The angle formed by the two hands have a measure less than 1/4 turn
How to relate the measure of the angle to 1/4 turn?From the question, we have the following parameters that can be used in our computation:
A clock with the hour hand at 12 and the minute hand at 2
The turn represented by the above is represened as
Turn = (2 * 30)/360
When simplified, we have
Turn = 1/6
Next, we have
Angle at the turn = 1/4
1/6 is less than 1/4
This means that the angle formed by the two hands have a measure less than 1/4 turn
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Help Quickly! Use the table. Estimate the total deer population for year 8.
A. about 1,815 deer
B. about 2,467 deer
C. about 1,934 deer
D. about 2,081 deer
2081 is the estimated population of the deer as per the given table.
We assume that the characteristics of the sample of the deer population match the characteristics of the population as a whole. This will be the case if the sample is random: each deer is equally likely to be included in the sample.
So, if 85 of the 110 marked deer show up in the sample, we assume that the sample is 85/110 of the entire population.
For a sample size of 1608 deer, that means the population is estimated to be ...
1608 = 85/110 × population
population = 1608 × 110/85 = 2081
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State all possible conditions that must be true for j and k so that the product of the expression is negative -2jk
The product -2jk is negative if and only if either j or k is negative (but not both). Therefore, the possible conditions for j and k are:
j < 0 and k > 0
j > 0 and k < 0
For the expression -2jk to be negative, at least one of the factors j or k must be negative, since the product of two positive numbers is always positive, and the product of two negative numbers is positive as well. Therefore, the possible conditions for j and k are:
j is negative and k is positive.
j is positive and k is negative.
In other words, if j and k have opposite signs, their product will be negative. However, if both j and k are positive or both are negative, their product will be positive. It's important to note that there are infinite possibilities for j and k that satisfy these conditions, since j and k can take on any real value as long as one is negative and one is positive.
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1. A cube of sugar is 2 cm wide. Calculate the num- ber of cubes in a box 720 cm².2. Calculate the amount of air in a room 6 m long, 5 m wide and 3 m high.3. The area of one side of a cuboid is 360 cm². What is the length, if the width is 1.5 cm? 4What is the volume of a container if it contains 12 boxes each 2.5 cm by 3 cm by 4.5 cm?5. A tank contains 4 500/ of water. Find the depth of the tank if its base area is 300 m².
(35)
In the grid to the left, a portion of the circle whose
center is the origin and whose radius is 10 is
drawn. Use it to help you answer the following
questions.
a. What is true about every point that lies on this circle?
b. Algebraically show that the point (6, 8) lies on the circle.
The circle is:[tex]x^2+y^2 = 5^2 = 25[/tex]This circle has center (0,0) and radius 5 units. Therefore, it is a circle with a radius of 5 units, and every point that lies on the circumference of this circle is 5 units away from the center of the circle.
the distance between any point on the circle and the center of the circle is always 5 units. This is because the equation of a circle is
[tex](x-a)^2+(y-b)^2=r^2[/tex]
where the center is (a,b) and the radius is r units. In this case,
a=b=0 and r=5.
Algebraically show that the point (6, 8) lies on the circle.
To show that the point (6, 8) lies on the circle, we need to substitute the values of x and y in the equation of the circle and verify whether the equation holds true or not.So,
substituting x=6 and y=8 in the equation of the circle, we
[tex]get:6^2 + 8^2 = 36 + 64 = 100[/tex]
Now, we can see that the LHS of the equation is equal to 100, which is also equal to the square of the radius of the circle. Therefore, the point (6, 8) lies on the circumference of the circle with center (0,0) and radius 5 units.
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Help! How to solve the x on logX=(log27)/(log5)
Thank you!
The solution to the given logarithmic expression is: x = 111.63
How to solve Logarithmic problems?The logarithmic form of expression is written as [tex]log_{a} c = b[/tex]. This is simply a rearrangement of the specific exponential form, aᵇ = c. Thus, we can say that exponential equation could be written as a logarithm.
We want to solve the logarithmic expression given as:
log x = [tex]\frac{log 27}{log 5}[/tex]
log x = [tex]\frac{log 3^3}{log 5}[/tex]
log x = [tex]\frac{3 log 3}{log 5}[/tex]
log x = 2.0478
x = [tex]10^{2.0478}[/tex]
x = 111.63
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Johnny uses a wheelbarrow to move planting soil to a delivery truck. The volume of planting soil that fits in the wheelbarrow measures
2
2 feet by
3
3 feet by
1.5
1.5 feet. The delivery truck measures
11
11 feet by
8
8 feet and is
6
6 feet tall. Johnny puts planting soil in the delivery truck until the truck is
70
70% full.
What is the minimum number of times Johnny needs to use the wheelbarrow until the delivery truck is
70
70% full?
The minimum number of times Johnny needs to use to the wheelbarrow until the delivery truck is filled up to 70%, whereby the shape of the truck is a rectangular prism is about 41 times
What is a rectangular prism?A rectangular prism is a three dimensional geometric figure with three pairs of parallel facing sides, and perpendicular adjacent faces.
Whereby the wheelbarrow and the truck are rectangular prisms, we get;
The dimensions of the wheel barrow are;
2 feet by 3 feet by 1.5 feet
The dimensions of the truck are;
11 feet by 8 feet by 6 feet
The amount of soil John puts in the truck = 70% of the volume of the truck
Therefore;
The amount of soil John puts in the truck = 11 feet × 8 feet × 6 feet × 70%
11 feet × 8 feet × 6 feet × 70% = 528 ft³ × 70% = 369.6 ft³
The number of times to use the wheelbarrow, n, is therefore;
n = 369.6 ft³ ÷ (2 ft × 3 ft × 1.5 ft) ≈ 41.0
The minimum number of times Johnny needs to use the wheelbarrow until the delivery truck is 70% filled is therefore 41 = 41 times
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Determine f(4) for A piecewise function f(x) = x^3 x<-3
2x^2-9 -3 ≤ x≤ 4
5x+4 x>4
PLEASE SHOW ALL WORK!!!!!!!!!!!!!!
23
24
41
64
thank you!
Solve 125 + 20w− 20w = 43 + 37w− 20w
Answer:
[tex]w=\frac{82}{17}[/tex]
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Decimal form: 4.82352941
having a great day and thx for your inquiry :)
Please help me find the equation to this in standard form equation ASAP
The equation of the line in the graph passing through the points (-2,1) and (6,7) is [tex]y = \frac{3}{4}x + \frac{5}{2}[/tex].
What is the equation of the line?The slope-intercept form is expressed as;
y = mx + b
Where m is slope and b is the y-intercept.
From the graph, the line passes through point (-2,1) and (6,7).
First, we determine the slope:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1} \\\\m = \frac{7 - 1}{6-(-2)} \\\\m = \frac{6}{6+ 2} \\\\m = \frac{6}{8} \\\\m = \frac{3}{4}[/tex]
Now, plug the slope m = 3/4 and point (-2,1) into the point-slope form:
( y - y₁ ) = m( x - x₁ )
[tex]y - 1 = \frac{3}{4}(x - (-2)) \\\\y - 1 = \frac{3}{4}(x + 2)\\\\y - 1 = \frac{3}{4}x + \frac{3}{2} \\\\y = \frac{3}{4}x + \frac{3}{2} + 1\\\\y = \frac{3}{4}x + \frac{5}{2}[/tex]
Therefore, the euation of the line is [tex]y = \frac{3}{4}x + \frac{5}{2}[/tex].
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A person buys a phone for $88 and signs up for a single-line phone plan with 2000 monthly anytime minutes. The plan costs $118.96 per month. Write an equation that can be used to determine the total cost
C(t) of this phone plan for t months. Then, find the cost for 22 months, assuming that the number of minutes the person uses does not exceed 2000 per month.
Answer: The total cost will be equal to $2839.16. The expression to calculate the total cost is 119.92(m)+81=C(t).
What is an expression?
Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that a person buys a phone for $81 and signs up for a single-line phone plan with 2000 monthly anytime minutes. The plan costs $119.92 per month.
The expression will be formed as below:-
119.92(m)+81=C(t)
119.92(23)+81=C(t)
2839.16=C(t)
Therefore, the total cost will be equal to $2839.16.
Enter the number that belongs in the green box
The number that belongs in the green box is 45.65
How to find the number that belongs in the green boxFrom the question, we have the following parameters that can be used in our computation:
The triangle
If the number that belongs in the green box is x, then we have
6.78/sin(29) = 10/sin(x)
Take the inverse of both sides
sin(29)/6.78 = sin(x)/10
This gives
sin(x) = 10 * sin(29)/6.78
Evaluate
sin(x) = 0.7151
Take the arc sin of both sides
x = 45.65
Hence, the number that belongs in the green box is 45.65
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When calculating the cost of a good or service, you often have to consider price markups and discounts. Consider these two statements regarding a
discounted item:
• The list price of the item is 80 percent of the original price.
• The price of the item has been reduced by 80 percent.
Write a pair of linear equations using variables of your choice to prove that these two statements are not equivalent. Explain how a calculation for
change in percentage (increase or decrease) is different from a calculation that involves multiplying by percentages. Why is the wording of percentage
problems so important? Give examples to illustrate your point.
20 points:D
Answer:
Step-by-step explanation:
Let’s assume the original price of the item is “x.” Then, using the first statement, the list price of the item is 80% of the original price, or 0.8x. If there is a discount applied, let’s say “d,” then the discounted price would be (1-d)(0.8x).
Using the second statement, if the price of the item has been reduced by 80%, then the discounted price would be 0.2x. This can be expressed as (1 - 0.8)(x).
So, we have the following two equations:
(1 - d)(0.8x) = 0.2x
0.64x - 0.8dx = 0.2x
Simplifying this equation, we get:
0.44x = 0.8dx
d = 0.55
This means that the discount applied in the first statement is 55%, not 80%.
The calculation for change in percentage (increase or decrease) involves finding the difference between two values and expressing it as a percentage of the original value. This is different from multiplying by percentages, which involves finding a percentage of the original value and subtracting or adding it to the original value.
The wording of percentage problems is important because it can affect the way the problem is interpreted and the calculation that is used to solve it. For example, the phrase “increased by 50%” could be interpreted as multiplying the original value by 1.5, while the phrase “increased to 50%” could be interpreted as finding 50% of the original value and adding it to the original value.
Examples:
A shirt is on sale for 30% off its original price of $50. The discounted price is (1-0.3)($50) = $35.
A company’s revenue increased from $100,000 to $120,000. The percentage increase in revenue is ((120,000 - 100,000) / 100,000) x 100% = 20%.
What is the y -intercept of y=-5x
Thank you for the help
The y-intercept of the line [tex]y = -5x \ is \ 0[/tex].
The equation of a line in slope-intercept form is given by [tex]$y = mx + b$[/tex], where [tex]$m$[/tex] represents the slope and [tex]$b$[/tex] represents the y-intercept. In the equation [tex]$y = -5x$[/tex], the coefficient of [tex]x \ \ is \ -5[/tex], which represents the slope of the line.
To find the y-intercept, we set [tex]$x$[/tex] equal to [tex]$0$[/tex] and solve for [tex]$y$[/tex]. Substituting [tex]$x = 0$[/tex] into the equation gives us [tex]$y = -5(0) = 0$[/tex].
Hence, the y-intercept of the line [tex]y = -5x \ is \ 0[/tex]. In the graph, the line passes through the origin [tex]$(0,0)$[/tex], indicating that it intersects the y-axis at [tex]$y = 0$[/tex]. This means the line passes through the point [tex]$(0, 0)$[/tex] on the coordinate plane. The y-intercept is the point at which the line crosses the y-axis.
The y-intercept is a crucial point on a line as it helps determine its starting position on the y-axis. In the graph, you can visually observe that the line passes through the origin, confirming the y-intercept of [tex]$0$[/tex].
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Calculator
A point is selected at random inside the given figure.
What is the probability the point will be in the region labeled A?
Enter your answer, as a fraction in simplest form, in the box.
P(A) =
Basic
5 in.
B
3 in.
A
C
4 in.
3 in.
D
4 in.
The probability the point will be in the region labeled A is 2/15 if point is selected at random inside the given figure.
Given that a point is selected at random from inside the given figure.
We are to find the probability that the point will be in the region labeled B.
From the figure, we note that the regions A, B and D are rectangles and the region C is a square.
The areas of all the regions are calculated as follows:
Area of region A is 5×(3+4) =35 sq in
Area of region B is 3×4 = 12 in
Area of region C is 4² = 16 sq in
Area of region D is 3×(4+5)= 27 sq. in
Therefore, the probability that the randomly chosen point will lie in the region B is given by P
P = 12/35+12+16+27
=12/90
=2/15
Hence, the probability the point will be in the region labeled A is 2/15
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NO LINKS!!!! URGENT HELP PLEASE!!!
Please help me with these problems
Answer:
[tex]\sf g(x) = f(x\; \boxed{+ 3}\;) \;\boxed{- 6}[/tex]
Step-by-step explanation:
A translation is a transformation that moves every point of a figure the same distance and in the same direction. This means that the size, shape, and orientation of the figure are preserved, but its position is changed.
From inspection of the given diagram, we can see that the size, shape and orientation of the graph of function g is the same as that of the graph of function f, but its position has changed. Therefore, the transformation is a translation.
We can use the vertex of both graphs to determine the translation.
The vertex of function f is the origin (0, 0).The vertex of function g is (-3, -6).Therefore, the graph of function f has been moved 3 units left and 6 units down to create the graph of function g.
When we move "a" units left, we add the value of "a" to the x-value of the function.
When we move "a" units down, we subtract the value of "a" from the function.
Therefore:
[tex]\sf g(x) = f(x\; \boxed{+ 3}\;) \;\boxed{- 6}[/tex]
(1) 6/6 ✓ (2) 4- 12 cm 9 cm The shape below is made from 4 of these triangles. 15 cm, Work out the area of the shape. Diagram NOT accurately drawn 888 Diagram NOT accurately drawn Onk 20 21-1744-8 30x4+2=6 (7+7)+2-
The perimeter of this solid is 72 cm.
How to calculate the perimeter of this triangle?In Mathematics and Geometry, the perimeter of a triangle can be calculated by using this mathematical equation:
P = a + b + c
Where:
P represents the perimeter of a triangle.a, b, and c represents the side lengths of a triangle.Since the shape was formed by combining four (4) of these triangles, we can logically deduce the following side lengths;
Side length = 12 - 9 = 15 - 12
Side length = 3 cm.
Therefore, the perimeter of this solid can be calculated as follows;
Perimeter of solid = 4(15) + 4(3)
Perimeter of solid = 60 + 12
Perimeter of solid = 72 cm.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
In ΔTUV, t = 22 inches, u = 79 inches and ∠V=51°. Find ∠U, to the nearest degree.
The measure of angle U is given as follows:
m < U = 66º.
What is the law of cosines?The Law of Cosines states that for any triangle with sides a, b, and c and angle C opposite to side c, the following equation is true to obtain the missing length:
c² = a² + b² - 2abcos(C)
Hence the length of side v is obtained as follows:
v² = 22² + 79² - 2 x 22 x 79 x cosine of 51 degrees
v² = 4537.48
[tex]v = \sqrt{4537.48}[/tex]
v = 67.36.
By the law of sines, we have that:
sin(51º)/67.36 = sin(U)/79
Hence the measure of angle U is obtained as follows:
sin(U) = 79 x sine of 51 degrees/67.36
sin(U) = 0.9114
m < U = arcsin(0.9114)
m < U = 66º.
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Jamal works at the recreation center 15 hours a week during the school year. He earns $8.75 an hour. in a typical month, he works 63 hours. Calculate his monthly taxes below.
Gross Monthly Income
Monthly Federal Income Tax (10%)
Monthly Social Security (FICA) (6.2%)
Monthly Medicare (1.45%)
Monthly State Tax (4%)
Monthly Local Tax (0.1 %)
Total Monthly Deductions
CA CA EA EA CA
S
Jamal's NMI =
Jamal's Net Monthly Income (NMI) is $431.40.
To calculate Jamal's Net Monthly Income (NMI)We need to calculate his gross income and all the monthly deductions first.
Gross Income = Hourly Rate x Total Hours Worked = $8.75/hour x 63 hours = $551.25
Monthly Federal Income Tax = Gross Income x Federal Tax Rate = $551.25 x 0.10 = $55.125
Monthly Social Security (FICA) = Gross Income x FICA Rate = $551.25 x 0.062 = $34.13625
Monthly Medicare = Gross Income x Medicare Rate = $551.25 x 0.0145 = $7.987625
Monthly State Tax = Gross Income x State Tax Rate = $551.25 x 0.04 = $22.05
Monthly Local Tax = Gross Income x Local Tax Rate = $551.25 x 0.001 = $0.55125
Monthly Federal Income Tax + Monthly Social Security (FICA) + Monthly Medicare + Monthly State Tax + Monthly Local Tax = Total Monthly Deductions
= $55.125 + $34.13625 + $7.987625 + $22.05 + $0.55125
= $119.85
Net Monthly Income (NMI) = Gross Income - Total Monthly Deductions
= $551.25 - $119.85
= $431.40
Therefore, Jamal's Net Monthly Income (NMI) is $431.40.
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A company makes chocolate candies in a shape of a solid sphere. Each piece of candy has a diameter of 9 centimeters. If a box contains 10 pieces of candy, how much chocolate does the box contain?
Answer:
10
Step-by-step explanation:
the answer is in the question
An insurance actuary tracks the customer mass and the dosage of a certain medicine prescribed to customers. An approximate least-squares regression line was used to predict the dosage, in milligrams; from a given costumer mass, in kilograms. Interpret the residual for the customer indicated in the scatter plot.
The residual measures the difference between the predicted and observed dosage, indicating if the customer received more or less medication than expected based on their mass.
The residual in this context refers to the difference between the predicted dosage of the medicine, based on the least-squares regression line, and the actual dosage observed for a specific customer. It indicates how much the actual dosage deviates from the expected dosage based on the customer's mass.
In the scatter plot, the residual for a particular customer represents the vertical distance between the observed data point (the actual dosage) and the regression line (the predicted dosage).
If the residual is positive, it means the observed dosage is higher than the predicted dosage, indicating that the customer received a higher dosage of the medicine than expected based on their mass.
Conversely, if the residual is negative, it means the observed dosage is lower than the predicted dosage, indicating that the customer received a lower dosage than expected based on their mass.
Interpreting the residual requires considering the magnitude of the deviation. A larger residual suggests a greater difference between the observed and predicted dosages, indicating a potentially significant variation from the regression model.
A smaller residual indicates a closer alignment between the observed and predicted dosages, suggesting that the regression model provides a more accurate estimation.
Overall, analyzing the residuals helps assess the effectiveness of the regression model in predicting the dosage of the medicine based on customer mass and identifies any outliers or discrepancies in the data that may need further investigation.
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Convert 2553 base 10 to base 7
Step By Step explanation
The conversion of 2553 base 10 to base 7 is 10305 base 7.
We are given that;
The value= 2553 base 10
Now,
To convert 2553 base 10 to base 7, we need to divide 2553 by 7 repeatedly and write down the remainders. The final answer will be the remainders read from bottom to top. Here are the steps:
Divide 2553 by 7. The quotient is 364 and the remainder is 5. Write down 5.
Divide 364 by 7. The quotient is 52 and the remainder is 0. Write down 0 below 5.
Divide 52 by 7. The quotient is 7 and the remainder is 3. Write down 3 below 0.
Divide 7 by 7. The quotient is 1 and the remainder is 0. Write down 0 below 3.
Divide 1 by 7. The quotient is 0 and the remainder is 1. Write down 1 below 0.
Therefore, by conversion the answer will be 10305 base 7.
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Let f(x) = 5 sin(x). Describe the graph of each of the following in terms of the graph of f.
1. g(x) = 5 sin(x) +4
2. h(x) = 5 sin(x + 7)
3.k(x) = 20 sin(x) + 10
4. m(x) = 5 sin(4x - 1)
I
g(x) shifts the graph vertically upward by 4 units,h(x) shifts the graph horizontally to the left by 7 units,k(x) scales the graph vertically by a factor of 20 and shifts it vertically upward by 10 units and m(x) compresses the graph horizontally by a factor of 1/4 and shifts it horizontally to the right by 1 unit.
To describe the graph of each function in terms of the graph of f(x) = 5 sin(x), we will analyze how each transformation affects the original graph.
1. g(x) = 5 sin(x) + 4:
Adding a constant value of 4 to the function f(x) shifts the graph vertically upward by 4 units. The amplitude and period of the graph remain the same.
2. h(x) = 5 sin(x + 7):
Adding a constant value of 7 inside the sine function causes a horizontal shift to the left by 7 units. This means the graph is shifted 7 units in the opposite direction of the sign (left in this case). The amplitude and period remain unchanged.
3. k(x) = 20 sin(x) + 10:
Multiplying the entire function by a constant of 20 scales the graph vertically, stretching it vertically by a factor of 20. Additionally, adding a constant value of 10 shifts the graph vertically upward by 10 units.
The amplitude remains the same, but the graph is vertically elongated and shifted upward.
4. m(x) = 5 sin(4x - 1):
Inside the sine function, the value of 4 stretches the graph horizontally by a factor of 1/4. This results in a shorter period, meaning the graph oscillates more frequently.
The value of -1 inside the sine function causes a horizontal shift to the right by 1 unit. Therefore, the graph is compressed horizontally and shifted 1 unit to the right. The amplitude remains the same.
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Raquel informed her stockbroker that she wanted to buy a certain amount of stock. The broker informed her that because of the margin requirement of 55% she would need at least $825 in cash what is the dollar value of the stock that Raquel wants to purchase?
The dollar value of the stock that Raquel wants to purchase is $1,833.33.
If the margin requirement is 55%, then the amount of cash wanted is 45% of the total value of the inventory.
Consequently, we will set up the following equation like this:
0.45x = 825
Wherein:
x is the dollar value of the stock Raquel wants to purchase.
To solve for x, we are able to divide both aspects of the equation by way of 0.45:
x = 825 ÷ 0.45
x = $1,833.33
Therefore, the dollar value of the stock that Raquel wants to purchase is $1,833.33.
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pls help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
[tex]\huge\mathcal{\fcolorbox{Aqua}{azure}{\red{➳Answer}}}[/tex]
Base of the Parallelogram=14m
Height of the Parallelogram=8m
∴ Are of the Parallelogram= Base × height
= (14×8) sq. m
=112 sq.m
Now,
Diameter of the circle (unshaded portion)=8m
Radius of the circle= Diameter/2 =8/2 m= 4m
So, radius=4m
∴ Area of the circle = πr²
=(22/7 × 4 × 4)sq.m
=352/7 sq.m
=50.2857 sq.m
=50.286 sq.m
∴ Are of the Unshaded portion= Are of the Parallelogram - Area of the circle
=(112-50.286) sq.m
= 61.714 sq.m (Ans)
∴The area of the shaded portion is 61.714 sq.m
Hope it helps you
[tex]\red{\rule{200pt}{5pt}}[/tex]
[tex]\bold{Thank ~you~:)}[/tex]
___________________________________
Given:-
Base of the Parallelogram=14m
Height of the Parallelogram=8m
∴ Are of the Parallelogram= Base × height
= (14×8) sq. m
=112 sq.m
Now,
Diameter of the circle (unshaded portion)=8m
Radius of the circle= Diameter/2 =8/2 m= 4m
So, radius=4m
∴ Area of the circle = πr²
=(22/7 × 4 × 4)sq.m
=352/7 sq.m
=50.2857 sq.m
=50.286 sq.m
∴ Are of the Unshaded portion= Are of the Parallelogram - Area of the circle
=(112-50.286) sq.m
= 61.714 sq.m (Ans)
∴The area of the shaded portion is 61.714 sq.m
___________________________________
Make the above person as brainlist :)
Thankyou :DQuestion content area top Part 1 A new cylindrical can with a diameter of 6 cm is being designed by a local company. The surface area of the can is 140 square centimeters. What is the height of the can? Estimate using 3.14 for , and round to the nearest hundredth. Apply the formula for surface area of a cylinder .
The height of the can is approximately 23.33 cm.
We have,
The formula for the surface area of a cylinder.
S = 2πr² + 2πrh
where S is the surface area, r is the radius, h is the height, and π is pi (approximately 3.14).
In this case, we know that the diameter of the can is 6 cm, which means that the radius is half of that or 3 cm.
We also know that the surface area is 140 square centimeters.
So,
140 = 2π(3²) + 2π(3)(h)
Simplifying:
140 = 18π + 6πh
Dividing both sides by 6π:
23.333... = h
Rounding to the nearest hundredth:
h ≈ 23.33 cm
Therefore,
The height of the can is approximately 23.33 cm.
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Mary pays income tax according to the graduated schedule shown below.
If taxable income
But not over-
The tax is:
is over-
10% of the amount over 50
$782.50 plus 15% of the amount over 7,825
$4,386 25 plus 25% of the amount over 31,850
$15.698.75 plus 28% of the amount over
77,100
SO
$7,825
$31,850
$77,100
$160,850
$349,700
$7,825
$31,850
$77,100
$160,850
$349,700
Mark this and return
no limit
$39,148.75 plus 33% of the amount over
160,850
$101.469 25 plus 35% of the amount over
349,700
If Mary's taxable income is $68,562, how much income tax does she owe, rounded to the nearest dollar?
a. $13,564
b. $17,140
c. $21,527
d. $12,349
Save and Exit
Next
3
Submit
We find that Mary owes $13,564 in income tax. So the correct option is (a) $13,564. Option a
Mary's taxable income falls between $31,850 and $77,100. This means we apply the tax rate relevant to this bracket, which is $4,386.25 plus 25% of the amount over $31,850.
First, we need to subtract $31,850 from Mary's income to find the amount that we need to apply the 25% tax rate to:
$68562 - $31850 = $36712
Next, we take 25% of this result:
0.25 * $36712 = $9178
Then we add the base tax for this bracket ($4,386.25) to this result to get the total tax:
$4386.25 + $9178 = $13564.25
Rounding this to the nearest dollar, we find that Mary owes $13,564 in income tax. So the correct option is (a) $13,564.
Option a
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Owners of a recreation area are filling a small pond with water. They are adding water at a rate of 32 liters per minute. There are 600 liters in the pond to start. Let W represent the total amount of water in the pond (in liters), and let T represent the total number of minutes that water has been added. Write an equation relating W to T Then use this equation to find the total amount of water after 13 minutes.
If owners of a recreation area are filling a small pond with water. The total amount of water after 13 minutes is 1016 liters.
What is the amount of water?Let the total amount of water in the pond = W
Let the total number of minutes that water has been added = T
The equation relating W to T Is:
W = 600 + 32T
Where:
600= initial amount of water in the pond
32T = additional water added over time
Now let find the total amount of water in the pond after 13 minutes
Substitute T = 13 into the equation:
W = 600 + 32(13)
W = 600 + 416
W = 1016
Therefore the total amount of water is 1016 liters.
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simplify
2x^2+8-4x+3x-6x^2+7
Answer: -4x^2-x+15
Step-by-step explanation:
Combine like terms: 2x^2 and -6x^2 combine to -4x^2.
Combine like terms: -4x and 3x combine to -x.
Combine like terms: 8 and 7 combine to 15.
The simplified expression is -4x^2-x+15.
Net worth is the number of goods or services that can be purchased with
several units of currency.
O False
O True
Answer:
False
Step-by-step explanation:
Net worth is a combination of everything you own.
This includes the amount of money you have, or have ever made, plus your house, vehicle, belongings, etc.
8. How can we prove that cos = sin(90-) ? Write your proof below.
it can be seen in
с
A
0
B
We can conclude that cosθ = sin(90° - θ) for any right triangle with angle θ and its complementary angle (90° - θ).
To prove that cosθ = sin(90° - θ), we can use the properties of right triangles and their angles.
Consider a right triangle ABC, where angle A is θ, angle B is (90° - θ), and angle C is 90°.
According to the definition of trigonometric functions in a right triangle:
- cosθ = adjacent side (AB) / hypotenuse (AC)
- sin(90° - θ) = opposite side (AB) / hypotenuse (AC)
From the given definitions, we can see that both cosθ and sin(90° - θ) have the same ratio of side lengths, which is AB/AC.
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