On solving the provided question, we can say that the trigonometry sin3θcos2θ+cos3θsin2θ = 4sin3(1−2cos2θ)+sinθ
What is trigonometry?The area of mathematics knοwn as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, arοund the third century BC. frοm the use of geometry in astronοmical study.
The area of mathematics knοwn as exact methods deals with specific trigonometric functions and hοw they might be used in calculations. There are six popular trigonοmetric functions in trigonometry. Sine, cosine, tangent, cοtangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics οf triangles, particularly right triangles, is called trigonοmetry. The study of geοmetry, however, is the characteristics of all geοmetric figures.
the trigonometry
sin3θcos2θ+cοs3θsin2θ=4sin3(1−2cos2θ)+sinθ
Use the variation cοs2θ=1−sin2θ to express sin(5θ) in terms of sinθ
sin5θ=4sin3θ(1−2(1−sin2θ))+sinθ(8(1−sin2θ}
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Find the value of x for the following
Answer:
x = -5
Step-by-step explanation:
Since both horizontal lines are parallel, the marked angles are corresponding angles and are congruent. This, we can set them equal to each other:
47 = 10x + 97
Next, isolate “x” to find the value of “x”:
47 - 97 = 10x
-50 = 10x
-5 = x
Consider the problem: Minimize cx subject to Ax >= b, x >= 0. Suppose that one component of the vector b, say bi, is increased by one unit to bi + 1. a. What happens to the feasible region? b What happens to the optimal objective value?
A) If the change in b results in a smaller feasible region, then the optimal objective value will either remain the same or increase.
B) If the change in b results in a larger feasible region, then the optimal objective value may remain the same or decrease.
In linear programming, the objective is to minimize or maximize an objective function subject to certain constraints. One common constraint is that the solution must be in the feasible region, which is defined by the set of all solutions that satisfy the constraints.
Recall that the constraints are given by Ax >= b, where A is a matrix of coefficients and x is a vector of variables. If we increase one component of b, say bi, then the set of solutions that satisfy the constraints will change. Specifically, any solution that previously satisfied Ax >= b may no longer satisfy the constraints, since the left-hand side of the inequality is fixed while the right-hand side has increased. In other words, the feasible region may shrink or shift in response to the change in b.
Now let's consider the effect on the optimal objective value. Recall that the objective function is given by cx, where c is a vector of coefficients. The optimal objective value is the minimum (or maximum) value of cx over all solutions in the feasible region. If we increase one component of b, then the optimal objective value may or may not change, depending on the specifics of the problem.
To see why, let's think about what happens to the feasible region. As we noted above, the feasible region may shrink or shift in response to the change in b. If the optimal solution was previously at the boundary of the feasible region, then it may no longer be feasible, and the optimal objective value will increase. On the other hand, if the optimal solution was previously in the interior of the feasible region, then it may still be feasible, and the optimal objective value will remain the same.
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Serenity is making beaded jewelry with no more than 920 beads she currently has in stock. Bracelets use 15 beads
and necklaces use 70 beads.
x= the number of bracelets
y = the number of necklaces
The inequality is written as 15x + 70y ≤ 920. Then the region below the line is the solution to inequality.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Serenity is assembling beaded jewelry with no more than 920 beads she presently has in inventory. Bracelets use 15 beads and necklaces use 70 beads.
Let 'x' be the number of bracelets and 'y' be the number of necklaces. Then the inequality is given as,
15x + 70y ≤ 920
The region below the line is the solution to inequality.
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Lenart Corporation has provided the following data for its two most recent years of operation: Manufacturing costs: Variable manufacturing cost per unit produced: Direct materials $ 13 Direct labor $ 5 Variable manufacturing overhead $ 5 Fixed manufacturing overhead per year $ 90,000 Selling and administrative expenses: Variable selling and administrative expense per unit sold $ 6 Fixed selling and administrative expense per year $ 61,000 Year 1 Year 2 Units in beginning inventory 0 1,000 Units produced during the year 10,000 9,000 Units sold during the year 9,000 8,000 Units in ending inventory 1,000 2,000
Answer: To calculate the total cost of the units in beginning inventory for each year, we need to multiply the number of units by the per-unit cost:
Year 1: Cost of units in beginning inventory = 0 units * $13 + $5 + $5 = $0
Year 2: Cost of units in beginning inventory = 1,000 units * ($13 + $5 + $5) = 1,000 * $23 = $23,000
To calculate the total cost of the units produced during each year, we need to multiply the number of units by the per-unit cost:
Year 1: Cost of units produced = 10,000 units * ($13 + $5 + $5) = 10,000 * $23 = $230,000
Year 2: Cost of units produced = 9,000 units * ($13 + $5 + $5) = 9,000 * $23 = $207,000
To calculate the total cost of the units sold during each year, we need to multiply the number of units sold by the per-unit cost:
Year 1: Cost of units sold = 9,000 units * ($13 + $5 + $5 + $6) = 9,000 * $29 = $261,000
Year 2: Cost of units sold = 8,000 units * ($13 + $5 + $5 + $6) = 8,000 * $29 = $232,000
To calculate the total variable manufacturing costs for each year, we need to sum the costs of the units in beginning inventory, units produced, and units sold:
Year 1: Total variable manufacturing costs = $0 + $230,000 + $261,000 = $491,000
Year 2: Total variable manufacturing costs = $23,000 + $207,000 + $232,000 = $462,000
To calculate the total fixed manufacturing overhead costs for each year, we need to add the fixed manufacturing overhead per year to the total variable manufacturing costs:
Year 1: Total manufacturing costs = $491,000 + $90,000 = $581,000
Year 2: Total manufacturing costs = $462,000 + $90,000 = $552,000
To calculate the total variable selling and administrative expenses for each year, we need to multiply the number of units sold by the variable selling and administrative expense per unit:
Year 1: Total variable selling and administrative expenses = 9,000 units * $6 = $54,000
Year 2: Total variable selling and administrative expenses = 8,000 units * $6 = $48,000
To calculate the total selling and administrative expenses for each year, we need to add the fixed selling and administrative expenses per year to the total variable selling and administrative expenses:
Year 1: Total selling and administrative expenses = $54,000 + $61,000 = $115,000
Year 2: Total selling and administrative expenses = $48,000 + $61,000 = $109,000
Step-by-step explanation:
Please help this those.
The values of x and y are 30 and 80
The value of x is 63The slope of GH is 0How to determine the values of x and yFrom the question, we have the following parameters that can be used in our computation:
The parallel line and the transversal
The value of y is calculated as
y + 25 = 105 ---- alternate angle theorem
So, we have
y = 80
For x, we have
3x - 15 + 105 = 180 --- coresponding angle
So, we have
3x = 90
Divide
x = 30
How to determine the value of xHere, we make use of
2x + 54 = 180 --- sum of alternate interior angles
So, we have
2x = 126
Divide
x = 63
The slope of line GHThis is calculated as
Slope = (y2 - y1)/(x2 - x1)
So, we have
Slope = (6 - 6)/(5 - 2)
Slope = 0
Hence, the slope is 0
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PLSSSS HELP ME ASAP I DONT UNDERSTAND THIS
Jon filled up the tank of his semitruck with 240 gallons of fuel and set out to deliver a shipment of vegetables. His truck uses an average of 0.15 gallons of fuel for each mile he drives. You can use a function to approximate the amount of fuel in Jon's tank after he drives x miles.
Write an equation for the function. If it is linear, write it in the form f(x)=mx+b. If it is exponential, write it in the form f(x)=a(b)^x.
Answer:
Step-by-step explanation:
Step 1: Understanding the Problem
The problem involves finding an equation to approximate the amount of fuel in Jon's semitruck after he drives x miles. Jon started with 240 gallons of fuel and his truck uses 0.15 gallons of fuel for each mile he drives.
Step 2: Writing the Equation
We know that the amount of fuel in Jon's tank decreases as he drives. So, we can write the equation as:
f(x) = 240 - 0.15x
This equation says that the amount of fuel in Jon's tank after he drives x miles is equal to 240 gallons (the amount of fuel he started with), minus 0.15 gallons for each mile he drives.
Step 3: Interpreting the Equation
The function f(x) = 240 - 0.15x is a linear equation, which means that it is a straight line on a graph. The value 240 is the y-intercept, which means that when x = 0, the y-value of the function is 240 (the amount of fuel in Jon's tank when he starts driving). The value -0.15 is the slope of the line, which tells us how much the y-value decreases for each unit increase in x (in this case, how much the fuel decreases for each mile Jon drives).
Step 4: Conclusion
So, the equation f(x) = 240 - 0.15x can be used to approximate the amount of fuel in Jon's semitruck after he drives x miles. The equation is linear and can be written in the form f(x) = mx + b, where m = -0.15 (the slope of the line) and b = 240 (the y-intercept).
Use the rational zeros theorem to list all possible rational zeros of the following.
Answer:
[tex]\sf \dfrac{p}{q}=\dfrac{\pm1}{\pm1},\dfrac{\pm1}{\pm3},\dfrac{\pm7}{\pm1},\dfrac{\pm7}{\pm3}=\pm 1, \dfrac{\pm1}{\pm3},\pm 7, \dfrac{\pm7}{\pm3}[/tex]
Step-by-step explanation:
Given polynomial:
[tex]f(x)=-3x^3-5x^2+x-7[/tex]
Rational Root TheoremIf P(x) is a polynomial with integer coefficients and if p/q is a root of P(x), then p is a factor of the constant term of P(x) and q is a factor of the leading coefficient of P(x).
Possible p-values
Factors of the constant term: ±1, ±7
Possible q-values
Factors of the leading coefficient: ±1, ±3
Therefore, all the possible values of p/q:
[tex]\sf \dfrac{p}{q}=\dfrac{\pm1}{\pm1},\dfrac{\pm1}{\pm3},\dfrac{\pm7}{\pm1},\dfrac{\pm7}{\pm3}=\pm 1, \dfrac{\pm1}{\pm3},\pm 7, \dfrac{\pm7}{\pm3}[/tex]
Substitute each possible rational root into the function:
[tex]x=-1 \implies f(-1)=-3(-1)^3-5(-1)^2+(-1)-7=-10[/tex]
[tex]x=1 \implies f(1)=-3(1)^3-5(1)^2+(1)-7=-14[/tex]
[tex]x=-7 \implies f(-7)=-3(-7)^3-5(-7)^2+(-7)-7=770[/tex]
[tex]x=7 \implies f(7)=-3(7)^3-5(7)^2+(7)-7=-1274[/tex]
[tex]x=-\dfrac{1}{3} \implies f\left(-\dfrac{1}{3}\right)=-3\left(-\dfrac{1}{3}\right)^3-5\left(-\dfrac{1}{3}\right)^2+\left(-\dfrac{1}{3}\right)-7=-\dfrac{70}{9}[/tex]
[tex]x=\dfrac{1}{3} \implies f\left(\dfrac{1}{3}\right)=-3\left(\dfrac{1}{3}\right)^3-5\left(\dfrac{1}{3}\right)^2+\left(\dfrac{1}{3}\right)-7=-\dfrac{22}{3}[/tex]
[tex]x=-\dfrac{7}{3} \implies f\left(-\dfrac{7}{3}\right)=-3\left(-\dfrac{7}{3}\right)^3-5\left(-\dfrac{7}{3}\right)^2+\left(-\dfrac{7}{3}\right)-7=\dfrac{14}{9}[/tex]
[tex]x=\dfrac{7}{3} \implies f\left(\dfrac{7}{3}\right)=-3\left(\dfrac{7}{3}\right)^3-5\left(\dfrac{7}{3}\right)^2+\left(\dfrac{7}{3}\right)-7=-70[/tex]
As f(p/q) ≠ 0, none of the possible rational roots are actual roots of the given polynomial.
At a hair salon, each womab is charged $15 for a cut and 35$ for a color. how much money will the salon earn if w women grt a cut and a color?
=$50
Step-by-step explanation:
Total amount to be earn
if one women cut and add a colour
35$ + 15$
= $50
The salon earn if the women get a cut and a colour is $50.
What is Total amount?There are many meanings of total, but they all have something to do with completeness. A total is a whole or complete amount, and "to total" is to add numbers or to destroy something.
In math, you total numbers by adding them: the result is the total. If you add 8 and 8, the total is 16. If a car is totalled in an accident, it has been completely destroyed. A total defeat is a complete and utter defeat with no chance of recovering. The total resources of a company are all its resources, everything it has.
Step-by-step explanation:
Total amount to be earn
if one women cut and add a colour
35$ + 15$
= $50
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5x-2w+t
T=8
W=1/2
X=3
Answer:
So the value of 5x-2w+t, with x=3, w=1/2, and t=8 is 22.
Step-by-step explanation:
Given,
The equation is
5x-2w+t
and also given the
x=3
w=1/2
and t=8
Now ,
if we substitute the value of x,w and t,
We get,
5 × 3 - 2 × (1/2) + 8
= 15 - 1 + 8
= 22
So the value of 5x-2w+t, with x=3, w=1/2, and t=8 is 22.
Jll company in 2012 had sales of 800,000 in 2022 sales were up 75% . Calculate the sales for 2021.
Answer:
860,000.
Step-by-step explanation:
If the sales in 2022 were up 75% from 800,000, the sales in 2022 would be 800,000 + (800,000 * 75%) = 800,000 + 600,000 = 1,400,000.
To find the sales for 2021, we'll have to use the average annual growth rate to find the sales in between 2012 and 2022.
Let's assume that the sales grew linearly, so the average annual growth rate would be (1,400,000 - 800,000) / (2022 - 2012) = 600,000 / 10 = 60,000.
The sales in 2021 would then be 800,000 + 60,000 = 860,000.
A rectangular room is 2 meters longer than it is wide, and its perimeter is 24
meters. Find the dimension of the room.
The length is : _____ meters and the width is _____
meters.
If a rectangular room is 2 meters longer than it is wide, and its perimeter is 24 meters then the dimensions of the room: 7 meter x 5 meter
What is the perimeter?Perimeter is a mathematical term, it indicates total outer boundary of a figure, we define it only for two dimensional figures.
Perimeter = Sum of length of the all the sides
Let x be the width of the room in meters.
Then the length of the room is 2 meters longer, which means it is x+2 meters.
In this case, we know that the perimeter is 24 meters.
So we can set up an equation:
Perimeter = 2Length + 2Width
Substituting the values we know:
24 = 2(x+2) + 2x
Simplifying the equation:
24 = 2x + 4 + 2x
24 = 4x + 4
20 = 4x
x = 5
So the width of the room is 5 meters, and the length is x+2 = 7 meters.
Therefore, the dimensions of the room are 7 meters by 5 meters.
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Binomial distribution calculation
If n=5 and p=0.7, find P(x=4)
Give at least 4 decimal places.
The binomial distribution P( x = 4 ) if n = 5 and p = 0.7 is 0.3602.
What is the binomial distribution?Binomial probability distribution determines the probability of a discrete random variable.
Given that;
n = 5p = 0.7p( x = 4 )Using the formula, probability mass function;
P( X = x ) = ⁿCₓPˣ( 1 - P )ⁿ⁻ˣ
P( X = x ) = ⁵Cₓ × 0.7ˣ × ( 1 - 0.7 )⁵⁻ˣ
Now for P( x = 4 )
P( X = 4 ) = ⁵C₄ × 0.7⁴ × ( 1 - 0.7 )⁵⁻⁴
P( X = 4 ) = ⁵C₄ × 0.7⁴ × ( 1 - 0.7 )
P( X = 4 ) = 5 × 0.2401 × 0.3
P( X = 4 ) = 0.3602
Therefore, the value of P( x = 4 ) is 0.3602.
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Line A (y = 3x + 1) is transformed into
Line B (y=2x-7). Which best describes
the new slope and y-intercept?
The slope is[ ? ],
and the line is shifted[ ? ]
steeper
flatter
Answer:
The new slope is 2,
New y-intercept is - 7
Line is flatter since slope has reduced
Step-by-step explanation:
Need help answering this question
Answer:
24 people
Step-by-step explanation:
German : 4 + (4/2) = 6
Norwegian : 4 + 4 + (4/2) = 10
Italian : 4 + 4 = 8
Add them all :
6 + 10 + 8 = 24
In figure measurement angle one equals 6X +7°, measurement angle two equals 5X +13°, and measurement angle for equals 12 X +9° different incorrectly says that measurement angle four equals 73°. What is the measurement for? What mistake my era friend have made
The value of x is 11.78.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
In a figure, the four angles sum must equal 360.
Now,
The four angles are:
6x + 7, 5x + 13, 12x + 9, and 73
Solve for x.
6x + 7 + 5x + 13 + 12x + 9 + 73 = 360
23x + 89 = 360
23x = 360 - 89
23x = 271
x = 11.78
Thus,
x is 11.78.
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Complete question:
In the figure measurement angle 1 is 6x + 7°, measurement angle 2 equals 5x + 13°, and measurement angle 3 equals 12x + 9° and measurement angle 4 equals 73°.
What is the value of x?
I need help with this math question
The value of the variables in the parallelogram are such that:
x = 58 y = 63. 5How to find the variables ?This is a parallelogram which means that angles on the same line will add up to 180 degrees.
The value of x is therefore:
( x - 5 ) + ( 2x + 11 ) = 180
3x + 6 = 180
x = ( 180 - 6 ) / 3
x = 58
The value of y is:
2 y + ( 58 - 5 ) = 180
2 y = 180 - 53
y = 127 / 2
y = 63.5
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3
10
x 100 = 0,3 x 100 =
Answer:
The answer is thirty (30)
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
You have a credit card with a balance of $1,367.90 at a 9.5% APR. You pay $400.00 each month on the
due date until the card is paid off. How many months does it take to pay off the card, and what is the total
amount paid including interest?
Be sure to include in your response: answer and steps
Answer:
Step-by-step explanation:
The solution to this problem involves calculating the monthly interest and reducing the balance accordingly each month until the balance reaches zero. Here are the steps:
Calculate the monthly interest: First, we need to calculate the monthly interest rate. We can do this by dividing the APR by 12. The monthly interest rate is 9.5% / 12 = 0.7917%.
Calculate the interest charge for the first month: The interest charge for the first month is the balance multiplied by the monthly interest rate. In this case, the interest charge is $1,367.90 x 0.7917% = $10.87.
Calculate the new balance: Next, we need to subtract the payment from the balance and add the interest charge to determine the new balance. The new balance after the first payment is $1,367.90 - $400.00 + $10.87 = $978.87.
Repeat the steps for subsequent months: Repeat the process of calculating the monthly interest charge and the new balance for each subsequent month until the balance reaches zero.
Keep track of the number of months: As we repeat the steps, keep track of the number of months it takes to pay off the card.
Here is a summary of the calculations:
Month Balance Interest Payment New Balance
1 $1,367.90 $10.87 $400.00 $978.87
2 $978.87 $7.74 $400.00 $586.61
3 $586.61 $4.62 $400.00 $191.23
4 $191.23 $1.50 $400.00 $-208.27
It takes 4 months to pay off the card, and the total amount paid including interest is $1,367.90 + $10.87 + $7.74 + $4.62 + $1.50 = $1392.73.
g(a)= -3a² + a
h(a) = 3a +4
Find (3g - 2h)(0)
A) 12
C) -8
B) -50
D) -38
Answer:yo no se come ablar ingles
Step-by-step explanation:
Write an equation for a rational function with the given characteristic.
Vertical asymptotes at x = -2 and x = 3, x-intercepts at (-4,0) and (-1,0), y-intercepts at (0,4)
f(x) =
The rational function with the given characteristics is:
f(x) = -6(x + 4)*(x + 1)/[(x - 2)*(x + 3)]
How to write the rational function?We want to write a rational function with the given characteristics, first we want to have vertical asymptotes at x = -2 and x = 3, then the denominator must be:
(x - 2)*(x + 3)
We also want to have x-intercepts at (-4,0) and (-1,0), this means that the numerator must be:
a*(x + 4)*(x + 1)
Where a is a real number, then the rational function is:
f(x) = a*(x + 4)*(x + 1)/[(x - 2)*(x + 3)]
Now we want to have an y-intercept at (0, 4)
Then we must have:
f(0) = 4 = a*(0 + 4)*(0 + 1)/[(0 - 2)*(0+ 3)]
4 = a*4/-6
(-6/4)*4 = a
-6 = a
The rational function is:
f(x) = -6(x + 4)*(x + 1)/[(x - 2)*(x + 3)]
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This question is due today. Could someone possibly help me.
Applying the triangle proportionality theorem, QR = 17½.
What is the Triangle Proportionality Theorem?The triangle proportionality theorem states that when a line is constructed parallel to one side of a triangle and intersects the remaining two sides at two different points, the two sides of the triangle will be divided in equivalent proportions.
Therefore:
SQ/PS = TQ/TR
SQ = 5
PS = 2
TQ = ?
TR = 5
Plug in the values:
5/2 = TQ/5
Cross multiply:
2TQ = 25
TQ = 25/2
TQ = 12½.
QR = TQ + TR
QR = 12½ + 5
QR = 17½
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Solve -4(r-2/3)+4<-8. Show your work
Please help quickly I will give brainly and do step by step explanation thanks!
Answer:
11/3
Step-by-step explanation:
-4(r-2/3)+4<-8
-4r+8/3+4<-8
8/3+4<-8+4r
8/3+4+8<4r
44/3<4r
44/12=r
11/3=r
Write the first five terms of the arithmetic sequence. Find the common difference d and write the nth term of the sequence as a function of n.
a1
= 300, ак + 1 = ак - 20
The first five terms of the arithmetic sequence are 300, 280, 260, 240, 220 and the common difference d is 20
What is arithmetic sequence?An arithmetic sequence in algebra is a sequence of numbers where the difference between every two consecutive terms is the same.
Given is an arithmetic sequence, [tex]a_{k+1} = a_k-20[/tex] and [tex]a_1 = 300[/tex],
we need to find the first five terms,
a₂ = a₁-20
a₂ = 300-20
a₂ = 280
a₃ = a₂-20
a₃ = 260
a₄ = a₃ - 20
a₄ = 240
a₅ = a₄ - 20
a₅ = 220
aₙ = aₙ₊₁ - 20
d = 20
Hence, the first five terms of the arithmetic sequence are 300, 280, 260, 240, 220 and the common difference d is 20
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The measure of angle 4 is 120°, and the measure of angle 2 is 35°.
Triangle A B C. Angle A is 2, angle B is 1, angle C is 3. The exterior angle to angle B is 5, and the exterior angle to angle C is 4.
What is the measure of angle 5?
95°
105°
130°
155°
The measure of angle that is an exterior angle to B is 95°.
What are exterior angles?The angle created by any extended side of a triangle and its neighboring side is referred to as the external angle of a triangle. A triangle has three external angles. It should be noticed that every outside angle and corresponding interior angle constitute a linear pair. We are aware that a triangle's internal angle is created when its sides come together at its apex.
Given that,
The measure of angle 4 is 120°, and the measure of angle 2 is 35°.
Triangle A B C. Angle A is 2, angle B is 1, and angle C is 3. The exterior angle to angle B is 5, and the exterior angle to angle C is 4.
The sum of an interior and exterior angle is 180°,
∠4 + ∠3 = ∠1 + ∠5 = ∠2 + ∠6 = 180°
and ∠2+ ∠1 +∠3 = 180°
Also, ∠3 = 180 - ∠4
∠3 = 180 - 120 = 60°
Substitute the values,
∠2+ ∠1 +∠3 = 180°
35 + ∠1 + 60 = 180
∠1 = 180 - 95
∠1 = 85°
Now, ∠1 + ∠5 = 180
∠5 = 180 - 85
∠5 = 95°
Hence, the measure of angle that is an exterior angle to B is 95°.
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The correct question is:
Answer: A) 95 Degrees
Step-by-step explanation:
What is 1/5 (3+2+5)^2
PLEASE GIVE BRAINLIEST!
thank you and have a good day :)
Answer:
20
Step-by-step explanation:
1/5(3+2+5)^2
3+2+5 = 10
10^2 = 100
100/5 = 20
The default rate on government-guaranteed student loans at a certain private 4-year institution is 7 percent. The college extends 10 such loans. (a) What is the probability that none of them will default? (b) That at least three will default? (c) What is the expected number of defaults?
The probability that none of them will default 0.0066
What is probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
(a) If 1,000 student loans are made, what is the probability of fewer than 50 defaults?
It's a binomial problem but the large n requires using a normal approximation.
mean = np = 1000*0.07 = 70
std = sqrt(npq) = sqrt(70*0.93) = 8.0685
z(50) = (50-70)/[8.0685] = -2.4788
P(# of defaults < 50) = P(z<-2.4788) = 0.0066
(b) More than 100?
z(100) = (100-70)/8.0685 = 3.7182
P(defaults > 100) = P(z>3.7182) = 0.00010035
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Correct question
The default rate on government-guaranteed student loans at a certaing public 4-year institution is 7% (a) If 1,000 student loans are made, what is the probability of fewer than 50 defaults? (b) More than 100? Show your work carefully.
y=x²-4x+6 List a. b. c. (1 pt) Find y: (2 pts) *** S Editing V
The value of a, b, and c are 1, -2, and 6 respectively.
The y-intercept of this quadratic function is 6.
The axis of symmetry of this quadratic function is 1.
The vertex of this quadratic function is (1, 5).
How to calculate the axis of symmetry of a quadratic function?Mathematically, the axis of symmetry of a quadratic function can be calculated by using this mathematical expression:
Axis of symmetry, Xmax = -b/2a
Where:
a and b represents the coefficients of the first and second term in the quadratic function.
For the given quadratic function f(x) = x² - 2x + 6, we have:
Axis of symmetry, Xmax = -b/2a
Axis of symmetry, Xmax = -(-2)/2(1)
Axis of symmetry, Xmax = 2/2 = 1.
Vertex (h, k) = (1, 5).
In Mathematics, the y-intercept of any graph such as a quadratic function, generally occur at the point where the value of "x" is equal to zero (x = 0).
y-intercept = 6.
Lastly, we would create a table and then graph the quadratic function as follows;
x y
0 6
2 2
5 11
Read more on quadratic function here: brainly.com/question/13159926
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Complete Question:
Quadratic Function f(x) = x² - 2x + 6 2.
1. List a, b, and c.
2. Find the axis of symmetry.
3. Find the vertex.
4. What is the y-intercept?
5. Create a table and graph.
4 x 9.5 using distributive method
Answer: 38
Step-by-step explanation:
4 x 9.5 can also be seen as 2 (2 x 4.75)
To solve this,
1) 2 x 2 = 4
2) 2 x 4.75 = 9.5
4 x 9.5 = 38.
Simple ways without distributive property is just 4 x 9.5 which is equal to 38.
If it is like 4(9.5) then the answer would be 4 * 9.5 which is 38. But if you were asking about this, 4(9 + 5) then these would be the steps.
So, distributive property is A(B + C) so A = 4 and B = 9 and C = 5.
So the setup would be 4(9 + 5).
And in order to solve this we have to distribute the 4 to 9 and 5. And after that, we remove the parenthesis. So, we get 36 + 20. And that would equal 56. So,
Answer = 56or
Answer = 38
please help me.
please here is the picture.
The functions are matched as follows -
y = √x ⇒ d. Square root
y = |x| ⇒ g. Absolute value
y = x² ⇒ h. Quadratic
y = 1/x² ⇒ f. Reciprocal Squared
y = 1/x ⇒ b. Reciprocal
y = x³ ⇒ a. Cubic
y = ∛x ⇒ e. Cube root
y = x ⇒ c. Linear
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The first function is given as -
y = √x
Since, this function contains a square root symbol, so it is a square root function.
The second function is given as -
y = |x|
Since, this function contains absolute value symbol, so it is a absolute value function.
The third function is given as -
y = x²
Since, this function contains power of 2 and x is squared, so it is a quadratic function.
The fourth function is given as -
y = 1/x²
Since, this function contains power of 2, x is squared and the value is reciprocal of x², so it is a reciprocal squared function.
The fifth function is given as -
y = 1/x
Since, this function contains reciprocal value of x, so it is a reciprocal function.
The sixth function is given as -
y = x³
Since, this function contains power of 3 and x is cubed, so it is a cubic function.
The seventh function is given as -
y = ∛x
Since, this function contains a cube root symbol, so it is a cube root function.
The second function is given as -
y = x
Since, this function contains y equal to x, so it is a linear function.
Therefore, all the different functions are identified.
To learn more about function from the given link
https://brainly.com/question/2284360
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el avión más grande el airbus a380 tiene una longitud de 239 ft 6 pulgadas una embarga dura de 261 ft y 10 pulgadas y una altura de 79 ft 1pulgada expresa estás dimensiones en metros
