The average speed of a car decreased by 3 miles per hour every successive 8-minute interval. If the car traveled 4.8 miles in the sixth 8-minute interval, what was the average speed of the car, in miles per hour, in the first 8-minute interval?
Answer:
13.5 mi/h
Step-by-step explanation:
The average speed of the car can be written as
[tex]v=\frac{d}{t}[/tex]
where
d = 4.8 miles is the total distance covered
[tex]t=6\cdot (8 min) = 48 min \cdot \frac{1}{60}=0.8 h[/tex] is the time elapsed
So the average speed is
[tex]d=\frac{4.8}{0.8}=6 mi/h[/tex]
We also know that the total time consists of 6 8-minutes interval, and the speed of the car decreased by 3 mi/h each interval.
Calling [tex]v_1[/tex] the average speed in the 1st interval, we have:
[tex]v_2=v_1-3\\v_3=v_1-6\\v_4=v_1-9\\v_5=v_1-12\\v_6=v_1-15[/tex]
The average speed in each interval can be written as [tex]v_i=\frac{d_i}{t}[/tex], where [tex]d_i[/tex] is the distance covered in each interval and [tex]d_i = 8 min =0.133 h[/tex] is the duration of each interval, so we can write
[tex]\frac{d_2}{t}=\frac{d_1}{t} -3 \rightarrow d_2 = d_1 -3t[/tex]
And similarly,
[tex]d_3=d_1-6t\\d_4=d_1-9t\\d_5=d_1-12t\\d_6=d_1-15t[/tex]
Since the total distance is [tex]d=d_1+d_2+d_3+d_4+d_5+d_6[/tex], we have:
[tex]d=6d_1 - 3t-6t-9t-12t-15t=6d_1-45t[/tex]
And since we know that
d = 4.8 miles
and t = 0.133h, we can find d1:
[tex]d_1=\frac{d+45t}{6}=\frac{4.8+(45)(0.133)}{6}=1.8 mi[/tex]
So the average speed in the first 8-minute interval is:
[tex]v_1=\frac{d_1}{t_1}=\frac{1.8}{0.133}=13.5 mi/h[/tex]
What is the first step in solving the equation
x^2-16/25=0
What is the second step in solving the equation?
Answer:
First Step: separate x^2 from -16
Second Step: add -16/25 to the other side.
Step-by-step explanation:
x^2 - 16/25 = 0
^^ this might be easier if you separate x^2 and -16
First Step-
so rewrite the problem as x^2/25 -16/25 = 0
then...
Second Step-
add -16/25 to the other side. This makes it: x^2/25 = 16/25
Continuation-
Now, you can multiply 25 on both sides to cancel it out.
so you have x^2 = -16
Message me if you want to solve for x.
The difference of a number and 8
Answer:8
Step-by-step explanation:
miss johnson is buying new chair and a table for the senior center. she has 150 to spend. she bought one table for $68 and each chair costs $18 which inequality shows the number of chairs, x, she can buy
A. 18x + 68 ≤ 150
B. 18x + 68 ≥ 150
C. 68x + 18 ≤ 150
D. 68x + 18 ≥ 150
The lines below are perpendicular. If the green line has a slope of -3, what is
the slope of the red line? Enter your answer as an integer or fraction in lowest
terms.
Answer:
⅓
Step-by-step explanation:
For two perpendicular lines,
m1 × m2 = -1
-3 × m2 = -1
m2 = -1/-3
m2 = 1/3
Find the value of this expression.
2(4+1)-3x6
A) -9
B) -8
C) 8
D) 36
E) 42
Answer:
B) -8
Step-by-step explanation:
2*5-18=10-18=-8
Answer:
B
Step-by-step explanation:
4+1 = 5
2*5 = 10
3*6 = 18
10-18=-8
What is the slope of (2,4) and (6,7) ?
Answer:
(7-4)/(6-2)= 3/4
Step-by-step explanation:
Answer:
3/4
Step-by-step explanation:
Rise/ Run = (7-4)/(6-2) = 3/4
Pleaseeeeeeee help me
Answer:
x = 24
Step-by-step explanation:
10:8
10(3) = x(3)
x = 8
30 : 24
Solve for ddd: d+\left(-5.004\right)=2.826d+(−5.004)=2.826d, plus, left parenthesis, minus, 5, point, 004, right parenthesis, equals, 2, point, 826 d =d=
Answer:
The value of [tex]'d'[/tex] is 7.83.
Step-by-step explanation:
Given:
[tex]d+(-5.004)=2.826[/tex]
We need to solve for [tex]'d'[/tex] .
Solution:
[tex]d+(-5.004)=2.826[/tex]
Now we know that;
By the rule of Addition and subtraction for positive and negative numbers
when a positive and negative signs are met then the result is negative.
So we can say that;
[tex]d-5.004=2.826[/tex]
Now Adding both side by 5.004 using addition property of equality we get;
[tex]d-5.004+5.004=2.826+5.004\\\\d= 7.83[/tex]
Hence The value of [tex]'d'[/tex] is 7.83.
Answer:
7.83
Step-by-step explanation:
Khan academy
plz rate 5 stars and press thanks. :)
from least to greatest -2.1,-2,-3,0 help plz
Answer:
-3, -2.1, -2, 0
Step-by-step explanation:
Least to greatest
Hope this helped you!
Answer:
-2,2-2.1,-3,0 that's your
3. Given that (5,12, 13) is a Pythagorean triple, which of the following isn't a Pythagorcan
triple?
(1) (10, 24, 26)
(3) (50,120,130)
(2) (10, 17, 18)
(4) (15, 36, 39)
Answer:
(2) (10,17,18)
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
Well, let’s use a cancelling technique.
We know that 10, 24, 26 is just 5, 12, 13 multiplied by 2. So that works! And 50, 120, 130 is just 5, 12, 13 multiplied by 10. So that also works! And 15, 36, 39 is just 5, 12, 14 multiplied by 3. Therefore 2 is our answer...
Evaluate the following:
ln ex + 1
A) x-2
B) y+1
C) x+1
Pls help, I don't understand this :(
Answer:
I believe the answer is C, x+1 :)
A group of students auditioned for a theater performance and 3/4 of the group less six students made up the cast of 42 students. Write an equation to represent the total number of students who auditioned, t.
Answer:
3/4x-6=42
x=64
Step-by-step explanation:
Let the number of students be x hence 3/4 of this number will be 3/4x
Since the number was 42 if they were 3/4x less six, it means minus six hence
3/4x-6=42
Therefore, the equation will be
3/4x-6=42
Solving the equation
3/4 x=42+6=48
3/4x=48
X=62
At barlow school 4/9 of the 873 students are boys at willow school 2/3 of the 630 students are girls which school has the greater number of boys and by how many
Answer:
There are 178 more boys in Barlow school as compared to Willow school.
Step-by-step explanation:
We are given the following in the question:
Barlow school:
Total number of students = 873
Number of boys =
[tex]=\dfrac{4}{9}\times 873 = 388[/tex]
Willow school:
Total number of students = 630
Number of girls =
[tex]=\dfrac{2}{3}\times 630 = 420[/tex]
Number of boys =
Total number of students - total number of girls
[tex]=630-420 = 210[/tex]
Thus, Barlow school has greater number of boys than Willow school.
Difference between the number of boys =
[tex]=388-210\\=178[/tex]
Thus, there are 178 more boys in Barlow school as compared to Willow school.
There are 6 crayons in a box. Only one of them is gold. A crayon is selected at random. Find the probability that it is not gold.
Answer:
1/6
Step-by-step explanation:
Answer:
5/6 or 83.33%
Step-by-step explanation:
There are 6 total crayons but only one is gold. The other five aren't. If you were to randomly pick one you'd have a 1/6 chance(16.67%)to pull out the gold crayon. That means there is a 5/6(83.33%)chance that you wouldn't pull out the gold one.
Only the ones that are circle. I NEED THEM QUICK PLEASE
Answer:
10
Step-by-step explanation:
183.35
what is the standard form of y=6(x-3)²-2
Answer:
B
Step-by-step explanation:
y = 6(x^2-6x+9)-2
y = 6x^2-36x+54-2
y = 6x^2-36x+52
The standard form of the given quadratic equation y=6(x-3)²-2 is y = 6x² - 36x + 52 after expanding the squared binomial and simplifying.
Explanation:The student has asked for the standard form of the quadratic equation y=6(x-3)²-2. The standard form of a quadratic equation is ax² + bx + c = 0. To rewrite the given equation in standard form, expand the squared binomial and simplify:
Expand the binomial: y = 6(x² - 6x + 9) - 2.Distribute the 6: y = 6x² - 36x + 54 - 2.Simplify the constants: y = 6x² - 36x + 52.So, the standard form of the given equation is y = 6x² - 36x + 52.
Learn more about Standard Form of a Quadratic Equation here:https://brainly.com/question/16956708
#SPJ2
Simplify -3xy 3 + 7xy 3 + (-xy 3) + (-3xy 3
(−3x)(y3)+7xy3+(−x)(y3)+(−3x)(y3) = 0
If the zeros of a quadratic function are 3 and 8, what are the factors of the function?
Answer:
(x-3)(x-8)
Step-by-step explanation:
the zero are what cancel out the factors.
Answer:
(x-8) and (x - 3)
Step-by-step explanation:
Enjoy your day:)
There are 16 baseball games per day at Lansing's annual baseball tournament, which lasts 10 days. Estimate the number of baseball games during the tournament by rounding the larger number to the nearest ten.
To estimate the total number of games during the baseball tournament, round the daily games (16) to the nearest ten (20) and multiply by the number of days (10), resulting in an estimated 200 games.
To estimate the number of baseball games during Lansing's annual baseball tournament, we can round the larger number to the nearest ten and then multiply it by the number of days in the tournament. The larger number, representing the number of games per day, is 16. Rounding 16 to the nearest ten gives us 20. As the tournament lasts 10 days, we calculate the total by multiplying these two numbers.
Estimated total number of games = Rounded number of games per day x Number of days in the tournament
Estimated total number of games = 20 x 10
Estimated total number of games = 200 games.
In order to answer the following question, please use the following image down below:
Find the value of x.
X=(Blank)
What is the value of X? Please show all the work on how you got your answer.
(If you can't explain your work, then it's fine. The only thing that I'm asking for is for you to show the work alongside your answer)
Answer:
23
Step-by-step explanation:
(x-3)(9) = (10)(18)
9x - 27 = 180
9x = 207
x = 23
I need help ASAP please (radical expressions)
Answer:
D
Step-by-step explanation:
Using the rule of radicals
[tex]\frac{\sqrt{a} }{\sqrt{b} }[/tex] = [tex]\sqrt{\frac{a}{b} }[/tex]
Given
[tex]\frac{14\sqrt{14} }{7\sqrt{2} }[/tex] ← cancel 14 and 7
= 2 × [tex]\sqrt{\frac{14}{2} }[/tex]
= 2[tex]\sqrt{7}[/tex] → D
Use technology or a z-score table to answer the question.
The number of baby carrots in a bag is normally distributed with a mean of 94 carrots and a standard deviation of 8.2 carrots.
Approximately what percent of the bags of baby carrots have between 90 and 100 carrots?
Answer: 46%
Step-by-step explanation:
Since the number of baby carrots in a bag is normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = the number of baby carrots in the bag.
µ = mean
σ = standard deviation
From the information given,
µ = 94 carrots
σ = 8.2 carrots
The probability that a bag of baby carrots have between 90 and 100 carrots is expressed as
P(90 ≤ x ≤ 100)
For x = 90,
z = (90 - 94)/8.2 = - 0.49
Looking at the normal distribution table, the probability corresponding to the z score is 0.31
For x = 100,
z = (100 - 94)/8.2 = 0.73
Looking at the normal distribution table, the probability corresponding to the z score is 0.77
Therefore,
P(90 ≤ x ≤ 100) = 0.77 - 0.31 = 0.46
The percent of the bags of baby carrots that have between 90 and 100 carrots is
0.46 × 100 = 46%
I need help with transversals!’
Answer:
∠ TWV = 106°
Step-by-step explanation:
∠ TWV and ∠ SVW are same- side interior angles and are supplementary, thus
∠ TWV + ∠ SVW = 180°, that is
3x - 5 + 2x = 180
5x - 5 = 180 ( add 5 to both sides )
5x = 185 ( divide both sides by 5 )
x = 37
Thus
∠ TWV = 3x - 5 = 3(37) - 5 = 111 - 5 = 106°
subtract 7/9 from 4 / 9
Answer:
3/9
Step-by-step explanation:
You just substract the numerator :) So, 7-4= 3
Help asap please due tomorrow
Answer:
The first one is 15.75 lbs or 15 3/4. The second one is 28 years old. The third one is$9.90 each t-shirt
Step-by-step explanation:
For the first one you multiply 18 by 14 and you get 252. Then there is 16 ounces in a pound so you divide by 16. Then you get 15.75. So that is your answer. The 2nd one you take 84 and multiply it by 1/6 then since she is twice the age of her sister you multiply by 2. so it would look like: 84 times 1/6= 14
14 times 2 = 28. So she is 28 years old. The third one you take 32 and subtract it by 12.20. You will be left with 19.8. Then both t-shirts cost the same so you would divide 19.8 by 2. You are left with 9.9. So the answer is $9.90. Sorry this took 10 minutes.
Answer:
15.75lb of hotdogs
Amy is 28 years old
she paid $9.90 for each shirt.
Step-by-step explanation:
1) we multiply the number of packages by how much each package weighs. which gives us 252ounces we can then convert ounces to pounds by multiplying by 0.0625pounds/1ounce which gives us 15.75lb
2) amy's age is her fathers age devided by 6 which gives us fourteen. we know Hannah's age is twice Amy's age, so we multiply 14 by two, 14X2=28
3) we subtract the money Rose spent on the poster from the overall amount rose spent. $32.00-$12.20=$19.80. so we know Rose spent $19.80 on t-shirts, since we also know she bought two equaly priced t-shirts we can devide $19.80 by 2, $19.80/2=$9.90, therfore, she spent $9.90 on each shirt.
Maria has a metal candle holder without a top that has a height of 3 cm and a radius of 3 cm how much metal was used to make holder?
Answer:
27pi cm^2
Step-by-step explanation:
Answer:
27 Pi cm2
Step-by-step explanation:
I NEED HELP THIS IS DUE IN 15 mins PLSSS SOMEBODY HELP ME!!!!!
Answer:
[tex] Standard \: form :\:y= {x}^{2} - 4x - 5\\
Factored\: from:\:y = (x + 1) (x - 5)[/tex]
Step-by-step explanation:
[tex]y = (x - 2)^{2} - 9 \\ y= {x}^{2} - 4x + 4 - 9 \\ \red{ \boxed{ \bold{y= {x}^{2} - 4x - 5}}} \\ is \: in \: standard \: form \\ \\ y = (x - 2)^{2} - 9 \\ y = (x - 2)^{2} - {3}^{2} \\ y = \{(x - 2) + 3\} \{(x - 2) - 3 \} \\ y = \{x - 2 + 3\} \{x - 2- 3 \} \\ \purple{ \boxed{ \bold{y = (x + 1) (x - 5)}}} \\ is \: in \: factored \: form[/tex]
A square root of paper 150 millimeters on a side is folded in half along a diagonal. The result is a 45° -45° -90° triangle. What is the length of the hypotenuse of this triangle in millimeters? Write your answer in simplified radical form, if necessary.
Answer:
The length of the hypotenuse of this triangle is 150√2 mm.
Step-by-step explanation:
Consider the square ABCD shown in the image below.
The sides are 150 mm each.
All the angles of a square are 90°.
Now The square is folded in half along the diagonal BD.
The angles A, B and D are: 45°, 45° and 90°.
The hypotenuse of the right angled triangle is BD.
Compute the length of BD using the pythagoras theorem as follows:
[tex]BD^{2}=AB^{2}+AD^{2}\\=150^{2}+150^{2}\\=2\times 150^{2}\\BD=\sqrt{2\times 150^{2}}\\=150\sqrt{2}[/tex]
Thus, the length of the hypotenuse of this triangle is 150√2 mm.
The common ratio in a geometric series is 4 and the first term is 3.
Find the sum of the first 8 terms in the series.
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Answer:
The sum of the first 8 terms in the series is 65535.
Step-by-step explanation:
We have,
The common ratio in a geometric series, r = 4
First term of GP is, a = 3
It is required to find the sum of the first 8 terms in the series. The sum of first n terms of a GP is given by :
[tex]S_n=\dfrac{a(r^n-1)}{r-1}, r>1[/tex]
Here, n = 8
[tex]S_8=\dfrac{3\times ((4)^8-1)}{4-1}\\\\S_8=65535[/tex]
So, the sum of the first 8 terms in the series is 65535.