Answers:0m/s
Step-by-step explanation: once she has completed one lap, displacement is 0, therefore her velocity is 0m/s
The average velocity of her is zero.
Average velocity;Average velocity is defined as the change in position or displacement (∆x) divided by the time intervals (∆t) in which the displacement occurs.
Given
A runner runs around a track consisting of two parallel lines 96 m long connected at the ends by two semicircles with a radius of 49 m.
She completes one lap in 100 seconds.
The formula is used to find average velocity is;
[tex]\rm Average \ velocity=\dfrac{Change \ in \ displacement }{Change \ in \ time \ interval}[/tex]
Here, the runner displacement is zero.
Therefore,
[tex]\rm Average \ velocity=\dfrac{Change \ in \ displacement }{Change \ in \ time \ interval}\\\\\rm Average \ velocity=\dfrac{0 }{100}\\\\\rm Average \ velocity=0[/tex]
Hence, the average velocity of her is zero.
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Which is the equation in slope-intercept form for the line that passes through (-1,5) and is parallel to 3x + 2y = 4?
A. y = 2/3x + 7/2
B. y = -2/3x + 7/2
C. y = 3/2x - 7/2
D. y = -3/2x + 7/2
Answer: -3/2x + 7/2
Step-by-step explanation:
for parallel lines; m₁ = m₂
the gradient of the given line is -3/2
2y= -3x + 4
y = -3/2x + 2
therefore the gradient of the parallel line is -3/2
hence the equation is y-y₁ = m(x-x₁)
y-5 = -3/2(x+1)
y - 5 =-3/2x - 3/2
y = -3/2x -3/2 + 5
y = -3/2x + 7/2
If f(x) = 2x – 1 and g(x) = – 2, find [g ◦ f](x).
Answer:
[tex][g\circ f](x)=-2[/tex]
Step-by-step explanation:
By the definition
[tex][g\circ f](x)=g(f(x))[/tex]
You are given
[tex]f(x)=2x-1\\ \\g(x)=-2[/tex]
So,
[tex][g\circ f](x)=g(f(x))=g(2x-1)=-2[/tex]
Help with slope intercept!
It the second equation. I used subsitution to find that out.
The second one y = 1/2x + 3/4 is the correct answer. I first graphed the two points then started graphing the equations to find which line went through those two points.
HELP PLZZZZ! thank you
1. Same length.
2.vertically opposite angle.
3.BAC =BDE
4.AC = DE
Hope this helps you ___!!❤
Gabriel is making a mixture of compost and soil to use for a special plant. He wants his final mix to be 2 parts compost to 6 parts potting soil. He wants to end up with 10 kilograms of mix.
how many kilograms of compost should Gabriel use?
Answer:
5/2 kg
Step-by-step explanation:
The ratio here is 2:6. 2 plus 6 is 8.
Then (2/8) times 10 kg represents the amount of compost needed; that comes to 20/8 kg, or 10/4 kg, or 5/2 kg.
Gabriel should use 2.5 kilograms of compost to create a 10-kilogram mix that has a ratio of 2 parts compost to 6 parts potting soil.
Gabriel is making a mixture for a special plant which requires a ratio of 2 parts compost to 6 parts potting soil. He aims to make 10 kilograms of this mix in total. To calculate the amount of compost he should use, we first have to find the total number of parts in the mix:
Add the parts of compost to the parts of potting soil: 2 parts (compost) + 6 parts (soil) = 8 parts (total).
Determine the weight of each part: 10 kilograms (total mix) / 8 parts = 1.25 kilograms per part.
Multiply the weight of each part by the number of parts for compost: 1.25 kilograms per part × 2 parts (compost) = 2.5 kilograms of compost.
Therefore, Gabriel should use 2.5 kilograms of compost for his special plant mix.
Find the value of x to the nearest tenth
Check the picture below.
make sure your calculator is in Degree mode.
Answer:
The opposite side x is 7
Step-by-step explanation:
Step one
From the given expression in the picture
We can estimate x by applying the
SOH CAH TOA rule on the triangle
Since we have one side and one angle given
step two
From the given picture we have
We have θ and adjacent side given
Hence we need to apply
tan θ= opposite/adjacent =
Tan 35°=x/10
Step three
From 4 figure table or calculator
tan 35° is 0.7
0.7=x/10
x=0.7*10
x= 7
What is (f ⋅ g)(x)?
f(x) = x^4 − 9
g(x) = x^3 + 9
(f ⋅ g)(x) =
Answer:
x⁷ + 9x⁴ - 9x³ - 81
Step-by-step explanation:
(f⋅g)(x) is just another way of writing f(x) ⋅ g(x).
f(x) ⋅ g(x)
(x⁴ - 9) (x³ + 9)
If you wish to simplify:
x⁷ + 9x⁴ - 9x³ - 81
What is the quotient (6x4 − 15x3 + 10x2 − 10x + 4) ÷ (3x2 + 2)?
2x + 6
2x − 6
2x + 4
2x − 4, r = 1
Answer:
The quotient is [tex]2x^2-5x+2[/tex]
Step-by-step explanation:
We want to simplify:
[tex]\frac{6x^4-15x^3+10x^2-10x+4}{3x^2+2}[/tex]
We factor the numerator to get:
[tex]\frac{(x-2)(2x-1)(3x^2+2)}{3x^2+2}[/tex]
We cancel out the common factors to get:
[tex](x-2)(2x-1)[/tex]
Therefore the quotient is [tex]2x^2-5x+2[/tex]
The Sudsy car wash loses $40 on rainy days and gains $150 on sunny days. If the probability of rain is 15%, what its he expected value of the net profit?
-40*.15 + 150*(1-.15)= 121.50
Given the probabilities of sunny and rainy days and the respective profits, the Sudsy car wash's expected net profit per day, considering the rain probability, is $121.5.
Explanation:The subject of the question is about Expected Value, a concept in Probability Theory. Considering the Sudsy car wash's situation, we know that it loses $40 on rainy days and gains $150 on sunny days. The probability of having a rainy day is given as 15%, which means the probability of having a sunny day is 85% (100% - 15%).
The expected value of the net profit can be calculated by the formula for Expected Value: E[X] = ∑[x*P(X=x)]. In the context of this problem, we can write out the expected value E[N] of the net profit N as E[N] = (-$40 * 0.15) + ($150 * 0.85) = -$6 + $127.5 = $121.5. So, it is expected that the Sudsy car wash will have a net profit of $121.5 per day, on average.
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I found an odd thing idk what I’m doing wrong, I think i calculated it right but?
Because 3.14 * 30^2 * 110 = 310860 just as 3.14 * 900 * 110 since its pi and 900 is just 30x30, but when I input the actual TT pi symbol or do pi * 900 * 110 a result of 311017
am I an idiot?
Answer:
Step-by-step explanation:
No, you're not an idiot. You are just misunderstanding pi. Pi is an irrational number, meaning it goes on forever. Literally, forever, with no end. Some weird guy actually memorized the first 100,000 places of it or something crazy like that. Anyway, if you use 3.14 you have rounded so incredibly, that you lose a lot of your precision. Your calculator uses the first 9 places of the decimal or something like that.
Valentina has a 30% chance of randomly drawing a blue marble from a bag. If she does the random drawing 50 times, how many times can she expect to get a blue marble
A-30
B-5
C-35
D-15
Answer:
d
Step-by-step explanation:
30% of 50 is 15 because 30 % means 30out of 100
and if you half 100 you also half 30
Valentina, with a 30% probability, can expect to draw a blue marble 15 times out of 50 draws. This is calculated by multiplying the total number of draws by the probability of drawing a blue marble.
Explanation:The question revolves around the concept of probability. The probability of an event is the measure of the likelihood that the event will occur. In Valentina's case, she has a 30% chance of drawing a blue marble. Therefore, if she were to draw a marble 50 times, we would expect her to draw a blue marble 30% of those 50 times. Probability is often expressed as a fraction or decimal, and in this case, 30% translates to 0.30 in decimal form.
To calculate how many times we can expect Valentina to draw a blue marble, we multiply the total number of draws (50) by the probability of drawing a blue marble (0.30).
So, 0.30 * 50 = 15.
Therefore, Valentina can expect to draw a blue marble 15 times out of 50 draws.
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For a certain font, the scale factor is 1.414 and one of the scale sizes is 1.999. What is the next larger scale size ?
Sorry this is a little late, but I hope it'll still help someone in the near future.
The next larger scale size is 2.827
Hope this helps :)
Answer:
Next larger scale size = 2.827
Step-by-step explanation:
For a certain font scale factor is 1.414 and one of the scale size is 1.999.
so we have to find the next larger scale size.
Since scale factor will be defined as the ratio of larger scale size of the font and smaller font size.
[tex]\text{Scale factor}=\frac{\text{Larger font size}}{\text{smaller font size}}[/tex]
1.414 = [tex]\frac{\text{Larger font size}}{1.999}[/tex]
Larger font size = 1.414 × 1.999 = 2.8266 ≈ 2.827
Next larger scale size = 2.827
Triangles are formed in a cube by connecting three vertices.
Which triangles are right triangles? Check all that apply.
1. triangle AEG
2. triangle AEH
3. triangle DAE
4. triangle BFH
5. triangle GDH
6. triangle CFG
7. triangle DFH
8. triangle BCF
Answer:
B: triangle AEH
C:triangle DAE
E: triangle GDH
F: triangle CFG
H: triangle BCF
Step-by-step explanation:
just took the unit test hope it helps ;)
Right angle triangles are triangle AEG , triangle AEH , triangle DAE , triangle BFH , triangle CFG , triangle BCF .
Right angle triangle :
A Right triangle states that if one of the angles of a triangle is a right angle - 90º .
So , In the figure given below we get :
→ In triangle AEG : the angle between AE and AG is 90 ^ º .
→ In triangle AEH : the angle between AE and EH is 90 ^ º .
→ In triangle DAE : the angle between DA and AE is 90 ^ º .
→ In triangle BFH : the angle between BF and FH is 90 ^ º .
→ In triangle GDH : the angle at G , D and H is 60 ^ º .
→ triangle CFG : the angle between CG and GF is 90 ^ º .
→ triangle DFH : the angle between sides is not 90^ º .
→ triangle BCF : the angle between BC and BF is 90 ^ º .
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Mary’s parents gave her $60 as pocket money to meet her daily expenses. She spent $20 on clothes and $10 on food. She wishes to buy some books, also. If each book costs $3 each, solve the inequality to find how many books she can buy. Question 5 options: at the most 10 at least 10 10 at the most 5
Answer: The correct option is
(A) at the most 10.
Step-by-step explanation: Given that Mary’s parents gave her $60 as pocket money to meet her daily expenses. She spent $20 on clothes and $10 on food.
Also, she wishes to buy some books and each book costs $3.
We are to solve the inequality to find the number of number of books that she can buy.
Let the number of books that Mary can buy be n.
Then, according to the given information, we have
[tex]20+10+n\times3\leq 60\\\\\Rightarrow 30+3n\leq 60\\\\\Rightarrow 3n\leq 60-30\\\\\Rightarrow 3n\leq 30\\\\\Rightarrow n\leq \dfrac{30}{3}\\\\\Rightarrow n\leq 10.[/tex]
Thus, Mary can buy at most 10 books.
Option (A) is CORRECT.
Please please help me
Answer:
y = 13
Step-by-step explanation:
If it's a parallelogram then its consecutive angles are supplementary (add up to 180°).
6x - 12 + 132 - x = 180°,
5x + 120 = 180
5x = 60
x = 12
6x - 12 = 6(12) - 12 = 72 - 12 = 60
Parallelogram, opposite angles are equal
so
6y + 18 = 6x - 12
6y - 18 = 60
6y = 78
y = 13
A company launches 4 new products.
The market price, in dollars, of the four products after a different number of years, x, is shown in the following table:
Product 1 | f(x)=3^x |$3 | $9| $27
Product 2 | g(x)= x^2+4| $5 | $8 | $13
Product 3 |h(x)=3x+8| $11| $14| $17
Product 4 | j(x) = x^3| $1 | $8 | $27
Based on the data table, for which product does the price eventually exceed the others?
A. product 1
B. Product 2
C. Product 3
D. Product 4
Answer:
A. product 1
Step-by-step explanation:
An exponential function (with a base larger than 1) will eventually exceed the value of any polynomial function. Product 1 has a price described by an exponential function, so its price will exceed all others. (One only need to compute the values for x=4 to see this.)
_____
The attachment extends the table and plots the functions up to the point where Product 1 exceeds the others.
The second side of a triangular deck is 6 feet longer than the shortest side and a third side that is 6 feet shorter than twice the length of the shortest side. If the perimeter of the deck is 56 feet, what are the lengths of the three sides?
Answer:
14 ft20 ft22 ftStep-by-step explanation:
Let s represent the length of the shortest side. Then the other two sides are ...
s +62s -6The perimeter is the sum of the lengths of the three sides, so is ...
56 ft = s + (s+6) + (2s-6) = 4s . . . . collect terms
14 ft = s . . . . . . . divide by the coefficient of s
The shortest side is 14 ft; the second side is 20 ft; the third side is 22 ft.
Final answer:
Using the given information about the sides of the triangular deck and its perimeter, we set up an equation to solve for the shortest side and then used that to find the lengths of the other two sides. The three sides of the triangular deck are 14 feet, 20 feet, and 22 feet.
Explanation:
To solve the problem, we need to set up an equation based on the given information. Let's define the shortest side of the triangle as x feet. According to the problem, the second side is x + 6 feet, and the third side is 2x - 6 feet. The perimeter of the triangle is the sum of the lengths of all three sides, which is given as 56 feet.
We can set up the following equation:
x + (x + 6) + (2x - 6) = 56
Combining like terms, we get:
4x = 56
Divide both sides by 4:
x = 14
Now we can find the lengths of the sides:
The shortest side: 14 feet
The second side: 14 + 6 = 20 feet
The third side: 2(14) - 6 = 22 feet
Please help............... :)
Answer:
False
Step-by-step explanation:
Let's list all the odd numbers less than 15.
13, 11, 9, 7, 5, 3, 1
Prime numbers are numbers that can only be multiplied by 1 and themselves. But, we can see, that 9 can be multiplied by 3 and 3, making it a not-prime number (sorry I don't remember the exact name for that, I'm blanking out).
The number 9 makes that statement false.
Hope I helped! ouo.
~Potato.
Copyright Potato 2019.
Answer:
False
Step-by-step explanation:
Consider the odd numbers less than 15
1, 3, 5, 7, 9, 11, 13
A prime number has only 2 factors, namely 1 and itself
9 has factors : 1, 3, 9 ← not Prime
The statement is therefore False
Please help me answer this
Answer:
C
Step-by-step explanation:
As with most problems of this type, you need to draw an actual line that has approximately the same number of data points on each side of it. If you'll do that you'll see that this line crosses the y-axis at approx. y = 4. Only Answer C has that y-intercept.
12. (07.06 LC) A library building is in the shape of a rectangle. Its floor has a length of (3x + 5) meters and a width of (5x − 1) meters. The expression below represents the area of the floor of the building in square meters: (3x + 5)(5x − 1) Which of the following simplified expressions represents the area of the floor of the library building in square meters? (5 points) 28x − 5 15x2 − 5 15x2 + 28x − 5 15x2 + 22x − 5
ANSWER
[tex]15 {x}^{2} + 22x - 5[/tex]
EXPLANATION
It was given that, the length of the rectangular building is
[tex](3x + 5) \: meters[/tex]
and the width of the is
[tex](5x - 1) \: meters[/tex]
The area of a rectangular building is calculated using the formula for finding the area of a rectangle.
[tex]A = l \times w[/tex]
Since the dimensions are given in terms of x, the area is also a function of x,
[tex]A(x) = (3x +5 )(5x - 1)[/tex]
We expand to get,
[tex]A(x) = 3x(5x - 1) + 5(5x - 1)[/tex]
[tex]A(x) = 15 {x}^{2} - 3x + 25x - 5[/tex]
[tex]A(x) = 15 {x}^{2} + 22x - 5[/tex]
meters square
Answer:
D. 15x^2 + 22x -5
Step-by-step explanation:
I just took the test
Please help me out please
Answer:
w = 54°
Step-by-step explanation:
w is the inscribed angle subtended on the same arc with measure of 108°
w is half the size of the central angle, that is
w = 0.5 × 108° = 54°
What is the slope of this graph?
Write your answer as a decimal (with one decimal place or as a simplified fraction
Answer:
slope = -0.5
Step-by-step explanation:
Answer:
slope = change in y / change in x
slope = 0 -3.5 / 7 -0
slope = -3.5 / 7
slope = -.5
Step-by-step explanation:
Brody and four of his friends purchased tickets to a movie. The total was $32. How much did each person spend on their ticket? Use the equation 5x = 32 to solve.
x = $6.00
x = $6.40
x = $27.00
x = $160.00
Nadir saves $1 the first day of a month, $2 the second day, $4 the third day, and so on. He continues to double his savings each day. Find the amount that he will save on the fifteenth day.
$16,384
$29
$32,768
$8192
ANSWER
$16,384
EXPLANATION
From the question we have that,
Nadir saves $1 the first day of a month, $2 the second day, $4 the third day, and so on.
This forms a geometric sequence,
[tex]1,2,4,...[/tex]
The first term of this sequence is
[tex]a = 1[/tex]
The common ratio is
[tex]r = \frac{2}{1} = \frac{4}{2} = 2[/tex]
The general term of a geometric sequence is given by the formula:
[tex]f(n) = a {r}^{n - 1} [/tex]
To find the 15th term, we plug in a=1, r=2 and n=15.
[tex]f(15) = 1 {(2)}^{15 - 1} [/tex]
[tex]f(15) = {2}^{14} [/tex]
[tex]f(15) = 16384[/tex]
The amount he will save on the 15th day is $16,384
is anyone willing to answer this question?
ANSWER
[tex]4(x + 6)(x - 2)[/tex]
EXPLANATION
The given rational expression is:
[tex] \frac{1}{ {x}^{2} + 4x - 12} + \frac{3x}{4x - 8} [/tex]
We can factor the denominators to obtain:
[tex] \frac{1}{(x + 6)(x - 2) } + \frac{1}{4(x - 2)} [/tex]
The common denominator is least common multiples of the denominators.
The common denominator is of the given rational expression is
[tex]4(x + 6)(x - 2)[/tex]
Assume that the probability of a driver getting into an accident is 7.6%, the average cost of an accident is $16,412.05, and the overhead cost for an e company per insured driver is $105. What should be this drivers insurance premium?
Answer:
1,352.32
Step-by-step explanation:
If you take 7.6 and multiply it to 16,412.05 (.076)(16,412.05), you get 1,247.32. You then add the overhead cost of 105 to get 1352.32. (Apex verified too)
The drivers insurance premium is:
$ 1352.3158
Step-by-step explanation:The probability of a driver getting into an accident is 7.6%.
The average cost of an accident is $16,412.05.
This means that the expected amount that will be paid to each of the driver by the company on accident will be: 0.076×16412.05
= $ 1247.3158
Also, the overhead cost for an e company per insured driver is $105.
This means that the insurance premium of driver is:
= 105+1247.3158
= $ 1352.3158
One hundred football players were asked how many broken bones they have suffered. The probability distribution shows the probability of the number of bones broken by a football player.
What is the probability that a football player has suffered more than 3 broken bones?
Enter your answer, as a decimal, in the box.
Answer:
0.25
Step-by-step explanation:
The probability that a football player has suffered more than 3 broken bones is equal to the probability they suffered 4 or 5.
P(x>3) = P(4 or 5)
P(x>3) = P(4) + P(5)
P(x>3) = 0.10 + 0.15
P(x>3) = 0.25
There is a beach ball with radius 24cm and a ping pong ball with radius 4cm. Find how many times greater the volume of the beach ball is as that of the ping pong ball.
It is 36 times greater.
It is 128 times greater.
It is 6 times greater.
It is 216 times greater.
Answer:
216
Step-by-step explanation:
What decimal is represented by this expanded form?
2×10,000+7×1,000+4×100+9×1+3×1/10+8×1/1,000
Answer:
27,409.308
Step-by-step explanation:
Compute the given sum. If you're really stuck, your calculator can help you.
Noa was paid a 25 percent commission for selling a used car If she was paid $1,631.24, what was the selling price of the car?
Answer:
$6,524.96
Step-by-step explanation:
Take the commission total which is $1631.24 divide it by 25% or .25.
$1,631.24 ÷ .25=$6,524.96 cost of the used car
Check your answer by taking your answer and multiple it by 25%.
$6,524.96 (cost of the car) × .25 =$1,631.24 commission
Answer:
$6,524.96
Step-by-step explanation:
Step One: Because the amount she is paid is the 25% commission, multiply the 1,631.24 by 4 ( 4 because she is paid 1 out of 4 parts of the total selling price)
Step Two: the answer is 6,524.96