Eileen was 600 feet away from the finish line before the race began.
Step-by-step explanation:
Step 1; Eileen rode at a speed of 20 feet per second whereas Andrew rode at a speed of 15 feet per second. So for every second that passes the distance in between decreases by 5 seconds. Assume x is the number of seconds at which the distance in between is 0. The distance in between at the beginning of the race is 150 feet due to the headstart.
Distance between them = Decreasing distance every second × x
150 feet = 5 feet/ second × x
x = 150 feet / 5 feet/second = 30 seconds.
So it takes Eileen 30 seconds to cover the distance between her and Andrew and cross the finishing line at the same time.
Step 2; The race lasted for 30 seconds so we can find the distance Andrew and Eileen traveled by multiplying their speed per second with the total number of seconds.
Distance Andrew traveled = speed per second × total number of seconds
= 15 feet per second × 30 seconds = 450 feet
Distance Eileen traveled = speed per second × total number of seconds
= 20 feet per second × 30 seconds = 600 feet
Graph plot;
The X-axis is time with 5 seconds for each cm
the y-axis is distance with 100 feet for each cm.
Eileen's plot (0,0), (5,100), (10,200), (15,300), (20,400), (25,500), (30,600).
Andrew's plot (0,150), (5,225), (10,300), (15,375), (20,450), (25,525), (30,600).
find the slope of the line that contains the points named A(3,2) B(7,8)
Answer:
Step-by-step explanation:
slope=y₂-y₁/x₂-x₁
[tex]\frac{8-2}{7-3}=\frac{6}{4}\\\\=\frac{3}{2}[/tex]
Two vertices of a right triangle have coordinates (9, 1) and (6, -1).
Select each ordered pair that could be the coordinates of the third vertex.
(6,9)
(6, 1)
(1, -1)
(9, -1)
Answer:
(6,1), (9,-1)
Step-by-step explanation:
In points (6,1) and (9,-1) a right angle can be formed.
solve the following system of equations
-2x+y=1
-4x+y=-1
Answer:
x = 1
y =
Step-by-step explanation:
-2x + y=1
-4x + y=-1
-2 (2) x + (2) y = (2) 1 (multilply by 2)
-4x + y=- 1
-4x + 2y = 2
-4x + y = -1
minus side by
y = 3
x =
Answer:
(1, 3).
Step-by-step explanation:
-2x + y = 1
-4x + y = -1 Subtract :
-2x - (-4x) = 1 - (-1)
-2x + 4x = 2
2x = 2
x = 1.
Substitute x = 1 in the first equation:
-2(1) + y = 1
-2 + y = 1
y = 1 + 2
y = 3.
Suppose y varies directly with x , if y =-14 when x = -7 , what is the value of x when y =22
Sandra bought 3 pounds of sweet potatoes for $4.71. What is the cost per pound of the sweet potatoes?
Which associations best describe the scatter plot?
Select each correct answer.
linear association
positive association
negative association
nonlinear association
Answer:
all the above conclude in a scatter plott does it have linear relation was it a positive or negative and it could be a random scatter plot so nonlinear association
The associations that best describe the scatter plot are: C. Negative association A. linear association
What are the Positive and Negative Associations on a Scatter Plot?On a scatter plot, if one variable increases or decreases as the other increases or decreases, it shows a positive association.
On the other hand, if one variable increases as the other decreases, it is a negative association.
Also, if the points are along a straight line, the association is linear.
Thus, in the scatter plot given, as time increases, distance decreases.
Therefore, the associations that best describe the scatter plot are: C. negative association A. linear association
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Sales Tax
nbsp Selling Price nbsp
nbsp Rate of Sales Tax nbsp
nbsp Sales Tax nbsp
$70.00
3%
?
The sales tax for an item priced at $70.00 with a tax rate of 3% is $2.10. This can be found by multiplying the selling price by the tax rate.
Explanation:To find the amount of sales tax, you can multiply the selling price by the rate of sales tax. In your case, the selling price is $70.00 and the rate of sales tax is 3%. So, your calculation will look like this: $70.00 * 0.03 (because 3% is the same as 0.03 when used in a calculation). The result of this multiplication will be the amount of sales tax. So, the sales tax for an item which costs $70.00 at a tax rate of 3% is $2.10.
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125% of e is 30. What is e?
125% of e is 30 means then the value of e is 24.
Step-by-step explanation:
By simplifying the given statement we can write it as[tex]\frac{125}{100}[/tex] [tex]\times e = 30[/tex]
So to find the e, we should keep e on one side the take the remaining terms on the other side. So after rearranging, we can obtain the equation e = [tex]\frac{30\times100}{125}[/tex]So now canceling the favorable terms we can get 24.The unknown number e from the given question is 24
How to find percentage125% of e is 30
125 / 100 × e = 30
1.25e = 30
divide both sides by 1.25e = 30 / 1.25
e = 24
Therefore, the unknown number e from the given question is 24
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The diameter of the circle above is 32 in. What is the circumference of the circle? Use = 3.14.
Answer:
8.3776 this is the circumference
Step-by-step explanation:
Answer:
the answer is 100.48 yd
Find the variance for the given data. Round your answer to one more decimal place than the original data. The billing rates for six dental procedures are listed below: $663 $273 $410 $622 $174 $374
Answer:
The variance is 30698.6
Step-by-step explanation:
The billing rates for six dental procedures are listed below:
$663
$273
$410
$622
$174
$374
The mean is given by:
[tex]\bar X=\frac{663+273+410+622+174+374}{6}=\frac{2516}{6}=419.333[/tex]
The variance is given by:
[tex]\sigma^2=\frac{\sum(x-\bar x)^2}{n}[/tex]
[tex]\sigma^2=\frac{(663-419.333)^2+(273-419.333)^2+(410-419.333)^2+(622-419.333)^2+(174-419.333)^2+(374-419.333)^2}{6}[/tex]
[tex]\sigma^2=30698.56[/tex]
Therefore the variance is 30698.6
The variance for the given set of data points, which are billing rates for dental procedures, is $35439.73. The variance is calculated as the average of the squared differences from the mean.
Explanation:The subject of this question is the variance, which is a statistical characteristic used in mathematics to measure how much individual numbers in a set diverge from the average. So, to find the variance for this given data follow these steps:
Find the mean of the data. This is done by adding all the numbers together and then dividing by the number of numbers. The mean in this case is $427.67 ($(663 + 273 + 410 + 622 + 174 + 374) / 6$). Subtract each number in the set by the mean, and then square the result. The squared differences are $55427.23$, $23856.23$, $312.23$, $37804.23$, $64368.23$, and $2870.23$, respectively. The variance is the mean of these squared differences. Adding them all up and dividing by 6 (the total number of numbers in the set) gets us a variance of $35439.73$ rounded to two decimal places. Learn more about Variance here:https://brainly.com/question/33654267
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You estimate that there are 66 cars in a parking lot. The actual number of cars is 75
.a. Find the percent error.
b.What other estimate gives the same percent error? Explain your reasoning
A. The percent error is 12%.
B. If you were to count 84 cars when there were only 75 it would also have the same percent error.
Step-by-step explanation:
Step 1; From the given data I measured the number of cars lower than its actual count. I counted the number of cars as 66 while it was 75. So my measurement was off by 9 counts. My percent error is given by dividing the difference in values by the actual value multiplied by 100.
% error = (difference in values / actual value) × 100
My % error = (75 - 66)/ 75 × 100 = 9/75 × 100 = 12%.
Step 2; My percent error was 13.6363%. I counted the cars lower then there were so to find another similar estimate I just add the percent error to the actual number of cars.
Similar % error = Actual value + 12% = 75 + 12% = 75 + 9 = 84 cars.
Final answer:
To calculate the percent error, use the formula (|Estimated Value - Actual Value| / Actual Value) x 100%. For an estimate of 66 compared to an actual value of 75, the percent error is 12%. An estimate of 84 cars would also produce a 12% percent error because it shares the same distance from the actual value as the original estimate, just in the opposite direction.
Explanation:
The question asks to find the percent error of an estimation and to determine another estimate with the same percent error. To calculate percent error, you use the formula: Percent Error = (|Estimated Value - Actual Value| / Actual Value) × 100%. Applying the given values, we get: Percent Error = (|66 - 75| / 75) × 100% = (9 / 75) × 100% = 12%.
To find another estimate with the same percent error, we can manipulate the percent error formula. Let x represent the new estimate. Thus, 12% = (|x - 75| / 75) × 100%. Solving for x gives two solutions: x = 66 (the given estimate) or x = 84. This means an estimate of 84 cars would also result in a 12% percent error, because it is 9 units away from the actual value, similar to the original estimate.
The reasoning is based on the symmetrical property of the absolute value function used in the percent error calculation, which indicates that the error margin above and below the actual value are equivalent.
Round 227 to the nearest 100
Which expression is equivalent to StartRoot 200 EndRoot?
2 StartRoot 10 EndRoot
10 StartRoot 2 EndRoot
10 StartRoot 20 EndRoot
100 StartRoot 2 EndRoot
Answer:
b) √200 = 10√2
Step-by-step explanation:
Here, the given expression is: √200
Simplifying the given expression, we get:
200 = 2 x 2 x 2 x 5 x 5
⇒ 200 = (2)² x (5) ² x 2
Taking ROOT both sides, we get:[tex]\sqrt{200} = \sqrt{(2)^{2} \times (5)^{2} \times 2}\\\implies \sqrt{200} = \sqrt{(2)^{2} } \times \sqrt{(5)^{2} } \times \sqrt{(2) } = 2 \times 5 \times \sqrt{2}\\ = 10 \sqrt {2}\\\implies \sqrt{200} = 10 \sqrt {2}[/tex]
Hence, √200 = 10√2
Answer:
B is the answer
Step-by-step explanation:
B for e2020
How to find the solution to an f(x)=g(x) equation
1.) Set the equation equal to each other
2.) Solve for y by itself and simplify the equation
3.) Solve for when x=0 to find the x-value
4.) Plug that x-value back into one of the equation to find the y-value.
Which graph represents the solution set of the compound inequality Negative 4 less-than-or-equal-to 3x minus 1 and 2 x + 4 less-than-or-equal-to 18?
A number line goes from negative 10 to positive 10. A closed circle appears at negative 1 and positive 7. The number line is shaded from negative 1 to positive 7.
A number line goes from negative 10 to positive 10. A closed circle appears at negative 7 and positive 1. The number line is shaded from negative 7 to positive 1.
A number line goes from negative 10 to positive 10. A closed circle appears at negative 1. The number line is shaded from negative 1 toward negative 10.
A number line goes from negative 10 to positive 10. A closed circle appears on positive 7. The number line is shaded from positive 7 toward positive 10.
Answer:
A number line goes from negative 10 to positive 10. A closed circle appears at negative 1 and positive 7. The number line is shaded from negative 1 to positive 7.
Step-by-step explanation:
The set of compound inequality are - 4 ≤ 3x - 1 and 2x + 4 ≤ 18.
Now, - 4 ≤ 3x - 1
⇒ 3x ≥ - 3
⇒ x ≥ - 1
And, 2x + 4 ≤ 18
⇒ 2x ≤ 14
⇒ x ≤ 7
Therefore, the solution will be 7 ≥ x ≥ - 1
Hence, the graph that shows the solution is 'a number line goes from negative 10 to positive 10. A closed circle appears at negative 1 and positive 7. The number line is shaded from negative 1 to positive 7'. (Answer)
Answer:
Graph A is your answer.
Step-by-step explanation:
A food stand sold hamburgers, ice cream cones, and hot dogs at a football game. Hamburgers were sold for $3.25, ice cream cones were sold for $2.50, and hot dogs were sold for $1.75. The total number of hamburgers, ice cream cones, and hot dogs sold was 104, and the total amount of money from these items was $248.75. If $80.50 was made just from selling hot dogs, how many ice cream cones were sold?
Answer y=27
27 ice cream cones were sold
12. Write an equation to solve for the following strip diagram:
421
158
628
Equation:
on:
Answer:
[tex]c + 421 + 158 = 628[/tex]
[tex]c + 579 = 628[/tex]
[tex]c = 49[/tex]
Area of 4.24 3 3
In a triangle
Answer:
4.5
Step-by-step explanation:
We can use heron's formula in this case:
let perimeter/2 be represented by [tex]p\\[/tex]
let [tex]a, b, c[/tex] represent each side length
[tex]p=\frac{ 4.24+3+3}{2} = 5.12[/tex]
Heron's formula is as follows:
[tex]Area=\sqrt{p(p-a)(p-b)(p-c)}[/tex]
Plug your numbers into the formula!
[tex]Area = \sqrt{5.12(5.12-4.24)(5.12-3)(5.12-3)}=\sqrt{5.12(0.88)(2.12)(2.12)}[/tex]
=[tex]4.5[/tex]
A basketball player made 17 out of 20 free throws at practice. What percent of the free throws did the player miss?
Answer:
The correct answer is 85%.
If a basketball player made 17 out of 20 free throws at practice then 85% of the free throws did the player miss.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that a basketball player made 17 out of 20 free throws at practice
We need to find the percent of the free throws did the player miss.
We find this by finding the product of x/100 with 20 which is equal to 17.
x/100 × 20=17
Now we have to find the value of x which is the percentage.
2x/10=17
0.2x=17
Divide both sides by 0.2
x=17/0.2
x=85%
Hence, if a basketball player made 17 out of 20 free throws at practice then 85% of the free throws did the player miss.
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Need help with simplifying this question
[tex]{3}^{ - 3} [/tex]
hope this helps :)
Yo sup??
[tex](3^6)^-^1^/^2\\=3^6^*^(^-^1^/^2^)\\=3^(^-^3^)\\[/tex]
Therefore your answer is option A ie
A.3^(-3)
Hope this helps.
Analyze the following pattern
1, 2, 5, 10, 17,....
what's the 8th term of the pattern
Answer:
50
Step-by-step explanation:
Add the next odd number to get the next term
1
1+1=2
2+3 =5
5 + 5 = 10
10 + 7 = 17
17 + 9 = 26
26 + 11 = 37
37 + 13 = 50
The dimensions of a portable kennel can be expressed as width x, length x + 0.4, and height x − 0.2? What are the dimensions of a portable kennel with a volume of 7.4 ft3? Use a graphing calculator to solve. Round the dimensions to the nearest tenth.
Answer:
[tex]L=2.3\ ft\\W=1.9\ ft\\H=1.7\ ft[/tex]
Step-by-step explanation:
we know that
The volume of a portable kennel (rectangular prism) is equal to
[tex]V=LWH[/tex]
where
[tex]L=(x+0.4)\ ft\\W=x\ ft\\H=(x-0.2)\ ft[/tex]
[tex]V=7.4\ ft^3[/tex]
substitute the given values in the formula of volume
[tex]7.4=(x+0.4)(x)(x-0.2)[/tex]
Apply distributive property right side
[tex]7.4=x(x^2-0.2x+0.4x-0.08)[/tex]
[tex]7.4=x(x^2+0.2x-0.08)[/tex]
[tex]7.4=x^3+0.2x^2-0.08x[/tex]
[tex]x^3+0.2x^2-0.08x-7.4=0[/tex]
Solve the cubic equation by graphing
using a graphing tool
The solution is x=1.9
see the attached figure
Find the dimensions
substitute the value of x
[tex]L=(1.9+0.4)=2.3\ ft\\W=1.9\ ft\\H=(1.9-0.2)=1.7\ ft[/tex]
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The box plots show the weights, in pounds, of the dogs in two different animal shelters.
Which is true of the data in the box plots? Select three choices.
The median weight for shelter A is greater than that for shelter B.
The median weight for shelter B is greater than that for shelter A.
The data for shelter A are a symmetric data set.
The data for shelter B are a symmetric data set.
The interquartile range of shelter A is greater than the interquartile range of shelter B.
Answer:
The median weight for shelter A is greater than that for shelter B.Step-by-step explanation:
In statistics, a box plot is a graphic method to display the quartiles of a distribution, where the line inside the body refers to the median.
So, in this case, you can observe that the median of shelter A is 21, and the median of shelter B is 18. That means the median of shelter A is greater than the median of shelter B.
Therefore, the right answer is first choice:
The median weight for shelter A is greater than that for shelter B.Box plot shows 5 description of the data set it is representing. The true statements for the given data sets' box plots are:
The data for shelter A are a symmetric data set.The interquartile range of shelter A is greater than the interquartile range of shelter B.How does a boxplot shows the data points?A box plot has 5 data description.
The leftmost whisker shows the minimum value in the data.The rightmost whisker shows the maximum value in the data.The leftmost line in the box shows the first quartile.The middle line shows the median, also called second quartile.The last line of the box shows the third quartile.How to find the interquartile range?IQR(inter quartile range) is the difference between third and first quartile.
For the given data set, we see that the middle line of first graph is right to the middle line of the lower graph, thus, Median of B < Median of A (18 < 22) (since as we go right, the magnitude of numbers increases)
Data is symmetric if the median is in the mid of the box plot and the box is mid to the line connecting both whiskers(since then the frequencies are more likely to be distributed symmetric to the middle).
Thus, B is symmetric but A isn't
IQR of A = Q3 - Q1 = 28 - 17 = 11IQR of B = Q3 - Q1 = 20 - 16 = 4Thus, IQR A > IQR B (here Q3 is third quartile and Q1 is first quartile).
Thus, the correct statements for the given box plots is:
The data for shelter A are a symmetric data set.The interquartile range of shelter A is greater than the interquartile range of shelter B.Learn more about box plot here:
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Manuela works as a security guard. She makes $15 per hour. Her employers deduct $125 from her weekly check to cover insurance and takes. If Manuela receives at least $205 in her weekly paycheck, what is the feast number of hours she works in a week
Answer:
At least 22 hours in a week.
Step-by-step explanation:
Given: Manuela make $15 per hour.
Her employers deduct $125 from her weekly check.
Manuela receives at least $205 in her weekly paycheck.
Lets assume, Manuela working hour in a week be "x".
We know, Total amount on week paycheck= [tex]Hourly\ pay\times number\ of\ hours- Deduction[/tex]
Now, forming an inequality to determine weekly pay of Manuela.
⇒ [tex]15\times x- 125\geq 205[/tex]
⇒[tex]15x-125\geq 205[/tex]
Adding both side by 125
⇒[tex]15x\geq 205+125[/tex]
⇒[tex]15x\geq 330[/tex]
Divinding both side by 15
⇒[tex]x\geq \frac{330}{15}[/tex]
∴[tex]x \geq 22\ hours[/tex]
Hence, Manuela works at least 22 hours per week.
a pilot is flying at 10,000 feet and wants to take the plane up to 20,000 feet over the next 50 miles. what should be his angle of elevation to the nearest
The angle of elevation is 2.17°
Step-by-step explanation:
First change value in miles to value in feet
1 mile =5280 ft
50 miles = 5280*50 =264000 ft
Apply the formula for tangent of an angle where the opposite side is 10,000 ft and the adjacent side is 264000 ft
Tan Ф = O/A
= 10,000/264000
=0.03787878787
Tan ⁻(0.03787878787) = 2.17°
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If you knew that two angles were complementary and were given the measure of one of those angles, would you be able to find the measure of the other angle? Explain your reasoning.
If we knew that two angles were complementary and were given the measure of one of those angles, then we can find the measure of the other angle by subtracting the given measure of one angle from 90
Solution:
Given that,
If you knew that two angles were complementary and were given the measure of one of those angles, would you be able to find the measure of the other angle
Yes we can find the measure of another angle
Complementary angles:
Complementary angles are two angles whose sum is 90 degrees
Therefore, if measure of one angle is given, then we can find the measure of another angle
Measure of another angle = 90 - measure of one angle
Example:
If x and y are complementary angles
Given that measure of angle x is 45 degrees
Then we can say,
According to complementary angles definition
x + y = 90
45 + y = 90
y = 90 - 45
y = 45
Thus measure of other angle y is found to be 45 degrees
Knowing the measure of one angle in a pair of complementary angles allows you to find the measure of the other angle because the sum of their measures is equal to 90 degrees.
Explanation:Yes, you would be able to find the measure of the other angle. This is because in geometry, two angles are said to be complementary if the sum of their measures is equal to 90 degrees. Thus, knowing the measure of one angle allows you to find the measure of the other angle by subtracting the known angle from 90.
For instance, if you were told one angle measures 35 degrees and you know the two angles are complementary, you could calculate the measure of the other angle as follows: 90 - 35 = 55 degrees. So, the other angle measures 55 degrees.
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NEED HELP Solve.
y=2x-6
4x-2y=14
Answer:
No solution
Step-by-step explanation:
Replace occurrences of y in 4x - 2y = 14 with 2x - 6
y = 2x - 6
4x - 2 (2x - 6) = 14
Simplify left side
y = 2x - 6
12 = 14
Since 12 is not equals to 14, There is no solution
find all of the points of the form (x −1) which are 4 unit from the point (3,2)
Answer:
[tex](3+2\sqrt{2},2+2\sqrt{2}),(3-2\sqrt{2},2-2\sqrt{2})[/tex]
Step-by-step explanation:
[tex]Points\ are\ of\ the\ form\ (x,x-1)\\\\Distance\ of\ these\ points\ from\ (3,2)=4\\\\\sqrt{(x-3)^2+(x-3)^2}=4\\\\\sqrt{(x-3)^2+(x-1-2)^2}=4\\\\\sqrt{2(x-3)^2}=4\\\\2(x-3)^2=16\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ square\ both\ the\ sides\\\\(x-3)^2=\frac{16}{2}\\\\(x-3)^2=8\\\\(x-3)=\pm 2\sqrt{2}\ \ \ \ \ \ \ \ \ \ \ square\ root\ both\ the\ sides\\\\x=3\pm 2\sqrt{2}\\\\When\ x=3+2\sqrt{2}\ \ \Rightarrow x-1=3+2\sqrt{2}-1=2+2\sqrt{2}\\\\When\ x=3-2\sqrt{2}\ \ \Rightarrow x-1=3-2\sqrt{2}-1=2-2\sqrt{2}[/tex]
Is -8-2(3+2n)+7n equivalent to -30-13n. Explain why or why not.
No, -8 - 2(3 + 2n) + 7n is not equivalent to -30 - 13n
Step-by-step explanation:
Let us revise the operation of the negative and positive numbers
(-) + (-) = (-)(-) × (-) = (+)(-) + (+) = the sign of greatest [(-) if the greatest is (-) or (+) if the greatest is (+)](-) × (+) = (-)(-) - (+) = (-)(+) - (-) = (+)∵ The expression is -8 - 2(3 + 2n) + 7n
- Simplify it
∵ 2(3 + 2n) = 2(3) + 2(2n) = 6 + 4n
∴ -8 - 2(3 + 2n) + 7n = -8 - (6 + 4n) + 7n
- Multiply the bracket by (-)
∴ -8 - (6 + 4n) + 7n = -8 - 6 - 4n + 7n
- Add the like terms
∴ -8 - (6 + 4n) + 7n = (-8 - 6) - 4n + 7n
∴ -8 - (6 + 4n) + 7n = -14 + 3n
∴ -8 - 2(3 + 2n) + 7n is equivalent to -14 + 3n
∵ -14 + 3n ≠ -30 - 13n
∴ -8 - 2(3 + 2n) + 7n is not equivalent to -30 - 13n
No, -8 - 2(3 + 2n) + 7n is not equivalent to -30 - 13n
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Evaluate g(x) = 5x + 7 for x = 9
Answer:
g(9) = 52
Step-by-step explanation:
Step 1: Identify the function
g(x) = 5x + 7 is the function
Step 2: Set x to 9 in the function
g(9) = 5(9) + 7
Step 3: Multiply
g(9) = 45 + 7
Step 4: Add
g(9) = 52
Answer: g(9) = 52