The area of the shape given which is a circle is; 38.465 in²
How to find the Area of the Circle?The area of a circle is π multiplied by the square of the radius. The area of a circle(A) when the radius 'r' is given is πr².
Area = πr²
The parameters are;
radius; r = 3¹/₂ inches = ⁷/₂ inches
Thus;
Area = π * (⁷/₂)²
Area = π * 49/4
Area = 3.14 * 49/4
Area = 38.465 in²
That's the area of the circle shape given.
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product p of three numbers x ,y,and z
Answer:
p = x(y)(z)
Step-by-step explanation:
product is multiplication.
multiplication has no specific order.
Camden is working two summer jobs, making $10 per hour babysitting and making $18 per hour lifeguarding. In a given week, he can work no more than 14 total hours and must earn no less than $180. If Camden worked 9 hours lifeguarding, determine the minimum number of whole hours babysitting that he must work to meet his requirements.
If there are no possible solutions, submit an empty answer.
Answer: 2 hours babysitting
Step-by-step explanation:
18 x 9 = 162
180-162= 18
meaning he'd have to work 2 hours babysitting to get to meet his requirement.
hours used = 11
hours left= 3
Use the distributive property to evaluate 4(2x - 1) when x = 6.
O44
04
40
O 47
The value of the expression 4(2x - 1) when x = 6 is 44. Option A
What are algebraic expressions?Algebraic expressions are defined as expressions that are made up of coefficients, terms, variables, factors and constants.
They are also identified with arithmetic operations, such as;
AdditionMultiplicationDivisionSubtractionBracketParenthesesFrom the information given, we have that;
4(2x - 1)
expand the bracket, we get;
8x - 4
Substitute the value of x as , we have;
8(6) - 4
Multiply
48 -4
Subtract the values
44
Hence, the value is 44
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Can someone Solve this?
- 2 ( m + 1 ) = 10
Answer:
m = -4
Step-by-step explanation:
-2 ( m + 1 ) = 10
( m + 1 ) = 10 / -2
m + 1 = -5
m = -4
What is the approximate horizontal distance between Amelia and Brendon? Explain your reasoning
The approximate angle of elevation if Brendan looks up at the tower is 20.03°
What is an elevation?The angle of elevation in math is "the angle formed between the horizontal line and the line of sight when an observer looks upwards is known as an angle of elevation".
We know that, sinθ = opposite/hypotenuse
Here, sinx° = 50/146
sinx° =0.34246575342
x = sin⁻¹(0.34246575342)
x = 20.0271724581
x = 20.03°
Therefore, the approximate angle of elevation if Brendan looks up at the tower is 20.03°
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"Your question is incomplete, probably the complete question/missing part is:"
Amelia and Brendon are both on the ground looking at The top of a tower point D. Amelia is at point A and Brendan is at point B.
What is the approximate angle of elevation in Brendan looks up at the tower explain your reasoning.
Which of the following complexe numbers is equal to (4 + 3i)(5 - 2i)?
20 + i
20+6i
26 + i^2
26 + 7i
Answer:
The product of (4 + 3i)(5 - 2i) can be calculated using the distributive property:
(4 + 3i)(5 - 2i) = 4 × 5 + 4 × -2i + 3i × 5 + 3i × -2i
= 20 - 8i + 15i - 6i^2
= 20 + 7i - 6(-1)
= 26 + 7i
So the answer is (4) 26 + 7i.
I believe the answer is (d) 26 + 7i.
Sue has 18 sweets.
Tony also has 18 sweets.
Sue gives Tony x sweets.
Sue then eats 5 of her sweets.
Tony then eats half of his sweets.
Write expressions for the number of sweets Sue and Tony now have.
Sue:
Tony:
Answer:
Step-by-step explanation:
18-5=13
18-9=9
our jobs are to be done on four different machines. The cost in rupees of
producing ith on the jth machine is given below. Assign the jobs to different machines
so as to minimise the total cost.
Jobs
M1
M2
M3
M4
J1
15
11
13
15
J2
17
12
12
13
J3
14
15
10
14
J4
16
13
11
17
The total optimal solution based on the information will be 49 rupees.
How to calculate the valueHere, four jobs and four machines are given, with the assignment matrix.
Find out the each row minimum element and subtract it from that row
Find out the each column's minimum element and subtract it from that column.
This assignment problem is being solved using Hungerian Method as the optimal solution is:
J1 to M2, J2 to M4, J3 to M1 and J4 to M3. The total optimal cost is:
= 11 + 13 + 14 + 11
= 49 rupees
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You made a big batch of slime for all of your friends. You have 7.2 cups of slime and 36 containers. What is the unit rate? (How much is in each container?) Enter your answer as a decimal in the box. The units are cups per container. Do not put the units.
Using the unitary method, we found that the unit rate of slime is 0.2 cups per container.
What is meant by the unitary method?
The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, and then multiplying that value to determine the required value. Recognizing the units and values is crucial when using the unitary technique to a problem.
Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. The unitary approach must be applied whenever we need to determine the ratio of one quantity to another.
Given,
Number of cups of slime = 7.2
Number of containers = 36
Unit rate = Amount of slime in each container
Using the unitary method we can find the unit rate.
7.2 cups = 36 containers
1 container = 7.2/36 = 0.2 cups.
Therefore using the unitary method, we found that the unit rate of slime is 0.2 cups per container.
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If f(x) = 2x² - x - 6 and g(x) = x² - 4, find f(x) = g(x).
OA.
B.
C.
2x+3
2
2x-3
#+2
2x+3
#+2
O D. 22-2
Jhayq
Answer:
Step-by-step explanation:
To find the value of x such that f(x) = g(x), we need to set the two functions equal to each other and solve for x.
First, let's define the variables:
f(x) = 2x² - x - 6 is a quadratic function with x as the variable.
g(x) = x² - 4 is also a quadratic function with x as the variable.
Now, to find the value of x such that f(x) = g(x), we set the two functions equal to each other:
2x² - x - 6 = x² - 4
Next, we simplify this equation by subtracting x² from both sides:
x² + x - 10 = 0
This is a quadratic equation, which we can solve for x using either the quadratic formula or by factoring.
Let's try factoring:
x² + x - 10 = (x + 5)(x - 2) = 0
So either x + 5 = 0 or x - 2 = 0. Solving for x, we find that:
x = -5 or x = 2
These are the two values of x such that f(x) = g(x).
A bag of garden soil weighs 42 pounds and holds 2 cubic feet. Find the weight of 15 bags in kilograms and the (((volume of 15 bags in cubic yards.)))
Answer:
he weight of 15 bags of garden soil in kilograms is 285.75 kilograms, and the volume of 15 bags in cubic yards is 1.111 cubic yards.
Step-by-step explanation:
To find the weight of 15 bags in kilograms, we can first convert the weight of one bag from pounds to kilograms and then multiply by the number of bags:
1 pound = 0.453592 kilograms
So the weight of one bag in kilograms is:
42 pounds * 0.453592 kilograms/pound = 19.05 kilograms
The weight of 15 bags in kilograms is:
15 bags * 19.05 kilograms/bag = 285.75 kilograms
To find the volume of 15 bags in cubic yards, we can first convert the volume of one bag from cubic feet to cubic yards and then multiply by the number of bags:
1 cubic yard = 27 cubic feet
So the volume of one bag in cubic yards is:
2 cubic feet / 27 cubic feet/cubic yard = 2 / 27 = 0.07407 cubic yards
The volume of 15 bags in cubic yards is:
15 bags * 0.07407 cubic yards/bag = 1.111 cubic yards
Therefore, the weight of 15 bags of garden soil in kilograms is 285.75 kilograms, and the volume of 15 bags in cubic yards is 1.111 cubic yards.
A bank is offering 2.5% simple interest on a savings account. If you deposit $5000, how much interest will you earn in 4 years?
• $50,000
• $500
• $125
• $12,500
[tex] \large \blue{ \large\tt{C ) \$500}}[/tex]
_____________
[tex] \: [/tex]
Given:-
[tex] \rm{Principal= \bold {5000}}[/tex][tex] \rm{Time= \bold 4}[/tex][tex] \rm{Intrest Rate= \bold { 2.5}}[/tex][tex] \: [/tex]
By using formula:-
[tex] \boxed{ \rm{ \pink{Simple \: interest= \frac{Principal × Time × Rate}{100}}}}[/tex]
[tex] \: [/tex]
Solution:-
[tex] \rm{SI = \frac{PTR}{100} }[/tex][tex] \: [/tex]
[tex] \rm{SI= \frac{50 \cancel{00}×4×2.5}{1 \cancel{00}} }[/tex][tex] \: [/tex]
[tex] \rm{SI=50×4×2.5}[/tex][tex] \: [/tex]
[tex] \underline{\boxed{ \rm{ \red{SI= 500}}}}[/tex][tex] \: [/tex]
hope it helps!:)
Answer: the answer is c.$500 hope that helps !
Step-by-step explanation: I took the test
The inside diameter of a randomly selected piston ring is a random variable with mean value 11 cm and standard deviation 0.02 cm. Suppose the distribution of the diameter is normal. (Round your answers to four decimal places.)
(a) Calculate P(10.99 ? X ? 11.01) when n = 16.
(b) How likely is it that the sample mean diameter exceeds 11.01 when n = 25?
a) P(10.99 ≤ X ≤ 11.01) = 0.9544
b) Probability that the sample mean diameter exceeds 11.01 when n = 25 is 0.0062.
We are given the following in the question:
Mean, μ = 11 cm
Standard Deviation, σ = 0.02 cm
We are given that the distribution of diameter is a bell-shaped distribution that is a normal distribution.
Formula: z = (x - μ)/σ
a) P(10.99 ≤ X ≤ 11.01 when n = 16)
Standard error due to sampling = σ/n = 0.02/√16 = 0.005
P(10.99 ≤ X ≤ 11.01) = P((10.99 - 11)/0.005 ≤ z ≤ (11.01 - 11)/0.005)
= P(-2 ≤ z ≤ 2) = 0.9772-0.0228
= 0.9544 = 95.44%
b) P(sample mean diameter exceeds 11.01 when n = 25)
Standard error due to sampling = σ/n = 0.02/√25 = 0.004
P(x > 11.01) = P(z > (11.01 - 11)/0.004) = P(z > 2.5)
= 1 - P(z ≤ 1) = 1 - 0.9938 = 0.0062 = 0.62%
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Graph the function f(x) = -x² - 2. Complete the table of function values below. x f(x) -2 -1 0 1 2 Use the graphing tool to graph the function.
The graph of the quadratic function is on the image at the end.
How to graph the quadratic function?Here we want to graph the quadratic function:
f(x) = -x² - 2
To do so, we can complete the table of values by evaluating the function.
if x = ±2 then:
f(±2) = -(±2)² - 2 = -4 - 2 = -6
if x = ±1
f(±1) = -(±1)² - 2 = -1 - 2 = -3
if x = 0
f(0) = -(0)² - 2 = - 2 = -2
Then we have the points:
(-2, -6), (-1, -3), (0, -2), (1, -3), (2, -6)
Now just graph these points and connect them with a curve. The graph of the parabola is below.
In the last several weeks, 66 days saw rain and 98 days saw high winds. In that same time period, 31 days saw both rain and high winds. How many days saw either rain or high winds?
133 days saw either rain or high winds.
What is Probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
Example: If an experiment has 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event will be as follows:
Probability(Event) = Favorable Outcomes/Total Outcomes = x/n
P(r) = 66 days
P(w) = 98 days
P(both) = 31 days
P(r or w) = P(r) + P(w) - P(both)
P(r or w) = 66 + 98 - 31
P(r or w) = 133 days
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One cubic foot holds 7.48 gallons of water, and 1 gallon of water weighs 8.33 pounds. How much does 2.2 cubic feet of water weigh:
In pounds?
In tons?
So far I Havn't received the correct answer yet.
1/4 (8x plus 2) = 20
Answer:
x = 9.75
Step-by-step explanation:
1 / 4 * ( 8x + 2) = 20
( 8x + 2) = 20 / (1/4)
8x + 2 = 20 * 4
8x + 2 = 80
8x = 78
x = 9.75
Answer:
x=39/4 (39 over 4 as a fraction)
Scenario #1: Raul.
raul is a saver. he sets aside $100 per month during his career of 40 years to prepare for retirement. He does not like the idea of investing because he prefers to minimize his risk as much as possible so he puts his money in a savings account, which earns 1.5% interest per year.
1. what is the total balance in the account after 40 years?
2. how much of a total did Raul contribute himself?
3. how much money did Raul make through compound interest in this savings account?
4. identify one way Raul could have increased the total amount of money he made over 40 years. Explain your reasoning..
After 40 years, the account has a total balance of $49.450.80.
What is an interest?Any loans or borrowings come with interest. the portion of the loan's value that lenders use to calculate interest. By lending money (via a bond or certificate of deposit, for instance), or by depositing funds into an interest-bearing bank account, consumers can earn interest.
here, we have,
Let's assume that he starts with $0 in the account and makes a monthly contribution of $100 for 40 years, which is equal to 40 x 12 = 480 months.
The total contributions would be $100 x 480 = $48,000.
The interest earned on the account balance can be calculated as follows:
Interest = Account balance * Interest rate
At the end of each year, the interest is added to the account balance. So, after 40 years, the balance would be:
Year 1: $48,000 * 1.5% = $720
Balance = $48,000 + $720 = $48,720
Year 2: $48,720 * 1.5% = $730.80
Balance = $48,720 + $730.80 = $49,450.80
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Multiply the following radicals and simplify your answer.
2√6⋅−3√12
what is the area of this polygon?
Answer:
27.5 square units
Step-by-step explanation:
You want to know the area of the composite shape shown in the graph.
CompositionThe shape can be decomposed into a parallelogram and a triangle. Each has the same base, 5 units.
The parallelogram has a height of 3 units, so its area is ...
A = bh
A = (5)(3) = 15 . . . . square units
The triangle has a height of 5 units, so its area is ...
A = 1/2bh
A = 1/2(5)(5) = 12.5 . . . . square units
The total area of the figure is the sum of the areas of its parts:
total area = (15 units²) +(12.5 units²) = 27.5 units²
The area of the polygon is 27.5 square units.
The ratio of horizontal distance to height of the ramp is 15:1. A builder has a roll of nonslip rubber mat that is 15 feet long. Does he have enough forever to cover the Ramp completely?
Answer:
No. The length of the ramp is [tex]\sqrt{226[/tex] The rubber mat will be too short
Step-by-step explanation:
There are marbles of four different colors in a bag. The
ratio of red to white to blue marbles is 3:4:5. There are half
as many green marbles as there are blue marbles. What is
the least possible number of marbles in the bag?
(A) 12
(B) 24
(C) 29
(D) 58
Answer:
(C) 29
Step-by-step explanation:
Which of the following equations listed below are linear equations?
Only Equation I is a linear equation. A linear equation is defined as an equation where the highest power of the variable is 1, and the relationship between the variables is a straight line.
What is Straight line?
A straight line is a type of geometric shape that is defined as a line with no curvature, extending infinitely in both directions. In other words, it is a one-dimensional object that extends indefinitely without bending or curving. Straight lines are often represented mathematically as y = mx + b, where m is the slope (or gradient) of the line and b is the y-intercept.The slope determines the steepness of the line, and the y-intercept determines where the line crosses the y-axis. Straight lines play a crucial role in mathematics, especially in geometry and linear algebra.
Only Equation I is a linear equation.
A linear equation is defined as an equation where the highest power of the variable is 1, and the relationship between the variables is a straight line. In Equation I, P is equal to 4 times s, so the highest power of the variable (s) is 1, making this a linear equation.
In Equation II, the right-hand side of the equation contains a single constant ($3), not a variable, and therefore it is not a linear equation.
Equation III is not a linear equation because it is just a constant equal to 2 and does not contain a variable.
So the answer is: 1. Equation I, only.
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In the spinner below, each sector is equal in size.
If you spin the spinner 7 times, what is the prediction for the number of times it will not land on blue?
B
4
5
6
7
The number of times it is not land on the blue color sector is 7-1 = 6
What is a probability?A probability is defined as the ratio to the number of required outcomes to the total number of outcomes of an event.
The spinner is divided into 7 sectors, in which each sector is equal in size.
Among 7 sectors two of of them are blue in color.
We have to calculate that how many times the spinner not landing on the blue color sector.
For that we have to calculate the possible outcome for the blue color sector for 1 spin.
For 1 spin , the number of possible outcomes = 7.
Number of required outcomes = 2.
Probability of number of spins on blue sector for 1 spin = 2/7.
Probability of number of spins on blue sector for 7 spin = 7*(2/7) = 2.
Standard deviation = [tex]\sqrt{\frac{2}{7} *\frac{5}{7} }[/tex]= 0.4518.≅0.452.
Standard error=root(7)*0.452= 1.19≅1.2
Expected value =2-1.2 = 0.8 ≅1
Therefore the expected value is 1.
Number of times it will land on the blue color sector is 1.
Hence, the number of times it is not land on the blue color sector is 7-1 = 6.
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Find the average rate of change of the function on the intervals specified for a real number h F(x) =6x^2 + 5. On [ x,x+h]
Step-by-step explanation:
The average rate of change of a function on an interval [x, x + h] is given by the formula:
(F(x + h) - F(x)) / h
For the function F(x) = 6x^2 + 5, the average rate of change on the interval [x, x + h] is:
(F(x + h) - F(x)) / h = (6(x + h)^2 + 5 - (6x^2 + 5)) / h = (6(x^2 + 2xh + h^2) - 6x^2 + 5) / h = (6(2xh + h^2)) / h = (12xh + 6h^2) / h
So the average rate of change of the function on the interval [x, x + h] is (12xh + 6h^2) / h for a real number h.
Find the exact value of x
Answer:
When it comes to right trangles, to find the value of x, what ever 9 plus x is, it is equal to 24.
You want to subtract 9 and 24 to get the x value:
24 - 9 = 15
x = 15
Step-by-step explanation:
Hope it helps! =D
Hi there, here's your answer:
Given a right angled triangle
With the hypotenuse as 24 units and one of the legs as 9 units
To find:
The 3rd side denoted as 'x'
Solution:
We use Pythagoras Theorem:
[tex]a^2 + b^2 = c^2[/tex]
Where a and b are the legs and c is the hypotenuse.
We know the value of c and b
And a = x
Thus,
[tex]x^2 = c^2 - b^2[/tex]
[tex]x^2 = 576 - 81\\[/tex]
[tex]== > x^2 = 495\\[/tex]
Or
[tex]x = \sqrt{495} = 3\sqrt{55} = 22.248[/tex] units
Hope it helps! Please mark as Brainliest!
Which represents the solution to the inequality 5.1(3+2.2x)>-14.25-6(1.7x+4)?
X=<-2.5
x>2.5
(-2.5,~)
(-~,2.5)
Step-by-step explanation:
Hope it helps :) #CarryOnLearning
Complete the sentence below.
0.075 is a hundred times smaller than
Answer:
0.075 is a hundred times smaller than 7.5
Step-by-step explanation:
How many pounds are in 1
1⁄2 pounds and 8 ounces?
There are
pounds in 1 pounds and 8 ounces.
The solution is
n ID:
The number of pounds in [tex]1\frac{1}{2}[/tex] pounds and and 8 ounces is 2 pounds.
What is Unit of Measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
We know that 1 pound = 16 ounces.
As there are [tex]1\frac{1}{2}[/tex] pounds=1.5×16= 24 ounces.
The total number of ounces in [tex]1\frac{1}{2}[/tex] pounds and 8 ounces is
24+8
32 ounces.
Now let us convert Ounces to pounds.
we divide the number of ounces by 16.
Therefore, 32 ounces is equal to 32/16 = 2 pounds.
Hence, 2 pounds will be there in [tex]1\frac{1}{2}[/tex] pounds and 8 ounces
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Talking on the telephone causes cancer.
6. There are marbles of four different colors in a bag. The
ratio of red to white to blue marbles is 3:4:5. There are half
as many green marbles as there are blue marbles. What is
the least possible number of marbles in the bag?
(A) 12
(B) 24
(C) 29
(D) 58
Answer:
(C) 29
Step-by-step explanation:
Answer:
the least possible number of marbles in the bag is 12.
Step-by-step explanation:
As for the question about the marbles, let's call the number of red marbles "x". Then the number of white marbles is 4x, the number of blue marbles is 5x, and the number of green marbles is (1/2) * 5x = 2.5x.
The total number of marbles in the bag is x + 4x + 5x + 2.5x = 12.5x.
To find the least possible number of marbles, we need to find the smallest possible value of x, which will give us the smallest total number of marbles. Since x represents the number of red marbles, it must be a positive integer. The smallest positive integer value of x is 1.
So, if there is one red marble, there are 4 white marbles, 5 blue marbles, and 2.5 green marbles. The total number of marbles in the bag is 1 + 4 + 5 + 2.5 = 12.5.
Therefore, the least possible number of marbles in the bag is 12.