Final answer:
Susie was 20 meters behind Andy when he reached the finish line in the 100-meter race.
Explanation:
To determine how many meters Susie was behind Andy at the moment Andy reached the finish line during the 100-meter race, let's consider the information given:
Andy finished the race.
Blaise was 10 meters behind Andy at that moment.
Susie was 10 meters behind Blaise when Blaise finished the race.
When Blaise reached the finish line, Andy would have already finished since Blaise was behind by 10 meters. However, at the moment Andy finished, Susie was also behind Blaise, who was 10 meters from finishing. Hence, Susie was 10 meters (the distance Blaise was behind Andy) + 10 meters (the distance Susie was behind Blaise at her finish) = 20 meters behind Andy when he finished the race.
In conclusion, Susie was 20 meters behind Andy when Andy reached the finish line.
What is AB? There’s an image of the triangle above
A research firm conducted a survey of 49 randomly selected Americans to determine the mean amount spent on coffee during a week. The sample mean was $20 per week. The population distribution is normal with a standard deviation of $5. What is the point estimate of the population mean? Using the 95% level of confidence, determine the confidence interval for μ.
The point estimate of the population mean is $20 per week. The 95% confidence interval, using a z-score of 1.96, ranges from $18.20 to $21.80.
Explanation:The subject of this question deals with the statistical concept of confidence intervals. The point estimate of the population mean is simply the sample mean, which is $20 per week. To calculate the confidence interval for the population mean (μ), we first need to understand that for a 95% level of confidence, the z-score (standard score) is 1.96. This is derived from statistical tables or a z-distribution.
The confidence interval is then calculated with the formula:
(sample mean - (z-score * (standard deviation/√sample size)), sample mean + (z-score * (standard deviation/√sample size))
Substituting the known values in, the 95% confidence interval for μ is ($18.20, $21.80).
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The point estimate of the population mean is the sample mean of $20 per week. Using the given standard deviation and applying the formula for a 95% confidence interval, we determine the confidence interval for the population mean to be ($18.6, $21.4).
The point estimate of the population mean ( μ) is the sample mean which is $20 per week. To calculate the confidence interval, we can use the formula for a 95% confidence interval when the population standard deviation ( σ) is known:
CI = Y ± Z*( σ/ √n)
Given that σ = $5, n = 49, Z for a 95% confidence level is approximately 1.96. Plugging these values into the formula, we get the confidence interval:
CI = 20 ± 1.96*(5/√49)
CI = 20 ± 1.96*(5/7)
CI = 20 ± 1.96*(0.714)
CI = 20 ± 1.4
CI = (18.6, 21.4)
Therefore, the 95% confidence interval for the population mean ( μ) is ($18.6, $21.4).
Jen borrowed $1500 from her parents for car repairs. She plans to take 10% of her $450 weekly income to pay them back. At this rate, how many weeks will it take her to pay off the long?
Answer:
34 weeks
Step-by-step explanation:
450* 10% (0.10) = 45
1500/45 = 33.333
But you need to round up, so 34 weeks
Machine A and machine B both make car parts.
Machine A makes 7 parts every 10 minute.
Machine B makes 16 parts every 17 minuets.
On Monday
Machine A makes parts for 12 hours.
Machine B makes parts for 10 hours.
Work out the total number of parts made by two machines on Monday. Show your working
Answer:
Machine A=504 parts in 12h
Machine B=564 parts in 10 h
Step-by-step explanation:
please find the attached picture for steps
Answer:
Part A is 504
Part B is 564.7
Step-by-step explanation:
Rates given
A=7 parts every 10 minutes
We know its 1 hour for every 60 minutes
12 hr x 60 min\1 hr is 720 minutes
720 min times 7 part divide by 10 minutes is 504 parts
B= 16 parts every 17 minutes
10 hr times 60 min divide by 1 hour is 600 minutes
600 min times 16 parts divide by 17 minutes is 564.7 parts
A cube has an edge lenght of 9 centimeters.
If the side length is increased by a factor of 3, how much larger is the perimeter of a face of the new cube?
A 72cm
B 72cm^2
C 108cm
D 108cm^2
Answer: A
Step-by-step explanation:
Took quiz
Answer:
The correct answer is A on edg
Step-by-step explanation:
Use the formula for continuously compounded interest, A = Pert, to find the annual interest rate for an $8000 investment that earns $410.17 in one year.
a. 7%
b. 6%
c. 5%
d. 4%
Answer:
c 5%
Step-by-step explanation:
8000 + 410.7 = 8000 e^(r)
e^r = 1.05127125
r lne = ln1.05127125
r = 0.05006316309 × 100
5%
Answer:
C 5%
Step-by-step explanation:
I hope this is what you need
In circle G, r = 3 units. Maria draws a circle with double the area of circle G. What is the area of Maria's circle? 6Pi units squared 9Pi units squared 12Pi units squared 18Pi units squared
Answer: 18pi unit squared
Step-by-step explanation:
Area of a circle = πr2
Radius of Circle G= 3units
Area of circle G= πr2
= π (3×3)
= 9π unit squared
Maria draws a circle with double the area of circle G. This will be:
2 × 9π
= 18π2
= 18pi unit squared
Answer:
18*pi units squared.
Step-by-step explanation:
The area of a circle can be calculated with the following formula:
Area = pi * r^2
Where r is the radius.
The circle G have a radius of 3 units, so its area is:
Area1 = pi * r^2 = pi * 3^2 = 9*pi
If the circle that Maria draws has double the area, so her circle have a area of:
Area2 = 2 * Area1 = 2*9*pi = 18*pi units squared.
During a particular week, the art museum had 1,600 visitors, and that was 40% of the total number of visitors for the month. How many total visitors did the art museum have that month?
Answer:
4000
Step-by-step explanation:
this can be found by using the equation
1600/x = 40/100
cross multiply
40x = 160000
simplify
x= 4000
To find the total number of visitors the art museum had in the month, divide 1,600 by 0.4.
Explanation:To find the total number of visitors the art museum had in the month, we can use the given information. We know that 1,600 visitors represents 40% of the total number of visitors for the month. To find the total number of visitors, we can set up the following equation:
1,600 = 0.4 * total number of visitors
To solve for the total number of visitors, we divide both sides of the equation by 0.4:
total number of visitors = 1,600 / 0.4 = 4,000
Therefore, the art museum had a total of 4,000 visitors that month.
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A triangle has a perimeter of 20 cm. It is dilated by a scale factor of 4/5. What is the perimeter of the dilation?
Answer:
i believe it to be 16. Im not sure though
Step-by-step explanation:
help please!, i need help
Answer:
The answer to your question is 5
Step-by-step explanation:
Rate of change of a linear function is the slope of the function.
To find the answer:
1.- Find two points of the line
A = (2, 4)
B = (1, -1)
2.- Write the formula of the slope
m = (y2 - y1) / (x2 - x1)
3.- Identify the values of x1, y1, x2 and y2
x1 = 2 y1 = 4 x2 = 1 y2 = -1
4.- Substitution
m = (-1 - 4) / (1 - 2)
5.- Simplification
m = -5/-1
6.- Result
m = 5
1. What is the circumference of the circle
below?
11 cm
Samir bought 3 pounds of cement to repair the cracks in his sidewalk. Each crack needs to be filled with 2 ounces of cement. Part A How can he convert 3 pounds to ounces? Use the drop-down menus to explain. 3 by . Part B How many cracks can he repair? Enter your answer in the box. cracks
Answer:
24 cracks will be filled
Step-by-step explanation:
Here, the first question asks how to convert 3 pounds to ounces.
we can do this using a mathematical approach. To convert pounds to ounces, we need to know that there are 16 ounces in a pound. so to convert pounds to ounces, we just need to multiply the number of pounds we have by 16 to get the equivalent number of ounces.
The second question asks to give the number of cracks that be repaired.
From the question, we were made to know that each of the cracks would eat up 2 pounds of cement to be filled.
Let’s calculate the amount of cement we have. That would be 3 * 16 = 48 ounces of cement.
The amount of cracks to be filled is thus 48 ounces/2 ounces = 24 cracks
The two cones are congruent
A
Determine the unknown measures of the cones,
units
units
units
5.2
B
units 3
6.2
V242 units
VD units
Answer: if you’re talking about the one on edge it’s:
3.1
4.2
5.2
42
Step-by-step explanation:
The cones are congruent so just copy the other cone and find the radius (dividing the diameter by 2)
Answer as a power of 6
The value of [tex]\(10^2 - 4^3\)[/tex] is [tex]\(6^2\)[/tex], equivalent to 36.
To solve this expression, first, let's calculate each part:
[tex]$10^2 = 10 \times 10 = 100$[/tex]
[tex]$4^3 = 4 \times 4 \times 4 = 64$[/tex]
Now, we can substitute these values into the expression:
[tex]$10^2 - 4^3 = 100 - 64 = 36$[/tex]
Now, we need to express 36 as a power of 6. We can see that [tex]$36 = 6^2$[/tex], so:
[tex]$36 = 6^2$[/tex]
Therefore, the value of [tex]$10^2 - 4^3$[/tex] as a power of 6 is [tex]$6^2$[/tex]
Please help me!!
2(5– x)3 – 11=151
Answer:
x = -22
Step-by-step explanation:
2(5– x)3 – 11 = 151
(10 - 2x)3 - 11 = 151
30 - 6x = 162
-6x = 132
x = -22
Did you know that the outdoor temperature can e found by counting the chirps made by crickets? According to the Farmer's Almanac, the formula C = StartFraction n Over 3 EndFraction + 4 relates degrees celsius (C) to the number of cricket chirps (n) in 25 seconds. One night while camping, Charlie counts 51 chirps in 25 seconds. What is the temperature in degrees Celsius?
Answer:
the answer is 21
Step-by-step explanation:
.
Answer:
21 is correct, & for some reason my answer was deleted... so strange, am I right ?
square root of 48 plus square root of 3
Answer:
2313
Step-by-step explanation:
what are all the functions that have no real number solution
4x^2+100=0
3x^2-9=0
x^2+1=0
6x^2-216=0
x^2-49=0
Answer:
Step-by-step explanation:
hello :
two equations have no real number solution :
x²+1=0 : bcause x²= - 1 false x²≥ 0
4x²+100 =0 : because x² = -25 false x²≥ 0
The functions that have no real solutions include the given equations.
Explanation:The functions that have no real number solutions in the given equations are:
4x² + 100 = 03x² - 9 = 0x² + 1 = 06x² - 216 = 0x² - 49 = 0For these equations, the solutions are complex numbers or no solution at all. In the first equation, there are no real solutions, while the others have complex solutions. For example, the second equation has solutions x = ±3i, where i is the imaginary unit.
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What is the answer to
–3x2+7=-2x
Step-by-step explanation:
-6 + 7 = 2x
1 =2x
If you have to find the value of x then
1/2 = x
estimate 196 divided0.499
Answer:
392
Step-by-step explanation:
round 0.499 up to 0.5, then divide 196 by 0.5 and your answer is 392.
In 2017, the entire fleet of light‑duty vehicles sold in the United States by each manufacturer must emit an average of no more than 86 milligrams per mile (mg/mi) of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) over the useful life ( 150,000 miles of driving) of the vehicle. NOX + NMOG emissions over the useful life for one car model vary Normally with mean 80 mg/mi and standard deviation 4 mg/mi. (a) What is the probability that a single car of this model emits more than 86 mg/mi of NOX + NMOG? (Enter your answer rounded to four decimal places.)
Answer:
probability that a single car of this model emits more than 86 mg/mi of NOX + NMOG = 0.8668
Step-by-step explanation:
mean, μ = 80 mg/mi
Standard deviation, [tex]\sigma = 4 mg/mi[/tex]
probability that a single car of this model emits more than 86 mg/mi of NOX + NMOG
[tex]P(X > x ) = P(z > \frac{x - \mu}{\sigma})[/tex]
[tex]P(X > x ) =1 - P(z < \frac{x - \mu}{\sigma})[/tex]
[tex]P(X > 86 ) =1 - P(z < \frac{86 - 80}{4})[/tex]
P(X > 86) = 1 - P(z < 1.5)
From the standard normal table, P(z < 1.5) = 0.9332
P(X > 86) = 1 - 0.9332
P(X > 86) = 0.0668
round your answer to the nearest hundredth
Answer:
8.54
Step-by-step explanation:
3*3=9
8*8=64
9+64=73
Square root of 73= 8.54
A circle has a circumference of 28.26 units. What is the diameter of the circle?
Answer:
Diameter of circle is 9 units.
Answer:
2 x radius
Step-by-step explanation:
Find the volume of a cylinder that has a radius of 7 and a height of 16. Leave your answer in terms of
π.a0
Step-by-step explanation:
volume =π r*2 h
sub r=7, h =16,
volume = 49(16)π
=784π
The probability that Alma makes a three-point shot in basketball is 20 % 20%20, percent. For practice, Alma will regularly shoot a series of these shots until she makes one. She's curious how many shots it will typically take her to get her first successful shot. She simulated 50 5050 trials of three-point shots where each shot had a 0.2 0.20, point, 2 probability of being made, and in each trial, she counted how many shots it took to get the first successful shot.
Complete Question: Check the file attached to this document to see the complete question
Answer:
P(X < 7) = 0.76
Step-by-step explanation:
Counting properly from the diagram attached to the question,
number of trials it took her to make less than 7 shots(i.e. 0 to 6 shots) = 38
The total number of trials she made = 50
Probability that it takes fewer than 7 shots to get her first successful shot, P(X < 7) = (number of trials it took to make less than 7 shots)/(Total number of trials)
P(X < 7) = 38/50
P(X < 7) = 0.76
Answer:
0.76
Step-by-step explanation:
Please help me!!!!! How do you get 67.3 and 112.7 from .9228
I attached the problem with the answer but not all the work.
In will make the first answer the brainlyest
Answer and Step-by-step explanation:
You are correct in that we need to use the Law of Sines: [tex]\frac{c}{sinC} =\frac{b}{sinB}=\frac{a}{sinA}[/tex].
Here, when we use the Law of Sines, we have: [tex]\frac{28}{sin(63)}=\frac{29}{sinB}[/tex].
Cross multiply:
(sinB) * 28 = (sin63) * 29
28sinB ≈ 25.839
sinB ≈ 0.9228
Now, in order to solve for B, we need to use inverse sin ([tex]sin^{-1}[/tex]):
[tex]sin^{-1}(sinB)=sin^{-1}(0.9228)[/tex]
The sines on the left cancel out, and we're left with:
B ≈ 67.3 degrees
Now, one thing to keep in mind when doing Law of Sines is that there is potentially more than one answer possible for the degree measure. The other degree measure can be found by subtracting this one from 180:
180 - 67.3 = 112.7 degrees.
Hope this helps!
Answer:
67.3° , 112.7°
Step-by-step explanation:
sinx = 0.9228
Take inverse of sin, you get:
x = 67.3389176683
Since sin is positive in first two quadrants, second angle is:
180 - 67.3389176683
= 112.6610823317
Find the 39th term of the arithmetic sequence
–66, - 68, – 70, ..
Answer:
Preview
Enter a mathematical expression (more..)
a boln. Video
Answer:
-142
Step-by-step explanation:
You seem to have an arithmetic sequence with first term -66 and common difference (-68-(-66)) = -2. The general term of such a sequence is given by ...
an = a1 +d(n -1) . . . . . for first term a1 and common difference d
We want to evaluate this equation for a1 = -66, d = -2, n = 39:
a39 = -66 -2(39 -1) = -66 -76 = -142
The 39th term is -142.
A student rolled 8 number cubes and counted the total amount of even numbers to simulate the number of questions she might guess correctly on a true/false test with 8 questions. The dot plot below shows the results of one hundred trials. Based on this data, which number of correct answers is most likely?
Answer:
The number of correct answers most likely is 3
Step-by-step explanation:
A Dot Plot is a histogram form of chart used to represent small amount of data in which the values are small discrete countable variables. It is a graphical display of data using dots and graph like scales to show count (relationships) within a group or a category.
Here from the box plot, we have that the number with the highest frequency is 3. Therefore, the number of correct answers most likely is 3.
A man drove his car 396 miles on Monday and 476 miles on Tuesday. How many miles did he drive altogether?
Marta looked at the results for the USA in the 2004 summer Olympics and noticed that the number of silver medals was 6 fewer (less) than twice the number of bronze medals. She also saw that the number of gold medals was four more than the number of silver medals. If the USA won 52 medals in total that year, how many of each type did they win?
Answer: They won 22 gold, 18 silver and 12 bronze.
Step-by-step explanation: Suppose gold is g, silver is s and bronze is b.
The number of silver was 6 less than twice of bronze: s = 2b - 6
Gold was 4 more than silver: g = s + 4
Total is 52: g + s + b = 52
We have 3 equations and 3 variables. To determine each one:
s = 2b - 6 (1)
g = s + 4 (2)
g + s + b =52 (3)
Substitute (1) in (2):
g = 4 + 2b - 6
g = 2b - 2 (4)
Using (1) and (4), substitute in (3)
2b - 2 +2b - 6 + b = 52
5b = 52+8
b= [tex]\frac{60}{5}[/tex]
b = 12
With b, we find s:
s = 2.12 - 6
s = 18
With s, we find g:
g = 4 + 18
g = 22
Therefore, the team won 22 gold, 18 silver and 12 bronze.
Answer:
Gold : 22 medals , Silver : 18 medals, Bronze : 12 medals
Step-by-step explanation:
Solution:-
- Denote the total number of medals won by USA, T = 52
- The number of bronze medals = x
- The number of silver medals = y
- The number of gold medals = z
- We are given that number of silver medals (y) was 6 fewer (less) than twice the number of bronze medals (x). So the mathematical representation of this observation would be:
y = 2x - 6
- Similarly, the number of gold medals (z) was four more than the number of silver medals (y). So the mathematical representation of this observation would be:
z = y + 4
- The total number of medals T:
T = x + y + z
- We have 3 equations and 3 unknowns. Solve the equations simultaneously,
z = 2x - 6 + 4 = 2x - 2
T = x + ( 2x - 6 ) + ( 2x - 2)
52 = 5x - 8
5x = 60
x = 12 bronze medals
z = 2x - 2
z = 2*12 - 2
z = 22 gold medals
z = y + 4
y = 22 - 4
y = 18 silver medals