Answer:
Step-by-step explanation:
area=4×22/7×14²=4×22×28=2464 units²
The surface area of a sphere with a radius of 14 is 2464 square units. When considering significant figures, this is rounded to 2500 square units to match the two significant digits of the given radius.
To find the surface area of a sphere with a radius of 14, using the given value of 22/7 for , the formula A = 4*pi*r2 is used. Plugging in the numbers:
A = 4 * (22/7) * (14)²
A = 4 * (22/7) * 196
A = 4 * 22 * 28
A = 88 * 28
A = 2464
Thus, the surface area of the sphere is 2464 square units.
Why wont anybody help me :(
PLEASE MARK BRAINLIEST!
Answer:
Don't worry friend! I am here to help you!
Step-by-step explanation:
I tried answering as many questions as I could, but the ones I didn't answer, I didn't know how to solve.
Please understand that I am here to help you and others on brainly!
I hope this makes you feel better!
- sincerelynini
A survey of 500 farmers showed that of the farmers, 121 grew only wheat, 113 grew only corn, 90 grew only oats, 199 grew wheat, 60 grew wheat and corn, 57 grew wheat and oats, and 182 grew corn. Determine the number of farmers who a) grew at least one of the three. b) grew all three, c) did not grow any of the three, d) grew exactly two of the three
Answer:
Step-by-step explanation:
Let x represent the number of farmers that grew all three crops.
Let y represent the number of farmers that grew corn and oat.
The Venn diagram representing the scenario is shown in the attached photo.
W represents the subset for wheat
C represents the subset for corn
O represents the subset for oat
199 grew wheat. It means that
121 + 57 - x + x + 60 - x = 199
238 - x = 199
x = 238 - 199
x = 39
182 grew corn. It means that
113 + 60 - x + x + y - x = 182
173 + y - x = 182
y = 182 - 173 + 39
y = 48
a) the number of farmers who grew at least one of the three would be
121 + 113 + 90 + 57 - x + 48 - x + 60 - x + x
= 121 + 113 + 90 + 57 - 39 + 48 - 39 + 60 - 39 + 39 = 411
b) the number of farmers that grew all three would be
x = 39
c) the number of farmers who did not grow any of the three would be
500 - 411 = 89
d) the number of farmers who grew exactly two of the three would be
60 - x + 57 - x + 48 - x
= 60 - 39 + 57 - 39 + 48 - 39
= 21 + 18 + 9
= 48
The number of farmers who grew at least one of the crops is 328, all three is not stated, none of the three is 172 and exactly two of them is 117.
Explanation:To solve this problem, we have to understand Venn Diagrams and set theory. When adding up counts for different categories, it is important to not double count any item.
The number of farmers who grew at least one of three crops (wheat, corn, oats) can be determined by the sum of all the individual and intersection categories. However, we subtract the counts that have been mentioned twice.
a) At least one: (121 wheat only + 113 corn only + 90 oats only + 199 wheat + 60 wheat&corn + 57 wheat&oats + 182 corn) - (2*(60 wheat&corn) + 2*(57 wheat&oats) + 2*(182 corn&-)) = 328
b) All three: There is no clear information about farmers growing all three crops. We may assume it to be 0, as it is not stated.
c) None of three: The survey includes 500 farmers, if 328 grow at least one crop, then the number of farmers that did not grow any of the three is 500 - 328 = 172
d) Exactly two: 60 grew wheat and corn, 57 grew wheat and oats. Hence 117 farmers grew exactly two of the three crops.
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The body temperatures of a group of healthy adults have a bell-shaped distribution with a mean of 98.38°F and a standard deviation of 0.48°F. Using the empirical rule, find each approximate percentage below.
a. What is the approximate percentage of healthy adults with body temperatures within 3 standard deviations of the mean, or between 97.05°F and 99.57°F?
b. What is the approximate percentage of healthy adults with body temperatures between 97.89°F and 98.73°F?
Answer:
a) The problem says that this represent the values within 3 deviations from the mean and using the empirical rule we know that on this case we have 68% of the data on this interval.
b) For this case we can use the z score formula again:
[tex] z_1= \frac{98.73-98.38}{0.48}=0.729[/tex]
[tex] z_2= \frac{97.89-98.38}{0.48}=-1.020[/tex]
For this case we want this probability:
[tex] P(97.89<X<98.73) =P(-1.02<Z<0.729)= P(Z<0.729)-P(Z<-1.02)=0.767-0.154= 0.613[/tex]
So the approximate percentage of temperatures between 97.89F and 98.73F is 61.3%
Step-by-step explanation:
The empirical rule, also referred to as "the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ)". The empirical rule shows that 68% falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).
For this case we know that the body temperatures for a group of heatlhy adults represented with the random variable X follows this distribution:
[tex] X \sim N(\mu =98.38F, \sigma=0.48 F)[/tex]
Part a
For this case we can use the z score formula to measure how many deviations we are within the mean, given by:
[tex] z=\frac{x-\mu}{\sigma}[/tex]
If we find the z score for the values given we got:
[tex] z_1= \frac{99.57-98.38}{0.48}=2.479[/tex]
[tex] z_2= \frac{97.05-98.38}{0.48}=-2.771[/tex]
The problem says that this represent the values within 3 deviations from the mean and using the empirical rule we know that on this case we have 68% of the data on this interval.
Part b
For this case we can use the z score formula again:
[tex] z_1= \frac{98.73-98.38}{0.48}=0.729[/tex]
[tex] z_2= \frac{97.89-98.38}{0.48}=-1.020[/tex]
For this case we want this probability:
[tex] P(97.89<X<98.73) =P(-1.02<Z<0.729)= P(Z<0.729)-P(Z<-1.02)=0.767-0.154= 0.613[/tex]
So the approximate percentage of temperatures between 97.89F and 98.73F is 61.3%
f the line passing through the points (1, a) and (5, −2) is parallel to the line passing through the points (2, 8) and (−5, a + 7), what is the value of a?
Answer:
[tex]a=-6[/tex]
Step-by-step explanation:
Line 1: (1, a) and (5, −2)
slope of the line is
[tex]slope = \frac{y_2-y_1}{x_2-x_1} =\frac{-2-a}{5-1} =\frac{-2-a}{4}[/tex]
Line 2: (2, 8) and (−5, a + 7)
slope of the line is
[tex]slope = \frac{y_2-y_1}{x_2-x_1} =\frac{a+7-8}{-5-2} =\frac{a-1}{-7}[/tex]
when the lines are parallel then slopes are equal
[tex]\frac{a-1}{-7} =\frac{-2-a}{4}[/tex]
cross multiply it
[tex]4(a-1)=-7(-2-a)[/tex]
[tex]4a-4=14+7a[/tex]
subtract 4a from both sides
[tex]-4=14+3a[/tex]
[tex]-18=+3a[/tex]
divide both sides by 3
[tex]a=-6[/tex]
A ________ is a numerical quantity computed from the data of a sample and is used in reaching a decision on whether or not to reject the null hypothesis.
1. significance level2. critical value3. test statistic4. parameter
Answer:
3. Test Statistic
A test statistic is a numerical quantity computed from the data of a sample and is used in reaching a decision on whether or not to reject the null hypothesis.
The numerical quantity computed from the data of a sample and used in reaching a decision on whether or not to reject the null hypothesis is called; 3.Test statistic.
When we are dealing with hypothesis testing, it is pertinent to note that we have terms like sample size, sample mean, population size, population mean, test statistic, significance level, critical value, standard deviation e.t.c.Now, among all those terminologies, the one that we always calculate first after defining the hypothesis is the test statistic. The test statistic is the one that is computed from which we will get the p-value to know whether to reject the null hypothesis or not.Read more about test statistic at; https://brainly.com/question/15980493
Use the sample data and confidence level to construct the confidence interval estimate of the population proportion p. n equals 500 comma x equals 150 comma 95 % confidencen=500, x=150, 95% confidence nothingless than
Answer:
(0.2599,0.3401)
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 500
x = 150
[tex]\hat{p} = \dfrac{x}{n} = \dfrac{150}{500} = 0.3[/tex]
Confidence interval:
[tex]\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
[tex]z_{critical}\text{ at}~\alpha_{0.05} = \pm 1.96[/tex]
Putting the values, we get:
[tex]0.3\pm 1.96\sqrt{\dfrac{0.3(1-0.3)}{500}} = 0.3 \pm 0.0401 =(0.2599,0.3401)[/tex]
The 95% confidence interval is (0.2599,0.3401).
A Sociology student investigated the association between a country’s Literacy Rate and Life Expec- tancy, and then drew the conclusions listed below. Explain why each statement is incorrect. (Assume that all the calculations were done properly.)
a) The determines 64% of the Life Expectancy for a country.
b) The slope of the line shows that an increase of 5% in will produce a 2-year improvement in
Answer:
Step-by-step explanation:
(a) R2 does not determine the level of correlation between two variables in statistics but rather it is used to determine the level of variance in a dependent variable that is explained by an independent variable. It is also known as coefficient of determination.
Pearson's correlation coefficient (r) will better explain a direct relationship between a country's literacy rate and life expectancy and the value obtained will better explain option a
(b) The slope of the line can predict an improvement in life expectancy but cannot guarantee this improvement. And as such, the use of the word "will" suggests a form of guarantee which is wrong in interpreting slopes.
Which would best display the following data if you wanted to display the numbers which are outliers as well as the mean? [4, 1, 3, 10, 18, 12, 9, 4, 15, 16, 32]
Stem and Leaf plot would be the best choice to display the given data if we want to display the numbers which are outliers as well as the mean.
Hence option C is correct.
Given, representation of outliers and mean.
Data: [4, 1, 3, 10, 18, 12, 9, 4, 15, 16, 32]
Stem and Leaf plot would be the best choice to display the given data if we want to display the numbers which are outliers as well as the mean.
Therefore option C is correct.
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Options for question :
1) Pie Graph
2) Bar Graph
3) Stem and Leaf Plot
4) Line Chart
5) Venn Diagram
A box and whisker plot is the best choice to display data including outliers and the mean in mathematics. It clearly shows the median, quartiles, and outliers. The mean can be depicted as an additional point.
Explanation:In the field of mathematics, to display the data with outliers and the mean, a box and whisker plot is the most suitable graph. This type of graph can highlight outliers and also show the mean. For instance, our given data [4, 1, 3, 10, 18, 12, 9, 4, 15, 16, 32] when plotted on a box and whisker plot would display the median (the line inside the box), the quartiles (the ends of the box), and outliers (points outside the whiskers). The mean can additionally be added as a separate point on the plot.
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Flight 725 left New York at 10:28 a.m. flying north. Flight 245 left from the same airport at 11:18 a.m. flying south at one hundred twenty kph less than three times the speed of flight 725. At 1:06 p.m. they are 1,030 kilometers apart. What is the average rate of speed for Flight 245?
A) 165 kph
B) 395 kph
C) 365 kph
D) 345 kph
E) 155 kph
F) 175 kph
Answer:
Step-by-step explanation:
Let x represent the average speed of flight 725.
Flight 725 left New York at 10:28 a.m. flying north.
Flight 245 left from the same airport at 11:18 a.m. flying south at one hundred twenty kph less than three times the speed of flight 725. This means that the speed of flight 245 is
3x - 120
At 1:06 p.m. they are 1,030 kilometers apart. This means that total distance travelled by both planes would be 1030
Between 10:28am and 1:06pm, the number of hours would be 2hr 38 minutes = 2 + 38/60 = 2.63 hours
Distance = speed × time
Total distance travelled by flight 725 = x × 2.63 = 2.63x
Between 11:18am and 1:06pm, the number of hours would be 1hr 48 minutes = 1 + 48/60 = 1.8 hours
Distance = speed × time
Total distance travelled by flight 245 = x × 1.8 = 1.8(3x - 120)
5.4x - 216 + 2.63x = 1030
8.03x = 1030 + 216 = 1246
x = 1246/8.03 = 155 kph
Suppose your manager indicates that for a normally distributed data set you are analyzing, your company wants data points between z = − 1.6 z=-1.6 and z = 1.6 z=1.6 standard deviations of the mean (or within 1.6 standard deviations of the mean). What percent of the data points will fall in that range?
Answer:
89.04% of the data points will fall in the given range of z = − 1.6 and z = 1.6
Step-by-step explanation:
We are given a normally distributed data.
We have to find the percentage of data that lies within the range z = − 1.6 and z= 1.6
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
[tex]P(-1.6 \leq z \leq 1.6)\\= P(z \leq 1.6) - P(z \leq -1.6)\\\text{Calculating the value from standard normal table}\\= 0.9452 - 0.0548 = 0.8904= 89.04\%[/tex]
89.04% of the data points will fall in the given range of z = − 1.6 and z= 1.6
Final answer:
Approximately 89.04% of data points fall within 1.6 standard deviations of the mean in a normally distributed set, calculated using the empirical rule and Z-table for the standard normal distribution.
Explanation:
To find the percentage of data points that fall between z-scores of -1.6 and 1.6, we use the properties of the standard normal distribution. Based on the empirical rule (also known as the 68-95-99.7 rule), we know that approximately 68% of data points lie within 1 standard deviation, 95% within 2 standard deviations, and 99.7% within 3 standard deviations of the mean in a normal distribution.
Since our z-scores are between -1 and 2, we will look at the percentages for these intervals. Typically, a z-score of 1.6 would correspond to a value between the percentages for 1 and 2 standard deviations from the mean. Using a Z-table or standard normal distribution curve calculator, we find that a z-score of 1.6 gives us approximately 0.4452 (or 44.52%) to the left of the z-score and 0.4452 to the right. Therefore, the total area between -1.6 and 1.6 is 2 × 0.4452, which is approximately 0.8904 (or 89.04%). Thus, approximately 89.04% of the data points will fall within 1.6 standard deviations from the mean in a normally distributed data set.
In one month, Rama and Siham ran for a total of 670 minutes. If Rama spent 60 fewer minutes running than Siham did, for how many minutes did Siham run?
Answer:
Siham ran for 305 minutes
Step-by-step explanation:
Let
Siham Ran for time = X
Siham Ran for time = X-60
According to given condition
X + (X-60) = 670
X + X - 60 = 670
2X = 670-60
2X = 610
X = 610/2
X = 305
So Siham ran for 305 minutes only
Use the given conditions to write an equation for the line in point-slope form and general form.
Passing through left parenthesis negative 5 comma 5 right parenthesis(−5,5) and parallel to the line whose equation is 6 x minus 5 y minus 9 equals 0
Answer:
The answer to your question is below
Step-by-step explanation:
Data
P (-5, 5)
Parallel to 6x - 5y - 9 = 0
Process
1.- Find the equation of the line
6x - 5y = 9
-5y = -6x + 9
y = -6/-5 x + 9/-5
y = 6/5 x - 9/5
slope = 6/5, as the lines are parallels, the slope is the same.
2.- Get the equation of the new line
y - y1 = m(x - x1)
y - 5 = 6/5 (x + 5)
y - 5 = 6/5x + 6
y = 6/5x + 6 + 5
y = 6/5x + 11 Point-slope form
5y - 25 = 6(x + 5)
5y - 25 = 6x + 30
6x - 5y + 30 + 25 = 0
6x - 5y + 55 = 0 General form
The equation of the line that passes through (-5,5) and is parallel to 6x - 5y - 9 = 0 can be written in point-slope form as y - 5 = (6/5)(x + 5) and in general form as -6x + 5y - 55 = 0.
Explanation:To write an equation for the line that passes through the point (-5,5) and is parallel to the line 6x - 5y - 9 = 0, we first need to find the slope of the given line. By rewriting the equation in slope-intercept form (y = mx + b), we can identify the slope (m). The equation 6x - 5y - 9 = 0 can be rewritten as y = (6/5)x + 9/5, so the slope of the line is 6/5. Since parallel lines have the same slope, the slope of our new line is also 6/5.
Next, we use the point-slope form of the equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line (here (-5,5)) and m is the slope. Substituting these values into the equation gives us y - 5 = (6/5)(x + 5).
To express this in general form (Ax + By + C = 0), we rearrange the equation: multiply both sides by 5 to clear the fraction, resulting in 5(y - 5) = 6(x + 5), which simplifies to 5y - 25 = 6x + 30. Rearranging gives -6x + 5y - 55 = 0.
PLEASE HELP!!!
Find MG.
∆EGF~∆EML.
Answer:
[tex]MG=56\ units[/tex]
Step-by-step explanation:
step 1
Find the value of x
we know that
If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
In this problem we have that
∆EGF~∆EML
so
[tex]\frac{EG}{EM}=\frac{EF}{EL}[/tex]
substitute the given values
[tex]\frac{5x+2}{16}=\frac{126}{28}[/tex]
solve for x
[tex]5x+2=\frac{126}{28}(16)[/tex]
[tex]5x+2=72\\5x=70\\x=14[/tex]
[tex]EG=5x+2=5(14)+2=72\ units[/tex]
step 2
Find MG
we know that
[tex]MG=EG-EM[/tex]
substitute
[tex]MG=72-16=56\ units[/tex]
Andy and Diane want to buy a new van. They are allowed $5,500 for their present car. They also made a down payment of $2,300. They still owe 40% of the regular price of the car. What is the regular price of the car
Answer:
The regular price of the car is $13,000.
Step-by-step explanation:
i) let the price of the van Andy and Diane want to buy be $x.
ii) they get $5,500 for their present car
iii) they also make a down payment of $2,300.
iv) therefore $x = $0.4x + $5,500 + $2,300
therefore $0.6x = $7,800
therefore $x = $[tex]\frac{7800}{0.6}[/tex] = $13,000
The regular price of the car is $13,000.
Find the sides of a triangle if two of its sides are equal, the third side is 1 1 3 cm longer than the others, and its perimeter is 5 2 5 cm.
Answer: [tex]137\dfrac{1}{3}\ cm,\ 137\dfrac{1}{3}\ cm,\ 250\dfrac{1}{3}\ cm[/tex]
Step-by-step explanation:
Let x be the equal sides of the triangle .
The , the third side would be x+113 cm.
The perimeter is the sum of all sides of a triangle.
So , The perimeter of triangle would be x+x+(x+113)= 3x+113 --------(1)
Since , it is given that the perimeter of triangle is 525. -----(2)
So from (1) and (2) , we have
[tex]3x+113=525\\\\ 3x=525-113=412\\\\ x=\dfrac{412}{3}=137\dfrac{1}{3}[/tex]
Then, third side = [tex]137\dfrac{1}{3}+113=250\dfrac{1}{3}\ cm[/tex]
Hence , the sides of a triangle are:[tex]137\dfrac{1}{3}\ cm,\ 137\dfrac{1}{3}\ cm,\ 250\dfrac{1}{3}\ cm[/tex]
Answer: 1 16/45, 1 16/45, 2 31/45
Step-by-step explanation:
Say x is the equal side of the triangle.
The third side would be x+113 cm.
The perimeter is the sum of all sides of a triangle.
So, the perimeter of the triangle would be x+x+(x+113)= 3x+113
Since the triangle's perimeter is 5 2/5, 3x + 1 1/3 = 5 2/5.
1 1/3 is 1 5/15. 5 2/5 is 5 6/15. 5 6/15 - 1 5/15 = 4 1/15.
This means 3x = 4 1/15.
4 1/15 = 61/15
3x = 61/15
To make 3x into x, you can multiply it by 1/3.
3x*1/3 is x. 61/15*1/3 = 61/45.
x = 1 16/45 because 61/45 = 1 16/45.
The longer side is x + 1 1/3 so you have to add 1 1/3 to 1 16/45 which is
2 31/45.
So, the sides are 1 16/45, 1 16/45 and 2 31,45.
A large company wants to admiister a satisfaction survey to its current customers. using their customer database the company radoml selects 60 customers and asks them about their elvel of satifcation with the company. What type of sampling is used?
Answer:
The sampling used is simple random sampling.
Step-by-step explanation:
Consider the provided information.
Types:
Simple random sample is a subset of the population chosen from a larger set. Every person is selected by chance and randomly.Systematic sampling: list of elements is counted off.Convenience sampling: data which is readily available is used. That is, the first people are running into by the surveyor.Cluster sampling: divide the population into groups, usually geographically.Stratified sampling: divide population into groups called strata. but this time population might be separated into males and females.Here, randomly selected 60 customers, Thus, the sampling used is simple random sampling.
True or False. The larger the distance between two adjacent numbers in the five‑number summary, the more spread out the data in that interval.
Answer: Its True
Step-by-step explanation:
The statement is true because the Percentages are preferred and also they are easier to compare than counts.
You have $11.50 to buy boxes of crackers for a party. A box of crackers costs $2.30. Which inequality represents the number x of boxes of crackers you can buy?
STEP-BY-STEP EXPLANATION:
Let be x the number of boxeds of crackers you can buy
If each box has a cost of $2.30 and you have $11.50
we can represent this into this equation
2.30x= 11.50
x=[tex]\frac{11.50}{2.30}[/tex]
x=5
You can buy 5 boxes of crackers
Find the value of x please help.
Answer:
x=11
Step-by-step explanation:
[tex]\frac{5x}{3x-3} =\frac{44}{24} =\frac{11}{6} \\33x-33=30x\\33x-30x=33\\3x=33\\x=11[/tex]
The price of milk has been increasing over the last month. Audrey believes there is a positive correlation between the number of predicted storms and the price of milk.
Number of Storms Predicted Milk Price
1 $2.70
3 $2.89
4 $3.50
6 $3.88
7 $3.91
Use the table to determine the average rate of change from 3 to 6 storms.
Answer:
0.33
Step-by-step explanation:
So we find the difference between the price of milk at 6 storms and the price of milk at 3 storms.
3.88 - 2.89= 0.99
Then we divide the difference by 3 to find the average rate of change for each storm between 3 to 6.
0.99 ÷3= 0.33
So the answer is 0.33.
The average rate of change from 3 to 6 storms is 0.33
What is Correlation?A correlation exists as a statistical measurement that expresses the extent to which two variables are linearly related (suggesting they change together at a constant rate). It's a familiar tool for defining simple relationships without making a statement about cause and effect.
To solve this example use this rule :
Δx/Δy
x exists the amount that changed. so Δx=0,99.
The storm stands to 3 to 6 so find the difference for x: for the 3rd and 6th members of the table... 3.88-2.89=0.99
Now,
0.99/Δy
Because require to find from 3 to 6, Δy=3,
When finding both, rate of change with :
0.99/3=0.33.
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wo crafty bacteria fall into a pot of milk which has recently been sterilized. They reproduce at a rate of 4% per day. Determine how many bacteria will be present after 100 days.
Final answer:
After 100 days, there will be approximately 7.18 bacteria present.
Explanation:
To determine the number of bacteria that will be present after 100 days, we need to calculate the exponential growth of the bacteria. The bacteria reproduce at a rate of 4% per day, which means the population will double every 25 days (since 100 divided by 4 is 25).
To calculate the final population, we can use the formula N = N₀ * [tex](1 + r/100)^t[/tex], where N is the final population, N₀ is the initial population, r is the growth rate, and t is the time in days.
In this case, the initial population is 2 (assuming there are initially only two bacteria), the growth rate is 4%, and the time is 100 days.
Plugging in these values,
we get [tex]N = 2 * (1 + 4/100)^{100} = 2 * (1.04)^{100}[/tex]nal population of approximately 7.18 bacteria. Therefore, there will be approximately 7.18 bacteria present after 100 days.
Write a polynomial function of least degree with integral coefficients that has the given zeros
Answer:
[tex]x^{4}[/tex] + 3x² - 4
Step-by-step explanation:
Note that complex zeros occur in conjugate pairs
If 2i is a zero then - 2i is a zero
The zeros are x = 1, x = - 1, x = 2i, x = - 2i, thus the factors are
(x - 1), (x + 1), (x - 2i) and (x + 2i)
The polynomial is expressed as the product of the factors, thus
f(x) = (x - 1)(x + 1)(x - 2i)(x + 2i) ← expanding in pairs
= (x² - 1)(x² - 4i²) → i² = - 1
= (x² - 1)(x² + 4) ← distribute
= [tex]x^{4}[/tex] + 4x² - x² - 4
= [tex]x^{4}[/tex] + 3x² - 4
Pam brought water to the soccer game.She had 12 containers.She put 4 liters of water in each container.How many liters of water did Pam bring to the soccer game?
Answer:
48 liters
Step-by-step explanation:
You should multiply the number of containers by the number of liters in each container.
12 x 4 = 48
Pam brought 48 liters of water to the soccer game.
In triangle EFG the measure of angle E is four times the measure if angle F. The measure of angle G is 18 degrees less than the measure of angle E. What is the measure of each angle?
Answer:
Step-by-step explanation:
In our triangle, angles E + F + G = 180 degrees. If angle E is 4 times the measure of F, and G is 18 less than E, then
F is x,
E is 4x, and
G is 4x - 18
Add these all together and set the sum equal to 180:
x + 4x + 4x - 18 = 180
Combining like terms:
9x - 18 = 180 and
9x = 196 so
x = 22
That means that
F = 22,
E = 4(22) = 88 and
G = 4(22) - 18 = 88 - 18 = 70
Since 22 + 88 + 70 do in fact equal 180 you can be fairly certain that your answer is correct! (It is correct...trust me!)
What type of pay is modeled below?
A) commission pay. B) hourly pay with a bonus. C) hourly pay without a bonus. D) piece rate.
The model shown in the graph describes a piece rate. Correct option is D.
Let us take a point (3, 60) in the given graph.
The function which model this is y=kx.
Let us plug in y as 60 and x as 3.
60=3k
Divide both sides by 3:
k=20
So, y=20x.
The model is proportional function, if the x value increases then y value increases.
Similarly, if x value decreases the y value decreases.
Hence, the model shown in the graph describes a piece rate. option D is correct.
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Answer:
Hourly pay without a bonus
Step-by-step explanation:
I just took the test
A shipment of computer monitors, some weighing 25lb and the others weighing 40lb each, has a total weight of 680lb. If there are 20 monitors altogether, how many weigh 40lb?
Answer:
The answer to your question is 12 monitors
Step-by-step explanation:
Data
v = monitors weighing 25 lb
f = monitors weighing 40 lb
Total weight = 680 lb
Total monitors = 20
Process
1.- Write equations
v + f = 20 ------------------ (l)
25v + 40f = 680 -----------------(II)
2.- Solve the system by elimination
Multiply equation l by -25
-25v - 25f = - 500
25v + 40f = 680
0 + 15 f = 180
Solve for f
f = 180 / 15
f = 12
3.- Find the value of v
v + 12 = 20
v = 20 - 12
v = 8
4.- Conclusion
There are 12 monitors weighing forty lb
There are 8 monitors weighing 25 lb
Buthaina is thinking of a number.The number is greater than two hundred twenty-five. Her number is less than 2 hundreds,2 tens, and 7 ones.What is Buthaina's number?
Answer:
The number is 226.
Step-by-step explanation:
Let the number be x.
Given:
The number is greater than two hundred twenty-five.
So we can say that;
[tex]x>225[/tex] equation 1
Also Given:
Her number is less than 2 hundreds,2 tens, and 7 ones.
Now we can say that 2 hundreds,2 tens, and 7 ones is equal to 227
So now the number is less than 227.
[tex]x<227[/tex] equation 2
From equation 1 and equation 2 we can say that;
[tex]225<x<227[/tex] equation 3
Also,
[tex]225<226<227[/tex] equation 4
Comparing equation 3 and 4 we get;
[tex]x=226[/tex]
Hence The number is 226.
The following data show the distances (in miles) from the homes of off-campus statistics students to the college. Create a stem plot using the data. 0.5; 0.7; 1.1; 1.2; 1.2; 1.3; 1.3; 1.5; 1.5; 1.7; 1.7; 1.8; 1.9; 2.0; 2.2; 2.5; 2.6; 2.8; 2.8; 2.8; 3.5; 3.8; 4.4; 4.8; 4.9; 5.2; 5.5; 5.7; 5.8; 8.0 Which are the outliers?
Answer:
See the plot below.
For this case we can consider as an outlier the value 8.0 since is far away from the other points
Step-by-step explanation:
For this case we can create the stem plot like this:
Stem Leaf
0 | 5 7
1 | 1 2 2 3 3 5 5 7 7 8 9
2 | 0 2 5 6 8 8 8
3 | 5 8
4 | 4 8 9
5 | 2 5 7 8
6 |
7 |
8 | 0
Notation : "1 |1 means 1.1 for example and 3|5 means 3.5"
By definition an outlier is "an observation that lies an abnormal distance from other values in a random sample from a population"
For this case we can consider as an outlier the value 8.0 since is far away from the other points
An equilateral triangle has a height of 10 feet. How long is one of its sides? (Note: In an equilateral triangle, all sides have the same length.)
Answer:
side length is [tex]\frac{20\sqrt{3} }{3}[/tex] feet
Step-by-step explanation:
An equilateral triangle has a height of 10 feet. the height of the triangle is the perpendicular bisector to the base
so it forms a two right angle triangle
the triangle formed is a 30-60-90 degree triangle
the diagram is attached below
Let x be the side if the equilateral triangle
sin(theta)=opposite by hypotenuse
[tex]sin(60)=\frac{10}{x}[/tex]
[tex]\frac{\sqrt{3}}{2} =\frac{10}{x}[/tex]
cross multiply
[tex]\sqrt{3} x=20[/tex]
[tex]x=\frac{20}{\sqrt{3} } =\frac{20\sqrt{3} }{3}[/tex]
The length of the side of an equilateral triangle with a height of 10 feet is approximately 11.54 feet. This is determined by applying the properties of a 30-60-90 triangle which is a half of an equilateral triangle.
Explanation:The problem is asking to solve for the side (s) of an equilateral triangle given the height (h). An equilateral triangle can be divided into two 30-60-90 right triangles. In such a triangle, the ratio between the hypotenuse (which is the side of the equilateral triangle) and the longer leg (which is half of the height) is 2:√3. Therefore, if the height is 10 feet, then the side length would be (2/√3)*h.
Step 1: Recognize that the triangle is a 30-60-90 triangle.
Step 2: Apply the ratio between the sides in a 30-60-90 triangle, 2:√3.
Step 3: Multiply the height by 2/√3 to get the length of one side which equals about 11.5 feet.
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A train drove the distance of 440 feet in 20 seconds. Select ALL the unit rates that are equivalent to the speed of the model airplane. (Use page 26 unit of measure chart to help.)
Answer:
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