Answer:
Volume = 264 cm³Step-by-step explanation:
Formula:
Let b be the base (circle) of the cone
and h be the height of the cone
[tex]\text{volume of the cone} =\frac{1}{3} \times b\times h[/tex]
……………………………………………
→ b = π × r²
= π × 6²
= (22÷7) × 36
= 113.142857142857 cm²
→ h = 7
[tex]\text{volume of the cone} =\frac{1}{3} \times b\times h[/tex]
The volume = (1÷3)×(113,142857142857)×(7)
= 264 cm³
===================
METHOD 2 :
Volume = (1÷3)×(22÷7)×36×7
= (1÷3)×22×36
= 22×12
= 264
Simplify the following: 9 – 2(x - 5) = x + 10
Answer:
x = 3
Step-by-step explanation:
Hello!
We can distribute the parenthesis and solve for x.
Solve9 - 2(x - 5) = x + 109 - 2x + 10 = x + 1019 - 10 = 3x9 = 3xx = 3The value of x is 3.
We can plug it back in to check if it works.
Check9 - 2(x - 5) = x + 109 - 2(3 - 5) = 3 + 109 - 2(-2) = 3 + 109 + 4 = 3 + 1013 = 13Correct!
Answer:
[tex]\huge\boxed{\sf x = 3}[/tex]
Step-by-step explanation:
Given equation:9 - 2(x - 5) = x + 10
Distribute
9 - 2x + 10 = x + 10
Subtract 10 to both sides
9 - 2x = x
Add 2x to both sides
9 = x + 2x
9 = 3x
Divide 3 to both sides
9/3 = 3x/3
3 = x
OR
x = 3[tex]\rule[225]{225}{2}[/tex]
multiply: (a+b),(a+b) and (a+b)
Answer:
Here,
[tex](a + b) [(a + b)(a + b)][/tex]
[tex](a + b)( {a}^{2} + 2ab + {b}^{2} )[/tex]
[tex]a( {a}^{2} + 2ab + {b}^{2} ) + b( {a}^{2} + 2ab + {b}^{2} )[/tex]
[tex] {a}^{3} + {2a}^{2} b + {ab}^{2} + {a}^{2} b + {2ab}^{2} + {b}^{3} [/tex]
[tex] {a}^{3} + 3 {a}^{2} b + {3ab}^{2} + {b}^{3} [/tex]
Thus,[tex](a+b)^3=a^3+3a^2b+3ab^2+b^3[/tex]
Thus, in case of multiplication of a binomial or a trinomial by a binomial or a trinomial each term of the binomial or the trinomial should multiply each term of the given binomial or the trinomial and if needed, simplification should be performed.
Which of the following functions best fits the data shown in the scatterplot below? y=100x+2y is equal to 100 x plus 2 y=20x2+10y is equal to 20 x squared plus 10 y=4x+8y is equal to 4 to the x th power plus 8 y=2x+5y is equal to 2 to the x th power plus 5
The equation of the scatter plot is (a) y = 100x + 2
How to determine the equation of the scatterplot?The line of best fit of the scatter plot passes through the points
(x,y) = (0,2) and (1,102)
Start by calculating the slope using:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{102 - 2}{1 - 0}[/tex]
m = 100
The equation is then calculated as:
y = m(x - x1) + y1
This gives
y = 100(x -0) + 2
Evaluate
y = 100x + 2
Hence, the equation of the scatter plot is (a) y = 100x + 2
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6. Dana measured the height of her
bedroom wall to be 3 yards tall. Which of
these is closest to the equivalent
measurement?
Answer:
9 feet, 108 inches, 274.32 cm, 2.7432 meters
Step-by-step explanation:
Not enough information is given to answer.
You didn't provide the list of "these" to choose from, but I can just list some potential answers I could see being an option.
3 yards = 9 feet [1 yard = 3 feet. 3 yards = 9 feet]
9 feet is also 108 inches [1 foot = 12 inches. 9 feet = 108 inches]
3 yards = 108 inches
{There are 91.44 cm in a yard} (1 yard = 91.44 cm. 3 yards = 274.32 cm),
3 yards = 274.32 cm
3 yards = 2.7432 meters (1 yard = 0.9144 meters; 3 yards = 2.7432 meters)
SO CONFUSED PLEASE SOMEONE EXPLAIN! DUE SOON AND NEED HELP!!!!!!!! QUESTION IN PICTURE BELOW
Answer:
=> Apply law of cosine
[tex]c^2=a^2+b^2-2abcos\left(C\right)[/tex]
=> input value
[tex]z^2=6.5^2 + 9.4^2-\left(6.5\right)\left(9.4\right)\left(cos\left(131\right)\right)[/tex]
=> simplify
[tex]z=\sqrt{\left(6.5^2+\:9.4^2\right)-\left(6.5\right)\left(9.4\right)\left(-0.65605902899\right)}[/tex]
=> calulcation
[tex]z=\sqrt{-61.1\cos \left(131^{\circ \:}\right)+130.61},\:z=-\sqrt{-61.1\cos \left(131^{\circ \:}\right)+130.61}[/tex]
=> apply rule: Distance must be greater than 0
which is about 14.51828
PLEASE ILL GIVE 25 POINTS ANS MARK BRAINIEST IF SOMEONE GIVES ME THE RIGHT ANSWER PLEASE PLEASE PLWASE
Answer:
Circumference: 25.12m
Area: 50.24 [tex]m^{2}[/tex]
Step-by-step explanation:
Formula for circumference of a circle: C=[tex]\pi d[/tex] or C=[tex]2\pi r[/tex] since the diameter is double the radius
C=3.14*2*4=3.14*8=25.12
Formula for area of a circle: A=[tex]\pi r^{2}[/tex]
A=3.14*[tex]4^{2}[/tex]=3.14*4*4=3.14*16=50.24
find the radius of a circle whose arc length is 55 m and its central angle measure if 5 radians
Answer:
Step-by-step explanation:
To solve this question, we can use the formula [tex]S=\theta r[/tex], where [tex]S[/tex] is the arc length, [tex]\theta[/tex] is the central angle of the sector in radians, and [tex]r[/tex] is the radius.
In this situation, we know that [tex]S=55[/tex] and [tex]\theta=5[/tex]
This means that [tex]55=5r \longrightarrow \boxed{r=11}[/tex]
Solve f(-4) for f(x) = 7x - 4x
f(-4)= [?]
Enter
ternational Academy of Science. All Rights Reserved.
Answer:
-12
Step-by-step explanation:
What you have to do is plug -4 into the function as a puzzle. So, replace all x with -4.
f(-4) = 7(-4) - 4(-4) = -28 + 16 = -12
f (-4) = 7x ( 1-4 ) - 4 (-4)
= -28 + 16
= -12
What is a equation example?
An equation is a mathematical statement this is made from two expressions related by an equal sign. for instance, 3x – 5 = 16 is an equation. solving this equation, we get the fee of the variable x as x = 7.
A declaration of the equality of mathematical expressions. An expression representing a chemical reaction by using chemical symbols. equation.
Conclusion: There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form. We review all three in this article.
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What is the median of 3,4,5,5,7,8
The regular hexagon has a radius of 4 in.
A regular hexagon has a radius of 4 inches.
What is the approximate area of the hexagon?
24 in.2
42 in.2
48 in.2
84 in.2
Given the radius of the regular hexagon, its area is approximately 42in².
Hence, option B) is the correct answer.
What is the approximate area of the hexagon?Given that;
Radius of the regular hexagon = 4inArea A = ?Since a regular hexagon can be divided into six equal triangle, we will determine the area of a single triangle and then multiply the area by 6 to get the area of the regular hexagon.
Angle of one triangle in the regular hexagon = 360°/6 = 60°.
To determine the height, we divide the triangle into two equal half, making a right angled triangle with hypotenuse 4in, Base 4in/2 = 2in.
We find the perpendicular height using Pythagoras theorem
h = √( (4)² - (2)² )
h = √( 16 - 4 )
h = √( 12 )
h = √( 2² × 3 )
h = 2√3
Now, we determine the area of a single triangle.
Area = (1/2) × base × height
Area = 0.5 × 4 × 2√3
Area = (4√3)in²
Now, to get the area of the regular hexagon, we multiply the area of the triangle by 6
Area of regular hexagon = 6 × (4√3)in²
Area of regular hexagon = 24(√3)in²
Area of regular hexagon = 41.57in² ≈ 42in²
Given the radius of the regular hexagon, its area is approximately 42in².
Hence, option B) is the correct answer.
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Answer: b
Step-by-step explanation:
The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample of 50 business travelers is selected and each traveler is asked to provide a rating for the Miami International Airport. The ratings obtained from the sample of 50 business travelers follow. 6, 4, 6, 8, 7, 7, 6, 3, 3, 8, 10, 4, 8 7, 8, 7, 5, 9, 5, 8, 4, 3, 8, 5, 5, 4 4, 4, 8, 4, 5, 6, 2, 5, 9, 9, 8, 4, 8 9, 9, 5, 9, 7, 8, 3, 10, 8, 9, 6 Develop, a, 95%, confidence, interval, estimate, of, the, population, mean, rating, for, Miami.
Using the t-distribution, it is found that the 95% confidence interval for the population mean rating for Miami is (5.73, 6.95).
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 50 - 1 = 49 df, is t = 2.0096.
Considering the given sample, the other parameters are given as follows:
[tex]\overline{x} = 6.34, s = 2.16, n = 50[/tex]
Hence, the bounds of the interval are:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 6.34 - 2.0096\frac{2.16}{\sqrt{50}} = 5.73[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 6.34 + 2.0096\frac{2.16}{\sqrt{50}} = 6.95[/tex]
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Which of the following statements must be true about parallelogram ABCD?
Options are below
Answer: [tex]\angle A+\angle D=180^{\circ}[/tex]
Step-by-step explanation:
Adjacent angles of a parallelogram are always supplementary.
Work out (5*10^3)*(9*10^7).
Give your answer in standard form.
Work out (7*10^5) / (2*10^2).
Give your answer in standard form.
Answer:
(5*10^3)*(9*10^7) = 4.5*10^11
(7*10^5) / (2*10^2) = 3.5*10^3
Step-by-step explanation:
calculate 5 multiply by 9
5*9=45
the multiple of the power in the same base of number is calculated by using addition(+)
(10^3)*(10^7) = 10^(3+7)
= 10^10
in standard form, it should be written as x*10^n, and x is only allowed from 1-9, so
45*(10^10)
= (4.5*10^1) * (10^10)
= 4.5*10^(1+10)
= 4.5*10^11
calculate 7 divide by 2
7/2=3.5
the dividing of the power in the same base of number is calculated by using subtraction(-)
(10^5)/(10^2)
= 10^(5-2)
= 10^3
in standard form, it should be written as x*10^n, and x is only allowed from 1-9, so
3.5*10^3
Answer:
→ (5×10³)×(9×10⁷) = 4.5 × 10¹¹→ (7×10⁵) / (2×10²) = 3.5 × 10³Step-by-step explanation:
(5×10³)×(9×10⁷)
= 5×10³×9×10⁷
= 5×9×10³×10⁷ (commutative property)
= (5×9)×(10³×10⁷) (associative property)
= 45 × 10³⁺⁷
= 45 × 10¹⁰. (Exponent property)
= 4.5 × 10¹¹
…………………………………………
(7×10⁵) / (2×10²)
= (7/2) × (10⁵/10²)
= 3.5 × 10⁵⁻²
= 3.5 × 10³
A class sold tickets to their school play. Each of the 232323 students in the class sold 444 tickets. The cost of each ticket was \$7$7dollar sign, 7.
How much money did the class earn by selling tickets to the play?
\$
Answer:
the class earned $722059884
Step-by-step explanation:
because each person sold 444 tickets and there was 232323 students
=232323×444
=103151412
because 103151412 tickets were sold and a ticket cost $7
=103151412×7
=722059884
John Pelson's weekly net pay is $972.11. His weekly deductions are $185.00 for FIT; 5% of gross for SIT; 2% of gross for CIT; Social Security and Medicare; $64.00 for health insurance; and $25.00 for charity? Find the weekly gross pay
Based on the calculations below, the weekly gross pay of John Pelson is $1,339.90.
How to calculate gross pay?Let G represents weekly gross pay. The gross pay can now be calculated as follows:
Net pay = G – FIT – SIT – CIT - Health insurance – Charity ……………….. (1)
Substitute all the relevant values into the equation (1) and solve as follows:
$972.11 = G – $185.00 – 0.05G – 0.02G – $64.00 – $25.00
$972.11 + $185.00 + $64.00 + $25.00 = G – 0.05G – 0.02G
$1,246.11 = (1 – 0.05 – 0.02)G
$1,246.11 = 0.93G
G = $1,246.11 / 0.93
G = $1,339.90
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I don’t quite understand this problem could someone help me please
Answer:
[tex]\frac{7\sqrt{65}}{65}[/tex]
Step-by-step explanation:
Cosine is the ratio of the side adjacent to the angle and the right triangle hypotenuse.
[tex]cos[/tex] B = [tex]\frac{7}{\sqrt{65}}[/tex] = [tex]\frac{7\sqrt{65}}{65}[/tex]
what is the mean of 12342634
Answer:
Mean = 3.125 ≈ 3.13
Step-by-step explanation:
Mean = Sum of numbers = 1 + 2 + 3 + 4 + 2 + 6 + 3 + 4 = 25 = 3.125≈3.13
Amount of number 8 8
If-5x + 4y = -3 is a true equation, what would be the value of
-6(-5x+4y)?
Answer:
Step-by-step explanation:
-5x+4y=-3
-6(-5x+4y)=-6×(-3)=18
The ratio of the one leg of
the right triangle to the other
leg of the right triangle must
be 8:7. Determine the
greatest length of one leg of
the right triangle given the
other leg of the right triangle
is 10.5 feet.
Answer:
12 ft
Step-by-step explanation:
We assume right triangle ABC with the right angle being at B. We are given that the ratio of AB/CB = 8/7, and one leg is 10.5. Let's call the other leg is X. We don't know which leg is which so assume both. Then
(a) assume the X leg is the longer
8 / 7 = X / 10.5
(8 * 10.5) / 7= X
X = 12
OR (b) assume the X leg is the shorter
8/7 = 10.5 / X
(8X / 7) = 10.5
8X = 10.5 * 7
8X = 73.5
X = 9.1875
(a) is the greater so (a) wins
Question 2 On the line that passes through point C, mark a point D that is distinct from point C. Use the slope formula along with coordinates of points to find the slopes of and . Show your work.
The slope formula along with coordinates of points ( p,q) and (x,y) [tex]m = \dfrac{y-q}{x-p}[/tex].
What is the slope of a straight line?A slope tells how vertical a line is.
The more the slope is, the more the line is vertical. When the slope is zero, the line is horizontal.
To find the slope, we take the ratio of how much the line's height increases as we go forward or backward on the horizontal axis.
This is because the more the height of the line to the amount we walk or run on the horizontal axis, the more the slope is.
The slope of a line that passes through points ( p,q) and (x,y)
Its slope would be:
[tex]m = \dfrac{y-q}{x-p}[/tex]
Slope of parallel lines are same. Slopes of perpendicular lines are negative reciprocal of each other.
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Given that ƒ(x) = 3x, identify the function g(x) shown in the figure.
A)
g(x) = −(1∕3)x
B)
g(x) = 3−x
C)
g(x) = −3−x
D)
g(x) = −3x
Answer: D
Answer:
the answer is D
hope it will help
I need help. This is an ixl
Answer: 2
Step-by-step explanation:
We will first pull the data values.
0, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3
Now, we will find the middle data value. This is the median.
0, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3
/, /, /, /, /, 2, /, /, /, /, /
Our median is 2.
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HELP PLEASE! THIS IS DUE SOON! HELP ME! QUESTION BELOW!
Answer:
A) x = 113°
Explanation:
Given three sides: 6.4 cm, 5.8 cm, 10.2 cm
Use the cosine rule:
c² = a² + b² - 2ab cos(C)
Insert/put variables:
[tex]\rightarrow \sf 10.2^2 = 5.8^2 + 6.4^2 - 2(5.8)(6.4) cos(x)[/tex]
[tex]\rightarrow \sf -74.24 cos(x) = 10.2^2 - 5.8^2 - 6.4^2[/tex]
[tex]\sf \rightarrow -74.24 cos(x) = 29.44[/tex]
[tex]\rightarrow \sf cos(x) = \dfrac{29.44}{-74.24}[/tex]
[tex]\rightarrow \sf x = cos^{-1}(-\dfrac{23}{58})[/tex] = 113.36° ≈ 113° (rounded to nearest degree)
E
6m
10m
8m
F
1.1
Calculate the length of the following
a)
DG
b)
EF
1.2 Determine the value of x
1.3
Given 17sinA-15-0 and 0° SA≤90°
Determine the values of the following with the aid of a diagram
a)
tan A
b)
1-cosA
c)
cos¹ A-cosecA
1.4 Simplify the following fraction WITHOUT USING A CALCULATOR
tan 45°.sin 30°-cot45°
sec 60⁰
මමමමම
(1)
(4)
(2)
(5)
(23)
The value of the tanA is 15/8, and the value of the 1 - cosA is 9/17 after calculating the base length which is 8 units.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
Here the diagram and some data are missing.
But using Pythagoras or trigonometric ratio we can find the length.
We have:
17sinA-15-0
sinA = 15/17
Using Pythagoras theorem:
Base length = √(17² - 15²) = 8 units
= tanA = 15/8
= 1 - cosA = 1 - 8/17 = 9/17
We can find the rest of the trigonometric ratio.
Thus, the value of the tanA is 15/8, and the value of the 1 - cosA is 9/17 after calculating the base length, which is 8 units.
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If the probability that a person over 40-year-old is diabetic, is 0.55
and the probability that a person has hypertension is 0.62. If a person
is selected randomly, find the probability that he is diabetic and and has hypertension
Answer:
0.341
Step-by-step explanation:
Multiply the probabilities: 0.55 * 0.62 = 0.341
Zoe thinks of a number. She multiplies it by 3 and adds 4. She gets the same answer when she adds 5 to the number and then multiplies the result by 2.
a. Write an equation, using n for Zoe's number.
b. Solve your equation to find Zoe's number.
Answer:
Zoe's number is 6
Step-by-step explanation:
Let the number be 'n'
a) Multiply 'n' by 3 ⇒ n*3 = 3n
Add 4 to '3n' ⇒ 3n + 4
Add 5 to 'n' ⇒ n +5
Multiply (n+ 5) by 2 ⇒ (n +5)*2 = 2n + 5*2 = 2n + 10
3n + 4 = 2n + 10
b) 3n + 4 = 2n + 10
Subtract 4 form both sides
3n = 2n + 10 - 4
3n = 2n + 6
Subtract 2n from both sides
3n - 2n = 6
[tex]\sf \boxed{\bf n = 6}[/tex]
Answer:
21 is probably the best answer
Select the correct answer.
Over which interval of the domain is function h decreasing?
25?
Answer:
the function is only increasing.
Step-by-step explanation:
20. THOUGHT PROVOKING There are 100 coins in a bag.
Only one of them has a date of 2010. You choose
a coin at random, check the date, and then put the
coin back in the bag. You repeat this 100 times. Are
you certain of choosing the 2010 coin at least once?
Explain your reasoning.
Answer:
yes
Step-by-step explanation:
yes, because there is a 99/1 chance. also, you can put 50 2010 coins in.
The table contains data for six students in a running club: time run in minutes, x, and the corresponding average speed in mph, y.
A 2-column table with 6 rows. Column 1 is labeled x with entries 25, 28, 30, 31, 33, 40. Column 2 is labeled y with entries 7.5, 6, 5.5, 5, 4.5, 4.5.
The regression line shows a:
negative trend line with a strong relationship.
negative trend line with a weak relationship.
positive trend line with a strong relationship.
positive trend line with a weak relationship.
Finding the correlation coefficient, it is found that the regression line shows a:
negative trend line with a strong relationship.
What is a correlation coefficient?It is an index that measures correlation between two variables, assuming values between -1 and 1.If it is positive, the relation is positive, that is, they are direct proportional. If it is negative, they are inverse proportional.If the absolute value of the correlation coefficient is greater than 0.6, the relationship is strong.Inserting the values of a table, the x-values as 25, 28, 30, 31, 33, 40, and the y-values as 7.5, 6, 5.5, 5, 4.5, 4.5, the coefficient is of -0.85, which is negative and strong.
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Inserting the values of a table, the x-values as 25, 28, 30, 31, 33, 40, and the y-values as 7.5, 6, 5.5, 5, 4.5, 4.5, the coefficient is -0.85,
The table contains data for six students in a running club: time run in minutes, x, and the corresponding average speed in mph, y.
Finding the correlation coefficient, it is found that the regression line shows a: negative trend line with a strong relationship.
What is a correlation coefficient?It is an index that measures the correlation between two variables, assuming values between -1 and 1.
If it is positive, the relationship is positive, that is, they are directly proportional. If it is negative, they are inversely proportional.
If the absolute value of the correlation coefficient is greater than 0.6, the relationship is strong.
Inserting the values of a table, the x-values as 25, 28, 30, 31, 33, 40, and the y-values as 7.5, 6, 5.5, 5, 4.5, 4.5, the coefficient is -0.85, which is negative and strong.
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Select the correct answer.
This system of equations relates the ticket price, in dollars, for seats in the silver (x) and gold (y) sections at a rock concert.
x + 2y = 82
3x + y = 96
By how much does the price of a ticket for the gold section exceed the price for a ticket for the silver section?
A.
$6
B.
$8
C.
$10
D.
$12
E.
$14
Answer:
$12
Step-by-step explanation:
x+2y=82........(1)
3x+y=96.........(2)
y=96-3x...........(3)
x+2y=82
x+2(96-3x)=82
x+192-6x=82
-5x=82-192
-5x=-110
x=-110÷-5
x=22
y=96-3x
y=96-3(22)
y=96-66
y=30
Therefore,x=22 and Y=30
so silver= x =22
gold= y = 30
y=30;x=22
=30-22
-12
Therefore $12