Answer:
Sample response: Volume represents the amount of space an object takes up. Surface area represents the area of the outside surface of the object. If you need to find the amount of space something takes up, or the amount to fill something, find the volume. If you want to find how much is needed to cover something, find the surface area.
Step-by-step explanation:
If they are asking for volume, they are wanting to know how much can go inside the object....If they are asking for surface area.....the are wanting to know about the outside only.
The volume is equal to the product of area and height of shape.
The total area occupied by the surfaces of an object is called its surface area.
What is a volume?"A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder or a sphere."
What is surface area?"The total area occupied by the surfaces of an object is called its surface area."
Different shapes have different volumes. In 3d geometry, we have studied the various shapes and solids such as cube, cuboid, cylinder, cone, etc., that are defined in three dimensions. For all these shapes, we are going to learn to find the volume.
The formula to calculate the volume of a solid in a three-dimensional space, is to find the product of dimensions. Basically, the volume is equal to the product of area and height of shape.
Volume = Base Area x Height
For shapes having flat surfaces such as cube and cuboid, it is easy to find the volume. But for curved shapes like cone, cylinder and sphere, we have to consider the dimensions of its curved surface as well, such as radius or diameter.
In geometry, different 3D shapes have different surface areas which can be easily calculated using the formulas that we will be learning in this article. The surface area is classified into two categories:
1. Lateral surface area or Curved surface area
2. Total surface area
There is a different surface area formula for every geometrical shape, but the idea behind all is to get the total area occupied by all the faces of the objects.
The total surface area considers all the faces of the 3D shape including the flat surfaces and the curved surfaces, while the lateral surface area is calculated to find the area occupied by the curved surface of the shape. It does not include the area of the bases. A sphere is one 3D figure which has only one round surface with no flat base.
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Write whether the following pair of linear
equations is consistent or not: x+y=14 & X-y=4
Answer:
The linear equation is consistent
Step-by-step explanation:
X+y=14....(1)
X-y=4....(2)
Add (1) and (2)
2x=28
Divide both sides by 2
x=14
Substitute the value for x into (1)
14+y=14
Substrate 14 from both sides
y=0
So the linear equation is consistent
what is the answer ?????????
Answer:
Option C, (2, 6)
Step-by-step explanation:
Step 1: Find the solution
They intersect at the x-value 2 and the y-value 6.
So... the answer is (2, 6)
Answer: Option C, (2, 6)
Drag each value to the correct location on the table.
Identify whether each cube root or square root lies between 2 and 3, 4 and 5, or 9 and 10.
Answer:
see attached
Step-by-step explanation:
Each cube root or square root lies:
∛800: Between 2 and 3
∛101: Between 4 and 5
∛90: Between 4 and 5
∛20: Between 2 and 3
√7: Between 2 and 3
√20: Between 4 and 5
√90: Between 9 and 10
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
Here are the steps to find whether each cube root or square root lies between 2 and 3, 4 and 5, or 9 and 10:
Start with the first cube root or square root, ∛800.
Estimate the value of the root.
For ∛800, we can estimate that it's between 8 and 9, since 8 cubed is 512 and 9 cubed is 729.
So, ∛800 must be somewhere in between.
Determine which range the estimated value falls into.
Since 8 is between 2 and 3, ∛800 must also be between 2 and 3.
Repeat the process for the remaining cube roots and square roots, using the same ranges.
Here are the results:
∛800: Between 2 and 3
∛101: Between 4 and 5
∛90: Between 4 and 5
∛20: Between 2 and 3
√7: Between 2 and 3
√20: Between 4 and 5
√90: Between 9 and 10
Thus,
Four of the roots lie between 2 and 3, two lies between 4 and 5, and one lies between 9 and 10.
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What is the volume of the cylinder? Express the answer in terms of .
d = 8 cm
h = 18 cm
Recall the formula V = 2h
The volume of the cylinder is,
⇒ Volume = 904.32 cm³
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
Height of cylinder = 18 cm
Diameter of cylinder = 8 cm
Hence, Radius of cylinder = 4 cm
Now, We know that;
The volume of the cylinder is,
⇒ Volume = πr²h
Substitute the given values, we get;
⇒ Volume = 3.14 × 4² × 18
⇒ Volume = 904.32 cm³
Thus, The volume of the cylinder is,
⇒ Volume = 904.32 cm³
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Find the value of t in the equation t + 5 + 3t = 1
--------------------------------------------------------
t + 5 + 3t = 1
Group like terms:
t+3t+5= 1
Add similar elements:
4t+5=1
Subtract 5 from both sides:
4t+5-5 = 1-5
Simplify:
4t= -4
Divide both sides by 4:
4t/4 = -4/4
Simplify:
t= -1
Your Answer Is t= -1
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Please answer this question
Answer:
B
Step-by-step explanation:
A- 2/15 + 1/3 = 7/15-0.46
B- 6/7-1/3=11/21-0.52
Answer: B is closer to 1/2
Step-by-step explanation:
I hope the explanation in the diagram helps
a coin is tossed and an eight sided die numbered 1 through 8 is rolled. find the probability of tossing a head and then rolling a number greater than 4
Answer:
The answer is 4.
Step-by-step explanation:
There are 16 possible outcomes of this, and of those, only 4 of them result in the coin landing on heads and landing on a number that is greater than 4.
Factor. 3ab-6b^2-2bc+ac
(Thank you, please explain all steps)
Answer:
(3b + c)(a - 2b)
Step-by-step explanation:
Given
3ab - 6b² - 2bc + ac ← Rearranging
= 3ab + ac - 6b² - 2bc (factor the first/second and third/fourth terms )
= a(3b + c) - 2b(3b + c) ← factor out (3b + c) from each term
= (3b + c)(a - 2b)
Answer:
(a-2b)(3b-c)
Step-by-step explanation:
3ab-6b^2-2bc+ac
Let's rearrange
3ab+ac-6b^2-2bc
Let's factorise
a(3b+c)-2b(3b+c)
(a-2b)(3b+c)
Since the answer cannot be solved further
The answer is (a-2b)(3b+c)
Which of the following equations represents a line that is parallel to the line that passes through the points below?
(-3,6) (9,2)
Answer:
See below
Step-by-step explanation:
Two lines are parallel if they have the same slope but different y-intercepts. So the slope that can be formed given the points (-3,6) and (9,2) is (9-(-3))/(2-6)=12/-4=-3
With y=-3x+b, we need b, which can be found by plugging in either point:
2=-3(9)+b
2=-27+b
29=b
So the y-intercept therefore cannot be 29 but it can be any real number.
So the equation y=-3x+2 works, y=-3x+3, y=-3x+4, and so on....
Melanie knew that the perimeter of the soccer field was 1/6 miles.Her goal was to walk 2 miles while watching her sisters game.If she walked around the field 13 times,did she reach her goal?Tell how
Answer:
Yes, she has reached her goal.
Step-by-step explanation:
I know this because you have to multiply 1/6 by 13 to get 13/6, which is equal to 2 1/6. Since 2 1/6 is greater than 2, she has reached her goal.
Equation: 1/6×13= 2 1/6
Comparing statement: 2 < 2 1/6
PLEASE ANSWER i WILL PUT MOST BRAINLIEST!
Bottles of mango juice are assumed to contain 275 milliliters of juice. There is some variation from bottle to bottle because the filling machine is not perfectly precise. Usually, the distribution of the contents is approximately Normal. An inspector measures the contents of seven randomly selected bottles from one day of production. The results are 275.4, 276.8, 273.9, 275.0, 275.8, 275.9, and 276.1 milliliters. Do these data provide convincing evidence at α = 0.05 that the mean amount of juice in all the bottles filled that day differs from the target value of 275 milliliters? (4 points)
Group of answer choices
Because the p-value of 0.0804 is greater than the significance level of 0.05, we fail to reject the null hypothesis. We conclude the data provide convincing evidence that the mean amount of juice in all the bottles filled that day does not differ from the target value of 275 milliliters.
Because the p-value of 0.0804 is greater than the significance level of 0.05, we reject the null hypothesis. We conclude the data provide convincing evidence that the mean amount of juice in all the bottles filled that day differs from the target value of 275 milliliters.
Because the p-value of 0.1609 is greater than the significance level of 0.05, we fail to reject the null hypothesis. We conclude the data provide convincing evidence that the mean amount of juice in all the bottles filled that day does not differ from the target value of 275 milliliters.
Because the p-value of 0.1609 is greater than the significance level of 0.05, we reject the null hypothesis. We conclude the data provide convincing evidence that the mean amount of juice in all the bottles filled that day differs from the target value of 275 milliliters.
Because the p-value of 1.5988 is greater than the significance level of 0.05, we fail to reject the null hypothesis. We conclude the data provide convincing evidence that the mean amount of juice in all the bottles filled that day does not differ from the target value of 275 milliliters.
Answer:
The correct option is;
c. Because the p-value of 0.1609 is greater than the significance level of 0.05, we fail to reject the null hypothesis. We conclude the data provide convincing evidence that the mean amount of juice in all the bottles filled that day does not differ from the target value of 275 milliliters.
Step-by-step explanation:
Here we have the values
μ = 275 mL
275.4
276.8
273.9
275
275.8
275.9
276.1
Sum = 1928.9
Mean (Average), = 275.5571429
Standard deviation, s = 0.921696159
We put the null hypothesis as H₀: μ₁ = μ₂
Therefore, the alternative becomes Hₐ: μ₁ ≠ μ₂
The t-test formula is as follows;
[tex]t=\frac{\bar{x}-\mu }{\frac{s}{\sqrt{n}}}[/tex]
Plugging in the values, we have,
Test statistic = 1.599292
[tex]t_{\alpha /2}[/tex] at 7 - 1 degrees of freedom and α = 0.05 = ±2.446912
Our p-value from the the test statistic = 0.1608723≈ 0.1609
Therefore since the p-value = 0.1609 > α = 0.05, we fail to reject our null hypothesis, hence the evidence suggests that the mean does not differ from 275 mL.
Answer:
Because the p-value of 0.1609 is greater than the significance level of 0.05, we fail to reject the null hypothesis. We conclude the data provide convincing evidence that the mean amount of juice in all the bottles filled that day does not differ from the target value of 275 milliliters.
Step-by-step explanation:
I took the quiz and got it right
Can you help me out plzzz
Answer:
x=31.6
Im not sure since i have not taken a trig course yet, but i know the basics:
Tangent is opposite over adjacent, and in respect to this angle, (31 degrees) the opposite side is 19 and adjacent is x.
Tan(31) = 19/x
Solve for x...use a calculator to find tan(31)
(Credit to google for the pic)
Find the area of a circle with a radius of 3.2 centimeters. Use the pi key and round to nearest tenth.
By what percent will the fraction change if its numerator is
increased by 25% and its denominator is increased by 20%?
Answer:
The fraction increase by ( [tex]0.047=4.7\:\%[/tex] ) if its numerator is
increased by 25% and its denominator is increased by 20%.
Step-by-step explanation:
Let 'n' be the numeratorLet 'd' be the denominatorAs
[tex]100\%\mathrm{\:in\:fractions}=\:1[/tex]
[tex]25\%\mathrm{\:in\:fractions}=\:\frac{1}{4}[/tex]
[tex]20\%\mathrm{\:in\:fractions}=\frac{1}{5}[/tex]
so
Increase in 25% means
[tex]100\%\:+25\%\:=\frac{5}{4}[/tex]
Increase in 20% means
[tex]100\%\:+20\%\:=\frac{6}{5}[/tex]
Thus the fraction becomes
[tex]\:\frac{\frac{5}{4}\times \:n}{\frac{6}{5}\times \:d}[/tex]
[tex]=\frac{\frac{5}{4}n}{\frac{6d}{5}}[/tex]
[tex]\mathrm{Divide\:fractions}:\quad \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\times \:d}{b\times \:c}[/tex]
[tex]=\frac{5n\times \:5}{4\times \:6d}[/tex]
[tex]=\frac{25n}{24d}[/tex]
[tex]=1.0417\left(\frac{n}{d}\right)[/tex]
[tex]=1\left(\frac{n}{d}\right)+0.047\left(\frac{n}{d}\right)[/tex]
As
[tex]0.047=4.7\:\%[/tex]
Therefore, the fraction increase by ( [tex]0.047=4.7\:\%[/tex] ) if its numerator is
increased by 25% and its denominator is increased by 20%.
Rewrite the quadratic function f(x)=-3(x-4)^2+5 in standard form
Answer:
f(x) = 3x² - 24x + 53
Step-by-step explanation:
Given
f(x) = 3(x - 4)² + 5 ← expand the factor using FOIL
= 3(x² - 8x + 16) + 5 ← distribute by 3 and simplify
= 3x² - 24x + 48 + 5
= 3x² - 24x + 53 ← in standard form
A triangle has an area of 24 meters squared and base length of 8m. Find the height.
Answer:
h = 6
Step-by-step explanation:
Since 1/2 times the base length times the height equals the area, just work your way backwards to get the answer!
It looks like this
(1/2)8 * h = 24
First multiply 1/2 by 8 to get 4
then divide 4 out of both sides so that h = 6!
Thank me later :)
Answer:
6 is the answer
Step-by-step explanation:
A waiter at a restaurant receives a 15% tip on a $25 bill. At the same restaurant, a waitress receives a 20% tip on a $20 bill.
Who gets the larger tip? By how much?
Answer:
The waitress who received 20% of $20 gets a larger tip.
The waitress who received 20% of $20 gets $4.00 tip, and the waitress who received 15% of $25 gets a tip of $3.75
Step-by-step explanation:
To get 15% of 25, you multiply it by .15, giving you your answer.
To get 20% of 20, you multiple it by .20, giving you your answer.
Answer:
the second waiter gets a larger tip by $0.25
Step-by-step explanation:
15% of $25 is $3.75
the first waiter only got a $3.75 tip.
20% of $20 is $4
the second waiter got a $4 tip
the second waiter got $0.25 more than the first.
i hope this helps! :)
What number is 1/100 of the value of 2.6
Answer:
0.026
Step-by-step explanation:
The number gotten from 1/100 of the value of 2.6 is; 0.026
Decimals and Fractions
We want to find 1/100 of the value of 2.6. This means that we will multiply 2.6 by 1/100.
⇒ 2.6 × 1/100
Multiply both numerator and denominator by 10 to get;
26/1000
Now, when we divide 26 by 1000, we will get a decimal which is; 0.026
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(8x^2+22x+19) divided by (2x+3)
find the quotient and remainder
Quotient=4x+5
Remainder=4
hope this will help u..
Answer: quotient =4x+5
remainder =4
Step-by-step explanation:
Looking at the diagram below
Quotient =4x+5
Remainder =4
Elsa saving money to buy a game so far she had saved $36 which is 3/4 of the total cost of the game how much does the game cost
Answer:
$48
Step-by-step explanation:
To figure out how much the game costs in total, we first need to divide $36 by 3 (3 is the numerator).
36 / 3 = 12
The number 12 is how much each quarter is worth as shown below.
1/4 = 12
2/4 = 24
3/4 = 36
4/4 = ?
To find the answer, all we do is add 12 to 36.
12 + 36 = $48
Answer:
$48
Step-by-step explanation:
Let x represent the cost of the game
$36 = 3/4 x
Divide both sides by 3/4
$36/3/4 = x
$36 *4 / 3 = x
$48 = x
Therefore, the game costs $48
NEED HELP BRANLIEST TO FIRST ANSWER
Compare the quadratic function represented by the table to the function represented by the graph to determine which statement is true.
A) The tabled function has a lower minimum value.
B) The tabled function has a greater maximum value.
C) The graphed function has a lower minimum value.
D) The graphed function has a greater maximum value.
x f(x)
−4 −15
−2 −3
0 1
2 −3
4 −15
5 −24
Answer:
B
Step-by-step explanation:
Based on the diagram, what is the value of x?
Answer:
is it 57
Step-by-step explanation:
Answer:
x = 57
Step-by-step explanation:
x and 57° are vertical angles and congruent, thus
x = 57
In January, Toby's bookstore sold books. In February, he sold 20% more books. How many books did he sell in February?
Answer:
For me to answer the question you will have to put another number
18) Write an equation of the line that is perpendicular to the line y = 4x - 10 that passes through the point (-16, 2). A) y = - 1 4 x - 2 B) y = -4x + 6 C) y = - 1 4 x + 2 D) y = 4x + 2
The equation of the line that is perpendicular to y = 4x - 10 and passes through the point (-16, 2) is y = -1/4x - 2, which is option A.
Explanation:The student is asking for the equation of a line that is perpendicular to the given line y = 4x - 10 and passes through the point (-16, 2). The slope of the given line is 4, and the slope of a line perpendicular to it will be the negative reciprocal, which is -1/4. Using the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept, we substitute the slope -1/4 and the point (-16, 2) to find b.
Plugging in the point, we get:
2 = (-1/4)(-16) + b
2 = 4 + b
b = 2 - 4
b = -2
So, the equation of the line is y = (-1/4)x - 2. The correct answer is option A) y = -1/4x - 2.
To find the line perpendicular to ( y = 4x - 10 ) passing through (-16, 2), its equation is[tex]\( y = -\frac{1}{4}x - 2 \)[/tex], option A.
The correct option is a)[tex]\(y = -\frac{1}{4}x - 2\).[/tex]
To find the equation of the line that is perpendicular to the given line (y = 4x - 10), we first need to determine the slope of the given line, because perpendicular lines have slopes that are negative reciprocals of each other.
The given line (y = 4x - 10) is in the slope-intercept form (y = mx + b), where (m) is the slope. In this case, the slope of the given line is (m = 4).
The negative reciprocal of (4) is [tex]\(-\frac{1}{4}\)[/tex]. This will be the slope of the perpendicular line.
Now, we use the point-slope form of a line, which is [tex]\(y - y_1 = m(x - x_1)\),[/tex]where [tex]\((x_1, y_1)\)[/tex] is a point on the line and \(m\) is the slope.
Given the point ((-16, 2)), we substitute (x_1 = -16) and (y_1 = 2) into the point-slope form and the slope[tex]\(m = -\frac{1}{4}\):[/tex]
[tex]\[ y - 2 = -\frac{1}{4}(x - (-16)) \][/tex]
[tex]\[ y - 2 = -\frac{1}{4}(x + 16) \][/tex]
Now, we can simplify and rewrite this equation in slope-intercept form (y = mx + b):
[tex]\[ y - 2 = -\frac{1}{4}x - 4 \][/tex]
[tex]\[ y = -\frac{1}{4}x - 4 + 2 \][/tex]
[tex]\[ y = -\frac{1}{4}x - 2 \][/tex]
So, the equation of the line that is perpendicular to (y = 4x - 10) and passes through the point ((-16, 2)) is option A) [tex]\(y = -\frac{1}{4}x - 2\).[/tex]
Colton has a 1/20 probability of winning the race. Logan has a 15% probability of winning. Who has the greater chance of winning?
A Colton
B Logan
C They have an equal chance
Answer:
Logan has the greater probability of winning
Step-by-step explanation:
Colton=1/20
=0.05
So the probability of Colton is 0.05
Logan=15%
=15/100
=0.15
So the probability of Logan is 0.15
When comparing the two,it was observed that the Logan has greater probability of winning
finding the area of a square is the same as finding the area of rectangle,
That is true, you multiply the length by the width in a rectangle, and you do the same in a square.
Austin just got hired for a new job and will make $80,000 in his first year. Austin
was told that he can expect to get raises of $1,500 every year going forward. How
much money in salary would Austin make in his 19th year working at this job? Round
to the nearest tenth (if necessary).
Answer:
$107,000
Step-by-step explanation:
Austin's salary in his 19th year will include his base pay and 18 raises:
$80,000 + 18×$1500 = $107,000
Austin's salary in his 19th year would be $107,000.
A building casts a shadow that is 420 meters long. At the same time, a person who is 2 meters tall casts a shadow that is 24 meters long. How tall is the building?
Answer:
35 Meters
Step-by-step explanation:
Ratio is 12
What I mean by that is 2 turns into 24 because you multiply 12 to it. Same thing for 420, except for the fact that you divide it (working backwards). So 420 divided by 12 equals 35:) Enjoy your day
Answer:
the answer is 35 meters.
Helpp!!!!
Evaluate (x+5)^2+8 for x=-2
A. 12
B. 33
C. 17
D. 57
∆DEF has vertices D(1, 4), E(3, 5), and F(2, 1). If you reflect ∆DEF across the x-axis, what will be the coordinates of the vertices of the image ∆D′E′F′?
A.) D′(–1, –4), E′(–3, –5), and F′(–2, –1)
B.) D′(–1, 4), E′(–3, 5), and F′(–2, 1)
C.) D′(4, –1), E′(5, –3), and F′(1, –2)
D.) D′(1, –4), E′(3, –5), and F′(2, –1)
Answer:
D
Step-by-step explanation:
When reflecting points across the x axis, and x coordinate remains the same and y-coordinates become the opposite of the original.
Answer:
it is D
Step-by-step explanation: