Answer:
C) (-4, 2)
Step-by-step explanation:
Answer:
The center is ( -4,2) and the radius is 4
Step-by-step explanation:
The equation of a circle can be written as
( x-h) ^2 + ( y-k) ^2 = r^2 where ( h,k) is the center and r is the radius
(x+4)^2 + (y - 2)^2 = 16
(x- -4)^2 + (y - 2)^2 = 4^2
The center is ( -4,2) and the radius is 4
Instructions: Find the Measure of the indicated angle to the
nearest degree.
Answer:
? = 35
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan ? = opp /adj
tan ? = 33/48
Take the inverse tan of each side
tan ^ -1 ( tan ? ) = tan ^ -1 ( 33/48)
? =34.50852299
? = 35
I need this answered in ONE minute
Place the indicated product in the proper location on the grid. Write your answer in descending powers of x. (x^ 2 + 3x + 1)(x^2 + x + 2)
Answer:
[tex]x^4 + 4x^3 + 6x^2 + 7x + 2[/tex]
Step-by-step explanation:
We are asked to multiply the given polynomials.
[tex](x^ 2 + 3x + 1) \times (x^2 + x + 2)[/tex]
Multiply each term of the first polynomial to each term of the second polynomial.
[tex]x^ 2 \times (x^2 + x + 2) = x^4 + x^3 + 2x^2[/tex]
[tex]3x \times (x^2 + x + 2) = 3x^3 + 3x^2 + 6x[/tex]
[tex]1 \times (x^2 + x + 2) = x^2 + x + 2[/tex]
Add the results
[tex](x^4 + x^3 + 2x^2) + (3x^3 + 3x^2 + 6x) + ( x^2 + x + 2)[/tex]
Combine the like terms
[tex]x^4 + 4x^3 + 6x^2 + 7x + 2[/tex]
The answer is written in descending powers of x.
The slope of the line below is 4 . Which of the following is the point slope form of that line ? ( top answer gets )
Answer:
C
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = 4 and (a, b) = (- 3, - 4) , thus
y - (- 4) = 4(x - (- 3)) , that is
y + 4 = 4(x + 3) → C
A recent national survey found that high school students watched an average (mean) of 7.8 movies per month with a population standard deviation of 0.5. The distribution of number of movies watched per month follows the normal distribution. A random sample of 30 college students revealed that the mean number of movies watched last month was 7.3. At the 0.05 significance level, can we conclude that college
Answer:
Step-by-step explanation:
Given that :
Mean = 7.8
Standard deviation = 0.5
sample size = 30
Sample mean = 7.3 5.4772
The null and the alternative hypothesis is as follows;
[tex]\mathbf{ H_o: \mu \geq 7.8}[/tex]
[tex]\mathbf{ H_1: \mu < 7.8}[/tex]
The test statistics can be computed as :
[tex]z = \dfrac{X- \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \dfrac{7.3- 7.8}{\dfrac{0.5}{\sqrt{30}}}[/tex]
[tex]z = \dfrac{-0.5}{\dfrac{0.5}{5.4772}}[/tex]
[tex]z = - 5.4772[/tex]
The p-value at 0.05 significance level is:
p-value = 1- P( Z < -5.4772)
p value = 0.00001
Decision Rule:
The decision rule is to reject the null hypothesis if p value is less than 0.05
Conclusion:
At the 0.05 significance level, there is sufficient information to reject the null hypothesis. Therefore ,we conclude that college students watch fewer movies a month than high school students.
The area of a triangle is 1.440 cm^2? The base of the triangle is 5 times the height. What is the height of the triangle?
12 cm
24 cm
46 cm
60 cm
Answer:
The answer is option B
24cmStep-by-step explanation:
Area of a triangle is
[tex] \frac{1}{2} \times b \times h[/tex]
Where b is the base
h is the height
The base of the triangle is 5 times the height is written as
b = 5h
Area of the triangle is 1440cm²
[tex]1440 = \frac{1}{2} \times 5h \times h[/tex]
[tex]1440 = \frac{1}{2} 5 {h}^{2} [/tex]
[tex]2880 = 5 {h}^{2} [/tex]
Divide both sides by 5
[tex] {h}^{2} = 576[/tex]
Find the square root of both sides
[tex]h = \sqrt{576} [/tex]
h = 24cmHope this helps you
2/3 (m-1/2) +3= m/3-7 Please Explain (Will give brainliest)
Answer:
m= -29
Step-by-step explanation:
This is a bit of a complex equation, but let's work through it.
2/3 (m-1/2) +3= m/3-7
First, we need to distribute the 2/3.
(2/3)(m)+(2/3)(−1/2)+3=m/3+−7
Now we simplify that.
2/3m+−1/3+3=1/3m+−7
We can now combine like terms.
2/3m+8/3=1/3m+−7
The goal is to isolate the variable, so we should subtract 1/3m from both sides.
1/3m+8/3=−7
Lets keep going! We can subtract 8/3 from both sides.
1/3m=-29/3
Well now we know what 1/3 of m is, but we want to know what m is. So we can multiply both sides by three to finally find out what m is!
m=-29
We did it! m=-29
Macy has a new beaded necklace. 26% of the 50 beads on her necklace are blue. How many
beads are there on Macy's necklace that are not blue?
Answer: 37
Step-by-step explanation:
Given that:
Total number of beads on her necklace = 50
Percentage of blue beads = 26%
Therefore, number of blue beads :
Percentage number of blue beads × total number of beads on necklace
Number of Blue beads = 26% × 50
= 0.26 × 50 = 13
Number of Blue beads = 13
Therefore, number of beads that aren't blue :
Total number of beads - number of blue beads
50 - 13 = 37
Number of beads that aren't blue = 37
please help :) Which number is greater than 3.14159 × 10 to the 4 power? A. 5,678,889 B. 9.897752 x 10 to the 6 power C. 71,224,900 D. 2.468 × 10 to the 7 power
Answer: C. 71,224,900
Based on the power, move the decimal point that many spaces to the right. (e.g., If it's 7.9 × 10^3, then move the decimal three spaces to the right, and you'd get 7900.)
3.14159 × 10^7 = 31415900
9.897752 × 10^6 = 9897752
2.468 × 10^7 = 24680000
Out of all the numbers mentioned in the question, 71,224,900 is the only one that's greater than 3.14159 × 10^7 = 31415900.
Which is a qualitative graph? On a coordinate plane, a line with positive slope goes through points (negative 1, 0) and (0, 3). On a coordinate plane, points are at (0, 2), (1, 3), (2, 2.5), (3, 3), (4, 4), and (4.5, 5). A graph has time on the x-axis and height on the y-axis. The graph increases to point A, increases to point B, and then decreases to point C. A graph has time on the x-axis and height on the y-axis. Segment A increases, segment B is increases, and segment C decreases.
Answer:
(-1,0), (0,3) and (2,2.25)
Step-by-step explanation:
The qualitative graph is as follows:
A(-1,0) ------> B(0,3) ------> C(2,2.25)
Hence, slope = (2.25 - 0)/(2 - (-1)) = 2.25/3
∴ slope = 0.75
Except for the option graph on a coordinate plane, a line with a positive slope goes through points (negative 1, 0) and (0, 3), all the graph is qualitative. Options B, C, and D are correct.
What is a qualitative graph?The kind of graph that shows the quality curve such as decreasing and increasing events, is called a qualitative graph or curve.
Here,
1. On a coordinate plane, a line with a positive slope goes through points (negative 1, 0) and (0, 3), since this graph does not represent any data as well as also constantly increasing between two points so it is not a qualitative graph.
Similarly,
Graphs B, C, and D have an increasing and decreasing order, so all are qualitative graphs.
Thus, except for graph A all the graphs are qualitative graphs.
Learn more about qualitative graphs here:
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can someone please help me
Answer:
B
Step-by-step explanation:
Because this equation is just a normal greater than symbol, it has to be a dotted line.
This graph starts at -2 and goes up 1 and right 3(this cancels out C as an option)
Than you shade the region with the larger number vaules, since it is greater than.
The mean one-way commute to work in Chowchilla is 7 minutes. The standard deviation is 2.4 minutes, and the population is normally distributed. What is the probability of randomly selecting one commute time and finding that: a). P (x < 2 mins) _____________________________ b). P (2 < x < 11 mins) _____________________________ c). P (x < 11 mins) ________________________________ d). P (2 < x < 5 mins) _______________________________ e). P (x > 5 mins)
Answer:
The answer is below
Step-by-step explanation:
Given that:
The mean (μ) one-way commute to work in Chowchilla is 7 minutes. The standard deviation (σ) is 2.4 minutes.
The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
a) For x < 2:
[tex]z=\frac{x-\mu}{\sigma}=\frac{2-7}{2.4} =-2.08[/tex]
From normal distribution table, P(x < 2) = P(z < -2.08) = 0.0188 = 1.88%
b) For x = 2:
[tex]z=\frac{x-\mu}{\sigma}=\frac{2-7}{2.4} =-2.08[/tex]
For x = 11:
[tex]z=\frac{x-\mu}{\sigma}=\frac{11-7}{2.4} =1.67[/tex]
From normal distribution table, P(2 < x < 11) = P(-2.08 < z < 1.67 ) = P(z < 1.67) - P(z < -2.08) = 0.9525 - 0.0188 = 0.9337
c) For x = 11:
[tex]z=\frac{x-\mu}{\sigma}=\frac{11-7}{2.4} =1.67[/tex]
From normal distribution table, P(x < 11) = P(z < 1.67) = 0.9525
d) For x = 2:
[tex]z=\frac{x-\mu}{\sigma}=\frac{2-7}{2.4} =-2.08[/tex]
For x = 5:
[tex]z=\frac{x-\mu}{\sigma}=\frac{5-7}{2.4} =-0.83[/tex]
From normal distribution table, P(2 < x < 5) = P(-2.08 < z < -0.83 ) = P(z < -0.83) - P(z < -2.08) = 0.2033- 0.0188 = 0.1845
e) For x = 5:
[tex]z=\frac{x-\mu}{\sigma}=\frac{5-7}{2.4} =-0.83[/tex]
From normal distribution table, P(x < 5) = P(z < -0.83) = 0.2033
ASAP PLEASE A box contains 6 red, 3 white, 2 green, and 1 black (in total 12) identical balls. What is the least number of balls necessary to take out randomly (without looking) to be sure of getting at least one red ball?
Answer:
7 is the least.
Step-by-step explanation:
Their are 12 balls, and 6 of them are red. if you are to pick every single ball except the red ones, you cut the number of balls in half, and are left with 6 red balls, and 6 balls picked. Your next pick must be a red ball, making 7 picks.
Dax is buying coffee for 5 5 people in his office. He also leaves a $2.00 $ 2.00 tip for the barista. If his total, with tip, is $18.25, $ 18.25 , how much is each cup of coffee, not including the tip? Enter your answer as a decimal, like this: 42.53
Answer:
$3.25
Step-by-step explanation:
To get the price of one cup of coffee without including Dax's two dollar tip, the first step is to subtract 2 from 18.25.
18.25 - 2= 16.25
16.25 is price of the five cups of coffee that Dax bought without the two dollar tip. The final step is to get the price of one cup of coffee which is basically:
16.25 ÷ 5 = 3.25
The cost of each cup of coffee is $3.25.
What is an expression?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.
To get the price of one cup of coffee without including Dax's two-dollar tip, the first step is to subtract 2 from 18.25.
18.25 - 2= 16.25
16.25 is the price of the five cups of coffee that Dax bought without the two-dollar tip. The final step is to get the price of one cup of coffee which is basically:
16.25 ÷ 5 = $3.25
Hence, the cost will be $3.25.
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Please answer this question now
Answer:
Area of the triangle = 469.4 ft²
Step-by-step explanation:
By applying Sine rule in the given triangle WXY,
[tex]\frac{\text{SinW}}{\text{XY}}=\frac{\text{SInY}}{\text{WX}}=\frac{\text{SinX}}{\text{WY}}[/tex]
Since m∠X + m∠Y + m∠W = 180°
m∠X + 40° + 27° = 180°
m∠X = 180° - 67°
m∠X = 113°
Now substitute the measures of sides and angles given in the picture,
[tex]\frac{\text{Sin27}}{\text{XY}}=\frac{\text{SIn40}}{38}=\frac{\text{Sin113}}{\text{WY}}[/tex]
[tex]\frac{\text{Sin27}}{\text{XY}}=\frac{\text{SIn40}}{38}[/tex]
XY = [tex]\frac{38\text{(Sin27)}}{\text{Sin40}}[/tex]
XY = 26.84
Area of the triangle = [tex]\frac{1}{2}(\text{XY})(\text{XW})(\text{SinX})[/tex]
= [tex]\frac{1}{2}(26.84)(38)(\text{Sin113})[/tex]
= 469.42
≈ 469.4 ft²
The FDA recommends that Americans get on average 3,000mg of salt in their daily diet. Suppose that you are interested in testing if Americans' average daily intake is different from 3,000mg. What is the correct null and alternative hypothesis statements?
Answer:
Null hypothesis; H0: μ = 3000
Alternative Hypothesis; Ha: μ ≠ 3000
Step-by-step explanation:
We are told that the FDA recommends that Americans get on average 3,000mg of salt in their daily diet.
Now we want to test this claim of whether Americans truly get an average of 3,000mg of salt in their daily diet.
Thus, the hypotheses is as follows;
Null hypothesis; H0: μ = 3000
Alternative Hypothesis; Ha: μ ≠ 3000
Null hypothesis; H0: μ = 3000
Alternative Hypothesis; Ha: μ ≠ 3000
Calculation of the null and alternative hypothesis:Since
The FDA recommends that Americans get on average 3,000mg of salt in their daily diet.
So, here the hypothesis be like
Null hypothesis; H0: μ = 3000
Alternative Hypothesis; Ha: μ ≠ 3000
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linear system please help 60 points * please please please help will give brainlist
Answer:
1. a. b = - 8
b. x = 8
c. x = 11
d. x = 5
2. 12 soccer balls and 8 basketballs can be purchased.
Step by step explanation
a. [tex] - 14 + 6b + 7 - 2b = 1 + 5b[/tex]
Calculate the sum
[tex] - 7 + 6b - 2b = 1 + 5b[/tex]
Collect like terms
[tex] 7 + 4b = 1 + 5b[/tex]
Move variable to L.H.S and change it's sign
Similarly, Move constant to R.H.S and change its sign
[tex]4b - 5b = 1 + 7[/tex]
Collect like terms
[tex] - b = 8[/tex]
Change the signs on both sides of the equation
[tex]b = - 8[/tex]
-----------------------------------------------------------------
b. [tex] \frac{5x + 10}{ - 6} = - 5[/tex]
Apply cross product property
[tex]5x + 10 = - 5 \times ( - 6)[/tex]
Multiply the numbers
[tex]5x + 10 = 30[/tex]
Move constant to R.H.S and change its sign
[tex]5x = 30 - 10[/tex]
Calculate the difference
[tex]5x = 20[/tex]
Divide both sides of the equation by 5
[tex] \frac{5x}{5} = \frac{20}{5} [/tex]
Calculate
[tex]x = 4[/tex]
----------------------------------------------------------------
c. [tex] - 15 = \frac{ - 8x - 17}{7} [/tex]
Apply cross product property
[tex] - 15 \times 7 = - 8x - 17[/tex]
Multiply the numbers
[tex] - 105 = - 8x - 17[/tex]
Swap the sides of the equation
[tex] - 8x - 17 = - 105[/tex]
Move constant to R.H.S and change its sign
[tex] - 8x = - 105 + 17[/tex]
Calculate
[tex] - 8x = - 88[/tex]
Change the signs on both sides of the equation
[tex]8x = 88[/tex]
Divide both sides of the equation by 8
[tex] \frac{8x}{8} = \frac{88}{8} [/tex]
Calculate
[tex]x = 11[/tex]
------------------------------------------------------------------
D. [tex]5 = 6x + 5(x - 10)[/tex]
Distribute 5 through the parentheses
[tex]5 = 6x + 5x - 50[/tex]
Collect like terms
[tex]5 = 11x - 50[/tex]
Swap both sides of the equation
[tex]11x - 50 = 5[/tex]
Move constant to R.H.S and change its sign
[tex]11x = 5 + 50[/tex]
Calculate the sum
[tex]11x = 55[/tex]
Divide both sides of the equation by 11
[tex] \frac{11x}{11} = \frac{55}{11} [/tex]
Calculate
[tex]x = 5[/tex]
------------------------------------------------------------------
2.
Solution,
No.of students in soccer = x
No.of students in basketball = y
Total no.of students = 20
i.e x + y = 20 → equation ( i )
Cost of soccer ball = $ 7
Cost of basketball = $ 10
Total budget = $ 164
i.e 7x + 10 y = 165 → equation ( ii )
In equation ( i ),
x + y = 20
Move 'y' to R.H.S and change its sign
x = 20 - y
Put the value of x in equation ( i )
[tex]7(20 - y) + 10y = 164[/tex]
[tex]140 - 7y + 10y = 164[/tex]
[tex]3y = 164 - 140[/tex]
[tex]3y = 24[/tex]
[tex]y = \frac{24}{3} [/tex]
[tex]y = 8[/tex]
Now, put the value of y in equation ( i ) ,
x + y = 20
[tex]x + 8 = 20[/tex]
[tex]x = 20 - 8[/tex]
[tex]x = 12[/tex]
Hence, 12 soccer balls and 8 basketballs can be purchased.
Hope this helps...
Best regards!!
Answer:
1. b = -8
2. x = 8
3. x = 11
4. x = 5
hope that helpwd
Please help find these angle for me plz!
Answer:
<DEF = 40°<EBF = <EDF = 56°<DCF = <DEF =40°<CAB = 84°Step-by-step explanation:
In triangle DEF, we have:
Given:
<EDF=56°
<EFD=84°
So, <DEF =180° - 56° - 84° =40° (sum of triangle angles is 180°)
____________
DE is a midsegment of triangle ACB
( since CD=DA(given)=>D is midpoint of [CD]
and BE = EA => E midpoint of [BA] )
According to midsegment Theorem,
. (DE) // (CB) "//"means parallel
. DE = CB/2 = FB =CF
___________
DEBF is a parm /parallelogram.
Proof: (DE) // (FB) [(DE) // (CB)]
AND DE = FB
Then, <EBF = <EDF = 56°
___________
DEFC is parm.
Proof: (DE) // (CF) [(DE) // (CB)]
And DE = CF
Therefore, <DCF = <DEF =40°
___________
In triangle ACB, we have:
<CAB =180 - <ACB - <ABC =180° - 40° - 56° =84° (sum of triangle angles is 180°)
[tex]HOPE \: THIS \: HELPS.. GOOD \: LUCK![/tex]
ANSWER ASAP #6 on WILL GIVE BRAINIEST TO ANSWER FIRSTTT
Answer:
20 m/s
Step-by-step explanation:
Assuming initial velocity is 0:
[tex]v_{f} = v_{i} + at[/tex]
[tex]v_{f} = at[/tex]
[tex]v_{f} =[/tex] 4m/s^2 * 5s = 20 m/s
Answer:
If you accelerate at 4 m/s/s for 5 seconds you accelerate by 20 m/s. Therefore, you started out at 3 m/s.
Step-by-step explanation:
The value 4 is a lower bound for the zeros of the function shown below.
f(x) = 4x^3 – 12x^2 – x + 15
A) True
B) False
Answer:
False roots are x = -1 or x = 5/2 or x = 3/2
Step-by-step explanation:
Solve for x:
4 x^3 - 12 x^2 - x + 15 = 0
The left hand side factors into a product with three terms:
(x + 1) (2 x - 5) (2 x - 3) = 0
Split into three equations:
x + 1 = 0 or 2 x - 5 = 0 or 2 x - 3 = 0
Subtract 1 from both sides:
x = -1 or 2 x - 5 = 0 or 2 x - 3 = 0
Add 5 to both sides:
x = -1 or 2 x = 5 or 2 x - 3 = 0
Divide both sides by 2:
x = -1 or x = 5/2 or 2 x - 3 = 0
Add 3 to both sides:
x = -1 or x = 5/2 or 2 x = 3
Divide both sides by 2:
Answer: x = -1 or x = 5/2 or x = 3/2
Answer:
False
Step-by-step explanation:
f(x) = 4x³ - 12x² - x + 15
Set output to 0.
Factor the function.
0 = (x + 1)(2x - 3)(2x - 5)
Set factors equal to 0.
x + 1 = 0
x = -1
2x - 3 = 0
2x = 3
x = 3/2
2x - 5 = 0
2x = 5
x = 5/2
4 is not a lower bound for the zeros of the function.
please help me with this math question
Answer:
5.50 years
Step-by-step explanation:
A = P[tex](1 + \frac{r}{n})^{nt}[/tex]
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
3178 = 2000(1+.086/2)^2t
t = 5.499904413
An object traveled for 3 hours at a rate of 30 mile/hr, and then for another 2 1/4 hours at a rate of 10 1/2 miles/hr. How many total miles did the object travel?
Answer:
113.625 miles
Step-by-step explanation:
3 hours at a rate of 30 mile/hr : 3*30=90 miles
2 1/4 hours at a rate of 10 1/2 miles/hr= 2 1/4 *10 1/2= 2.25*10.5=23.625
total miles the object traveled : 90+23.625=113.625 miles
A cone fits inside a square pyramid as shown. For every cross section, the ratio of the area of the circle to the area of the square is StartFraction pi r squared Over 4 r squared EndFraction or StartFraction pi Over 4 EndFraction. A cone is inside of a pyramid with a square base. The cone has a height of h and a radius of r. The pyramid has a base length of 2 r. Since the area of the circle is StartFraction pi Over 4 EndFraction the area of the square, the volume of the cone equals StartFraction pi Over 4 EndFraction the volume of the pyramid or StartFraction pi Over 4 EndFractionStartFraction pi Over 4 EndFraction (StartFraction (2 r) (h) Over 3 EndFraction) or One-sixthπrh. StartFraction pi Over 4 EndFraction the volume of the pyramid or StartFraction pi Over 4 EndFractionStartFraction pi Over 4 EndFraction (StartFraction (2 r) squared (h) Over 3 EndFraction) or One-thirdπr2h. StartFraction pi Over 2 EndFraction the volume of the pyramid or StartFraction pi Over 2 EndFraction or Two-thirdsπr2h. StartFraction pi Over 2 EndFraction the volume of the pyramid or StartFraction pi Over 4 EndFraction or One-thirdπr2h.
The question above is not well arranged. Please find the well arranged question below for proper understanding.
Complete Question:
A cone fits inside a square pyramid as shown. For every cross section, the ratio of the area of the circle to the area of the square is StartFraction pi r squared Over 4 r squared EndFraction or StartFraction pi Over 4 EndFraction.
A cone is inside of a pyramid with a square base. The cone has a height of h and a radius of r. The pyramid has a base length of 2 r.
Since the area of the circle is StartFraction pi Over 4 EndFraction the area of the square, the volume of the cone equals
A. StartFraction pi Over 4 EndFraction the volume of the pyramid or StartFraction pi Over 4 EndFractionStartFraction pi Over 4 EndFraction (StartFraction (2 r) (h) Over 3 EndFraction) or One-sixthπrh.
B. StartFraction pi Over 4 EndFraction the volume of the pyramid or StartFraction pi Over 4 EndFractionStartFraction pi Over 4 EndFraction (StartFraction (2 r) squared (h) Over 3 EndFraction) or One-thirdπr²h.
C. StartFraction pi Over 2 EndFraction the volume of the pyramid or StartFraction pi Over 2 EndFraction or Two-thirdsπr²h.
D. StartFraction pi Over 2 EndFraction the volume of the pyramid or StartFraction pi Over 4 EndFraction or One-thirdπr²h.
Answer:
B. StartFraction pi Over 4 EndFraction the volume of the pyramid or StartFraction pi Over 4 EndFraction (StartFraction (2 r) squared (h) Over 3 EndFraction) or One-thirdπr²h = 1/3πr²h
Step-by-step explanation:
We have two geometric shapes in the question.
a) A cone and b) a square pyramid
The cone has a height of h and a radius of r. The pyramid has a base length of 2 r.
The volume of a cone =1/3πr²h
Where πr² = Area of the circle at the base of the cone
Hence, Volume of a cone = 1/3 × Area of the circular base of a cone × Height
The volume of a square pyramid = 1/3a²h
Where a² = Area of the square base of the pyramid
Hence, Volume of a square pyramid = 1/3 × Area of the square base of a pyramid × height(h)
Base area of a cone / Base area of a square pyramid = π/4
Base area of a circle = Base area of a pyramid × π/4
Volume of a cone = 1/3πr²h
Volume of a cone = 1/3 × Base area of a square pyramid × π/4 × h
Note that:
Volume of a square pyramid = 1/3a²h
= 1/3 × Base area of a square pyramid × height
Hence,
Volume of a cone = Volume of a square pyramid × π/4
= StartFraction pi Over 4 EndFraction the volume of the pyramid
Or
Where a = base length = 2r
Volume of the square pyramid = 1/3 × 2r² × h = 1/3 × 4r²h
Volume of a cone = Volume of a square pyramid × π/4
Substituting = 1/3 × 4 × r²× h × π/4
Volume of a cone = 1/3 πr²h
Or
Volume of a cone = Volume of a square pyramid × π/4
Volume of a square pyramid when base length is 2r = 1/3 × (2r)² × h = (2r²)h/3
Substituting (2r²)h/3 for volume of a square pyramid in volume of a cone , we have:
Volume of a cone = π/4 × 2r²h/3
=
StartFraction pi Over 4 EndFractionStartFraction pi Over 4 EndFraction (StartFraction (2 r) squared
Therefore, Option B is correct
Answer:
B
Step-by-step explanation:
Three students used factoring to solve a quadratic equation? The equation was solve correctly by ______.The solutions of the equation are__________.
Answer:Keith
x=5,x=12
Step-by-step explanation:
Answer:
the answers are keith and -5,-12
Step-by-step explanation:
I just took the test and got a 5/5 the other person is incorrect.
Miriam is setting up a fishing game in a kiddie pool for her niece's birthday party. The pool has a circular base with a diameter of 4 feet and a height of 0.75 feet. She wants to fill the pool halfway so there is plenty of space left for the plastic fish. Approximately how many cubic feet of water does she need? 9.4 1.5 2.4 4.7
Answer:
4.7 feet³ of water
Step-by-step explanation:
Diameter of 4 feet
Radius = 2 feet
Height = 0.75 feet
Formula for Volume = 2·[tex]\pi[/tex]·radius·height
But she only wants to fill half, so divide by 2, cancels the 2 in the formula for volume, giving us: [tex]\pi[/tex]·radius·height
[tex]\pi[/tex]·2·0.75 = 4.71 feet³
Points A(-l, y) and B(5,7) lie on a circle with centre 0(2, -3y). Find the values of y. Hence, find the radius of the circle
Answer:
The answer is below
Step-by-step explanation:
Points A(-l, y) and B(5,7) lie on a circle with centre O(2, -3y). This means that AB is the diameter of the circle and OA = OB = radius.
For two points X([tex]x_1,y_1[/tex]) and Y([tex]x_2, y_2[/tex]), the coordinates of the midpoint (x, y) between the two points is given as:
[tex]x=\frac{x_1+x_2}{2},y=\frac{y_1+y_2}{2}[/tex].
For A(-l, y) and B(5,7) with center O(2, -3y), the value of y can be gotten by:
[tex]For\ x\ coordinate:\\2=\frac{-1+5}{2}\\ 2=2.\\For\ y\ coordinate:\\-3y=\frac{y+7}{2}\\ -6y=y+7.\\-6y-y=7\\-7y=y\\y=-1[/tex]
The value of y is -1. Therefore A is at (-1, -1) and O is at (2, -3(-1))= (2, 3)
The radius of the circle = OA. The distance between two points X([tex]x_1,y_1[/tex]) and Y([tex]x_2, y_2[/tex]) is given as:
[tex]|OX|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\Therefore\ the\ radius \ |OA|\ is :\\|OA|=\sqrt{(2-(-1))^2+(3-(-1))^2}=\sqrt{25}=5[/tex]
The radius of the circle is 5 units
There are 86{,}40086,40086, comma, 400 frames of animation in 111 hour of anime. How many frames are there per second? There are 3600 seconds in one hour
Answer
24 frames per second
Step-by-step explanation:
Total frames=86,400
Total time=1 hour
Find frame per second
1 hour= 60 minutes*60 seconds
1 hour=3600 seconds
Frame per second=Total frames/Total number of seconds
=86,400/3600
=24 frames per second
Find the equation of the line.
Answer:
y = [tex]-\frac{1}{3}x+5[/tex]
Step-by-step explanation:
Let the equation of the given line is,
y = mx + b
where 'm' = slope of the line
b = y-intercept of the line
Since slope of a line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is represented by,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
If the points are (0, 5) and (-3, 6),
Slope of the line 'm' = [tex]\frac{6-5}{-3-0}[/tex]
= [tex]-\frac{1}{3}[/tex]
y-intercept of the line 'b' = 5
Therefore, equation of the given line will be,
y = [tex]-\frac{1}{3}x+5[/tex]
Help..... please math
Answer:
Ones: 91
Hundredths: 91.20
Step-by-step explanation:
All numbers that comprises the digits, 91.20, have place value.
The 9 in the digit has a place value of tens, i.e. 9*10 = 90.
The 1 has a place value of one's, i.e. 1*1 = 1
The 2, after the decimal point to the right, has a place value of tenth, i.e. 1*10-¹ = ⅒ = 0.1
While the zero has a place value of hundredth.
Therefore, the digits, in the ones place = 91
In the hundredths place = 91.20
The table below lists some of the characteristics of the houses on Katrina’s street. Characteristics of Homes For Sale on Katrina’s Street Bedrooms Acres of land Sale price Appraised value Property tax 2 0.17 $230,000 $200,000 $1,220 2 0.20 $210,000 $220,000 $1,232 3 0.20 $275,000 $250,000 $1,400 4 0.24 $275,000 $275,000 $1,540 4 0.52 $360,000 $310,000 $1,736 4 0.75 $350,000 $320,000 $1,792 5 1.23 $375,000 $350,000 $1,960 Which relationship describes a function?
Answer:
your welcome and hope this helps
A student wants to determine if there is a difference in the pricing between two stores for health and beauty supplies. She recorded prices from both stores for each of 10 different products. Assuming that the conditions for conducting the test are satisfied, determine if there is a price difference between the two stores. Use the alphaequals0.1 level of significance. Complete parts (a) through (d) below. A B C D E F G H I J Store 1 5.94 7.47 3.79 1.74 1.73 2.88 4.75 3.15 2.92 3.77 Store 2 5.96 7.97 3.97 1.72 1.96 2.49 4.74 3.75 2.99 3.61
Answer:
There is no price difference between the two stores.
Step-by-step explanation:
The dependent t-test (also known as the paired t-test or paired samples t-test) compares the two means associated groups to conclude if there is a statistically significant difference amid these two means.
In this case a paired t-test is used to determine if there is a price difference between the two stores.
The hypothesis for the test can be defined as follows:
H₀: There is no price difference between the two stores, i.e. d = 0.
Hₐ: There is a price difference between the two stores, i.e. d ≠ 0.
From the information provided the sample mean and standard deviation are:
[tex]\bar d=-0.464\\\\S_{d}=1.019[/tex]
Compute the test statistic value as follows:
[tex]t=\frac{\bar d}{S_{d}/\sqrt{n}}=\frac{-0.464}{1.019/\sqrt{10}}=-1.4399\approx -1.44[/tex]
The test statistic value is -1.44.
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.
The degrees of freedom is:
n - 1 = 10 - 1 = 9
Compute the p-value of the test as follows:
[tex]p-value=2\cdot P(t_{\alpha/2, (n-1)}>-1.44)[/tex]
[tex]=2\cdot P(t_{0.10/2, 9}>-1.44)\\=2\times 0.092\\=0.184[/tex]
*Use a t-table.
The p-value of the test is 0.184.
p-value= 0.184 > α = 0.10
The null hypothesis was failed to be rejected.
Thus, it can be concluded that there is no price difference between the two stores.