The radius changing when the volume is 8in^3/min by: -512π /30 in³ /min.
How to find the radius?First step is to find the radius changing over time at a constant rate
dr/dt = 10-12 /30
= -2/30 in/min
Now let find the how fast is the radius changing using this formula
dV/dt = 4πr²(dr/dt)
Where,
r =8
Hence,
dV/dt = 4π (8in)² × -2/30 in/min
dV/dt = 4π (64in) × -2/30 in/min
dV/dt = -512π /30 in³ /min
Therefore the change in radius is -512π /30 in³ /min.
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Given the following probabilities, algebraically determine if Events A and B are:• mutually exclusive or non-mutually exclusive• independent or dependent.P(A) =P(B) 0.75P(A U B)'U0.15
We know that:
[tex]\begin{gathered} P(A\cup B)^{\prime}=1-P(A\cup B) \\ P(A\cup B)^{\prime}=1-P(A)+P(B)-P(A\cap B) \end{gathered}[/tex]Plugging the values given we have that:
[tex]\begin{gathered} 0.15=1-0.8+0.75-P(A\cap B) \\ P(A\cap B)=1-0.8+0.75-0.15 \\ P(A\cap B)=0.8 \end{gathered}[/tex]Now, since the probability of the intersection is not zero this means that the events are non-mutually exclusive.
The sphere is _____ cubic centimeters bigger than the cube. (Round to the nearest cubic centimeter.)
ANSWER
The sphere is 10762 cubic centimeters bigger than the cube.
EXPLANATION
We want to find the difference in the volumes of the sphere and the cube.
To do this, we have to find the volumes of the sphere and cube and subtract that of the cube from the sphere.
The volume of a sphere is given as:
[tex]V=\frac{4}{3}\pi r^3[/tex]where r = radius
The radius of the sphere is 15 centimeters. Therefore, the volume of the sphere is:
[tex]\begin{gathered} V=\frac{4}{3}\cdot\pi\cdot15^3 \\ V\approx14137\operatorname{cm}^3 \end{gathered}[/tex]The volume of a cube is given as:
[tex]V=s^3[/tex]where s = length of the side
The length of the side of the cube is 15 centimeters. Therefore, the volume of the cube is:
[tex]\begin{gathered} V=15^3 \\ V=3375\operatorname{cm}^3 \end{gathered}[/tex]Therefore, the difference in the volumes of the sphere and cube is:
[tex]\begin{gathered} V_d=V_s-V_c \\ V_d=14137-3375 \\ V_d=10762\operatorname{cm}^3 \end{gathered}[/tex]Therefore, the sphere is 10762 cubic centimeters bigger than the cube.
f(x) = x ^ 2 + ax + bf(x) has m zeros, and f[f(x)] has M zeros,So M - m will never be ____A. 0B. 1C. 2D. 3
First, notice that the expression for f(f(x)) is the following:
[tex]f(f(x))=(x^2+ax+b)^2+a(x^2+ax+b)+b[/tex]notice that the first term is a quadratic expression with exponent 2. This means that f(f(x)) has 4 zeros.
Since f(x) has 2 zeros (since its quadratic), we have that M-m = 4-2 = 2, thus, M-m will never be 0, 1 or 3
A coffee shop receives a box of cups and lids. The box weighs less than 42 ounces. Each cup weighs 0.5 ounce, and each lid weighs 0.25 ounce.
Choose the inequality that shows the possible contents of the box.Use c for
the number of lids
The inequality that shows the possible contents of the box is 0.5c + 0.25l < 42
What is inequality?Inequality, defined as "the state of not being equal, particularly in status, rights, and opportunities," is a central concept in social justice theories. However, it is prone to misunderstanding in public debate because it means different things to different people. Some distinctions, however, are universal.
The expression 5x 4 > 2x + 3 resembles an equation, but the equals sign has been replaced by an arrowhead. It's an example of inequity. This means that the left part, 5x 4, is greater than the right part, 2x + 3. We'll be looking for x values for which the inequality holds true.
The definition of inequality is that two things are not equal.
One of the things could be less than, greater than, less than or equal to the other things, or greater than or equal to the other things.
p ≠ q means that p is not equal to q
p < q means that p is less than q
p > q means that p is greater than q
p ≤ q means that p is less than or equal to q
p ≥ q means that p is greater than or equal to q
Therefore, The inequality that shows the possible contents of the box is 0.5c + 0.25l < 42
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You pick a card at random. Without putting the first card back, you pick a second card at rando 4 5 6. What is the probability of picking an odd number and then picking an odd number? Simplify your answer and write it as a fraction or whole number.
Given data:
The three numbers on the cards are 4, 5, 6.
The probability of picking an odd number and then picking an odd number is,
[tex]\begin{gathered} P=\frac{1}{3}\times\frac{0}{2} \\ =0 \end{gathered}[/tex]Thus, the probability of picking an odd number and then picking an odd number is 0.
40% of the students on the field trip love the museum. If there are 20 students on the field trip, how many love the museum?
well, what's 40% of 20?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{40\% of 20}}{\left( \cfrac{40}{100} \right)20}\implies 8[/tex]
The triangle shown below are similar. which line segment corresponds to RS?
B) TS
1) Since these triangles are similar then we can write out the following ratios according to the Thales Theorem:
[tex]\frac{RS}{TS}=\frac{RO}{TU}[/tex]2) So these line segments must share the same ratio
3) Hence, the answer is TS
Answer:
TS
Step-by-step explanation:
of the trains that recently pulled into Westford Station, 16 were full and 4 had room for morepassengers. What is the experimental probability that the next train to pull in will be full?Write your answer as a fraction or whole number
The formula for probabilty is given by; the Probability of an event(A) is the number of favorable outcomes divided by the total number of outcomes possible in a scenario. It can also be denoted by the formula:
[tex]P(A)=\frac{Number\text{ of Favorable Outcome}}{\text{Total Number of }Outcome}[/tex]In our problem we have 16 trains that are full and 4 which are not, therefore there are a total number of 20 trains in the Westford Station.
The number of favorable outcome is equal to the number of trains that are full since it is the one asked in our question as the one which is more favored to come, according to the question.
Therefore, the number of favorable outcome = number of full trains = 16, and
The Total number of Outcome = total number of trains that may pull over to Westford Station = 20
Therefore the experimental probability that a full train will pull over in the station is;
[tex]\begin{gathered} P(A)=\frac{Number\text{ of Favorable Outcome}}{\text{Total Number of Outcome}}\text{ = }\frac{16}{20} \\ P(A)=\frac{16}{20}=\frac{4}{5} \\ P(A)=\frac{4}{5} \end{gathered}[/tex]Therefore there is a probabilty of 4/5 or 80% that a full train will pull over the station.
Can anyone help me? I don't know the answer.
By means of the area formula for a square, the square has an area of 4 / 49 square meters (approx. 0.0816 square meters).
What is the area of the square?
Herein we find a representation of a solid square in the figure, whose side length measure (l), in meters, is known, and whose area (A), in square meters, has to be found. Dimensionally speaking, the area unit is the square of length unit.
The area formula of the square is shown below:
A = l²
If we know that the side length of the square has a measure of 2 / 7 meters (l = 2 / 7 m), then the area of the triangle is equal to:
A = (2 / 7 m)²
A = 4 / 49 m²
A ≈ 0.0816 m²
The area of the square is 4 / 49 square meters (approx. 0.0816 square meters).
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According to the graph, what is the value of the constant in the equation below?A.2B.0.667C.3D.1.5
Solution
- The constant being asked for is the slope of the graph.
- The formula for finding the slope of a graph is:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ where, \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are the points on the line} \end{gathered}[/tex]- The points on the graph that we will use are:
[tex]\begin{gathered} (x_1,y_1)=(2,3) \\ (x_2,y_2)=(4,6) \end{gathered}[/tex]- Thus, we can find the constant as follows:
[tex]\begin{gathered} m=\frac{6-3}{4-2} \\ \\ m=\frac{3}{2}=1.5 \end{gathered}[/tex]Final Answer
The constant(slope) is 1.5 (OPTION D)
What is the mean before the rent ? What is the mean after the change ?
Given:
The data set of the monthly rent paid by 7 tenants
990, 879, 940, 1010, 950, 920, 1430
We will find the mean of the data:
Mean = Sum/n
n = 7
Sum = 990+879+940+1010+950+920+1430 = 7119
Mean = 7119/7 = $1017
One of the tenants change from 1430 to 1115
The mean after the change will be as follows:
Sum = 990+879+940+1010+950+920+1115 = 6804
n = 7
Mean = 6804/7 = 972
So, the answer will be:
Mean before the change = 1017
Mean after the change = 972
use your formula to determine the height of a trapezoid with an area of 24 square centimeters and base length of 9 cm and 7 cm
Answer
The height of the trapezoid = 3 cm
Explanation
The area of a trapezoid is given as
Area = ½ (a + b) h
where
a and b = base lengths of the trapezoid
a = 9 cm
b = 7 cm
h = height of the trapezoid = ?
Area = 24 cm²
Area = ½ (a + b) h
24 = ½ (9 + 7) h
24 = ½ (16) h
24 = 8h
8h = 24
Divide both sides by 8
(8h/8) = (24/8)
h = 3 cm
Hope this Helps!!!
The equation 8x+8y=16 in slope-intercept form
Create a "rollercoaster using the graphs of polynomials with real and rational coefficients.
The coaster ride must have at least 3 relative maxima and/or minima.
The coaster ride starts at 250 feet (let this be your y-intercept).
The ride dives below the ground into a tunnel (under the x-axis) at least once.
The graph must have at least one even multiplicity, two real solutions, and two imaginary solutions.
The polynomial that represents the rollercoaster, using the Factor Theorem, is given as follows:
y = 400(x - 1)²(x + 1)(x² + 0.1)(x + 5).
What is stated by the Factor Theorem?The Factor Theorem states that a polynomial function with zeros [tex]x_1, x_2, \codts, x_n[/tex], also represented by factors [tex]x - x_1, x - x_2, \cdots x - x_n[/tex] is given by the rule presented as follows:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient of the polynomial function with the given roots.
For this problem, the requirements are as follows:
At least 3 relative maxima and/or minima -> derivative of 3rd order -> 4 unique rootsy-intercept of 250 feet -> controlled by the leading coefficient.The roots will be given as follows:
Root at x = 1 with even multiplicity -> (x - 1)².Real solution at x = -1 -> (x + 1).Two imaginary solutions -> (x² + 0.1).Unique root at x = -5 -> (x + 5).Hence the function is:
y = a(x - 1)²(x + 1)(x² + 0.1)(x + 5).
At x = 0, the function assumes a value of 250, hence the leading coefficient is obtained as follows:
0.5a = 200.
a = 400.
Thus the function is:
y = 400(x - 1)²(x + 1)(x² + 0.1)(x + 5).
Which has the desired features, as shown by the image at the end of the answer.
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Sketch and calculate the area enclosed by y² = 8-x and (y + 1)² = −3+x.
The area enclosed by y² = 8 - x and (y + 1)² = −3 + x is 243.
We are given y² = 8 - x and (y + 1)² = −3 + x.
To sketch and calculate the area enclosed, find the intersection points:
y² = 8 - x ⇒ x = 8 - y²
Substitute x = 8 - y² in (y + 1)² = −3 + x:
(y + 1)² = −3 + 8 - y²
y² + 2y + 1 = −3 + 8 - y²
2y² + 2y - 4 = 0
y² + y - 2 = 0
(y - 1) (y + 2) = 0
y = 1, -2
Substitute y = 1, -2 in x = 8 - y²:
When y = 1, x = 8 - (1) ⇒ x = 7
When y = -2, x = 8 - (-2)² ⇒ x = 4
Thus, the point of intersection is (4, -2) and (7, 1).
Graph of the region enclosed by y² = 8 - x and (y + 1)² = −3 + x:
The area of the enclosed region is given by:
A = [tex]\int \, \int \,dA[/tex]
[tex]=\int\limits^7_{-2} \, \int\limits^{3+ (y+1)^{2} } _{8 - y^{2} } \, dxdy[/tex]
[tex]=\int\limits^7_{-2} \, (x)^{3+ (y+1)^{2} } _{8 - y^{2} } \, dy[/tex]
[tex]=\int\limits^7_{-2} \, [{(3+ (y+1)^{2} )} -({8 - y^{2} })] \, dy[/tex]
[tex]=\int\limits^7_{-2} \, {(2 y^{2} + 2y -4) } \, dy[/tex]
[tex]=(\frac{2y^3}{3} + \frac{2y^2}{2} -4y)^7_{-2}[/tex]
[tex]=\frac{686}{3} + 49 - 28 + \frac{16}{3} - 4 - 8[/tex]
= 343
Hence, the area enclosed by y² = 8 - x and (y + 1)² = −3 + x is 243.
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Use vertical multiplication to find the product of: x2 + 3x + 2 x x - x2-1 O - A. ** - 3x4 – x2-3x+ - *- 2 O B. x + 2x4 – x2-3x2 – 3x-2 - C. + 3x4 - X2-3x2-3x O D. +2x4- *° - 3x2 - 3x-2 x
Use vertical multiplication as shown below
Therefore, the answer is x^5+2x^4-x^3-3x^2-3x-2, option B
What is the exponential form of the logarithmic equation?5= log base .9 .59049
Given:
[tex]5\text{ }=\text{ log}_{0.9}0.59049[/tex]To find:
to convert from logarithmic form to exponential form
[tex]\begin{gathered} If\text{ logarithmic form:} \\ a\text{ = log}_bC \\ E\text{xponential form:} \\ b^a\text{ = C} \\ \\ The\text{ base of the log will become the base of the expoenent on the other side} \\ \text{The exponent will be the number of the other side of the equation} \end{gathered}[/tex][tex]\begin{gathered} Applying\text{ same rule:} \\ 0.9^5\text{ = 0.59049} \end{gathered}[/tex]Find the value of x in the triangle shown below.=2°31770
The sum of all the angles in a triangle is always 180°.
We can write the equation and solve for the missing angle:
[tex]31^o+77^o+x=180^o[/tex]Solving for x:
[tex]\begin{gathered} x=180^o-31^o-77^o \\ \\ x=72^o \end{gathered}[/tex]The measure of the unknown angle is 72 degrees.
4(2x + 3) = 3x + 3 + 2x
We operate as follows:
[tex]4(2x+3)=3x+3+2x\Rightarrow8x+12=5x+3[/tex][tex]\Rightarrow3x=-9\Rightarrow x=-3[/tex]The value of x is -3.
if there are 7 teams and every teams plays everyone once how many games total played
This is a problem about combinations where the order doesn't matter. The solution is usually written as 7C2 (seven choose two) and has the value
[tex]\frac{7!}{(7-2)!2!}=21[/tex]Comment: 7C2 is the answer to the question "How many pairs (in our case, these pairs are seen as games played) can we form from a group of 7 things?".
Question 2b: NAME THE Y-INTERCEPTy = -2(x - 3)^2
The given equation corresponds to a parabola:
[tex]y=-2(x-3)^2[/tex]The y-intercept of the parabola is the point when it crosses the y-axis, at this point x=0, to determine this value you have to replace the formula with x=0 and calculate the value of y:
[tex]\begin{gathered} y=-2(0-3)^2 \\ y=-2(-3)^2 \end{gathered}[/tex]Solve the exponent first, then the multiplication
[tex]\begin{gathered} y=-2(-3)^2 \\ y=-2\cdot9 \\ y=-18 \end{gathered}[/tex]The y-intercept for the given function is (0,-18)
Simplify (a + 15) •2
(a + 15) •2
Multiply each term in the parentheses by 2
a*2 + 15*2
2a + 30
How much would $200 interest compounded monthly be worth after 30 years
Given:
Principal (P)=$200
Rate of interest (r) =4%
time (t)=30 years
Number of times compounded per year(n) = 12
Required- the amount.
Explanation:
First, we change the rate of interest in decimal by removing the "%" sign and dividing by 100 as:
[tex]\begin{gathered} r=4\% \\ \\ =\frac{4}{100} \\ \\ =0.04 \end{gathered}[/tex]Now, the formula for finding the amount is:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Put the given values in the formula, we get:
[tex]A=200(1+\frac{0.04}{12})^{12\times30}[/tex]Solving further, we get:
[tex]undefined[/tex]Complex numbers may be applied to electrical circuits. Electrical engineers use the fact that resistance R toelectrical flow of the electrical current I and the voltage V are related by the formula V = RI. (Voltage ismeasured in volts, resistance in ohms, and current in amperes.) Find the resistance to electrical flow in a circuitthat has a voltage V = (40+30i) volts and current I = (-5+ 3i) amps._+_i/_Note: Answer in the forma + bi/c. If b is negative make sure to put a negative sign in the answer box.
we have the formula
[tex]\begin{gathered} V=RI \\ R=\frac{V}{I} \end{gathered}[/tex]substitute given values
[tex]R=\frac{40+30i}{-5+3i}[/tex]Remember that
To divide complex numbers, multiply both the numerator and denominator by the conjugate of the denominator
the conjugate of the denominator is (-5-3i)
so
[tex]\begin{gathered} R=\frac{40+30\imaginaryI}{-5+3\imaginaryI}*\frac{-5-3i}{-5-3i}=\frac{-40(5)-40(3i)-30i(5)-30i(3i)}{25-9i^2}=\frac{-200-120i-150i-90i^2}{25-9(-1)}=\frac{-110-270i}{34} \\ \\ R=\frac{-110-270\imaginaryI}{34} \\ simplify \\ R=\frac{-55-135\imaginaryI}{17} \end{gathered}[/tex]Provide the missing reasons with proof. Given: AB/DB = CB/EBProve: ∆ABC~∆DBE
Answer:
Statement 1. AB/DB = CB/EB
Reason 1: Given
Statement 2: ∠ABC = ∠BDE
Reason 2: Vertical angles
Statement 3: ∆ABC~∆DBE
Reason 3: SAS (side - angle - side)
Explanation:
It is given that AB/DB = CB/EB. So, we can say that the ratio of side AB to DB is equal to the ratio of side CB to EB. This made these sides similar.
Additionally, ∠ABC and ∠BDE are vertical angles because they are opposite angles formed when two lines intersect. Vertical angles have the same measure so, ∠ABC = ∠BDE.
Now, we can say that the triangles ABC and DBE are similar by SAS (Side-Angle-Side). Because two sides are similar and the angle between them is congruent.
Therefore, the answer is
Statement 1. AB/DB = CB/EB
Reason 1: Given
Statement 2: ∠ABC = ∠BDE
Reason 2: Vertical angles
Statement 3: ∆ABC~∆DBE
Reason 3: SAS (side - angle - side)
e dist Since the radius is an imaginary value, the equation is not a real circle. the cece - 4x + 2) + ( + 8y + (-2) + + 4) = -5 2-5 r-rs-115 lisch Pe squares for each quadratic, list the center and radius, then graph each circle ahs 12.3 llowing: it tort 'onics Ibolas It wh 121, the at of anslated center: 2 - 40 = 4 (b) x² + y2 - 4x = 0 2 27 822
The general equation of a circle is given by
[tex](x-h)^2+(y-k)^2=r^2[/tex]where (h,k) is the center of the circle and r is the radius
x² + y² -2x - 8y = 8
x² - 2x + y² - 8y = 8
(x² - 2x + ) + (y² -8y + ) = 8
Add square of half of the coefficient of x in the first paenthesis and the half of the square of the coefficient of y in the second parenthesis
Then add the two squaes at the right-hand side of the equation
(x² -2x +1 ) + (y² -8y + 16 ) = 8 + 1+ 16
(x-1)² + (y-4)² = 25
comparing this with the general equation
Center is ( 1, 4)
Radius is 5
The circle above is rotated about the axis as shown. What shape is formed?cylinderconedonutsphere
The answer is a donut.
A donut or Toroid is formed when you rotate an circle by a rotation axis displaced of the center of the circle.
Answer:
Step-by-step explanation:
donut
With the points (8. 4) (-6, -6) (-10, 12) (2,-4). What are the new points if thescale factor of dilation is X?
With the points (8. 4) (-6, -6) (-10, 12) (2,-4). What are the new points if the
scale factor of dilation is X?
we know that
The rule of the dilation of a point is equal to
(x,y) -------> (ax, ay)
with a scale factor a
so
In this problem
the scale factor is x
therefore
(8. 4) --------> (8x. 4x)
Given the equation of the circle, identify the center and radius (x + 1) ^ 2 + (y - 1) ^ 2 = 36
The form of the equation of the circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex](h, k) is the center
r is the radius
Let us compare it with the given equation to find the center and the radius
[tex](x+1)^2+(y-1)^2=36[/tex]From the comparing
h = -1
k = 1
r^2 = 36
Find the square root of 36 to get r
[tex]\begin{gathered} r=\sqrt[]{36} \\ r=6 \end{gathered}[/tex]The center is (-1, 1) and the radius is 6
8 ( 11 - 2b ) = -4 ( 4b - 22 )
Problem
8 ( 11 - 2b ) = -4 ( 4b - 22 )
Solution
We can distribute the terms in the equation and we got:
88 -16b = -16b +88
If we add 16b in boh sides we got:
88 =88
Then for this case we can conclude that this equation has infinite solutions