The volume of the cylinder is 238. 7m³
How to determine the valueThe formula that is used for calculating the cross-sectional area of a cylinder is expressed with the equation;
A = πr²
Such that;
A is the area of the cylinder.r is the radius.From the information given, we have that;
17 = 3.14 × r²
Divide the values
r² = 5. 414
Find square root
r = 2.33 m
The volume of a cylinder is given as;
Volume = πr²h
Substitute the values
Volume = 3.14 × 2.33² × 14
Multiply the values
Volume = 238. 7m³
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the amount harry is paid each day, f(x), is a function of the number of hours, x, he works. the function f(x)=10x+25 models this situation. harry can work, at most, 4 hours each day. what is the best domain of the function in this context?
The total amount paid to harry in past week, is 299.28.
We know that,
Amount is the sum or the total value.
For example, if A purchase 2 kg rice at the price of 40 rs/kg, the amount will be 40×2= 80 rs.
Given that,
The amount paid to Harry for 1 hour = $8.60
Since, Harry worked for 33 hours,
So, The amount paid to Harry for 33 hours = 8.60×33=283.8
Harry gets half times more amount than hourly rate and also gets bonus for last 3 days
So for last 3 days the extra amount paid to Harry
= 3×1/2×8.60+3×1/10×8.60
= 12.9+2.58
=15.48
So the total amount paid to harry = 283.8+15.48=299.28
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complete question:
Harry is paid £8.60 per hour for the first 30 hours he works each week. After 30 hours he is paid 1 and a half times the hourly rate.
Last week Harry worked 33 hours. He was also paid a bonus of 1/10 of his earnings
Calculate how much in total Harry was paid last week
Find each angle and arc measure.
⌢
mDGF= degrees
(50 POINTs will give BRAINIEST FOR EFFORT)
Answer: 226
Step-by-step explanation:
The angle is half of the arc angle
so mDGF is 2 times as big as the angle
mDGF=113*2
mDGF=226
Applying the Right Triangle Altitude Theorem. Which similarity statement is true?
The true similarity statement are using Right Triangle Altitude Theorem :
ΔABD similar to ΔBCD
ΔABC similar to ΔADB
ΔABC similar to ΔBDC
Two triangles are said to be similar if the triangles are of the same shape but different size. The angles of the triangle will be equal and the sides are proportional.
By the Right Triangle Altitude Theorem,
If the altitude of a triangle is drawn to the hypotenuse of a right angled triangle, then the triangles formed by the division are similar to each other and both are similar to the original triangle.
Using this,
ΔABD similar to ΔBCD
ΔABC similar to ΔADB
ΔABC similar to ΔBDC
Hence the true statements are ΔABD similar to ΔBCD, ΔABC similar to ΔADB, ΔABC similar to ΔBDC.
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The complete question is given below.
In Martha's food storage, she has 13 cans of chicken noodle soup, 15 cans of tomato soup, and 17 cans of mushroom soup. If she randomly chooses a can of soup from her food storage, what is the probability it is a can of tomato soup?
Answer:
1/3
Step-by-step explanation:
p(event) = (number of desired outcomes)/(total number of outcomes)
total number of outcomes = 13 + 15 + 17 = 45
number of desired outcomes = 15
p(can of tomato soup) = 15/45 = 1/3
Help me solve and show my work please
The simplified form of trigonometric functions by trigonometric formulas are listed below:
Case 1: 0.5√(2 - √3)
Case 2: (0.5√2) / (1 + 0.5√2)
Case 3: sin 6x
Case 4: sin θ
How to simplify and evaluate trigonometric functions
In this problem we must simplify and evaluate trigonometric functions by means of trigonometric formulas. The first two expressions must be simplified and evaluated by of half angle formulas:
Case 1
sin 15° = √[(1 - cos 30°) / 2]
sin 15° = √[(1 - √3 / 2) / 2]
sin 15° = √[(2 - √3) / 4]
sin 15° = 0.5√(2 - √3)
Case 2
tan 22.5° = sin 45° / (1 + cos 45°)
tan 22.5° = (0.5√2) / (1 + 0.5√2)
The last two expressions are simplified and evaluated by double angle formulas:
Case 3
2 · sin 3x · cos 3x
sin 6x
Case 4
2 · sin 0.5θ · cos 0.5θ
sin θ
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URGENT!! ILL GIVE BRAINLIEST! ALONG WITH 100 POINTS!!!!
If you know what question this is please answer I couldn’t fit everything in the picture :(
Restaurant
No commute 3
0-1 Hr Commute 10
> 1 Hr Commute 28
Sum 41
The correct groupings for each probability are given below as follows:
The probability that you have more than a 1 hour commute: Marginal-57/134 = 42.5% chanceThe probability that you make a home-cooked meal and you have more than a 1-hour commute: Joint-7/134 = 5% chanceThe probability that you eat at a restaurant given that you have no commute: Conditional-3/37 = 8% chanceThe probability that you get takeout food: Marginal-50/134 = 37% chanceThe probability that you eat at the restaurant and have no commute: Joint probability 3/134 = 2% chanceThe probability that you commute 0-1 hour given that you get take-out food: Conditional-18/50 = 36% chanceWhat is joint probability?The possibility of two events occurring simultaneously and at the same time is known as joint probability.
Joint probability is the likelihood that event Y will take place at the same time as event X.
An example of a joint probability is the probability that you eat at the restaurant and have no commute
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maria and joan went shopping. maria bought 3 pair of jeans that each cost the same amount and 4 t-shirts that each cost the same amount. joan bought 2 pair of jeans that each cost the same amount, and 1 t-shirts that each cost the same amount. what is the cost of the jeans and shirts
Result:
The total cost of the jeans and shirts = 5(x + y)
How do we determine the cost?Let's use variables (x and y) to show the total cost of one pair of jeans and one T-shirt, respectively.
Let x = the cost of one pair of jeans.
Let y = e the cost of one T-shirt.
Given:
Maria bought 3 pairs of jeans and 4 T-shirts, all at the same price. That is:
3x = cost of Maria's jeans
4y = cost of Maria's T-shirts
Joan bought 2 pairs of jeans and 1 T-shirt, all at the same price. That is:
2x = cost of Joan's jeans
y = cost of Joan's T-shirt
To find the total cost of all they bought, add up the costs:
Total cost = Maria's cost + Joan's cost
Total cost = 3x + 4y + 2x + y
Total cost = 5x + 5y
So the total cost is 5 times the sum of the cost of one pair of jeans and one T-shirt.
Simplify the expression by factoring out a common factor of 5, and we get:
Therefore, total cost = 5(x + y)
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Write each number in scientific notation
Answer:
There is nothing to write about my brother
Step-by-step explanation:
There is a scientific notation moment when shrek had to hit the griddy and said "i said right foot creep"
Find the area of the shaded region.
80°
5 cm
A≈ [?] cm²
Enter a decimal rounded to the nearest tenth.
[tex]\textit{area of a segment of a circle}\\\\ A=\cfrac{r^2}{2}\left( ~~ \cfrac{\pi \theta }{180}-\sin(\theta ) ~~ \right) ~~ \begin{cases} r=radius\\ \theta = \stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=5\\ \theta =80 \end{cases} \\\\\\ A=\cfrac{5^2}{2}\left( ~~ \cfrac{\pi (80) }{180}-\sin(80^o ) ~~ \right)\implies A=\cfrac{25}{2}\left(\cfrac{4\pi }{9}- \sin(80^o) \right) \\\\\\ A=\cfrac{50\pi }{9}-\cfrac{25\sin(80^o)}{2}\implies A\approx 5.1~cm^2[/tex]
Which of the following ratios would form a proportion with Two-thirds?
a.
Three-fourths
c.
StartFraction 12 Over 15 EndFraction
b.
StartFraction 6 Over 9 EndFraction
d.
One-third
The proportion equivalent with Two-thirds would be 6/9.
Since we know that the proportion is a fraction of a total amount, and the measures are related using a rule of three.
The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
We are given that the proportion with Two-thirds
If you actually divide it’ll make since , so first we want to divide the 2 , then you want to multiply the third of the two
2/3 x 3/3
6/9
thus, the answer will be 6/9.
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An ordinary fair dice is a cube with the numbers 1 through 6 on the sides
The probability values are P(A) = 0.722 and P(B) = 0.50
Calculating the probability valuesFrom the question, we have the following parameters that can be used in our computation:
A fair die
The sample space of the events are
A = Sum is greater than 5
B = Sum is an even number
From the sample space of the sum of outcomes, we have
n(A) = 26
n(B) = 18
So, we have
P(A) = 26/36 = 0.722
n(B) = 18/36 = 0.50
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1-The tangent line to the curve y = x³ at point A(a, a³) intersects the curve at point B. Let
R be the area of the region bounded by the curve and the tangent line. The tangent line at B
intersects the curve at another point C. Let S be the area of the region bounded by curve and
the second tangent line. How are the areas R and S related?
Answer:
The areas R and S are equal.
Step-by-step explanation:
Since, the tangent line to the curve y = x³ at point A(a, a³) is given by y = 3a²(x - a) + a³. This line intersects the curve at point B(a, a³), and we can find the x-coordinate of point B by setting y = 3a²(x - a) + a³ equal to x³ to get the equation x³ - 3a²x + 3a³ - a³ = 0. Using the fact that x = a is a root of this equation, we can factor it as (x - a)³ = 0, which implies that the curve and the tangent line are tangent at point B.
The slope of the tangent line at point B is 3a², so the equation of the tangent line at point B is y = 3a²(x - a) + a³. This line intersects the curve at another point C, and we can find the x-coordinate of point C by setting y = 3a²(x - a) + a³ equal to x³ to get the equation x³ - 3a²x + 3a³ - a³ = 0. Using the fact that x = a is a root of this equation, we can factor it as (x - a)³ = 0, which implies that the curve and the tangent line are tangent at point C.
The region bounded by the curve and the tangent line at point A is a triangle with base a - (a - a) = 0 and height a³ - a³ = 0, so its area is 0. The region bounded by the curve and the tangent line at point B is a triangle with base a - a = 0 and height a³ - a³ = 0, so its area is also 0. Therefore, the areas R and S are both equal to 0, which means they are equal to each other.
Gwen has $50 in a savings account that earns 5% annually. The interest is not compounded. How many years will it take for her to have $57.50 in her
account?
Answer:
3 years
Step-by-step explanation:
1. Find 5 percent of 50.
5 percent of 50 is 2.5.
However, we are talking about money so we will say 2.50.
2. Add to 50 until you reach your desired number.
50 + 2.50 = 52.50
52.50 +2.50 = 55
55+2.50 = 57.50
Finally we have reached 57.50. It took us 3 equations to get there and therefore took 3 years.
The Mackinac Bridge in Michigan is 1158 meters long. The Tsing Ma Bridge in Hong Kong is 97 meters longer than the Golden Gate Bridge in California. Together, all three bridges have a length of 3815 meters. How long is the Tsing Ma Bridge?
Lenght of Tsing Ma Bridge in Hong Kong is, 1,377 meters
Given that;
The Mackinac Bridge in Michigan is 1158 meters long.
And, The Tsing Ma Bridge in Hong Kong is 97 meters longer than the Golden Gate Bridge in California.
Let the length of Golden Gate Bridge = x
Then, Lenght of Tsing Ma Bridge in Hong Kong = x + 97
Since, Together, all three bridges have a length of 3815 meters.
Hence, We get;
1158 + x + (x + 97) = 3815
1255 + 2x = 3815
2x = 2,560
x = 1,280 meters
Thus, Lenght of Tsing Ma Bridge in Hong Kong = x + 97
= 1280 + 97
= 1,377 meters
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I don’t understand this problem
The area of the composite figure is equal to 521.080 square milimeters.
How to determine the area of a composite figure
In this problem we have the representation of a composite figure, whose area should be found. This figure is the consequence of the combination of three figures: a semicircle, a rectangle and a triangle. The area formulas for each case are introduced below:
Semicircle
A = 0.5π · r²
Where r is the radius, in milimeters.
Rectangle
A = b · h
Triangles
A = 0.5 · b · h
Where:
b - Base, in milimeters.h - Height, in milimeters.A - Area, in square milimeters.Now we proceed to compute the area of the composite figure:
A = 0.5π · (10 mm)² + (20 mm) · (14 mm) + 0.5 · (12 mm) · (14 mm)
A = 50π mm² + 280 mm² + 84 mm²
A = 521.080 mm²
RemarkThe statement is absent. Complete statement is introduced below:
Find the area of the figure.
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Which of the following represents the symmetric property of equality?
A) If a = b and b = c, then a = c
B) If a = b, then ac = bc
C) If a = b, then b = a
D) a(b + c) = ab + ac
Answer:
C) a = b ⇒ b = a
Step-by-step explanation:
You want to identify the statement that represents the symmetric property of equality.
A.If a = b and b = c, then a = c. This is the transitive property of equality.
B.If a = b, then ac = bc. This is the multiplication property of equality.
C.If a = b, then b = a. This is the symmetric property of equality.
D.a(b +c) = ab +ac. This is the distributive property of multiplication over addition.
Maria is creating a new art piece on canvas. (The canvas is represented in the picture below as
rectangle ARTS). She knows the base edge of the canvas, ST, measures 4 ft. And the distance of
diagonal AT measures 8.5 ft. What is the area of Maria’s canvas? Show all work.
The Area of Maria's canvas is 30 ft.
Area of Maria's canvas, we need to know the length of the other side of the rectangle. We can use the Pythagorean theorem to find this length. Let's call it SA.
According to the problem statement, the base edge ST measures 4 ft, and the diagonal AT measures 8.5 ft. Using the Pythagorean theorem, we have:
[tex]AT^2 = ST^2 + SA^2\\8.5^2 = 4^2 + SA^2\\72.25 = 16 + SA^2\\56.25 = SA^2\\SA = \sqrt{56.25}\\SA = 7.5\ ft[/tex]
Now we know that the length of the canvas is 7.5 ft, and the width is 4 ft. Therefore, the area of Maria's canvas is:
Area = length x width
Area = 7.5 ft x 4 ft
Area = 30 square feet
Therefore, the area of Maria's canvas is 30 square feet.
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(x)<0 over and what other interval?
The other interval is (-1.1, 0.9)
In a graph of any function, values of f(x) are represented by the values on the y-axis for the different input values on x-axis.
For the given graph, values of f(x) are less than zero.
That means interval in which the values of the function are negative for the different values of x.
Negative values of the given function are in the intervals (-∞, -3), (-1.1, 9).
Therefore, from the given options, Option (4) will be the answer.
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The complete question is
F(x)<0 over (-∞, -3) and what other interval?
O (-2.4, - 1.1)
O (-3, - 1.1)
O (-1.1, 2)
O (-1.1, 0.9)
Yoshi is driving across the United States. If Yoshi's map is 20 inches across, and the United States is 3,000 miles across, what is the scale of the map?
What is the range of |x|-7?
Answer:
3 2/5 +(3/2+3/5)×6/5÷3/2-10 1/2× 2/2
Garnier's Opera House is a revival of the________style.
Romantic
Gothic
Renaissance
Baroque
Answer: Garnier's Opera House is a revival of the Baroque style.
The measure of weights of 15 students is normally distributed with a sample mean of 6 and standard deviation of 5. Find the 95% confidence interval for the mean.
The 95% confidence interval for the mean is [3.23, 8.76].
What is the confidence of interval?
The confidence of interval of the mean is calculated as follows;
Confidence interval = σ ± (t-value x μ)
where;
σ is the sample meanμ is the standard errorThe standard error is calculated as follows:
μ = std / √n
μ = 5 / √15
μ = 1.29
Based on this value we will check the distrbution table, for the t-value of 95% confidence;
= 2.145.
Confidence interval = σ ± (t-value x μ)
= 6 ± (2.145 x 1.29)
= [3.23, 8.76]
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what is the area of triangle ADC, if A is (-1, 3), D is (-1, 7), and C is (0, 4)?
Answer:
e
Step-by-step explanation:
g
(2/5)y-5=-2.5
What's y
Answer: Y = 6.5
Step-by-step explanation:
What transformations take the graph of f(x) = e^x to f(x) = -e^x -2?
The transformations of the given functions is vertical shift 2 units down.
Given that, the function is f(x)=-eˣ to f(x)=-eˣ-2.
To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.
Parent Function: f(x)= −eˣ
Horizontal Shift: None
Vertical Shift: Down 2 Units
Reflection about the x-axis: None
Vertical Compression or Stretch: None
Therefore, the transformations of the given functions is vertical shift 2 units down.
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solve for x
2x^2/3+9x^1/3= -4
The solution of the equation is x=0.08813 or 3.90664.
We have,
2x² / 3 + 9[tex]x^{1/3[/tex] = -4
Now, solving the equation for x
2x² + 27[tex]x^{1/3[/tex] = -12
Now, taking cube on both side we get
(2x² + 27[tex]x^{1/3[/tex] )³= -12³
Now, simplifying we get
19683x = -1728 -864x² -144[tex]x^4[/tex]-8[tex]x^6[/tex]
So, x=0.08813 or 3.90664
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Can someone help with this?
Answer: the real zero of this equation is 5/3.
A closet in Shivani's house is 2 yards by 1 yard. How much would it cost to put a new floor in the closet if the flooring costs $38.00 per square yard?
The amount it would cost to put a new floor in the closet is $76.00
Calculating how much it would cost to put a new floor in the closetFrom the question, we are to calculate how much it would cost to put a new floor in the closet
From the given information,
A closet in the house is 2 yards by 1 yard.
To determine how much it would cost to put a new floor in the closet,
First,
We calculate the area of the closet
Area of the closet = 2 yard × 1 yard
Area of the closet = 2 square yards
Now,
From the given information,
The flooring costs $38.00 per square yard
Thus,
The amount it would cost to put a new floor in the closet is
2 × $38.00
= $76.00
Hence,
The amount it would cost is $76.00
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Find the maximum value of C=4x+2y subject to the following restraints x>2 x<5 y>1 y<6
The required maximum value of C is 16, and it occurs when x = 3 and y = 2.
To find the maximum value of C = 4x + 2y subject to the restraints x > 2, x < 5, y > 1, and y < 6, we can use the method of Lagrange multipliers.
First, we set up the Lagrangian function L as follows:
L = 4x + 2y - λ₁(x - 2) - λ₂(x - 5) - λ₃(y - 1) - λ₄(y - 6)
where λ1, λ2, λ3, and λ4 are Lagrange multipliers.
Next, we take the partial derivatives of L with respect to x, y, λ1, λ2, λ3, and λ4, and set them equal to zero:
∂L/∂x = 4 - λ₁ - λ₂ = 0
∂L/∂y = 2 - λ₃ - λ = 0
∂L/∂λ₁ = x - 2 = 0
∂L/∂λ₁ = 5 - x = 0
∂L/∂λ₃ = y - 1 = 0
∂L/∂λ₄ = 6 - y = 0
Solving these equations simultaneously, we get:
λ₁ = 1, λ₂ = 3, λ₃ = 1, λ₄ = 1, x = 3, y = 2
Therefore, the maximum value of C is:
C = 4x + 2y = 4(3) + 2(2) = 16
So, the maximum value of C is 16, and it occurs when x = 3 and y = 2.
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Please help me out! :D
Answer:
A
Step-by-step explanation: