we use the pooled proportion when we calculate the standard error for the difference in proportions when performing a hypothesis test whne When the variances of both populations are the same
The standard error for the distinction within the proportions is calculated utilizing the population proportions but in cases where the population proportions are unknown, we utilize the test proportions to calculate the standard error. In the case of hypothesis testing, we are mindful of the population proportions whereas in evaluating the confidence interval for the distinction between the proportions we have no thought of the population proportions. So, the standard error for a hypothesis test of distinction in two proportions is distinctive from the standard error for a certain interval of the difference in two proportion.
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please hep me asap!!!
find the equation of the line in slope-intercept form. e through (−5, 6) with slope = 2
Answer:
Step-by-step explanation:
Slope-intercept form is y=mx+b where m is your slope and b is your y-intercept.
To find your equation with what you are given, you have to plug in your values.
(-5, 6) = (x, y) so plug -5 in where there is x and 6 in where there is y
then your slope, m, is 2 so plug 2 in where there is m.
so it should look like
6=2(-5)+b, now you are solving for b.
6 = -10+b
+10 +10
___________
16 = b Then take the values and plug back into the slope intercept formula, y=mx+b.
Plug 16 in for b and 2 in for m (m represents slope and they told us the slope =2)
*you no longer need the y and x values because you only use those to solve for m or b, in this case b, so leave y and x in your equations*
y=2x+16
the sum of the measures of the angles in the triangle is 180 degrees. what is the measure of each angle? write and solve an equation
If sum of the measures of the angles in the triangle is 180 degrees then
measures of each angle is 60 degrees.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Given,
The sum of the measures of the angles in the triangle is 180 degrees
By angle sum property, sum of the measures of the angles in the triangle is 180 degrees
Let the measure of angle be x
x+x+x= 180 degrees
3x=180
Divide both sides by 3
x=180/3
x=60
Hence each angle measures 60 degrees.
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write the inverse: if the 2 smallest sides sum to be larger than the 3rd side, then it is a triangle.
Using the properties of conditional statements we can write the inverse of the statement as ": if the 2 smallest sides sum is not larger than the 3rd side, then it is not a triangle."
The statement is given as if the sum of two sides is greater than the third side then it is a triangle.
Now for the inverse we have to convert the given line into double negative.
Hence we get:
If the 2 smallest sides sum is not larger than the 3rd side, then it is not a triangle
Conditional statements are part of mathematical reasoning, a vital skill that enables students to evaluate a given hypothesis without reference to a particular context or meaning. Simply put, when a scientific research or allegation is studied, the logic isn't truly founded on an individual's perspective. Deductions and evidence must have factual and scientific foundations.
the various types of conditional statements are:
When the conditional statement's hypothesis and conclusion are both untrue, it is referred to as an inversion of the statement.If both a hypothesis and a conclusion are false at the same time, the statement is contrapositive.A statement is said to be biconditional when it is both conditional and converse at the same time, satisfying both conditions as true.Top learn more about inverse of a statement visit:
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Darnell spent 10 hours doing homework. Marie did homework for 4/5 as many
hours as Darnell did. How many hours did Marie spenddoing homework?
Marie did her homework in 8 hours.
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Answer:
the shorter leg = 9mm
the longer leg = 12mm
the hypotenuse is 15mm
Step-by-step explanation:
x^2 +(x+3)^2 =(x+6)^2
x^2 + x^2 + 6x +9=x^2 + 12x +36
x^2-6x-27=0
(x+3)(3-9)=0
x=-3 (impossible) ... or x=9
Which congruence postulate could prove TriangleAEM = TriangleDEN
Triangle AEM is congruent to triangle DEN by SAS congruence criterion.
What do you mean by congruence of triangle?
Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. If moved, they coincide with one other. The sign of congruence is’ ≅’. After proving triangles congruent, the remaining dimension can be predicted without actually measuring the sides and angles of a triangle.
In triangle AEM and triangle DEN
AE = DE (Given)
ME = NE (As In triangle MEN , angle M = angle N and sides opposite to equal angles are equal)
angle MEA = angle NED (Vertically opposite angles)
Triangle AEM ≅ Triangle DEN (By SAS congruence criterion)
Therefore, both the trinagles are congruent by SAS congruence criterion.
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A cat’s heart beats approximately 45 times in 15 seconds. At this rate how many times does the cat′s heart beat per second?
Work Shown:
45 beats = 15 seconds
45/15 beats = 15/15 seconds
3 beats = 1 second
To convert to beats per minute (bpm), multiply by 60.
Given ∠4≅∠14, which lines, if any, must be parallel based on the given information? Justify your conclusion. Responses a∥b, converse of the same-side interior angles theorem a is parallel to b, , converse of the same-side interior angles theorem a∥b, converse of the alternate interior angles theorem a is parallel to b, , converse of the alternate interior angles theorem a∥b, converse of the corresponding angles theorem a is parallel to b, , converse of the corresponding angles theorem not enough information to make a conclusion not enough information to make a conclusion Two horizontal, parallel lines, line c and line d, where line c is above line d. These lines are intersected by two diagonal parallel lines, line a and line b. Line a is to the left of line b. The angles created by each intersection are numbered. From top left, going clockwise, the angles where line a intersects line c are labeled eleven, ten, nine, and twelve. The angles where line b intersects line c are labeled seven, six, five, and eight. The angles where line a intersects line d are labeled fifteen, fourteen, thirteen and sixteen. The angles where line b intersects line d are labeled three, two, one and four. Skip to navigation
If ∠4 ≅ ∠14, then the lines that must be parallel are a and b and so we can say that; a∥b, Converse of the Alternate Interior Angles Theorem
What are Interior Angles?Interior angles are basically the pair of angles created on the inner side of the parallel lines and right on the opposite sides of the transversal when two parallel lines are intersected by a transversal .
We are told that ∠4 ≅ ∠14, which lines,
If a transversal connects two parallel lines, we know that the corresponding angles and vertically opposite angles are equivalent.
Thus, angle 4 is congruent to angle 14.
Therefore, we can deduce the following;
Angle 15 is a corresponding angle to angle 3 and so we can write that;
∠15 ≅ ∠3
Angle 15 is a vertically opposite angle to angle 13 and so we can write that; ∠15 ≅ ∠13
By transitive property of equality, we can say that;
∠3 ≅ ∠13 [Alternate interior angles]
Thus, we have ∠4 ≅ ∠14
Therefore, we conclude that a∥b, Converse of the Alternate Interior Angles Theorem.
Hence, the correct answer would be an option (B).
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a large company states in its promotional literature that 74% of its employees have college degrees. assume this claim is true. if 3 employees are selected at random from this company, what is the probability that at least 1 of the selected employees will not have a college degree?
The probability of having at least one employee not have a college degree is 0.595
Here it is given that the 74% of employees have a college degree.
Hence, the probability of one employee having a college degree is
74/100
= 0.74
The probability that an employee does not have a college degree is
1 - 0.74
= 0.26
Hence
The above problem is clearly a Binomial distribution. with n = 120 and p = 0.26
"success" is when one employee does not have a college degree.
Therefore the probability that at least 1 employee does not have a college degree is
P(X≥1)
= 1 - P(X = 0)
A binomial distribution with sample n and probability p has a PMF
ⁿCₓ X pˣ X (1 - p)ⁿ⁻ˣ
where x is a random variable
Here
n = 3
p = 0.28
x = 0
Hence we get
³C₀ X 0.26⁰ X (0.74)³
0.405
Therefore,
P(X≥1)
= 1 - 0.405
= 0.595
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An investor borrows r11500 to buy a computer and is charged interest at an annual rate of 6 %per annum compounded quarterly. the loan has to be paid in 3 years. calculate the amount of loan that is outstanding at the end of 2 years
The loan amount at the end of 2 years is Rs. 12,127 .
In the given question we have, amount Rs. 11500 is borrowed by investor at the interest rate of 6% per annum.
compund interest is defined as the addition of interest to the principal of loan.
principal (P) = 11500
If interest is compunded quarterly then time(t) = 3 years = 12 , rate ( r%) = 6/4% = 2/3 %
Using the formula of Amount ,
Amount = P( 1 + r / 100) ᵗ
= 11500( 1 + 2/ 300)⁸
= 12127.83 ~ 12128
compound interest = Amount - principal =
12128- 11500 = Rs. 628
So, An investor has to pay total Rs. 12128 at the end of 2- year.
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Answer the following answer
As per given data of at least 48inches height is required to ride in amusement park , Michael is 42 inches tall and grow 1/2 in. every month then total months after which Michael can ride is 12 months.
As given in the question,
Minimum height require to ride in amusement park = at least 48 inches
Present height of Michael is 42 inches tall
Increase in height every month 1/2 inch.
Let 'm' months taken by Michael to ride in amusement park.
Required equation is:
48 = 42 + (1/2)m
⇒(1/2)m = 48 -42
⇒ m = 6×2
⇒ m =12 months
Therefore, for the given data of at least 48inches height is required to ride in amusement park , Michael is 42 inches tall and grow 1/2 in. every month then total months after which Michael can ride is 12 months.
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-8x-7=33 ''solve it ''
Answer:
Step-by-step explanation:
-8x-7=33
+7 +7
-8x=40
x=-5
Find all rational roots.
x(3x − 4) (x − 5) = 0
The rational roots of the given equation x(3x − 4) (x − 5) = 0 are x = 0, 4/3 and 5
What is Rational Number?
Numbers that may be expressed in the form p/q, where p and q are integers and q0, are considered rational numbers. Because fractions cannot have a negative numerator or denominator, they differ from rational numbers in this respect. Because of this, the numerator and denominator of a fraction are whole numbers (denominator 0), unlike in the case of rational numbers, when they are both integers.
So to convert a fractional to reduce form we have to divide by 10 to power how many digits thereafter decimal point, and make sure that numerator or denominator doesn't have common divisible.
x(3x − 4) (x − 5) = 0
So we can put every term equal to zero to find it's root.
1st case, x = 0
2nd, 3x-4 = 0
3x = 4
x= 4/3
3rd, x-5 = 0
x = 5
Hence, the rational roots of the given equation are x = 0, 4/3 and 5
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how many ways are there to select a set of 8 donuts from 3 varieties? donuts of the same variety are indistinguishable.
There are 336 to select a set of 8 donuts from 3 varieties, where the donuts of the same variety are indistinguishable.
here the total number of 8 donuts of a set needs to make from a given variety of 3, since here the orders so, we need to use permutations.A permutation of a set is an arrangement of its individuals into a grouping or direct order, or in the event that the set is as of now ordered, a modification of its elements. It alludes to the act or preparation of changing the direct arrange of a requested set. Permutations vary from combinations, which are determinations of a few individuals of a set in any case of an order.
the formula for permutations is :
P(n,r) = n! /(n-r)! , here n i=8 and r = 3
P(8,3) = 8! /(8-3)!
= 8* 7*6= 336
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Description of End behavior "-x^4-x^3+3x^2+2x+6"
The end behavior of the function is f(x) → -∞, as x→ -∞ and f(x) → -∞, as x→ +∞.
What is the end behavior of a function?A polynomial function's final behavior is how its graph behaves as x gets closer to positive or negative infinity.
The graph's final behavior is determined by a polynomial function's degree and leading coefficient.
For extremely big or very tiny values, the leading coefficient is more important than the other function coefficients. Therefore, it is sufficient to forecast the function's final behavior based on the sign of the leading coefficient.
The given function is -x⁴ -x³ +3x² +2x +6
The degree of the given function is even and the leading coefficient is negative. So,
End behavior is given by
f(x) → -∞, as x→ -∞
f(x) → -∞, as x→ +∞
The graph looks as follows:
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Factor completely, than place the factors in the proper location on the grid
Y^2x -y^x-20
Answer: Cannot be factored
Step-by-step explanation:
= Factor Y^2x -y^x-20
= Cannot be factored
Megan bought 60 donuts for study club. She told the worker at the donut
shop that she wanted 60% of the donuts to be chocolate glazed. How
many of the donuts should be chocolate-glazed? (hint - simplify)
Out of 60 donuts there are 36 chocolate-glazed donuts.
What is donuts?
A leavened, fried dough product is known as a doughnut or donut. It is a common sweet snack that can be made at home or bought in bakeries, supermarkets, food stands, and franchised specialty retailers. It is produced in a variety of ways.
Given: Megan bought 60 donuts for study club.
She told the worker at the donut shop that she wanted 60% of the donuts to be chocolate glazed.
Let the total donuts are 60.
And the 60% of 60 are,
60 x 0.6 = 36
Therefore, 36 donuts are chocolate - glazed.
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which of the following is a polynomial?
Answer:
Option D
Step-by-step explanation:
This is because it contains the sum of the same variable to different powers.
Quadrilateral PONY is rotated 180° about the origin.
Draw the image of the rotation
The given quadrilateral PONY is rotated to 180° as P'O'N'Y' and its coordinates are:
P': (2, -7)O': (2, -3)N': (6, -3)Y': (5, -6)What is rotation?A transformation in geometry is an action that moves, flips, or modifies a shape to produce a new shape. A rotation is an example of a transformation where a figure is rotated a set number of degrees around a fixed point (referred to as the center of rotation).The circular motion of an item around a center or axis is the definition of rotation in mathematics. The rotation of the earth on its axis is one of the best examples of rotation in nature.So, rotate the given quadrilateral at 180° as follows:
Given quadrilateral: PONY
P: (7, -2)O: (3, -2)N: (3, -6)Y: (6, -5)Rotate to 180° and plot as follows:
Quadrilateral after rotation: P'O'N'Y'
P': (2, -7)O': (2, -3)N': (6, -3)Y': (5, -6)(Refer to the graph attached below)
Therefore, the given quadrilateral PONY is rotated to 180° as P'O'N'Y', and its coordinates are:
P': (2, -7)O': (2, -3)N': (6, -3)Y': (5, -6)Know more about rotation here:
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Answer:
P': (2, -7)
O': (2, -3)
N': (6, -3)
Y': (5, -6)
Step-by-step explanation:
WILL GIVE BRAINLIST TO BEST ANSWER! EASY POINTS
write the point slope form of the equation of the line through the given points.
through (-5, -1) and (-4, -5)
Answer:
y+1=-4(x+5)
Step-by-step explanation:
it changed to point slope form so now it’s different
the equation is y-y1=m(X-x1)
y-(-1)=m(x-(-5)
y+1=m(x+5)
Now to find slope y2-y1/x2-x1
-5+1/-4+5
-4/1
-4 is the slope so we just fill it in
y+1=-4(x+5)
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The vertex of the parabola is at (-2, 2), the line of symmetry of the parabola is at x = -2 and the parabola is open downwards
From the given parabola
The vertex of the parabola is at (-2, 2)
The vertex of the parabola is defined as the the point at the intersection of the parabola and its line of symmetry.
The line of symmetry is at x = -2
The parabola is open downwards
Hence, the vertex of the parabola is at (-2, 2), the line of symmetry of the parabola is at x = -2 and the given parabola is open downwards
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Which capital letters in the word TRANSFORMATION produce the same letter after being rotated 180°?
The capital letters of the word TRANSFORMATION are rotated 180 degrees, they generate the same letter are I, N, O and S.
Define the term rotation?Geometry can be used to determine the meaning of rotation in mathematics. As a result, it is described as the movement of an object round the center or an axis.The point of rotation is the point where the object is rotated.An angle of rotation is the degree of rotation calculated in degrees.It is possible to rotate clockwise or counterclockwise. If an item needs to be rotated, there are several methods for doing so:
90 degrees counterclockwise90° counterclockwise180 degrees counterclockwiseanticlockwise 180 degreesWhen the capital letters of the word TRANSFORMATION are rotated 180 degrees, they generate the same letter: I, N, O and S.
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What is the value of log10 1000000000
Answer:
9 i think
Step-by-step explanation:
Find the value of the variables in each figure. Explain your reasoning.
The value of the variables x and y in each figure are 28 and 46.3 respectively.
What are supplementary angles?Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line.
Therefore,
5x + 40 = 180,
5x = 180 - 40
5x = 140
x = 28
Also,
(3y-1 ) and 40 are corresponding angles, thus
40 + 3y - 1= 180 ,
3y = 180 - 40 + 1
3y = 139
y = 46.3
Thus, the value of the variables x and y in each figure are 28 and 46.3 respectively.
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HELP!!
Find three consecutive odd integers that twice the sum of the second and the third is 43 more than three times the first
Answer: 31, 33, 35
Step-by-step explanation:
Can someone help me with this please! I really need it done
increase the amount of the ingredients by 5 and by 20
Using simple mathematical operations, the missing values are as follows:
(B) Dijon Mustard: 18g
Increased by 20 = 360g(C) Barbeque sauce: 70g
Increased by 5 = 350gIncreased by 20 = 1,400g(D) Worcestershire sauce: 10.35g
Increased by 5 = 51.75gIncreased by 20 = 207g(E) Kosher salt: 1.5g
Increased by 5 = 7.5gIncreased by 20 = 30g(F) Ground black pepper: 2.3g
Increased by 5 = 11.5gIncreased by 20 = 46g(G) Crushed red pepper: 1.15g
Increased by 5 = 5.75gIncreased by 20 = 23gWhat do we mean by mathematical operations?A mathematical "operation" is the process of calculating a value utilizing operands and a math operator.There are predefined rules associated with the math operator's symbol that must be applied to the supplied operands or numbers.The order of operations is a rule that outlines the proper steps to take when analyzing a mathematical equation.We can recall the PEMDAS steps in the following order: Parentheses, Exponents, Multiplication, Division (from Left to Right), Addition, and Subtraction (from left to right).So, we can calculate missing values as follows:
(B) Dijon Mustard: 18g
Increased by 20 = 18×20 = 360g(C) Barbeque sauce: 70g
Increased by 5 = 70×5 = 350gIncreased by 20 = 70×20 = 1,400g(D) Worcestershire sauce: 10.35g
Increased by 5 = 10.35×5 = 51.75gIncreased by 20 = 10.35×20 = 207g(E) Kosher salt: 1.5g
Increased by 5 = 1.5×5 = 7.5gIncreased by 20 = 1.5×20 = 30g(F) Ground black pepper: 2.3g
Increased by 5 = 2.3×5 = 11.5gIncreased by 20 = 2.3×20 = 46g(G) Crushed red pepper: 1.15g
Increased by 5 = 1.15×5 = 5.75gIncreased by 20 = 1.15×20 = 23gTherefore, using simple mathematical operations, the missing values are as follows:
(B) Dijon Mustard: 18g
Increased by 20 = 360g(C) Barbeque sauce: 70g
Increased by 5 = 350gIncreased by 20 = 1,400g(D) Worcestershire sauce: 10.35g
Increased by 5 = 51.75gIncreased by 20 = 207g(E) Kosher salt: 1.5g
Increased by 5 = 7.5gIncreased by 20 = 30g(F) Ground black pepper: 2.3g
Increased by 5 = 11.5gIncreased by 20 = 46g(G) Crushed red pepper: 1.15g
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A circle has a circumference of 3.143.143, point, 14 units.
What is the diameter of the circle?
Use 3.14 for \piπpi and enter your answer as a decimal.
The diameter of the circle is 4.45 units.
What is circle?
A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. Every line that passes through the circle forms the line of reflection symmetry. Also, it has rotational symmetry around the centre for every angle.
A line segment having both the endpoints on the circle and is the largest chord of the circle is called diameter.
Given,
the circumference of circle = 14 units
circumference = πd
14 = 3.14(d)
14/3.14 = d
d = 4.45
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Which of the following is the independent variable of F(G(x))?
O A. V
• B. x
• C. F(x)
• D. F(G(x))
Answer:
D
Step-by-step explanation:
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The maximum area is 640,000.
Given fencing yards = 3200
let the length be x and the width be y
The parameter of the rectangle is given as;
2(L + B),that is
2(x + y) = 3200
x + y = 1600
y = 1600-x
let the area of the rectangle be A, then
A = x y
A = x(1600-x)
A = 1600x - x^2
finding the maximum derivative of A with respect of x
da/dx = 1600 - 2x
set da/dx to zero,
1600 - 2x = 0
1600 = 2x
x = 1600/2
x =800
substitute the value of x = 800 in to y
y = 1600 - 800
y = 800
The maximum area is 800 x 800
Therefore Maximum area = 640,000.
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