Find the area of this figure.
Use 3.14 for pi.
Round answer to the nearest hundredth.
Area = ____ ft2
The total area of the figure, which includes a rectangle and a semicircle, is 29.00ft². This is achieved by calculating the individual areas of the rectangle and semicircle, and then adding them together.
Explanation:The figure in question is composed of a rectangle and a semicircle. The area of a rectangle is found by multiplying its length by its width, so the area of the rectangle part is 7.2ft * 3.4ft = 24.48ft². The area of a semicircle is found using the formula ½πr², where r is the radius of the circle. In this case, the diameter of the semicircle is the same as the width of the rectangle (3.4ft), so the radius will be half of that (1.7ft). Therefore, the area of the semicircle is ½π(1.7ft)² = 4.52ft² (rounded to the nearest hundredth). So, the total area of the figure is the sum of the rectangle and the semicircle area, which equals to 24.48ft² + 4.52ft² = 29.00ft².
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The area of the figure which is composed of a semi-circle and a rectangle is approximately 23.24 ft².
What is the area of the composite figure?The figure in the image is composed of a semi-circle and a rectangle.
The area of a semicircle is expressed as;
A = 1/2 × πr²
The area of a rectangle is expressed as;
Area = length × width
From the diagram;
Diameter = 3.4 ft
Radius r = 1.7 ft
Width of the rectangle = 3.4ft
Length = 7.2ft - 1.7ft = 5.5ft
Now, to determine the area of the figure, we sum the area of the semi-circle and the area of the rectangle.
Area = ( 1/2 × πr² ) + ( length × width )
Plug in the values:
Area = ( 1/2 × 3.14 × 1.7² ) + ( 5.5 × 3.4 )
Area = ( 1/2 × 3.14 × 2.89 ) + ( 5.5 × 3.4 )
Area = 4.5373 + 18.7
Area = 23.24 ft²
Therefore, the total area has a measure of 23.24 ft².
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A telemarketer will make 25 calls in one hour. the probability of making a sale on any given call is .09. what is the probability that he will make at least one sale during the hour? (answer to the third decimal place.)
What is the value of 60 tens?
You would multiply 60 times 10.
Hope it helped!:)
Suppose a and b are independent events if P(A) =0.4 and P(B) =0.45 what is P(A*B)?
Answer:
P(A*B) = 0.18
Step-by-step explanation:
Given : We are given that a and b are independent events .
P(A) = 0.4
P(B) = 0.45
Solution :
Since , A and B are independent events so by
[tex]P(A*B) = P(A\cap B)=P(A)\ast P(B)[/tex]
⇒[tex]P(A*B) = 0.4\times 0.45[/tex]
[tex]P(A*B) = 0.18[/tex]
Thus, [tex]P(A*B) = 0.18[/tex]
classify the quadrilateral using the name that best describes it.
An exponential function is graphed for all real numbers. This includes which of the following sets of numbers?
In addition to linear, quadratic, rational, and radical functions, there are exponential functions. Exponential functions have the form f(x) = bx, where b > 0 and b ≠ 1. Just as in any exponential expression, b is called the base and x is called the exponent.
An example of an exponential function is the growth of bacteria. Some bacteria double every hour. If you start with 1 bacterium and it doubles every hour, you will have 2x bacteria after x hours. This can be written as f(x) = 2x.
Before you start, f(0) = 20 = 1
After 1 hour f(1) = 21 = 2
In 2 hours f(2) = 22 = 4
In 3 hours f(3) = 23 = 8
and so on.
With the definition f(x) = bx and the restrictions that b > 0 and that b ≠ 1, the domain of an exponential function is the set of all real numbers. The range is the set of all positive real numbers. The following graph shows f(x) = 2x.
Jennifer has carpet in her square bedroom. She decides to also purchase carpet for her living room which is rectangular in shape and 9 feet longer than her bedroom. The area of the carpet required in the living room is given by the quadratic expression below, where x represents the side length, in feet, of the carpet in the bedroom. Match each part of the expression with what it represents. Tiles :
1 the width of the carpet in the living room
2 the length of the carpet in the living room
3 the area of the carpet in the bedroom
4 the increase in the area of carpet needed for the living room
Pairs :
1 the second-degree term of the expression x2 + 9x
2 the monomial, x, a factor of the expression x2 + 9x
3 the first-degree term of the expression x2 + 9x
4 the binomial, (x + 9), a factor of the expression x2 + 9x
Answer:
1. the width of the carpet in the living room
Ans. The monomial, x, a factor of the expression x2 + 9x
2 the length of the carpet in the living room
Ans . the binomial, (x + 9), a factor of the expression x2 + 9x
3 the area of the carpet in the bedroom
Ans. the second-degree term of the expression x2 + 9x
4. the increase in the area of carpet needed for the living room
Ans. the first-degree term of the expression x2 + 9x
Step-by-step explanation:
Jennifer has carpet in her square bedroom.
Formula of area of square = [tex]a^2[/tex]
Where a is the side length
Side length of her bedroom is x
Area of the bedroom is [tex]x^2[/tex]
So, area of carpet for bedroom is [tex]x^2[/tex]
She decides to also purchase carpet for her living room which is rectangular in shape and 9 feet longer than her bedroom. (no change in width)
So, length of living room = 9+x
Width = x
Area of living room = [tex]x*(9+x)[/tex]
[tex]=x^{2} +9x[/tex]
So, increase in area of carpet for living room in comparison to the area of carpet for bedroom is 9x
1. the width of the carpet in the living room
Ans. The monomial, x, a factor of the expression x2 + 9x
2 the length of the carpet in the living room
Ans . the binomial, (x + 9), a factor of the expression x2 + 9x
3 the area of the carpet in the bedroom
Ans. the second-degree term of the expression x2 + 9x
4. the increase in the area of carpet needed for the living room
Ans. the first-degree term of the expression x2 + 9x
Erika has three pieces of ribbon. Each peice is 25 yards long.she needs to cut pieces that are 22inches long. What is the greatest number of 22-inch pieces that she can cut from the three pieces of ribbon?
Erika has three pieces of ribbon, each of 25 yards' length.
Then in total she has 3·25=75 yards of ribbon.
Since 1 yd = 36 in, then 75 yd = 75·36=2700 in.
Now she needs to cut pieces that are 22 inches long, thus
[tex]2700:22=122\dfrac{16}{22}[/tex] pieces.
Answer: she can cut from the three pieces of ribbon 122 pieces that are 22 inches long.
Graph y=(x+2)^2-3
Show Vertex
Answer:
-3,2
Step-by-step explanation:
just took the test edge 2020
Simplify this algebraic expression
Z-4/4+8
A. Z-7
B.z+7
C.z+9
D.z-3
A ski resort can manufacture enough machine-made snow in 12 h to open its steepest run, whereas it would take 36 h of naturally falling snow to provide enough snow. if the resort makes snow while it is snowing naturally, how long will it take until the run can open?
If the resort makes snow while it is snowing naturally then for 9 hours it will take until the run can open.
What is an arithmetic operation?The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the given information in the question,
The pace at which a resort creates snow is t/12,
the rate at which snow falls naturally is t/36.
(1/12) + (1/36) = (1/t)
Take LCM,
(3/36) + (1/36) = (1/t)
1/t = 4/36
4t = 36
t = 9 hours.
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Solve the exponential equation algebraically and use a graphing utility
400/1+e^-x= 350
Use the compound interest formula to find the future value A for the following values.
P= $ 1,500
i = 0.075
n= 26
In a rhombus, an altitude from the vertex of an obtuse angle bisects the opposite side. Find the measures of the angles of the rhombus.
The angles of the rhombus determines the inclination of the sides of the
rhombus.
The correct response;The measures of the four angles of the rhombus are 60°, 60°, 120°, and 120°.Method used to arrive at the above response;Given;The altitude of the rhombus bisects the opposite side.
The angle of the rhombus at the vertex point of the altitude = An obtuse angle
Required:The measure of the angles of the rhombus
Solution:The length of the sides of a rhombus are equal.
The opposite angles of a rhombus are equal.
Let x represent the length of a side of the rhombus, we have;
The bisector from the vertex of the obtuse angle = An altitude
The angle the altitude forms with the side it bisects = 90°
Therefore;
The triangle formed by the altitude, half the bisected side and the side of the rhombus adjacent to the bisected side = A right triangle
The hypotenuse side to the right triangle = The side of the rhombus
Let θ represent the angle opposite the altitude, and between the sides of
the rhombus, in the right triangle by trigonometric ratios, we have;
[tex]\displaystyle cos(\theta) = \mathbf{\frac{Adjacent}{Hypotenuse}}[/tex][tex]\displaystyle cos(\theta) = \frac{0.5 \cdot x}{x} = 0.5[/tex]
θ = arccos(0.5) = 60°
Therefore, two acute (opposite) angles of the rhombus are 60°
The two obtuse angles of the rhombus are each = (360° - 2×60°) ÷ 2 = 120°
The angles of the rhombus are 60°, 60°, 120°, 120°.Learn more about trigonometric ratios here:
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Zane bought two shirts for$26 each.Three shirts for $19.25 each.And one pair of jeans for$68.50.
How much did he spend?
Write an expressions?
Solve the system of equations using the linear combination method.
{4x−3y=12
7x−3y=3
Enter your answers in the boxes.
x =
y =
Answer:
x = -3
y = -8
Step-by-step explanation:
I took the test
The length of a rectangle is 8 cm more than 3 times its width. The perimeter of the rectangle is 64 cm. Show the equation that would be used to find the dimensions of the rectangle.
To find the dimensions of a rectangle with length '8 cm more than 3 times the width' and a perimeter of 64 cm, form the equation 2(3W+8) + 2W = 64. Solving for W gives the width, which can be substituted into the equation 3W+8 to give the length.
Explanation:The subject of the question is algebra, specifically how to form equations based on word problems involving geometric shapes. The rectangle problem you've given can be solved using the formulas for the perimeter of a rectangle.
The perimeter 'P' of a rectangle is given by P=2(length) + 2(width). In the problem, the length 'L' is given as 8 cm more than 3 times the width 'W', or L=3W+8. The perimeter 'P' is stated as 64 cm, so substituting our equation for length into the perimeter equation, we get 2(3W+8) + 2W = 64. This equation will yield the width of the rectangle. To get the length, you simply substitute the width into the length equation.
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Natalia paid $38.95 for three medium sized pizzas and a salad. Solve an equation to find the cost of one pizza,p, if Natalia paid $11.98 for the salad
The linear equation is defined as the equation, which can be represented in the form of y=mx+b.
The cost of one pizza is $ 8.99.
Given that,
Cost of salad = $ 11.98Let the cost of pizza be x.The three pizzas cost will be 3x. The total cost of the food items = $ 38.95Now, using the linear equation formula:
Total cost = Cost of three pizzas + Cost of Salad
Substituting the values, the equation becomes:
$ 38.95 = 3x + $ 11.98
$ 38.95 - $ 11.98 = 3x
$ 26.97 = 3x
x = [tex]\dfrac{26.97}{3}[/tex]
x = $8.99
Therefore, the value of each pizza is $8.99.
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Harrison High School has 768 students. In 6 years, it is projected to have 1,157 students. What is the projected average rate of change per year in students over this time period?
What is the constant of variation for the quadratic variation? 0.1y = 3x2
Answer:
The constant of variation for the given quadratic equation is, 30
Step-by-step explanation:
One of the form of a quadratic equation is written as:
[tex]y = kx^2[/tex] ....[1]
where k is the coefficient and for this case the constant of variation.
In order to obtain the answer for the given equation, we write the given equation to the form above.
[tex]0.1y=3x^2[/tex] or
[tex]y=(\frac{3}{0.1})x^2[/tex] or
[tex]y=30x^2[/tex]
Comparing this equation with equation [1], to get the value of k;
k=30.
therefore, the constant of variation is, 30.
Devin borrowed $1,058 at 13 percent for nine months.
What will he pay in interest?
How much is his total payment?
What will be his monthly payment?
Solve –19 = x – 4. A. x = –76 B. x = 25 C. x = –15 D. x = –23
Answer:
The answer is : -15 (C)
Step-by-step explanation:
–19 = x – 4
x - 4 = -19
x = -19 + 4
x = -15
1. A/an _______ triangle has all three angles measuring less than 90°. A. right B. obtuse C. scalene D. acute
Find the shortest distance, d, from the point (8, 0, −6) to the plane x + y + z = 6. d =
The distance between the point P( 8 , 0 , -6 ) to the plane x + y + z = 6 is
d = ( 4 / √3 )
What is the distance between a point and a plane?
The distance between a point and a plane is the smallest perpendicular distance between the point and the plane in question. In other words, the length of the perpendicular parallel to the normal vector dropped from the given location to the provided plane is the shortest distance between two points.
Let the point be P( x₀ , y₀ , z₀ )
Let the plane be Ax + By + Cz + D = 0
The distance between point P and plane is
d = | Ax₀ + By₀ + Cz₀ + D | / √ ( A² + B² + C² )
Given data ,
Let the point be P( x₀ , y₀ , z₀ ) = P ( 8 , 0 , -6 )
Let the equation of plane be x + y + z = 6
A = 1
B = 1
C = 1
D = -6
Now , the distance between the point and the plane is given by ,
d = | Ax₀ + By₀ + Cz₀ + D | / √ ( A² + B² + C² )
Substituting the values in the equation , we get
d = | 8 + 0 + ( -6 ) + ( -6 ) | / √ ( 1 + 1 + 1 )
d = | 8 - 6 - 6 | / √3
d = | -4 | / √3
d = 4 / √3
Therefore , the value of d = 4 / √3
Hence , The distance between the point P( 8 , 0 , -6 ) to the plane
x + y + z = 6 is d = ( 4 / √3 )
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what is the area of this parallelogram?
44cm^2
55cm^2
99cm^2
220cm^2
(I forgot to put the picture on this one)
D. (4cm) F. 5cm C.
(11cm)
A. 5cm E 4cm B.
~~~~~~~~~~~~~~~~~~
what is the area of this parallelogram?
10.35cm^2
12.5cm^2
20.25cm^2
30.6cm^2
help me asap please let me down
The game of european roulette involves spinning a wheel with 37 slots: 18 red, 18 black, and 1 green. a ball is spun onto the wheel and will eventually land in a slot, where each slot has an equal chance of capturing the ball. gamblers can place bets on red or black. if the ball lands on their color, they double their money. if it lands on another color, they lose their money.
Answer:
a) Expected amount of winnings = -$0.084
Standard deviation = $3.00
b) Expected amount of winnings = -$0.084
Standard deviation = $1.73
c) The expected winnings for both cases is exactly the same, but the spread of the wins about the expected value/mean is low in the case (b) compared to case (a).
So, with the expected winnings using the method in (a) and (b) the same, the risk associated with betting $3 dollar per game is higher because it has a higher standard deviation. This points to higher spread of losses and wins betting $3 once than betting $1 three different times.
Step-by-step explanation:
(a) Suppose you play roulette and bet $3 on a single round. What is the expected value and standard deviation of your total winnings?
It's either one wins or not with a bet of $3.
We can then obtain the probability mass function.
Random variable X represents the amount of winnings.
- If one bets $3 and picks the right colour, the person wins $6.
X = amount of winnings = 6 - 3 = $3
probability of winning = (18/37) = 0.486
- If one bets $3 and picks the wrong colour, then the person wins $0.
X = amount of winnings = 0 - 3 = -$3
Probability of losing = (19/37) = 0.514
The probability mass function is then
X | P(X)
3 | 0.486
-3 | 0.514
E(X) = Σ xᵢpᵢ
xᵢ = each variable
pᵢ = probability of each variable
E(X) = (3×0.486) + (-3×0.514) = -$0.084
Standard deviation = √(variance)
Variance = Var(X) = Σx²p − μ²
μ = E(X) = -0.084
Σx²p = (3²×0.486) + [(-3)² × 0.514] = 9
Variance = 9 - (-0.084)² = 8.993
Standard deviation = √8.993 = 2.999 = $3
(b) Suppose you bet $1 in three different rounds. What is the expected value and standard deviation of your total winnings?
With a bet of $1,
It's either one wins or not with a bet of $1.
We can then obtain the probability mass function.
Random variable X represents the amount of winnings.
- If one bets $1 and picks the right colour, the person wins $2.
X = amount of winnings = 2 - 1 = $1
probability of winning = (18/37) = 0.486
- If one bets $1 and picks the wrong colour, then the person wins $0.
X = amount of winnings = 0 - 1 = -$1
Probability of losing = (19/37) = 0.514
The probability mass function is then
X | P(X)
1 | 0.486
-1 | 0.514
E(X) = Σ xᵢpᵢ
xᵢ = each variable
pᵢ = probability of each variable
E(X) = (1×0.486) + (-1×0.514) = -$0.028
For 3 rounds of $1, the expected amount of winnings = 3 × -0.028 = -$0.084
Variance = Var(X) = Σx²p − μ²
μ = E(X) = -0.028
Σx²p = (1²×0.486) + [(-1)² × 0.514] = 1
Variance = 1 - (-0.028)² = 0.999216
Variance for combining 3 independent distributions = Σ λᵢ²σᵢ²
Variance of 3 rounds of $1 bets = 3[1²× var(X)] = 3 × var(X) = 3 × 0.999216 = 2.997648
Standard deviation = √(variance) = √(2.997648) = $1.73
(c) How do your answers to parts (a) and (b) compare? What does this say about the riskiness of the two games?
The expected winnings for both cases is exactly the same, but the spread of the wins about the expected value/mean is low in the case (b) compared to case (a).
So, with the expected winnings using the method in (a) and (b) the same, the risk associated with betting $3 dollar per game is higher because it has a higher standard deviation. This points to higher spread of losses and wins betting $3 once than betting $1 three different times.
Hope this Helps!!!
Find all zeros of the function and write the polynomial as a product of linear factors. f(x) = 3x4 + 4x3 + 13x2 + 16x + 4
Shelley compared the number of oak trees to the number of maple trees as part of a study about hardwood trees in a woodlot. She counted 9 maple trees to every 5 oak trees. Later in the year there was a big problem and many trees died. New trees were planted to make sure there was the same number of trees as before the big problem. The new ratio of the number of maple trees to the number of oak trees is 3:11. After planting new trees, there were 132 oak trees. How many more maple trees were in the woodlot before the big problem than after the bug problem? Explain.
Prior to the major issue, the woodlot had 72 more maple trees than it had after.
To solve this problem
Assuming x is a positive constant, we can represent the initial number of oak trees as 5x and the initial number of maple trees as 9x.
Prior to the problem, the ratio of maple trees to oak trees was 9:5, which produced the following equation:
[tex](9x)/(5x) = 9/5[/tex]
Later, the new ratio changed to 3:11 after new trees were planted to replace the original amount of trees. After planting, 132 oak trees were reported to have been planted. We so established the equation:
11y = 132
Solving for y:
y = 132/11 = 12
Now, we can find the new number of maple trees:
3y = 3 * 12 = 36
There were 36 maple trees when new trees were planted.
Before the problem, there were 9x as many maple trees as there were.
9x = 9 * 12 = 108
The difference between the original and new number of maple trees is:
108 - 36 = 72
So, Prior to the major issue, the woodlot had 72 more maple trees than it had after.
Find the perimeter of a polygon with sides 11ft 7ft 18ft 22ft 14ft and 23.5ft
Perimeter of a polygon is equal to sum of all sides of the polygon
Sides of the polygons are 11 ft, 7 ft, 18 ft, 22 ft, 14 ft and 23.5 ft
Sum of all sides of the polygon is given by = 11 ft + 7 ft + 18 ft + 22 ft + 14 ft + 23.5 ft
= 95.5 ft
Perimeter of a polygon = 95.5 ft
Hope this helps..!!
Thank you :)