Sydney can row a canoe at a speed of 5 mph in still water.
Let x represent Sydney's speed in still water. When rowing upriver, her effective speed will be (x - 2) mph because she's going against the current, which flows at 2 mph. When rowing downriver, her effective speed will be (x + 2) mph, since she's going with the current.
According to the problem, the time it takes her to row 6 miles upriver is the same as the time it takes her to row 14 miles downriver. We can set up the equation using the formula time = distance / speed:
6 / (x - 2) = 14 / (x + 2)
To solve for x, first cross-multiply:
6(x + 2) = 14(x - 2)
Expand:
6x + 12 = 14x - 28
Now, rearrange and solve for x:
12 + 28 = 14x - 6x
40 = 8x
x = 5
So, Sydney can row a canoe at a speed of 5 mph in still water.
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What value of x is in the solution set of 2x– 3 > 11 – 5x?
-3
0
2
4
Answer:
the answer is x > 2
Step-by-step explanation:
Answer:
The answer is D : 4.
Step-by-step explanation:
=2x-3>11-5x
=2x-3+5x>11
=7x-3>11
=7x>11+3
=7x>14
=7x/7>14/7
=x>2
By simplifying the problem, you can see that "x" must be greater than 2. Therefore, eliminating all other possible answers that are shown, but 4.
I answered the same questions with the same exact wording and explanation so please don't report any answers that are the same as this one, they are all mine and written by me.
Solve for x: −3|2x + 6| = −12 (1 point)
x = 1 and x = 5
x = −1 and x = −5
x = −9 and x = 3
No solution
Answer:
x = -1 and x = -5
Step-by-step explanation:
Part 1
−3|2x + 6| = −12
1. divide -3 by -3 and -12 by -3
|2x + 6| = 4
2. subtract 6 from 6 and 6 from 4
2x = -2
3. divide 2x by 2 and -2 by 2
answer: -1
Part 2
−3|2x + 6| = 12
1. divide -3 by -3 and 12 by -3
|2x + 6| = -4
2. subtract 6 from 6 and 6 from -4
2x = -10
3. divide 2x by 2 and -10 by 2
answer: -5
hope this helps!
Express your answer as a polynomial in standard form.
f(x) = 2x² + 3x + 12
g(x) = 5x - 6
Find: (gof)(x)
The answer as a polynomial in standard form is 50x² - 45x +66.
What are polynomials?A polynomial is an expression in mathematics that solely uses the operations of addition, subtraction, multiplication, and powers of positive-integer variables. It consists of indeterminates and coefficients. The polynomial x2 4x + 7 is an illustration of a single indeterminate x polynomial. Sums of terms with the pattern k x n—where k is any positive integer and n is an arbitrary number—are known as polynomials. A polynomial is something like 3x+2x-5. Polynomials: An introduction In this video, basic terms such terms, degrees, standard form, monomial, binomial, and trinomial are covered. Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an equation made up of variables, constants, and exponents (No division operation by a variable).
g(x) = 5x - 6
So,
f(x) = 2(5x - 6)² + 3(5x - 6) + 12
= 2( 25x² + 36 - 60x ) + 15x - 18 + 12
= 50x² + 66 - 45x
= 50x² - 45x +66
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the area of a circle is 100 Pi find the circumference in terms of Pi
Answer:
The formula for the area of a circle is given by Pi * r^2, where r is the radius of the circle. If the area of the circle is 100 Pi, we can solve for the radius:
100 Pi = Pi * r^2
r^2 = 100
r = 10
The formula for the circumference of a circle is given by 2 * Pi * r. Substituting the value of r = 10, we get:
C = 2 * Pi * r = 2 * Pi * 10 = 20 * Pi
So, the circumference of the circle is 20 Pi.
What is 3x+12 = 10x-15
Answer: 3.85714285714=x
Step-by-step explanation:
3x+12=10x-15
-3x -3x
12=7x-15
+15 +15
27=7x
27/7=7x/7
3.85714285714=x
:)
Because the Texas Constitution does not have a "necessary and proper" clause, _________. a. government powers are almost unlimited b. much of what is included in the constitution is improper c. the governor has to make the laws d. government is limited to what is in the constitution Please select the best answer from the choices provided A B C D
Answer:
The answer is D.
Step-by-step explanation:
Edge
divide 6q by q please solve this and help me to get out of this
Step-by-step explanation:
the answer is 6
please mark me brainliest
Answer:
\( \frac{6q}{q} \\ \frac{6 \times q}{q} \\ when \: q \: is \: divided \: by \: q \: then \: the \: remainder \: is \: 1 \\ 6 \times 1 \\ 6\)
Events D and E are independent, with P(D)- 0.6 and P(D and E) - 0.18. Which of the following is true? A. P(E)- 0.12 B. P(E) = 0.4 C. P(D or E)-0.28 D. P(D or E) 0.72 E. P(D or E)-0.9
The correct statement is: A. P(E) = 0.3. The probability of event E, denoted as P(E), is equal to 0.3.
To determine the correct answer, let's analyze the given information.
We know that events D and E are independent, which means that the occurrence of one event does not affect the probability of the other event happening.
Given:
P(D) = 0.6
P(D and E) = 0.18
Since events D and E are independent, the probability of both events occurring (P(D and E)) can be calculated as the product of their individual probabilities:
P(D and E) = P(D) * P(E)
Substituting the given values:
0.18 = 0.6 * P(E)
To find the value of P(E), we can rearrange the equation:
P(E) = 0.18 / 0.6
P(E) = 0.3
Therefore, the correct answer is A. P(E) = 0.3.
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describe the sample space in terms of the condition (functional or defective) of each nozzle after a year. let ""f"" denote a functional nozzle after a year and ""d"" denote a defective one.
The sample space, in terms of the condition (functional or defective) of each nozzle after a year, can be represented using the symbols "f" and "d" to denote a functional and defective nozzle, respectively.
The possible outcomes in the sample space can be described as a combination of these symbols. For example, if we have three nozzles, the sample space could include outcomes such as "fff" (all three nozzles are functional), "dfd" (the first and third nozzles are functional, while the second one is defective), "ffd" (the first two nozzles are functional, while the third one is defective), and so on.
Each outcome in the sample space corresponds to a particular arrangement or configuration of functional and defective nozzles after a year. The sample space encompasses all the possible combinations and provides a comprehensive representation of the different outcomes that can occur.
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New game You pay 10 and roll a 6 die. If you get a you win 50 If not, you get to roll again. If you get a 6 this time, you get your 10 back.
a) Create a probability model for this game.
b) Find the expected value and standard deviation of your prospective winnings.
c) You play this game five times. Find the expected value and standard deviation of your average winnings.
d) 100 people play this game. What's the probability the person running the game makes a profit?
a) Probability model
P(40) = 1/6
P(0) = 5/36
P(-10) = 25/36
b) E(X) = -5/18
standard deviation = 18.331
c) standard deviation = 91.65
d) Probability = 0.560
From the question, we have
a) X = -10, 0 or 40 for your winnings (or losses). The corresponding probabilities are:
P(40) = 1/6
P(0) = (5/6)(1/6) = 5/36
P(-10) = 1 - 1/6 - 5/36 = 25/36
b) E(X) = (-10)(25/36) + 0(5/36) + 40(1/6) = -5/18
E(X^2) = (100)(25/36) + 1600(1/6) = 3025 / 9
Var(X) = E(X^2) - [E(X)]^2 = 3025 / 9 - (-5/18)^2 = 108875 / 324
standard deviation = sqrt [Var X] = 119043 / 6494 =18.331
c) E(X) = (-10)(25/36) + 0(5/36) + 40(1/6) = -5/18
5 * E(X) = - 25/18
standard deviation = 5 * 18.331 = 91.65
d) Probability :
P(X < 0) = P{ z < [0 - (-5/18)] / [(119043 / 6494) / sqrt 100] } = P(z < 0.1515) = 0.560
Probability:
Possibility is referred to as probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is.
Complete question:
From the Data at Hand to the World at Large 4. New game You pay $10 and roll a die. If you get a 6, you win $50. If not, you get to roll again. If you get a 6 this time, you get your $10 back. a) Create a probability model for this game. b) Find the expected value and standard deviation of your prospective winnings. c) You play this game five times. Find the expected value and standard deviation of your average winnings. d) 100 people play this game. What's the probability the person running the game makes a profit?
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Hard question: there are many partially mixed strategy Nash equilibria here. Try to think of when players are indifferent between their strategies. In each of the following games, find all the pure and mixed strategy Nash equilibria. Golden Balls Player 2 Split Player 1 Split 50,50 Steal 100,0 Steal 0,100 0,0
in the Golden Balls game, there is only one pure strategy Nash equilibrium, which is (Split, Split).
In the Golden Balls game, there are two players, Player 1 and Player 2. Each player can choose to either "Split" or "Steal." The payoffs for each possible combination of actions are as follows:
If both players choose Split, they both receive a payoff of 50.
If Player 1 chooses Steal and Player 2 chooses Split, Player 1 receives 100, and Player 2 receives 0.
If Player 1 chooses Split and Player 2 chooses Steal, Player 1 receives 0, and Player 2 receives 100.
If both players choose Steal, they both receive a payoff of 0.
To find all the pure strategy Nash equilibria, we need to identify any strategies where neither player has an incentive to deviate unilaterally.
Pure Strategy Nash Equilibria:
(Split, Split): This is a pure strategy Nash equilibrium because if both players choose Split, neither player can improve their payoff by unilaterally changing their strategy to Steal.
Now let's consider mixed strategy Nash equilibria, where players randomize between their available strategies.
Mixed Strategy Nash Equilibrium:
To find the mixed strategy Nash equilibrium, we need to examine whether there exists a probability distribution over strategies that maximizes the expected payoff for each player, given the other player's strategy.
In this case, there is no mixed strategy Nash equilibrium since Player 2's expected payoff from choosing Split is always lower than the expected payoff from choosing Steal, regardless of the probabilities assigned to each strategy by Player 1. Similarly, Player 1's expected payoff from choosing Split is always lower than the expected payoff from choosing Steal, regardless of the probabilities assigned to each strategy by Player 2.
Therefore, in the Golden Balls game, there is only one pure strategy Nash equilibrium, which is (Split, Split).
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Help stuck on this question
Answer:
< b = 73°
Step-by-step explanation:
The angle with a measure of < 73° has the same measure as < b because they are vertical angles. Two angles are vertical angles if they are opposite angles formed by the intersection of two lines. Vertical angles are congruent.
Therefore, the correct answer is: < b = 73°
what is two fifths of 30,000 miles squared?
pls help this is due in like 10 minutes
Answer: 12,000 \(mi^{2}\)
Step-by-step explanation:
30,000 x 2/5 (0.4 in decimal form) = 12,000
Answer: 12000 miles
Step-by-step explanation:
30000*2/5 = 12000 miles
What is the equation for the least square regression line where the independent or predictor variable is sepal length and the dependent or response variable is sepal width for iris setosa?
The equation for the least square regression line can be used to model the relationship between the independent variable (sepal length) and the dependent variable (sepal width) for the iris setosa species.
The least square regression line is represented by the equation:
y = mx + b
where y is the predicted value of the dependent variable (sepal width), x is the value of the independent variable (sepal length), m is the slope of the line, and b is the y-intercept. To find the values of m and b, you would need a dataset of sepal length and sepal width measurements for the iris setosa species. By using statistical software or calculators, you can perform a linear regression analysis on the dataset to obtain the values of m and b. These values can then be plugged into the equation to obtain the least square regression line for sepal width based on sepal length. The equation for the least square regression line with sepal length as the independent variable and sepal width as the dependent variable for iris setosa is y = mx + b, where y is the predicted value of sepal width, x is the sepal length, m is the slope of the line, and b is the y-intercept. The equation for the least square regression line, also known as the linear regression line, allows us to model the relationship between two variables by fitting a straight line to a given set of data points. In this case, we are interested in predicting the sepal width (dependent variable) based on the sepal length (independent variable) for the iris setosa species. To find the equation for the least square regression line, we need to perform a linear regression analysis on a dataset of sepal length and sepal width measurements for iris setosa. This analysis calculates the values of the slope (m) and the y-intercept (b) of the line that best fits the data. Once we have the values of m and b, we can plug them into the equation y = mx + b to obtain the least square regression line. This line represents the best-fit line that minimizes the sum of the squared differences between the observed values of sepal width and the predicted values based on sepal length.
In conclusion, the equation for the least square regression line with sepal length as the independent variable and sepal width as the dependent variable for iris setosa is y = mx + b. This equation allows us to predict the sepal width based on the sepal length by using the values of the slope (m) and y-intercept (b) obtained through a linear regression analysis on a dataset of iris setosa measurements.
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1. If f(x) = (3x-2)/(2x+3), then f'(x) =
Answer:
\(f'(x)= \frac{13}{(2x+3)^2}\\\)
Step-by-step explanation:
\(f(x)= \frac{3x-2}{2x+3} \\\)
\(f'(x)=\frac{dy}{dx} = \frac{d}{dx}(\frac{3x-2}{2x+3})\\ f'(x)= \frac{(2x+3)\frac{d}{dx}(3x-2)-(3x-2)\frac{d}{dx}(2x+3) }{(2x+3)^{2} } \\f'(x)= \frac{(2x+3)(3)-(3x-2)(2)}{(2x+3)^{2} } \\\)
\(f'(x)= \frac{6x+9-6x+4}{(2x+3)^{2} }\\ f'(x)= \frac{13}{(2x+3)^2}\\\)
pelase man hel me im dying miserably
The scatter plot for the above data is attached accordingly. The results fro the scatter plot shows that the there is little or no correlation between the two data examined.
What is a scatter graph?A scatter plot is a graphic or mathematical diagram that uses Cartesian coordinates to show the values of two variables for a set of data. If the points are coded, an additional variable can be displayed.
A scatterplot shows the correlation between two quantitative variables measured for the same individual. The values of one variable are displayed on the horizontal axis and the values of the other variable are displayed on the vertical axis.
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Which of the following statements is true? (A) A parameter is a number that describes some characteristic of a sample. (B) An unbiased estimator is any statistic that is taken from a sample chosen by random methods. (C) A sampling distribution is the distribution of a statistic calculated from all possible samples of the same size from the same population. (D) The variability of a population distribution will decrease as the sample size increases. (E) A normal approximation can always be used for the sampling distribution of pas long as the sample size is greater than 30.
The true statement among the options is (C) A sampling distribution is the distribution of a statistic calculated from all possible samples of the same size from the same population.
Option (A) is incorrect because a parameter describes a characteristic of a population, not a sample. Option (B) is incorrect because an unbiased estimator is a statistic that produces an estimate that is, on average, equal to the true value of the parameter being estimated. It is not related to the method of sampling. Option (D) is incorrect because the variability of a population distribution does not depend on the sample size. Option (E) is incorrect because the normal approximation can only be used for the sampling distribution if the population is normally distributed or if the sample size is large enough to satisfy the central limit theorem, which typically requires a sample size greater than 30 for moderate to large variability.
C) A sampling distribution is the distribution of a statistic calculated from all possible samples of the same size from the same population.
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what is BE in the figure
Answer:
I honestly don't understand what is being asked
Answer:
25
Step-by-step explanation:
B is second in the English alphabet and E is on the 5th positions on this same English alphabet
A future interest usually exists in conjunction with which of the following real property interests at the time that it is the interest granted?
A future interest in real property typically exists in conjunction with a present interest in that same property at the time the future interest is granted.
What is a future interest?
Future interests are created when a property owner grants an interest in their property that will take effect at a later time, such as after their death or the expiration of a lease.
These interests are typically created in the form of a trust or a will, and they can be used to ensure that property is distributed according to the owner's wishes, to provide for the future needs of family members, or to protect property from creditors or other claims.
Examples of future interests include remainders, reversions, and executory interests.
Complete questin:
A future interest usually exists in conjunction with which of the following real property interests at the time that it is the interest granted?
1) future interest
2) protect property
3) both a and b
4) None of these
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The principal P is borrowed at a simple interest rate r for a period of time t. Find the loan's future value A, or the total amount due at time t. P = $20,000, r = 5.5%
the loan's future value or the total amount due at time t is $23,300 if the loan is borrowed at a simple interest rate of 5.5% for a period of 3 years.
The principal P is borrowed at a simple interest rate r for a period of time t. Find the loan's future value A, or the total amount due at time t. P = $20,000, r = 5.5%
The formula for calculating the future value of a simple interest loan is:
FV = P(1 + rt)
where FV represents the future value, P is the principal, r is the interest rate, and t is the time in years. Therefore, using the given values: P = $20,000 and r = 5.5% (or 0.055) and the fact that no time is given, we cannot determine the exact future value.
However, we can find the future value for different periods of time. For example, if the time period is 3 years:
FV = $20,000(1 + 0.055 × 3) = $20,000(1.165) = $23,300
Therefore, the loan's future value or the total amount due at time t is $23,300 if the loan is borrowed at a simple interest rate of 5.5% for a period of 3 years.
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i don't know how to solve this problem. please help.
Answer:
$2.71 + 4j = $6.75
j = $1.01
Step-by-step explanation:
$2.71 + 4j = $6.75
4j = 6.75 - 2.71 = 4.04
j = 4.04/4 = $1.01
Answer:
$6.75 = $2.71 + 4j
j = $1.01
Step-by-step explanation:
The total amount of money Ava spent was $6.75. We can make this one side of an equation.
The other side of the equation can be what Ava bought for that $6.75. We know that she bought $2.71 of oranges and 4 juice bottles, so we can add these on the other sides of the equation.
\(\$6.75 = \$2.71 + 4j\)
To solve this equation for \(j\), we can first subtract $2.71 from both sides.
\(\textrm{ } \ \$6.75 = \$2.71 + 4j\\\underline{-\$2.71} \ \ \ \ \underline{-\$2.71 \ \ \ \ }\)
\(\$4.04 = 4j\)
Finally, we can divide both sides by 4.
\(\$4.04 = 4j\\\overline{\ \ \ 4\ \ \,} \ \ \ \ \overline{\: 4 \:}\)
\(\$1.01 = j\)
\(\boxed{j = \$1.01}\)
Aline read a report saying 39% of teachers in the United State were members of a labor union. She wants to test whether this holds true for teachers in her state, so she is going to take a random sample of teachers and see what percent of them are members of a union. Let p represent the proportion of teachers in her state that are members of a union. Write an appropriate set of hypotheses for her significance test.
Answer:
H0: p= 0.39 vs Ha: p ≠ 0.39
Step-by-step explanation:
She wants to test whether this holds true for teachers in her state.
The test is the formulated into the hypotheses.
The null hypothesis would be
H0: p= 0.39 against the claim Ha: p ≠ 0.39
The null hypothesis tells that the the proportion of teachers in her state that are members of a union is equal to the proportion of teachers in the US that are members of the labor union.
against the claim
That the the proportion of teachers in her state that are members of a union is not equal to the proportion of teachers in the US that are members of the labor union.
hi help me (2·4)²= this is other (6:2)²+
Answer:
(2·4)² = 64 / (6*2)² = 144
Step-by-step explanation:
Follow PEMDAS :
Parenthesis first, so:
2 * 4
==> 8
Then Exponent:
8 ^2
==> 64
(2·4)² = 64
Do the same for (6:2)² :
Parenthesis first :
6 * 2
==> 12
Then Exponent:
12^2
==> 144
(6:2)² = 144
Answer:
1. 64 is the answer.2. 144 is the answerStep-by-step explanation:
First, multiply the numbers inside the parenthesis. So
1. 2*4 = 8
2. 6*2 = 12
Next, Use the exponents
1. 8^2
2. 12^2
Finally, solve using exponents.
1. 8^2 = 64
2. 12^2 = 144
So 64 and 144 is the answer.
Hope this helped,
Kavitha
ms tunnicliffe is making jam for the county fair blackberries cost 5.50 per kg sugar cost 65c per kg 15 glass jars cost 5.85 she uses 16kg of blackberries and 10kg of sugar to make 15 jars of jam calculate the total cost to make the 15 jars
Therefore , the solution of the given problem of unitary method comes out to be total cost for to make 15 jars is 12,386.25 euroes.
What exactly is a unitary method?After calculating the size of a small slice, multiply the quantity by two to complete a task using the unitary technique. Simply expression, the unit variable technique works to separate a coded item from a certain group or collection of groups. For instance, 40 pens would cost Rs. 400 (or 400 pounds, $1.01). It's possible that one country will have total control over the method employed to do this. Almost every living creature has a distinctive quality.
Here,
Given :
cost of blackberry = 88 euroes
cost of sugar = 650 euroes
Jam bottles costs =87.75
total cost for to make 15 jars is
=> 15 * (87.75+650+88)
=> 15 * 825.75
=> 12,386.25 euroes
Therefore , the solution of the given problem of unitary method comes out to be total cost for to make 15 jars is 12,386.25 euroes.
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Maria wanted to bring back 5 million grains of sand from her trip to the beach. Each grain of sand weighs approximately 6.7 x 10^-7 kg. How heavy is the bag of sand that Maria brings home?
a
Multiply (5,000,000 x 6.7 x 10^-7) = (5 x 10^6) x (6.7 x 10^-7) = (5 x 6.7) x (10^(6 + - 7)) = 33.5 x 10^-1 = 3.35 kg
b
Multiply 5 x (6.7 x 10^-7) = 33.5 x 10^-7 = 3.35 x 10^-6 kg
c
Multiply (5,000,000 x 6.7 x 10^-7) = (5 x 10^6) x (6.7 x 10^-7) = (5 x 6.7) x (10^(6 + 7)) = 33.5 x 10^13 = 3.35 x 10^14 kg
d
Divide (5,000,000 / 6.7 x 10^-7) = (5 x 10^6) / (6.7 x 10^-7) = (5 / 6.7) x (10^(6 - 7)) = .74 x 10^-1 = 0.074 kg
PLEASE HELP
Answer:
3.35
Step-by-step explanation:
5,000,000*6.7 * 10^-7
= 5 * 10^6 * 6.7*10^-7
= 33.5 * 10^-1
= 3.35
The weight of 5 million grains of sand is 3.35 kg.
Option A is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Weight of each grain of sand = 6.7 x \(10^{-7}\) kg
Weight of 5 million grains of sand.
= 5,000,000 x 6.7 x \(10^{-7}\) kg
= 5 x \(10^6\) x 6.7 x \(10^{-7}\)
= 33.5 x \(10^{-1}\) kg
= = 3.35 kg
Thus,
The weight of the total grain of sand is 3.35 kg.
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suppose you have a weak argument with all false premises. given this information, what do you know about the conclusion of this argument?
A weak argument with all false premises tells us that the conclusion is not supported by valid reasoning and should be examined carefully before accepting it.
If an argument has all false premises, then it is not a sound argument. The conclusion of such an argument cannot be trusted as it is based on false information. In other words, a weak argument with all false premises does not provide any logical or factual support for its conclusion, and the conclusion itself is likely to be false.
It is important to note that even if the conclusion happens to be true, it cannot be inferred from false premises. This is because the truth of a conclusion depends on the truth of its premises. If the premises are false, then the conclusion cannot be relied upon.
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Smithsonian national zoological park in d.c. has 15 toucans and 60 parrots. what is the ratio of the number of toucans to the number of parrots at the zoo?
The ratio of the number of toucans to the number of parrots at the Smithsonian National Zoological Park is 1:4, indicating that there is one toucan for every four parrots at the zoo.
To determine the ratio of the number of toucans to the number of parrots at the Smithsonian National Zoological Park, we can use the concept of a ratio, which compares two quantities. In this case, the two quantities are the number of toucans and the number of parrots.
Given that the zoo has 15 toucans and 60 parrots, we can express the ratio of toucans to parrots as:
15 toucans : 60 parrots
To simplify this ratio, we can divide both the number of toucans and parrots by the greatest common divisor (GCD) to obtain the simplest form.
The GCD of 15 and 60 is 15. Dividing both quantities by 15, we get:
15 toucans ÷ 15 : 60 parrots ÷ 15
This simplifies to:
1 toucan : 4 parrots
Therefore, the ratio of the number of toucans to the number of parrots at the Smithsonian National Zoological Park is 1:4.
This ratio indicates that for every toucan at the zoo, there are four parrots. It gives a relative comparison of the quantities of these two bird species present in the park.
It's important to note that ratios can also be expressed in different forms, such as fractions or percentages. In this case, the ratio 1:4 can also be written as 1/4 or 25% (since 1 out of 4 is 25%).
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If f(x)=2x+1 and g(x)=x−5, find f(x)+g(x) to complete the polynomial
Answer:
\(\huge\boxed{\sf 3x -4}\)
Step-by-step explanation:
Given functions:f(x) = 2x + 1g(x) = x - 5Add both equations.
f(x) + g(x):= 2x + 1 + x - 5
Combine like terms
= 2x + x + 1 - 5
= 3x - 4\(\rule[225]{225}{2}\)
Answer:
f(x) + g(x) = 3x - 4
Step-by-step explanation:
The problem is,
→ f(x) + g(x)
Let's solve the problem,
→ f(x) + g(x)
→ (2x + 1) + (x - 5)
→ 2x + 1 + x - 5
→ (2x + x) + (1 - 5)
→ 3x +(-4)
→ 3x - 4
Hence, answer is 3x - 4.
monique and tara each make an ice-cream sundae. monique gets 3 scoops of cherry ice-cream and 1 scoop of mint chocolate chunk ice-cream for a total of 84g of fat. tara has 1 scoop of cherry and 3 scoops of mint chocolate chunk for a total of 60g of fat. how many grams of fat does 1 scoop of each type of ice cream have?
The amount of fat in Cherry ice-cream is 24 grams.
The amount of fat in the Mint Chocolate Chunk ice-cream is 12 grams.
Writing data into equations using Algebra,3C + M = 84...(1)C + 3M = 60...(2)
Multiplying equation (2) by 3 and then subtracting equation (1) from
the result gives, 3 * (C +3M) = 3 × 603C + 9M = 180...(3)(3C + 9M = 180) - (3C + M = 84) = 8M =96M= 12
The amount of fat in the Mint Chocolate Chunk ice-cream, M = 12
grams C + 12*3 = 60C = 60-36 = 24
The amount of fat in Cherry ice-cream C = 24 grams As a result, Cherry ice cream contains 24 grams of fat and Mint Chocolate Chunk ice cream contains 12 grams of fat.
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Nora was offered a job that paid a salary of $40,000 in its first year. The salary was set to increase by 3% per year every year. If Nora worked at the job for 21 years, what was the total amount of money earned over the 21 years, to the nearest whole number?
The total amount of money earned by Nora salary over the 21 years is approximately $1,848,000.
To find the total amount of money earned by Nora over 21 years, we need to calculate the salary for each year and then sum them up.
In the first year, Nora's salary is $40,000.
In the second year, her salary will be increased by 3%, so it will be:
$40,000 + 3% of $40,000 = $40,000 + $1,200 = $41,200.
In the third year, her salary will again increase by 3%, so it will be:
$41,200 + 3% of $41,200 = $41,200 + $1,236 = $42,436.
We can continue this process for each year, adding 3% of the previous year's salary to calculate the next year's salary.
To calculate the total amount of money earned over the 21 years, we need to sum up the salaries for each year. Here's the calculation:
Total = $40,000 + $41,200 + $42,436 + ... (21 terms)
To simplify the calculation, we can use the formula for the sum of an arithmetic series:
Total = (n/2) * (2a + (n - 1)d)
where:
n = number of terms (21 in this case)
a = first term ($40,000)
d = common difference (3% of the previous year's salary)
Plugging in the values:
Total = (21/2) * [2(40,000) + (21 - 1)(0.03)(40,000)]
Simplifying further:
Total = (21/2) * [80,000 + 20(0.03)(40,000)]
= (21/2) * [80,000 + 2,400(40,000)]
= (21/2) * [80,000 + 96,000]
= (21/2) * 176,000
= 21 * 88,000
= 1,848,000
Therefore, the total amount of money earned by Nora salary over the 21 years is approximately $1,848,000.
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