13students;it had already said it.
A mail carrier can deliver mail to 36 houses in 30 minutes. Mark wants to determine how many houses the carrier can deliver mail to in 7.5 minutes at this rate. He thinks that to find the answer, he should do the following.
1. First divide 36 houses by 30 minutes to find a unit rate of 1.2 houses per minute.
2. Then multiply 1.2 houses per minute by 7.5 minutes to get 9 houses.
Mark's method is correct, because even though it is impossible to deliver mail to 1.2 houses in minute, it represents the unit rate of houses per minute .
Is Mark's method correct?The first step is to determine the unit rate of houses per minute. This can be done by dividing 36 houses by 30 minutes.
36/30 = 1.2 houses per minute
The second step is to multiply 1.2 by 7.5: 1.2 x 7.5 = 9 houses
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10 - 13x + 2 in words
The simplification of the equation above in words is = Twelve minus thirteen X.
Simplification of an equationIn mathematics, coefficients are those numbers that multiplies a variable. For example in 13x, the coefficient is 13 which multiplies a variable known as X.
The equation given is,
10 - 13x + 2
Arrange the digits without a coefficient together.
That is ,
10+2 -13x
12 - 13x
Therefore the simplification of the given equation in words is Twelve minus thirteen X.
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Evaluate functions from their graph Problem g(3) =
See attached for the correct answer!
The notation g (3), left parenthesis, 3 refers to the output of the function when the input is x=. If the point (3, b) is on the graph, then g (3) =b.
We should look for the point on the graph whose x- coordinate is 3 is the point )3, 4).
The point on the graph whose x-coordinate is 3 is the point (3,4).
Therefore, g (3) = 4
The value of g(3) is g(3) = 4
How to evaluate the function?The function value is given as:
g(x)
The notation g(3) implies that:
We determine the value of g(x) when x = 3
From the graph, the function has a point at (3,4)
This means that:
When x = 3, g(x) = 4
i.e. g(3) = 4
Hence, the value of g(3) is g(3) = 4
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Explain how to determine if Carlos’s allowance is directly proportional to the number of chores he completes.
A 2-column table with 3 rows. Column 1 is labeled number of chores with entries 10, 13, 15. Column 2 is labeled Allowance with entries 75 dollars, 97 dollars and 50 cents, 112 dollars and 50 cents.
Using a proportional relationship, it is found that Carlos earns an allowance of $7.5 for each chore that he completes.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
In this problem, the constant is:
k = 75/10 = 97.5/13 = 112.5/15 = 7.5.
Hence Carlos earns an allowance of $7.5 for each chore that he completes.
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Express the confidence interval (0.065,0.143) in the form of p - E
The confidence interval expressed in the form p - E is:
(0.104 - 0.039, 0.104 + 0.039).
What are the mean and the margin of error of a confidence interval?The mean is the mean of the bounds, hence:
p = (0.065 + 0.143)/2 = 0.104.
The margin of error is the difference between the bounds and the mean, hence:
E = 0.104 - 0.065 = 0.143 - 0.104 = 0.039.
Hence the interval in the desired format is:
(0.104 - 0.039, 0.104 + 0.039).
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If cot theta = 3/2, what is the value of csc theta?
The value of csc theta is [tex]\frac{3. 61}{2}[/tex]
How to determine the valueIt is important to note that the ratio for cot is given as;
Cot theta = adjacent/opposite
cosec theta = hypotenuse/opposite
If cot theta = 3/2, then
Adjacent = 3
Opposite = 2
Using Pythagoras theorem, we have
Hypotenuse square = opposite + adjacent square
[tex]H = \sqrt{2^2 + 3^2}[/tex]
[tex]H = \sqrt{4 + 9}[/tex]
[tex]H = 3. 61[/tex]
Cosec theta = [tex]\frac{3. 61}{2}[/tex]
Thus, the value of csc theta is [tex]\frac{3. 61}{2}[/tex]
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Answer:
3.16/2
Step-by-step explanation:
Have a great day
Linear functions f(x) and g(x) have been combined by addition and multiplication. The table shows values for the sum, s(x), and product, p(x).
Which statements correctly compare the sum and product? Check all that apply.
Both functions have a constant rate of change.
The sum is linear and the product is quadratic.
The x-intercepts are the same.
The sum has one y-intercept and the product has two x-intercepts.
Both functions decrease for x ≥ 2.
The statements that correctly compare the sum and product of the function are:
The sum is linear and the product is quadratic.The sum has one y-intercept and the product has two x-intercepts.What is a linear function?A linear function simply means a function that represents a straight line on the coordinate plane.
In this case, the sum is linear and the product is quadratic while the sum has one y-intercept and the product has two x-intercepts.
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This table reflects the result of a survey conducted in a town to find out the number of cars of a particular color.
Which of the following ranges would be appropriate to use in order to represent the numerical data on the vertical axis of a Bar Graph?
A. 10 to 20
B. 20 to 100
C. 0 to 50
D. 0 to 30
the range that would be the most appropriate to represent the numerical data on the vertical axis is B. 20 to 100.
what range would be most appropriate?the table is not included but the range of 20 to 100 is most appropriate for the number of cars in town with a particular color.
this is because towns would normally have between hundreds and thousands of cars which means that cars of a particular color would be between 20 and 100 at least.
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The range that would be the most approx to represent the numerical data on the vertical axis is B. 20 to 100.
Bar graph :
Bar graphs are the pictorial representation of data (generally grouped), in the form of vertical or horizontal rectangular bars, where the length of bars is proportional to the measure of data
The range that would be the most approximately to represent the numerical data on the vertical axis is B. 20 to 100.
because
it is not possible to have zero number of cars that have a particular color,
in That way, we can eliminate options C and D .
in option A the range is too small which is not possible.
the table is not included but the range of 20 to 100 is most appropriate for the number of cars in town with a particular color.
this is because towns would normally have between hundreds and thousands of cars which means that cars of a particular color would be between 20 and 100 at least.
Which of the following characteristics describe the graph of an exponential function?
Answer:
A GENERAL NOTE: CHARACTERISTICS OF THE GRAPH OF THE PARENT FUNCTION
f
(
x
)
=
b
x
An exponential function with the form
f
(
x
)
=
b
x
,
b
>
0
,
b
≠
1
, has these characteristics:
one-to-one function
horizontal asymptote:
y
=
0
domain:
(
−
∞
,
∞
)
range:
(
0
,
∞
)
x-intercept: none
y-intercept:
(
0
,
1
)
increasing if
b
>
1
decreasing if
b
<
1
Step-by-step explanation:
hope it helps you
A jar contains 100ml of a mixture of oil and water in the ratio 1:4. Enough oil is added to make the ratio of oil to water 1:2. How much water must be added to make the ratio oil to water 1:3?
Answer:
40 ml of water must be added.Step-by-step explanation:
Initial volume of mixture is 100 ml with oil to water ratio of 1 : 4.
First, let's find the volume of each component.
If the oil is x then water is 4x according to ratio and their sum is 100 ml:
x + 4x = 1005x = 100x = 20So, we have 20 ml of oil and 80 ml of water.
Now, let's added volume of oil be y. Then we have the ratio:
(20 + y)/80 = 1/220 + y = 40y = 20So, we have 40 ml of oil and 80 ml of water.
Lastly, let's added water be z. Then we have the ratio:
40/(80 + z) = 1/380 + z = 120z = 40We must add 40 ml of water.
A state uses a combination of three letters (A-Z) followed by three digits (0-9) for their license plates. How many different license plates are possible? (Exact steps shown for credit)
A state uses a combination of three letters (A-Z) followed by three digits (0-9) for their license plates. So, there are 17576000 license plates can be made.
Given that, license plates consists of 3 letters followed by 3 digits.
Let the numbers on license plates be N
Let the letters on license plates be L
So, the license plate consisting of 3 letters and 3 digits will be LLLNNN.
Letters can be anything from A to Z.
There are 26 letter combinations for the first letter. That is applicable for the following 2 letters.
So, the combination for letters = 26×26×26 = 17576
Numbers can be anything from 0 to 9.
There are 10 combinations for each place.
So, the combination for numbers = 10×10×10 = 1000
Now, the combination for letters and numbers= 17576×1000
= 17576000
Therefore, 17576000 license plates can be made.
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9. For Investment Plan A to C, solve for the future value at the end of the term based on the
information provided.
Investment Plan Principal
A
$7,500
B
$53,000
C
$19,000
Interest Rate
8% compounded quarterly
6% compounded monthly
5.75% compounded semi-annually
Term
3 years
4
years and 3 months
6 years and 6 months
The future value of Investment A is 9511.81
The future value of Investment B is 68,351.02
The future value of Investment C is29.067.07.
What are the future values?When an amount earns a compound interest, it means that both the amount invested and the interest rate already accrued increases in value at the next compounding date. For example, if interest is compounded quarterly, both the amount invested and the interest accrued increases every quarter.
The formula for calculating future value:
FV = P (1 + r)^nm
FV = Future value P = Present value R = interest rate m = number of compoundingN = number of yearsInvestment A = 7500 x [(1 + (0.08/4)]^(4 x 3) = 9511.81
Investment B = 53,000 x [(1 + (0.06/12)]^[(4 x 12) + 3) = 68,351.02
Investment C = 19,000 x [(1 + (0.0575/2)]^{6 x 2) + 6/2) = 29.067.07
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What is the domain of the function given below
Answer:
c. [-1, infinity)
Step-by-step explanation:
the domain the interval or set of valid x values (while the range is the same for the valid y values).
what is the smallest value of x we see for the graph ?
for x values we need to look left and right.
and the more left the value, the smaller it is.
so, in other words, what is the left-most x value e can find ?
x = -1
that is the "starting point" of the function. there is no functional value for any smaller x.
and then clearly, the function goes on and on to the right without any boundary in sight. so, it keeps going to the right in all eternity, that means it goes to infinity.
therefore the answer.
keep in mind that "infinity" is not a number, only a concept. so, when writing "infinity" at an interval end, it is not included (and we use a round bracket).
SKETCHPAD
Question 5
Given AABC shown on the coordinate plane below.
AA"B"C" = Ro (T(-4,3)(ABC))
90°
Draw AA'B'C'' if
You may use different colors for the separate transformations. Indicate your final
answer. Feel free to use the Dynamic Geometry Tool to complete the
transformations.
The attached figure represents the image of A"B"C" after the transformation
How to transform the triangle?The transformation rule is given as:
A"B"C" = Ro90° (T(-4,3)(ABC))
This means that we rotate the triangle 90 degrees clockwise, and then translate the triangle
From the figure, the coordinates of ABC are
A = (-1, 2)
B = (1, 4)
C = (3, -1)
The rule of 90 degrees clockwise rotation is
(x,y) ⇒ (y,-x)
So, we have
A' = (2, 1)
B' = (4, -1)
C' = (-1, -3)
The translation of the triangle by T(-4,3) is
(x,y) ⇒ (x - 4, y + 3)
So, we have
A'' = (-2, 4)
B'' = (0, 2)
C'' = (-5, 0)
See attachment for the image of the transformation
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Which of the following functions best describes this graph?
Answer:
C
Step-by-step explanation:
We can use process of elimination
D is incorrect because the roots are 3 and -4 and there are no negative roots visible
B is wrong because the roots -3 and -6 are both negative
You can factor A into (x-2)(x-3) and the roots are 2 and 3 but the roots on the graph look closer to 3 and 6
For C it can be factored as (x-6)(x-3) so the roots are 3 and 6 which look accurate
( 13/7 ) ^2
[answer in fraction form]
Answer:
[tex]\frac{169}{49}[/tex]
Step-by-step explanation:
Square the top and bottom numbers in the fraction
13^2 = 169
7^2 = 49
169/49
How many fewer people live in Elmira than White Plains
Population density implies the number of an object, items, or people that can be found in a unit area at a particular time. Therefore, the number of fewer people that live in Elmira than in White Plains is 27,653.
Population density implies the total number of objects, items, or people that exist in a unit area or a place at a particular time. So that the number of people that exist in a place, area, city, or country can be referred to as population, in a particular period.
Thus in the given question, it can be deduced that;
The population of people living in White Plains =56,853
The population of people living in Elmira = 29,200
So, the difference in the population between the two cities can be determined as;
= 56,853 - 29,200
= 27,653
Thus, the number of fewer people living in Elmira than in White Plains is 27,653
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Find the axis of symmetry:
Picture is below.
Answer:
x = -3
Step-by-step explanation:
Axis of symmetry:Axis of symmetry is the vertical line that divides the parabola into two equal halves and it passes through the vertex of the parabola.
From the graph, Vertex (-3, 4)
Axis of symmetry: x = -3
f(x) = √2x
g(x) = √8x
Find (f g)(x). Assume x ≥ 0.
OA. (f g)(x) = 4x
OB. (f g)(x) = 8x
O C. (f g)(x) = 4√√x
OD. (f.g)(x) = √/10x
Answer:
Step-by-step explanation:
hello :
f(x) = √(2x)
g(x) = √(8x)
(f g)(x) = f(x)×g(x) =√(2x)×√(8x) = √(16x²) =4/x/
x ≥ 0: /x/ = x (f g)(x) = 4x......(answer : A)
Find the equation of the line through point (−2,−1) and perpendicular to 5x+6y=−6
Answer:
Step-by-step explanation:
eq. of any line perpendicular to 5x+6y=-6 is
5y-6x=c
where c is a constant.
it passes through (-2,-1) so
5(-1)-6(-2)=c
c=-5+12=7
so reqd. eq. is 5y-6x=7
or 6x-5y=-7
or
slope of given line =-5/6
slope of reqd. line=6/5
eq. of line through (-2,-1) with slope 6/5 is
y+1=6/5(x+2)
5y+5=6x+12
5y=6x+12-5
or 5y=6x+7
or
6x-5y=-7
Select all of the following that are quadratic equations.
5x-1=3x+8
5 x- 3 = 0
x²-2x = 4x+1
2x²+12 x = 0
x³-6x² + 8 = 0
9x²+6x-3=0
The quadratic equations among all the options given are [tex]x^{2} -2x=4x+1[/tex],[tex]2x^{2} +12x=0[/tex] and [tex]9x^{2} +6x-3=0[/tex].
Given six equations as under:
5x-1=3x+85 x- 3 = 0x²-2x = 4x+12x²+12 x = 0x³-6x² + 8 = 09x²+6x-3=0We are required to find the quadratic equations among the above equations.
Quadratic equations are those equations in which the highest power of the variable present in the equation is 2.
It is in form of [tex]ax^{2} +bx+c=0[/tex].
In our options quadratic equations are [tex]x^{2} -2x=4x+1[/tex],[tex]2x^{2} +12x=0[/tex] and [tex]9x^{2} +6x-3=0[/tex].
5x-1=3x+8: It is not a quadratic equation as the highest power is 1.
5 x- 3 = 0:It is also a linear equation not quadratic equation.
x³-6x² + 8 = 0:It is a cubic equation not a quadratic equation.
Hence the quadratic equations among all the options given are [tex]x^{2} -2x=4x+1[/tex],[tex]2x^{2} +12x=0[/tex] and [tex]9x^{2} +6x-3=0[/tex].
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Solve the logarithmic equation by writing in exponential form or by
graphing.
log (5-2x) = 0
Answer:
Hello,
Step-by-step explanation:
[tex]log(5-2x)=0\\\\\ \Longleftrightarrow\ 10^{log(5-2x)}=10^0\\\\\\\Longleftrightarrow\ 5-2x=1\\\\\Longleftrightarrow\ 2x=5-1\\\\\\\Longleftrightarrow\ x=\dfrac{4}{2}\\\\\\\Longleftrightarrow\ \boxed{x=2}\\[/tex]
Which equations can be used to find the lengths of the legs of the triangle? Select three options. 0.5(x)(x + 2) = 24 x(x + 2) = 24 x2 + 2x – 24 = 0 x2 + 2x – 48 = 0 x2 + (x + 2)2 = 100
The equations that can be used to find the lengths of the legs of the triangle are as follows:
100 = (x + 2)² + x²24 = 0.5 × (x + 2)(x)x² + 2x - 48 = 0How to find the equation of a right triangle?The equation that can be used to find the length of the leg of the right triangle uses Pythagoras theorem,
Therefore,
c² = a² + b²
where
c = hypotenuse sidea and b are the other legsTherefore,
10² = (x + 2)² + x²
100 = (x + 2)² + x²
Therefore, using the area of a triangle,
area of a triangle = 1 / 2 bh
where
b = baseh = heightTherefore,
area of the triangle = 1 / 2 × (x + 2)(x)
24 = 0.5 × (x + 2)(x)
24 = x² + 2x / 2
cross multiply
48 = x² + 2x
x² + 2x - 48 = 0
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Determine the output voltage of the op-amp circuit shown below:
The output voltage of the op-amp circuit shown is -5v.
What is voltage?It should be noted that voltage is the electric potential difference between two points l.
In this case, the output voltage will be:
= -5 × i
where I = 1.
Voltage = -5 × 1
= -5v
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If f(x) = x and g(x) = 2, what is (fog)(x)?
Step-by-step explanation:
=fog(x)
−2x=0
x(x−2)=0
x=0,2
Find the area of the figure.
What is the y-intercept of the liner function? (y=3x-2)
The y-intercept of the linear function y = 3x - 2 is -2
How to determine the y-intercept?The function is given as
y = 3x - 2
The above function is a linear function, and the y-intercept is the point on the graph, where x = 0 i.e. the point (0, y)
As a general rule, linear functions are those functions that have constant rates or slopes
Next, we set x to 0, and calculate y to determine the value of the y-intercept
y = 3(0) - 2
Remove the bracket in the above equation
y = 3 * 0 - 2
Evaluate the product of 3 and 0 i.e. multiply 3 and 0
y = 0 - 2
Evaluate the difference of 0 and -2 i.e. subtract 0 from 2
y = -2
The above means that the value of y when x is 0 is -2
Hence, the y-intercept of the linear function y = 3x - 2 is -2
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What are the fourth roots of -3+3√3i?
Enter your answer by filling in the boxes. Enter the roots in order of increasing angle measure in simplest form.
By De Moivre's formula, we have the following four roots: [tex]z_{1} = 1.565 \cdot \left(\cos \frac{\pi}{6} + i\,\sin \frac{\pi}{6} \right)[/tex], [tex]z_{2} = 1.565\cdot \left(\cos \frac{2\pi}{3} + i\,\sin \frac{2\pi}{3} \right)[/tex], [tex]z_{3} = 1.565\cdot \left(\cos \frac{7\pi}{6}+i\,\sin \frac{7\pi}{6} \right)[/tex] and [tex]z_{4} = 1.565\cdot \left(\cos \frac{5\pi}{3} + i\,\sin \frac{5\pi}{3} \right)[/tex].
How to determine a fourth root of a complex numberAccording to complex analysis, the fourth roots of a complex number can be found by De Moivre's formula:
[tex]\sqrt[n]{z} = \sqrt[n]{r}\cdot \left[\cos \left(\frac{\theta + 2\pi\cdot i}{n} \right)+ i\,\sin \left(\frac{\theta + 2\pi\cdot i}{n} \right)\right][/tex], for [tex]i = \{0, 1, ..., n - 1\}[/tex] (1)
Where:
r - Magnitude of the complex number.θ - Direction of the complex number, in radians.First, we find the magnitude and direction of the complex number:
[tex]r = \sqrt{(-3)^{2}+(3\sqrt{3})^{2}}[/tex]
r = 6
[tex]\theta = \tan^{-1} \left(\frac{3\sqrt{3}}{-3} \right)[/tex]
[tex]\theta = \frac{2\pi}{3} \,rad[/tex]
Now we find the four quartic roots of the complex number:
[tex]z_{1} = 1.565 \cdot \left(\cos \frac{\pi}{6} + i\,\sin \frac{\pi}{6} \right)[/tex]
[tex]z_{2} = 1.565\cdot \left(\cos \frac{2\pi}{3} + i\,\sin \frac{2\pi}{3} \right)[/tex]
[tex]z_{3} = 1.565\cdot \left(\cos \frac{7\pi}{6}+i\,\sin \frac{7\pi}{6} \right)[/tex]
[tex]z_{4} = 1.565\cdot \left(\cos \frac{5\pi}{3} + i\,\sin \frac{5\pi}{3} \right)[/tex]
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In the year 2000, The U.S. Budgeted $25,003 million for Natural Resources and Environment. In 2014, they budgeted $40,156 million. What was the absolute and relative change in environmental spending from 2000 to 2014?
Using it's concepts, we have that:
The absolute change was of $15,153 million.The relative change was of 60.60%.What is the absolute change of two values?The absolute change between two values is given by the absolute value of the difference between two values.
In this problem, the values are of $40,156 million, which is the final value, and $25,003 million, which is the initial value, hence the absolute change is:
A = 40,156 - 25,003 = $15,153 million.
What is the relative change?The relative change is the absolute change multiplied by 100% and divided by the initial value, hence:
(15,153/25,003) x 100% = 60.60%.
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The following data show the height, in inches, of 11 different plants in a garden:
9
4
10
9
5
2
22
10
3
3
5
After removing the outlier, what does the mean absolute deviation of this data set represent?
On average, the height of a plant varies 2.8 inches from the mean of 6 inches.
On average, the height of a plant varies 3.2 inches from the mean of 5 inches.
On average, the height of a plant varies 2.8 inches from the mean of 5 inches.
On average, the height of a plant varies 3.2 inches from the mean of 6 inches.
On average, the height of a plant varies 3.2 inches from the mean of 6 inches.
What does the mean absolute deviation represent?An outlier is a number that is way smaller or way larger than that of other numbers in a data set. The outlier is 22.
Mean absolute deviation = (1/n) x ∑ l x - m(x) l
Mean without the outlier : (9 + 4 + 10 + 9 + 5+ 2 + 10 + 3 + 3+ 5) / 10 = 6
(1/10) x ∑ l (9 - 6) + (4 - 6) + (10 - 6) + (9 - 6) + (5 - 6) + (2 - 6) + (10 - 6) + (3 - 6) + (3 - 6) + ( 5 - 6) = 3.2
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