Answer:
[tex]\huge\boxed{\sf 157.1 \ units^2}[/tex]
Step-by-step explanation:
Diameter = 20
Radius = Diameter/2 = 20/2 = 10
Area of semicircle:[tex]\displaystyle =\frac{\pi r^2}{2} \\\\r = 10\\\\= \frac{\pi (10)^2}{2} \\\\= \frac{100 \pi}{2} \\\\= \frac{314.2}{2} \\\\= 157.1 \ units^2\\\\\rule[225]{225}{2}[/tex]
Insert a monomial such that each expression can be rewritten as the square of a sum or the square of a difference.
0.01 b²+.....+100 c²
0.01 b²+____+100 c²
The monomial that completes the expression 0.01 b²+.....+100 c² is 2bc
How to determine the monomial that completes the expression?From the question, we have the following parameters that can be used in our computation:
0.01 b²+.....+100 c²
Complete the expression with a variable
So, we have
0.01 b² + x + 100 c²
The given terms of the expression are factors/multiples of 10
By trial and error, we make use the following representation
0.01 b² + x + 100 c² = (0.1b + 10c)²
Expand the expression
0.01 b² + x + 100 c² = 0.01 b² + 2bc + 100 c²
Evaluate the like terms
x = 2bc
Hence, the monomial is 2bc
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48.49 ÷ 0.4
Round your answer to the nearest hundredth.
Answer:
121.23
Step-by-step explanation:
48.49/0.4 = 121.225
121.225 rounding into nearest hundredth = 121.23
For the figure below, suppose
∠3 = 30°
and
∠7 = 97°.
Find the measures (in degrees) of the other angles.
∠1 =
°
∠2 =
°
∠4 =
°
∠5 =
°
∠6 =
°
∠8 =
°
[tex]\angle 1=150^{\circ}[/tex] (linear pair)
[tex]\angle 2=30^{\circ}[/tex] (vertical angles)
[tex]\angle 4=150^{\circ}[/tex] (linear pair)
[tex]\angle 5=83^{\circ}[/tex] (linear pair)
[tex]\angle 6=97^{\circ}[/tex] (vertical angles)
[tex]\angle 8=83^{\circ}[/tex] (linear pair)
1. What is the decay factor?
From 2000 to 2013, the value of the U.S. dollar was shrinking. The value of the U.S. dollar
over time v(t) can be modeled by the following formula:
1.36(0.9758)', where t is the number of years since 2000.
0.9758 is the decay factor of the model
How to determine the decay factor?Given that:
The value of the U.S. dollar over time v(t) can be modeled by the following formula:
v(t) = 1.36(0.9758)^t , where t is the number of years since 2000
The form of the exponential decay models is f(t) = ab^t
where,
a is the initial value, b is the decay factor and t is the time
Comparing f(t) = ab^t with v(t) = 1.36(0.9758)^t :
a = 1.36
b = 0.9758
Therefore, the decay factor is 0.9758
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the equation of the normal to the 2x² + 2y² -4x +4y =12 at the point (-1,1) is
To find the equation of the normal to the given curve at the point (-1,1), you can use the following steps:
Rewrite the given equation in the form "y = mx + b," where m is the slope of the curve and b is the y-intercept.
Find the slope of the curve at the point (-1,1). This can be done by taking the derivative of the equation and evaluating it at x = -1.
The slope of the normal line at the point (-1,1) is the negative reciprocal of the slope of the curve at that point. Calculate this value.
Use the point-slope formula to write the equation of the normal line in the form "y - y1 = m(x - x1)," where (x1, y1) is the point (-1,1) and m is the slope of the normal line.
Substitute the values for x1, y1, and m into the point-slope formula to obtain the final equation of the normal line.
For example, if the given equation is 2x^2 + 2y^2 - 4x + 4y = 12, you can follow these steps:
Rewriting the equation in slope-intercept form, we get: y = -x + 2
Taking the derivative of the equation, we get: y' = -1
The slope of the normal line is the negative reciprocal of the slope of the curve, which is 1/-1 = -1
Using the point-slope formula, we get: y - 1 = -1(x + 1)
Substituting the values into the point-slope formula, we get: y - 1 = -1x - 1
Thus, the equation of the normal line at the point (-1,1) is y - 1 = -1x - 1.
Find the root of the polynomial by factoring
(if you can give steps that’d be great)
Step-by-step explanation:
[tex]x + \frac{75}{4} (x) = 0[/tex]
[tex] \frac{79x}{4} = 0[/tex]
[tex]x = 0[/tex]
4
If figure ABCD is congruent to MNOP, what
is the length of PM?
6
A
F
H
D 7 C
6789
10
10
8
8
P
N
M
The length of the PM is 6 if ABCD is congruent to MNOP.
What do you mean by congruent?When it comes to geometry, two figures or objects are said to be congruent if they are the same size and shape, or if one is the mirror image of the other.
More specifically, two sets of points are said to be congruent if—and only if—they can be changed into one another by an isometry, which is a combination of rigid motions including translation, rotation, and reflection. This indicates that either object may be exactly aligned with the other object by moving and reflecting it, but not by resizing it. If we can cut out and then perfectly match up two separate plane figures on a piece of paper, they are then congruent. I'm allowed to turn the paper over.
Here both the given figures are congruent figures. So, their shape and size must be equal.
Therefore from the two figures, PM=DA
So, PM=6
Therefore, the length of the PM is 6 if ABCD is congruent to MNOP.
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[tex]\sqrt{2x-6 =x-3\\[/tex]
The value of x in the quadratic equation using mathematical operations is 4±√19
What are Quadratic EquationsTo solve this problem, we have to use some mathematical operations to find the value of x.
In this process, we have to remove the square root and solve for x. This will eventually result to a quadratic equation
In the equation given;
√(2x - 6) = x - 3
Square both sides
(√(2x - 6)² = (x - 3)²
This will eliminate the square root
2x - 6 = (x - 3)²
Open the bracket on the right hand side
2x - 6 = x² - 6x - 9
Collect like terms
x² - 6x - 9 - 2x + 6 = 0
x² - 8x - 3 = 0
Solving for x
x = 4±√19
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A local company offers you an opportunity to sell discount cards. You will have to pay the company a one-time setup fee of $320. Each card will cost you $6. How many cards would you have to sell before your average total cost per card falls to $10?
Answer:
80 cards would have to sold before your average total cost per card falls to $10
Step-by-step explanation:
To find the number of cards you would have to sell to bring the average total cost per card down to $10, you can use the following formula:
number of cards = setup fee / (average total cost per card - cost per card)
Plugging in the values given in the problem, we get:
number of cards = $320 / ($10 - $6)
Solving this equation gives us:
number of cards = $320 / $4
Dividing 320 by 4 gives us a result of 80, so you would have to sell 80 cards before your average total cost per card falls to $10
Another approach is setting it up as y = mx+b
$10 = (320 + 6x) / x
Where x is the number of cards that you need to sell.
Solving for x, we get:
$10x = 320 + 6x
4x = 320
x = 80
"Question 60
Find the probabilities below using a standard 52 card deck.
By using the concept of probability, it can be calculated that-
1) P(Ace [tex]\cup[/tex] 5) = [tex]\frac{8}{52}[/tex]
2) P(Ace [tex]\cap[/tex] 5) = 0
3) P([tex]Even^c[/tex]) = [tex]\frac{20}{52}[/tex]
4) P(Even [tex]\cup[/tex] Black) = [tex]\frac{36}{52}[/tex]
5) P(Face [tex]\cap[/tex] Diamond) = [tex]\frac{3}{52}[/tex]
What is probability?
Probability gives us the information about how likely an event is going to occur
Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.
Probability of any event is greater than or equal to zero and less than or equal to 1.
Probability of sure event is 1 and probability of unsure event is 0.
1) Number of ace card = 4
Number of '5' card = 4
P(Ace [tex]\cup[/tex] 5) = [tex]\frac{4}{52} + \frac{4}{52}[/tex]
= [tex]\frac{8}{52}[/tex]
2) P(Ace [tex]\cap[/tex] 5) = 0
3) Number of odd numbered cards = [tex]5 \times 4[/tex] = 20 (Assuming the ace is odd)
Probability of getting an odd numbered card = [tex]\frac{20}{52}[/tex]
P([tex]Even^c[/tex]) = [tex]\frac{20}{52}[/tex]
4) Number of black coloured even numbered card = 10
Number of even numbered card = 20
Number of card of black colour = 26
P(Even [tex]\cup[/tex] Black) = [tex]\frac{20}{52} + \frac{26}{52} - \frac{10}{52}[/tex]
= [tex]\frac{36}{52}[/tex]
5) Number of face cards of diamond = 3
P(Face [tex]\cap[/tex] Diamond) = [tex]\frac{3}{52}[/tex]
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1/3 + 2/3
Please help! This is due tomorrow and I need it now
Answer: 1
Step-by-step explanation:
Answer:
1 or 3/3
Step-by-step explanation:
There is a common denominator (bottom number) so you add straight across.
1+2=3 so it is 3/3, which is a whole, making it 1.
What is the value of x in the equation 2/3 (1/2×+ 12) = 1/2(1/3x +14) - 32
Answer:
Step-by-step explanation:
x = 174
what is (3z+1)+(1+7z)
Answer:
10z + 2
Step-by-step explanation:
combine the like terms
3z + 7z = 10z
1 + 1 = 2
10z + 2
Rewrite 1 1/5 using fifths
1 1/5 - 1/3
= __ /__ - 1/3
The value of mixed fraction 1(1/5) using fifths is 6/5.
How may a number be written as a mixed number?
Divide the numerator by the denominator in step 1.The quotient should be expressed as a whole number in step 2. Input the numerator and denominator as the remainder and the divisor, respectively in step 3.As an illustration, we convert 7/3 into a mixed fraction form by using the instructions provided.
[tex]1\frac{1}{5}[/tex] = [(5 * 1) + 1]/5
= (5 + 1) / 5
= 6/5
Hence, The value of mixed fraction 1(1/5) using fifths is 6/5.
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In the fall of 1996, tuition and registration fees for undergraduates at the University of California, Davis was $1411. In the fall of 2018, tuition and fees
were $14,402. Find the percent increase. Round your answer to the nearest tenth percent
% increase
To find the percent increase, we need to calculate the difference between the new tuition and fees and the old tuition and fees, and then divide this difference by the old tuition and fees and multiply by 100%.
The difference between the new tuition and fees of $14,402 and the old tuition and fees of $1411 is $14,402 - $1411 = $12,991.
The percent increase is: ($12,991/$1411) * 100% = 9.2 * 100% = 920%
Therefore, the percent increase in tuition and fees between the fall of 1996 and the fall of 2018 was 920%, rounded to the nearest tenth percent.
3.
The angles of a triangle are 120°, (x + 16)°, and x°.
What is the value of x?
Pls explain how you get the answer
The triangle has a value of x=22°.
What is a triangle?The three vertices of a triangle make it a three-sided polygon. The angles of the triangle are formed by the three sides' end-to-end connections at a point. 180 degrees is the sum of the triangle's three angles.
Having three sides, a triangle is a form. Each kind of triangle has a unique name. The size of the angles and side lengths determine what kind of triangle it is (corners). Triangles can be classified as equilateral, isosceles, or scalene depending on how long their sides are.
The sum of all the angles in a triangle must be °
120° + (x+16)° + x° = 180°
2x + 136° = 180°
2x = 180° - 136°
2x° = 44°
x = 22°
The triangle has a value of x=22°.
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✓
The principal P is borrowed and the loan's future value A at time t is given. Determine the loan's simple interest rater.
P = $6000.00, A = $6180.00, t = 1 year
% (Round to the nearest tenth of a percent as needed.)
please help proportional relationship easy needed now !!
The equations representing the proportional relationships between two variables:
k = 5 · hk = (5 / 4) · hk = (1 / 5) · hWhat are the equations of proportional relationship for each table of values?
In this problem we find three cases of tables showing proportional relationships between two variables. Proportional relationships are represented by equations of the form:
y = k · x
Where:
x - Independent variable.y - Dependent variable.k - Proportionality factor.Each table represents a proportional relationship if and only if each pair of variables has one and same proportionality factor. After a quick inspection, we find the following features:
The first table has a proportionality factor of 5. The equation is k = 5 · h.The second table has a proportionality factor of 5 / 4. The equation of k = (5 / 4) · h.The third table has a proportionality factor of 1 / 5. The equation of k = (1 / 5) · h.To learn more on proportional relationships: https://brainly.com/question/12917806
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helppp me please. i did my points but I need help on the rest
By using linear equation, it can be calculated that
New Solution #1 : (-6, 1) is a solution because when you plug it into the original equation x + 3y = -3, the equation simplifies to -3 = -3
New Solution #2: (-9, 2) is a solution because when you plug it into the original equation x + 3y = -3, the equation simplifies to -3 = -3
What is linear equation?
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Equation of line : x + 3y = -3
Putting y = 1
x + 3 [tex]\times[/tex] 1 = -3
x = -3 - 3
x = -6
Putting y = 2
x + 3 [tex]\times[/tex] 2 = -3
x + 6 = -3
x = -3 - 6
x = -9
New solutions (-6, 1) and (-9, 2)
New Solution #1 : (-6, 1) is a solution because when you plug it into the original equation x + 3y = -3, the equation simplifies to -3 = -3
New Solution #2: (-9, 2) is a solution because when you plug it into the original equation x + 3y = -3, the equation simplifies to -3 = -3
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Complete the inequality for this graph.
y < [?]
Answer: y < 2
Step-by-step explanation:
What is the area of triangle UVW?
Answer:
30 units²
Step-by-step explanation:
Triangle Area = 1/2bxh
Base (b) = 12 units
Height (h) = 5 units
let's apply the formula1/2 × 12 × 5 =
6 × 5 =
30 units²
At the beginning of each quarter, rupees 2000 is deposited in the savings account which pays an interest of 10% p.a compounded quarterly. Find the balance in the account after 5 years.
Fill in the blanks below in order to justify whether or not the mapping shown represents a function.
The mapping diagram above a function since
in where there
The mapping diagram above is a function since there are no two values in set B where there is only one mapping from Set A.
What is a function?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
In the example provided, each element in Set A is mapped to one specific element in Set B.
Set A stands for the domain, whereas Set B stands for the range. There would be exactly one value in the range for each value in the domain as a result.
Hence, the mapping diagram above is a function since there are no two values in set B where there is only one mapping from Set A.
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For each of the following equations, solve for the variable. If there are multiple solutions, separate them by a comma.
Answers should be integers, fractions, radicals, or in exponential form. No decimals!
1/7㏒ (x-1) + 3㏒ (2)
x=______
3㏑(ω+6) = 5㏑ (6)
ω=____
The solutions to the x and w variables are x = 2097153 and w = (6)⁻²/⁵
How to determine the solution to the variables?From the question, we have the following parameters that can be used in our computation:
1/7log(x - 1) = 3log(2)
3 ln(w + 6) = 5 ln(6)
Solving the equation (1), we have the following equation
1/7log(x - 1) = 3log(2)
Multiply both sides of the equation by 7
So, we have the following representation
log(x - 1) = 21log(2)
Apply the power rule of logarithm
log(x - 1) = log(2)²¹
By comparison, we have
x - 1 = (2)²¹
Evaluate the exponent
x - 1 = 2097152
So, we have
x = 2097153
Solving the equation (2), we have the following equation
3 ln(w + 6) = 5 ln(6)
Multiply both sides of the equation by 1/3
So, we have the following representation
ln(w + 6) = 5/3 ln(6)
Apply the power rule of logarithm
ln(w + 6) = ln(6)³/⁵
By comparison, we have
w + 6 = (6)³/⁵
So, we have
w = (6)⁻²/⁵
Hence, the solutions are x = 2097153 and w = (6)⁻²/⁵
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Select all the correct locations on the table.
Classify each situation as an exponential growth, exponential decay, or linear relationship.
A catering company purchased a delivery van
for $25,000. After 2 years, the value of the van
was $17,500. After 4 years, the value of the van
was $12,250.
At the beginning of the day, a laptop had 100%
battery life. After 3 hours, the laptop had 60%
battery life. After 6 hours, it had 20% battery life.
A tiger reserve had an initial population of
20 tigers. After 5 years, the population was
30 tigers. After 10 years, the population was
45 tigers.
exponential growth
exponential decay
linear
The required answer choices are (i)exponential decay (ii) linear and (iii) exponential growth
What are exponential growth and exponential decay?
Quantities that fluctuate quickly are subject to exponential growth and decay. The idea of geometric progression has been used to infer exponential growth and decay. Exponential growth or exponential decay are terms used to describe quantities that vary exponentially rather than continuously.
From question,
1) The first question is like, initially delivery van price is $25,000 after 2 years, the value of the van becomes $17,500
This means it is decaying. The difference between the initial price and after 2 years price is $7500.
To be linear, further after 2 years, or from start after 6 years, the price should be $10000. But it is given to be $12250.
Thus exponential decay.
2) In the second, Initially, a laptop had 100% battery life. After 3 hours, the laptop has 60% battery life. Thus the loss in 3 hours is (100 - 60) = 40%.
After 4 hours, the loss is (60 -20) = 40%
As the loss is the same in equal intervals of time, the decay is linear.
3) In the third one, A tiger reserve had an initial population of 20 tigers.
After 5 years the population was 30 tigers, thus the growth is (30-20) =10.
After 10 years, the population was 45 tigers. Thus the growth is (45-30) = 15.
Thus the increase is non-linear, and so is exponential growth.
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This is the question in the picture
The inequality for the value of y can be given as -1/8 < -2/3y, where y < 3/16.
What is inequality?Inequality shows relation between two expression which are not equal to each others.
Let the required number is y.
To find the inequality that represents the -1/8 is less than the product of -2/3 and number y.
The product of -2/3 and y = -2/3y
The inequality for the y can be written as,
-1/8 < -2/3y
Solve for the value of y,
1/8 > 2/3 y
3/16 > y
Or y < 3 / 16
The required inequality is -1/8 < -2/3y, where y < 3/16.
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During a sale, a store offered a 25% discount on a bed that originally sold for $890. After the sale, the discounted price of the bed was marked up by 25%. To the nearest whole number, what percent of the original price was the price after markup?
The percent of the original price was the price after markup will be 6.29%.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
During a deal, a store offered a 25% rebate on a bed that initially sold for $890. After the deal, the limited cost of the bed was increased by 25%.
The marked-up price is given as,
⇒ $890 x (1 - 0.25) x (1 + 1.25)
⇒ $890 x 0.75 x 1.25
⇒ $834
The percentage is given as,
P = [(890 - 834) / 890] x 100
P = (56 / 890) x 100
P = 0.0629 x 100
P = 6.29%
The percent of the original price was the price after markup will be 6.29%.
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Answer: 94%
Step-by-step explanation:
Find what percent of the original price this represents:
$834.375 / $890 = 0.9375
0.9375 × 100 = 93.75%
93.75% ≈ 94%
Round to the nearest whole number
The price after markup was 94% of the original price.
URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
Answer:
False
A sphere is 3 dimensional.
In a recipe for fizzy grape juice, the ratio of cups of sparkling water to cups of grape juice concentrate is 3 to 1
Answer:
Yes it is
Step-by-step explanation:
Sum of -5a + 6 and 3a + 2
Answer:
:)
Step-by-step explanation:
-5a + 6 + 3a + 2
Combine like terms:
-5a + 3a + 6 + 2
2a + 8 is your answer, you can't simplify it further
----------------------------------------------------------------------------------------------------------
If you want to solve for the a value:
-5a + 6 = 3a + 2
Subtract 2 from both sides
-5a + 6 = 3a + 2
- 2 - 2
-5a + 4 = 3a
(The +2 and -2 cancel each other out, it makes 0)
Add +5a to both sides
-5a + 4 = 3a
+5a +5a
(The -5a and +5a cancel each other out, it makes 0)
4 = 8a
Divide by 8 on both sides
4/8 (OR 1/2 OR 0.5) = a
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