Answer:
The five-number summary of the data represented by the given box plot is: Min: 72, Q1: 76, Median: 79, Q3: 80.5, Max: 84. Therefore, the correct option is: Min: 72, Q1: 76, Median: 79, Q3: 80.5, Max: 84.
Step-by-step explanation:
Daisy has a box of sea glass that has a mass or 1 1/2 kilograms.the box has a mass of 235 grams when it is empty. What is the mass of the sea glass in grams?
The mass of the sea glass in the box is 1265 grams.
To find the mass of the sea glass in grams, we need to subtract the mass of the empty box from the total mass of the box with the sea glass. Let's convert all the units to grams for consistency.
Mass of the empty box = 235 grams
Total mass of the box with sea glass = 1 1/2 kilograms = 1.5 kilograms = 1500 grams
To determine the mass of the sea glass, we subtract the mass of the empty box from the total mass:
Mass of the sea glass = Total mass of the box with sea glass - Mass of the empty box
Mass of the sea glass = 1500 grams - 235 grams
Performing the subtraction:
Mass of the sea glass = 1265 grams
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Using a t-distribution table or software or a calculator, report the t-statistic which is multiplied by the standard error to form the margin of error for the following cases: a. 90% confidence interval for a mean with 8 observations. b. 90% confidence interval for a mean with 18 observations. c. 99% confidence interval for a mean with 18 observations.
a. The t-value is 1.895.
b. The t-value is 1.734.
c. The t-value is 2.898.
To calculate the t-statistic for a confidence interval, we first need to determine the degrees of freedom (df), which depends on the sample size minus one. We can then use a t-distribution table, software, or calculator to find the t-value at the desired confidence level and degrees of freedom.
a. For a 90% confidence interval with 8 observations, the degrees of freedom is 7. Using the t-distribution table or calculator,
b. For a 90% confidence interval with 18 observations, the degrees of freedom is 17. Using the t-distribution table or calculator,
c. For a 99% confidence interval with 18 observations, the degrees of freedom is 17. Using the t-distribution table, software, or calculator,
Note that as the sample size increases, the degrees of freedom increase and the t-value approaches the value of the standard normal distribution for large sample sizes. This means that for large sample sizes, we can use the z-value instead of the t-value in confidence interval calculations.
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how many zero pairs are in 9+ (-16)?
There are no zero pairs in the expression.
To calculate the number of zero pairs in statement 9 + (-16), we need to clarify the expression and determine any matching positive and negative numbers.
In this respect, 9 and -16 have unlike signs. To simplify, we can rewrite the expression as 9 - 16, which is similar to adding the opposite of 16.
Here, let's look for zero pairs. A zero pair incorporate a positive and negative number that cancel each other out and occur in a sum of zero.
In the expression 9 - 16, there are no identical positive and negative numbers.
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Determine the percentile of 6.2 using the following data set.
4.2 4.6 5.1 6.2 6.3 6.6 6.7 6.8 7.1 7.2
Your answer should be an exact numerical value.
The percentile of 6.2 is |
%.
The percentile of 6.2 in the given data set is 40%.
To determine the percentile of 6.2 in the given data set, we can use the following steps:
Arrange the data set in ascending order:
4.2, 4.6, 5.1, 6.2, 6.3, 6.6, 6.7, 6.8, 7.1, 7.2
Count the number of data points that are less than or equal to 6.2. In this case, there are 4 data points that satisfy this condition: 4.2, 4.6, 5.1, and 6.2.
Calculate the percentile using the formula:
Percentile = (Number of data points less than or equal to the given value / Total number of data points) × 100
In this case, the percentile of 6.2 can be calculated as:
Percentile = (4 / 10) × 100 = 40%
The percentile of 6.2 in the sample data set is therefore 40%.
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What is the total amount and the amount of interest earned on $6,500 at 6% for 25 years?
Total Amount Interest Amount
compounded annually
compounded semiannually
compounded quarterly
V
Answer:
The total amount with annual compounding is 23,304.79 .
The interest with annual compounding is $18,304.79.
The total amount with semi annual compounding is 24,005.10.
The interest with semi annual compounding is $19,005.10.
The total amount with quarterly compounding is 24,377.20.
The interest with quarterly compounding is $19,377.20.
What are the total amount and interest?
The formula for determining the total amount is:
FV = PV(1 + r/m)^nm
Where:
FV =total amount
PV = amount deposited
r = interest rate
n = number of years
m = number of compounding
Interest = FV - amount deposited
FV = 5000 x (1.08)^20 = 23,304.79
Interest = 23,304.79 - 5000 = $18,304.79
FV =5000 x (1.08/2)^(2 x 20) =24,005.10
Interest = 24,005.10 - 5000 = $19,005.10
FV =5000 x (1.08/4)^(20 x 4) =24,377.20
Interest = 24,377.20 - 5000 = $19,377.20
Step-by-step explanation:
19
Select the correct answer.
This table represents function f.
0
2
I
f(x)
0
-2
If function g is a quadratic function that contains the points (-3, 5) and (0, 14), which statement is true over the inter
-3
-4.5
-2
-2
-1
-0.5
1
-0.5
3
-4.5
OA. The average rate of change of fis less than the average rate of change of g.
O B.
The average rate of change of fis more than the average rate of change of g.
'O C.
The average rate of change of fis the same as the average rate of change of g.
OD. The average rates of change of f and g cannot be determined from the given information.
The average rate of change of f(x) is less than average rate of change of g(x). Then the correct option is A.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
The function f(x) is given in the table, then the rate of change of the function f(x) will be
[tex]\text{Rate of change of f(x)} = \dfrac{(-2 + 4.5)}{(-2 + 3)}[/tex]
[tex]\text{Rate of change of f(x)} = 2.5[/tex]
If function g is a quadratic function that contains the points (-3, 5) and (0, 14).
Then the rate of change of the function g(x) will be
[tex]\text{Rate of change of g(x)} = \dfrac{(14 - 5)}{(0 + 3)}[/tex]
[tex]\text{Rate of change of g(x)} = \dfrac{9}{3}[/tex]
[tex]\text{Rate of change of g(x)} = 3[/tex]
Thus, the average rate of change of f(x) is less than average rate of change of g(x).
Then the correct option is A.
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A shop gives an offer saying '20% discount on all products and if your bill amount (after the discount) is more than Rs 1000,
then you will get further discount of 20% on the bill amount).
Aditi buys goods worth Rs 2400 by marking price. What is the amount she needs to pay?
Answer:
Step-by-step explanation:
To calculate the amount Aditi needs to pay, we need to apply the discounts step by step based on the given offer.
Step 1: 20% discount on all products
The marked price of the goods is Rs 2400. Applying a 20% discount means she will get a reduction of 20% of the marked price.
20% of Rs 2400 = (20/100) * Rs 2400 = Rs 480
After the first discount, the new bill amount is Rs 2400 - Rs 480 = Rs 1920.
Step 2: Additional 20% discount on the bill amount if it exceeds Rs 1000
The new bill amount after the first discount is Rs 1920. If this amount exceeds Rs 1000, Aditi will get a further discount of 20% on this bill amount.
Since Rs 1920 is greater than Rs 1000, we can apply a 20% discount to it.
20% of Rs 1920 = (20/100) * Rs 1920 = Rs 384
The final amount Aditi needs to pay after both discounts is Rs 1920 - Rs 384 = Rs 1536.
Therefore, Aditi needs to pay Rs 1536.
cindy bought 7/8 yard of ribbon at a craft store. Jacob bought 4/5 the length of ribbon as Cindy. How many yards of ribbon did Jacob buy?
Jacob bought 0.7 yards of ribbon.
To find out how many yards of ribbon Jacob bought, we need to determine 4/5 of the length of ribbon that Cindy bought.
Cindy bought 7/8 yard of ribbon. To find 4/5 of this length, we multiply 7/8 by 4/5:
(7/8) * (4/5) = (7 * 4) / (8 * 5) = 28/40
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 4:
(28/4) / (40/4) = 7/10
Therefore, Jacob bought 7/10 yard of ribbon.
However, we can convert this fraction to a mixed number or decimal to express it in yards.
To convert 7/10 to a mixed number, we divide the numerator (7) by the denominator (10):
7 ÷ 10 = 0 with a remainder of 7
So, 7/10 is equivalent to 0 7/10 or 0.7 yards.
Therefore, Jacob bought 0.7 yards of ribbon.
In summary, Jacob bought 7/10 yard or 0.7 yards of ribbon.
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I am trying to figure out how you would read 2.1 as time would it be hours, minutes, or seconds?
Answer: seconds
Step-by-step explanation:
Millman’s golfing group is terrific for a group of amateurs. Are they ready to turn pro? Here’s the data. (Hint: Remember that the lower the score [in golf], the better!)
Milkman’s Group: size 9, average score 82, standard deviation 2.6
The pros: size 500, average score 71, standard deviation 3.1
Based on the average scores and standard deviations, it appears that Millman's group still has room for improvement before they can reach the level of professional golfers.
To determine whether Millman's golfing group is ready to turn pro, we can compare their performance to that of professional golfers. Based on the provided data, Millman's group consists of 9 amateurs with an average score of 82 and a standard deviation of 2.6.
On the other hand, the professional golfers consist of 500 individuals with an average score of 71 and a standard deviation of 3.1.
To make a meaningful comparison, we can look at the average scores of the two groups. The average score is an indicator of the overall performance, with lower scores being better in golf.
In this case, the professional golfers have an average score of 71, while Millman's group has an average score of 82. This suggests that the professional golfers perform better, on average, than Millman's group.
However, it is also essential to consider the standard deviation, which measures the variability of scores within each group. A smaller standard deviation indicates less variation and greater consistency in performance.
The professional golfers have a standard deviation of 3.1, while Millman's group has a standard deviation of 2.6. This suggests that Millman's group has slightly less variation in scores compared to the professional golfers.
Overall, based on the average scores and standard deviations, it appears that Millman's group still has room for improvement before they can reach the level of professional golfers.
The professional golfers demonstrate better performance, on average, and a slightly higher variability in scores compared to Millman's group. Therefore, it would be advisable for Millman's group to continue refining their skills and striving to improve their scores before considering turning pro.
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Question 1 (1 point)
Caroline wants to create a helix shape by using the screw modifier. Unfortunately,
when she tries the screw modifier, it keeps spinning her model around an axis
without any vertical movement. What does she need to change to get the vertical
movement that will give it a helix-like shape?
Screw option needs to be set to something greater than 0.
Screw option needs to be set to 0.
Screw option needs to be set to something less than 0.
Screw option needs to be turned off.
Question ? (1 point) ✓ Saved
The correct answer is Screw option needs to be set to something greater than 0.
To get the vertical movement and create a helix-like shape using the screw modifier, Caroline needs to change the screw option to something greater than 0.
The screw option determines the amount of vertical displacement or height of the helix shape.
By setting the screw option to a value greater than 0, Caroline can control the vertical movement of the model as it spirals along the axis, resulting in a helix-like shape.
Therefore, the correct answer is:
Screw option needs to be set to something greater than 0.
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The first three steps in determining the solution set of
the system of equations algebraically are shown.
y=x²-x-3
y=-3x + 5
Step
1
2
3
Equation
x²-x-3=-3x+5
0=x²+
+2x-8
0=(x-2)(x+4)
What are the solutions of this system of equations?
O (-2,-1) and (4, 17)
O (-2, 11) and (4, -7)
O (2, -1) and (-4, 17)
(2, 11) and (-4,-7)
The solutions of the system of equations are (2, -1) and (-4, 17)
The given system of equations is:
y = x² - x - 3
y = -3x + 5
To find the solutions, we need to solve these equations simultaneously.
Set the equations equal to each other:
x² - x - 3 = -3x + 5
Simplify and rewrite the equation in standard form:
x² - x + 3x - 3 - 5 = 0
x² + 2x - 8 = 0
Factor the quadratic equation:
(x - 2)(x + 4) = 0
Now we can solve for x by setting each factor equal to zero:
x - 2 = 0 or x + 4 = 0
Solving for x, we get:
x = 2 or x = -4
To find the corresponding y-values, we substitute these x-values into either of the original equations. Let's use equation 1):
For x = 2:
y = (2)² - 2 - 3 = 4 - 2 - 3 = -1
For x = -4:
y = (-4)² - (-4) - 3 = 16 + 4 - 3 = 17
As a result, the system of equations has two solutions: (2, -1) and (-4, 17).
The right responses are therefore (2, -1) and (-4, 17).
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what is the answer and how do I figure it out
Answer:
[tex]\frac{3}{7}[/tex] < [tex]\frac{3}{5}[/tex]
Step-by-step explanation:
[tex]\frac{3}{7}[/tex] ? [tex]\frac{3}{5}[/tex]
We have to get both fractions with the same denominator to compare them.
[tex]\frac{3}{7}[/tex] = [tex]\frac{15}{35}[/tex]
[tex]\frac{3}{5}[/tex] = [tex]\frac{21}{35}[/tex]
[tex]\frac{15}{35} < \frac{21}{35}[/tex]
So, [tex]\frac{3}{7}[/tex] < [tex]\frac{3}{5}[/tex]
Place point Q on the graph to indicate an unemployment rate of 100 percent, point R to indicate full employment, and point S to indicate where the U.S. economy usually operates.
In a Production Possibility Curve (PPC) with product output Y on the vertical axis and product output X on the horizontal axis the following points are described as follows.
Explanation for PPC- Point Q represents an unemployment rate of 100 percent. It is located at the origin, where both axes intersect, indicating no product output due to complete unemployment.
- Point R signifies full employment and is located at the maximum product output on the X-axis, showing the economy's capacity when all resources are fully utilized.
- Point S indicates where the US economy typically operates, within the usual range of product output levels on the X-axis, reflecting a balanced unemployment rate that includes frictional and structural unemployment.
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what is the value of x in the triangle
Answer:
7
Step-by-step explanation:
In an 30-60-90 right triangle, the longer leg is the shorter leg multiplied by [tex]\sqrt{3}[/tex]
So [tex]7\sqrt{3} =x*\sqrt{3[/tex]
[tex]7=x[/tex]
x=7
Answer:
A. 21
Step-by-step explanation:
This is a 30-60-90 triangle, where you have one 30° angle, one 60°, and one 90° (aka right) angle.
The sides of a 30-60-90 triangle adhere to the following rules:
The side opposite the 30° angle is the shortest side and we can call its length "x".The side opposite the 60° angle is the medium length side and its length is given by x * √3. This means its length is the product of the length of the side opposite the 30° angle and √3.The side opposite the 90° (right) angle is the longest side (aka the hypotenuse) and its length is given by 2x. This means its length is twice the length of the side opposite the 30° angle.Since 7√3 is the length of the side opposite the 30° angle, the entire expression represents x.
Since the length of the side opposite the 60° angle is given by x * √3, the length of this side is (7√3)(√3).
Simplifying gives us 7*3, which is 21.
Thus, the value of x in the triangle is 21 (answer choice A.)
Solve the quadratic by taking square roots.
32=25x^2-4
Hello!
[tex]32 = 25x^2 - 4\\\\32 + 4 = 25x^2\\\\36 = 25x^2\\\\25x^2 - 36 = 0\\\\x = \dfrac{-b \±\sqrt{b^2 - 4ac} }{2a} \\\\\\x = \dfrac{-0 \±\sqrt{0^2 - 4 \times 25 \times (-36) } }{2 \times 25} \\\\\\x = \dfrac{\±60}{50} \\\\\boxed{x = \±\frac{6}{5} }[/tex]
Juan, standing at one focus of a whispering gallery; is 20 ft from the nearest
wall. His friend is standing at the other focus, 80 ft away. How high is its elliptical
ceiling at the center?
Fill in the blank:
The elliptical ceiling is
ft high at the center.
Give your answer to the nearest whole ft (no decimal places).
The elliptical ceiling is approximately 30 ft high at the center.
To find the height of the elliptical ceiling at the center, we can use the properties of an ellipse.
In this case, the two foci of the ellipse represent the positions where Juan and his friend are standing.
The distance between the two foci is 80 ft, and Juan is 20 ft away from the nearest wall.
This means that the sum of the distances from any point on the ellipse to the two foci is constant and equal to 80 + 20 = 100 ft.
Since Juan is standing at one focus and the distance to the nearest wall is given, we can determine the distance from Juan to the farthest wall by subtracting the distance to the nearest wall from the sum of the distances.
Distance from Juan to the farthest wall = 100 ft - 20 ft = 80 ft.
The height of the elliptical ceiling at the center is equal to half of the distance between the nearest and farthest walls.
Height of elliptical ceiling = (80 ft - 20 ft) / 2 = 60 ft / 2 = 30 ft.
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answer ASAP I will brainlist and i will answer two questions on your page
Using row operations to write the augmented matrix, the value of x, y and z are 2, -12 and 11
What is the solution to the system of equations?To solve the system using row operations, we'll write the augmented matrix and perform row operations to transform it into row-echelon form. Here are the steps:
1. Write the augmented matrix for the system of equations:
[1 1 -1 | 1]
[4 -1 1 | 9]
[1 -3 2 | -14]
2. Perform row operations to transform the matrix into row-echelon form:
R2 = R2 - 4R1
R3 = R3 - R1
[1 1 -1 | 1]
[0 -5 5 | 5]
[0 -4 3 | -15]
3. Perform row operations to further transform the matrix into row-echelon form:
R2 = -R2/5
R3 = -4R2 + R3
[1 1 -1 | 1]
[0 1 -1 | -1]
[0 0 -1 | -11]
4. Perform row operations to obtain a diagonal of 1s from left to right:
R1 = R1 + R3
R2 = R2 + R3
[1 1 0 | -10]
[0 1 0 | -12]
[0 0 -1 | -11]
5. Perform row operations to transform the matrix into reduced row-echelon form:
R3 = -R3
[1 1 0 | -10]
[0 1 0 | -12]
[0 0 1 | 11]
The resulting matrix corresponds to the system of equations:
x + y = -10
y = -12
z = 11
Therefore, the solution to the given system of equations is x = -10 - y, y = -12, and z = 11.
So, the solution is x = -10 - (-12) = 2, y = -12, and z = 11.
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please help quick
Which of the following are solutions to the quadratic equation? Check all that
apply.
The correct solutions to the quadratic equation are:
c. -8
e. 2
To determine the solutions to the quadratic equation 2x^2 + 6x - 10 = x^2 + 6, we need to solve for x.
First, let's simplify the equation by combining like terms:
2x^2 + 6x - 10 - x^2 - 6 = 0
x^2 + 6x - 16 = 0
Now, we can solve this quadratic equation by factoring or by using the quadratic formula.
By factoring:
(x + 8)(x - 2) = 0
Setting each factor equal to zero, we get:
x + 8 = 0 --> x = -8
x - 2 = 0 --> x = 2
So, the solutions to the quadratic equation are x = -8 and x = 2.
Now, let's check the given options:
a. -2: This value is not a solution to the equation.
b. 1/3: This value is not a solution to the equation.
c. -8: This value is a solution to the equation.
d. -1/2: This value is not a solution to the equation.
e. 2: This value is a solution to the equation.
f. 8: This value is not a solution to the equation.
The following are the proper answers to the quadratic equation: c. -8 e.2
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How much money has to be invested at 2.9% interest compounded
continuously to have $34,000 after 18 years?
A. $20,173.31
B. $20,211.34
C. $20,249.07
D. $20,186.02
Answer:
None of the given options (A, B, C, D) match the correct investment amount.
Explaination:
A = P * e^(rt),
where:
A = the future amount (in this case, $34,000),
P = the principal amount (the initial investment),
e = Euler's number (approximately 2.71828),
r = the interest rate (2.9% expressed as a decimal, so 0.029),
t = the time period (18 years).
We can rearrange the formula to solve for P:
P = A / e^(rt).
Now we can plug in the given values and calculate the investment amount:
P = $34,000 / e^(0.029 * 18).
Using a calculator, we can evaluate e^(0.029 * 18) and divide $34,000 by the result to find the investment amount.
Calculating e^(0.029 * 18) gives us approximately 1.604.
P = $34,000 / 1.604 ≈ $21,179.55
En una ciudad se midió la temperatura a las 7:00 am y el valor fue de 15°C, luego se midió a las 3:00 pm el valor fue de 24°C. Partiendo del nivel de medición de esta variable, en qué proporción excede una temperatura de la otra, analice su respuesta.
The proportion by which the later temperature exceeds the earlier temperature is 3/5 or 3:5.
In what proportion does one temperature exceed the other?To determine the proportion by which one temperature exceeds the other, we need to calculate the difference between the two temperatures and express it as a proportion of the starting temperature.
First, calculate the temperature difference between 7:00 am and 3:00 pm:
temperature difference = 24°C - 15°C = 9°C
Now, express the temperature difference as a proportion of the starting temperature (15°C).
Proportion = Temperature difference / Starting temperature
Proportion = 9/15
Proportion = 3/5
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Question in English
In a city the temperature was measured at 7:00 am and the value was 15°C, then it was measured at 3:00 pm the value was 24°C. Starting from the level of measurement of this variable, in what proportion does one temperature exceed the other, analyze your answer.
What is the difference quotient of the function f(x) = 12x + 1?
The difference quotient of the function f(x) = 12x + 1 is 12.
The difference quotient of a function measures the average rate of change of the function between two points. To find the difference quotient of the function f(x) = 12x + 1, we can follow these steps:
Select two points on the function, let's call them x and x + h, where h is a small positive value.
Evaluate the function at those two points to get the corresponding y-values. For f(x) = 12x + 1, we have:
f(x) = 12x + 1
f(x + h) = 12(x + h) + 1
Calculate the difference quotient by subtracting the values and dividing by h:
[f(x + h) - f(x)] / h
= [(12(x + h) + 1) - (12x + 1)] / h
= [12x + 12h + 1 - 12x - 1] / h
= (12h) / h
= 12
In this case, since the function is linear with a slope of 12, the difference quotient is constant and equal to the slope of the function. This means that for every unit increase in x, the function f(x) increases by 12.
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(Comparing Data LC)
The histograms display the frequency of temperatures in two different locations in a 30-day period.
When comparing the data, which measure of variability should be used for both sets of data to determine the location with the most consistent temperature?
A IQR, because Sunny Town is symmetric
B IQR, because Beach Town is skewed
C Range, because Sunny Town is skewed
D Range, because Beach Town is symmetric
IQR, because Sunny Town is symmetric should be used for both sets of data to determine the location with the most consistent temperature?(option a).
1. The question asks for the measure of variability that should be used to determine the location with the most consistent temperature when comparing the data from two different locations.
2. The first option, A, suggests using the Interquartile Range (IQR) because Sunny Town is symmetric. This means that the data in Sunny Town is evenly distributed around the median, indicating consistency in temperatures.
3. The second option, B, proposes using the IQR because Beach Town is skewed. Skewness implies an asymmetrical distribution, which may indicate less consistency in temperatures.
4. The third option, C, suggests using the Range because Sunny Town is skewed. Skewed data in Sunny Town might imply a larger spread and less consistency in temperatures.
5. The fourth option, D, recommends using the Range because Beach Town is symmetric. However, symmetric data indicates consistency, making the Range less suitable as a measure of variability.
6. Considering the explanations for each option, the best choice is A, IQR, because Sunny Town is symmetric. The symmetric distribution suggests that the temperatures in Sunny Town are consistent and evenly distributed around the median.
7. Therefore, the measure of variability that should be used for both sets of data to determine the location with the most consistent temperature is the IQR, as indicated by option A.
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Combine like terms I need help pls!!!!
Answer:
21 - 12p
Step-by-step explanation:
I hope this helps and I'm super sorry if I'm wrong!
write the standard form of the equation of a circle with radius 2 and )-14,-13).
Answer:
11? I'm so sorry if it's incorrect. I apologize.
point D i ain’t the interior of ABC . what is m/ DBC
Answer:
36.5°--------------------------------
Angles ABD and DBC form a linear pair, hence their sum is 180°.
Set up an equation and solve for x:
3x + 22 + x - 4 = 1804x + 18 = 1804x = 162x = 40.5Substitute 40.5 for x and find the measure of ∠DBC:
m∠DBC = 40.5 - 4 m∠DBC = 36.5A company has recently been hiring new employees. Today the company has 32% more employees than it did a year ago. If there are currently 69,300 employees, how many employees did the company have a year ago?
Answer:
52500
Step-by-step explanation:
Let there be x employees in the previous year
Now, the company has 32% more employees whis is 69300
i.e.
[tex]x + \frac{32}{100} x = 69300\\\\ \implies\frac{132x}{100} = 69300 \\\\\implies 132x = 6930000\\\\\implies x = \frac{6930000}{132}\\[/tex]
⇒ x = 52500
There were 52500 employees in the previous year
What is the surface area of a triangular with 6, 7cm 4cm 12cm
The surface area of the given triangle is approximately 33.74 square centimeters.
To calculate the surface area of a triangle, we need the lengths of two sides and the included angle between them. However, in this case, you provided the lengths of all three sides (6 cm, 7 cm, and 12 cm).
To determine the surface area, we can use Heron's formula, which is applicable to triangles with all three side lengths known.
Heron's formula states that the surface area (A) of a triangle with side lengths a, b, and c is given by:
[tex]A = \sqrt(s \times (s - a) \times (s - b) \times (s - c))[/tex]
where s is the semi perimeter of the triangle, calculated as:
s = (a + b + c) / 2
Plugging in the given side lengths, we have:
s = (6 cm + 7 cm + 12 cm) / 2 = 25 / 2 = 12.5 cm
Now we can substitute the values into Heron's formula:
[tex]A = \sqrt(12.5 cm \times (12.5 cm - 6 cm) \times (12.5 cm - 7 cm) \times (12.5 cm - 12 cm))[/tex]
[tex]= \sqrt(12.5 cm \times 6.5 cm \times 5.5 cm \times 0.5 cm)[/tex]
= √(1137.5 cm^4)
≈ 33.74 cm^2
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Jake drives a tractor from one town to another, a distance of 120 kilometers. He drives 6 kilometers per hour faster on the return trip, cutting 1 hour off the time. How fast does he drive each way?
The speed of Jake's initial trip is x = 24 kilometers per hour, and the speed of the return trip is x + 6 = 30 kilometers per hour.
Let's assume that Jake's speed during the initial trip is represented by "x" kilometers per hour.
On the return trip, he drives 6 kilometers per hour faster, so his speed can be represented as "x + 6" kilometers per hour.
To find the time taken for each trip, we can use the formula Time = Distance / Speed.
For the initial trip, the time taken is 120 kilometers divided by x kilometers per hour, which gives us 120/x hours.
On the return trip, the time taken is 120 kilometers divided by (x + 6) kilometers per hour, which gives us 120/(x + 6) hours.
According to the problem, the return trip takes 1 hour less than the initial trip. So we can set up the equation:
120/x - 1 = 120/(x + 6)
To solve this equation, we can multiply both sides by x(x + 6) to eliminate the denominators:
120(x + 6) - x(x + 6) = 120x
Simplifying this equation:
120x + 720 - x² - 6x = 120x
Combining like terms:
x² + 6x - 720 = 0
Now we can solve this quadratic equation by factoring or using the quadratic formula. By factoring, we find:
(x + 30)(x - 24) = 0
This gives us two potential solutions: x = -30 or x = 24.
Since speed cannot be negative, we discard the solution x = -30.
Therefore, the speed of Jake's initial trip is x = 24 kilometers per hour, and the speed of the return trip is x + 6 = 30 kilometers per hour.
So, Jake drives at a speed of 24 kilometers per hour on the initial trip and 30 kilometers per hour on the return trip.
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what does a fraction that is horizontally compressed versus vertically compressed look like?
Answer:
Fractions are like pancakes: you can flatten them horizontally or vertically. Horizontal flattening means you shrink the x-value by multiplying it by a huge number before doing anything else. Vertical flattening means you squish the y-value by multiplying the whole function by a tiny number. For example, if f (x) = x^2, then f (2x) is horizontally flattened by 2 and f (0.5x^2) is vertically flattened by 0.5. Don't worry, it's not rocket science, it's just math.