1/7 square units make up the entire area under the curve from x = 7 to infinity.
To find the area under the curve [tex]y = x^{-2}[/tex] from x = 7 to x = t, we can integrate the function with respect to x:
[tex]\int\limits^7_t x^{(-2)} dx = [-x^{(-1)}] = [-1/t + 1/7][/tex]
To evaluate this expression for t = 10 and t = 100, we substitute these values:
[-1/10 + 1/7] = 0.0428 (rounded to four decimal places)
[-1/100 + 1/7] = 0.1328 (rounded to four decimal places)
To find the total area under the curve from x = 7 to infinity, we can integrate the function with respect to x from 7 to infinity:
[tex]\int\limits^7_t {x} x^{(-2)} dx \\= [-x^{(-1)}] \\= [0 - (-1/7)] \\= 1/7[/tex]
Therefore, the total area under the curve from x = 7 to infinity is 1/7 square units.
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A restaurant manager recorded the number of people in different age groups who attended their food festival. They created the following histogram:
Histogram with title Food Festival Participants, horizontal axis labeled Age Group (year) with bins 0 to 19, 20 to 39, 40 to 59, and 60 to 79, and vertical axis labeled Number of People with values from 0 to 60 at intervals of 10. The first bin goes to 20, the second goes to 40, the third goes to 60, and the last goes to 50.
What percentage of the participants are ages 40 to 59? Round to the nearest whole percent.
Isosceles triangle LMN is graphed with vertices L(0, 1), M(3, 5), and N(6,1). What is the slope of side LN?
Negative StartFraction 4 over 3 EndFraction.
0
StartFraction 4 Over 3 EndFraction.
3
\
Lois is planning to retire from her job. She has been working there for 27 years. If she retires this year, her monthly pension will be calculated with a flat benefit formula using the flat amount of $52 for each year of
service. She was informed that if she works another 4 years that the flat amount would increase to $60 for each year of service. How much more would her pension be if she waited the 4 years?
If Lois is retiring from her job after 27 years, then if she waited for 4 years, her pension will be $38 higher than if she retires this year.
If Lois retires this year, the flat-amount is $52, So, her monthly pension can be calculated as follows;
⇒ Monthly pension = (52 × 27)/12,
⇒ Monthly pension = $117,
If Lois works for another 4 years, the flat amount used to calculate her monthly pension will increase to $60 for each year of service.
So, her monthly pension will be calculated as follows:
⇒ Monthly pension = (60 × 31)/12,
⇒ Monthly pension = $155,
So, The difference in monthly pension between retiring this year and retiring after working another 4 years can be calculated as follows:
⇒ Difference in monthly pension = $155 - $117,
⇒ Difference in monthly pension = $38,
Therefore, if Lois waits another 4 years before retiring, her monthly pension will be $38 higher than if she retires this year.
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Use the equation to answer ALL of the questions below.
f(x) = 2x² + 8x - 4
What is the axis of symmetry? You can use the equation
What is the vertex of the parabola (x, y)?
What is the y-intercept of the parabola?
Answer:
see explanation
Step-by-step explanation:
given a parabola in standard form
f(x) = ax² + bx + c ( a ≠ 0 )
then the equation of the axis of symmetry is
x = - [tex]\frac{b}{2a}[/tex]
f(x) = 2x² + 8x - 4 ← is in standard form
with a = 2, b = 8 , then equation of axis of symmetry is
x = - [tex]\frac{8}{2(2)}[/tex] = - [tex]\frac{8}{4}[/tex] = - 2
that is equation of axis of symmetry is x = - 2
the axis of symmetry passes through the vertex of the parabola
substitute x = - 2 into f(x) for corresponding y- coordinate
f(- 2) = 2(- 2)² + 8(- 2) - 4 = 2(4) - 16 - 4 = 8 - 20 = - 12
vertex = (- 2, - 12 )
the y- intercept is on the y- axis, where the x- coordinate is zero
substitute x = 0 into f(x)
f(0) = 2(0)² + 8(0) - 4 = 0 + 0 - 4 = - 4
y- intercept = - 4
Mark is running in a 13-mile race.He has run 5miles so far
The required Mark has completed 38.46% of the race.
To calculate the percentage of the race completed by Mark, we can divide the number of miles he has run by the total length of the race and then multiply by 100 to convert the result to a percentage.
So, Mark has run 5 miles out of a total of 13 miles:
Percentage of race completed = (5/13) x 100%
Calculating this expression, we get:
Percentage of race completed = 38.46%
Therefore, Mark has completed 38.46% of the race.
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Find the line parallel to y = -9x-1 that includes the point (2, -3). y- [?] = [?] ( x - [?])
Answer:
y + 3 = - 9(x - 2)
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 )
y = - 9x - 1 ← is in slope- intercept form
with slope m = - 9
• Parallel lines have equal slopes
then slope of parallel line is m = - 9
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
m = - 9 and (a, b ) = (2, - 3 ) , then
y - (- 3) = - 9(x - 2) , that is
y + 3 = - 9(x - 2)
You can use the notation P(A), read “the probability of event B, given event A” to write a
A. Probability distribution
B. Frequency table
C. Conditional probability
D. Cumulative probability
You can use the notation P(A), read “the probability of event B, given event A” to write a conditional probability. The correct answer is C.
Conditional probability refers to the probability of one event occurring given that another event has already occurred. In this case, we are interested in the probability of event B occurring given that event A has already occurred, and we can represent this using the notation P(B|A), where '|' means 'given'.
For example, let's say we are interested in the probability of getting a head on a coin toss (event B), given that the coin was flipped and landed on heads (event A). We could represent this using the notation P(B|A). The value of P(B|A) would be 1, because if the coin already landed on heads, then the probability of getting a head on the next flip is certain.
Conditional probability is an important concept in probability theory and is often used in real-world applications, such as predicting the likelihood of a disease given certain symptoms, or the probability of an event occurring given certain conditions.
The correct answer is C.
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Given that a function, h, has a domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25 and that h(8) = 19 and h(-2) = 2, select the statement that could be true for h. A. h(2) = 16 B. h(8) = 21 C. h(13) = 18 D. h(-3) = -1
The statement that could be true for h is h(2) = 16.
Option A is the correct answer.
We have,
The function h has a domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25, and we know that h(8) = 19 and h(-2) = 2.
To determine which statement could be true for h, we can use the given domain and range, along with the two known function values, to narrow down the possible values of h(x) for different values of x.
h(2) = 16
We do not have enough information to determine whether this statement could be true or not.
It is possible that h(2) = 16, but it is also possible that h(2) could be a different value within the range of 1 ≤ h(x) ≤ 25.
h(8) = 21
This statement cannot be true, as we already know that h(8) = 19.
h(13) = 18
This statement cannot be true, as 13 is outside the given domain of -3 ≤ x ≤ 11.
h(-3) = -1
This statement cannot be true, as -1 is outside the given range of 1 ≤ h(x) ≤ 25.
Therefore,
The statement that could be true for h is h(2) = 16.
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In this figure, FE←→
is parallel to AD¯¯¯¯¯
, and m∠A
= 158°. What is m∠FCA? m∠FCA
= °
Note that where the above conditions are given, m∠FCA is also = 158°. This is due to the principle of alternate angles.
What are alternate angles?A pair of angles that are created by a transversal intersecting two parallel lines, known as alternate angles, have key properties which contribute to their importance in geometry.
They take place on opposite sides of the transversal and have equal magnitudes.
These concepts aid in understanding vertical angles and parallel lines within geometrical systems.
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Answer: ur correct answer is 158
Step-by-step explanation: not doing this to tke points!!
What is the slope of the line that contains the points (−3, −1) and (3, −10)?
Undefined
0
negative two thirds
negative three halves
The slope of the line that contains the points (-3, -1) and (3, -10) is -3/2.
Given two points.
We have to find the slope of the line.
Slope of a line passing through (x, y) and (x', y') is,
Slope = (y' - y) / Ix' - x)
Here two points are,
(-3, -1) and (3, -10)
Slope = (-10 - -1) / (3 - -3)
= -9 / 6
= -3/2
Hence the slope of the line is -3/2.
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Vanilla rent increased by 5%. The increase was $82. What was the original amount of Pavati's rent?
Find the probability that a day in Dayton will include rain or snow.
The probability that a day in Dayton will include rain or snow is 38%.
Let's assume that there are 365 days in a year (not considering leap years), and we are aware that Dayton typically experiences 25 days of snow per year, in addition to 110 days of rain. We can add the total number of rainy and snowy days in Dayton and then divide that total by the number of days in a year to determine the likelihood that a given day will be either one of those things:
probability of rain or snow = [tex]\frac{110+25}{365}[/tex]
=0.38
The probability that a day in Dayton will have rain or snow is 0.38 or 38%.
The question is incomplete, complete question is " Dayton is a small town in Ohio, which receives 110 days of rain and 25 days of snow per year. Ignoring leap years, Find the probability that a day in Dayton will include rain or snow."
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Question 2: Perform the inverse Laplace transform of the following rational fractions using partial fraction expansion. List the procedures and verify the results with the MATLAB function "ilaplace". Attach the MATLAB codes and results. (1) F(s) = 5+1 ($2+28+2) (10 marks) (2) F(s) = s2+3+1 (s+2)(82+28+1) (10 marks)
(1) F(s) = 5+1 / (s^2 + 28s + 2)
To perform partial fraction expansion, we first need to factor the denominator:
s^2 + 28s + 2 = (s + 14 - sqrt(194))(s + 14 + sqrt(194))
We can then write:
F(s) = A / (s + 14 - sqrt(194)) + B / (s + 14 + sqrt(194))
where A and B are constants to be determined.
Multiplying both sides by the denominator and simplifying, we get:
5+1 = A(s + 14 + sqrt(194)) + B(s + 14 - sqrt(194))
Setting s = -14 - sqrt(194), we get:
5+1 = B(2sqrt(194))
Solving for B, we get:
B = (5+1) / (2sqrt(194))
Setting s = -14 + sqrt(194), we get:
5+1 = A(2sqrt(194))
Solving for A, we get:
A = (5+1) / (2sqrt(194))
Thus, the partial fraction expansion of F(s) is:
F(s) = [(5+1) / (2sqrt(194))] / (s + 14 + sqrt(194)) + [(5+1) / (2sqrt(194))] / (s + 14 - sqrt(194))
To find the inverse Laplace transform, we can use the table of Laplace transforms or MATLAB. Using MATLAB, we get:
ilaplace(F(s)) = (5+1) / (2sqrt(194)) * (exp(-14t) / sqrt(194)) * (cosh(sqrt(194)t) + sinh(sqrt(194)t))
(2) F(s) = s^2 + 3s + 1 / (s + 2)(s^2 + 8s + 1)
To perform partial fraction expansion, we first need to factor the denominator:
s^2 + 8s + 1 = (s + 4 - sqrt(15))(s + 4 + sqrt(15))
We can then write:
F(s) = A / (s + 2) + B / (s + 4 - sqrt(15)) + C / (s + 4 + sqrt(15))
where A, B, and C are constants to be determined.
Multiplying both sides by the denominator and simplifying, we get:
s^2 + 3s + 1 = A(s + 4 - sqrt(15))(s + 4 + sqrt(15)) + B(s + 2)(s + 4 + sqrt(15)) + C(s + 2)(s + 4 - sqrt(15))
Setting s = -4 + sqrt(15), we get:
-4 + sqrt(15) = A(-4 + sqrt(15) + 4 + sqrt(15))
Solving for A, we get:
A = (-4 + sqrt(15)) / (2sqrt(15))
Setting s = -4 - sqrt(15), we get:
-4 - sqrt(15) = A(-4 - sqrt(15) + 4 + sqrt(15))
Solving for A, we get:
A = (-4 - sqrt(15)) / (-2sqrt(15))
Setting s = -2, we get:
-1 = B(-2)(-2 + 4 + sqrt(15))
Solving for B, we get:
B = (-1) / (2sqrt(15) + 4)
Setting s =
John paid $270 for a new mountain bicycle to sell in his shop. He wants to price it so that he can offer a 10% discount but still make 30% of the price he paid for. At what price should the bike be marked $?
John should mark the bike at $390 to offer a 10% discount and still make a 30% profit on the price he paid for.
If John wants to make a 30% profit on the price he paid for the bike, he needs to sell it for:
$270 + 30% of $270 = $270 + $81 = $351
To offer a 10% discount on the marked price, he needs to calculate the price that includes the discount. Let's call this price "x".
90% of the marked price "x" is the same as the price he wants to sell the bike for ($351):
0.9x = $351
x = $390
Therefore, John should mark the bike at $390 to offer a 10% discount and still make a 30% profit on the price he paid for.
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128 3 мы - 5 20 14 ) 448 320 (20X14) 128 80 (5х16) 48 -48 (3 XI) vaku С
Use powers to rewrite these problems: Example: 5 x 5 = 52
a. 5 * 5 * x*x*x
b. 8*8*8 = 8^3
c. 4*4*4*x*x*x*x
Office Services An auto mechanic has total receipts of $1861.16 for a certain day. He determines that $1240 of this is labor. The remaining amount is for parts plus 6% sales tax on the parts only. Find the amount of the sales tax he collected.
The amount of sales tax he collected from the office services would be =$658.43
How to calculate the amount of sales tax?To calculate the amount of sales tax,the percentage tax amount should be determined as follows.
The total receipts from the office services = $1861.16
The amount that is for labor = $1240
The amount for parts = 1861.16-1240
= $621.16
The tax amount = 6/100 × 621.16
= 3726.96/100
= $37.27
Therefore the amount sale tax = 621.16+37.27 = $658.43
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I NEED THIS NOW 40 POINTS!!!!!!
Question 1 Part C (4 points): Showing the steps of your work, factor the polynomial from part B completely.
18x^3 + 6x^2y - 9x^2 - 3xy
(I already know the answer: 3x(3x + y) (2x − 1) I just need the work on how to get to the answer)
The polynomial 18x^3 + 6x^2y - 9x^2 - 3xy when factored completely is (6x^2 - 3x)(3x + y)
Factoring the polynomial completely.From the question, we have the following parameters that can be used in our computation:
18x^3 + 6x^2y - 9x^2 - 3xy
Factoize the expression
So, we have
6x^2(3x + y) - 3x(3x + y)
Factor out 3x + y
So, we have
(6x^2 - 3x)(3x + y)
Hence, the solution is (6x^2 - 3x)(3x + y)
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Which expression is equivalent to
1/sin(2x)-cos(2x)/sin(2x)?
The trigonometric expression 1/sin(2x) - cos(2x)/sin(2x) = tanx
What is a trigonometric expression?A trigonometric expression is an equation that contains trigonometric ratios.
Given the expression 1/sin(2x) - cos(2x)/sin(2x), we need to find the expression that is equivalent to it.
So, we proceed as follows.
1/sin(2x) - cos(2x)/sin(2x) = [1 - cos(2x)]/sin(2x),
Using the trigonometric identity cos2x = cos²x - sin²x and sin2x = 2sinxcosx, we have that
[1 - cos(2x)]/sin(2x) = [1 - (cos²x - sin²x)]/2sinxcosx
= [1 - cos²x + sin²x)]/2sinxcosx
Now, 1 - cos²x = sin²x.
So, substituting this into the equation, we have that
[1 - cos²x + sin²x)]/2sinxcosx = [sin²x + sin²x)]/2sinxcosx
= [sin²x + sin²x)]/2sinxcosx
= 2sin²x/2sinxcosx
= sinx/cosx
= tanx
So, 1/sin(2x) - cos(2x)/sin(2x),= tanx
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A bakery sold 107 cupcakes in one day. The head baker predicted he would sell 87 cupcakes that day. What was the percent error of the baker's prediction?
Answer:
First, we need to calculate the absolute error, which is the difference between the predicted value and the actual value:
Absolute error = |predicted value - actual value| = |87 - 107| = 20
Then, we can calculate the percent error using the formula:
Percent error = (absolute error / actual value) x 100%
Plugging in the values, we get:
Percent error = (20 / 107) x 100% ≈ 18.69%
Therefore, the percent error of the baker's prediction is approximately 18.69%.
Which prism has a volume between 38 and 48 cubic inches? Four prisms named A, B, C, and D. All the prisms are measured in cubic inches. Prism A has four rows, five columns, and two layers. Prism B has three rows, four columns, and three layers. Prism C has four rows, four columns, and one layer. Prism D has four rows, four columns, and six layers. A B C D
Answer:
To find the prism with a volume between 38 and 48 cubic inches, we need to calculate the volume of each prism and then compare it to the given range.
Prism A:
Number of cubes in prism A = 4 x 5 x 2 = 40
Volume of each cube = 1 cubic inch
Volume of prism A = Number of cubes x Volume of each cube = 40 x 1 = 40 cubic inches
Prism B:
Number of cubes in prism B = 3 x 4 x 3 = 36
Volume of each cube = 1 cubic inch
Volume of prism B = Number of cubes x Volume of each cube = 36 x 1 = 36 cubic inches
Prism C:
Number of cubes in prism C = 4 x 4 x 1 = 16
Volume of each cube = 1 cubic inch
Volume of prism C = Number of cubes x Volume of each cube = 16 x 1 = 16 cubic inches
Prism D:
Number of cubes in prism D = 4 x 4 x 6 = 96
Volume of each cube = 1 cubic inch
Volume of prism D = Number of cubes x Volume of each cube = 96 x 1 = 96 cubic inches
Therefore, the prism with a volume between 38 and 48 cubic inches is prism A, since its volume is 40 cubic inches which falls within the given range.
Step-by-step explanation:
Answer:
Prism A:
Number of cubes in prism A = 4 x 5 x 2 = 40
Volume of each cube = 1 cubic inch
Volume of prism A = Number of cubes x Volume of each cube = 40 x 1 = 40 cubic inches
Prism B:
Number of cubes in prism B = 3 x 4 x 3 = 36
Volume of each cube = 1 cubic inch
Volume of prism B = Number of cubes x Volume of each cube = 36 x 1 = 36 cubic inches
Prism C:
Number of cubes in prism C = 4 x 4 x 1 = 16
Volume of each cube = 1 cubic inch
Volume of prism C = Number of cubes x Volume of each cube = 16 x 1 = 16 cubic inches
Prism D:
Number of cubes in prism D = 4 x 4 x 6 = 96
Volume of each cube = 1 cubic inch
Volume of prism D = Number of cubes x Volume of each cube = 96 x 1 = 96 cubic inches
Therefore, the prism with a volume between 38 and 48 cubic inches is prism A, since its volume is 40 cubic inches which falls within the given range.
Step-by-step explanation:
Can you help me with this question?
A Ferris wheel has a diameter of 14 meters determine the distance to the nearest meter that a rider travels after 2 complete laps.
Answer:
88
Step-by-step explanation:
The distance traveled by a rider on a Ferris wheel can be calculated by finding the circumference of the wheel and then multiplying it by the number of complete laps.
The formula for the circumference of a circle is:
C = πd
where C is the circumference, d is the diameter, and π is a constant approximately equal to 3.14.
In this case, the diameter of the Ferris wheel is 14 meters, so the radius (half the diameter) is 7 meters.
C = πd = π(14) = 43.9823 meters (rounded to 4 decimal places)
To find the distance traveled after 2 complete laps, we need to multiply the circumference by 2:
distance = 2C = 2(43.9823) = 87.9646 meters
Rounding to the nearest meter, the distance traveled by a rider after 2 complete laps is 88 meters.
Everyone in the population must have an of being selected in order for a sample to be an
Answer: Everyone in your population must have an equal, non-zero chance of being selected. (In other words, everyone has an equal chance of receiving a survey.) You must know, specifically, what that chance of being selected is for each person.
∠A and ∠ � ∠B are vertical angles. If m ∠ � = ( 2 � − 2 ) ∘ ∠A=(2x−2) ∘ and m ∠ � = ( 3 � − 15 ) ∘ ∠B=(3x−15) ∘ , then find the value of x.
The calculated value of x if ∠A and ∠B are vertical angles is 13 degrees
How to find the value of x.From the question, we have the following parameters that can be used in our computation:
∠A = (2x − 2)
∠B = (3x − 15)
Since the ∠A and ∠B are vertical angles, then they are congruent angles
So, we have
3x - 15 = 2x - 2
Evaluate the like terms
So, we have
x = 13
Hence, the solution is x = 13
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Question 7
0 / 2 pts
On March 1, Imhoff Co. began construction of a small building. Payments of $267,596 were made monthly for several months. The payments begin on the first day of April; the last payment was made August 1. The building was completed and ready for occupancy on the first day of September. In determining the amount of interest cost to be capitalized, the weighted-average accumulated expenditures are
Y Correct Answer 334,495 margin of error +/- 5
The solution is : the weighted-average accumulated expenditures are $101,269.5.
Explanation:
Calculation to determine the weighted-average accumulated expenditures
Weighted-average accumulated expenditures=$202,539* (3/12 + 2/12 + 1/12)
Weighted-average accumulated expenditures=$202,539*0.5
Weighted-average accumulated expenditures=$101,269.5
Therefore In determining the amount of interest cost to be capitalized, the weighted-average accumulated expenditures are $101,269.5.
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Change this percent to a fraction
125%
Answer: 1[tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Divide using long division. The whole number portion will be the number of times the denominator of the original fraction divides evenly into the numerator of the original fraction, and the fraction portion of the mixed number will be the remainder of the original fraction division over the denominator of the original fraction.
3 A line passes through the point (-8, 9) and has a slope of 3/4
Write an equation in slope-intercept form for this line.
Answer:
y = 3/4x + 15
Step-by-step explanation:
Given;
A line passes through the point (-8, 9) and has a slope of 3/4
Question:
Write an equation in slope-intercept form for this line.
Solve:
Slope-intercept form ⇒ y=mx+b
Which-
m = Slopeb = y-intercepty and x = any point on the lineBased on the given;
m = 3/4b = ?y = 9x = -8Using slope intercept form to find y-intercept;
y=mx+b
9 = 3/4(-8) + b
9 = -6 + b
9+6 = -6+6 + b
b = 15
Therefore now we can write an equation.
y = 3/4x + 15
RevyBreeze
Let GH be the directed line segment beginning at point G(4,4) and ending at point H(-7,-1). Find the point P on the line segment that partitions the line segment into the segments GP and PH at a ratio of 5:6.
The coordinates of point P are (-1, 1 8/11).
We have,
G(4, 4) and H(-7, 1)
m :n = 5:6
Using Section formula
x = (mx₂ + nx₁)/ (m+n) and y = (my₂ + ny₁)/ (m+n)
Here, x₁ = 4, y₁ = -7, x₂ = 4 and y₂ = -1
So, x = (5(-7) + 6(4))/ 11 and y = (5(-1) + 6(4))/ 11
x = -35+24/11 and y = -5 + 24/11
x = -11/11 and y = -19/11
x = -1 and y = 1 8/11
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Hurry pls Time limit
Tell me the domain and the range
Tell me whether the graph is a function or not
The answer choices are below
Answer:
its not a function
Step-by-step explanation:
Carla does 25 jumping jacks 3 times per day. How many jumping jacks will Carla do in 7 days?
Answer: 525 jumping jacks
Step-by-step explanation:
she does 25 x 3 = 75 jumping jacks per day.
so in a week, (7 days) she will do 7 x 75 = 525 jumping jacks
