Answer:
zero
Step-by-step explanation:
You want Amy Van's average velocity when she swims 50 m to the end of the pool and back.
Average velocityAverage velocity is the ratio of the change in position to the amount of time over which that change occurs. When Amy ends up where she started, she has not changed position at all, so her average velocity is ...
Vave = (change in position)/time = 0/time = 0
Her average velocity is zero.
In an all boys school, the heights of the student body are normally distributed with a
mean of 67 inches and a standard deviation of 5 inches. Using the empirical rule,
determine the interval of heights that represents the middle 95% of male heights
from this school.
The interval of heights calculated by using empirical rule which represents the middle 95% of male heights from this school is between 57 inches and 77 inches.
What is Empirical rule?
Empirical rule has three rule of statement based on the normal distribution and they as as follows:
1) About 68% of the x values lie between 1 standard deviation below and above the mean.
2) About 95% of the x values lie between 2 standard deviations below and above the mean.
3) About 99.7% of the x values lie between 3 standard deviations below and above the mean.
According to the question, let us assume 'x' be a random variable representing the heights of males from this school. With the mean and standard deviation given, then the Empirical Rule number two states that the:
From the information given,
mean = 67 inches
Standard deviation = 5 inches
We want to determine where 95% of x values lies. This is 2 standard deviations from the mean Therefore,
2 standard deviations = 2 × 5 = 10 inches
The heights are
67 - 10 = 57 inches and
67 + 10 = 77 inches
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Decide
{(8,0), (5,7), (9,3), (3,8)}
if each relation is a function.
Since each input value (domain) leads to only one output value, therefore each relation classifies as a function.
An ordered pair set is known as a relation. Each ordered pair's collection of first components is known as the domain, and its set of second components is known as the range.
A function (f) is a relation that gives each value in the domain a single value from the range.
Its given that - (8,0), (5,7), (9,3), (3,8)
Mapping:
Domain Range
8 → 0
5 → 7
9 → 3
3 → 8
In other words, classify the relationship as a function if each input value (domain) results in just one output value. Do not classify the connection as a function if any domain produces two or more outputs.
As a result, the relationship given is a function.
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how to solve a sequence
For the first sequence
Let a1 = 2
2, 9, 16, 23, ...
Recursive Formula
[tex]a_n=a_{n-1}+7[/tex]Explicit Formula
[tex]a_n=2+7(n-1)[/tex]For the second sequence
Let a1 = 2
2, 14, 98, 686, ...
Recursive Formula
[tex]a_n=7(a_n-1)[/tex]Explicit Formula
[tex]a_n=2\cdot7^{n-1}[/tex]X+87°+2x degrees i need to solve for angle 2x
Answer:
62
Step-by-step explanation:
x + 87 and 2x are linear pair angles.
Sum of linear pair angles is 180,
x + 87 + 2x = 180
x + 2x + 87 = 180
3x + 87 = 180
3x = 180 - 87
3x = 93
x = 93 / 3
x = 31
2x
= 2 * 31
= 62
consider the three circles, where R represents the radius of each circle which statement is true?
If two shapes are similar to each other, they have the same shape, but not necessarily the same size.
All circles are similar to each other. All points on the circumference of any circle are equidistant from its center.
The ratio of the radii of the pair of circles will give the scale factor.
The correct option is the SECOND OPTION.
decide if you think the method described would result in a good random sample, and explain your answer. random phone numbers are dialed in a given area code to survey people as to whether or not they've needed the services of a food pantry to feed their families.
The given situation represents a random sample because, in statistics, a simple random sampling refers to the subset of individuals chosen from a larger set called population, where the sample is chosen randomly.
In this case, the dialed number are a random event, so it can be called a simple random sample.
If the probability that a vaccine you took will protect you from getting the flu is 0.977, what is the probability that you will get the flu?
Probability that you will get the flu =
Answer:
Step-by-step explanation:
0.033
Need help on this question thanks
The linear regression equation is y = 15430.5034 + 301.2586x .
What is the substitution method?The algebraic technique for resolving multiple linear equations at once is called the substitution method. As the name implies, this method involves substituting a variable's value from one equation into another. The first stage in the substitution approach is to determine any variable's value in terms of the other variable from one equation. If there are two equations, x + y=7 and x - y=8, for instance, we can deduce from the first equation that x=7-y. The substitution approach is applied in this manner as the first stage. There are three steps in the substitution technique: For each variable, solve a single equation. Solve the other equation by substituting (plugging in) this expression. Find the corresponding variable by substituting the value back into the original equation.
∑x = 56
∑ y = 109453.5
∑ x² = 760
∑ x × y = 1093064.7
Substitute the upper values
6a + 56b = 109453.5
56a + 760b = 1093064.7
Solve the above 2 equations
a = 15430.5034
b = 301.2586
Now substitute the values in y = a + bx
y = 15430.5034 + 301.2586x
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Liz does screen-printing. When she screen-prints a batch of T-shirts, there is an initial set-up time of 15 minutes. After that, it takes 3 minutes to print each shirt. How long does it take to screen-print a batch of 14 shirts?
The time taken to screen-print a batch of 14 shirts are 42 minutes
In the above question, it is given that,
Lizz does screen-printing and she screen-prints a batch of T-shirts
The time taken in initial set-up to screen print the first t-shirt is = 15 minutes
After that,
The time taken in screen printing further t-shirts of the batch is = 3 minutes
We need to find the time taken to screen-print a batch of 14 shirts = 3 x 14 = 42 minutes
Hence, the time taken to screen-print a batch of 14 shirts are 42 minutes
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3x^3-15x-13/x+2
Using synthetic division
The quotient when [tex]3x^{3} -15x-13[/tex] is divided by (x+2) using the synthetic division is ([tex]3x^{2} -6x-3[/tex]) and remainder is -7.
According to the question,
We have the following expressions:
[tex]3x^{3} -15x-13[/tex] is divided by (x+2)
First, we will look at some of the rules of the synthetic division:
We have to make the quotient in such a way that it is same as the term with the highest power in the dividend.
We change signs after solving using one complete term of the quotient.
We have to solve this using the synthetic division method:
x+2 )[tex]3x^{3} -15x-13[/tex]( [tex]3x^{2} -6x-3[/tex]
[tex]3x^{3} +6x^{2}[/tex]
_-___-_____
[tex]-6x^{2} -15x-13[/tex]
[tex]-6x^{2} -12x[/tex]
+ +
_________
-3x-13
-3x-6
+ +
_______
-7
Hence, the quotient when [tex]3x^{3} -15x-13[/tex] is divided by (x+2) using the synthetic division is ([tex]3x^{2} -6x-3[/tex]) and remainder is -7.
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what is the area of a triangle with a base of 9units and a height of 7units ?
The area of a triangle is given by
[tex]A=\frac{1}{2}\cdot b\cdot h[/tex]Where b is the base and h is the height of the triangle.
Let us substitute the given values of base and height into the above formula
[tex]\begin{gathered} A=\frac{1}{2}\cdot b\cdot h \\ A=\frac{1}{2}\cdot9\cdot7 \\ A=\frac{63}{2} \\ A=31.5 \end{gathered}[/tex]Therefore, the area of the triangle is 31.5 square units.
Are the triangles congruent using AAS?
True
False
What is a(b(x)) if a(x) = 3x 2 and g(x) = -3x + 1?
The equivalent composite function of the given one is expressed as; -9x + 5
What is a function?Function is a type of relation, or rule, that maps one input to specific single output. Composite functions are also known as function of a function.
Given the following functions as;
a(x) = 3x+2 and
b(x) = -3x + 1
To determine the value of a(b(x));
a(b(x)) = a(-3x+1)
a(b(x)) = 3(-3x+1) + 2
a(b(x)) = -9x + 3 + 2
a(b(x)) = -9x + 5
Therefore, This gives the equivalent composite function of the given one.
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please help me out thanks
The value for the A³ matrix will be [tex]A^{3} = \left[\begin{array}{ccc}75&0 \\0&1\end{array}\right][/tex]
In the given question, it is stated that A is a given matrix. We have to find out the values of A³. This can be done by product of A*A*A. The product should follow the properties of the Matrix. First, we will find out the value of A². So calculating, we get:
=> [tex]A^{2} = \left[\begin{array}{ccc}-5&-1\\0&1\end{array}\right] * \left[\begin{array}{ccc}-5&-1\\0&1\end{array}\right][/tex]
=> [tex]A^{2} = \left[\begin{array}{ccc}-25+0 &1 -1\\0+0&0 + 1\end{array}\right][/tex]
=> [tex]A^{2} = \left[\begin{array}{ccc}-25 &0\\0&1\end{array}\right][/tex]
Now we will calculate the value of A³. We can calculate the value of A³ by using the values of A² because we know that A³ = A².A. So, after calculating we get:
=> [tex]A^{3} = \left[\begin{array}{ccc}-25&0\\0&1\end{array}\right] * \left[\begin{array}{ccc}-5&-1\\0&1\end{array}\right][/tex]
=> [tex]A^{3} = \left[\begin{array}{ccc}75+0&0 + 0\\0+0&0+1\end{array}\right][/tex]
=> [tex]A^{3} = \left[\begin{array}{ccc}75&0 \\0&1\end{array}\right][/tex]
Hence we get value for [tex]A^{3} = \left[\begin{array}{ccc}75&0 \\0&1\end{array}\right][/tex]
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Temperature (°C) Number of People Day х у 1 20 280 2 24 360 3 36 450 4 32 420 5 2 28 400 ON 38 500 7 34 475 8 26 520 Question: The table shows data for the number of people using a swimming pool over 8 days in summer, and the corresponding maximum temperature (in degrees Celsius) on each day. A Find the equation of the line of best fit for the data. Round decimals to the nearest tenth. B. Can a set of data have more than one line of best fit? Why or why not?
First Step: Calculate the mean of the values in X and Y
[tex]\begin{gathered} \bar{x}=\frac{20+24+36+32+28+38+34+26}{8}=29.75 \\ \bar{y}=400.625 \end{gathered}[/tex]Second step: we have to find the sum of Squares and sum of products
Third step: find the linear equation
[tex]\begin{gathered} Y=aX+b, \\ a=\frac{SP}{SS}=\frac{3201.25}{275.5}=11.61978 \\ b=\bar{y}-a\cdot\bar{x}=54.93648 \\ Y=11.61978X+54.93648 \end{gathered}[/tex]If OA-OB-OC and if AOB = 9x + 20, BOC = 7x - 6 and AOC = 142 find BOC
The angle BOC has a measure of 50 degrees
How to evaluate the measure of the angle?From the question, the given parameters about the angles are:
OA-OB-OCAOB = 9x + 20BOC = 7x - 6AOC = 142The above parameters implies that
AOC = AOB + BOC
Next, we substitute the angle measurements in the above equation
So, we have
142 = 9x + 20 + 7x - 6
Evaluate the like terms
So, we have the following equation
142 = 16x + 14
Evaluate the like terms again
So, we have the following equation
16x = 128
Divide both sides by 16
x = 8
Substitute x = 8 in BOC = 7x - 6
BOC = 7 x 8 - 6
Evaluate
BOC = 50
Hence, the measure of the angle is 50 degrees
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The angle BOC has a measure of 50 degrees
What is Angle?An angle is formed when two straight lines or rays meet at a common endpoint
If OA-OB-OC and if AOB = 9x + 20, BOC = 7x - 6 and AOC = 142
We need to find BOC
We have AOC = AOB + BOC
142=9x + 20+7x-6
142=16x+14
Subtract 14 from both sides
142-14=16x
128=16x
Divide both sides by 16.
8=x
Now put x value in BOC = 7x - 6
BOC = 7x - 6
=7(8)-6
=56-6
BOC=50
Hence If OA-OB-OC and if AOB = 9x + 20, BOC = 7x - 6 and AOC = 142 then BOC=50.
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Write an equation in point-slope form for the line that passes through the point with the given slope.
(2, 1); m=−32
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ - 32 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies {\Large \begin{array}{llll} y-\stackrel{y_1}{1}=\stackrel{m}{- 32}(x-\stackrel{x_1}{2}) \end{array}}[/tex]
Find :
1) (-50+1)÷49
Answer: The answer is -1
Use the slope-intercept form to graph the equation 2x - 5y = - 15.
To do this, this equation must be taken to the form
[tex]\begin{gathered} y=mx+b \\ \text{Where} \\ m\colon\text{Slope oth the line} \\ b\colon\text{ intercept with the y-axis} \end{gathered}[/tex]So,
[tex]\begin{gathered} 2x-5y=-15 \\ \text{ Substract 2x from both sides of the equation} \\ 2x-5y-2x=-15-2x \\ -5y=-15-2x \\ \text{Divide by -5 from both sides of the equation} \\ \frac{-5y}{-5}=\frac{-15}{-5}-\frac{2}{-5}x \\ y=3+\frac{2}{5}x \\ y=\frac{2}{5}x+3 \end{gathered}[/tex]Then a positive slope of 2/5 tells you that for every 2 units on the y-axis there are 5 units on the x-axis. And 3 tells you that the line intercepts the y-axis at 3.
t's find profit or loss percents. C. P. = Rs 200, S. P. = Rs 220
Answer:
10% profit
Step-by-step explanation:
since the item was sold for more than it cost, this is a profit
percent profit = [tex]\frac{P}{C}[/tex] × 100%
profit P = SP - CP = Rs 220 - Rs 200 = Rs 20 , then
% profit = [tex]\frac{20}{200}[/tex] × 100% = 0.1 × 100% = 10%
parallelogram ABCD is below. m < D = 130° and m < B = (3x-1.5)° . solve for x and round to the nearest whole number.
Given:
m∠D = 130 degrees
m∠B = (3x - 1.5) degrees
Let's solve for the value of x.
A parallelogram is a quadilateral that has equal opposite angles and equal opposite sides.
Since a parallelogram has equal opposite angles, measure of angle D and measure of angle B are equal.
Thus, we have the equation:
m∠B = m∠D
(3x - 1.5) = 130
Solve for x.
Remove the parentheses:
3x - 1.5 = 130
Add 1.5 to both sides:
3x - 1.5 + 1.5 = 130 + 1.5
3x + 0 = 131.5
3x = 131.5
Divide both sides by 3:
[tex]\begin{gathered} \frac{3x}{3}=\frac{131.5}{3} \\ \\ x=43.83\approx44 \end{gathered}[/tex]Therefore, the value of x rounded to the nearest whole number 44
ANSWER:
44
Which number is enquivalent to 6/10
We have the fraction 6/10
For finding the equivalent number, we divide 6 by 10:
6 / 10 = 0.6
0.6 is the equivalent number
We have 6 in the numerator and 10 in the denominator, if we calculate any mathematical operation to both, we will find the equivalent fractions.
Let's see two examples:
1. Let's divide by 2:
6 divided by 2 is 3; and 10 divided by 2 is 5. Then our new equivalent fraction is
[tex]\frac{3}{5}[/tex]2. Let's multiply by 3:
6 multiplied by 3 is 18; 10 multiplied by 3 is 30. Then a second equivalent fraction is:
[tex]\frac{18}{30}[/tex]We can calculate additional equivalent fractions, using the same operation for both: numerator and denominator.
For calculating the equivalent fraction in hundreds, we will use the initial decimal equivalent we calculated at the beginning: 0.6
0.6 = 6/10 and we multiply it by 10 numerator and denominator
6 * 10 = 60 and 10 * 10 = 100. Then the fraction is 60/100
20 divided by 10 is 2 and 100 divided by 10 is 10, so the equivalent fraction is 2/10
This case is exactly the same than the previous we solved:
?/10 = 120/100
As you can see the first fraction is notated in tens and the second is notated in hundreds. Therefore, if you divide 120 between 10, what is the result?
Please Help!!!Use division to determine if the binomial is a factor. Show all work (x^3+7x^2+16x+12) ; (x+2)
Clearly, we can see that x+2 is a factor of the given polynomial.
Using the point (-5, 4) has one endpoint, State a possible location of the other endpoint given the line segment is 7 units long. Apply the distance formula to create a possible endpoint(s) from a given location.
EXPLANATION
Since the line segment is 7 units long, we can apply the following relationship:
(x_1+ 7 , y_1) = (x_2 , y_2)
[tex](-5+7)=2[/tex]The coordinate of the endpoint is as follows:
[tex](x_{endpoint},y_{endpoint})=(2,4)[/tex]We can get to this point by applying the distance formula as follows:
[tex]distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Applying the square power to both sides:
[tex]7^2=(x_2-(-5))^2+(y_2-4)^2[/tex]Subtracting numbers:
[tex]49=(x_2+5)^2+(y_2-4)^2[/tex]Now, if the x_2 coordinate is -3, the value of y_2 will be as follows:
[tex]49=(-3+5)^2+(y_2-4)^2[/tex][tex]49=4+(y_2-4)^2[/tex]Subtracting -4 to both sides:
[tex]45=(y_2-4)^2[/tex]Applying the square root to both sides:
[tex]\sqrt{45}=y_2-4[/tex]Adding +4 to both sides:
[tex]4+\sqrt{45}=y_2[/tex]In conclusion, the equation to get the coordinate from a given point is,
[tex]49=(x_{2}+5)^{2}+(y_{2}-4)^{2}[/tex]A scientist mixes water (containing no salt) with a solution that contains 15% salt. She wants to obtain 105 ounces of a mixture that is 5% salt. How many ounces of water and how many ounces of the 15% salt solution should she use?
Let's call X the ounces of water and Y the ounces of the salt solution.
Of she
what is the value that will correctly replace the missing part? 6(2x + 4) = ? + 24
Answer:?=12x
Step-by-step explanation: 6(2x+4)=?+24, 6 x 2x= 12x. 6 x 4= 24, 24 is already in the equation, so 12x is our missing number.
Write each number
1. 1,000 more than 3,872
The value for a number that is 1000 more than 3,872 will be 4,872
In the given question, it is stated that we have to find out the value of the expression given. The expression states that we have to find out a number that is 1000 more than 3872.
This can easily be done. To find out the value for a number that is 1000 greater than 3872, we just need to add the value to the number i.e. we need to add 1000 to 3872. Let the new number be 'x'.
So, by solving this condition, we get
=> x = 3872 + 1000
=> x = 4872
Here we get x = 4872.
Hence, 1000 more than 3,872 will be 4,872.
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a pancakes recipe asks for 3 and 1 half times as much milk as flour. if 4 and two thirds cups of milk is used, what quantity of flour would then be needed, according to the recipe?
A pancakes require 3.5 cups of milk and 1 cup of flour, or a ratio of 3.5:1 or a fraction of
(3.5) / (1)
If you have 4.6 cups of milk you need x cups of flour
Set up a ratio of
[tex]\frac{3.5}{1}=\frac{4.6}{x}[/tex][tex]x=\frac{4.6}{3.5}[/tex][tex]undefined[/tex]
The total amount of candy sold at Cassandra's Candy Corner can be represented by the function C(x) = 4x3 + 16x2 + 60x + 648, where x represents the number of years since the store opened. The amount of types of candy can be modeled by the linear function T(x) = 2x + 12. Which expression represents the amount of candy sold each year per type at Cassandra's Candy Corner?
4x3 + 16x2 + 58x + 636
4x3 + 16x2 + 62x + 660
2x2 – 4x + 54
2x2 + 4x + 54
The expression which correctly represents the amount of candy sold each year per type at Cassandra's Candy corner is; 2x2 – 4x + 54.
Polynomial divisionIt follows from the task content that the expression which shows the amount of candy sold each year per type is to be determined.
Since, the function, C (x) = 4x³ + 16x² + 60x + 648 represents the total amount of candy sold while, T(x) = 2x + 12 represents the amounts of types of candy.
Therefore, the amount of candy sold each year per type is; C(x) ÷ T(x).
Hence, the result of the polynomial division as in the attached image is; 2x² - 4x + 54.
Ultimately, the amount of candy sold each year per candy is represented by the expression; 2x² - 4x + 54.
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1. Find the amount of tax owed: vacant land valued at $24,000.00; assessed at 18%; taxed at $11.00 per hundred dollars worth of property.
The amount of tax owed is $ 6,960.
It is given in the question that:-
Vacant land value = $ 24,000
Tax percentage = 18 %
Tax per hundred dollars = $ 11
We have to find the tax owed.
Tax = (18/100)*24000 = $ 4,320
Tax per hundred for $ 24000 land = 11*(24000/100) = $ 2,640
Hence, total tax owed = $ 4,320 + $ 2,640 = $ 6,960
Percentage
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100.
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