A cone and a pyramid have equal heights and volumes. If the base area of the pyramid is 154cm^2, find the radius of the cone
Answer:
√154/π
Step-by-step explanation:
thể tích nón = thể tích hình chóp
1/3πr².h=1/3S.h
πr²=154(rút gọn h và 1/3)
=> r=√154/π
The radius of the cone is 7 cm if the cone and a pyramid have equal heights and volumes.
What is a cone?It is defined as a three-dimensional shape in which the base is a circular shape and the diameter of the circle decreases as we move from the circular base to the vertex.
[tex]\rm V=\pi r^2\dfrac{h}{3}[/tex]
We have:
A cone and a pyramid have equal heights and volumes.
154 = πr²
π = 22/7
r = 7 cm
Thus, the radius of the cone is 7 cm if the cone and a pyramid have equal heights and volumes.
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11. Find the 5th term of the sequence defined by the given rule. (1/2 point)
f(n) = 6n + 4
Answer:
34
Step-by-step explanation:
n = 5
f(5) = 6(5)+4
f(5)=34
The fifth term of the sequence is equal to 34.
What is arithmetic progression?The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression.
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given expression is f(n) = 6n + 4. The value of the fifth term will be calculated as,
n = 5
f(5) = 6(5)+4
f(5)=34
Therefore, the fifth term of the sequence is equal to 34.
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HELP WILL GIVE BRAINLYIST
Answer:
The parent cubic function has been vertically stretched by a factor of 4.
Equation:G(x)= 4[tex]\sqrt[3]{x}[/tex]
Answer: Option B
OAmalOHopeO
I NEED THE ANSWER SOON PLEASE!!?!?! hopefully someone sees this
Answer:
1 and 1/25
Step-by-step explanation:
Please help!! The question is the image below VVV
Answers are also images after the picture.
Step-by-step explanation:
When adding two fractions with different bases (bottom numbers), we can use this function:
[tex]\frac{a}{b} + \frac{c}{d} = \frac{ad + cb}{bd}[/tex]
So, to apply this to the given question:
[tex]\frac{x+3}{x-6} +\frac{1}{x-2}[/tex]
= [tex]\frac{(x+3)(x-2)+(1)(x-6)}{(x-6)(x-2)}[/tex]
From the given answers, we see we don't need to simplify the resulting base number, which makes things a lot easier.
Multiply top using: (a + b)(c + d) = ac + ad + bc + bd= [tex]\frac{[(x*x) + (x*-2)+(3*x)+(3*-2)]+(x-6)}{(x-6)(x-2)}[/tex]
Simplify.= [tex]\frac{[x^2 -2x+3x-6]+(x-6)}{(x-6)(x-2)}[/tex]
Remove parentheses.= [tex]\frac{x^2 -2x+3x-6+x-6}{(x-6)(x-2)}[/tex]
Simplify again.= [tex]\frac{x^2 +2x-12}{(x-6)(x-2)}[/tex]
Now if we wanna be a little smart, we can see that from here, the only answer that has x^2 and something else, is A. But, just for show, lets factor.
Factor.= [tex]\frac{x(x+2)}{(x-6)(x-2)}[/tex]
Answer:
A) [tex]\frac{x(x+2)}{(x-6)(x-2)}[/tex]
Find Term 20 for the sequence a= 4 6 8 10......
4,6,8,10 are in A.P
a=4d=2[tex]\\ \rm\Rrightarrow a_n=a+(n-1)d[/tex]
[tex]\\ \rm\Rrightarrow a_20=4+(20-1)2[/tex]
[tex]\\ \rm\Rrightarrow a_20=4+19(2)[/tex]
[tex]\\ \rm\Rrightarrow a_20=4+38[/tex]
[tex]\\ \rm\Rrightarrow a_20=42[/tex]
5. Given a test in which there is overlap of the test results for diseased and non-diseased individuals (e.g., normal individuals are found who have test results ranging in value from 8 to 15, and diseased individuals are found who have test results ranging in value from 12 to 25, so that in the range of values 12 to 15 there are both normal and diseased individuals), if the current cutoff value lies in the range of this overlap and you move the cutoff value toward the normal population (lower numbers in this example), the true negative numbers will _____________________ . (5 points)
Answer:
True negative numbers are considered as diseased individual. So, the true negative numbers will increase
Step-by-step explanation:
True negative numbers are considered as diseased individual. So, the true negative numbers will increase.
Consider the probability that no more than 28 out of 304 students will not graduate on time. Choose the best description of the area under the normal curve that would be used to approximate binomial probability.
a. Area to the right of 27.5
b. Area to the right of 28.5
c. Area to the left of 27.5
d. Area to the left of 28.5
e. Area between 27.5 and 28.5
Solution :
Here the probability that exactly 28 out of 304 students will not graduate on time. That is
P (x = 28)
By using the normal approximation of binomial probability,
[tex]$P(x=a) = P(a-1/2 \leq x \leq a+1/2)$[/tex]
∴ [tex]$P(x=28) = P(28-1/2 \leq x \leq 28+1/2)$[/tex]
[tex]$=P(27.5 \leq x \leq 28.5)$[/tex]
That is the area between 27.5 and 28.5
Therefore, the correct option is (e). Area between 27.5 and 28.5
1. Coach Jensson wants to celebrate the final win of the
school's baseball season with a trip to the local fast food
place. The team buys 22 delicious tacos and 17 orders
of savory nachos for $71.05. A few of the players are still
hungry, so the coach buys 10 more tacos and 5 more
orders of nachos for $27.25. If you don't consider tax,
what is the price of a taco and the price of an
order of nachos ?
6 less than six times a number is 42 what is the number
Answer:
x = 8
General Formulas and Concepts:
Pre-Algebra
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
6x - 6 = 42
Step 2: Solve for x
[Addition Property of Equality] Add 6 on both sides: 6x = 48[Division Property of Equality] Divide 6 on both sides: x = 8Answer: -6
Step-by-step explanation:
We can create an equation based on the info given.
6-6x=42 Now you solve for x, the unknown number.
-6 -6 Subtract 6 on both sides
-6x=36
/-6 /-6 Divide by -6 on both sides
x=-6
The number is -6.
- 18 = -3x + 6
Plz help
Answer:
8 =x
Step-by-step explanation:
- 18 = -3x + 6
Subtract 6 from each side
-18-6 = -3x+6-6
-24 = -3x
Divide each side by -3
-24/-3 = -3x/-3
8 =x
Answer:
x= 8
Step-by-step explanation:
[tex]\sf{}[/tex]
=> -3x+6 = -18
=> -3x+6-6= -8-6
=> -3x= -24
=> x= 8
please help me with geometry
Answer:
x = 7
Explaination:
ABC = 40°
and BD bisects the angle so ABD = 20°
so 3x-1=20
solving for x gets us
x = 7
Let x represent the average annual salary of college and university professors (in thousands of dollars) in the United States. For all colleges and universities in the United States, the population variance of x is approximately σ2
= 47.1. However, a random sample of 15 colleges and universities in Kansas showed that x has a sample variance σ2 = 83.2. Use a 5% level of significance to test the claim that the variance for colleges and universities in Kansas is greater than 47.1. Use the traditional method. Assume that a simple random sample is selected from a normally distributed population.
a. Check requirements.
b. Establish H0 and H1 and note the level of significance.
c. Find the sample test statistic.
d. Find Critical Value.
e. Conclude the test and interpret results.
Answer:
Kindly check explanation
Step-by-step explanation:
Given that :
The hypothesis :
H0 : σ²= 47.1
H1 : σ² > 47.1
α = 5% = 0.05
Population variance, σ² = 47.1
Sample variance, s² = 83.2
Sample size, n = 15
The test statistic = (n-1)*s²/σ²
Test statistic, T = [(15 - 1) * 83.2] ÷ 47.1
Test statistic = T = [(14 * 83.2)] * 47.1
Test statistic = 1164.8 / 47.1
Test statistic = 24.73
The degree of freedom, df = n - 1 ; 10 = 9
Critical value (0.05, 9) = 16.92 (Chisquare distribution table)
Reject H0 ; If Test statistic > Critical value
Since ; 24.73 > 16.92 ; Reject H0 and conclude that variance is greater.
write
the following numbers using Roman numerals 20
Step-by-step explanation:
xx is the Roman number of 20
Form a polynomial whose zeros and degree are given.
Zeros: - 2, 2, 6; degree: 3
Type a polynomial with intéger coefficients and a leading coefficient of 1 in the box below.
f(x)=(Simplify your answer.)
Answer:
[tex]f(x) = (x + 2)(x - 2)(x - 6)[/tex]
[tex]f(x) = ({x}^{2} + 4)(x - 6)[/tex]
[tex]f(x) = {x}^{3} - 6 {x}^{2} + 4x - 24[/tex]
Step-by-step explanation:
Multiply factors.
Which of the two functions below has the smallest minimum y-value?
f(x) = 4(x - 6)4 + 1
g(x) = 2x3 + 28
O A. g(x)
B. f(x).
C. The extreme minimum y-value for f(x) and g(x) is --
D. There is not enough information to determine
Answer:
Answer A
Step-by-step explanation:
[tex]\displaystyle \lim_{n \to -\infty} (3x^3+28)=-\infty\\\\minimum\ of \ f(x)=6\\\\Answer\ A[/tex]
Which expression represents the perimeter of the rectangle above? . 6x + 3. 10x + 6. 8x² + 6x. 12x + 6
There is no any image of rectangle
HURRY PLEASE!!!!!
All of the following expressions are equal except ____. 1/4^3 4^2/4^5 4^5/4^2 4^-3
Answer:
4^5/4^2
Step-by-step explanation:
We know 1/a^b = a^-b
a^b/ a^c = a^(b-c)
1/4^3 = 4^-3
4^2/4^5 = 4^(2-5) = = 4^-3
4^5/4^2 = 4^(5-2) = 4^3
4^-3
Answer:
[tex]4^{5}/5^{2}[/tex] = not the same
Step-by-step explanation:
you have the equations
[tex]1/4^{3} = 0.015625\\\\4^{2}/4^{5} = 16/1024 = 0.015625\\\\4^{5}/4^{2} = 1024/16 = 65\\\\4^{-3} = 0.015625[/tex]
the value of 5/121^1/2
Answer:
√5/121
Step-by-step explanation:
formula: a^½=√a
(⁵/¹²¹)^½=√⁵/¹²¹
Determine the indicated term in the following arithmetic sequences.
1.) a subscript 5: {2, 5, 8, ...}
2.) a subscript 20: {4, 8, 12, ...}
3.) a subscript 18: {0,20,40,60, ...}
Answer:
[tex]a_5= 14[/tex]
[tex]a_{20}= 80[/tex]
[tex]a_{18}= 340[/tex]
Step-by-step explanation:
Solving (a):
We have:
[tex]a_1=2[/tex] --- first term
[tex]d = 5 -2 = 3[/tex] common difference
The 5h term is:
[tex]a_n= a_1 + (n - 1)d[/tex]
[tex]a_5= 2+ (5 - 1)*3[/tex]
[tex]a_5= 14[/tex]
Solving (b):
We have:
[tex]a_1 = 4[/tex] --- first term
[tex]d = 8 -4 = 4[/tex] common difference
The 20h term is:
[tex]a_n= a_1 + (n - 1)d[/tex]
[tex]a_{20}= 4+ (20 - 1)*4[/tex]
[tex]a_{20}= 80[/tex]
Solving (c):
We have:
[tex]a_1 = 0[/tex] --- first term
[tex]d = 20 -0 = 20[/tex] common difference
The 18th term is:
[tex]a_n= a_1 + (n - 1)d[/tex]
[tex]a_{18}= 0+ (18 - 1)*20[/tex]
[tex]a_{18}= 340[/tex]
The measurements of a circular object are given in the ratio table.
a. Find the missing dimensions of other circular objects by completing the ratio table.
b. Graph the pairs of values.
Answer:
answer hajandtb Tj.yfs5bsyb
What is the equation of the line that passes through (-3,-1) and has a slope of 2/5? Put your answer in slope-intercept form
A: y= 2/5x -1/5
B: y= 2/5x +1/5
C: y= -2/5x -1/5
Answer:
y = 2/5x + 1/5
Step-by-step explanation:
y = 2/5x + b
-1 = 2/5(-3) + b
-1 = -6/5 + b
1/5 = b
how many ways can this be done. if a committee of 5 people from 7 men and 8 women?
Answer:
3003 ways
Step-by-step explanation:
(7+8)C5
= 15C5
= 15!/(5!10!)
= 3003
if x and y are linear pair of angel then x +y=
Answer: x + y = 180²
Step-by-step explanation:
A linear pair is a pair of adjacent, supplementary angles.
Adjacent means next to each other.
Supplementary means that the measures of the two angles add up to equal 180 degrees.
Therefore, by definition, if x and y are linear pairs of angles, then x + y = 180.
1. Plot the following points by hand or using an online graphing calculator. What is the function that best fits the points?
(0, 3), (1, 6), (2, 12), (3, 24)
•Linear
•Exponential
•Quadratic
The weight of an object above the surface of the Earth varies inversely with the square of the
distance from the center of the Earth. If a body weighs 50 pounds when it is 3,960 miles from
Earth's center, what would it weigh if it were 4,015 miles from Earth's center?
Answer:
weight =48.71228786pounds
Step-by-step explanation:
[tex]w = \frac{k}{ {d}^{2} } \\ 50 = \frac{k}{ {3960}^{2} } \\ \\ k = 50 \times {3960}^{2} \\ k = 50 \times 15681600 \\ k = 784080000 \\ \\ w = \frac{784080000}{ {d}^{2} } \\ w = \frac{784080000}{16120225} \\ \\ w = 48.71228786 \\ w = 48.7pounds[/tex]
If a body weighs 50 pounds when it is 3,960 miles from Earth's center, it would weigh approximately 48.547 pounds if it were 4,015 miles from Earth's center, according to the inverse square law formula.
We know the inverse square law formula:
W₁ / W₂ = D²₂ / D²₁
Where W₁ is the weight of the body at the initial distance D₁, and W₂ is the weight at the final distance D₂.
So we have,
W₁ = 50
D₁ = 3,960
D₂ = 4015
We know that the body weighs 50 pounds when it is 3,960 miles from Earth's center,
So we can plug in those values as follows:
50 / W₂ = (4,015)²/ (3,960)²
To solve for W₂, we can cross-multiply and simplify as follows:
W₂ = 50 x (3,960)² / (4,015)²
W₂ = 50 x 15,681,600 / 16,120,225
W₂ = 48.547 pounds (rounded to three decimal places)
Therefore, if the body were 4,015 miles from Earth's center, it would weigh approximately 48.547 pounds.
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X
у
Which equation could be used to create the data shown in the
table?
1
5
O y = 5x
4
17
O y = 5x + 1
5
21
O y = 4x + 1
7
29
O y = x + 4
9
37
Answer:
C
Step-by-step explanation:
The equation that represents the table is y=4x+1
yesterday kofi earned 50cedis mowing lawns. today kofi earned 60% of what he earned yesterday mowing lawns.How much did kofi earned mowing lawns today?
Answer:
30 cedis
Step-by-step explanation:
todays earning = yesterdays earning * 60/100
50 * 60/100 =30
Jordan buys sandals and sunglasses for a trip to the beach. The sunglasses cost $6. The sandals cost 3 times as much as the sunglasses. How much do the sandals cost?
Answer:
18 dollars
Step-by-step explanation:
sunglasses = 6 dollars
sandals = 3 * sunglasses
= 3 * 6 dollars
= 18 dollars
2. The cost of 5 pen is Rs 1200, find the cost of 1 pen.
Step-by-step explanation:
cost of 5 pen is Rs 1200,
cost of 1 pen is 1200/5 = Rs 240
Answer:
Rs 240
Step-by-step explanation:
1200÷5=240
