Answers
The exponential function passes through the points (-1,4/5) and (1,20) will be y = 4 × [tex]5^{x}[/tex].
What is an exponential function?In mathematics, an exponential function is a relationship of the type y = ax, where x is an independent variable that spans the entire real number line and is expressed as the exponent of a positive number.
In other meaning, an exponential function is that function above which a variable x has imposed.
Suppose the exponential function as
y = a[tex]e^{bx}[/tex]
Substitute, (-1,4/5)
4/5 = a[tex]e^{-b}[/tex] (1)
Substitute, (1,20)
20 = a[tex]e^{b}[/tex] (2)
Multiply (1) with (2)
(4/5)20 = a[tex]e^{-b}[/tex] × a[tex]e^{b}[/tex]
4 × 4 = a²
a = 4
Substitute, a = 4 into (2)
20 = 4[tex]e^{b}[/tex]
[tex]e^{b}[/tex] = 5
Take log on both sides of the above equation,
ln [tex]e^{b}[/tex] = ln 5
b = ln 5
Substitute a = 4 and b = ln 5 into y = a[tex]e^{bx}[/tex]
y = 4 e^(x(ln 5)) = 4 e^(ln5^x)
y = 4 × [tex]5^{x}[/tex]
Hence "The exponential function passes through the points (-1,4/5) and (1,20) will be y = 4 × [tex]5^{x}[/tex]".
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Related Questions
2. Sandy Sellers works 30 hours per week
with an hourly rate of pay of $15.00 per
hour. She has deductions from each
paycheck of 12% for federal income tax,
2.84% for North Carolina income tax, 6.2%
for Social Security, and 1.45% for Medicare.
What is Sandy's net take home pay each
week?
Answers
Answer:
$348.79
Step-by-step explanation:
You want to know Sandy Sellers' net weekly pay if she earns $15 per hour for 30 hours' work and has deductions of ...
12% federal tax2.84% NC tax6.2% SS1.45% Medicare.Gross PaySellers' net pay will be her gross pay, less the taxes. Those taxes are all percentages of her gross pay.
gross pay = (hourly rate) × (hours worked)
gross pay = ($15.00/hour) × (30 hours) = $450
DeductionsThe deductions from her pay total ...
12% +2.84% +6.2% +1.45% = 22.49% . . . . of her gross pay
The dollar amount of the deductions is ...
0.2249 × $450 = $101.205 ≈ $101.21
Net PayThen Sellers' net pay is ...
net = gross - deductions
net = $450 -101.21 = $348.79
Sandy Sellers' take-home pay each week is $348.79.
Whenever he is injured and unable to play, Patrice Bergeron likes to earn a little extra cash by doing some tutoring. He currently charges $50/hr and has 20 students that he works with. He has discovered that for every $5/hr he increases the price, he loses one student.
Answers
The revenue function of Patrice Bergeron earnings is R(x) = (50 + 5x)(20 -x)
How to determine the revenue function?From the question, we have the following parameters that can be used in our computation:
Charges = $50
Students = 20
Also, we have:
For every $5/hr he increases the price, he loses one student.
This means that
Charges = 50 + 5x
Students = 20 - x
So, the revenue equation is
R(x) = Charges * Students
Substitute the known values in the above equation, so, we have the following representation
R(x) = (50 + 5x)(20 -x)
Hence, the function is R(x) = (50 + 5x)(20 -x)
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Complete question
Whenever he is injured and unable to play, Patrice Bergeron likes to earn a little extra cash by doing some tutoring. He currently charges $50/hr and has 20 students that he works with. He has discovered that for every $5/hr he increases the price, he loses one student.
What is the revenue function
What is the function rule? Select the correct choice and fill in any answer boxes in your choice below.
A. y=_____
(Simplify your answer. Use integers or fractions for any numbers in the expression.)
B. There is no function rule.
Answers
B. There is no function rule
An art class is making a mural for their school which has a triangle drawn in the middle. The length of the bottom of the triangle is . Another side is 8 more than times the length of the bottom of the triangle. The last side is more than the bottom of the triangle. Write and simplify an expression for the perimeter of the triangle.
Answers
Let's call the length of the bottom of the triangle x. The length of another side of the triangle is 8 more than 3 times the length of the bottom of the triangle, or 3x + 8. The last side of the triangle is y, where y is more than x.
The perimeter of the triangle can be expressed as:
x + (3x + 8) + y
Simplifying this expression gives:
4x + 8 + y
Therefore, the perimeter of the triangle can be expressed as the sum of 4 times the length of the bottom of the triangle, 8, and the length of the last side of the triangle, y.
PLS HELP 10 POINTS!!
Perpendicular to the y-axis and has the point of (-4,5)
Answer choices
Y=5
Y=-4
X=5
X=-4
Answers
The line passes through Y=5. Correct option is A.
What is a perpendicular line?Two lines are perpendicular to each other if they are at right angle
to each other.
Given, line is perpendicular to Y-axis and passes through (-4,5).
Therefore, the given line is parallel to X-axis and passes Y-axis at y=5.
Hence, the given line passes through Y=5.
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Gina changes the amount of milk she purchases depending on whether it costs $1,$1.50, or $1.75 a pound. What other information do we need to come up with her demand curve for milk?
Select the correct answer below:
whether her milk consumption goes up or down with price
how much milk she buys in total
whether or not she switches to a substitute when the price is high
how much milk she buys at each price point
Answers
The information that we need to come up with her demand curve for milk is D how much milk she buys at each price point
What is a demand curve?A demand curve is a graph that shows the relationship between a commodity's price and the amount that is desired at that price. Demand curves can be applied to the price-quantity relationship for either a specific consumer or for every consumer in a given market.
Individual demand curves and market demand curves are the two types of demand curves. It shows a graphic depiction of the demand schedule. It should be noted that based on the information, the quantity is needed. The correct option is D.
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use an appropriate taylor series to find the first four nonzero terms of an infinite series that is equal to ln(5/3).
Answers
The appropriate Taylor series for an infinite series with the first four nonzero terms equal to ln(5/3) is 0/1!, 0/2!, 0/3!, and 0/4! .......
What is taylor series?An infinite sum of words that are expressed in terms of a function's derivatives at a single point is known as the Taylor series or Taylor expansion of a function in mathematics. Near this point, the function and the sum of its Taylor series are equivalent for the majority of common functions. The polynomial or function of an infinite sum of terms is the Taylor series. The exponent or degree of each succeeding term will be greater than the exponent or degree of the one before it.
The formula is:
∑n=0 to ∞(fⁿ(a)(x-a)ⁿ)/n!
Here,
∑n=0 to ∞(fⁿ(a)(x-a)ⁿ)/n!
at n=1,
=0/1!
at n=2,
=0/2!
at n=3,
=0/3!
at n=4,
=0/4!
Appropriate taylor series for first four nonzero terms of an infinite series that is equal to ln(5/3) is 0/1!, 0/2!, 0/3!, 0/4!.......
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Solve equation with rational exponents. Check all proposed solutions.
8x^3/2-56=0
Answers
Answer: x=3√14
Step-by-step explanation:
Of the 20 students in Mr . Evans class , 45% of them brought their lunches. Which of the following is the number of students who brought their lunches ?
Answers
Answer: 9 because 45% of 20 is 9
PLS HURRY 30 PTS Write the math sentence as an equation: Negative six times the sum of a number and 18.3 is 27.9
−6(r + 18.3) = 27.9
−6(r − 18.3) = 27.9
−6r + 18.3 = 27.9
−6r − 18.3 = 27.9
Answers
Answer: A
Step-by-step explanation:
From the statement.
Times = Multiplication
The sum of a number and 18.3 = (r + 18.3)
Equals = 27.9
Therefore,
-6 x (r + 18.3) = 27.9
Need help, please!
Suppose you will perform a test to determine whether there is sufficient evidence to support a claim of a linear correlation between two variables. Find the critical values of r given the number of
pairs of data in and the significance level a
n=14,a=0.01
A: r=0.661
B: r= +- 0.532
C: r= 0.684
D: r= +- 0.661
Answers
Answer:
c or b
Step-by-step explanation:
the midpoint of AB is at (0,4). If A=(3,0), find B.
Answers
If the midpoint of AB is at (0,4). and A = (3,0) then B is at point (-3, 8)
How to find point BThe formula to determine the center point of a straight line using the coordinates of its endpoints is known as the midpoint formula in coordinate geometry.
The formula is of the form
X= (x₂ - x₁)/2
Y = (y₂ - y₁)/2
solving for B (x₂, y₂)
0 = (x₂ + 3)/2
0 = x₂ + 3
x₂ = -3
4 = (y₂ + 0)/2
8 = y₂ + 0
y₂ = 8
point B = (-3, 8)
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To multiply a decimal number by 10,
O move the decimal point one place to the right.
move the decimal point two places to the right.
O move the decimal point one place to the left.
O move the decimal point two places to the left.
Answers
Answer:
[tex]\huge{\boxed{\text{A) move the decimal point one place to the right}}}}[/tex]
Step-by-step explanation:
Think about the following scenarios
4.00 * 10
529.00 * 10
4 * 10 = 40 (4.00 * 10 = 40.0)
529 * 10 = 5290 (5290.00 * 10 = 5290.0)
As you can see, the decimal point is moving one space to the right when multiplying by ten.
In the decimal system, moving the decimal point one place to the right multiplies by ten, while moving the decimal point one place to the left multiplies by 1/10.
Hope it helps :) and let me know if you want me to elaborate.
Explanation is edge
I’m a computer graphics design program, Mario created a segment with endpoints at ( 1, 5) and ( 7, 3). He then reflected the segment about a vertical line through the segment’s own midpoint. WHAT ARE THE COORDINATES OF THE ENDPOINTS OF THE NEW SEGMENTS?
A. (5, 1) and (3, 7)
B (7, 5) and (1, 3)
C. (7, 3) and (1, 5)
D. (5, 1) and (7, 3)
Answers
The coordinates of the endpoints after the transformation is (c) (7, 3) and (1, 5)
How to determine the coordinates of the endpointsFrom the question, we have the following parameters that can be used in our computation:
Segment with endpoints at (1, 5) and (7, 3)
Also from the question, we have:
The points are reflected the segment about a vertical line through the segment’s own midpoint
When this is done, this means that the points would swap positions
So, we have the following representations
(1, 5) and (7, 3) ⇒ (7, 3) and (1, 5)
Hence, the coordinates of the endpoints is (c) (7, 3) and (1, 5)
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Given the equation v over 9.4 equals 13.7, solve for v.
4.3
23.1
128.87
128.78
Answers
Therefore the solution to the given question is option d)128.78 for this particular equation.
What is Equation?Many different definitions exist for a mathematical equation. In algebra, a statement that mathematically establishes the equality of two mathematical expressions is known as an equation.. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal." Mathematical variables are used in even the most fundamental and straightforward algebraic equations.
Here,
=> v/9.4 = 13.7
=> v = 13.7*9.4
=> v= 128.78
Therefore the solution to the given question is option d)128.78 for this particular equation
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pat radigan wants to purchase a new home for $312,500. pat puts 20% down and will finance the remainder of the purchase. compare the following two mortgage options he has: 20 years at 6.5% or 25 years at 7.0%.
Answers
Difference in interest paid = $82,740.52
Total interest paid for 25 year loan interest - Total interest paid for 20 year loan interest
According to the given information
A.
Monthly payment for 20 year mortgage [tex]& $=$ PMT $\left(6.5 \% / 12,20^* 12,-312500^* 0.8\right)$ & $=$ PMT $($ rate, nper, $-$ pv $)$ \[/tex]\
Monthly payment for 25 year mortgage [tex]& $=$ PMT $\left(7 \% / 12,25^* 12,-312500^* 0.8\right)$ & $=$ PMT(rate,nper,-pv) \\[/tex]
B
Total cost of interest for 20 year mortgage [tex]& $=(\mathrm{B} 2 * 20 * 12)-(312500 * 0.8)$ \\[/tex]
Total cost of interest for 25 year mortgage [tex]$=(\mathrm{B} 3 * 25 * 12)-(312500 * 0.8)$ &[/tex]
C.
Difference in interest paid [tex]& $=\mathrm{B} 7-\mathrm{B} 6$ &[/tex] = Total interest for 25 year loan-total interest for 20 years
A.
Monthly payment for 20 year mortgage [tex]& $\$ 1,863.93$ & $=$ PMT(rate,nper,-pv) \\[/tex]
Monthly payment for 25 year mortgage [tex]& $\$ 1,766.95$ & $=$ PMT(rate,nper,-pv) \\[/tex]
B.
Total cost of interest for 20 year mortgage = [tex]& $\$ 197,343.88$ & $=$[/tex] total monthly payments-loan taken
Total cost of interest for 25 year mortgage = [tex]& $\$ 280,084.40$ & $[/tex] = total monthly payments-loan taken
C.
Difference in interest paid = $82,740.52
Total interest paid for 25 year loan interest - Total interest paid for 20 year loan interest
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Please help work due at 11:59( look at photo for answer choices)
Answers
The vertex labels of Δ QRT are : ∠2 label is Q, ∠8 label is T and the remaining vertex label is R. The vertex labels for ΔSTR are: ∠5 label is S, ∠9 label is R and the remaining label is T.
What is a triangle?The polygon having three sides and three vertices are known as triangle.
If we separate the two triangles as shown in the figure. We can find the vertex labels with the help of the angles marked in the figure.
For Δ QRT, the vertex labels are:
∠2 is Q, ∠1 is R and ∠8 is T
Similarly. for ΔSTR, the vertex labels are:
∠5 is S, ∠6 is T, and ∠9 is R
Hence, For Δ QRT, we can label as ∠2 is Q, ∠1 is R and ∠8 is T and for ΔSTR we can label as ∠5 is S, ∠6 is T, and ∠9 is R.
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Carmen made $209 for 11 hours of work.
At the same rate, how much would she make for 8 hours of work?
Answers
Answer:
Step-by-step explanation:
First find the hourly rate Carmen makes. You can find it by dividing the amount she made by the number of hours she worked
209 / 11 = 19
Now multiply that rate by the amount of hours you want to figure out.
19 * 8 = 152
Answer: $152
Step-by-step explanation:
Divide 209 by 11 to find how much money she gets for 1 hour of work ($19) then multiply that value by 8.
Let a dilation be defined by a scale factor s and center of dilation (x,y). Each of the options below represents a dilation of a polygon according to the given values of s,x and y. Which of the following dilations produce an image congruent to its pre-image. Select all that apply.
Answers
s = 1, x = 0, y = 3 and s = 1, x = 2, y = 0 produce an image congruent to its pre-image so option C and D are correct
What is dilation?
Dilation is the increase or decrease in the size of a figure by a scale factor. Rigid transformations preserve the shape of a figure. Examples of rigid transformation are reflection, rotation and translation.
Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. However, there is a variation in the shape's size. The initial form should be stretched or contracted during a dilatation. The phrase "scale factor" describes this transition.
Enlargement is the term used when a dilatation results in a bigger picture.Reduction occurs when a dilatation results in a smaller picture.Dilation is said to be a rigid transformation if the scale factor is equal to one.
Therefore the dilation by a scale factor of one produce an image congruent to its pre-image.
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What is the probability of flipping a coin 50 times and getting tails 22 times or fewer? Round your answer to the nearest tenth of a percent.
Answers
The probability of flipping a coin 50 times and getting tails 22 times or fewer is given as follows:
A. 24%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].The parameters for the binomial distribution are given as follows:
n = 50, p = 0.5.
Hence the mean and the standard deviation are obtained as follows:
[tex]\mu = 50 \times 0.5 = 25[/tex][tex]\sigma = \sqrt{50 \times 0.5 \times 0.5} = 3.54[/tex]Using continuity correction, the probability of 22 or fewer tails is the p-value of Z when X = 22.5, hence:
Z = (22.5 - 25)/3.54
Z = -0.71
Z = -0.71 has a p-value of 0.2709.
Which is closest to 24%.
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Question 21 Suppose that 12 inches of wire costs 36 cents. At the same rate, how much (in cents) will 5 inches of wire cost?
Answers
Answer: To determine how much 5 inches of wire would cost at the same rate as 12 inches of wire, we can first determine the rate at which the wire is being sold by dividing the cost of the wire by the length of the wire:
36 cents / 12 inches = 3 cents/inch
We can then use this rate to determine the cost of 5 inches of wire by multiplying the rate by the length of the wire:
3 cents/inch * 5 inches = 15 cents
Therefore, 5 inches of wire would cost 15 cents at the same rate as 12 inches of wire.
A local movie theater has a movie lovers club. After paying a membership fee,
all ticket purchases are discounted. The cost after buying 5 movie tickets is $48.75. The
cost after buying 7 movie tickets is $58.25. Write an equation in slope-intercept form to
represent the data. Describe what the slope and intercept mean. Use the equation to
find the total cost after buying 12 tickets.
Answers
Answer: 57 dollars, hope this helps!
Find the quotient of 6x^3-+18x^2-18x+12 , x-2
Answers
In linear equation, 96 is the quotient.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
f(x) = 6x^3-+18x^2-18x+12
x - 2 = 0
x = 2
f( x) = 6 * 8 + 18 * 4 - 18 * 2 + 12
= 48 + 72 - 36 + 12
= 132 - 36
= 96
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Aunt Georgia agreed to pay 40% of the cost of the new UMSHQYGT 2000, which costs $649.99. Does Kayan have enough money in the bank to get the phone?
Answers
Kayan will have enough money in the bank to get the phone.
Will Kayan have enough money?It is important to note that percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
Since Aunt Georgia has $1000 and bought a gadget for $300, the remaining amount will be:
= $1000 - $300
= $700
Therefore, since also agreed to pay 40% of the cost of the new UMSHQYGT 2000, which costs $649.99, she will have money left. This will be:
= $700 - $649.99
= $50.01
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Complete question
Aunt Georgia has $1000 and bought a gadget for $300 She also agreed to pay 40% of the cost of the new UMSHQYGT 2000, which costs $649.99. Does Kayan have enough money in the bank to get the phone?
Write the systems of equations from the table below and find the solution?
Answers
The system of equations is y = 4x - 3 and y = -1/3x + 4 and the solution is (21/13, 45/13)
How to determine the system of equations?From the question, we have the table of values as the parameters that can be used in our computation:
From the table, we have
Table 1
(x, y) = (0, -3) and (4, 13)
A linear equation is represented as
y = mx + c
Where
Slope = m
c = y when x = 0
This means that
c = -3
So, we have
y = mx - 3
The point (4, 13) implies that
13 = m * 4 - 3
So, we have
4m = 16
m = 4
So, the equation is
y = 4x - 3
Table 2
(x, y) = (0, 4) and (4, 6)
A linear equation is represented as
y = mx + c
This means that
c = 4
So, we have
y = mx + 4
The point (4, 6) implies that
6 = m * 4 + 4
So, we have
4m = -2
m = -1/3
So, the equation is
y = -1/3x + 4
Substitute y = -1/3x + 4 in y = 4x - 3
-1/3x + 4 = 4x - 3
So, we have
-x + 12 = 12x - 9
Evaluate the like terms
13x = 21
Divide
x = 21/13
y = -1/3x + 4 implies that
y = -1/3 x 21/13 + 4
So, we have
y = -7/13 + 4
Evaluate
y = 45/13
So, the solution is (21/13, 45/13)
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Which inequality does the graph represent?
A two-dimensional graph with an x-axis and a y-axis is given. A dotted line is passing through the co-ordinates (1,0), and (-1,2). The region below the dotted line is shaded in grey.
A. y < –x – 1
B. y < –x + 1
C. y < x – 1
D. y < x + 1
Answers
The inequality that the graph represent is y < -x + 1. The correct option is B. y < –x + 1
Determining the inequality that represents a graphFrom the question, we are to determine the inequality that represents the given graph.
From the given information,
The line is passing through the coordinates (1, 0) and (-1, 2).
Using the formula for the equation of a line,
Using the formula,
(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)
Then,
(y - 0)/(x - 1) = (2 - 0)/(-1 - 1)
y/(x-1) = 2/-2
y/(x -1) = -1
y = -1(x -1)
y = -x + 1
Since the line is dotted and the shaded region is below the line, the inequality becomes
y < -x + 1
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A plane slices a double-napped cone parallel to the base of the cone. Which conic section is formed?
Answers
Answer:
Parabola
Step-by-step explanation:
A conic section is a curve obtained by the intersection of a plane with the surface of a (double-napped) cone, When the plane is parallel to the edge of one cone.
Thus, The intersection is a parabola.
Answer: degenerate hyperbola
Step-by-step explanation:
degenerate hyperbola because its the thickest of the plane so it can be formed.
Please help, picture of question is attached
Answers
Bearing is a topic that deals with angles and distance. Thus, the required answers to the given question are:
i. Distance of 1034.2 miles
ii. Bearing of [tex]158^{o}[/tex]
The speed of an object is the rate of movement of the object with time.
speed = [tex]\frac{distance}{time}[/tex]
So that:
distance = speed x time
i. In the given question; let the initial distance covered be represented by d, so that:
d = 250 x 2
= 500 miles
ii. Let the second distance covered by the pilot be represented by D, so that:
D = 300 x 2
= 600 miles
iii. Thus let the distance to the starting point be represented by x. From Cosine rule, we have:
[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] - 2abCos C
[tex]x^{2}[/tex] = [tex]500^{2}[/tex] + [tex]600^{2}[/tex] - 2(500 x 600)Cos [tex]140^{o}[/tex]
= 250000 + 360000 - 600000(-0,7660)
= 610000 + 459600
= 1069600
x = [tex]\sqrt{1069600}[/tex]
= 1034.22
x = 1034.2 miles
Using the Sine rule to determine the required internal angle, we have:
[tex]\frac{a}{Sin A}[/tex] = [tex]\frac{c}{Sin C}[/tex]
[tex]\frac{500}{Sin A}[/tex] = [tex]\frac{1034.22}{Sin 140}[/tex]
Sin A = [tex]\frac{500*0.6428}{1034.22}[/tex]
= 0.3108
A = [tex]Sin^{-1}[/tex] 0.3108
= 18.11
A = [tex]18^{o}[/tex]
To determine angle B, we have:
140 + 18 + B = 180 (sum of angles in a triangle)
158 + B = 180
B = 180 - 158
= 22
B = [tex]22^{o}[/tex]
Thus, the required bearing is 180 - 22 = 158
Therefore the distance and bearing required to fly to starting point are 1034.2 miles and [tex]158^{o}[/tex] respectively.
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Tami earned 71 out of 80 points on a test. What percentage did Tami earn on the test?
Answers
Answer:
88.75% is the percentage Tami earned.
A fair die with its faces numbered from 1 to 6 will be rolled. Which of the following is the best interpretation of the probability that the number landing face up will be less than three?
For many rolls of the die, the long- run relative frequency of a number less than three landing face app is 1/3.
Answers
For many of the rolls die, the long run relative frequency of a number less than 3 landing face up is 1/3.
What is relative frequency?
The proportion of outcomes where a specific event occurs to all trials, not in a hypothetical sample space but in a real experiment, is known as the empirical probability, relative frequency, or experimental probability of an event.
Given that, Only two integers (1 and 2) are smaller than 3, hence their relative frequency will be 2/6=1/3.
The best way to interpret the data is thus,
For many rolls of the die, the long- run relative frequency of a number less than three landing face up is1/3.
Hence option A is correct which is for many of the rolls die, the long run relative frequency of a number less than 3 landing face up is 1/3.
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