Tommy and Zach will be 16 miles apart after 2.90 hours.
Let the time taken for Tommy and Zach to run until they are 16 miles apart be t hours.
Tommy runs North at a speed of 5 miles per hour.
Therefore, the distance covered by Tommy in t hours is 5 multiplied by t hours:
=5t miles
Zach runs East at a speed of 8 miles per hour.
Zach started running 2 hours later so that he would run for (t - 2) hours.
Distance covered by Zach in (t - 2) hours running at a speed of 8 miles per hour :
=8(t - 2) miles
Since they are now 16 miles apart, Pythagoras's theorem, a²+ b² = c², is applied.
[8(t - 2)]²+ (5t)² = 16²
64(t - 2)² + 25t² = 256
64(t² + 4 - 4t) + 25t² = 256
64t² + 256 - 256t + 25t² = 256
89t² -256t + 256 - 256 = 0
89t² - 256t = 0
t( 89t - 256) = 0
(89t - 256) = 0
9t = 256
= 256÷9
t = 2.90 hours
Therefore, for 2.90 hours, Zach and Tommy will be 16 miles apart.
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Dave drives a truck and can only drive 35 miles per day. If he drives 1,960 miles and gets paid $18 per day, how much money will he make?
Answer: $1008
Step-by-step explanation:
Since Dave can only drive 35 miles per day and he drives 1,960 miles, this means that the number of days he used for driving will be:
= 1960 / 35
= 56 days
Since he gets paid $18 per day, the amount that he will make will be:
= $18 × 56
= $1008
A salesman at a clothing store makes a sale to 30% of the customers he talks to, and wants to try out a new tecnique to see if he can change this rate. He decides to collect data for a few months on the percentage of customers he makes a sale to, and he is able to construct a 95% confidence interval of (.3095, .3275). Is there evidence at 5% significance that he has changed his average sales?
Answer:
Yes, we can conclude that average sales has changed.
Step-by-step explanation:
The null hypothesis, H0 : μ = 0.3
The alternative ; H0 : μ ≠ 0.3
The result of the 95% confidence interval of (.3095, .3275); This shows that the confidence interval is now between 30.95% and 32.75% ; since μ does not lie within the confidence interval value and the lower boundary of the confidence interval is > 30; we Can conclude with an evidence of 5% significance that his average sales as changed (increased).
We can reject H0 and conclude that μ > 0.3
Can y’all help me ?
Answer:
-2 is 4
Step-by-step explanation:
write an equation for the graph
Answer:
In standard form: y = 1(-2) + 2
Step-by-step explanation:
y=mx+b
m is the slope (calculate with rise over run, 2/2 is 1)
x is the x intercept (in this case -2)
b is the y intercept (in this case 2)
A ribbon of length 3meters is to be cut into strips of length 14centimeters. How many strips of lengths 14centimeters were cut? What length of ribbon remained?
Answer:
21
6 CM REMAINED
Step-by-step explanation:
Convert metre to centimetre
100 cm = 1 m
3 m = 3 x 100 = 300cm
strips cut = 300/14 = 21 would be cut with some remainders
Remainders = 300 - (14 x 21) = 6cm
anybody know the answer to this?
If xy + 12 = 6x + 7, find y if x =5.
Answer: look at the picture
Step-by-step explanation: Hope this help :D
Answer:
y=25
Step-by-step explanation:
If your grandmother had a cousin what would she be to you??
Answer:
Wouldn't he be like a second cousin or something?
Step-by-step explanation:
Answer:
I think she would be your second cousin.
Step-by-step explanation:
Hope this helps!!
Please mark this answer as Brainiest!!
Multiply. Write your answer as a fraction in simplest form.
−1(4/5)=
Answer: -4/5
Step-by-step explanation:
Any positive number/fraction multiplied by -1 will become negative
find the measure of each interior and exterior angles of a regular polygon with 48 sides
Answer:
172.5
may this will help you
Triangle PQR has vertices at the following coordinates: P(0, 1), Q(3, 2), and R(5, -4). Determine whether or not triangle PQR is a right triangle. Show all calculations for full credit.
Answer:
it's a right angled triangle
Line t and Δ??? and Δ??? are shown on the coordinate plane. Which statements are true? Select all that apply.
Answer:
1. True
2. True
3. True
4. False
5. True
6. False
4) Shruti covered a distance of 350.175 km in 7 days. How much distance did she
cover in 1 day?
Answer:
[tex]350.175 \div 7 \\ 50.025km[/tex]
what is the prime factor of 4400 by tree method
Answer:
The orange divisor(s) above are the prime factors of the number 4,400. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 5 x 5 x 11 = 4,400. It can also be written in exponential form as 24 x 52 x 111.
Step-by-step explanation:
Hope that this helps! :)
Have a great rest of your day/night!
Please thank me on my profile if this answer has helped you!
Find the length of the hypotenuse.
Answer:
25
Step-by-step explanation:
c-a=b
30-16=b
900-256=644
square root=25
Consider trapezoid SODA
Answer:
CPCTC
Step-by-step explanation:
If two triangles are similar, we can prove by CPCTC
At a recent charity event there was a range of admission charges:
Family (2 Adults + 2 Children)
Adult
Senior
Child (5 to 16 years)
Child under-5
$44
$14
$12
$10
Free
In addition it was possible to buy Family tickets before the event at the reduced cost of $40 per
family.
At the gate tickets to the value of $40 000 were purchased, and prepaid tickets added a further
$10000 to the total income. For every Family ticket sold on the day, 1 Adult, 1 Senior, and 3 Child
tickets were sold and 2 under-5 children were admitted free of charge.
How many people attended?
A
B
c
4400
4600
4650
5400
Answer:
5400
Step-by-step explanation:
Given data
Family (2 Adults + 2 Children) = $44
Adult = $14
Senior = $12
Child (5 to 16 years) = $10
Child under-5 = Free
At reduced price family buys ticket at = $40
Total prepaid ticket sold = $10,000
Value of ticket sold at the gate = $40,000
Determine how many people attended
first step : determine number of family that purchased the prepaid tickets
= 10,000 / 40 = 250 families
∴ number people who booked prepaid tickets = 250 * 4 = 1000 people
Next step : Determine the number of families that booked the ticket at the gate
let the number of families = y
40,000 = 44 y + 12y + 3y * 10 + 14y + 2y *0
40,000 = y ( 100 ) hence y = 40,000 / 100 = 400
∴ number of people = 400 * ( 4 + 1 + 1 + 3 + 2 ) = 400 * 11 = 4400
Number of people whom attended = 4400 + 1000 = 5,400
Find the area of the parallelogram. base is 10 and height is 8
Answer:
80
Step-by-step explanation:
8*10
Please help! hurry, It's 8 pm and I'm tired :(
Answer:
I’m pretty sure x=6
Step-by-step explanation:
Anyone know this cause my sister been lost for a day on this. I know it's nice t that hard to most of y'all but it's hard for her. ( will give big brain if I can)
Answer: The book tax is $1.10 and the video game is $3.40 so i'll let you figure this out
tell your sister that the nae nae frog has blessed her with the answer
Select the correct answer.
Which phrase describes one of the transformations on the graph of the parent cosine function resulting in function g?
g(0) = cos(21 - )
А.
a horizontal stretch by a factor of 2
B.
a horizontal shift right x units
C.
a horizontal shift right units
a horizontal compression by a factor of
D.
Reset
Nelu
Answer:
The answer is C! horrizontal shift right pi/2 units.
Step-by-step explanation:
I just took the test and got it right!
Help please, what's the interquartile range?
Solve for x. x= __________
Answer:
64
Step-by-step explanation:
160 + 136 = 296
360 - 296 = 64
Find the value of x.
Answer:
1
Step-by-step explanation:
An altitude is drawn from the vertex of an isosceles triangle, forming a right angle
and two congruent triangles. As a result, the altitude cuts the base into two equal
segments. The length of the altitude is 26 inches, and the length of the base is 9
inches. Find the triangle's perimeter. Round to the nearest tenth of an inch.
Answer: 61.8
Step-by-step explanation:
Answer:
85
Step-by-step explanation:
delta math
HELP ME PLZZ: Francesca is making a scale drawing of the mural on a wall in her school's hallway. The mural is 12 ft high and 135 ft long. She is using a sale of 3 cm for every 4 ft. What are the dimensions of her scale drawing?
Answer:
i think ur supposed to do 135 divided by 3?
Step-by-step explanation:
tell me if im right or wrong so then i can help
The height of the mural drawing is 9 inches while the length is 101.25 inches.
What is the scale factor?You must specify the extent of the shape's enlargement when describing one.
The scale factor is the ratio of two dimensions such that one figure is large and another is small.
The scale factor is done due to the unpractical measurement of any figure.
Hight of the mural = is 12 feet
⇒ 12 × 12 = 144 inches.
Length of mural = 135 feet
⇒ 1620 inches.
Now,
She is using 3 cm for every 4 feet(4×12 = 48 inches)
Scale factor = 3/48 = 1 : 16
Now,
Length of mural drawing = 144/16 = 9 inches.
Height of mural drawing = 1620/16 = 101.25 inches.
Hence "The height of the mural drawing is 9 inches while the length is 101.25 inches".
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PLZ HELP ME WITH ALL OF THESE QUESTIONS PLZ I WILL GIVE BRAINLIEST ANSWER
Answers:
1. This question is asking for the dilation, or division of each point by a factor of 3. This is shown in the results below:
A' = (-4/3, -2/3)
B' = (1/3, -1)
C' = (2/3, -5/3)
D' = (-1/3, 7/3)
2. This question is asking the same thing as the previous question except for new points and a new scale factor. The results are shown below:
A' = (3, 1)
B' = (-2, -2)
C' = (-4, 6)
D' = (1, -4)
3. This question is basically asking to multiply the area of the fence by two as shown with "extend the fence's range by a scale factor of 2." The results are shown below:
A' = (4, 6)
B' = (-6, 4)
C' = (4, -4)
4. This question is asking for the ratio of each side. Moreover, this means that the same side on both triangles must equal the same ratio. This is shown below:
75/24 = 25/8
60/18 = 10/3
The values of 25/8 and 10/3 are not the same, meaning that the scale ratio is not the same. These two triangles are NOT similar because of this.
5. This question is asking the same thing as question 4. The results are shown below:
10/5 = 2
10/5 = 2
As these values are the same, these two triangles ARE similar because of how the larger triangle is multiplied by a scale factor of 2.
what is the difference between (3.1,000) -(2.100)
Answer:
You just have to subtract the answer will equal 1
What percent of students have 3 or more siblings?
(The dot plot is also included)
Answer:
5
Step-by-step explanation:
if you count all the dots above 3, 4, 5 and 10 you will gte your answer :)
Enter
30
to
70 as a fully simplified ratio.
Answer:
3:7
Step-by-step explanation:
To simplify the ratio 30:70, we find the greatest common divisor of 30 and 70, and then we divide 30 and 70 by the greatest common divisor. The greatest common divisor that you can use to simplify 30:70 is 10. This means the answer to ratio 30:70 simplified is: 3:7.
Please mark me brainliest!