In system equation method,
a) Amount of red portion = 240 ml.
b) There are 300 mL of blue potion used and 100 mL of red potion used.
c) There is a ratio of 2 (blue potion):1 (red potion), there will be a 35% amount of magical syrup.
What is equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
(a) We can use a system equation here to solve this.
Let x=amount of red potion used
Let y=total amount of potion in solution
Then,
=>200 + x = y
=> 0.15(200) + 0.75x = 0.25y
0.15(200) because 15% of the blue potion=.15 and there is 200mL.
0.75x because 75% of the red potion=.75 and there is x amount of it
0.25y because we want 25% of the total potion=.25 and there is y amount of it.
We can substitute for y in the second equation:
=>0.15(200) + 0.75x = 0.25(200 + x)
=> 30 + 0.75x = 50 + 0.25x
=> -20 = -0.5x
=> x = 40
Knowing that x=40, we know that y=240, meaning our answer is 240.
b.) We can again use a system for this problem
Let x=Amount of red potion
Let y=Amount of blue potion
=> x + y = 400
=> 0.3(400) = 0.15y + 0.75x
0.3(400)=30% of the 400 mL
0.15y=15% of the magic syrup
0.75x=75% of the magic syrup
We can substitute for x in this equation:
=>120 = 0.15y + 0.75(400 - y)
120 = 0.15y + 300 - 0.75y
-180 = -0.6y
y = 300, x = 100
There are 300 mL of blue potion used and 100 mL of red potion used.
c.) Let x=amount of red potion
Let y=amount of blue potion
=> 0.15x + 0.75y = 0.35(x + y)
0.35(x+y) because the total amount of the potion is x+y
=>0.15x + 0.75y = 0.35x + 0.35y
0.4y = 0.2x
2y = x
Whenever there is a ratio of 2 (blue potion):1 (red potion), there will be a 35% amount of magical syrup.
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the objective of statistical process control (spc) is to question 38 options: 1) determine whether a batch of raw materials should be accepted or rejected 2) determine whether a batch of finished goods should be accepted or rejected 3) detect assignable cause variations versus normal random variations in the process 4) identify variable versus attribute measures
From the following option given, the correct option is option (3) - detect assignable cause variations versus normal random variations in the process.
The objective of statistical process control (SPC) is to monitor and control a process to ensure that it operates within its specifications and meets the desired quality level. One of the main goals of SPC is to distinguish between normal random variation in the process and variation that is caused by assignable or special causes.
By identifying and eliminating the assignable causes of variation, the process can be improved and the quality of the output can be maintained or improved over time. Therefore, the primary objective of SPC is to detect assignable cause variations versus normal random variations in the process.
Options 1, 2, and 4 are related to quality control and monitoring, but they do not capture the essence of what SPC is trying to achieve. SPC is focused on monitoring and improving the process, rather than simply accepting or rejecting batches of raw materials or finished goods or identifying variable versus attribute measures.
Therefore, the correct option is '3' - detect assignable cause variations versus normal random variations in the process.
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after graduation you achieve your dream of opneing your own art shop. how many wokers should you hire
Answer:
Step-by-step explanation:
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Introducing yourself well sets the stage for a professional conversation whether at a networking event, with a colleague or at the beginning of an interview. One tool that many people use to make introductions simple and effective is the elevator pitch.
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Jenn, a certified career coach, helps you tell a compelling story about who you are and where you are going in under two minutes.
Find the value of x.
The value of x from the triangle using the triangle proportionality theorem is 8.4
Calculating the values of x from the triangleGiven that we have the triangle
Using the triangle proportionality theorem, we have the following equivalent ratio
3.5 : 5 = x : 12
When this ratio is represented as a fraction, we have
3.5/5 = x/12
So, we have
x = 12 * 3.5/5
Evaluate the products
This gives
x = 8.4
Hence. the solution for x is 8.4
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the mean difference equals 1.2, the standard deviation of the difference equals 1.5, and n equals 25. what does t equal?
The value of t according to the given conditions equals 4.
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean.
The t-value can be calculated by dividing the mean difference by the standard error of the mean difference.
The formula for calculating t is:
t = (mean difference) / (standard deviation / sqrt(n))
Given that the mean difference equals 1.2, the standard deviation of the difference equals 1.5, and n equals 25.
Therefore the t-value can be calculated as follows:
t = (1.2) / (1.5 / sqrt(25)) = (1.2) / (1.5 / 5)= (1.2) / (0.3)= 4
Therefore, t equals 4.
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For babysitting, Nicole charges an initial fee of $15 plus $5 per hour. What will the cost be to hire Nicole for any number of hours?
the cost of hiring Nicole for any number of hours "h" will be $15 plus $5 multiplied by the number of hours you hire her for.
To find the cost of hiring Nicole for any number of hours, you need to know the hourly rate and add it to the initial fee.
According to the problem, Nicole charges an initial fee of $15 and $5 per hour. So if you hire Nicole for "h" hours, the cost will be:
Cost = Initial fee + Hourly rate x Number of hours
Cost = $15 + $5 x h
Therefore, the cost of hiring Nicole for any number of hours "h" will be $15 plus $5 multiplied by the number of hours you hire her for.
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The number of home runs a baseball player earned each season in his career are listed. 12, 14, 20, 21, 25, 29, 30, 30, 31, 32, 32, 39, 46 Which of the following box plots best represents the data given?
option (C) is the box plot that best represents the given data set.
Based on the given data set, the box plot that best represents the data is (C). Here are the reasons:
The median of the data set is 30, and this is represented by the line inside the box in all four options.
The box in option (C) ranges from 22.5 to 33.5, which includes the interquartile range (IQR) of the data set, which is from 16 to 37. This means that 50% of the data falls within this range, and the box in option (C) represents this well.
The whiskers in option (C) extend to the minimum and maximum values in the data set, which are 9 and 39 respectively. This means that none of the data points fall outside the whiskers.
The range of the number line in option (C) (7 to 46) and the tick marks (every one unit) also match the range and increments of the given data set.
Therefore, option (C) is the box plot that best represents the given data set.
Here is the visual representation of option (C):
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Geometry The length of a rectangle is 3 times its width. The area of the
rectangle is 170 square meters. Find the width. Round to the nearest
tenth of a meter. (Hint: Use A = lw.)
Rounding to the nearest tenth of a meter, we get the width of the rectangle to be approximately 7.5 meters.
What is area?Area is a measure of the size of a two-dimensional surface, such as the surface of a plane or a geometric shape. It is usually measured in square units, such as square meters (m²) or square feet (ft²).
Here,
Let's assume that the width of the rectangle is x meters. Then, according to the problem statement, the length of the rectangle is 3x meters. The area of a rectangle is given by the formula:
A = length x width
Substituting the values from the problem statement, we get:
170 = (3x) x (x)
Simplifying and solving for x, we get:
3x² = 170
x² = 56.67
x ≈ 7.5
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Question 2(Multiple Choice Worth 2 points)
(Comparing Data MC)
The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4,6,14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9,18, 20, and 22. There are two dots above 6, 10, 12,14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of variability to determine which bus is the most consistent. Explain your answer.
Bus 18, with an IQR of 16
Bus 47, with an IQR of 24
Bus 18, with a range of 16
Bus 47, with a range of 24
Bus 18 is the more consistent bus, due to the lower IQR.
What is the median?
The median is the value that divides a data sample, a population, or a probability distribution's upper and lower halves in statistics and probability theory. It could be referred to as "the middle" value for a data set.
Here, we have
For groups of 15 students, we have that:
The first half is composed of the first seven students, hence the first quartile is the fourth dot, which is the median of the first half.
The second half is composed of the last seven students, hence the first quartile is the eleventh dot, which is the median of the first half.
The quartiles for Bus 18 are given as follows:
Q1 = 12.
Q3 = 18.
Hence the IQR is of:
IQR = Q3 - Q1 = 18 - 2 = 16.
Hence, Bus 18 is the more consistent bus, due to the lower IQR.
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Which are real zeroes of this function?
x3 + 2x2 – 9x – 18
Write the standard equation for the hyperbola graphed above.
The hyperbola's standard equation is thus:[tex]((x - 5)^2) / 4 - ((y + 2)^2) / 1 = 1[/tex]as by the distance down the conjugate axis.
what is equation ?Variables, numbers, and mathematical operations like addition, subtraction, multiplication, and division are frequently included. Equations are used in many disciplines, including physics, engineering, economics, and finance, to describe connections between quantities and to solve problems. For instance, the formula "2x + 5 = 11" states that the number 11 is equal to the sum of the two variables x and 5. We can determine that x equals 3 by finding a solution for x. On the basis of mathematical relationships, equations enable us to locate unknown values and create predictions.
given
The hyperbola shown above has a center at and a horizontal transverse axis (5, -2). Its vertices are at (3, -2) and (8, -2), while its foci are at (2, -2) and (8, -2). (7, -2).
The typical equation for a hyperbola with a center at (h, k) and a horizontal transverse axis is:
((x - h)2) / a2 - ((y - k)2) / b2) equals one.
where an is the distance along the transverse axis from the center to a vertex, and b is the distance along the conjugate axis from the center to a point on the hyperbola.
In this instance, an equals 2, since the distance along the transverse axis between the center and a vertex is 2.
B = 1 because the distance down the conjugate axis from the hyperbola's center to any point is 1.
The hyperbola's standard equation is thus:[tex]((x - 5)^2) / 4 - ((y + 2)^2) / 1 = 1[/tex]as by the distance down the conjugate axis.
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PLEASE I NEED HELP
explain how this is a function
Answer:
This is a function because a function is anything that will give you an output when you give it an input, in this case you could give it an input of 0 and it will give you 2. if you give it 1 it will give you 3.
Step-by-step explanation:
:)
Find the solution set for the following system graphically:
2\3x+4 = y and y < 4x
Therefore, the solution set for the system is the point (1.8, 5.2).
What is graph?A graph is a collection of points, called vertices (or nodes), and a set of connecting lines, called edges, that connect pairs of vertices. Graphs are often used to represent relationships between objects, such as roads between cities, social connections between people, or links between web pages.
Graphs can be classified based on their properties, such as whether they are directed or undirected, whether they have loops (edges that connect a vertex to itself), or whether they are connected (all vertices can be reached from any other vertex).
by the question.
To solve this system of equations graphically, we need to plot the lines represented by each equation on a coordinate plane and find their intersection point (if it exists).
First, let's rearrange the first equation to solve for y:
[tex]y = (2/3)x + 4[/tex]
Now, we can plot this line by finding two points on it. For example, when x = 0, y = 4, and when x = 3, y = 6. We can then connect these points with a straight line.
[tex]y < 4x[/tex]. This is an inequality, so we'll shade the region below the line y = 4x. To plot the line itself, we can again find two points on it. When x = 0, y = 0, and when x = 1, y = 4. Connecting these points.
we need to shade the region below this line, since y is less than 4x. This region includes all points on the coordinate plane that satisfy y < 4x. We can shade it by drawing a dotted line along the line y = 4x and shading the region below.
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A computer costs $800. It loses
of its value every year after it is purchased. Time (years) Value of computer (dollars)
0 A
1 B
2 C
3 D
t E
Complete the table to show the value of the computer at the listed times. Do not include $ signs in your answer. A:
Question Blank 1 of 5
type your answer. , B:
Question Blank 2 of 5
type your answer. , C:
Question Blank 3 of 5
type your answer. , D:
Question Blank 4 of 5
type your answer. E:
Question Blank 5 of 5
type your answer
The value of the computer after 5 years is $189.84 and [tex]v = 800 * (3/4)^t[/tex] , where v is the value of the computer t years after it is purchased.
1. The computer costs $800 initially and loses 1/4 or 25% of its value every year. We can represent this decrease in value using the following formula:
[tex]v = 800 * (1 - 1/4)^t[/tex]
where v is the value of the computer t years after it is purchased. Simplifying this equation, we get:
[tex]v = 800 * (3/4)^t[/tex]
2. To find the value of the computer when t is 5, we can substitute t = 5 into the equation we derived in step 1:
[tex]v = 800 * (3/4)^5[/tex]
[tex]v = 800 * 0.2373[/tex]
[tex]v = 189.84[/tex]
This means that the value of the computer after 5 years is $189.84. This value is less than the initial cost of the computer, which was $800. It indicates that the computer has significantly depreciated in value over time, losing approximately 76% of its initial value.
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The complete question is :
A computer costs $800. It loses 1/4 of its value every year after it is purchased.
1. Write an equation representing the value, v, of the computer, t years after it is purchased.
2. Use your equation to find v when t is 5. What does this value of v mean?
What is the area of this parallelogram?
Answer:
112 square meters
Step-by-step explanation:
The base is 14 meters, and the height is 8 meters. So the area is 14 × 8 = 112 square meters.
3 extra squares can be shaded on this grid so that the resulting pattern has 4 lines of symmetry and rotational symmetry of order 4. Which 3 squares should be shaded?
The three extra squares that should be shaded to have a pattern with 4 lines of symmetry and a rotational symmetry of order 4 are E, H, N.
What requirements should be met?It is required for the new shape to have four lines of symmetry, which means that if the new shape is divided we can obtain four identical lines; moreover, it should have a rotational symmetry of order 4, which means that if we rotate the shape it will coincide with the original shape four times. Based on this, the squares that should be shaded are E, H, N.
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The volume of a right cylinder is V = πr²h, where r is the
radius of the base and h is the height of the cylinder. If the
volume of a cylinder is 48π cubic inches and the height of the
cylinder is 3 inches, then what is the radius of the cylinder in
inches?
The requried radius of the cylinder is 4 inches.
We are given the volume of the cylinder as 48π cubic inches and the height as 3 inches. So we can use the formula V = πr²h to solve for the radius.
48π = πr²(3)
16 = r²
r = ±4
Since the radius of a cylinder cannot be negative, we take the positive value of r, which is 4.
Therefore, the radius of the cylinder is 4 inches.
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If three coins are flipped, what is the probability of two heads and a tail coming up in any
order? Justify your answer by constructing a sample space using an organized list or a tree
diagram (or both).
The probability of getting two heads and one tail in any order is 3/8.
What is probability ?
Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. For example, the probability of flipping a coin and it landing heads up is 0.5, because there are two equally likely outcomes (heads or tails) and one of them is heads.
Probabilities can also be expressed as percentages or fractions. For instance, a probability of 0.25 can be expressed as a percentage of 25%, or as a fraction of 1/4.
According to the question:
The sample space for flipping three coins is:
HHH
HHT
HTH
THH
HTT
THT
TTH
TTT
where H represents heads and T represents tails.
Out of these eight outcomes, there are three outcomes in which two heads and one tail come up in any order: HHT, HTH, and THH. Therefore, the probability of getting two heads and one tail in any order is 3/8, or 0.375, which can also be written as a fraction.
To see why this is the case, you can also use a tree diagram to represent the sample space:
H T
/ \ / \
H T H T
/ \ / \ / \ / \
H T H T H T H T
Each branch represents the outcome of one coin flip, and the branches lead to the possible outcomes of flipping three coins. The outcomes with two heads and one tail are HHT, HTH, and THH, which occur in three out of the eight possible outcomes, as previously stated. Therefore, the probability of getting two heads and one tail in any order is 3/8.
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PLEASE HELP ME SOLVE THIS!!
Therefore, the rate/slope between the two given points is 60.
What is slope?In mathematics, slope refers to the steepness or incline of a line. It measures how much a line rises or falls over a certain horizontal distance, which is called the "run." Slope is usually denoted by the letter m and is defined as the ratio of the change in y (the vertical distance) to the change in x (the horizontal distance) between any two points on the line.
Here,
1. To find the rate/slope between the coordinates (1,60) and (2,120), we can use the slope formula:
slope = (change in y) / (change in x)
So, we have:
slope = (120 - 60) / (2 - 1)
= 60 / 1
= 60
2. The equation given is y = 65x, where x is the time in hours and y is the number of miles. To find the rate/slope, we can see that the equation is in the form of y = mx, where m is the slope. So, the slope of this equation is 65. Therefore, the rate/slope for the given equation is 65.
3.The slope of the graph is the change in y over the change in x for any two points on the line, whereas the slope of the equation is the coefficient of x. In this case, the slope of the graph is not given, so we cannot compare it directly to the slope of the equation.
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What are the solutions of the equation 3x² – 5x + 2 = 0? U C D 1 and 2 1 and Homb -1 and -2 -1 and -2
Answer:
1and 2/3
Step-by-step explanation:
using the factorization method
the product of the equation is positive 6(3×2)
then we find the factors of 6 which give us the product 6 and the sum of-5
the factors are-3 and -2
we then substitute negative 5 with these factors
it then be 3x^2-3x-2x+2=0
then we group factorise
we will have 3x(x-1)-2(x-1)=0
we find the common factors of the 2 groups
we will then have (x-1)(3x-2)=0
then we equate the both brackets to 0
(x-1)=0 and(3x-2)=0
for the first bracket add 1 both sidesand the second add 2 both sides and divide by 3
Answer two questions about Equations A AA and B BB: A . 5 x = 3 x B . 5 = 3 A. B. 5x 5 =3x =3 1) How can we get Equation B BB from Equation A AA? Choose 1 answer: Choose 1 answer: (Choice A) Add/subtract the same quantity to/from both sides A Add/subtract the same quantity to/from both sides (Choice B) Add/subtract a quantity to/from only one side B Add/subtract a quantity to/from only one side (Choice C) Multiply/divide both sides by the same non-zero constant C Multiply/divide both sides by the same non-zero constant (Choice D) Multiply/divide both sides by the same variable expression D Multiply/divide both sides by the same variable expression 2) Based on the previous answer, are the equations equivalent? In other words, do they have the same solution? Choose 1 answer: Choose 1 answer: (Choice A) Yes A Yes (Choice B) No B No
1) The answer is C) MuItipIy/divide bοth sides by the same nοn-zerο cοnstant.
2)The sοIutiοn tο bοth equatiοns is the same.
What is equatiοn?EquivaIent equatiοns are aIgebraic equatiοns that are having identicaI rοοts οr sοIutiοns.
1) Tο get Equatiοn B BB frοm Equatiοn A AA, we need tο muItipIy/divide bοth sides οf Equatiοn A AA by the same nοn-zerο cοnstant. In this case, we can muItipIy bοth sides by 5/3 tο get:
5/3 * 5x = 5/3 * 3x
SimpIifying, we get:
25/3 x = 15/3 x
Which is Equatiοn B BB.
Therefοre, the answer is C) MuItipIy/divide bοth sides by the same nοn-zerο cοnstant.
2) Yes, the equatiοns are equivaIent. When we muItipIy bοth sides οf Equatiοn A AA by 5/3, we are essentiaIIy muItipIying the entire equatiοn by 1, since 5/3 divided by 5/3 is equaI tο 1. Therefοre, the sοIutiοn tο bοth equatiοns is the same.
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A stop sign casts a shadow as shown in the
figure. How tall is the light pole to the nearest
tenth of a foot?
The answer of the given question based on the right angle triangle is , the height of the light pole to the nearest tenth of a foot is 9.3 feet.
What is Right angle triangle?A right-angled triangle, also known as a right triangle, is a triangle that has one angle equal to 90 degrees. The side opposite right angle is called hypotenuse, and other two sides is called legs. The leg opposite to a particular acute angle is known as the opposite side, and the leg adjacent to it is known as the adjacent side.
The Pythagorean theorem is a fundamental theorem that applies to all right-angled triangles. It states that square of hypotenuse of right-angled triangle is equal to sum of squares of its two legs
To determine the height of the light pole, we can use similar triangles.
Let's call height of light pole be "x". Then we have:
(height of stop sign) / (length of stop sign's shadow) = (height of light pole)/(length of light pole's shadow)
Substituting the given values, we have:
8/12 = x/14
Simplifying this equation, we get:
x = (8/12) * 14 = 9.33 feet
Therefore, the height of the light pole to the nearest tenth of a foot is 9.3 feet.
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Hi! Can you help my question i really need it. (Please don't answer if you don't know)
The statements and reasons that completes the table that proves the triangles are congruent are;
1. 1. Given, 2. Alternate interior angles theorem, 3. SAS Postulate
2. 1. Given, 2. All right angles are congruent, 3. Definition of midpoint, 4. ASA Postulate
3. 1. [tex]\overline{TM}[/tex] ≅ [tex]\overline{PR}[/tex], 2. [tex]\overline{TM}[/tex] ≅ [tex]\overline{RP}[/tex], 3. ∠M ≅ ∠R, and ∠T ≅ ∠P, 4. ΔTEM ≅ ΔTER
What are congruent triangles?Congruent triangles are triangles that have exactly the same shape and size.
The completed the tables that prove the congruence of the triangles are presented as follows;
1. Statements Reasons
1. [tex]\overline{AB}[/tex] ≅ [tex]\overline{DC}[/tex] [tex]{}[/tex] 1. Given
2. [tex]\overline{AC}[/tex] ≅ [tex]\overline{AC}[/tex] [tex]{}[/tex] 2. Reflexive property
3. [tex]\overline{AB}[/tex] || [tex]\overline{DC}[/tex] [tex]{}[/tex] 3. Given
4. ∠BAC ≅ ∠DCA [tex]{}[/tex] 4. Alternate interior angles theorem
5. ΔABC ≅ ΔCDA [tex]{}[/tex] 5. SAS Postulate
2. Statement [tex]{}[/tex] Reasons
1. [tex]\overline{RS}[/tex] ⊥ [tex]\overline{ST}[/tex]; [tex]\overline{TU}[/tex]⊥ [tex]\overline{ST}[/tex] 1. Given
2. m∠S = 90°; m∠T = 90° [tex]{}[/tex] 2. Definition of right angles
3. ∠S ≅ ∠T [tex]{}[/tex] 3. All right angles are congruent angles
4. V is the midpoint of [tex]\overline{ST}[/tex] 4. Given
5. [tex]\overline{SV}[/tex] ≅ [tex]\overline{TV}[/tex] 5. Definition of midpoint
6. ∠RVS ≅ ∠UVT [tex]{}[/tex] 6. Vertical angles are congruent
7. ΔRSV ≅ ΔUTV [tex]{}[/tex] 7. ASA Postulate
3. The completed statements in the table are provided as follows;
Statement [tex]{}[/tex] Reason
1. [tex]\overline{TM}[/tex] ≅ [tex]\overline{PR}[/tex] [tex]{}[/tex] 1. Given
2. [tex]\overline{TM}[/tex] ║ [tex]\overline{PR}[/tex] 2. Given
3. ∠M ≅ ∠R [tex]{}[/tex] 3. If two parallel lines are cut by a
∠T ≅ ∠P transversal then alternate interior
[tex]{}[/tex] angles are congruent
4. ΔTEM ≅ ΔPER [tex]{}[/tex] 4. ASA
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PLEASE ANSWER I HAVE 10 MINS
What is the mean of this data set?
A set of data showing the lengths of string in inches. The data includes the following values: 6, 5, 8, 4, 9, 7, 5, 7, 4, 8, 7, 6.
5
five and three fourths
6
six and four-twelfths
(Mean means the average value in a data set; found by adding all numbers in the set and dividing by the number of values in the set)
A set of information displaying string lengths in inches. The values in the data are as follows: 6, 5, 8, 4, 9, 7, 5, 7, 4, 8, 7, 6. This data set's mean is 6.
To find the mean of the data set, we need to add up all the values and then divide by the total number of values.
Adding up all the values:
[tex]6 + 5 + 8 + 4 + 9 + 7 + 5 + 7 + 4 + 8 + 7 + 6 = 76[/tex]
There are 12 values in the data set, so we divide the sum by 12:
76/12 = 6.33 (rounded to two decimal places)
Therefore, the mean of the data set is 6.33.
Therefore the correct answer is thus 6.
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write a equation of a line that goes through (1,2) that is perpendicular to y=-4x+6
Answer:
4y = x + 7.
Step-by-step explanation:
The slope of a line perpendicular to a line of slope m = -1/m
So the slope of the required line = -1/ (-4) = 1/4.
y - y1 = m(x - x1)
y - 2 = 1/4(x - 1)
y = 1/4(x - 1) + 2
y = 1/4x - 1/4 + 2
y = 1/4x + 7/4
4y = x + 7
Which one represents the magnitude and direction angle of the vector shown?
answer is c
The correct answer is: √(6² + 2²), and tan⁻¹(2/6) represents the magnitude and direction angle of the vector.
What is Pythagoras' Theorem?
Pythagoras' theorem is a fundamental principle in geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
The magnitude of a vector is the length of the vector. For a vector that passes from the origin to the point (6,2),
the magnitude can be calculated using the Pythagorean theorem, which states that for a right triangle with legs of length a and b and hypotenuse of length c,
c² = a² + b².
In this case, the vector is the hypotenuse of a right triangle with legs of length 6 and 2, so the magnitude is:
magnitude = √(6² + 2²) = √(40) = 2*√(10)
The direction angle of a vector is the angle that the vector makes with the positive x-axis, measured counterclockwise. The direction angle can be calculated using the inverse tangent function, which is the inverse of the tangent function. In this case, the direction angle is:
direction angle = tan⁻¹(2/6) = tan⁻¹(1/3)
Therefore, the correct answer is: √(6² + 2²), and tan⁻¹(2/6) represents the magnitude and direction angle of the vector.
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POR is a right-angled triangle.
R
x
18 cm
15 cm
(b) Work out the size of the angle marked x.
Give your answer correct to 1 decimal place.
Q
The measure of angle x in the right triangle is 33.6 degrees.
How to find the angle of a right angle triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
The triangle PQR is a right angle triangle. Therefore, let's find the angle x using trigonometric ratios as follows:
cos x = adjacent / hypotenuse
where
adjacent = 15 cm
hypotenuse = 18 cm
Therefore,
cos x = 15 / 18
x = cos⁻¹ 0.83333333333
x = 33.5607646704
Therefore,
x = 33.6 degrees
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help!!!!
the possible answers are below:
a: x=-1/4, y=-1/2
b: x=-1/2, y= -1/4
c: x=1/2, y=1/4
d: x= 1/4, y= 1/2
Answer: Based on the graph, I believe that the answer is a. x = -1/4, y = -1/2
Step-by-step explanation:
Which function is represented by the graph below?
24
3+
101
O f(x) = e.x O f(x) = log x ○ f(x) = e) Of(x) = lnx
The graph below is a graph of a function in the form of f(x) = eˣ,
where ‘e’ is the mathematical constant known as Euler's number and is approximately equal to 2.718.
What is a exponential function?An exponential function has an output that increases rapidly with increasing inputs.
This function is an exponential function, which means that the output increases at an exponential rate as the input increases.
The graph shows that the output, which is represented by the y-axis, increases rapidly as the input, which is represented by the x-axis, increases.
This is a characteristic of an exponential function, which is why this graph is a representation of the function f(x) = eˣ.
The other three functions, f(x) = e.x, f(x) = log x and f(x) = ln x, do not represent the graph as they are not exponential functions.
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Can someone help Asap
Step-by-step explanation:
I answered this on the other question
The center is (1,-4)
The new center is
(-4,-6)
The equation of the center is
[tex](x + 4) {}^{2} + (y + 6) {}^{2} = 16[/tex]
What is the volume of a hemisphere with a radius of 7.1 in, rounded to the nearest tenth of a cubic inch?
A hemisphere with a 7.1-inch radius has a volume of 2478.8 cubic inches.
To calculate a hemisphere's volume, use the following formula:
V = (2/3) × π × r³
where r is the radius of the hemisphere, and π (pi) is a mathematical constant approximately equal to 3.14159.
Substituting the given value of the radius, r = 7.1 inches, into the formula, we get:
V = (2/3) × π × 7.1³
V ≈ 2.094 × π × 7.1³ (rounded to three decimal places)
V ≈ 2.094 × 3.141 × 357.911
V ≈ 2478.796 cubic inches
Therefore, the volume of the hemisphere with a radius of 7.1 inches is approximately 2478.796 cubic inches. Rounded to the nearest tenth of a cubic inch, the volume is 2478.8 cubic inches.
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