Ame, Devon, Micah, and Shawna ran in a long distance race. The graph shows their progress during the race.
Distance (meters)
B. Devon
Legend
Time (minutes)
Which runner started out fast, then ran the rest of the race at a slower rate of speed?
OA Ame
Oc. Micah
OD. Shawna
Ame
Devon
Micah
Shawna

We can condense and find n's solution: 3n + 24 = 2n - 4

Since n = -14, the unknowable number is also -14.

A mathematical expression called an algebraic expression includes variables, integers, and mathematical operations including addition, subtraction, multiplication, and division. Algebraic expressions can be straightforward, like "2x," or they can be more complicated, like

[tex]3x^2+4y-5[/tex].

Variables are used to represent unknown quantities and have a range of possible values. In problems requiring unknown values or to represent connections between quantities, algebraic expressions are widely used.

A mathematical expression that includes variables, constants, and operations involving algebra (addition, subtraction, etc.) is known as an algebraic expression. Terms comprise expressions.

To know more about variables, visit:

brainly.com/question/17344045

#SPJ1

Answer:

The Fundamental Counting Principle states that if there are n ways to do one thing and m ways to do another, then there are n x m ways to do both things together. This principle can be applied to find the total number of possible outcomes in a given situation.

For example, if you have 3 shirts, 4 pants, and 2 shoes to choose from, and you want to find the total number of possible outfits you can make, you would use the Fundamental Counting Principle as follows:

Number of possible outfits = (number of shirt choices) x (number of pants choices) x (number of shoe choices)

= 3 x 4 x 2

= 24

Therefore, there are 24 possible outfits that you can make from the given choices of shirts, pants, and shoes.

Answer:

finding the perimeter, you sumthe distance all round that is 7+7.5+17.8+6=38.3

38.3 is the perimeter

The probability of the given situation through which the given relation is satisfied is 0.78

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain to occur.

The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For example, if you flip a fair coin, there are two possible outcomes: heads or tails. The probability of getting heads is 1/2, or 0.5, since there is one favorable outcome (heads) out of two possible outcomes (heads or tails).

Probabilities can also be expressed as percentages or fractions. For example, a probability of 0.25 can be expressed as 25%, or as a fraction of 1/4.

Probability theory is a branch of mathematics that deals with the analysis of random events and the quantification of uncertainty. It has applications in a wide range of fields, including statistics, physics, finance, and engineering.

Flexible hour work = 78%

Don't Know = 9%

Rigid hour = 13%

The probability of that 4 people choose flexible hour for work is,

0.78

To know more about probability visit:

https://brainly.com/question/30034780

#SPJ1

Answer: To find the longest route for Eric to fly, we need to add up the distances for each option and compare them.

Option A: San Francisco to Denver to Chicago to New Jersey

Total distance = 698 + 678 + 965 = 2,341 miles

Option B: Non-stop from San Diego to New Jersey

Total distance = 2,786 miles

Option C: Non-stop from San Diego to New Jersey

Total distance = 2,786 miles

Option D: San Francisco to Denver to Chicago to New Jersey

Total distance = 698 + 678 + 965 = 2,341 miles

Therefore, the longest route for Eric to fly is Option D, from San Francisco to Denver to Chicago to New Jersey, which is 2,341 miles. This is longer than the non-stop flight from San Diego (Option B) by 445 miles. Therefore, the answer is (D) the flight from San Francisco by 445 miles.

Step-by-step explanation:

5. The real zero occurs located

6. The x-coordinate at which a relative minimum occurs is at

In the context of a graph of a function

A real zero, also known as a root or a solution, is a value of the independent variable (usually denoted as x) for which the value of the dependent variable (usually denoted as y) is equal to zero.

Geometrically, a real zero corresponds to the x-coordinate of a point where the graph of the function intersects the x-axis.

A relative minimum, on the other hand, is a point on the graph where the function has a local minimum value.

Geometrically, a relative minimum corresponds to a point where the graph changes from decreasing to increasing, and is located at the bottom of a valley or a trough.

Learn more about real zero at

https://brainly.com/question/31017255

#SPJ1

Answer:

10 feet

Step-by-step explanation:

Let's start by finding the current area of the deck:

Area = length x width = 20 ft x 10 ft = 200 sq ft

If Ian increases each dimension by the same amount, let's call this amount "x", then the new dimensions of the deck will be:

Length = 20 ft + x

Width = 10 ft + x

The new area of the deck will be:

New Area = (20 ft + x) x (10 ft + x)

We know that Ian wants the new area to be triple the original area of 200 sq ft, so:

New Area = 3 x 200 sq ft

New Area = 600 sq ft

Substituting this into the equation above and solving for "x", we get:

(20 ft + x) x (10 ft + x) = 600 sq ft

200 + 30x + x^2 = 600

x^2 + 30x - 400 = 0

(x + 40) (x - 10) = 0

We discard the negative solution, and we get:

x = 10 ft

Therefore, Ian should increase each dimension by 10 feet to triple the area of his deck.

To confirm, we can check the original area of the deck which is 20 ft x 10 ft = 200 sq ft.

If Ian increases each dimension by 10 feet, the new dimensions of the deck will be 30 ft x 20 ft. The new area of the deck will be 30 ft x 20 ft = 600 sq ft. This is triple the original area of the deck (200 sq ft), which is what we wanted to achieve.

Therefore, increasing each dimension by 10 feet will triple the area of the deck as required.

Ian should increase both the sides by 10 feet each.

This is a simple mathematics problems related to the topic of mensuration.

Firstly we calculate the current area of the deck:

Area of the deck (rectangle) = l x b

Area of the deck (rectangle) = 20 x 10

Area of the deck (rectangle) =  200 square feet

Since Ian wants to triple the area of the deck, the required area is 600 square feet.

We now look at pairs of numbers multiplying which will give us 600:

(1,600) (2,300) (3,200) (4,150) (5,120) (6,100) (8,75) (10,60) (12,50) (15,40) (20,30) (25,24)

Out of the above pairs only one pair fulfils Ian's criteria to increase the length and breadth of the deck by equal measure, i.e., (20,30). So, Ian should increase the length and breadth of his deck by 10 feet each.

To know more about Mensuration,

https://brainly.com/question/14269400

Answer: y = 4

Step-by-step explanation:

Let x= -4 and solve for y given our equation.

[tex]y= \frac{-4}{4} + 5\\y = -1 + 5\\y = 4\\[/tex]

Answer:

  51.5

Step-by-step explanation:

You want the median of the data set {55, 44, 40, 55, 48, 44, 58, 67}.

There are an even number of elements in the set of data, so the median will be the average of the middle two.

Sorted into increasing order, the data set is ...

  {40, 44, 44, 48, 55, 55, 58, 67}

The middle two elements are (48, 55). Their average is ...

  median = (48 +55)/2 = 103/2 = 51.5

The median of the data is 51.5.

<95141404393>

Answer:

the value of $s$ is 13.

Step-by-step explanation:

We are given that $r=9$ and $4r+3s=75$. We can use the value of $r$ to find $s$.

Substituting $r=9$ into the second equation, we get:

$4(9) + 3s = 75$

Simplifying the left-hand side, we get:

$36 + 3s = 75$

Subtracting 36 from both sides, we get:

$3s = 39$

Dividing both sides by 3, we get:

$s = 13$

Therefore, the value of $s$ is 13.

The intervals on which the function Is constant are [-4, -3] and [3, 6]

A function is considered constant over an interval if the function has the same output for all the inputs within that interval.

In other words, the function does not change over that interval.

Using the above as a guide, we have the following:

The function does not change over the intervals [-4, -3] and [3, 6]

Hence, the intervals are [-4, -3] and [3, 6]

Read more about functions at

https://brainly.com/question/28532394

#SPJ1

The mean decreases from the original value.  The median stays the same.

(a) To find the new mean, we need to add up all the numbers in the list (except for the 523 that changed to 424) and divide by the number of schools (which is still 9). So the new mean is:

(164 + 225 + 227 + 250 + 261 + 268 + 277 + 379 + 424) / 9 = 272.89

The mean decreases from the original value.

(b) To find the new median, we need to arrange the numbers in order again:

164, 225, 227, 250, 261, 268, 277, 379, 424

The median is the middle value, which is still 261. So the median stays the same.

Learn more about mean at https://brainly.com/question/1136789

#SPJ1

Answer:

1000

Step-by-step explanation: 7+3{-1+5[2-(-9-7)4]+2} can be simplified as follows:

First, we need to solve the innermost parentheses first: -9-7 = -16

So, 7+3{-1+5[2-(-16)4]+2} becomes 7+3{-1+5[2+64]+2}

Next, we need to solve the brackets: 2+64 = 66

So, 7+3{-1+5[66]+2} becomes 7+3{-1+330+2}

Now, we need to solve the innermost parentheses again: -1+330 = 329

So, 7+3{329+2} becomes 7+3*331

Finally, we need to multiply: 3*331 = 993

So, the final answer is 7+993 = 1000.

Therefore, the value of the given expression is 1000.

[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ x^{-2}\implies \cfrac{1}{x^2}\hspace{5em} {\Large \begin{array}{llll} \ne \end{array}}\hspace{5em}-x^2[/tex]

Answer:  there are 13 rows of seats in the theater.

Step-by-step explanation: Concurring to the issue, the number of lines is 3 less than the number of seats in each push. So, the number of lines can be communicated as "x - 3".

We know that the theater can situate 208 individuals, so the entire number of seats can be communicated as "x times (x - 3)".

Hence, we are able type in the condition as:

x(x - 3) = 208

Expanding the condition, we get:

x^2 - 3x - 208 =

Presently, ready to unravel this quadratic condition to discover the esteem of "x" which speaks to the number of seats in each push:

Utilizing the quadratic equation:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = -3, and c = -208

x = (-(-3) ± sqrt((-3)^2 - 4(1)(-208))) / 2(1)

x = (3 ± sqrt(841)) / 2

x = (3 ± 29) / 2

Ready to disregard the negative arrangement, so:

x = (3 + 29) / 2

x = 16

Hence, the number of seats in each push is 16.

And, the number of columns can be communicated as "x - 3":

Number of columns = 16 - 3 = 13

The diagram of the Gateway Arch on the coordinate plane, analyzed using quadratic equations indicates;

1. The vertex point is (50, 630)

2. The solution point are; (20, 0), and (80, 0)

3. Vertex form; f(x) = -0.7·(x - 50)² + 630

4. Factored form; f(x) = -0.7·(x - 20)·(x - 80)

A quadratic equation is an equation of the form f(x) = a·x² + b·x + c

1. The vertex obtained from the graphical diagram of the Gateway Arch indicates that the point corresponding to the vertex point is; (50, 9 × 70 = 630)

The vertex point is; (50, 630)

2. The solution are the points the curve of the Gateway intersects the x-axis, which are points where the y-axis values are zero, therefore;

The solutions are; (20, 0), and (80, 0)

3. The vertex form of a quadratic equation is; f(x) = a·(x - h)² + k

Where;

(h, k) = The coordinates of the vertex

Therefore;

(h, k) = (50, 630)

f(20) = 0 = a·(20 - 50)² + 630

a·(20 - 50)² = -630

a = -630/((20 - 50)²) = -630/900 = -7/10

a = -7/10 = -0.7

The vertex form quadratic equation is therefore; f(x) = -0.7·(x - 50)² + 630

4. The factored form of a quadratic equation is; f(x) = a·(x - r₁)·(x - r₂)

r₁ = 20, and r₂ = 80, a obtained from the vertex is; a = -0.7

The factored form is therefore; f(x) = -0.7·(x - 20)·(x - 80)

Learn more on the factored form of a quadratic equation here: https://brainly.com/question/25094938

#SPJ1

Answer:94.2

Step-by-step explanation: i think

Answer:

To find the point that best represents 331% of the distance between 0 and 1, we need to first calculate 331% of the distance between 0 and 1, which is:

331% of (1 - 0) = 3.31 * (1 - 0) = 3.31

So we want to find the point on the number line that is 3.31 units away from 0.

Looking at the number line, we can see that the distance between W and X is 1 unit, the distance between X and Y is 1/3 unit, and the distance between Y and Z is 2/3 unit.

Therefore, the point that best represents 331% of the distance between 0 and 1 is the point that is 1 unit away from 0 and then an additional 0.31 units away from that point. This point is on the segment between W and X, and is closer to X.

So, the point that best represents 331% of the distance between 0 and 1 is Point X.

Therefore, the answer is (B) Point X.

The length of XY uisng the midpoint theorem is 40 units

The midpoint theorem states that if a line segment is drawn connecting the midpoints of two sides of a triangle, then that line segment is parallel to the third side of the triangle, and its length is half the length of the third side.

In this case, we have a triangle XYZ, and points A, B, C are the midpoints of sides XY, YZ, and ZX respectively.

By the midpoint theorem, we know that AB is parallel to ZX and has a length of half of ZX.

Similarly, BC is parallel to XY and has a length of half of XY, and AC is parallel to YZ and has a length of half of YZ.

We are given that BC has a length of 20, and we want to find the length of XY.

Using the midpoint theorem, we know that

XY is twice the length of BC

So

XY = 2 * BC = 2 * 20 = 40.

Therefore, the length XY is 40 units

Read more about line segments at

https://brainly.com/question/24778489

#SPJ1

The total, rounded to the nearest ten dollars, is $74,730 as $500 is the monthly payment, and the annual interest rate is 2%.

The term "amount" can be used to denote a quantity or overall value, such as the overall value of a product or the overall number of elements in a collection. It is an all-encompassing phrase that may be applied to a certain amount or sum in a variety of settings.

given

Applying the formula for the annuity's future value:

FV is equal to Pmt [tex]x [(1 + r/n)(n*t) - 1] / (r/n).[/tex]

where:

$500 is the monthly payment, and the annual interest rate is 2%, or 0.02 percent. There are 12 compounding periods every year (monthly)

If t = number of years, then 11

Inserting the values:

[tex]FV = 500 x [(1 + 0.02/12)^(12*11) - 1] / (0.02/12)[/tex]

FV ≈ $74,730

The total, rounded to the nearest ten dollars, is $74,730 as $500 is the monthly payment, and the annual interest rate is 2%.

To know more about amount visit :-

brainly.com/question/8082054

#SPJ1

Answer:

The third option:

Points: A, B, C, D

Line segments: AB, AD, AC, DC, BC

Answer:  Vertex is (0,8)        

The answer of the given question based on the Critical value is , , the critical value to for the confidence level c = 0.99 and sample size n = 22 is 2.819.

In statistics, the critical value is a value that is used to determine whether to reject the null hypothesis in a hypothesis test. It is based on the chosen level of significance, which is the maximum probability of making a Type I error (rejecting a true null hypothesis). The critical value is determined by the sampling distribution of the test statistic, which is often a t-statistic or z-statistic, depending on the test and the characteristics of the population being studied.

To find the critical value t for a 99% confidence level and a sample size of 22, we need to use a t-distribution table or a calculator.

Using a t-distribution table with 21 degrees of freedom (n-1), we find that the critical value for a 99% confidence level is approximately 2.819.

Therefore, critical value for confidence level c = 0.99 and sample size n = 22 is 2.819 (rounded to nearest thousandth).

To know more about Null hypothesis visit:

https://brainly.com/question/30404845

#SPJ1

Answer:

A parallelogram with congruent diagonals, a parallelogram with a right angle, a parallelogram with perpendicular diagonals.

Step-by-step explanation:

By definition, a rectangle is nothing but a parallelogram with one right angle. One of the properties of a rectangle is that its perpendiculars are congruent. Finally, the diagonals of a rectangle are congruent (this can be proved by finding congruent triangles split by the diagonals, using CPCTC, etc.).

Answer: The area of the door can be calculated as:

Area of door = width x height

= 0.9 m x 2.1 m

= 1.89 square meters

The area of one window can be calculated as:

Area of window = width x height

= 1.5 m x 1.2 m

= 1.8 square meters

Since there are four windows, the total area of the four windows is:

Total area of four windows = 4 x Area of window

= 4 x 1.8 square meters

= 7.2 square meters

Therefore, the total area of the door and the four windows is:

Total area = Area of door + Total area of four windows

= 1.89 square meters + 7.2 square meters

= 9.09 square meters

Hence, the total area of the door and the four windows is 9.09 square meters.

Step-by-step explanation:

Therefore, the Trigonometric Ratios for Ø are: sin Ø = -20/√(1241), cos Ø = 21/√(1241), tan Ø = -20/21 csc Ø = -√(1241)/20, sec Ø = √(1241)/21, cot Ø = -21/20.

The following are the ratio formulas right now: The definition of sine or sin is "perpendicular/opposite/hypotenuse." Adjacent/Hypotenuse = cosine or cos = Base/Hypotenuse. tangent, tan, or tan = perpendicular, base = opposite, or adjacent.

We can find the hypotenuse by applying the Pythagorean theorem to the problem:

h² = (-20)² + 21²

h² = 841 + 400

h² = 1241

h = √(1241)

So, the hypotenuse is √(1241).

Now we can use the trigonometric ratios:

sin Ø = opposite/hypotenuse = -20/√(1241)

cos Ø = adjacent/hypotenuse = 21/√(1241)

tan Ø = opposite/adjacent = -20/21

csc Ø = 1/sin Ø = -√(1241)/20

sec Ø = 1/cos Ø = √(1241)/21

cot Ø = 1/tan Ø = -21/20

Therefore, the trig ratios for Ø are:

sin Ø = -20/√(1241)

cos Ø = 21/√(1241)

tan Ø = -20/21

csc Ø = -√(1241)/20

sec Ø = √(1241)/21

cot Ø = -21/20

To know more about Trigonometric Ratios visit:-

https://brainly.com/question/25122832

#SPJ1

The probability of drawing a black card is P(draw a black card) = 0.3 or 30%.

Probability is a branch of mathematics that deals with the study of random events and the likelihood or chance of their occurrence. It is the measure of how likely or unlikely it is for an event to happen. The probability of an event is a number between 0 and 1, where 0 means that the event is impossible, and 1 means that the event is certain to occur.

Probability can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For example, if we want to calculate the probability of flipping a coin and getting heads, we divide the number of ways to get heads (1) by the total number of possible outcomes (2), which gives us a probability of 1/2 or 0.5.

Probability is used in many real-world applications, such as in the fields of finance, insurance, and engineering, to make informed decisions based on the likelihood of an event occurring. It is also used in statistical analysis to make inferences about a population based on a sample of data.

The total number of cards in the deck is:

Total number of cards = number of black cards + number of red cards = 33 + 77 = 110

The probability of drawing a black card is given by:

P(draw a black card) = (number of black cards) / (total number of cards) = 33 / 110

Therefore, the probability of drawing a black card is:

P(draw a black card) = 0.3 or 30%

To know more about card visit:

https://brainly.com/question/14611704

#SPJ9

Answer:

C) 4

Step-by-step explanation:

Answer: 26

Step-by-step explanation:

this is how i solve this first divide 19.5 by 3/4 (0.75) therefore the answer to this problem is 26 i hope this help please make me brianlist that would help

To identify whether a fraction is a terminating decimal or not, we can use the division operation and divide numerator by denominator. For example, 1/8 is a terminating decimal expansion as the quotient after dividing 1 by 8 is 0.125. Is 7/8 a terminating decimal? The decimal representation of 7/8 is 0.875. So, it is a terminating decimal.