Option (a) is correct.
What is a equation?statement of equality between two expressions consisting of variables and/or numbers. In essence, equations are questions, and the development of mathematics has been driven by attempts to find answers to those questions in a systematic way.
Given that,
The given equation are
y=2x-13 ........(1)
2x+6y=-8 ........(2)
Solve the equation by elimination method
From equation (1)
y-2x = -13
From equation (2)
Now,
y-2x = -13
6y+2x = -8
adding both equation
7y = -21
y = -3
substitute the value of y in equation (1)
y = 2x-13
-3 = 2x-13
-3+13 = 2x
2x = 10
x = 5
Hence, The coordinate (5,-3) is a solution to both equations.
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A sample of 342 students at a university is surveyed. The students are classified according to gender ("female" or "male"). They are also classified according tomajor ("blology", "business", "engineering", "mathematics", or "computer science"). The results are given in the contingency table below.Biology Business Engineering Mathematics Computer scienceFemale4623501837Male4815461544What is the relative frequency of male students in the sample?Round your answer to two decimal places.0Х5.?
The relative frequency of an event is the quotient of the division between the event and the total number of the sample
From the given table
Add the numbers of males to find their total
[tex]48+15+46+15+44=168[/tex]Then add the numbers of females and males to find the total of the sample
[tex]168+46+23+50+18+37=342[/tex]Now, divide the number of males by the total to find the relative frequency
[tex]\begin{gathered} R\mathrm{}F=\frac{168}{342} \\ R\mathrm{}F=0.4912280702 \end{gathered}[/tex]Round it to 2 decimal places, then
The relative frequency of the male students = 0.49
Question at position 3
Write the expression as a sum and/or difference of logarithms with all variables to the first degree
[tex]ln\sqrt{8t^{4} v^{2}[/tex]
The expression as a sum and/ or difference of logarithms is [tex]\frac{In8}{2} + 2 . In t + In v[/tex]
Given,
Write the expression as a sum and/or difference of logarithms with all variables to the first degree.
[tex]In\sqrt{8t^4v^2}[/tex]
Convert to exponential form
= [tex]In(8t^4v^2)^\frac{1}{2}[/tex]
Simplify using exponent rule with same exponent [tex](ab)^n = a^n . b^n[/tex]
= [tex]In (8^\frac{1}{2} . (t^4)^\frac{1}{2}(v^2)^\frac{1}{2} )[/tex]
Apply laws of logarithms to simplify the expression.
= [tex]In 8^\frac{1}{2} + In(t^4)^\frac{1}{2} + In(v^2)^\frac{1}{2}[/tex]
Express the logarithm of a power of an expression as the power times the logarithm of the expression.
= [tex]\frac{1}{2} . In8 + In(t^4)^\frac{1}{2} + In(v^2)\frac{1}{2}[/tex]
=[tex]\frac{1}{2} . In8 + \frac{1}{2} . In(t^4) + \frac{1}{2} .In(v^2)[/tex]
Multiply the monomials
[tex]\frac{In8}{2} + \frac{1}{2} . 4 . In t + \frac{1}{2} . 2 . In v[/tex]
= [tex]\frac{In8}{2} + 2 . In t + \frac{1}{2} . 2 . In v[/tex]
= [tex]\frac{In8}{2} + 2 . In t + In v[/tex]
Hence, The expression as a sum and/ or difference of logarithms is [tex]\frac{In8}{2} + 2 . In t + In v[/tex]
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There are two numbers whose sum is 50. Three times the first is 5 more than twice the second. What are the numbers?
The two numbers whose sum is 50 and three times the first is 5 more than twice the second are 21 and 29.
What do you mean by sum?
A summation, also known as a sum, is the outcome of adding two or more numbers or quantities. There could be only two terms, or there could be one hundred, thousand, or a million. There are summations with an infinite number of terms.
Let the two numbers be X and Y.
There are two condition given in the question through which we can form a system of equation containing two equations.
First condition: The sum of the numbers is 50.
Therefore,
X + Y = 50
Second Condition: Three times the first is 5 more than twice the second
Therefore,
3X = 2Y + 5
We get the system of equation:
X + Y = 50
3X = 2Y + 5
Solving this system of equation
3X - 5 = 2(50 - X)
3X - 5 = 100 - 2X
X = 105/5
X = 21
Putting the value of X in one of the equation:
Y = 50 - X
Y = 50 - 21
Y = 29
Therefore, two numbers are 21 and 29
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A cosine function has an amplitude of 1/4 , period of pi/2, horizontal shift of 2pi, and vertical shift of -4.
What is the y-value of the positive function when x = 2π?
y = ?
The value of y when y = y = 0.25sin(4(x+2π))-4. and x = 2pi is -4.
Some functions (like Sine and Cosine) repeat forever and are called Periodic Functions.The Amplitude is the height from the center line to the peak (or to the trough).The Phase Shift is how far the function is shifted horizontally from the usual position.The Vertical Shift is how far the function is shifted vertically from the usual position.
We can have all of them in one equation:
y = A sin(B(x + C)) + D
amplitude is A
period is 2π/B
phase shift is C (positive is to the left)
vertical shift is D
So, for the given question we have amplitude is 0.25, period is 2π/4, phase shift is 2π, vertical shift is -4
So,
y = 0.25sin(4(x+2π))-4.
when x = 2π
y = 0.25sin(16π)-4
y = 0-4
y = - 4
Therefore, y = 0.25sin(4(x+2π))-4, and its y - value when x = 2π is -4.
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11A family went out to dinner. The cost of their meal was $689, before sales tax and tip.A sales tax of 8% was added.(a)The family then tipped 20% on the amount after the sales tax was added,Part AWhat was the amount, rounded to the nearest cent, of just the sales tax?Show all of your work and record your final answer in the space below.Click the box below to type your math work and answer.On the right side of the box, click thebutton to start a new line.
The cost of the meal before the sales tax and tip= $689
Sales tax = 8%
The family then tipped 20% on the ammount after the sales was added
PART A
The amount of the sales tax can be calculated as follows
Amount of sales tax = sales tax * the amount of the meal
Amount of sales tax = 8% x $689
Amount of sales tax = 8/100 x 689
Amount of sales tax = 0.08 x 689
Amount of sales tax = $55.12
Therefore, the amount of sales tax is $55.12
PART B
What is the total amount paid by the family after adding the tax sales and 20% tipping
The cost of the meal = $689
Amount of sales tax = $55. 12
20% tipping on the amount after the sales tax was added
Amount of the meal after the sales has been added = $689 + $55.12
Amount of the meal after the sales tax has been added = $744. 12
20% tipping of the total amount = 20% x 744.12
= 20/100 x 744.12
= 0.2 x 744.12
= $148.82
The total amount paid by the family = 689 + 55.12 + 148.82
The total amount = $892.94
Therefore, the family paid a total amount of $892.94
15) What is the range of the following set of points: {(3, 4), (7,-2), (11, -8)}? Al{-8, -2,3,7,11} B {3,7, 11} C{-8, -2,4} D{-19, -9,1}
The range is the set of y-values of the points given.
The points given are:
{(3, 4), (7,-2), (11, -8)}
The range would be:
4, -2, and -8
Range = {4,-2,-8}
Option C
What is the degree of the second term in this polynomial
The degree of the second term in the polynomial;
[tex]5x^{27}+5x^{19}+9x^9[/tex]is 19
write an equation of a line m= -7 b= -11
Answer:
y= -7x-11
Step-by-step explanation:
m= -7 (gradient)
b= -11 (y-intercept)
write in the form of y=mx+b
y=-7x-11
consider functions f and g. f(x) = -x^3g(x) = | 1/8x-1| what is the value of ( g • f)(4)a: -9b: -1/8 c: 9 d: 1/8
The solution:
Given the functions:
[tex]\begin{gathered} f(x)-x^3 \\ \\ g(x)=|\frac{1}{8}x-1| \end{gathered}[/tex]Required:
To find the value of g(f(4))
Step 1:
Substitute 4 for x in f(x).
[tex]f(4)=-(4)^3=-64[/tex]Step 2:
Substitute -64 for x in g(x).
[tex]\begin{gathered} g(-64)=|\frac{1}{8}(-64)-1| \\ \\ g(-64)=|(1\times-8)-1| \\ \\ g(-64)=|-8-1|=|-9|=9 \end{gathered}[/tex]Therefore, the correct answer is 9 [option C]
Hi, can you help me with this Exercise , please!
The weekly cost C of producing x units in a manufacturing process is given by
[tex]C(x)=60x+750[/tex]The number of units x produced in t hours is given by
[tex]x(t)=50t[/tex](a) The composite function C(x(t)) is given by
[tex]\begin{gathered} C(x)=60x+750 \\ C(x(t))=60(50t)+750 \\ C(x(t))=3000t+750 \end{gathered}[/tex]The function C(x(t)) gives us the cost of production for t hours.
(b) The number of units produced in 4 hours is given by
[tex]\begin{gathered} x(t)=50t \\ x(t)=50(4) \\ x(t)=200 \end{gathered}[/tex]200 units will be produced in 4 hours.
(c) Let us graph the function C(x(t)) = 3000t + 750 to find the value of t for which the cost increases to $15,000
As you can see, the value of t is 4.75 hours when the cost is $15,000.
Therefore, 4.75 hours must elapse until the cost increases to $15,000.
QuestRecently, More Money 4U offered an annuity that pays 6.6% compounded monthly. If $1,504 is deposited into this annuity every month, how much is in the account after 11 years? How much of this is interest?Type the amount in the account: $(Round to the nearest dollar.)
ANSWER
Amount = $3102.75
Interest = $1598.75
EXPLANATION
The annuity pays 6.6% compounded monthly.
The formula for an Amount compounded at a rate of r after t years is given as:
[tex]A\text{ = P(1 + }\frac{r}{n})^{nt}[/tex]where P = principal (amount deposited) = $1,504
r = rate = 6.6% = 0.066
n = 12 (12 months in a year)
t = number of years = 11 years
Therefore, the amount in the account after 11 years is:
[tex]A\text{ = 1504(1 +}\frac{0.066}{12})^{12\cdot\text{ 11}}[/tex][tex]\begin{gathered} A=1504(1+0.0055)^{132} \\ A\text{ = 1504(}1.0055)^{132} \\ A\text{ = 1504 }\cdot\text{ 2.063} \\ A\text{ = \$3102.75} \end{gathered}[/tex]That's the amount in the account after 11 years.
This means that the amount of interest after 11 years is the amount after 11 years minus the amount that was there initially:
Interest = 3102.75 - 1504
Interest = $1598.75
8 Write the equation of the line in standard form, point-slope form, and slope-intercept form. 4 -2 DELL
step 1
Find the slope
we need two points
take the points (0,3) and (1,0)
m=(0-3)/(1-0)
m=-3
step 2
Find the equation of the line in slope intercept form
y=mx+b
we have
m=-3
b=3
substitute
y=-3x+3step 3
Find the equation of the line in point slope form
y-y1=m(x-x1)
we have
m=-3
point (0,3)
y-3=-3(x-0)
y-3=-3xstep 4
standard form
AX+By=C
we have
y=-3x+3
3x+y=3 -----> standard formCan someone please help me with this problem? I’ll give brainliest
Answer:
Step-by-step explanation:
gee girls generation
Write the correct inequality for the following statement and then solve for the given number of
yards.
You have found a used car and your parents have agreed to pay the first
$750 for you. You have a summer job mowing yards for $25 per yard.
Write and inequality that will calculate the number of yards (y) you will
have to mow to get to at least the cost (C) of the car.
If the car cost a total of $4500 how many yards will you have to mow?
The inequality that will calculate the number of yards (y) you will have to mow to get to at least the cost (C) of the car is 25y + 750 ≥ C.
If the car costs a total of $4500 number of yards you will have to mow is 150 yards at least.
What is inequality in math?In mathematics, a statement of an order relationship between two integers or algebraic expressions (greater than, greater than or equal to, less than, or less than or equal to) is called an Inequality.
Given:
Price of the car paid by your parents = $750
You have a summer job mowing yards for $25 per yard.
We have to determine an inequality that will calculate the number of yards (y) you will have to mow to get to at least the cost (C) of the car.
So, the required inequality is
25y + 750 ≥ C
Now, the Cost of the car given is $4500.
Substituting this in the inequality to find the number of yards,
25y + 750 ≥ 4500
Subtracting 750 from both sides
25y ≥ 3750
Dividing both sides by 25,
y ≥ 150
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Someone help me out pls!
Answer:
look my photo. hope it can help
Each of 5 students wishes to buy a particular textbook, but only 2 textbooks are available. How could one express the number of ways those textbooks could be distributed among the students?
The way that expresses the number of ways those textbooks could be distributed among the students is ⁵C₂.
What is combination?Combinations are also referred to as selections. Combinations imply the selection of things from a given set of things. In this case, we intend to select the objects. This can be illustrated by ⁿCr
Combination formula will be:
ⁿCr = n! / ((n – r)! r!)
n = the number of items.
r = how many items are taken at a time
In this case, each of 5 students wishes to buy a particular textbook, but only 2 textbooks are available. This will be illustrated as ⁵C₂.
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There are ten ways (which are ⁵C₂ = 10) to distribute those textbooks could be among the students in this situation.
What is the Combination?Combinations indicate the choosing of items from a predetermined list of items.
The combination is given by the relation, ⁿCₓ = n!/{x!(n-x)!}
The quantity is given by n. and x is equal to how many objects are taken at once.
Each of the five students in this situation wants to purchase a specific textbook, but there are only 2 books available.
The expression for the number of possible distributions of such textbooks among the students is
⇒ ⁵C₂
⇒ 10
Hence, there are ten ways to distribute those textbooks could be among the students.
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Help me please, it’s due in 10 minutes!
Answer: x<2 or (−∞,2)
Step-by-step explanation:
Write the number positioned at point D.
PLS HELP ( geometry) and please explain the steps tyy
Answer: The line parallel to y = -2x + 5 that passes through the point(1,1)
Has the same slope, m but a different y intercept (0,b)
So lets start by using the given point (1, 1) and the slope intercept form of the line to calculate b
y = mx + b
m = -2
1 = -2(1) + b
1 = -2 + b
Add 2 to both sides of the equation to solve for b
1 + 2 = b
3 = b
The line is
y = -2x + 3
Step-by-step explanation:
Assume that all interest is simple interestBerger Car rental borrow $8500 at 4% interest to cover the increase cost of the auto insurance find the term of the loan if the interest is $170.
we know that
The formula of simple interest is equal to
[tex]I=P(rt)[/tex]In this problem
we have
I=$170
P=$8,500
r=4%=4/100=0.04
t=?
substitute given values in the formula
[tex]\begin{gathered} 170=8,500(0.04t) \\ Solve\text{ for t} \\ t=\frac{170}{8,500*0.04} \\ t=0.5\text{ years} \end{gathered}[/tex]therefore
0.5 years=6 months
The answer is 6 months
f(2x)
13
-5
2
-3
What is x?
The solution for the given equivalent equation f(2x) is 10.
What is equation?
In mathematics, the term equation can be defined as the two algebraic expression which are equal to each other. This method is used to calculate the values of the parameters in the problems.
According to the question, the given equivalent equation is as follows:
Equivalent equation: f(2x) = 3x + 3 = x + 13
By using the addition-subtraction property, to generate the equivalent equations.
3x + 3 = x + 13, 3x = x + 10, 2x = 10, and x = 5
Now, f(2x) = 2x = 10
Hence, the solution for the given equivalent equation is 10.
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The correct equation is: f(2x) = 3x + 3 = x + 13
Bryant measured a house and made a scale drawing the scale he used was 1 inch = 1 foot what scale factor does the drawing use?
The scale factor which is being used by this drawing is 1 : 12.
What is scale factor?A scale factor can be defined as the ratio of two (2) corresponding length of sides or diameter in two similar geometric figures such as equilateral triangles, river, planets in our solar system, etc.
Mathematically, the scale factor of a geometric figure can be calculated by using tis formula:
Scale factor = Dimension of image/Dimension of original figure
Generally speaking, an appropriate conversion factor to an equal value must be used when it is necessary to perform any mathematical conversion.
Conversion:
1 inch = 1 foot
12 inches = 1 foot
Therefore, the scale factor for this drawing is 1 : 12.
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The following table shows a proportional relationship between wand z.318z 2. 545819Write an equation to describe the relationship between w and z.
when w = 18 then z =2
take ratio,
k = 18/2
k = 9
when w =45 then z = 5
take ratio
k = 45/5
k = 9
now it is clear that the constant of proportionality is k = 2
so, the relation between w and z is
w = k z
put k = 9
w = 9z
so, the relation between w and z is w = 9z
what is the price of a line jacket at discount Heaven?
The price of the lined jacket at discount heaven is 32.
To find the price of the lined jacket at the house of denim we use the rule of three.
[tex]\begin{gathered} 35.25\rightarrow100 \\ x\rightarrow10 \end{gathered}[/tex]Then the discount is:
[tex]x=\frac{10\cdot35.25}{100}=3.525[/tex]Hence, the price of the lined jacket at house of denim is:
[tex]35.25-\text{3}.525=31.725=\text{31}.73[/tex]Therefore, the price of the lined jacket at house of denin is $31.73.
Passes through the coordinates -2,2 parallel to the line whose slope is -1
The equation of the line is y-2x= 6.
Here the problem we are dealing with is related to the slope of the line, where, a slope of a line is the alter in the y coordinate about the alter in the x coordinate. The net change in the y-coordinate is spoken to by Δy and the net change in the x-coordinate is spoken to by Δx. The equation for the slope of a straight line is given by y − y1 = m(x − x1), where m is the slope and (x1,y1) are the points that pass through it,whereas the slope-intercept form of the line is given by y = mx + b, where b is the y-intercept. Since if two lines are parallel at that point it said the slope of both those lines are equal i.e m₁= m₂
Since it is given that the coordinates (-2,2) and the slope of the parallel to it, m=2
so the equation for the line is
=>y − y1 = m(x − x1)
=>y − 2 = 2(x +2)
=>y − 2 = 2x+4
=>y-2x= 6
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Find the eqaution of the line that passes through the coordinates -2,2 parallel to the line whose slope is -1.
A regular polygon is shown.
15 sided regular polygon
Determine the measure of one of its angles.
156°
168°
2,340°
2,700°
The measure of the given polygon's angle is 2340°
Polygons are two-dimensional closed objects in geometrical mathematics where n number of line segments cross each other to generate n number of vertices. A triangle is a polygon with three sides, for instance.
In an n-sided polygon, there are n inner angles.
The total of all interior angle measurements in a polygon is always constant and is denoted by the notation "n" for the number of sides in the polygon.
the formula is ;
Sₙ = ( n - 2 ) 180°
Here in question n is given as 15
Thus Sₙ = ( n - 2 ) 180° becomes
Sₙ = ( 15 - 2) 180
13 × 180
= 2340 °
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Answer:
it is really A 156 i took the test and got an 100%
Step-by-step explanation:
Now move the red distribution at the top to the right so that its mean is approximately 375 and then look at the middle and bottom distributions. Based on the location of 0 in the bottom distribution (meaning no difference in the means) what is the best conclusion?
Based on the location of 0 in the bottom distribution (meaning no difference in the means), the best conclusion is:
A- The distribution of differences between the sample means of each group has a mean at or near zero making it likely the two groups are not statistically different.
What is a distribution?In mathematics, distribution describes the probability that a system or a data set will take on a specific value or set of values.
Probability distribution shows how data values are distributed. It is also known as statistical distribution because it demarcates values into common and uncommon (left and right), making a bell-shaped normal distribution.
Thus, when there is no difference in the means, the best conclusion of the statistical distribution is Option A.
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Question Completion with Answer Options:A- The distribution of differences between the sample means of each group has a mean at or near zero making it likely the two groups are not statistically different.
B- The distribution of differences between the sample means of each group has a mean at or near 325 making it likely the two groups are not statistically different.
C- The distribution of differences between the sample means of each group has a mean at or near zero making it likely the two groups are statistically different.
D- The distribution of differences between the sample means of each group has a mean at or near 325 making it likely the two groups are statistically different.
7. Each set of numbers below represents the lengths of three line segments.
Which set represents line segments that could be connected to form a triangle:
A. (1, 2, 3)
B. (3, 4, 5)
C. (1, 10, 100)
D. (1, 2, 5)
E. (1, 3, 4)
F. (1, 20, 100)
Please don't just give a letter choice as an answer. There are more questions like this one and I'd like to understand how to do it : )
Answer:
B: (3, 4, 5)
Step-by-step explanation:
You want to know which segment lengths could be used to form a triangle.
Triangle inequalityThe triangle inequality requires the sum of the two short sides of a triangle exceed the length of the longest side.
A: 1+2 = 3 . . . not a triangle
B: 3+4 > 5 . . . forms a triangle
C: 1+10 < 100 . . . not a triangle
D: 1+2 < 5 . . . not a triangle
E: 1+3 = 4 . . . not a triangle
F: 1+20 < 100 . . . not a triangle
__
Additional comment
The above expression of the triangle inequality seems to be the one most commonly used in algebra and geometry courses.
The triangle inequality can also be seen to be expressed as ...
a + b ≥ c . . . . . . where a, b, c are side lengths in any order
The "equal to" case allows triangles of zero height. (They look like a line segment.) Using that formulation, triples A and E in your answer list will also be considered to form a "triangle."
Please Help . I'm Running Out Of Time!
-5/4 can be shown as -1 1/4, and plotted on the number line as the first quarter tick past -1. Its opposite, 1 1/4, is the same way, the first quarter tick past 1.
Answer: On the plot line 5/4 is 5 tic marks passed 0 so -5/4 would be 6 tic marks before. Hope this helps
If this is wrong I am deeply sorry.
Use the graph below for this question: graph of parabola going through negative 3, negative 1 and 5, negative 1. What is the average rate of change from x = −3 to x = 5? (1 point) A) −1
B) 0
C) 1
D) 8
The average rate of change of the function at the interval x = -3 to x = 5 has a value of (b) 0
How to calculate the average rate of change f?From the question, we have the following points
Parabola going through (-3, -1) and (5, -1).
Also from the question, the interval is given as
x = −3 to x = 5
This interval can also be represented as
(a, b) = (-3, 5)
The points in the question can be expressed as
f(a) = f(-3) = -1
f(b) = f(5) = -1
The value of the average rate of change of the graph at the interval is then calculated as
Rate = [f(b) - f(a)]/[b - a]
Substitute the known values in the above equation
So, we have the following equation
Rate = [f(5) - f(-3)]/[5 + 3]
So, we have the following equation
Rate = [-1 + 1]/[5 + 3]
Evaluate the above quotient
Rate = 0
Hence, the average rate of change of function f is (b) 0
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