In a paint-drying situation with a null hypothesis H0: μ = 73 and an alternative hypothesis Ha: μ < 73, a random sample of n = 25 observations is taken. We are given x = 72.3 and σ = 6. We need to determine (a) how many standard deviations below the null value x = 72.3 is, (b) the conclusion using α = 0.005, (c) the value of Φ(70) for α = 0.005, (d) the required sample size to ensure Φ(70) = 0.01, and (e) the probability of a type I error when α = 0.01 and n = 100.
(a) To determine the number of standard deviations below the null value x = 72.3, we calculate z = (x - μ) / σ. Plugging in the values, we have z = (72.3 - 73) / 6, giving us z = -0.12.
(b) To make a conclusion using α = 0.005, we calculate the test statistic z = (x - μ) / (σ / √n) and compare it to the critical value. The critical value for α = 0.005 in a left-tailed test is approximately -2.576. If the calculated test statistic is less than -2.576, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
(c) To find Φ(70) for α = 0.005, we calculate the test statistic z = (70 - μ) / (σ / √n) using the values provided. Then we find Φ(z) using a standard normal distribution table.
(d) To determine the required sample size for Φ(70) = 0.01, we find the z-score corresponding to Φ(70) = 0.01 using a standard normal distribution table. We then rearrange the formula for the test statistic z = (x - μ) / (σ / √n) to solve for n.
(e) To calculate the probability of a type I error when α = 0.01 and n = 100, we find the test statistic z = (x - μ) / (σ / √n) and compare it to the critical value for a left-tailed test. The probability of a type I error is the area under the curve to the left of the critical value.
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Evaluate 3x for x = -2, x = 1, and x = 3.
A) 1/9, 3,27
B) ¹/3, 0, 9
C) 9,3, 27
D) 1/9, 9, 27
Answer:
A) 1/9, 3, 27
Step-by-step explanation:
i think you mean 3^x (and not 3x).
because otherwise none of the answer options withdraw makes any sense.
3^-2 = 1/(3²) = 1/9
3¹ = 3
3³ = 27
_____ is a quantitative statistical analysis that compares and combines the results of individual but similar studies.
"Meta Analysis" is a quantitative statistical analysis that compares and combines the results of individual but similar studies.
What is meta analysis?A quantitative statistical analysis of numerous distinct but related experiments or research to assess the statistical significance of the pooled results.
Some characteristics of meta analysis are-
The statistical method for merging data from various studies is called meta-analysis. Meta-analysis can be used to pinpoint this common impact when the treatment effect (or effect size) is constant from one trial to the next. Meta-analysis can be performed to determine the cause of variance in the effect when it differs between studies.Regulatory agencies occasionally demand a meta-analysis as part of the approval process, which pharmaceutical companies employ to obtain clearance for new medications. Meta-analysis is used by clinicians and applied researchers in a variety of sectors, including medicine, education, psychology, criminal justice, and many more, to identify which therapies are most effective.To know more about Meta-analysis, here
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First consider the system of equations y = -1/2 x + 1 and y = x - 5. Then consider the system of inequalities y > -1/2x+1 and y < x-5. When comparing the number of solutions in each of these systems, which statement is true?
Both systems have an infinite number of solutions.
The system of equations has more solutions.
The system of inequalities has more solutions.
Both systems have only one solution.
we conclude that the system of inequalities has more solutions than the system of equations.
What can we conclude about the two given systems?We have the system of equations:
y = (-1/2)*x + 1
y = x - 5
And the system of inequalities:
y > (-1/2)*x + 1
y < x - 5
First, if you look at the first system you can see that we have two non-parallel lines, so that system has only one solution.
Now let's look at the system of inequalities, we can get solutions like:
x = 10
y = 1
1 > (-1/2)*10 + 1 = -4
1 < 10 - 5 = 5
So both inequalities are true, which means that the point (10, 1) is a solution.
And also is the point (11, 1), and (12, 1), and infinite other points.
Then we conclude that the system of inequalities has more solutions than the system of equations.
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Drag the values to the correct locations to write this series using sigma notation and find the sum of the terms. Not all values will be used.
45 + [45 − 2.5] + ⋯ + [45 − 4(2.5)]
Answer:
[tex]\displaystyle \\\sum_{k=0}^4 45-2.5k=200[/tex]
Step-by-step explanation:
We start off with the term 45 and decrease by 2.5 each term, ending with four 2.5's subtracted from 45.
Therefore, our index starts at k=0 and ends at 4. The general term can be defined then as [tex]\displaystyle \\\sum_{k=0}^4 45-2.5k[/tex] and evaluating yields 200.
Which set describes the domain of p(h)? {h| 0 ≤ h ≤ 40} {h| 0 ≤ h ≤ 60} {p(h)| 0 ≤ p(h) ≤ 1,400} {p(h)| 0 ≤ p(h) ≤ 1,800}
The set {h| 0 ≤ h ≤ 60} describe the domain of p(h).
According to the statement
We have given that the brenton gets paid $20 per hour for the first 40 hours he works in a week. For any hours above that, he is paid overtime at $30 per hour.
and we have to find that the those set which describes the domain of p(h).
So,for this purpose
In this case, the domain represents the set of hours he is permitted to work
From the question, we understand that he cannot work more than 60 hours
This means that, the least number of hours to work is 0, and the highest is 60
So, the domain is 0 to 60
When represented properly, the domain of P(h) is (b) {h| 0 ≤ h ≤ 60}.
So, The set {h| 0 ≤ h ≤ 60} describe the domain of p(h).
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Disclaimer: This question was incomplete. Please find the full content below.
Question:
Brenton’s weekly pay, P(h) , in dollars, is a function of the number of hours he works, h. He gets paid $20 per hour for the first 40 hours he works in a week. For any hours above that, he is paid overtime at $30 per hour. He is not permitted to work more than 60 hours in a week. Which set describes the domain of P(h)? {h| 0 ≤ h ≤ 40} {h| 0 ≤ h ≤ 60} {P(h)| 0 ≤ P(h) ≤ 1,400} {P(h)| 0 ≤ P(h) ≤ 1,800
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Answer:
B.{h|0<h<60}
Step-by-step explanation:
Create a factorable polynomial with a GCF of 5z. Rewrite that polynomial in two other
equivalent forms. Explain how each form was created. (10 points)
The polynomial is P(z) = 5z * (z - 1) and the equivalent forms are P(z) = 5z^2 - 5z and P(z) = -5z + 5z^2
How to create the polynomial?The GCF is given as:
GCF = 5z
This means that the polynomial can be represented as:
P(z) = GCF * Another factor
We can make use of the following function
P(z) = 5z * (z - 1)
Expand
P(z) = 5z^2 - 5z
Rewrite as:
P(z) = -5z + 5z^2
Hence, the polynomial is P(z) = 5z * (z - 1) and the equivalent forms are P(z) = 5z^2 - 5z and P(z) = -5z + 5z^2
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A rectangle’s area is 18 m2 it perimeter is 18 m one side is
Step-by-step explanation:
hello : here is an solution
A box contains colored jelly beans. There are 14 red, 6 yellow, and x blue jelly beans in the bag. If the probability of drawing a yellow jelly beans is 1/4, what is the value of x?
Answer:
4
Step-by-step explanation:
If the probability of drawing a yellow jelly beans is 1/4, the box is has 1/4 yellow jellybeans.
1/4b=6
b=24
14+6+x=24
20+x=24
x=4
Answer:
36 blue jelly beans
Step-by-step explanation:
We can find the total number of jelly beans by adding all red, yellow, and blue jelly beans together.
14+6+x
This simplifies to 20+x
For probability, it is (the number of things you want)/(the total number of things there are).
If the probably of drawing a yellow jelly bean is 1/4, we can set up this equation:
[tex]\frac{14}{20+x}=\frac{1}{4}[/tex]
We can cross multiply:
[tex]20+x=14(4)\\x+20+56\\x=36[/tex]
There are 36 blue jelly beans.
can someone helpp cuz this is confusing me
Answer:
4. b) an angle
5. b) the angles of a triangle
6. b) opposite, hypotenuse and adjacent
Step-by-step explanation:
4. To find sine, cosine, tangent, you use the sin, cos, tan key of the calculator.
If you are given the value of the sin, cos, tan, and you are looking for the angle, then you use the second function of the calculator.
Answer: b) angle
5. angles of a triangle
6. The sides that form the right angle are the legs. In trig, there is an angle of interest, so to distinguish between the legs, one leg is called the adjacent leg, and the other leg is called the opposite leg. The side opposite the right angle is the hypotenuse.
Answer: opposite, hypotenuse and adjacent
Please help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
a) x = 1.5 or x = -0.3
b) x = 5 or x = -8
Explanation:
Quadratic formula:
[tex]\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \quad when \:\: ax^2 + bx + c = 0[/tex]
Here given equation: 5x² - 6x - 2 = 0
Identify variable constants: a = 5, b = -6, c = -2
Putting these values into equation:
[tex]\sf x = \dfrac{ -(-6) \pm \sqrt{(-6)^2 - 4(5)(-2)}}{2(5)}[/tex]
[tex]\sf x = \dfrac{ 6 \pm \sqrt{36 + 40}}{10}[/tex]
[tex]\sf x = \dfrac{ 6 \pm \sqrt{76}}{10}[/tex]
[tex]\sf x = \dfrac{ 3\pm \sqrt{76}}{5}[/tex]
[tex]\sf x = \dfrac{ 3+ \sqrt{76}}{5} \quad or \quad \dfrac{ 3- \sqrt{76}}{5}[/tex]
In one decimal point:
[tex]\sf x = 1.5 \quad or \quad -0.3[/tex]
b) Here use "middle term split" method
⇒ x² + 3x = 40
relocate
⇒ x² + 3x - 40 = 0
The factors of 40 are 8 and 5
⇒ x² + 8x - 5x - 40 = 0
factor common terms
⇒ x(x + 8) - 5(x + 8) = 0
collect into groups
⇒ (x - 5)(x + 8) = 0
set to zero
⇒ x - 5 = 0 or x + 8 = 0
relocate
⇒ x = 5 or x = -8
Step-by-step explanation:
a) The quadratic formula can help find answers to a quadratic equation when it is equal to 0. The formula is [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex] for a quadratic equation of the form [tex]ax^2+bx+c=0[/tex].
In this question, a is 5, b is -6, and c is -2. Let's put them in the equation and solve.
[tex]x=\frac{6\pm\sqrt{(-6)^2-4(5)(-2)}}{2(5)}\\x=\frac{6\pm\sqrt{36+40}}{10}\\x=\frac{6\pm\sqrt{76}}{10}\\x=\frac{6\pm2\sqrt{19}}{10}\\x=\frac{3\pm\sqrt{19}}{5}[/tex]
This means that the value of x is both [tex]\frac{3+\sqrt{19}}5[/tex] and [tex]\frac{3-\sqrt{19}}5[/tex], since both values make x equal to 0. Putting both into the calculator, we get that [tex]x=1.5[/tex] or [tex]x=-0.3[/tex].
b) We can easily solve this equation using factoring, which turns a quadratic into two factors, and finds the solutions by setting both to 0. This will only work if the quadratic is equal to 0.
[tex]x^2+3x-40=0[/tex]
Now, we have to find two numbers that add to 3 and multiply to -40. The numbers 8 and -5 work, as 8-5=3 and 8*-5 is -40.
we can now make our factors x+8 and x-5
[tex](x+8)(x-5)=0[/tex]
If two numbers, say A and B, are being multiplied and equal 0, then either A is 0, or b is 0, or both. Similarly, if x+8 and x-5 are being multiplied and equal 0, either x+8 = 0, or x-5=0.
[tex]x+8=0\\x=-8[/tex] [tex]x-5=0\\x=5[/tex]
This makes our solutions x=-8 and x=5.
If you are not familiar with factoring or the process I have went through above, I highly recommend learning about it.
Joe is thinking of an integer. The opposite of his number is greater than
the number itself. Which of the following must be true of Joe’s number?
Answer: Joe's number is a negative number.
Since the number's opposite is greater in value, the number's value is in the negatives.
PLEASE HELP ASAP!!!!
The location of the points on Cartesian plane are listed below:
Figure 1: A(x, y) = (0, 4), B(x, y) = (5, 0)
Figure 2: A(x, y) = (8.5, 4), B(x, y) = (2.5, 1.5)
How to write coordinates in a rectangular system
A point on a Cartesian plane can be represented by rectangular system of coordinates with the form:
(x, y)
Where:
x - Distance along the x-axis respect to origin.y - Distance along the y-axis respect to origin.Now we proceed to represent each point:
Figure 1: A(x, y) = (0, 4), B(x, y) = (5, 0)
Figure 2: A(x, y) = (8.5, 4), B(x, y) = (2.5, 1.5)
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can someone pls help me on this
Answer:
The answer is X=3/4 or -1/2
Please help. will give brainliest
Answer:
the 4th answer option. W = 153°, P = 71°
Step-by-step explanation:
PQRS ~ TUVW
that means both figures are similar.
and that means that the angles at the corresponding vertexes are the same, and all 4 corresponding sides (and any other pair of corresponding lines like diagonals) have the same scaling factor.
we see due to the proportions of the different parts of the shapes
U corresponds to Q.
T corresponds to P.
W corresponds to S.
V corresponds to R.
therefore, as the angle at S = 153°, so is W.
and as the angle at T = 71°, so is P.
7. In a regular polygon, adjacent interior and exterior angles are congruent
What is the name of the polygon?
(1) triangle
(2) rectangle
(4) hexagon
lor
(3) square
Answer:
This would be true for a rectangle and a square.
Step-by-step explanation:
Rectangles and square have 90 angles. The exterior angles would also equal 90 because 90 + 90 is 180. An interior angle and the exterior angle are supplements (add together to 180).
Can you help me with the exercise 3. A 3.B and the number 5. Too please .
3a) The coordinate of R after dilation is; R' = (-6, 21)
3b) The coordinate of T after dilation is; T' = (1, 3)
5) A dilation by a scale factor of 2 followed by a translation right 1 up 3.
How to carry out dilation in Transformation?3a) We are given the coordinates of the rectangle as;
Q(-2, -1), R(-2, 7), S(4, 7), T(4, -1)
Now, we are told that R(-2, 7) is dilated about the origin with a scale factor of 3. Thus;
R' = (-2 *3), (3 * 7)
R' = (-6, 21)
3b) We are now told that T(4, -1) is dilated by a scale factor of 1/2 with R as center of origin. R has a coordinate of (-2, 7). Thus;
Coordinate of T' = (-2, 7) + ¹/₂((4, -1) - (-2, 7))
Coordinate of T' = (-2, 7) + ¹/₂(6, -8)
Coordinate of T' = (-2, 7) + (3, -4)
Coordinate of T' = (1, 3)
5) We can see that LN is 2 units while L'N' is 4 units and so we can say scale factor in the transformation of ΔLMN to ΔL'M'N' is 2.
Now, if we apply scale factor of 2 to coordinates of N before transformation, we will have; 2(3, 1) = (6, 2)
Comparing to N' which is (5, 5) we can say that it was shifted up by 3 units and right by 1 unit.
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Jared made a 15 minute phone call yesterday that cost $0.90. how long will jared be on the phone today if the call cost $1.32, assuming the rate of the cost remains constant
help quick, it's based on polynomials .
Find the area of the shape
Answer:
Step-by-step explanation:
I got you first you want to get some little ceasers
If a client is exercising for 150 minutes per week (30 minutes, 5 days per week), then a 10% increase in volume would result in how many minutes total per week
It takes 165 minutes per week if 10% increase in volume for an exercising client.
How much is the 10% increase in the volume?A client is exercising for 150 minutes per week. I.e., 30 minutes, 5 days per week.
So, 10% increase results,
30 minutes × 10% = 3
So, the increased minutes per day = 30 + 3 = 33 minutes/day.
How many minutes total per week results if a 10% increase in the volume?After the 10% increase, the minutes per day = 33 minutes
Since 5 days a week, he does exercise, the total minutes per week
= 33 × 5 = 165 minutes.
So, a 10% increase in volume would result in 165 minutes total per week.
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If ABC is reflected across the y-axis, what are the coordinates of C?
A. (6,-3)
B. (3,-6)
C. (-6,-3)
D. (-6,3)
Answer:
Step-by-step explanation:
The correct answer would be C (-6,3). The y axis is the bold line going up and down on the middle of the page. If you were able to pick up triangle and flip it over the y axis. Point C would land at (-6,3).
Also, you can see that point C is six spaces to the right of the y axis. That means when we flipped it over the axis, it will now be six paces to the right of the y axis. Since the point did not go up or down when you flipped it. It is still 3 spaces above the x axis.
Answer:
D (-6, 3)
Step-by-step explanation:
the point C is originally (6, 3).
that means the x coordinate is 6, the y coordinate is 3.
now, if we reflect (= mirror) that point across the y axis, that means we mirror it to the other side of the y axis.
the y axis is the vertical coordinate axis in the middle of the graph.
so, what is going to happen to the point ?
will the y coordinate change ? no. the point will move over to the other side of the y line in the same "height" as before. nothing will move it higher or lower.
so, it will keep the same y coordinate : 3.
will the x coordinate change ? oh, yes. because the point will move from the right of the y axis to the left of the y axis. and it will be the same distance to the left as it was originally to the right.
so, +6 turns into -6 (as the y axis represents x=0).
In a right triangle, one acute angle is 22 degrees less than 3 times the other acute angle. What is the measure of the larger acute angle
The measure of the acute angles are 62° and 28° .
What is the larger acute angle in a right triangle?The Triangle Angle Sum Theorem states that the sum of all interior angles in a triangle is . Additionally, the Right Triangle Acute Angle Theorem states that the two non-right angles in a right triangle are acute; that is to say, the right angle is always the largest angle in a right triangle.Let x represent the measure of one of the acute angles of the right angle triangle.
Let y represent the measure of the other acute angle of the right angle triangle.
One of the acute angles in a right triangle measures 22 degrees less than 3 times the other acute angle. This means that
x = 3y - 22
The sum of two acute angles in a right triangle is 90 degrees.
We write as
x + y = 90 - - - - - - - (1)
Substituting x = 3y - 22 into equation 1, it becomes
3y - 22 + y = 90
4y = 90 + 22= 112
y = 112/4 = 28
x = 90 - y = 90 - 28
x = 62
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Refer to Table 9-8. Suppose that the data in the table above reflect the price levels in the economy. What is the inflation rate in between 2017 and 2018
The inflation rate between 2017 and 2018 is 2.86%.
What is the inflation rate?
Inflation rate is used to determine the rate at which the general price levels in an economy is increasing with the passage of time.
The inflation rate = (2018 CPI / 2017 CPI) - 1
(180 / 175) - 1 = 0.0286 = 2.86%
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Which equation has an a-value of 1 a b-value of -3 and a c-value of -5
The equation which has the values as given in the task content is; y= x² -3x -5.
What is the quadratic equation with the given values?By convention, the general form representation of a quadratic equations is;
y = ax² + bx +c.
Hence, it follows that when the equation has an a-value of 1 a b-value of -3 and a c-value of -5, the equation is; y= x² -3x -5.
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Find the mode of the following data: 18, 17, 12, 14, 8, 21, 10, 11, 19, 20, 10, 5, 17, 12, 10, 20  A. 16  B. 14  C. 13  D. 10
Answer:
D.10
Step-by-step explanation:
Mode is the number that is repeated the most as we can see the number 10 is there 3 times in the data. 13 isn't there, 14 is only there once and 16 is also not there
In a(n) _____________ design, two or more treatments are alternated relatively quickly on a regular schedule.
In a(n) reversal design, two or more treatments are alternated relatively quickly on a regular schedule.
Reversal designs are used to observe the impact of a remedy on the conduct of a single player. The participant is observed time and again previous to remedy to establish a baseline stage of behavior.
One ought to not use a reversal layout with behaviors that aren't reversible. For instance, if you train a person to fish, that man or woman is not probable to forget about how to fish, making a reversal design a negative preference for evaluating your fishing intervention.
Reversal layout: reversing among remedies (e.g., baseline, treatment, NCR, treatment, NCR, remedy, and many others.) Withdrawal design: reversing among treatment and no treatment (e.g., baseline, remedy, baseline, treatment, etc.)
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What is the term for breaking a larger number apart into smaller numbers that can be multiplied together to get a specific result? entanglement factorization interference superposition i don't know this yet.
The term for breaking a number into smaller sections and multiplying these numbers is factorization.
What is factorization?This is a common method used in math that implies breaking a big number into smaller ones and then multiplying the numbers. This multiplication should lead you to the original number.
What is an example of factorization?120 can be broken as 12 and 10, then 12 × 10 = 120
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2^4n × 2^ 2n = 512
What is the value of n.
Step-by-step explanation:
[tex] {2}^{4n} \times {2}^{2n} = 512[/tex]
[tex] {2}^{4n} \times {2}^{2n} = {2}^{9} [/tex]
[tex] {2}^{4n + 2n} = {2}^{9} [/tex]
[tex]6n = 9[/tex]
[tex]n = \frac{3}{2} [/tex]
make m the subject!
A single die is rolled twice. The set of 36 equally likely outcomes is {(1, 1), (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}. Find the probability of getting two numbers whose sum is greater than 9. Group of answer choices 6
The probability of getting two numbers whose sum is greater than 9 is [tex]\frac{5}{36}[/tex].
What is probability?Probability is a measure of the possibility that an event will occur in a Random Experiment. Probability is expressed as a number between 0 and 1, where 0 denotes impossibility and 1 denotes certainty. The higher the likelihood of an occurrence, the more probable it will occur.To find the probability of getting two numbers whose sum is greater than 9:
The set of 36 equally likely outcomes is {(1, 1), (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
Set of numbers greater than 9:
{(5, 5), (5, 6), (6, 4), (6, 5), (6, 6)}
Formula:
Favorable event / Total number of events = [tex]\frac{5}{36}[/tex]
Therefore, the probability of getting two numbers whose sum is greater than 9 is [tex]\frac{5}{36}[/tex].
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A number is chosen at random from the first 100 positive integers. find the probability that the number is divisible by 5. 1/10 1/5 1/4
The probability that the number chosen is divisible by 5 is; 1/5.
What is the probability that the number chosen is divisible by 5?It follows from the task content that the number of possible outcomes in the probability event is; 100. Additionally, the number of required outcomes is 20 as only 20 numbers are divisible by 5.
Ultimately, the required probability is; 20/100 = 1/5.
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