\( \huge\quad\qquad\underline{{\sf Answer}}\)
Let's solve ~
\(\qquad \sf \dashrightarrow \: - 4 \sqrt{135} + 7 \sqrt{15} \)
\(\qquad \tt \dashrightarrow \: - 4 \sqrt{5 \times3 \times 3 \times 3} + 7 \sqrt{15} \)
\(\qquad \tt \dashrightarrow \:( - 4 \times 3) \sqrt{5 \times 3} + 7 \sqrt{15} \)
\(\qquad \tt \dashrightarrow \: - 12 \sqrt{15 } + 7 \sqrt{15} \)
\(\qquad \tt \dashrightarrow \: - 5 \sqrt{15} \)
A vendor is thinking about changing the number of sweatshirts he brings to
an event. To make sure he doesn't run out, he plans to bring more of the size
most likely to be sold.
The table shows the number of sweatshirts of each size sold at the vendor's
last event and the number he had for sale.
Which size should he bring more of?
A. Medium
B. X-Large
C. Small
D. Large
The size he should bring more of is small and is denoted as option C.
What is Sale?This is a term which refers to the number of goods sold within a given period of time.
Given that, a vendor is thinking about changing the number of sweatshirts he brings to an event.
To make sure he doesn't run out, he plans to bring more of the size most likely to be sold.
we need to determine that which size should he bring more of,
So, here according to the table,
Small size has the smallest remaining which is 9 when the difference between the number sold and number put up for sale is calculated.
This is therefore why bringing more of small size will ensure he doesn't run out of stock in the next event as more people prefer it.
Hence, the size he should bring more of is small and is denoted as option C.
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Graph the linear equation.
x - 2y = - 2
The graph of the linear equation can be seen in the image below.
How to graph the linear equation?Here we have the linear equation:
x - 2y = -2
To graph it, we need to find two points that belong to the line, and then we can graph these and connect them with a line.
If x = 0, we have:
0 - 2y = -2
y = -2/-2 = 1
if x = 1 then:
1 - 2y = -2
1 + 2 = 2y
3 = 2y
3/2 = y
Then we have the points (0, 1) and (1, 3/2), now just graph these points on a coordinate axis and then connect them with a line, we will get:
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using the gcf and the distributive property find the sum of 34+51
it would be 75 ur welcome
event A includes outcomes 1,3,5.
event b includes 2,4,3,5.
event c includes outcomes 1,2,3.
which outcome would be included in the intersection of A and C'?
Answer:
Outcome 5 will be included in the intersection of A and C'
Step-by-step explanation:
The outcomes included in C' would be any outcomes not included in C.
Since C includes {1, 2, 3}, C' will include {4, 5}. The only outcome of C' that can be found in A is outcome 5.
Please answer this correctly
Answer:
Mean
Step-by-step explanation:
In a bag there are 3 red marbles, 2 yellow marbles, and 1 blue marble. What is the likelihood of a yellow marble being selected on the first draw?
likely
unlikely
even chance
certain
Therefore, it is not even chance, but it is also not very unlikely. It is moderately likely that a yellow marble will be selected on the first draw.
What is Probability?Probability is a branch of mathematics that deals with the study of random events and their likelihood of occurring. It is a measure of the likelihood or chance of an event happening. Probability is expressed as a number between 0 and 1, where 0 means the event is impossible, and 1 means the event is certain.
In other words, probability is a way of quantifying uncertainty. It is used in various fields, such as statistics, physics, finance, engineering, and more, to help make predictions and decisions based on uncertain information. Probability theory provides a set of rules and tools for analyzing and manipulating random variables and events, and for calculating the probability of complex events.
The likelihood of a yellow marble being selected on the first draw can be calculated by dividing the number of yellow marbles by the total number of marbles in the bag:
likelihood of selecting a yellow marble = number of yellow marbles / total number of marbles
So, in this case, the likelihood of selecting a yellow marble on the first draw is:
likelihood of selecting a yellow marble = 2 / (3 + 2 + 1) = 2/6 = 1/3
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A man, a woman, and their four children randomly stand in a row for a family picture. What is the probability that the parents will be standing next to each other?
Answer:
Required probability = 2 / 11
Step-by-step explanation:
Sample space of 5 person = 11!
One woman one man arrangement = 2!
Arrangement without woman = 10!
Required probability = [2!][10!] / [11!]
Required probability = 2 / 11
The probability that the parents will be standing next to each other is 2/11
Probability is the likelihood or chance that an event will occur.
Probability = Expected outcome/Sample spaceGiven a woman, man and their four children, if their parents will be standing next to each other, that makes it 5 people. The sample space for 5 people is 11!
The parent arrangement is 2!If they are arranged without the woman, the expected event will be 10!Pr(parents standing next to each other) = 2!10!/11!
Pr(parents standing next to each other) = 2*10!/11*10!
Pr(parents standing next to each other) = 2/11
Therefore the probability that the parents will be standing next to each other is 2/11
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15/32 multiplied by 4
Answer:
15/8
Step-by-step explanation:
15/32 * 4 = 15/8
Reflect (6,-4) across the -axis. Then reflect the result across the -axis. What are the coordinates of the final point?”
The coordinates of the final point after the reflections across the x-axis twice is (6, -4)
What are the coordinates of the final point?Reflecting a point across the x-axis means that we keep the x-coordinate the same, but change the sign of the y-coordinate.
So reflecting (6,-4) across the x-axis gives us the point (6,4).
Reflecting this result again across the x-axis means that we keep the x-coordinate the same, but change the sign of the y-coordinate again.
So reflecting (6,4) across the x-axis gives us the point (6,-4).
Therefore, the final point after both reflections is (6, -4).
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Rewrite the equation `6y=2x+12`into slope intercept form.
Answer:
y=1/3x+2
Step-by-step explanation:
................
Answer:
y=1/3x+2
Step-by-step explanation:
slope intercept form: y=xm+b
6y=2x+12
/6 /6
y=2/6x+2
y=1/3x+2
have a great day!
5. Share $1200 among Carl, Stacy and Peter so that Stacy gets three times as much as Peter and Peter gets half the amount that Carl gets.
Using the concept of proportion and substitution with the total money to be divided given, The answer is Carl gets $480, Stacy gets $720, and Peter gets $240.
What do you mean by proportion?Proportion refers to the relationship between two or more quantities or values, often represented as a ratio or fraction. It can also refer to the relative size or scale of something in relation to something else. In mathematics, a proportion is an equation that states that two ratios are equal. For example, "the ratio of apples to oranges is 2:3" can be written as the proportion "2/3 = x/y," where x and y represent the number of apples and oranges. In statistics, a proportion is a measure of the frequency with which an event occurs, often expressed as a decimal or percentage.
What do you mean by substitution method?The substitution method is a technique used to solve systems of equations, which are sets of two or more equations containing multiple variables. The basic idea behind the substitution method is to solve for one variable in terms of the others in one equation, and then substitute that expression into the other equations. This can be done by isolating one variable by adding or subtracting other variables from both sides of the equation, and then using the resulting equation to express that variable as a function of the others. Once one variable is expressed in this way, it can be substituted into the other equations, allowing us to solve for the other variables.
S = 3P (Stacy gets three times as much as Peter)
P = C/2 (Peter gets half the amount that Carl gets)
C + S + P = 1200
We can substitute the first equation into the second one to get:
S = 3(C/2)
Now we can substitute the second equation into the first one to get:
C + 3(C/2) + C/2 = 1200
We can simplify this equation by multiplying out the 3(C/2) term and combining like terms to get:
5C/2 = 1200
Now we can solve for C by multiplying both sides by 2/5:
C = 480
Now that we know C = $480, we can use the earlier equations to find S and P:
S = 3P = 3(480/2) = $720
P = C/2 = 480/2 = $240
So Carl gets $480, Stacy gets $720, and Peter gets $240.
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the 4.1 m of concrete is made into the shape of a cylinder. The base has radios 0.5 metres. work out the height of the cylinder ( photo attached)
Answer:
5.22m
Step-by-step explanation:
Rearrange the formula - volume = π × r² × h:
h = volume ÷ (π × r²)
volume = 4.1m³r = 0.5Plug in the numbers:
h = 4.1 ÷ (π × 0.5²)
h = 5.22028... ≈ 5.22m
Hope this helps!
Solve 0=4x^2+12x+9. Simplify the expression to solve the equation. X=
Answer:
x = - 3/2
Step-by-step explanation:
4x^2 + 12x + 9 = 0
(2x + 3)^2 = 0
2x + 3 =0
2x = -3
= - 3/2
The solution is, x = - 3/2
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, given that,
4x^2 + 12x + 9 = 0
(2x + 3)^2 = 0
2x + 3 =0
2x = -3
x= - 3/2
Hence, The solution is, x = - 3/2.
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HELPPP ASAPPPP PLEASEEE
Answer:
with the years labeled on the horizontal axis and the number of hours labeled on the vertical axis. The graph shows that the number of hours spent watching TV declined steadily over the 5-year period, starting at around 1750 hours in Year 1 and falling to around 1300 hours in Year 5. The graph also shows a clear, downward-sloping trend from Year 1 to Year 5.
Step-by-step explanation:
Mathematics
Find the rate
What percent of 200 is 50?
What percent of 50 is 40?
What percent of 10 is 6?
200 is what percent of 200?
What percent of 800 is 200?
Show your solution, HELP PLS ASAP!!!
I'LL GIVE 20 POINTS!!
Answer:
Step-by-step explanation:
25%
80%
60%
100%
25%
What is the answer to this?
The lamp shades diameter is 12 inches. About how long does the fabric need to be to cover the entire lamp shade?
Answer: 37.68
Step-by-step explanation:
Since the diameter is 12 inches, you have to multiply it by pi (π) for the final answer, the circumference aka the whole thing
So:
C=πd
(12)(3.14)
=37.68
Please help with this equation, it would really help me. Thank you.
Answer:
the volume should be 2/15
r marks in percent. other earns Rs 27,000 and spends Rs 10,800 every month. Express her expenditure in percent. (ii) Calculate her saving
The expenditure of the man in percent is 40% and his savings is Rs16200 .
In the question ,
it is given that ,
amount earned by the man = Rs 27000
amount spend by the man = Rs 10800
So , the expenditure in percent can be calculated using the formula ,
we get ,
= (expenditure)/(total earning) × 100
= 10800/27000 × 100
= 0.4 × 100
= 40%
the savings = earning - expenditure
savings = 27000 - 10800
= 16200
Therefore , The expenditure of the man in percent is 40% and his savings is Rs16200 .
The given question is incomplete , the complete question is
A man earns Rs 27,000 and spends Rs 10,800 every month. Express her expenditure in percent also calculate his savings .
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A meter is a unit of length approximately equal to 39.37 inches. If someone is 77 meters tall, what is his or her approximate height in inches?
Answer:
It is 3031.49 Inches.
Step-by-step explanation:
77 times 39.37
= 3031.49
What is greater 1.0275 or 1.029
Answer:
1.029 is greater than 1.0275
Step-by-step explanation:
Answer:
1.029
Step-by-step explanation:
What is greater 1.0275 or 1.029
.027 < .029
So, 1.029 is greater.
show full solutions.15. Name the indicated parts of this diagram.
Given:
A circle with a center at C.
Required:
We need to find the names of the given parts.
Explanation:
Recall that radius is a line segment extending from the center of a circle to the circumference.
Line segment AC extends from the center C of a circle to the circumference.
\(AC=Radius\)Recall that the arc of a circle is defined as the part of the circumference of a circle.
AE is the part of the circumference of a circle.
\(AE=Arc\)Recall that a straight line segment joins and is included between two points on a circle.
D and E are two points on a circle.
A straight line DE line segment joins and is included between two points D and E on a circle.
\(DE=Chord\)Recall that meeting a curve or surface in a single point if a sufficiently small interval is considered a straight line tangent to a curve.
AB is tangent.
\(AB=Tangent\)Recall that an inscribed angle is an angle with its vertex "on" the circle, formed by two intersecting chords.
\(\measuredangle ADE=\text{ Inscribed angle.}\)Recall that a central angle is an angle formed by two radii with the vertex at the center of the circle.
\(\measuredangle ACE=\text{ Central angle}\)Recall that an angle formed by an intersecting tangent and chord has its vertex "on" the circle.
\(\measuredangle\measuredangle CAB=\text{ Tangent Chord Angle}\)Final answer:
\(AC=Radius\)\(AE=Arc\)\(DE=Chord\)\(AB=Tangent\)\(\measuredangle ADE=\text{ Inscribed angle.}\)\(\measuredangle ACE=\text{ Central angle}\)\(\measuredangle\measuredangle CAB=\text{ Tangent Chord Angle}\)what is a measurement
Answer:
Its the instrument that measures unknown quality of goods.
Step-by-step explanation:
Answer:
The size, length, width, surface, height or volume of a object.
A measurement is the size, length, width, surface height or volume of a object.
Sample measurements:
1 foot 1 yard1 inch1 gram1 pound1 ounceHope it helps!
MA.7.DP.1.4
A group of friends has been given $800 to host a party. They must decide how much money
will be spent on food, drinks, paper products, music and decorations.
Part A. As a group, develop two options for the friends to choose from regarding how to
spend their money. Decide how much to spend in each area and create a circle
graph for each option to represent your choices.
Part B. Mikel presented the circle graph below with his recommendations on how to
spend the money. How much did he choose to spend on food and drinks? How
much did he choose to spend on music?
Party Spending Proposal
Mail
17%
Paper Products
Answer: $130 money did Brenda and Hazel have all together before buying decorations and snacks.
Here, we have,
You want to know Brenda and Hazel's combined money when the ratio of their remaining balances is 1 : 4 after Brenda spent $58 and Hazel spent $37. They had the same amount to start with.
Setup
Let x represent the total amount the two women started with. Then x/2 is the amount each began with, and their fnal balance ratio is ...
(x/2 -58) : (x/2 -37) = 1 : 4
Solution
Cross-multiplying gives ...
4(x/2 -58) = (x/2 -37)
2x -232 = x/2 -37 . . . . . . eliminate parentheses
3/2x = 195 . . . . . . . . . . . . add 232-x/2
x = (2/3)(195) = 130 . . . . . multiply by 2/3
Brenda and Hazel had $130 altogether before their purchases.
Alternate solution
The difference in their spending is $58 -37 = $21.
This is the same as the difference in their final balances.
That difference is 4-1 = 3 "ratio units", so each of those ratio units is $21/3 = $7.
Their ending total is 1+4 = 5 ratio units, or $35.
The total they started with is $58 +37 +35 = $130.
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complete question:
Brenda and Hazel decide to throw a surprise party for their friend, Aerica. Brenda and Hazel each go to the store with the same amount of money. Brenda spends $58 on decorations, and Hazel spends $37 on snacks. When they leave the store, the ratio of Brenda’s money to Hazel’s money is 1 : 4. How much money did Brenda and Hazel have all together before buying decorations and snacks?
A number is chosen at random from 1 to 50. Find the probability of selecting numbers less than 33
Answer:
75%Step-by-step explanation:
Students at two high schools were asked about their plans after graduation. The table displays the results for 300 students at Henderson High School. The bar graph displays the results for 300 students at Johnson High School. Which Statement about the results from Henderson High School and johnson high school must be true?
Armed force and other for Henderson high school is greater than
Johnson High School.
The mode for each school is college.
Options F and G are the correct answer.
We have,
The number of students in Henderson High School.
Work = 96
College = 114
Armed forced = 48
Other = 42
The number of students in Johnson High School.
Work = 30
College = 40
Armed forced = 15
Other = 15
From the information,
The number of students in Work for Henderson High School is greater than Johnson High School.
Now,
Henderson High School:
Armed force and other = 48 + 42 = 90
Mode = college
Johnson High School.
Armed force and other = 15 + 15 = 30
Mode = college
Thus,
Armed force and other for Henderson high school is greater than
Johnson High School.
The mode for each school is college.
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R
8
7
6
2
-6-5-4-3-2-14
A
S
T
1 2 3 4 5 6 x
H
Question Details
*REQUIRED 15
1. To earn full credit, you must show ALL
of your steps and calculation leading to
your solution. You will be assessed on
your mathematical communication, use
of mathematics and accuracy of your
results.
Find the area of the parallelogram.
View Rubric
The required area of the parallelogram is 36√2 square units.
How to find the area of parallelogram?To find the area of the parallelogram, we can use the formula:
Area = base x height
where the base is one of the sides of the parallelogram, and the height is the perpendicular distance between the base and the opposite side.
First, we need to find the length of one of the sides of the parallelogram. Let's take RS as the base.
RS = √[(2-(-4))² + (6-4)²] = √(6² + 2²) = √40 = 2√10
Next, we need to find the height of the parallelogram corresponding to the base RS. To do this, we need to find the distance between the line RS and the point T.
The equation of the line RS can be found using the slope-intercept form:
y - y1 = m(x - x1)
where (x1, y1) is one of the points on the line, and m is the slope of the line. Let's take R(-4, 4) as the point on the line. The slope of RS can be found as:
m = (6 - 4) / (2 - (-4)) = 1/3
Using point-slope form, the equation of RS is:
y - 4 = 1/3(x - (-4))
Simplifying, we get:
y = x/3 + 16/3
To find the distance between the line RS and point T(6,2), we need to find the perpendicular distance between T and the line RS. We can use the formula for the distance between a point and a line:
distance = |ax1 + by1 + c| / √(a² + b²)
where a, b, and c are the coefficients of the equation of the line in the standard form (Ax + By + C = 0), and (x1, y1) is the point.
Converting the equation of RS to the standard form, we get:
-2x + y - 8 = 0
Using this equation, we can find the distance between T and RS as:
distance = |(-2)(6) + (1)(2) - 8| / √((-2)² + 1²)
= 18/√5
the area of the parallelogram is:
Area = base x height = RS x distance between T and RS = 2√10 x 18/√5 = 36√2 = 36√2 square units.
So the area of the parallelogram is 36√2 square units.
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i need help asap
than you!
The highest height for the daily rainfall were for 5 and 6 inches
How to Interpret Dot Plots?Dot plots are used to present data in the form of points or small circles. It is similar to a simplified histogram or bar graph in that the height of the bar made up of points represents the numerical value of each variable. Dot plots are used to represent small amounts of data.
From the given dot plot, we see the number of times for each height of rainfall.
Thus, we see that the highest number of times of rainfall height was from that of 5 and 6 inches.
Thus, we conclude those were the highest heights for the daily rainfall.
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An amount was invested at % r per quarter. What value of rwill ensure that accumulated amount at the end of one year is 1.5 times more than amount invested? Correct to 2 decimal places
Answer:
42.67%
Step-by-step explanation:
The annual growth factor for interest at annual rate r compounded quarterly is ...
(1 +r/4)^4
You want that value to be 1.5:
1.5 = (1 +r/4)^4
1.5^(1/4) = 1 +r/4
(1.5^(1/4) -1) = r/4
4(1.5^(1/4) -1) = r ≈ 0.426728
The rate r must be about 42.67%.
_____
Comment on the wording
We interpreted the problem to mean the end-of-year amount is 1.5 times the beginning-of-year amount. That is, it is "1.5 times the amount invested."
The word "more" is typically used when addition is involved. For example, "25% more" means 25% of the original is added to the original. We occasionally see "more" where "x times more" is intended to mean "x times", rather than "x times the amount, added to the original amount."
for each parallel lines. you are given the measure of one angle
Answer:
The question is not complete
From the top of a building 30 meters high, the angle of elevation to the top of a monument is found to be equal to the angle of depression to the foot of the monument. Find the height of the monument.
The height of the monument is 30 meters.
We have,
Let's assume the height of the monument is "h" meters.
From the top of the building, the angle of elevation to the top of the monument is equal to the angle of depression to the foot of the monument. This forms a right triangle with the building, the monument, and the ground.
In this triangle, the opposite side of the angle of elevation is the height of the building, which is given as 30 meters.
The opposite side of the angle of depression is the height of the monument, which is "h" meters.
Since the angles of elevation and depression are equal, the triangle is an isosceles triangle.
Therefore, the opposite sides are equal in length.
By setting up the equation:
h = 30
Thus,
The height of the monument is 30 meters.
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