It is to be noted that the volume of Emma's storage tank is: 785.3cubic feet.
What is the rationale for the above calculation?
Start by calculating the area of the base of the storage tank. The area of a circle is calculated by: A = π*r², where r is the radius of the circle.
Where:
π = 22/7
r = radius of the circular base
Recall that for Emma’s cylindrical storage tank, the radius of the base is 5 feet.
So we replace this value in the formula and calculate the area of the base, which is equal to:
A = π*5²
A = 22/7 * 5²
= 78.5714285714
[tex]\approx[/tex] 78.54 square feet.
Now we need to compute the volume of the cylindrical storage tank. The volume of a cylinder is calculated by:
V = π*r²*h,
where r is the radius of the circle and h is the height of the cylinder.
Recall that for Emma’s tank, the height is 10 feet. Hence,
We substitute these values in the formula and calculate the volume, which is equal to:
V = π*5²*10 = 785.4 cubic feet.
Therefore, Emma’s cylindrical storage tank has a capacity of 785.4 cubic feet.
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What is the height of the flag pole?
the height of the flag pole should be 108 inches.
g(n)-50-15n
Complete the recursive formula of g(n).
g(1) =
g(n) = g(n-1)+
Answer:
-65
Step-by-step explanation:
Substitute: g (1) =_50-15
Calculate the sum or difference:
Answer=-65
Please help
Whats 9^2-10=
Answer: The correct answer would be 71.
step-by-step explanation:
9^2 - 10 =
Calculate the exponents: 9^2 : 81
Then subtract 81 by 10
81 - 10 = 71
Select the function(s) that have a domain of (- infinity, positive infinity)
Exponential Function
Cubic Function
Quadratic Function
Reciprocal Function
Linear Function
Absolute Function
Logarithmic Function
Square Root Function
Cube Root Function
Constant Function
Step-by-step explanation:
Exponential Function, example y=e×;
Cubic Function, example y=x³;
Quadratic Function, example y=x²;
Linear Function, example y=x-1;
Absolute Function, example y=|x|;
Cube Root Function, example y=∛x;
Constant Function, example y=2.
An exponential function f(x)=ab^x passes through the points (0,10000) and (3,3430). What are the values of a and b ?
a=
b=
The values of a and b for the exponential function are given as follows:
a = 10000.b = 0.1143.How to obtain the values of a and b for the exponential function?The standard definition of an exponential is given as follows:
y = ab^x.
In which the meaning of the parameters a and b is given as follows:
a is the initial value of the function, meaning that when x = 0, y assumes a value of a.b is the rate of change of the exponential function, meaning that when x is increased by one, y is multiplied by b.The function passes through the points (0,10000), hence the value of the parameter a is given as follows:
a = 10000.
The function also passes through the point (3,3430), hence the value of the parameter b is obtained as follows:
10000b³ = 3430
b = cubic root of (3430/10000)
b = (3430/10000)^1/3
b = 0.1143.
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For the polynomial below, what is the coefficient of the term with the power of
3?
x^3+1/3 x^4+6x+5
A. 5
B. 0
C. 6
D. 1
Answer: The coefficient of the term with the power of 3 is (D. 1)
Step-by-step explanation:
The power of 3 is x^3. When there's no number besides x, we can think of it as an imaginary 1. So, therefore, it's D-1.
Which expression is equivalent to 200k¹5, if k + 0?
O A. 2k¹225
O B. 2k5 25
O c.
O D.
8k5/25
8kv/25
Answer: Choice B
[tex]2k^5\sqrt[3]{25}[/tex]
================================================
Work Shown:
[tex]\sqrt[3]{200k^{15}}\\\\\sqrt[3]{8*25k^{5*3}}\\\\\sqrt[3]{8*25(k^5)^3}\\\\\sqrt[3]{8(k^5)^3*25}\\\\\sqrt[3]{8(k^5)^3}*\sqrt[3]{25}\\\\2k^5\sqrt[3]{25}[/tex]
------------------------
Explanation:
The goal is to factor the radicand in such a way that we pull out perfect cube factors.
Notice that 200 = 8*25 and 8 is a perfect cube (since 2^3 = 8). It is the largest perfect cube factor of 200.
We can rewrite the k^15 as k^(5*3) which is equivalent to (k^5)^3
Once these perfect cube factors are pulled out, they cancel with the cube root to get what you see above.
Find the value of z.
108°
40°
z=[?]°
Answer:32
Step-by-step explanation:
Assuming this is a triangle, there are three sides.
All sides of a triangle must add up to 180 degrees
180-108-40 = 32
What is greater 7/8 or 5/6?
Answer:
7/8
Step-by-step explanation:
First, we need to get 7/8 and 5/6 to the same denominator which is 48. 7/8 becomes 42/48 whilst 5/6 becomes 40/48
we can simply put them both with the same denominator and check, the larger numerator will be it.
so hmmm let's multiply one by the denominator of the other
[tex]\cfrac{7}{8}\hspace{5em}\cfrac{5}{6} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{7}{8}\cdot \cfrac{6}{6}\implies \cfrac{42}{48}\hspace{5em}\cfrac{5}{6}\cdot \cfrac{8}{8}\implies \cfrac{40}{48}\hspace{9em}\boxed{\cfrac{42}{48} ~~ {\Large \begin{array}{llll} > \end{array}}~~ \cfrac{40}{48}}[/tex]
HELP THANK YOU SO MUCH
Kyle works at a local music store. The store receives a shipment of new CDs in a box. In the shipment, there are 10 country CDs5 rock CDs12 hip hop CDs, and 3 jazz CDs. What is the probability that the first CD that Kyle pulls from the box will NOT be hip hop?
A. 3/5
B. 2/5
C. 12/30
D. 17/30
The probability of not pulling hip hop CDs is equal to 3/5. The correct option is (A).
What is probability?Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.
The probability of any event always lies in the close interval of 0 and 1 [0,1].
The zero value of probability indicates that the event will not happen while its value equal to one indicate that it will happen.
Given that,
The number of country, rock, hip hop, and jazz CDs are 10, 5, 12 and 3 respectively.
Then, the total number of CDs are 10 + 5 + 12 + 3 = 30
Now, the probability of not selecting hip hop is equal to the probability of selecting the remaining types of CDs which is given as,
P(Not hip hop CDs) = (10 + 5 + 3)/30
= 18/30
= 3/5
Hence, the probability that the first CD that Kyle pulls from the box will not be hip hop is 3/5.
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What is the area of the triangle?
7 cm
10 cm
Area = [?] cm²
Enter
Answer:
35 cm²
Step-by-step explanation:
Base of triangle = 10 cm
Height of triangle = 7 cm
Area of triangle = 1/2 x (base x height)
= 1/2 x (10 x 7)
= 1/2 x 70
= 35
So, area is 35 cm²
Factor 2x^4-5x^3+6x^2-15x completely over the set of integers
[tex]2x^4 - 5x^3 + 6x^2 - 15x \\ \\ =x(2x^3 - 5x^2 + 6x-15) \\ \\ =x(x^2(2x-5)+3(2x-5)) \\ \\ =\boxed{x(2x-5)(x^2+3)}[/tex]
Suppose z varies directly with x and inversely with the square of y. If z = 12 when x what is z when x = 7 and y = 8?
what is z?
the initial statement here is
z
∝
x
y
2
to convert to an equation multiply by k the constant
of variation
⇒
z
=
k
x
y
2
to find k use the given condition
z
=
18
when
x
=
6
and
y
=
2
z
=
k
x
y
2
⇒
k
=
y
2
z
x
=
4
×
18
6
=
12
equation is
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
∣
∣
∣
2
2
z
=
12
x
y
2
2
2
∣
∣
∣
−−−−−−−−−−−−−
when
x
=
8
and
y
=
9
z
=
12
×
8
81
=
32
27
Carrie is creating a painting for art class. The width of the canvas is 5 inches greater than the height of the canvas. Write a simplified equation in terms of h (the height) for the perimeter, p, of the canvas. (Please show work!)50 points!!!!!!
Length is 4 ft and width is is 3ft.
What is width ?
The "size" of a body is measured in geometry by its mean width; for more information on the various body measures, see Hadwiger's theorem. One must take into account -dimensional hyperplanes parallel to a specific direction in where is the n-sphere.
[tex]\begin{aligned}& w^2+(w+1)^2=5^2 \\& \frac{w^2+w^2+2 w+1}{}=25 \\& 2 w^2+2 w-21\end{aligned}[/tex]
[tex]\begin{aligned}& 2 w^2+2 w-24=0 \\& w^2+w-12=0\end{aligned}[/tex]
[tex]\begin{gathered}(w-3)(w+4)=0 \\w=3,-4\end{gathered}[/tex]
The width must be three because we can't have negative widths. Since the length is four feet, we have the dimensions of our poster.
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In how many ways can the digit in the number 7,600,000 be arranged
Answer:Answer to Solved In how many ways can the digits in the number 7, ... Question: In how many ways can the digits in the number 7, 600,000 be arranged?
1 answer
·
Top answer:
Concept used : The number of permutations (arrang...
Step-by-step explanation:
Calculate the distance between the points P=(-1, -1) and A=(2, 7) in the coordinate plane. Round your answer to the nearest hundredth.
Using the distance formula, [tex]AP=\sqrt{(-1-2)^2+(-1-7)^2} \approx \boxed{8.54}[/tex]
13. Find (f . g)(x) if f(x)=7x³-5x²+42x-30 and g(x)=7x-5.
(f . g)(x)=49x⁴-269x²-150
(f . g)(x)=49x⁴+269x²+150
(f . g)(x)=49x⁴-70x³+319x²-420x+150
(f. g)(x)=49x⁴+70x³-319x²+420x-150
(f . g)(x) is multiplication of f(x) and g(x). So,
(f. g)(x) = [tex]49x^{4}-70x^{3}+319x^{2} -420x+150[/tex] . Option (c) is correct answer.
How to multiply two functions?A new function that is the product of the original two functions is created when two independent functions are multiplied together.
To multiply two functions together, perform these steps:
Each term in the first function should be multiplied by each term in the second function.Combine related terms to produce the desired function.The highest-order term in the new function should come first.In given question we have two functions
f(x) = 7x³-5x²+42x-30
g(x) = 7x - 5
we need to find (f.g)(x) that is nothing but multiplication of f(x) and g(x).
So multiplying both the functions, we get
(f.g)(x) = f(x). g(x)
=( 7x³-5x²+42x-30)*(7x - 5)
=(49[tex]x^{4}[/tex]-35x³-35x³+25x²+294x²-210x-210x+150)
= [tex]49x^{4}-70x^{3}+319x^{2} -420x+150[/tex]
So, option (c) is correct answer.
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PLEASE HELP WILL MARK BRAINLIEST..Write a polynomial function of least degree with rational coefficients so that P(x) = 0 has the given roots.
x= -2, x=7
P(x)=
A polynomial function of least degree with rational coefficients so that P(x) = 0 has the given roots is P(x)=x²-5x-14
What is a polynomial function?A function is said to as polynomial when a variable in an equation, such as a quadratic equation or cubic equation, etc., has only positive integer exponents or non-negative integer powers. One polynomial with an exponent of 1 is 2x+5, for instance. One that has more than two algebraic terms is referred to as a polynomial expression. Polynomial is a monomial or binomial that is repeatedly added, as the name suggests.
A mathematical expression containing one or more algebraic terms, where each algebraic term is made up of a constant multiplied by one or more variables raised to a nonnegative integral power.
x= -2, x=7
Given,
P(x) = 0
This polynomial function has the roots,
x= -2, x=7
So,
(x+2)(x-7)
We have to multiply both of them we get,
P(x)=(x+2)(x-7)
0=x²-5x-14
x²-5x-14=0
Therefore, P(x)=x²-5x-14 is the polynomial function.
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A sample of 200g of an isotope decays to another isotope according to the function A(t)= 200е⁻⁰⁰⁵⁴⁺ ,where t is the time in years
(a) How much of the initial sample will be left in the sample after 25 years?
(b) How long will it take the initial sample to decay to half of its original amount?
(a) After 25 years, about __g of the sample will be left.
(Round to the nearest hundredth as needed.)
After 25 years, about 52g of the sample will be left and the sample never reaches half of its original amount
How to determine the sample after 25 yearsFrom the question, we have the following parameters that can be used in our computation:
A(t)= 200е⁻⁰⁰⁵⁴⁺
Also from the question, we have
The variable t represents the number of years
This means that
t = 25, in this case
So, we have
A(25)= 200е⁻⁰⁰⁵⁴ ˣ ²⁵
Evaluate the above equation
A(25)= 51.848052128
Approximate
A(25) = 52
This means that the remaining sample is 52 grams
When the sample decays to reach half the initial valueHere, we have
A(t) = 0.5 * 200
A(t) = 100
Substitute the known values in the above equation, so, we have the following representation
200е⁻⁰⁰⁵⁴⁺ = 100
Divide both sides by 100
е⁻⁰⁰⁵⁴⁺ = 0.5
Take the natural logarithm of both sides
0.054t = -0.69314718056
So, we have
t = -0.69314718056/0.054
Evaluate
t = -13
Time cannot be negative
This means that it never reaches half of its original amount
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Help solve systems of equations
Answer:
b!vch I am up b!vch I am up b!vch I am up
Help Please!!
Line q has an equation of y+7=9(x+4). Line r is perpendicular to line q and passes through (9,–10). What is the equation of line r?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
The equation of line r, in slope-intercept form, is: y = -1/9x - 9.
How to Write the Equation of a Line in Slope-intercept Form?The equation that represents a line, in slope-intercept form, is expressed or written as:
y = mx + b, where the slope is m, and the y-intercept is b.
The slope of line q, with the equation y + 7 = 9(x + 4) is 9. The negative reciprocal of 9 is -1/9. This means line r that is perpendicular to line q and passes through (9, -10) has a slope, m = -1/9.
To write the equation of the line in slope-intercept form, first, substitute m = -1/9 and (a, b) = (9, -10) into y - b = m(x - a):
y - (-10) = -1/9(x - 9)
y + 10 = -1/9(x - 9)
Rewrite in slope-intercept form:
y + 10 = -1/9x + 1
y = -1/9x + 1 - 10
y = -1/9x - 9
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HELP! 10 POINTS!!!!
Where are the residual values shown on a residual plot?
A) on the y-axis
B) on the x-axis
C) on the line of best fit
D) on the x and y-axis
The coordinate on which the residual values are shown on a residual plot is: A) on the y-axis.
What is a residual value?A residual value can be defined as a difference between the measured (given or observed) value from a residual plot (scatter plot) and the predicted value from a residual plot (scatter plot).
Mathematically, the residual value of a data set can be calculated by using this formula:
Residual value = given value - predicted value
In Mathematics, the independent variable (fitted values) are generally plotted on the x-axis of a residual plot (scatter plot) while the residual value is plotted on y-axis of a residual plot (scatter plot).
In conclusion, a line of best fit simply refers to a trend line on a residual plot (scatter plot).
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There are two right circular cylinders. The radius of the first cylinder is 3 centimeters, and its height is 5 centimeters. The radius of the second cylinder is 15 centimeters, but its height is also 5 centimeters. What is the ratio of the volume of the second cylinder to the volume of the first cylinder?
The ratio of the volume of the second cylinder to the volume of the first cylinder is 25.
To find the ratio of the volume of the second cylinder to the volume of the first cylinder, we need to calculate the volumes of both cylinders and then compare them.
The formula to calculate the volume of a right circular cylinder is given by V = πr^2h, where V represents the volume, r is the radius, and h is the height.
For the first cylinder:
Radius (r₁) = 3 centimeters
Height (h₁) = 5 centimeters
Volume of the first cylinder (V₁) = π * (3 cm)^2 * 5 cm
= 45π cm³
For the second cylinder:
Radius (r₂) = 15 centimeters
Height (h₂) = 5 centimeters
Volume of the second cylinder (V₂) = π * (15 cm)^2 * 5 cm
= 1125π cm³
To find the ratio of the volumes, we divide the volume of the second cylinder by the volume of the first cylinder:
Ratio = V₂ / V₁
= (1125π cm³) / (45π cm³)
= 25
Therefore, the ratio of the volume of the second cylinder to the volume of the first cylinder is 25.
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Evaluate b(-7), when b(c) = 2c³5c² - 6c - 13.
Answer:
168015
Step-by-step explanation:
b(c) = 2c³5c² - 6c - 13
b(7)=2(7)³5(7)²-6(7)-13
b(7)=2(343)5(7)²-6(7)-13
b(7)=(686) 5(49)-6(7)-13
b(7)=(686) (245)-6(7)-13
b(7)=(686) (245) -42-13
b(7)=168070-42-13
b(7)=168028-13
b(7)=168015
(Usually this is how you would solve it but because there was no sign between the 2c^35c^2 I got sort of confused so I just multiplied, if wrong I'm sorry..)
[tex]b(-7)=-168041[/tex].
Step-by-step explanation:1. Write the function.[tex]b(c)=2c^{3} 5c^{2} -6c-13[/tex]
2. Substitute "c" by "-7" in the function.[tex]b(-7)=2(-7)^{3} 5(-7)^{2} -6(-7)-13[/tex]
3. Calculate.[tex]b(-7)=2(-343) 5(49) -(-42)-13\\ \\b(-7)=-168070 +42-13\\ \\b(-7)=-168041[/tex]
which of the following inference tests is not appropriate for a comparison of two means in a causal comparative study?
a. The Mann-Whitney U test
b. ANOVA
c. Chi-Square
d. A t test for independent means
The Mann-Whitney U test is not appropriate for a comparison of two means in a causal comparative study.
What is Mann-Whitney U test?To determine if two samples are likely to come from the same population, researchers employ the Mann Whitney U test, also known as the Mann Whitney Wilcoxon Test or the Wilcoxon Rank Sum Test (i.e., that the two populations have the same shape). When a continuous level variable is measured across all observations in two groups and we wish to test if the distribution of this variable differs between the two groups but we are unable to assume normality in both groups, we use the Mann-Whitney test.
Here,
Mann-Whitney test In a causal comparative investigation, comparing two means is not acceptable using the U test.
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Brayden runs a farm stand that sells raspberries and grapes. Yesterday Brayden sold 44 pounds of raspberries and 43 pounds of grapes for a total revenue of $217. Today he sold 45 pounds of raspberries and 18 pounds of grapes for a total revenue of $144. Write a system of equations that could be used to determine the price of each pound of raspberries and the price of each pound of grapes. Define the variables that you use to write the system
Step-by-step explanation:
44r + 43g = 217
45r + 18g = 144
r = a pound of raspeberries
g = a pound of grapes
help meeeeeeeeeee pleaseee
(a) 794g of the initial sample will be left in the sample after 25 years. (b) Time taken to decay to half of its original amount is 3.39 years.
Isotopes(200g) are atoms that have the same number of protons in their nucleus, but a different number of neutrons. This means that they have the same atomic number, but a different atomic mass. Because of this, isotopes have different physical and chemical properties. Isotopes can be stable, meaning that they do not undergo radioactive decay, or they can be unstable, meaning that they will undergo radioactive decay over time.
(a) Substituting 25 for t in the expression, we get:
[tex]A(25) = 200e^{0.0541 \times 25}[/tex]
[tex]= 200e^{1.3525}[/tex]
Thus, after 25 years, there will be
[tex]200e^{1.3525} = 2003.97[/tex]
794 g of the initial sample left in the sample.
(b) We want to find t such that
[tex]A(t) = 200e^{0.0541}[/tex]
= 100.
Solving for t, we get:
[tex]= 200e^{0.0541} \times t=100[/tex]
Dividing both sides by 200 and applying the natural logarithm to both sides, we get:
0.0541 × t = ln(0.5)
Therefore,
[tex]t = \frac{ln(0.5)}{0.0541}[/tex]
= 3.39 years.
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I need 1/8 turned into a percentage but rounded to the nearest whole number.
Answer: 12.5%
Explain:
There are two main ways to express a fraction as a percentage:
-Divide 100 by the numerator, and then multiply both numerator and denominator by the answer.
-Convert the fraction to a decimal first, then multiply the answer by 100.
Write a linear equation
representing a line passing
through points (3, 5) and (-8,
5).
Hello,
I hope you and your family are doing well!
The answer is y = 5 (See below for the explanation).
To find a linear equation representing a line passing through two points, you can use the slope-intercept form of the equation, which is written as y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis).
To find the slope of the line, you can use the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates of the two given points, we get:
m = (5 - 5) / (-8 - 3) = 0 / -11 = 0
Since the slope of the line is 0, the line is horizontal and passes through both points at the same y-value (5). The x-intercept (the point at which the line crosses the x-axis) is not relevant in this case.
Therefore, the linear equation representing this line is y = 5.
Happy Holiday & New Year!
Please give this answer 5 stars and brainliest if you find it helpful.
Best,
Answer:
y=5
Step-by-step explanation:
y=mx+b
if you put your two point on a graft, they are on same line for the y-intersept. So if that is true then your answer has to y=5
What are the x- and y-coordinates of point C, which partitions the directed line segment from A to B into the ratio 3:10? Round to the nearest tenth, if necessary.
x = ____
y = ____Choose matching definition
a. (-3.5, 2.3)
b. (1.2, -4.7)
c. -2.6
5.2
d. (-4, -5)
The x- and y-coordinates of point C, which partitions the directed line segment from A to B into the ratio 3:10 are (-2.6,5.2).
A line segment in geometry has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a line that links two places. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction. A ray has only one endpoint and an endlessly long another end, as opposed to a line segment that has two ends.
If a point (x,y) divides the line segment joining the points A(x1,y1) and B (x2,y2) is in the ratio m:n, then
[tex]x=\frac{mx2+nx1}{m+n} \\y=\frac{my2+ny1}{m+n} \\[/tex]
Here,
m:n = 3:10
The endpoint of line AB are at: A(-4,8) and B(2,-4)
We substitute the given values to obtain:
x= 3*2+10*(-4)/3+10
x= -34/13
x= -2.6
and
y= 3*(-4)+10*(8)/3+10
y= 68/13
y= 5.2
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