The solution is, the simplification of the expression is:
{16 - 9x^2 + 14x}
Here, we have,
given that,
the expression:
{√49 + [√81 - x (9x - 14)]}
now, we have to simplify this expression:
{√49 + [√81 - x (9x - 14)]}
={7 + [9 - x (9x - 14)]}
={7 + [9 - 9x^2 + 14x]}
={7 +9 - 9x^2 + 14x}
={16 - 9x^2 + 14x}
Hence, The solution is, the simplification of the expression is:
{16 - 9x^2 + 14x}
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Find the slope of a line that is perpendicular to: x − y = 0
-1 is the value of the slope.
To find the slope of a line that is perpendicular to the line x - y = 0, we need to find the slope of the given line first.
To do this, we can rearrange the equation x - y = 0 to solve for y:
x - y = 0
y = x
So the given line has a slope of 1 since the coefficient of x is 1.
Since a line perpendicular to this line will have a slope that is the negative reciprocal of the slope of the given line, we can find the slope of the perpendicular line by taking the negative reciprocal of 1:
the slope of the perpendicular line = -1/1
the slope of the perpendicular line = -1
Therefore, the slope of a line that is perpendicular to the line x - y = 0 is -1.
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If a rectangle is made up from points (-2,-1), (4,-1), (4,3),
The value of coordinates of fourth vertex of rectangle is, (0, 3)
We have to given that;
A rectangle is made up from points (-2,-1), (4,-1), (4,3),
Since, Midpoints of the points are same both diagonal.
Hence, Let the fourth vertex = \(x, y)
Midpoint of point (- 2, - 1) and (4, 3) is,
(- 2 + 4) / 2,. (- 1 + 3) / 2
(2, 1)
Midpoint of (x, y) and (4, - 1) is,
(x + 4)/2, (y - 1)/2
Which is same as (2, 1).
Hence, We can compare as;
(x + 4) / 2 = 2
x + 4 = 4
x = 0
y - 1 / 2 = 1
y - 1 = 2
y = 3
Thus, The value of coordinates of fourth vertex of rectangle is, (0, 3)
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Complete question is,
If a rectangle is made up from points (-2,-1), (4,-1), (4,3),
Then, The value of fourth coordinate is?
What is the smallest whole number that rounds to 2,560 to the nearest ten?
The requreid smallest whole number that rounds to 2,560 to the nearest ten is 2,565. When we round 2,565 to the nearest ten, we get 2,570, which is the desired result.
When rounding a number to the nearest ten, look at the digit in the tens place. If that digit is 5 or greater, we round up by adding 1 to the digit in the hundreds place. If that digit is less than 5, round down by keeping the digit in the hundreds place the same.
In the given question, 2,560 rounded to the nearest ten would be,
2,560 rounded up to 2,560 + 10 = 2,570.
Therefore, the smallest whole number that rounds to 2,560 to the nearest ten is 2,565. When we round 2,565 to the nearest ten, we get 2,570, which is the desired result.
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What is the volume of the solid?
A. 12 yd³
B. 14 yd³
C. 22 yd³
D. 5 yd³
Answer:
(1/2)(4)(3)(2) = 12 cubic yards
The correct answer is A.
what will be the answer
1) Using the Law of Syllogism, we can combine statement 1 and statement 3 to conclude that Sally weighs more than Jill's car:
If something weighs more than 2000 pounds, then it weighs more than Jill’s car.
Sally weighs more than 2000 pounds.
Therefore, Sally weighs more than Jill's car.
2) Using the Law of Detachment, we can apply statement 2 to our conclusion from the Law of Syllogism to conclude that Sally is too heavy for the bridge:
If something weighs more than Jill’s car, then it is too heavy for the bridge.
Sally weighs more than Jill's car.
Therefore, Sally is too heavy for the bridge.
What is the Law of Syllogism and the Law of Detachment?The Law of Syllogism opines that if two conditional statements have the same terms, then we can combine them to form a conclusion.
The Law of Detachment states that if a conditional statement is true and its hypothesis is true, then its conclusion is also true.
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What’s the probability that event A or B takes place?
The probability that event A or B takes place is P ( A ∪ B ) = 4/13
Given data ,
Let the probability of event A happening P ( A ) = 1/13
Let the probability of event B happening P ( B ) = 3/13
And , the probability of event A and B happening P ( A ∩ B ) = 0
So , from the probability rule ,
The probability that event A or B takes place is P ( A ∪ B ) and
P ( A ∪ B ) = P ( A ) + P ( B ) - P ( A ∩ B )
On simplifying , we get
P ( A ∪ B ) = 1/13 + 3/13 - 0
P ( A ∪ B ) = 4/13
Hence , the probability is 4/13
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A line passes through the point (-4, -8) and has a slope of -5/4 Write an equation in point-slope form for this line.
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-8})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{5}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-8)}=\stackrel{m}{- \cfrac{5}{4}}(x-\stackrel{x_1}{(-4)}) \implies y +8 = - \cfrac{5}{4} ( x +4)[/tex]
A normally-distributed population has a mean μ = 32 and a standard deviation σ = 7. For a set of samples of size 8 taken from this population, about 99.7% of the means will be in what interval?
The standard error of the mean δ for a sample of size n is calculated as:
δ = σ / √(n)
where σ is the population standard deviation and n is the sample size.
For a sample of size 8 taken from a normally-distributed population with a mean of 32 and a standard deviation of 7, the δ is:
δ = 7 / √(8) ≈ 2.475
The 99.7% confidence interval for the sample mean is given by:
x ± 3 Substituting the values, we get:
32 ± 3(2.475)
where x is the sample mean.
Substituting the values, we get:
32 ± 3(2.475)
which simplifies to:
[24.575, 39.425]
Therefore, about 99.7% of the sample means taken from this population will fall within the interval [24.575, 39.425].
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(100 POINTS + BRAINLIEST) A box has 1 red marble, 1 blue marble, and 4 green marbles of the same shape and size. Dan draws a marble randomly from the box, replaces it, and then draws another marble randonmy What is the probability of drawing two green marbles in a row? Explain your answer.
The probability of drawing two green marbles in a row is 4/9.
Given that, a box has 1 red marble, 1 blue marble, and 4 green marbles.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.
Number of favorable outcomes = 4
Total number of outcomes = 6
Probability of drawing 1st green marble = 4/6
= 2/3
Probability of drawing 2nd green marble = 4/6
= 2/3
Probability of drawing two marbles = 2/3 × 2/3
= 4/9
Therefore, the probability of drawing two green marbles in a row is 4/9.
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Solve the following simultaneous equation using algebra
6x + 3y =45
On Solving the equations "6x + 3y = 45" and "2x - 2y = 6", we get that the solution is x = 6 and y = 3.
An "Equation" is defined as a mathematical statement which shows the equality of "two-expressions", which are separated by equal sign.
To solve the simultaneous equations:
6x + 3y = 45 ...equation(1)
2x - 2y = 6 ...equation(2)
We Multiplying the equation(2) by 3, we get:
⇒ 6x - 6y = 18,
Subtracting this equation to the first equation, we get:
⇒ 6x + 3y - 6x + 6y = 45 - 18,
⇒ 9y = 27,
⇒ y = 3,
Now, we can substitute this value of "y" into any of the original equations to find "y". Let's use the first equation:
⇒ 6x + 3y = 45,
Substituting y = 3, we get:
⇒ 6x + 3(3) = 45,
⇒ 6x + 9 = 45,
⇒ 6x = 45 - 9,
⇒ x = 6,
Therefore, the solution to the simultaneous equations is x = 6 and y = 3.
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The given question is incomplete, the complete question is
Solve the following simultaneous equation
6x + 3y = 45 and 2x - 2y = 6.
7
The venue for an outdoor summer concert was divided into 35 sections. The event planner randomly chose 8 sections and counted
the number of ice chests in the section, as shown below.
48, 51, 26, 73, 51, 48, 26,51
Assuming that the sample was representative of the entire venue, what was the mean number of ice chests in a section?
The mean number of ice chests in a section is 46.75.
How do we find the mean number of ice chests?The mean is the average or the most common value in a collection of numbers. In statistics, it is a measure of central tendency along median and mode..
To find the mean number of ice chests in a section, we need to calculate the sum of the ice chests and then divide total number of sections sampled.
Sum of ice chests = 48 + 51 + 26 + 73 + 51 + 48 + 26 + 51
Sum of ice chests = 374
Mean number of ice chests will be:
= (Sum of ice chests) / (Total number of sections sampled)
= 374 / 8
= 46.75
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How many days with 9 workers
Answer: 9.66666667
Step-by-step explanation:
To find the number of days it would take to build a similar house, we would need to create a proportion.
Workers: 27:9
Days: 29:?
Let's simplify.
Workers: 3:1
Days: 29:?
Now, we divide 29 by 3 to see how many days it would take to build a similar house.
29/3=9.666666667 (9.6 repeating)
So, your answer would be 9.6
Hope this helps!
The following data sets show the number of shoppers on four weekends in a month at different hours of the day. Identify the weekend whose data best shows asymmetric distribution.
First: 9, 7, 8, 6, 7, 8, 7, 6, 8, 7, 9, 7, 8, 5, 10, 5, 10, 8, 7, 7
Second: 15, 13, 12, 15, 14, 13, 15, 16, 14, 13, 15, 15, 15, 17, 18, 12, 18, 15, 17, 16
Third: 11, 18, 17, 14, 15, 9, 16, 12, 13, 15, 14, 12, 15, 17, 16, 14, 13, 11, 10, 9
Fourth: 18, 17, 18, 19, 18, 17, 16, 18, 17, 19, 18, 17, 17, 16, 16, 15, 15, 16, 15, 17
The second data set best shows asymmetric distribution.
To identify the weekend whose data best shows asymmetric distribution, we need to look for the data set that is skewed, or "lopsided", meaning it has a longer tail on one side than on the other.
We can begin by creating a histogram for each of the data sets to visualize their distributions
The second data set, however, shows a clear skew to the left, with a longer tail of observations on the left side of the center than on the right side.
This makes the second data set the one that best shows asymmetric distribution.
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The pair of values below is from a direct variation. Find the missing value.
(3,8),(18,y)
y= ?
Answer:
the missing value is y = 48.
Step-by-step explanation:
In a direct variation, the ratio of the two variables remains constant. We can use this fact to find the missing value y:
y / 18 = 8 / 3
To solve for y, we can cross-multiply:
y = 18 * 8 / 3
y = 48
Therefore, the missing value is y = 48.
How does Tom's ploy to get other boys to do his work
for him create suspense?
OA. through Tom's explanation the difficult parts of
work
O B. through Tom's use of persuasion and trickery to
get the work done
O C. through Tom's consideration of exchanging toys
and marbles for the work
O D. through Tom's description about completing the
work and doing a good job
Tom's ploy to get other boys to do his work: through Tom's use of persuasion and trickery to get the work done. Option B
How does Tom's ploy to get other boys to do his workThe reader is left wondering if Tom will be caught and punished for his conduct because he uses persuasion and deceit to persuade other lads to perform his work for him.
The reader is also left wondering whether the other lads will finally grasp what Tom is up to and cease assisting him, or whether they will continue to be duped by him. The use of persuasion and cunning adds a sense of danger and risk-taking to the situation, heightening the story's tension.
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PLEASE HELP THANK YOU HURRY FAST
The solution of the equation 1/(x-3) + 1/(x+5) = 1/3 is x=-3, x=7, option D is correct
The given equation is 1/(x-3) + 1/(x+5) = 1/3
Take LCM on left hand side
(x+5)+(x-3)/(x-3)(x+5)= 1/3
2x+2/(x-3)(x+5) = 1/3
2(x+1)/(x-3)(x+5) = 1/3
6(x+1)=(x-3)(x+5)
6x+6 = x²+5x-3x-15
6x+6 = x²+2x-15
x²+2x-6x-15-6=0
x²-4x-21=0
x² -7x+3x-21=0
x(x-7)+3(x-7)
(x+3)(x-7)
The solutions are x=-3, x=7
Hence, the solution of the equation 1/(x-3) + 1/(x+5) = 1/3 is x=-3, x=7, option D is correct
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Insert commas and write the number name in international system of numeration
The number name of 97600305 in international system of numeration Ninety-Seven Million, Six Hundred Thousand, Three Hundred and Five.
The number 97600305 can be written with commas as,
Place the commas after hundred.
That is after 305.
Read as three hundred five.
then place the commas after thousands.
Place the comma after 600.
Read as six hundred thousands.
and place the comma after million.
that is after 97.
Read as Ninety-Seven Million.
Combine all and write in the international system of numeration,
The number 97600305 is read as,
Ninety-Seven Million, Six Hundred Thousand, Three Hundred and Five.
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The given question is incomplete, I answer the question in general according to my knowledge:
Write the number name for the numeral 97600305 by inserting commas and write the number name in international system of numeration.
Robert has a pond in his backyard. How much land does the pond take up? if he were to put a fence around the pond, how much fencing would he need?
The requried amount of fencing needed t cover the pond in this backyard is 319.36 meters.
A figure of Robert's backyard has been shown, we have to determine the perimeter of his backyard,
The perimeter of backyard = 2L + 2[πw/2]
The perimeter of backyard = 2*78 + 2[π*52/2]
The perimeter of the backyard = 319.36 meters
Thus, the requried amount of fencing needed t cover the pond in this backyard is 319.36 meters.
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14. Find the volume of the hemisphere. Round to the
nearest tenth.
The volume of the hemisphere as given in the task content to the nearest tenth is; 718.4 mm³.
What is the volume of the hemisphere as given in the task content?It follows from the task content that the volume of the hemisphere as represented in the attached image is to be determined.
Since the volume of the hemisphere is given by;
V = 2/3πr³
where radius = diameter/2 = 14/2 = 7.
Consequently, the volume, V is;
V = 2/3 × π × 7³
V = 718.4 mm³.
Ultimately, the volume is; 718.4 mm³.
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A set of data has a normal distribution with a mean of 55 and a standard deviation of 9. Find the percent of data within the following interval.
from 28 to 82
The percent of data within the given interval is.
(Type an integer or a decimal.)
The percent of data within the following interval from 28 to 82 is 99.73%
Calculating the percent of data of values from the the z-scoresFrom the question, we have the following parameters that can be used in our computation:
Mean = 55
Standard deviation = 9
Scores = from 28 to 82
So, we have
z = (28 - 55)/9 = -3
z = (82 - 55)/9 = 4
This means that it is between a z-score of -3 and a z-score of 3
This is represented as
Probability = (-3 < z < 3)
Using a graphing calculator, we have
Probability = 0.9973
Express as percentage
Probability = 99.73%
Hence, the probability is 99.73%
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.- Para hallar el volumen de una esfera, el valor de su radio se debe
elevar a la potencia 3 y este resultado debe ser multiplicado por-
Un balón esférico tiene como volumen 1000 x 7 centímetros
cúbicos, ¿cuánto mide su radio?
3
A) 10 centímetros.
B) 300 centímetros.
C) 1,000 centímetros.
R) 3,000 centímetros.
3
TU.
5. Lakita's test scores are 87, 96, 81, and 89.
What score does she need on the last test in
order to average 90 on her tests?
[5]
Answer: 97
Step-by-step explanation:
Average: All the numbers added divided by the number of numbers
Start adding the smallest grade in her notes: 87+96+81+89+81= 434/5= 86.8
Keep adding 1 to the last grade until you find a number that gives us an average of 90.
87+96+81+89+97+ 450
Then divide it by the amount of grades
450/5= 90
A primary credit card holder's card has an APR of 11.99%. The current monthly balance, before interest, is $6,299.59. The
cardholder makes a payment of $350 the first 11 months and then pays off the balance at the end of the 12th month. How much
interest did the credit card holder pay?
O$123.02
O$562.73
O $211.04
O$559.56
The total interest that the credit card holder paid at 11.99% APR for $6,299.59 is D. $559.56.
How the interest is determined:The total interest is a function of the APR, the principal, and the period involved.
The total interest can be determined using an online finance calculator with some adjustments.
N (# of periods) = 11 months
I/Y (Interest per year) = 11.99%
PV (Present Value) = $6,299.59
PMT (Periodic Payment) = $-350
Results:
FV = $-2,979.39
Sum of all periodic payments = $-3,850.00
Total Interest = $529.80
12th Month Interest = $29.76 ($2,979.39 x 11.99% x 1/12)
Total interest up to the 12th month = $559.56 ($529.80 + $29.76)
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Select the correct sentences in the passage. Which statements are true? Any two squares are either similar or congruent. If two lines are parallel, they never intersect. If all the angles of a polygon are congruent, then it is a square. The intersection of two lines always forms 4 congruent angles. A line can be drawn through any two distinct points.
The correct sentences in the passage are option A, option B, and option E.
Any two squares are either similar or congruent. If two lines are parallel, they never intersect.A line can be drawn through any two distinct points.Let's check all the options, then we have
Any two squares are either similar or congruent. The statement is true.
If two lines are parallel, they never intersect. The statement is true.
If all the angles of a polygon are congruent, then it is a square. The statement is false because a regular polygon has an equal angle but it may be a pentagon, hexagon, etc.
The intersection of two lines always forms 4 congruent angles. The statement is false because opposite angles are the same. But if adjacent angles become the same, then the statement will be true.
A line can be drawn through any two distinct points. The statement is true.
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4. The scale drawing of a baby blanket has the dimensions of 6 inches by 10 inches. The dimensions of the actual baby blanket are 30 inches by 50
inches.
What is the scale of the drawing?
The scale factor of the given drawing is expressed as: 1:5
How to find the scale factor?We are given the dimensions of the scale drawing of the blanket as:
Length = 10 inches
Width = 6 inches
We are given that the actual dimensions of the baby blanket are:
Length = 50 inches
Width = 30 inches
The size by which a shape is enlarged or reduced is called as its scale factor. It is used when we need to increase the size of a 2D shape, such as circle, triangle, square, rectangle, etc. If y = Kx is an equation, then K is the scale factor for x.
The scale factor is:
50/10 = 30/6 = 5
Thus, we have 1:5
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A manufacturing machine has a 2% defect rate.
If 7 items are chosen at random, what is the probability that at least one will have a defect?
Answer:7.02
Step-by-step explanation: cause im right
A tennis ball can in the shape of a right circular cylinder holds three tennis balls snugly. If the radius of a tennis ball is
3.5 cm, what percentage of the can is not occupied by tennis balls?
The percentage of the can that is not occupied by tennis balls is______%.
(Type an integer, fraction, or mixed number.)
The percentage of the can that is not occupied by tennis balls is approximately 80.14%.
We have,
The volume of the can = The volume of the cylinder - The volume of the three tennis balls.
The volume of the cylinder.
V(cylinder) = πr²h
where r is the radius and h is the height of the cylinder.
Since the can holds three tennis balls snugly, the height of the cylinder is equal to three times the diameter of a tennis ball.
= 3 × 2(3.5 cm)
= 21 cm.
V(cylinder)
= π (3.5 cm)² (21 cm)
= 2709.38 cm³
The volume of one tennis ball.
V (ball) = (4/3)πr³
where r is the radius of the tennis ball. Thus,
V(ball) = (4/3)π(3.5 cm)³ = 179.594 cm³
The total volume of the three tennis balls is:
V(3balls) = 3 V(ball)
= 3(4/3) π (3.5 cm)³
= 538.782 cm³
The volume of the can not be occupied by tennis balls.
V(not occupied) = V(cylinder) - V(3 balls)
= 2709.38 - 538.782
= 2170.598 cm³
The percentage of the can that is not occupied by tennis balls.
percentage = (V(not occupied / V(cylinder)) × 100%
= (2170.598 cm^3/2709.38 cm^3) × 100%
= 80.14%
Therefore,
The percentage of the can that is not occupied by tennis balls is approximately 80.14%.
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A
Find the recursive definition
of this sequence.
3, 10, 17, 24
an = an-1 + 10
a1 = 3
B
an = 10an-1
a₁ = 3
C
an = an-1+7
a₁
a₁ = 3
Hello! Here are the recursive definitions of the given sequence:
A) The sequence is increasing by 7 for each term, so the recursive definition can be written as:
a1 = 3
an = an-1 + 7
So, the recursive definition of the sequence is: 3, 3+7=10, 10+7=17, 17+7=24, ...
B) The second option given, "anan-1 + 10 a1 = 3" is not a recursive definition of the sequence.
C) The third option given, "San = 10an-1" is also not a recursive definition of the sequence because it uses a different variable 'S' instead of 'a'.
Find the value of x for the following
The length x in the similar triangle is 7.06 units.
How to find the side of similar triangle?Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other.
Therefore, let's use the similarity of the triangle to find the value of x in the triangle.
Hence, using the proportion,
y / 8 = 8 / 17
cross multiply
17y = 64
y = 64 / 17
y = 3.76470588235
y = 3.76
Therefore,
17 - 3.76 = 13.24
Hence,
13.24 / x = x / 3.76
cross multiply
x² = 49.7824
x = √49.7824
x = 7.05566439111
Hence,
x = 7.06 units
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A clothing eCommerce company has an Average Order Value of USD 65. It costs the company USD 35 to produce the clothes in the average order and USD 15 to ship it to the customer. What is the Average Order's Gross Profit?
USD 65
USD 30
USD 15
USD 50
The Average Order's Gross Profit for the clothing eCommerce company in this scenario is USD 15.
For the Average Order's Gross Profit for the clothing eCommerce company in this scenario, we need to subtract the cost of production and shipping from the Average Order Value as;
⇒ Gross Profit = Average Order Value - Cost of production - Cost of shipping Gross Profit
⇒ Gross Profit = USD 65 - USD 35 - USD 15
⇒ Gross Profit = USD 15
Therefore, the Average Order's Gross Profit for the clothing eCommerce company in this scenario is USD 15.
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