The required value of x for the rational expression x-4/4+x to become undefined is x = -4
What is a rational expression?Rational expressions are defined as fractions of algebraic expressions, such as ax + b / cx + d.
Here,
A fraction to become undefined must consist of zero in its denominator,
So
Given expression = x - 4 / 4 + x
The above expression can be undefined if and only if 4 + x = 0
x = -4
Thus, the required value of x for the rational expression x-4/4+x to become undefined is x = -4.
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In a certain game, Auntie Hall has four boxes B1, B2, B3, B4, exactly one of which contains a valuable gemstone; the other three contain cups of yogurt. You are told the probability the gemstone lies in box Bn is n/10 for n = 1, 2, 3, 4.Initially you may select any of the four boxes; Auntie Hall then opens one of the other three boxes at random (which may contain the gemstone) and reveals its contents. Afterwards, you may change your selection to any of the four boxes, and you win if and only if your final selection contains the gemstone. Let the probability of winning assuming optimal play be m/n, where m and n are relatively prime integers. Compute 100m + n.
The probability of winning, assuming optimal play, is m/n, where m and n are relatively prime integers. Then 100m + n is 11.
To find the probability of winning assuming optimal play, we need to find the probability that we choose the correct box after we know what is in the other box. Let X be the event that the gemstone is in box B1. Then P(X) = 1/10.
After Auntie Hall opens a box, the probability of X changes. Let Y be the event that the opened box contains yoghurt. Then P(Y) = 2/3.
Given Y, the probability of X changes to P(X | Y) = P(X) / (P(X) + P(X complement given Y)). We can use Bayes' theorem:
P(X | Y) = P(Y | X) × P(X) / P(Y)
Since the box that Auntie Hall opens is selected randomly, P(Y | X) = 2/3 for each X complement. Thus,
P(X | Y) = 1/10 × 2/3 / (2/3) = 1/10
The probability of winning is the same regardless of whether we switch boxes or not, so the probability of winning is 1/10.
So, 100m + n = 100 × 1/10 + 1 = 11, and the answer is 100m + n = 100 × 1/10 + 1 = 11.
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A camera has a listed price of $704.95 before tax. If the sales tax rate is 9.75%, find the total cost of the camera with sales tax included.
Answer:
773.68
Step-by-step explanation:
1.0975*704.95 ~= $773.68
Answer:
Step-by-step explanation:
camera listed price $704.95
sales tax rate is 9.75%
total price with tax will be
$704.95×(1+9.75%) = $773.68
jefferson is plotting the verticles of an isoceles right triangle on a coordinate graph. he has plotted the two points shown. where should he plot the third point
To form an isosceles triangle Jefferson should plot the third point at (4,2).
What is an isosceles triangle?Any triangle with two sides that have the same length is said to be an isosceles triangle. If the two sides of a triangle are congruent, then the angle across from them must likewise be, according to the theorem that explains the isosceles triangle. As a result, the two angles of an isosceles triangle that are on opposite sides with equal numbers are equal in size.
Given, Jefferson is plotting the vertices of an isosceles right triangle on a coordinate graph.
the given points are,
(-2,-4) (4,-4)
Let, x₁ = -2, y₁ = -4
x₂ = 4, y₂ = -4
distance between (-2,-4) (4,-4) is given as,
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
= √[(4 - -2)² + (-4 - -4)²]
= √[(4 + 2)² + (-4+ 4)²]
= √[(6)² + (0)²]
= √[(6)²
= 6
now verifying with other options,
1). For points (-2, -9),
Distance between (-2, -4) and (-2, -9) = √[(-2 + 2)² + (-4 + 9)²] = √5
Similarly, distance between (4, -4) and (-2, -9) = √[(4 +2)² + (-4 + 9)²] = √61
side is not equal. So the triangle is not isosceles.
2). For a point (3, 1),
Distance between (3, 1) and (-2, -4) = √[(3 + 2)² + (1 + 4)²] = 5√2
Distance between (3, 1) and (4, -4) = √[(3 - 4)² + (1 + 4)²] = 26
side is not equal. So the triangle is not isosceles.
3). For a point (-2,0),
Distance between (-2, 0) and (-2, -4) = √[(-2 + 2)² + (-4 + 0)²] = 4
Distance between (-2, 0) and (4, -4) = √[(-2 - 4)² + (0 + 4)²] = 2√13
side is not equal. So the triangle is not isosceles.
4). For a point (4, 2),
Distance between (4, 2) and (-2, -4) = √[(4 + 2)² + (2 + 4)²] = 6√2
Distance between (4, 2) and (4, -4) = √[(4 - 2)² + (2 + 4)²] = 6
Sides are equal so the triangle formed is an isosceles triangle.
Therefore, the third coordinate is (4, 2).
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The complete question is,
Jefferson is plotting the vertices of an isosceles right triangle on a coordinate graph. He has plotted the two points shown. Where should he plot the third point?
The point is on the graph is (-2,-4) (4,-4)
The options is
(-2,-9)
(3,1)
(-2,0)
(4,2)
Given that f(x) = 5x + 4 and g(x)=x³, find (fog)(-5).
Answer:
Step-by-step explanation:
fog)oh(x) = fo(goh)x. 3) If f(x) and g(x) are one-one functions, then gof(x) is also one-one function. 4) If f(x) and g(x) are on-to functions, then gof(x) is also on-to function. 5) If f(x) and g(x) are bijective functions, then gof(x) is also a bijective function.
40 points for 2 questions.
Please help me :)
3 persons A, B, C independently fire at a target. What is the probability that
a. Exactly one of them hits the target,
b. At least one of them hits the target?
Given: Probability of hitting the target. P(A) = 2/5, P(B) = 1/4, P(C) = 1/2.
2. Company provides to their clients the following products: accidental insurance and
health insurance.
If 55% of male clients opt for accidental insurance and 65% of female clients opt for
health insurance, then what is the probability that health insurance contract is chosen if
60% of the company’s clients are females?
The probabilities are given as follows:
1. a. Exactly one hits the target: 7/20.
1. b. At least one hits the target: 31/40.
2. Health insurance is chosen: 0.57 = 57%.
How to obtain the probabilities?The outcomes with exactly one person hitting the target are given as follows:
A hits (3/5 probability), while B and C do not (3/4 and 1/2 probability).B hits (1/4 probability), while A and C do not (2/5 and 1/2 probability).C hits (1/2 probability), while B and C do not (3/4 and 1/2 probability).Hence the probability is obtained as follows:
p = 3/5 x 3/4 x 1/2 + 1/4 x 2/5 x 1/2 + 1/2 x 3/4 x 1/2
p = 9/40 + 2/40 + 3/40
p = 14/40
p = 7/20.
The probability that none hits the target is of:
3/5 x 3/4 x 1/2 = 9/40.
Hence the probability of at least one hitting is of:
1 - 9/40 = 40/40 - 9/40 = 31/40.
The percentages associated with health insurance are given as follows:
45% of 40% (male clients).65% of 60% (female clients).Hence:
p = 0.45 x 0.4 + 0.65 x 0.6
p = 0.57.
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what is the perimeter of a regular pentagon whose sides are 6 incges long
Answer: 30inches
Step-by-step explanation:
P=5a
a=side length
P=5(6)
5*6=30
The area of a diving board is 40 square feet. The perimeter is 44 feet. What are the dimensions of the diving board?
Answer:
diving board has a length of 20 feet and a width of 2 feet
Step-by-step explanation:
diving board has a length of 20 feet and a width of 2 feet
Area = length (l) x width (w)
lw = 40
Perimeter = 2l + 2w
we can solve for 'l' and have:
l = 40/w
now substitute 40/w in for 'l' in the perimeter formula to get:
2(40/w) + 2w = 44
distribute through by 2 to get:
80w + 2w² = 44w
we can create the quadratic equation: 2w²-44w + 80 = 0
we can factor out a 2 to get:
2(w² - 22w + 40) = 0
2(w-20)(w-2) = 0
w = 20 and 2
NEED ASAP PLEASE!!!!! A vertical number line is given.
A vertical number line starting at negative 5.5 with tick marks every one half unit up to positive 1.5. The value negative 3.75 is labeled.
When scuba diving, a student recorded the value plotted in the image. If 0 represents sea level, which of the following is true about the value?
A. The student is −3.75 ft above sea level, and the absolute value is 3.75 ft.
B. The student is 3.75 ft above sea level, and the absolute value is 3.75 ft.
C. The student is −3.75 ft below sea level, and the absolute value is 3.75 ft.
D. The student is 3.75 ft below sea level, and the absolute value is 3.75 ft.
The truth about the position of the student scuba diving using absolute value concept is;
D. The student is 3.75 ft below sea level, and the absolute value is 3.75 ft.
How to interpret the absolute value?The absolute value (or modulus) | x | of a real number x is defined as the non-negative value of x without regard to its sign. For example, the absolute value of 5 is 5, and the absolute value of −5 is also 5. The absolute value of a number may be thought of as its distance from zero along real number line.
Thus, if negative 3.75 is marked on the number line, from the given options, we can say that if we apply the definition above that |-3.75| = 3.75ft below the sea level
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17. the shaft is supported at its ends by two bearings a and b and is subjected to the forces applied to the pulleys fixed to the shaft. determine the resultant internal loadings acting on the cross section at point d. the 400-n forces act in the -z direction and the 200-n and 80-n forces act in the y direction. the journal bearings at a and b exert only y and z components of force on the shaft.
The resultant normal force at point D along the x-direction is [tex]F_D_x=0[/tex] and the resultant shear force at point D along the y-direction is [tex]F_D_y=154.29N[/tex]
Consider the equilibrium of the shaft.
Resolve the forces along the y-direction.
[tex]R_A_y+R_B_y=200+200+80+80R_A_y+R_B_y=560-----(1)[/tex]
Take moments about point B and about the z-axis:
[tex]R_A_y*1.4=2*100*0.7+2*80*0.4\\\\R_A_y=245.71[/tex]
Substitute the above value in equation (1).
[tex]245.71+R_B_y=560\\\\R_B_y=314.29N[/tex]
Resolve the forces along the z-direction.
[tex]R_A_z+R_B_z=385+385R_A_z+R_B_z=770-----(2)[/tex]
Take moments about point B and about the y-axis:
[tex]R_A_z*1.4=2*385*1.1\\\\R_A_z=605N[/tex]
Substitute the above value in equation (2).
[tex]605+R_B_z=770\\\\R_B_z=165N[/tex]
a) The resultant normal force at point D along the x-direction is
[tex]F_D_x=0[/tex]
b) The resultant shear force at point D along the y-direction is
[tex]F_D_y-R_B_y+2*80=0\\\\F_D_y-314.29+160=0\\F_D_y=154.29N[/tex]
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Identify the solid formed by a given net.
A: Cylinder
B: Cone
C: Rectangular pyramid
D: Rectangular prism
The solid formed by a given net is cylinder.
What is Three dimensional shape?
a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
The net has two circles and one rectangle.
The net of a cylinder is formed of two circles, with one attached to each end of a rectangle.
A cylinder is a 3D shape with a circular cross section and a curved surface. It has no straight edges
Hence, the solid formed by a given net is cylinder.
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Val is going to plant d vegetable seeds in one garden and 2d+6 vegetable seeds in another. How many seeds is going to plant?
There are 3d + 6 seeds is going to plant.
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
We have to given that;
Val is going to plant d vegetable seeds in one garden and 2d+6 vegetable seeds in another.
Hence, The total vegetable seeds to plant is,
⇒ d + (2d + 6)
⇒ d + 2d + 6
⇒ 3d + 6
Thus, The total vegetable seeds to plant is, (3d + 6)
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If each quadrilateral below is a square, find the missing measures. the square STUV, TU=15 Find VU= SU= TV= SW=
Answer:
VU = 15, SU = 21.21 or 15[tex]\sqrt{2}[/tex], TV = 21.21 or 15[tex]\sqrt{2}[/tex], and SW = 10.6 or [tex]\frac{15\sqrt{2} }{2}[/tex].
Step-by-step explanation:
VU = 15 by the properties of a square.
To find SU and TV we need to use the rule: the diagonal for a square of side length s is: (√2)s
Then the diagonals for our square are: TV = SU = (√2)*15 = 21.2
SW is just the diagonal divided by 2, so SW = 10.6
The other answers are in radical form, but you can put either the number or radical version.
Why does the arc of length π/6 on the unit circle correspond to the point ( square root of 3 over 2, 1/2 ) on the unit circle? Explain without using trigonometric functions (sine, cosine, tangent, cosecant, secant, cotangent). Hint: Review the previous discussions.
The arc of length π/6 on the unit circle can be visualized as one-sixth of a full circle with a radius of 1 unit. The unit circle is defined as a circle with a radius of 1 unit centered at the origin (0, 0) in a coordinate plane.
What does the mathematical term "arc" mean?
An "arc" in mathematics is a straight line that connects two endpoints. An arc is typically one of a circle's parts. In essence, it is a portion of a circle's circumference. A curve contains an arc.
To locate the point on the unit circle that corresponds to the end of the arc, we can use the concept of polar coordinates. In polar coordinates, a point on the unit circle is defined by its distance from the origin (r) and its angle with the positive x-axis (θ), as shown in the diagram below.
[diagram here]
For the arc of length π/6 on the unit circle, the angle θ is π/6 and the distance from the origin (r) is 1 unit.
Therefore, the point on the unit circle that corresponds to the end of the arc can be represented in rectangular coordinates as (r * cos(θ), r * sin(θ)), where cos(θ) and sin(θ) are the cosine and sine of the angle θ, respectively.
Substituting the values for r and θ, we have:
x = 1 * cos(π/6) = sqrt(3) / 2
y = 1 * sin(π/6) = 1/2
So, the point on the unit circle that corresponds to the end of the arc of length π/6 is (sqrt(3) / 2, 1/2).
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19. An event that is certain to occur has a probability of _________________.
An event that is certain to occur has a probability of 1
What is probability in math?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
Hence we an say that 0 and 1 are two extreme values in probability.
When an even is certain to occur the probability is 1 however when the event will not occur the probability is zero.
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A music company offers a loan to buy a drum set for $1500. The simple interest is 11.8% and the loan will be paid in equal monthly payments fo
years. What is the monthly payment?
The monthly payment is $
1
The monthly payment on the principal is $33.22
What is the monthly paymentA monthly payment is a regular installment made by a borrower to a lender in order to pay off a debt over a period of time. It is typically used to repay loans such as mortgages, car loans, or personal loans, and is usually calculated based on the loan's interest rate, principal amount, and loan term (the number of months over which the loan will be repaid).
The formula of monthly payment is given as;
The formula for calculating the monthly payment on a loan is:
M = P * (r(1 + r)^n) / ((1 + r)^n - 1)
Where:
M = monthly payment
P = the principal amount of the loan = $1500
r = the monthly interest rate (expressed as a decimal) = 11.8%
n = the number of payments (in months) = 60 months
Substituting the values into the formula;
Monthly Payment = $ 33.22
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Complete Question:
A music company offers a loan to buy a drum set for $1500. The simple interest is 11.8% and the loan will be paid in equal monthly payments for 5
years. What is the monthly payment?
Find the area of the shaded region y=2x^2-4x
The area of the region between x = 0 and x = 2 of the curve y = 2x² - 4x is given as follows:
2.64 square units.
How to obtain the area?The area of a curve y = f(x) between an interval from x = a to x = b is obtained by the definite integral of f(x) from x = a to x = b.
The curve in this problem is given as follows:
y = 2x² - 4x.
The integral is given as follows:
I(x) = 0.67x³ - 2x².
The bounds are given as follows:
x = 0 and x = 2.
Applying the Fundamental Theorem of Calculus, the definite integral is given as follows:
A = |I(2) - I(0)|.
A = |0.67(2)³ - 2(2)²|
A = 2.64 square units.
Missing InformationThe shaded region is between x = 0 and x = 2.
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Answer #4 for brainliest and 20 points!!
Maggie and her classmates are making cupcakes in baking class. Their teacher divides a bag of candy flowers evenly among 6 students at the table. Each student gets 3 candy flowers to use for decorating.
In linear equation, Each student, including Maggie, will receive 3 candy flowers to use for decorating their cupcakes.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
6 students * 3 candy flowers/student = 18 candy flowers.
This is 18 candy flowers / 6 students = 3 candy flowers/student.
Each student, including Maggie, will receive 3 candy flowers to use for decorating their cupcakes.
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In spherical geometry, state an equality involving the sum of the angles of a triangle, using x, y, and x as the angles. Find a formula for the area of a triangle in spherical geometry. Help pls I’m desperate.
Answer:
In spherical geometry, the sum of the angles of a triangle is always greater than 180 degrees. The formula for this is:
x + y + z > 180 degrees
where x, y, and z are the angles of the triangle.
The formula for the area of a triangle in spherical geometry is given by:
A = R^2 * (θ1 + θ2 + θ3 - π)
Where A is the area of the triangle, R is the radius of the sphere, θ1, θ2, θ3 are the angles of the triangle in radians, and π is the constant pi.
It's important to note that this formula is based on the triangle's spherical excess which is the amount by which the sum of the triangle's angles exceeds 180 degrees.
a) The inequality is,
⇒ x + y + z > 180°
b) Area of spherical ΔXYZ is,
⇒ A = r² (α + β + у - pi),
where, r is the radius of the sphere and α, β, and y are the angles of the triangle in radians.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Now, the sum of the angles of a triangle is greater than 180 degrees.
Hence, The actual sum of the angles is given by;
x + y + z = π + A,
where A is the area of the triangle measured in radians.
And, As for the formula for the area of a triangle in spherical geometry, it is given by the formula;
⇒ A = r² (α + β + у - pi),
where, r is the radius of the sphere and α, β, and y are the angles of the triangle in radians.
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Think back to the interest rates you wrote down for federal loans in
Resource #6. How did those interest rates compare to those you saw for
private loans in the 2nd article you read? Were the private loan interest
rates surprising to you? Why or why not?
Answer:
Step-by-step explanation:
u cant explain it
what is a Mandelbrot set?
Salut/Hello!
Answer:
The Mandelbrot set is the set of values [tex]c[/tex] in the complex plane for which the orbit of the critical point [tex]z = 0[/tex] under iteration of the quadratic map
[tex]z_{n+1} = z_{n}^{2} + c[/tex] remains bounded.
I hope it was helpful! :]
Answer:
A Mandelbrot set is a mathematical set of points in the complex plane, the boundary of which forms a fractal shape. The set is composed of all complex numbers c for which the complex-valued iterative equation zn+1 = zn2 + c does not tend to infinity as n tends to infinity. The set is named after the mathematician Benoit Mandelbrot, who studied it in the 1970s and is considered to be one of the most famous and studied fractal shapes in mathematics.
Task 6
misc. 7%
gifts &
entertainment
12%
clothes 5%
savings
10%
debt 5%
housing 30%
Spending Guidelines
(% of net incomes)
food 20%
transportation
11%
Brenna has a job where she makes a
net semimonthly income of $2,640.
She lives in an apartment where rent
is cheap at $800 per month and heat
is included. Her electricity bill
averages $90 per month.
1: What is Brenna's monthly net income?
2: How much does she spend on housing
per month?
3: If Brenna puts the money she saves on
housing in a savings account, how much
will she save each month? Each year?
Brenna's monthly net income is $2,640.
What is Brenna's monthly net income?Brenna spends $800 per month on housing.If Brenna puts the money she saves on housing in a savings account, she will save $800 per month and $9,600 per year.Brenna's monthly net income is $2,640.This figure is calculated by taking her semimonthly net income of $2,640 and multiplying it by two since she is paid semimonthly.Brenna spends $800 per month on housing.This figure is calculated by multiplying her rent of $800 by one since she does not need to worry about heating costs. If Brenna puts the money she saves on housing in a savings account, she will save $800 per month and $9,600 per year.This figure is calculated by taking her monthly housing costs of $800 and multiplying it by twelve since she will not be spending it every month.This money can then be put into a savings account to earn interest and grow over time.To learn more about budgeting refer to:
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Please help!!
See picture for details!
sin(A) =
cos(A) =
tan(A)=
sec(A)
csc(A) =
cot(A) =
Answer:
Step-by-step explanation:
In the diagram there are two vertex A & B
Let us assume the 3rd vertex to be C
AB is the hypotenuse which is 8
AC is the adjacent side which is 6
CB is the opposite side. Let us assume it to be x for now
[tex]hypotenuse^{2} = opposite^{2} +adjacent^{2}[/tex]
[tex]8^{2} =x^{2}+6^{2} \\64=x^{2} +36\\x^{2} =64-36=28\\x=2 \sqrt{7}[/tex]
sinA=CB/AB = 2[tex]\sqrt{7[/tex] /8
CosA=AC/AB=6/8
TanA=sinA/CosA=CB/AC=2[tex]\sqrt{7}[/tex]/6
Similarly,
CosecA=1/SinA
SecA=1/CosA
CotA=1/TanA
find the width of a rectangle with perimeter of 64cm and. length of 18 cm
A rectangular piece of paper has a 64 cm perimeter. The width is 8 cm if the length is three times.
What is a perimeter?A perimeter is a closed path that encompasses, surrounds, or delineates something, whether it be a two-dimensional shape or a one-dimensional length.A circle's or an ellipse's circumference is its furthest boundary. There are various useful situations where knowing the perimeter is useful. The radius of a shape's edge is known as the perimeter. Discover how to calculate a shape's perimeter by multiplying its side lengths.The measurement of a shape's perimeter is its length. It takes adding the lengths of all four sides to determine a rectangle's or square's perimeter.The correct option is A 8 cm
Given: Perimeter of a rectangular piece of paper = 64 cm
Length =3 × Width
Let the width be x cm
[tex]\Rightarrow$ Length $=3 \times \mathrm{cm}[/tex]
[tex]\because$ Perimeter $=2($ length $+$ width $)=2(3 x+x)=8 x \mathrm{~cm}$[/tex]
[tex]$\Rightarrow 8 x=64 \Rightarrow x=8$[/tex]
[tex]\therefore$ Width is $8 \mathrm{~cm}$[/tex]
The complete question is:
The perimeter of a rectangular piece of paper is 64 cm. If the length is three times its width, find its width.
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Calculate the degrees of freedom for a one-sample t test with 2,822 U.S. adults between the ages of 15 and 64 in the sample.o
The degrees of freedom for a one-sample t test with 2,822 U.S. adults in the sample is 2821.
What is the calculation of degrees of freedom for a one-sample t test with 2,822 U.S. adults?The degrees of freedom (df) for a one-sample t test with 2,822 U.S. adults as the sample size can be calculated as follows:Step by step explanation:The degrees of freedom (df) is the number of independent observations in the sample that can be used to estimate the population parameters.In a one-sample t test, the sample size (n) is subtracted from the degrees of freedom.Therefore, df = n - 1 = 2822 - 1 = 2821.So the degrees of freedom for a one-sample t test with 2,822 U.S. adults in the sample is 2821.To learn more about degree of freedom refer:
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Choose the most convenient method to graph the line x−y=1.
Which of the following represents the ratio of the short leg to the hypotenuse
in the right triangle shown below?
On solving the provided question, we can say that the ratio of the short leg to the hypotenuse in the right triangle is 1;2
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
the ratio of the short leg to the hypotenuse in the right triangle is
1;2
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a cell phone company charges $35 per month for an unlimited data plan and charges a one time $100 activation fee. your parents will only spend a maximum of $485 on a phone for you. write and solve an inequality that represents the total months (m) your parents will pay for the phone
Answer:
Step-by-step explanation:
set the months as X
base on the question information, we have
35X + 100 ≤ 485
then we can have
35x ≤ 485 -100
35x≤385
x≤385/35
x≤11
thus, we can say, the total month is 11 months the parents will pay for the phone
For each point of the function f(x), determine the corresponding point for the transformed function:
y = -3f(x+2).
Write answer as ordered pair.
Points on f(x):
(-4,5), corresponding point:
(-2,3), corresponding point:
(1,-2), corresponding point:
(3,-4), corresponding point:
The corresponding point for the transformed function are:
Ordered pair (-4, -9).
Ordered pair (-2, 0).
Ordered pair (1, 12).
Ordered pair (3, 36).
How to determine the corresponding point for the transformed function?In order to determine the corresponding point for the transformed function, we would have to substitute the given value of x (x-value) into the transformed function and then evaluate.
When the x-value = -4, the corresponding point for the transformed function is:
y = -3f(x + 2)
y = -3f(-4 + 2)
y = -3f(-2)
y = -3(3)
y = -9.
When the x-value = -2, the corresponding point for the transformed function is:
y = -3f(x + 2)
y = -3f(-2 + 2)
y = -3f(0)
y = 0
When the x-value = 1, the corresponding point for the transformed function is:
y = -3f(x + 2)
y = -3f(1 + 2)
y = -3f(3)
y = -3(-4)
y = 12.
When the x-value = 3, the corresponding point for the transformed function is:
y = -3f(x + 2)
y = -3f(3 + 2)
y = -3f(5)
y = 36
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the equation of line y=-4x pass through the origin of coordinates
True, line y = -4x passes through the origin of coordinates.
Graph of the line is attached below.
What is line?A line is a one-dimensional figure, which has length but no width. A line is made of a set of points which is extended in opposite directions infinitely.
Given equation of the line,
y = -4x
Line passes through the origin
So, Coordinates of the origin (0, 0) should satisfy the above equation.
0 = -4(0)
0 = 0
LHS = RHS
Hence, line y=-4x pass through the origin of coordinates.
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