(a) Use slope-intercept form to write an equation of the line that passes through the given point and has the given slope.
(b) Write the equation using function notation where .
Answers
The equation of the line is y = 3x/2 - 8 and can be rewritten using function notation as f(x) = 3x/2 - 8
Slope intercept form:
The slope-intercept form of a line is given by
y = mx + c
Where 'm' is slope and c in y-intercept
Here we have
The coordinate of points (0, -8) and slope (m) = 3/2
As we know the formula for slope intercept form is y = mx + c
Where 'm' is the slope
=> y = (3/2)x + c
=> -8 = 3/2(0) + c
=> c = - 8
Hence, Equation of the line is y = 3/2(x) + (-8)
=> y = 3x/2 - 8
The equation can be rewritten using function notation as follows
=> f(x) = 3x/2 - 8
Therefore,
The equation of the line is y = 3x/2 - 8 and can be rewritten using function notation as f(x) = 3x/2 - 8
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Related Questions
What is the height of the parallelogram?
12 m
A = 186 m²
Answers
Answer: 15.5
Step-by-step explanation:
H = A/B
= 186/12
= 15.5
a pharmaceutical company investigating whether drug stores are less likely than food markets to remove over-the-counter drugs from the shelves when the drugs are past the expiration date found a p-value of 2.8%. this means that:
Answers
qwerty
2.8% the answer is 2.8% and b is 2.8%
Jennifer bought 14.75 gallons of gasoline for her car at a cost of $2.95 a gallon. which is closest to the amount she paid for the gasoline?
Answers
The total amount paid by Jennifer for 14.75 gallons of gasoline at the cost of $2.95per gallons is equal to $43.51.
Total gallons of gasoline bought by Jennifer for her car = 14.75 gallons
Cost of gasoline per gallons = $2.95
The total amount Jennifer paid for the gasoline is equal to,
Amount paid by Jennifer
= Number of gallons of gasoline x Cost per gallon
Substitute the value in the formula we get,
⇒ Amount paid by Jennifer = 14.75 gallons x $2.95/gallon
⇒ Amount paid by Jennifer = $43.5125
⇒ Amount paid by Jennifer = $43.51
Therefore, the closest amount Jennifer paid for the gallons of gasoline is equal to $43.51.
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miguel went to a movie theater and bought a large bag of popcorn that cost $10.49. to avoid spending too much money in all, he determined that he could spend up to $5.51 on a drink. let x represent how much money miguel wanted to spend in all. which inequality describes the problem?
Answers
The inequality that represents Miguel's spending limit is $16.00 ≤ x.
Let x represent the total amount of money Miguel wants to spend. We know he spent $10.49 on popcorn and can spend up to $5.51 on a drink.
To find the inequality, we can add these two amounts together and set it less than or equal to x, since x represents the maximum amount he wants to spend. Mathematically, we can write:
$10.49 + $5.51 ≤ x
Simplifying this inequality, we get:
$16.00 ≤ x
This means that Miguel can spend up to $16.00 in total on the popcorn and drink combined. If he spends more than $16.00, he will have exceeded his limit.
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Kyle is playing a game where he rolls a number cube twice and flips a coin twice. The number cube is labeled 1 to 6. The coin can land on heads or tails.
If the number cube lands on 5 both times and the coin lands on heads both times, Kyle wins a prize. What is the probability that Kyle wins the prize?
Answers
The chance of rolling two 5s and flipping two heads can be calculated by multiplying the odds together because each cube and coin flip is independent. the probability that Kyle wins the prize is [tex]1/144[/tex]
What is the probability?The probability of rolling a 5 on a number cube is 1/6, and the probability of flipping heads on a coin is 1/2.
Since each roll of the cube and flip of the coin is independent, we can find the probability of rolling two 5's and flipping two heads by multiplying the probabilities together:
P(rolling two 5's and flipping two heads) = P(rolling a 5) * P(rolling a 5) * P(flipping heads) * P(flipping heads)
[tex]= (1/6) \times (1/6) \times (1/2) \times (1/2)[/tex]
[tex]= 1/144[/tex]
Therefore, the probability that Kyle wins the prize is ,[tex]1/144[/tex] or approximately [tex]0.0069[/tex] (rounded to four decimal places).
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64x=8
What is the value of x that makes the equation true.
Answers
Answer:
x=8
Step-by-step explanation:
8 x 8 = 64
You can find this answer by using inverse operations.
64/8 = 8
To check your work, you can multiply...
8x8 = 64.
Hope this helps!
please help me im begging (ignore the cat hair)
Answers
Step-by-step explanation:
The circumference of a circle is given by the formula:
C = πd
where d is the diameter of the circle and π is a mathematical constant approximately equal to 3.14159.
In this case, the diameter of the circle is 58, so we can substitute this value into the formula:
C = πd
C = π(58)
C ≈ 182.09
Therefore, the circumference of the circle with diameter 58 is approximately 182.09 units. Note that the units of measurement were not specified in the question, so the units of the answer will depend on the units used for the diameter.
abc is a right triangle with points a 2,5 b 2,0 and c x,0. if the area of abc is 25 square units, what us the equation of ac?
Answers
As the given abc is a right triangle with points a(2, 5), b(2, 0), and c(x, 0). The area of 'abc' is 25 square units. and the equation of AC is x = 5√5.
The equation of ac has to be found. Since triangle ABC is right-angled, it can be shown that
AC² = AB² + BC²
Finding the lengths of AB and BC before using the Pythagorean theorem to find AC.
Using the distance formula,
AB =√(5²+0²)
= √25
= 5,
And BC = √(x²+0²)
= √x²
= x.
Area of a right triangle = ½(base × height)
Here base = AB and height = BC,
So, ½ × 5 × x = 25
⇒ 5x = 50
⇒ x = 10
Now, to find AC, use the Pythagorean Theorem.
AC² = AB² + BC²
= 5² + 10²
= 25 + 100
= 125AC
= √125
= 5√5
Thus, the equation of AC is x = 5√5. Answer: x = 5√5.
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find the amount due on the loan round to the nearest cent.
principal= $4,000
rate =7 1/2 %
time in months = 3
Answers
Answer:
The first step is to calculate the interest that accrues over the 3-month period:
Interest = Principal x Rate x Time
= $4,000 x 0.075 x (3/12)
= $75
The amount due on the loan is the sum of the principal and interest:
Amount due = Principal + Interest
= $4,000 + $75
= $4,075
Rounding to the nearest cent gives: $4,075.00
WILL GIVE BRAINLY
If sin (x) =3 cos(x), then what is sin(x) times cos (x)?
Answers
sin^2(x) + cos^2(x) = 1
Dividing both sides by cos^2(x):
tan^2(x) + 1 = sec^2(x)
Substituting sin(x) = 3cos(x) into the left-hand side:
tan^2(x) + 1 = (1/9)sec^2(x)
Multiplying both sides by cos^2(x):
(sin(x)/cos(x))^2 + cos^2(x) = (1/9)(1/cos^2(x))
Expanding the left-hand side:
sin^2(x)/cos^2(x) + cos^2(x) = 1/9cos^2(x)
Rearranging and factoring out cos^2(x):
sin^2(x) = (1/8)cos^4(x)
Multiplying both sides by cos(x):
sin^2(x)cos(x) = (1/8)cos^5(x)
Using the identity sin(x)cos(x) = (1/2)sin(2x):
(1/2)sin(2x) = (1/8)cos^5(x)
Multiplying both sides by cos(x):
(1/2)sin(2x)cos(x) = (1/8)cos^6(x)
Using the identity sin(2x) = 2sin(x)cos(x):
sin(x)cos(x) = (1/16)cos^6(x)
Therefore, sin(x)cos(x) is equal to (1/16)cos^6(x).
i dont know how yo do this question
Answers
Step-by-step explanation:
2x + 2y = 28 <=====given
x * y = 40 <===given ..... re-arrange to :
y = 40 / x <===substitute this 'y' into the first equation
2x + 2 ( 40/x) = 28 <=====solve for x
2x^2 -28x + 80 = 0
x^2 -14x +40 = 0
(x -10)(x-4) = 0 shows x = 10 or 4 then y = 4 or 10
dimensions 10 and 4 inches
Answer:
4 or 10 inches
Step-by-step explanation:
I added a photo of my solution
Hudson is a waiter at a restaurant. Each day he works, Hudson will make a guaranteed wage of $30, however the additional amount that Hudson earns from tips depends on the number of tables he waits on that day. From past experience, Hudson noticed that he will get about $13 in tips for each table he waits on. How much would Hudson expect to earn in a day on which he waits on 18 tables? How much would Hudson expect to make in a day when waiting on t tables?
Answers
The total amount of money earned by Hudson in a day on which he waits on 18 tables is $264.
The total amount of money earned by Hudson in a day on which he waits on t tables is $(30 + 13t).
How to determine Hudson's earnings in a day on which he waits on 18 tables?Based on the information provided above, we can logically deduce that a linear equation that models the total amount of money earned by Hudson at this restaurant is represented by the following function:
y = 30 + 13t
Where:
t represent the number of tables he waits on that day.y represent the total earnings.When the number of tables he waits on that day is equal to 18, Hudson's total earnings can be calculated as follows;
y = 30 + 13t
y = 30 + 13(18)
y = $264.
When the number of tables he waits on that day is t tables, Hudson's total earnings can be calculated as follows;
y = 30 + 13t = $(30 + 13t).
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L(-1,6), M(5,8), N(0,2), P(-8,12)
Determine whether the quadrilateral is a parallelogram using the specific method. (Distance formula)
Answers
Yes, the quadrilateral is a parallelogram. To prove this using the distance formula method, we need to show that opposite sides of the quadrilateral are equal in length.
We can calculate the distance between each pair of points using the distance formula:
d = [tex]\sqrt{((x2 - x1)^2 + (y2 - y1)^2)}[/tex]
Using this formula, we get:
d(LM) = √[tex]((5 - (-1))^2 + (8 - 6)^2)[/tex] = √(36 + 4) = √(40) = 2√(10)
d(NP) = √[tex]((-8 - 0)^2 + (12 - 2)^2)[/tex] = √(64 + 100) = √(164) = 2√(41)
d(LN) = √[tex]((0 - (-1))^2 + (2 - 6)^2)[/tex] = √(1 + 16) = √(17)
d(MP) = √[tex]((-8 - 5)^2 + (12 - 8)^2[/tex]) = √(169 + 16) = √(185)
We can see that d(LM) = d(NP) and d(LN) = d(MP), which means that opposite sides of the quadrilateral are equal in length. Therefore, the quadrilateral is a parallelogram.
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a pair of headphones originally costs 95$ and is on sale for 70$ what is the percent change in the price of the headphones? be sure to show whether it is a percent increase or decrease.
Answers
The percent decrease in the price of the headphones is 26.32%.
Explanation:
To find the percent change in price, we can use the following formula:
percent change = (new value - old value) / old value * 100%
In this case, the old value is the original price of the headphones, which is $95.
The new value is the sale price, which is $70. Plugging these values into the formula, we get:percent change = (70 - 95) / 95 * 100%
percent change = -25 / 95 * 100%
percent change = -0.2632 * 100%
percent change = -26.32%
The negative sign indicates that the price has decreased, and the magnitude of the percent change is 26.32%, which means that the sale price is 26.32% lower than the original price.
the cpa practice advisor reports that the mean preparation fee for federal income tax returns was . use this price as the population mean and assume the population standard deviation of preparation fees is .
Answers
The CPA Practice Advisor reports that the mean preparation fee for federal income tax returns was 261. Use this price as the population mean and assume the population standard deviation of preparation fees is 120.
We need to find the probability of selecting a random sample of 20 tax returns and a standard deviation of the sample preparation fees of 50 or less.
We use the central limit theorem that states that, regardless of the shape of the population, the sampling distribution of the sample means approaches a normal distribution with mean μ and standard deviation
σ/√n
where μ is the population mean, σ is the population standard deviation, and n is the sample size.
Therefore, we have:
[tex]\mu = 261\]\\sigma = $120\]\\n = 20\][/tex]
[tex]S.E.= \frac{\sigma}{\sqrt{n}}\\S.E =\frac{\ 120}{\sqrt{20}}\\S.E =26.83[/tex]
The probability of selecting a random sample of 20 tax returns and a standard deviation of the sample preparation fees of 50 or less is given by:
[tex]P(Z < \frac{X - \mu}{S.E})\][/tex]
where X is the sample mean, μ is the population mean, and S.E is the standard error of the mean.
To calculate the probability, we standardize the distribution of the sample means using the z-score formula, i.e.,
[tex]\[z = \frac{X - \mu}{S.E} = \frac{\50 - \261}{\26.83} = -7.91\][/tex]
Therefore, the probability of selecting a random sample of 20 tax returns and a standard deviation of the sample preparation fees of 50 or less is zero because the z-score is less than the minimum z-score (i.e., -3.89) that corresponds to the probability of selecting a random sample of 20 tax returns and a standard deviation of the sample preparation fees of 50 or less.
Thus, it is impossible to obtain such a sample.
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the probability is approximately 0.6 that in a randomly selected week, they will make a combined total less than what amount?
Answers
There is a probability of around 60% that during a week picked randomly, the combined sum of their earnings will be below $0.2533.
The given probability is a measure of the chances that the occurrence of an event will happen. In the context of the question, we want to calculate the combined total of earnings that are less than a certain amount. We know that the probability is approximately 0.6. Therefore, the answer is given by the value that satisfies this condition.
That is, P(X < a) = 0.6where X represents the combined total earnings of a randomly selected week, and a is the required amount.
To solve for a, we can use the cumulative distribution function (CDF) of X. The CDF gives the probability that X is less than or equal to a. Therefore, CDF(a) = P(X ≤ a)
The complement of this probability isP(X > a) = 1 - CDF(a)
We know that P(X < a) = 0.6, which is equivalent to (X ≤ a) = P(X < a) + P(X = a) = 0.6 + 0 = 0.6
Therefore, P(X > a) = 1 - CDF(a) = 1 - P(X ≤ a) = 1 - 0.6 = 0.4
Now we can use a calculator to find the value of a that corresponds to P(X > a) = 0.4.
For example, if we use a calculator, we get a value of a = 0.2533 (rounded to four decimal places).
Therefore, the probability is approximately 0.6 that in a randomly selected week, they will make a combined total of less than $0.2533.
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PLEAaSE HELP PLSSSS!!!!!
Answers
Answer:
= 58/33
= 1 25/33
Step-by-step explanation:
12/11 - (-2/3) =
= 12/11 + 2/3
= 36/33 + 22/22
= 58/33
= 1 25/33
emme takes a quiz for her anthropology 401e course. there are 9 multiple-choice questions on the test with 4 answer choices, only one of which is correct. emme has not studied for the test, so she just randomly guesses the answers. what is the probability that emme answers exactly 3 questions correctly? enter your answer as a decimal with four significant digits
Answers
The probability that Emme answers exactly 3 questions correctly is 0.1961.
Since each question has four answer choices and only one is correct, the probability of Emme randomly guessing the correct answer for each question is 1/4 = 0.25. Emme needs to answer exactly 3 out of the 9 questions correctly, so we use the binomial distribution with n = 9 and p = 0.25 to calculate the probability:
P(X = 3) = (9 choose 3) * (0.25)^3 * (0.75)^6
Using a calculator, we get:
P(X = 3) = 0.1961
Therefore, the probability that Emme answers exactly 3 questions correctly is 0.1961.
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Write the compound inequality that represents the statement. The quotient of a number y and 3, less 2 is between –7 and 4.
Solve the compound inequality.
Answers
The compound inequality is -7 < y/3 - 2 < 4 and the solution is -15 < y < 18
identifying and solving the compound inequalityTo write the compound inequality that represents the statement, we can first translate the words into symbols:
The quotient of a number y and 3, less 2: y/3 - 2
Is between -7 and 4: -7 < y/3 - 2 < 4
So the compound inequality that represents the statement is:
-7 < y/3 - 2 < 4
To solve this compound inequality, we can first add 2 to all parts of the inequality:
-7 + 2 < y/3 - 2 + 2 < 4 + 2
Simplifying, we get:
-5 < y/3 < 6
To isolate y/3, we can multiply all parts of the inequality by 3:
-15 < y < 18
Therefore, the solution to the compound inequality is: -15 < y < 18
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A fish tank, in a shape of rectangular prism, measures
100 cm × 60 cm X40 cm. The water level reached the blvoo eveD gror vIs midpoint of the base (the 50 cm mark), when the tank was tilted to rest on a 60 cm edge, as shown in the
100
diagram on the right. What would be the depth of the water, if the tank is returned to its horizontal position (resting on its 60 cm × 100 cm base)?
Answers
When the tank is tilted, the water level reaches the midpoint of the 60 cm side, which is 30 cm from the bottom of the tank. This means that the height of the water is 30 cm.
To find the depth of the water when the tank is returned to its horizontal position, we need to use the concept of similar triangles. The two triangles formed by the water level and the sides of the tank are similar, because they have the same angles.
Let x be the depth of the water in centimeters when the tank is returned to its horizontal position. Then we have:
(40 - x) / 60 = 30 / 50
Simplifying this equation, we get:
40 - x = 36
x = 4
Therefore, the depth of the water in the fish tank when it is returned to its horizontal position is 4 cm.
Solve the equation x² = 4.
Do u know what is x ?
Answers
Answer:
x= 2
Step-by-step explanation:
² means times the number itself 2 times.
2×2=4
Polygon ABCD with vertices at A(1, −1), B(3, −1), C(3, −2), and D(1, −2) is dilated to create polygon A′B′C′D′ with vertices at A′(4, −4), B′(12, −4), C′(12, −8), and D′(4, −8). Determine the scale factor used to create the image.
1/4
1/2
2
4
Answers
The scale factor used to create the dilated polygon is 4.
What is scaler factor?
Scale factor is a numerical ratio that describes how much a geometric figure has been enlarged or reduced. It is the ratio of the length of a side, diagonal, or any other linear dimension of the new (dilated) figure to the corresponding dimension of the original figure.
The distance between two points can be calculated using the distance formula: [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.[/tex]
To determine the scale factor, we need to compare the distances between corresponding points in the original and dilated polygons. Let's start by finding the distance between points A and B in the original polygon:
[tex]$d_{AB}=\sqrt{(3-1)^2+(-1+1)^2}=\sqrt{4}=2$[/tex]
Now let's find the distance between corresponding points A' and B' in the dilated polygon:
[tex]$d_{A'B'}=\sqrt{(12-4)^2+(-4+4)^2}=\sqrt{64}=8$[/tex]
To find the scale factor, we divide the corresponding distances:
[tex]$scale\ factor=\frac{d_{A'B'}}{d_{AB}}=\frac{8}{2}=4$[/tex]
Therefore, the scale factor used to create the dilated polygon is 4.
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consider rolling two dice. which of the following describe two events that are collectively exhaustive? multiple select question. event 1: a value of 6 or more. event 2: a value of 8 or less. event 1: a value of 9 or more. event 2: a value of 7 or less. event 1: a value of 7 or more. event 2: a value of 6 or less. event 1: rolling an even number. event 2: rolling an odd number.
Answers
Two events that are collectively exhaustive are event 1: a value of 6 or more and event 2: a value of 7 or less.
These events are collectively exhaustive because the events cover the entire possible range of values of the dice rolls. If one of these events does not occur, then the other event must occur. This means that the sum of the dice rolls is either 6 or less, or it is greater than 6. This means that the sum of the dice rolls is either 7 or more, or it is less than 7.
Another set of events that are collectively exhaustive are event 1: rolling an even number and event 2: rolling an odd number. These events are collectively exhaustive because the events cover the entire set of possible outcomes of rolling two dice. If one of these events does not occur, then the other event must occur. This means that the sum of the dice rolls is either even or odd. This means that the sum of the dice rolls is not both even and odd at the same time.
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Evaluate
8
�
−
1
+
0. 5
�
8a−1+0. 5b8, a, minus, 1, plus, 0, point, 5, b when
�
=
1
4
a=
4
1
a, equals, start fraction, 1, divided by, 4, end fraction and
�
=
10
b=10b, equals, 10
Answers
The evaluation of the algebraic expression 8a-1+0.5b when a=1/4 and b=10 is 6.
We are given an expression 8a−1+0.5b8, and we are asked to evaluate it when a = 1/4 and b = 10. Substituting these values, we get:
8(1/4) - 1 + 0.5(10) = 2 - 1 + 5
Simplifying the expression on the right-hand side, we get:
8a−1+0.5b8 = 6
Therefore, when a = 1/4 and b = 10, the value of the expression 8a−1+0.5b8 is 6.
This means that if we substitute the given values for a and b, the resulting expression will have a value of 6. It is important to correctly substitute the values before evaluating the expression to obtain the correct answer.
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____The given question is incomplete, the complete question is given below:
Evaluate 8 a − 1 + 0.5 b 8a−1+0.5b8, a, minus, 1, plus, 0, point, 5, b when a = 1 4 a= 4 1 a, equals, start fraction, 1, divided by, 4, end fraction and b = 10 b=10b, equals, 10.
Determine the equation of the circle graphed below.
Answers
Answer:
Step-by-step explanation:
Circle centre: (4,7)
Radius: 3
Equation is:
[tex](x-h)^2+(y-k)^2=r^2[/tex] (where (h,k) is center, r is radius)
[tex](x-4)^2+(y-7)^2=3^2[/tex]
[tex](x-4)^2+(y-7)^2=9[/tex] (This is the general standard form )
in expanded form,
[tex](x^2-8x+16)+(y^2-14y+49)=9[/tex]
[tex]x^2+y^2-8x-14y+56=0[/tex]
Note: Unless stated either form is an acceptable answer.
Jhoney ate 3 apples and have 2 left how much did he eat?
Answers
By probability , 3 Apples are left .
What does a probability simple definition entail?
A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
The probability is a metric for determining how likely an event is to occur. It gauges how likely an event is. The probability equation is stated by the following notation: P(E) = Number of Favorable Outcomes/Number of Total Outcomes.
Jhoney ate = 3 apples
= 2 left
he eat = ³C₂
= 3!/(3-2)! 2!
= 3
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a bag contains a collection of distinguishable marbles. the bag has two red marbles, four green ones, one lavender one, six yellows, and five orange marbles. hint [see example 7.] how many sets of four marbles include exactly two green marbles? (note that this means there must be two other non-green marbles as well).
Answers
Therefore, the total number of sets of four marbles, including exactly two green marbles, is 720.
The given bag contains a total of [tex](2+4+1+6+5)=18[/tex] marbles.
There are two possibilities of selecting two green marbles and the other two marbles in a set, as shown below;GG -- NN (No Green Marbles)GG -- RR (No Green Marbles)GG -- YY (No Green Marbles)GG -- OO (No Green Marbles)GG -- GL (Lavender)GG -- RG (Red)GG -- OG (Orange)
The first two options have no green marbles; thus, they are eliminated. We can select non-green marbles in C(16,2) = 120 ways, then multiply by C(4,2) = 6 to choose two green marbles out of four.So, the total number of such sets is
[tex]120 × 6 = <<120*6=720>>720.[/tex]
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If you have 4 purple marbles and 8 yellow marbles in a bag. What is the probability of getting a purple marble
Answers
You have a 4/12 probability.
Dan had 50% fewer stickers than Jeff. After Jeff gave 20 of his stickers to Dan, Dan had 40% fewer stickers than Jeff (had after he gave away 20 of his stickers). How many stickers did Dan have at first?
Answers
Dan had 50% fewer stickers than Jeff. After Jeff gave 20 of his stickers to Dan, Dan had 40% fewer stickers than Jeff. Dan had 320 stickers first.
Dan had 50% fewer stickers than Jeff.
After Jeff gave 20 of his stickers to Dan, Dan had 40% fewer stickers than Jeff (had after he gave away 20 of his stickers).
How many stickers did Dan have at first?
The total number of stickers that Jeff had is denoted by J, and the total number of stickers that Dan had is denoted by D.
In order to solve the question, let us first represent the given data mathematically:
J = 1.5D; D+20 = 0.6(J-20)
We have 2 equations and 2 unknowns, J and D.
We can solve these equations using simultaneous linear equations.
Substitute the first equation in the second equation:
D+20=0.6(J-20)
⇒ D+20=0.6J-12
⇒ D=0.6J-32
Now substitute the value of D in the first equation:
J=1.5D
⇒ J=1.5(0.6J-32)
⇒ J=0.9J-48.
Therefore, J=480
The total number of stickers that Jeff had initially was 480.
Now, to calculate the total number of stickers that Dan had, we can use the equation
J=1.5D:J=1.5D
⇒ 480=1.5D
⇒ D=320
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given that kw for water is 2.4×10−14 at 37 ∘c, calculate the ph of a neutral aqueous solution at 37 ∘c, which is the normal human body temperature.
Answers
6.81 is the Ph of a neutral aqueous solution.
To calculate the pH of a neutral aqueous solution at 37°C with a KW of 2.4×10⁻¹⁴, follow these steps:
1. Identify that in a neutral aqueous solution, the concentrations of hydrogen ions (H⁺) and hydroxide ions (OH⁻) are equal. Therefore, [H⁺] = [OH⁻].
2. Use the KW expression, which is the product of [H⁺] and [OH⁻] concentrations. In this case, KW = 2.4×10⁻¹⁴.
3. Since [H⁺] = [OH⁻], you can rewrite the KW expression as KW = [H⁺]². Now, solve for [H⁺] by taking the square root of KW: [H⁺] = sqrt(KW) = sqrt(2.4×10⁻¹⁴).
4. Calculate the square root: [H⁺] ≈ 1.55×10⁻⁷ M.
5. Use the pH formula: pH = -log[H⁺]. Plug in the [H⁺] value: pH = -log(1.55×10⁻⁷).
6. Calculate the pH: pH ≈ 6.81.
The pH of a neutral aqueous solution at 37°C with a KW of 2.4×10⁻¹⁴ is approximately 6.81.
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