Answer:
The volume of cone z has the same base area as cylinder y but its height is 3 times the height of cylinder y have the same volume.
Step-by-step explanation:
The volume of a cylinder having base area 'A' and height 'H' is given by V = AH, and the volume of a cone having the same base area as the cylinder i.e. A and height 3 times the height of the cylinder i.e. 3H is given by [tex]V' = \frac{1}{3} A(3H) = AH[/tex].
So, V = V'
Hence, the volume of cone z has the same base area as cylinder y but its height is 3 times the height of cylinder y have the same volume. (Answer)
June uses 12 eggs to make cupcakes. She uses 4 eggs for each batch of
cupcakes. Which expression can be used to find the number of batches she
makes?
12 - 4
12 +4
12:4
12 x 4
Done
Answer:
12/4=3
Step-by-step explanation:
12/4
The expression that could be used to find the no of batches she makes is [tex]= 12\div 4[/tex]
Given that,
June uses 12 eggs to make cupcakes. She uses 4 eggs for each batch of cupcakes.Based on the above information, the calculation is as follows:
[tex]= 12\div 4[/tex]
= 3
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-7(2x - 4) - 7= 3(x - 5)+ 4x - 9 distribute and combine like terms
kim is saving monyfor a trip this summer. She already has some money in her savings account and will add the same amount to her account each week. At the end of 2 weeks, Carla has $130. At the end of 8 weeks, she has $280. Write a linear function in the form y = mx + b to represent the amount of money, m, that Carla has saved after w weeks.
The linear function represents the amount of money, m, that Carla has saved after w weeks is m = 25 w + 80
Step-by-step explanation:
Carla is saving money for a trip this summer. She already has some money in her savings account and will add the same amount to her account each week
At the end of 2 weeks, Carla has $130At the end of 8 weeks, she has $280Write a linear function in the form y = m x + b to represent the amount of money, m, that Carla has saved after w weeks
The linear equation is y = m x + b, where m is the slope of the line and b is the y-intercept
The formula of the slope is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] , where [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] are 2 points on the line
∵ The slope is the rate of change of y and x
∴ The same amount of money that Carla add every week = m
∵ At the end of 2 weeks, Carla has $130
∴ The first point is (2 , 130)
∵ At the end of 8 weeks, she has $280
∴ The second point is (8 , 280)
∵ [tex]m=\frac{280-130}{8-2}=\frac{150}{6}=25[/tex]
∴ The same amount of money that Carla add every week = $25
∵ The amount of money that Carla saved after w week is m
∴ m = 25 w + b, where b is the initial amount of money that she
saved in her account
To find b substitute w and m by the coordinates of one of the two
given points, let us use the first point
∵ w = 2 and m = 130
∵ m = 25 w + b
∴ 130 = 25(2) + b
∴ 130 = 50 + b
- Subtract 50 from both sides
∴ 80 = b
∴ m = 25 w + 80
The linear function represents the amount of money, m, that Carla has saved after w weeks is m = 25 w + 80
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Gail bought 5 pounds of oranges ans 2 pounds of bananas for $14. Her husband later bought 3 pounds of oranges ans 6 pounds of bananas for $18. What was the cost per pounds of the oranges and the bananas?
Answer:
Step-by-step explanation:
5r + 2b = 14 (5 lbs of oranges and 2 lbs of bananas = $14)
3r + 6b = 18 (3 lbs of oranges and 6 lbs of bananas = $18)
Let's use the elimination method. Multiply the first equation by -3:
-15r - 6b = -42
3r + 6b = 18
-----------------
12r = 24
Divide by 12:
r = 2
Answer:
The price per pound of the oranges is $ 2.
The price per pound of the bananas is $ 2.
Step-by-step explanation:
A system of linear equations is a set of equations that have more than one unknown. The unknowns appear in several of the equations, but not necessarily in all. In these equations the unknowns are related to each other.
In this case a system of equations is applied. For that, you must first define the unknowns (or also called variable):
x: price per pounds of the orange y: price per pounds of the bananaThe price of the 5 pounds of oranges, whose price is "x", and 2 pounds of bananas, whose price is "y", bought by Gail must add $ 14. Then expressed in an equation this represents: 5*x+2*y=14 Equation (A)
The price of the 3 pounds of oranges, whose price is "x", and 6 pounds of bananas, whose price is "y", bought by her husband must add $ 18. Then expressed in an equation this represents: 3*x+6*y=18 Equation (B)
Equation A and equation B form the equation system, where the variables are "x" and "y", which are the price of an orange and a banana:
[tex]\left \{ {{5*x+2*y=14} \atop {3*x+6*y=18}} \right.[/tex]
One of the ways to solve a system of equations is through the substitution method. This method consists of isolating one of the unknowns (for example, "x") and replacing its expression in the other equation. In this way, a first degree equation is obtained with the other variable, "y".
In this case, x is isolated from the first equation, obtaining:
5*x+2*y=14
5*x=14-2*y
[tex]x=\frac{14-2*y}{5}[/tex]
[tex]x=\frac{14}{5} -\frac{2}{5}*y[/tex] Equation (C)
Replacing this equation (C) in the other equation you get:
[tex]3*[\frac{14}{5} -\frac{2}{5} *y]+6*y=18[/tex]
Isolating the value of "y" you get:
[tex]3*\frac{14}{5} -3*\frac{2}{5} *y+6*y=18[/tex]
[tex]\frac{42}{5} -\frac{6}{5} *y+6*y=18[/tex]
[tex]-\frac{6}{5} *y+6*y=18-\frac{42}{5}[/tex]
[tex]\frac{24}{5} *y=\frac{48}{5} \\[/tex]
[tex]y=\frac{\frac{48}{5} }{\frac{24}{5} }[/tex]
[tex]y=\frac{48}{5} *\frac{5}{24} \\[/tex]
y=2
Remembering that "y" is the price per pounds of the banana, then it is possible to say that the price per pound of the banana is $ 2.
Replacing the value of the variable "y" in equation (c) and isolating the value of the variable "x" gives:
[tex]x=\frac{14}{5} -\frac{2}{5}*2[/tex]
[tex]x=\frac{14}{5} -\frac{4}{5}[/tex]
[tex]x=\frac{14-4}{5}=\frac{10}{5}[/tex]
x=2
Remembering that "x" is the price per pounds of the oranges, then it is possible to say that the price per pound of the oranges is $ 2.
Segment endpoints: (0,0) and (0,20) midpoint
Answer:
is is 20
Step-by-step explanation:
associated press online provided information from a fiscal analyst stating that during the past 20 years, the average after tax income of the wealthiest 1% of americans had grown from $263,700 to $677,900. what was the percent increase? Round to the nearest percent.
Answer:
The percent increase is 157%
Explanation:
Average after tax income 20 years before: $263,700
Average after tax income after 20 years: $677,900
Increased average after tax income : $677,900-$263,700
=$414,200
Hence,
Percent increase = [tex]\frac{Increased amount}{original amount} \times 100[/tex]
=[tex]\frac{414,200}{263,700} \times 100[/tex]
=157.07%
After Rounding off:
=157%
157% is the percent increase
The largest cross-section of the sphere shown has an approximate area of 28.27 cm2, what is the approximate volume of the sphere? A) 14.14 cm3 B) 113.1 cm3 C) 226.2 cm3 D) 904.78 cm3
Answer:
B) 113.1 cm³
Step-by-step explanation:
The cross-section of a sphere is a circle. The area of a circle is:
A = πr²
The largest cross section passes through the center of the sphere, where the radius of the circle equals the radius of the sphere.
28.27 = πr²
r = 3.00
The volume of the sphere is therefore:
V = 4/3 π r³
V = 4/3 π (3.00)³
V = 113.1
Answer:
B
Step-by-step explanation:
5
Which of the following measures could be 432
square inches?
A the width of a car
B the area of a doormat
Cthe volume of a suitcase
D the perimeter of a classroom
Answer:
B
Step-by-step explanation:
When we see "square inches" in a statement (or squared centimeters, meters, feet, etc) this refers to an area measure. So we need to find which of the options are areas.
A is not, as it is width, is a longitude measure. I could never be in square inches.
C is volume and it measure should be in cubic inches. So, not.
D is perimeter and is the sum if the lengths of different sides of a figure, so is also in inches, not square inches.
Finally, B is the area, so is our only chance. B in correct.
Label each pair of triangles with the postulate or theorem that proves the triangles are congruent.
Answer:
We can conclude that Δ ABC ≅ Δ DEF by SSS postulate.
Step-by-step explanation:
Δ ABC and Δ DEF are congruents because:
1. Their sides AB and DE are equal (9 units = 9 units)
2. Their sides BC and EF are equal (5 units = 5 units)
3. Their sides AC and DF are equal (10 units = 10 units)
Now, we can conclude that Δ ABC ≅ Δ DEF by SSS postulate.
Composite figures are two or more figures combined. When finding the surface area, you cannot simply find the separate surface areas and add them. What face(s) do you have to exclude from the total surface area? Explain.
Step-by-step explanation:
You must exclude any intersecting faces (faces that are shared), because these faces are not on the surface.
For example, an ice cream cone can be approximated as a composite figure of a hemisphere on top of a cone. The circular base of the hemisphere and the circular base of the cone are intersecting, so you must exclude it when finding the surface area.
Answer:When two figures are placed together, one of each of their surfaces meets. The surfaces come together on the inside of the figure, and are no longer a part of the surface. These surfaces are a part of the individual figures’ surface area, but not of
Step-by-step explanation:
Did the test (this is the sample response)
10x - 26y=-38
6x + 13y=28
Answer:
[tex]\displaystyle [\frac{9}{11}, 1\frac{111}{143}][/tex]
Step-by-step explanation:
{10x - 26y = −38
{6x + 13y = 28
½[10x - 26y = −38]
{5x - 13y = −19 >> New Equation
{6x + 13y = 28
___________
[tex]\displaystyle \frac{11x}{11} = \frac{9}{11}[/tex]
[tex]\displaystyle x = \frac{9}{11}[/tex][Plug this back into both equations above to get the y-coordinate of 1 111⁄143]; [tex]\displaystyle 1\frac{111}{143} = y[/tex]
I am joyous to assist you anytime.
Review the image and two-column proof below. Which of the following represents a valid reason for statement #2? opposite angles of a parallelogram are equal opposite sides of a parallelogram are equal all three faces are congruent both bases of the prism are congruent
A valid reason is :opposite sides of a parallelogram are equal
Step-by-step explanation:
It is possible to notice that RUTS is a parallelogram where RU=TS and RS = UT.
When you introduce a diagonal RT you form triangles RUT and TSR.
∠URT = ∠STR ----alternate angles
∠UTR=∠SRT------alternate angles
RU║ST and RS║UT
RT=TR -----Common
ΔRUT ≡ ΔTSR by AAS theorem
hence RS=UT matching sides of congruent triangles
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Answer:
opposite sides of a parallelogram are equal
Step-by-step explanation:
got it right on odyssey
the mean amount of money spent per week on gas by a sample of 25 drivers was found to be $57.00 with a standard deviation of $2.36. assuming the population distribution is normally distributed construct and interpret a 90% confidence interval for the mean amount of money spent on Gas per week
Answer:
See below
Step-by-step explanation:
To construct a confidence interval we use the following formula:
ci = (sample mean) +- z*(sd)/[n^(1/2)]
The sample mean is 57, the standard deviation is 2.36, n s 25 and z is the upper (1-C)/2 critical value for the standard normal distribution. Here, as we want a confidence interval at a 90% we have (1-C)/2=0.05 we have to look at the 1-0.05=0.95 value at the normal distribution table, which is 1.65 approximately. Replacing all these values:
ci = 57 +- 1.65*(2.36)/[25^(1/2)]
ci = 57 +- 3.894*/(5) = 57 +- 0.78
ci => (56.22 , 57.78)
9. Find the distance between the point P(-12,-2)
and Q(3,6).
Hint: a sketch is useful.
Answer:
Distance between points [tex]P(-12,-2)[/tex] and [tex]Q(3,6)[/tex] is 17 units
Step-by-step explanation:
Given points:
[tex]P(-12,-2)[/tex]
[tex]Q(3,6)[/tex]
To determine the distance between points P and Q.
Steps to be carried out:
1) Plot the points P and Q on graph.
2) Construct a line from P towards right horizontally and a line from Q downwards vertically such that they meet at point [tex]O(3,-2)[/tex]
3) Join PQ thus forming a right triangle POQ.
4) We can find the distance of sides OP and OQ by counting the units between the points.
OP=[tex]|-12-3|=|-15|=15\ units[/tex]
OQ=[tex]|6-(-2)|=|6+2|=8\ units[/tex]
4)Now, we can apply Pythagorean theorem for triangle POQ.
[tex]PQ^2=OP^2+OQ^2[/tex] [ [tex]Hypotenuse^2=Leg1^2+Leg 2^2[/tex]]
[tex]PQ^2=15^2+8^2[/tex]
[tex]PQ^2=225+64[/tex]
[tex]PQ^2=289[/tex]
Taking square root both sides:
[tex]\sqrt{PQ^2}=\sqrt{289}[/tex]
[tex]PQ=17\ units[/tex] [We take only the positive value as distance is always positive.
∴ Distance between points [tex]P(-12,-2)[/tex] and [tex]Q(3,6)[/tex] is 17 units
Question 2 of 20 :
Select the best answer for the question.
2. Simplify (3a4 - 2a2 + 5a - 10) - (2a4 +
4a2 + 5a - 2).
O A. a4 – 6a² – 8
O B. a4 + 4a? + 10a - 12
O C. 5a4 + 4a3 + 3a? + 10a - 12
O D. a4 + 2a? + 10a - 12
Answer:
A
Step-by-step explanation:
(3a^4-2a^2+5a-10)-(2a^4+4a^2+5a-2)
a^4-6a^2-8
The group of points {(0, 1), (0, 5), (2, 6), (3, 3)} is not a function, but the group of points {(1, 4), (2, 7), (3, 1), (5, 7)} is a function. What do you notice about the two groups of points? What do you think it means to be a function?
The first group of points is not a function due to repetition of elements in domain while second group of points is a function because no element of domain is repeated in any ordered pair.
Step-by-step explanation:
Why {(0, 1), (0, 5), (2, 6), (3, 3)} is not a function?
A relation is said to be a function if there is no repetition in the first elements of each ordered pair. In this group of points, 0 is repeated in two ordered pairs (0, 1), (0, 5) so it is not a function.
Why {(1, 4), (2, 7), (3, 1), (5, 7)} is a function?
The given group of points is a function because there is no repetition in first elements of each ordered pair i.e. there is not repetition in domain so it is a function
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Answer:
AB = 9.6 cm
Step-by-step explanation:
ΔAPQ and ΔABC are similar triangles, thus ratio of corresponding sides are equal, that is
[tex]\frac{AP}{AB}[/tex] = [tex]\frac{PQ}{BC}[/tex], substitute values
[tex]\frac{8}{AB}[/tex] = [tex]\frac{10}{12}[/tex] ( cross- multiply )
10AB = 96 ( divide both sides by 10 )
AB = 9.6 cm
Calculate the percent error
1. Jerri estimates that 30 people would attend the dinner event but only 25 people attended.
2. Gene estimated the length of the fence to be 150 feet, but the actual measurement was 142 feet.
Answer:
Therefore, the percent error in 1. 20%
and the percent error in 2. 6%
Step-by-step explanation:
Given:
1. In estimation of 30 people only 25 people attended.
2. In estimated length of 150 feet the measurement was 142 feet.
Now, in first case for the percent error we would calculate the difference between the people attended:
[tex]30-25=5[/tex]
And then, we will get the percentage error :
[tex]\frac{5}{25} \times 100[/tex]
[tex]\frac{500}{25}[/tex][tex]=20[/tex].
Therefore, the percentage error is 20%.
Now, in second case for the percent error we would repeat the above process as done in first case:
[tex]150-142=8[/tex]
And then:
[tex]\frac{8}{142}\times 100[/tex]
[tex]\frac{800}{142}[/tex][tex]=5.63[/tex]
Therefore, the percentage error is 6% (approximately).
Therefore, the percent error in 1. is 20%
and the percent error in 2. is 6%
6=1 -2n +5 -4n please help get right for Hw struggling hsusns
Answer:
n=0
Step-by-step explanation:
6=1-2n+5-4n
Combine like terms
6=-6n+6
now move the +6 to other side
0=-6n
so divide to remove the n from the -6
0=n
No worries I tested it it's right! I hope :/
PLEASE HELP ME SOLVE THIS 7TH GRADE MATH PROBLEM, THANK YOU!
Answer:
The correct answer is s = 27.
Step-by-step explanation:
This problem already gives us an equation so all we need to do is plug in the numbers:
c = 39.95 + 0.15(s + r) becomes 53.45 = 39.95 + 0.15(s + 63). Now to solve:
53.45 = 39.95 + 0.15(s + 63)
13.50 = 0.15(s + 63) Subtract 39.95 from both sides
13.50 = 0.15s + 9.45 Distribute 0.15 to s and 63
4.05 = 0.15s Subtract 9.45 from both sides
27 = s Divide both sides by 0.15
Hope this helps,
❤A.W.E.S.W.A.N.❤
What is the simplified form of
(X/3-y/4)/(x/4+y/3) ? (6 points)
Option 2: [tex]\frac{4x-3y}{3x+4y}[/tex] is the right answer
Step-by-step explanation:
Given fraction is:
[tex]\frac{\frac{x}{3}-\frac{y}{4}}{\frac{x}{4}+\frac{y}{3}}[/tex]
To solve the fraction, Taking LCM in denominator and numerator
[tex]=\frac{\frac{4x-3y}{12} }{\frac{3x+4y}{12}}[/tex]
When the numerator and denominator both have fractions, the simplified form is obtained be multiplying the numerator with reciprocal of the denominator. So,
[tex]= \frac{4x-3y}{12} * \frac{12}{3x+4y}\\=\frac{4x-3y}{3x+4y}[/tex]
Hence,
Option 2: [tex]\frac{4x-3y}{3x+4y}[/tex] is the right answer
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what is highest common factor of 98 and 42
Answer:
So the greatest common factor 42 and 98 is 14.
7.
The school cafeteria sells corn chips for $0.80 and
potato chips for $0.60. On Tuesday they sold 121
bags earning $80.80. How many of each item did
they sell?
The cafeteria sold 41 corn chips and 80 potato chips.
Step-by-step explanation:
Let,
Corn chips = x
Potato chips = y
Price of corn chips = $0.80
Price of potato chips = $0.60
According to given statement;
x+y= 121 Eqn 1
0.80x+0.60y=80.80 Eqn 2
Multiplying Eqn 1 by 0.80
[tex]0.80(x+y= 121)\\0.80x+0.80y=96.80\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 2 from Eqn 3
[tex](0.80x+0.80y)-(0.80x+0.60y)=96.80-80.80\\0.80x+0.80y-0.80x-0.60y=16\\0.20y=16[/tex]
Dividing both sides by 0.20
[tex]\frac{0.20y}{0.20}=\frac{16}{0.20}\\y=80[/tex]
Putting y=80 in Eqn 1
[tex]x+80=121\\x=121-80\\x=41[/tex]
The cafeteria sold 41 corn chips and 80 potato chips.
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What is the value of the expression below? (6¼) x (6¼) x (6¼) x (6¼)
Answer:
6
Step-by-step explanation:
The expression [tex]6^{\frac{1}{4}}\times 6^{\frac{1}{4}}\times6^{\frac{1}{4}}\times6^{\frac{1}{4}}[/tex] can be simplified by applying power properties.Particulary, there is a property known as "power of a product property" that states that, when there is a product of a series of numbers that share the same base "a", [tex]a^n\times{a^m}\times{a^j}[/tex], the result of the multiplications is [tex]a^{m+n+j}[/tex].Then,in this particular case [tex]6^{\frac{1}{4}}\times 6^{\frac{1}{4}}\times6^{\frac{1}{4}}\times6^{\frac{1}{4}}[/tex] equals [tex]6^{\frac{1}{4} +\frac{1}{4} +\frac{1}{4} +\frac{1}{4} }=6^1=6[/tex]if x=3t-8 and y=4+t, what equation expresses y in terms of x?
Final answer:
To express y in terms of x, rearrange the equations to isolate y. The equation expressing y in terms of x is (4x + 20)/3.
Explanation:
To express y in terms of x, we need to isolate y in the given equations.
From the first equation, x = 3t - 8, we can rearrange to solve for t: t = (x + 8)/3.
Substituting this expression for t into the second equation, y = 4 + t, gives us y = 4 + (x + 8)/3. Simplifying further, we have y = (4x + 20)/3.
The adjacent sides of a parallelogram measure 11 cm and 5cm, and one angle measure 50 °6’. Find the area of the parallelogram
Answer:
42.5 square centimeters
Step-by-step explanation:
The area of the parallelogram is
[tex]A=a\cdot b\cdot \sin \alpha,[/tex]
where a and b are adjacent sides and [tex]\alpha[/tex] is inckuded angle.
In your case,
[tex]a=11\ cm\\ \\b=5\ cm\\ \\ \alpha=50^{\circ}6'[/tex]
Thus,
[tex]A=11\cdot 5\cdot \sin 50^{\circ}6'\approx 42.5\ cm^2[/tex]
85 students went on a field trip. three buses were filled and 25 students traveled in cars. how many students were in each bus?
Answer:
28 students
Step-by-step explanation:
you get 28.3 if you divide 85 by 3
Rachel can finish the job in 5 hours, while Carl can finish the same job in 8 hours. How long will it take them to finish the job together? It is not 3.333 hours
They both will finish the work in 3.07 hours
Step-by-step explanation:
Time taken by Rachel = 5 hours
Work done by Rachel in one hour = 1/5
Time taken by Carl = 8 hours
Work done by Carl in one hour = 1/8
Let x hours be the time taken by both to do work
Then 1/x will be the work done by both in one hour
So,
[tex]\frac{1}{5} + \frac{1}{8} = \frac{1}{x}[/tex]
Taking LCM
[tex]\frac{8+5}{40} = \frac{1}{x}\\\frac{13}{40} = \frac{1}{x}\\13x = 40\\x = \frac{40}{13}\\x = 3.07\ hours[/tex]
They both will finish the work in 3.07 hours
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Answer:
12 hrs
Step-by-step explanation:
X/30+x/48=1
common denominator
x/1440+x/1440
2x/1440=1
2x=1440
x=720
when you convert to hrs you get 12
What decimal is equal to 4/25
Answer:
0.16
Step-by-step explanation:
Use long division
Answer:
0.16
Step-by-step explanation:
4÷25 = 0.16
Question 2
In the diagram, BCD is a straight line. AD = 2V3 cm
Work out the exact length of CD. Give your answer in the form
a + bv3 where a and b are integers
Not drawn
accurately
2V3 cm
Answer:
[tex]CD=(3-\sqrt{3})\ cm[/tex]
Step-by-step explanation:
step 1
Find the length side AB
In the right triangle ABD
[tex]sin(30\°)=\frac{AB}{AD}[/tex]
[tex]AB=sin(30\°)(AD)[/tex]
we have
[tex]AD=2\sqrt{3}\ cm[/tex]
[tex]sin(30\°)=\frac{1}{2}[/tex]
substitute
[tex]AB=\frac{1}{2}(2\sqrt{3})[/tex]
[tex]AB=\sqrt{3}\ cm[/tex]
step 2
Find the length side BD
In the right triangle ABD
[tex]cos(30\°)=\frac{BD}{AD}[/tex]
[tex]BD=cos(30\°)(AD)[/tex]
we have
[tex]AD=2\sqrt{3}\ cm[/tex]
[tex]cos(30\°)=\frac{\sqrt{3}}{2}[/tex]
substitute
[tex]BD=\frac{\sqrt{3}}{2}(2\sqrt{3})[/tex]
[tex]BD=3\ cm[/tex]
step 3
Find the length side BC
In the right triangle ABC
we know that
BC=AB -----> is an 45°-90°-45° triangle
therefore
[tex]BC=\sqrt{3}\ cm[/tex]
step 4
Find the length side CD
we know that
[tex]BD=BC+CD\\CD=BD-BC[/tex]
substitute the values
[tex]CD=(3-\sqrt{3})\ cm[/tex]