After dilation, the size of the image will change and the shape of the image will be same
Dilating an image means the changing the size of the image, but the shape of the image will be same
Dilation is the process of changing the size of the image without changing the shape of the image
The image after the dilation is called as the pre image.
The dilation can be done by using the scale factor or normally increase or decrease the size,
If the dilation of an image done by scale factor, the size is increased or decreased according to the value of scale factor. If it is greater than 1 the size increases and if it is between 0 and 1 the size decreases
Therefore, size of the image will change after the dilation
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In triangle def, if m∠d = (2x)°, m∠e = (2x − 4)°, and m∠f = (x 9)°, what is the value of x? 35 37 44 71
Option A is correct, the required simplified value of the x is given as 35.
In triangle DEF, if m∠D = (2x)°, m∠E = (2x − 4)°, and m∠F = (x + 9)°.
for the triangle sum of the interior angles is equal to 180°.
∠D + ∠E + ∠F = 180
2x + 2x - 4 + x + 9 = 180
5x + 5 = 180
5x = 175
x = 35
Thus, the required simplified value of the x is given as 35.
The sum of the measures of the interior angles of a triangle in Euclidean space is continually 180 stages. This reality is equal to Euclid's parallel postulate. This permits the determination of the degree of the 1/3 perspective of any triangle, given the measure of angles. An exterior perspective of a triangle is an attitude that is a linear pair (and subsequently supplementary) to an indoor angle.
The degree of an exterior perspective of a triangle is the same as the sum of the measures of the 2 indoor angles that aren't adjoining to it; this is the outside perspective theorem. The sum of the measures of the 3 exterior angles (one for every vertex) of any triangle is 360 degrees.
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A random variable x has a mean of 120 and a standard deviation of 15. A random variable y has a mean of 100 and a standard deviation of 9. If x and y are independent, approximately what is the standard deviation of x - y ?.
The standard deviation of x - y is 12
X and Y are independent random variables
For random variable X, mean =120 and standard deviation =15
For random variable Y, mean =100 and standard deviation = 9
Let D be the difference of standard deviation of X and Y.
Variance can be defined as the square of standard deviation.
Hence, Variance of X = (standard deviation of X)2 = (15)2 = 225
And, variance of Y = (standard deviation of Y)2 = (9)2 = 81
SD(X - Y) = sqrt(SD(X)2 - SD(Y)2)
Hence, D = sqrt(225 - 81) = sqrt(14) = 12
Hence, the standard deviation of x - y is 12
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What are the 4 types of slopes of a line?
The four types of the slope of a line are positive, negative, zero, and undefined also known as infinite slope.
A line that is growing when seen from left to right has a positive slope.
A line that is declining when seen from left to right has a negative slope.
When seen from left to right or the other way around, a line with a zero slope is neither increasing nor decreasing. The slope of a horizontal line is zero, to put it simply.
The line is neither moving left nor right, as in the case of a vertical line, if the slope is undefined or infinite. A vertical line's slope might be either + ∞ or - ∞.
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What is the value and value of 6?
The value is nothing but the worth of each digit depending on where it lies in the number and the value of 6 is 6
We know that the value in mathematics is nothing but the worth of each digit depending on where it lies in the number.
We calculate the value of number by multiplying the place value and face value of the digit.
Value = Place Value × Face Value
Place value is the value of the column in which the number is. Each column in a number holds a different place value.
For exa., consider a number 574. Here, the place value of the digit 7 is tens and the place value of 5 is hundreds.
The face value of any digit is the same digit.
For above number 574, the face value of 7 is 7, face value of 5 is 5.
Now, we need to find the value of 6.
The place value for 6 is 1 (units place) and the face value = 6
so, the value of 6 = 1 * 6
= 6
Therefore, the value of 6 is 6
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A line that includes the point (0, -1) has a slope of 1. What is its equation in
slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y = x - 1
Step-by-step explanation:
A line that includes the point (0, -1) has a slope of 1. What is its equation in
slope-intercept form?
slope-intercept form : y = mx + b where m is slope and b is the y-intercept.
you are give:
slope = 1
y-intercept = -1
y = mx + b
y = 1x + (-1)
y = x - 1
Draw a line of fit using (5,35) and (10,30)
The equation of a line in two-dimensional space is typically given in the form y is mx + b.
What is equation of a line ?The equation of line in two-dimensional space is typically given in the form y = mx + b, where m is the slope of the line and b is the y-intercept, the point where the line crosses the y-axis. For example, the equation y = 3x + 2 describes a line with slope 3 and y-intercept (0, 2).Alternatively, the equation of a line can also be given in the slope-intercept form, which is the same as the standard form except that the slope and y-intercept are written explicitly. For example, the equation of the line y = 3x + 2 can also be written as slope = 3, y-intercept = 2.The equation of a line can also be given in the point-slope form, which is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. For example, the equation of a line with slope 2 passing through the point (3, 4) would be y - 4 = 2(x - 3).There is also the general form of the equation of a line, which is given by the equation Ax + By + C = 0, where A and B are the coefficients of the x and y terms and C is the constant term. For example, the equation 2x - 3y + 4 = 0 is in the general form.To learn more about equation of line refer :
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An art teacher has 2,532 crayons. He plans to give 12 crayons to each student who takes his class. How many students take his art class?
Answer:
The art class is attended by 211 students, each one with 12 crayons.
Step-by-step explanation:
Total crayons = 2532
If the teacher gives 12 crayons, then:
Total students = 2532/12 = 211
arturo can have pizza for dinner on any two of the next six days. how many different ways can he select the days on which to have pizza?
the 15 different ways can he select the days on which to have pizza
What is combination?
A combination is a choice made in mathematics from a group of different elements when the order of the choices is irrelevant (unlike permutations). For instance, if three fruits, such as an apple, an orange, and a pear, are supplied, there are three possible pairings of the two: an apple and a pear. Formally speaking, a k-combination of a set S is a subset of S's k unique components. In other words, two combinations are the same if and only if they have the same members. (It is not important how the individuals in each set are arranged.) The quantity of k-combinations for a set with n components
Arturo can have pizza for dinner on any two of the next six days.
he select the days on which to have pizza
So the number of ways c(6 2)
= [tex]\frac{6!}{4!2!}[/tex]
=[tex]\frac{30}{2}[/tex]
=15 ways
Hence the 15 different ways can he select the days on which to have pizza.
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Solve for t:
-18 = -3t−18=−3t
The value of t in -18 = -3t is 6.
What is the equation?A formula known as an equation uses the equals sign to denote the equality of two expressions. In essence, equations are questions, and the motivation for the development of mathematics has been the systematic search for the answers to these questions.
Given:
-18 = -3t
Solve the above equation as shown below,
Multiply both sides by -1
-18 × (-1) = -3t × (-1)
18 = 3t
Divide both sides by 3 we get,
18 / 3 = 3t / 3
t = 6
Therefore, the value of t in -18 = -3t is 6.
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In the figure below, JK¯¯¯¯¯ is parallel to LM¯¯¯¯¯¯ . Suppose that JKLM will be reflected in the y-axis, then translated 3 units down to produce J'K'L'M'. Which statement is true? Responses J'K'¯¯¯¯¯¯¯ will be parallel to L'M'¯¯¯¯¯¯¯¯ . J ' K ' ¯ will be parallel to L ' M ' ¯ . J'K'¯¯¯¯¯¯¯ will be perpendicular to JK¯¯¯¯¯ . J ' K ' ¯ will be perpendicular to J K ¯ . J'K'¯¯¯¯¯¯¯ will be perpendicular to L'M'¯¯¯¯¯¯¯¯ . J ' K ' ¯ will be perpendicular to L ' M ' ¯ . J'K'¯¯¯¯¯¯¯ will be parallel to JK¯¯¯¯¯ .
The resultant of the reflection will be JK parallel to J'K'
What is transformation ?
resizing an object is accomplished through a change called dilation. The objects can be enlarged or shrunk via dilation. A shape identical to the source image is created by this transformation. The size of the form does, however, differ. A dilatation ought to either extend or contract the original form. The scale factor is a phrase used to describe this transition.
The scale factor is defined as the difference in size between the new and old images. An established location in the plane is the center of dilatation. The dilation transformation is determined by the scale factor and the center of dilation.
Given JK parallel to LM
and it is reflected back by the y-axis.
So the resultant will be JK p[arallel to J'K'
Hence, The resultant of the reflection will be JK parallel to J'K'
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Find the midpoint of the line segment with the given endpoint. (9,-7),(-9,5)
PLEASE HELPPP
Answer:
[tex](0,-1)[/tex]
Step-by-step explanation:
[tex]\left(\frac{-9+9}{2}, \frac{5-7}{2} \right)=(0, -1)[/tex]
g an inverted conical tank has a height of 18 feet and a diameter of 6 feet. water is flowing into the cone at a rate of 24 cubic feet per second. at what rate is the height of the water in the tank increasing when there is 10 feet of water in the tank.
The rate at which the height of the tank is increasing when there is 10 feet of water in the tank is 2.75 ft/sec .
In the question ,
it is given that ,
the height of the conical tank is =18 feet ,
the radius of the tank is = 6/2 = 3 feet .
the rate at which the water is flowing is = 24 cubic feet per second .
that is dv/dt = 24 .
the ratio of height and radius is
h/r = 18/3
h/r = 6
r = h/6
we know that the Volume of Conical tank is = (πr²h)/3
On substituting r = h/6 and differentiating with respect to time "t" ,
we get ,
dv/dt = (π/108)×3×h²×dh/dt
substituting the value of h = 10 and dv/dt = 24 ,
we get ,
24 = (π/108)×3×10²×dh/dt
dh/dt = (24 * 36)/100π
= 2.7501
≈ 2.75 ft/sec .
Therefore , the rate of change of the height of the tank is 2.75 ft/sec .
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What is 5/4 X 5/3 X 5/6 = also how many times can 5 go into the answer
how do you solve x=-54
what are two requirements that must be satisfied to perform a chi-square test (such as the test of homogeneity, the goodness-of-fit test, and the test of independence of proportions)?
The two requirements that must be satisfied to perform a chi-square test are All Ei>=1 and no more than 20% of the Ei are less than 5.
What is chi-square?
In order to establish if the expected and actual findings are well-fitting, the statistical test known as chi-square compares the differences between categorical variables from a random sample.
For the given equation,
To perform a chi-square test,
All Ei>=1 and no more than 20% of the Ei are less than 5
Hence, these two are the important requirements to carry out the chi-square goodness of fit test.
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when studying the relationship between test performance and length of sleep (the night before), which type of measurement is being examined?
When studying the relationship between test performance and length of sleep (the night before), measure of association type of measurement is being examined.
What is measure of association?
Measure of association in statistics any of various factors or coefficient used to quantity a relationship between two or more variables.
Measure of association are used in various fields of research but are specially common in the areas of Epidermiology and Psycology, where they frequently are used to quantity relationships between exposures and behaviours.
Here length of sleeping and test performance is behavioural based relationship. It can best studied through measure of association.
Hence, when studying the relationship between test performance and length of sleep (the night before), measure of association type of measurement is being examined.
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How do you find the domain and range of a quadratic graph?
To find the domain, we look around the x-axis from left to right because domain is about inputs and the range is partly determined by the pivotal point, or vertex.
In the given question we have to explain, how we can find the domain and range of a quadratic graph.
We are only interested in the horizontal aspect of the graph because domain is about inputs. The x-axis from left to right in search of areas where the graph doesn't exist in order to view the domain.
The range is partly determined by the pivotal point, or vertex. The parabola's opening direction is the other. The range is all real integers bigger than or equal to the range's y-coordinate if a quadratic function opens up. All real integers less than or equal to the range's y-coordinate are in the range if a quadratic function opens downward.
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A bicycle store costs $2700 per month to operate. The store pays and average of $60 per bike. The average selling price of each bicycle is $90. How many bicycles must the store sell each month to break even?
I need the 500th term of the 7 count sequence 24,31,38,45,52
The 500th term of the 7 count sequence 24,31,38,45,52 is 3517.
How to calculate the sequence?It should be noted that this is an arithmetic sequence. The formula is represented as:
a + (n - 1) d
where
a = first term
n = number of terms
d = common difference
Since the numbers are 24,31,38,45,52, the common difference is (3 - 25) = 7
The 500th term will be:
a + (n - 1) d
24 + (500 - 1) × 7
= 24 + (499 × 7)
= 24 + 3493
= 3517
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How do you find the range of a graph without graphing?
The method to find the range of the graph without graphing is explained below .
In the question ,
we have to explain how can we find the range of the graph without graphing .
we know that the Range of the function is the set of all its outputs.
let us understand it with the help of example .
So ,let y = 2-√(-3x+2) ,
we know that the result of the root function is always non negative ,
So , √(-3x+2) ≥ 0,
Multiply with -1 on both the sides ,
we get ,
-√(-3x+2) ≤ 0
Adding 2 to both sides
2 - √(-3x+2) ≤ 2
y ≤ 2
So ,the range will be (-∞ , 2] .
Therefore , the process to find the range is explained above .
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Which polynomial correctly combines the like terms and expresses the given polynomial in standard form?
9xy3 – 4y4 – 10x2y2 + x3y + 3x4 + 2x2y2 – 9y4
Answer:
Combined like terms- 9xy3−13y4+x3y+3x4−8x2y2
Simplified- 3x4+x3y−8x2y2+9xy3−13y4
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
lol
an anova procedure is used for data that was obtained from five sample groups each comprised of six observations. the degrees of freedom for the critical value of f are
The degrees of freedom for the critical value F are (k-1,n-k).
Assume there are 4 sample groups, i.e.
k=4.
Also suppose that each of the four groups contains five observations.
So,
n=4*5
n=20
critical value F has degrees of freedom
(k-1,n-k)
( 4-1:20-4)
(3: 16).
Therefore , the degrees of freedom for the critical value of F is (3.16).
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the sum of two numbers is 15. one number is 4 times the other. letimage andimage represent the two numbers. which system of equations correctly represents this problem?
The two numbers are 3 and 12 when 15 is the result of sum two numbers. One to two are compared in a 4:1 ratio.
Given that,
15 is the result of adding two numbers. One to two are compared in a 4:1 ratio.
We have to find which two numbers are they.
We know that,
Let take x and y to denote the two numbers
We get
x + y = 15 ----->equation(1)
x = 4y ----->equation(2)
Substitute the 4y in equation(1)
(4y) + y = 15
5y = 15
Divide both sides by 5
y = 3.
Substitute y=3 in equation(2)
x=4(3)
x = 12
Therefore, The two numbers are 3 and 12 when 15 is the result of adding two numbers. One to two are compared in a 4:1 ratio.
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Henry is standing 4 feet from the base of a tree in his yard. The tree is 14 feet tall. What is the angle of elevation the point on the ground where he is standing, to the top of the tree? Round to the nearest tenth?
Answer:
Here
Step-by-step explanation:
54.5°
Answer:
63.4
Step-by-step explanation:
First, find the height of the tree relative to Henry by subtracting his height from the tree's height: 14 feet - 4 feet = <<14-4=10>>10 feet
Next, use the formula for finding the angle of elevation: tan(angle) = opposite side / adjacent side
Since the opposite side is the tree's height relative to Henry and the adjacent side is the distance between Henry and the tree, plug in the values: tan(angle) = 10 feet / 4 feet
Solve for the angle: tan(angle) = 2.5
Since the inverse tangent function is used to find the angle given the tangent value, find the inverse tangent of 2.5: angle = tan^-1(2.5) = 63.4 degrees
Round to the nearest tenth: 63.4 degrees rounded to the nearest tenth is 63.4 degrees. Answer: {63.4}.
you and a friend are riding your bikes to a restaurant that you think is east; your friend thinks the restaurant is north. you both leave from the same point, with you riding 16 mph east and your friend riding 8 mph north. after you have travelled 3 mi, at what rate is the distance between you and your friend changing?
The distance between you and your friend changing is 20 MPH for the bike riding.
Let x be the distance you've got got traveled, y be the space your buddies has traveled, and z be the space among you and your pal. From the hassle it's far obvious that dxdt is 16 mph and dydt is 12 mph.
Recall the system for the time given distance and velocityt=d v and the system for the space given time and velocityd=vt The time elapsed if you have traveled 4 miles ist=416=14 hrNow, the space your pal has traveled isd=(12)(14)=3 mi.Hence, x=4 and y=3.An equation bearing on all of the variables is z2=x2+y21)that's primarily based totally at the Pythagorean Theorem.Computing for z given x=4 and y=3z2=32+42z=√32+42=5Differentiating (1) with appreciate to time tz2=x2+y22zdzdt=2xdxdt+2ydydtzdzdt=xdxdt+ydydtNote that the hassle is requesting the charge of extrade of the space among you and your pal, that's dzdt. Rewriting the equation abovezdzdt=xdxdt+ydydtdzdt=xdxdt+ydydtz2)Plugging in x=4, y=3, and z=5, and dxdt=16 and dydt=12 to (2)dzdt=xdxdt+ydydtz=(4)(16)+(3)(12)5=20Thus, the space among you and your pal when you travel 4 miles is converting at a charge of 20 mph.Read more about distance;
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Is the sum of two whole numbers is always less than their product?
No. The sum of 2 whole numbers is not always less than their product.
A whole number is any positive integer running from 0 to infinity.
When we take up any 2 whole numbers and consider 0 or 1 as one of them, the sum of the 2 whole numbers is ging to be more than the product.
When we consider 1 number to be 0, the sum of the numbers will be the number itself. The product will be 0. Hence the sum is greater than the product.
Example- 0 and 25.
0 + 25
= 25
0 X 25
= 0
0 < 25
If we consider one number to be 1. The product of any number and 1 will be the number itself. Adding 1 to any number will in turn increase it. Hence, the sum is greater than the product.
Example- 1 and 78
1 + 78 = 79
1 X 78 = 78
Hence the sum of two whole numbers is not always less than the product.
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question 91 pts nine percent of americans have rh-negative o blood type. in a random sample of 200 americans, what is the probability that the sample proportion with rh-negative o blood types will be less than 12% (round off to second decimal place)?
The probability that the sample proportion with rh-negative o blood types will be less than 12% is 0.93.
Given:
91 pts nine percent of Americans have rh-negative o blood type.
In a random sample of 200 Americans, what is the probability that the sample proportion with rh-negative o blood types will be less than 12% = ?
Using central limit theorem,
P(p cap < p) = P(Z<p cap-p/√p(1-p)/n)
so,
P(p cap < 0.12) = P(Z<0.12-0.09/√(0.09×0.91/200)
= P(Z<1.4825)
= 0.9309 (from Z table)
= 0.93 (Rounded to second decimal place)
Hence we get the required answer.
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Owen decides to buy a 2-pack of almond butter. He notices that each jar in the pack has 84 servings, and each serving has 20 milligrams of sodium. He estimates that the 2-pack has a total of about 320 milligrams of sodium. Does that sound about right?
Pls tell me which option to pick
*Yes
*No its too much
*No it's to less
The estimation done by Owen is wrong because he estimated the amount of sodium very low.
What is estimation?Estimation is a process or way to roughly calculate the answer or solution of a given problem or question, estimation gives an approximate solution for a question.
Given that, Owen decides to buy a 2-pack of almond butter. He notices that each jar in the pack has 84 servings, and each serving has 20 milligrams of sodium.
Since, there are 20 mg of sodium in 1 serving,
Therefore, in 84 serving = 84x20 = 1680 mg of sodium.
And, there are 2 packs, therefore total amount of sodium in 2 packs = 1680x2 = 3360 mg
We calculated the amount of sodium to be 3360 mg, which is larger than the estimation of Owen.
Hence, Owen's estimation for amount of sodium is wrong.
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15/5+1/2x(-4/7) solve
Answer:
(21-2x)/12
Step-by-step explanation:
15/5+1/2x(-4/7)=
15/5+x/2(-4/7)=
3+(-4/7)x/2=
3-(4/7)x/2=
3-(4x/(7*2))=
3-(4x/14)=
(3-4x/14)*14/14=
42/12 - 4x/14 =
(42-4x)/14=(21-2x)/12
suppose that x is uniformly distributed on the interval from 0 to 1. consider a random sample of size 4 from x. what is the joint probability density function of the sample?
The joint probability density function of the sample is 1
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
The likelihood that a population parameter will be less than a given value when the null hypothesis is true is expressed as the p-value, also known as a probability value or a measure of significance, for a particular statistical model.
Every Xi has distribution as shown below:
f(xi) = 1, 0<xi<1
When all Xis are independent, then the following is true.
f(x1,x2,x3,x4) = f(x1) f(x2) f(x3) f(x4)
= 1, for all xi between 0 and 1
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