Acceleration is the rate of change of velocity over time
The sled travels 100 meters in the first 10 seconds of its motion
How to determine the distanceThe acceleration function is given as:
[tex]a = \frac 1{500}(20t^2 - t^3)[/tex]
When t = 10, we have:
[tex]a = \frac 1{500}(20*10^2 - 10^3)[/tex]
[tex]a = 2[/tex]
The distance at 10 seconds is then calculated as;
[tex]S = ut +\frac 12 at^2[/tex]
Where:
u = initial velocity = 0
So, we have:
[tex]S = 0 *10 +\frac 12 * 2 * 10^2[/tex]
[tex]S =100[/tex]
Hence, the sled travels 100 meters in the first 10 seconds of its motion
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If a triangle has side lengths a, b, and c, and if a^2 + b^2 = c^2, then the converse of the Pythagorean theorem says that the triangle is a(n)
A. equiangular triangle
B. scalene triangle
C. equilateral triangle
D. right triangle
two thirds of a number is negative six. find the number
Answer:
-9
Step-by-step explanation:
Two-thirds of a number is negative six. The number is -9. Let the number is x, 2/3x =-6, x=-6x3/2=-9.
Which sentence describes a way to determine the missing number number in the pattern?
Answer:
70910 not sure
Step-by-step explanation:
70.91 x 10 = 709.1 70.91 x 100 = 7,091 70.91 x 1,000 =
Consider the following confidence interval interpretation: We are 98% confident that the true mean laptop screen size is between 19.2 and 21.4 inches. Is this interpretation of a confidence interval correct or incorrect
Answer:
Incorrect
Step-by-step explanation:
This interpretation is incorrect because it states that 98% of the data is with in the confidence interval.
or 98% of the laptop have screen size between 19.2 and 21.4 inches
However, the interpretation would have been correct if it would have stated as - Value of the population mean i.e mean size of the laptop screen lies within the confidence interval.
Abigail is using blocks to build a tower. The blocks are 3 inches, 4 inches, and 8 inches tall. She has stack 3 blocks. How many different heights are possible for the tower?
9514 1404 393
Answer:
10
Step-by-step explanation:
Possible tower heights using 3 blocks are ...
{9, 10, 11, 12, 14, 15, 16, 19, 20, 24}
There are 10 different heights possible.
_____
Each block can be used 1, 2, or 3 times.
Using a 3 in block as the smallest, we have ...
3+3+3 = 9
3+3+4 = 10
3+3+8 = 14
3+4+4 = 11
3+4+8 = 15
3+8+8 = 19
Using a 4-in block as the smallest, we have ...
4+4+4 =12
4+4+8 = 16
4+8+8 = 20
And ...
8+8+8 = 24
explanation would be appreciated, last word is indicated.
Answer:
AC = 28
Step-by-step explanation:
Ok, we know that:
Points A, B, and C are collinear.
Point B is between A and C.
We want to find the length AC (distance between A and C), if we know that:
AB = 16
BC = 12
Ok, knowing that B is between the other points, we know that:
AB + BC
defines the total length of the segment that connects the 3 points.
Thus, if we define this segment as a length, we only use the endpoints, A and C.
Then we have that:
AB + BC = AC
now we can solve this:
16 + 12 = AC
28 = AC
A populations instantaneous growth rate is the rate at which it grows for every instant in time. Function r gives the instantaneous growth rate of a bacterial culture x hours after the start of an experiment How many hours after the experiment began was the instantaneous growth rate equal to 0? r(x)=0.01(x+2)(x^2 -9) A. 9 B. 2 C. 0 D. 3
Answer:
3
Step-by-step explanation:
r(x) = 0.01(x + 2)(x^2 - 9)
We are looking fo the value of x at which r(x) = 0.
We set the function equal to 0 and solve for x.
0.01(x + 2)(x^2 - 9) = 0
Divide both sides by 0.01. Factor x^2 - 9 as the difference of two squares.
(x + 2)(x + 3)(x - 3) = 0
x + 2 = 0 or x + 3 = 0 or x - 3 = 0
x = -2 or x = -3 or x = 3
Since we are looking for a time after the experiment started, and it started at x = 0, we discard the negative answers, and we keep x = 3.
Answer: 3
Answer:
3
Step-by-step explanation:
EDMENTUM
7056 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows and the number of plants in each row
Answer:
84 rows
84 plants on each row
Step-by-step explanation:
Given
[tex]Plants = 7056[/tex]
Required
The number of rows
Since the number of rows (r) and the plants on each row (p) are the same, then the area to be planted on is:
[tex]Plants = r * p[/tex]
Where
[tex]r =p[/tex]
So, we have:
[tex]Plants = r * r[/tex]
[tex]Plants = r^2[/tex]
This gives:
[tex]7056 = r^2[/tex]
Take square roots
[tex]84 = r[/tex]
Rewrite
[tex]r = 84[/tex]
Round 3,872.3155 to the nearest hundred
Answer:
3,872.316
Step-by-step explanation:
Answer:
to nearest hundreds it would be: 3,900
Step-by-step explanation:
872 it closer to 900 than 800
The hypotenuse of a right triangle is 13 ft long. The longer leg is 7 ft longer than the shorter leg. Find the side lengths of the triangle.
Answer:
The shorter leg is five feet, the longer leg is 12 feet, and the hypotenuse is 13 feet.
Step-by-step explanation:
Let the shorter leg be x.
Since the longer leg is seven feet longer than the shorter leg, the length of the longer leg can be modeled by (x + 7).
Since the triangle is a right triangle, we can use the Pythagorean Theorem, given by:
[tex]a^2+b^2=c^2[/tex]
Where a and b are the side lengths and c is the hypotenuse.
The hypotenuse is 13 and the legs are x and (x + 7). Substitute:
[tex](x)^2+(x+7)^2=(13)^2[/tex]
Square:
[tex]x^2+x^2+14x+49=169[/tex]
Simplify:
[tex]2x^2+14x-120=0[/tex]
We can divide both sides by two:
[tex]x^2+7x-60=0[/tex]
Factor:
[tex](x-5)(x+12)=0[/tex]
Zero Product Property:
[tex]x-5=0\text{ or }x+12=0[/tex]
Solve for each case:
[tex]x=5\text{ or } x=-12[/tex]
Since lengths cannot be negative, we can ignore the negative answer. So, our only solution is:
[tex]x=5[/tex]
The shorter leg is five feet, the longer leg will be (5 + 7) or 12 feet. And the hypotenuse is 13 feet as given.
What is the relation between the variables in the equation
X^4/y=7?
a. x varies inversely as y
b. x4 varies directly as y
c. y varies directly as x4
d. y varies inversely as x4
Answer:
b. x^4 varies directly as y.
Step-by-step explanation:
x^4 = 7×y
x^4 is proportional to y.
The parent function f(x) 3 to the square root of x is transformed to g(x)=2f(x-3). Which is the graph of g(x)?
Answer:
the answer is B
Step-by-step explanation:
Person A leaves his home to visit his cousin, person B, who lives 243 miles away. He travels at an average rate of 46 miles per hour. One half-hour later, person B leaves her house to visit person A, traveling at an average rate of 64 miles per hour. How long after person B leaves will it be before they meet?
plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz help me i really do need the help
Each of the problems below was solved incorrectly, for each problem, find the mistake in the work/ answer. Explain what the mistake is, and find the correct answer.
Explain the mistake:
Find the correct answer(equation):
2. Find the value of x
Explain the mistake:
Find the correct answer(equation):
3. Find the value of x
Explain the mistake:
Find the correct answer(equation):
Question 1
The mistake is that vertical angles are congruent, and don't always add up to 180 degrees.[tex]5x=100 \longrightarrow x=20[/tex]Question 2
Angles that add to form a right angle add to 90 degrees, not 180 degrees.[tex]3x+39=90 \longrightarrow 3x=51 \longrightarrow x=17[/tex]Question 3
Angles that add to form a right angle add to 90 degrees, not 180 degrees.[tex]3x+39=90 \longrightarrow 3x=51 \longrightarrow x=17[/tex]Help me pls and thanks important!!!!
Answer:
33
1/2(83-50)=25
83-x=50
x=33
Solve one-sixth ÷ 6 = ___
Answer:6/6
Step-by-step explanation:
1/6 divide 6
Keep
Flip
Change
your gonna keep 1/6 as a fraction
then flip the second fraction so 6 would’ve been 6/1 but it’s gonna flip so it should look like this 1/6
after you will change the sign so the division will become multipliaction so it should look like 1/6 x 6/1 which will equal to 6/6
HELP!!!
A spherical baseball has a diameter of 5 inches and weighs 7 grams per cubic inch. What is the closest weight of the baseball rounded to the nearest gram?
Answer:
69
Step-by-step explanation:
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How many 1/6 cup serving of rice and in 2/3 cup of rice
Answer:
4 serving cups
Step-by-step explanation:
Given
[tex]Serving\ cup = \frac{1}{6}[/tex]
[tex]Rice\ cup = \frac{2}{3}[/tex]
Required
The number of serving cup (n)
This is calculated by dividing the rice cup by the serving cup
[tex]n = \frac{Rice\ cup}{Serving\ cup}[/tex]
[tex]n = \frac{2/3}{1/6}[/tex]
Rewrite as:
[tex]n = \frac{2}{3} \div \frac{1}{6}[/tex]
Change to multiplication
[tex]n = \frac{2}{3} * \frac{6}{1}[/tex]
[tex]n = \frac{12}{3}[/tex]
[tex]n=4[/tex]
A science teacher wrote the table of values below.
Amount of Hydrogen vs. pH
pH, f(x)
Amount of Hydrogen, X
(in moles per liter)
1
10
1
2
1
100
3
3
1
1,000
4
1
10.000
-
5
1
100,000
Which function models the data in the table?
Answer:
B
Step-by-step explanation:
Took quiz
The logarithmic function for the teacher who wrote the table of values with amount of hydrogen and pH level is given by f ( x ) = log ( 1/x )
What is Logarithm?The power to which a number must be increased in order to obtain another number is known as the logarithm. A power is the opposite of a logarithm. In other words, if we subtract an exponentiation from a number by taking its logarithm
The properties of Logarithm are :
log A + log B = log AB
log A − log B = log A/B
log Aⁿ = n log A
Given data ,
Let the function be represented as f ( x )
Now , the values of x are
x = { 1/10 , 1/100 , 1/1000 , 1/10000 , 1/100000 }
where x represents the amount of Hydrogen in moles per liter
And the values of f ( x ) = { 1 , 2 , 3 , 4 , 5 }
where y represents the pH level
So , when x = 1/10 , f ( x ) = 1
And , the logarithmic equation is given as
f ( x ) = log ( 1/x )
when x = 1/1000
f ( 1/1000 ) = log ( 1/1/1000 )
f ( 1/1000 ) = log ( 1000 )
f ( 1/1000 ) = 3
Therefore , the value of f ( x ) is log ( 1/x )
Hence , the logarithmic equation is f ( x ) = log ( 1/x )
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If A = {x x is an even integer), B = {xx is an odd integer), C = {2, 3, 4, 5), and D = {8, 9, 10, 11), list the element(s) of the following set.
AND
An D= { } (Use a comma to separate elements in the set.)
Answer:
AnD = {8,10}
Step-by-step explanation:
A = {2, 4, 6, 8 ,10 ...}
B = {1, 3, 5, 7 ,9 ...}
C = {,2 ,3 ,4 ,5 ...}
D = { 8, 9 ,10 ,11 ...}
AnD = {8, 10}
can someone answer this please
Answer:
x = 14
Step-by-step explanation:
Please note, the word trapezium is a synonym for the word trapezoid.
This problem gives one the area of the trapezoid, a well as one of the measurements of a base and the height of the figure. One is asked to find the length of the other base. This can be done by using the formula to find the area of a trapezoid. This formula is the following,
[tex]A=(h)(\frac{b_1+b_2}{2})[/tex]
Where (A) represents the area of a trapezoid, ([tex]b_1[/tex]) and ([tex]b_2[/tex]) represents the bases and (h) represents the height. Substitute in the given values and solve for the unknown base.
[tex]b_1=7\\h=6\\A=84[/tex]
[tex]A=(h)(\frac{b_1+b_2}{2})\\[/tex]
Substitute,
[tex]84=6(\frac{7+b_2}{2})\\[/tex]
Inverse operations,
[tex]84=6(\frac{7+b_2}{2})[/tex]
[tex]14=\frac{7+b_2}{2}[/tex]
[tex]28=7+b_2[/tex]
[tex]14=b_2[/tex]
If you answer this you will get 100 points pls answer hurry it’s due in 20 mins
Answer:
Option B, medianStep-by-step explanation:
We see the data is not uniform. One of the prices is very high compared to the others. Since there is an outlier, the median is the best measure of central tendency.
This is the second option.
Identify the relationship between sampling error and sample size.
Answer:
as the sample size increases, the margin of error decreases
If x + y =6, y +z = 7 and z + x =9, what is the average (arithmetic mean) of
x,y and z?
Answer:
[tex]\frac{22}{3}[/tex]
Step-by-step explanation:
x + y + y + z + z + x = 2x + 2y + 2z = 22
x + y + z = 22
22 ÷ 3 = [tex]\frac{22}{3}[/tex]
If 3 is added to a number and the sum is multiplied by 7,gives 91 as result. Find the number.
Answer:
10
Step-by-step explanation:
10+3 = 13
13 x 7 = 91
Answer:
7(3x)=91
21x=91
x=91/21
Compute the loss of head and pressure drop in 200 ft of horizontal 6-in diameter asphalted cast iron pipe carrying water with a mean velocity of 6 ft/s. For water: rho = 1.94 slug/ft3 and μ = 2.09x10-5 slug/ft-s (ν = μ/rho). Assume ε = 0.0004 ft.
Answer:
The answer is below
Step-by-step explanation:
12 inches = 1 ft.
6 inches = 6 inches * (1 ft./12 inches) = 0.5 ft.
Therefore the diameter of the cast iron (D) = 6 inches = 0.5 ft.
The area of cast iron (A) = πD²/4 = π(0.5)²/4 = 0.196 ft²
The velocity (V) = 6 ft./s, the acceleration due to gravity (g) = 32.2 ft./s²
ε/D = 0.0004 ft./ 0.5 ft. = 0.0008
Using the moody chart, find the line ε/D = 0.0008 and determine the point of intersection with the vertical line R = 2.7 * 10⁵. Hence we get f = 0.02.
The head loss (h) is:
[tex]h_f=f*\frac{L}{d}* \frac{V^2}{2g}=0.02*\frac{200\ ft}{0.5\ ft} *\frac{(6\ ft/s)^2}{2*32.2\ ft/s^2}=4.5\ ft[/tex]
The pressure drop (Δp) is:
Δp = ρg[tex]h_f[/tex] = [tex](62.4\ lbf/ft^3)(4.5\ ft)= 280\ lbf/ft^2[/tex]
Sue believes that the two cylinders shown in the diagram have equal volumes. Is Sue correct? Explain why or why not
Sui believes that the two cylinders have an equal volume is correct.
The volume of cylinder = Base area×Height
=(πr²)×(height)
This is also true for oblique cylinder.
Both cylinders have same height and radius also so, both cylinders have equal volume.
V=πr²h
V=π×(5)²×11.5
V=903.208m³
It can also be visualized that the oblique cylinder have circular pieces. These pieces can be solid together to form a regular cylinder with the same height (i.e. 11.4 m). So both the cylinders have equal volume.
What is a cylinder?A cylinder is a three-dimensional shape in geometry. A cylinder is round and has a top and bottom in the shape of a circle. The top and bottom are flat and always the same size.
Thus, Sue is correct, and it's true that the two cylinders shown in the diagram have equal volumes.
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find the smallest number by which 2925 should be divided to be a perfect square
Answer: 13
Step-by-step explanation:
Given
The number is 2925
The prime factorization of 2925 is
[tex]\Rightarrow 2925=3\times 3\times 5\times 5\times 13\\\Rightarrow 2925=3^2\times 5^2\times 13[/tex]
To make 2925 a perfect square, we have to eliminate 13 from it, so divide 2925 by 13 to make it a perfect square
The perfect Sqaure becomes [tex](3\times 5)^2=225[/tex]
What sample size is needed to give a margin of error within in estimating a population mean with 95% confidence, assuming a previous sample had .
Answer:
[tex]n = (\frac{1.96\sqrt{\pi(1-\pi)}}{M})^2[/tex]
The sample size needed is n(if a decimal number, round up to the next integer), considering the estimate of the proportion [tex]\pi[/tex](if no previous estimate use 0.5) and M is the desired margin of error.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
Needed sample size:
The needed sample size is n. We have that:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]M = 1.96\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]\sqrt{n}M = 1.96\sqrt{\pi(1-\pi)}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{\pi(1-\pi)}}{M}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96\sqrt{\pi(1-\pi)}}{M})^2[/tex]
[tex]n = (\frac{1.96\sqrt{\pi(1-\pi)}}{M})^2[/tex]
The sample size needed is n(if a decimal number, round up to the next integer), considering the estimate of the proportion [tex]\pi[/tex](if no previous estimate use 0.5) and M is the desired margin of error.
What is the volume of the cylinder below?
3