The area of a circle with the value of its circumference as 60cm is 286. 38cm²
How to determine the area of the circleThe formula for determining the formula for circumference of a circle is expressed as;
Circumference = 2 πr
Given that;
π has a fractional value of 22/ 7 and a decimal value of 3. 14r is the radius of the circleNow, we have to substitute the value of circumference of the circle as 60cm
We have;
60 = 2 πr
Now, substitute the value for π into the equation, we have;
60 = 2× 3.14r
Multiply the values, we get;
60 = 6.28r
Make 'r' the subject of formula in the equation
r = 60/6.28
r = 9.55cm
But we know that e formula for area of a circle is expressed as;
Area = πr²
Now, substitute the value of radius into the formula, we have;
Area = 3. 14(9.55)²
Find the squares
Area = 3.14(91.2025)
Multiply the values by expanding the bracket
Area = 286. 38cm²
Hence, the area is 286. 38cm²
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see the picture instead:
Find the maximum value of the function for the polygonal convex set determined by the given system of inequalities.
see the picture instead :(
The maximum value of the function is at (8, 7).
The inequalities are :4x + 4y ≥ 28-2x + 6y ≤ 26-6x + 2y ≥ -34The objective function is f(x, y) = 7x + 6y.Convert the above inequalities into equations and plot them on the graph, and find the coordinates of their intersection as shown in the graph attached below.Shade the side of the area which satisfies the inequality. Do this for every inequality.Now we check the corner points which fall within the first quadrant as well as in the shaded region of the inequalities.We obtain three points (2, 5), (8, 7), and (6, 1).We will now check which point gives us the maximum value of our objective function.f(2, 5) = 7(2) + 6(5) = 44f(8, 7) = 7(8) + 6(7) = 98f(6, 1) = 7(6) + 6(1) = 48The function achieves its maximum value at (8, 7).To learn more about inequalities, visit :
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pls help ill give brainly
The slope of this straight line is equal to: A. 2
What is a slope?A slope is also referred to as gradient and it's typically used to describe both the direction, ratio, and steepness of the function of a straight line based on its coordinates or points.
How to calculate the slope of a line?Mathematically, the slope of any straight line can be calculated by using this formula;
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
By critically observing the given graph, we can logically deduce the following points:
Point (x, y) = (1, 1) Point (x, y) = (-1, -3)Note: Each interval on this graph represents 1 unit.
Substituting the given points into the formula, we have;
Slope = Δy/Δx
Slope = (-3 - 1)/(-1 - 1)
Slope = -4/-2
Slope = 2
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I don’t know 6-8 I need help. Please do not write random I fr need help
In functions, value of x = 45 and y = 45
What is function in math?
A quantitative expression, rule, or law that describes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions occur widespread, and they are essential for defining physical links in the sciences.6) x = 15
y = 49
3x = 3 * 15 = 45
y - 4 = 49 - 4 = 45
7) 3x + 23 = 4x
4x - 3x = 23
x = 23
y = 4 * 23 = 92°
8) y + 12 = 5x °
3x + 50 =
According to the question
y + 12 = 3x + 50
5x = 3x + 50
2x = 50
x = 25
y + 12 = 5x °
y = 5 * 25 - 12
y = 125 - 12 = 113
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María Fernanda buys a bag of cookies that contains 7 chocolate chip cookies, 5 peanut butter cookies, 6 sugar cookies and 8 oatmeal cookies.
What is the probability that María Fernanda reaches in the bag and randomly selects 2 chocolate chip cookies from the bag?
Based on the number of cookies in the bag of cookies, if María Fernanda is to reach in and select 2 chocolate chip cookies, the probability of that happening is 6.46%
How to find the probability?The events that María Fernanda picks one chocolate chip cookie and then another, are both independent events.
To find the probability of independent events, the formula is:
= Independent event probability 1 x Independent probability 2
Find the total number of cookies:
= 7 chocolate chip cookies + 5 peanut butter cookies + 6 sugar cookies + 8 oatmeal cookies
= 26 cookies
The probability of two chocolate cookies being picked by María Fernanda is:
= Number of chocolate cookies / Number of total chips x Number of chocolate cookies left / Number of cookies left
= 7 / 26 x 6 / 25
= 42 / 650
= 21 / 325
= 6.46%
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A bag of sweets weighs 120g and costs
£0.89. It contains 14 gummy bears, 6 jelly
beans and 4 chocolate buttons.
What is the ratio of bears:beans:buttons in
it's simplest form?
The ratio of bears:beans: buttons in the simplest form is 7:3:2
Mathematicians use the term "ratio" to compare two or more numbers. It serves as a comparison tool to show how big or tiny an amount is in relation to another.
Weight of sweet bag = 120g
Cost of a sweet bag = 0.89 euros
Number of gummy bears = 14
Number of jelly beans = 6
Number of chocolate buttons = 4
The ratio of bears:beans:buttons = 14:6:4
Dividing the ratio by 2 throughout we get:
Ratio of bears:beans:buttons = 7:3:2
So, In its simplest form, the ratio of bears to beans to buttons is 7:3:2.
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is -4 a solution for the equation?
5x(2-4)=2(5x-4)
please explain ur answer/show work. :)
Answer:
x=[tex]\frac{2}{5}[/tex]
Step-by-step explanation:
5x(2-4)=2(5x-4)
1. First we expand the brackets
10x-20x=10x-8
2. we can simplify the equation to
-10x=10x-8
3. we want to find the value of x so we get all of the x on one side so we would -10x on both side
-20x=-8
4. to find the value of x we divide each side by -20 this gives us
x=[tex]\frac{8}{20}[/tex]
(it's not a negative as the negative cancel each other out as negative divided by negative gives us positive)
5. However we can simplify the fraction by dividing the top and bottom by 4 (this is because the highest common factor for both number is 4) this gives
x=[tex]\frac{2}{5}[/tex]
6. Therefore -4 is not a solution for the equation
In the country of United States of Heightlandia, the height measurements of ten-year-old children are
approximately normally distributed with a mean of 54.6 inches, and standard deviation of 5.7 inches.
What is the probability that the height of a randomly chosen child is between 55.15 and 68.35 inches? Do not
round until you get your your final answer, and then round to 3 decimal places.
Answer=
(Round your answer to 3. decimal places.)
After being exposed to an electromagnetic shrinking machine, joe's height decreased by 120cm over 1.5 seconds. his height decreased by the same amount each second.
Main Answer:
Height decreased in 1 second is 80 cm
Explanation:
The total amount of height decreased is 120.
Total amount of time taken is 1.5 s.
Height decreased in 1 second = [tex]\frac{120}{1.5}[/tex]
⇒ [tex]\frac{1200}{15}[/tex]
⇒ 80 cm
Therefore, height decreased in 1 second is 80 cm.
could i get another hand please:)
The expression [tex]\sqrt{n}[/tex] which is the third option represents the side length, in feet, of the bulletin board.
It is given in the question that the area of the bulletin board is n square feet.
We have to find the expression that represents the side length, in feet, of the bulletin board.
Let the side, in feet of the bulletin board be x.
We know that,
Area of a square =[tex]side^2[/tex]
We have, side = x
Hence we can write,
Area of a square = [tex]x^2[/tex] square feet
Hence,
[tex]x^2=n[/tex]
Square rooting on both sides, we get
[tex]\sqrt{x^2}=\sqrt{n}\\\\x=\sqrt{n}[/tex]
Hence the expression [tex]\sqrt{n}[/tex] which is the third option represents the side of the square bulletin.
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The game of chess is played on a square shaped board. If the length of one edge is 2m[4thpower]n what is the area of the board
Step-by-step explanation:
if I understand correctly, one side of the square is 2m⁴n.
so, the area of the square is
side² = (2m⁴n)² = 4m⁸n²
because
(2m⁴n)² = 2m⁴n × 2m⁴n
and that is 4m⁸n²
Which measure of spread is the most appropriate for the data set represented by the graph?
Number of Chocolates
11-
10-
9
8-
7 9
S
ST
3
2-
1 2
3
4 5 678
Number of Children
9 10 11
your answer is B
your welcome
What is the difference?
− 3 − 6
Answer:
-9
Step-by-step explanation:
If you find the -6 point on the number line and move to the left three spaces, you stop at -9. You are taking away three spaces from an already negative number. So, you move to the left to show you subtracting something.
Hope this helps! :)
Answer:
-9
Step-by-step explanation:
Using absolute value (6+3) you can add -6 to -3.
There are 12 bags of apples on a market store. The main number of apples in each bag is eight. The table shows the number of apples in 11 of the bags. Calculate the number of apples in the bag.
The main number of apples in each bag is eight therefore 12 bags contain 96 apples.
What is basic algebra ?The area of mathematics known as algebra aids in the representation of circumstances or problems as mathematical expressions. To create a meaningful mathematical expression, it takes variables like x, y, and z together with mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in every discipline of mathematics, including trigonometry, calculus, and coordinate geometry.
Given that :There are 12 bags of apples on a market store. The main number of apples in each bag is eight
Eight apples on average fit into each bag.
We need to figure out how many apples are in the 12 bag.
The total number of apples is 8×12 = 96.
Therefore, 12 bags contain 96 apples.
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Phyllis invested $9,500 a portion earning a simple interest rate of 7 1/5% per year and the rest earning a rate of 7% per year. After 1 year the total interest earned on these investments was $677. How much money did she invest at each rate?
Using simple interest, it is found that the amounts invested are given as follows:
$2,350 at a rate of 7.2%.$6,650 at a rate of 7%.Simple InterestSimple interest is used when there is a single compounding per time period, usually measured in years.
The amount of money after t years in is modeled by:
A(t) = P(1 + rt)
In which:
P is the initial amount of the investment.r is the interest rate of the investment, as a decimal.The interest accrued over t years is:
I(t) = Prt.
For this problem, we have that:
She had two investments totaling $9500, hence P and 9500 - P.The rates are of [tex]r_1 = 0.072, r_2 = 0.07[/tex].From the interest earned, we have that:
[tex]I_1 + I_2 = 677[/tex]
In which:
[tex]I_1 = 0.072P[/tex][tex]I_2 = 0.07(9000 - P)[/tex]Replacing both these relations in the sum of interests, we have that:
0.072P + 0.07(9000 - P) = 677
0.002P = 677 - 0.07(9000)
P = (677 - 0.07(9000))/0.02
P = 2350.
Hence she invested $2,350 at a rate of 7.2% and $6,650 at a rate of 7%, as 9000 - 2350 = 6650.
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Select all the digital construction tools that do the same job as a straightedge.
-Line
-Segment
-Point plotted on an object
-Point of intersection
-Circle with center through point
The correct answers are line and segment.
Find the differential dy in each of the followings:
y = 2t² +t+1
Answer:
4t + 1.
Step-by-step explanation:
Use the General form of the differential:
If y = ax^n,
dy/dx = anx^(n-1)
So:-
y = 2t^2 + t + 1
dy.dt = 2*2t^(2-1) + t^(1-1) + 0
= 4t + 1.
pls do number 20!! i mark as brainliest
Answer:
10
Step-by-step explanation:
I'm going to estimate [tex]\sqrt{30}[/tex]. Because root 25 is 5 and root 26 is 6, root 30 is around 5.5. 5.5 + 6.2 is around 10.
Don't say you are going to mark as brainliest if you don't have brainliest.
Simplify: [(x – 2) ^2(x + 2)] ^2
The value of the expression : [(x – 2) ^2(x + 2)] ^2 will be (x³ - 4x² + 10x + 8)².
How to illustrate the information?It should be noted that the information simony wants us to multiply the expressions that are given. In this case, they can be computed individually. This will be:
(x - 2)² = (x - 2)(x - 2)
= x² - 2x - 2x + 4.
= x² - 4x + 4
This will be:
(x² - 4x + 4)(x - 2)
= x³ - 2x - 4x² + 8x + 4x - 8
= x³ - 4x² + 10x + 8
We will then square the above value. This will be (x³ - 4x² + 10x + 8)².
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14.549 - (8.131 + 3.7024)
Answer: 2.7156
Step-by-step explanation:
Using Bidmas: we do the brackets first so 8.131 + 3.7024 = 11.8334
Then 14.549 - 11.8334 = 2.7156
Hope this helps :)
Answer:
Step-by-step explanation:
help please i don't understand this
Sounds at 85 dBA can cause hearing loss if listened to for more than 8 hours. Sounds above 85 dBA can damage your hearing more quickly. For every 3-dB increase in noise levels above 85 dBA, the safe listening time is cut in half. You can, for example, listen to sounds at 85 dBA for up to 8 hours.
What is meant by decibel?The decibel (dB) is 10 times the decimal logarithm of the ratio of two variables' values. Decibels are calculated using a logarithm, which allows very large or very small relationships to be represented with a conveniently small number. The decibel, abbreviated dB, is the scale's unit. Sound intensity as a reference ( = 10 ^{ -12 } Watts per square meter.) The decibel (dB) is a logarithmic unit of measurement for sound level. It is also widely used in electronics, communications, and signals. The dB is a logarithmic measure of a ratio. Power, sound pressure, voltage, or intensity are all examples of ratios.A noise or sound level of 85 decibels is equivalent to that of a food blender, heavy traffic while driving, a noisy restaurant, or a movie theater. As you can see, we are exposed to high noise levels in a variety of situations in our daily lives.To learn more about decibel, refer to:
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How do I answer this question?
The surface area of the regular pyramid is 151.9 m².
How to find the surface area of a pyramid?The surface area of the regular pyramid can be found as follows:
surface area of the pyramid = A + 1 / 2 ps
where,
A = base areap = perimeter of the bases = slant heightTherefore,
A = 61.9 m²
p = 6 × 5 = 30 m
s = 6m
Hence,
surface area of the pyramid = 61.9 + 1 / 2 × 30 × 6
surface area of the pyramid = 61.9 + 180 / 2
surface area of the pyramid = 61.9 + 90
surface area of the pyramid = 151.9 m²
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solve this equation
[tex] \frac{33}{3} = c + 2[/tex]
Answer:
c=9
Step-by-step explanation:
[tex]11=c+2 \\ \\ c=9[/tex]
() A bookmark has an area of 160 square centimeters. Its perimeter is 56 centimeters.
What are the dimensions of the bookmark?
The dimensions of the bookmark is 14cm.
What is area and perimeter of square?The perimeter of a shape is the space surrounding it. Space inside a shape is measured by area. Learn how to compute the area and perimeter of various forms. The perimeter of a square is equal to four times the length of its side, and its area is equal to the square of that length. As a result, the square's perimeter will be as follows: perimeter = 4 x side = 4 area units. As a result, given a square's size, we can determine its perimeter.
Given data
Area = 160cm
Perimeter = 56
Area = side²
Perimeter = 4(a)
Putting values in perimeter
Perimeter = 4a
56 = 4a
a = [tex]\frac{56}{4}[/tex]
a = 14
The dimensions of the bookmark is 14cm.
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Jesse and amir were assigned the same book to read. jesse started reading on saturday, and he is reading 30 pages a day. amir didn't start until sunday, but he is reading 35 pages a day.
He will read 210 pages of the book and it will take Amir 6 days to catch up with Jesse
Day Jesse started reading: Saturday
Number of pages read by Jesse each day: 30 pages
Day Amir started reading: Sunday
Number of pages read by Amir each day: 35 pages
Let x represent the number of days Amir has been reading and y represent the number of pages he has read
Formulating the equation for Amir we get:
y = 35*x
y = 35x
The equation for Jesse will be:
y = 30*(x+1)
y = 30(x+1)
Equating both equations we get:
35x = 30(x+1)
35x = 30x +30
5x = 30
x=6
So, the number of pages read will be 210 and it will take 6 days for Amir to catch up with Jesse
Although a part of your question is missing, you might refer to this full question: Jesse and Amir were assigned the same book to read. Jesse started reading on Saturday, and he is reading 30 pages a day. Amir didn't start until Sunday, but he is reading 35 pages a day. How many days will it take Amir to catch up to Jesse, and how many pages will they each have read? Write an equation to represent the number of pages Amir has read. Use x to represent the number of days Amir has been reading and y to represent the number of pages he has read
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help with geometry please.
Answer:
Surface area: 432 Area: 576
Step-by-step explanation:
Surface area fomula: 2lh+2wl+2wh
Area formula:lh
For each event, write the sample space and tell how many outcomes there are. Roll a standard number cube. Then flip a quarter. How many outcomes are there?
The total number of outcomes is 12.
An outcome is a potential outcome of an experiment or trial in probability theory.
Each conceivable result of a specific experiment is distinct, and many results are incompatible (only one outcome will occur on each trial of the experiment). The components of a sample space are all the potential results of an experiment. There is a chance that outcomes will occur with probabilities between 0 and 1. (inclusively). In a discrete probability distribution whose sample space is finite, each result is assigned a certain probability. A continuous distribution, on the other hand, only allows non-zero probabilities to be assigned to ranges of events, with all individual outcomes having zero probability.When a number cube is rolled there are 6 distinct outcomes {1,2,3,4,5,6} = 6
Again when a quarter is flipped then there are two possible outcomes {heads , tails } = 2
The total number of outcomes = 6 × 2 = 12
Hence there are 12 distinct outcomes.
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Juan's company spent $2,350 on an event, They spent
about $1,500 on food and about $900 on entertainment,
What could the actual cost of the food and entertainment be?
work.
Show your work!!
The actual cost of the food and entertainment be $2,400.
What is defined as the actual cost?The sum of money paid to obtain a product or asset is referred to as the actual cost in accounting. The actual cost is exactly as it sounds like. This cost may be a historical, previous, or current day product cost. You may be wondering what other costs exist aside from the actual cost of a product. Keep in mind that in managerial accounting, costs are budgeted and forecasted.For the given question;
The amount spent by Juan's company = $2,350.
The amount spent of the food = $1,500.
The amount spent on entertainment = $900.
Thus, the actual amount will be;
Actual amount = food + entertainment
Actual amount = $1,500 + $900
Actual amount = $2,400.
Thus, the actual cost of the food and entertainment be $2,400.
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A box is filled with 14 blue cards, 2 brown cards, and 4 green cards. A card is chosen at random from the box. What is the probability that the card is not
brown?
Write your answer as a fraction in simplest form.
Answer:
18/20
Step-by-step explanation:There are 20 total cards and 2 are brown so answer would be 18/20.
Drag a number to each box to complete the product. Numbers may be used more than once.
0.476
4.76
47.6
476
4,760
Equation Product
476 × 0.001
0.476 × 10¹
4.76 × 10³
47.6 x 0.1
476 x 0.001 = 0.476
0.476 x 10¹ = 4.76
4.76 x 10³ = 4,760
47.6 x 0.1 = 4.76
We have to find the following products of the equations.
The basic rule for multiplication between numbers with decimal points can be described through some examples first.
Decimal point is shifted leftwards up to the power of 10 which is divided with it. Also decimal point is shifted rightwards when multiplied with powers of 10.
Now we will find the product for each equation:
For 476 × 0.001, 0.001 = 1/1000
Therefore, 476 × 0.001 = 476 × 1/1000 = 0.476 [decimal point shifted left]
For 0.476 × 10¹ = 0.476 × 10 = 4.76 [decimal point shifted right]
For 4.76 × 10³ = 4.76 x 1000 = 4760 [decimal point shifted right]
For 47.6 x 0.1 = 47.6 x 1/10 = 4.76 [decimal point shifted left]
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Any buyer of a new sports car has to pick between 2 of 5 options for seat colors and 3 of 4 options for dashboard accessories. how many different combinations of colors and dashboard options are available to this buyer?
There are 40 different combinations of colors and dashboard options available to this buyer.
Combination is a counting technique where the order of the selected items from a collection does not matter. The formula in finding the number of combinations when ‘r’ items are chosen out of a total of ‘n’ objects.
nCr = n! / [r! (n - r)!]
If there are 2 of 5 options for seat colors, then using the formula, the number of combinations for the seat color is:
5C2 = 5! / [2! (5 - 2)!]
5C2 = 120 / 12
5C2 = 10
If there are 3 of 4 options for dashboard accessories, then using the formula, the number of combinations for the dashboard accessories is:
4C3 = 4! / [3! (4 - 3)!]
4C3 = 24 / 6
4C3 = 4
Multiplying the two results will give the total number of different combinations of colors and dashboard options available.
combination = 10 x 4
combination = 40
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