Answer:
0.125 took test
Step-by-step explanation:
Volume of the resultant solid will be 0.125 times of the original solid.
Volume scale factor of a rectangular solid:If the sides of a rectangle solid is dilated by a scale factor 'k',Volume of the solid will be given by the expression,
Volume = (k)³(Volume of the original solid)
If a rectangular solid is dilated by a scale factor 'k' = 0.5
Volume of the resultant solid = (0.5)³(Volume of the original solid)
= 0.125(Volume of the original solid)
Therefore, volume of the resultant solid will be 0.125 times of the original solid.
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The product of three whole numbers is 120 how many different possibilities are there for the three whole numbers
Solution:
It is given that,
Product of three Whole numbers = 120
Factorizing 120 into Prime Factors
120 = 2 ×2 ×2×3×5
Number of Possibilities
=Arrangement of 5 things which are numbers(2,2,2,3,5) when 3 of them are equal
= [tex]\frac{5!}{3!}=\frac{5 \times 4 \times 3!}{3!}=5 \times 4 =20[/tex]
The radius of a cylinder is increased by a factor of 5. The height is not changed.
What is the effect of the increase on the volume of the cylinder?
A) The volume of the cylinder increases by a factor of 5.
B) The volume of the cylinder increases by a factor of 25.
C) The volume of the cylinder increases by a factor of 15.
D) The volume of the cylinder increases by a factor of 10.
When the radius of a cylinder is increased by a factor of 5, the volume of the cylinder increases by a factor of 25.
Explanation:The volume of a cylinder can be calculated using the formula V = πr2h, where V is the volume, r is the radius, and h is the height. In this case, the radius of the cylinder is increased by a factor of 5, but the height remains the same. Let's consider the original radius as r and the increased radius as 5r. The volume of the original cylinder is πr2h, and the volume of the new cylinder is π(5r)2h.
Simplifying the expression for the volume of the new cylinder, we get V' = 25πr2h. Comparing the volume of the new cylinder to the volume of the original cylinder, we can see that the volume has increased by a factor of 25. Therefore, statement B is correct: The volume of the cylinder increases by a factor of 25.
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The correct answer is B) The volume of the cylinder increases by a factor of [tex]25.[/tex]
Let's analyze the relationship between the volume of a cylinder and its dimensions.
The volume [tex]\( V \)[/tex] of a cylinder is given by the formula:
[tex]\[ V = \pi r^2 h \][/tex]
where:
[tex]\( r \)[/tex] is the radius of the cylinder,
[tex]\( h \)[/tex] is the height of the cylinder.
Given that the height [tex]\( h \)[/tex] remains unchanged, if the radius [tex]\( r \)[/tex] is increased by a factor of [tex]5[/tex], the new radius [tex]\( r' \)[/tex] becomes[tex]\( 5r \).[/tex]
Now, let's compare the volumes before and after the increase in radius:
1. Original Volume [tex](\( V_{\text{original}} \))[/tex]
[tex]\[ V_{\text{original}} = \pi r^2 h \][/tex]
2. New Volume [tex](\( V_{\text{new}} \))[/tex]
After increasing the radius by a factor of [tex]5[/tex], the new radius [tex]\( r' = 5r \)[/tex].
[tex]\[ V_{\text{new}} = \pi (5r)^2 h = \pi (25r^2) h \][/tex]
Now, compare [tex]\( V_{\text{new}} \)[/tex] with [tex]\( V_{\text{original}} \)[/tex]
[tex]\[ \frac{V_{\text{new}}}{V_{\text{original}}} = \frac{\pi (25r^2) h}{\pi r^2 h} = \frac{25r^2 h}{r^2 h} = 25 \][/tex]
An hourglass consists of two sets of congruent composite figures on either end. Each composite figure is made up of a cone and a cylinder, as shown below:
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Each cone of the hourglass has a height of 18 millimeters. The total height of the sand within the top portion of the hourglass is 54 millimeters. The radius of both cylinder and cone is 8 millimeters. Sand drips from the top of the hourglass to the bottom at a rate of 10π cubic millimeters per second. How many seconds will it take until all of the sand has dripped to the bottom of the hourglass?
68.3
38.4
268.8
230.4
Which equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4)? Check all that apply.
y = –x – 2
2x + 5y = −10
2x − 5y = −10
y + 4 = –(x – 5)
y – 4 = (x + 5)
Writing [tex]5x-2y=-6[/tex] in slope-intercept form:
[tex]5x-2y=-6\\5x+6=2y\\\frac{5x+6}{2}=y\\y=\frac{5}{2}x +3[/tex]
The slope of the line is the number before "x", which is [tex]\frac{5}{2}[/tex].
The slope of the perpendicular to this line is the negative reciprocal of this.
So the slope of perpendicular is [tex]-\frac{2}{5}[/tex].
To find the equation of the perpendicular line, we need a point. It is given as [tex](5,-4)[/tex] where [tex]x_{1}=5[/tex] and [tex]y_{1}=-4[/tex].
Now we use the point-slope form of a line to figure out the equation:
[tex]y-y_{1}=m(x-x_{1})[/tex]
Plugging in the values of [tex]x_{1}[/tex] and [tex]y_{1}[/tex] and [tex]m=-\frac{2}{5}[/tex], gives us:
[tex]y-(-4)=-\frac{2}{5}(x-5)\\y+4=-\frac{2}{5}x+2\\y+\frac{2}{5}x=2-4\\y+\frac{2}{5}x=-2[/tex]
Multiplying everything by 5 [to get rid of the denominator] and re-arranging gives us:
[tex]y+\frac{2}{5}x=-2\\5y+2x=-10\\2x+5y=-10[/tex].
THIS IS THE SECOND OPTION.
ANSWER: [tex]2x+5y=-10[/tex]
If you answer (making sense) and explain (so I can understand) you will be awarded! Please help ASAPA
Solve y=x^2 + 7 for x
Final Answer:
The solutions to the equation [tex]\( y = x^2 + 7 \)[/tex] for x are: [tex]\[ x = +\sqrt{y - 7} \quad \text{and} \quad x = -\sqrt{y - 7} \][/tex]
Explanation:
To solve the equation [tex]\( y = x^2 + 7 \)[/tex] for x, you want to isolate x on one side of the equation. Here are the steps to do so:
1. **Subtract 7 from both sides**:
To isolate the [tex]\( x^2 \)[/tex] term, we first remove the constant term on the right side by subtracting 7 from both sides of the equation.
[tex]\( y - 7 = x^2 + 7 - 7 \)[/tex]
This simplifies to:
[tex]\( y - 7 = x^2 \)[/tex]
2. **Take the square root of both sides**:
To solve for x, you need to get rid of the square on the x term. This is done by taking the square root of both sides. Remember that when you take the square root of both sides of an equation, you must consider both the positive and negative square roots.
[tex]\( \sqrt{y - 7} = \pm\sqrt{x^2} \)[/tex]
Simplifying the right side (since the square root and square operations are inverses of each other), we get:
[tex]\( \sqrt{y - 7} = \pm x \)[/tex]
3. **Solve for x**:
We now have two solutions for x, a positive and a negative one, because squaring a positive or a negative number both give a positive result. Therefore, we write:
[tex]\( x_1 = +\sqrt{y - 7} \\\\ \( x_2 = -\sqrt{y - 7} \)[/tex]
So, the solutions to the equation [tex]\( y = x^2 + 7 \)[/tex] for x are:
[tex]\[ x = +\sqrt{y - 7} \quad \text{and} \quad x = -\sqrt{y - 7} \][/tex]
Remember that you can only take the square root of a non-negative number in real numbers. So if y - 7 is negative, the solutions for x would be complex numbers.
help me please. Find the values of x and y that make these triangles congruent by the HL Theorum.
A. x=2, y=1
B. x=3, y=2
C. x=1, y=2
D. x=2, y=3
36 years old. His son is 8 years old. In how many years will Bruce be three times as old as his son?
the law of cosines is used to find the value of m. m2 = 272 + 182 ??? 2(27)(18)cos(28??) m2 = 729 + 324 ??? (972)cos(28??) m2 = 1053 ??? (972)cos(28??) To the nearest whole number, the value of m is .
the law of cosines establishes:
c² = a² + b² - 2 ab cos C
in this problem
a=27
b=18
C=28°
c=m
m² = 27² + 18² - 2*(27)*(18)* cos(28°)
m² = 729 + 324 - 972* cos(28°)
m² = 1053 - 972* 0.8829
m² = 194.82-------------> m=13.96-----------> 14
the answer is m=14 units
In 1985, there was 285 cell phones subscribers in the small town of centerville.After 1985, the number of subscribers increased by 75% per year. How many cell phones subscribers were in centerville in 1994 ?
The manager of a convenience store wishes to determine how many cartons of eggs are damaged in shipment and delivery. For ten shipments of 1000 cartons of eggs, she examines every 50th carton to see how many cartons contain cracked eggs.
Identify the population and the sample
a.
population: 1,000,000 cartons of eggs
sample: every 50th carton in each shipment
c.
population: 10 shipments of 1000 cartons of eggs
sample: every 50th carton in each shipment
b.
population: 1,000,000 cartons of eggs
sample: the 50th carton of eggs
d.
population: 10 shipments of 1000 cartons of eggs
sample: the 50th carton of eggs
Answer:
Option c. Population: 10 shipments of 1000 cartons of eggs
sample: every 50th carton in each shipment.
Step-by-step explanation:
First we find out population :
For ten shipments of 1000 cartons of eggs. In other words in each 10 shipments there are 1000 cartons of eggs.
Therefore, 1000 × 10 = 10,000 cartons of eggs.
Population : 10,000 cartons of eggs
Now it is given that she examines every 50th carton to see how many cartons contain cracked eggs.
Hence, Sample would be every 50th carton in each shipment.
In option a and b given cartons of eggs are 1,000,000, so they would be eliminated and in option d it is given that sample is only 50th carton of eggs
Therefore, option c would be correct.
Solve for x
Please help quick
A cylinder with a radius of 1 cm and a height of 21 cm has the same volume as a cone with a height of 7 cm. What is the radius of the cone?
Which of the following is a cubic binomial
A.w^3-6w^2+9
B.7a^3+4a^-2
C.-y^3+3y^5
D.x^2-2x^3
How long will it take for 750 mg of a sample of radium-225, which has a half-life of about 15 days, to decay to 68 mg?
A. ≈ 50 days
B. ≈ 54 days
C. ≈ 48 days
D. ≈ 52 days
Answer:
52 Days
Step-by-step explanation:
A news reporter wants to estimate the percentage of registered voters who will vote for a particular candidate in an upcoming election.
Which statement describes a method that will help him accurately estimate this percentage?
He could ask his readers to respond to a survey that asks which candidate the reader will vote for and then calculate the percentage of people who say that they will vote for the particular candidate.
He could ask employees at the newspaper which candidate each will vote for, and then calculate the percentage who will vote for the particular candidate.
He could contact every resident in the town, ask whether the resident will vote for the particular candidate, and then calculate the percentage of residents who say they will vote for the particular candidate.
He could take a random sample of registered voters, and then calculate the percentage of the sample who will vote for the particular candidate.
Answer: The answer is d
Step-by-step explanation: I took this test
What are the domain and range of the function f(x)=1/4(x^3+6x^2+5x-4)
Answer:
Domain and Range of f(x) is all real numbers i.e [tex](-\infty, \infty)[/tex]
Option 4 is correct.
Step-by-step explanation:
Given the function
[tex]f(x)=\frac{1}{4}(x^3+6x^2+5x-4) [/tex]
we have to find domain and range of the above function.
The domain of a function is the complete set of possible values of the independent variable i.e of x. The denominator function can't be equals to 0 when taking the values of x.
[tex]f(x)=\frac{1}{4}(x^3+6x^2+5x-4) [/tex]
Here the function defines at each and every value of x therefore
Domain of f(x) is all real numbers i.e [tex](-\infty, \infty)[/tex]
The range of a function is the complete set of all resulting values of the dependent variable i.e of y, after substituting the values of the domain.
Range of f(x) is all real numbers i.e [tex](-\infty, \infty)[/tex]
Option 4 is correct.
Answer:
d all infinities
Step-by-step explanation:
true or false 120% of a whole number is always greater than the number? and why?
The Art Store sells three types of art pencil sets. The profit is $8.45 on watercolor pencil sets, $6.19 on pastel pencil sets and $4.62 on charcoal pencil sets. There are two branches of the Art Store. The number of sales of pencil sets for each store are shown in the table below.
Set Type
Sales for Westside Branch
Sales for Downtown Branch
watercolor
132
74
pastel
56
48
charcoal
119
126
Which store had the most profit and what was the total profit of that store?
Answer:
c
Step-by-step explanation:
Sammy is 5 feet 3 inches tall. He casts a shadow that is 31 feet 6 inches long. He is standing next to a stop sign that casts a shadow that is 40 feet 6 inches long. How tall is the stop sign in feet and inches.
Mister Stein is pushin 2.25 lb of meat that cost $2.80 per pound how much change should Mr Stein receive if he gives the cashier 20.00$
Answer:
13.7 and dang dude is really pushin big P
Step-by-step explanation:
What is the vertex of the parabola?
A. (-1,0)
B. (0,-3)
C. (1,-4)
D. (3,0)
Option C is correct, the vertex of the parabola is (1, -4).
What is Conic section?Any curve produced by the intersection of a plane and a right circular cone is called as Conic section.
A parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.
The vertex is either the highest point or the lowest point on the parabola depending on whether the parabola opens upward or downward.
In this case, since the parabola opens upward, we can see that
the vertex is the lowest point on the parabola which is (1,-4).
Hence, Option C is correct, the vertex of the parabola is (1, -4).
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Tabitha is trying to find the equation of a line perpendicular to y = 1 over 2 x − 5 in slope-intercept form that passes through the point (2, −7). Which of the following equations will she use?
Answer:
[tex]y=-2x-3[/tex]
Step-by-step explanation:
we know that
If two lines are perpendicular
then
the product of their slopes is equal to minus one
so
[tex]m1*m2=-1[/tex]
Step 1
Find the slope of the given line
we have
[tex]y=\frac{1}{2}x-5[/tex]
the slope of the given line is equal to
[tex]m1=\frac{1}{2}[/tex]
Step 2
Find the slope of the line perpendicular to the given line
[tex]\frac{1}{2}*m2=-1[/tex]
[tex]m2=-2[/tex]
Step 3
Find the equation of the line into slope intercept form
[tex]y=mx+b[/tex]
we have
[tex]m=-2[/tex]
[tex]point(2,-7)[/tex]
substitute and solve for b
[tex]-7=-2*(2)+b[/tex]
[tex]-7=-4+b[/tex]
[tex]b=-7+4=-3[/tex]
The equation of the line is equal to
[tex]y=-2x-3[/tex]
Which of these states had a flat state income tax in 2009
Apex
A.Michigan
B.New Hampshire
C.South Carolina
D.Georgia
Answer:
The correct answer is:
Michigan.
Michigan is the state that had a flat state income tax in 2009.
Step-by-step explanation:
A flat tax (short for flat-rate tax) is a tax system with a constant marginal rate, usually applied to individual or corporate income.
Flat tax benefits higher income brackets progressively due to decline in marginal value.
The state that had a flat state income tax in 2009 is:
Michigan.
Michigan is a flat-tax state that levies a state income tax of 4.25%
https://s3.amazonaws.com/algebranation/testyourself_uploads/MAFS9/9.029.png
Answer:
x = 14
x = negative 2
x = 2
x = negative 14
Step-by-step explanation:
What's the explicit formula HELP
a lab is growing bacteria in a culture dish. the amount of bacteria in the dish doubles every 3 hours. initially, there are 500 bacteria in the dish. how many are in the dish after 9 hours
a. 4,500 bacteria
b. 4,000 bacteria
c. 1,500 bacteria
d. 13,500 bacteria
Answer:
1,500 bacteria so answer C
Step-by-step explanation:
Can someone help me please?
what set of transformations could be applied to rectangle ABCD to create A’B’C’D’?
A)Reflected over the x-axis and rotated 180 degrees
B)Reflected over the y-axis and rotated 180 degrees
C)Reflected over the x-axis and rotated 90 degrees counterclockwise
D)Reflected over the y-axis and rotated 90 degrees counterclockwise
Rectangle ABCD has vertices A(-4,2), B(-4,1), C(-1,1) and D(-1,2).
1. Apply the reflection over the x-axis that has a rule
(x,y)→(x,-y).
Then
A(-4,2)→A''(-4,-2);B(-4,1)→B''(-4,-1);C(-1,1)→C''(-1,-1);D(-1,2)→D''(-1,-2).2. The second transformation is rotation by 90° counterclockwise about the origin. This transformation has a rule
(x,y)→(-y,x).
Then
A''(-4,-2)→A'(2,-4);B''(-4,-1)→B'(1,-4);C''(-1,-1)→C'(1,-1);D''(-1,-2)→D'(2,-1).As you can see these points are exactly those frome the diagram.
Answer: 1st transformation is reflection over the x-axis and second transformation is rotation by 90° counterclockwise about the origin.
Your turn: Use the triangle given. What is the value of sin Θ?