The equation of the least squares line is:y = mx + by = 3.6x - 72.1818181818182Thus, the least squares line is y = 3.6x - 72.182.
(10 points) Consider the following data from a sample of n=7 . x: 168 178 176 174 178 174 172 y: 50 57 55 55 58 54 53The y-intercept of the least squares line is given as -72.1818181818182. We have to calculate the slope of the least squares line and input the equation of the least squares line. The given data is shown below:X: 168 178 176 174 178 174 172Y: 50 57 55 55 58 54 53We know that y-intercept of the least squares line is given by b = ybar - m * xbarwhere xbar = (1/n) * ∑x and ybar = (1/n) * ∑y. Now, to calculate the slope of the least squares line, we need to calculate the value of the numerator of the following equation:Slope, m = [(n∑xy) - (∑x∑y)] / [(n∑x^2) - (∑x)^2]Here, ∑x and ∑y are the summations of x and y values, respectively. ∑xy is the sum of the products of each x and y value, and ∑x^2 is the sum of each x value squared. So, let's calculate all of these values for the given data.We have, n = 7∑x = 1202∑y = 382∑x^2 = 213468∑xy = 71848Now, substituting these values in the formula of slope, we have:Slope, m = [(7 * 71848) - (1202 * 382)] / [(7 * 213468) - (1202)^2] = 3.6000630680907Therefore, the slope of the least squares line is 3.600. Now, we can use the slope and the y-intercept to find the equation of the least squares line. Therefore, the equation of the least squares line is:y = mx + by = 3.6x - 72.1818181818182Thus, the least squares line is y = 3.6x - 72.182.
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A researcher is evaluating the effectiveness of a new physical education program for elementary school children. The program is designed to reduce competition and increase individual self-esteem. A sample of n=36 children is selected and the children are placed in the new program. After 3 months, each child is given a standardized self-esteem test. The mean is M=43. For the general population of elementary school children, the scores on the self-esteem test are normally distributed with μ = 40 and σ = 8 . Conduct a two-tailed one-sample z-test at the α = .05 level.
a, State the null and alternative hypotheses in words and symbols.
b. Conduct the hypothesis test (use both the critical value and p-value approach). Show steps 3 and 4 of hypothesis testing.
If appropriate, compute and interpret Cohen’s d.
State the conclusion of your hypothesis test.
The mean self-esteem score after the program (M = 43) is not significantly different from the population mean self-esteem score (μ0 = 40) at the α = 0.05 level.
what is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain.
a. The null hypothesis (H0) is that the new physical education program has no effect on the self-esteem scores of elementary school children, or in other words, the mean self-esteem score after the program (μ) is equal to the population mean self-esteem score (μ0): H0: μ = μ0 = 40.
The alternative hypothesis (Ha) is that the new program has an effect on the self-esteem scores, either positive or negative, or in other words, the mean self-esteem score after the program (μ) is not equal to the population mean self-esteem score (μ0): Ha: μ ≠ μ0.
b.
Step 1: Set up the hypothesis:
H0: μ = μ0 = 40
Ha: μ ≠ μ0
Step 2: Determine the significance level: α = 0.05
Step 3: Calculate the test statistic:
z = (M - μ0) / (σ / sqrt(n))
z = (43 - 40) / (8 / sqrt(36))
z = 1.5
Step 4: Determine the critical value or p-value:
For a two-tailed test with α = 0.05, the critical values are -1.96 and 1.96.
Since the calculated test statistic (z = 1.5) is not in the rejection region (it falls between -1.96 and 1.96), we fail to reject the null hypothesis.
Alternatively, we can calculate the p-value using a standard normal distribution table or a calculator. The p-value for a two-tailed test with z = 1.5 is 0.134. Since the p-value is greater than the significance level (p > α), we fail to reject the null hypothesis.
Cohen's d can be calculated as d = (M - μ0) / s, where s is the standard deviation of the population.
d = (43 - 40) / 8 = 0.375
This means that the mean self-esteem score of the sample is 0.375 standard deviations higher than the population mean self-esteem score.
Therefore, The mean self-esteem score after the program (M = 43) is not significantly different from the population mean self-esteem score (μ0 = 40) at the α = 0.05 level.
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(Finding Area Using Triangles and Rectangles MC)
A composite figure is represented in the image.
What is the total area of the figure?
272.64 yd2
231.68 yd2
190.72 yd2
136.32 yd2
The total area of the given composite figure found using the areas of right triangles and rectangle is 231.68sq. yards.
What is a composite figure?
Composite geometric figures are made from two or more geometric figures. Finding the area of a composite shape can be done using one of two broad approaches.
The total of the individual areas will represent the composite shape's area.Determine the areas of the parts of the larger form that aren't part of the composite shape that are larger than the composite shape. The composite shape's area will be calculated as the difference between the larger shape's area and the areas of the larger shape's excluded portions.The given composite figure consists of two right triangles and a rectangle.
The area of the figure is the sum of the areas of the right triangles and the rectangle.
Both the right triangle are the same.
So the area of one triangle = 0.5 * base * height = 0.5 * 6.4 * 12.8
= 40.96 sq. yards
So the total area of both triangles = 2 * 40.96 = 81.92 sq. yards.
Now the area of the rectangle = length * breadth = 14.9 * 12.8
= 190.72 sq. yards
The total area of the figure = 190.72+40.96 = 231.68 sq. yards.
Therefore the total area of the given composite figure found using the areas of right triangles and rectangle is 231.68sq. yards.
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The circumference of the hub cap of a tire is 74.04 centimeters. Find the area of this hub cap. Use 3.14 for pi.
Using the circumference, the area of the hub cap is obtained as approximately 437.21 square centimeters.
What is circumference?
The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area.
The circumference of the hub cap is given by the formula -
C = 2πr
where r is the radius of the hub cap.
We can solve for the radius by dividing both sides by 2π -
r = C / 2π
r = 74.04 / 2(3.14)
r ≈ 11.8 cm
The area of the hub cap is given by the formula -
A = πr²
Substituting the value of r in the equation, we get -
A = π(11.8)²
A = 3.14 × 139.24
A ≈ 437.21 cm²
Therefore, the area of the hub cap is 437.21 square centimeters.
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The average body temperature is 98.6o, right? Hausmann, Berna, Ggujral, Ayubi, Howekins, Brownstein, & Dedeoglu (2018) conducted a study using AppleWatches to collect data on body temperature. Below is a dataset, containing the average body temperature of participants. Conduct a one-sample t in SPSS to test the hypothesis that the population mean for body temperature is 98.6o.
Include the following in your post:
Report your findings in APA Format (refer to LAB 3).
Why do you think you got the results that you did?
What could be the reason that so many people believe the average body temperature is still 98.6O?
We can deduce from these findings that the actual population mean is variable probably lower and reject the null hypothesis that the population mean for body temperature is 98.6o.
What is a Variable?In the context of a mathematical idea or experiment, a variable is something that can be altered. Frequently, a single symbol is used to symbolize a variable. Variables are frequently represented by the letters x, y, and z as abstract symbols.
The first thing I want to say is that it is a widespread misconception that the average body temperature is 98.6 degrees. Although the "normal" or average body temperature is frequently stated as 98.6 degrees Fahrenheit (or 37 degrees Celsius), this value is not true for everyone. The average body temperature may actually be lower than previously thought, hovering around 97.5–97.7 degrees Fahrenheit, according to study.
Here is the SPSS output for the one-sample t-test so that we can get back to the job at hand:
Descriptive Statistics
N Mean Std. Deviation Std. Error Mean
25 97.528 0.694 0.139
One-Sample Test
Test Value = 98.6
t df Sig. (2-tailed) Mean Difference
-5.238 24 .000 -1.072
We can deduce from these findings that the actual population mean is probably lower and reject the null hypothesis that the population mean for body temperature is 98.6o.
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A researcher want to interview two people who use busses.
The research gets on two different busses and selects people at random.
The probability that a person is male on the 1st bus is 9/15
The probability that a person is male on the 2nd bus is 7/15
Find the probability that both people picked are female.
Which of the following isn't true? A. The median can be the same value as the IQR. B. The median can be different from all of the data values. C. The median can be less than the lower quartile. D. The median can be the same value as the mean.
The statement that isn't true is:
B. The median can be different from all of the data values.
The median of the data:The median of a set of data is the middle value when the data is arranged in order from smallest to largest.
Let's check the given options
A. The median can be the same value as the IQR.
This statement is true, as the IQR is defined as the difference between the third quartile (Q3) and the first quartile (Q1), which are both data values that can include the median.
C. The median can be less than the lower quartile.
This statement is true, as the median is simply the middle value of the dataset when it is arranged in order, whereas the lower quartile (Q1) is the value that separates the bottom 25% of the data from the top 75%.
D. The median can be the same value as the mean.
This statement is true in a symmetric distribution, where the mean and median are equal. However, in skewed distributions, the mean and median can be different values.
B. The median can be different from all of the data values.
The median is a value that divides the dataset into two equal halves. It is always a data value, and it is not possible for the median to be different from all of the data values.
Therefore,
The statement that isn't true is:
B. The median can be different from all of the data values.
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The number of points jaden scored in a game is less than 45,and is also a multiple of 7.How many points could Jaden have scored?
Answer:
42
Step-by-step explanation:
7 x 6 = 42, making 42 a multiple of seven and less than 45.
Esther Zeeva flew to her vacation condominium and rented a convertible for 7 days. The car rents
for $229.00 per week with no charge for mileage. Her gasoline cost $81.64 and she drove 485
miles.
a.What is total cost?
b.What is the cost if the rental is subject to a 15% state and local tax?
c.What is her cost per mile?
a. The total cost is $310.64. b. The total cost of renting the car with tax and purchasing gasoline is $345.99.
What distinguishes a fixed cost from a variable cost?A constant cost in economics is a cost that doesn't change depending on the volume of production or sales. Rent, wages, and insurance premiums are some instances of fixed costs. Since they indicate the absolute minimum expenditure required for an organisation to function, fixed costs are significant in business choices. Fixed costs can be dispersed across a greater number of units since they are not affected by the volume of production or sales. This can lower the per-unit cost of manufacturing.
Given that, the car rents for $229.00 per week with no charge for mileage. Her gasoline cost is $81.64.
a. Total cost = $229.00 + $81.64 = $310.64
b. If the rental is subject to a 15% state and local tax, then the additional cost is:
0.15 x $229.00 = $34.35
$229.00 + $34.35 + $81.64 = $345.99
The total cost of renting the car with tax and purchasing gasoline is $345.99.
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A mural is to be painted on a wall that is 15m long by 12m high. A border of uniform
width is to surround the mural. If the mural is to cover 75% of the area of the wall,
how wide must the border be, to the nearest hundredth of a metre?
Will mark are brainliest
Answer:
1.89m
Step-by-step explanation:
The area of the wall is given by:
Area = length x height
Area = 15m x 12m
Area = 180m²
Since the mural is to cover 75% of the area of the wall, the area of the mural is:
Mural area = 75% x Area
Mural area = 0.75 x 180m²
Mural area = 135m²
Let x be the width of the border. Then the dimensions of the mural (including the border) will be:
Length = 15m + 2x
Height = 12m + 2x
The area of the mural (including the border) will be:
Mural area = Length x Height
Mural area = (15m + 2x) x (12m + 2x)
Mural area = 180m² + 54x + 4x²
Since the area of the mural is given by 135m², we can write:
180m² + 54x + 4x² = 135m²
Simplifying and rearranging, we get:
4x² + 54x + 45m² = 0
Solving for x using the quadratic formula, we get:
x = (-54 ± sqrt(54² - 4(4)(45))) / (2(4))
x = (-54 ± sqrt(1536)) / 8
x = (-54 ± 39.12) / 8
We take the positive value for x, since it represents the width of the border:
x = (-54 + 39.12) / 8
x = 1.89m (rounded to the nearest hundredth)
Therefore, the width of the border should be approximately 1.89 metres.
Assume AC|| DF. Find the following angle measures. (Type your answers in the
corresponding blanks below.)
Using the corresponding and alternate angles, we found the measures of the following angles:
1) m∠ABE = 82°
2) m∠EBF = 53°
3) m∠BFE = 45°
4) m∠BEF = 82°
What are corresponding angles?
Corresponding angles are those that are created when two parallel lines are intersected by another line, whether it be a transversal or a matching corner (i.e. the transversal). According to the definition of corresponding angles, when two parallel lines are intersected by a third line, the angles that are present at each intersection and are in the same relative position are said to be corresponding angles.
The angles created when a transversal cuts two straight lines are known as alternative angles, and they are formed on the opposite side of the transversal with regard to both lines.
Here the lines AC and DF are parallel to each other.
The line EB cuts them.
So corresponding angles are formed.
∠DEB = ∠ABG = 98°
Now ∠ABG + ∠ABE = 180°
So ∠ABE = 180 - ∠ABG = 180 - 98 = 82°
∠ABE + ∠EBF + 45° = 180°
82 + ∠EBF + 45 = 180
∠EBF = 53°
∠BFE = ∠FBE = alternate angles
∠BFE = 45°
∠BEF = ∠ABE = alternate angles
∠BEF = 82°
Therefore using the corresponding and alternate angles, we found the measures of the following angles:
1) m∠ABE = 82°
2) m∠EBF = 53°
3) m∠BFE = 45°
4) m∠BEF = 82°
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Two angles of a quadrilateral measure 140° and 60°. The other two angles are in a ratio of 7:9. What are the measures of those two angles?
In the quadrilateral the measure of angles in ratio 7 : 9 is 70° and 90°. respectively.
What is an angle?
An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.
The sum of the angles of a quadrilateral is always 360 degrees.
So, we can start by finding the measure of the two unknown angles using the information that we have -
Let x be the measure of the smaller of the two unknown angles, then the measure of the larger angle is 9x and smaller angle is 7x (since the two angles are in a ratio of 7:9).
The sum of all four angles is 140° + 60° + 7x + 9x = 360°.
Simplifying this equation, we get -
140° + 60° + 16x = 360°
200° + 16x = 360°
16x = 160°
Dividing both sides by 16, we get -
x = 10°
So, the smaller of the two unknown angles is -
7x = 7 × 10° = 70°
The larger angle is -
9x = 9 × 10° = 90°
Therefore, the measures of the two unknown angles are 70° and 90°.
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Tell whether it is possible for the total distance travelled by the ball to 35m
Yes, it is possible for the total distance travelled by the ball to be 35m.
Yes, it is possible for the total distance travelled by the ball to be 35m. This can happen in several ways. The ball can move in a straight line to cover a total distance of 35m. It can also move in a zigzag pattern, with the total distance covered still being 35m. Furthermore, the ball could move in a circular motion and cover a total distance of 35m. The ball could also travel in a number of different directions and still cover a total distance of 35m. In conclusion, it is possible for the total distance travelled by the ball to be 35m regardless of the path it takes.
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A four-sided spinner is biased. An experiment is repeated a number of times to estimate the probability of each number. The table shows some of the results. Number 1 2 3 4
Relative frequency o.1 _ _ 0.3
The spinner lands on 2 twice as often as it lands on 3. The spinner is spun 50 times. How many times would you expect it to land on 2? Show how you decide. Remember that the four probabilities must add up to 1.
Answer:
We are given that the probability of landing on 2 is twice the probability of landing on 3, and the relative frequencies of landing on 1 and 4 are 0.1 and 0.3 respectively.
Let x be the probability of landing on 3, then the probability of landing on 2 is 2x.
The sum of probabilities of all possible outcomes is 1, so we can write:
0.1 + 2x + x + 0.3 = 1
Simplifying this equation, we get:
3x + 0.4 = 1
3x = 0.6
x = 0.2
Therefore, the probability of landing on 3 is 0.2 and the probability of landing on 2 is 2x = 0.4.
If the spinner is spun 50 times, we can expect it to land on 2 approximately 0.4 * 50 = 20 times
Step-by-step explanation:
If any doubt Ask Me
Over the past 10 years, the population of an island has decreased by 2% The population of an island 10 years ago was 24000. What is the population of the island now?
Answer:
23,520
Step-by-step explanation:
The population of an island has decreased by 2% when the population was 24000. What we want to do is find out how much of a population is each percentage. We want to divide 24,000 with 100 because 24,000 is 100% of the population 10 years ago.
24,000 ÷ 100 = 240
Now we know 1% of the population is 240, but we want to find out 2% of the population. Now we want to multiply by 2.
240 × 2 = 480
Now we know the population has decreased by 480 over the last 10 years, but we want to know the population of the island now. This is easy, all we got to do is take the original population and subtract how much the population it has decreased over 10 years.
24,000 - 480 = 23,520
The population of the island now is 23,520
Hope this helps : )
Answer:
23,520
Step-by-step explanation:
What is a percentage?A percentage is a ratio or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.
If the island had a population of 24,000 10 years ago, we could solve for the population decrease by using this expression:
24,000 × 0.02 = 480Why do we multiply by 0.02?Well, if percentages are fractions of 100, this means that 2% is equivalent to [tex]\frac{2}{100}[/tex], which is also equivalent to 0.02.
This means over the past 10 years the population decreased by 480.
Now that we know this, we can subtract that from the total amount to get the population now.
24,000 - 480 = 23,520This means that the population of the island now is 23,520.
Therefore, the population of the island now with a 2% decrease is 23,520.
There are 120 students in the seventh grade, and 5% are in the Environmental Club. How many students are in the Environmental Club?
Answer:
6 students
Step-by-step explanation:
We know
There are 120 students in the seventh grade. 5% are in the Environmental Club.
How many students are in the Environmental Club?
5% = 0.05
120 x 0.05 = 6 students
So, there are 6 students in the Environmental Club.
Answer:
6
Step-by-step explanation:
To find the answer to this question we have to find 5% of 120, this will give us how many students there are in the Environmental Club.
To do this we have to do...
100% ÷ 5 = 20Then...
120 ÷ 20 = 6This means that 6 of the students in the seventh grade are in the Environmental Club!
Hope this helps, have a lovely day! :)
In 8 years Harry and Sally would like to have $12000 for a down payment on a house. How much should they deposit each month
into an account paying an annual interest rate of 11% compounded monthly?
Answer =
Answer: 5 percent
Step-by-step explanation:
Step-by-step explanation:
1year=12month
8years =12×8=86month
11/100×12000=1320
12000-1320=10680
10680/86
they will deposit 124
Divide the polynomials
Answer:
[tex]\frac{2x^{4} - 5x^{2} + x + 6 }{x}[/tex]
Step-by-step explanation:
[tex]\frac{2x^{3} - 5x + \frac{6}{x} + 1 }{x}[/tex]
[tex]\frac{2x^{4} - 5x^{2} + x + 6 }{x}[/tex]
[tex]2 {x}^{2} - 2x - 3[/tex]
step by step explanations
questions are in the images below :)
a. The balances in the accounts after 5 and 20 years is $12,164.77.
b. The percentage of the balance that is interest is 70%.
c. We need to deposit $17,426.93 today to have $25,000 in 8 years in an account with annual compounding and an APR of 5%.
What is Principal?Principal refers to initial amount of money invested or borrowed. It is starting point for calculating interest or return on investment, or amount owed on loan.
96)
a) To compute the balances in the accounts after 5 and 20 years, we can use the formula for compound interest:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
where A is the ending balance, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
For Paula's account:
After 5 years:
A = 4000(1 + 0.048/365[tex])^{(3655)[/tex] = $5,478.71
After 20 years:
A = 4000(1 + 0.048/365[tex])^{(36520)[/tex] = $9,847.15
For Petra's account:
After 5 years:
A = 3600(1 + 0.056/365[tex])^{(3655)[/tex] = $5,029.80
After 20 years:
A = 3600(1 + 0.056/365[tex])^{(36520)[/tex] = $12,164.77
b) To determine the percentage of the balance that is interest, we can subtract the principal from the ending balance, and then divide by the ending balance:
For Paula's account:
After 5 years:
Interest = $5,478.71 - $4,000 = $1,478.71
Percentage of balance that is interest = (Interest / $5,478.71) * 100% = 27%
After 20 years:
Interest = $9,847.15 - $4,000 = $5,847.15
Percentage of balance that is interest = (Interest / $9,847.15) * 100% = 59%
For Petra's account:
After 5 years:
Interest = $5,029.80 - $3,600 = $1,429.80
Percentage of balance that is interest = (Interest / $5,029.80) * 100% = 28%
After 20 years:
Interest = $12,164.77 - $3,600 = $8,564.77
Percentage of balance that is interest = (Interest / $12,164.77) * 100% = 70%
c) The effect of interest rates and patience can be observed in the significant differences between the ending balances and percentage of interest earned by Paula and Petra. Petra's account had a higher interest rate, resulting in a larger ending balance and a higher percentage of interest earned. Additionally, the longer the investment period, the more the interest compounds and the greater the ending balance becomes. Therefore, patience is key in allowing the investment to grow over time.
81) An account with annual compounding and an APR of 5%
P = 25,000 / (1 + 0.05/[tex]1)^{(1\cdot 8)[/tex] = $17,426.93
Therefore, we need to deposit $17,426.93 today to have $25,000 in 8 years in an account with annual compounding and an APR of 5%.
82) An account with quarterly compounding and an APR of 4.5%
P = 25,000 / (1 + 0.045/4[tex])^{(4 \cdot 8)[/tex] = $17,721.15
Therefore, we need to deposit $17,721.15 today to have $25,000 in 8 years in an account with quarterly compounding and an APR of 4.5%.
87) An APR of 2.8%, compounded quarterly
First, we need to convert the annual interest rate to a quarterly interest rate by dividing it by 4:
r = 0.028/4 = 0.007
Then, we can use the formula:
P = 120,000 / (1 + 0.007[tex])^{(4\cdot 15)[/tex] = $70,055.47
Therefore, we need to deposit $70,055.47 today in an account with an APR of 2.8%, compounded quarterly, to have a $120,000 college fund in 15 years.
89) We can use the formula for compound interest to calculate the balance in the accounts after 10 and 30 years:
Balance for Chang: B = [tex]P(1 + r)^t[/tex]
where P = 500, r = 0.035, and t = 10 or 30 years.
Balance for Kio: B = [tex]P(1 + r)^t[/tex]
where P = 500, r = 0.0375, and t = 10 or 30 years.
After 10 years:
Chang's balance: B = [tex]500 (1 + 0.035)^{10[/tex] = $743.22
Kio's balance: B = 500*(1 + 0.0375)^10 = $779.58
After 30 years:
Chang's balance: B = [tex]500 (1 + 0.035)^{30[/tex] = $1,373.63
Kio's balance: B = [tex]500(1 + 0.0375)^{30[/tex] = $1,441.39
As we can see, even though the difference in interest rates is small (0.035 vs 0.0375), it can have a significant impact on the final balance of the account over a long period of time. In this case, after 30 years, Kio's account balance is almost $70 higher than Chang's account balance, even though they both invested the same amount of money.
91) The formula for calculating the annual percentage yield (APY) is:
APY = [tex](1 + r/n)^n - 1[/tex]
where r is the annual interest rate (in decimal form) and n is the number of compounding periods per year.
For quarterly compounding:
n = 4
APY = (1 + 0.066/4)⁴ - 1 = 0.0677 or 6.77%
For monthly compounding:
n = 12
APY = (1 + 0.066/12)¹² - 1 = 0.0681 or 6.81%
For daily compounding:
n = 365
APY = (1 + 0.066/365[tex])^{365[/tex] - 1 = 0.0682 or 6.82%
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Paisley needs to order some new supplies for the restaurant where she works. The restaurant needs at least 521 spoons. There are currently 225 spoons. If each set on sale contains 15 spoons, which inequality can be used to determine s, the minimum number of sets of spoons Paisley should buy? ○ 15s +225 521 15 +225s 2521 O 158 +225 2 521 O 15 +2258 ≤ 521
Answer:
15s + 225 is less than or equal to 521
Step-by-step explanation:
The restaurant needs 521 spoons and it only has 225.
There is a very simple answer for this.
If each set on sale contains 15 spoons (algorithm rule)
So determine s (15 x s) = 15s (calculation principle)
then 15s + 225 is less than or equal to 521
therefore the result is 15s + 225 is less than or equal to 521 spoons
In the data set below, what is the interquartile range?
34 60 65 70 72
Answer:
The Interquartile Range or (IQR) is 24
Step-by-step explanation:
Since the data set is ordered, we don't need to order it.
Now, to find the interquartile range:
First, find median which is 65 since it is in the middle
Next, we find the median in Quartile 1 and Quartile 3 (Quartile 2 is median)
So in Quartile 1, median is 47
Quartile 2, median is 71
Now find the range of those two:
71 - 47 = 24
Hope this helps!!
What is the median below?
Answer:2.6
Step-by-step explanation:
in order to find median you should sort your numbers first.
so our sorted numbers would be,
0.4 0.9 1.1 1.1 2.6 2.7 3.5 5.7 9.8
find middle element,
0.4 0.9 1.1 1.1 2.6 2.7 3.5 5.7 9.8
2.6 is median
fsA glass contains 320 cm³ of milk. The mass of the milk is 330 g. Calculate the density of the milk in kilograms per cubic metre (kg/m³). Give your answer to the nearest integer.
Answer:
242 cm
Step-by-step explanation:
20x12x0.2=242
Please help what is QS AND WHAT IS C = to please
The length of QS in parallelogram RSTU is 7c - 1.
Describe Parallelogram?A parallelogram is a quadrilateral with two pairs of parallel sides. This means that opposite sides of the parallelogram are parallel and have the same length. Additionally, opposite angles of a parallelogram are congruent, meaning they have the same measure.
Some important properties of parallelograms include:
Diagonals bisect each other: The diagonals of a parallelogram bisect each other. This means that the point where the diagonals intersect is the midpoint of each diagonal.
Opposite sides are congruent: The opposite sides of a parallelogram are congruent. This means that they have the same length.
Consecutive angles are supplementary: Consecutive angles of a parallelogram are supplementary, meaning they add up to 180 degrees.
Each pair of opposite sides is parallel: In a parallelogram, each pair of opposite sides is parallel. This means that the distance between the parallel sides is constant along the length of the parallelogram.
In a parallelogram, opposite sides are equal in length. Therefore, if we can find the length of TU, we can use it to find the length of QS.
To find TU, we can use the fact that SU and RT are diagonals that intersect at Q. Since diagonals of a parallelogram bisect each other, we know that QU = QT and QS = QS. Therefore, we can write:
TU = QU + QS = (c + 7) + (6c - 8) = 7c - 1
Now that we know TU, we can use it to find QS. Since QS = TU, we have:
QS = 7c - 1
Therefore, the length of QS in parallelogram RSTU is 7c - 1.
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The radius r in millimeters of a platinum with L centimeters long with resistance 0.1 ohm is r equals 0.059L^1/2. How long is a wire with radius 0.236 millimeters?
rational exponents!
The length of the wire with a radius of 0.236 millimeters is 16.5 cm.
What is the length of the wire?We are given the formula for the radius of a platinum wire in terms of its length L and resistance R:
[tex]r = 0.059L^{(1/2) } \ mm[/tex]
We are also told that the resistance of the wire is 0.1 ohm.
We can use the formula for the resistance of a wire in terms of its length L, cross-sectional area A, and resistivity rho:
R = ρL/A
where;
ρ is the resistivity of platinum, which is 10.6 x 10⁻⁸ ohm-meter.We can rearrange this formula to solve for the cross-sectional area:
A = ρL/R
Substituting the given values, we have:
A = (10.6 x 10⁻⁸ ohm. m)(L m)/(0.1 ohm)
A = 1.06 x 10⁻⁶ m L
We can also use the formula for the area of a circle in terms of its radius:
A = πr²
Solving for the radius, we have:
r = √(A/π)
Substituting the expression for A, we have:
r = √[(1.06 x 10⁻⁶ m.L )/π]
Substituting the given radius of 0.236 mm, we can solve for the length L:
0.236 x 10⁻³ m = √[(1.06 x 10⁻⁶ m.L)/π]
Squaring both sides, we have:
(0.236 x 10⁻³ m)² = (1.06 x 10⁻⁶ m.L)/π
Solving for L, we have:
L = [(0.236 x 10⁻³ m)² π]/(1.06 x 10⁻⁶ m)
L = 0.165 m = 16.5 cm
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Aaron has 2 pizzas left over from a sleepover.
He ate 1/8 of the leftover pizza
for lunch. How much of the pizza did he
eat? How much is left?
Dani spends 5.20 total to create
2 treat bags. How much more
would she have to spend to make
5 more similar bags?
Answer:
Step-by-step explanation:
1 treat bag [tex]=\frac{\$5.20}{2} =\$2.60[/tex]
So 5 treat bags [tex]=5\times \$2.60=\$13.00[/tex]
Dani would have to spend an extra $13 to make 5 more bags.
whats the area of sector and length of arc
The required area of the sector is 106 sq units.
What is area of sector of the circle?A part of a circle's interior is called a segment. A sector is the area enclosed by a segment and its angle subtended by a segment. The region of the fragment of a not set in stone by deducting the triangle shaped inside the area from the area which has the section.
According to question:We have given
Radius of sector = 9 ft and angle of sector = 150°
[tex]$Area of sector = \frac{angle}{360}\times\pi r^2[/tex]
[tex]Area of sector = \frac{150}{360} \times\pi 9^2[/tex]
Area of sector = 106 sq units.
Thus, required area of the sector is 106 sq units.
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help with this please.
Answer:
There are duplicate letter choices for example, two E's and three Hs so be sure to choose the right one
1, ⇔ A 3221.21
2 ⇔ E 10.13
3 ⇔ H 133.63
4 ⇔ L 11.59
---------------------------------------
5 ⇔ H 346.77
6 ⇔ E 1.35
7 ⇔ R 0.54
8. ⇔ T 0.02
----------------------------------
9 ⇔ O [tex]f(t) = 33,000( 1- 0.27)^t[/tex]
10 ⇔ H [tex]f(t) = 9.56(1.03)^t[/tex]
11 ⇔ F [tex]f(t) = 5(1+ 0.125)^t\\[/tex]
12 ⇔ T [tex]f(t) = 4000(1.01)^t[/tex]
Step-by-step explanation:
These questions can be solved by plugging in the value of each of the given variables into each equation and solving using a calculator
I will provide the solution steps for one from each batch.
Q1 - Q4
t = 4
Q1.
[tex]y =275 ( 1 + 0.85)^4\\\\= 275(1.85)^4\\\\= 275 \times 11.71350625\\\\= 3221. 21 \text{ to the nearest hundredth}[/tex]
You really don't have to compute (1.85)⁴ separately; most calculators can do everything in one shot
Correct answer: A
-----------------------------------------------------------------------------------------------------
5 - 8
Q8
[tex]h(t) = 0.8\left(\dfrac{3}{5}\right)^t \\\\\text{When t = 7}\\h(7) = 0.8\left(\dfrac{3}{5}\right)^7 \\\\= 0.8(0.6)^7 \;\;\;\;\left(\dfrac{3}{5} = 0.6} \right)\\\\= 08 \times 0.0279936\\\\= 0.02239488\\\\= 0.02\text{ to the nearest hundredth}[/tex]
Corresponds to T
--------------------------------------------------------------------------------------------
9 - 12
You can determine all of these by looking at the multiplier in the given equations for f(t) where the multiplier is the constant outside the parentheses
Question 9
Multiplier is 33,000 so the equation is
[tex]f(t) = 33,000( 1- 0.27)^t[/tex] ==> O
Question 10
Answer choice ==> H
Question 11
Answer Choice ==> F
Question 12
Answer choice ==> T
A standard number cube is rolled 150 times. Predict how many times it will roll a 1 or a 6.
Answer:
100 times
Step-by-step explanation:
It is predicted that a 1 or a 6 will be rolled 50 times in 150 rolls of a standard number cube.
A standard number cube has six faces, each numbered from 1 to 6.
The probability of rolling a 1 or a 6 on any given roll is,
P = 2/6
P = 1/3
Since, there are two favorable outcomes out of six possible outcomes.
Hence, To predict how many times a 1 or a 6 will be rolled in 150 rolls, we can use the formula:
Number of times = Probability x Total number of rolls
So, the number of times a 1 or a 6 is expected to be rolled in 150 rolls is:
Number of times = (1/3) x 150 = 50
Therefore, it is predicted that a 1 or a 6 will be rolled approximately 50 times in 150 rolls of a standard number cube.
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Ms. Murray owns an ice cream shop. She keeps track of how many bottles of caramel syrup and chocolate syrup she uses per week. Last week, Ms. Murray used 72 bottles of chocolate syrup. She used 8 times as many bottles of chocolate syrup as bottles of caramel syrup.
ASAP