The translation of a function and coordinates are given below..
What is translation?It is the movement of the shape in the left, right, up, and down directions.
The translated shape will have the same shape and shape.
There is a positive value when translated to the right and up.
There is a negative value when translated to the left and down.
We have,
The following functions:
y = x²
y = 2x
The transformation is:
Translate two units to the left.
So,
y = (x - 2)²
y = 2(x - 2)
Translation 5 units up.
y = x² + 5
y = 2x + 5
The following coordinates:
Translate 2 units to the right.
(1, 4) = (1 + 2, 4) = (3, 4)
(5, 8) = (5 + 2, 8) = (7, 8)
Translation 5 units down.
(1, 4) = (1, 4 - 5) = (1, -1)
(5, 8) = (5, 8 - 5) = (5, 3)
Thus,
The translation of a function and coordinates are given above.
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2.
In isosceles triangle RST shown below, RS = RT,
M and N are midpoints of RS and RT, respectively,
and MN is drawn. If MN = 3.5 and the perimeter
of ARST is 25, determine and state the length of
NT.
The length of the segment NT is 4.5 units
What is isosceles triangle?
An isosceles triangle is one that has two sides of equal length.
The angles opposite to equal sides are equal.
Let RM=x, then MS=RN=NT=x ( because RS = RT )
RS=RT =2x
RST and RMN are two similar triangles
So, we have
ST/MN = RT/NT
=> ST/3.5 = 2x/x
=> ST/3.5 = 2
=> ST = 2*3.5 = 7
Given , perimeter = 25
=> RS+ST+RT = 25
=> 2x+ST+ 2x = 25
=> 4x + 7 = 25
=> 4x= 25-7 = 18
=> x=18/4 = 4.5
NT=x= 4.5 units
The length of the segment NT is 4.5 units
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which of the following is the best interpretation of the power of a significance test? responses power is the probability of detecting an effect if no effect exists. power is the probability of detecting an effect if no effect exists. power is the probability of detecting an effect if an effect exists. power is the probability of detecting an effect if an effect exists. power is the probability of detecting an effect whether or not an effect exists. power is the probability of detecting an effect whether or not an effect exists. power is the probability of not detecting an effect if no effect exists. power is the probability of not detecting an effect if no effect exists. power is the probability of not detecting an effect if an effect exists.
The power in a significance test is the probability of detecting a true effect, while the probability of making a type II error is the complementary probability of power.
A significance test is a statistical method used to determine whether an observed difference or effect is statistically significant or simply due to chance.
Power is defined as the probability of detecting an effect in a significance test if an effect truly exists. In other words, it is the probability of correctly rejecting the null hypothesis (H0) when the alternative hypothesis (Ha) is true. The null hypothesis assumes that there is no significant difference between two groups, while the alternative hypothesis states that there is a significant difference.
Mathematically, power is calculated using the following formula:
Power = 1 - β
Where β is the probability of making a type II error, which is the probability of failing to reject the null hypothesis when the alternative hypothesis is true. In other words, it is the probability of not detecting an effect when an effect truly exists.
Therefore, power and β are complementary probabilities. If power is high, β is low, and vice versa. A significance test with a low power has a higher chance of making a type II error, meaning that it can fail to detect a real effect. Conversely, a test with a high power has a lower chance of making a type II error, meaning that it can detect a real effect more accurately.
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15. Miss Jackson wrote this number sentence on the board.
7x = 36
Which procedure could be used to find a value for x that will make the number
sentence true?
A. Subtract 7 from 7x, and subtract 7 from 36.
B. Multiply 7x by 7, and multiply 36 by 7.
C. Divide 7x by 7, and divide 36 by 7.
D. Add 7 to 7x, and add 7 to 36.
NEED THIS ASAP
Find m/EFG.
m/EFG
Answer: 41 degrees
Step-by-step explanation:
121-39=82
82/2=41
there are two urns containing colored balls. the first urn contains 50 red balls and 50 blue balls. the second urn contains 30 red balls and 70 blue balls. one of the two urns is randomly chosen (both urns have equal probability of being chosen) and then a ball is drawn at random from one of the two urns. if a red ball is drawn, what is the probability that it came from the first urn?
If a red ball is drawn from two urns containing colored balls , then the probability that it came from the first urn is 0.625 or 62.5% .
Let A = the event that the first urn is chosen, and
B is = the event that a red ball is drawn.
We have to find P(A|B), which means , the probability that the first urn was chosen given that a red ball was drawn.
So , By Bayes' theorem:
we have , P(A|B) = P(B|A) × P(A) / P(B) ;
Since each urn has an equal probability of being chosen, we have P(A) = P(B) = 1/2 ; and
the probability of drawing a red ball is the same regardless of which urn was chosen.
We need to find P(B|A), the probability of drawing a red ball from the first urn is 50/100 = 0.5 ;
To find P(B), the overall probability of drawing a red ball, we can use the law of total probability:
that is ; P(B) = P(B|A) × P(A) + P(B|A') × P(A') ;
where A' = event that the second urn was chosen.
Now , we find P(B|A'), which is the probability of drawing a red ball from the second urn is = 30/100 = 0.3 ;
We know that P(A') = 1/2 = 0.5 , because there are only 2 urns.
So , we have : P(A|B) = P(B|A)×P(A) / P(B) ;
= (0.5×0.5) / (0.5×0.5 + 0.3×0.5)
= 5/8
= 0.625
Therefore, the probability that the red ball came from the first urn is 0.625 or 62.5% .
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The function P(n) = 108 + 10 log(n) gives the
total sound power in decibels when n drill presses are operating in a factory. What is the total sound power, to the nearest decibel, when three drill presses are operating?
112.8 is the the total sound power, when three drill presses are operating
What is a function?A relation is a function if it has only One y-value for each x-value.
Given that a function P(n) = 108 + 10 log(n) gives the total sound power in decibels when n drill presses are operating in a factory.
We need to find the total sound power, to the nearest decibel, when three drill presses are operating
We have to consider n as 3
P(3) = 108 + 10 log(3)
=108+10×0.477
=108+4.77
=112.77
Hence, 112.8 is the the total sound power when three drill presses are operating
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Oliver tries to cut a piece of metal 30 centimeters long the price of metal ends up being 29. 4 centimeters long what is the percent error
The percent error in the specified situation is 2%.
The actual length of the metal is 30 centimeters, and the measured length is 29.4 centimeters. The difference between the actual and measured lengths is:
30 - 29.4 = 0.6 centimeters
The absolute error is the magnitude of this difference:
|0.6| = 0.6 centimeters
To find the percent error, we divide the absolute error by the actual value and multiply by 100:
percent error = (absolute error / actual value) x 100%
= (0.6 / 30) x 100%
= 2%
Therefore, the percent error is 2%.
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Use synthetic division to find the result when 4x^4-7x^3+7x^2-12x+15 is divided by x-1. If there is a remainder, express the result in the form q(x)+r(x)/b(x)
When given expression (4x⁴-7x³+7x²-12x+15)/(x-1) is solved, result in the form q(x)+r(x)/b(x) will be -7x² + 4 + 19/(x-1).
What precisely are expressions?Expressions in mathematics are mathematical statements that are made up of at least two sentences that contain numbers, variables, or both, and are connected by an operator. Addition, subtraction, multiplication, and division are examples of mathematical operations. For example, x + y is an equation that separates the terms x and y by an addition operator. There are two sorts of expressions in mathematics: numerical expressions, which include simply numbers, and algebraic expressions, which contain both numbers and variables.
e.g. A number is 6 times larger than another number, x. This statement may be expressed mathematically as x/2 + 6. Complex issues are solved using mathematical expressions.
Now,
Given expression to solve is (4x⁴-7x³+7x²-12x+15)/(x-1)
then dividing this
=4x⁴/x-1-7x³/x-1+7x²/x-1-12x/x-1+15/x-1
=4x³-3x²+4x-8+7/x-1 in form of q(x)+r(x)/b(x)
= 4x⁴/x-1-7x³/x-1+7x²/x-1-12x/x-1+15/x-1
= -7x² + 4 + 19/(x-1)
hence,
When given expression (4x⁴-7x³+7x²-12x+15)/(x-1) is solved, result in the form q(x)+r(x)/b(x) will be -7x² + 4 + 19/(x-1).
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Simplify g³ x g³‼️‼️‼️
Answer:
[tex]g^6[/tex]
Step-by-step explanation:
When multiplying exponents, for example
[tex]x^2 * x^5[/tex]
Their power values are added together to get
[tex]x^2 * x^5 = x * x * x* x* x* x* x = x^7[/tex]
Answer:
[tex]g^6[/tex]
Step-by-step explanation:
because, [tex]g^3*g^3[/tex] is basically [tex]g^(^3^+^3^)[/tex] which is [tex]g^(^6^)[/tex] = [tex]g^6[/tex]
recent report suggests the proportion of general us population who believe in extraterrestrial life is 0.47. choose the appropriate null and alternative hypothesis that tests whether the proportion of college students who believe in extraterrestrial life in greater than the general population?
The null hypothesis assumes that the proportion of college students who believe in extraterrestrial life is the same or lower than the general population
The appropriate null and alternative hypothesis that tests whether the proportion of college students who believe in extraterrestrial life is greater than the general population can be expressed as follows:
Null hypothesis: The proportion of college students who believe in extraterrestrial life is equal to or less than the general population, or
H0: p <= 0.47
Alternative hypothesis: The proportion of college students who believe in extraterrestrial life is greater than the general population, or
Ha: p > 0.47
where p is the true proportion of college students who believe in extraterrestrial life.
In other words, the null hypothesis assumes that the proportion of college students who believe in extraterrestrial life is the same or lower than the general population (i.e., there is no difference between the two populations), while the alternative hypothesis assumes that the proportion of college students who believe in extraterrestrial life is higher than the general population.
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Let’s see who gets this right..
Pls show your work thank you will mark the Brainliest
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
According to graph, the value of p(x) = 8, when x = -2, as this point lies on the curve ~
Now, put the value of x in each of the choices provided to check if its equal to 8.
[tex]\qquad \sf \dashrightarrow \: p( x) = (0.35) {}^{x} [/tex]
[tex]\qquad \sf \dashrightarrow \: p( - 2) = (0.35) {}^{ - 2} [/tex]
[tex]\qquad \sf \dashrightarrow \: p( - 2) = \dfrac{1}{(0.35 ){}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: p( - 2) = \dfrac{1}{0.1225} [/tex]
[tex]\qquad \sf \dashrightarrow \: p( - 2) = 8.1632[/tex]
[tex]\qquad \sf \dashrightarrow \: p( - 2) \approx 8[/tex]
Since the value satisfy the first equation, the correct choice will be (A)
Fatina uses 7.8 pints of white paint and blue paint to paint her bedroom walls 3/5 of this amount is white paint and the rest is blue paint how many pints of blue paint did she use to paint her bedroom walls
Using the fractional value of blue paint to white paint, the number of pints of blue paint Fatina used to paint her bedroom walls is 3.12 pints.
What is a fractional value?A fractional value is a proportional quantity of the whole value.
Fractional values are depicted in decimals, fractions, or percentages.
The total quantity of white and blue paints used on the bedroom walls = 7.8 pints
The fraction of the white paint = 3/5
The fraction of the blue paint = 2/5 (1- 3/5)
2/5 of 7.8 = 3.12 pints
Thus, proportionately, we can conclude that the blue paint Fatina used was 3.12 pints.
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Kathy uses 3.12 pint of white paint to paint her bedroom walls
How many pints of blue paint did she use?Total amount of paint ( Blue and white paint)= 7.8 pints
Amount of blue paint=3/5 x 7.8 = 4.68Pints
amount of white paint = Total amount of paint - amount of blue paint
= 7.6 pints - 4.68 pints
=3.12 pint of white paint
In conclusion, she uses 3.12 pint of white paint to paint her bedroom walls
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Match the functions with their periods. y = - 3 tan 3 x y = 6 sin 3 x y = - 4 cot x 4 y = 2 cos 2 x 3 y = - 2 3 sec x 5 3 π arrowRight 2 π 3 arrowRight π 3 arrowRight 10 π arrowRight
The functions are matched with their periods as follows:
y = - 3 tan 3 x has a period of π/3.y = 6 sin 3 x has a period of 2π/3.y = - 4 cot x 4 has a period of π.y = 2 cos 2 x 3 has a period of 3π.y = - 2 3 sec x 5 has a period of 2π/5.What is the rationale for the above responses?The period of a trigonometric function is the smallest positive value of "T" for which the function repeats itself.
Note that to determine the period of a function, we need to identify how the function changes over one cycle. The period can then be obtained by dividing the length of the cycle by the number of complete cycles in the full range of the function.
1) y = - 3 tan 3 x: The period of the tangent function is π/b, where b is the coefficient of x. So, the period of y = - 3 tan 3 x is π/3.
2) y = 6 sin 3 x: The period of the sine function is 2π/b, where b is the coefficient of x. So, the period of y = 6 sin 3 x is 2π/3.
3 )y = - 4 cot x 4: The period of the cotangent function is π/b, where b is the coefficient of x. So, the period of y = - 4 cot x 4 is π.
4) y = 2 cos 2 x 3: The period of the cosine function is 2π/b, where b is the coefficient of x. So, the period of y = 2 cos 2 x 3 is 3π.
5 )y = - 2 3 sec x 5: The period of the secant function is 2π/b, where b is the coefficient of x. So, the period of y = - 2 3 sec x 5 is 2π/5.
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A baker initially makes 10 loaves of bread and sells 2 loaves each day.
What equation models the situation, where x is time in days and y is number of loaves?
Y=2x+10
Y=2x-10
Y=-2x+10
Y=-2x-10
Answer:
y = 2x + 10
Step-by-step explanation:
y = 2x + 10
y is the total number of loaves of bread.
x is the number of days.
If the baker baked for ten days, he would have 30 loaves of bread
y = 2x + 10
y = 2(10) + 10
y = 20 + 10
y = 30
If he baked for 50 days, he would have baked 110 loaves
y = 2x + 10
y = 2(50) + 10
y = 100 + 10
y = 110
And so on and so on...
Diego’s history teacher writes a test for the class with 30 problems. The test is worth 50 points and has two types of problems: multiple choice worth 1 point each, and short answer problems worth 3 points each. How many short answer questions are in the test? Explain or show you reasoning. Diego’s history teacher writes a test for the class with 30 question. The test is worth 50 points and has two types of questions: multiple choice worth 1 points each, and short answer problems worth 3 points each. How many short answer questions are in the test? Explain or show you reasoning
there are 10 short answer questions on the test, we get this answer after solving.
Let's assume that the number of multiple choice questions on the test is "m", and the number of short answer questions is "s".
From the given information, we can set up a system of equations:
m + s = 30 (The total number of questions on the test is 30)
1m + 3s = 50 (The total number of points on the test is 50)
To solve for "s", we can use the first equation to find "m" in terms of "s":
m = 30 - s
Then we can substitute this expression for "m" into the second equation:
1(30 - s) + 3s = 50
Simplifying and solving for "s", we get:
30 - s + 3s = 50
2s = 20
s = 10
Therefore, there are 10 short answer questions on the test.
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Complete Question
Diego’s history teacher writes a test for the class with 30 question. The test is worth 50 points and has two types of questions: multiple choice worth 1 points each, and short answer problems worth 3 points each. How many short answer questions are in the test? Explain or show you reasoning.
12. Solve the problem.
According to a college survey, 22% of all students work full time. Find the mean for the
number of students who work full time in samples of size 16.
00.2
03.5
04.0
02.8
The mean for the number of students who work full-time in
samples of size 16 are 3.5.
What is the expected value?We understand The expected value, also known as the expected average in the field of probability theory, is a generalization of the weighted average.
Given, 22% of all students work full-time, per a college poll.
Now, If we choose a sample of 16 students the mean number of students working full-time is,
= 16(22/100)
= 16×0.22
= 3.5.
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The formula area of a trapezoid is A=1/2 h(b_1+b_2) solve for b_1
Please help ASAP
Answer: b1 = [tex]\frac{2A}{h} -b2[/tex]
Step-by-step explanation:
Algebra my friend...Algebra
So:
A = 0.5h(b1+b2)
A/(0.5h) =b1+b2
.: A/(0.5h) - b2 = b1
In other words:
b1 = [tex]\frac{A}{0.5h} -b2[/tex]
The 0.5 in the denominator can be rearranged to get the final answer:
b1 = [tex]\frac{2A}{h} -b2[/tex]
What is the equation of a horizontal line passing through the point (−3, 8)
which of the following is a difference between panel and pooled cross-sectional data? group of answer choices a panel data set consists of data on different cross-sectional units over a given period of time while a pooled data set consists of data on the same cross-sectional units over a given period of time. a panel data set consists of data on the same cross-sectional units over a given period of time while a pooled data set consists of data on different cross-sectional units over a given period of time a panel data consists of data on a single variable measured at a given point in time while a pooled data set consists of data on the same cross-sectional units over a given period of time. a panel data set consists of data on a single variable measured at a given point in time while a pooled data set consists of data on more than one variable at a given point in time.
From the following, a panel data set consists of data on the same cross-sectional units over a given period of time while a pooled data set consists of data on different cross-sectional units over a given period of time is the difference between panel and pooled cross-sectional data.
Panel data refers to samples of the same cross-sectional units observed at multiple points in time.
For example we will follow the same set of households X, Y and Z, for each time period we collect data i.e. in 1990 and we will also interview the same households in 1995.
Pooled data occur when we have a “time series of cross sections,” but the observations in each cross section do not necessarily refer to the same unit.
For example we will take household income data on households X, Y and Z, in 1990. And then we will take the same income data on households G, F and A in 1995. Although we are interested in the same data, we are taking different samples (using different households) in different time periods.
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In 10 words or fewer, write your own definition of slope.
Answer: An incline, a slant up or down.
Step-by-step explanation:
Calculate x in the following ratio: x : 4 = 54 : 3
Answer:
x = 72
Step-by-step explanation:
x : 4 = 54 : 3
express the ratios in fractional form
[tex]\frac{x}{4}[/tex] = [tex]\frac{54}{3}[/tex] = 18 ( multiply both sides by 4 to clear the fraction )
x = 4 × 18 = 72
PLEASE HELP! O is the centre of a sphere and has coordinates (2, -3,5). If AB is a diameter of the sphere
and A has coordinates (5, 1, 1), find the coordinates of B. Give your answer as an ordered
triple (x, y, z).
Answer:
(-2, -6, -6)
Step-by-step explanation:
The center of the sphere, O, and point A, are located on the same diameter of the sphere, AB. Thus, the line segment joining these two points is the radius of the sphere. Therefore, the length of the line segment, OA = OB = r, where r is the radius of the sphere.
We can find the length of the line segment, OA, using the distance formula:
√((5 - 2)^2 + (1 + 3)^2 + (1 - 5)^2) = √(3^2 + 4^2 + (-4)^2) = √49 = 7
Since OA = OB = 7, the coordinates of B can be found by subtracting the radius, 7, from the x, y, and z-coordinates of point A:
B = (5 - 7, 1 - 7, 1 - 7) = (-2, -6, -6)Therefore, the coordinates of B are (-2, -6, -6).
a. Starting with the number 10, build a sequence of 5 numbers.
Answer:
Step-by-step explanation:
10, 20, 30, 40, 50
Solve for x. P S (6x-21)° T Q R
Answer:
x = 11
Step-by-step explanation:
You want to know the measure of x in a square marked with one portion of the bisected corner angle as being (6x -21)°.
AngleWe presume quadrilateral PQRS is a square, so each of the corner angles is 90°, and each of the diagonals bisects the corner angles. That mean ...
(6x -21)° = 90°/2
6x = 66 . . . . . . . . . . divide by °, add 21
x = 11 . . . . . . . . . . . divide by 6
amy invested $223 in the banck and a year later has $280,98 . by what percent has changed
Andrea is three times Nick's age. In 10 years, Andrea will be twelve years older than Nick.
What are their ages now?
Answer:
Nick is 6
Andrea is 18
Step-by-step explanation:
Sounds like a system of equations
Letting...
a = Andrea
n = Nick
Since she's 3 times the age, the first equation will be
a = 3n
Since in 10 years, Andrea will be 12 years older than Nick, we can write
a = n + 12
Since we have two a = ,we can set them equal to each other
3n = n + 12
Subtracting n
3n - n = 12
Now combining the n's (n is the same as 1n)
2n = 12
And last but not least, we can divide by 2
n = 6... so Nick is 6 right now.
Going back to our first equation of a = 3n, if we plug 6 in
a = 6(3) = 18.
Making Andrea 18 right now
A stamp book contains a mixture of 27c second class stamps and 32c first class stamps. The
total value of stamps in the book is exactly $6.00.
How many 27c stamps are there in the book?
A 5
B 8
C 10
D 12
E 22
Answer:
8
Step-by-step explanation:
Let's call the number of 27c stamps in the book "x". The number of 32c stamps in the book would then be $6.00 / $0.32 = 18.75 stamps, but since stamps come in whole numbers, we'll round down to 18 stamps. So the total number of stamps in the book is x + 18.
The total value of the 27c stamps is $0.27 * x. The total value of the 32c stamps is $0.32 * 18 = $5.76. The total value of both stamp types is $6.00, so we have the following equation:
$0.27x + $5.76 = $6.00
Solving for x:
$0.27x = $0.24
x = $0.24 / $0.27 = 8.89 stamps, rounded down to the nearest whole number, which is 8 stamps.
So the answer is B) 8.
If each base angle in an isosceles triangle is 10 degrees larger then the vertex angle, find the measure of the vertex angle.Write the equation how to use to solve for the vertex angle?
The measure of the vertex angle is 53.3degrees, the equation is 3x+20=180.
What is an isosceles right angled triangle?It has two equal sides, and those two equal sides make 90 degrees (right angle) internally. The triangles on either side of the diagonals are isosceles and congruent.
Given;
Each base angle in an isosceles triangle is 10 degrees larger then the vertex angle.
The addition of the internal angles of triangle is 180
So, let vertex angle be x
The other two sides will be x+10,
x+x+10+x+10=180
3x+20=180
x=160/3
x=53.3
Therefore, the vertex angle of the triangle will be 53.3degrees.
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A retailer sells chemistry sets for $21 that were acquired at a cost of $15. What percentage is the mark-up?
The percentage for the markup for the wheelbarrow is 40%.
It is important to note that the percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100
In this case, the retailer sells wheelbarrows for $21 that were acquired at a cost of $15. The markup will be:
The amount paid to purchase an article or the price at which an article is made is known as its cost price. Selling Price: The price at which an article is sold is known as its selling price.= Selling price - Cost price
= $21 - $15
= $6
Markup percentage will be:
= Markup / Cost price × 100
= [tex]\frac{6}{15}[/tex]× 100%
=0.4*100%
= 40%
Therefore, the percentage for the markup is 40%.
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