Two​ joggers, one averaging 5 mph and one averaging 4 ​mph, start from a designated initial point. The slower jogger arrives at the end of the run 35 minutes after the other jogger. Find the distance of the run.

The number of unique ways to complete a quiz with 5 questions and 4 possible answers to each question is [tex]4^5[/tex], or 1024.

This can be calculated using exponential notation, which states that a number raised to the power of another number is equal to the number multiplied by itself that many times. In this case, 4 to the power of 5 is equal to 4 x 4 x 4 x 4 x 4, or 1024.

In other words, the number of unique ways to answer a quiz with 5 questions and 4 possible answers to each question is equal to 4 multiplied by itself 5 times. This can also be written using the exponential notation as [tex]4^5[/tex]. There are 1024 unique ways to complete a quiz with 5 questions and 4 possible answers to each question.

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The equations obtained from evaluation of the data in the table and the predicted cost of hiring the DJs are as follows;

Part B

The equation representing the cost of hiring Celinda is; c = 36·h + 16

The equation representing the cost of hiring Brian is; c = 38·h + 4

Part C

The cost of hiring Celinda for 5 hours is $196

Cost of hiring Brian for 5 hours is $194

A linear equation is an equation that has an highest index of 1.

Part B

The first difference in the cost of hiring each DJ is presented as follows;

Celinda; 160 - 124 = 124 - 88 = 88 - 52 = 36

Brian; 156 - 118 = 118 - 80 = 80 - 42 = 38

The first difference are constant, therefore, the relationship are linear, which can be represented by linear equations.

The difference between the subsequent values in the number of hours of 1 indicates that we get;

Slope of the equation for Celinda = 36

The equation representing the total cost for Celinda is therefore;

Where c represents the cost and h represents the number of hours, we get;

c - 52 = 36·(h - 1)

c = 36·h - 36 + 52

The equation for Brian, with a slope of 38, is therefore;

c - 42 = 38·(h - 1)

c = 38·h - 38 + 42 = 38·h + 4

Part C

The cost of hiring each DJ for 5 hours is therefore;

h = 5

The cost of hiring Celinda for 5 hours is; c = 36 × 5 + 16 = 196

The cost of hiring Celinda for 5 hours is $196

The cost of hiring Brian for 5 hours can be obtained by plugging in h = 5 in the equation; c = 38·h + 4

Therefore; c = 38 × 5 + 4 = 194

The cost of hiring Brian for 5 hours is $194

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Player 3 is more likely to hit the ball than Player 2 because P(Player 3) > P(Player 2). Option D

Probability is a mathematical concept that describes the likelihood of an event happening in a given set of circumstances. It is expressed as a number between 0 and 1, with 0 indicating an impossible event and 1 indicating a certain event. The closer the probability is to 1, the higher the likelihood of the event happening.

If we arrange the fractions in decreasing order we would have;

5/7 > 6/9 > 6/11

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The set of observations on a variable measured at successive points in time or over successive periods of (c) time series .

A Time Series is a set of observations on a variable that is measured at successive points in time or over successive periods.

Which means that the values of the variable that are recorded at regular intervals or successive points, such as daily, weekly, monthly, or annually, and are analyzed to identify the patterns, trends, and relationships over time.

The Time series analysis can be used in various fields, including economics, finance, engineering, and the natural sciences, to make predictions, identify cause-and-effect relationships, and inform decision-making.

The given question is incomplete , the complete question is

A set of observations on a variable measured at successive points in time or over successive periods of

(a) geometric series

(b) time invariant set

(c) time series

(d) logarithmic series

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The equation representing the temperature y in degrees Fahrenheit at x hours after sunset is:

y = -2x + 4

Since the temperature changes linearly with time after sunset, we can represent the temperature as a linear equation:

y = mx + b

where y is the temperature in degrees Fahrenheit, x is the number of hours after sunset, m is the rate of change of temperature and b is the y-intercept.

Given that at 2 hours before sunset, the temperature is 0°F and at 2 hours after sunset, the temperature is -4°F, we can use these points to find m and b.

At x = -2: y = 0°F

At x = 2: y = -4°F

So, m = (y2 - y1) / (x2 - x1) = (-4°F - 0°F) / (2 - (-2)) = -2°F/hour

And, b = y - mx = 0°F - (-2°F/hour * -2) = 4°F

Therefore, the equation representing the temperature y in degrees Fahrenheit at x hours after sunset is:

y = -2x + 4

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The best tool for collecting data on which gas pump is used most frequently by customers would be a check sheet.

A check sheet is a simple tool used to collect and categorize data in a structured manner. In this case, the operator can use a check sheet to keep track of which gas pump is being used by customers by marking each time a customer uses a certain pump.

The operator can then tally the marks to determine which pump is used most frequently. This method provides an easy and efficient way to collect data and quickly see patterns and trends in the data.

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--The given question is incomplete; the complete question is

"A gas station operator is interested in determining which gas pump is used most frequently by customers. The best tool for collecting this data would be a

Run chart.

Check sheet.

Histogram.

Pareto diagram."--

Answer:

Z+12a−z+8+12−+8

Step-by-step explanation:

Z+8−6(z−2a)+5z

+8−6(−2)+5

Z+8−6(−2a+z)+5z

+8−6(−2+)+5

Z+8−6(−2a+z)+5z

+8−6(−2+)+5

Z+8+12a−z+8+12−

Answer:

Z + 8 + 12a − z

12a + 8

Step-by-step explanation:

The result of [tex] \frac{x - 3}{8} [/tex] is x = 8k + 3

To solve the fraction [tex] \frac{x - 3}{8} [/tex], you need to isolate the fraction on one side of the equation. Then, multiply both the numerator and denominator by the same number to make the denominator equal to 1. Finally, simplify the fraction by dividing the numerator by the denominator. The steps are as follows:

[tex] \frac{x - 3}{8} = k[/tex], where k is a constant.

Then, [tex](x - 3) \times {8}^{ - 1 } = k[/tex].

This simplifies to x-3 = 8k.

Finally, you have x = 8k + 3. This is the solution to the fraction [tex] \frac{x - 3}{8} [/tex].

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250g tin of coffee: 29.99/250 = R0.12 per gram

750g tin of coffee: 69.99/750 = R0.09 per gram

750g tin of coffee is better value for money.

A geometric random variable is the number of 5s when rolling a die 35 times. (option 1)

This is due to the fact that rolling a 5 on any given roll has a probability of 1/6, and the number of 5s can be determined by counting the number of successes (rolling a 5) prior to the first failure (not rolling a 5).

If you roll a number other than 5, the expected number of unsuccessful iterations is 1/2pq, where p is the probability of success (1/6) and q is the probability of failure (5/6). Additionally, this can be expressed as (1-p)/p. Therefore, when rolling a die 35 times, the expected number of 5s is 35, or (1-1/6)/(1/6).

We can use the formula for the expected value of a geometric random variable, E[X] = (1-p)/p, where p is the probability of success, to demonstrate this mathematically. p is 1/6 in this case.

E[X] = (1-1/6)/(1/6) = 35 can be obtained by substituting this number into the formula. This indicates that 35 is the anticipated number of 5s after rolling a die 35 times.

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Complete Question:

which of the following random variables is geometric?

Bar graph. This type of graph is ideal for comparing the number of sneakers sold by brand, as it clearly displays the numerical differences between them. It is also easy to interpret and visually appealing.

A bar graph is the best choice for displaying the number of sneakers sold by brand for the month. Bar graphs are used to compare data and show the differences between them. Each brand would be represented by its own bar, and the length of each bar would be determined by the number of sneakers sold. The bars can be labeled with the brand's name, and a numerical scale would be used at the bottom of the graph to indicate the number of sneakers sold. The data can be organized by either the number of sneakers sold (descending) or by the brand name (alphabetically). The bar graph would be easy to interpret and visually appealing. It is also a great way to compare the performance of different brands in a given period.

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The equation of the circle that meets the specified requirements is x^2 + y^2 = 89, with the center at the origin and going through P(5, 8).

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10.

Here,

The equation of a circle with center at the origin (0,0) and passing through the point (x1,y1) can be found using the distance formula.

The distance between a point (x1, y1) and the origin (0,0) is given by:

sqrt((x1-0)^2 + (y1-0)^2) = sqrt(x1^2 + y1^2)

Let's call the radius of the circle r. We know that the distance between the point (x1,y1) and the origin is equal to r. So, we can set up the equation:

sqrt(x1^2 + y1^2) = r

Substituting the values x1 = 5 and y1 = -8, we have:

sqrt(5^2 + (-8)^2) = r

Solving for r, we get:

r = sqrt(5^2 + (-8)^2) = sqrt(25 + 64) = sqrt(89)

Finally, we can write the equation of the circle in standard form using the center (0,0) and radius r:

(x - 0)^2 + (y - 0)^2 = r^2

x^2 + y^2 = r^2

x^2 + y^2 = 89

The  equation of the circle that satisfies the stated conditions that is center at the origin, passing through P(5, −8) is x^2 + y^2 = 89.

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Answer:

there were 13 dogs with ticks but not fleas.

Step-by-step explanation:

Let's call the number of dogs with fleas "x" and the number of dogs with ticks "y".

From the information given, we know:

x = 40 (dogs with fleas)

x + y = 75 (total number of dogs)

y = 27 (dogs with ticks)

So, the number of dogs with ticks but not fleas is equal to y - the number of dogs with both:

y - 14 = 27 - 14 = 13

Therefore, there were 13 dogs with ticks but not fleas.

Answer:

x = 8, y = 1

Step-by-step explanation:

11x - 20y = 28 ...(1)
3x + 4y = 36
or 15x + 20y = 180 ...(2)
Adding (1) and (2),
26x = 208
Or x = 8
Now, 3x + 4y = 36
3(8) + 4y = 36
4y = 36 - 32 = 4
so y = 1

To determine the price of the keyboard with the coupon, we need to know how much Tiana spent. Let's call the original price of the keyboard "x".

According to the coupon, Tiana will receive a discount of $150 for every $500 spent. So, if she spends x dollars, she will receive a discount of (x/500) * $150.

The price of the keyboard with the coupon will then be x - (x/500) * $150.

Since the original price is not specified, we cannot determine the exact price of the keyboard with the coupon.

The amount of the down payment is:     $ 108.08

Step-by-step explanation:

It is given that:

You purchase a new LCD monitor for $1,351.

You put a 8% down payment and $59.56 per month on a 24 month purchase plan.

This means that the down payment made is 8% of the total amount of the LCD monitor.

i.e.

The amount of the down payment= 8% of 1,351

i.e.

The amount of the down payment= 0.08 of 1,351

i.e.

The amount of the down payment=0.08×1,351

i.e.

The amount of the down payment= $ 108.08

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In linear equation, The carbohydrate intake ranges between 129-286g

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                          Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

A diet with adequate proteins and carbohydrates can be given to an athlete (2-3 hours) before a sport.

Generally, 2-3g/kg body weight of Carbohydrates can be included in the diet (depending on the weight and height.

Here, the person weighs 86kgs (assuming the majority of the bodyweight is muscle mass)

Therefore, average carbohydrate intake can be – 85* 2 = 170g; or, 85*3 = 255g

Thus, the carbohydrate intake ranges between 129-286g

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Cost of 15 liters of paint is, 630 Rs.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

Five liters of paint cost = 210 Rs.

Hence, We get;

Cost of 1 liters of paint = 210/5

                                   = 42 Rs.

So, Cost of 15 liters of paint is,

⇒ 15 × 42

⇒ 630 Rs.

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A scatter plot in Excel is the type of chart that can plot a point at its Cartesian coordinates using an x-coordinate and a y-coordinate.

The type of chart in Excel that plots a point at its Cartesian coordinates using an x-coordinate and a y-coordinate is a Scatter Plot. A scatter plot is a type of graph in which individual data points are represented by dots on a graph. Each data point has two coordinates: the x-coordinate and the y-coordinate, which are used to plot the point on the graph.

In Excel, to create a scatter plot, you need to first select your data, then go to the Insert tab and click on the Scatter chart button. You can then choose the type of scatter plot you want to create. Once the chart is created, you can add data labels to show the x-coordinate and y-coordinate of each data point.

In summary, a scatter plot in Excel is the type of chart that can plot a point at its Cartesian coordinates using an x-coordinate and a y-coordinate.

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Tiffany didn't deposit any more money and didn't withdraw any,

her balance is $1,413.82.

Compound interest is computed as interest on the principle of an account plus any accrued interest.

Compound interest can be calculated using the following formula:

x = P(1 + r/n[tex])^{nt}[/tex]

,where x = compound interest

P = principal (the initial deposit or loan amount)

r = annual interest rate

n = the number of compounding periods per unit of time

t = the number of time units the money is invested or borrowed for

Given:

Tiffany makes some extra money selling vinyl's to teachers.

She deposited the $1,245 extra money into an account that earned 3.7% interest that was compounded annually.

First, convert R as a percent to r as a decimal

r = R/100

r = 3.7/100

r = 0.037 rate per year,

Then solve the equation for A

A = P(1 + r/n[tex])^{nt}[/tex]

A = 1,245.00(1 + 0.037[tex])^{3.5}[/tex]

A = $1,413.82

Therefore, the amount is $1,413.82.

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Answer:

Step-by-step explanation:

2+2=4

y = 1/2 x + 1

y = 3/2x + 4        Use first equation to sub in for y

1/2 x + 1  = 3/2 x + 4

-3 = x      then use this value in one of the equations to calc  y

y = 1/2 x + 1

y = 1/2 (-3) + 1 =  - 1/2

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \pounds 3100\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years\dotfill &3 \end{cases} \\\\\\ I = (3100)(0.08)(3) \implies I = 744[/tex]

The length GF in the rhombus is 26.4 and the value of x in the square is 12

The given shape is a rhombus

The diagonals of a rhombus intersect at 90 degrees

This means that

GF^2 = 21^2 + 16^2

So, we have

GF^2 = 697

This gives

GF = 26.4

The given shape is a square

The vertex of a square has a measure of 90 degrees

This means that

11x - 32 = 90

So, we have

11x = 132

This gives

x = 12

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Answer:

To subtract the two mixed numbers, we need to convert both mixed numbers to improper fractions.

So,

8/9 = 72/81 (by multiplying both numerator and denominator by 9)

and

4/6 = 40/60 = 2/3 (by multiplying both numerator and denominator by 10/10)

So,

72/81 - 2/3 = (72 * 3 - 2 * 81) / (81 * 3) = (216 - 162) / 243 = 54/243.

So,

8/9 - 4/6 = 54/243.

Answer:

Step-by-step explanation:

ok so basically you want to turn 8/9 and 4/6 into decimals. When your done turning them into decimals subtract them.

you can also simplify the fractions and then subtract them!

Sorry tried my best hope this helps! :)

The area of the oil spill after 2 hours is 300 square  meters

A rate of change describes the rate at which one quantity changes in relation to another quantity.

Since the oil spill spreads 25 square meters every 1/6 hour. We can write:

rate = 25/(1/6) = 150 square meters per hour

In 2 hours:

area = 2 * 150

area = 300 square meters

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Answer:

false

Step-by-step explanation:

Answer:

1. subtract 12 to the right side and remove the 12 from the left.

You will have -4x=-16

2. divide -4x and  -16 by -14

ANSWER= 4

Step-by-step explanation:

Answer:

Problem 1: the price of one adult ticket is $8.25 and the price of one student ticket is $30.75

Problem 2: there were 10.33 students in each van and 152.67 students in each bus.

Step-by-step explanation:

Problem 1:

Let's call the price of an adult ticket as "a" and the price of a student ticket as "s". We know that on the first day the total cost was $39 and they sold 1 adult ticket and 1 student ticket, so we have the equation:

a + s = 39

And on the second day, the school took $105 from selling 9 adult tickets and 8 student tickets, so we have the equation:

9a + 8s = 105

We can use these two equations to solve for "a" and "s".

Solving for "a":

9a + 8s = 105

a - s = -39

8a = 66

a = $8.25

So the price of one adult ticket is $8.25.

Solving for "s":

a + s = 39

a = $8.25

s = 39 - 8.25 = $30.75

So the price of one student ticket is $30.75.

Problem 2:

Let's call the number of students in each van as "v" and the number of students in each bus as "b". We know that the senior classes at High School A rented and filled 2 vans and 2 buses with 326 students, so we have the equation:

2v + 2b = 326

And High School B rented and filled 11 vans and 6 buses with 233 students, so we have the equation:

11v + 6b = 233

We can use these two equations to solve for "v" and "b".

Solving for "v":

2v + 2b = 326

11v - 6b = -233

-9v = -93

v = 10.33 students in each van

Solving for "b":

2v + 2b = 326

2(10.33) + 2b = 326

20.66 + 2b = 326

2b = 326 - 20.66 = 305.34

b = 152.67 students in each bus

So there were 10.33 students in each van and 152.67 students in each bus.

According to the above, to draw a 1:2 scale we must divide the figure in 2.

The scale model is a way of drawing a figure that is smaller or larger in size. In this case, the size would be smaller, 1:2 means that for each unit of measurement (cm) of the original figure, there are 2 units on the scale.

According to the above, if the circle has a 12cm radius, then the scale model would have a 6cm radius, that is, it would be smaller than the original as shown in the second image.

Note: This question is incomplete. Here is the complete information:

Draw a scale of 1:2 of the following figure:

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