Michele wanted to measure the height of her school’s flagpole. She placed a mirror on the ground 48 feet from the flagpole, then walked backwards until she was able to see the top of the pole in the mirror. Her eyes were 5 feet above the ground and she was 12 feet from the mirror. Using similar triangles, find the height of the flagpole to the nearest tenth of a foot. Find the geometric mean of the pair of numbers. A. 20 ft B. 38.4 ft C. 55 ft D. 25 ft
Ned has scored 84 points in the first 6 games of the basketball season. How many points per game has Ned scored?
Answer:
84/6=14
Step-by-step explanation:
read the answer
Jane is having difficulty deciding whether to put her savings in the Mystic Bank or in the Four Rivers Bank. Mystic offers a 12% rate compounded quarterly, and Four Rivers offers 14% compounded semiannually. Jane has $40,000 to invest and expects to withdraw the money at the end of five years. Using the tables in the Business Math Handbook that accompanies the course textbook, determine which one of the following is the best deal.
A. Four Rivers
B. Mystic
C. Mystic for last two years
D. Four Rivers for first two years
How many liters of a 10% alcohol solution must be mixed with 90 liters of a 60% solution to get a 30% solution?
Find the next three terms in the patter 9, 4, -1, -6, -11....then describe the pattern
The graph of f(x) = log x + 3 is the graph of
g(x) = log x translated 3 units a)up b)down c)left D) right
Answer:
A)up
Step-by-step explanation:
Given : f(x)=log x +3
g(x)= log x
To Find :
The graph of f(x) = log x + 3 is the graph of g(x) = log x translated 3 units
a)up
b)down
c)left
d) right
Solution:
Rule: f(x)→f(x)+b
So, the graph f(x) is translated up by b units
So, on comparing given f(x) with rule , we can say that the graph g(x) is translated up by 3 units
Thus option A is correct.
Hence The graph of f(x) = log x + 3 is the graph of g(x) = log x translated 3 units up
63 POINTS!!!!!
Please help fast 1.4t-0.4(t-3.1)=5.8
t= what
which of the following is a solution set to 4|x+3|
Solve formula please
c=PI*d
divide both sides by PI to get d by itself
d = c/PI
What does information meanins
Identify the expressions and the value that are equivalent to 6 times 5 squared.
The value that is equivalent to 6 times 5 squared is 150.
What is an expression?In mathematics, an expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, division, and exponentiation) that represents a mathematical relationship or a quantity.
Expressions in mathematics can be evaluated or simplified to produce a single value or to represent a more simplified form of the original expression.
6 times 5 squared can be written in a few different ways:
6 x 5²
6 x 25
150
So the expressions that are equivalent to 6 times 5 squared are:
6 x 5²
6 x 25
The value that is equivalent to 6 times 5 squared is 150.
To know more about an expression follow
https://brainly.com/question/1859113
#SPJ2
A salesperson makes a base salary of $2000 a month. Once he reaches $40,000 in total sales, he earns an additional 5% commission on the amount in sales over $40,000. Write a piecewise-defined function to model the salesperson's total monthly salary (in $) as a function
Answer:
The piecewise-defined function to model the salesperson's total monthly salary (in $) is,
[tex]f(x)=\begin{cases}2000 & \text{ if } x\leq 40,000 \\2000+0.05(x-40000) & \text{ if } x>40000\end{cases}[/tex]
Step-by-step explanation:
It is given that the salesperson makes a base salary of $2000 a month. Once he reaches $40,000 in total sales, he earns an additional 5% commission on the amount in sales over $40,000.
Let the x represents the amount of sales and f(x) represents the salary of salesperson.
It means till the sale of $40,000, the salary of the salesperson is constant, i.e., $2000.
[tex]f(x)=2000[/tex] for [tex]x\leq 40,000[/tex]
He will get commision of 5% on the amount in sales over $40,000.
[tex]f(x)=2000+\frac{5}{100}(x-40000)[/tex] for [tex]x>40,000[/tex]
Therefore the piecewise-defined function to model the salesperson's total monthly salary (in $) is,
[tex]f(x)=\begin{cases}2000 & \text{ if } x\leq 40,000 \\2000+0.05(x-40000) & \text{ if } x>40000\end{cases}[/tex]
The piecewise-defined function to model the salesperson's total monthly salary (in $) as a functionis [tex]\boxed{f\left( x \right)=\left\{\begin{gathered}2000{\text{ if }}x \leqslant 40000 \hfill\\2000 + 0.05\left( {x - 40000} \right){\text{ if }}x > 40000 \hfill\\\end{gathered}\right.}[/tex].
Further explanation:
The piecewise defined function is defined as a function that takes different values in different interval. It is defined on the sequence of intervals.
Given:
The base salary is [tex]\$ 2000[/tex].
He will earn [tex]5\%[/tex] additional commission on the amount sales over [tex]\$ 40000[/tex].
Explanation:
The base salary of a salesperson in a month is $2000.
If the salesperson reaches to $40000, he will earns 5% additional commission on the amount sales over [tex]\$ 40000[/tex].
The person get [tex]\$ 2000[/tex] if sale less than [tex]\$ 40000[/tex].
[tex]f\left( x \right) =2000{\text{ for }}x \leqslant 40000[/tex].
The value of the function for less than $40000 is [tex]f\left( x \right)=2000[/tex].
If he sales over 40000 the amount he will get can be expressed as follows,
[tex]f\left( x \right)=2000+\dfrac{5}{{100}}\left( {x - 40000} \right)[/tex] for[tex]x > 40000.[/tex]
The value of the function for greater than 40000 is [tex]f\left( x \right)=2000 + \dfrac{5}{{100}}\left({x - 40000} \right)[/tex].
The piecewise-defined function to model the salesperson's total monthly salary (in $) as a functionis [tex]\boxed{f\left( x \right)=\left\{\begin{gathered}2000{\text{if }}x \leqslant 40000\hfill\\2000 + 0.05\left( {x - 40000}\right){\text{if }}x > 40000 \hfill \\\end{gathered}\right.}[/tex]
Learn more:
1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Linear Equation
Keywords: solving equation, inverse operation, isolate, variable, addition property, good guess, solution, order of operations, reverse order, two solution, linear equation.
The number n(t) of people in a community who are exposed to a particular advertisement is governed by the logistic equation. initially, n(0) = 500, and it is observed that n(1) = 1000. solve for n(t) if it is predicted that the limiting number of people in the community who will see the advertisement is 50,000. (round all coefficients to four decimal places.)
Rounding the coefficients to four decimal places:
[tex]\[ n(t) = 50000 \times \left(1 - e^{-20.2020t + 0.0101}\right) \][/tex]
The logistic equation governing the number of people exposed to the advertisement in the community is given by:
[tex]\[ \frac{{dn}}{{dt}} = kn \left(1 - \frac{n}{M}\right) \][/tex]
Where:
n(t) is the number of people exposed to the advertisement at time t
k is the growth rate constant
M is the limiting number of people who will see the advertisement
Given:
[tex]\( n(0) = 500 \)[/tex]
[tex]\( n(1) = 1000 \)[/tex]
[tex]\( M = 50000 \)[/tex]
We first need to find the growth rate constant \( k \):
[tex]\[ 1000 = 500 \times \left(1 - \frac{500}{50000}\right) \times k \][/tex]
[tex]\[ 1000 = 500 \times \left(1 - \frac{1}{100}\right) \times k \][/tex]
[tex]\[ 1000 = 500 \times \frac{99}{100} \times k \][/tex]
[tex]\[ k = \frac{1000 \times 100}{500 \times 99} \][/tex]
[tex]\[ k = \frac{2000}{99} \][/tex]
Now, we integrate to find [tex]\( n(t) \)[/tex]:
[tex]\[ \int \frac{{dn}}{{n(1 - \frac{n}{50000})}} = \int \frac{{2000}}{{99}} dt \][/tex]
[tex]\[ -\ln|1 - \frac{n}{50000}| = \frac{{2000}}{{99}}t + C \][/tex]
Using the initial condition [tex]\( n(0) = 500 \)[/tex], we find[tex]\( C \)[/tex]:
[tex]\[ -\ln|1 - \frac{500}{50000}| = 0 + C \][/tex]
[tex]\[ -\ln\left(\frac{99}{100}\right) = C \][/tex]
So, the equation becomes:
[tex]\[ -\ln|1 - \frac{n}{50000}| = \frac{{2000}}{{99}}t - \ln\left(\frac{99}{100}\right) \][/tex]
Solving for n(t) :
[tex]\[ |1 - \frac{n}{50000}| = e^{-\frac{{2000}}{{99}}t + \ln\left(\frac{99}{100}\right)} \][/tex]
[tex]\[ 1 - \frac{n}{50000} = e^{-\frac{{2000}}{{99}}t + \ln\left(\frac{99}{100}\right)} \][/tex]
[tex]\[ \frac{n}{50000} = 1 - e^{-\frac{{2000}}{{99}}t + \ln\left(\frac{99}{100}\right)} \][/tex]
[tex]\[ n(t) = 50000 \times \left(1 - e^{-\frac{{2000}}{{99}}t + \ln\left(\frac{99}{100}\right)}\right) \][/tex]
This is the solution for [tex]\( n(t) \)[/tex]. Now, rounding the coefficients to four decimal places:
[tex]\[ n(t) = 50000 \times \left(1 - e^{-20.2020t + 0.0101}\right) \][/tex]
highest common factor of 92 and 42
The Greates Common Factor (GCF) is: 2
You can always share this solution
two different ways to find the value of the expression 5.4 * 1.17 * 100 that do not require you to First multiply 5.4 X 1.17
How do I write 19.4 in expanded form
To write 19.4 in expanded form, you can break down the number into its place values. The digit 1 is in the tens place, the digit 9 is in the ones place, and the digit 4 is in the tenths place. Therefore, 19.4 in expanded form is 10 + 9 + 0.4.
Explanation:To write 19.4 in expanded form, we break down the number into its place values. The digit 1 is in the tens place, the digit 9 is in the ones place, and the digit 4 is in the tenths place. So, we can write 19.4 in expanded form as 10 + 9 + 0.4.
Learn more about Expanded form here:https://brainly.com/question/25632734
#SPJ11
some hot dogs come in packages of 8.Why would a baker of hot dog buns packages 7 hot dog buns to a package
. Which is equivalent to a drink made with 3 ounces of 80-proof vodka?
Find the distance between the points on a number line -7, -54
since they are both negative numbers just subtract 7 from 54
54-7 = 47
If a coin is tossed 4 times, and then a standard six-sided die is rolled 2 times, and finally a group of four cards are drawn from a standard deck of 52 cards without replacement, how many different outcomes are possible?
[tex]\(1138368400\)[/tex] different outcomes possible when considering all the events together.
Coin Toss: Since each toss is independent of the others, the total number of outcomes for 4 tosses is:
[tex]\(2 \times 2 \times 2 \times 2 = 2^4 = 16\)[/tex].
Die Roll: A standard six-sided die has 6 faces, each with a different number from 1 to 6. When the die is rolled once, there are 6 possible outcomes. If the die is rolled 2 times, the number of different outcomes is:
[tex]\(6 \times 6 = 6^2 = 36\)[/tex]
Card Draw: When drawing a card from the deck, there are 52 possible outcomes. If a second card is drawn without replacing the first, there are now 51 possible outcomes for the second card (since one card has already been drawn). Continuing this pattern, for the third card, there are 50 possible outcomes, and for the fourth card, there are 49 possible outcomes.
The number of different outcomes for drawing 4 cards without replacement is: [tex]\(52 \times 51 \times 50 \times 49\)[/tex].
[tex]\[ \text{Total Outcomes} = (\text{Coin Toss Outcomes}) \times (\text{Die Roll Outcomes}) \times (\text{Card Draw Outcomes}) \][/tex]
[tex]\[ \text{Total Outcomes} = 16 \times 36 \times (52 \times 51 \times 50 \times 49) \][/tex]
[tex]\[ \text{Total Outcomes} = 6^2 \times 52 \times 51 \times 50 \times 49 \][/tex]
[tex]\[ \text{Total Outcomes} = 36 \times 52 \times 51 \times 50 \times 49 \][/tex]
[tex]\[ \text{Total Outcomes} = 36 \times 31625400 \][/tex]
[tex]\[ \text{Total Outcomes} = 1138368400 \][/tex]
Suppose there are two full bowls of cookies. bowl #1 has 10 chocolate chip and 30 plain cookies, while bowl #2 has 20 of each. our friend stacy picks a bowl at random, and then picks a cookie at random. we may assume there is no reason to believe stacy treats one bowl differently from another, likewise for the cookies. the cookie turns out to be a plain one. how probable is it that stacy picked it out of bowl #1?
The that stacy picked it out of bowl #1 is 0.6
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
Bowl 1 has 10 chocolate chip and 30 plain cookies, while Bowl #2 has 20 of each.
So, P[tex](H_1|E)[/tex]
= P( E| [tex]H_1[/tex]) P([tex]H_1[/tex]) / [ P( E| [tex]H_2[/tex]) P([tex]H_2[/tex] )+ P( E| [tex]H_1[/tex]) P([tex]H_1[/tex])
= (0.75 x 0.5) / (0.75 x 0.5 + 0.5 x 0.5)
= 0.375 / (0.375 + 0.25)
= 0.6
Hence, the probability is 0.6
Learn more about Probability here:
https://brainly.com/question/30034780
#SPJ5
1. Given a segment with endpoints A and B, what figure can you construct using the steps below?
Step 1: Draw a ray with endpoint C.
Step 2: Open the compass to the length of AB.
Step 3: With the same compass setting, put the compass point on point C. Draw an arc that intersects the ray. Label the point of intersection D.
a. a perpendicular bisector
b. a congruent segment
c. an angle bisector
d. a congruent angle
2. Given a segment with endpoints A and B, what figure can you construct using the steps below?
Step 1: Put the compass point on A and draw a long arc. Be sure the opening is grater than 1/2 AB.
Step 2: With the compass on the same setting, put the compass point on B and draw another long arc. Label the points where the two arcs meet as X and Y.
Step 3: Draw XY. Label the point of intersection of AB and XY as M, the midpoint of AB.
a. a perpendicular bisector
b. a congruent segment
c. an a
1. For that accurate reason, CD and AB will be congruent. the answer here is B) A congruent segment. 2. Option (A) is the right answer. We can construct a perpendicular bisector usind the given steps.
How to find the correct steps?1. Form opening the compass to the length of AB you are setting the radius of the circle the compass could create to the same length of AB then by intersecting with the ray C, we have to copied the length of AB to ray C.
For that accurate reason, CD and AB will be congruent.
Therefore, The answer here is B) A congruent segment.
2. Given a segment with endpoints A and B.
By using the construction step we will draw the following figure that represents a perpendicular bisector XY of line segment AB.
Hence, Option (A) is the right answer. We can construct a perpendicular bisector usind the given steps.
Learn more about this concept here;
https://brainly.com/question/2485485
#SPJ2
Convert 1/3 and 4/5 to a decimal. Are both of them repeating or terminating?
1/3 = 0.33333 ( repeating)
4/5 = 0.8 (terminating)
A number changed to 12.6 after it was rounded to what place was the number rounded what would the answer be
17 - 8.63 find the sum please thank you
How do I solve this equation? I need a refresher on Algebra.
What is the approximate base area of the resulting figure?
Area of a circle: A = πr2
Answer: [tex]78.5\ cm^2[/tex]
Step-by-step explanation:
From the given we can see that there is a rectangle is rotated about a line bisecting its length in segment of 5 cm in each.
Since the base will be a circle, then the area of the base will be :-
[tex]\text{Area of base}=\pi r^2\\\\\\\Rightarrow\text{Area of base}=3.14\times(5)^2\\\\\\\Rightarrow\text{Area of base}=78.5\ cm^2[/tex]
Hence, the base area of the resulting figure = [tex]78.5\ cm^2[/tex]
The approximate base area of the rectangle is rotated about a line bisecting its length in segments of 5 cm in each is 78.5.
From the given, we can see that there is a rectangle is rotated about a line bisecting its length in segments of 5 cm in each.
Since the base will be a circle, then the area of the base will be
What is the area of the base?
A=pir^2
Where r is the radius of the circle.
A=3,14(5)^2
A=78.5.
Therefore, the approximate base area of the resulting figure is 78.5.
To learn more about the area visit:
https://brainly.com/question/25292087#SPJ3
1.5x - 3y = 6 (solve for y)
An equation is formed of two equal expressions. The value of y for the given equation is (1.5x - 6)/3.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
1.5x - 3y = 6
Subtract 1.5x from both the sides of the equation,
1.5x - 3y - 1.5x = 6 - 1.5x
-3y = 6 - 1.5x
Divide both the sides of the equation by -3,
-3y/(-3) = (6 - 1.5x)/(-3)
y = (1.5x - 6)/3
Hence, the value of y for the given equation is (1.5x - 6)/3.
Learn more about Equation here:
https://brainly.com/question/14686792
#SPJ2
how many more kilometers in 4320 than 7200
if f(x)=4-x^2 and g(x)=6x, which expression is equivalent to (g-f)(3)?
To find (g-f)(3), evaluate g(3) and f(3), then subtract f(3) from g(3).
Explanation:To find (g-f)(3), we need to subtract the function f(x) from g(x) and then evaluate the result at x = 3. Let's first simplify the expressions for f(x) and g(x):
f(x) = 4 - x^2
g(x) = 6x
Now substitute these into (g-f)(3) and simplify:
(g-f)(3) = g(3) - f(3)
= 6(3) - (4 - 3^2)
= 18 - (4 - 9)
= 18 - (-5)
= 23
Therefore, (g-f)(3) is equivalent to 23.
Learn more about Evaluating functions here:https://brainly.com/question/12056604
#SPJ2