The scale factor for the measurements on the map would be 11 x 10 ⁻⁵.
What is scale factor?Scale factor is used to compare the size of two objects. Mathematically, we can write -
{K} = S{O1}/S{O2}
Given is that the distance between home and school is 4.5 miles. On a map it shows the distance to be 9 cm.
The distance between home and school : 4.5 miles.
On the map the distance between home and school is 9 cm.
We can write the scale factor as -
{K} = (9 x 5.5 x 10 ⁻⁵)/4.5
{K} = 11 x 10 ⁻⁵
Therefore, the scale factor for the measurements on the map would be 11 x 10 ⁻⁵.
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Adan can do a piece of work in 3 days, Bernie in 4 days, and Cynthia in 6 days each working alone.
How long will it take them to do it working together?
Please include how you did it.
Answer:
1 day and 8 hours
Step-by-step explanation:
Adan does 1/3 work each day,
Bernie does 1/4 work each day, and
Cynthia does 1/6 work each day
combined they accomplish 3/4 each day
therefore it would take them 1 day and 8 hours
By adding the individual work rates of Adan, Bernie, and Cynthia, we find that they could complete the task in a total time of 1.5 days when working together.
Explanation:In this question, the rates at which Adan, Bernie, and Cynthia can complete a piece of work are given. This information can be used to calculate how long it would take for them to complete the work together.
Adan can do the job in 3 days, so his work rate is 1/3 of the job per day. Bernie's work rate is 1/4 of the job per day, and Cynthia's work rate is 1/6 of the job per day.
The combined work rate of Adan, Bernie, and Cynthia per day would be the sum of their individual work rates which is (1/3 + 1/4 + 1/6). This sums up to 4/6 or 2/3. The time required for them to finish the job together is the reciprocal of the total work rate which is 3/2 and that equals to 1.5 days.
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25 students in a high school health class are asked to write down what foods they ate last week. Of the 25
students, 14 write steak, 6 write chicken, and 5 write both steak and chicken. Using this information, answer
each of the following questions,
Let S be the event that a randomly selected student writes steak and C be the event that a randomly selected
student writes chicken.
What is P(S), the probability that a student writes steak?
What is P(C), the probability that a student writes chicken?
What is P(S and C), the probability that a student writes steak and chicken?
What is P(S or C), the probability that a student writes steak or chicken?
The probability of event S(students writing steak) was calculated as 14/25, event C(students writing chicken) as 6/25, while both occurring(S and C) as 5/25. From these the combined probability of either of these two events occurring(S or C) was determined by summing the individual probabilities and subtracting the combined one thus, 14/25+6/25-5/25.
Explanation:The subject matter relates to the field of probability in Mathematics, focusing on two independent events namely, S (student writes steak) and C (student writes chicken). Here, the total number of students 25 serves as our sample space.
The probability of event S, P(S), is equal to the number of students who write steak over the total number of students. So, P(S) = 14/25. The probability of event C, P(C), is similarly calculated. That is, P(C) = 6/25.The probability that both events S and C occur, denoted as P(S and C), can be obtained by the division of the number of students who write both steak and chicken by the total number of students. So, P(S and C) = 5/25.The probability that either event S or C occur, written as P(S or C) is calculated by adding the probabilities of each event and then subtracting the probability of them occurring together. Thus, P(S or C) = P(S) + P(C) - P(S and C) = 14/25 + 6/25 - 5/25.Learn more about Probability here:https://brainly.com/question/32117953
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Teresa is maintaining a camp fire. She can keep the fire burning for 4 hours with 6 logs. How many logs does Teresa need to maintain the fire for 18 hours?
Answer:
27
Step-by-step explanation:
Set up the equation as a ration 4*6 = 18*y
Cross multiply you get 108/4y= 27 logs
Greg is buying a bike on a payment plan. The equation y=20x+600 models the amount he has left to pay, where x is the number of weeks and y is the amount of money owed in dollars. Lin is also buying a bike on a payment plan. The bike costs 500. She will pay 25 each week. Which statement correctly compares Greg's function and Lin's function.
We can conclude that the amount owned by Greg is greater than that of Lin. Plus, Greg Also took an additional loan of $600. Lin will pay of the debt in x = 20 weeks, but since no data is given for Greg, it is not possible to determine the time it will cost him to return money.
What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
The equation of a straight line can be also written as -
Ax + By + C = 0
By = - Ax - C
y = (- A/B)x - (C/A)
We have the following problem -
Greg who is buying a bike on a payment plan. The equation y = 20x + 600 models the amount he has left to pay, where [x] is the number of weeks and [y] is the amount of money owed in dollars. Lin is also buying a bike on a payment plan. The bike costs 500. She will pay 25 each week.
The equation for Greg payment plan -
y = 20x + 600
models the amount he has left to pay, where [x] is the number of weeks and [y] is the amount of money owed in dollars.
Similarly, the equation that represents the money owned by Lin -
y = 500 - 25x
[x] is the number of weeks and [y] is the amount of money remaining to be paid in dollars.
Refer the graph of both situations.
The amount owned by Greg is greater than that of Lin. Plus, Greg Also took an additional loan of $600. Lin will pay of the debt in x = 20 weeks, but since no data is given for Greg, it is not possible to determine the time it will cost him to return money.
Therefore, we can conclude that the amount owned by Greg is greater than that of Lin. Plus, Greg Also took an additional loan of $600. Lin will pay of the debt in x = 20 weeks, but since no data is given for Greg, it is not possible to determine the time it will cost him to return money.
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Two wires with lengths of 448 cm and 616 cm are to be cut into pieces of all the same length without a remainder. Find the greatest possible length of the pieces?
SOMEBODY PLZ HELP!!! wih this question.
The greatest possible length for the pieces into which two wires of lengths 448 cm and 616 cm can be cut without a remainder is 56 cm, which is the Greatest Common Divisor of the two lengths.
For the lengths given, 448 cm and 616 cm, the GCD can be found using the Euclidean algorithm.
Divide 616 by 448 and find the remainder: 616 / 448 gives a quotient of 1 and a remainder of 168.
Next, divide the former divisor (448) by the remainder (168) to get a new quotient and remainder: 448 / 168 gives a quotient of 2 and a remainder of 112.
Repeat this process using the previous remainder: 168 \/ 112 gives a quotient of 1 and a remainder of 56.
Continue the process: 112 / 56 gives a quotient and remainder of 2 and 0, respectively.
Therefore, the greatest possible length for equally-sized pieces of wire without remainder is 56 cm.
Tobin is solving the equation 3(x - 1.25) = 11.25. His work is shown below.
What mistake did Tobin make?
a
Tobin did not make a mistake.
b
Tobin should have subtracted 3.75 from each side.
c
Tobin did not distribute the 3 correctly.
d
Tobine should have divided by 3.
Answer:
b
Step-by-step explanation:
in training for a race, each day aylin ran 1.5% further than the day before. if on the 27th day of training she ran approx 6 miles approx how many miles did she run on the first day of training? Round to the nearest integer
Answer: 5%
Step-by-step explanation:
Simplify the expression. Use standard polynomial format.
x(2x + 3) + (x - 3)(x - 4)
Answer:
x(2x + 3) + (x - 3) (x - 4) = 3x²- 4x + 12
Step-by-step explanation:
Expand:
x(2x + 3): 2x² + 3x
2x² + 3x + (x - 3) (x - 4)
Expand:
(x - 3) (x - 4): x²- 7x + 12
2x² + 3x + x²- 7x + 12
Simplify:
2x² + 3x + x² - 7x + 12: 3x² - 4x + 12
= 3x² - 4x +12
Find the measure of arc DBC in circle P.
Answer:
122°
Step-by-step explanation:
The measure of arc DBC in circle P is calculated thus:
DBC = 180° - 58° (sum of angles on a straight line)
DBC = 122°
Therefore, the measure of arc DBC in circle P is 122°.
Note,
Line BD is a straight line; thus, sum of angles on a straight line is 180°.
Angle BPC is 58°. To determine angle DPC, we subtract 58° from 180°, such that, 180° - 58° = 122°.
Write an equation m=1/3 through (4,4)
Answer:
y - 4 = 1/3(x - 4)
y - 4 = 1/3x - 4/3
y - 12/3 = 1/3x - 4/3
y = 1/3x + 8/3
Step-by-step explanation:
The slope of a line can be expressed in the form y = mx + b. Given m = 1/3 and a point (4,4), we can substitute these into the equation to find b. The equation of the line is thus y = 1/3x + 8/3.
Explanation:In mathematics, an equation of a line is often written in the slope-intercept form, which is y = mx + b. The term 'm' represents the slope of the line, while 'b' is the y-intercept.
In the question, the value 'm' is provided as 1/3, and one point through which line passes is (4,4). We can substitute the value of 'm' and the coordinates of the point into the equation to solve for 'b'.
So, y = mx + b becomes 4 = (1/3)*4 + b. Simplify this to solve for b, hence b=4-(4/3) which gives 'b' as 8/3.
Therefore, the equation of the line becomes y = 1/3x + 8/3.
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A square has sides with lengths of (x - 2) units. A rectangle has a length of x units and a width of
(x - 4) units.
Which statements about the situation are true? Select all that apply.
The area of the square is greater than the area of the rectangle.
B
The area of the square is (x2 - 4) square units.
The value of x must be greater than 4.
The difference in the areas is 4x -4.
The area of the rectangle is (x2 - 4x) square units.
Final answer:
The correct statements are the area of the rectangle is x^2 - 4x square units, the difference in areas is 4x - 4, and if x > 4, the area of the square could be greater than, equal to, or less than the area of the rectangle, depending on x.
Explanation:
When analyzing the given geometric shapes, a square with sides of length (x - 2) and a rectangle with dimensions x by (x - 4), a number of true statements can be identified:
The area of the square is (x - 2)2 or x2 - 4x + 4 square units.
The area of the rectangle is x(x - 4) or x2 - 4x square units.
If x > 4, then the area of the square could be greater than, less than, or equal to the area of the rectangle, depending on the value of x.
The difference in the areas is (x - 2)2 - (x(x - 4)) which simplifies to 4x - 4.
Therefore, the correct statements are that the area of the rectangle is (x2 - 4x) square units, and if x is greater than 4, the area of the square could be greater than the area of the rectangle, depending on x. The difference in the areas is indeed 4x - 4. However, the area of the square is not (x2 - 4) square units as previously stated.
Write an algebraic expression for: the product of 12 and x divided by the sum of 4 and x
Answer:
12x / (4+x)
Step-by-step explanation:
product of 12 and x
12x
Divided by
12x /
sum of 4 and x
(4+x)
12x / (4+x)
Answer:
12x/(4+x)
Step-by-step explanation:
product of 12 and x: 12x
divided by
the sum of 4 and x: 4 + x
12x/(4+x)
pleasee help mee
12sin(x)-5cos(x)=6,5
We turn -5,12 into polar coordinates. It's a Pythagorean Triple so
r = 13 Ф=arctan(-12/5) + 180° ( in the second quadrant )
so -5 = 13 cos Ф, 12 = 13 sin Ф
12 sin x - 5 cos x = 6.5
13 sinФ sin x + 13 cos Ф cos x = 6.5
13 cos(x - Ф) = 6.5
cos(x - Ф) = 1/2
cos(x - Ф) = cos 60°
x - Ф = ± 60° + 360° k integer k
x = Ф ± 60° + 360° k
x = 180° + arctan(-12/5) ± 60° + 360° k
That's the exact answer;
x ≈ 180° - 67.38° ± 60° + 360° k
x ≈ 122.62° ± 60° + 360° k
x ≈ { 62.62°, 182.62°} + 360° k, integer k
Steven purchases a bowl. THe diameter of the bowl is 14cm. What is the area of the bowl?
Answer: 153.86cm
Step-by-step explanation:
A bowl represents a circle
Area of a circle is pir2
But here we are given the diameter as 14
Diameter = 2radii
14=2r
R=14/2
R=7
So radius of the bowl is 7cm
Back to the formula
Area of a circle is pir2
Pi=3.14
Substitute for each value
Area= 3.14×7^2
Area= 3.14×49
Area= 153.86cm
Area= ~154cm
Answer 7?
Im not 100% sure. It is probably wrong
Are the data shown in this line plot skewed left, skewed right, or not skewed? 45 47 49 51 53 55
Answer:
it is skewed left
Step-by-step explanation:
i know it looks like more of the data is on the right side then you think it is skewed right but it is always the opposite.
hope i helped
In a sample of people in the school district, 16 out of 25 favored building a new football stadium. If 6,000 people vote in the next local election, how many are likely to vote in favor of the new football stadium based on this sample?
Using the sample proportion of 64% favoring the new stadium, we predict that approximately 3,840 out of 6,000 voters would vote in favor of the new football stadium.
In the sample provided, 16 out of 25 people favored building a new football stadium, which is a proportion of 64% favoring the stadium. To predict how many people are likely to vote in favor of the new football stadium in the local election with 6,000 voters, we use this sample proportion.
The calculation is straightforward:
First, convert the percentage to a decimal: 64% = 0.64.Then, multiply the total number of voters by this decimal: 0.64 * 6,000 = 3,840.Based on the sample, approximately 3,840 people are likely to vote in favor of building the new football stadium in the next local election.
The swimming club went to a swim meet in another town. They took 3 cars and 2 vans. There were 5 people in each car and 4 people in each van. How many people went on the trip?
WOILL GIVE BRAINLIST!!! :))
To find the total number of people who went on the trip, add the number of people in the cars and vans together.
Explanation:To find the total number of people who went on the trip, we need to calculate the number of people in each car and each van and then add them together.
In each car, there were 5 people, so 3 cars would have a total of 3 x 5 = 15 people.
In each van, there were 4 people, so 2 vans would have a total of 2 x 4 = 8 people.
To find the total number of people, we add the number of people in the cars and the number of people in the vans: 15 + 8 = 23.
Therefore, a total of 23 people went on the trip.
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15. The vertices of A DEF are D(0,0), E(0,7), and F(6,3).
Find the coordinates of the orthocenter of A DEF.
Orthocenter of a triangle with one vertex at the origin D(0,0), E(0,7), F(6,3)
The orthocenter is the meet of the altitudes.
DE is the line x=0. That's the y axis. The altitude is the perpendicular through F(6,3), so is the horizontal line y=3.
DF is the line
6y=3x
y=(1/2)x
Perpendicular through E(0,7) is
y - 7 = (-2)(x - 0)
y = -2x + 7
That's the other altitude. Intersecting with y=3
3 = -2x + 7
-4 = -2x
x = 2
y = 3
Answer: orthocenter is (2,3)
Please help on number 5, multiple choice
Answer: Post a picture of the question.
Step-by-step explanation:
What type of triangle has three angles whose measure are less than 90°?
Answer:
acute
Step-by-step explanation:
it is an acute triangle
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P.S. Hello from Russia :^)
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Find all pairs of natural numbers which can be the solution to the equation:
xy = 18
please help me I need help
Answer:
[tex] |28 - x| = 0 \\ 28 - x = 0 \\ - x = - 28 \\ x = 28[/tex]
Answer:
x = 28.
Step-by-step explanation:
|28 - x| = 0
28 - x = 0
28 = x.
The absolute value makes no difference to the result as we have 0 on the right side.
What is the circumference of the circle? if the diameter is 33 Please help
Answer:
C = 33pi or approximately 103.62
Step-by-step explanation:
The circumference of a circle is given by
C = pi *d where d is the diameter
C = pi*33
We can approximate pi by 3.14
C = 33*3.14
103.62
Answer:
103.62 units
Step-by-step explanation:
Radius = 33/2 = 16.5 units
Circumference = 2 × 3.14 × 16.5
= 103.62
Wheel A has a diameter of 25.4 inches. Wheel B has a diameter of 22.5 inches. About how much farther will Wheel A travel in one rotation than Wheel B? Use 3.14 for pi. Round your answer to the nearest whole number.
Wheel A will travel a distance of approximately 9 in more than wheel B in one rotation.
Explanation:
Given:
Diameter of wheel A, d₁ = 25.4 in
Radius of wheel A, r₁ = 12.7 in
Diameter of wheel B = 22.5 in
Radius of Wheel B, d₂ = 11.25 in
Distance travelled by A = ?
In one rotation, the distance travelled by a wheel is equal to its circumference.
Circumference of a wheel = 2πr
Circumference of wheel A = 2πr₁
= 2 X 3.14 X 12.7 in
= 80 in
Circumference of wheel B = 2πr₂
= 2 X 3.14 X 11.25 in
= 71 in
Therefore, wheel A will travel a distance of approximately 9 (80 - 71 in) in more than wheel B in one rotation.
The larger wheel with a diameter of 25.4 inches travels approximately 9 inches farther in one rotation than the smaller wheel with a diameter of 22.5 inches.
To determine how much farther Wheel A will travel in one rotation compared to Wheel B, we need to calculate the difference in their circumferences, since the circumference of a wheel determines the distance it covers in one rotation. The formula for the circumference of a circle is C = (pi * d), where C is the circumference and d is the diameter of the wheel.
First, we calculate the circumferences of both wheels:
Wheel A: C = (pi * d) = 3.14 * 25.4 inches = 79.756 inches.
Wheel B: C = (pi * d) = 3.14 * 22.5 inches = 70.65 inches.
Now, to find how much farther Wheel A travels than Wheel B in one rotation, we subtract the circumference of Wheel B from that of Wheel A:
Difference in distance = Circumference of Wheel A - Circumference of Wheel B = 79.756 inches - 70.65 inches = 9.106 inches.
When rounding to the nearest whole number, the difference is approximately 9 inches.
Which is the value of g(-5) if g(x)=3.4x-8?
At a carnival, 700 tickets were sold for a total amount of $5000. An adult ticket cost $10 and a children's ticket cost $5. Find the number of adult tickets (x) and the number of children's tickets (y) sold.
Answer: 400 adult tickets and 300 kids tickets
Step-by-step explanation:
Four students took a national standardized test for which the mean was 500 and the standard deviation was 100. If a student's value was 1:75 on the test, what was the student's score?
a. 675
c. 645
b. 650
d.700
Answer:
560 has 0.6 z-value, 450 has -0.5 z-value, 640 has 1.4 z-value, 530 has 0.3 z-value
Step-by-step explanation:
I had this qution on a test on time
please mark me as brainliest
Answer: The answer is A) 675
Step-by-step explanation: Take each answer choice and subtract it from 500 and divide by 100 until one of them gives you the answer of 1.75
help me!!!! study island question.
Answer:
D
Step-by-step explanation:
1/4=3/12
1/3=4/12
4/12 +3/12= 7/12
7/12 divided by 3/1
7/12 x 1/3
=7/36 of a pound
Write the equation of the line that passes through the points (-2, 3) and (-2, 5).
Answer:
x = -2
Step-by-step explanation:
We can find the slope of the line using
m = (y2-y1)/(x2-x1)
= (5-3)/(-2- -2)
(5-3)/(-2+2)
2/0
The slope is undefined since the denominator is zero
This means we have a vertical line
This is in the form x=
We have points with x=-2 so
x = -2
The side of a ramp is to be painted. The ramp has a
length of 11.1 feet, reaches a height of 1.5 feet, and
runs 11 feet on the ground. What is the area of the
space that will be painted? If necessary, round to the
nearest tenth.
The area of the painted space is
square
11.1 ft
1.5 ft
feet
11 ft
Please Help!!
Answer:
8.3
Step-by-step explanation: