The difference in the salary Cynthia will earn working as a camp counselor instead of a lifeguard after x hours (f − g)x = 5x - 25.
What is a function?A function can be defined as the set of inputs that results in output.
Given, Cynthia earns 20 dollars per hour working as a camp counselor plus an additional 25 dollars as a bonus which is f(x) = 20x + 25, and as a lifeguard 15dollars per hour and an additional 50 dollars bonus which is g(x) = 15x = 50.
We know (f - g)x = f(x) - g(x).
∴ The difference in the salary Cynthia will earn working as a camp counselor instead of a lifeguard after x hours is f(x) - g(x).
= (20x + 25) - (15x + 50).
= 20x - 15x + 25 - 50.
= 5x - 25.
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Write the equation for g(x)
The equation of the graph of g is represented by y - 6 = (x-2)²
The very first step in balancing a variable equation is to correctly identify the specific values of the variables that lead to equality.
The equation's solutions are the specific values of the unknown variables that perfectly satisfy the equality, which are often referred to as the variables for which the particular equation must be solved. Identity equations and conditional equations are the two types of equations. The variables all have the same identity for all conceivable values. A conditional equation can only be true in particular situations where the values of the variables match. The equals sign is an important symbol that is used in mathematical formulas to denote the equality of two expressions.The graph of the function is f is y = x²
Now we can see that the graph of g is translated to 2 units to the right and 6 units up.
We know from the properties of translation that when the graph moves 2 units to the right we get the equation as y = (x-2)²
Again when the graph moves 6 units up wards the graph changes by
y - 6 = (x-2)²
Therefore the equation of g is y - 6 = (x-2)²
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15% of x=20% of y what is x:y?
The ratio of x:y is 4:3.
What is ratio?Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categories ratios. Part to whole ratio is one, while part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings.
For instance, a class has a 12:15 boy-to-girl ratio, but the part-to-whole ratio refers to the relationship between a particular group and the entire. For instance, five out of every ten people enjoy reading. As a result, the ratio of the portion to the total is 5: 10, meaning that 5 out of every 10 persons enjoy reading.
Given:
15% of x=20% of y
So,
15 / 100 × x = 20 / 100 × y
3 / 20x = 1/5y
x / y = 1/5 x 20/3
x / y = 4/3
Hence, the ratio of x:y is 4:3.
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Finding Missing Angles !
Answer: m11= 180-90= 90 (linear pair)
m12= 180-90= 90 (linear pair)
m13= 90 linear pair
Alex and Patty are tracking the number of steps they walk. Alex records that he can walk 5750 steps in 50 minutes. Patty
writes the equation y = 1142, where y is the number of steps and x is the number of minutes she walks, to describe her
step rate. This week, Alex and Patty each walk for a total of 4 hours. Who walks more steps? How many more?
walks
more steps.
By solving the equation we can conclude that Andre (36,000 steps) walks more than Priya (35,400 steps).
What are equations?A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 = 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this article, let's learn more about math equations.So, the distance that Andre traveled.
He demonstrated his ability to take 6000 steps in 50 minutes.
The pace at which Andre can walk is:
= 6000/50= 120 steps per minuteThe 5 hours in minutes conversion: 5 × 60 minutes = 300 minutes
Then,
The distance traveled by Andre is:
120 × 300 = 36000 stepsSo, Andre walks 36000 steps.And, Priya enters the formula y = 118x.Where x represents the number of minutes and y is the number of steps.
The formula to convert 5 hours to minutes is:
x = 5 × 60 minutesx = 300 minutesReplace x with its value in the equation:
y = 118xy = 118 × 300y = 35400 steps35400 steps are taken by Priya.
Therefore, by solving the equation we can conclude that Andre (36,000 steps) walks more than Priya (35,400 steps).
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The correct question is given below:
Andre and Priya are tracking the number of steps they walk. Andre records that he can walk 6000 steps in 50 minutes. Priya writes the equation y=118x, where y is the number of steps and x is the number of minutes she walks, to describe her step rate. This week, Andre and Priya each walked for a total of 5 hours. Who walks more steps?
Select the correct answer.
This table represents function f.
If function g is a quadratic function that contains the points (-3, 5) and (0, 14), which statement is true over the interval (-3, 0]?
The average rate of change of f is less than the average rate of change of g.
The average rates of change of f and g cannot be determined from the given information.
Te average rate of change of f is the same as the average rate of change of g
The average rate of change of f is more than the average rate of change of g
The average rate of change of f is less than the average rate of change of g.
What is average rate ?
This expression represents the average rate of change of the function f over the range a≤x≤b is less than or equal to x, and is less than or equal to b:
f(b)−f(a) / b - a
It is the average amount by which the function changed per unit throughout that time period.
Here, in Average rate of change in function g over [-3, 0]
=> a = -3, b = 0
=> f(a) = 5 , f(b) = 14
Average rate of change = (14 - 5) / (0 - (-3))
= 3
Now, in Average rate of change in function f over [-3, 0]
=> a = -3, b = 0
=> f(a) = -3, f(b) = 0
Average rate of change = (0 - (-3)) / (0 - (-3))
= 1
Therefore, The average rate of change of f is less than the average rate of change of g.
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solve each system of inequalities
Answer:
x < 6
Step-by-step explanation:
x/3 + x/4 < 7 | * 12
4x + 3x < 84
7x < 84 | : 7
x < 12
1 - x/6 > 0
1 > x/6 | * 6
6 > x
x < 6
x < 6 and x < 12 gives x < 6
I need help finding the perimeter
Answer:
Perimeter (to the nearest tenth) = 24.3
Step-by-step explanation:
Using the math tool graph your points on the graph and connect them to each other. You should have something like this (look at the first image)* [note the scale of my graph is one but I skip the odd numbers] From there you can count the distance from those points. To find the distance from point R to Q and from point Q to S you can simply count the number of square from those points. For instance from point R to point Q is 9 units and from point Q to point S is 5 units (look at the second image) To find the distance from point R to point S you do the Pythagorean theorem since this triangle is a right triangle which is Leg² + Leg² = Hypothnose². Let line segments RQ and QS be the legs and let line segment RS be the hypothnose. Since the square root of the hypothnose is an irrational number we take advantage of round to the nearest tenth so 10.295... will become 10.3. (In case you're confused follow the steps of the third image)To find the perimeter of the triangle you add all of the sides together so the formula for solving for it would be P = 9 + 5 + 10.3 which is 24.3. The perimeter is 24.3. (The foruth and last image shows all the work)write 0.0000072 in scientific notation
Answer:
7.2 × 10^-6
Step-by-step explanation:
7.2 are the two last digits of the notation
and the reason its to the power of -6 is because there are 6 digits until you reach 7
The diagram shows a lawn with a fence along one edge.
12 m
Fence
17 m
20 m
One can of weedkiller can cover 100 square metres.
Each can costs £19.75
Work out the total cost of the cans of weedkiller needed to cover the lawn.
You must show some working.
59.25 euros is the the total cost of the cans of weedkiller needed to cover the lawn
What is Trapezium?A trapezium is a convex quadrilateral with exactly one pair of opposite sides parallel to each other
The figure that is formed is the following with the respective measurements, now to calculate the area we need the height, for Pythagoras we have:
17 ²= h ² + 8 ²
h ² = 289 - 64
h ² = 225
h = 15
now the figure area is as follows:
A = h × (b + a) / 2
b long side 20 m and short side 12 cm, replacing:
A = 15 × (12 + 20) / 2
A = 240 m²
We are told that each can of weed killer can cover up to 100m ^ 2
Thus:
240/100 = 2.4, so you would need 3 cans of weedkiller
each can costs 19.75, which means that the total cost is:
19.75 × 3 = 59.25 euros
Hence 59.25 euros is the the total cost of the cans of weedkiller needed to cover the lawn.
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A. No, because one x-value corresponds to two different y-values.
B. Yes, because there are two x-values that are the same.
C. No, because two of the y-values are the same.
D. Yes, because every x-value corresponds to exactly one y-value.
Answer:
its A
Step-by-step explanation:
:)
1) Calculate the perimeter of
this triangle
7cm
4cm
10cm
6cm
Answer:
27
Step-by-step explanation:
length+base+heigth+breath
=6cm+10cm+4cm+7cm
=27cm
but I am not very sure so when it is correct the give me thanks or rate the answer so I will know it is correct
x³-8x+8 =0
[tex]x ^3 - 8x + 8 = 0[/tex]
ezzzzzzzzzzzzzzzzzzz
I need help on this 3rd grade homework
Pls help
The correct option or equation that applies to the given situation is 7*6 = (4*6) + (3*6).
According to the question,
We have the following information:
Akela drew smaller arrays to find the product of a larger array.
Now, we have two figures where one has 6*3 boxes (6 horizontal boxes and 3 horizontal boxes) and in the second figure we have 6*4 boxes (6 horizontal boxes and 4 vertical boxes).
Now, to find the correct option, we will look for these two in options:
So, the option that has both of them is 7*6 = (4*6) + (3*6).
Now, we can verify whether the sides of the equation given are correct or not.
We have:
7*6 = 42
On right hand side, we have:
(4*6) + (3*6)
24+18
42
Hence, the correct option is 4th one.
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Gabriel practices for a local marathon. If the
marathon is 42.195 kilometers long, how
many miles does Gabriel need to run in order
to condition himself? Round the answer to
the nearest tenth.
(1 mile ≈ 1.61 kilometers)
Answer:
26.208 miles
Step-by-step explanation:
42.195 / 1.61 = 26.208 miles
a playground is rectangular with a length of 7/8 miles. If the area of the play ground is 8/20 miles what is the width.
Answer: Width = 8/20 ÷ 7/8 = 8/20 x 8/7 = 16/35 Therefore, the width will be 16/35 miles. Hope you do great :) !
If the knowledge that an event a has occurred implies that a second event b cannot occur, then the events a and b are said to be.
If the knowledge that an event "a" has occurred implies that another event "b" cannot occur, then the events "a" and "b" are said to be disjoint events.
As per the question statement, the knowledge that an event "a" has occurred implies that another event "b" cannot occur.
We are required to determine the characteristic name for the above mentioned events.
Now as per the Probability Theory in Mathematics, two events are said to be "mutually exclusive" or "disjoint" if they cannot occur at the same time or simultaneously.And here, if event "a" occurs, even "b" does not, implying the fact that, events "a" and "b" cannot occur simultaneously. Hence, as per the above definition of disjoint events, the events "a" and "b" are be disjoint.
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Is the following shape a rectangle? How do you know?
Simplify: 4/x-2/x^2+1-2/x+1
On simplifying the given expression 4/x-2/x^2+1-2/x+1 we get solution as (2x^2 + 2x - 2)/x^2.
What is the meaning of simplifying a n equation?
To simplify a phrase, create an equivalent expression without any terms that are identical. The expression will then be rewritten using the fewest terms feasible.
We have given:
[tex]\frac{4}{x} - \frac{2}{x^2} +1 - \frac{2}{x} + 1[/tex]
Adding the numbers:
[tex]\frac{4}{x} - \frac{2}{x^2} - \frac{2}{x} + 2[/tex]
Making a common denominator:
[tex]\frac{4x}{x^2} - \frac{2}{x^2} - \frac{2x}{x^2} + \frac{2x^2}{x^2}[/tex]
Combining the values with common denominator:
[tex]\frac{2x^2 + 2x - 2}{x^2}[/tex]
This the the simplified result of the given expression.
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Can someone help me solved the highlighted question please. Ill give brainliest. Check attatched photo
Applying logarithm properties, the solution of the highlighted question is given as follows:
x = 4.
What is the solution for the equation?The logarithmic equation is given as follows:
[tex]\log_{a}(x + 2) = \frac{1}{3}\log_{a}{8} + \log_{a}{3}[/tex]
First, we apply the power rule, meaning that the multiplying coefficient of the logarithm can be the power of the given term, hence:
[tex]\frac{1}{3}\log_{a}{8} = \log_{a}{8^{\frac{1}{3}}} = \log_{a}{\sqrt[3]{8}} = \log_{a}{2}[/tex]
Then the equivalent expression is:
[tex]\log_{a}(x + 2) = \log_{a}{2} + \log_{a}{3}[/tex]
Now we apply the product rule, as the sum of two logarithms of same base can be written as a single logarithm, keeping the base and multiplying the terms.
Hence the equivalent expression is:
[tex]\log_{a}(x + 2) = \log_{a}{(2 \times 3)}[/tex]
[tex]\log_{a}(x + 2) = \log_{a}{6}[/tex]
The logarithm function is one-to-one, meaning that if they have the same input, they will have the same output, hence we can solve for x as follows:
x + 2 = 6
x = 6 - 2
x = 4.
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$55 set of headphones for 15% off. What is amount of discount? What is the total amount you pay?
Answer:
discount = $8.25 Total=$46.75
Step-by-step explanation:
[tex]\frac{x}{55}[/tex] = [tex]\frac{15}{100}[/tex] 55.00-8.25= $46.75
[tex]\frac{100x}{100}[/tex] = [tex]\frac{825}{100}[/tex] total= $46.75
x=8.25
discount = 8.25
Answer: The discount is $8.25, the total price you pay is $46.75
Step-by-step explanation:
To find the discount, you multiply the decimal of the percent, which is .15 by the total. So 55*.15=8.25. That is how much of a discount you get.
To find the total amount you pay after the discount you simply subtract the discount from the total, so 55-8.25=46.75
each individual in a random sample of high school and college students was cross-classified with respect to both political views and marijuana usage. does the data support the hypothesis that political views and marijuana usage level are independent within the population?
Since X² (68.732) > X²₀.₀₁ (13.277), we reject the null hypothesis and conclude that There is evidence that political views and level of marijuana usage are related.
The alternative hypothesis states that political beliefs and marijuana use depend on one another within the population, contrary to the null hypothesis that asserts these two variables are independent.
H₀ : Pij = Pi · Pj ; i = 1, 2, 3 ; j = 1, 2, 3
Ha : at least one Pij ≠ Pi · Pj
We want to test whether there is a relationship between political views and marijuana usage levels. The results of a random sample of size n = 1353 are derived from the following formula;
e = (Row total) x (Column total) /Total sample size
We are told to use the 0.01 level of significance to test the null hypothesis. Thus, α = 0.01. The table has r = 3 rows and c = 3 columns. An r × c table has degrees of freedom df = (r - 1) x (c - 1). So, a 3×3 table has degrees of freedom df = (3 - 1) x (3 - 1) = 4. From formula the df = 4 and α = 0.01, χ²₀.₀₁ = 13.277. Reject the null hypothesis if X² ≥ 13.277 where
x² =Σ(a - e)²/e
Substituting the observed and expected frequencies summarized in the table above into the formula for x², we get
X² = 68.732
Rejection Region → X² ≥ 13.277
Test statistic → X² = 68.732
Since X² (68.732) > X²₀.₀₁ (13.277), we reject the null hypothesis and conclude that There is evidence that political views and level of marijuana usage are related.
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x+3 is greater than or equal to 2x-6 solve
The solution for x + 3 is greater than or equal to 2x - 6 is x ≤ 9.
Given,
x + 3 is greater than or equal to 2x - 6
That is,
x + 3 ≥ 2x - 6
Solve for x in this solution.
So,
x + 3 ≥ 2x - 6
Here,
6 + 3 ≥ 2x - x
Then,
9 ≥ x
That is,
The solution for x + 3 is greater than or equal to 2x - 6 is x ≤ 9.
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what is the answer of (3/8)^-2
[tex](\frac{3}{8} )^{-2}[/tex]
[tex](\frac{8}{3})^{2}[/tex]
[tex](\frac{8}{3} )\times(\frac{8}{3} )[/tex]
[tex]\frac{8\times8}{3\times3}[/tex]
[tex]\frac{64}{9}[/tex] or [tex]7.1111111[/tex]
In circle Q with the measure of arc ⌢=118∘PR⌢ =118 ∘ , find m∠PQRm∠PQ
Explanation
We are given the measure of arc PR = 118°.
We are required to find m∠PQR.
We know that an arc measure is an angle the arc makes at the center of a circle. Therefore, we have:
[tex]\begin{gathered} obtuse\text{ }m\angle PQR=118\degree \\ obtuse\text{ }m\angle PQR+reflex\text{ }m\angle PQR=360\degree\text{ }\lbrace angles\text{ }at\text{ }a\text{ }point\rbrace \\ reflex\text{ }m\angle PQR=360\degree-obtuse\text{ }m\angle PQR \\ reflex\text{ }m\angle PQR=360\degree-118\degree \\ reflex\text{ }m\angle PQR=242\degree \end{gathered}[/tex]Hence, the answer is:
[tex]\begin{gathered} obtuse\text{ }m\angle PQR=118\degree \\ reflex\text{ }m\angle PQR=242\degree \end{gathered}[/tex]But since Q is the measure of the angle, then the final answer is 118°.
is equivalent to /x-
20 For the function w, w(9) = -7, and w(-7)= 9. If y = w(x), what is the value of y when
X = -7?
Record your answer and fill in the bubbles on your answer document.
The value of y when x = -7 according to the function defined y = w(x) is; 9.
What is the value of y when x = -7 as required in the task content?It follows from the task content that the value of y when x = -7 is to be determined according to the given expression; y = w(x).
Since it follows from the task content that;
y = w(x)
Therefore, it follows that when; x = -7; we have;
y = w(-7).
However, recall from the function instances given that; w(-7) = 9;
Therefore, y = w(-7) = 9.
Ultimately, the value of y when x = -7 as required in the task content is; 9.
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50779 / 590 remainder
Answer:
39.
Step-by-step explanation:
50779 divided by 590 is 86, with a remainder of 39.
Find the value of x in each case.
The algebraic expression should often take one of the following forms: addition, subtraction, multiplication, or division. Bring the variable to the left and the remaining values to the right to determine the value of x. To determine the outcome, simplify the values.
How do you find the value of x?In algebra, the letter "x" is frequently used to denote an unknown value. It is referred to as a "variable" or occasionally a "unknown. "x is a variable in x + 2 = 7, but we can figure out its value if we try! The order in which you perform operations in arithmetic and algebra is governed by a number of laws.The Commutative, Associative, and Distributive Laws are the three that receive the most attention.People have discovered over time that the sequence of the numbers has no bearing on the results of addition or multiplication.4x+2x+5x+50= 180
= 6x+5x+50 =180
combine 6x and 5x
= 11x
11x+50= 180
subtract 50 both sides
11x = 180- 5
= 130
11x=130
x= 130/11
11.81
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Johnny found a sick abandoned kitten in his yard. It was very malnourished and he decided to nurse it back to health. He started feeding the kitten enough food to help it gain weight. On average the kitten was gaining 4 ounces per day. After 6 days in Johnny's care, the cat weighed 73 ounces. Determine how many days until the kitten will weighs 105 ounces.
Answer:9 days
Step-by-step explanation:A lot of division is required, but because 8.75 probably isn't an answer, I rounded up to 9.
What percentage of this shape is shaded?
Answer: there is no picture again. just take a good guess
Step-by-step explanation:
at a delicatessen, ham costs $2.49 per pound and swiss cheese costs $3.79 per pound. The customer has $9.50 to spend on 2 pounds of ham and some cheese. how much cheese can she purchase? write an equation and solve it.
The customer can purchase 1.19788 pounds of cheese (approximately 1.2 pounds).
How much cheese can she purchase?We are given with the cost of ham is $2.49 per pound and
Cost of swiss cheese is $3.79 per pound.
So, the cost of 2 pounds of ham will be given as-
= 2× $2.49
= $4.98
Since, the customer has a total of $9.50 to spend on 2 pounds of ham and some cheese,
∴ Let the number of pounds of cheese she can purchase be x.
Then the equation will be this:
2.49*2 + 3.79*x = 9.50
4.98 + 3.79x = 9.50
Subtracting 4.98 from each side we get-
4.98 -4.98 + 3.79x = 9.50-4.98
3.79x = 4.54
x [tex]=\frac{4.54}{3.79}[/tex]
x = 1.19788 pounds of cheese (approximately 1.2 pounds).
Hence, the customer can purchase 1.19788 pounds of cheese (approximately 1.2 pounds).
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