The height of rock 4 seconds after it was thrown is 168 ft.
What is speed?Speed is measured as distance moved over time.
Speed = Distance/ Time.
Here, given that,
we have
a rock is thrown off a bridge 40 feet above a river at an initial velocity of 96 feet per second.
The height h, in feet, of the rock
t seconds after it was thrown can be modeled by the function
h(t)=-16t^2 +96t+40.
where
h -----> is the height in feet of the rock
t -----> the time in seconds
For , t=4, we get,
substitute the value of t in the function and find the value of h
h(4)=-16×4^2 +96×4+40.
So, h= 168
Hence, the height of rock 4 seconds after it was thrown is 168 ft.
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What does log of e mean?
The Power e is to which a number should be raised to get the specified number is called the logarithm of that specific number. For example, the logarithm to the base of 10 of 1000 is 3 because 10 raised to the power 3 is 1000.
The logarithmic function is the reverse of the Mathematical function of the exponential function. The logarithmic function is log ax = y is equal to x = ay.
There are mainly two types of logarithms normally used in Mathematics. They are one is common logarithms and second natural logarithms.
The log number ‘e’ is an irrational Mathematical constant and is mostly used as the base of natural logarithms. The number ‘e’ is the only unique number in mathematics whose value of natural logarithm is equal to unity.
The value of log ‘e’ was calculated in 1683 by Jacob Bernoulli.
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cos(-0)=3, sin 0 <0
What is the value of sin ?
2√3/ 3
√6/3
-2 √3/3
-√6/3
On solving the provided question we can say that - here in trigonometry [tex]sinx(2cosx - 1) = 0\\[/tex] => sinx = 0 and 2 cosx -1 =0
what is trigonometry?The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures.
[tex]sin 2x - sinx = 0\\-sinx + 2cosx sinx=0\\sinx(2cosx - 1) = 0\\[/tex]
sinx = 0 and 2 cosx -1 =0
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How do you start elimination with 3 variables?
The goal of elimination is to remove one of the variables by combining the equations together.
Let's say we have an equation with 3 variables:
a + b + c = 0
The goal of elimination is to remove one of the variables by combining the equations together.
Multiply the first equation by a number, n, such that nb + nc = 0
For example:
Let n = -2
-2b + -2c = 0
Add the two equations:
a + b + c = 0
-2b + -2c = 0
a - b = 0
Solve for b:
a - b = 0
b = a
Therefore, the final equation is:
a + a + c = 0
2a + c = 0
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In the diagram, two circles, each with center $D$, have radii of $1$ and $2$. The total area of the shaded region is $\frac5{12}$ of the area of the larger circle. How many degrees are in the measure of (the smaller) $\angle ADC$
Angle ADC = 120 degrees.
What is area of sector?A certain portion of a circle that is created based on two radius of the same circle and one arc. Area of sector for a circle with radius r is given by π r²Ф/ 360°
What is the angle of ADC in the smaller circle?
Given, two circles of radius 1 unit and 2 unit which have same center D.
We know area of a circle = π r²
Area of larger circle = π 2² = 4π
it is said that the total area of the shaded region that means area of a particular sector is 1/12 of the area of the larger circle.
area of sector, ACD = 1/12 ×4π
as per the question, the ACD sector is located in the smaller circle that has radius 1 unit.
formula for area of sector ACD = π r² ×Ф/360°
where,Фis the central angle of ACD sector
and Ф = ADC
from the above statement, 4π/12 = π r² ADC/360
ADC = 1/3×360°
ADC = 120 degrees
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What is equivalent to 4 6?
The fraction which is equivalent to 4/6 is 8/12 as asked in the question.
2 x 4 = 8 and
3 x 4 = 12
Therefore, they satisfies the condition of an equivalent numbers.
Equivalent numbers are those which on reducing to it's lowest terms gives the same number.
Other example , 2/4 is equivalent number to 8/16 .
Equivalent fractions are those fractions which has different numerators and denominators but the same value when reduced to their lowest terms. For, example 2/4 and 3/6 are comparable fractions because they both equal 12.
A fraction is a portion of a number written in terms of numerator and denominator. Equivalent fractions represent the same percentage of the whole.
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What is the prouduct of 2 and 0.73
Answer:
1.46
Step-by-step explanation:
We can represent this problem as an array of dots, where each dot represents 0.73 units.
⚫️ ⚫️
We can see that the resulting product of 2 × 0.73 is just the sum of two dots. We can represent this in equation form as:
0.73 + 0.73
Finally, we can execute the addition by adding the tenths and hundredths of each number separately, then adding everything together at the end.
tenths + hundredths
(0.70 + 0.70) + (0.03 + 0.03)
1.40 + 0.06
1.46
Which expression is equivalent to –3 – 3x – 1 x? 2x – 4 –2x 4 –2x – 4? 4 – 2x
The expression equivalent to -3 - 3x -1x is 4 - 2x.
An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.
To get to this you can combine like terms:
-3 - 3x - 1x = -3 - (3x + 1x)
= -3 - (4x)
= -3 - 4x
= -4x - 3
= 4 - 2x
Hence 4 - 2x is equivalent to -3 - 3x -1x
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What is the volume, in cubic in, of a rectangular prism with a height of 3in, a width of 10in, and a length of 2in
On solving the provided question, we can say that w = 10 in; l = 2 in; volume of prism = WL = 10 X 2 = 20 in sq
what is prism?The definition of a prism in geometry is a polyhedron with an n-sided polygonal base, a second base that is a shifted copy of the first base, and n additional faces (necessarily all parallelograms), with two Connect the corresponding sides of the base. Translations of the base are all cross sections that are parallel to it. A prism is a two-sided, solid, three-dimensional object. It consists of equal cross-sections, flat sides, and identical bases. A prism has faces that are parallelograms or rectangles without bases. A prism is a homogenous, solid, transparent, refracting object enclosed by two planes that are obliquely angled to one another. Two triangular faces and three parallel rectangular faces make up a typical prism. They are constructed of either glass.
here,
w = 10 in
l = 2 in
volume of prism = WL = 10 X 2 = 20 in sq
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Graph the systems of equations.
{2x+y=8
−x+2y=6
Need help really fast thank you so much!
Use the Line tool to graph the lines.
Answer:
x = 2
y = 4
Step-by-step explanation:
-x+6=-2(x+2)-5
Solve for x
Answer:
x = -15
Step-by-step explanation:
-x+6=-2(x+2)-5
Solve for x
-x + 6 = -2(x + 2) - 5
-x + 6 = -2x - 4 - 5
x = -15
------------------------
check- (-15) + 6 = -2(-15 + 2) - 5
21 = 21
the answer is goodx = -15
what is the percent change from 99 to 71?
To calculate the percent change of two numbers such as 99 to 71, you use the Percent Change Formula, where a is the start value and b is the end value. When we insert a = 99 and b = 71 in the formula above, then we get the following that we can simplify and solve to get the percent change from 99 to 71.
Change ≈ -28.2828%
Select the interval where f is negative.
Answer: A
Step-by-step explanation:
Based on the graph, we know that it is negative if it is under the x-axis. It is also indicated by the negative labels.
A: correct
Looking at choice A, it says the interval is from -4<x<-2. This means we have to find x=-4 and x=-2. On the graph, that interval is below the x-axis, so it is negative.
B: incorrect
Looking at choice B, it says the interval is from -1<x<1. This means we have to find x=-1 and x=1. On the graph, that interval is above the x-axis, so it is positive, not negative.
C: incorrect
Looking at choice C, it says the interval is from 2<x<4. This means we have to find x=2 and x=4. On the graph, that interval is above the x-axis, so it is positive, not negative.
Therefore, A is the correct answer.
A company i expanding it building area from 18,000 quare feet to 25,380 quare feet. What i the percentage increae of the area of the building pace?
41% is the percentage increase of the area of the building pace.
What is percentage?When the denominator is 100, percentages are really just fractions. We place the percent sign (%) next to the number to indicate that the number is a percentage.
Comparing two amounts while rebasing the second amount to 100 is the simplest way to use percentages. The word percentage comes from the Latin term per centum, which means "by the hundred." In the 16th century, the Latin term made its way into English. It was later abbreviated to %.
A company is expanding it building area from 18,000 square feet to 25,380 square feet.
= (25,380 - 18,000)
= 7,380
Now,
= 7,380 / 18,000
= 0.41
the percentage increase of the area of the building pace: 0.41 / 100 = 41%
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For the function Y= X +4 what is the output value if three is the input value
Answer: 7
Step-by-step explanation:
1. You need to know that the input value means the x-value, which means x = 3.
2. Input 3 in the function
3. Solve 3+4
4. 3+4 = 7
Answer:
put y=4 then four comes with- and 4-3=2
The cost to hire a tent consists of two parts. $c + $d per dayThe total cost for 4 days is $27. 10 and for 7 days is $34. 30. Write down two equations in c and d and solve them
The cost to hire a tent consists of a fixed cost of $17.50 and a variable cost of $2.40 per day.
Let's call the total cost of hiring a tent for 4 days as T4, and the total cost of hiring a tent for 7 days as T7.
The first equation is the cost for 4 days:
T4 = c + 4d
The second equation is the cost for 7 days:
T7 = c + 7d
We know the values of T4 and T7 from the problem statement:
T4 = $27.10 and T7 = $34.30
We can now use these two equations and their corresponding values to solve for c and d:
Substitute the value of T4 into the first equation:
$27.10 = c + 4d
Substitute the value of T7 into the second equation:
$34.30 = c + 7d
Now we have a system of two equations with two variables (c and d).
Subtract 4d from both sides of the first equation:
$27.10 - 4d = c
Subtract c from both sides of the second equation:
$34.30 - c = 7d
Now we can substitute the value from step 4 into step 5:
$34.30 - $27.10 + 4d = 7d
7d = $34.30 - $27.10 + 4d
3d = $7.20
d = $7.20 / 3 = $2.40
Now we have the value of d, we can substitute it back into the first equation to find the value of c:
$27.10 = c + 4d
$27.10 = c + 4($2.40)
$27.10 = c + $9.60
c = $27.10 - $9.60
c = $17.50
Therefore, c= $17.50 and d= $2.40
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A spinner is divided into 6 equal regions, numbered 10 through 15. An arrow is spun and lands on one of the numbers. What are the odds of the arow landing on a number that is greater than 10?
A.
0.1667
B.
0.333
C.
0.667
D.
0.833
Answer: Option D (0.833)
Step-by-step explanation:
There are 6 possible outcomes when the arrow is spun, and 5 of those outcomes correspond to the arrow landing on a number greater than 10 (the numbers 11, 12, 13, 14, and 15).
Therefore, the probability of the arrow landing on a number greater than 10 is 5/6, or about 0.833
What is quadrant 3 on a graph?
The lower left-hand corner of the graph is the third quadrant.
It contains the negative values of both x and y.
Quadrant
The axes of a two-dimensional Cartesian system divide the plane into four infinite regions called quadrants, each bounded by two half-axes.
Cartesian system
A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length.
coordinates
Coordinates are numbers which determine the position of a point or a shape in a particular space.
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You have to pay 25% income tax on all of the money you make. If you made $3000 this month, how much did you have to pay in taxes this month?
Please answer ASAP! :{
You get 20 points! :)
Answer: 750
Step-by-step explanation:
3000/4= 750
750
HELP PLEASE 10 POINTS!
pls explain
a. 160 is what percentage of 40?
b. 40 is 160% of what number?
c. What number is 40% of 160?
Answer:
a) 400% b) 1/4 c) 64
Step-by-step explanation:
Answer:
a. 400%
b. 25
c. 64
Step-by-step explanation:
a. 160 ÷ 40/100
160 × 100 / 40
4 × 100 = 400%
b. 40 ÷ 160%
40 ÷ 160/100
40 × 100/160 = 25
c. 40% × 160
40/100 × 160
4 × 16 = 64
What are the 4 steps in solving simple problems in mathematics?
The 4 steps in solving simple problems in mathematics is explained below.
According to the author called Polya created his famous four-step process for problem solving that one is used all over to aid people in problem solving
The first and foremost Step is to understand the problem which includes identification of the unknowns and figure out what the problem tells you is important and then we have to identify any information that is irrelevant to the problem.
Then the nest step is to Devise a plan which means that Look for a pattern and then by using it we have to make a table, diagram or chart and then write an equation.
Then we have to move onto the next steps that is to carry out the plan which means the process of solving the question.
Then the final step is to Look back problem that is none other than check and interpret its reliability of the solution
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1. The population average fuel efficiency of U.S. light vehicles for 2005 was 21 mpg. If the standard deviation of the population was 2.9 and the gas ratings were normally distributed, what is the probability that the mean for a random sample of 25 light vehicles is under 20 mpg
The probability that the mean mpg for a random sample of 25 light vehicles is 0.042341
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.
z = (x-μ)/σ/n, where
x is the raw score = 20 mpg
μ is the population mean = 21 mpg
σ is the population standard deviation = 2.9
n = random number of samples [tex]x < 20[/tex]
[tex]= z = 20 - 21/2.9/\sqrt{25} \\= z = -1/2.9/5\\= z = -1.72414\\[/tex]
P-value from Z-Table:
[tex]P(x < 20) = 0.042341[/tex]
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Where is graph increasing and decreasing?
The graph is increasing when the graph has positive slope and the graph is decreasing when the graph have a negative slope .
What is Slope ?
The slope of any line can be calculated by using any two distinct points on the line. The slope of a line formula calculates the ratio of the vertical change to horizontal change between two distinct points of the line.
that means , let the two points on the line be [tex](a,b)[/tex] , [tex](c,d)[/tex] . So , the slope will be calculated as : Slope(m) = [tex]\frac{d-b}{c-a}[/tex] .
(i) When the slope of the graph is positive , it indicates that the graph rises when moving from left to right , Hence , the graph is increasing .
(ii) When the slope of the graph is negative , it indicates that the graph falls when moving from left to right , Hence , the graph is decreasing .
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The spinner is spun 75 times. What is the experimental probability of spinning the given result? Round your answer to the nearest hundredth if necessary. Outcome A B C D Frequency 20 11 14 30 B or C
The experimental probability of spinning of B or C is 1/3.
In the given question, the spinner is spun 75 times.
We have to find the experimental probability of spinning of B or C.
The given data is:
Outcome A B C D
Frequency 20 11 14 30
Total frequency = 20 + 11 + 14 + 30
Total frequency = 75
The probability of spinning B = Frequency of B/Total Frequency
The probability of spinning B = 11/75
The probability of spinning C = Frequency of C/Total Frequency
The probability of spinning C = 14/75
Now the experimental probability of spinning of B or C;
P(B or C) = P(B) + P(C)
P(B or C) = 11/75 + 14/75
P(B or C) = (11 + 14)/75
P(B or C) = 25/75
P(B or C) = 1/3
Hence, the experimental probability of spinning of B or C is 1/3.
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On a negatively skewed curve, which is true?
a.The median is lower than the mode which is lower than the mean. b.The mean, median, and mode are the same. c.The mean is lower than the median which is lower than the mode. d.The mode is lower than the mean which is lower than the median. e.The mean is lower than the mode which is lower than the median.
The mean of negatively skewed data is smaller than the median. If the data are displayed symmetrically, the distribution is not skewed regardless of tail length or thickness. So, option d. is correct.
What do you mean by skewed curve?A skew curve is a type of statistical distribution in which the data are unevenly distributed. This is often called an asymmetric distribution, meaning that the two halves of the curve look different. A skewed curve can be either positively or negatively skewed, depending on the direction in which the data points are shifted. Positively skewed curves tend to have long tails to the right, while negatively skewed curves tend to have long tails to the left. This type of distribution is common in real-world data such as income and wealth distributions.
A negatively skewed curve is indicated by the negative tail of the chart. This means that the data points are likely to be below average. Therefore, the mean is lower than the mode, which is lower than the median. The mean is the arithmetic mean of all data points, the mode is the most common value, and the median is the midpoint of the data points.
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Pls help me with math
Answer:1
Step-by-step explanation:;
Given points V(10;2) and N (-7;9).
Determine the coordinates of vectors VN and NV
VN =( ; )
NV = ( ; )
Solve the system of inequalities by graphing. If there is no solution, click on "No solution".
3x+y≥3
x≤-1
:)
ggggggggggggrssdfffffffffffffffffffffffffffffffffrsssssssssshggh
Find the 7th term of the geometric sequence whose common ratio is 3/2 and whose first term is 5
The 7th term of the geometric sequence is 3675/64.
A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a constant called the common ratio.
The 7th term of a geometric sequence can be found using the formula:
a_n = a_1 * (r)^(n-1) where a_1 is the first term of the sequence, r is the common ratio, and n is the position of the term in the sequence.
Given that the common ratio is 3/2 and the first term is 5, we can substitute these values into the formula:
a_7 = 5 * (3/2)^(7-1)
After solving the expression we get:
a_7 = 5 * (3/2)^6 = 5* (243/64) = 15*243/64 = 3675/64
So the 7th term of the geometric sequence is 3675/64.
Therefore, the 7th term of the geometric sequence is 3675/64.
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Find the value of b.
Image is below please explain and give correct answer !!
The value of b is degree 104.we can find by using vertically opposite theorem.
What is vertically opposite in maths?Vertical Angles are when two lines intersect each other then the opposite angles formed due to intersection are called vertical angles or vertically opposite angles. A pair of vertically opposite angles are always equal to each other.The point where they meet is called a vertex.
How do we identify opposite angles?Vertical opposite angles that are opposite each other when two lines cross are also known as vertical angles because the two angles share the same corner. Opposite angles are also congruent angles meaning they are equal or have the same measurement.
Now we have
(b-308)=(-2b+4)
b+2b=4+308
3b=312
b=104
Hence the value of b is 104 degree.
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We take a sample of 80 observations from a large population with a mean of 1460 and a standard deviation of 270. The probability that the sample mean is between 1300 and 1400 is:
The probability that the sample mean is between 1300 and 1400 is approximately 1.34%.
We can use the Central Limit Theorem and the standard normal distribution to calculate the probability that the sample mean is between 1300 and 1400. The Central Limit Theorem states that as the sample size increases, the distribution of the sample means will approach a normal distribution, regardless of the distribution of the population.
Since we have a sample of 80 observations, we can assume that the sample mean follows a normal distribution with a mean of 1460 (the population mean) and a standard deviation of:
Standard deviation of the sample mean
= population standard deviation ÷ [tex]\sqrt {sample size[/tex]
[tex]= 270 \div \sqrt{80} = 27[/tex]
So the standard deviation of the sample mean is 27.
We can now standardize the interval between 1300 and 1400 by subtracting the mean and dividing it by the standard deviation of the sample mean.
[tex]Z_1[/tex] = (1300 - 1460) / 27 = -2.59
[tex]Z_2[/tex] = (1400 - 1460) / 27 = -2.22
We need to find the area under the standard normal distribution curve between Z1 and Z2.
Using a standard normal table or a calculator with the standard normal distribution function, we can find the probability that a random variable from the standard normal distribution is between -2.59 and -2.22. This probability is approximately 0.0134 or 1.34%.
Therefore, the probability that the sample mean is between 1300 and 1400 is approximately 1.34%.
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