a, With df = 6, the rejection region of t = 0.098. b. With df = 12, the rejection region of t = 0.049. c. With df = 25, the rejection region to the left of t = 2.060 and to the right of t = 0.019. d, The probability of making a Type I error is 0.05 for all cases, assuming a significance level of α = 0.05.
a. T > 1.440 where df = 6
To find the probability of T > 1.440, we need to calculate the area under the curve to the right of 1.440 in the t-distribution with df = 6.
Using a t-table or statistical software, we can find that the area to the right of 1.440 for df = 6 is approximately 0.098.
Therefore, the probability of making a Type I error is 0.098.
b. T < -1.782 where df = 12
To find the probability of T < -1.782, we need to calculate the area under the curve to the left of -1.782 in the t-distribution with df = 12.
Using a t-table or statistical software, we can find that the area to the left of -1.782 for df = 12 is approximately 0.049.
Therefore, the probability of making a Type I error is 0.049.
c. T < -2.060 or T > 2.060 where df = 25
To find the probability of T < -2.060 or T > 2.060, we need to calculate the combined area under the curve to the left of -2.060 and to the right of 2.060 in the t-distribution with df = 25.
Using a t-table or statistical software, we can find that the area to the left of -2.060 for df = 25 is approximately 0.019. The area to the right of 2.060 is also approximately 0.019.
Therefore, the total probability of making a Type I error is 0.019 + 0.019 = 0.038.
d, For each of parts a through c, the probability of making a Type I error is determined by the significance level (α) chosen for the hypothesis test.
If we assume a significance level of α = 0.05 (commonly used in hypothesis testing), then the probability of making a Type I error is 0.05 for all three cases.
In other words, if the null hypothesis is true (no effect or no difference), there is a 5% chance of incorrectly rejecting it and concluding there is an effect or a difference in the population based on the sample evidence alone.
It's important to note that the specific probability of Type I error depends on the chosen significance level, and different significance levels will result in different probabilities of Type I error.
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One circle has a circumference of 12x cm. Another circle has a circumference of 32 cm. What is the ratio of the
adius of the smaller circle to the radius of the larger circle?
O 3:8
O 8:3
O 1:3
O 3:1
56:23
21
The ratio of the radius of the smaller circle to the radius of the larger circle as required in the task is; 3:8.
What is the ratio of the radius of the smaller circle to the radius of the larger circle?It follows from the task content that the circumference of the smaller circle is; 12cm while that of the bigger circle is; 32cm.
Since, the circumference of a circle is directly proportional to the radius of the circle from the formula; C = 2πr.
The ratio is therefore; 12:32, in which case, when expressed in its simplest form is; 3:8.
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On a coordinate plane, a solid straight line has a positive slope and goes through (0, negative 1) and (3, 0). Everything above and to the left of the line is shaded.
Which linear inequality is represented by the graph?
y ≤ One-thirdx − 1
y ≥ One-thirdx − 1
y < 3x − 1
y > 3x − 1
The graphed inequality is:
[tex]y \geq \frac{1}{3}*x - 1[/tex]
Which linear inequality is represented by the graph?We know that the line is solid, and the region above and to the left is shaded, then the inequality is of the form:
y ≥ line.
Now we need to get the linear equation.
It is of the form;
y = a*x + b
Where a is the slope and b is the y-intercept. Because it passes through (0, -1), we know that the y-intercept is -1.
And knowing that the line passes through (0, -1) and (3, 0), the slope is:
[tex]a = \frac{- 1 - 0}{0 - 3} = \frac{1}{3}[/tex]
Then the inequality is:
[tex]y \geq \frac{1}{3}*x - 1[/tex]
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What is the simplified form of startroot startfraction 48 over 192 endfraction endroot?
By the use of factor decomposition and algebra properties, we conclude that the rational number 48/192 is equal to the rational number 1/4.
How to simplify rational numbers
In this question we should simplify a rational number into its simplest form based on two facts. First, that all natural numbers except 1 and the prime numbers are products of prime numbers and, second, the simplification of the fraction can be done by using the following algebra property:
(a · c)/(b · c) = a/b, where a, b, c are natural numbers. (1)
Along with power properties.
Now we proceed to simplify the rational number:
48/192 = (2⁴ × 3) / (2⁶ × 3)
48/192 = 1 / 2²
48/192 = 1 / 4
By the use of factor decomposition and algebra properties, we conclude that the rational number 48/192 is equal to the rational number 1/4.
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Answer:
4
Step-by-step explanation:
Subtract.
3 x - z + 9
3 x - 16 y - z + 9
3 x + z + 9
Answer:
1)3×-8
-24
Step-by-step explanation:
2)bshejejnenenejejkejehrh
Approximately ___% of a district’s students that are eligible for free and reduced meals are homeless at any given time.
Percentages are used to show the fraction of a thing. For example, if 5 students out of 20 like math, the percentage is 5/20 x 100= 25%
What is a Percentage?This refers to the number of ratios that is described as a fraction of 100 and is denoted by the sign %.
Hence, we can see that although your question is incomplete, I gave you a general overview of percentages for a better understanding of the concept.
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Solve each of the following equations show the solution on a number line check your answers 5-|n-1|=-2
n=8
n=-6
What is a number line?A number line is a horizontal line with evenly spaced number increments. The numbers on the line will determine how the number on the line can be answered.
The numbers on the number line increase as one moves from left to right and decrease as one moves from right to left.
Solution for the above equation 5-|n-1|=-2What is the modulus?A modulus function is a function that returns the absolute value of a number or variable. It yields the magnitude of the number of variables. It is also known as an absolute value function. This function's output is always positive, regardless of the input.
Open modulus with a positive sign.
5-|n-1|=-2
-|n-1|=-2-5
n+1= 7
n= 8
Open modulus with a negative sign.
5-|n-1|=-2
-|n-1|=-2-5
n-1= -7
n= -6
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Which measure represents the standard deviation of the sample means and is used in place of the population standard deviation when
the population parameters are unknown?
The measure represents the standard deviation of the sample means and is used in place of the population standard deviation when the population parameters are unknown is; t-test.
Which measure is used when the population parameters are unknown?A hypothesis test for a population mean when In the case that the population standard deviation, σ, is unknown, carrying out a hypothesis test for the population mean is done in similarly like the population standard deviation is known. A major distinctive property is that unlike the standard normal distribution, the t-test is invoked.
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Answer:
standard error of the mean
Step-by-step explanation:
Plato/Edmentum
A boat with some water at its bottom was found leaking again. Assume that water goes into the boat at a constant rate. 3 hours are needed to get all the water out of the boat when 10 people work together. It takes 8 hours to get all the water out if 5 people work together. How many people are needed to get all the water out in 2 hours
The Number of people is 12 when time taken is 2 hours.
According to the statement
Time taken when 10 people works is 3 hours
Time taken when 5 people works is 8 hours
Then we have to find the number of peoples when time taken is 2 hours.
So, average time that for which single person works is 180 min/ 10 = 18 min.
It means the average time for single person works is 18 min in case of 10 people.
and one thing is clear that the number of people is greater than 10 people when time taken is 2 hours.
So, The Number of people is 12 when time taken is 2 hours.
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Select the correct expressions.
A ladder that is 25 feet long is leaning against a pillar. The vertical height from the base of the pillar to the top of the ladder is 24 feet. Which
expressions represent the angle, 8, that the bottom of the ladder makes with the ground?
(answer options shown below)
Answer:
sin-1 (24/25).
Step-by-step explanation:
We are given the opposite side to the given angle (24 ft) and the hypotenuse (25 ft) .
sin = opposite / hypotenuse
- so it is sin-1 (24/25).
What is the height, x, of the equilateral triangle shown?
60°
60°
10 in.
60°
O A. 5in.
O B.
OC. 10in.
OD. 10√3in.
5√/3in.
Answer:
B
Step-by-step explanation:
Drop an altitude. Either of the two resulting right triangles with legs of length 5 and x and a hypotenuse of 10.
By the Pythagorean theorem, it follows that the answer is B.
A _______ probability of an event is a probability obtained with knowledge that some other event has already occurred.
A conditional probability of an event tells us that the event has already occured.
Given a _______ probability of an event is a ............. other event has already occurred.
We have to fill the blank with appropriate term or word associated with probability.
The right term is conditional.
Conditional probability of an event is a probability obtained with knowledge that some other event has already occured.
It is denoted as P(A I B).
It satisfies the following equation:
P(AIB)=P(A and B ) / P(B)
where P( A and B) is the probability of A and B together.
Hence conditional probability of an event is obtained with knowledge that some other event has already occured.
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What's the explicit rule for the sequence 3, -6, 12, -24, 48, ...?
Answer:
[tex]a_{n}[/tex] = 3 [tex](-2)^{n-1}[/tex]
Step-by-step explanation:
there is a common ratio between consecutive terms , that is
- 6 ÷ 3 = 12 ÷ - 6 = - 24 ÷ 12 = 48 ÷ - 24 = - 2
this indicates the sequence is arithmetic with explicit rule
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
here a₁ = 3 and r = - 2 , then
[tex]a_{n}[/tex] = 3 [tex](-2)^{n-1}[/tex]
Answer:
[tex]\sf \dfrac{-3}{2}(-2)^n[/tex]
Step-by-step explanation:
Explicit formulas are used to represent all the terms of the geometric sequence with a single formula.
[tex]\sf \boxed{\bf t_n = ar^{n-1}}[/tex]
a is the first term.
r is the common ratio.
r = second term ÷ first term.
3 , - 6 , 12, - 24, 48 ,........
a = 3
r = -6 ÷ 3 = -2
[tex]\sf t_n = 3*(-2)^{(n-1)}\\\\[/tex]
[tex]\sf = 3*(-2)^{n}*(-2)^{-1}\\\\ =3*(-2)^n*\dfrac{-1}{2}\\\\= \dfrac{-3}{2}(-2)^n[/tex]
Check:
[tex]\sf t_1 =\dfrac{-3}{2}*(-2)^1=\dfrac{-3}{2}*(-2) = 3\\\\\\t-2 = \dfrac{-3}{2}*(-2)^2 = \dfrac{-3}{2}*4=-6\\\\\\t_3=\dfrac{-3}{2}*(-2)^3=\dfrac{-3}{2}*(-8)=12[/tex]
Need help with this problem
put into quadratic formula
Answer: [tex]\frac{-7+\sqrt{49-4(15)(-12)} }{30}[/tex]
Step-by-step explanation:
Use the quadratic formula:
[tex]\frac{-b+-\sqrt{b^{2}-4(ac) } }{2a}[/tex]
Substitute the values, A = 15, b = 7, c = -12
[tex]\frac{-7+-\sqrt{7^{2}-4*(15*-12) } }{2*15}[/tex]
Simplify to answer:
[tex]\frac{-7+49-4(15)(-12)}{30}[/tex]
I hope this helps!
Question 1 of 21
Which of the following steps would you perform to the system of equations
below so that the equations have equal x-coefficients?
4x+2y = 4
12x+y = 22
O A. Divide both sides of the top equation by 3
B. Multiply both sides of the top equation by 3
C. Multiply both sides of the bottom equation by 3
OD. Divide both sides of the bottom equation by 2
PLEASE HELP ME! FAST
The quadrants in which all the coordinates given are located is; As explained below.
How to Identify Quadrants in coordinates?1) (2, 4) is located in Quadrant I where both x and y-values are positive.
2) (0, -3) is located in Quadrant II where x - values are positive but y-values are negative.
3) (-1, 1/2) is located in Quadrant IV.
4) (-2 1/2, -7) is located in Quadrant III where x and y values are both negative.
5) (0, 6) is located in Quadrant I where both x and y-values are positive.
6) (-5, 0) is located in Quadrant IV where x is negative but y is positive.
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Find the product -2/9(-5/3) I-Ready math
The product of the given fractions, -2/9(-5/3), is: 10/27.
How to Find the Product of Two Fractions?Given the fractions, -2/9(-5/3), recall that minus multiplied by minus equals plus.
So therefore, the product of the two fractions would be a positive number. Thus:
-2/9(-5/3) = (-2 × -5)/(9 × 3)
-2/9(-5/3) = 10/27
Therefore, the product is: 10/27.
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8
45°
Find the value of x.
A. 4
B. 8√√2
2
X
C. 4√2
D. 8√√2
45°
Hello,
Pythagorean theorem :
x² = 8² + 8²
x² = 64 + 64
x² = 128
x = √128
x = √(64 × 2)
x = √(8² × 2)
x = 8√2
→ Answer D
Kira exercises no less than 40 minutes per day. Use t to represent Kira's amount of exercise (in minutes per day).
Kira's time exercising every day can be represented as t ≥ 40 because she exercises for 40 minutes or more.
How can this situation be represented?This situation can be represented with an inequality. An inequality is an expression that is used to represent variables. This type of expression uses symbols such as >, < or ≥ to represent different variable values.
What inequality is represented in this situation?The expression is: t ≥ 40The inequality represented in this situation implies that Kira exercises is equal or more time than 40 minutes every day.
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Which of the following represents the divisor and the dividend for the
synthetic division problem below?
-1)29 7
OA. x+1 and 2x² +9x+7
OB. x+1 and -2*² -9x-7
OC. x-1 and 2x² +9x +7
OD. x-1 and -2*² -9x-7
The dividend is [tex]2x^2+9x+7[/tex] while the divisor is x + 1
Option A is correct
Division of polynomial using synthetic divisionThe coefficient outside the division block is -1.
This means that the divisor = x + 1
Also, the coefficients of the dividend are:
2, 9, 7
The highest exponent is 2 since there are three terms in the polynomial. Three terms show that the expression is a quadratic expression
Therefore, the dividend is [tex]2x^2+9x+7[/tex]
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Activity in this activity, you will first find the squares of positive and negative numbers. then you will determine whether the solution to an equation is a perfect square. question 1 part a complete the table by squaring each positive x-value listed.
The complete table is shown below.
What is square root?A number's square root is the factor that can be multiplied by itself to yield that number. The square root of, the end square root is the symbol for the square root. Finding an integer's square root is the inverse of squaring a number.Complete the table as follows:
[tex]2^{2} = 2*2 = 4\\3^{2} = 3*3 = 9\\4^{2} = 4*4 = 16\\5^{2} = 5*5=25\\6^{2} =6*6=36\\7^{2} =7*7=49\\8^{2} =8*8=64\\9^{2} =9*9=81\\10^{2} =10*10=100\\11^{2} =11*11=121[/tex]
Therefore, the complete table has been shown.
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The question you are looking for is here:
Complete the table by squaring each positive x-value listed 2, 3,4,5,6,7,8,9,10,11.
Please help. was due 2 days ago
Answer:
[tex]x=-\frac{1}{2},\frac{5}{2}[/tex]
Step-by-step explanation:
1) Split the second term in [tex]4{x}^{2}-8x-5[/tex] into two terms.
1- Multiply the coefficient of the first term by the constant term.
[tex]4\times -5=-20[/tex] to -8 and multiply to -−20?
2 and −10
3 - Split -8x as the sum of 2x and -10x.
[tex]4x^2+2x-10x-5[/tex]
2) Factor out common terms in the first two terms, then in the last two terms.
[tex]2x(2x+1)-5(2x+1)=0[/tex]
3) Factor out the common term [tex]2x+1[/tex].
[tex](2x+1)(2x-5)=0[/tex]
4) Solve for [tex]x[/tex].
1 - Ask: When will (2x+1)(2x-5) equal zero?
When 2x + 1 = 0 or 2x - 5 = 0
2 - Solve each of the 2 equations above.
[tex]x=-\frac{1}{2},\frac{5}{2}[/tex]
Which rule describes the composition of transformations that maps δbcd to δb"c"d"? translation of 5 units x, negative 6 units y composition reflection across y = negative x reflection across y = negative x composition translation of 5 units x, negative 6 units y. translation of 6 units x, negative 5 units y composition reflection across the y-axis reflection across the y-axis composition translation of 6 units x, negative 5 units y
The rule which describe the composition of transformations that
maps ΔBCD to ΔB"C"D" is:
Reflection across the y-axis composition translation of 6 units x,
negative 5 units y ⇒ last answer
Step-by-step explanation:
Let us revise the reflection across the y-axis , horizontal translation
and vertical translation
1. If point (x , y) is reflected across the y-axis, then its image is (-x , y)
2. If point (x , y) is translated h units to the right, then its image is
(x + h , y), if translated h units to the left, then its image is (x - h , y)
3. If point (x , y) is translated k units up, then its image is (x , y + k),
if translated k units down, then its image is (x , y - k)
∵ The vertices of triangle BCD are (1 , 4) , (1 , 2) , (5 , 3)
∵ The vertices of triangle B'C'D' are (-1 , 4) , (-1 , 2) , (-5 , 3)
∵ The x-coordinates of the vertices of Δ B'C'D' have the same
magnitude of x-coordinates of Δ BCD and opposite signs
∴ Δ B'C'D' is the image of Δ ABC after reflection across the y-axis
∵ The vertices of triangle B'C'D' are (-1 , 4) , (-1 , 2) , (-5 , 3)
∵ The vertices of triangle B''C''D'' are (5 , -1) , (5 , -3) , (1 , -2)
∵ The image of -1 is 5 and the image of -5 is 1
∴ The x-coordinates of the vertices of triangle B'C'D' are added by 6
∵ The image of 4 is -1 , image of 2 is -3 and the image of 3 is -2
∴ The y-coordinates of the vertices of triangle B'C'D' are subtracted
by 5
∴ Δ B"C"D" is the image of Δ B'C'D' by translate 6 units to the right
and 5 units down ⇒ (x + 6 , y - 5)
The rule which describe the composition of transformations that
maps ΔBCD to ΔB"C"D" is:
Reflection across the y-axis composition translation of 6 units x,
negative 5 units y
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The composition of transformations that maps BCD to B"C"D" is described by the following rule:
Composition translation of 6 units x, negative 5 units y across the y-axis last response
Let us rewrite the y-axis reflection, horizontal translation, and vertical translation.
1. If point (x, y) is mirrored across the y-axis, the image of that point is (-x , y)
2. If point (x, y) is translated h units to the right, its image is (x + h, y), and if it is translated h units to the left, its image is (x + h, y) (x - h , y)
3. If point (x, y) is translated k units up, its image is (x, y + k), but if it is translated k units down, its image is (x , y - k)
∵ Triangle BCD has (1, 4) vertices, (1, 2) vertices, and (5, 3) vertices. Triangle B'C'D' has (-1, 4) vertices, (1, 2) vertices, and (5, 3) vertices. The x-coordinates of the B'C'D' vertices have the same magnitude as the x-coordinates of BCD and opposite signs. B'C'D' is the picture of ABC after it has been reflected across the y-axis.
The vertices of triangle B'C'D' are (-1, 4), (-1, 2), (-5, 3), (1, -2)
The vertices of triangle B"C"D" are (5, -1), (5, -3), (1, -2)
The x-coordinates of the triangle B'C'D' vertices are added by 6.
The image of 4 is -1, the image of 2 is -3, and the image of 3 is -2.
The y-coordinates of triangle B'C'D' vertices are subtracted by 5.
∴ Δ B"C"D" is the image of Δ B'C'D' by translating 6 units to the right
and 5 units down ⇒ (x + 6 , y - 5)
The rule which describe the composition of transformations that
maps ΔBCD to ΔB"C"D" is:
Reflection across the y-axis composition translation of 6 units x,
negative 5 units y
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Which values of x would make a polynomial equal to zero if the factors of the
polynomial were (x-5) and (x-6)?
A. -5 and 6
B. 5 and 6
C. 5 and -6
D. -5 and -6
If the factors of the polynomial were (x-5) and (x-6), the values of x that would make the polynomial equal to zero would be 5 and 6.
5 - 5 = 0
6 - 6 = 0
Assuming the polynomial is (x-5)(x-6), if one factor is 0 then anything multiplied by 0 is still 0.
Hope this helps!
what is x and y? i am having trouble finding what x and y are
Answer:
x = 10
y =10√2
Step-by-step explanation:
45° - 45° - 90° triangle:The ratio of the sides of 45°- 45° - 90° triangle is a : a : a√2
The side opposite to angle 45° is a
a = 10
⇒ x = a
[tex]\sf \boxed{\bf x = 10}[/tex]
The side opposite to 90° is a√2
y = a√2
= 10√2
[tex]\sf \boxed{\bf y= 10\sqrt{2}}[/tex]
Answer:
y = 14.1 or 10√2Step-by-step explanation:
is an isosceles right triangle, so x = 10
to find y we use pythagoras
y = √(10²+10²)
y = √200
y = 14.1 or 10√2
Petra opens her mail one day to find that an anonymous donor has given her $3000 cash. (woohoo!) she sets aside $1000 to refurnish her apartment, and decides to invest the other $2000. unfortunately, the value of the stock swhe invested in started going down almost as soon as she invested her money. if the stock decreases at a rate of 15% per year for eight years, how much is the stock worth when she sells it eight years later?
The stock worth when she sells it eight years later $545, If the stock decreases at a rate of 15% per year for eight years.
According to the question,
Petra opens her mail one day to find that an anonymous donor has given her $3000 cash. She sets aside $1000 to refurnish her apartment, and decides to invest the other $2000.
If the stock decreases at a rate of 15% per year for eight years. In order to find the stock worth when she sells it eight years later we have the formula
Value of stock after 'n' years = Principal[1-Rate/100]ⁿ
Value of stock after '8' years = 2000[1-15/100]⁸
= 2000[1-0.15]⁸
=2000[0.85]⁸
=2000[0.2725]
=545$
Hence, the stock worth when she sells it eight years later $545, If the stock decreases at a rate of 15% per year for eight years.
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which of the following is the product of the rational expression shown below
Answer:
B
Step-by-step explanation:
[tex]\frac{x}{x-3}[/tex] × [tex]\frac{2x}{x+5}[/tex] ( no factors cancel on numerator / denominator )
= [tex]\frac{x(2x)}{(x-3)(x+5)}[/tex]
= [tex]\frac{2x^2}{x^2+2x-15}[/tex]
What is the y-value of point A? On a coordinate plane, point A is 6 units to the right and 1 unit up.
Answer:
1
Step-by-step explanation:
Points on a coordinate plane are written as (x,y) coordinates. The vertical axis is the y axis. If your point is "one unit up" its y-value is 1. (The horizontal axis is the x-axis. The x-value is 6.)
What is the degree of the polynomial? 5x² + 8x³ + 4- 6x² - 3x5
Answer:
The degree of polynomial is 5.
Step-by-step explanation:
I suppose the polynomial is [tex]\displaystyle{5x^2+8x^3+4-6x^2-3x^5}[/tex]. To find the which degree this polynomial is, we consider the highest exponent of the term which is [tex]\displaystyle{3x^5}[/tex], the 5 is our highest degree of the term and thus, 5 is our highest degree of polynomial.
Answer:
5
Step-by-step explanation:
I'm assuming that the 5 in "3x5" is supposed to be a exponent. The degree of the polynomial is the greatest of the exponents (powers) of its various terms.
I can find the 3 third side of the triangle
Answer:
15
Step-by-step explanation:
First side is 20
Second side is 20 * (3/2), as it is 1 and 1 half times longer than the first
Second side is 30(as calculated above)
65-20-30 = 15
The revenue earned from tourists in Florida was:
2018 – $4 381 million
2019 – $3 607 million
What is the percentage decrease in revenue from tourists to Florida?
Select one answer
A) 17.67%
B) 21.46%
C) 82.33%
D) 121.46%