If all other quantities are unchanged, a decrease in the sample size will lead to a wider confidence interval.
What is a sample size?
Sample size refers to the number of observations or measurements that are taken from a larger population as part of a statistical study. In statistical analysis, a sample is a subset of the population being studied, and the sample size is the number of observations or units of analysis included in the sample.
A decrease in the sample size will lead to a wider confidence interval in the construction of confidence intervals.
In statistical inference, a confidence interval is a range of values that is estimated to contain the true value of a population parameter with a certain level of confidence. The width of the confidence interval depends on several factors, including the sample size, the level of confidence, and the variability of the data.
In general, as the sample size increases, the precision of the estimate of the population parameter improves, and the width of the confidence interval decreases. Conversely, as the sample size decreases, the precision of the estimate decreases, and the width of the confidence interval increases.
Hence, if all other quantities are unchanged, a decrease in the sample size will lead to a wider confidence interval.
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Reagan created a model of a rectangular flag.
Her model is 13 inches long.
It is a model of a flag that is 39 inches long.
How many times wider is the actual flag than Reagan's model?
The actual flag is
times wider than Reagan's model.
Actual Flag
39 inches
Reagan's
Model
13 inches
CLEAR
CHECK
The number of times that the actual flag is wider than the Reagan's model would be = 3 times.
What is rectangle?A rectangle is defined as a type of quadrilateral that has opposite sides that are parallel and equal to each other and all four angles are right angles.
The actual length of the rectangular flag = 39 inches long.
The length of Reagan's model = 13 inches.
To find the number of times wider than the actual flag the model is, use the formula:
= Length of actual flag / Length of model
= 39/13 = 3.
Therefore, the number of times that the actual flag is wider than the Reagan's model is 3 times.
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I need help with my math homework
You are shown TUV below whose measure is 76°. Draw an angle bisector of
LTUV by clicking a dragging a ray out from the vertex at U.
Click and drag to draw a ray from the yellow dot.
To redraw, click and drag from the yellow dot again.
m/TUV = 76⁰
The bisector of the angle TUV is attached below.
What is an angle?
In Euclidean geometry, an angle is the shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
The steps to draw a bisector of an angle:
1) Cross both rays with an arc. Place the compass point at the vertex of the angle after opening it to any width. Swing the compass so the pencil creates an arc that spans the angle's two rays.
2) Make a vertical arc inside. Place the compass such that the point is at the spot where the first ray and the first arc connect. Swing the compass to create an arc that fits inside the angle.
3) To intersect the first interior arc, draw a second interior arc. Move the point to the spot where the first arc crosses the second ray without altering the compass's breadth. Draw an internal arc by swinging the compass and intersecting it with the initial interior arc you drew.
4) From the vertex to the spot where the arcs meet, draw a line. To make sure the line is exact, use a straightedge. This line cuts the angle in half.
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Find the area of the figure. (Sides meet at right angles.)
7 in
2 in
5 in
8 in
4 in
5 in
2 in
7 in
Answer:
36
Step-by-step explanation:
Brody runs a farm stand that sells strawberries and grapes. Each pound of strawberries sells for $2.50 and each pound of grapes sells for $2. Brody made $160 from selling a total of 72 pounds of strawberries and grapes. Graphically solve a system of equations in order to determine the number of pounds of strawberries sold, x,x, and the number of pounds of grapes sold, yy.
The number of pounds of strawberries sold and the number of pounds of grapes sold is 32 and 20 respectively.
What is equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given that the selling price of strawberries each pound = $2.50,
The selling price of grapes each pound = $2
The total earning = $160
Let x is the no of a pound of strawberries and y is the no of a pound of grapes sold, then equation will be,
x = y + 12 and 2.50x + 2y= 160
Solve the equation by substitution method;
x = 32 and y = 20
Therefore, the number of pounds of strawberries sold is 32
the number of pounds of grapes sold is 20.
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A = {red, blue, green, yellow, orange} B = {pink, blue, purple, yellow, green} Find A ⋂ B.
According to the given sets, A ⋂ B = {blue, green, yellow}.
What are sets?A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets.
A set is a mathematical model for a collection of various things.
A ⋂ B:
A set called an intersection B has components that are found in both sets A and B.
The intersection of sets A and B is shown by the symbol, which is interpreted as "An intersection B" and written as A⋂B.
The set of components shared by all sets is the intersection of two or more sets.
So, we have:
A = {red, blue, green, yellow, orange}
B = {pink, blue, purple, yellow, green}
A ⋂ B which means common elements:
A ⋂ B = {blue, green, yellow}
Therefore, according to the given sets, A ⋂ B = {blue, green, yellow}.
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Please give an answer, and thinking. Thank you.
Answer:
see explanation
Step-by-step explanation:
- 1x + 4y = 12 , that is
- x + 4y = 12 ( add x to both sides )
4y = 12 + x ( divide each term by 4 )
y = 3 + [tex]\frac{1}{4}[/tex] x
Lupe says that the product
of 4 and any number is even.
Does her statement make
sense? Explain.
Answer:
I'm not to sure what the answer is
Lupe's statement seems quite fair
When multiplied by 4, any number's pair
An even product will be produced
By this rule, we are not reduced
For example, take the number 6
Multiply it by 4, and what do you get?
The answer is 24, a multiple of 2
This confirms Lupe's statement is true
In conclusion, Lupe's statement rings true
It makes perfect sense, through and through
The product of 4 and any number
Will always be an even number.
First person to answer gets a Brainilest!!!Solve this math questions of the picture.
Answer: S wanted points I
Step-by-step explanation:
POSSIBLE POINTS: 25
Ashanti has two bank accounts. Account A has $800, and she withdraws $50 per month for food.
Account B has $100, and she adds $30 per month from babysitting. When does account A and B have
the same amount of money in it?
Ron got a cell phone rate of C(a)=0.22+0.10a. Graph the cost per minute. How much will a five minute call cost?
The cost of the five-minute call will be equal to $0.72.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Ron got a cell phone rate of C(a)=0.22+0.10a. The cost of a five-minute call will be calculated as,
Cost = 0.22+0.10a
Cost = 0.22 + ( 5 x 0.10 )
Cost = 0.22 + 0.50
Cost = $0.72
The five-minute call will cost $0.72.
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In two or more complete sentences, explain how to use ordered pairs of points in f(x) = 2x + 5 and g(x)= x-5/2 to determine if f(x) and g(x) are inverses of each other. PLEASE EXPLAIN WITH WORDS IN TWO SENTENCES I NEED HELP ASAP
Answer:
See below.
Step-by-step explanation:
The given functions f(x) and g(x) are linear functions. Therefore, their inverses are a reflection about the line y = x.
The mapping rule for reflecting a point about the line y = x is:
(x, y) → (y, x)To determine if f(x) and g(x) are inverses of each other:
Input the x-value of the ordered pair into one function.Input the y-value of the ordered pair as the x-value of the other function.If the y-value of one function equals the x-value of the other function (and the x-value of one function equals the y-value of the other function), the functions are inverses of each other.
Given functions:
[tex]\begin{cases}f(x) = 2x+5\\\\g(x)=\dfrac{x-5}{2} \end{cases}[/tex]
Ordered pair: (2, 9)
Substitute x = 2 into f(x):
[tex]\implies f(2)=2(2)+5=9[/tex]
Substitute x = 9 into g(x):
[tex]\implies g(9)=\dfrac{9-5}{2}=2[/tex]
Therefore, the functions are inverses of each other since the x-value of function f equals the y-value of function g, and the y-value of function f equals the x-value of function g.
1 Select the correct answer. A group of 8 friends (5 girls and 3 boys) plans to watch a movie, but they have only 5 tickets. How many different combinations of 5 friends could possibly receive the tickets? A. 13 B. 40 C. 56 D. 64 Reset Next
The different combinations of 5 friends could possibly receive the tickets are 56.
What is combination?
A combination is a choice made from a set of distinct items in mathematics where the order of the choices is irrelevant.
The definition of a combination is "An arrangement of objects where the order in which the objects are chosen does not matter." A combination is a "selection of things" where the importance of the order of the things is negligible.
Given:
A group of 8 friends (5 girls and 3 boys) plans to watch a movie.
We have to find the different combinations of 5 friends could possibly receive the tickets.
Here there are total 8 friends.
We have to select 5 from 8 in 8C5 ways.
[tex]8_C_5 = \frac{8!}{5!*(8-5)!} \\8_C_5 = \frac{8!}{5!*3!} \\8_C_5 = \frac{6*7*8}{1*2*3}\\ 8_C_5 = 56[/tex]
Hence, the different combinations of 5 friends could possibly receive the tickets are 56.
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Here are yesterday's high temperatures (in Fahrenheit) in 13 U.S. cities.
50, 51, 55, 55, 59, 59, 64, 67, 67, 74, 77, 78, 80
Notice that the temperatures are ordered from least to greatest.
Give the five-number summary and the interquartile range for the data set.
Five-number summary
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum:
Interquartile range:
Answer:
To find the five-number summary for a set of data, we need to find the minimum, first quartile, median, third quartile, and maximum of the data. To find the interquartile range, we subtract the first quartile from the third quartile.
The minimum temperature in the list is 50 degrees Fahrenheit. The maximum temperature is 80 degrees Fahrenheit. To find the median, we need to first find the middle value in the list. Since there are 13 temperatures in the list, the middle value is the seventh temperature, which is 64 degrees Fahrenheit.
To find the first and third quartiles, we need to divide the list into two halves at the median. The first half of the list contains the first six temperatures, and the second half contains the last six temperatures. The median of the first half of the list is the average of the third and fourth temperatures, which is 55 degrees Fahrenheit. The median of the second half of the list is the average of the sixth and seventh temperatures, which is 61.5 degrees Fahrenheit.
Therefore, the five-number summary for this data set is:
Minimum: 50
Lower quartile: 55
Median: 64
Upper quartile: 61.5
Maximum: 80
The interquartile range is the difference between the upper and lower quartiles, which is 61.5 - 55 = 6.5.
Shana makes a 3 gallon batch of lemonade. Each 1 gallon batch requires 2.5 pints of fresh lemon juice. How many cups of lemon juice will Shana need for 3 batches?
what is the slope of the line
Answer:
a) 9/5
Step-by-step explanation:
Formula we use,
→ Slope (m) = (y2 - y1)/(x2 - x1)
Now required slope will be,
→ m = (y2 - y1)/(x2 - x1)
→ m = (-16 - 2)/(-10 - 0)
→ m = (-18)/(-10)
→ m = 18/10
→ [ m = 9/5 ]
Hence, the slope is 9/5.
What is the geometric mean of 7 and 12? 09.5
02/21
04√21
Answer:
9.16
Step-by-step explanation:
formula for Geometric mean is
b = √a × √c
a = 7 and c = 12
b = √ 7×12
b = √84
b = 9.16
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27 km equals about how many miles?
27 kilometers to miles
1 kilometer = 0.621371 miles
27 kilometers * 0.621371 miles = [tex]\fbox{16.777 miles}[/tex]
Which number line models the expression 1/8-(-3/4) ?
Answer: 7/8
Step-by-step explanation:
Please help with question 1.
Answer:
reflection over the y-axistranslation left 4, down 3Step-by-step explanation:
You want two transformations that will map segment AB to segment A"B", where the points are A(1, 1), B(5, 3), A"(-5, -2), B"(-9, 0).
ReflectionWe notice that the difference B-A is (5 -1, 3 -1) = (4, 2), and the difference B"-A" is (-9 -(-5), 0 -(-2)) = (-4, 2). These values have the same magnitudes, so we know no dilation is involved. The sign of the x direction of the segment has been reversed, which means the segment has been reflected horizontally. (B" is left of A", where B is right of A.)
Reflection over any vertical line will do, but the simplest is reflection over the y-axis.
The first transformation can be reflection over the y-axis.
TranslationThe reflected line segment will be ...
(x, y) ⇒ (-x, y)
A(1, 1) ⇒ A'(-1, 1)
B(5, 3) ⇒ B'(-5, 3)
The value that must be added to A' to move it to A" is ...
A" -A' = (-5, -2) -(-1, 1) = (-5 -(-1), -2-1) = (-4, -3) . . . . . . left 4, down 3
Similarly, the value that must be added to B' to move it to B" is ...
B" -B' = (-9, 0) -(-5, 3) = (-9 -(-5), 0 -3) = (-4, -3) . . . . . . left 4, down 3
That is, the entire segment A'B' can be moved to A"B" by a translation left 4 and down 3.
The second transformation can be translation left 4 and down 3.
__
Additional comment
The translation left could be accomplished by reflection over the line x = -2 instead of the y-axis.
The movement of the line segment could be accomplished in one transformation by rotation 126.87° clockwise about the point (-1.25, -2). The exact angle is arctan(-4/3) in the second quadrant.
Sarah made a floral arrangement with 60% roses. If there were a total of 25 flowers in the arrangement, how many roses?
Answer:
Step-by-step explanation:
turn percentage into decimal :
60/100 = 0.6
Then times it by how many flowers there are :
0.6×25 = 15
And your answer should be 15.
Consider the two expressions 6x^3 + 9x^2 + 4x + 7 and 3x^2 + 2 + 6x^3 + 6x^2 + 4x + 5.
a) Show that the two expressions represent equal numbers when x=10.
b) Explain why these two expressions do not represent equal numbers when x = -3/2.
c) Show that these two expressions represent equal numbers for all x other than x = -3/2.
When x = 10 the equations are equal and when x gets any value the two equations are equal.
What is equation ?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."
The equals sign is a part of mathematical expressions known as equations. Often, algebra is used in equations. When a calculation requires an exact number but you don't know it, algebra is utilized.
When x = 10 the equation becomes
6x³ + 9x² + 4x + 7
6(10)³ + 9(10)² + 4(10) + 7
= 6000 + 900 + 40 + 7
= 6947
6x³ + 3x² + 6x² + 4x + 5 + 2
= 6x³ + 9x² + 4x + 7
= 6(10)³ + 9(10)² + 4(10) + 7
= 6000 + 900 + 40 + 7
= 6947
Both the equations are equal when x = 10
When x = -3/2 the equation becomes
6x³ + 9x² + 4x + 7
6(-3/2)³ + 9(-3/2)² + 4(-3/2) + 7
= -20.25 + 20.25 + 6 + 7
= 13
6x³ + 3x² + 6x² + 4x + 5 + 2
= 6x³ + 9x² + 4x + 7
= 6(-3/2)³ + 9(-3/2)² + 4(-3/2) + 7
= -20.25 + 20.25 + 6 + 7
= 13
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use implicit differeniation to find dy/dx x^2+xy+y^2+1=0
The differentiation of the given function x² + xy + y² + 1 = 0 will be 2x + y + dy/dx(x + 2y) = 0.
What is the rate of change?The rate of change is the change of a quantity over 1 unit of another quantity.
Most of the time the rate of change is the change with respect to time.
As per the given,
x² + xy + y² + 1 = 0
Take the first derivative on both sides with respect to x as,
d/dx(x² + xy + y² + 1) = d/dx(0)
2x + xdy/dx + ydx/dx + 2ydy/dx + 0 = 0
2x + x(dy/dx) + y + 2y (dy/dx) = 0
2x + y + dy/dx(x + 2y) = 0
Hence "The provided function x2 + xy + y2 + 1 = 0 will be differentiated as 2x + y + dy/dx(x + 2y) = 0.".
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Two tailors, Zoe and Wanda, sit down to do some embroidery. Zoe can embroider 2 shirts per hour, and Wanda can get through 6 shirts per hour. In addition, the tailors had previously finished some shirts. Zoe has already completed 14 shirts, and Wanda has completed 6 shirts. Zoe and Wanda decide to take a break when they have finished the same total number of shirts. How long will that take? How many shirts, in total, will each tailor have finished?
After 2 hours, Zoe and Wanda will complete the same total number of shirts.
Each tailor will finish 18 shirts.
What is linear equation?
An algebraic equation of the form y=mx+b is referred to as a linear equation. m is the slope, and b is the y-intercept, and all that is involved is a constant and a first-order (linear) term. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Given that,
Zoe can embroider 2 shirts per hour, and Wanda can get through 6 shirts per hour. Zoe has already completed 14 shirts, and Wanda has completed 6 shirts.
Assume that after x hours they have finished the same total number of shirts.
The number of shirts that Zoe finished is
Z(x) = 14 + 2x ....(i)
The number of shirts that Wanda finished is
W(x) = 6 + 6x ...(ii)
When they make same number of shirts, then Z(x) = W(x)
14 + 2x = 6 + 6x
6 + 6x = 14 + 2x
Subtract 2x from both sides:
6x - 2x = 14 - 6
4x = 8
Divide both sides by 4
x = 8/4
x = 2.
Putting x = 2 in Z(x) = 14 + 2x:
Z(2) = 14 + (2×2)
Z(2) = 18
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One number is 5 more than twice another and their sum is 23. Find the numbers.
The value of the numbers 'x' and 'y' will be 6 and 17, respectively.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
One number is 5 more than twice another and their sum is 23.
Let the two numbers be 'x' and 'y'. Then the equations are given as,
y = 2x + 5 ...1
x + y = 23 ...2
From equations 1 and 2, then we have
x + 2x + 5 = 23
3x + 5 = 23
3x = 23 - 5
3x = 18
x = 6
Then the value of the variable 'y' will be given as,
6 + y = 23
y = 23 - 6
y = 17
The value of the numbers 'x' and 'y' will be 6 and 17, respectively.
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A parabola has an axis of symmetry at x = 5/12. The distance between its roots is 13/6. What is the equation of the parabola?
Answer:
The axis of symmetry of a parabola is the line that divides the parabola into two mirror images. This line always passes through the vertex of the parabola. For a parabola with an axis of symmetry at x = 5/12, the vertex of the parabola is at the point (5/12, 0).
The distance between the roots of a parabola is the distance between the x-coordinates of the two points where the parabola crosses the x-axis. In this case, the distance between the roots is 13/6.
To find the equation of the parabola, we can use the vertex form of the equation, which is given by y = a(x - h)^2 + k, where (h, k) is the coordinates of the vertex and a is a constant. In this case, the coordinates of the vertex are (5/12, 0) and the constant a can be determined using the distance between the roots.
To find a, we can use the fact that the distance between the roots of a parabola is equal to the square root of the product of the coefficients of the quadratic terms in the equation. In the vertex form, the coefficient of the x^2 term is a, so we can set up the following equation to find a:
(13/6)^2 = a * (5/12)^2
Solving for a, we find that a = -1/3.
Therefore, the equation of the parabola is y = -1/3(x - 5/12)^2.
A school is painting its logo in the shape of a triangle in the middle of its sports field. The school wants the height of the triangle to be feet. The area of the logo must be at most 14 square feet. (The school doesn't want to buy more paint.) Write an inequality that describes the possible base lengths (in feet) of the triangle.
Use b for the base length of the triangular logo.
The inequality that describes the base length of the triangle is b ≤ 28/h
How to determine the inequality that describes the base length of the triangle?From the question, we have the following parameters that can be used in our computation:
Base = bHeight = hArea = At most 14 square feetThe area of a triangle can be calculated using the following formula
Area = 1/2 * Base * Height
Substitute the known values in the above equation, so, we have the following representation
Area = 1/2 * b * h
Evaluate the products
Area = 1/2bh
Recall that
Area = At most 14 square feet
This means that
Area ≤ 14
So, we have
1/2bh ≤ 14
Multiply through by 2
bh ≤ 28
Divide both sides by h
b ≤ 28/h
Hence, the inequality is b ≤ 28/h
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this is serious pls help ASAPPPPPPPPPPPPPPPPPPPPPP its due in 25 mins
Answer:
14,641
Step-by-step explanation:
11^4 = 11 × 11 × 11 × 11 = 121 × 11 × 11 = 1331 × 11 = 14,641
Answer:
14,641
Step-by-step explanation:
10^4 = 10000
11^4 > 10 ^4 so A is the answer
Unit rate reasoning down
In the unit rate between two units, the denominator is always one.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
Unit rate is written in a fraction form where the denominator is always one.
Example:
6 miles in 3 minutes.
This can be written as,
6 miles = 3 minutes
Dividing 3 on both sides.
2 miles = 1 minute
= 2 miles per minute
Thus,
In the unit rate between two units, the denominator is always one.
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Select the correct answer.
Which list orders the angles of triangle ABC from smallest to largest measure?
B
OA.
B.
O C.
OD.
130
180
ZA, ZC, ZB
ZC, ZA, ZB
ZB, ZC, ZA
ZA, 2B, 2C
120
Answer:
<B, <C, <A
Step-by-step explanation:
The order from smallest to largest angle is the same as the order from shortest to longest opposite side.
Sides from shortest to longest:
120, 130, 180
Angles from smallest to largest:
<B, <C, <A