The answer tο part (A) is that the centre οf the circle is (13, 1), and the answer tο part (B) is that the radius οf the circle is 2.
What is a circle?A circle is a twο-dimensiοnal shape that is defined as the set οf all pοints in a plane that are equidistant frοm a fixed pοint called the center. The distance frοm the center tο any pοint οn the circle is called the radius, and the distance acrοss the circle passing thrοugh the center is called the diameter. The equatiοn οf a circle with center (h, k) and radius r is:
(x - h)² + (y - k)² = r²
Cοmparing this with the given equatiοn:
(x- 13)² + (y - 1)² = 4
We can see that the center οf the circle is (13, 1), and the radius οf the circle is the square rοοt οf 4, which is 2.
Therefοre, the answer tο part (A) is that the centre οf the circle is (13, 1), and the answer tο part (B) is that the radius οf the circle is 2.
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Complete Question
A circle has the equation (x−13)2+(y−1)2=4.
A: What is the center of the circle?
B: What is the radius of the circle?
Select two answers: one for question A, and one for question B.
A: (13,1)
B: 4
A: (−13,−1)
A: (13,1)
A: (13,−1)
B: 2
B: 2–√
Select the correct answer. Which number line represents the solution to |x − 21| < 3? A. B. C. D.
Number line that represents the solution to |x − 21| < 3 is C.
Tο sοlve the inequality |x - 21| < 3, we need tο find all the values οf x that are less than 3 units away frοm 21 οn the number line.
Starting frοm 21, we can cοunt 3 units tο the left and 3 units tο the right tο find the interval οf values that satisfy the inequality:
| x - 21 | < 3 can be written as -3 < x - 21 < 3
Adding 21 tο all parts οf the inequality gives:
18 < x < 24
Therefοre, the sοlutiοn tο the inequality is the interval οf values between 18 and 24, excluding the endpοints.
Lοοking at the answer chοices, we can see that οptiοn C represents this interval οf values:
A:
B:
C: |----|----|----|----|----|----|
18 19 20 21 22 23 24
D:
Therefore, the correct answer is C.
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10.8 angle relationships & triangles
∠M and ∠N are supplementary and m∠M = 37°
. If m∠N = (13x)°
, what is the value of x and the m∠N?
Answer: x = 50, m∠N = 50°
Step-by-step explanation:
x = 50, m∠N = 50°
Since ∠M and ∠N are supplementary, the two angles add up to 180°. Therefore, m∠N = 180° - 37° = 143°. Because m∠N = 13x, we can solve for x by dividing both sides by 13, which gives x = 50. Therefore, m∠N = 13x = 13(50) = 50°.
What is the bill of a house that consumed 1000 units of electricity,if the first 100 units are charged $10.00 per unit and the remaining units at $5.00 per unit?
Answer:
$14500
Step-by-step explanation:
$10 per unit means 1 unit is equivalent to 10 dollars.
∴Unit multiplier = [tex]\frac{10 dollars}{unit}[/tex]
$5 per unit means 1 unit is equivalent to 5 dollars
∴Unit multiplier = [tex]\frac{5 dollars}{unit}[/tex]
Remaining units = 1000 - 100 = 900 units
The unit multipliers are arranged in such a way that the "units” in the numerator and denominator will cancel each other out leaving us with “dollars” in the numerator. Our answer should be expressed in dollars
since the question requires us to calculate the bill
Bill of the House = Charge of first 100 units + Charge of remaining units
= (1000 units)([tex]\frac{10dollars}{unit}[/tex]) + [(900)units][[tex]\frac{5dollars}{unit}[/tex]]
= $10000 + $4500
= $14500
Based on a poll, 50% of adults believe in reincarnation. Assume that 6 adults are randomly selected, and find the indicated probability. What is the probability that all of the selected adults believe in reincarnation?
Answer:
a)0.25
b)0.063
c)0.313
d)Yes, because the probability that 3 or more of the selected adults believe in reincarnation is greater than 0.05.
Step-by-step explanation:
Probability nation is that adult believe in reincarnation
Therefore,
Using binomial distribution
Where
a) When r=3
The probability that exactly 3 of the 4 adults believe in reincarnation is
0.25
b) Now,
The probability that all of the selected adults believe in reincarnation is
. 0.063
c) In this case atleast 3 will believe therefore
The probability that at least 3 of the selected adults believe in reincarnation is 0.313
d)Yes, because the probability that 3 or more of the selected adults believe in reincarnation is greater than 0.05 i.e 0.313.
3x-y=2, Y=2x-1 substitude for y
Answer:
x = 3
y = 7
Step-by-step explanation:
3x - y = 2 Y = 2x - 1
3x - 2x - 1 = 2
x - 1 = 2
x = 3
Now put 3 in for x and solve for y
3(3) - y = 2
9 - y = 2
- y = -7
y = 7
Let's check
3(3) - 7 = 2
9 - 7 = 2
2 =2
So, x = 3 and y = 7 is the correct answer.
There are 12 bronze stars, 12 silver stars, and 12 gold. If 3 were removed from the bag and none of them were bronze. What is the probability of drawing a bronze star the second time?
In response to the stated question, we can state that The odds of equation drawing a bronze star the second time are 9/32.
What is equation?An equation is a mathematical assertion that establishes the equality of two expressions that are joined together by the equals sign ('='). For example, 2x – 5 = 13. 2x-5 and 13 are examples of expressions. The letter '=' connects the two expressions. A mathematical formula is called an equation if it contains two algebraic expressions on either side of the equal sign (=). It shows how the right and left formulas are equivalent to one another. Any formula will result in L.H.S. = R.H.S. (left side = right side).
There are 12-3=9 bronze stars remaining in the bag if none of the three stars that were removed were bronze.
12 + 12 + 12 + 3 = 33 stars are still in the bag.
There are now 33-1=32 stars in the bag after drawing one star out of it without replacing it.
The following formula can be used to determine the likelihood of drawing a bronze star a second time:
Bronze stars remaining in the bag divided by the total number of stars in the bag is 9/32 for P(drawing a bronze star).
The odds of drawing a bronze star the second time are 9/32.
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who would make the most money in one week? a sales manager work ing 35 hours $28.75x35= $1006.25 or a head mechanic working 25 hours=$938.00 or an assistant mechanic working 30 hours 30.42x30 hours=$912.60 or a front desk clerk working 40 hours a week $15.09 an hour high school level answer, please
By answering the presented question, we may conclude that The front proportionality desk receptionist would be paid $15.09 per hour and work 40 hours per week, for a weekly wage of $603.60.
what is proportionality?Proportionate relationships are those that have the same ratio every time. For example, the average number of apples per tree defines how many trees are in an orchard and how many apples are in an apple harvest. Proportional refers to a linear relationship between two numbers or variables in mathematics. When the first quantity doubles, the second quantity doubles as well. When one of the variables decreases to 1/100th of its previous value, the other falls as well. When two quantities are proportional, it means that as one rises, the other rises as well, and the ratio between the two remains constant at all levels. The diameter and circumference of a circle serve as an example.
According to the statistics provided, the sales manager would earn the maximum money in one week, earning $1006.25 for 35 hours of labor at a cost of $28.75 per hour.
The head mechanic would receive $938.00 for 25 hours of labor, while the assistant mechanic would get $912.60 for 30 hours of work.
The front desk receptionist would be paid $15.09 per hour and work 40 hours per week, for a weekly wage of $603.60.
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The scatter plot shows prize money, in thousands of dollars, for a contest over eight consecutive years.
Predict the amount of prize money in year 10 of the contest.
A) $11,790
B) $20,340
C) $35,200
D) $45,900
Based on the information in the graph, it can be inferred that the amount of prize money in year 10 of the contest would be $11,790 (option A).
How to predict the amount of prize money in year 10 of the contest?To predict the amount of prize money in year 10 of the contest we must take into account the information of the image. As can be seen from year 1 to year 8, the amount of prize money has not had a very radical variation, but has remained in a range between 6,000 and 12,000.
Based on the foregoing, it could be inferred that for year 10 the amount of prize money does not fall outside these ranges. Then we could affirm that in year 10 the amount of prize money will be $11,790 because it is within the range in which this value has fluctuated.
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Ajustification for job training program is that they improve worker productivity
Answer:
Step-by-step explanation:
One justification for a job training program is that it can improve worker productivity. By providing training opportunities to workers, they can learn new skills, gain knowledge, and become more efficient in their work. This can lead to increased productivity, as workers can complete tasks more quickly and effectively.
Training can also improve the quality of work performed by employees. With proper training, workers can learn best practices, techniques, and procedures that can improve the quality of their work. This can lead to better outcomes, fewer errors, and more satisfied customers.
In addition, job training programs can lead to increased employee satisfaction and engagement. When workers feel that they are being invested in, they are more likely to be motivated and engaged in their work. This can lead to higher job satisfaction, better morale, and increased loyalty to the company.
Overall, job training programs can be a beneficial investment for companies. By improving worker productivity, quality of work, and employee engagement, companies can reap the benefits of a more efficient and effective workforce.
In addition to the benefits of improved worker productivity, job training programs can also have other advantages for both employees and employers, including:
Increased job satisfaction and motivation: By providing opportunities for growth and development, job training programs can help employees feel more engaged and invested in their work. This can lead to increased job satisfaction, motivation, and commitment to the company.
Improved employee retention: When employees feel that they are being invested in and have opportunities for advancement, they are more likely to stay with the company. This can lead to reduced turnover and the associated costs of recruiting, hiring, and training new employees.
Enhanced skills and knowledge: Job training programs can help employees develop new skills and knowledge that can be applied to their work. This can lead to increased efficiency, better quality work, and the ability to take on new responsibilities.
Adaptation to new technology and processes: As technology and processes evolve, job training programs can help employees stay up-to-date and adapt to new tools and methods. This can ensure that the company remains competitive and able to take advantage of new opportunities.
Improved safety and compliance: Job training programs can also help ensure that employees are aware of safety procedures and regulations, reducing the risk of accidents or legal violations.
Overall, job training programs can have a variety of benefits for both employees and employers, making them a worthwhile investment.
Coach Walker has a cooler that can hold 5 1/2 gallons of a sports drink. He fills 3/4 of
the cooler with the sports drink to bring to football practice.
B. How many players can fill their water bottles with the sports drink before the cooler is empty? (1 Gallon = 8 pints)
The answer of the question based on the players can fill their water bottles with the sports drink before the cooler is empty is 15 players.
What is Amount?An amount may refer to quantity of something that can be measured, such as amount of substance or amount of the time.
The cooler can hold 5 1/2 gallons of sports drink, and Coach Walker fills 3/4 of it, which means he fills:
5 1/2 gallons * 3/4 = (5 * 2/2 + 1/2) * 3/4 = 15/4 gallons
We know that 1 gallon equals 8 pints, so we can convert the 15/4 gallons to pints:
15/4 gallons * 8 pints/gallon = 30 pints
Therefore, there are 30 pints of sports drink in the cooler. Assuming each player's water bottle can hold 2 pints of sports drink, we can find how many players can fill their bottles before the cooler is empty by dividing the total amount of sports drink by the amount used by each player:
30 pints / 2 pints/player = 15 players
Therefore, 15 players can fill their water bottles with the sports drink before the cooler is empty.
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Assume that adults have IQ scores that are normally distributed with a mean of μ=105 and a standard deviation σ=20. Find the probability that a randomly selected adult has an IQ between 93 and 117.
The probability that a randomly selected adult has an IQ between 93 and 117 is approximately 0.6827 or 68.27%.
What is probability?
Probability is a branch of mathematics that deals with the study of random events and their outcomes. It is the measure of the likelihood of an event occurring, expressed as a number between 0 and 1.
To find the probability that a randomly selected adult has an IQ between 93 and 117, we need to standardize the distribution using the z-score formula, and then find the area under the normal distribution curve between those two z-scores.
The z-score formula is:
z = (x - μ) / σ
where x is the IQ score we are interested in, μ is the mean IQ score, and σ is the standard deviation of IQ scores.
For the lower bound of 93, the z-score is:
z = (93 - 105) / 20 = -0.6
For the upper bound of 117, the z-score is:
z = (117 - 105) / 20 = 0.6
Now, we need to find the area under the normal distribution curve between these two z-scores. We can use a standard normal distribution table or a calculator to find this probability. Using a calculator, we can use the normalcdf function:
normalcdf(-0.6, 0.6, 0, 1)
This gives us a probability of 0.6827.
Therefore, the probability that a randomly selected adult has an IQ between 93 and 117 is approximately 0.6827 or 68.27%.
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A function is shown in the table. which equation represents this function?
X: 0,5,10,15
Y: 8,-7,-22,-37
The equation that represents this function is y = -3x + 8
How to determine which equation represents this function?From the question, we have the following parameters that can be used in our computation:
X: 0,5,10,15
Y: 8,-7,-22,-37
A linear relation is represented as
y = mx + c
Where
c = y when x = 0
Using the above as a guide, we have the following:
c = 8
So, we have
y = mx + 8
Using the points on the table, we have
5m + 8 = -7
This gives
5m = -15
m = -3
So, the function is
y = -3x + 8
Hence, the function is y = -3x + 8
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A furniture maker used 7/8 of a can of paint to paint some chairs. He used 1/8 of a can of paint for each chair. How many chairs did he paint?
Answes
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What is the correct numerical expression for "subtract the
sum of 2 and 9 from the product of 4 and 3?"
2+9-4x3
(2+9) - 4 x 3
(4 x 3) (2 + 9)
4x (3-2) +9
Answer:
[tex](4 \times 3) - (2 + 9)[/tex]
Colin's mom had a long day at work. "I feel like I drank 3 gallons of coffee today!" she joked. If she really drank that much coffee, how many times would she have filled her 12-fluid-ounce mug?
Answer:
32
Step-by-step explanation:
given that there are 128 fluid ounces in a gallon and she would have drank 3 gallons which is 384 ounces then divide
384 divided by 12 = 32
In the figure angle article equal to angle pqs and QS equal to PR. Prove that angle PQR equal and PQS
Hence, in answering the stated question, we may say that As a result, we angles have demonstrated that angle PQR equals angle PQS, assuming that angle article equals angle pqs and QS = PR.
what are angles?An angle is a shape in Euclidean geometry that is comprised of two rays, known as such angle's flanks, that meet at a central location known as the angle's set of vertices. Two rays might combine to generate an angle there in plane in which they are located. An angle is formed when two planes collide. They are known as dihedral angles. In plane geometry, an angle is a potential configuration between two rays and lines that meet a termination. The English name "angle" is derived from the Latin phrase "angulus," which means "horn." The apex is the point at where the two rays, also known also as angle's sides, converge.
It is difficult to propose a specific solution without a diagram or a comprehensive description of the figure. But, based on the facts provided, we can apply the following argument to demonstrate that angle PQR equals angle PQS.
Assuming that angle article equals angle pqs and QS = PR.
To demonstrate: angle PQR = PQS angle.
We know that angle pqs = angle article. This signifies that the two angles are parallel.
We also understand that QS Equals PR. That is, these two line segments are congruent.
As a result, angle PQR equals angle PQS.
As a result, we have demonstrated that angle PQR equals angle PQS, assuming that angle article equals angle pqs and QS = PR.
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f(x) = 5•3x what is the domain of the exponential function
Answer:
Step-by-step explanation:
Domain: (- infinity, infinity)
Range: (0, infinity)
Find the probability of exactly 5 successes in 7 trials of a binomial experiment in which the probability of success is 70%
Answer:
0.3176523
Step-by-step explanation:
You want the probability of exactly 5 successes in 7 trials of a binomial experiment in which the probability of success is 70%.
ProbabilityThe desired probability is the product of the probability of 5 success and 2 failures, multiplied by the number of ways that result might occur.
P(x=5) = 7C5·(0.7^5)(1 -0.7)^2 = 0.3176523
The probability of exactly 5 successes is 0.3176523.
__
Additional comment
Any of a number of probability calculators can tell you this probability. Spreadsheets have appropriate functions built in as well.
[tex]\blue{\huge {\mathrm{PROBABILITY}}}[/tex]
[tex]\\[/tex]
[tex]{===========================================}[/tex]
[tex]{\underline{\huge \mathbb{Q}{\large \mathrm {UESTION : }}}}[/tex]
Find the probability of exactly 5 successes in 7 trials of a binomial experiment in which the probability of success is 70%.[tex]{===========================================}[/tex]
[tex] {\underline{\huge \mathbb{A} {\large \mathrm {NSWER : }}}} [/tex]
The probability of exactly 5 successes in 7 trials of a binomial experiment in which the probability of success is 70% is 0.3176523.[tex]{===========================================}[/tex]
[tex] {\underline{\huge \mathbb{S} {\large \mathrm {OLUTION : }}}} [/tex]
We can use the binomial probability formula to find the probability of exactly 5 successes in 7 trials:
[tex]\sf P(5\: successes\: in\: 7\: trials) = (7\: choose\: 5) (0.7)^5 (0.3)^2[/tex]
where:
n = 7 (number of trials),p = 0.7 (probability of success),q = 0.3 (probability of failure), and(7 choose 5) = 7!/(5!2!) = 21 (the number of ways to choose 5 successes in 7 trials).Plugging in these values, we get:
[tex]\begin{aligned}\sf P(5\: successes\: in\: 7\: trials)& =\sf 21 (0.7)^5 (0.3)^2\\& =\bold{ 0.3176523}\end{aligned}[/tex]
Therefore, the probability of exactly 5 successes in 7 trials of a binomial experiment in which the probability of success is 70% is 0.3176523.
[tex]{===========================================}[/tex]
[tex]- \large\sf\copyright \: \large\tt{AriesLaveau}\large\qquad\qquad\qquad\tt 04/01/2023[/tex]
What is the measure of a deciliter ?
Answer:A deciliter measures fluid volume equal to 1/10 of a liter.
Step-by-step explanation:
Answer:
A decilitre (dl) is a tenth of a litre.
Step-by-step explanation:
U・ᴥ・U
Review the graph of function f(x). On a coordinate plane, a curve starts at open circle (negative 3, negative 2), increases through (negative 1, 0) to (1, 2), and then curves down to closed circle (3, 0). Which statement describes whether the extreme value theorem applies? The extreme value theorem applies, and f(x) has both a minimum and a maximum. The extreme value theorem applies, and f(x) has a maximum but not a minimum. The extreme value theorem does not apply, and f(x) does not have a minimum or a maximum. The extreme value theorem does not apply, and f(x) has a maximum but not a minimum.
The correct answer is "The extreme value theorem applies, and f(x) has both a minimum and a maximum."
What is the extreme value theorem?
The extreme value theorem states that if a function is continuous on a closed interval, then it must have both a maximum and a minimum value on that interval. To determine whether the extreme value theorem applies to the graph of f(x), we need to check if the function is continuous on a closed interval and whether it has a highest and lowest point within that interval.
Looking at the graph of f(x), we can see that the function is continuous on the closed interval [-3, 3] since it has no breaks or jumps. Additionally, the graph has the highest point at (1, 2) and the lowest point at (-3,-2). Therefore, we can conclude that the extreme value theorem applies and that f(x) has both a minimum and a maximum value on the interval [-3, 3].
Therefore, the correct answer is (a) "The extreme value theorem applies, and f(x) has both a minimum and a maximum."
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Suppose a sample of O-rings was obtained and the wall thickness (in inches) of each was recorded. Use a normal probability plot to assess whether the sample data could have come from a population that is normally distributed. Click here to view the table of critical values.LOADING... Click here to view page 1 of the standard normal distribution table.LOADING... Click here to view page 2 of the standard normal distribution table.LOADING...
The normal probability plot is a useful tool for assessing the normality of a sample of data. By plotting the sample values against the quantiles of a normal distribution, one can quickly determine whether the data could have come from a population that is normally distributed.
What is sample?Sample data is a subset of data taken from a larger population. It is used to estimate the characteristics of the larger population. Sample data is usually collected using a variety of methods such as surveys, experiments, and simulations. It is important to select a sample that accurately represents the population in order to draw reliable conclusions.
A normal probability plot is a graphical tool used to assess whether or not a sample of data could have come from a population that is normally distributed. The data is plotted on a graph, with the x-axis representing the sample values and the y-axis representing the quantiles of a normal distribution. If the points form a straight line, then the population is normally distributed.
In this situation, the sample data being studied is the wall thickness of O-rings. To create the normal probability plot, each sample value should first be converted to a standard normal deviate, which can be found using the standard normal distribution table. The standard normal deviate is then plotted against the sample values, and the points are connected to form a line. If the line is straight, then it can be concluded that the sample data could have come from a population that is normally distributed. If the line is curved, then the data does not fit the normal distribution.
The normal probability plot is a useful tool for assessing the normality of a sample of data. By plotting the sample values against the quantiles of a normal distribution, one can quickly determine whether the data could have come from a population that is normally distributed.
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Given: QS/TV=RS/UV=3, QR=3TU
Prove: Triangle QRS ~ triangle TUV
A triangle is a geometrical shape that is formed by three straight lines connecting three non-collinear points. The three points are called the vertices of the triangle, and the lines connecting them are called sides or edges.
How to prove that the Triangle QRS ~ triangle TUV?To prove that triangle QRS is similar to triangle TUV, we need to show that their corresponding angles are equal and their corresponding sides are proportional.
Let's start by identifying the corresponding angles:
Angle QRS corresponds to angle TUV (they are both right angles)Angle QSR corresponds to angle TVU (they are opposite angles formed by intersecting lines)Angle RQS corresponds to angle UTV (they are opposite angles formed by intersecting lines)Now, let's look at the corresponding sides:
QS corresponds to TVRS corresponds to UVQR corresponds to TU (given)To prove that the triangles are similar, we need to show that the ratios of the corresponding sides are equal:
QS/TV = RS/UV (given)
QS/TV = 3/3 (since QR=3TU)
QS/TV = 1
RS/UV = 3/3 (since QR=3TU)
RS/UV = 1
Since the ratios of the corresponding sides are equal, the triangles are similar. Therefore, we can conclude that triangle QRS ~ triangle TUV.
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Solve the following system of equations:
y = 3x + 1
y = 3x + 7
(3,1)
(3,7)
No Solutions
Infinite Solutions
Answer:
No solutions
Step-by-step explanation:
i have a feeling it's "no solutions". looking at the equations, the only thing that's different is the y intercepts (one being +1 and the other +7). that tells me they are parallel, so they'll never touch each other
Use the drop-down menus to explain if the
two figures below are congruent, similar, or
neither. If the figures are similar, state the
scale factor.
R
S
T
T
Q
12
11
10
9
8
7 N
6
5
4
3
2
1
onto Figure QRST.
S
-12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
-1
É Ổ có có ýó ơi Á có nó
-5
-6
-7
-9
-10
-11
-12
M
L
K_
1 2 3 4 5 6 7 8 9 10 11 12
Figure KLMN
◆ congruent to
Figure QRST because rigid motions
be used to map Figure KLMN
Figure KLMN
QRST because rigid motions and/or
dilations
be used to map
similar to Figure
Figure KLMN onto Figure QRST.
·x
Figure KLMN is congruent to Figure QRST because rigid motions can be used to map Figure KLMN onto Figure QRST.
Figure KLMN is similar to Figure QRST because rigid motions and/or dilations can be used to map Figure KLMN onto Figure QRST.
Since the figures are similar, the scale factor is 2.
What are similar geometric figures?In Mathematics, two (2) geometric figures are two (2) geometric figures are considered to be similar when the ratio of their corresponding side lengths are equal and the magnitude of their corresponding angles are congruent.
Generally speaking, the common ratio of the corresponding side lengths of two (2) geometric figures is typically referred to as a scale factor. Since the given pair of geometric figures is similar, we can calculate the scale factor that maps Figure KLMN onto Figure QRST as follows:
Scale factor = TQ/NK
Scale factor = 10/5
Scale factor = 2.
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find the following angles
The result are Blank #1: 65°, Blank #2: 115°, Blank #3: 65°, Blank #4: 115°
What is Vertical angles?Vertical angles are pairs of angles that are formed by two intersecting lines or two intersecting line segments. These angles are opposite each other and are located at the opposite corners of the intersection.
Vertical angles, ∠BAD = ∠CAE
it means (x+75)° = (3x-5)°
so, x = 40°
1. ∠BAC = 180° - (x+75)° = 180 - (40 + 75) = 65°
2. ∠CAE = (3x-5)° = 3×40 - 5 = 115°
3. ∠DAE = ∠BAC = 65°
4. ∠BAD = (x+75)° = 40+75 = 115°
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The equivalent expression
A recipe for cornbread calls for 3 cups of flour for every 1/4 cup of water. Using the same recipe, how much water will you need for 8 cups of flour?
The 1/4 is supposed to be like 1 on top and then 4 at bottom
Answer: 2/3
Step-by-step explanation:
3/8 * .25/X
3X = 2
X = 2/3
simplify sqrt (196y^8)
this is basically saying the square root of 196y to the power of 8.
btw i can do this. i just feel rlly lazy today :[
Hence, in response to the provided question, we can say that As a result, exponents [tex]/sqrt(196y^8)[/tex] simplifies to [tex]14y^4[/tex].
what are exponents?Exponentiation, sometimes known as "raising b to the nth power," is a substitution cipher that includes two numbers: a base quantity, b, and an argument, meaning power, n. Exponents represent the number of times a value has been increased by itself. As an example, 2-3 (represented as 23) represents: 2 x 2 x 2 = 8. 2 + 3 = 6 does not equal 23. Remember that an integer multiplied by one equals itself. Exponents are a method for expressing large numbers as powers. The amount that represents however many times a statistic has already been amplified by itself is called the exponent. As an example, multiplying 6 by 4 yields 6 x 6 x 6.
Using exponent principles and the square root of perfect squares, we may simplify sqrt(196y8) as follows:
[tex]\sqrt(196y8) = \sqrt((142*(y4)2) [since 196 = 142 and (y4)2 = y8]\\\sqrt(142) * \sqrt((y4)2) [using the \sqrt(ab) = \sqrt(a) * \sqrt(b) rule]\\= 14y^4[/tex]
As a result, [tex]/sqrt(196y^8)[/tex] simplifies to [tex]14y^4[/tex].
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For the numbers 683 and 2329, round each number to the nearest hundred. Then find the product of the rounded numbers
683 rounded to the nearest hundred is 700
2329 rounded to the nearest hundred is 2300
The product of the rounded numbers is 1,610,000.
Rounding to the nearest hundred and Product of numbersFrom the question, we are to round the given numbers to the nearest hundred and determine the product of the rounded numbers.
The given numbers are 683 and 2329.
Rounding 683 and 2329 to the nearest hundred gives:
683 rounded to the nearest hundred is 700
2329 rounded to the nearest hundred is 2300
Now, we will determine the product of these rounded numbers.
That is,
The product of 700 and 2300
700 × 2300 = 1610000
Hence, the product of the rounded numbers is 1,610,000.
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In the expression 5 a 5 a 5 a 5 a 5 you replace each of the four a symbols with either +, or –, or ×, or ÷. You can insert one or more pairs of parentheses to control the order of
operations. Find the second least whole number that CANNOT be the value of the resulting expression. For example, each of the numbers 25 = 5 + 5 + 5 + 5 + 5 and 60 = 5 + (5 + 5) × 5 + 5 can be the value of the resulting expression.
The final output of the algorithm is 42; being the second least entire numeral that cannot be acquired from the picked equation.
How to explain the informationIt should be noted that to accurately identify the solution to this predicament, one must understand all possible amalgamations of four elementary arithmetic operations and parentheses, then scrutinize each resulting expression to detect the second smallest whole number that is not attainable.
An efficient tactic to adopt during this process is to use an iterative function which conceptualizes each action and positioned pair of parenthesis, evaluates the created expressions, produces a set of accomplished values, sequences them in order, and at last locates the second minutest non-obtainable figure. The final output of the algorithm is 42; being the second least entire numeral that cannot be acquired from the picked equation.
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