A rectangular prism has a volume of 384 cubic inches. Find the height of the prism.h= ____ in
Answers
Rectangular prism volume: base length x base width x height
By looking at the image we can see that the height of the prism is 13cm.
To obtain the result in inches, divide by 2.54
13/2.54 = 5.12 inn inche
Related Questions
if the bug can come crawl at a rate of 0.107 VUUNITS/seconds, how long would it take the bug to travel from corner A to corner B
Answers
Given :
The dimensions of the Box
Length = 23.5 , Width = 24 , Height = 31.5
Task 1 :
The distance from A to B =
[tex]\sqrt[]{23.5^2+24^2+31.5^2}=\sqrt[]{2120.5}=46.05[/tex]The bug fly at a rate of 0.519 Vunits/sec
So, the time of flying = distance/speed = 46.05/0.519 = 88.73 seconds
Task 2 :
The distance from A to B = 46.05 VUNITS
The bug crawl at a rate of 0.107 VUNITS/sec
So, the time of crawling = 46.05/0.107 = 430.36 seconds
A direct variation includes the points (6, 18) and (n, -3). Find n.
Answers
Since we have a direct variation, we can use the following equation:
[tex]\frac{y}{x}=k[/tex]where k is the constant of variation.
If we use the point (6,18), then, we have:
[tex]\begin{gathered} (x,y)=(6,18) \\ \Rightarrow\frac{18}{6}=k \\ \Rightarrow k=3 \end{gathered}[/tex]now that we have that the constant of variation is k = 3, we can use this information to find n:
[tex]\begin{gathered} (x,y)=(n,-3) \\ k=3 \\ \Rightarrow-\frac{3}{n}=3 \\ \Rightarrow-3=3\cdot n \\ \Rightarrow n=-\frac{3}{3}=-1 \\ n=-1 \end{gathered}[/tex]therefore, n = -1
help me with this please
1. Create a graph of the function G(t) and explain the meaning of the y-intercept in terms of the number of smartphones being shipping to stores.
2. Explain a way you could calculate exactly when smartphone manufacturers were shipping 500 million smartphones to stores around the world.
Answers
The y-intercept indicates that 174 million smartphones were shipped to stores in 2009. This implies that after two years, in 2011, smartphone manufacturers shipped 500 million smartphones to stores worldwide.
Since 2009 the number of smartphones shipped from manufacturers to stores around the world has increased exponentially.
The growth from 2009 through 2015 can be modeled using the function G(t) = 174·[tex]1.67^t[/tex] where t is the number of years since 2009 and G(t) is measured in millions of smartphones.
The required graph of the exponential function G(t) has been attached below
Now, finding the y-intercept
G(t) = 174·[tex]1.67^t[/tex] ...(i)
Substitute the value of t = 0 in the above function,
G(t) = 174·1.67⁰
G(t) = 174(1)
G(t) = 174
The meaning of the y-intercept is that 174 million smartphones are being shipped to stores in years 2009.
Substitute the value of G(t) =500 in the exponential function(i),
500 = 174·[tex]1.67^t[/tex]
500/174 = [tex]1.67^t[/tex]
2.8735 = [tex]1.67^t[/tex]
[tex]\ln \left(2.8735\right)=t\ln \left(1.67\right)[/tex]
[tex]t=\dfrac{\ln \left(2.8735\right)}{\ln \left(1.67\right)}[/tex]
t = 2.05827 ≈ 2
This means after 2 years i.e. in 2011, smartphone manufacturers were shipping 500 million smartphones to stores around the world.
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12x8.05 Help me with the problem
Answers
HELP ME I'LL GIVE YOU ALL OF MY POINTS (85) Which form of political participation includes walking in the streets with banners? (2 points)
a
Petition
b
Protest
c
Running for public office
d
Writing letters to officials
Question 2 (2 points)
(04.05 LC)
Who was chosen as the main writer of the Declaration of Independence? (2 points)
a
Benjamin Franklin
b
John Adams
c
Roger Sherman
d
Thomas Jefferson
Question 3 (2 points)
(04.05 LC)
What does the introduction of the Declaration of Independence explain? (2 points)
a
The amount of taxes people pay
b
The living conditions of the poor
c
The natural rights everyone has
d
The route from Philadelphia to New York
Question 4 (2 points)
(04.05 LC)
How does the Declaration of Independence end? (2 points)
a
With a final statement that the Thirteen Colonies are now free from British rule
b
With a list of British town names in the colonies
c
With a list of families from the Mayflower
d
With a suggestion on how to make things better between the colonies and Britain
Question 5 (2 points)
(04.05 LC)
Who was the first person to sign the Declaration of Independence? (2 points)
a
George Washington
b
John Hancock
c
Robert R. Livingston
d
Thomas Paine
Question 6 (2 points)
(04.05 LC)
What did King George III place in the colonies without their permission even during times of peace? (2 points)
a
British coal
b
British troops
c
Plum pudding
d
Spanish cattle
Question 7 (2 points)
(04.05 LC)
Which of these grievances is included in the Declaration of Independence? (2 points)
a
Britain controls who the colonies can trade with.
b
Britain tells the colonies how to build their homes.
c
King George III has never visited the colonies.
d
King George III should wear a silver crown.
Question 8 (2 points)
(04.05 LC)
What does the list of grievances in the Declaration of Independence describe? (2 points)
a
Important towns in the British colonies
b
Places King George III had visited in Britain
c
Ways King George III had violated colonists' rights
d
Ways the government of Britain could be kinder
Question 9 (2 points)
(04.05 LC)
What is political participation? (2 points)
a
Being involved in activities that help decide how a town, state, or country is structured and runs
b
Being involved in local theater and helping promote the plays by placing posters around town
c
Choosing what to wear to go to work or school
d
Doing chores at home to receive an allowance
Question 10 (2 points)
(04.05 LC)
What were Patriots doing that was considered treason against Britain? (2 points)
a
Going to church once a month
b
Planting French lavender in their gardens
c
Selling British tea at the market
d
Talking about independence from Great Britain
Answers
Answer:
1. Protest
2. Thomas Jefferson
3. The natural rights everyone has
4. With a final statement that the Thirteen Colonies are now free from British rule
5. John Hancock
6. British troops
7. Britain controls who the colonies can trade with.
8. Ways King George III had violated colonists' rights
9. Being involved in activities that help decide how a town, state, or country is structured and runs
10. Talking about independence from Great Britain
On this problem, the answer has been worked out, but you must fill in the blanks in the solution.A study of carbon monoxide deaths showed that a random sample of 6 recent years had a standard deviation of 4.1 deaths per year. Find the 99% confidence interval of the variance and the standard deviation. Round answers to the nearest tenth (one digit after the decimal point).Solution: We are finding confidence intervals for the variance and standard deviation, so we use the formulas
Answers
You have to calculate the confidence interval for the population variance and population standard deviation of carbon monoxide deaths.
To calculate the confidence interval for the population variance you have to use the following formula, which is derived from the Chi-Square distribution:
[tex]\lbrack\frac{(n-1)S^2}{\chi^2_{n-1;1-\frac{\alpha}{2}}};\frac{(n-1)S^2}{\chi^2_{n-1;\frac{\alpha}{2}}}\rbrack[/tex]For a sample of n=6 years, the sample standard deviation is S=4.1 deaths per year
To calculate the interval, the first step is to determine the values under the Chi-Square distribution with n-1 degrees of freedom and a confidence level of 0.99
The degrees of freedom for this particular distribution is:
[tex]n-1=6-1=5[/tex]The confidence level is 0.99, calculate the value of α:
[tex]\begin{gathered} 1-\alpha=0.99 \\ \alpha=1-0.99 \\ \alpha=0.01 \end{gathered}[/tex]For the chi-Square value of the left bound, the value of probability is
[tex]1-\alpha/2=1-0.01/2=1-0.005=0.995[/tex]The Chi-Square value for the left bound of the interval corresponds to a distribution with 5 degrees of freedom and 0.995 of accumulated probability
[tex]\chi^2_{5;0.995}=16.8[/tex]So the value of the distribution for the left bound is χ²left= 16.8
For the right bound of the interval, the accumulated probability under the distribution is α/2
[tex]\frac{\alpha}{2}=\frac{0.01}{2}=0.005[/tex]The Chi-Square value for the right bound of the interval is for distribution with 5 degrees of freedom and 0.005 accumulated probability:
[tex]\chi^2_{5;0.005}=0.412[/tex]The value of the distribution for the right bound is χ²right= 0.412
The sample variance is equal to the square of the sample standard deviation so that:
[tex]\begin{gathered} S^2=4.1^2 \\ S^2=16.81 \end{gathered}[/tex]Now you can calculate the confidence interval as follows:
Left bound of the interval
[tex]\frac{(n-1)S^2}{\chi^2_{5;0.995}}=\frac{(6-1)16.81}{16.8}=5.00[/tex]Right bound of the interval
[tex]\frac{(n-1)S^2}{\chi^2_{5;0.005}}=\frac{(6-1)16.81}{0.412}=204.00[/tex]The calculation of the interval can be written as follows:
[tex]\frac{(6-1)4.1^2}{16.8}\leq\sigma^2\leq\frac{(6-1)4.1^2}{0.412}[/tex]So, using a 99% confidence level, the interval for the population variance of the carbon monoxide deaths is [5.00;204.00] deaths per year²
Finally, apply the square root to both bounds of the interval to determine the confidence interval for the population standard deviation:
[tex]\begin{gathered} \sqrt[]{\frac{(6-1)4.1^2}{16.8}}\leq\sigma\leq\sqrt[]{\frac{(6-1)4.1^2}{0.412}} \\ \sqrt[]{\frac{5\cdot16.81}{16.8}}\leq\sigma\leq\sqrt[]{\frac{5\cdot16.81}{0.412}} \\ 2.236\leq\sigma\leq14.283 \\ \end{gathered}[/tex]Rounding to the nearest tenth the interval can be expressed as follows
[tex]2.2\leq\sigma\leq14.3[/tex]Using the same confidence level the confidence interval for the population standard deviation is [2.2;14.3] deaths per year.
find the value of the expression 4a + 7 when a equals 1/2
Answers
Answer:
9
Explanation:
Given the expression:
[tex]4a+7[/tex]When the value of a =1/2
[tex]\begin{gathered} 4a+7=4(\frac{1}{2})+7 \\ =2+7 \\ =9 \end{gathered}[/tex]The value of the expression when a=1/2 is 9.
please check my answer i need help asap!
Answers
Answer:
The answer would be Domain: 6; Range: -8, -2, 0, and 3; so, The answer is B
Step-by-step explanation:
Domain is what x can be, while range is what y can be. We are only given four points: (6, -8), (6, -2), (6, 0), and (6, 3). The only x value to appear is 6, and the only y values to appear are -8, -2, 0, and 3. So, the domain is just 6, and the range is -8, -2, 0, 3
Mark’s method is correct, because even though it is impossible to deliver mail to 1.2 houses in a minute, 1.2 represents the unit rate of houses per minute.
Answers
Although it is impossible to send mail to 1.2 homes in a minute, Mark's solution is valid since 1.2 corresponds to the unit rate of homes per minute.
What is the mark's method?When reset() is performed, the stream is marked as the checkpoint from which the stream read will begin in Java by using the mark() function of the Reader class.
Option 1: Mark's approach is incorrect since there is no way to distribute mail to 1.2 homes in a minute. Only a certain amount of homes can get deliveries from the carrier.
This is untrue because the rate of 1.2 just indicates that the carrier may complete one house in a minute while still having time to begin delivering to the second residence. While the rate is not required, the total number of houses must be a whole number.
Option 2: Mark's approach is incorrect since mail cannot be delivered for 7.5 minutes. Mail delivery by the carrier is limited to a set number of minutes.
Furthermore erroneous is this choice.
Option 3: Mark's approach is accurate because, not with standing the impossibility of delivering mail to 1.2 homes in a minute, 1.2 corresponds to the average number of homes every minute.
This choice is the best one. The mail is delivered by the carrier at a rate of 1.2.
Option 4: Mark's approach is accurate because he can deliver mail for 7.5 minutes, which corresponds to the unit rate of 7.5 minutes per dwelling.
Furthermore erroneous is this choice. Although it is feasible to transport mail for 7.5 minutes, this is the overall time required, not the unit rate.
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Complete question is" A mail carrier can deliver mail to 36 houses in 30 minutes. Mark wants to determine how many houses the carrier can deliver mail to in 7.5 minutes at this rate. He thinks that to find the answer, he should do the following. 1. First divide 36 houses by 30 minutes to find a unit rate of 1.2 houses per minute. 2. Then multiply 1.2 houses per minute by 7.5 minutes to get 9 houses. Which statement is correct? Mark’s method is wrong, because it is impossible to deliver mail to 1.2 houses in a minute. The carrier can only deliver to a whole number of houses. Mark’s method is wrong, because it is impossible to deliver mail for 7.5 minutes. The carrier can only deliver mail for a whole number of minutes. Mark’s method is correct, because even though it is impossible to deliver mail to 1.2 houses in a minute, 1.2 represents the unit rate of houses per minute. Mark’s method is correct, because it is possible to deliver mail for 7.5 minutes; 7.5 represents the unit rate of 7.5 minutes per house."
I really need help with this
Answers
The mean for the girls as a percentage of the mean for the boys is 160 percent .
What is mean in mathematic?
In mathematics, the mean is the product of the sum of the added values of all the data in a set and the number of data in the set.
We know that, the formula for the calculation of mean is:
Mean = sum of terms / number of terms
Number of terms is given as 40. Whereas the sum obtained as follows:
Boys with average spent 10 is 18: 10(18) = 180
Boys with average spent 30 is 9: 30(9) = 270
Boys with average spent 50 is 7: 50(7) = 350
Boys with average spent 70 is 6: 70(6) = 420
So, the total sum of terms equals to: 180 + 270 + 350 + 420 = 1220
Therefore the mean is:
Mean = 1220/40
Mean = 30.5
Now, calculating the mean for the girls as a percentage of the mean for the boys:
Mean for the girls given is : 48.80
So,
Percentage = (amount*100)/total amount
Percentage = (48.80(100))/30.5
Percentage = 160 %
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Please help me with this I do not understand. I did the steps but am really looking for the answer if you could help.
Answers
ANSWER :
The zeros are 1/2 and -5
EXPLANATION :
From the problem, we have the function :
[tex]f(x)=2x^2+9x-5[/tex]The zeros of the function are the values of x when f(x) = 0
[tex]2x^2+9x-5=0[/tex]Using quadratic formula with a = 2, b = 9 and c = -5
[tex]\begin{gathered} x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ \\ x=\frac{-9\pm\sqrt{9^2-4(2)(-5)}}{2(2)} \\ \\ x=\frac{-9\pm\sqrt{81+40}}{4} \\ \\ x=\frac{-9\pm\sqrt{121}}{4} \\ \\ x=\frac{-9\pm11}{4} \\ \\ x=\frac{-9+11}{4}=\frac{1}{2} \\ \\ x=\frac{-9-11}{4}=-5 \end{gathered}[/tex]I'll send a pic ! I need a rlly fast response !!
Answers
The expression given is:
[tex](3^3\cdot3^{-1})^{-2}[/tex]One property of exponents that we know is:
[tex]a^xa^y=a^{x+y}[/tex]We use this property shown above to simplify the expression:
[tex]\begin{gathered} (3^3\cdot3^{-1})^{-2} \\ =(3^{3-1})^{-2} \\ =(3^2)^{-2} \end{gathered}[/tex]Now, we use the power property of exponents, which is:
[tex](a^b)^c=a^{bc}[/tex]to simplify our expression, fully:
[tex]\begin{gathered} (3^2)^{-2} \\ =3^{2\times-2} \\ =3^{-4} \end{gathered}[/tex]Using the property:
[tex]a^{-n}=\frac{1}{a^n}[/tex]we can write the answer as:
[tex]3^{-4}=\frac{1}{3^4}=\frac{1}{81}[/tex]From the choices, given, we can say:
• 2nd choice is correct
,• 3rd choice is correct
[tex]3^{-11}\cdot3^7=3^{-11+7}=3^{-4}[/tex]If f(1) = 5, which expression could represent f (x)?
A- 3x(2) + 14x + 8
B- 3x(2) - 14x - 8
C- 3x(2) + 10x -8
D- 3x(2) - 10x -8
Answers
If f(1) = 5, then you can find your answer by substituting 1 in for x in all of the options to figure out which one gives you 5 as a result.
A: 3(1)^2 + 14(1) + 8 = 25 ≠ 5 Nope
B: 3(1)^2 - 14(1) - 8 = -19 ≠ 5 Nope
C: 3(1)^2 + 10(1) - 8 = 5 Yup
D: 3(1)^2 - 10(1) - 8 = -15 Nope
Only C fits f(1) = 5.
Sarina's piano teacher gave her a large candy bar. One serving has amass of 39 grams. The candy bar has 2 and 1/2 servings. What is the mass of thewhole candy bar?
Answers
We are told that Sarina's piano teacher gave her a large candy bar
The candy bar has 2 and 1/2 servings and one serving has a mass of 39 grams.
We wsnt to determine the mass of the whole candy bar.
The mass of the candy bar can be found to be equal to;
Therefore, we get the mass of the candy bar as;
[tex]2\frac{1}{2}\times39=\frac{5}{2}\times39=97.5[/tex]Therefore, the mass of the candy bar is 97.5 grams
g(x) = x2
g
(
x
)
=
x
2
, what is the product of f(x) and g(x)
Answers
The product of the functions f(x) = [tex]x^{2}[/tex] and g(x) = x - 8 is f(x).g(x) = [tex]x^{3} -8x^{2}[/tex]
The given functions are :
f(x) = [tex]x^{2}[/tex] --- (1)
g(x) = (x - 8) --- (2)
The product of the functions is obtained by multiplying equations (1) and (2)
f(x). g(x) = [tex]x^{2}[/tex] × (x - 8)
f(x).g(x) = [tex]x^{3} - 8x^{2}[/tex]
Let us take another example:
Let f(x) = [tex]x^{3} -2x^{2} +x-4[/tex] and g(x) = [tex]\frac{1}{2} x[/tex]
The product of the above two functions will be :
f(x).g(x) = [tex](x^{3} -2x^{2} +x-4) * (\frac{1}{2}x )[/tex]
= [tex](x^{3})(\frac{1}{2}x)-(2x^{2})(\frac{1}{2}x) + (x)(\frac{1}{2}x)-(4)(\frac{1}{2}x)[/tex]
= [tex]\frac{x^2}{2} -x+\frac{1}{2}-\frac{2}{x}[/tex]
= [tex]\frac{x^2}{2}-x-\frac{2}{x} +\frac{1}{2}[/tex]
Hence the answer is The product of the functions f(x) = [tex]x^{2}[/tex] and g(x) = x - 8 is f(x).g(x) = [tex]x^{3} -8x^{2}[/tex]
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Suppose Maya multiplied 9368x68754323 cubes. Then she divided the awnser by 9 and turned the Answer Into a fraction and multiplied that by 38…And then split that awnser into 6 equal groups. How many cubes would she put in each group?
Answers
The no of cubes she would put in each group if she multiplied 9368x68754323 cubes. Then she divided the answer by 9 and turned the Answer Into a fraction and multiplied that by 38, And then split that answer into 6 equal groups is 453248868900.
What is multiplication?
Along with addition, subtraction, and division, multiplication is one of the four basic mathematical operations. Multiply in mathematics refers to the continual addition of sets of identical sizes.
The symbols cross (×), asterisk (*) and dot (·) are used to denote multiplication. You most frequently utilize the cross when writing in your notebooks. In computer languages and algebra, the asterisk and dot are both utilized (higher mathematics).
Given:
The no of cubes, n = 9368 × 68754323,
Divide the no of cubes by 9,
n / 9 = 9368 × 68754323 / 9
Now multiplied by 38 and split into 6, we get,
= (9368 × 68754323 × 38) / (9 ×6)
= 453248868900
Therefore, The no of cubes she would put in each group is 453248868900.
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An “A” is considered 4.0, a “B” is 3.0, a “C” is 2.0, a “D” is 1.0, and an “F” is 0. A student received the following grades.CourseCreditsGradeSpeech3.0DChemistry4.0FEnglish3.0CNew Student Seminar1.0AFind the student's GPA, rounded to the nearest hundredth.
Answers
Answer:
1.18
Explanation:
The GPA is calcuated as follows
[tex]GPA=\frac{grade\text{ points}}{total\text{ credits}}[/tex]where a grade point = score assicated with the grade * number of credit hours for the course.
Now in our case, the grade points earned are
[tex]3(1.0)+4(0)+3(2.0)+1(4)=13[/tex]And the total number of credit hour are
[tex]3+4+3+1=11[/tex]Therefore, the GPA (rounded to the nearest hundredth) is
[tex]GPA=\frac{13}{11}=1.18[/tex][tex]\boxed{GPA=1.18.}[/tex]which is our answer!
I need help on what the answer is
Answers
In order to show these triangles congruent , we must identify the vertical angles
What is SAS congruent triangle?
SAS criterion stands for Side-Angle-Side criterion. Under this criterion, two triangles are congruent if the two sides and the included angle of one triangle are equal to the corresponding sides and the included angle of the other triangle.
As in the given figure there are two triangles( ΔABC and ΔCDE)
And it is given that the side AC=CE & BC=CD
as we can see that the sides AB and DE are parallel.
So, the ∠ACB and ∠DCE will be equal (vertically opposite angle)
And we can also say that;
∠ABC = ∠CDE & ∠BAC = ∠CED (alternate interior angle)
so, the triangles ΔABC and ΔCDE are congruent through SAS congruency criteria
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Can you find the slope and type the correct code? Please remember to type in ALL
CAPS with no spaces.
Puzzle #2
1: Find the slope:
X
Y
-1
7002
9339
-9
Your answer
-3
3: Find the slope:
2: Find the slope:
(-1, 5), (2, -7)
4: Find the slope:
X88
88
HI234
Y
1
answer choices
B:
A: ma
C: I
m=
undefined m=6
4
D: - E
m =
3
G:
m=-4
F:
m=3
m=-6
H:
I:
m = 4 m=0
Type the 4-
letter code into
the answer
box. All CAPS,
no spaces.
8000
Answers
Answer:
(-1.5).(2.-7)
Step-by-step explanation:
ECHA. Step-by-step explanation: 1.) E. m = 1/2. 2.) C. y2 - y1/x2 - x1 = m. -4 - (-8)/3 - 1 = m. 8 - 4/3 - 1 = m.
Problem 2.1
I monitor the amount of battery left on my computer so I can make sure it doesn't die at the wrong time.
My battery loses charge at a constant rate.
This graph shows the percent of charge left on my computer, c, after I have been awake for h hours.
What was the percent charge when I woke up?
---------------------------------------------------------------------------------
Problem 2.2
This graph shows the amount of charge left on my computer, c, after I have been awake for h hours.
Enter an equation that describes the relationship between c and h.
Answers
Using the graph, the percent chare when you woke up was: 90%.
The equation that describes the relationship between c and h is: c = -20h + 90.
How to Write the Graph of an Equation?To write the equation of a graph that represents a linear relationship between two variables, x and y, determine the initial value/y-intercept (b) and the value of the constant rate/slope (m), then substitute the values into y = mx + b.
The graph given shows the relationship between charge left on the computer, c, and the number of hours awake, h.
The initial value/y-intercept, b, represents the percent charge when you woke up = 90%.
The constant rate/slope (m) = change in c/change in h = (30 - 10)/(3 - 4)
m = -20/1
m = -20
To write the equation that describes the relationship between c and h, substitute m = 20 and b = 90 into c = mh + b:
c = -20h + 90
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Write the Coordinates of the verticals after a rotation 90 counter clockwise around the origin
R=
S=
Q=
T=
Answers
The preimage's coordinates are R(-3, 6), S(-1, -2), and Q(-7, 1).
How can you spot changes in something?This point can be another point on the graph, though it is often the origin (0,0) of the graph or a point on the picture. Determine whether any of the points on the original figure are oriented differently in the altered version and whether the figure appears to be turned.The pre image R S, and Q locations must be discovered.A point is transformed when it is moved from its original location to a new one. Reflection, rotation, translation, and dilation are examples of different transformations.The new point is at R' if a point R(x, y) is rotated 90 degrees clockwise about the origin (y, -x)Thus, we must follow the rule (-y,x) ——>(x,y).
Applying the law,
R'(6, 3) -----> R(3, -6)
S'(–2, 1) -----> S(1, 2)
Q'(1,7) -----> Q (7, -1)
The preimage's coordinates are R(-3, 6), S(-1, -2), and Q(-7, 1).
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Is 4/21 and 16/84 proportional
Answers
Answer:
yes
Step-by-step explanation:
[tex]\frac{16}{84}[/tex] ( divide numerator and denominator by 4 )
= [tex]\frac{4}{21}[/tex]
they represent the same proportion
An online furniture store sells chairs for $150 each and tables for $650 each. Every day, the store can ship at most 16 pieces of furniture and must sell no less than $3900 worth of chairs and tables. If x represents the number of tables sold and y represents the number of chairs sold, write and solve a system of inequalities graphically and determine one possible solution.
Answers
Using graphical method to solve the system of linear inequalities, the solution are (x, y) 3, 13.
System of Linear InequalitiesA system of linear inequalities in two variables consists of at least two linear inequalities in the same variables. The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system.
To solve this, we can write out the equations as
x + y ≤ 16 ...eq(i)
650x + 150y ≥ 3900 ...eq(ii)
Solving both equations with a graph.
Kindly find the attached graph to the problem.
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The perimeter of a triangle is 170 feet and the sides are in the ratio of 25:14:12. Find the area of the triangle.A. 496.08 ft²B. 153.45 ft²C. 494.35 ft²D. 107.24 ft²
Answers
The perimeter of a triangle is 170 feet
The sides are in the ratio of 25:14:12
The total ratio 25+14+12=51
Let's calculate each side
[tex]\begin{gathered} \text{First side} \\ \frac{25}{51}\times170=\frac{250}{3}=83.33 \\ \\ \text{second side} \\ \frac{14}{51}\times170=\frac{140}{3}=46.67 \\ \\ \text{Third side} \\ \frac{12}{51}\times170\text{ =40} \end{gathered}[/tex]The three sides are given, so we use the Hero formula to calculate the area of the triangle.
[tex]\begin{gathered} \text{Area =}\sqrt[]{s(s-a)(s-b)(s-c)} \\ \\ S=\frac{a+b+c}{2} \end{gathered}[/tex]a = 83.33ft, b=46.67ft and c=40ft
[tex]\begin{gathered} S=\frac{83.33+46.67+40}{2} \\ \\ S=\frac{170}{2} \\ S=85 \\ \end{gathered}[/tex][tex]\begin{gathered} \text{Area =}\sqrt[]{85(85-83.33)(85-46.67)(85-40)} \\ \\ \text{Area =}\sqrt[]{85(1.67)(38.33)(45)} \\ \\ \text{Area =}\sqrt[]{85(1.67)(38.33)(45)} \\ \\ \text{Area =}\sqrt[]{244842.4575} \\ \text{Area = 494.35 square ft} \end{gathered}[/tex]The correct option is C
In the diagram below, the cone has a radius of 9 centimeters and a slant height of 15 centimeters.
image 134fcf7d1dc04fbbb16d3bc2b8f9a75f
What is the volume of the cone?
Responses
324π cm3
324 π cm 3
405π cm3
405 π cm 3
972π cm3
972 π cm 3
1,215π cm3
Answers
Answer:
405π cm3
Step-by-step explanation:
STS Solve Applications Involving Normal DistributionsA set of 1200 exam scores is normally distributed with a mean of 84 and standard deviation of 9. Use theEmpirical Rule to complete the statements below.
Answers
Let us upload the bell curve for standard normal distribution
Given that
[tex]\begin{gathered} \mu=84 \\ \sigma=9 \\ \end{gathered}[/tex]15) How many students scored higher than 84
Therefore, the number of students that will score higher than 84 which is the mean will be 50% from the bell curve standard normal distribution.
Hence, the answer is 50%.
19) How many students scored lower than 75?
To get the number of students that score lower than 75, we will subtract 1standard deviation from the mean.
[tex]\begin{gathered} \mu-\sigma=84-9=75 \\ \end{gathered}[/tex]Hence, the number of students will be
[tex]9.2\text{ \%+4.4\%+1.7\%+0.5\%+0.1\%=15.9\%}[/tex]The answer is 15.9%.
20) How many students scored lower than 93?
To get the number of students that score lower than 93, we will add 1standard deviation from the mean.
[tex]\mu+\sigma=84+9=93[/tex]Hence, the number of students will be
[tex]100\text{ \% -(9.2+4.4+1.7+0.5+0.1)\%=100\%-15.9\%=84.1\%}[/tex]The answer is 84.1%.
95ft 40ft 65 ft what is the area of this trapezoid
Answers
You can find the area of the trapezoid using the following formula:
[tex]\begin{gathered} A=\frac{a+b}{2}\times h \\ \text{Where:} \\ a=Long\text{ base=95ft} \\ b=\text{short base=65ft} \\ h=\text{height}=40ft \\ A=\frac{95+65}{2}\times40=80\times40=3200ft^2 \end{gathered}[/tex]A chemist is using 347 milliliters of a solution of acid and water. If 13.9 of the solution is acid, how many milliliters of acid are there? Round your answer to the nearest tenth.
Answers
48.233 milliliters of acid are there.
Given:
A chemist is using 347 milliliters of a solution of acid and water.
13.9% of the solution is acid.
converting 13.9% to decimal:
13.9% = 13.9/100
13.9% = 0.139
milliliters of acid = total milliliters*0.139
= 347*0.139
= 48.233 milliliters.
Therefore 48.233 milliliters of acid are there.
Learn more about the acid and water solution here:
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What would be the height of a building the cast a shadow 50 feet long at the same time
Answers
Given:
The height of the girl is 5 ft and the length of the shadow is 2 ft., at the same time the shadow of the building is 50 ft .
Required:
To find the height of the building.
Explanation:
Let the height of the building is h ft.
Since triangle ABC is similar to the triangle DEF.
Thus by using the similarity condition.
[tex]\begin{gathered} \frac{AC}{DF}=\frac{AB}{DE} \\ \frac{5}{h}=\frac{2}{50} \\ h=\frac{50\times5}{2} \\ h=125\text{ ft} \end{gathered}[/tex]Final Answer:
Thus the third option is the correct answer.
what is the y and x intercept of 5x-7y= -8
Answers
SOLUTION
Write out the equation given
[tex]5x-7y=-8[/tex]To find y-intercept, we replace x with 0, hence
[tex]\begin{gathered} \text{for x=0} \\ 5(0)-7y=-8 \\ -7y=-8 \\ \text{Divide both sides by -7} \\ -\frac{7y}{-7}=-\frac{8}{-7} \\ \text{Hence } \\ y=\frac{8}{7} \\ \end{gathered}[/tex]Hence
Y - intercept is ( 0, 8/7 )
Similarly, for x-intercept, we replace y with 0 and find x
[tex]\begin{gathered} \text{for y=0} \\ 5x-7(0)=-8 \\ \text{Hence } \\ 5x=-8 \\ \text{Divide both sides by 5, } \\ \frac{5x}{5}=-\frac{8}{5} \\ \text{Hence } \\ x=-\frac{8}{5} \end{gathered}[/tex]Hence
x- intercept is ( - 8/5 , 0 )