To make sure the flip is in unison after 4 seconds should the flip occur, as given by option C: 4 seconds.
We have given that,
Two gymnasts are running toward each other in a floor routine, and they plan to precisely time a flip to stay synchronized for the audience.
What does synchronized motion mean?Synchronized motion is a motion of two or more system which goes in synchronization with each other.
For this case, the flip will occur such that both gymnasts are synchronized and the flip is in unison (simultaneous).
For that, we need the time(x) and the height (y) same.
Since the motion paths are:
[tex]y=-(x-5)^2+3[/tex]
[tex]y=-3(x-3)^2+x+1[/tex]
Therefore, we need to find the values of x for which the same y comes as output.
Let x = t be the time for which the height y is the same, then:
[tex]-(t-5)^2+3=-3(t-3)^2+t+1[/tex] = height achieved by both gymnasts.
Solving it further:
[tex]-(t-5)^2+3=-3(t-3)^2+t+1[/tex]
t=4,t=1/2
Assuming they planned to do a flip after an integral number of time in seconds, the correct option is t = 4 seconds.
Thus, to make sure the flip is in unison after 4 seconds should the flip occur, as given by the option C: 4 seconds.
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pls help! i need an explanation and the steps that show how it’s solved too. tysm!
Answer:
true
Step-by-step explanation:
6(6(13x-2)
36(13x-2)
468x-72
please mark brainliest :D
Answer:
True
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=3x-7\\g(x)=13x-2\\h(x)=6x\end{cases}[/tex]
[tex]h(h(g(x)))[/tex] is a composite function.
Composite functions are when the output of one function is used as the input of another.
Therefore, the given composite function means to substitute the function g(x) in place of the x in function h(x), then substitute this in place of the x in function h(x).
Step 1
Substitute the function g(x) in place of the x in function h(x):
[tex]\begin{aligned}h(x) & = 6x\\\implies h(g(x)) & =6(g(x))\\& = 6(13x-2)\\ & = 78x-12\\\end{aligned}[/tex]
Step 2
Now substitute the above in place of the x in function h(x):
[tex]\begin{aligned}h(x) & = 6x\\\implies h \left(h(g(x))\right) & =6(h(g(x)))\\& = 6(78x-12)\\& = 468x-72\end{aligned}[/tex]
Therefore, the statement is true.
To carry out the composite function in one step:
[tex]\begin{aligned}h(x) &=6x\\\implies h(h(g(x))) & = 6\:(h(g(x)))\\& = 6(6(g(x)))\\& = 6( 6(13x-2))\\& = 6(78x-12)\\& = 468x-72\end{aligned}[/tex]
What method of matrixes would be used for this question? ( Inverse Matrices, Cramer's Rule, Gaussian Elimination, and Gauss-Jordan Elimination)
John had $24,500 to invest. He divided the money into three different accounts. At the end of the first year he had made a total of $1,300 in interest between the three accounts. If the first account earned 4% interest on its original amount for the year, the second account earned 5.5% interest on its original amount for the year, and the third account earned 6% interest on its original amount for the year. Also, the amount of money in the first account was 4 times the amount in the second account. How much had he originally placed in each account?
Answer:
The method of matrixes that would be used for this question is Gaussian Elimination.
Step-by-step explanation:
Gaussian Elimination is a method of solving linear equations by transforming them into upper triangular form. In this case, we want to solve for the original amount of money placed in each account, which can be represented by variables x, y, and z. We can set up the equations as follows:
4x + 5.5y + 6z = 1,300
x + y + z = 24,500
4x = y
We can then use Gaussian Elimination to solve for x, y, and z.
Which table matches the graph below
The table that matches the graph shown is the second table.
How to depict the table?It should be noted that in the graph, there's a quadratic equation. The form is given as ax² + bx + c.
When x = 0, y = 2. When x = 1, y is a number between 3 and 4. In the second table x we have y(1) = 7/2. This is in the range.
The graph is attached.
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A landscaping company is hired to mow the grass for several large properties. The total area of the properties combined is 1,345 acres. The rate at which one person can mow is as follows:
ŷ = 1350 – 1.2x where x is the number of hours and ŷ represents the number of acres left to mow.
How many acres will be left to mow after 20 hours of work?
How many acres will be left to mow after 100 hours of work?
How many hours will it take to mow all of the lawns? (When is ŷ = 0?)
Using the given linear function, we have that:
After 20 hours, 1326 acres will be left to mow.After 100 hours, 1230 acres will be left to mow.It will take 1125 hours to mow all the lawns.What is the linear function?
The linear function for the number of acres left to mow after x hours is given as follows:
y = 1350 - 1.2x.
After 20 hours, the number acres is given as follows:
y = 1350 - 1.2(20) = 1326.
After 100 hours, the number acres is given as follows:
y = 1350 - 1.2(100) = 1230.
The time it takes to mow all the lawns is given by:
1350 - 1.2x = 0.
1.2x = 1350
x = 1350/1.2
x = 1125 hours
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How many three-letter "words" can be made from 7 different letters "FGHIJKL" if...
a) Repetition of letters is allowed?
b) Repetition of letters is not allowed?
Answer:
343
Step-by-step explanation:
How many three-letter ”words” can be made from 7 letters FGHIJKL” if repetition of letters (a) is allowed? (b) is not allowed? Solution: (a) If repetition is allowed each letter can be any of the 7. So number ways is 7 × 7 × 7=73 = 343
Answer: See below
Step-by-step explanation:
Given:
The letters FGHIJKL
To find:
The number of three letter words can be formed if repetition is allowed (or) if repetition is not allowed
[tex]$$(a) If repetition is allowed:Total no of three letter words can be made$$=7_{C 1} x 7_{C 1} x 7_{C 1}=7^{3}=343$$(b) If repetitions is not allowed :Total no of three letter words can be made without repetition is $$\begin{gathered}=7_{C 1} \times 6_{C 1} \times 5_{C 1} \\=7 x 6 \times 5=210\end{gathered}$$[/tex]
Find the product of the given polynomials
(5r+8-6r)(4+2r-7)
A.2r^2+13r-24
B.-2r^2-24r+19
C.-2r^2+19r-24
D.2r^2+19r+24
Answer:
C
Step-by-step explanation:
(5r + 8 - 6r)(4 + 2r - 7) ← collect like terms inside each parenthesis
= (8 - r)(2r - 3)
each term in the second factor is multiplied by each term in the first factor.
8(2r - 3) - r(2r - 3) ← distribute parenthesis
= 16r - 24 - 2r² + 3r ← collect like terms
= - 2r² + 19r - 24
Translate and solve: the product of
p
and
−
2.5
is
4.8
Answer:
p = 7.3
Step-by-step explanation:
Equation: p - 2.5 = 4.8
add 2.5 to both sides:
P - 2.5 + 2.5 = 4.8 + 2.5
simplify
P = 7.3
hope that helps! :)
Given: 1.1 1.2 1.3 f(x) = 8 +4 x-8
Write down the domain and range off.
Write down the equations of the asympotes of f
Sketch the graph of f clearly showing the intercepts with the axes and the asymptotes.
Answer:
Did you mean " f(x)=8+4^{x-8} ? " The function you entered was linear, meaning there would be no asymptote.
D: (-∞, +∞)
R: (8, +∞)
Horizontal asymptote at y=8
No vertical asymptote
The volume of a fish tank is 50 cubic feet. if the density is 0.2 fish over feet cubed, how many fish are in the tank? 5 10 125 250
Answer: 10
Step-by-step explanation:
I just took the test!! :)
Write the augmented matrix of the system of equations given below. (10 points)
−2 + 2 − = −13
−3 − + = 7
− + 3 − 2 = 0
The augmented matrix of the system of equations is [tex]\left[\begin{array}{ccc}-2&2&-1\\-3&-1&1\\-1&3&-2\end{array}\right] \left[\begin{array}{c}13&7\\0\end{array}\right][/tex]
How to determine the augmented matrix?The system of equations is given as:
-2x + 2y - z = 13
-3x - y + z = 7
-x + 3y - 2z = 0
Remove the variables x, y and z
-2 2 -1 13
-3 -1 1 7
-1 3 -2 0
Express as matrix
[tex]\left[\begin{array}{ccc}-2&2&-1\\-3&-1&1\\-1&3&-2\end{array}\right] \left[\begin{array}{c}13&7\\0\end{array}\right][/tex]
Hence, the augmented matrix of the system of equations is [tex]\left[\begin{array}{ccc}-2&2&-1\\-3&-1&1\\-1&3&-2\end{array}\right] \left[\begin{array}{c}13&7\\0\end{array}\right][/tex]
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Complete question
Write the augmented matrix of the system of equations given below. (10 points)
-2x + 2y - z = 13
-3x - y + z = 7
-x + 3y - 2z = 0
if anyone knows how to answer this do so pleass
Answer:
x = 4.08
Step-by-step explanation:
As we now, from Trigonometric Identities
that [tex]tan(\alpha )=\frac{Opposite}{Adjacent}[/tex]So for our Problem , [tex]\alpha =27[/tex] , [tex]Opposite=x[/tex] , [tex]Adjacent = 8[/tex]
by substituting , then [tex]tan(27)=\frac{x}{8}[/tex]
by multiplying both sides by 8 , then [tex]x=8tan(27)=4.0762=4.08[/tex]
The area of the parallelogram below is ____ square meters. A parallelogram with height labeled with 7 meters. The top horizontal side is labeled 6 meters. The base of the left triangle formed by the height is 2 meters. Numerical Answers Expected
The area of the parallelogram in the image given is: 42 m².
What is the Area of a Parallelogram?Area of a parallelogram = base × height
Given the parameters:
Base = 6 metersHeight = 7 metersArea of the parallelogram = (6)(7)
Area of the parallelogram = 42 m²
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Taylor earned the following scores on her first ten quizzes. What would she need to earn on the eleventh test in order to have a mean score of 87? 78, 92, 98, 87, 86, 72, 92, 81, 86, 92
A mean is an arithmetic average of a set of observations. The score that Taylor needs to make in her eleventh test for the average to be 87 is 93.
What is Mean?A mean is an arithmetic average of a set of observations. it is given by the formula,
Mean = (Sum of observations)/Number of observations
The score earned by Taylor in her first 10 test are 78, 92, 98, 87, 86, 72, 92, 81, 86, 92. Also, she wants the average to be 87, therefore, we can write,
(78 + 92 + 98 + 87 + 86 + 72 + 92 + 81 + 86 + 92 + x)/11 = 87
864 + x = 957
x = 93
Hence, The score that Taylor needs to make in her eleventh test for the average to be 87 is 93.
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c. Divide 45 into three parts which are in A.P. Such that the pr oduct of last two is 300.
A fixed deposit receipt initiallypurchased for #1,500,000 for 4years has a maturity value of #1,300,000. What is the simple interest rate per year?
Answer:
11 3/13% per annum
Step-by-step explanation:
to find rate= 100×simple interest ÷ (principal ×time)
simple interest=total amount - principal
=1,500,000-1,300,000
=200,000
=200,000 ×100÷ 1,300,000×4
=3 11/13% per annum
What fraction of this shape is shaded?
Time
Running
Give your answer in its simplest form.
Find the area of the triangle if b = 8 inches and h = 4 inches
The area of triangle is 16 square inches.
what is Area of Triangle?Area of triangle is half times the product of base and height.
i.e., A-= 1/2 *b *h
Given:
b= 8 inches, h= 4 inches
Now, Area of triangle
= 1/2*b*h
= 1/2 * 8 *4
=1/2*32
=16.
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Which linear inequality is represented by the graph?
Answer:
y>2/3+3
Step-by-step explanation:
Answer:
y<2/3x+3
Step-by-step explanation:
1. Find the slope, the slope is 2/3
2. Find the y-intercept, the y intercept is 3
3. Make an linear equation out of it, y=2/3x+3
4. Dotted or solid? Its dotted which means the answer has to be greater or less than, not equal or less than or equal or greater than
5. Test you have 2 answer choices y<2/3x+3 or y>2/3x+3, input the origin (0,0)
0<2/3(0)+3, 0<3 which is true
0>2/3(0)+3 0>3 which is false
So y<2/3x+3 is the right answer. :)
What is the inverse of
F(x) =5x/3+ 5
The inverse function of f(x) = 5x/3 + 5 is f-1(x) = 3x/5 - 3
How to determine the inverse?The function is given as:
f(x) = 5x/3 + 5
Rewrite as:
y = 5x/3 + 5
Swap x and y
x = 5y/3 + 5
Subtract 5 from both sides
x - 5 = 5y/3
Multiply through by 3
3x - 15 = 5y
Divide through by 5
y = 3x/5 - 3
Express as inverse function
f-1(x) = 3x/5 - 3
Hence, the inverse function of f(x) = 5x/3 + 5 is f-1(x) = 3x/5 - 3
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!!HELP!! PLEASE I NEED THIS DONE IN AN HOUR IF ANYONE CAN HELP
Answer:
the 1st answer is x = 5, the 2nd answer is x = 7, the 3rd answer is x = 4, the 4th answer is: x = 4, the 5th answer is the exact form: x = - 1/3 but the decimal form is: x = - 0.3, the 6th answer is x = 3.
Brainliest?
The data below represents the relationship between the number of incidences of UFO sightings in late 1930s and early 1940s. Draw a scatter plot for the data.
Year of Incidence
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
Number of Incidences (percent)
0.9
0.8
0.8
1.3
1.4
1.2
1.7
1.8
1.6
1.5
1.5
a.
A graph has years of incidence on the x-axis from 1932 to 1948, and incidence on the y-axis, from 0 to 10. Points are around (1936, 0.9), (1937, 0.8), (1938, 0.8), (1939, 1.3), (1940, 1.4), (1941, 1.2), (1942, 1.7), (1943, 1.8), (1944, 1.6), (1945, 1.5), (1946, 1.5).
c.
A graph has years of incidence on the x-axis from 1932 to 1948, and incidence on the y-axis, from 0 to 10. Points are around (1936, 0.9), (1937, 0.8), (1938, 0.8), (1939, 1.3), (1940, 1.4), (1941, 1.2), (1942, 1.7), (1943, 1.8), (1944, 1.6), (1945, 1.5).
b.
A graph has years of incidence on the x-axis from 1932 to 1948, and incidence on the y-axis, from 0 to 10. Points are around (1936, 0.9), (1937, 1.7), (1938, 0.8), (1939, 1.3), (1940, 1.4), (1941, 1.2), (1942, 1.7), (1943, 1.8), (1944, 1.6), (1945, 1.5), (1946, 1.5).
d.
A graph has years of incidence on the x-axis from 1932 to 1948, and incidence on the y-axis, from 0 to 10. Points are around (1936, 0.9), (1937, 0.8), (1939, 1.3), (1940, 1.4), (1941, 1.2), (1942, 1.7), (1943, 1.8), (1944, 1.6), (1945, 1.5), (1946, 1.5).
The description of graph of the data about relationship of UFO sightings in late 1930s and early 1940s will be :A graph has years of incidence on the x-axis from 1932 to 1948, and incidence on the y-axis, from 0 to 10. Points are around (1936, 0.9), (1937, 0.8), (1938, 0.8), (1939, 1.3), (1940, 1.4), (1941, 1.2), (1942, 1.7), (1943, 1.8), (1944, 1.6), (1945, 1.5), (1946, 1.5).
Given:
Year of incidence percent
1936 0.9
1937 0.8
1938 0.8
1939 1.3
1940 1.4
1941 1.2
1942 1.7
1943 1.8
1944 1.6
1945 1.5
1946 1.5
We have been given the percentages of different years. The points will be (1936,0.9) , (1937,0.8) , (1938,0.8) , (1939,1.3) , (1940,1.4) , (1941,1.2) , (1942,1.7), (1943,1.8) , (1944,1.6) , (1945,1.5) , (1946,1.5).
We have to just plot the points on the graph to find scatter plot. It is called scatter plot as the points are not in line but they are scattered.
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Barn Yard Inc. is a wholesaler that stocks engine components and tests equipment for the commercial aircraft industry. A new customer has placed an order for eight high-bypass turbine engines, which increase fuel economy. The variable cost is $1.6 million per unit, and the credit price is $1.725 million each. Credit is extended for one period, and based on historical experience, payment for about one out of every 200 such orders is never collected. The required return is 1.8% per period.Suppose that customers who don’t default become repeat customers and place the same order every period forever. Further assume that repeat customers never default.
The NPV is positive, therefore, this order can be placed.
How to calculate the NPV?The calculation of probability of default will be:
= 1 / 200 = 0.005
We use NPV formula to find out whether the order should be filled or not
NPV = -Variable cost per unit +[(1-π)(price of equipment/1+percentage of return)]
= -$1.6 million +[(1-0.005)($1.725m/1.018)]
= -$1.6m + $1.6860
= 0.0860 million
As NPV is positive this order can be placed.
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Word problem involving conversion between compound units...
A business based in South Africa pays a consultant in the U.S. 1,570,000 rand per year. Assume that the conversion is 1 rand to 0.074 dollars. What is the
consultant's salary in dollars per month?
First fill in the two blanks on the left side of the equation using two of the ratios. Then write your answer rounded to the nearest hundredth on the right side o
the equation.
Ratios:
1 rand
0.074 dollars
1,570,000 rand
1 yr
0.074 dollars
1 rand
1 yr
12 mo
0
0
I need help with this math problem.
Using proportions, it is found that the consultant's salary in dollars per month is of $9,681.67.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
A business based in South Africa pays a consultant in the U.S. 1,570,000 rand per year. Considering the conversion rate, his salary in dollars per year is given as follows:
S = 1570000 x 0.074 = $116,180.
Since a year has 12 months, his salary in dollars per month is given by:
Sm = $116,180/12 = $9,681.67.
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using this diagram, find x and y
Answer:
x=13
y=11
Step-by-step explanation:
3y+5+52=90
3y=90-57
3y=33
y=33/3=11
4x=52
x=52/4=13
3y+5 and 52 are complementary
3y+5+52=903y+57=903(y+19)=90y+19=30y=11Apply angle sum property
4x+3(11)+5+90=1804x+33+5=904x+38=904x=52x=13A boat is heading towards a lighthouse, whose beacon-light is 148 feet above
the water. The boat's crew measures the angle of elevation to the beacon, 8°.
What is the ship's horizontal distance from the lighthouse (and the shore)?
Round your answer to the nearest hundredth of a foot if necessary.
Answer:
feet
Submit Answer
attempt 1 out of 2 / problem 2 out of max 4
Answer:
x = 1053.07 ft
Step-by-step explanation:
So if you look at the diagram I drew it might become a bit more apparent what you have to do. For this problem you'll need to use one of the six trigonometric functions. In this case you know the angle and the opposite side of the angle, and you need the adjacent side. The trigonometric function tan is defined as [tex]\frac{oppposite}{adjacent}[/tex]. So let's plug in the known values:
[tex]tan(8) = \frac{148}{x}[/tex]
multiply both sides by x
[tex]tan(8) * x = 148[/tex]
Divide both sides by tan(8)
[tex]x=\frac{148}{tan(8)}[/tex]
Calculating tan of 8 degrees using a calculator
[tex]x=\frac{148}{0.141}[/tex]
Simplify
x = 1053.07 ft
Order the quotients of these expressions from least to greatest.
42.6 ÷ 70
42.6 ÷ 0.7
426 ÷ 70
42.6 ÷ 0.07
Please answer all parts as I know the answers but need the work to go with them. Thus, I believe some answers are correct. Thank you!
The approximate 95 % confidence interval for p is found by the formula
p^ ± Z∝/2 √p^q^/n
The sample size n can be found by the
The formula
n= (Z∝/2)² p^q^/e²
The approximate 95 % confidence interval for p is 0.165; 0.243
This indicates 95 % confidence interval level.
A sample of 6239 nonprofits should be surveyed
Solution
Part a:
Sample Proportion p^= 84/412= 0.2038 ≅ 0.204
q^ = 1-p^= 1.0 -0.204= 0.796
The degree of confidence is 95% so z∝/2= 1.96
Putting the values
p^ ± Z∝/2 √p^q^/n
0.204 ± 1.96 √0.204(0.796)/ 412
0.204 ± 0.0389
0.1650 ; 0.2429
0.165; 0.243
The approximate 95 % confidence interval for p is 0.165; 0.243
Part B
This indicates 95 % confidence interval level.
Part C
With ± 0.01 of 0.95 Confidence interval gives range 0.94 to 0.96
For 0.96 interval Z∝/2 = 2.054
For 0.94 interval Z∝/2 = 1.8808
and error e= 0.01
For solving n the formula is
n= (Z∝/2)² p^q^/e²
and e= 0.01
Putting the values
n= 1.96²(0.204)(0.796)/ 0.01²
n= 6238.1437≅ 6238.14
A sample of 6239 nonprofits should be surveyed.
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If the cost of 5m of cloth is Rs 375,find the cost of 80m of cloth
Step-by-step explanation:
If the cost of 5m cloth is Rs.375
Then cost of 80m cloth is (80m× Rs 375)÷ 5m
then the cost of is 6000 Rs. you can use the criss cross method
5m = 375 Rs
80m = ?
80 × 375 = (30,000) ÷5
?= 6000
Divide. Write the quotient in lowest terms.
Answer:
11/12
Step-by-step explanation:
2 3/4 ÷ 3
11/4 ÷ 3
11/4 × 1/3
11/12
Answer:
Hello! The answer is 11/12.
Step-by-step explanation:
Convert improper fractions:
[tex]2\frac{3}{4} \\= \frac{11}{4}[/tex]
Change 3 to its reciprocal:
[tex]\frac{1}{3}[/tex]
Multiply:
[tex]\frac{11}{4} * \frac{1}{3} \\= 11/12[/tex]
A line passes through the point (8, -1) and has a slope of
Write an equation in slope-intercept form for this line.
The equation in slope intercept form is y = - 1 / 4 x + 1
How to find the slope intercept equation?Using slope intercept form,
y = mx + b
where
m = slopeb = y-interceptTherefore,
m = - 1 / 4
it passes through (8, -1)
Hen e,
-1 = - 1 / 4 (8) + b
-1 = - 2 + b
b = -1 + 2
b = 1
Therefore,
y = - 1 / 4 x + 1
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