We have two cones.
They have a scale factor of 8:27.
This ratio relates elements in one dimension: radius, height, slant height.
This can be expressed for the height for example as:
[tex]\frac{h_2}{h_1}=\frac{8}{27}[/tex]If this is the ratio between the linear elements, then the ratio for the volume will be the cube of the linear ratio.
Then, we can find the ratio for the volumes as:
[tex]\frac{V_2}{V_1}=(\frac{8}{27})^3=\frac{512}{19683}[/tex]Answer: if the scale factor of the cones is 8/27, the ratio of their volumes is 512/19683.
translate the sentence into an equation four Less than the product of 3 and a number is 6 use the variable w for the unknown number
Answer:
3w - 4 = 6
Explanation:
Let us call t
Books are on sale for25% off. The discountis $4. What is theregular price of thebook?
We know that the value of the discount is equal to $4 and that it represents 25% of the original value. To find the regular price we can apply a rule of three in such a way that $4 is related to 25% in the same proportion that "x" is related to 100%, where "x" is the regular price of the book. We have:
[tex]\frac{4}{x}=\frac{25}{100}[/tex]Doing the cross product we have:
[tex]\begin{gathered} 25\cdot x=4\cdot100 \\ x=\frac{4\cdot100}{25}=16 \end{gathered}[/tex]The regular price of the book is $16.
For the polynomial f(X)=2x^3-9x^2+11x-20AsX -> -♾️,f(X) -> ♾️, calculate the end behavior
Answer:
The polynomial is given below as
[tex]f(x)=2x^3-9x^2+11x-20[/tex]Definition of end behavior:
The end behavior of a function f describes the behavior of the graph of the function at the "ends" of the x-axis. In other words, the end behavior of a function describes the trend of the graph if we look to the right end of the x-axis (as x approaches +∞ ) and to the left end of the x-axis (as x approaches −∞ ).
Step 1:
Figure out the domain of the function
The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0.
[tex]\begin{gathered} f(x)=2x^3-9x^2+11x-20 \\ the\text{ domain of the function is given below as} \\ -\inftyStep 2:Limit the polynomial to -∞ and +∞
[tex]\begin{gathered} \lim_{x\to\infty}f(x)=2x^3-9x^2+11x-20=\infty \\ as\text{ x}\rightarrow+\infty,f(x)\rightarrow+\infty \end{gathered}[/tex][tex]\begin{gathered} \lim_{x\to-\infty}f(x)=2x^3-9x^2+11x-20=-\infty \\ as\text{ x}\rightarrow-\infty,f(x)\rightarrow-\infty \end{gathered}[/tex]Hence,
The end behavior of the polynomial is given below as
[tex]\begin{gathered} as\text{ x}\rightarrow+\infty,f(x)\rightarrow+\infty \\ as\text{ x}\rightarrow-\infty,f(x)\rightarrow-\infty \end{gathered}[/tex]xP(x)00.1510.320.330.25Find the mean of this probability distribution. Round your answer to one decimal place.
The mean of a probability distribution can be found by applying the formula:
[tex]\mu=\sum_^x\cdot P(x)[/tex]By replacing the given values, we obtain:
[tex]\begin{gathered} \mu=0*0.15+1*0.3+2*0.3+3*0.25 \\ \mu=0+0.3+0.6+0.75 \\ \mu=1.65\approx1.7 \end{gathered}[/tex]The answer is 1.7
I need to know what numbers to use to find the volume. Can you answer this one as an example, then I can solve the rest.
The volume of a triangular pyramid is given by
[tex]V=\frac{1}{3}\times A\times H[/tex]where H is the heigh of the pyramid and A is the base of the triangular base. In our case,
[tex]H=14mm[/tex]and the base area is
[tex]\begin{gathered} A=\frac{1}{2}base\times\text{height} \\ A=\frac{1}{2}11\times10.6mm \\ A=58.3mm^2 \end{gathered}[/tex]where
Then, by substituting our last result into the volume formula, we have
[tex]\begin{gathered} V=\frac{1}{3}\times A\times H \\ V=\frac{1}{3}\times58.3\times14 \end{gathered}[/tex]which gives
[tex]V=272.0666mm^3[/tex]Therefore, by rounding to the nearest thousandth, the answer is: 272.067 cubic milimeters
If the flow into a reservoir is 15 cubic feet per second, how long will it take to fill a 1,000,000 gallon reservoir? (1 cubic foot = 7.48 gallons
Evaluate. Write your answer as an integer or as a decimal rounded to the nearest hundredth. cos 37° = ____
The value of cos 37° is,
[tex]\cos 37\degree=0.798[/tex]Rounding to the nearest hundredth,
[tex]\cos 37\degree=0.80[/tex]Aziz reads 1/2 a book in 2/3 months find the unit rate
Find the volume of the figure. Express answers in terms of ,
then round to the nearest whole number.
6 in.
8 in.
The volume of the cone that Illustrated is 168π inches.
How to calculate the volume of a cone?It is important to note that the volume of a cone will be calculated thus:
Volume of a cone = 1/3πr²h
In this case, the height is 14 inches while the radius is 6 inches.
The volume will be:
= 1/3πr²h
= 1/3 × π × (6)² × 14
= 168π inches³
Therefore the volume is 168π inches³.
The complete question is attached.
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For the following polynomial function, use the remainder theorem to find f(k).
f(x)=2x5-7x³ - 13x² - 25; k= 3
Answer:
-267
Step-by-step explanation:
The answer is : f ' (3) = -267
Write Yes or No to indicate whether 10x -3+ 2x -5 and 4(3x-2) is equivalent
As given by the question
There are given that the two-equation
[tex]10x-3+2x-5\text{ and 4(3x-2)}[/tex]Now,
From the first equation
[tex]\begin{gathered} 10x-3+2x-5=12x-8 \\ =4(3x-2) \end{gathered}[/tex]Hence, the correct answer is YES.
(X+2) is raised to the fifth power period the third term of the expansion is:
Solution
- The Binomial expansion formula is given by:
[tex](x+y)^n=\sum_{k=0}^n(^nC_k)x^{n-k}y^k[/tex]- Applying this formula to our expression, we have:
[tex](x+2)^5=^5C_ox^5(2^0)+^5C_1x^4(2^1)+^5C_2x^3(2^2)+...[/tex]- From the above, we can see that the 3rd term is
[tex]^5C_2x^3(2^2)=C(5,2)x^32^2[/tex]Final Answer
The answer is
[tex]C(5,2)x^32^2\text{ \lparen OPTION 3\rparen}[/tex]which of the following is a function?a. (2, 5),(5,2),(0,0)b.(2,5),-9,0)c.(-9,2)(0,-9)d.(2,5),(5,-9),(2,0)
Problem
which of the following is a function?
a. (2, 5),(5,2),(0,0)
b.(2,5),-9,0)
c.(-9,2)(0,-9)
d.(2,5),(5,-9),(2,0)
Solution
For this case we need to satisfy that for each value we have just one value of y and if we analyze one by one the options we have:
a. (2, 5),(5,2),(0,0)
For this case is a function we satisfy the definition
b.(2,5),(-9,0)
This is a function based on the definition
c.(-9,2)(0,-9)
This is a function satisfy the condition
d.(2,5),(5,-9),(2,0)
This is not a function since for x=2 we have two values of y
Can you please help me out with a question
Step 1: Problem of ages
Step 2: Concept
1.
12x + 8 = 2 x (5x + 13 )
12x + 8 = 10x + 26
12x - 10x = 26 - 8
2x = 18
x = 18/2
x = 9
2. m = 12 x 9 + 8
= 108 + 8
= 116
3.
m
m = 45 + 13
= 58
Therefore
= 2 x 32
= 64
Final answer
X = 9
mSR = 116
mST = 64
m
Given the system below. What is the x value of the solution? 3х + 5 = 8 y = x + 8
Answer
x = 1
y = 9
Explanation
3x + 5 = 8
y = x + 8
3x = 8 - 5
3x = 3
Divide both sides by 3
(3x/3) = (3/3)
x = 1
y = x + 8
y = 1 + 8
y = 9
Hope this Helps!!!
Find the value of x such that the trapezoid has an area of 52
Consider the following trapezoid
The formula to find the area of this trapezoid is given by the formula
[tex]A=\frac{h(b+B)}{2}[/tex]In this case, we have h=8, b=x and B=10. So the formula for our trapezoid is given by
[tex]A=\frac{8\cdot(x+10)}{2}=4\cdot(x+10)[/tex]We are told that the area should be 52, so we end up with the following equation
[tex]4\cdot(x+10)=52[/tex]now, we should solve this equation for x. To do so, we start by dividing by 4 on both sides. So we get
[tex]x+10=\frac{52}{4}=\frac{26\cdot2}{2\cdot2}=\frac{26}{2}=13[/tex]Now, we subtract 10 on both sides, so we get
[tex]x=13-10=3[/tex]large-scale production.6. You deposit $1000 a year into an account. This account earns 8% interest compounded yearly.(20 points)a) how much will you have after 10 years?) How much total money did you put in the account.c) How much total interest did you earn?
Apply the compound interest formula:
A = P (1 + r/n)^ nt
Where:
A=amount after n years
P = initial principal = 1000
r= interes rate ind ecimal form = 8/100 = 0.08
n= number of times the interest is compounded annualy = 1
t= years
a. After 10 years:
A = 1000 (1 + 0.08)^10
A = 1000 (1.08)^10
A= $2,158.93
b. interest earnt
2,158.92 - 1000 = $1,158.93
4x - 9y = 8 x - intercept = ?
4x-9y=8
x intercept:
we have to find the coordinate (x,0)
Replace y=0 and solve for x_
4x-9(0) =8
4x=8
Divide both sides by 4
4x/4 =8/4
x= 2
x-intercept = 2
Need help ⅝ + ¾ / -2 / 3 - ⅚A. 2 1/16B. 11 / 12C. -2 1/16D. - 11/12
Here, we want to solve the given expression
To do this, we will follow the order in which the order of solution is to come
The order is; BODMAS
We start with bracket, order , division, multiplication, addition and subtraction
We start with the divison between the second and the third term
That would be;
[tex]\frac{+3}{4}\times\frac{-3}{2}\text{ = }\frac{-9}{8}[/tex]From here, we can then proceed to add up/subtract the terms;
[tex]\frac{5}{8}-\frac{9}{8}-\frac{5}{6}[/tex]we proceed to get the lowest common multiple of the denominator
This is 24
We now divide 24 by each of the denominator and multiply each of the numerator by the result of the division
That would be;
[tex]\frac{3(5)-3(9)-5(2)}{24}\text{ = }\frac{15-27-10}{24}\text{ = }\frac{-22}{24}\text{ =-}\frac{11}{12}[/tex]What value of x would prove a || b (19x - 13) (6x - 7) a.8 b.9 c.10 d. 11
The lines a and b are cut by a transversal, which means if a and b are parallel lines, then
[tex]\begin{gathered} 19x-13+6x-7=180 \\ \text{This is because the angle that corresponds to 19x-13 is a supplementary angle alongside }6x-7 \\ \text{Therefore, if 6x-7+supplement=180, then} \\ \text{Supplement and 19x-13 are corresponding angles} \\ \text{Hence;} \\ 19x-13+6x-7=180 \\ \text{Collect all like terms} \\ 19x+6x=180+13+7 \\ 25x=200 \\ \text{Divide both sides by 25} \\ x=8 \end{gathered}[/tex]The correct answer is option A; x = 8
What is the axis of symmetry for the quadratic equation from Question 1: f(x) = 0.5(x+3)(x-7)?
We know that for an equation of the form:
[tex]f(x)=ax^2+bx+c[/tex]the axis of symmetry is given by:
[tex]x=-\frac{b}{2a}[/tex]In this case, where our formula is given by the equation:
[tex]f\mleft(x\mright)=0.5\mleft(x+3\mright)\mleft(x-7\mright)[/tex]we want to multiply all the factors so we can work with the form of the first equation. We do this using the distributive property:
0.5 (x + 3) = 0.5 · x + 0.5 · 3
= 0.5x + 1.5
Then, in the equation:
[tex]\begin{gathered} f(x)=0.5(x+3)(x-7) \\ \downarrow \\ f(x)=(0.5x+1.5)(x-7) \end{gathered}[/tex]Now, multiplying both (0.5x + 1.5) and (x - 7) we have that:
[tex]\begin{gathered} f(x)=(0.5x+1.5)(x-7) \\ \downarrow \\ f(x)=(0.5x+1.5)\cdot x-(0.5x+1.5)\cdot7 \end{gathered}[/tex]Now, finding the product of
(0.5x + 1.5)x, we have that:
[tex]\begin{gathered} \mleft(0.5x+1.5\mright)x \\ =0.5x\cdot x+1.5\cdot x \\ =0.5x^2+1.5x \end{gathered}[/tex]Replacing in the equation:
[tex]\begin{gathered} f(x)=(0.5x+1.5)\cdot x-(0.5x+1.5)\cdot7 \\ \downarrow \\ f(x)=0.5x^2+1.5x-(0.5x+1.5)\cdot7 \end{gathered}[/tex]On the other hand, finding the product of
-(0.5x + 1.5) · 7,we have that
-(0.5x + 1.5) · 7 = -0.5x · 7 - 1.5 · 7
= -3.5x - 10.5
Replacing in the equation:
[tex]\begin{gathered} f(x)=0.5x^2+1.5x-(0.5x+1.5)\cdot7 \\ \downarrow \\ f(x)=0.5x^2+1.5x-3.5x-10.5 \\ f(x)=0.5x^2-2x-10.5 \end{gathered}[/tex]Then, we have that
a = 0.5,
b = -2
and
c = -10.5
Then, using the equation for the axis of symmetry, we have that:
[tex]\begin{gathered} x=-\frac{b}{2a} \\ \downarrow \\ x=-\frac{(-2)}{2\cdot0.5} \\ x=\frac{2}{2\cdot0.5}=\frac{1}{0.5} \\ \downarrow \\ x=2 \end{gathered}[/tex]Which of the following notations correctly describe the end behavior of thepolynomial graphed below?
End behavior is described as the direction of which the tails of a polynomial or parabola point towards. End behavior can be used to predict additional factors of the function.
As we can see, we have a downward facing polynomial. This polynomial therefore sends both ends towards a negative value.
For each side of the graph, we have negative infinity and positive infinity.
The left side of the graph approaches negative infinity whereas the right side of the graph approaches positive infinity.
Since in both conditions the parabola points downwards, when the graph approaches either negative infinity or positive infinity, the value of the end behavior is also approaching further negative values.
This means that our end behavior can be represented as:
[tex]\begin{gathered} x\rightarrow\infty,f(x)\rightarrow-\infty \\ x\rightarrow-\infty,f(x)\rightarrow-\infty \end{gathered}[/tex]I don't know how to interpret the residual (-1.3829)What should I say? the equation of the least-squares regression line is ŷ = 0.4684X + 64.69888
A Residual is just the difference between the observed value in an experiment or survey and the value predicted by the regression line.
This means that the Residual can be calculated using the formula:
[tex]\begin{gathered} r=y-\hat{y} \\ \text{where,} \\ y=\text{observed value} \\ \hat{y}=\text{predicted value} \end{gathered}[/tex]Thus, if we are told that a piece of data has a residual of -1.3829, it means that the difference between one of the observations from the experiment or survey conducted and the value predicted by the regression line is -1.3829.
Mathematically,
[tex]-1.3829=y-\hat{y}[/tex]
What is 78,400,000 expressed in scientific notation?A.78.4 x 10*5B.7.84 x 10*7C.78.4 x 10*6D.784 x 10*4
Solution:
Given:
[tex]78,400,000[/tex]
Scientific notation is a way of writing very large or very small numbers.
A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.
Hence, we move the decimal points such that the number is between 1 and 10 and then multiply it by a power of 10.
Thus,
Hence, the decimal point was moved 7 times to make the number fall between 1 and 10.
The number becomes 7.84 and the power of 10 to which is multiplied is 10 to power 7 because the decimal was moved 7 times.
Hence,
[tex]78,400,000=7.84\times10^7[/tex]Therefore, option B is correct.
Which line is parallel to the line given below y=-(5/2)x-7A. 2x+5y = -5B. 2x - 5y =30C. 5x+2y= 4D. 5x - 2y =8
Answer:
C. 5x+2y= 4
Explanation:
Two lines are parallel if their slopes are the same.
To determine the line that is parallel, express each of the options in the slope-intercept form.
[tex]\begin{gathered} A.2x+5y=-5\implies5y=-2x-5\implies y=-\frac{2}{5}x-1 \\ B.2x-5y=30\implies5y=2x-30\implies y=\frac{2}{5}x-6 \\ C.5x+2y=4\implies2y=-5x+4\implies y=-\frac{5}{2}x+2 \\ D.5x-2y=8\implies2y=5x-8\implies y=\frac{5}{2}x-4 \end{gathered}[/tex]The only equation with a slope of -5/2 is Option C.
The parallel line is 5x+2y= 4.
In a state's Pick 3 lottery game, you pay $1.27 to select a sequence of three digits (from 0 to 9), such as 544. If you select the same sequence of three digits that are drawn, you win and collect $378.82. Complete parts (a) through (e).
A. All the possible selections are
[tex]10\times10\times10=1000[/tex]B. The probability of winning is
[tex]\frac{1}{1000}=0.1\%[/tex]C. The net profit is
[tex]378.82-1.27=377.55[/tex]D. Expected value
[tex]\frac{999}{2}=499.5\text{ }\approx500[/tex]The conic section below isa.a circleb.an ellipseC.a parabolad.a hyperbolae.a degenerate
An ellipse is a shape that resembles an oval or a flattened circle.
An ellipse looks as shown below:
This looks like the image in the question.
Therefore, the conic section is an ellipse.
OPTION B is cor
g (x) = -3x^4 + 6x^2 – xHow do I find the inverse function
We find the inverse function as follows, solving for y (Assuming g(x) as y):
The function is incredbly complex given the x^4, the x^2 and the x since there is not an easy way to factor it.
Explaining:
When you have a function:
[tex]f(x)=6x-8[/tex](Here f(x)=y) You will determine the inverse function by solving for x:
[tex]y=6x-8\Rightarrow y+8=6x\Rightarrow\frac{y+8}{6}=x\Rightarrow g(y)=\frac{y+8}{6}[/tex]Here g(y) is going to represent the inverse function of f(x)
Which of the following shows the prime factorization of using exponential notation?
Remember that
The number 36 in prime factorization is given by
[tex]\begin{gathered} 36=(2)(2)(3)(3) \\ 36=2^23^2 \end{gathered}[/tex]the pitch of the roof is its slope. find the pitch.
Let's draw a rough drawing of what's needed to be solved.
x is the pitch of the roof and we need to solve for x.
This is a right triangle so we can use the Pythgaorean Theorem to solve it.
It states that in a right triangle, the Sum of the Squares of its legs is equal to the square of its Hypotenuse.
The hypotenuse is x
The legs are 16 and 14
Thus, we can write:
[tex]\begin{gathered} x^2=14^2+16^2 \\ x^2=452 \\ x=\sqrt[]{452} \\ x=\sqrt[]{4}\sqrt[]{113} \\ x=2\sqrt[]{113} \end{gathered}[/tex]