Please answer this picture

Answer:

In summary, the faster cyclist cycles at a speed of 18 mi/h since they travel 36 of the 54 miles in 2 hours while cycling twice as fast as the slower cyclist.

Explanationn:

The two cyclists are 54 miles apart and heading toward each other.

One cyclist cycles 2 times as fast as the other. We will call the faster cyclist A and the slower cyclist B.

They meet 2 hours after starting. This means they travel a total distance of 54 miles in 2 hours.

Since cyclist, A cycles 2 times as fast as cyclist B, cyclist A travels 2/3 of the total distance, and cyclist B travels 1/3 of the total distance.

In two hours, cyclist A travels (2/3) * 54 miles = 36 miles.

We need to find the speed of cyclist A in miles per hour.

Speed = Distance / Time

So the speed of cyclist A is:

36 miles / 2 hours = 18 miles per hour

Therefore, the speed of the faster cyclist is 18 mi/h.

Sorry for bad handwriting

if i was helpful Brainliests my answer ^_^

The year when the population becomes zero is 2020.2

We know that the population decreases at a constant rate, so it is modeled by a line:

y = ax + b

Where a is the slope and b is the y-intercept.

Here we have two points (2010, 5100) and (2012, 4100)

The slope is the quotient between the differences of the y-values and the x-values, then:

a = (4100 - 5100)/(2012 - 2010) = -1000/2 = -500

We can write.

y = -500*x + b

We know that when x = 2010, y = 5100, replacing that we get:

5100 = -500*2010 + b

b = 5100 + 500*2010 = 1,010,100

Then:

y = -500*x + 1,010,100

And it is zero when:

0  = -500*x + 1,010,100

x = 1,010,100/500

x = 2020.2.

That is the year when the pópulation becomes zero.

Learn more about linear equations at:

https://brainly.com/question/1884491

#SPJ1

The Math Club raised $400.

To find out how much money the Math Club raised, we need to determine the percentage of the total amount raised that corresponds to the Math Club's portion.

Let's assume the Math Club raised "x" amount of money. The total amount raised by all five clubs is $2000.

According to the incomplete circle graph, the Math Club's percentage is missing, but we know the percentages for the other clubs: Computer Club raised 15%, Gardening Club raised 18%, Art Club raised 30%, and Spanish Club raised 17%.

To find the missing percentage for the Math Club, we subtract the percentages of the other clubs from 100%:

Missing percentage = 100% - (15% + 18% + 30% + 17%) = 100% - 80% = 20%

Now we can set up a proportion to determine the amount raised by the Math Club:

(x / $2000) = 20% / 100%

Cross-multiplying:

x = ($2000 * 20%) / 100%

Simplifying:

x = $400

For more such questions on Math Club

https://brainly.com/question/31896144

#SPJ8

The perimeter of the rhombus in this problem is given as follows:

19.8 units.

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

The diagonal length can be obtained as follows:

RU + UT = 7.

Applying the Pythagorean Theorem, the side length is obtained as follows:

x² + x² = 7²

2x² = 49

[tex]x = \sqrt{\frac{49}{2}}[/tex]

x = 4.95.

Then the perimeter is given as follows:

P = 4 x 4.95

P = 19.8 units.

More can be learned about the perimeter of a polygon at https://brainly.com/question/3310006

#SPJ1

The histogram in the school newspaper report provides a visual summary of the commute distances for a sample of 24 students at the major university in Southern California, supporting the students' claims of a housing crunch and long commutes.

According to the study reported in the school newspaper, a histogram was used to summarize the commute distances for a sample of 24 students at the major university in Southern California.

A histogram is a graphical representation that displays the distribution of a dataset by organizing it into intervals or bins along the horizontal axis and showing the frequency or count of observations in each bin on the vertical axis.

The histogram provides valuable insights into the commute distances of the university's students and helps assess the housing crunch issue.

By analyzing the histogram, university officials can gain a better understanding of the distribution of commute distances and identify any patterns or concentrations that may indicate the severity of the problem.

The histogram should provide information about the range of commute distances and the frequency of students within each interval.

It allows university officials to visualize the distribution and assess whether there is a significant portion of students facing long commutes due to the lack of housing near campus.

The officials can use the histogram to determine the central tendency measures such as the mean or median commute distance, which can provide a representative value of the typical commute for the student population.

Additionally, they can examine the spread or variability of the data to understand if there are extreme cases or if most students face similar distances.

By studying the histogram, university officials can gather quantitative evidence to support the students' claims of a housing crunch.

This information can guide their decision-making process in addressing the issue, such as implementing policies to increase affordable on-campus housing options or exploring partnerships with nearby housing providers.

In summary, the histogram in the school newspaper report provides a visual representation of the commute distances of a sample of 24 students at the university.

It serves as a valuable tool for university officials to analyze the housing crunch problem and make informed decisions to alleviate the commuting burden on the students.

For similar question on histogram.

https://brainly.com/question/30564854  

#SPJ8

Is not possible to define a radius  nor a diameter in a trapezium.

Radius and diameter are two measures defined for circles.

Radius is the distance between the center and any point in the circumference, and the diameter is the distance between two opposite points in the circumference (so it does not need to be 3D to have radius/diameter).

At the same time, a trapezium is not a circle, is a quadrilateral, so it can't have any of these.

To get the area use the formula:

Area = (base1 + base2)*height / 2

Learn more about trapeziums:

https://brainly.com/question/1410008

#SPJ1

Answer$535.50

Step-by-step explanation:

15% is equal to .15

So, multiply 600.00x .15=90

                   600.00 - 90.0=510.
                   510. 00x .05=25.50

                   510.00+25.50=535.50

                   Your answer is $535.5

The units of each product that Cane should produce to maximize profits will be 62000 units of Beta and 7600 units of

Alpha.

               Alpha Beta

Selling price 130 90

Variable cost 78 48

Contribution margin 52 42

Pound per unit 5 2

Contribution margin per pound 10.4 21

                      Pound                   Unit

Beta 62000*2 = 124000 62000

Alpha 38000 38000/5 = 7600

Total 162000

Maximum contribution margin = (38000*10.4+124000*21) = 2999200

Highest price = 10.4+5 = 15.40 per pound

Learn more about profit on

https://brainly.com/question/1078746

#SPJ1

The angle C in the triangle is 34.05 degrees.

The sum of angles in a triangle is 180 degrees. The angle in a triangle can be found using cosine law as follows:

Therefore, let's find the unknown angle in the triangle as follows;

c² = a² + b² - 2ab cos C

Hence,

4² = 5² + 7² - 2 × 7 × 5 cos X

16 = 25 + 49 - 70 cos X

16 = 74 - 70 cos X

16  - 74 = -70 cos X

-58 = -70 cos X

cos X = 58 / 70

X = cos⁻¹ 0.82857142857

X = 34.0478785629

X = 34.05 degrees

learn more on cosine law here: brainly.com/question/21297672

#SPJ1

Answer:

y = (2x + 5)(2x + 3)

Step-by-step explanation:

y = 4x² + 16x + 15

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 4 × 15 = 60 and sum = + 16

the factors are + 10 and + 6

use these factors to split the x- term

y = 4x² + 10x + 6x + 15 ( factor the first/second and third/fourth terms )

y = 2x(2x + 5) + 3(2x + 5) ← factor out (2x + 5) from each term

y = (2x + 5)(2x + 3)

since multiplication is commutative , then could be

y = (2x + 3)(2x + 5)

Answer:

Therefore, the correct answer is: x < 23.

Step-by-step explanation:

To solve the inequality x - 5 + 2 < 20, we can simplify it step by step:

x - 5 + 2 < 20

Combine like terms:

x - 3 < 20

Add 3 to both sides of the inequality:

x - 3 + 3 < 20 + 3

Simplify:

x < 23

The solution to the inequality is x < 23.

Therefore, the correct answer is: x < 23.

Answer and Step-by-step explanation:

Please see the photo for the solution :)

Let's represent the number with the variable "x". According to the given property, we can write the following equation:

3(x + 4) < 7x

Now, let's solve this inequality to find the range of numbers that satisfy the property.

3x + 12 < 7x

Subtract 3x from both sides:

12 < 4x

Divide both sides by 4 (since the coefficient of x is 4):

3 < x

So, the range of numbers that satisfy the given property is x > 3.

Therefore, any number greater than 3 will satisfy the condition. For example, 4, 5, 6, 7, 8, etc.Step-by-step explanation:

The vertices of the image triangle N'M'O' are N'(5, 2), M'(2, 1), and O'(3, 3).

To determine the vertices of the image N'M'O' after reflecting triangle NMO over the line x = -1, we need to apply the reflection transformation to each vertex.

For a reflection over the line x = -1, we can find the image of a point (x, y) by finding its reflection as (2(-1) - x, y).

Applying this transformation to each vertex of triangle NMO, we get:

N' = (2(-1) - (-5), 2) = (5, 2)

M' = (2(-1) - (-2), 1) = (2, 1)

O' = (2(-1) - (-3), 3) = (3, 3)

The vertices of the image triangle N'M'O' are N'(5, 2), M'(2, 1), and O'(3, 3).

For more such questions on Triangle

https://brainly.com/question/1058720

#SPJ8

Answer:

C. (n+5)(n-5)

Step-by-step explanation:

Select the expression that is equivalent to (n²-25)

Let's check each option. A and B are wrong, so we only check C & D.

C. (n + 5) (n - 5)

n² - 5n + 5n - 25

n² - 25

D. (n - 5)²

(n - 5) (n - 5)

n² - 5n - 5n + 25

n² - 10n + 25

So, the correct answer is C. (n+5)(n-5)

An output value for (fog)(x) is 55/(x² + 2x).

Domain = (-∞, 1) U (-2, 0) U (0, ∞) or {x|x ≠ 0, -2}.

In this exercise, we would determine the corresponding composite function of f(x) and g(x) under the given mathematical operations in simplified form as follows;

(fog)(x) = 5/(x + 2) × 11/x

(fog)(x) = 55/x(x + 2)

(fog)(x) = 55/(x² + 2x)

For the restrictions on the domain, we would have to equate the denominator of the rational function to zero and then evaluate as follows;

x² + 2x ≠ 0

x² ≠ -2x

x ≠ -2

Domain = (-∞, 1) U (-2, 0) U (0, ∞) or {x|x ≠ 0, -2}.

In conclusion, we can reasonably infer and logically deduce that x must not be equal to 0 and -2.

Read more on function here: brainly.com/question/10687170

#SPJ1

It is not accurate to make a blanket statement that the U.S. always has a lower unemployment rate than other countries. The unemployment rates can differ significantly based on specific circumstances, making it important to examine the relevant data and context before drawing conclusions.

The statement "The unemployment rate in the U.S. tends to be lower than in other countries" is subjective and cannot be definitively categorized as true or false without further context and data analysis.

Unemployment rates vary across countries due to a multitude of factors, such as economic conditions, labor market policies, demographics, and government interventions. While it is true that at certain times the unemployment rate in the U.S. may be lower than in some other countries, it is not universally true in all circumstances.

Comparing unemployment rates between countries requires a comprehensive analysis of various factors and data points, including the specific time period, the methodology used for calculating unemployment, and the demographic and socio-economic characteristics of each country. Additionally, economic conditions can fluctuate over time, leading to variations in unemployment rates.

Therefore, it is not accurate to make a blanket statement that the U.S. always has a lower unemployment rate than other countries. The unemployment rates can differ significantly based on specific circumstances, making it important to examine the relevant data and context before drawing conclusions.

for such more question on unemployment rate

https://brainly.com/question/13280244

#SPJ8

The radius of the circle is 25 inches. The length of arc with a central angle of 138° is 115π/6 in

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

The length of an arc with a central angle Ф with circle radius (r) is given by:

Length of arc = (Ф/360) * 2πr

Given the length of arc as 115π/6 in and angle of 138°, hence:

Length of arc = (Ф/360) * 2πr

Substituting:

115π/6 = (138/360) * 2πr

r = 25 inches

The radius of the circle is 25 inches.

Find out more on equation at: https://brainly.com/question/29174899

#SPJ1

Answer:

slope = - [tex]\frac{3}{2}[/tex] , y- intercept = 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

3x + 2y = 14 ( subtract 3x from both sides )

2y = - 3x + 14 ( divide through by 2 )

y = - [tex]\frac{3}{2}[/tex] x + 7 ← in slope- intercept form

with slope m = - [tex]\frac{3}{2}[/tex] and y- intercept c = 7

Answer:

B

Step-by-step explanation:

Yes, because for each input there is exactly one output. You can have two of the same x values but you cannot have 2 of the same y values. if you have two of the same y values, it is not a function as it doesn't pass the vertical line test.

The total cost of the pita bread and hummus dips will be $305.00.

To determine the cost of the pita bread and hummus dips, Toula can use the following expressions:

Cost of pita bread:

Number of crates needed = (150 bags) / (50 bags/crate) = 3 crates

Cost of each crate = $15.00

Total cost of pita bread = (Number of crates needed) × (Cost of each crate) = 3 crates × $15.00/crate = $45.00

Cost of hummus dips:

Number of boxes needed = (65 containers) / (5 containers/box) = 13 boxes

Cost of each box = $20.00

Total cost of hummus dips = (Number of boxes needed) × (Cost of each box) = 13 boxes × $20.00/box = $260.00

Therefore, the expressions Toula can use to determine the costs are:

Cost of pita bread = 3 crates × $15.00/crate

Cost of hummus dips = 13 boxes × $20.00/box

The total cost will be the sum of the costs of pita bread and hummus dips:

Total cost = Cost of pita bread + Cost of hummus dips

Total cost = $45.00 + $260.00

Total cost = $305.00

Therefore, the total cost of the pita bread and hummus dips will be $305.00.

for such more question on cost

https://brainly.com/question/8993267

#SPJ8

Answer:

-1 - 6x = x - 15

Add 15 to both sides using the addition property of equality.

14 - 6x = x

14 = 7x

2 = x

D) -1 - 6x + 15 = x - 15 + 15

Answer and Step-by-step explanation:

Please refer to the photo for the solution!

Answer:

A

Step-by-step explanation:

the axis of symmetry passes through the vertex

its equation x = - 5 is the x- coordinate of the vertex

substitute x = - 5 into f(x) for corresponding y- coordinate

f(- 5) = - (- 5)² - 10(- 5) + 16

       = - 25 + 50 + 16

      = - 25 + 66

     = 41

coordinates of vertex = (- 5, 41 )

Answer:

Step-by-step explanation:

True, the surface area of the cylinder is 100units²

The surface area of a three-dimensional object is the sum of the area of all the outer surfaces, it is also measured in square units.

The surface area of a cylinder is expressed as;

SA = 2πrh + 2πr²

where 2πr² is the area of the bases

2πrh = lateral area

75 = 2 × 3.14 × 6 × r

r = 75/37.68

r = 1.99 unit

base area = 2 × 3.14 × 1.99²

= 25 units ( nearest whole number)

The surface area = 75+25

= 100units²

Therefore the surface area of the cylinder to nearest whole number is 100units².

learn more about surface area of cylinder from

https://brainly.com/question/16519513

#SPJ1

Answer:

A round pencil is sharpened at both ends the hight of the pencil is 16cm the length of the pencil is 1cm the radius of the two sharpened ends is 16cm 1.2cm

Calculate the volume using the value 22/7. 

Step-by-step explanation:

a) Heather contributed $135,000 and Lesley contributed $150,000 to their accounts.

b) Heather's investment is approximately $273,714.17, while Lesley's investment is approximately $191,048.18 when they are 65 years old.

c) Heather has more money by approximately $82,665.99 at age 65.

a) To find out how much money Heather and Lesley contributed to their accounts, we need to calculate the total contributions made by each of them.

Heather:

Heather started investing at age 20 and stopped at age 65, contributing $3000 annually. The number of years she contributed is (65 - 20) = 45 years.

Total contributions by Heather = $3000 × 45 = $135,000.

Lesley:

Lesley started investing at age 40 and stopped at age 65, contributing $6000 annually. The number of years she contributed is (65 - 40) = 25 years.

Total contributions by Lesley = $6000 × 25 = $150,000.

Therefore, Heather contributed $135,000 and Lesley contributed $150,000 to their respective accounts.

b) To calculate the value of their investments at age 65, we can use the formula for compound interest:

Future Value = Principal × (1 + interest rate)^number of years

Heather:

Principal (initial investment) = $3000

Interest rate = 7.5% = 0.075 (converted to decimal)

Number of years = 65 - 20 = 45

Future Value of Heather's investment = $3000 × (1 + 0.075)^45

Lesley:

Principal (initial investment) = $6000

Interest rate = 7.5% = 0.075 (converted to decimal)

Number of years = 65 - 40 = 25

Future Value of Lesley's investment = $6000 × (1 + 0.075)^25

Calculating these values:

Future Value of Heather's investment = $3000 × (1.075)^45 ≈ $273,714.17

Future Value of Lesley's investment = $6000 × (1.075)^25 ≈ $191,048.18

c) To determine who has more money at age 65 and by how much, we compare the future values of their investments.

Heather's investment value at age 65 = $273,714.17

Lesley's investment value at age 65 = $191,048.18

Therefore, Heather has more money at age 65, and the difference in their investments is approximately $273,714.17 - $191,048.18 = $82,665.99.

for such more question on Heather's investment

https://brainly.com/question/1400500

#SPJ8

The statement "There is one outlier, indicating an abnormally large number of books were checked out on that day" is true based on the data set.

To determine if there are any outliers in the given data set of the number of books checked out from a library during the first two weeks of the month, we can examine the values and look for extreme values that deviate significantly from the rest of the data.

The data set is as follows:

19, 10, 15, 99, 12, 18, 15, 16, 12, 13, 18, 17, 19, 13

To identify outliers, we can use different methods, such as the interquartile range (IQR) or z-scores. Let's calculate the IQR to determine if there are any outliers:

Arrange the data set in ascending order:

10, 12, 12, 13, 13, 15, 15, 16, 17, 18, 18, 19, 19, 99

Calculate the first quartile (Q1) and third quartile (Q3):

Q1 = 13 (median of the lower half)

Q3 = 18 (median of the upper half)

Calculate the interquartile range (IQR):

IQR = Q3 - Q1 = 18 - 13 = 5

Define the lower and upper boundaries for outliers:

Lower bound = Q1 - 1.5 * IQR = 13 - 1.5 * 5 = 5.5

Upper bound = Q3 + 1.5 * IQR = 18 + 1.5 * 5 = 25.5

Based on these calculations, any value below 5.5 or above 25.5 would be considered an outlier.

Looking at the data set, we can see that there is indeed one outlier, which is the value 99. It is significantly larger than the rest of the values and falls above the upper bound.

Therefore, the statement "There is one outlier, indicating an abnormally large number of books were checked out on that day" is true based on the data set.

for such more question on data set

https://brainly.com/question/4219149

#SPJ8