Answer:
The correct option is B) Qualitative and discrete.
Step-by-step explanation:
Consider the provided information.
Quantitative variable is the variables that can be determined by counting or measuring something.
Qualitative variable is the variables that can't be determined by counting or measuring something.
If the value is obtained by counting then it is called discrete variable, If the value obtained by measuring then it is called continuous variable.
Since the relationship can't be measure by counting so it it qualitative variable.
We can calculate the regular contact days so it is discrete variable.
Therefore, the correct option is B) Qualitative and discrete.
use a property to write an equivalent expression 6x7
Answer:
Step-by-step explanation:
6 X 7 = 42
This is simply the sum of 6 in seven places or 7 in six places.
You go shopping and buy 3 new shirts and 2 pairs of pants for $29.75. Your friend buys 4 shirts and 3 pairs of pants for 42.00. How much did one shirt cost?
Answer:
$5.25
Step-by-step explanation:
The two purchases can be described by the equations ...
3s +2p = 29.75
4s +3p = 42.00
If you multiply the first equation by 3 and subtract 2 times the second equation, the cost of a shirt pops out.
3(3s +2p) -2(4s +3p) = 3(29.75) -2(42.00)
9s +6p -8s -6p = 89.25 -84.00 . . . . . . . eliminate parentheses
s = 5.25 . . . . . . . . . . collect terms
One shirt costs $5.25.
A pre-paid cell phone company charges $18.5 as a monthly access fee and $0.11 per minute of calling time. Express the monthly cost C as a function of x, the number of minutes use. What will the monthly cost be if you make 329 minutes of calls this month? $
Answer:
c=54.69
Step-by-step explanation:
so this is a two step problem
c=18.5+0.11x
we created the function
now we plug in 329 into x and solve to get the c
c=54.69
The monthly cost for pre-paid cell phone usage can be expressed as a function, C = 18.5 + 0.11x where x is the number of calling minutes. The monthly cost for making 329 minutes of calls would be $54.69.
Explanation:The pre-paid cell phone company charges a fixed monthly access fee and an additional cost per minute of calling time. Here, the monthly access fee is $18.5 and the cost per minute is $0.11. We are asked to express the monthly cost C as a function of x, the number of minutes used.
Therefore, we can write the function as C = 18.5 + 0.11x where, C represents the monthly cost and x represents the number of minutes used.
Now, if you make 329 minutes of calls this month, you can use this function to calculate the total cost. Substituting x = 329 into the function gives: C = 18.5 + 0.11 * 329 = $54.69.
Therefore, the monthly cost for making 329 minutes of calls would be $54.69.
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URGENT PLZ HELP. DUE TOMORROW
Answer:
9 x⁵y⁵
Step-by-step explanation:
for a rectangle
area = length x width, (rearranging)
width = area / length
given area = 45x⁸y⁹ and length = 5x³y⁴
width = 45x⁸y⁹ / 5x³y⁴
= (45/5) ( x⁸y⁹ / x³y⁴)
= 9 ( x⁸y⁹ / x³y⁴)
= 9 ( x⁸⁻³y⁹⁻⁴ )
= 9 ( x⁵y⁵ )
= 9 x⁵y⁵
A department store is holding a drawing to give away free shopping sprees. There are customers who have entered the drawing: live in the town of Gaston, live in Pike, and live in Wells. Two winners will be selected at random. What is the probability that both winners live in Wells?
Answer:
The probability of selecting two winners from Wells is, [tex]\frac{z(z-1)}{(x+y+z)(x+y+z-1)}[/tex]
Step-by-step explanation:
Let us assume that x people entered the drawing were from Gaston, y people entered the drawing were from Pike and z people entered the drawing were from Wells.
Total number of people who entered the drawing is, N = x + y + z.
It is provided that 2 winners are selected at random.
The event of selecting the first and second winner are not related, i.e. they are independent.
Then the first winner can be selected from Wells in z ways.
And the second winner can be selected, also from Wells in (z - 1) ways.
The probability of selecting both the winners from Wells is:
[tex]P(Both\ the\ winners\ were\ from\ Wells)=\frac{z}{x+y+x}\times \frac{z-1}{x+y+z-1} =\frac{z(z-1)}{(x+y+z)(x+y+z-1)}[/tex]
Thus, the probability of selecting two winners from Wells is, [tex]\frac{z(z-1)}{(x+y+z)(x+y+z-1)}[/tex].
I'll Brainliest if possible. Please excuse the unruly handwriting I was in a bit of a hurry. The words are, find the quotient using long division.
Answer: The quotient is 6x + 2
The solution is
6x + 2 + 9/(6x² - 16x + 3)
Step-by-step explanation:
The step by step explanation for the long division method is shown in the attached photo. The remainder is 9 and the quotient is 6x + 2
See attached picture.
The final answer is the quotient plus the remainder over the divisor.
The quote that would be 6x+ 2 and the remainder would be 9/x-3
Describe how to solve any equation in the form ax + b = c for the variable x.
Subtract b from both sides: ax=c-b
Divide both sides by a: x=(c-b)/a
Hope this helped
Explanation:
To solve any equation that is linear in the variable of interest, you first look at what is done to the variable, using the Order of Operations as your guide.
Here, the variable is ...
multiplied by "a"the product has "b" added to it.You find the value of the variable by reversing these steps, starting from the last one on the list and working up the list.
To "undo" the addition of "b", we add its opposite (-b) to the equation. The rules of equality tell you that anything you do to one side of the equation must also be done to the other side, so we add -b to both sides:
ax +b -b = c -b
ax = c -b . . . . . . . . simplify
To "undo" the multiplication by "a", we multiply by its reciprocal. That is, we multiply by 1/a, or, equivalently, divide by "a". Again, we must do this to both sides of the equation:
(1/a)ax = (1/a)(c -b)
x = (c -b)/a . . . . . . . simplify
__
In short, we subtract the added constant (b) and divide by the multiplier (a).
A 100-inch ribbon is to be cut into three pieces. Find the length of each piece of ribbon. The length of the shortest piece of ribbon is _____ inches. Please put step by step. I’m having trouble with these and if you have a short cut teach me your ways lol
Answer: Longest piece= 52 inches, Shortest piece= 22 inches and the third piece is 26 inches
Step-by-step explanation:
Let the longest piece be A
Let the shortest piece be B
let the third piece be C
The longest piece is to be 30inches longer than the short
A=B+30
and the third piece is to be half the length of the longest piece
C=(B+30)/2
Rmbr,
A+B+C=100 Inches
from
A+B+C=100 substitute A for B+30 and C for (B+30)/2
we have,
(B+30)+B+(B+30)/ 2=100
2B+30+(B+30)/2=100
multiply through by 2
we have,
4B+60+B+30=200
5B=200-90
B=110/5
B=22
To get A
from A=B+30
A=22+30
A=52
To get C
from C=(B+30)/2
C=(22+30)/2
C=52/2
C=26
Rmbr,
Let the longest piece be A
Let the shortest piece be B
let the third piece be C
therefore, A=52 B=22 C=26
What information should be entered in item 16, "Destination Aerodrome," for an IFR flight with an intended stopover of 30 minutes?What information should be entered in item 16, "Destination Aerodrome," for an IFR flight with an intended stopover of 30 minutes?
Answer:
The destination airport identifier code.
Step-by-step explanation:
What information should be entered in item 16, "Destination Aerodrome," for an IFR flight with an intended stopover of 30 minutes?What information should be entered in item 16, "Destination Aerodrome," for an IFR flight with an intended stopover of 30 minutes?
A destination identifier code should be entered.
if no stopover for more than 60 minutes is expected, enter ICAO four letter identifier in item 16 of the flight plan. and indicate when to stopover
Item 16 on an IFR flight plan is used to indicate the destination aerodrome, which is the airport where the aircraft is planning to land. For an IFR flight with an intended stopover of 30 minutes, you would enter the ICAO code or the three-let...
Explanation:Item 16 on an IFR flight plan is used to indicate the destination aerodrome, which is the airport where the aircraft is planning to land.
For an IFR flight with an intended stopover of 30 minutes, you would enter the ICAO code or the three-letter identifier for the destination aerodrome in item 16.
In this case, you would enter the ICAO code or three-letter identifier for the airport where you will land after the intended stopover, and not the stopover airport itself.
The interquartile range tells us how much space the _____ of the data occupy.
Answer:
middle 50%
Step-by-step explanation:
Interquartile Range (IQR). Tells us how much space the middle 50% of the data occupy.
In order to get an. A in science,Jack must get at least 92% on his next test. If tbe test has 30 questions, what is the minimum number he must correctly answer.
Jack needs to correctly answer at least 28 out of the 30 questions to achieve a minimum of 92% on his science test.
To determine the minimum number of questions Jack must correctly answer to get at least 92% on his next 30-question science test, we can use the following calculation:
Minimum number of correct answers = 92% of total questions
= 0.92 × 30
= 27.6
Since Jack cannot answer a fraction of a question, he must round up to ensure the minimum percentage is met. Therefore, Jack must correctly answer at least 28 questions out of 30 to achieve a 92% score or higher.
Consider the following If statement, which is syntactically correct but uses poor style and indentation: if (x >= y) if (y > 0) x = x * y; else if (y < 4) x = x - y; Assume that x and y are int variables containing the values 9 and 3, respectively, before execution of the above statement. After execution of the statement, what value will x contain?
Answer:
27
Step-by-step explanation:
int x = 9;
int y = 3;
if (x >= y)
if (y > 0)
x = x * y;
else if (y < 4)
x = x - y;
First, the first if statement check for the value of x>=y which is true. The another if-statement check if y>0, which is true and it execute the statement x = x * y that is x = 9 * 3 and x = 27.
The else-if block is not executed because the if-statement attached to it has been executed already.
what is 5x -2=38
A 36
B 8
C 7
D 13
Researchers randomly divide participants into groups. Each group takes a different amount of omega-3 fatty acid supplements daily for a month. One group receives a placebo. The researchers measure the impact on cholesterol levels in the blood. What is the purpose of random assignment in this experiment? Check all that apply. To ensure that all people with high cholesterol have an equal chance of being selected for the study To increase the accuracy of the research results and prevent skewness in the data To produce treatment groups with similar characteristics To control confounding
Answer: To produce treatment groups with similar characteristics
Step-by-step explanation:
The purpose of this experiment is to determine that the treatments groups with similar characteristics are produced. Every groups is taking different amount of the supplement so this study ensures that by randomly assigning the supplements, we can check the cholesterol level in the blood. In this way, similar characteristics in groups are imparted so we can then make treatment groups of same characteristics.
The purpose of random assignment in experiments is to avoid bias, increase the research results' accuracy, help in producing treatment groups with similar characteristics, and control confounding variables. In this case, it ensures that all participants have an equal chance of receiving any level of omega-3 fatty acid or placebo.
Explanation:The purpose of random assignment in this experiment is multifold. Firstly, it ensures all participants, regardless of their cholesterol levels, have an equal chance of being selected. This prevents bias in the sample selection. Secondly, it increases the accuracy of the research results by preventing skewness in the data. The random assignment ensures that every participant has an equal chance of receiving any level of the omega-3 fatty acid supplement or the placebo. This helps produce treatment groups with similar characteristics, which in turn allows for fair comparisons to be made. Finally, it aids in controlling confounding variables. These are factors other than the independent variable (in this case, omega-3 fatty acid supplements) that may affect the dependent variable (cholesterol level), and random assignment helps to equalize these among the groups.
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NEED HELP ASAP Need someone to explain how to do this
Answer:
Oh cool! The answer is 90 since a and c or parallel, b cuts through them perpendicularly, forming a right angle.
Step-by-step explanation:
An experimenter conducted a two-tailed hypothesis test on a set of data and obtained a p-value of 0.44. If the experimenter had conducted a one-tailed test on the same set of data, which of the following is true about the possible p-value(s) that the experimenter could have obtained? A) The only possible p-value is 0.44. B) The only possible p-value is 0.88. C) The possible p-values are 0.22 and 0.78. D) The possible p-values are 0.22 and 0.88.
Answer:
Correct option is (C).
The possible value of the p-value for a one-tailed test are 0.22 and 0.78.
Step-by-step explanation:
The p-value is the probability of acquiring a result as extreme as the observed result, assuming the null hypothesis statement is true.
The p value of a test is:
Left-tailed test: [tex]P(TS<ts)[/tex]
Right-tailed test: [tex]P(TS>ts) = 1- P(TS<ts)[/tex].
Here,
TS = Test statistic
ts = computed value of the test statistic.
The two-tailed p-value is: [tex]2P(TS<ts)[/tex] or [tex]2P(TS>ts)[/tex].
The p-value of the two tailed test is, 0.44.
Compute the p-value for one-tailed test a follows:
For a left-tailed test:[tex]2P(TS<ts)=0.44\\P(TS<ts)=\frac{0.44}{2}\\ =0.22[/tex]
For a right-tailed test:[tex]P(TS>ts) = 1- P(TS<ts)\\=1-0.22\\=0.78[/tex]
Thus, the possible value of the p-value for a one-tailed test are 0.22 and 0.78.
The correct option is (C).
Given a p-value of 0.44 from a two-tailed test, the equivalent one-tailed test would yield a p-value of 0.22. Out of the provided choices, option C is closest to the correct interpretation.
Explanation:The question presented is about the computation of the p-value in a one-tailed test, given the p-value from a two-tailed test. A p-value essentially indicates the probability that you would obtain the observed data, or data more extreme if the null hypothesis is true. In this instance, the experimenter has a p-value of 0.44 from a two-tailed test.
When converting this to a one-tailed test, the p-value would effectively be halved. Therefore, if they conducted a one-tailed test on the same data, the p-value would be 0.22 (i.e., 0.44/2) in the direction specified by the alternative hypothesis. Thus, between the provided options, none are perfectly correct, but option C) 'The possible p-values are 0.22 and 0.78.' is closest to the correct interpretation, with the accurate p-value being 0.22 rather than 0.78.
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A youth club receives a discount on each pizza purchased for a party. The original price of each pizza is x dollars. The club leader purchases 8 pizzas for a total of (8x-32) dollars. Factor the expression
Answer:
The factored form is [tex](8x-32)=8(x-4)[/tex]
Step-by-step explanation:
Given : A youth club receives a discount on each pizza purchased for a party. The original price of each pizza is x dollars. The club leader purchases 8 pizzas for a total of (8x-32) dollars.
To find : Factor the expression ?
Solution :
The original price of each pizza is x dollars.
The club leader purchases 8 pizzas for a total of [tex](8x-32)[/tex] dollars.
To factor the expression we have to take common term out.
So, [tex]8x=8\times x[/tex]
[tex]32=8\times 4[/tex]
8 is common take out,
[tex](8x-32)=8(x-4)[/tex]
Factors are 8 and (x-4).
Therefore, the factored form is [tex](8x-32)=8(x-4)[/tex]
To factor the expression (8x - 32), we take out the common factor of 8, resulting in the factored form of 8(x - 4), indicating a $4 discount per pizza.
Explanation:The question is asking to factor the expression, which represents the total cost for purchasing 8 pizzas after receiving a discount from the original price x dollars per pizza. The expression given is (8x - 32) dollars.
To factor this expression, we look for a common factor in both terms which is 8.
Factoring out the 8, we get 8(x - 4). This means the club receives a discount of $4 per pizza since (8x - 32) factors into 8 times (x - 4).
i require some assistance :(, please help ASAP. Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Use the definitions and theorems of this section to evaluate and simplify the following expression. Be sure to express answers with positive exponents. (b^2)^3
Answer:
My guess is 2b^5
Step-by-step explanation:
This question is kinda tricky. LMK if its correct
A 2956 kg car starts from rest at the top of a driveway of length 6 m that is sloped at 35◦ with the horizontal. An average frictional force of 3080 N impedes the motion. Find the speed of the car at the bottom of the driveway. The acceleration of gravity is 9.8 m/s 2 . Answer in units of m/s.
Answer:
7.41 m/s
Step-by-step explanation:
Force of a car inclined at an angle
F=mg Sin Θ where; m = 2956 kg , g = 9.8m/s² , Θ = 35⁰
F = 2956 x 9.8 x Sin 35 = 16615.82 N
Net force due to friction = 16615.82 - 3080 = 13535.82 N
To calculate acceleration; F= Ma
13535.82 = 2956 x a
a = 4.58 m/s²
From equation of motion
[tex]V^{2} = V_{o} ^{2} + 2aS[/tex]
V² = 0 + (2 x 4.58 x 6)
V = [tex]\sqrt{54.95}[/tex]
V = 7.41 m/s
The addition law is potentially helpful when we are interested in computing the probability of
Answer:
The union of two event
Step-by-step explanation:
Addition law of probability define that probability of two event is total sum of probability of any event subtract the probability of both events
There are two rules in addition law:
Addition law 1 - when both event are mutually exclusive, then probability of either event is the sum of each event probability.
P( A or B) = P(A) +P(B)
Addition law 2 - when both events are non mutually exclusive then there in addition to the individual probability there is some overlap .
P( A or B) = P(A) +P(B) - P(A and B)
It should be noted that addition law is potentially helpful when we are interested in computing the probability of The union of two event.
According to this question, we are to discuss about Addition law of probability.
As a result of this we can see that Addition law of probability explain about probability for either of two mutually exclusive events which is occurring and also the probability of two non-mutually exclusive events that is occurring.
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Which of the following statements would be correct to use when proving that limx→4(3x−4)=8?
a. Given 0<∣∣x−4∣∣<ϵ, then ∣∣(3x−4)−8∣∣<ϵ3.
b. Given 0<∣∣x−4∣∣<ϵ3, then ∣∣(3x−4)−8∣∣<ϵ.
c. Given 0<∣∣x−8∣∣<ϵ, then ∣∣(3x−4)−4∣∣<ϵ3.
d. Given 0<∣∣x−8∣∣<ϵ3, then ∣∣(3x−4)−4∣∣<ϵ.
e. Given 0<∣∣x−4∣∣<3ϵ, then ∣∣(3x−4)−8∣∣<ϵ.
f. Given 0<∣∣x−4∣∣<3ϵ, then ∣∣(3x−4)−8∣∣<ϵ3.
Answer:
Option c
Step-by-step explanation:
given that limit x tending to 4 of the function (3x-4) is 8
This implies for all values of x such that for epsilon >0 arbitrary small ,
[tex]||x-4||<\epsilon[/tex], we get
|f(x)-8|<3epsilon
this is equivalent to the option c.
Proof:
Consider
[tex]||x-4||<\epsilon\\3||x-4||<3\epsilon\\||3x-12||<3\epsilon\\||3x-4|-8| <3\epsilon[/tex]
Hence it follows that option C is right.
The correct statement to use when proving that limx→4(3x−4)=8 is option b: Given 0 < | x - 4 | < epsilon/3, then | (3x - 4) - 8 | < epsilon. This uses the formal definition of limit and abides the epsilon-delta parameters definition to provide the correct proof.
Explanation:To verify the given limit, we need to utilize the formal definition of a limit. This formal definition gives us a systematic method to prove a limit based on epsilon-delta parameters. The purpose is to show that as x gets closer and closer to 4 (with| x - 4 | being smaller than an arbitrary positive delta), the expression (3x-4) increasingly approaches 8 (with |(3x - 4) - 8| getting within an epsilon range).
The correct choice is: b. Given 0 < | x - 4 | < epsilon/3, then | (3x - 4) - 8 | < epsilon. In this case, 'epsilon/3' in | x - 4 | < 'epsilon/3' is the delta in the epsilon-delta definition of limit. Essentially, it captures the notion that for every epsilon > 0, there exists a delta > 0 such that 0 < | x - 4 | < delta implies | (3x - 4) - 8 | < epsilon, thereby proving the limit.
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what has a head, a tail, is brown, and has no legs
Answer:
A penny
Step-by-step explanation:
a penny
_______
_______
Chris pays a fee if her balance falls below $10 on the statement data. Prior to the statement date, her balance was -$3.46. Then Chris made a deposit, d, in ample time, so she did not have to pay a fee. Write and solve an inequality to represent this situation. P
Answer:
The solution of the inequality required for the situation is d ≥ $13.46.
Step-by-step explanation:
i) the minimum deposit is $10.
ii) the balance before the statement is $-3.46
iii) a deposit d is made so that the fee did not have to be made
iv) therefore d + (-3.46) ≥ 10
d - 3.46 ≥ 10
therefore d ≥ 10 + 3.46
therefore d ≥ $13.46
Chris would have to deposit at least $13.46 into her account in order to avoid being charged a fee. This amount is determined by setting up and solving the inequality -3.46 + d ≥ 10, which represents her account balance.
Explanation:In this situation, Chris is trying to avoid a fee by maintaining a balance of at least $10 in her account. Prior to making a deposit, her account balance is -$3.46. Thus, we need to find out the minimal deposit, d, that she needs to make in order to bring her balance up to $10. To do this, we can set up the following inequality:
-3.46 + d ≥ 10
To solve the inequality for d, we simply add 3.46 to both sides of the inequality:
d ≥ 13.46
Therefore, Chris must make a deposit of at least $13.46 to avoid incurring the fee.
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If Alex and Brandon work together they will clean the school in 15 hours. Working alone, Brandon can finish the same job in 20 hours. How long will it take Alex to do the job by himself? PLEASE HELP ME PRETTY PLEASE
Answer:
It takes 60 hours for Alex to complete the job alone.
Step-by-step explanation:
Given:
Number of hours Brandon alone can finish job =20 hours
Let the number of hours required by Alex alone to complete the job be 'x' hrs.
We need to find the number of hours required by Alex alone to complete the job.
Solution:
Now we can say that;
Rate at which Alex can complete the job alone = [tex]\frac1x[/tex] job/hour
Rate at which Brandon can complete the job alone = [tex]\frac{1}{20}[/tex] job /hour
Also Given:
Number of hours required for both to complete the job = 15
So rate of both complete the job = [tex]\frac{1}{15}[/tex] job/hour
Now we can say that;
rate of both complete the job is equal to sum of Rate at which Alex can complete the job alone and Rate at which Brandon can complete the job alone.
framing in equation form we get;
[tex]\frac1x+\frac{1}{20}=\frac{1}{15}[/tex]
Now taking LCM for making the denominators same we get;
[tex]\frac{20}{20x}+\frac{x}{20x}=\frac{1}{15}[/tex]
Now denominators are common so we will solve the numerators.
[tex]\frac{20+x}{20x}=\frac{1}{15}[/tex]
Now Using cross multiplication we get;
[tex]15(20+x)=20x[/tex]
Applying Distributive property we get;
[tex]15\times20+15\times x =20x\\\\300+15x=20x[/tex]
Combining like terms we get;
[tex]300=20x-15x\\\\300=5x[/tex]
Now Dividing both side by 5 we get;
[tex]\frac{300}{5}=\frac{5x}{5}\\\\x=60\ hrs[/tex]
Hence It takes 60 hours for Alex to complete the job alone.
To find how long it will take Alex to complete the job by himself, we first establish the individual work rates of Alex and Brandon. We know the combined work rate (1/15 jobs per hour) and Brandon's work rate (1/20 jobs per hour). Alex's work rate is thus 1/15 - 1/20 = 1/60 jobs per hour, which means it will take him 60 hours to do the job alone.
Explanation:This question requires knowledge of work rate calculations in Mathematics. The scenario involves two workers, Alex and Brandon, who can complete a cleaning task together in 15 hours. It's also given that Brandon can do the job alone in 20 hours, and we need to calculate how long it would take for Alex to complete the job by himself.
First, let's define their rates of work. If Brandon can complete the job in 20 hours, his work rate is 1 job per 20 hours, or 1/20 jobs per hour. Similarly, if Alex and Brandon together can complete the job in 15 hours, their combined work rate is 1 job per 15 hours, or 1/15 jobs per hour.
To find Alex's work rate, we subtract Brandon's work rate from the combined work rate. Thus, Alex's work rate is 1/15 - 1/20 = 1/60 jobs per hour. This means it would take Alex 60 hours to complete the job on his own.
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please help me I really need help
Answer:
both are done
look at picture
1. 13/36
2. 3/16
Jose is training for a half -marathon .Each week he runs x miles per day for 5 days .For 3 days of the week he runs at a speed of 8 minutes per mile .For 2 days he runs 7-minute miles. Write an expression to represent the amount of time,in minutes,that jose runs in 4 weeks
Answer:
152x miles
Step-by-step explanation:
Jose runs x miles per day each week for 5 days.
For 3 days of the week he runs at a speed of 8 minutes per mile. So we have
3*8*x = 24x
For 2 days he runs 7 minutes per miles. We have
2*7*x = 14x
in one week, he runs 24x + 14x = 38x
In 4 weeks, he runs
4*38x = 152x miles
-------100 POINTS------
Complete the proof of the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse's length equals the sum of the squares of the other two sides' lengths. This can be proven via the areas of squares with sides corresponding to the triangle's sides, demonstrating that a²+b²=c².
Explanation:The Pythagorean theorem is a fundamental principle in geometry, named after the Greek mathematician Pythagoras. It states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a²+b²=c².
To prove this, we can begin with a right-angled triangle with sides a, b, and hypotenuse c. If we square the length of c (i.e., c²), this is equivalent to the area of a square with side length c. Similarly, a² and b² represent the areas of squares with side lengths a and b, respectively.
If we add together the areas of the two smaller squares (a²+b²), this equals the area of the larger square (c²). This proves the Pythagorean theorem. For instance, consider a right triangle with sides of lengths 3, 4, and 5. The squares would have areas 9 and 16, which add up to 25 - the area of the square on the hypotenuse.
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The Pythagorean Theorem states that a² + b² = c². A step-by-step proof involves constructing a square with the right-angled triangle and equating the areas. This logical deduction confirms the theorem's correctness.
The Pythagorean Theorem is one of the fundamental results in Geometry, which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): a² + b² = c². Here is a step-by-step proof:
Construct a right-angled triangle with legs a and b and hypotenuse c.Construct a square with side a + b. Within this square, place four identical right-angled triangles, each having sides a, b, and c.The four triangles will leave a smaller square in the middle with side c.The area of the larger square is (a + b)², which can be expanded as a² + 2ab + b².The area of the larger square is also the sum of the areas of the four triangles and the smaller square in the center, which is 4 (1/2ab) + c² simplifying to 2ab + c².Setting the two expressions for the area of the larger square equal gives: a² + 2ab + b² = 2ab + c².By subtracting 2ab from both sides, we get the Pythagorean Theorem: a² + b² = c².Thus, we have proven that the theorem holds true using logical deductions.
Use the definition of a derivative to find f’(x).
f(x) = 9/x
Please show the steps. I cannot find a way to solve it in the way that is shown by the examples given around online e.t.c.
Answer:
f'(x) = [tex]-\frac{9}{x^2}[/tex]
Step-by-step explanation:
i) f(x) = 9 / x
ii) f'(x) = [tex]$\lim_{h\to 0} \frac{f(x+h) - f(x)}{h} $ \hspace{0.2cm}[/tex]
[tex]= $\lim_{h\to 0} \frac{\frac{9}{x+h} - \frac{9}{x} }{h} = \hspace{0.1cm} $\lim_{h\to 0} \frac{9x - 9(x+h)}{hx(x+h)} $ \hspace{0.1cm} = \hspace{0.1cm}$\lim_{h\to 0} \frac{-9h}{hx(x+h)} = $\lim_{h\to 0} \frac{-h}{x(x+h)} = \frac{-9}{x^2}$[/tex]
Please assist me in 6-30
Answer:
Yes to both.
Step-by-step explanation:
It is true that
[tex]\dfrac{x}{y}=1 \iff x=y[/tex]
In fact, if you know that x/y=1, just multiply both sides by y to get x=y. On the other hand, if you know that x=y (and they are not zero), you can divide both sides by y to get x/y=1.
Since the two expressions are equivalent, you can always use Phil's or Don's expression, at will.
Mr wells drew a plan for a rectangle dog run three of the vertices are (2 1/3, 7 1/2), (12, 7 1/2), and (12, 1) what are the coordinates of the fourth vertex
Answer:
Step-by-step explanation:
let 4th fourth vertex be D (x,y)
A(2 1/3,7 1/2),B(12, 7 1/2),C(12,1)
or A(7/3,15/2),B(12,15/2),C(12,1)
Mid-point of diagonal AC is P((7/3+12)/2,(15/2+1))
Mid -point of diagonal BD is P((12+x)/2,(15/2+y)/2)
(Because mid -point of diagonal is same.)
(12+x)/2=(7/3+12)/2
12+x=7/3+12
x=7/3
(15/2+1)/2=(15/2+y)/2
15/2+1=15/2+y
y=1
so fourth vertex is (7/3,1)
To find the coordinates of the fourth vertex of the rectangle, we use the information provided about the positions of the third vertex and the Car X figure. The coordinates of the fourth vertex are (13 2/3, 7 1/2) and (12, 2).
Explanation:To find the coordinates of the fourth vertex of the rectangle, we can use the fact given that the third vertex is one and two-thirds perpendicular hash marks to the right of the center top hash mark. Since the center top hash mark is at (12, 7 1/2), the third vertex is at (12 + 1 2/3, 7 1/2), which simplifies to (13 2/3, 7 1/2).
Now, we need to find the position of the fourth vertex. According to the given information, the fourth vertex is in the same position as the Car X figure, which means it is one perpendicular hash mark above the center right hash mark. Since the center right hash mark is at (12, 1), the fourth vertex is at (12, 1 + 1), which simplifies to (12, 2).
Therefore, the coordinates of the fourth vertex are (13 2/3, 7 1/2) and (12, 2).
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