Answers
Using equations of linear model function, the number of hours Jeremy wants to skate is calculated as 3.
How to Write the Equation of a Linear Model Function?The equation that can represent a linear model function is, y = mx + b, where m is the unit rate and b is the initial value.
Equation for Rink A:
Unit rate (m) = (35 - 19)/(5 - 1) = 16/4 = 4
Substitute (x, y) = (1, 19) and m = 4 into y = mx + b to find b:
19 = 4(1) + b
19 - 4 = b
b = 15
Substitute m = 4 and b = 15 into y = mx + b:
y = 4x + 15 [equation for Rink A]
Equation for Rink B:
Unit rate (m) = (39 - 15)/(5 - 1) = 24/4 = 6
Substitute (x, y) = (1, 15) and m = 6 into y = mx + b to find b:
15 = 6(1) + b
15 - 6 = b
b = 9
Substitute m = 6 and b = 9 into y = mx + b:
y = 6x + 9 [equation for Rink B]
To find how many hours (x) both would cost the same (y), make both equation equal to each other
4x + 15 = 6x + 9
4x - 6x = -15 + 9
-2x = -6
x = 3
The hours Jeremy wants to skate is 3.
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Related Questions
Suppose we write down the smallest (positive) $2$-digit, $3$-digit, and $4$-digit multiples of $7$.
What is the sum of these three numbers?
Answers
Step-by-step explanation:
Smallest two digit number which is multiple of 7 = 14 (7*2)
Smallest three digit number which is multiple of 7 = 105 (7*15)
Smallest four digit number which is multiple of 7 = 1001 (7*143)
Sum = 14+105+1001 = 1120.
The table shows a hot air balloon's height h , in feet, during a descent at various times t , in seconds.
Part A: Use the table's first two ordered pairs to find the hot air balloon's rate of change.
Part B: Is the rate of change constant? Explain.
Part C: What was the hot air balloon's height at the time the descent began?
Part D: Write , as a linear function of
.
Answers
Using a linear function, we have that:
A. The rate of change is of -12 feet per second.
B. The rate of change is constant.
C. The initial height is of 1210 feet.
D. The linear function is: h(t) = -12t + 1210.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.From the table, when x changes by 5 seconds, the height decreases by 60 feet, hence the slope is given by:
m = -60/5 = -12 feet per second.
Hence the function is:
h(t) = -12t + b.
When t = 5, h(t) = 1150, hence we use this to find the initial height.
h(t) = -12t + b.
1150 = -12(5) + b.
b = 1210.
Hence the linear function is:
h(t) = -12t + 1210.
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What is the ratio of 12 blue marbles and 20 red marbles
Answers
Answer:
12:20
Step-by-step explanation:
i hope the answer will help you
match each equation to one of the graphs
Answers
Answer:
I can only see one graph in that screenshot, so I graphed all of them. The one on your screenshot was B.
Based only on the information given in the diagram which congruence theorems or postulate could be given as reasons why LMN and OPQ
Answers
The congruence theorems or postulates could be given as reasons why LMN is congruent to OPQ are LA and AAS.
What is congruence theorems?Congruence theorems is one that explain that in a case whereby three sides of two triangles are equal to another, we can say they are congruent to each other.
From the given figure, there are two angles as well as one non-included side which is seen to be a congruent.
According to LA theorem , a triangle is congruent in a case whereby, leg as well as an acute angle of one right triangle of two right triangles are congruent to each other.
AAS theorem also explains that incase two angles and any of the side of a triangle are congruent to each other , the triangles are congruent.
Therefore, with these theorem, congruence theorems or postulates could be given as reasons why LMN is congruent to OPQ are LA and AAS.
CHECK THE FIQURE FOR THE COMNPLETE QUESTION
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Find the largest rational number r for which 5r ≤ 33.
Answers
Answer:
33/5 or 6.6
Step-by-step explanation:
Well the most 5r can be is 33, since it has the underline under it, so it's less than or equal to.
So set 5r equal to 33
5r = 33
Divide both sides by 33
r = 33/5
You can leave it in this form or convert it to a decimal which is 6.6
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation: }[/tex]
[tex]\mathsf{5r \leq 33}[/tex]
[tex]\huge\textbf{Simplifying it:}[/tex]
[tex]\mathsf{5r \leq 33}[/tex]
[tex]\huge\textbf{Divide \boxed{5} to both sides:}[/tex]
[tex]\mathsf{\dfrac{5r}{5}\leq \dfrac{33}{5}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{r \leq \dfrac{33}{5}}[/tex]
[tex]\mathsf{r \leq 6 \dfrac{3}{5}}[/tex]
[tex]\mathsf{r \leq 6.60}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{r \leq \dfrac{33}{5}}}[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
[tex]\large\textsf{The graph will be labeled down below for you :)}\downarrow[/tex]
Solve x 6x+2=2x-1 give your answer as a fraction in its simplest form
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathbf{6x + 2 = 2x - 1}[/tex]
[tex]\huge\textbf{SUBTRACT 2x to BOTH SIDES:}[/tex]
[tex]\mathbf{6x + 2 - 2x = 2x - 1 - 2x}[/tex]
[tex]\huge\textbf{Simplify it!}[/tex]
[tex]\mathbf{4x + 2 = -1}[/tex]
[tex]\huge\textbf{SUBTRACT 2 to BOTH SIDES:}[/tex]
[tex]\mathbf{4x + 2 - 2 = -1 - 2}[/tex]
[tex]\huge\textbf{Simplify it!}[/tex]
[tex]\mathbf{4x = -3}[/tex]
[tex]\huge\textbf{DIVIDE 4 to BOTH SIDES:}[/tex]
[tex]\mathbf{\dfrac{4x}{4} = \dfrac{-3}{4}}[/tex]
[tex]\huge\textbf{Simplify it!}[/tex]
[tex]\mathbf{x = \dfrac{-3}{4}}[/tex]
[tex]\mathbf{x = -\dfrac{3}{4}}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{x = -\dfrac{3}{4}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assigiment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]The table below shows the number of correct answers that students gave on a recent 5-question quiz. Which of the following statements is true? Number Correct 1 2 3 4 5 3 46 9 8 Frequency
Answers
The true statement about the number of correct answers is that the: A. median = mode.
How to calculate the mean?Mathematically, the mean for the number of correct answers can be calculated by using the following formula:
Mean = [F(x)]/n
Total frequency, n = 3 + 4 + 6 + 9 + 8 = 30.
F(x) = [(1 × 3) + (2 × 4) + (3 × 6) + (4 × 9) + (5 × 8)] = 105.
Mean = 105/30
Mean = 3.5.
For the median, we have:
The median for the number of correct answers is the average of the 15th and 16th number:
Median = (4 + 4)/2
Median = 8/2
Median = 4.
For the mode, we have:
The mode for the number of correct answers is the answer with the highest frequency, which is 4 with a frequency of 9.
Therefore, the true statement about the number of correct answers is that the median is equal to mode.
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Complete Question:
The table below shows the number of correct answers that students gave on a recent -question quiz. Which of the following statements is true?
A. median = mode
B. mode > median
C. mode < mean
D. mean > median Reset Selection
What are the medians for the height and weight distribution, respectively?
Answers
The median for height is: 167
The median for Weight is: 183
What is the Median of a Data Set?The middle value or the average of the two middle value of an ordered data set is the median of the data.
Given the following data:
Height: 178, 163, 174, 186, 154, 167, 167, 181, 159, 165, 177, 191, 158
Arranged in an ordered form, we would have:
54, 158, 159, 163, 165, 167, [167,] 174, 177, 178, 181, 186, 191
The middle value is 167. The median for height is: 167.
Weight: 157, 163, 190, 187, 183, 173, 184, 189, 193, 192, 177, 173, 168
Arranged in an ordered form, we would have:
157, 163, 168, 173, 173, 177, [183,] 184, 187, 189, 190, 192, 193
The middle value is 183. The median for weight is: 183.
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The difference......
Answers
Answer:
[tex] log_{7}(3) [/tex]
Step-by-step explanation:
According to the
Law of logarithms,[tex] log_{7}(18) \: - log_{7}(6) \\ \\ = \frac{ log_{7}(18) }{ log_{7}(6) } = log_{7}(3) [/tex]
use the interactive expression equivalent to 4x-4-2x+3.
Answers
Answer: x = 1/2
Step-by-step explanation:
4x - 2x - 4 + 3
2x - 1
x = 1/2
5. The function h(t) = 1 + 4t - 1.86t? models the height of a rock thrown upward on the planet Mars, where h(t) is height in meters and t is time in seconds. Use a graph to determine:
a. the maximum height the rock reaches
b. how long the rock will be above the surface
Answers
The maximum height the rock reaches 3.15 feet and the rock will be above the surface for 2.6 seconds
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
From the graph of the function h(t) = 1 + 4t - 1.86t²:
The maximum height the rock reaches 3.15 feet.
Time spent on air = 2.38 - (-0) = 2.38 seconds
The maximum height the rock reaches 3.15 feet and the rock will be above the surface for 2.6 seconds
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A rectangular prism with a base that is
5 inches by 4 inches and a height of 15 inches.
Answers
The surface area and the volume of the rectangular prism are 310 in² and 300 in³, respectively.
How to find the volume of a right rectangular prism?Suppose that the right rectangular prism in consideration be having its dimensions as 'a' units, 'b' units, and 'c' units, then its volume is given as:
V = a × b × c unit³
The surface area of the prism = 2[(5×4)+(15×4)+(15×5)]
= 310 inches²
The volume of the prism = 5 × 4 × 15
= 300 in³
Hence, the surface area and the volume of the rectangular prism are 310 in² and 300 in³, respectively.
The complete question is:
A rectangular prism with a base that is 5 inches by 4 inches and a height of 15 inches. Find the volume and the surface area of the rectangular prism?
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How many different strings can be made by shuffling the letters in DISCRETEMATHS?
Answers
Answer:
I found 14 but their might be more!
hope that helps! :)
Step-by-step explanation:
calculate the value of the sample variance of 13,−2,−2,−2,13,13,−5
Answers
Answer:
13, -2
Step-by-step explanation:
How many significant figures are in the measurement 1.050 l? a. 1 b. 2 c. 3 d. 4 please select the best answer from the choices provided a b c d
Answers
There are 4 significant figures in the measurement 1.050 (Option d)
What are significant figures?
Significant figures are the number of digits that add to the correctness of a value, frequently a measurement. The first non-zero digit is where we start counting significant figures. We can determine how many significant figures in a given numbers by counting the number of digits that are significant to indicate the quantity or value of something.
How the measurement 1.050 has 4 significant figures?
Since the quantity 1.050 starts with 1, that is a non-zero digit, we start counting the significant figures starting from this digit. Thus, 1 is the first significant digit here. 0, 5, and 0 are the second, third, and fourth significant digit respectively.
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Answer:
option D
Step-by-step explanation:
just took the test
Type the correct answer in each box. Use numerals instead of words. A group of students were surveyed about what they want to be when they grow up. The table provided shows the choices that the students made. Use the information in the table to answer the following questions. Round all answers to the nearest whole number. Teacher Doctor Athlete Boys 24 28 56 Girls 45 31 26 The marginal relative frequency of boys and girls who want to be a teacher is %. The joint relative frequency of girls who want to be an athlete is %. The conditional relative frequency of students that selected doctor, given that those students are boys is %.
Answers
The marginal relative frequency of boys and girls who want to be a teacher is 32 %. The joint relative frequency of girls who want to be an athlete is 25.4%. The conditional relative frequency of students that selected doctor, given that those students are boys is 51.85 %.
according to the question, the table given is
Teacher - Doctor - Athete
boys 24 28 56 Total boys = 108
girls 45 31 26 Total girls = 102
What is average?Average of the values is the ratio of total sum of values to the number of values.
Conditions
1) for boys and girls whom opt for teacher,
[tex]=\frac{69}{210} \\[/tex]
= 32%
2) for the girls who opt for athlete relative to girls,
[tex]=\frac{26}{102}[/tex]
= 25.4%
3) for the boys whom opt for doctors in boys
= [tex]\frac{28}{108}[/tex]
= 25.9%
Thus, The required values of conditions 1,2,3 is 32%, 25.4%, 25.9% respectively
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Answer:
the answer is 33. 12. and 26
Step-by-step explanation:
The function f(x) is graphed. It represents a translation of the square root function g(x) = .
What equation represents the graph of f(x)?
f(x) =
f(x) =
f(x) = – 1
f(x) = + 1
Answers
The equation that represents the graph of f(x) is [tex]f(x) = \sqrt {x - 1[/tex]
How to determine the equation of f(x)?The complete question is in the attached image
The parent square root function is:
[tex]g(x) = \sqrt x[/tex]
From the graph,
g(x) is shifted one unit right to get f(x)
This is represented as:
f(x) = g(x - 1)
So, we have:
[tex]f(x) = \sqrt {x - 1[/tex]
Hence, the equation that represents the graph of f(x) is [tex]f(x) = \sqrt {x - 1[/tex]
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Use the table to work out the values of a, b,
C, and d.
X
-3
-2
-1
0
1
2
3
y = 5x
—
a
3x² + 3
- 19
-5
3
b
C
d
Answers
Insert the -3 in the x’s in the equation on the top of the table
y= 5x -3x to the second power + 3
y= 5 (-3) -3(-3) to the second power + 3
Then continue to simplify the equation
y= -15 + 9 to the second power + 3
y= -15 + 84
y = 69
Y= 69 for the chart for -3
For b, c, and d insert the number in the x values and simplify like the previous equation.
If you are confused, feel free to ask questions. I hope this is effective and helps you in your studies.
During the first year of life, a whale gains about 30 tons of weight what is the average weight gain per month?
Answers
Step by step
We know 30 tons gained over 12 months
(1 year)
Divide total weight by 12 months to get average weight gain per month
30/12 = 2.5 tons per month
The square shown has a perimeter of 32 units. The square is rotated about line k. what is the circumfrence of the base
Answers
The circumference equal to 25 units
What is perimeter of square?The perimeter of square is 4 times the side.
P= 4* side
The perimeter of the square,
4x = P
Now P is = 32 units then,
32 units = 4(x)
x = 8 inches
So, the diameter of the cylinder formed by the rotation of 8 inches
Now, the circumference of the base is
C = 2πr = πD
If r =8 inches
C = π(8 units) = 8π units
C = 8(3.14) = 25.12 units
Hence, the circumference equal to 25 units
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-. A medical test has been designed to detect the presence of a certain disease. Among those who have the disease, the probability that the disease will be detected by the test is 0.95. However, the probability that the test will erroneously indicate the presence of the disease in those who do not actually have it is 0.04. It is estimated that 4% of the population who take this test have the disease .If the test administered to an individual is positive, what is the probability that the person actually has the disease? Suppose 20% of the people who were referred to a clinic for the test did in fact have the disease. If the test administered to an individual from this group is positive, what is the probability that the person actually has the disease?
Answers
Answer:
TV focusing urgency hangs amateur ushers sex tendency yachting
What is the domain indicated on the graph for each
portion of the piecewise function?
-2,
2x + 1,
--—-x,
f(x)=
Domain 1st piece
Domain 2nd piece
Domain 3rd piece
Answers
Step-by-step explanation:
try this option, all the details are in the attachment.
Two student clubs were selling t-shirts and school notebooks to raise money for an upcoming school event. In the first few minutes, club A sold 3 t-shirts and 2 notebooks, and made $19. Club B sold 1 t-shirt and 1 notebook, for a total of $8. Use the given matrix equation to solve for the cost of t-shirts and notebooks that were sold. Explain the steps that you took to solve this problem.
A matrix with 2 rows and 2 columns, where row 1 is 3 and 2 and row 2 is 1 and 1, is multiplied by matrix with 2 rows and 1 column, where row 1 is x and row 2 is y, equals a matrix with 2 rows and 1 column, where row 1 is 19 and row 2 is 8.
Answers
Using a system of equations, it is found that the cost of a t-shirt is of $3 and the cost of a notebook is of $5.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
The variables are given as follows:
Variable x: Cost of a t-shirt.Variable y: Cost of a notebook.Considering the costs of the purchases of Clubs A and B, the matrices give the equations as follows:
3x + 2y = 19.x + y = 8 -> y = (8 - x).Hence, replacing the second equation into the first:
3x + 2(8 - x) = 19
x = 3.
y = 8 - x = 8 - 3 = 5.
The cost of a t-shirt is of $3 and the cost of a notebook is of $5.
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2. What is the radius of a circle (rounded to the nearest tenth) that has a circumference of 87 cm?
O 10.5
27.7
13.8
5.3
Answers
3.
A = pi x r^2
48 = 3.141... x r^2
÷ by value of pi
15.278... = r^2
Square root the ans, to get r
Thus, R = 3.908..... So, radius is 3.9
2.
Circumference = pi x diameter
87. = 3.141... x d
÷ by value of pi
27.692............. = diameter
Radius is twice the diameter. So, divide diameter by 2 to find the radius.
27.692.....÷ 2 = 13.846...
Thus, radius is 13.8cm
Hope this helps!
A
<
Lennox had been scheduling employees based on the assumption that the
following distribution represented when people made purchases in his store.
Time slot
Predicted
percentage
8 a.m.-12 p.m.
25%
12-4 p.m.
40%
4-8 p.m. 8-12 a.m.
25%
10%
He took a random sample of 300 purchases and recorded their time slot so he
could test whether this was an accurate distribution. Here are his results:
Time slot 8 a.m.-12 p.m. 12-4 p.m. 4-8 p.m.
Purchases
75
120
90
Choose 1 answer:
8-12 a.m.
15
He wants to use these results to carry out a x² goodness-of-fit test to determine
if the distribution of time slots of the purchases disagrees with his assumed
distribution.
What are the values of the test statistic and P-value for Lennox's test?
Answers
The test value and the p value for the probability are 10.5 and 0.0148.
How to illustrate the probability?Based on the information, the observed and expected values will be:
Observed. Expected
75. 75
100. 120
90. 75
15. 30
The p value based on the test statistic from the distribution table will be 0.0148.
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Giselle works as a carpenter and as a
blacksmith.
She earns $20 per hour as a carpenter and
$25 per hour as a blacksmith. Last week,
Giselle worked both jobs for a total of 30
hours, and earned a total of $690.
How long did Giselle work as a
carpenter last week, and how long did
she work as a blacksmith?
Giselle worked as a carpenter for
hours and as a blacksmith for
hours last week.
Answers
Answer:
12 hours as a carpenter and 18 as a blacksmith.
Step-by-step explanation:
So she earns 20$ per hour as a carpenter. c can represent the amount of hours she worked as a carpenter, and the coefficient will be 20 (salary)
So she earns 25$ per hour as a blacksmith, b can represent the amount of hours she worked as a blacksmith, and 25 will be the coefficient (salary)
So we have the two equations:
c + b = 30
20c + 25b = 690
Now we can solve for c in terms of b and substitute that into the second equation:
Original equation:
c + b = 30
Subtract b from both sides
c = -b + 30
Original equation:
20c + 25b = 690
Substitute -b + 30 as c
20(-b + 30) + 25b = 690
Distribute the 20
-20b + 600 + 25b = 690
Simplify the equation
600 + 5b = 690
Subtract 600 from both sides
5b = 90
Divide both sides by 5
b = 18
Now plug this into either of the original equations to solve for c, but the first equation b + c = 30 is the easiest, so I'll use that equation
Original equation
b + c = 30
Substitute 18 as b
18 + c = 30
Subtract 18 from both sides
12 = c
•Mr. Jones and Mr. Thomas
entered into partnership
I with capital of $12600
and $19200 respectively.
after 3 months they!
were joined by Mr.Forson with a capital of $ 16200.It is agreed that the profit should be shared in proportion to their capitals.During the first 3 month of the year,………..
Answers
The profit should be shared in proportion to Mr Jones, Mr Thomas and Mr forson capitals in the ratio 21 : 32 : 27 respectively.
ProportionMr Jones capital = $12600Mr Thomas capital =$19200Mr forson capital = $16200Total capital = $12600 + $19200 + $16200
= $48,000
Mr Jones proportion = $12600 / $48,000
= 21/80
Mr Thomas proportion = $19200 / $48,000
= 32/80
Mr forson proportion = $16200 / $48000
= 27/80
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A freight train was supposed to travel 1300 miles in 50 hours. When the train had traveled 0.4 of this distance, it was delayed by 4 hours. What should the new speed of the train be to arrive on time?HELLPASAP
Answers
Answer:
The answer is 30 miles per hour
Step-by-step explanation:
1) From the question we can calculate the initial speed of the train
Initial speed = 1300 miles / 50 hours
= 26 miles / hour
2) Next, we can calculate the amount of distance already traveled:
Distance traveled = 1300 * 0.4
= 520 miles
3) Now let's calculate the amount of time it took to travel the 520 miles:
From point no. 1 we saw that it was traveling at the speed of 26 miles/ hour, so let's calculate the time elapsed.
Time elapsed = 520 miles / 26 hours
= 20 hours
But then again the text states the train was delayed by 4 hours, therefore the total time elapsed was 24 hours
4) Now to find the new speed required to arrive on time, we need to calculate how many hours and distance are left:
From point no. 2 we calculate the distance left
Distance left = 1300 - 520
= 780 miles
From point no. 3 we can calculate the amount of time left:
Time left = 50 - 24
= 26 hours
Finally, we can find the new speed required to arrive on time:
New speed = 780 miles / 26 hours
= 30 miles / hour
A rectangle has length of 10 mm. • and breadth 7mm calculate its perimeter YW
Answers
Answer:
34 mm
Step-by-step explanation:
P = 2 x (L + B) for a rectangle
P = 2 x (10 + 7) = 2 x 17 = 34