The hydrogen ion concentration [H+] for tomatoes with a pH of 4.86 is 1.67 x 10^-5 moles/liter.
The pH of a solution is defined as the negative logarithm (base 10) of the hydrogen ion concentration [H+]. Mathematically, pH = -log[H+].
Rearranging the equation, we get [H+] = 10^(-pH).
Substituting the given pH of 4.86 into the equation, we get [H+] = 10^(-4.86).
Evaluating the expression, we get [H+] = 1.67 x 10^-5 moles/liter. Therefore, the hydrogen ion concentration for tomatoes with a pH of 4.86 is 1.67 x 10^-5 moles/liter.
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Solve this equation
3x - 5 = -26
3x - 5 = -26
step 1:
subtract +5 on each side because you have to do the inverse operation
step 2:
3x= -21
step 3:
now divide 3 on each side
the answer is -7
Hope this helped!
TheOneAndOnlyLara~
Answer:
x=-7.
Step-by-step explanation:
Hi student! Let me help you out.
_________________
First, add 5 to both sides.
\(\sf 3x=-26+5\). Upon simplifying, we obtain this.
\(\sf 3x=-21\).
↪
Now divide both sides, by 3.
\(\sf x=-7\)
\(\therefore,\sf the \quad value \quad of \quad x \quad is \quad -7\). Which is our final answer.
⇨Hope that this helped! have a great day ahead! ⇦
Best Wishes!
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Heyy!!
Kiona fills a measuring cup with 3/4 cups f juice 3 times to make a punch. Write and solve a multiplication equation with a whole number and a fraction to show the total amount of juice Kiona uses.
Answer:
3/4 times 3
Step-by-step explanation:
9/4 in fraction form, so it equal 2 1/4. Hope this helps
A hypothesis can be differentiated from a theory because it is...
a. a specific prediction arising from the theory. c. it talks about how one specific variable affects d. all of the above.
A hypothesis can be differentiated from a theory because it is a specific prediction arising from the theory. The statement that is true is, a hypothesis can be differentiated from a theory because it is a specific prediction arising from the theory. A hypothesis is a suggested explanation of a phenomenon or observed data that is testable.
Hypotheses are more detailed, and are written to explain precisely what you think is going to occur in your research and the reason for that prediction. A hypothesis will be rejected if it does not fit the data, whereas a theory will be modified to fit the data.
A hypothesis is more like a forecast, and a theory is more like a law that explains how certain events operate. Thus, we can conclude that a hypothesis is a specific prediction arising from the theory.
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Determine the equation of the line below using the given point and slope. using variables x and y.Point : (1,0) , slope: m=0
Given
Point : (1,0) , slope: m=0
Step 1
\(y-y_1=m(x-x_1_{})for\text{rmula}\)\(\begin{gathered} x_1=1,y_1=0 \\ m=0 \\ \end{gathered}\)Step 2
we substitute into the formula
\(\begin{gathered} y-y_1=m(x-x_1) \\ \end{gathered}\)\(\begin{gathered} y-0=0(x-1) \\ y-0=0 \\ y=0 \end{gathered}\)The equation of a line is y = 0
James begins a savings plan in which he deposits $120 at the beginning of each month into an account that earns 10.2% interest annually or, equivalently, 0.85% per month. To be clear, on the first day of each month, the bank adds 0.85% of the current balance as interest, and then James deposits $120. Let B, be the balance in the account after the nth deposit, where Bo = $0. Complete parts (a) through (c) below. a. Write the first five terms of the sequence {B}. How should the terms of the sequence be found? A. Multiply the balance of the previous month by the monthly interest rate to find the interest of this month. Then add the the deposit to the interest of this month found earlier to find the balance of this month. B. Multiply the balance of the previous month by the monthly interest rate to find the interest of this month. Then add the the deposit and the interest of this month found earlier to the balance of the previous month to find the balance of this month. C. Multiply the balance of the previous month by the annually interest rate to find the interest of this month. Then add the the deposit and the interest of this month found earlier to the balance of the previous month to find the balance of this month. D. Multiply the balance of the previous month by the monthly interest rate to find the interest of this month. Then add the interest of this month found earlier to the balance of the previous month to find the balance of this month.
The correct way to find the terms of the sequence {B}, which represents the balance in James' account after each deposit, is by using option B. Multiply the balance of the previous month by the monthly interest rate to find the interest of this month. Then, add the deposit and the interest of this month found earlier to the balance of the previous month to determine the balance of this month.(option D)
In James' savings plan, the balance after the first deposit is $120, as he starts with $0. To find the balance after the second deposit, we multiply the previous balance ($120) by the monthly interest rate (0.0085), which gives us $1.02. Adding the deposit of $120 to this interest amount, we get $121.02 as the balance after the second deposit. Continuing this process, we find the following terms:
First deposit: $120
Second deposit: $121.02
Third deposit: $242.23
Fourth deposit: $364.69
Fifth deposit: $488.40
Each term is obtained by multiplying the previous month's balance by the monthly interest rate, adding the deposit amount, and summing it up. This approach reflects the compounding effect of interest on the account balance, resulting in an increasing balance over time.
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will mark for correct answer!!
SOLVE THE PROBLEM BY HAND 1(i)
and (ii) and also solve the problem in MATLAB AND SHOW THE OUTPUT
RESULTS
1. A discrete time signal is defined as x(n)={-3, 2,-2, 1, 5,-3, 6} i) Sketch the signal x (n), x (-n), x (2n), x (n/2), x (2n-3), x (2n+3), x (-n/2-2) and x(2-2n). ii) Energy of x(n).
a) 1. x(n) = {-3, 2, -2, 1, 5, -3, 6}, 2. x(-n) = {-6, 3, -5, 1, -2, 2, -3}, 3. x(2n) = {-3, -2, 5, 6}, 4. x(n/2) = {-3, -2, 1}, 5. x(2n-3) = {1, -2}, 6. x(2n+3) = {-2, 6}, 7. x(-n/2-2) = {-2, 1, 5, -3}, 8. x(2-2n) = {6, -3}
b) The energy of the given signal x(n) is 88.
i) To sketch the signal x(n), x(-n), x(2n), x(n/2), x(2n-3), x(2n+3), x(-n/2-2) and x(2-2n), we have to apply the given operations on the original signal x(n):
1. x(n) = {-3, 2, -2, 1, 5, -3, 6}
2. x(-n) = {-6, 3, -5, 1, -2, 2, -3}
3. x(2n) = {-3, -2, 5, 6}
4. x(n/2) = {-3, -2, 1}
5. x(2n-3) = {1, -2}
6. x(2n+3) = {-2, 6}
7. x(-n/2-2) = {-2, 1, 5, -3}
8. x(2-2n) = {6, -3}
ii) The energy of a discrete-time signal x(n) is defined as the sum of the squared magnitude of each sample of the signal that can be represented as:
E = ∑|x(n)|² from n=-∞ to n=+∞
For the given signal x(n)={-3, 2,-2, 1, 5,-3, 6}, the energy is
E = |-3|² + |2|² + |-2|² + |1|² + |5|² + |-3|² + |6|²
E = 9 + 4 + 4 + 1 + 25 + 9 + 36
E = 88
Therefore, the energy of the given signal x(n) is 88.
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A planner assembles party favor bags filled with glow sticks and temporary tattoos for a client. There are 24 glow sticks and 30 temporary tattoos to divide
evenly among the bags.
If there are no leftover items, what is the greatest number of bags the planner can assemble?
A. 6 bags
B.8 bags
C. 24 bags
D. 30 bags
Answer:
24
Step-by-step explanation:
you don't have more than 24 glow sticks so thats the most amount of bags you can have
Is (x-7) a factor of (x2-5x+14)?
Yes or no
Answer:
Step-by-step explanation:
Is the given equation factorable?
(x - 7)(x - 2) = x^ - 9x + 14 That doesn't work.
-7 * - 2 = 14 but the middle term is - 9 not - 5
x - 7 is not a factor of x^ - 5x + 14
What is?
Something very ugly (x - 2.5 +/- 2.783 i )
suppose a frequency distribution has the following consecutive classes: $20 up to $30 $30 up to $40 $40 up to $50 what is the class midpoint for the first class?
Answer:25
Step-by-step explanation:
One urn contains 6 blue balls and 14 white balls, and a second urn contains 12 blue balls and 7 white balls. An urn is selected at random, and a ball is chosen from the urn. (a) What is the probability (as a %) that the chosen ball is blue? (Round your answer to one decimal place.) (b) If the chosen ball is blue, what is the probability (as a %) that it came from the first urn? (Round your answer to one decimal place.)
(a) To find the probability of selecting a blue ball, we need to consider the probabilities from both urns.
The probability of selecting the first urn is 1/2 since there are two urns and one is chosen at random. The probability of selecting a blue ball from the first urn is 6/20 (6 blue balls out of a total of 20 balls).
The probability of selecting the second urn is also 1/2. The probability of selecting a blue ball from the second urn is 12/19 (12 blue balls out of a total of 19 balls).
To find the overall probability of selecting a blue ball, we can use the law of total probability:
P(blue) = P(First Urn) * P(blue | First Urn) + P(Second Urn) * P(blue | Second Urn)
P(blue) = (1/2) * (6/20) + (1/2) * (12/19)
Simplifying the expression, we get:
P(blue) = 0.25 + 0.3158
P(blue) = 0.5658
To convert to a percentage, we multiply by 100:
P(blue) = 56.58%
(b) Given that the chosen ball is blue, we want to find the probability that it came from the first urn.
Using Bayes' theorem, we can calculate:
P(First Urn | blue) = (P(blue | First Urn) * P(First Urn)) / P(blue)
P(First Urn | blue) = (6/20 * 1/2) / 0.5658
P(First Urn | blue) = 0.15 / 0.5658
P(First Urn | blue) ≈ 0.2654
To convert to a percentage, we multiply by 100:
P(First Urn | blue) ≈ 26.54%
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Please help ASAP 4 and 5 will mark brainliest and give 10 points
Answer
I know the answer to number 4 is No
Step-by-step explanation:
Because when you plug the coordinates (8,-44) into the equation y=-7x+6 it gives the wrong output of -50
The table shows the number of goals made by two hockey players.
Player A Player B
2, 3, 1, 3, 2, 2, 1, 3, 6 1, 4, 5, 1, 2, 4, 5, 5, 11
Find the best measure of variability for the data and determine which player was more consistent.
Player B is the most consistent, with an IQR of 3.5.
Player B is the most consistent, with a range of 10.
Player A is the most consistent, with an IQR of 1.5.
Player A is the most consistent, with a range of 5
Player B is the most consistent, with an IQR of 2. This means that 50% of their scores fell within the range of 3 to 5.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen
To determine which player was more consistent, we need to find the best measure of variability for the data. The two common measures of variability are range and interquartile range (IQR).
The range is the difference between the highest and lowest values in the data set. For Player A, the range is 6 - 1 = 5, and for Player B, the range is 11 - 1 = 10.
The interquartile range (IQR) is a measure of dispersion based on dividing the data into quartiles. It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1).
To find the IQR for each player, we first need to find the quartiles.
For Player A:
Arrange the data in order: 1, 1, 2, 2, 2, 3, 3, 3, 6
Find Q1: (2 + 2) / 2 = 2
Find Q3: (3 + 3) / 2 = 3
Calculate IQR: Q3 - Q1 = 3 - 2 = 1
For Player B:
Arrange the data in order: 1, 1, 2, 4, 4, 5, 5, 5, 11
Find Q1: (2 + 4) / 2 = 3
Find Q3: (5 + 5) / 2 = 5
Calculate IQR: Q3 - Q1 = 5 - 3 = 2
Therefore, Player B is the most consistent, with an IQR of 2. This means that 50% of their scores fell within the range of 3 to 5. In contrast, Player A has an IQR of 1, indicating that 50% of their scores fell within the range of 2 to 3.
Therefore, we can conclude that Player B was more consistent than Player A.
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which phrase represents this expression? (30 - 10) × 5
Answer:
100
Step-by-step explanation:
Equations in parentheses get solved first: 30-10=20 and 20x5=100
I'm not sure how to factor this
If the radius of a circle is 14 in, what is the diameter?
Answer:
28
Step-by-step explanation: radius is half the diameter
Step-by-step explanation:
In a circle
Radius (r) = 14 in
Diameter (d)
= 2 * r
= 2 * 14
= 28 in
Hope it will help :)❤
if the work required to stretch a spring 3 ft beyond its natural length is 15 ft-lb, how much work (in ft-lb) is needed to stretch it 18 in. beyond its natural length? give your answer in decimal form.
The amount of work needed to stretch the spring 18 in. from its natural position is 3.75 ft-lb.
According to the Hooke's Law, the work done on the spring is:
W = 1/2. k . x²
Where:
k = spring constant
x = displacement.
Notice that the work done is directly proportional to x².
Hence,
W₁ : W₂ = x₁² : x₂²
Parameters given:
W₁ = 15 ft-lb
x₁ = 3 ft
x₂ = 18 in. = 1.5 ft
Plug the above parameters into the ratio equation:
15 : W₂ = 3² : (1.5)²
W₂ = (1.5)² . 15 / 3² = 15/4 = 3.75 ft-lb
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2 Bea counts the number of red pencils in 7 boxes of pencils. The list shows her
data: 22, 28, 30, 28, 35, 30, 28. The mean is 26 red pencils per box. Based on
the MAD for the data set, would it be unlikely to get a box with 31 red pencils?
Show your work. Explain your reasoning.
2.29 is less than the MAD of 2.53, it would not be unlikely to get a box with 31 red pencils based on the MAD for the given data set.
What is the data set?To determine whether it would be unlikely to get a box with 31 red pencils based on the Mean Absolute Deviation (MAD) for the given data set, we first need to calculate the MAD.
Step 1: Calculate the mean of the data set
The given data set is: 22, 28, 30, 28, 35, 30, 28
The mean is calculated by adding up all the numbers and dividing by the total number of values:
Mean = (22 + 28 + 30 + 28 + 35 + 30 + 28) / 7 = 201 / 7 = 28.71 (rounded to two decimal places)
Step 2: Calculate the absolute deviations
The absolute deviation for each data point is calculated by finding the absolute difference between the data point and the mean:
|22 - 28.71| = 6.71
|28 - 28.71| = 0.71
|30 - 28.71| = 1.29
|28 - 28.71| = 0.71
|35 - 28.71| = 6.29
|30 - 28.71| = 1.29
|28 - 28.71| = 0.71
Step 3: Calculate the MAD
The MAD is the mean of the absolute deviations:
MAD = (6.71 + 0.71 + 1.29 + 0.71 + 6.29 + 1.29 + 0.71) / 7 = 17.71 / 7 = 2.53 (rounded to two decimal places)
Now, to determine whether it would be unlikely to get a box with 31 red pencils, we can compare 31 with the MAD. If the difference between 31 and the mean (28.71) is greater than the MAD (2.53), then it would be unlikely.
Difference = 31 - 28.71 = 2.29
Since 2.29 is less than the MAD of 2.53, it would not be unlikely to get a box with 31 red pencils based on the MAD for the given data set.
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PLEASE HELPPPPPPPPPPPPPP
Answer:
how can I help u sir...???
Plz hurry help will mark brainliest if given correct answers.
Consider the segments on the coordinate plane.
Which two statements are true?
A. The length of segment JK is 5 units.
B. The length of segment JK is 10 units.
C. The length of segment PQ is 5 units.
D. The length of segment PQ is 10 units.
E. The length of segment ST is 10 units.
Choose two of the correct answers
Answer:
Option (A) and Option (E)
Step-by-step explanation:
Length of a segment between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by,
Length = \(\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\)
Length of the segment between J(-8, 1) and K(-5, 5) will be,
JK = \(\sqrt{(-8+5)^2+(1-5)^2}\)
JK = \(\sqrt{9+16}\)
JK = 5 units
Length of segment between the points P(2, 8) and Q(7, 3) will be,
PQ = \(\sqrt{(2-7)^2+(8-3)^2}\)
PQ = \(\sqrt{25+25}\)
PQ = \(5\sqrt{2}\) units
Length of segment between the points S(-3, -10) and T(3, -2) will be,
ST = \(\sqrt{(-3-3)^2+(-10+2)^2}\)
ST = \(\sqrt{36+64}\)
ST = 10 units
Therefore, Option (A) and Option (E) are the correct options.
Explanation of how we can make (a) subject
Answer:
Step-by-step explanation:
Note: All calculations must be shown clearly at each step, Writing the results of the calculations only will not be taken into account. a) For the following sequence \( x[n]=[2,1,4,6,5,8,3,9] \) find
The range of the sequence is \(8\).
Let's calculate the requested values for the given sequence \(x[n] = [2, 1, 4, 6, 5, 8, 3, 9]\):
a) Find the mean (average) of the sequence.
To find the mean, we sum up all the values in the sequence and divide it by the total number of values.
\[
\text{Mean} = \frac{2 + 1 + 4 + 6 + 5 + 8 + 3 + 9}{8} = \frac{38}{8} = 4.75
\]
Therefore, the mean of the sequence is \(4.75\).
b) Find the median of the sequence.
To find the median, we need to arrange the values in the sequence in ascending order and find the middle value.
Arranging the sequence in ascending order: \([1, 2, 3, 4, 5, 6, 8, 9]\)
Since the sequence has an even number of values, the median will be the average of the two middle values.
The two middle values are \(4\) and \(5\), so the median is \(\frac{4 + 5}{2} = 4.5\).
Therefore, the median of the sequence is \(4.5\).
c) Find the mode(s) of the sequence.
The mode is the value(s) that occur(s) most frequently in the sequence.
In the given sequence, no value appears more than once, so there is no mode.
Therefore, the sequence has no mode.
d) Find the range of the sequence.
The range is the difference between the maximum and minimum values in the sequence.
The maximum value in the sequence is \(9\) and the minimum value is \(1\).
\[
\text{Range} = \text{Maximum value} - \text{Minimum value} = 9 - 1 = 8
\]
Therefore, the range of the sequence is \(8\).
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Holly Krech is planning for her retirement, so she is setting up a payout annuity with her bank. She wishes to receive a payout of $1,800 per month for twenty years. She must deposit $218,437.048 and the total amount that Holly will receive from her payout annuity will be $432,000.
A. How large a monthly payment must Holly Krech make if she saves for her payout annuity with an ordinary annuity, which she sets up thirty years before her retirement?
B. how large a monthly payment must she make if she sets the ordinary annuity up twenty years before her retirement?
A. To save for her payout annuity with an ordinary annuity set up thirty years before her retirement, Holly Krech must make a monthly payment of $175.97.
B. If she sets up the ordinary annuity twenty years before her retirement, Holly Krech must make a monthly payment of $432.00.
What is the monthly payment required for an ordinary annuity set up 30 years before retirement?To calculate the monthly payment for an ordinary annuity set up thirty years before retirement, we can use the formula for the present value of an ordinary annuity. Given the deposit amount of $218,437.048 and the total amount received from the annuity of $432,000, and solving for the monthly payment, we find that Holly must make a monthly payment of $175.97.
How much must be paid monthly for an ordinary annuity set up 20 years before retirement?For an ordinary annuity set up twenty years before retirement, we use the same formula for present value. With the deposit amount and total amount received unchanged, we solve for the monthly payment, which comes out to be $432.00.
It's important to note that the monthly payment increases when the annuity is set up closer to the retirement date. This is due to the shorter time period available for saving, resulting in a higher required contribution to reach the desired payout amount.
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What percent is represented by the shaded portion on this 10 × 10 grid?
A grid model has 100 squares. 76 squares are shaded.
StartFraction 7.5 Over 100 EndFraction percent
StartFraction 75 Over 100 EndFraction percent
7.5%
75%
Answer:
76%
Step-by-step explanation:
76 out of 100 is equal to 76%. This is the answer
Answer:
people are saying its b but maybe its d
Step-by-step explanation:
Calculations for the Determination of Ammonium Chloride The data from the data entry portion of the report has been copied into this section of the report for your convenience. Use the data to make the necessary calculations. [1] Mass of evaporating dish #1: 36.190 g [2] Mass of evaporating dish and original sample (g) : 37.020 g (2pts) Mass of original sample (g) [3) Mass of evaporating dish after subliming NH
4
( g) : 36.550 g (2pts) Mass of NH
4
Cl(g) (2pts) Percent of NH
4
Cl (\%) (4pts) B. Calculations for the Determination of Sodium Chloride [4] Mass of evaporating dish #2: 41.63 g [5] Mass of watch glass (g) : 47.84 g [6] Mass of evaporating dish #2, watch glass, and NaCl(g) : 89.510 g (2pts) Mass of NaCl(g) (2pts) Percent of NaCl(%)
[1] Mass of evaporating dish #1: 36.190 g
[2] Mass of evaporating dish and original sample: 37.020 g
To calculate the mass of the original sample, we subtract the mass of the evaporating dish from the total mass:
Mass of original sample = Mass of evaporating dish and original sample - Mass of evaporating dish
Mass of original sample = 37.020 g - 36.190 g
Mass of original sample = 0.830 g
[3] Mass of evaporating dish after subliming NH4Cl(g): 36.550 g
To calculate the mass of NH4Cl(g), we subtract the final mass of the evaporating dish from the initial mass:
Mass of NH4Cl(g) = Mass of evaporating dish - Mass of evaporating dish after subliming NH4Cl(g)
Mass of NH4Cl(g) = 36.190 g - 36.550 g
Mass of NH4Cl(g) = -0.360 g (Note: The negative value indicates an error in measurement or calculation. Please double-check the data provided.)
To calculate the percent of NH4Cl (%), we use the formula:
Percent of NH4Cl = (Mass of NH4Cl(g) / Mass of original sample) * 100
Percent of NH4Cl = (-0.360 g / 0.830 g) * 100
Percent of NH4Cl = -43.37% (Note: The negative value also suggests an error. Please review the data carefully.)
Moving on to the determination of Sodium Chloride:
[4] Mass of evaporating dish #2: 41.63 g
[5] Mass of watch glass: 47.84 g
[6] Mass of evaporating dish #2, watch glass, and NaCl(g): 89.510 g
To calculate the mass of NaCl(g), we subtract the sum of the masses of the evaporating dish #2 and the watch glass from the total mass:
Mass of NaCl(g) = Mass of evaporating dish #2, watch glass, and NaCl(g) - (Mass of evaporating dish #2 + Mass of watch glass)
Mass of NaCl(g) = 89.510 g - (41.63 g + 47.84 g)
Mass of NaCl(g) = 89.510 g - 89.47 g
Mass of NaCl(g) = 0.040 g
To calculate the percent of NaCl (%), we use the formula:
Percent of NaCl = (Mass of NaCl(g) / Mass of original sample) * 100
Percent of NaCl = (0.040 g / 0.830 g) * 100
Percent of NaCl = 4.82%
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can someone answer this now?
Answer:
x=10
Step-by-step explanation:
5x-10 and 3x+10
+10 +10
5x and 3x+20
-3x -3x
2x and 20
divide by 2 on both sides
x=10
please help please im giving so much
Answer:
D
Step-by-step explanation:
The highest number that divides exactly into two or more numbers. 3 and 9 cannot be divided by anything greater than 3.
Answer: i think its D.
Step-by-step explanation:
I need help please. Does any one know how to do this
The probability that a randomly selected muffin will be a banana nut muffin is; P(banana nut muffin) = 0.5
What is the probability of selection?From the table in the question, we are given;
Number of blackberry muffins = 10
Number of banana nut muffins = 25
Number of Chocolate chip muffins = 1
Number of blueberry muffins = 11
Number of pumpkin spice muffins = 3
Total number of muffins = 10 + 25 + 1 + 11 + 3
= 50
Probability = number of successful outcomes/Total number of outcomes
Thus;
P(banana nut muffin) = 25/50
= 0.5
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Solve for n.
3 ( n + 5 ) ≥ 3 n + 8
Answer:
\(3(n + 5) \geqslant 3n + 8 \\ 3n + 3 \times5 \geqslant 3n + 8 \\ 3n + 15 \geqslant 3n + 8 \\ 3n - 3n \geqslant 8 - 15 \\ 0n \geqslant - 7 \\ no \: solution \\ thank \: you\)
Answer:
\(7 \geqslant 0 \: \: \: \: or \: \: \: \: 0 \leqslant 7 \\ \)
Step-by-step explanation:
\(3(n + 5) \geqslant 3n + 8 \\ 3n + 15 \geqslant 3n + 8 \\15 - 8 \geqslant 3n - 3n \\ 7 \geqslant0 \\ \)
HELPPP.!!!
Answer choices:
−y ≥ x + 4
−3x + 3y ≤ −9
−y ≤ 3x + 4
−3x + 3y ≤ −9
y ≤ −x − 4
−x − y ≤ − 4
y ≤ −x + 4
−4x + 4y ≤ 16
Step-by-step explanation:
the second option.
you see that the steeper line has a slope of -3 (when x increases by 1 grid point, y decreases by 3 grid points, that makes the slope ratio of y/x = -3/1 = -3).
the slope is always the factor of x in an equation of
y = ax + b
the only equation provided in the answer options with slope -3 is
-y <= 3x + 4
because when we transform this into the general firm above, we need to multiply both sides by -1 (which flips the inequality symbol, by the way) :
y >= -3x - 4
there you have it. no other equation here can be transformed into this.
as a control we also look at the second equation :
-3x + 3y <= -9
3y <= 3x - 9
y <= x - 3
this has a slope of 1 (so, x and y both increase by the same amount), and the y-inteecept is -3 (the y value when x = 0). that also fits the graph.
so, it is all correct.