4. The probability of drawing 1 pink, 2 yellow and, stripped ball in succession without replacing the ball each time is (7/16) x (1/35) x (1/13) = 1/2540.
5. The probability that we roll a total of five if we are given that the total is less than nine is (1/36) / (4/36) = 1/4.
6. The probability that both cards are 7s is (6/36) x ($5 - $1) + (30/36) x (-$1) = -$0.17.
7. The expected value of the game is a loss of 17 cents per play.
Probabilities of Games4. The probability of drawing 1 pink ball, 2 yellow balls, and 1 stripped ball in succession is given by the product of the probabilities of drawing each ball without replacement.
The probability of drawing 1 pink ball is 7/16, the probability of drawing 2 yellow balls is (3/15) x (2/14) = 1/35 (because there are 3 yellow balls in the bag out of 15 total balls on the first draw, and 2 yellow balls out of 14 total balls on the second draw), and the probability of drawing 1 stripped ball is 2/13. Therefore, the probability of drawing 1 pink ball, 2 yellow balls, and 1 stripped ball in succession is:
(7/16) x (1/35) x (1/13) = 1/2540
5. If the total is less than nine, then there are only 4 possible outcomes: (1, 4), (2, 3), (3, 2), and (4, 1). The probability of rolling each of these outcomes is 1/36, since each die has 6 equally likely outcomes. The only outcome that adds up to 5 is (1, 4), which has probability 1/36. Therefore, the probability of rolling a total of 5, given that the total is less than nine, is:
(1/36) / (4/36) = 1/4
6. The probability of drawing a 7 on the first card is 4/52, since there are four 7s in a deck of 52 cards. Since the card is replaced, the probability of drawing a 7 on the second card is also 4/52. Therefore, the probability of drawing two 7s in a row is:
(4/52) x (4/52) = 1/169
7. The expected value of the game is the sum of the products of the outcomes and their probabilities. There are 6 x 6 = 36 possible outcomes, each with probability 1/36. Of these outcomes, 6 are winning outcomes (where both dice show the same number), and 30 are losing outcomes. The payout for a winning outcome is $5, and the cost of playing the game is $1. Therefore, the expected value is:
(6/36) x ($5 - $1) + (30/36) x (-$1) = -$0.17
Therefore, the expected value of the game is a loss of 17 cents per play.
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please help me on this
Answer:
[tex]\frac{4}{90}[/tex]
Step-by-step explanation:
[tex]\frac{4}{9}[/tex] - [tex]\frac{4}{10}[/tex]
to subtract the fractions we require them to have a common denominator
the LCM of 9 and 10 is 90
= = [tex]\frac{4(10)}{9(10)}[/tex] - [tex]\frac{4(9)}{10(9)}[/tex]
= [tex]\frac{40}{90}[/tex] - [tex]\frac{36}{90}[/tex]
= [tex]\frac{40-36}{90}[/tex]
= [tex]\frac{4}{90}[/tex]
Martín did the following work and found his surfing increased 50% from the first week to the second.
Percent of change= amount of change/Original amount = 9-6/6 = 3/6 =0.5.
0.5—->50%. Describe Martin’s method for finding percent change in your own words.
The surfing increased by 50% from the first week to the second. His method is correct.
What is the percentage change?The amount of any product is given as if it were a percentage of a hundred. The ratio is one-quarter of one hundred. % is an abbreviation for one hundred percent. It is represented by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
The Surfing 6 seconds to reach 9 seconds. Then the percentage is given as,
P = [(9 - 6) / 6] x 100
P = (3 / 6) x 100
P = 0.50 x 100
P = 50%
The surfing increased by 50% from the first week to the second. His method is correct.
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Determine whether each number is an integer, a rational number that is not an integer, or an irrational number. pls help very urgent
Integer: 12
Irrational numbers: -2√10 and √20
Rational numbers: 17/4, 0.25, and -77/11.
What are integers?Any positive or negative number without fractions or decimal places is known as an integer, often known as a "round number" or "whole number."
Given:
There are rational and irrational numbers in the image.
The numbers can be written in the form of p/q, where q is never zero is rational numbers.
And rest of the numbers are irrational numbers.
So, the solutions are given in the image below.
√144 = 12
0.25 = 25/100 = 1/4
Therefore, the solutions are given in the image below.
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Naomi has taken six science tests so far this year. The tests are out of 100 points, and she has gotten the following scores.
64, 88, 92, 86, 81, 92
What must Naomi score on her seventh test in order to raise her mean to an 85?
88
92
85
95
Answer:92
Step-by-step explanation:
[tex]\frac{64+88+92+89+81+92+x}{7} =85[/tex]
85 x 7 = 595
595 - 64 - 88 - 92 - 89 - 81 - 92 = 92
Answer:
Naomi needs to score a 92 on her seventh test to raise her mean to an 85.
Step-by-step explanation:
Let's call the score Naomi needs to get on her seventh test "x".
To find out what score she needs to raise her mean to 85, we can set up an equation:
(64 + 88 + 92 + 86 + 81 + 92 + x) / 7 = 85
We add up all her scores so far (64 + 88 + 92 + 86 + 81 + 92) and add the score she needs to get on her seventh test (x). We divide the sum by the total number of tests (7) to get the mean score of 85.
Simplifying the equation, we get:
503 + x = 595
Subtracting 503 from both sides, we get:
x = 92
Change 1.5 to fraction with working
Answer:
³/₂
Step-by-step explanation:
1.5 = ¹⁵/₁₀
= ³/₂
What does t-test assuming equal variances mean?
The t-test assuming equal variances means Pooled t-test in which variances of the two sample populations are equal.
The pooled t-test is the statistical procedure that assumes that population variances are equal. Finding a weighted average of the two independent sample variances is referred to as pooling. By combining data from samples from populations 1 and 2, we may estimate the common variance when there is solid evidence that population 1's variance is equal to population 2's variance.
Compare the ratio of the two sample standard deviations as a quick way to verify this. The ratio would be compared as: S1/S2. The ratio would be 1, or, in the event that the two are equal.
However, we cannot anticipate the ratio to be exactly 1, as they are samples and as a result, there will be some errors. Thus, the pooled t-test implies whether the null-hypothesis should be accepted or rejected.
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If the numerator of a fraction is multiplied by 4 and the denominator is reduced by 2,the result is 4. If the numerator of the fraction is increased by 15 and 2 subtracted from the double of the denominator, the result is 5/4. Find the fraction.
Answer:
To solve this problem, we need to start by setting up an equation. The equation should express the fact that the result of the two operations on the fractions is both 4 and 5/4.
We can do this by writing:
4x/(x-2) = 4
5x/2(x-2) = 5/4
Solving for x, we get x=16. Therefore, the fraction we are looking for is 4/14, since 4 times 16 divided by 16 minus 2 equals 4 and 5 times 16 divided by 2 times 16 minus 2 equals 5/4.
How Much Tax Will She Pay
The total amount of money Tegan paid for tax last year from her income of £48,300 is £4,830
How Much Tax did Tegan Pay?Tegan's income last year before tax = £48,300
Tegan's earnings is upto £43,000 and in excess of £48,300 - £43,000
= £5,300
Assume, Tegan's tax rate is 10% since her excess is not up to £11,000
Tegan's tax = 10% of £48,300
= 0.10 × 48,300
= £4,830
Ultimately, Tegan paid a total amount of £4,830 as tax last year.
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Given f(x) = 2x - 1, find the value of f(-1).
To find the value of f(-1), we simply need to substitute -1 for x in the function f(x) = 2x - 1 and evaluate:
f(-1) = 2(-1) - 1
= -2 - 1
= -3
Therefore, the value of f(-1) is -3.
Answer:
f=2x-1/x
Step-by-step explanation:
I hope this helps :) <3
Two furniture salesmen are comparing their salaries. Gert is paid R25,00 per hour plus a 15% commission on his total sales. Ben is paid R29,00 per hour plus a 10% commission on his total sales. Suppose each has sold R5 000 worth of furniture, compare their income over various periods of time to find out when they will earn the same. What will happen after that point? Who would have earned more before that point?
When sales are under $15,000, the current job pays less than the new offer. The new job offer is therefore favoured for sales below $15,000.
What is meant by linear equation?A linear equation, according to the definition, is an algebraic equation in which each term has an exponent of one and the graphed value of the equation is a straight line. Y=mx + b is a prime example of a linear equation. Ax+By=C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5. Finding both intercepts of an equation in this format is rather simple (x and y). A two-variable linear equation can be thought of as a linear relationship between x and y, or two variables where the value of one (often y) relies on the value of the other (usually x).a) Wc = 2000+.07S
b) Wn =2300+.05S
c) When the totals are similar, the sales level at which she would not care
2000 + .07S = 2300 + .05S
subtract .05S from both sides
2000 +.02S = 2300
subtract 2000 from both sides
.02S = 300
divide both sides by .02
S = 300/.02 = 15000
Sales of $15,000 equate to identical pay.
If we apply the same calculation, substituting less than for the = sign... The result of our equation is
2000 + .07S < 2300 + .05S
S < 15000
The present employment pays less than the new offer when sales are under $15,000. Therefore, the new job offer is preferred for sales below $15,000.
check: Let S = 10,000
Wc = 2000+.07(10000) = $2700
Wn = 2300 + .05(10000) = $2800
As can be seen, at sales of $10,000 the new job earns more.
The complete question is:
A salesperson receives a monthly salary $2000 plus commission of 7% of sales. she is offered a new job at $2300 per month plus commission of 5% os sales.
a) write a linear equation for her current wage W in terms of her monthly sales S.
b)write a linear equation for her monthly wage W of the job offer in terms of her monthly sales S.
c) what level of sales will make her indifferent between the two jobs? Which scheme is preferred when sales are below this level?
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PLEASE HELP WITH ALGEBRA!!!
A classmate simplified this rational equation. (Picture attached)
[tex]1 - \frac{2}{x+3} = \frac{x+1}{x-3}[/tex]
a) circle and explain the error in this simplifcation
b) show your work as you correct the error
Part (a)
The error happens on the 2nd step.
The student multiplied both sides by the LCD (x+3)(x-3) to clear out the fractions, but forgot about the first "1" at the very left.
=================================================
Part (b)
[tex]1 - \frac{2}{x+3} = \frac{x+1}{x-3}\\\\(x+3)(x-3)*1 - (x+3)(x-3)*\frac{2}{x+3} = (x+3)(x-3)*\frac{x+1}{x-3}\\\\(x+3)(x-3) - 2(x-3) = (x+1)(x+3)\\\\x^2-9 - 2x+6 = x^2+4x+3\\\\x^2-2x-3 = x^2+4x+3\\\\x^2-2x-3-x^2-4x-3=0\\\\-6x-6=0\\\\-6x=6\\\\x = 6/(-6)\\\\x = -1[/tex]
The answer is x = -1Check:
[tex]1 - \frac{2}{x+3} = \frac{x+1}{x-3}\\\\1 - \frac{2}{-1+3} = \frac{-1+1}{-1-3}\\\\1 - \frac{2}{2} = \frac{0}{-4}\\\\1 - 1 = 0\\\\0 = 0\\\\[/tex]
The answer is fully confirmed.
You can use a graphing tool like GeoGebra to visually confirm the answer.
Given the equation y = -2x + 4, complete the table.
0
1
2
3
Answer:
0: 4
1: 2
2: 0
3: -2
Step-by-step explanation:
To find out the values of 0, 1, 2 and 3 we have to substitute these numbers into the place of x
0...
y = -2(0) + 4 = 4
1...
y = -2(1) + 4 = 2
2...
y = -2(2) + 4 = 0
3...
y = -2(3) + 4 = -2
TIP:
We can see that there is a pattern of decreasing of 2 so to keep finding the following values we just have to keep subtracting 2. For any question like this, if we see a pattern to make it easier and quicker all we have to do is follow the pattern!
Hope this helps, have a lovely day! :)
I will give you a Brainliest
Answer:
192
Step-by-step explanation:
2x9=18
18x12=192
Brianna surveyed a representative sample of students at her school to collect data about the numbers of Internet-compatible devices they own. Use the data in the table. Select all the valid inferences.
Internet-Compatible Devices
Number of Devices Number of Students
1 18
2 25
3 or more 7
Students are more likely to own exactly 2 devices than any other number.
More students own 3 devices than own more than 3 devices.
Less than half as many students own 3 or more devices as compared to students who own 1 device.
10 more students own 1 device than own 3 or more devices.
None of the students own exactly 5 devices.
The statements, Students are more likely to own exactly 2 devices than any other number, Less than half as many students own 3 or more devices as compared to students who own 1 device and About 10 more students own 1 device than own 3 or more devices are true.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Students are more likely to own exactly 2 devices than any other number is
true because the number of students own exactly 2 devices is greater than the other categories.
Less than half as many students own 3 or more devices as compared to students who own 1 device is true because 18 students own 1 device, the half of them is 9, and the number of students own 3 or more devices is 7 which is less than 9.
About 10 more students own 1 device than own 3 or more devices is true because the difference between students own 1 device and those own 3 or more devices = 18 - 7 = 11 which is about 10 more.
Hence, the statements, Students are more likely to own exactly 2 devices than any other number, Less than half as many students own 3 or more devices as compared to students who own 1 device and About 10 more students own 1 device than own 3 or more devices are true.
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Answer the question for lots of points
The angle of depression from an airplane to the top of an air traffic control tower is 56°. If the tower is 320 feet tall and the the airplane is flying at an altitude of 7,450 feet, how far away is the airplane from the control tower? Round to the nearest tenth.
Find the angle of depression from the top of a lighthouse 275 feet above water to a boat 1,324 feet off shore. Round to the nearest whole number.
Answer:
1) 7995.9 feet
2) 12 degrees
Step-by-step explanation:
1)
We can start by drawing a diagram of the situation. Let's label the height of the tower as "h", the distance from the airplane to the tower as "d", and the angle of depression as 56°.
C (top of tower)
/|
/ |
/ |h
/ |
/θ |
A_____/_____|
d B
In this diagram, point A represents the airplane, point B represents the base of the tower, and point C represents the top of the tower. The angle θ is the angle of depression from the airplane to the top of the tower.
We can use trigonometry to solve for the distance "d" from the airplane to the tower. In particular, we know that:
tan(θ) = h / d
We can rearrange this equation to solve for "d":
d = h / tan(θ)
Substituting the values we know, we get:
d = 320 / tan(56°)
Using a calculator, we can evaluate this to get:
d ≈ 215.8 feet
However, the airplane is flying at an altitude of 7,450 feet, so we need to add this to the height of the tower to get the total distance from the airplane to the ground:
total distance = d + 320 + 7,450
Plugging in the value we found for "d", we get:
total distance ≈ 7995.8 feet
Rounding to the nearest tenth, we get:
total distance ≈ 7995.8 ≈ 7995.9 feet
2)
We can use the tangent function to find the angle of depression. Let theta be the angle of depression. Then:
tan(theta) = (275 / 1324)
We can solve for theta by taking the inverse tangent (or arctan) of both sides:
theta = arctan(275 / 1324)
Using a calculator, we find:
theta ≈ 11.92 degrees
Rounding to the nearest whole number, we get:
The angle of depression is approximately 12 degrees.
5/18 + 11/12
fractions
adding fractions with unlike denominators
Answer:
= 43.
Step-by-step explanation:
[tex] \frac{5}{18} + \frac{11}{12} \\ = 36 \times \frac{5}{18} + 36 \times \frac{11}{12} \\ = 2(5) + 3(11) \\ = 10 + 33 \\ = 43[/tex]
Note// the LCM for 18 and 12 is 36.
Anita uses one sheet of paper to make a calendar showing each month of the year. Draw Anita’s calendar. Show how she can divide her calendar so that each month is given the same space. What fraction of the calendar does each month receive
The requried, each month receives 1/12 of the calendar or about 8.33% of the total space.
What is the fraction?A fraction is a mathematical concept that can be used to express a portion of a whole or a number that can be written as the ratio of two integers.
Here,
Anita can start by drawing a large rectangle on the paper to represent the entire year. Then, she can divide the rectangle into 12 equal parts, each representing a month. One way to do this is to draw four vertical lines to divide the rectangle into five equal columns, and then draw three horizontal lines to divide each column into four equal rows.
Each of the 12 parts represents 1/12 or one-twelfth of the calendar. Therefore, each month receives 1/12 of the calendar, or about 8.33% of the total space.
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In the Diagram segment ad bisects angle bac
Since segment AD bisects angle BAC, the value of x is equal to 14.6.
What is an angle bisector?In Mathematics, an angle bisector can be defined as a type of line, ray, or segment, that bisects or divides a line segment exactly into two (2) equal angles.
By applying the angle bisector theorem to this triangle (ΔABC), we have:
AB/BD = AC/DC
19/x = 17/(20 - x)
17x = 19(20 - x)
17x = 380 - 19x
19x + 17x = 380
26x = 380
x = 380/26
x = 14.6.
In conclusion, we can reasonably infer and logically deduce that the value of x in triangle ABC is 14.6.
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100 POINTS!
Select the true statement that describes a right circular cone.
A right circular cone does not have a base.
A right circular cone has a rectangular face.
A right circular cone has one apex.
A right circular cone has 7 edges.
Answer:
C
Step-by-step explanation:
It makes the most sense.
Does a matrix have to be symmetric to be orthogonally diagonalizable?
No, a matrix does not have to be symmetric to be orthogonally diagonalizable. Orthogonal diagonalization is a property of square matrices that can be used to simplify calculations and solve certain types of problems.
A square matrix A is orthogonally diagonalizable if there exists an orthogonal matrix P and a diagonal matrix D such that A = PDP^T, where D contains the eigenvalues of A and P contains the corresponding eigenvectors.
A symmetric matrix is always orthogonally diagonalizable, meaning that there exists an orthogonal matrix P such that A = PDP^T, where D is a diagonal matrix containing the eigenvalues of A. However, not all matrices are symmetric and still can be orthogonally diagonalizable.
For a non-symmetric matrix, the eigenvectors and eigenvalues may not have certain symmetrical properties that make orthogonal diagonalization straightforward, but it is still possible to diagonalize the matrix. In such cases, we can use other techniques, such as the Schur decomposition, to obtain a similar diagonal form.
In summary, a matrix does not have to be symmetric to be orthogonally diagonalizable, but symmetric matrices are always orthogonally diagonalizable. Other techniques may be used for diagonalizing non-symmetric matrices.
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what is the value of 5g in mg?
The value of 5g in mg is 5000mg. This is because 1g is equal to 1000mg, and 5g is equal to 5 times that amount, or 5000mg.
When converting between different metric units of mass, the prefixes are used to denote the multiple of the base unit. In this case, the base unit is the gram, and the prefix we are using is 'milli', which is equal to one thousandth of the base unit. Therefore, in order to convert 5g to mg, the prefix 'milli' is multiplied by the base unit of grams, resulting in a value of 5000mg.When converting between metric units, it is important to remember that the decimal point moves right by a number of places equal to the number of zeroes in the prefix. For example, if we were converting 5g to kg, the prefix 'kilo' has three zeroes, so the decimal point would move three places to the right, resulting in a value of 0.005kg.When converting from a larger unit to a smaller unit, the numerical value will increase, and when converting from a smaller unit to a larger unit, the numerical value will decrease. In this case, we are converting 5g to mg, which is a smaller unit, so the numerical value of 5g increases to 5000mg.
Overall, the value of 5g in mg is 5000mg. This is because 1g is equal to 1000mg, and the prefix 'milli' is multiplied by the base unit of grams, resulting in a value of 5000mg.
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Millie is considering a zero closing cost loan. She wants to borrow $600,000 her lending institution is offering her a 3.49% loan for 25 years. She has the option of purchasing negative points, which will increase her apr by 0.125% for each 1% of her principal credited to her. To cover the bank's closing cost she will need to get 2 negative points. Determine Millie's breakeven time. Is this purchase of negative points a wise decision? Explain.
Breakeven's time is 31.7 years.
The loan term is only 25 years, so it is not a wise decision.
What is a percentage?The percentage means the required value out of 100.
It is calculated by dividing the required value by the total value and multiplying it by 100.
The percentage change is also calculated using the same method.
In percentage change, we find the difference between the values given.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
We have,
To determine if the purchase of negative points is a wise decision, we first need to calculate Millie's monthly payment with and without the negative points.
Without negative points:
Principal = $600,000
Interest rate = 3.49%
Loan term = 25 years or 300 months
Now,
Monthly Payment = $2,967.27
With negative points:
Millie needs to purchase 2 negative points to cover the bank's closing cost. Each negative point will increase her APR by 0.125%, so the new interest rate will be:
New interest rate.
= 3.49% + (2 x 0.125%)
= 3.49/100 + (2 x 0.125/100)
= 3.74%
Monthly Payment = $2,998.84
The breakeven time.
This is the amount of time it takes for the cost of the negative points to be offset by the savings in monthly payments.
The total cost of the negative points.
We see that,
Each negative point costs 1% of the principal.
Cost of negative points,
= 2 x $6,000
= $12,000
The breakeven time.
Monthly savings.
= $2,967.27 - $2,998.84
= -$31.57
i.e
The value is negative because the new monthly payment is higher.
So,
Breakeven time.
= $12,000 ÷ -$31.57
= 380.2 months
This is,
1 year = 12 months
so,
31.7 years
Thus,
Breakeven's time is 31.7 years.
The loan term is only 25 years, so it does not make sense to purchase the negative points.
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solve for x,
3x+10
3x+2
SOH CAH TOA TRIG RATIOS
Answer:
HI: 57.4 cm; KM: 0.4 mil
Step-by-step explanation:
Question 17:
ΔGHI is a right-angled triangle
where:
Side GI = Hypotenuse
α = 55°
With respect to 55° angle:
Side HI = Adjacent side
∴Trigonometric function used: Cosα (CAH)
Cos55° = [tex]\frac{Side HI}{100cm}[/tex]
Cross-multiplication is applied:
Side HI = (Cos55°)×(100 cm)
Side HI = 57.4 cm (Rounded to 3 significant figures)
Question 18:
ΔKLM is a right-angled triangle
where:
Side KL = Hypotenuse
β = 27°
With respect to 27° angle:
Side KM = Opposite side
∴Trigonometric function used: Sinβ (SOH)
Sin27° = [tex]\frac{Side KM}{0.8 mil}[/tex]
Cross-multiplication is applied:
Side KM = (Sin27°)×(0.8 mil)
Side KM = 0.4 cm (Rounded to 1 decimal places)
Situation:
A geologist in South America discovers a
bird skeleton that contains 61% of its
original amount of C-14.
N = Noe-kt
No = inital amount of C-14 (at time
t = 0)
N = amount of C-14 at time t
k = 0.0001
t = time, in years
Answer:
Step-by-step explanation:
Transcribed image text: Situation: Find the age of the bird skeleton to the nearest A geologist in South America discovers a bird skeleton that contains 74% of its original amount of C-14. Enter the correct answer. N-Noekt No-inital amount of C.14 (at time t 0) N amount of C-14 at time t k 0.000 t time, in years.
HJK and RST are supplementary angles. If HJK is 56 , what is the measure of RST?
Answer: The measure of RST is 124 degrees.
Step-by-step explanation:
If HJK and RST are supplementary angles, it means that their sum is equal to 180 degrees. So we can use this information to find the measure of RST.
HJK + RST = 180
Substituting HJK = 56, we get:
56 + RST = 180
Subtracting 56 from both sides, we get:
RST = 180 - 56
RST = 124
Therefore, the measure of RST is 124 degrees.
what is 2 + 2 equal and what are the steps to solving it
Answer: 4
Step-by-step explanation:
1+1=2 but if it is 2+2 then it would = 4
In 1997, a city had a population of 250,000 people. Each year since, the population has grown by 4.9%.
Let t be the number of years since 1997. Let y be the city's population.
Write an exponential function showing the relationship between y and t.
Amy has a job that pays according to the function P(h) = 9.5h. If Amy is only allowed to work
40 hours per week, what are the domain and range of the function P?
Answer:
well in 9.5 40 you have to multiply which is 40 times 9.5h
What is the value of 1 gallon in kg?
Answer:
kg = gal × 3.7854 × density.
Step-by-step explanation: