a-9b+c=17 (2)

64a-8b+c=12 (3)

Isolate the coefficient a, you have [tex]a=\frac{24+10b-c}{100}[/tex]. Replacing the variable a in equations 2 and 3, you have:

[tex]81* \frac{24+10b-c}{100}-9b+c=17 (2) \\\\ 64* \frac{24+10b-c}{100}-8b+c=12 (3)[/tex]

Simplifying, you can rewrite it as:

[tex]\frac{-90b+19c+1944}{100}=17 (2) \\ \frac{-40b+9c+384}{25}=12 (3)[/tex]

Next step, you should isolate the coefficient b from the previous equation 2. You have:

[tex]\frac{-90b+19c+1944}{100}=17\\ \\ -90b=1700-19c-1944\\ \\ -90b=-244-19c\\ \\ b=-\frac{-244-19c}{90} = \frac{244+19c}{90}[/tex]

[tex]b=\frac{(244+19c)}{90} (4)[/tex]

Replacing the variable b in the previous equation 3, you have:

[tex]\frac{-40*\frac{244+19c}{90}+9c+384 }{25} =12\\[/tex]. Multiplying both sides by 25, you find the coefficient c:

[tex]\frac{25*(-40(\frac{244+19c}{90})+9c+384)}{25}=12*25\\ \\ -40(\frac{244+19c}{90})+9c+384=300\\ \\ -4(\frac{244+19c}{9})+9c+384=300\\ \\ (\frac{-976-76c}{9})+9c+384=300\\ \\ -976-76c+81c+3456=2700\\ \\ -76c+81c=2700+976-3456\\ \\ 5c=220\\ \\ c=44[/tex]

From the previous equation 4, you finally find the coefficient b. See below.

[tex]b=\frac{244+19c}{90} \\ b=\frac{244+19*44}{90}\\ \\ b=\frac{244+836}{90}\\ \\ b=\frac{1080}{90}\\ \\ b=12[/tex]

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A correct solution for the following system of Inequalities is; (-2, 6)

What is the solution to the inequality graph?

From the graph, it represents two inequalities and we can say that the solution of the two inequalities is the coordinate of the point where both lines of the inequalities intersect each other.

In the given graph, the coordinate of the point where both lines intersect each other is expressed as;

(-0.5, 4.2)

Now, that coordinate is not among the options but then the solution to the inequality graph will be the region shaded purple which in this case the only correct one is the coordinate (-2, 6)

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According to the information in the graph, it can be inferred that the percentage of students who have brown eyes among the group that wears glasses is equivalent to 42.9% (option B).

How to calculate the percentage of students who have brown eyes in the group that wears glasses?

To calculate the percentage of students who have brown eyes in the group that wears glasses we must perform the following mathematical operation.

We must add all the values of the group that wears glasses

0.04 + 0.08 + 0.12 + 0.04 = 0.28

0.28 = 100%0.12 = X= 42.85%

According to the previous operation, the result must be approximated to 42.9% and the correct option would be B.

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Answer: The answer is 5

Step-by-step explanation:

-3-(-8)

-3+8

5

Answer: 5

Step-by-step explanation:

First the negative 3 adds to 8. Because if you see “- -“ it will be +. So we just have -3 + 8 = 5

21 = 3· 7

33 = 3·11

If 21 and 33 are two divisors, then so are 3, 7, 11, and 77. And 1 and the number itself are always divisors.

So, we have 1, 3, 7, 11, 21, 33, 77, and the number. That's eight divisors.

So the number is 3·7·11 = 231, the product of only the prime divisors of the number.

The energy in the pendulum as it swings from point A to point B

Potential energy is converted to kinetic energy.

Now, According to the question:

Energy is defined as the ability of an object to do work. Energy can be classified in two different types of energy, Kinetic and potential energy. This two may be the principal ones, but we can see how energy manifests in different ways in nature, like heat, chemical potential energy, solar energy, electric potential energy, and so on.

Energy is constantly changing from kinetic to potential energy, and vice-versa in a pendulum. At the lowest point of the pendulum swing, the pendulum will have reach a state of maximum kinetic energy. This due to it attaining the maximum speed the pendulum can reach due to it's movement. As the pendulum start to rise again, it will start to lose kinetic energy and will gain potential energy. This loss in kinetic energy will cause the pendulum to slow down until it reaches it's max height. At this point the pendulum will have converted all of it's kinetic energy to potential energy.

Hence, Potential energy is converted to kinetic energy.

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Answer:

13.9 miles

Step-by-step explanation:

We know

A group of hikers walked 8 7/10 miles to caribou cave and then 5 1/5 miles to silver stream. How far did they walk altogether

8 7/10 = 87/10

5 1/5 = 26/5

87/10 + 26/5 = 87/10 + 52/10 = 139/10 = 13.9 miles

So, they walked 13.9 miles.

Jade's mother is the sun of Jade because she motivated Jade against race and gender, class and privilege, and fear and courage. Something is discomforting about a sun that gives no heat but keeps shining. " In this comparison, Jade's mother is the sun. So the option 3 is correct.

While expressing the complicated emotions of an aspirational, devoted girl, Jade's narrative voice offers riveting insights on the intricacies of race and gender, class and privilege, and fear and courage. Watson's story, which brims with empathy and wisdom, extols the ability of creative expression to reimagine and transform the world.

The many individuals who find themselves in the world looking for themselves are addressed in Watson's exquisitely written book. Piecing Me Together is a novel about how young people deal with the struggles and pain of daily life while remaining entire and true to themselves. It is both timely and timeless.

The reason why Jade's mother is said to as the sun of Jade is because she inspired Jade to overcome prejudices related to class, privilege, and fear.

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The complete question is:

Consider this excerpt from chapter 39:

Something is discomforting about a sun that gives no heat but keeps shining. " In this comparison, who is the sun?

1. The tour guide

2. Maxine

3. Jade's mother

4. The symphony members

Answer:

The graph would look like this

Step-by-step explanation:

The amount of glass needed to cover a table measuring 0.8m long and 0.65m wide is (d) 0.52m²

How to determine the amount of the glass

from the question, we have the following parameters that can be used in our computation:

Length = 0.8 m

Width = 0.65 m

The area of a rectangle can be calculated using tge following equation

Area = Length * Width

substitute the known values in the above equation, so, we have the following representation

Area = 0.8 * 0.65

Evaluate

Area = 0.52

Hence, the amount is 0.52 square meters

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Answer:

To solve this problem we can use the formula for future value of an investment, which is:

FV = PV(1+r)^t

Where PV is the present value, r is the interest rate, t is the number of years, and FV is the future value.

In this case, we know that PV = $4,900, r = 3% = 0.03, and FV = $5,920.

So we can rearrange the formula to solve for t:

t = log(FV/PV) / log(1+r)

t = log($5,920 / $4,900) / log(1+ 0.03)

t ≈ 10.3 years

Therefore, it would take approximately 10.3 years for the account to reach $5,920.