Answer:
1.6
Step-by-step explanation:
To find the scale factor, we compare the image size to the pre-image size.
R'S' = 8 and RS = 5; this makes the scale factor 8/5, which is 1.6.
Dilation is a transformation that allows you to resize an object. Dilation is a technique for making items bigger or smaller. The scale factor that was used in the dilation is 1.6.
What is dilation?Dilation is a transformation that allows you to resize an object. Dilation is a technique for making items bigger or smaller. This transformation yields a picture that is identical to the original shape. However, there is a size discrepancy in the form.
Scale factor = Dimension of the new shape/Dimension of the original shape
Given that △R′S′T′ is the image of △RST under a dilation through point C. Also, given that RS=5 and R′S′=8. Therefore, the scale factor that was used in the dilation is,
Scale factor = Dimension of the new shape/Dimension of the original shape
Scale factor = R′S′ / RS = 8/5
= 1.6
Hence, the scale factor that was used in the dilation is 1.6.
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The banner over the finish line of a running race is 400. Centimeters long and 85 centimeters high. What is the area over the banner?
The sum of the ages of ruth and her mother is 77 years. the difference in their ages is 27 years. how old is each?
Find the sample standard deviation. round to the nearest tenth. 15 42 53 7 9 12 14 28 47
A circle in the standard (x, y) coordinate plane is tangent to the x-axis at 4 and tangent to the y-axis at 4. Which of the following is an equation of the circle?
a
(x − 4)2 + (y − 4)2 = 16
b
x2 + y2 = 16
c
(x + 4)2 + (y + 4)2 = 16
d
x2 + y2 = 4
e
(x − 4)2 + (y − 4)2 = 4
The equation of the circle is: is (x - 4)² + (y - 4)² = 16 Option A
How the equation of the circle was derivedTo find the equation of a circle tangent to the x-axis at (4, 0) and tangent to the y-axis at (0, 4)
Let's use the general form of the equation for a circle:
(x - h)² + (y - k)² = r²
Where (h, k) is the center of the circle, and r is the radius.
The center of the circle is (4, 4) because it's tangent to both the x-axis and y-axis at 4.
The radius can be found by the distance from the center to the point (4, 0) (which is on the x-axis):
r = √((4 - 4)² + (0 - 4)²) = √(0 + 16) = √16 = 4
So the equation of the circle is:
(x - 4)² + (y - 4)² = 4²
(x - 4)² + (y - 4)²= 16
The correct option is: a) (x - 4)² + (y - 4)² = 16
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Write an equation, in the slope intercept form, of the line with an x-intercept at (3 , 0) and a y-intercept at (0 , -5).
Hello : let A(3,0) B(0,-5)
the slope is : (YB - YA)/(XB -XA)
(-5-0)/(0-3) = 5/3
Subtract. Your answer should be a polynomial in standard form. (-9g^4+3g^2h+1) -(6g^4-3g^2h+h)
Write the decimal 3.59 as a mixed number in simplest form.
Which of the following will result in a rational answer?
A. multiplying pie by a fraction
B. adding the square root of a non perfect square to a whole number
C. adding the square root of a perfect square to pie
D. multiplying a fraction by a repeating decimal.
P.S. I asked a question 2 before this one, no one has answered it can someone do that?
Temperatures in the Gobi desert reach -40 F in the winter and 90 F in the summer. Find the range of the temperatures
add the 2 numbers together
40 + 90 = 130 degree range
SOMEONE PLEASE HELP ME ASAP!!!!!!!
Below is a data set consisting of 33 whole-number observations. Its five-number summary is:
(16,20,22,30,46).
What is the range of the data?
A. 6
B. 16
C. 24
D. 30
Below is a data set consisting of 33 whole-number observations. Its five-number summary is:
(16,20,22,30,46).
How many observations are strictly less than 20?
A wide variety of oak trees grow in the United States, In one study, a sample, of acorns was collected from different locations, and their volumes, in cm^3, were recorded. In the table are the summary statistics for these data:
Statistic | Value
N | 38
Mean | 3.0
Median | 1.8
St.Dev. | 2.6
Minimum | 0.3
Maximum | 10.5
1st Quartile | 1.1
3rd Quartile | 4.3
Describe a procedure that uses some or all of these summary statistics to determine whether outliers are present in the data.
Show the work using the procedure from the previous question to determine if there are outliers in these data.
To determine the number of observations below 24 in the given data set with a five-number summary, we find 25% of 33, yielding 8 observations.
To find the number of observations strictly less than 24, we need to understand the structure of the five-number summary: minimum (12), Q1 (24), median (38), Q3 (51), and maximum (69).
Since Q1 (24) represents the 25th percentile, it indicates that 25% of the observations lie below 24. Therefore, the number of observations strictly less than 24 is 25% of the total number of observations.
Given that there are 33 unique observations, we calculate 25% of 33 as:
[tex]\[ \text{Number of observations} = \frac{25}{100} \times 33 = 8.25 \][/tex]
As we can't have a fraction of an observation, we round down to the nearest whole number. Therefore, there are 8 observations strictly less than 24.
Hence, 8 observations are strictly less than 24 in the given data set.
This calculation involves understanding the position of Q1 in the data set and applying the concept of percentiles to determine the number of observations below a certain value.
The question probable maybe:
Given a data set consisting of 33 unique whole number observations, its five-number summary is: 12, 24, 38, 51, 69
How many observations are strictly less than 24 ?
1. The range of the data is 30.
2. The number of observations strictly less than 20 is the count of observations is 16.
3. Based on the IQR method, there are no outliers in the data.
Let's address each question one by one:
1. Range of the data:
The range of the data is the difference between the maximum and minimum values in the dataset. From the five-number summary given, we have:
Maximum = 46
Minimum = 16
So, the range is:
[tex]\[ \text{Range} = \text{Maximum} - \text{Minimum} = 46 - 16 = 30 \][/tex]
Therefore, the range of the data is 30. Hence, the correct answer is D. 30.
2. Observations strictly less than 20:
From the five-number summary, we know that 20 is the second quartile (median) of the dataset. Observations strictly less than 20 would fall in the first quartile. Therefore, we need to find the number of observations below the first quartile.
Given:
First Quartile = 16
Observations strictly less than 20 = Number of observations below the first quartile.
So, the number of observations strictly less than 20 is the count of observations below the first quartile, which is 16.
Now, for the third question:
To determine if outliers are present in the data, we can use the Interquartile Range (IQR) method.
The Interquartile Range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1).
[tex]\[ \text{IQR} = Q3 - Q1 \][/tex]
Any data point that falls below [tex]\( Q1 - 1.5 \times \text{IQR} \) or above \( Q3 + 1.5 \times \text{IQR} \)[/tex] is considered an outlier.
Given:
Q1 = 1.1
Q3 = 4.3
[tex]\[ \text{IQR} = Q3 - Q1 = 4.3 - 1.1 = 3.2 \][/tex]
Therefore, the lower bound for outliers is [tex]\( 1.1 - 1.5 \times 3.2 = -3.7 \)[/tex] (which is not relevant in this context), and the upper bound for outliers is [tex]\( 4.3 + 1.5 \times 3.2 = 9.9 \).[/tex]
Looking at the summary statistics:
- The minimum value is 0.3, which is within the range.
- The maximum value is 10.5, which is also within the range.
Hence, based on the IQR method, there are no outliers in the data.
Check my answer?
Students observed that their teacher's desk plant looked wilted on Monday morning compared to how it looked at the end of the day on Friday. Some students hypothesized that a warmer room temperature over the weekend caused the plant to wilt. Other students hypothesized that the lack of light caused the plant to wilt. Both hypotheses are valuable because they
A.) are reasonable and testable ---- (My answer)
B.) compare independent variables
C.) compare light and temperature
D.) are the only possible explanations.
Given that x is a whole number, Niram conjectured that x3>x2 .
What value is a counterexample to Niram's conjecture?
(a) −2
(b) 1/10
(c) 1
(d) 5
Answer:
The answer is 1.
Step-by-step explanation:
Took the test.
solve y=x^2+2 for x.
A clothing store offers a shirt in 5 colors, in long or short sleeves, with a choice of three different collars. How many ways can the shirt be designed? a. 20 c. 30 b. 25 d. 50
Answer:
30
Step-by-step explanation:
In his free time, Gary spends 8 hours per week on the Internet and 10 hours per week playing video games. If Gary has five hours of free time per day, approximately what percent of his free time is spent on the Internet and playing video games?
Answer:
He spent a total of 22.85+28.57 = 51.42 % of his free time o internet and videogames.
Step-by-step explanation:
If Gary has 5 hours of free time per day, he has 5*7=35 hours of free time per week.
Now, in the case of internet:
[tex]\frac{35h}{8h}= \frac{100}{x}[/tex]
[tex]x= \frac{8*100}{35}[/tex]
x= 22.85% spent on internet.
In the case of videogames:
[tex]\frac{35h}{10h}= \frac{100}{x}[/tex]
[tex]x= \frac{10*100}{35}[/tex]
x= 28.57% spent on internet.
The perimeter of a rectangular pig pen is 310 ft. The length is 15 ft greater than the width. Find the width
Find the number of real number solutions for the equation. x2 – 4x + 4 = 0
The quadratic equation x^2 - 4x + 4 = 0 has one real number solution, x = 2, which is a repeated solution since the discriminant of the equation is zero.
To determine the number of real number solutions for the equation x2
- 4x + 4 = 0, we can use the discriminant method. The discriminant D of a quadratic equation ax2 + bx + c = 0 is given by b2 - 4ac. For our equation, a = 1, b = -4, and c = 4.
Calculating the discriminant gives us D = (-4)2 - 4(1)(4) = 16 - 16 = 0. Since the discriminant is equal to zero, it indicates that there is exactly one real number solution, which means the quadratic has a perfect square trinomial, or the two real solutions are identical.
In this case, the solution to the equation can be found by factoring the quadratic as (x - 2)2 = 0, which implies that x = 2. Therefore, the equation x2 - 4x + 4 = 0 has one real solution, x = 2, which is repeated.
Michael is riding his bicycle. He rides at a speed of 8 kilometers per hour for 12.8 kilometers. For how many hours does he ride?
What is meant by the term financial planning?
please help me ASAP
What is the length of segment NS?
1 unit
2 units
4 units
6 units
Answer:
Option C. 4 units
Step-by-step explanation:
As we know median of a triangle intersect each other at a point in the ratio of 2.01.
Therefore, in Δ QNL,
[tex]\frac{NS}{SR}[/tex] = [tex]\frac{2}{1}[/tex]
[tex]\frac{(7x-3)}{(5x-3)}[/tex] = [tex]\frac{2}{1}[/tex]
By cross multiplication
(7x - 3) = 2(5x -3)
7x - 3 = 10x - 6
6 - 3 = 10x - 7x
3 = 3x
x = 1
Now length of NS
= (7x - 3)
= (7 × 1 - 3)
= (7 - 3)
= 4 units
Option C. 4 units is the answer.
Which of the following expressions is equivalent to 6m - 10?
2(3m + 5)
-2(5 - 3m)
2(3m - 10)
At what point on the curve x = t 3, y = 3t, z = t 4 is the normal plane parallel to the plane 6x + 6y − 8z = 1?
The coordinates of the point are x=3 / 4, y = 3 / 4, and z = 3 for the plane.
What is a plane?A plane is a two-dimensional Euclidean surface that extends indefinitely in mathematics. A plane is the two-dimensional equivalent of a point, a line, and space.
Given that the points are x = 3t, y = 3t and z = 4t. The equation of the plane is 6x + 6y -8z = 1.
Substitute the value of x,y, and z in the equation and solve for the value of 't'.
6x + 6y -8z = 1.
6 x 3t + 6 x 3t - 8 x 4t = 1
18t + 18t - 32t = 1
4t = 1
t = 1 / 4
The coordinates will be calculated as,
x = 3t = 3 x 1 / 4= 3 / 4
y = 3t = 3 x 1 / 4= 3 / 4
z = 4t = 4 x 3 / 4 = 3
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Juan is saving money for a new car. He has already saved $200 and plans to save $25 per week. This situation can be represented by the function f(x) = 200 + 25x, where x is the number of weeks. How much money has Juan saved after 8 weeks?
$200
$400
$600
$800
400 is the correct answer. I am too lazy to put an explanation, but trust me it's not 800, I just got it wrong.
3. Solve. 5 < x - 2 < 11
A. 5 < x < 11
B. 7 < x < 13
C. 7 < x < 11
D. 5 < x < 16
Sam made $198 last week cutting grass. He worked for 18 hours. How much did he make per hour? He thinks he made $12 per hour. True False
divide:
198/18 = 11
he made $11 per hour
so it's False, he did not make $12 per hour
Bruce wants to make sure that each tiger at the zoo has 1,000 square feet of space. He wants to write an equation to represent the relationship between the number of tigers, t, and the number of square feet of space, f. Based on this information, answer these questions. Write an equation to represent the relationship between the number of tigers, t, and the total number of square feet of space, f, if each tiger has 1,000 square feet of space.
Answer:
The equation that represents the relationship between the number of tigers and the total number of square feet of space is f = 1,000t.
Step-by-step explanation:
In a certain region the number of highway accidents increased by 20% over a four years. How many accidents were in the 2006 if there was 5120 in 2002? hint when the percent increases if you want the original 100% plus the additional 20%
Please help with the tennis court one.
Answer:
Length = 78 feet
Width = 36 feet
Step-by-step explanation:
In a study, a group of ten-year-old boys are fed doughnuts every morning for a week and then weighed to see how much weight they gained. which factor is the dependent variable?
In the stated experiment, the weight gain of the ten-year-old boys is the dependent variable. It is expected to change based on the consumption of doughnuts, which is the independent variable.
Explanation:
In the study described, where a group of ten-year-old boys are fed doughnuts every morning for a week and then weighed to see how much weight they gained, the dependent variable is the weight gain of the boys. The dependent variable is the outcome that is measured in an experiment or study. It is the factor that is expected to change as a result of changes to the independent variable, which in this case is the eating of doughnuts.
The dependent variable depends on the independent variable. For example, if the independent variable is the number of doughnuts eaten, the dependent variable (body weight) would likely change in response to the number of doughnuts consumed.
To illustrate this further, if we were to create a graph with the number of doughnuts eaten (independent variable) on the x-axis and the weight gained (dependent variable) on the y-axis, we could see if there is an exponential relationship or a different kind of correlation between these two variables. By understanding the dependent and independent variables, we can better interpret the results of studies and experiments.
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