Answers
The volume V of a cylinder with radius r and and height h is given by:
[tex]V=\pi r^2h[/tex]In this case,
[tex]r=10,h=25[/tex]Therefore, the volume is given by:
[tex]V=\pi\cdot10^2\cdot25\approx7854\text{ cm}^3[/tex]Hence, the required volume is 7854 cm³
Related Questions
what is the solution to the inequality 2x<20
Answers
The given expression is
[tex]2x<20[/tex]We just have to divide by 2
[tex]\begin{gathered} \frac{2x}{2}<\frac{20}{2} \\ x<10 \end{gathered}[/tex]Hence, the solution is all real numbers less than 10.Hello! I really need help with this ASAPFrom my ACT prep guide
Answers
Asymptotes for the given F(x) =( 2x^2-5x -3 )/(x^2-4x +3 ) is at :
1. x =1 (vertical) and y =1(horizontal)
( function is also undefined at (3; 7/2)
What is the Interquartile Range for the following data set?{5,6,7,3, 9, 8,3,1,6,7,7}
Answers
Answer:
Explanation:
The first step is to rearrange the data in ascending order. It becomes
1, 3, 5, 5, 6, 6, 7, 7, 7, 8, 9
Recall,
interquartile range, IQR = Q3 - Q1
where
Q1 is the lower quartile
Q3 is the upper quartile
Position of Q1 = 0.25(n + 1)
where
n = number of values = 11
Position of Q1 = 0.25(11 + 1) = 3
T
find the diameter of a circle with a circumference of 94.2 CM round your answer to the nearest whole number
Answers
The circumference of a circle is computed as follows
C = πD
where D is the diameter of the circle.
Replacing with C = 94.2, and solving for D,
94.2 = πD
94.2/π =D
30 = D
Find the sale price when the original price is $58 and the discount rate is 9%
Answers
When the discount rate is 9%, this means the sale price of the product will be 100% - 9% =91% the original price.
91% of $58 is
[tex]\frac{91}{100}\times58=52.78[/tex]The sale price after a discount rate of 9% is $52.78
I will show you the pic
Answers
Data Input
$22 in your bank account
+ 1.50 each week
$218 in causing account
- 13 echa week
t = week
Procedure
[tex]\begin{gathered} 22+1.50t=218-13t \\ 13t+1.50t=218-22 \\ 14.5t=196 \\ t=\frac{196}{14.5} \\ t=13.51 \end{gathered}[/tex]
The answer would be at t = 13.51 weeks
A board is 20 inches long. It must be cut into four pieces of equal length, and each of the three cuts will cause a waste of 1/2 inches. How long will each piece be after the Cuts are made
Answers
Let the length of each cut be x.
Therefore, the following equation holds true:
[tex]4x+3(\frac{1}{2})=20[/tex]Therefore,
[tex]\begin{gathered} 4x=20-\frac{3}{2}=18.5 \\ x=4.625\text{ inches} \end{gathered}[/tex]Therefore, the required length is 4.625
What are 6 different expressions that have the same value as 10 to the 8 power?(show using exponents,multiplication, and division)
Answers
Answer
(10²)⁴
(1/10⁻⁸)
10⁴ × 10⁴
10¹² ÷ 10⁴
1,000 × 100,000
10,000,000,000 ÷ 100
All of them are equal to 10⁸
Explanation
The laws of indices will help us solve this
- When a variable carries a power and is raised to an extra power, the answer is the variable carrying the product of these two powers.
- When a variable is raised to the power of a negative number, this is the same as 1 over that variable raised to the positive value of that power
- When the same variable, carrying different powers are multiplied with each other, then, the result is that same variable raised to the power of the sum of the two powers from before multiplication.
So, some of the ways to write expressions that will give 10 raised to the power of 8 include
First one
(10²)⁴ = 10⁸
Second one
(1/10⁻⁸) = 10⁻⁽⁻⁸⁾ = 10⁸
Third one
10⁴ × 10⁴ = 10⁴⁺⁴ = 10⁸
Fourth one
10¹² ÷ 10⁴ = 10¹²⁻⁴ = 10⁸
Fifth one
1,000 × 100,000 = 100,000,000 = 10⁸
Sixth one
10,000,000,000 ÷ 100 = 100,000,000 = 10⁸
Hope this Helps!!!
If 3x - 4y = 9, then x equals
Answers
Solution
Given
3x - 4y = 9
If we make x the subject of the formula,
adding 4y to both sides,
=> 3x = 9 + 4y
Dividing all through by 3,
=> x = 3 + 4y/3
[tex]\Rightarrow x=3+\frac{4y}{3}[/tex]Use the table to evaluate the given composite function (G o f)(-5)=
Answers
We were given that:
[tex]\begin{gathered} g(5)=2 \\ f(5)=-1 \end{gathered}[/tex]We will proceed to calculate (G o f)(-5), we have:
[tex]undefined[/tex]NO* 5GThe movement of the progress bar may be uneven because questions can be worth more or less(including zero) depending on your answer.The two triangles below are similar because IZA = MZEand mzB = mZF.EBADLOUISE L. HAYWhich option lists the other corresponding sideling
Answers
For two similar triangles, the corresponding angles are always congruent.
We know two pairs of corresponding angles:
m∠A=m∠E
m∠B=m∠F
As mentioned above, all corresponding angles are congruent, so the remaining pair must be equal:
m∠C=m∠D
Having established the corresponding pairs we can name both triangles. When you name the triangles, the letters of the corresponding vertices must be in the same position, starting with the first corresponding pair ∠A and ∠E the name of the triangles can be:
Following the order of the letters, you can determine the corresponding sides:
[tex]\begin{gathered} \bar{AB}\cong\bar{EF} \\ \bar{BC}\cong\bar{FD} \\ \bar{CA}\cong\bar{DE} \end{gathered}[/tex]The correct option is the second:
[tex]undefined[/tex]Find sin (t), cos(t), tan (t), csc (t), sec (t), cot (t)
Answers
In a unit circle, the trigonometric functions are as follows:
• sin t = y and csc t = 1/y.
,• cos t = x and sec t = 1/x
,• tan t = y/x and cot t = x/y
The vertices of △ABC are A(2, −3), B(−3, −5), and C(4, 1). For each translation,give the vertices of △A′B′C′.
Answers
A (2,-3)
B(-3,-5)
C(4, 1)
1. T (-2,3)
Add and subtract the new coordinates:
A′(2-2,-3+3) = (0,0)
B′(-3-2,-5+3)= (-5,-2)
C′(4-2,1+3) = (2,4)
2. T (-4,-1)
A′(2-4,-3-1) = (-2,-4)
B′(-3-4,-5-1)= (-7,-6)
C′(4-4,1-1) = (0,0)
3. T (4,6)
A′(2+4,-3+6) = (6,3)
B′(-3+4,-5+6)= (1,1)
C′(4+4,1+6) = (8,7)
What I’d the sum of the numbers 1 up to 200
Answers
SOLUTION
The given sum of numbers are
[tex]1+2+3+4+5+\cdots+200[/tex]Notice that this represents an arithmetic series with
First term a=1
Last term l=200
Number of terms n = 200
Using the arithmetic sum formula
[tex]S_n=\frac{n}{2}\lbrace a+l\rbrace[/tex]Substituting values gives
[tex]\begin{gathered} S_n=\frac{200}{2}(1+200) \\ S_n=100(201) \\ S_n=201,100 \end{gathered}[/tex]Therefore the total sum is 201,100
Determine which variable is the independent variable and which variable is the dependent variable. Write an equation, make a table, and plot the points from the table on the graph. Noah can type 40 words per minute. Let w be the number of words typed and m be the number of minutes spent typing.
Answers
w=40m
m is the independent variable.
w is the dependent variable.
Rearrange the equation so n is the independent variable.m +1 = -2(n + 6)m =
Answers
This question you just need to manipulate the equation, in a way the "m" is written as a function of n.
We start with the initial equation:
m + 1 = -2(n + 6)
This is pretty much given already. You just need to subtract "1" from both sides, and you'll get your "m" as a function of "n"
m(n) = -2(n+6) - 1
Rearranging:
m = -2n - 13
fill in the values of the table for the function shown
Answers
To find the value of y, we need to replace each of the values of x in the equation of the function.
For example for the first value of x, -8, replace x for -8, this way:
[tex]\begin{gathered} y=\sqrt[3]{x} \\ y=\sqrt[3]{-8} \\ y=-2 \end{gathered}[/tex]The first value of y is -2.
Follow the same procedure for the resting values of x:
[tex]\begin{gathered} y=\sqrt[3]{-1} \\ y=-1 \end{gathered}[/tex][tex]\begin{gathered} y=\sqrt[3]{0} \\ y=0 \end{gathered}[/tex][tex]\begin{gathered} y=\sqrt[3]{1} \\ y=1 \end{gathered}[/tex][tex]\begin{gathered} y=\sqrt[3]{8} \\ y=2 \end{gathered}[/tex]Now, fill in the table using the obtained values of y:
how can I use deductive reasoning to show that
Answers
Therefore,
[tex]\Delta PQS\cong\Delta RQS\text{ (SAS congruence rule.)}[/tex]So,
[tex]\angle P\cong\angle R[/tex]Solve the equation for x, and enter your answer in the box below. x + 15 = 36
Answers
SOLUTION
x + 15 = 36
You collect like terms by taking 15 to meet 36. When 15 crosses the = sign it becomes -15.
x = 36 - 15
x = 21
Is the value of makayla’s scooter growing or decaying A growingB decaying
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given exponential function
[tex]f\mleft(x\mright)=13500\cdot0.89^x[/tex]STEP 2: Explain the standard exponential function
Exponential function is given as
[tex]y=a\cdot b^x[/tex]where:
a is the initial or starting value of the function,
b is the growth factor or growth multiplier. b determines the rate at which the graph grows or decays.
STEP 3: Compare the given function with the standard exponential function
[tex]\begin{gathered} \text{By comparison,} \\ a=13500 \\ b=0.89 \end{gathered}[/tex]STEP 4: Mention the condition for determining a growth or decay in an exponential function.
If a is positive and b is greater than 1, then it is an exponential growth
If a is positive and b is less than 1 buth greater than 0, then it is an exponential decay.
STEP 5: Reach a conclusion
It can be seen from Step 3 that a is positive(13500) and b(0.89) is greater than zero but less than 1, therefore this implies according to the condition in step 4 that the value of the scooter is decaying.
(b) The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there are 1500 after 1 day, what is thesize of the colony after 3 days?Approximately mosquitoes(Do not round until the final answer. Then round to the nearest whole number as needed.)}.vix
Answers
Given:
The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there are 1500 after 1 day,
Required:
what is the size of the colony after 3 days?
Explanation:
We know
[tex]A=A_0e^{kt}[/tex][tex]\begin{gathered} Where, \\ A_0=\text{ Starting amount} \\ e=\text{ Euler's constant} \\ k=\text{ Amount of increase} \\ t=\text{ time} \end{gathered}[/tex]Now,
[tex]\begin{gathered} 1500=1000e^k \\ \frac{1500}{1000}=e^k \\ 1.5=e^k \\ ln1.5=klne \\ k=0.405 \end{gathered}[/tex]After 3 days
[tex]\begin{gathered} A=1000\times e^{(0.405\times3)} \\ A=1000\times e^{1.215} \\ A=1000\times3.370 \\ A=3370 \end{gathered}[/tex]Answer:
After 3 days there will be 3370 mosquitoes.
A scientist has two solutions, which has labeled solution A abd solution B . each salt contain she knowns that solution A is 60% salt and solution B is 85% salt. she want to obtain 180 ounces of a mixture that is 70% salt how many ounces of each solution should she use
Answers
To do this, you can first express the percentages as decimals, like this
[tex]\begin{gathered} 60\text{ \%}=\frac{60}{100}=0.6 \\ 85\text{ \%}=\frac{85}{100}=0.85 \\ 70\text{ \%}=\frac{70}{100}=0.7 \end{gathered}[/tex]Later, you can take
x = number of ounces of solution A
y = number of ounces of solution B
And build the following system of linear equations
[tex]\begin{gathered} \mleft\{\begin{aligned}x+y=180 \\ 0.6x+0.85y=0.7\cdot180\end{aligned}\mright. \\ \mleft\{\begin{aligned}x+y=180 \\ 0.6x+0.85y=126\end{aligned}\mright. \end{gathered}[/tex]To solve it you can use the substitution method, for example.
Solve for x from the first equation and substitute this value in the second equation
[tex]\begin{gathered} x+y=180 \\ \text{ Subtract y from both sides of the equation} \\ x+y-y=180-y \\ x=180-y \end{gathered}[/tex]Now substituting in the second equation
[tex]\begin{gathered} 0.6(180-y)+0.85y=126 \\ 108-0.6y+0.85y=126 \\ 108+0.25y=126 \\ \text{ Subtract 108 from both sides of the equation} \\ 108+0.25y-108=126-108 \\ 0.25y=18 \\ \text{ Divide both sides of the equation by }0.25 \\ \frac{0.25y}{0.25}=\frac{18}{0.25} \\ y=72 \end{gathered}[/tex]Now plug the value of y into the first equation
[tex]\begin{gathered} x+y=180 \\ x+72=180 \\ \text{ Subtract 72 from both sides of the equation} \\ x+72-72=180-72 \\ x=108 \end{gathered}[/tex]So,
[tex]\mleft\{\begin{aligned}x=108 \\ y=72\end{aligned}\mright.[/tex]Therefore, the scientist should use 108 ounces of solution A and 72 ounces of solution B.
Line 1 goes through the points (9,7) and (10,1). Line 2 passes through (4,4) and (10,5). Are the lines parallel or perpendicular?
Answers
perpendicular
Explanation
to solve this we need to find the slopes of the lines, and then compare the slopes
Step 1
find the slope of line 1
the slope is given by:
[tex]\begin{gathered} \text{slope}=\frac{change\text{ in y}}{\text{change in x}}=\frac{y_2-y_1}{x_2-x_1} \\ \text{where} \\ P1(x_1,y_1) \\ P2(x_2,y_2) \end{gathered}[/tex]P1 and P2 are 2 known points of the line,
so
Let
P1(9,7)
P2(10,1)
now, replace to find slope 1
[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ slope=\frac{1-7}{10-9} \\ \text{slope}=\frac{-6}{1} \\ \text{slope}_1=-6 \end{gathered}[/tex]Step 2
now, slope of line 2
Let
P1(4,4)
P2(10,5)
replace to find slope 2
[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ slope_2=\frac{5-4}{10-4}=\frac{1}{6} \\ slope_2=\frac{1}{6} \end{gathered}[/tex]Step 3
remember:
when 2 lines are parallel , the slope is the same,hence
[tex]\begin{gathered} \text{slope}_1=-6 \\ \text{slope}_2=\frac{1}{6} \\ \text{slope}_1\ne slope_2\rightarrow the\text{ lines are not parellel} \end{gathered}[/tex]now, 2 lines are perpendicular if
[tex]slope_1\cdot slope_2=-1[/tex]replace to check
[tex]\begin{gathered} slope_1\cdot slope_2=-1 \\ -6\cdot\frac{1}{6}=-1 \\ -1=-1\rightarrow true,\text{ so the lines are perpendicular} \end{gathered}[/tex]I hope this helps you
3. A park designer wanted to place a fountain so that it was close to both the slide and the swings. Refer to the coordinate grid shown. Each unit on the grid represents 100 ft Slide 0 2 8 12 7 Fountain Swings (a) Find the distance from the slide to the fountain. Show your work (b) Find the distance from the swings to the fountain Show your work.
Answers
In general, the distance between two points on the plane is given by the formula below
[tex]d((x_1,y_1),(x_2,y_2))=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]Therefore, in our case,
[tex]\begin{gathered} \text{slide}=(-2,0) \\ \text{fountain}=(-2,-2) \\ \text{ Swings}=(5,2) \end{gathered}[/tex]Thus,
[tex]\begin{gathered} d(slide,fountain)=\sqrt[]{(-2-(-2))^2+(0-(-2))^2}=\sqrt[]{0+2^2}=2 \\ \text{and} \\ d(swings,fountain)=\sqrt[]{(5-(-2))^2+(2-(-2))^2}=\sqrt[]{7^2}=7 \end{gathered}[/tex]The answer to part a) is 2*100ft=200ft
The answer to part b) is 7*100ft=700ft
Write an equation for a rational function with:
Vertical asymptotes at x = 2 and x = -4
x-intercepts at x = 1 and x = 4
y-intercept at 9
y=
Answers
The equation for a rational function with: Vertical asymptotes at x = 2 and x = -4. x-intercepts at x = 1 and x = 4. y-intercept at 9 is
[tex]y=-36\frac{(x - 1) (x - 4)}{(x - 2) (x +4)}[/tex]
How to determine the equation for a rational functioninformation gotten from the question
From the question given above, the following data were obtained:
Vertical asymptotes at x = 2 and x = -4x-intercepts at x = 1 and x = 4y-intercept at 9y =?Rational function means that the equation will be a fraction
The rational function that models the Vertical asymptotes at x = 2 and x = -4. x-intercepts at x = 1 and x = 4. y-intercept at 9 is written as follows
The numerator
x-intercepts at x = 1 and x = 4
x = 1 ⇒ (x - 1)
x = 4 ⇒ (x - 4)
This means the equation will have (x - 1) (x - 4) as the numerator
The denominator
Vertical asymptotes at x = 2 and x = -4
x = 2 ⇒ (x - 2)
x = -4 ⇒ (x + 4)
This means the equation will have (x - 2) (x + 4) as the denominator
y-intercept at 9
expressing the functions derived already gives
[tex]y=a\frac{(x - 1) (x - 4)}{(x - 2) (x +4)}[/tex]
substituting x = 0 and y = 9 and solving gives a
[tex]9=a\frac{(0 - 1) (0 - 4)}{(0 - 2) (0 +4)}[/tex]
[tex]9=a\frac{(4)}{(-8)}[/tex]
4a = 9 * -8
a = -36
The equation of the rational function is [tex]y=-36\frac{(x - 1) (x - 4)}{(x - 2) (x +4)}[/tex]
Learn more on equation for a rational function at :
https://brainly.com/question/28032338
#SPJ1
Find the volume I have a with radius four. 0 inches. Use three. 14 pi. Why are you answer to the nearest thousandth.
Answers
Given
Hemisphere
[tex]\begin{gathered} r=4 \\ \pi=3.14 \end{gathered}[/tex]The formula volume of Hemisphere
[tex]\begin{gathered} Volume\text{ of Hemisphere=}\frac{2}{3}\pi r^3 \\ \\ Volume\text{ of Hemisphere=}\frac{2}{3}\times3.14\times4^3 \\ \\ Volume\text{ of the hemisphere=133.9733} \end{gathered}[/tex]The final answer
Option B
[tex]133.973in^3[/tex]Question 5Ginny has $10,000 in a savings account earning 4% simple interest annually. Ginny plans on savingthis money for a long time. Let's calculate Ginny's Total account balance in 20 years.a $18
Answers
ANSWER
$18,000
EXPLANATION
Ginny has $10,000 in a savings account.
The interest is 4% simple interest.
We want to calculate Ginny's total account balance after 20 years.
To do this, we will first caluclate the interest and then we will add it to the initial balance.
To calculate Simple Interest, we use:
[tex]\text{Simple Interest = }\frac{P\cdot\text{ R }\cdot\text{ T}}{100}[/tex]P = principal = $10000
R = rate = 4%
T = time = 20 years
Therefore:
[tex]SI\text{ = }\frac{10000\cdot\text{ 4 }\cdot\text{ 20}}{100}\text{ = \$8000}[/tex]Therefore, her account balance after 20 years is:
Amount = $10000 + $8000 = $18,000
(a)For an algebra class, all students took a Unit 5 test. Their scores and the amount of hours they studied are contained in the graph belowa student. A trend line (line of best fit) is given.Time Spent Studying(Hours)a) For the trend line,what is the slope?b) For the trend line,what is the y-intercept?c) Create a slope-intercept equationfor the trend line:
Answers
Can someone please help me . is this right ?
Answers
5x-7(x+1)>-9
Using distributive property:
5x-7x-7>-9
Add like terms:
(5x-7x)-7>-9
-2x-7>-9
Add 7 to both sides:
-2x-7+7>-9+7
-2x>-2
Multiply both sides by (-1):
"Whenever you multiply or divide an inequality by a negative number, you must flip the inequality sign"
2x<2
Divide both sides by 2:
2x/2<2
x<1
So, for the arrow, the answer is left.
Kendra wrote the Pythagorean relationship as r ^ 2 = p ^ 2 + q ^ 2 for the triangle shown. Is she correct? Explain.
Answers
In the Pythagorean relationship,
The square of the hypotenuse is equal to the sum of the squares of the legs of the right angle
From the given figure
The hypotenuse is P
The two legs of the right angle are q and r
Then the Pythagorean relationship should be
[tex]p^2=r^2+q^2[/tex]Then she is not correct because she put r as the hypotenuse of the triangle and p, q are the legs of the right angle.