The statement 'The ratio 4/7 : 8/21 has a unit rate of 3/2.' is True.
In this question, we have been given a statement 'The ratio 4/7 : 8/21 has a unit rate of 3/2.'
We need to check whether the statement is True or False.
We have been given the ratio of two fractions.
4/7 : 8/21
We know that for any non zero real numbers a, b, c, d,
a/b : c/d = a/b × d/c
So, we can write given ratio as,
4/7 : 8/21
= 4/7 × 21/8
= 3/2
In the given statement, it is mentioned that, the ratio 4/7 : 8/21 has a unit rate of 3/2.
This means, the given statement is correct.
Therefore, the statement 'The ratio 4/7 : 8/21 has a unit rate of 3/2.' is True.
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Two mechanics worked on a car. The first mechanic charged $55 per hour, and the second mechanic charged $110 per hour. The mechanics worked for a combined total of 25 hours, and together they charged a total of $2200. How long did each mechanic work?
Answer:
25 Hours
Step-by-step explanation:
It says it in the text
Find the slope of the lined graph
The slope of the lined graph is 5 / 3
How to determine the slope
The formula for determining the slope of a line is expressed as;
Slope = y2 - y1/ x2 - x1
From the graph shown;
y1 = -1y2 = 4x2 = 3x1 = 0Now, let's substitute the values
Slope, m = 4 - (-1) / 3 - 0
Find the differences
Slope, m = 4 + 1/ 3
Slope, m = 5 / 3
Thus, the slope of the lined graph is 5 / 3
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The point (-2,8) is on the graph of y=f (x), which point must be on the graph of y=-f(x)
The point on the graph y = -f(x) is (-2 , -8)
According to the question the coordinates we have been given is (-2 , 8) and it is on the graph y = f(x)
That is we have been given that
f(-2) = 8 (1)
Now we have to find the point on the graph y = -f(x)
So we will choose the value of x = -2 in f(x)
Thus, putting the required value we get
y = - f(-2)
As the value of f(-2) is 8 from equation (1). we will equate the value in the above equation we get
y = -(8)
y = -8
Hence the point on the graph is (-2 , -8)
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Write an algebraic expression for the verbal description.
The discount d is 40% of the list price L.
Answer:
D = 0.4(L)
Step-by-step explanation:
D = 0.4(L)
Answer: 0.4L=d
Step-by-step explanation:
40%=0.4
0.4L=d ==> 40% of L, the listed price, is d, the discount.
Date
11. Write the fraction below as a decimal rounded
to the nearest hundredth.
25
7
Answer:
3.57
Step-by-step explanation:
25/7 is the same as 25÷7 which is 3.57
The composite bar chart Messages received shows the number of messages Tim received each day for five days.
a) How many texts did Tim receive on Monday?
b) How many emails did Tim receive on Thursday?
c) In total, what fraction of the messages were emails?
Give your answer in its simplest form.
We need to know about a composite bar chart to solve the question. The answer for (a) is Tim received 8 texts on Monday, (b) Tim received 4 emails on Thursday and (c) 0.52 of the messages were emails.
A composite bar chart is used when there are two sets of data that are connected and their frequencies are combined.In this question there are two sets of data emails and texts but both of them belong to the same category which is messages. For question (a) we can easily say from the diagram that the number of texts Tim received on Monday is 8.
For question (b) we need to find out the number of emails Tim received on Thursday, for this we have to look at the bar for Thursday and subtract the number of texts received from total number of messages to get the number of emails received that means, 15-11=4, so Tim received 4 emails on Thursday.
For question (c) we need to find the total number of messages received by Tim for five days, total number of emails received and then calculate the fraction of emails out of messages.
Total number of messages=14+16+14+15+14=73
Total number of emails=6+10+10+4+8=38
Fraction of emails over messages=[tex]\frac{38}{73}[/tex]=0.52
Thus 0.52 of the messages were emails.
We analysed the composite bar chart to find out the answers of the three questions, Tim received 8 texts on Monday,4 emails on Thursday and 0.52 of the messages were emails.
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Answer:
a= 5
b= 7
c=
Step-by-step explanation:
find the probability of a point chosen at random being in the shaded area of the diagram at the right
Answer: 1/9
Step-by-step explanation:
The area of the shaded region is [tex](4/2)^2 \pi =4\pi[/tex]
The area of the entire circle is [tex](6)^2 \pi=36\pi[/tex]
So, the probability is [tex]\frac{4\pi}{36\pi}=1/9[/tex]
10. f(3)=2x-5 Evaluate the function.
Answer should be written: f(3)=?
Type a response
2/1
The evaluation of function will give the result f(3) = 1
To find the value of function given in question, we will simply keep the desired value in place of variable x.
Rewriting the equation
f(3) = 2x - 5
Keep the value of x in equation, as given in question
f(3) = 2×3 - 5
Performing multiplication to find the value of x in equation given in question
f(3) = 6 - 5
Performing subtraction to find the value of x in equation given in question
f(3) = 1
Therefore, the result of evaluation of given function is f(3) = 1.
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HELPPPPPPOOOOOOPOOOOOOOOOOOPPPPPPPPPPPPPPPPPPPPPPPPOOOOOO
Answer:
In standars form it would look like so:
28,936
In expanded form it would look like so:
20,000 + 8,000 + 900 + 30 + 6
Step-by-step explanation:
Your welcome! Hope it helps! =D
Kelly works four hours a day on tickets and solves on average 38 tickets per day. Brian works five hours per day and solves 45 tickets per hour. Marvin works six hours a day on tickets and solves on average 59 tickets per day. Linda works five and a half hours a day on tickets and solves 53 tickets per day. Who solves the most tickets per hour?
Answer:
Marvin
Step-by-step explanation:
Kelly works four hours a day on tickets and solves on average 38 tickets per day.
38 tickets / 4 hours = 9.5 tickers per hour
_____________________
Brian works five hours per day and solves 45 tickets per hour.
45 tickets / 5 hours = 9 tickers per hour
_____________________________
Marvin works six hours a day on tickets and solves on average 59 tickets per day.
59 tickets / 6 hours = 9.83333 tickers per hour
______________________
Linda works five and a half hours a day on tickets and solves 53 tickets per day.
53 tickets / 5.5 hours = 9.6363637 tickers per hour
Who solves the most tickets per hour? Marvin at 9.833 tickets an hour
PLEASE HELP FAST I ONLY HAVE ONE HOUR!!!!!!!!
The residual plot represents a linear model because (a) there is no clear pattern
How to determine the if the residual plot represents a linear model?The given parameters are:
The graph
The table
For a residual plot to represent a linear model, the following must be true
The points on the residual plot must be randomly dispersed on the plot
This means that all residual plots that have random points are linear models
From the attached graph, we can see that the points on the graph are randomly dispersed
Hence, the residual plot represents a linear model because (a) there is no clear pattern
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In Exercises 11 and 12, find m/1, m/2, and m/3.
Explain your reasoning.
Answer:
11
m/1= 100, m/2 = 80, m/3 = 100
12
m/1 = 47, m/2= 133, m/3=47
Step-by-step explanation:
Number 11 uses Cointerior angle rule
Number 12 uses Cointerior angle rule and Corresponding angle rules
Which function is positive for the entire interval [–3, –2]? On a coordinate plane, a curved line with a minimum value of (0, negative 3) crosses the x-axis at (negative 3, 0) and (3, 0), and crosses the y-axis at (0, negative 3). On a coordinate plane, a curved line with a minimum value of (2, negative 3) crosses the x-axis at (negative 1, 0) and (5, 0), and crosses the y-axis at (0, negative 1.5). On a coordinate plane, a curved line with a minimum value of (2, 4) and a maximum value of (0.5, 6), crosses the x-axis at (negative 1.5, 0) and crosses the y-axis at (0, 5). On a coordinate plane, a curved line with a minimum value of (negative 1.75, negative 3.9) and a maximum value of (0, 2), crosses the x-axis at (negative 2.2, 0), (negative 0.75, 0), and (0.75, 0), and crosses the y-axis at (0, 2).
The function that is positive for the entire interval [-3,-2] is given by:
On a coordinate plane, a curved line with a minimum value of (2, negative 3) crosses the x-axis at (negative 1, 0) and (5, 0), and crosses the y-axis at (0, negative 1.5).
When a function is positive and when it is negative?We have to look at the graph of the function relative to the x-axis, as follows:
A function is positive when it is above the x-axis.A function is negative when it is below the x-axis.The graphs for this function are given at the end of the answer, and the only function for which it is positive, that is, above the x-axis, in the entire interval [-3,-2] is the second, hence the correct option is:
On a coordinate plane, a curved line with a minimum value of (2, negative 3) crosses the x-axis at (negative 1, 0) and (5, 0), and crosses the y-axis at (0, negative 1.5).
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PLEASE HELP FAST I ONLY HAVE ONE HOUR!!!!!
The type of model that would be the most appropriate would be the exponential model: An exponential model is appropriate because the relationship between days and the natural log of views is linear, and the residual plot does not show a clear pattern.
What is an exponential model?This is the term that is used to refer to the process that is known to show a growth that is double its rate of growth. That is, it is used to show that there is the existence of a speed up in the rate at which the data is growing and it would follow a particular patter. This can be shown as: y = ab^x.
What is a scatterplot?This is the term that is used to show the graphical representation that is done by showing the existing relationship that exists between two variables in a graph. That would be the x variable and the y variable.
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You have 2 positive numbers. One number is one-fifth of the other number. The difference between the two numbers is 308, find the numbers. PLEASE HELP
Answer:
[tex]77, 385[/tex]
Step-by-step explanation:
Start by writing the equations in symbolic form. I will represent one number with an x and the other with a y.
One number is one-fifth of the other number:
[tex]x=\frac{1}{5}y[/tex]
The difference between the two numbers is 308:
[tex]y-x=308[/tex]
This difference is positive, therefore I am assuming that y is the larger number. In the first equation, I made x a part of y, so this should check out.
Now we have a system of equations:
[tex]\left \{ {{x=\frac{1}{5}y } \atop {y-x=308}} \right.[/tex]
I will rewrite the first equation for simplicity:
[tex]5x=y[/tex]
Now, I will substitute y from the first equation for y in the second equation:
[tex]5x-x=308[/tex]
Simplify:
[tex]4x=308\\x=77[/tex]
Now, use x to find y using the second equation:
[tex]y-77=308\\y=385[/tex]
Now, I can check the solutions by plugging them into the first equation!
[tex]x=\frac{1}{5}y\\ 77=\frac{1}{5}(385)\\77=77[/tex]
The solution is correct!
3 in
4 in
2 in What is the area of the shape?
Solve the following inequality algebraically.
x²-16x +60 ≥ 0
Answer:
[tex] \sf \large \: x≤6 \: or \: x≥10[/tex]
Step-by-step explanation:
Let's solve your inequality step-by-step.
x2−16x+60≥0
Let's find the critical points of the inequality.
x2−16x+60=0
(x−6)(x−10)=0(Factor left side of equation)
x−6=0 or x−10=0(Set factors equal to 0)
x=6 or x=10
Check intervals in between critical points. (Test values in the intervals to see if they work.)
x≤6(Works in original inequality)
6≤x≤10(Doesn't work in original inequality)
x≥10(Works in original inequality)
You are to move from A to B, always moving
right or down along the lines. On how many
different paths can you go? [The number of paths
from A to various intersections has been included.
Answer:
70
Step-by-step explanation:
You want the number of paths from corner to corner on a 5×5 grid with no backtracking.
Pascal's triangleThe geometry of the problem matches that of Pascal's triangle, attached.
In the attached figure, the value at each node is the sum of the values above and to the left. This matches the counting process for paths that can be used to get to any particular point on the grid: the total number of ways to get there is the sum of the ways it can be approached from above and the ways it can be approached from the left.
The given grid has some numbers filled in. If we continue to assign values to nodes that are the sum of the values above and to the left, we find the node values match the upper left 5×5 array of values in the attachment.
The value at the lower right corner of that array is 70. That is, ...
there are 70 ways to get from A to B.
__
Alternate solution
The path taken will always have 8 steps. Of those, 4 must be to the right, and 4 must be down. The number of ways we can choose 4 of those 8 steps to be steps to the right is "8 choose 4" ...
C(8,4) = 8!/(4!(8-4)!) = (8·7·6·5)/(4·3·2·1) = 70
Of course, using Pascal's triangle is simply another way to find the value of C(n,k).
Graph the following line
X=0
Answer:
the line runs that aligns with the y-intercept
Step-by-step explanation:
1 + ((-2 / 3) - ((-9 / 2)
Bryan, Michael, and Han are painting a house. Working together, they can paint the house in 6 hr. Working alone, Bryan can paint a similar sized house in 15 hr and Han can paint a similar sized house in 18 hr. How many hours would it take Michael to paint a similar sized house working alone? Enter the answer to the nearest tenth.
Answer:
Step-by-step explanation:
11x+90=15x
The computation shows that Michael will take 22.5 hours to paint a similar sized house working
How to compute the value?Based on the information given, the appropriate equation to use will be:
= 1/15 + 1/18 + 1/Michael = 1/6
Add the two fractions on the left
11/90 + 1/Michael = 1/6
1/Michael = 1/6 - 11/90
Take the reciprocal
Michael = 45/2
Michael= 22.5
Michael will take 22.5 hours.
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The telephone company offers two billing plans for local calls. Plan 1 charges $21 per month for unlimited calls and Plan 2 charges $15 per month plus $0.06 per call.
a. Use an inequality to find the number of monthly calls for which Plan 1 is more economical than Plan 2.
b. Explain the meaning of the answer to part a.
a. Let x represent the number of monthly calls.
Answer:
Step-by-step explanation:
The number of monthly calls for which Plan 1 is more economical than Plan 2 is 200 calls
If more than 200 calls are made, the plan 1 charge will be more than plan 2.
Let the number of charges per month be x
If plan 2 charges $16 per month plus $0.04 per call, this is expressed as 0.04x + 16
Price that pan 1 charges = $24
If Plan 1 is more economical than Plan 2, this is expressed as:
0.04x + 16 > 24
Subtract 16 from both sides:
0.04x + 16 - 16 > 24 - 16
0.04x > 8
x = 6/0.04
x = 200
This shows that if more than 200 calls are made, the plan 1 charge will be more than plan 2.
Write a function g whose graph represents the
indicated transformation of the graph of f.
f(x)=2x-9; translation 6 units up
The translated function is g(x) =
Answer: g(x)=2x-3
Step-by-step explanation:
f(x)=2x-9
g(x)=2x-9+6 ==> Translate 6 units up
g(x)=2x-3
The governor of state A earns $47,535 more than the governor of state B. If the total of their salaries is $299,115, find the salaries of each.
18. The length of a rectangle is 7 cm more than the width. The perimeter is 78 cm. Find the rectangle's dimensions. What would be the formula to solve this?
The length of the rectangle is 21 cm and the width is 16 cm.
What is a rectangle?A rectangle is a quadrilateral having four sides and the sum of the angles is 180 in the rectangle the opposite two sides are equal and parallel and the two sides are at 90-degree angles.
The perimeter of the rectangle is defined as the sum of all the sides of the rectangle.
The formula to calculate the perimeter is,
P = 2 ( L + W)
Here
P = Perimeter
L = length of the rectangle
W = Width of rectangle
Given that the length of a rectangle is 7 cm more than the width. The perimeter is 78 cm.
The equations can be formed as,
L = 7 + W
P = 2(L+W)
78 = 2 ( 7 + W + W )
39 = 7 + 2W
W = 32/2
W = 16 cm
L = 7 + W
L = 7 + 16 = 21 cm
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Write a one-variable equation or inequality with variables on both sides to describe the problem situation. Complete Steps 1 - 3 in order.
Two drones are descending from the sky in vertical lines. A black drone is currently at an altitude of 1,170 feet and is dropping at a rate of 64 feet per minute. A white drone is at an altitude of 966 feet and is dropping at a rate of 52 feet per minute. How many minutes will it take for the two drones be at the same altitude? Use the variable `n` to represent the unknown quantity.
The number of minutes that it will take for the two drones be at the same altitude is 17 minutes.
How to illustrate the information?It should be noted that ablack drone is currently at an altitude of 1,170 feet and is dropping at a rate of 64 feet per minute. The expression will be:
1170 - 64m
The white drone is at an altitude of 966 feet and is dropping at a rate of 52 feet per minute. This will be 966 - 52m where m = number of minute
Therefore, we will equate both equations. This will be:
1170 - 64m = 966 - 52m
Collect like terms
-64m + 52m = 966 - 1170
12m = 204
Divide
m = 204 / 12
m = 17
Therefore, the number of minutes that it will take for the two drones be at the same altitude is 17 minutes.
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I don't have many points but I will make brainliest, thank you !!
Answer: The answer for question 48. is -9, The answer for question 49. is 1/2, the answer for question 50. is -2.25, and for question 51 it's 4/5
Step-by-step explanation:
How to solve question 48
1/2(-12-6)-3(5-3)
-6+3-15+9
-3-6
-9
How to solve question 49
(20/2)+10/(-10+20+30)
10+10/40
20/40
1/2
How to solve question 50.
3/4(-15+4)+(8+7)/(-3)
-45/4+3+15/-3
-11.25+3+15/-3
6.75/-3
-2.25
How to solve question 51
5(7)-(3+4)/-2^2-2^2+3^2
35-7/4+4+27
28/35
4/5
Hope this helped owo
If Zendaya travels $5 and 3/7 of a mile in 3 hours on her roller skates. How far will she
travel in 1 hour?
1 and 17/21 miles per hour
7/114 miles per hour
114/7 miles per hour
16 and 2/7 miles per hour
Zendaya will travel $ 1 and 17/21 of a mile per hour on her roller skates.
Zendaya travels $5 and 3/7 of a mile in 3 hours on her roller skates. We can simply write this statement in mathematical form as,
Total distance covered by Zendaya in 3 hours on her roller skates = $( 5 + ( 3/7 ) of a mile
Total distance covered by Zendaya in 3 hours on her roller skates = $ ( ( 35 + 3)/7 ) of a mile
Total distance covered by Zendaya in 3 hours on her roller skates = $ ( 38/7 )
Total distance covered by Zendaya in 1 hours on her roller skates = $ (( 38/7 )/3 ) = $ (38/21) of a mile
or we can write also write ( 38 /21 ) miles per hour as ( 1 and 17/21 ) miles per hour.
So, Zendaya will travel $ 1 and 17/21 of a mile per hour on her roller skates.
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K
ZRQT is a straight angle. What are mZRQS and
mZTQS?
mZRQS=
mZTQS=
ICCEID
R
30% /
(15x + 1)º
(10x + 4)º
Answer:
m∠RQS = 106°m∠TQS = 74°===============================
Use angle addition postulate:
m∠RQT = m∠RQS + m∠TQSSubstitute the values and solve for x:
180 = 15x + 1 + 10x + 4180 = 25x + 5175 = 25xx = 175/25x = 7Find the angle measures:
m∠RQS = 15*7 + 1 = 106m∠TQS = 10*7 + 4 = 74You need to make 12 servings of fried fish. Each serving takes 7.5 ounces of flour. How many ounces of flour do you need?