Carolina biked 1 mile more than twice the number of miles James biked. Carolina biked a total of 5 miles. Write an equation to determine how many miles James biked.

Answer:

21

Step-by-step explanation:

Since the girls have the same age, let their age be x.
Then, their average is

\(\frac{x+x}{2} = \frac{2x}{2} = x\)

Let \(S_{i}\) denote the age of 'i' girls.
Then, \(S_{8} = S_{6} + x + x - eq(1)\)

Also, we have,

\(\frac{S_{8}}{8} =15 - eq(2)\)

\(\frac{S_{6}}{6} =13 - eq(3)\)

Then eq(2):

(from eq(1) and eq(3))

\(\frac{S_{6} + 2x}{8} =15\\\\\frac{13*6 + 2x}{8} = 15\\\\78+2x = 120\\\\2x = 120-78\\\\x = 21\)

The average of the other two girls with equal age​ is 21

Considering their slopes, these two lines, Line 1 and Line 2, are perpendicular.

The slope, given by change in y divided by change in x, determines if the lines are parallel, perpendicular, or neither, as follows:

In this problem, the slopes are given as follows:

The multiplication is given by:

3 x -1/3 = -1.

Hence they are perpendicular.

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When Jevonte pulls the ladder 3 feet farther from the house, the ladder will reach approximately 10.15 feet up the Side of the house.

To solve this problem, we can use the Pythagorean theorem, which relates the lengths of the sides of a right triangle. In this case, the ladder, the distance from the house to the ladder, and the height along the side of the house form a right triangle.

Let's denote the distance Jevonte pulls the ladder as d. We want to find the new height, h, along the side of the house when the ladder is pulled 3 feet farther from the house.

According to the Pythagorean theorem, we have:

h^2 + (48 + d)^2 = 52^2

Simplifying the equation, we get:

h^2 + (48 + d)^2 = 2704

Expanding and rearranging the equation, we have:

h^2 + (d^2 + 96d + 48^2) = 2704

h^2 + d^2 + 96d + 2304 = 2704

h^2 + d^2 + 96d = 2704 - 2304

h^2 + d^2 + 96d = 400

Now we substitute the known values into the equation. We have d = 3 (since Jevonte pulls the ladder 3 feet farther) and h as the unknown.

h^2 + 3^2 + 96(3) = 400

h^2 + 9 + 288 = 400

h^2 + 297 = 400

h^2 = 400 - 297

h^2 = 103

Taking the square root of both sides, we get:

h = √103

Rounding to the nearest tenth of a foot, h ≈ 10.15 feet.

Therefore, when Jevonte pulls the ladder 3 feet farther from the house, the ladder will reach approximately 10.15 feet up the side of the house.

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Answer:

I am pretty sure the answer is 3. hope this helps

Answer:

e=3

Step-by-step explanation:

\(7(2e-1)-11=6+6e\\14e-7-11=6e+6\\14e-18=6e+6\\8e-18=6\\8e=24\\e=3\)

That is just one way to get to the answer, but basically just use pemdas, multiplying the parentheses and combining like terms. ;)

Answer:

58 degrees

Step-by-step explanation:

The answer is 58 degrees.

180 degrees in a triangle, subtract the angles of 65 and 57, you get 58 degrees.

180 - 57 -65 = 58

Answer:

5/2; 5

Step-by-step explanation:

The first box is m, which is the slope. To find the slope you do rise over run, so basically the change in x and y. You move up 5 and over 2, so m would be 5/2.

The second box is b, which is the y-intercept. To find the y-intercept, you just find where the line crosses the y-axis. That would be 5

We find that 28 child tickets were sold on Tuesday.

To determine the number of child tickets that were sold on Tuesday, let x be the number of child tickets that were sold. Then, the number of adult tickets sold was four times the number of child tickets sold. Thus, the number of adult tickets sold is 4x.

The cost of one child ticket is $6.50, and the cost of one adult ticket is $9.80. Therefore, the total sales can be represented by the equation:6.50x + 9.80(4x) = 1279.60

Simplifying this equation gives: 6.50x + 39.20x = 1279.60

Combining like terms, the equation can be further simplified to:

45.70x = 1279.60 Solving for x gives: x = 28

Therefore, 28 child tickets were sold on Tuesday

In conclusion, if we assume that the number of child tickets sold is x, then we can calculate the number of adult tickets sold to be 4x. By multiplying the number of child tickets sold by the price of one child ticket and the number of adult tickets sold by the price of one adult ticket and adding the two values together, we obtain the total sales equation. Using this equation, we solve for x by simplifying and combining like terms.

Therefore, we find that 28 child tickets were sold on Tuesday.

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Answer:

Step-by-step explanation:

First, we need to calculate how many cookies can the Bakery make in one minute.

So we use \(\dfrac{63}{9} = \dfrac{21}{3} = 7\) to find out that the rate is 7 cookies per minute.

So in 20 minutes, the bakery can make \(20*7=140\) cookies.

Step-by-step explanation:

First, we need to calculate how many cookies can the Bakery make in one minute.

So we use  to find out that the rate is 7 cookies per minute.

So in 20 minutes, the bakery can make cookies.

Answer:

140 cookies in 20 minutes

Answer:

Car As unit rate is --- ***57km/h***

Car Bs unit rate is --- ***70km/h***

Which car goes faster? --- ***Car B*

I hope this helps. u said 45 minutes, so i tried to some up with an answer. best of luck on ur work

Step-by-step explanation:

car a is 57 km in an hour, as 57t is equal to d. This, when d is 57 km will be 1 hr. So we are assuming that "t" is 1. Then d is 57. NOw lets check out car b. 140/2 is for 2 hrs, 210/3 for 3 hrs, and 280/4 for 4 hrs. This gives rate of 70 km in 1 hr.

The probability that Akira will choose apple pie and Paula will choose strawberry cheesecake for dessert is; B: 0.028

We are told that;

There are 6 dessert options menu.

Now, Akira and Paula like all of the choices equally. Thus, probability of selecting any of the 6 menus will be; P(select 1 menu) = 1/6

Thus, probability that they select the preferred menu written in the question is; P(both select 1 menu) = 1/6 * 1/6 = 0.028

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Answer:

1 7/8 inches is 1.875 in decimal form.

Answer:

3

Step-by-step explanation:

the rate of change of the function, or the slope is 3 because to get to one point from the other point in the line, you would have to go up 3 and over 1 (3/1) or just 3.

Hope this helps

The statement is true. If we take any two distinct prime numbers, and the number "1", these numbers will always be pairwise relatively prime.

Two numbers are said to be pairwise relatively prime if their greatest common divisor (GCD) is equal to 1. In this case, since we are considering distinct prime numbers, their GCD will always be 1 since prime numbers have no common factors other than 1 and themselves. Therefore, any two distinct prime numbers will be relatively prime.

Similarly, when we consider the number "1", it is relatively prime to any other number because its only divisor is 1. Hence, when "1" is paired with any prime number, the GCD will be 1.

In summary, whether we consider two distinct prime numbers or pair them with the number "1", the resulting numbers will always be pairwise relatively prime.

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Both f(t) and g(t) are of exponential order.

To show that a function f(t) is of exponential order, we need to find positive constants M and k such that:

|f(t)| <= M * e^(k*t) for all t >= t0, where t0 is some arbitrary constant.

Let's start by considering f(t) = t³ * sin(t). We can use the fact that |sin(t)| <= 1 to obtain an upper bound for f(t):

|f(t)| = |t³ * sin(t)| <= t³ for all t

Now we need to find k such that t³ <= M * e^(k*t) for all t >= t0. Taking logarithms of both sides yields:

ln(t³) <= ln(M * e^(kt)) = ln(M) + kt

Simplifying the left-hand side:

3 ln(t) <= ln(M) + k*t

Now we can choose M = 1 and k = 1 to obtain:

3 ln(t) <= ln(1) + t

3 ln(t) <= t

This inequality holds for all t >= 1, so we have shown that f(t) is of exponential order with M = 1 and k = 1.

Next, consider g(t) = t² * e^t. We can once again obtain an upper bound using the fact that e^t >= 1:

|g(t)| = |t² * e^t| <= t² * e^t for all t

To find M and k such that t² * e^t <= M * e^(k*t) for all t >= t0, we can again take logarithms of both sides:

ln(t² * e^t) <= ln(M * e^(kt)) = ln(M) + kt

Simplifying the left-hand side:

2 ln(t) + t <= ln(M) + k*t

Now we can choose M = 1 and k = 2 to obtain:

2 ln(t) + t <= ln(1) + 2t

2 ln(t) + t <= 2t

This inequality holds for all t >= 1, so we have shown that g(t) is of exponential order with M = 1 and k = 2.

Therefore, both f(t) and g(t) are of exponential order.

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Answer: $2624

Step-by-step explanation:

Well since it’s square yards that means find the area first and since it’s a square and your given 1 side then it’s 8(8)=64. So there’s 64 square yards and since it’s $41 per square yard then multiply 64(41) which will give you $2624

Answer:

x −2  −1   0   1   2

y −6 −4  −2  0  2

The graph of y=2x-2 is given in attachment and slope of given line is 2.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The given equation of the line is y=2x-2

We need to draw the graph of equation y=2x-2.

We need to find values of x and y to plot the graph.

If x=-2,

then y=-6

if x=-1

then y=-4

if x=0

then y=-2

if x=1

then y=0

if x=2

then y=2

if x=3

then y=4

Hence, the graph of y=2x-2 is given in attachment and slope of given line is 2.

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Answer:

Step-by-step explanation:

The equation for this surf instructors' price would be y = 8x + 12.

The y-intercept would be located at (0,12) as that is the initial price that the instructor charges before pricing hourly.

Hope this helps, but if you have any questions, please let me know. :)

according to the question

given data in the question,

the type of sample-

random stratified sampling

The usage of satisfied sampling may be required for a variety of distinct features.

The population is first split into two or more strata or subgroups in this kind of random sampling. Beginning with the sampling procedure, each unit is assigned to one stratum based on the unit's historical performance. Following that, separate random samples are chosen using a basic random sampling technique from each stratum, which contains a percentage of the population. that is, they are both mutually and jointly exhaustive.

The traits that we are evaluating are distinct from those of members of another stratum and similar to those of the sample unit stratum.

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the type of sample that proportionately reflects the relevant diversity of opinions in the population from which it is drawn is random stratified sampling

A sample is a condensed, controllable representation of a larger group. It is a subgroup of people with traits from a wider population. When population sizes are too big for the test to include all potential participants or observations, samples are utilized in statistical testing.

The sample size in statistics is a measurement of the total number of samples utilized in an experiment. The sample size is 50, for instance, if we are evaluating 50 samples of city dwellers who watch TV. It's also known as sample statistics.

Considering the query

the information in the query

a sample's type-

stratified sampling at random

For a number of unique traits, satisfied sampling may be necessary.

In this type of random sampling, the population is initially divided into two or more strata or subgroups. Each unit is categorized into a stratum at the start of the sampling process depending on its prior performance. A basic random sampling approach is then used to select distinct random samples from each stratum, which represents a portion of the population. they are mutually and jointly exhaustive, in other words.

The characteristics that we are examining are different from those of members of one stratum and comparable to those of the stratum that contains the sample unit.

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We have a sample of 28 data points. The sample mean is 30.0 and the sample standard deviation is 2.40. The confidence level required is 98%. Then, we calculate α by:

The confidence interval for the population mean, given the sample mean μ and the sample standard deviation σ, can be calculated as:

Where n is the sample size, and Z is the z-score for 1 - α/2. Using the known values:

Where (from tables):

Finally, the interval at 98% confidence level is:

Answer:

3

X is slope but the equation isnt set up proper

12x-4y=3

-12x -12x

-4y=-12x+3

/-4 /-4

y= 3x+3/-4

Answer:

3

Step-by-step explanation:

Answer:

the slope of the line represented by the table is y = 2/11x

Step-by-step explanation:

y = mx + b

slope: (y² - y¹) / (x² - x¹)

(4 - 2) / (22 - 11) = 2/11

plug in an x and y value to find b

y = 2/11x + b

2 = (2/11)(11) + b

2 = 2 + b

b = 0

the y-intercept is 0

your equation is y = 2/11x

The average number of viewers over the two weeks written in scientific notation is 3.85 × 10^8. option C

Average number of viewers over the two weeks = (First week + Second week) / 2

= {(3.6 x 10⁴) + (4.1 x 10⁴)} / 2

= {3.6 + 4.1 × 10^(4×4) } / 2

= (7.7 × 10^16) / 2

= 3.85 × 10^8

Therefore, the average number of viewers over the two weeks written in scientific notation is 3.85 × 10^8.

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Answer:

6

Step-by-step explanation:

Let the number be x.

1/3 × 12 = 2/3 × x

Multiply.

12/3 = 2/3x

4 = 2/3x

Multiply both sides by 3/2.

4 × 3/2 = x

12/2 = x

x= 6

Answer:

1/3 of 12 = 2/3 of 6

Step-by-step explanation:

1/3 · 12 = 2/3 · x

12/3 = 2x/3

Multiply 3 on both sides.

12 = 2x

12 ÷ 2 = x

6 = x

Answer:

Below.

Step-by-step explanation:

Comparing:

y = mx + c

y = 2x -   1

So m = 2 and c = -1.

The required arc length of sector VW is 8\(\pi\).

Given that, in a circle U, radius  UV = 9 and  central angle of sector m∠VUW = 160°.

To find the arc length of sector VW, we can use the formula:

Arc length = (central angle / 360) x circumference of the circle.

First,  find the circumference of the circle by the  formula for the circumference of a circle is given by:

Circumference = 2 x \(\pi\) x radius.

Circumference = 2 x \(\pi\) x 9 = 18π.

Now, let's find the arc length of sector VW using the central angle of 160 degrees:

Arc length = (160/360) x 18π

Arc length = (4/9) * 18\(\pi\) = 8\(\pi\).

Therefore, the arc length of sector VW is 8\(\pi\).

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Answer:

The answer is 115 degrees

Step-by-step explanation:

You would need to find out the total of the angles in the triangle first (75+40=115) then subtract that by 180 (180-115=65) Take that and subtract it from 180 (180-65) giving you 115 for the outside line.

The odd one out is the furthest to the right. the Nickels.

The first square is 25 cents. The second square is 25 cents. The third square is 15 cents.

I hope this helps you :D

Proportional reasoning can be used to make an estimate about a population using data from a sample by assuming that the sample is representative of the population as a whole.

Proportional reasoning involves using the relationship between different parts of a whole to estimate an unknown value.

To apply proportional reasoning to a population estimate, you would first need to gather a random sample of individuals from the population. Then, you could use the data from the sample to estimate the value of a particular characteristic or parameter for the entire population.

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