The final expression is:
[tex]18x + 4\sqrt{3x} - 10[/tex]
To multiply the given expression, we'll use the distributive property (also known as FOIL):
[tex](2\sqrt{3x}-2)(3\sqrt{3x}+5 )[/tex]
1. Multiply the first terms: [tex](2\sqrt{3x})(3\sqrt{3x}) = 6(3x) = 18x[/tex]
2. Multiply the outer terms: [tex](2\sqrt{3x})(5) = 10\sqrt{3x}[/tex]
3. Multiply the inner terms: [tex](-2)(3\sqrt{3x}) = -6\sqrt{3x}[/tex]
4. Multiply the last terms: [tex](-2)(5) = -10[/tex]
Now, combine the terms:
[tex]18x + 10\sqrt{3x} - 6\sqrt{3x} - 10[/tex]
Combine like terms (10√(3x) and -6√(3x)):
[tex]18x + 4\sqrt{3x} - 10[/tex]
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according to census the total number of male and female was 88,51,84,692, if number of male was 45,40,34,570what was the number of number of female population
According to census the total number of male and female was 88,51,84,692, if number of male was 45,40,34,570 the number of female population is 43,11,50,122.
To find the wide variety of girl population, we will subtract the quantity of male population from the full population.
Total population = 88,51,84,692
Number of male = 45,40,34,570
Number of female = Total population - Number of male
= 88,51,84,692 - 45,40,34,570
= 43,11,50,122
Therefore, the number of female population is 43,11,50,122.
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Please help math probabilities! ASAP 20 points and give brainliest!
Answer:
(1) = 1/3
(2) = 1/2
(3) = .14
Step-by-step explanation:
(1)
two number cubes are rolled:
probability that the first lands on a number less than 5 = 4/6 = 2/3
probability that the second lands on an even number = 3/6 = 1/2
probability for both number cubes = 2/3 * 1/2 = 2/6 = 1/3
(2)
tree diagram:
first coin second coin third coin
H H HHH
HHT
T HTH
HTT
T H THH
THT
T TTH
TTT
Theoretical probability of heads coming up exactly 2 times in 3 coin flips
= 4/8 = 1/2
(3)
probability that the first character is a letter = 1/7 = .1428
decimal rounded to the nearest hundredth = .14
Question
Given the ordered pairs below, determine which are solutions to the inequality x + y > 7.
(8, 7), (-4, 8), (−1, 8), (2, 3), (3, 5)
Enter your answer as a list separated by commas.
Answer:
(8,7) and ( 3,5)
Step-by-step explanation:
(8, 7):
8 + 7 = 15, which is greater than 7. So, (8, 7) is a solution.
(-4, 8):
-4 + 8 = 4, which is not greater than 7. So, (−4, 8) is not a solution.
(−1, 8):
-1 + 8 = 7, which is not greater than 7. So, (−1, 8) is not a solution.
(2, 3):
2 + 3 = 5, which is not greater than 7. So, (2, 3) is not a solution.
(3, 5):
3 + 5 = 8, which is greater than 7. So, (3, 5) is a solution.
Based on these evaluations, the correct solutions to the inequality x + y > 7 are: (8, 7), (3, 5).
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Which expression represents a cube root of 1 + i?
OVE (cos()+ i sin (24))
OVE (cos (37) + i sin (3))
/
O & (cos (4) + i sin (24))
V2 (cos (37) + 1 sin (37))
Answer:c
Step-by-step explanation is va cuz when your multiply:
Answer:
[tex]\sqrt[6]{2}\left(\cos\left(\frac{3\pi}{4}\right)+i\sin\left(\frac{3\pi}{4}\right)\right)[/tex]
Step-by-step explanation:
The analysis is as attached below.
What is the shaded area
Answer:
4,788
Step-by-step explanation:
Do you do college tests on gogle forms?
The shaded area is the total minus the unshaded. The total area is ( 8 * 12 ) * ( 5 * 12 ) or 96 * 60 = 5760. The unshaded area is 27 times 36, which is 972. Note that the picture is not to scale.
Use the information to complete the task.
A store wants to sell 5 kilograms of oranges in one week. The store has sold 12 kilograms of oranges so far. How many more kilograms of
oranges does the store need to sell?
Make an equation to show the number of kilograms of oranges that the store needs to sell. Move numbers and a symbol to the blanks to
make the equation. If there is no whole number, put a 0 in the first box.
-08
0
1
2
5
7
1²
8
711
10
The equation representing the number of kilograms of oranges that the store needs to sell is: Remaining kilograms = -7 kg.
To determine the number of kilograms of oranges that the store still needs to sell, we can subtract the amount of oranges already sold from the target amount of oranges.
Let's denote the target amount of oranges as T and the amount of oranges already sold as S.
According to the information given, the store wants to sell 5 kilograms of oranges in one week, so T = 5 kg.
The store has already sold 12 kilograms of oranges, so S = 12 kg.
To find the remaining amount of oranges that the store needs to sell, we subtract S from T:
Remaining oranges = T - S
Substituting the values, we have:
Remaining oranges = 5 kg - 12 kg
Calculating the difference, we get:
Remaining oranges = -7 kg
The result is -7 kg, indicating that the store has sold more oranges (12 kg) than the target amount (5 kg). Therefore, the store needs to sell an additional 7 kilograms of oranges to reach its target.
In the equation form, we can write it as:
Remaining kilograms = Target kilograms - Sold kilograms
= 5 kg - 12 kg
= -7 kg
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If the cost of my building is 85,000, my scrap value is 7,500 and the expected life is 31.5 years. What is the depreciation for one month. I'd like the answer and the formula.
205 was not the answer.
The depreciation for one month is approximately $205.03.
To calculate the depreciation for one month, we can use the straight-line depreciation method. The formula for straight-line depreciation is:
Depreciation per period = (Initial cost - Scrap value) / Expected life
Given that the cost of the building is $85,000, the scrap value is $7,500, and the expected life is 31.5 years, we can plug these values into the formula:
Depreciation per period = ($85,000 - $7,500) / 31.5
Simplifying the equation, we get:
Depreciation per period = $77,500 / 31.5
Dividing $77,500 by 31.5, the depreciation per period is approximately $2,460.32.
To find the depreciation for one month, we need to divide this amount by 12 (since there are 12 months in a year):
Depreciation per month = $2,460.32 / 12
Therefore, the formula for calculating the depreciation for one month using the straight-line method is: Depreciation per month = (Initial cost - Scrap value) / (Expected life in years * 12 months).
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Find the component form of AB with initial point A(8, -2) and terminal point B(-2, -2).
The component form of AB with initial point A(8, -2) and terminal point B(-2, -2) is (-10, 0).
To find the component form of vector AB with initial point A(8, -2) and terminal point B(-2, -2), we need to subtract the coordinates of point A from the coordinates of point B.
Let's calculate the components:
The x-component of AB is obtained by subtracting the x-coordinate of point A from the x-coordinate of point B:
x-component = x-coordinate of B - x-coordinate of A
= -2 - 8
= -10
The y-component of AB is obtained by subtracting the y-coordinate of point A from the y-coordinate of point B:
y-component = y-coordinate of B - y-coordinate of A
= -2 - (-2)
= -2 + 2
= 0
In vector notation, we can represent vector AB as AB = (-10, 0), where the x-component represents the horizontal displacement and the y-component represents the vertical displacement from point A to point B.
Geometrically, the vector AB can be visualized as the directed line segment from point A to point B, with a horizontal displacement of -10 units and no vertical displacement (0 units). The negative sign indicates that the direction of AB is from right to left along the x-axis.
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1.1.3. How many litres of milk does Lihle need to make 120 cupcakes? (2)
Lihle would need 30 liters of milk to make 120 cupcakes.
To determine the amount of milk Lihle needs to make 120 cupcakes, we can calculate the total milk requirement by multiplying the milk quantity per cupcake by the number of cupcakes.
Given that the recipe requires 250 milliliters (ml) of milk per cupcake, we can proceed with the calculation:
Convert milliliters to liters:
Since there are 1,000 milliliters in a liter, we divide 250 ml by 1,000 to get the milk quantity per cupcake in liters, which is 0.25 liters.
Multiply the milk quantity per cupcake by the total number of cupcakes: Multiply 0.25 liters (milk per cupcake) by 120 cupcakes.
0.25 liters/cupcake [tex]\times[/tex] 120 cupcakes = 30 liters.
Therefore, Lihle would need 30 liters of milk to make 120 cupcakes in a US curriculum class.
It's important to note that this calculation assumes the given milk requirement of 250 milliliters per cupcake and does not consider any other ingredients or variations in the recipe.
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The complete question may be like: Assuming that the recipe requires 250 milliliters (ml) of milk per cupcake, how many liters of milk does Lihle need to make 120 cupcakes in a US curriculum class?
El resultado de la operación X= 2/3+4/5+6/7+1/9
Hola!
2/3 + 4/5 + 6/7 + 1/9
= 6/9 + 4/5 + 6/7 + 1/9
= 7/9 + 4/5 + 6/7
= 7/9 + 28/35 + 30/35
= 7/9 + 58/35
= 245/315 + 522/315
= 767/315
Brothers Jason and Neil go out for pizza. Jason chooses a rectangular piece of pizza measuring 10 cm by 15 cm. Neil’s piece will be cut from a circular pizza with diameter 30 cm. Neil wants his piece to be the same size as Jason’s. What angle should be made at the centre of the pizza?
The angle at the center of the circular pizza should be approximately 240.01° to make Neil's piece the same size as Jason's rectangular piece.
To determine the angle that should be made at the center of the circular pizza to obtain a piece the same size as Jason's rectangular piece, we need to compare the areas of the two shapes.
The area of Jason's rectangular piece is given by length times width, which is 10 cm × 15 cm = 150 cm².
The area of Neil's circular piece is given by the formula for the area of a circle, which is π times the square of the radius (A = πr²). Since the diameter is 30 cm, the radius is half of that, which is 15 cm. Thus, the area of Neil's piece is π × (15 cm)² =225π cm².
To make Neil's piece the same size as Jason's, we set up the equation:
150 cm² = 225π cm²
Now we solve for π:
π = 150 cm² / (225 cm²)
π ≈ 0.6667
To find the angle, we use the relationship between angles and the fraction of the circle's circumference they cover. Since π represents the fraction of the circumference, the angle is:
Angle = π × 360° ≈ 0.6667 × 360° ≈ 240.01°
Therefore, the angle at the center of the circular pizza should be approximately 240.01° to make Neil's piece the same size as Jason's rectangular piece.
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Does the series converge or diverge? If it converges, what is the sum? Show your work.
Step-by-step explanation:
This is a geometric series where our common ratio is -1/2, and a is -4
Since r is less than -1, this series converges so
The sun is
[tex] \frac{ - 4}{1 + 0.5} [/tex]
[tex] \frac{ - 4}{1.5} = - \frac{8}{3} [/tex]
The sum is -8)3
Given the circle below with chords OP and QR. Find the length of PS. Round to
the nearest tenth if necessary.
Q
20
39
S
22
R
The value of segment SP in the circle is 13.4.
Given is a circle with chords OP and QR, intersecting S, where QS = 19, QS = 15 and SR = 17 we need to find the value of SP,
To find the value of SP, we can use the property of intersecting chords in a circle, which states that when two chords intersect inside a circle, the product of the segments of one chord is equal to the product of the segments of the other chord.
In this case, we have two chords OP and QR intersecting at point S. Let's denote the lengths of the segments as follows:
QS = 19
QS = x (where S is the intersection of QR and OP)
SR = 17
SP = y (the segment we want to find)
According to the property mentioned above, we have:
QS × QS = QR × SR
15 × 17 = 19 × SP
SP = 15 × 17 / 19
SP = 13.4
Hence the value of segment SP in the circle is 13.4.
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Helppp meee Pleaseee
Answer:
4
Step-by-step explanation:
I like to use the FOIL method! I've attached a quick picture of how it works below, but basically you multiply the first terms. Next, multiply the outside/outer terms. Then, multiply the inside/inner terms. Lastly, you multiply the last terms.
In this question, the binomial is (x + 2)².
You can expand this to be (x + 2)(x + 2).
When you expand it using the FOIL method, you get x times x, which is x².
Next, the outside/outer terms are x and 2, which is 2x.
Then, you multiply the inside/inner terms 2 and x, which is 2x.
Last, you multiply the last terms, which are 2 and 2, which is 4.
When you put them together, it looks like this:
x² + 2x + 2x + 4.
You can simplify this to x² + 4x + 4.
So your answer is 4.
Which transformation represents a reflection over the y = × line?
A. (x, y) - (-x, y)
B. (x, y) -+ (-x, -y)
C. (x,y) → (y, x)
D. (x, y) -+ (y, -x)
The transformation represents a reflection over the y = × line.
A. (x, y) → (-x, y)
A reflection over the y-axis is a transformation that flips a point or shape across the vertical line y = 0.
This means that points on the right side of the y-axis will be reflected to the left side, and vice versa.
Let's examine each option to determine which one represents a reflection over the y-axis.
A. (x, y) → (-x, y):
This transformation reflects the point across the y-axis.
For example, if we have a point (3, 2), after applying this transformation, it becomes (-3, 2).
This represents a reflection over the y-axis.
B. (x, y) → (-x, -y):
This transformation not only reflects the point across the y-axis but also flips it vertically.
For example, if we have a point (3, 2), after applying this transformation, it becomes (-3, -2).
This represents a reflection over the y-axis.
C. (x, y) → (y, x):
This transformation swaps the x and y coordinates of a point, which does not represent a reflection over the y-axis.
Instead, it represents a 90-degree rotation of the point.
D. (x, y) → (y, -x):
This transformation swaps the x and y coordinates of a point and negates the new x-coordinate.
It does not represent a reflection over the y-axis.
Instead, it represents a 90-degree rotation of the point in the counterclockwise direction.
Based on the explanations above, both options A and B represent a reflection over the y-axis.
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You will need ____ ml of the 90%
The required volume of 90% alcohol mixture required to prepare the 40% alcohol solution is 33.33mL
Proportion of mixtureVolume of 30% mixture = 300mL
Volume of 90% mixture = y
Percentage of alcohol solution needed = 40%
300(0.3) + y(0.9) = 40%
300(0.3) + 0.9y = 0.4(300)
90 + 0.9y = 120
Collect like terms
0.9y = 120 - 90
0.9y = 30
Divide both sides by 0.9 to isolate y
y = 30/0.9
y = 33.33 mL
Therefore, the volume of 90mL alcohol solution required to make the 40% alcohol mixture is 33.33mL.
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What is the value of the rational expression below when x is equal to 5? 15-x x-10 A. 10 B. -2 C. -10 D. 2
The correct answer is B. -2.
To evaluate the rational expression (15-x) / (x-10) when x is equal to 5, we substitute 5 for x in the expression:
(15 - 5) / (5 - 10)
Simplifying further:
(10) / (-5)
The simplified expression is -2.
Therefore, the value of the rational expression when x is equal to 5 is -2.
The correct answer is B. -2.
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53000 divided by ? = 53
Answer:
1000
Step-by-step explanation:
53*1000-53000 so it is correct answer
Hello!
[tex]\underline{\Large \textbf{Formula:}}\\\\\sf ~a\div~b=c\\\\b = \dfrac{a}{c} \\\\\\\underline{\Large \textbf{Application:}}\\\\ 53000~ \div~x~=~53\\\\x = \dfrac{5300}{53} \\\\x = 100\\\\\\\underline{\Large \textbf{Explanation:}}\\\\\\sf ~a\div~b=c\\\\\sf ~a\div~b~\times~b=c~\times~b\\\\a = c~\times~b\\\\a ~\div~c= c~\times~b~\div~c\\\\b = \dfrac{a}{c}\\\\\\\underline{\Large \textbf{Answer:}}\\\\\boxed{\Large \textbf{the number is 100}}[/tex]
Is r = 6 a solution to the inequality below? 10 < r
Answer:
No
Step-by-step explanation:
10 is not less than 6, so 10 < r when r=6 is not true.
The sum of the reciprocals of two consecutive even integers is 9/40
This can be represented by the equation shown.
1/x +1/x+2 =9/40
Use the rational equation to determine the integers. Show all work.
Answer:
Only integer solution is x=8
Step-by-step explanation:
[tex]\displaystyle \frac{1}{x}+\frac{1}{x+2}=\frac{9}{40}\\\\\frac{x+2}{x^2+2x}+\frac{x}{x^2+2x}=\frac{9}{40}\\\\\frac{2x+2}{x^2+2x}=\frac{9}{40}\\\\40(2x+2)=9(x^2+2x)\\\\80x+80=9x^2+18x\\\\0=9x^2-62x-80\\\\0=x^2-62x-720\\\\0=(x-72)(x+10)\\\\0=(x-8)(9x+10)\\\\x=8,\,x=-\frac{10}{9}[/tex]
Therefore, the only integer solution is x=8
a circle has a radius of 12 inches. find the area of the sector if its central angle is 60 degrees
What is the radius of a circle of circumference 2,74m
Answer:
Step-by-step explanation:
The formula to calculate the circumference of a circle is given by C = 2πr, where C represents the circumference and r represents the radius. Rearranging the formula, we have r = C / (2π).
Substituting the given circumference of 2.74 m into the formula, we get:
r = 2.74 m / (2π) ≈ 0.4367 m
Therefore, the radius of a circle with a circumference of 2.74 m is approximately 0.4367 meters.
Question 3 of 10
The estimate obtained from a sample of which of the following sizes would
most likely be closest to the actual parameter value of a population?
K
A. 75
OB. 15
O C. 150
OD. 45
The sample that would have an estimate that is likely closest to the actual value of the population is C. 150.
Why would this sample be better ?The size of the sample has a direct impact on the likelihood of obtaining an estimate that closely approximates the actual parameter value of the population.
In this context, a larger sample size, such as the one in option C with a magnitude of 150, is more inclined to yield an estimate that is nearest to the true parameter value. The rationale behind this lies in the fact that a larger sample size mitigates the effects of sampling error, resulting in a more accurate and representative depiction of the entire population. Consequently, the estimate derived from a sample of 150 would be expected to offer a higher level of precision and proximity to the actual parameter value.
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
The point (2, 5) is a solution to the system of equations: y = x + 2.
Let's test each system of equations:
y = x - 8
2x + y = 7
Substituting x = 2 and y = 5 into the equations:
5 = 2 - 8 (not true)
2(2) + 5 = 7 (not true)
The point (2, 5) is not a solution to this system of equations.
y = x + 2
y = x + 5
y = -1/2 * x + 6
y = 3x - 1
y = 2/3 * x + 6
Substituting x = 2 and y = 5 into the equations:
5 = 2 + 2 (true)
5 = 2 + 5 (not true)
5 = -1/2 * 2 + 6 (not true)
5 = 3 * 2 - 1 (not true)
5 = 2/3 * 2 + 6 (not true)
The point (2, 5) is a solution to the equation y = x + 2.
3y + 6x - 18 = 0
Substituting x = 2 and y = 5 into the equation:
3(5) + 6(2) - 18 = 0
15 + 12 - 18 = 0
27 - 18 = 0
9 = 0 (not true)
The point (2, 5) is not a solution to this equation.
Based on the tests, the point (2, 5) is a solution to the system of equations: y = x + 2.
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() Is the following a statistical question?
) How many legs does an ant have?
yes
No
Answer:
Yes!
Step-by-step explanation:
A statistical question is a question that can be answered by collecting data that vary
I need help quick plssss
Answer:
Grapes: 7/15 pound. Cherries: 1/6 pound.
Step-by-step explanation:
The total weight of the fruits is 7/10 of a pound. The weight of the grapes is 2/3 of the total weight. Therefore, the weight of the grapes is 2/3 * 7/10 = 14/30 = 7/15 of a pound. The weight of the cherries is 7/10 - 7/15 = 1/6 of a pound.
A dresser has 5 shelves. One shelf has x shirt and four shelves have y shirts. What is the total number of shirt in the dresser?
The total number of shirts in the dresser is: x+ 4y.
The total number of shirts in the dresser can be calculated by adding the number of shirts on each shelf.
The first shelf has x shirts.
Each of the other four shelves has y shirts.
Therefore, the total number of shirts in the dresser is:
x + y + y + y + y = x + 4y
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Question 2 of 20
Lexi wants to open an account where she can access the funds she needs to
pay her rent and other bills any time she wants. Which type of account would
be the best option for Lexi?
OA. A checking account
OB. A certificate of deposit
OC. A savings account
D. A money market account
SUBMIT
A Checking account will be the best option for lexi.
Given,
Lexi wants to open an account where she can access the funds she needs to pay her rent and other bills any time she wants.
Now,
Checking account:
A checking account offers easy access to your money for your daily transactional needs and helps keep your cash secure. Customers can typically use a debit card or checks to make purchases or pay bills.Standard checking account may be best for some, as it provides easy access to your funds and often has lower minimum balance requirements. Additionally, checking accounts may offer additional features, such as debit cards and online bill pay, that can make banking easier.Learn more about accounts,
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Give one pair of vertical angles and one pair of supplementary angles shown in the figure below.
Answer:
see explanation
Step-by-step explanation:
vertical angles are angles on the opposite side at a vertex of 2 lines.
1 and 6 , 2 and 5 , 3 and 8 , 4 and 7 are all vertical angles
supplementary angles sum to 180°
adjacent angles on a straight line sum to 180°
1 and 2 , 3 and 4 , 5 and 6 , 7 and 8 are examples of supplementary angles.
Film cameras allow a limited number of shots per role. How many images can a photographer typically shoot on a roll?
O A 30
OB. 36
OC. 25
O D. 50
OE 20
Film cameras allow a limited number of shots per role. 36 images can a photographer typically shoot on a roll. Thus, option A is the correct option.
The most cost-effective per shot is the roll, which typically yields 36 exposures. The 35mm format comes in a few different forms. On a roll of 35mm film, half-frame cameras may capture twice as many images at a smaller size.
Rolls of film typically have 24 or 36 exposures. The number of pictures you may take before loading a new roll may be limited as a result. However, some photographers view this as a benefit since it forces them to be more deliberate and exact when creating their images.
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