To represent the situation, the function can be written as f(t) = 35000 × (1 + 0.04)^t, where t represents the number of years into the future.
Explanation:To write a function in terms of t that represents the situation, we can start with the initial salary of $35,000 and then calculate the annual increase using the 4% growth rate.
We need to multiply the current salary by (1 + 0.04) to get the new salary for each year. The function can be written as:
f(t) = 35000 × (1 + 0.04)^t
Here, t represents the number of years into the future from the initial starting point.
For example, if you want to find the salary after 3 years, you can plug in t = 3 into the function.
A function that represents your annual salary starting at $35,000 and increasing by 4% each year,
[tex]S(t) = 35000 * (1 + 0.04)^t[/tex], where t is the number of years.
To create a function that represents your annual salary starting at $35,000 and increasing by 4% each year,
we use the formula for exponential growth,
[tex]final amount = initial amount * (1 + growth rate)^t^i^m^e.[/tex]
Given that your initial salary is $35,000 and the growth rate is 4% (or 0.04),
let's define the function S(t) where S represents your salary and t represents the number of years:
[tex]S(t) = 35000 * (1 + 0.04)^t[/tex]
the initial salary=$35,000.
Convert the percentage increase to a decimal,
4% becomes 0.04.
Set up the function using the formula for exponential growth,
which is initial amount multiplied by [tex](1 + growth rate) ^t[/tex]
Thus, for any year t, the function [tex]S(t) = 35000 * (1 + 0.04)^t[/tex] calculates your annual salary.
The graph shows a system consisting of a linear equation and a quadratic equation. What is the solution(s) to the system?
A (4,5) only
B (1,8) only
C (1,8) and (4,5)
D this system has no solution
Answer:
Option (C) is correct.
The solutions of the graph showing a system consisting of a linear equation and a quadratic equation are (1,8) and (4,5).
Step-by-step explanation:
Given : The graph showing a system consisting of a linear equation and a quadratic equation.
We have to find the solution(s) to the system.
Since , the solution(s) to the system are the points where the both linear equation and a quadratic equation intersect each other.
So from the graph given the linear equation intersect the quadratic equation at two points namely (1,8) and (4,5).
Thus, the solutions of the graph showing a system consisting of a linear equation and a quadratic equation are (1,8) and (4,5).
in a circle with a radius of 6 m, an arc is intercepted by a central angle of 7π4 radians. What is the arc length? Use 3.14 for π . Enter your answer as a decimal in the box. m
Answer:
The correct answer is 32.97 m.
Step-by-step explanation:
Verified by correct test results.
Janine wishes to conduct a poll to predict how many dance club members will vote for her for club president.
Which polling methods are likely to be biased?
Select each correct answer.
Janine chooses 5 members that plan on voting for her and asks each to select another 5 members. These 25 members are asked for whom they intend to vote.
Every 10th club member from a list of all members is selected and asked for whom the member intends to vote.
From a list of all club members, 25 members are selected at random and asked for whom they intend to vote.
Five of Janine's friends are selected and asked for whom they intend to vote.
The polling methods likely to be biased are when Option d. Five of Janine's friends are selected and asked for whom they intend to vote.
When conducting a poll, it is important to ensure the sampling method is random and representative. Here are the methods and their potential biases:
Janine chooses 5 members that plan on voting for her and asks each to select another 5 members. These 25 members are asked for whom they intend to vote. — This method is likely to be biased because it relies on the initial selection of supporters, which creates a non-random and unrepresentative sample.Every 10th club member from a list of all members is selected and asked for whom the member intends to vote. — This method is less likely to be biased as it uses systematic sampling, which is more representative of the entire population.From a list of all club members, 25 members are selected at random and asked for whom they intend to vote. — This method is unlikely to be biased because it employs a simple random sample, ensuring each member has an equal chance of being selected.Five of Janine's friends are selected and asked for whom they intend to vote. — This method is likely to be biased due to the convenience sampling of her friends, which is not representative of the entire club.Hence option D is likely to be biased.
Complete question:
Janine wishes to conduct a poll to predict how many dance club members will vote for her for club president.
Which polling methods are likely to be biased?
Select each correct answer.
a. Janine chooses 5 members that plan on voting for her and asks each to select another 5 members. These 25 members are asked for whom they intend to vote.
b. Every 10th club member from a list of all members is selected and asked for whom the member intends to vote.
c. From a list of all club members, 25 members are selected at random and asked for whom they intend to vote.
d. Five of Janine's friends are selected and asked for whom they intend to vote.
can someone please help me i don’t know this and i’m really stuck so please
BRAINLIEST!!!
Given the two functions,
What is the rate of change of each function? (the graph & the equation)
g(x) = 4x - 2
Which of these geometric figures can intersect to form a cross section? Check all that apply. 1.a line and a prism 2.a line and a rectangle 3.a point and a prism 4.a prism and a horizontal plane 5.a vertical plane and a pyramid Check all that apply
The geometric figures that intersect to form a cross-section are:
4. a prism and a horizontal plane 5. a vertical plane and a pyramidFor a cross-section to be formed, then the intersected figures must be a plane and a three-dimensional object.
From the list of given options, option (1) through (3) cannot be true;
This is so because: lines and points are not three-dimensional or planes
However, in options (4) and (5);
Vertical planes, horizontal planes and prism are planes or three-dimensional object.
Hence, the true options are (4) and (5)
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Shayla has 5 pets which is 3 more than half the number of pets Judy has. how many pets does Judy have
If 5a=-4b+5 and 3a=-2b+3, what is 6b?
PLZ HELP!!!!!! (WILL GIVE BRAINLIEST!!!!)
how many pairs of parallel sides does the quadrilateral appear to have
22. If triangle DEC equals about triangle BEC, which is true by CPCTC?
A. Angle EBC equals about angle EDC
B. Line AE equals about line EC
**C. Angle A equals about angle C
D. Line AE equals about line ED
I choose C but I’m Lost
Answer with explanation:
→Triangle DEC equals about Triangle B EC.
⇒The meaning of equal here,is that both the triangles that is, ΔDEC ≅ ΔB EC.
≡When Triangles are congruent,their corresponding sides and angles are equal .
Corresponding Sides which are equal by C P C TC:
1. BE = DE
2.BC =CD
3.EC, is Common.
Corresponding angles which are equal by C P C TC are:
1. ∠B EC=∠DEC
2. ∠ D CE=∠B CE
3.∠ E B C= ∠ E D C
Option A: ⇒Angle E BC equals about angle E DC
Sandy's orchard has only apple trees and pear trees and she is wanting to add some avocado trees. Currently, there are 4 apple trees for every 3 pear trees. She is wanting to plant enough avocado trees so that she has 2 avocado trees for every 5 pear trees in the orchard.
Sandy is planting 18 avocado trees, making the ratio of avocado trees to apple trees be to .
Answer:
3 to 10 OR 3:10
Step-by-step explanation:
The length of the minute hand is 200% of the length of the hour hand.
In 1 hour, how much farther does the tip of the minute hand move than the tip of the hour hand? Round your answer to the nearest hundredth.
A 4-inch minute hand would traverse 3.14 x 8 inches (25.12 in) on a clock, which is double the distance.
What is a circle?It is the centre of an equidistant point drawn from the centre. The radius of a circle is the distance between the centre and the circumference.
The length of the minute hand is 200% of the length of the hour hand.
In 1 hour, the tip of the minute hand move then the tip of the hour hand will be
You may put this to the test with numbers. If you have a clock with a 2-inch hour hand, it will travel 3.14 x 4 inches (12.56 in).
A 4-inch minute hand would traverse 3.14 x 8 inches (25.12 in) on a clock, which is double the distance.
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Alexander reads 1/8 of a book each night. how long will it take him to read 3/4 of the book?
Hansel makes the following statement: "I have an 80% chance of being selected as the captain of the baseball team and a 10% chance of being elected student body president." What is the probability that Hansel will be selected as the captain of the baseball team and will be elected student body president?
4%
8%
70%
90%
Answer:
Its 8%
Step-by-step explanation:
turn the percentages into decimals and multiply them its will give you 8%.
Answer:
8%
Step-by-step explanation:
all i did was devide 80 by 10, im not sure its correct but it got the right answer apparantly :)
If k1/2 = integer and k1/4 = integer, which is a possible value for k?
Answer:
D: 81
Step-by-step explanation:
Did the usa test prep
How do you find area like in this question I know already it’s d though I just need help figuring this out?
There are three questions. I'll give brainliest if you show your work for all three of them. Plz help and answer quickly!
What square root best approximates the point on the graph?
A square root of 5
A square root of 15
A square root of 28
A square root of 53
Hassan used the iterative process to locate the square root of 15 on the number line.
Which best describes Hassan’s estimation?
Hassan is correct because the square root of 15 is about 0.4
Hassan is correct because the point is on the middle of the number line.
Hassan is incorrect because the square root of 15 is less than 0.4
Hassan is incorrect because the point should be located between 0.1 and 0.2.
The point plotted on the number line is the square root of x.
What is the approximate value of x?
4
9
17
20
The square root which is best approximated by the point on the graph is given by: Option C: A square root of 28. Also, the square root of 15 lies between 3 and 4.
How to find the closest integer less than and greater than the square root of a number?The function [tex]y = \sqrt{x}[/tex] is strictly increasing function for x ≥ 0.
Assuming that all the values of x are ≥ 1, whenever there is increment in the value of 'x', the value of y increases too.
That means, we've got:
[tex]x_1 < x_2 < x_3 \implies \sqrt{x_1} < \sqrt{x_2} < \sqrt{x_3} \: \text{(such that } x_1 \leq 1)[/tex]
Perfect square are those integers whose square root is an integer.
Let x-a be the closest perfect square less than x,
and let x+b be the closest perfect square more than x, then we get:
x-a < x < x+b (no perfect square in between x-a and x+b, except possibly x itself).
Then, we get:
[tex]\sqrt{x-a} < \sqrt{x} < \sqrt{x+b}[/tex]
Thus, [tex]\sqrt{x-a}[/tex] and [tex]\sqrt{x+b}[/tex] are the closest integers, less than and more than the value of [tex]\sqrt{x}[/tex]. (assuming x is non-negative value).
Now, from the first graph, we see that the value of the square root is between 5 and 6, therefore, we have:
[tex]5 < \sqrt{x} < 6[/tex]
Now, squaring all the sides, we get:
[tex]25 < x < 36[/tex]
Thus, the number out of the given options, whose square root lies between 5 and 6 is given by: Option C: A square root of 28
It is because 25 < 28 < 36, and no other option satisfies this,
For square root of 15, the perfect squares closest to 15 are 9 and 16, therefore, we get:
[tex]\sqrt{9} < \sqrt{15} < \sqrt{16}\\\\3 < \sqrt{15} < 4[/tex]
Thus, the square root which is best approximated by the point on the graph is given by: Option C: A square root of 28. Also, the square root of 15 lies between 3 and 4.
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The function f(x) is graphed below.
Use the graph of the function to find, f(1).
A function assigns the value of each element of one set to the other specific element of another set. The value of f(1) is equal to 2.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
As the graph of a function is given. The value of the function when the value of x, which is the independent variable in the function is equal to 1 can be found by referring to the graph.
To know the value, check the value of the function when the value of x is 1. Therefore, when the value on the horizontal line is equal to 1.
Since the value of the function is equal to 2 for the instance when the value of x is 1.
Hence, the value of f(1) is equal to 2.
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Which module is not a function?
a large aquarium 18 inches deep holds 30 gallons of water. a small aquarium with the same shape holds 20 gallons of water. how deep is the small aquarium to the nearest inch?
What is a decimal in tenths that is less than 2.42 but greater than2.0
Which equation gives this number of 1/3 inches that are in 5/6 inch
The correct answer is [tex]\frac{5}{6}[/tex] inch.
To find the number of 1/3 inches that are in 5/6 inch, we need to convert both fractions to have a common denominator and then divide the numerators.
[tex]\text{Step 1: Find the LCM of 3 and 6}[/tex]
[tex]\text{LCM}(3, 6) = 6[/tex]
[tex]\text{Step 2: Convert the fractions to equivalent fractions with the denominator of 6}[/tex]
[tex]\frac{1}{3} = \frac{2}{6}[/tex]
[tex]\frac{5}{6} = \frac{5}{6}[/tex]
[tex]\text{Step 3: Divide the numerators of the equivalent fractions}[/tex]
[tex]\frac{5}{6} \div \frac{2}{6} = \frac{5}{2} = 2.5[/tex]
Therefore, there are [tex]2.5[/tex] one-third inches in [tex]\frac{5}{6}[/tex] inch.
stacy has hired tom to build her a doll house. The doll house will be a scale model of her home, and the scale will be 2 inches:3ft. The living room in stacy's house is 18 feet by 12 feet and has wall-to-wall carpeting. Hiw many square inches of carpeting will Tom need for thevliving room in Stacy's doll house?
To find the area of the living room in Stacy's doll house, we need to use the given scale of 2 inches:3ft.
Explanation:To find the area of the living room in Stacy's doll house, we need to use the given scale of 2 inches:3ft. First, we convert the dimensions of the living room from feet to inches. The dimensions of the living room in inches will be 18 feet * 12 inches/foot = 216 inches by 12 feet * 12 inches/foot = 144 inches.
Next, we multiply the dimensions by the scale factor of 2 inches:3ft. The dimensions of the living room in the doll house will be 216 inches * (2 inches/3ft) = 144 inches and 144 inches * (2 inches/3ft) = 96 inches.
Finally, we multiply the dimensions together to find the area: 144 inches * 96 inches = 13,824 square inches.
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Which graph represents the system of equations?
y=2x+1y=2x2+1
Graphing the system involves plotting points for both equations and identifying their intersections. The graph visually illustrates the simultaneous solutions to "y = 2x + 1" and "y = 2x^2 + 1.
Graphing the system of equations "y = 2x + 1" and "y = 2x^2 + 1" involves plotting points that satisfy both equations to identify their intersection. The first equation, "y = 2x + 1," represents a straight line with a slope of 2 and a y-intercept of 1. The second equation, "y = 2x^2 + 1," is a quadratic function, creating a parabolic curve.
To visualize their intersection, plot several points for each equation and observe where they coincide on the graph. For the linear equation, select x-values, calculate the corresponding y-values using the equation, and plot the points. For the quadratic equation, choose various x-values, calculate the corresponding y-values, and plot these points.
The intersection points on the graph represent solutions to both equations. Depending on the specific values chosen, the intersection may occur at one or more points.
The question probable may be:
Graph the following system of equations.
y=2x+1 y=2x^2+1
The two equations intersect at points (0, 1) and (1, 3).
Analyzing the Equations:
Equation 1: y = 2x + 1 represents a linear equation. This means the graph will be a straight line. The slope of the line is 2, and the y-intercept is 1.
Equation 2: y = 2x² + 1 represents a parabolic equation. This means the graph will be a U-shaped curve. Since the coefficient of the x² term (2) is positive, the parabola will open upwards. The y-intercept is also 1.
Identifying the Intersections:
To find the points of intersection, we can set the two equations equal to each other and solve for x:
2x + 1 = 2x² + 1
0 = 2x² - 2x
0 = 2x(x - 1)
The solutions are x = 0 and x = 1. We can then plug these x-values back into either equation to find the corresponding y-values:
y = 2(0) + 1 = 1 (for x = 0)
y = 2(1)² + 1 = 3 (for x = 1)
Therefore, the two equations intersect at points (0, 1) and (1, 3).
Complete and correct question:
Which graph represents the system of equations?
y=2x+1
y=2x²+1
The graph is attached below:
Which values in this data set are outliers?
61,53,21,48,78,84,56,52,58,62,63
Answer:
21, 84
Step-by-step explanation:
The sides of a triangle are 7, 4, n. If n is an integer, state the largest and smallest possible values of n.
smallest value-
largest value-
plz help
Smallest value and largest value of n is [tex]11 , 3[/tex].
The third side of a triangle has a range,
[tex]Sum\; of \;two\; other\; sides\geq n\geq Difference\; of\; the\; sides[/tex]
[tex]7+4\geq n \geq7-4[/tex]
[tex]11\geq n \geq 3[/tex]
Therefore
Largest[tex]=11[/tex]
Smallest[tex]=3[/tex]
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What series of transformations to quadrilateral ABCD map the quadrilateral onto quadrilateral EFGH to prove that ABCD≅EFGH ?
a reflection across x-axis, and then a translation 4 units left
a reflection across x-axis, and then a translation 4 units right
a reflection across y-axis, and then a translation 4 units right
a reflection across y-axis, and then a translation 4 units left
The correct series of transformations is a reflection across the x-axis, and then a translation 4 units left.
Let's start by labeling the vertices of quadrilateral ABCD as follows:
A(2, 4)
B(4, 5)
C(5, 4)
D(4, 1)
If we reflect quadrilateral ABCD across the x-axis, the new coordinates of the vertices will be:
A'(2, -4)
B'(4, -5)
C'(5, -4)
D'(4, -1)
Now, if we translate quadrilateral A'B'C'D' 4 units left, the new coordinates of the vertices will be:
E(-2, -4)
F(0, -5)
G(1, -4)
H(0, -1)
These are the coordinates of the vertices of quadrilateral EFGH.
Therefore, it can prove that for the transformation to quadrilaterals ABCD≅EFGH by reflecting quadrilateral ABCD across the x-axis and then translating it 4 units left.
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a train traveled 1/5 of the distance between two cities in 3/4 hour. at this rate, how many hours will it take the train to travel the entire distance between these two cities
Jimmy and his family are on their way to visit some family friends who live
780 miles away from them. Based on the route they chose, they expect to
complete their trip in three days. The distances and average speeds for the
first two days driven are shown below.
• First day: 4 hours at an average speed of 60 miles per hour
• Second day: 6 hours at an average speed of 65 miles per hour
If the average speed on the third day is 60 miles per hour, how many more
hours will it take for them to reach their family friends’ home?