The meaning of the slope in the linear function is given as follows:
B. Cars per minute.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.The slope of a linear function represents the rate of change of the output variable relative to the input variable.
The variables for this problem are given as follows:
Output: number of cars.Input: number of minutes.Hence the slope represents the rate of change of cars per minute, hence option B is correct.
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A basketball player makes 85% of her foul shots. If 10 of her foul shots are randomly selected, what is the probability that 8 of them are successful shots?
0.06
0.28
0.85
0.98
Answer: 0.28
Step-by-step explanation: Reviewed my quiz, got you covered
5.4 times 2 3/4 ???????????????????????????????????????????????????
Answer: In decimal form, 14.85
Answer in fraction form: 297/20
Step-by-step explanation:
Hexagon DEFGHI is translated on the coordinate plane below to create hexagon D′E′F′G′H′I′: Hexagon DEFGHI and Hexagon D prime E prime F prime G prime H prime I prime on the coordinate plane with ordered pairs at D 2, 5, at E 5, 5, at F 6, 3, at G 5, 1, at H 2, 1, at I 1, 3, at D prime negative 6, negative 2, at E prime negative 3, negative 2, at F prime negative 2, negative 4, at G prime negative 3, negative 6, at H prime negative 6, negative 6, at I prime negative 7, negative 4
Answer: To find the image of a figure under a translation, you need to apply the same translation to every point in the figure.
In this case, the image of hexagon DEFGHI is hexagon D′E′F′G′H′I′. To find the image of each point, you can apply the translation that maps point D to point D′.
For example, to find the image of point E under the translation, you can apply the same translation that maps point D to point D′:
Point D is located at (2, 5).
Point D′ is located at (-6, -2).
The translation that maps point D to point D′ is a translation 6 units to the left and 2 units down.
To find the image of point E under this translation, you can apply the same translation to point E:
Point E is located at (5, 5).
The image of point E is located at (5 - 6, 5 - 2) = (-1, 3).
You can follow the same process to find the images of the other points under the translation.
Alternatively, you can use the coordinates of point D and point D′ to find the translation vector that describes the translation. The translation vector is a displacement that describes the change in position of a point under the translation.
In this case, the translation vector is given by the displacement from point D to point D′:
Point D is located at (2, 5).
Point D′ is located at (-6, -2).
The translation vector is given by the displacement (-6 - 2, -2 - 5) = (-8, -7).
To find the image of any point under the translation, you can add the translation vector to the coordinates of the point. For example, to find the image of point E under the translation, you can add the translation vector to the coordinates of point E:
Point E is located at (5, 5).
The translation vector is (-8, -7).
The image of point E is located at (5 - 8, 5 - 7) = (-3, -2).
You can follow the same process to find the images of the other points under the translation.
Step-by-step explanation:
Show what a monomial expression looks like
Give me a monomial expression and solve it, step-by-step, thoroughly, show your work and explain with each step how your doing it
(New to this, thanks in advance for the extra help!!!)
Answer:
Refer to the step-by-step explanation.
Step-by-step explanation:
Come up with a monomial expression and solve it.
What is a monomial expression?A monomial expression is an algebraic expression that consists of a single term. It is an expression that can contain variables, constants, and non-negative integer exponents, but there should be no addition or subtraction between different terms.
Here are a few examples of an monomial expression:
5x-2xy²3a⁵7m³n²\(\hrulefill\)
Let's work with the monomial expression, 3x²y³z.
To solve this expression, I assume you would like to evaluate it for specific values of the variables x, y, and z. So let x=3, y=2, and z=1.
Plug these values into the expression:
3x²y³z
=> 3(3)²(2)³(1)
=> 3(9)(8)(1)
=> 27(8)(1)
=> 216(1)
=> 216
Thus, the expression is solved.
pls help ! Find the value of x.
Answer:
x=48
Step-by-step explanation:
They are vertical angles.
Help .....................
Answer:
1. 8 is bigger
2. -9 is bigger
3. 12 is bigger
Step-by-step explanation:
A college student takes the same number of credits each semester. She had 15 credits when she started, and after 4 semesters, she had 71 credits. Which of these expresses the rate at which she is earning credits?
Answer:
14 Semesters Per Credit
Step-by-step explanation:
The rate at which she is earning credits is 14 credits per semester.
What is an expression?
Expression in mathematic is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Here in this question it is given that a college student had 15 credits already when she started her college and at the end of 4 semesters she had 71 credits which means she earned in total 71 - 15 = 56 credits. And the credits she earned is divided equally into all the 4 semesters, Now the rate at which she is earning credits is :
total credits earned by her divided by number of semesters = 56/4 = 14 credits.
Therefore, the rate at which she is earning credits is 14 credits per semester.
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Professor A.B.C company opens his own company, Electronic Tutorial Services, and completes the following transactions in June:
6/1 A.B.C company invests 20,000 in the business.
6/3 Purchased 12,100 of equipment.
6/4 Paid 220 premium for an insurance policy.
6/6 Purchased office supplies on Account 140.
6/9 Purchased a new computer for 9,000. Paid 40% cash agreed to pay the remainder Later.
6/10 Billed student Omar 58 for tutorial services that were performed.
6/14 Paid for the supplies purchased on June 6th.
6/15 the owner suggested to purchased new Building for his company by 22,000
6/25 Received 85 cash from student Salim Ali for tutorial services performed.
6/30 Student billed on June 10 pays the amount due to A.B.C company.
6/30 A.B.C company withdraws 60 for personal use.
Required: Prepare the all Accounting Cycles
In June, A.B.C company invested $20,000, purchased equipment, paid insurance premium, bought office supplies, billed students for tutorial services, received cash, paid for supplies, withdrew personal funds.
Accounting Cycles:
1. June 1:
- A.B.C company invests $20,000 in the business.
- Prepare the journal entry:
- Debit: Cash ($20,000)
- Credit: Capital ($20,000)
2. June 3:
- Purchased equipment for $12,100.
- Prepare the journal entry:
- Debit: Equipment ($12,100)
- Credit: Cash ($12,100)
3. June 4:
- Paid $220 premium for an insurance policy.
- Prepare the journal entry:
- Debit: Insurance Expense ($220)
- Credit: Cash ($220)
4. June 6:
- Purchased office supplies on account for $140.
- Prepare the journal entry:
- Debit: Office Supplies ($140)
- Credit: Accounts Payable ($140)
5. June 9:
- Purchased a new computer for $9,000. Paid 40% in cash and agreed to pay the remainder later.
- Prepare the journal entry for the cash payment:
- Debit: Computer ($3,600) [40% of $9,000]
- Credit: Cash ($3,600)
- Prepare the journal entry for the remaining amount:
- Debit: Computer ($5,400)
- Credit: Accounts Payable ($5,400)
6. June 10:
- Billed student Omar $58 for tutorial services performed.
- Prepare the journal entry:
- Debit: Accounts Receivable ($58)
- Credit: Tutorial Services Revenue ($58)
7. June 14:
- Paid for the supplies purchased on June 6th ($140).
- Prepare the journal entry:
- Debit: Accounts Payable ($140)
- Credit: Cash ($140)
8. June 15:
- The owner suggested purchasing a new building for the company for $22,000.
- No journal entry is required at this point. It is a decision made by the owner.
9. June 25:
- Received $85 cash from student Salim Ali for tutorial services performed.
- Prepare the journal entry:
- Debit: Cash ($85)
- Credit: Accounts Receivable ($85)
10. June 30:
- Student billed on June 10 pays the amount due ($58).
- Prepare the journal entry:
- Debit: Cash ($58)
- Credit: Accounts Receivable ($58)
11. June 30:
- A.B.C company withdraws $60 for personal use.
- Prepare the journal entry:
- Debit: Withdrawals ($60)
- Credit: Cash ($60)
These transactions represent the accounting cycles for the given period.
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A bank features a savings account that has an annual percentage rate of r=3.3% with interest compounded quarterly. Maia deposits $10,000 into the account. What values should be used for p, r, and n? How much money will Maia have in the account in 9 years?
The used values are;
p = $10,000
r = 3.3%
n = 9 years
And, The amount after 9 years will be $14,593.
What is Simple interest?
A quick and easy method of calculating the interest charge on a loan is called a Simple interest.
Given that;
A bank features a savings account that has an annual percentage rate of r = 3.3% with interest compounded quarterly.
And, Maia deposits $10,000 into the account.
Now,
Since, The interest rate is for compounded quarterly.
So, The used formula is,
⇒ \(A = P (1 + \frac{r}{4} )^n^t\)
Here, P = $10,000
r = 3.3% = 0.033
n = 4
t = 9
Substitute all the values, we get the amount after 9 years,
⇒ \(A = P (1 + \frac{r}{4} )^n^t\)
⇒ A = $10,000 (1 + 0.033/4)³⁶
⇒ A = $10,000 (1 + 0.008)³⁶
⇒ A= 10,000 × (1.008)³⁶
⇒ A = 10,000 x 1.45
⇒ A = $14,593
Thus, The amount after 9 years will be $14,593.
Therefore, The used values are;
p = $10,000
r = 3.3%
n = 9 years
And, The amount after 9 years will be $14,593.
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A soccer field is a rectangle 50 meters wide and 80 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
The distance of the diagonal is 94.3 meters.
What is a diagonal?A diagonal is a line segment that joins the opposite corners of a polygon through its vertices. But it is not an edge.
The length and width of the soccer field is given by 80meters and 50 meters respectively.
The coach asks players to run from one corner to the other corner diagonally across.
To find the distance of the diagonal thus formed.
From the diagram consider the ΔABD, AB= 80 , BD=50 meters.
Then by Pythagoras theorem,
“In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides"
\(AD^{2} = AB^{2} +BD^{2}\)
= \(80^{2} + 50^{2}\)
= 6400 + 2500
= \(10\sqrt{89}\)= 94.3 meters.
Hence, the distance of the diagonal is 94.3 meters.
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i need help with this asap! will give brainiest if answered correctly
Answer:
Step-by-step explanation:
2
Can y’all help me with this!???? I’ll boost you up!
The equations have been computed below
How to illustrate the information?3(x + 2) + 11 = 5(x - 4)
3x + 6 + 11 = 5x - 20
Collect like terms
3x - 5x = -20 - 17
-2x = -37
x = 37/2
x = 18.5
6x + 4 = 3(3 - 2x)
6x + 4 = 9 - 6x
Collect like terms
6x + 6x = 9 - 4
12x = 5.
x = 5/12
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An objects _________
Question Progress
Homework Progress
46/229 Marks
Submit Answer
a) Factorise x² + 5x-14
b) Solve x² + 5x-14= 0
After solving the quadratic equation, the roots are (x - 2) and (x + 7).
What is a Quadratic function?To determine values for various parameters, quadratic functions are employed in a variety of engineering and scientific disciplines. A parabola is used to graphically illustrate them.
The direction of the curve is determined by the highest degree coefficient. Quadratic is a derivative of the term quad, which signifies square.
As per the given equation in the question,
x² + 5x - 14 = 0
b² - 4ac
5² - 4(1)(-14)
25 + 56 = 81
Use the equation,
-b ± \(\sqrt{b^2-4ac}/2a\)
Substitute the values,
(-5 + 9)/2 = 2 and,
(-5 - 9)/2 = -7
Therefore, the root will be (x - 2) and (x + 7).
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A box has a width of 10 cm and a length of 17 cm. The volume of the box is decreasing at a rate of 527 cubic cm per minute, with the width and length being held constant. What is the rate of change, in cm per minute, of the height when the height is 6 cm?
Round your answer to the nearest hundredth. (Do not include any units in your answer.)
Therefore, the rate of change, in cm per minute, of the height when the height is 6 cm is approximately -6 cm/min.
Given,The width of the box = 10 cm Length of the box = 17 cmThe volume of the box = 527 cubic cm/minWe need to find the rate of change, in cm per minute, of the height when the height is 6 cm.We know that the volume of the box is given as:V = l × w × h where, l, w and h are length, width, and height of the box respectively.It is given that the width and length are being held constant.
Therefore, we can write the volume of the box as
:V = constant × h Differentiating both sides with respect to time t, we get:dV/dt = constant × dh/dtNow, it is given that the volume of the box is decreasing at a rate of 527 cubic cm per minute.
Therefore, dV/dt = -527.Substituting the given values in the above equation, we get:
527 = constant × dh/dt
We need to find dh/dt when h = 6 cm.To find constant, we can use the given values of length, width and height.Substituting these values in the formula for the volume of the box, we get:
V = l × w × hV = 17 × 10 × hV = 170h
We know that the volume of the box is given as:V = constant × hSubstituting the value of V and h, we get:
527 = constant × 6 cm
constant = 87.83 cm/minSubstituting the values of constant and h in the equation, we get
-527 = 87.83 × dh/dtdh/dt = -6.0029 ≈ -6 cm/min
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Non Shaded Shaded
Area
Area
8
Find the radius
of the small circle
Answer:
The answer is 16pi or 50.3cm² to 1 d.p
Step-by-step explanation:
The non shaded=area of shaded
d=8
r=d/2=4
A=pir³
A=p1×4²
A=pi×16
A=16picm² or 50.3cm² to 1d.p
Answer:
3.45 cm (3 s.f.)
Step-by-step explanation:
We have been given a 5-sided regular polygon inside a circumcircle. A circumcircle is a circle that passes through all the vertices of a given polygon. Therefore, the radius of the circumcircle is also the radius of the polygon.
To find the radius of a regular polygon given its side length, we can use this formula:
\(\boxed{\begin{minipage}{6 cm}\underline{Radius of a regular polygon}\\\\$r=\dfrac{s}{2\sin\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)
Substitute the given side length, s = 8 cm, and the number of sides of the polygon, n = 5, into the radius formula to find an expression for the radius of the polygon (and circumcircle):
\(\begin{aligned}\implies r&=\dfrac{8}{2\sin\left(\dfrac{180^{\circ}}{5}\right)}\\\\ &=\dfrac{4}{\sin\left(36^{\circ}\right)}\\\\ \end{aligned}\)
The formulas for the area of a regular polygon and the area of a circle given their radii are:
\(\boxed{\begin{minipage}{6 cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{nr^2\sin\left(\dfrac{360^{\circ}}{n}\right)}{2}$\\\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)
\(\boxed{\begin{minipage}{6 cm}\underline{Area of a circle}\\\\$A=\pi r^2$\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}\)
Therefore, the area of the regular pentagon is:
\(\begin{aligned}\textsf{Area of polygon}&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(\dfrac{360^{\circ}}{5}\right)}{2}\\\\&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(72^{\circ}\right)}{2}\\\\&=\dfrac{\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}}{2}\\\\&=\dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}\\\\&=110.110553...\; \sf cm^2\end{aligned}\)
The area of the circumcircle is:
\(\begin{aligned}\textsf{Area of circumcircle}&=\pi \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\\\\&=\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\&=145.489779...\; \sf cm^2\end{aligned}\)
The area of the shaded area is the area of the circumcircle less the area of the regular pentagon plus the area of the small central circle.
The area of the unshaded area is the area of the regular pentagon less the area of the small central circle.
Given the shaded area is equal to the unshaded area:
\(\begin{aligned}\textsf{Shaded area}&=\textsf{Unshaded area}\\\\\sf Area_{circumcircle}-Area_{polygon}+Area_{circle}&=\sf Area_{polygon}-Area_{circle}\\\\\sf 2\cdot Area_{circle}&=\sf 2\cdot Area_{polygon}-Area_{circumcircle}\\\\2\pi r^2&=2 \cdot \dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\\end{aligned}\)
\(\begin{aligned}2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)-16\pi}{\sin^2\left(36^{\circ}\right)}\\\\r^2&=\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}\\\\r&=\sqrt{\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}}\\\\r&=3.44874763...\sf cm\end{aligned}\)
Therefore, the radius of the small circle is 3.45 cm (3 s.f.).
Which choices are equivalent to the expression below? Check all that apply.
4./6
O A. 96
B. 132.5
I C. 4../36
O D. 116.6
E. 196
OF V24
SUBMIT
Help! Which of the following side lengths would NOT make a right triangle?
Answer:
The Answer is 10, 50, and 54
Step-by-step explanation:
You want to figure this answer out by using the Pythagorean Theorem. If 10 squared plus 50 squared does not equal 54 squared, then those side lengths can not make a triangle.
Find A − B and B − A. (Enter your answers in list form. Enter EMPTY or ∅ for the empty set.)
The main answer is that without specific values or elements for sets A and B, we cannot determine the result of A - B and B - A.
To find A - B, we need to subtract the elements in set B from set A. Similarly, to find B - A, we need to subtract the elements in set A from set B.
However, I need the specific values or elements of sets A and B to perform the calculations. Could you please provide the values or elements of the sets?In order to perform set subtraction, we need the specific elements or values of sets A and B. Set subtraction involves removing the common elements between the sets.
Let's say set A is {1, 2, 3} and set B is {2, 3, 4}. To find A - B, we remove the elements in set B from set A. Thus, A - B would be {1}.
To find B - A, we remove the elements in set A from set B. Therefore, B - A would be {4}.
Please provide the values or elements of sets A and B, and I will be able to calculate A - B and B - A accordingly.
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A certificate of deposit often charges a penalty for withdrawing funds before the maturity date. If the penalty involves two months of interest, what would be tbe amount for early withdrawal on a CD paying 7 percent and valued at $18,000? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Penalty time = 2 months of interest = 2 x (7/100 x 18,000) = $2520.00
This serves as a deterrent to encourage individuals to leave their money in the CD until the maturity date.
Penalty = 2 months of interest = 2 x (Interest rate/100 x Value of CD)
= 2 x (7/100 x 18,000)
= $2520.00
A certificate of deposit (CD) is a financial product offered by banks and credit unions that allows an individual to deposit a certain amount of money for a fixed period of time, usually a few months to a few years. Most CDs will pay a higher rate of interest than a traditional savings account, but they come with certain restrictions. One of these restrictions is that if you withdraw funds from the CD before it reaches maturity, you will be charged a penalty time. This penalty usually involves two months of interest. Therefore, the amount of the penalty for early withdrawal on a CD with a value of $18,000 and paying 7 percent interest would be 2 x (7/100 x 18,000) = $2520.00. This serves as a deterrent to encourage individuals to leave their money in the CD until the maturity date.
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1,2,3,4,5 what is probability that an even number will be chosen?
Answer:
Step-by-step explanation:
step 1
100%/the total number = percent for one probability
100/5 = 20%
2 and 4 is even.
total even number * percent for one probability = total percent for even number
20% * 2 = 40%
therefore total even number is 40%
The probability is:
2/5Step-by-step explanation:
Remember the formula for probability:
\(\boxed{\!\!\boxed{\bold{Probability=\frac{Favourable~outcome}{total~outcomes}\quad}}\!\!}\)
In this case, the favourable outcome (an even number) is 2, because there are only 2 even numbers in the set.
As for the total outcomes, there are 5 of them, because we have 5 numbers total.
So the probability of choosing an even number is 2/5.
does anyone know the answer to this? 5x-(4+3x)
Answer:
2x-4
Step-by-step explanation:
5x-(4+3x)
5x-4-3x
5x-3x-4
2x-4
A laptop costs $1800. A shop is having a storewide 10% discount, How much does the laptop cost after the discount?
Answer:
$1620
Step-by-step explanation:
Given:
Original Cost ⇒ $1800
Discount ⇒ 10%
To Find:
How much does the laptop cost after the discount?
Solve:
$1800 × 10% = 180
$1800 - 180 = $1620 {Discount = subtract}
Hence, the Laptop cost after the discount is $1620
Kavinsky
One brand of cola co fizz is sold in packs of 4*500ml for 2.50 another brand colo is sold in packs of 10 330mlfo $2 which brand is more expensive
Based on the given information, the second brand, Cola, is the more affordable option in terms of cost per milliliter compared to Co Fizz.
To determine which brand of cola is more expensive, we need to compare the cost per unit volume for each brand.
For the first brand, Co Fizz, a pack contains 4 bottles, and each bottle has a volume of 500 ml. The cost of the pack is $2.50. Therefore, the total volume in a pack is 4 * 500 ml = 2000 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2.50 / 2000 ml = $0.00125 per ml.
For the second brand, Cola, a pack contains 10 bottles, and each bottle has a volume of 330 ml. The cost of the pack is $2. Therefore, the total volume in a pack is 10 * 330 ml = 3300 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2 / 3300 ml ≈ $0.000606 per ml.
Comparing the two brands, we can see that the cost per milliliter for Co Fizz is $0.00125, while the cost per milliliter for Cola is approximately $0.000606.
Since the cost per milliliter for Co Fizz is higher than the cost per milliliter for Cola, it can be concluded that Co Fizz is more expensive in terms of price per unit volume.
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Suppose you read a story that claims the government is conducting an investigation of corruption in a congressional district. On what type of data source is the claim in this story based?
a. These data are results of an observational study.
b. These data are collected by ongoing business activities.
c. These data are distributed by an organization.
d. These data are responses from a survey.
e. These data are outcomes of a designed experiment.
Answer:
a. These data are results of an observational study.
Step-by-step explanation:
In observational study, individuals are observed or certain outcomes are measured without the observer trying to affect the outcome of the observation. The results of an observational study can be random, and there final results might not be expected prior to the study. In observational study, the observer does not affect the study because of ethical concerns or logistical constraints. In the case of this question, the observer might be under the constraint of not having the political influence of a direct experiment.
Juwad picked 30 bags of apples on Monday and sold them at his fruit stand for $3.45 each.the following week he picked and sold 26bags
I do not understand this problem
Answer:
$89.70 or $192.30
Step-by-step explanation:
All you have to do is multiply 26 by 3.45 and you get your answer. Which if you use a calculator it would say 89.7, to find the answer you just add a zero to the end.
If you're doing the second answer you multiply 30 by 3.45, then you take 26 and multiply by 3.45, after that you add them together and you get your answer.
A certain department store keeps track of an age and an annual income of customers who have its credit card. From a sample of 820 of such customers the following descriptive statistics had been obtained: the average age was 41 years with the standard deviation of 16 years and the average annual income was $37,290 with the standard deviation of $2,850. The correlation between the age the annual income was found to be 0.34. Answer the following questions. (Round your answers to 2 places after the decimal point).
Calculate the value of a slope.
a) 309.23 $ per year of age
b) 60.56 $ per year of age
c) 192.43$ per year of age
d) None of the above
Answer: b) $60.56 per year of age
Step-by-step explanation: If the scatterplot of two variables shows a line and the correlation between them is strong, we can calculate a regression line.
Regression line is a line graph that best fits the data. Like any other line, its formula is given by
y = mx + b
with
m being the slope
b the y-intercept
The slope of the line, correlation and standard deviations of the two variables have the following relationship:
\(m=r\frac{S_{y}}{S_{x}}\)
where
r is correlation
\(S_{y}\) is standard deviation for the y data
\(S_{x}\) is standard deviation for the x data
For our problem:
r = 0.34
\(S_{y}=\) 2850
\(S_{x}=\) 16
Calculating
\(m=0.34(\frac{2850}{16})\)
m = 60.56
Slope for the regression line of annual income per year of age is 60.56.
PLS HELP ME I HAVE NO IDEA WHAT THESE ARE. If you can find all the answers and give me the words you would be a life saver
Answer:
SO EVERYONE WOULD SHOUT LOOK AT THE S CAR GO
Step-by-step explanation:
The brackets just mean to multiplye.g. 3(2)(5) is the same as 3 × 2 × 5When you get the answer, find in in the boxes below and write the letter of that equationI will not go through each question separately because it would take too long, but will give you the wordsFor the given values of n and d, find integers q and r such that n = dq + r and 0 ≤ r < d. n = −67, d = 8
Answer:
\(q = 8\)
\(r = 3\)
Step-by-step explanation:
Given
\(n = dq + r\)
\(0 \le r < d\)
\(n = 67\) --- not -67
\(d = 8\)
Required
Find q and r
Substitute values for d and b
\(n = dq + r\)
\(67 = 8 * q + r\)
\(67 = 8q + r\)
Make q the subject
\(q = \frac{67 - r}{8}\)
\(0 \le r < d\) means that r is less than 8 but greater than or equal to 0
And r and q are integers.
Let \(r = 3\)
\(q = \frac{67 - 3}{8}\)
\(q = \frac{64}{8}\)
\(q = 8\)
No other true values of r and q can be gotten.
What are the degrees of freedom associated with the factor(s) in this study design?
Answer:
The question is unclear and incomplete.
Let me explain the degrees of freedom in statistics.
Step-by-step explanation:
Statistically, degrees of freedom which is denoted as DF is the number of independent values that can vary in an analysis without breaking any constraints. It can also be referred to as the number of independent values that a statistical analysis can estimate.
Degrees of freedom also define the probability distributions for the test statistics of various hypothesis tests.
The degree of freedom has the formula:
DF = N - 1 where N number of random variables
DF = (R - 1) x (C - 1) Where R is the number of data values and C is the number of groups