one cyclist travels faster than the other. Therefore, the rate of the faster cyclist is (distance between towns) / (2 * hours) and the rate of the slower cyclist is also (distance between towns) / (2 * hours).
Let x = the rate of the faster cyclist, and y = the rate of the slower cyclist.
We can set up the equation:
x + y = (distance between towns) / (time they met)
x + y = (distance between towns) / (hours)
We can solve for x and y:
x = (distance between towns) / (2 * hours)
y = (distance between towns) / (2 * hours)
Therefore, the rate of the faster cyclist is (distance between towns) / (2 * hours) and the rate of the slower cyclist is also (distance between towns) / (2 * hours).
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As a social media employee, Darla is paid $150 a week plus $10 for every person that
he gets to subscribe to the website. This week, Darla wants her pay to be more than
$450. Website subscribers is defined by w.
Part A. Given 150 + 10w > 450 solve for the number of subscribers Darla needs to make.
Answer:
30
Step-by-step explanation:
Write the inequality as 150 + 10w > 450.
Then, solve. Draw a line on the inequality symbol, and cross out the 150. Subtract 150 from the other side. Then, divide the 10w by 10, to get w by itself. Since it's inverse operations, divide 450 by 10 as well.
You will get an answer of w > 30.
Thus, Darla needs 30 more subscribers.
Solve the following maximization problem graphically.
The solution to the maximization problem P(x, y) = 7x + 9y - 5 is 33.4
How to determine the solution to the maximization problem?From the question, we have the following parameters that can be used in our computation:
Objective function: P(x, y) = 7x + 9y - 5
Subject to: x ≥ 0
y ≥ 0
2x + 3y ≤ 12
3x + 2y ≤ 12
x + y ≥ 2
Next, we plot the graph of the constraints
The vertices of the feasible region are
(0, 2), (2, 0) and (2.4, 2.4)
Substitute (0, 2), (2, 0) and (2.4, 2.4) in P(x, y) = 7x + 9y - 5
So, we have
P(0, 2) = 7(0) + 9(2) - 5 = 13
P(2, 0) = 7(2) + 9(0) - 5 = 9
P(2.4, 2.4) = 7(2.4) + 9(2.4) - 5 = 33.4
Hence, the maximum value is 33.4
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from a square cadrboard sheet, a 5cm wide strip was cut away. the area of the remaining rectangle is 266 cm. find the original dimensions of the square cardboard sheet.
Answer: S=19cm
Step-by-step explanation:
area = s^2
s(s-5)=266
s^2-5s=266
s^2-5s-266=0
(s-19)(s+14)=0
s=19cm
19 x 19 = 266
The original dimensions of the square cardboard sheet is 19 x 19.
What is Quadratic Equation?ax² + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable, a≠0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
Given:
Let the length of each side of the original square cardboard be x cm.
After cutting off a strip of 3cm wide its dimension becomes
length = x cm and breadth= (x−5) cm
So, Area = x² - 5x
266 = x² - 5x
x² - 5x - 266= 0
x² - 19x + 14x - 266= 0
x(x - 19) + 14 (x - 19)= 0
(x- 19)( x + 14) = 0
x= 19, -14.
Hence, the original dimensions of the square cardboard sheet is 19 x 19.
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A triangle has sides with lengths of 15 kilometers, 17 kilometers, and 20 kilometers. Is it a right triangle?
Answer: no
Step-by-step explanation:
use pythagorean theorem.
you can use a^2+b^2=c^2
the biggest value is always c(the hypotenuse) -> c=20
a and b would be 15 and 17(doesn't matter which is which)
plug it into the equation -> 15^2+17^2=20^2
225+289=400
514≠400
so no, it's not a right triangle
What is in exponential form?
Answer:
We all must have heard the word “exponential” before. What does this word mean? Exponential means to become more and more rapid in growth. However, in mathematics, it represents a mathematical expression that has one or more exponents. Hence, we know it as an exponential form.
We can say that a thing may increase with an exponential rate when the increase becomes quicker and quicker as the thing which is talked about becomes larger.
Now let us learn more about the exponential form of numbers which is greatly used and applied in mathematics.
please help can’t figure out
Answer:
a=82°
b=32°
Step-by-step explanation:
x is the reflection of b
y is the reflection of a
The graph shows a function of the form f(x) = ax + b. Use the drop-down menus to complete the statements about the function, and then write an equation that represents this function. URGENT SOS
Answer:
- When x = 0, f(x) = -5
- Each time x increases by 1, f(x) increase by 3
- f(x) = 3x - 5
Step-by-step explanation:
m = slope of the graph
m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x{1}}[/tex]
m = [tex]\frac{4- (-5)}{3-0}[/tex]
m = [tex]\frac{9}{3}[/tex]
m = 3
[tex]y - y_{1} = m ( x - x_{1})[/tex]
[tex]y - (-5) = 3 ( x - 0 )[/tex]
[tex]y = 3x - 5[/tex]
The table shows the height of players in a basketball team
calculate the perimeter of the irregular shape 4cm 3cm 2cm 3cm 5cm 6cm 9cm
Answer:8 cm 6 cm 8 cm 6 cm The perimeter of the shape is 8 + 6 + 8 + 6 = 28cm.
Step-by-step explanation:
what would the slope of a line parrallel to 2x-y=-1 be?
Answer:
2
Step-by-step explanation:
2x - y = -1
-y = -2x - 1
y = 2x + 1
parallel line = same slope
A jazz band wants to sell $2,800 worth of tickets. If each ticket costs $70, how many tickets will the band have to sell to meet its goal?
Answer: 40 tickets
Step-by-step explanation:
Divide 2,800 by 7
40
7| 2800|
28
0
You get 40. The jazz band would need to sell 40 tickets to meet its goal.
Hope This Helps!:)write the expression using exponents. a⋅a⋅c⋅c =
The expression when expressed in its exponent is a²+c²
how to express a number in exponent form?In mathematics, we should understand that exponent tell the power to which a number is raise.
It shows the number of times a number multiplies itself to get the certain member.
The given expression is a*a*c*.
Using the law of multiplication that says when two or more numbers in the same base are multiplied, we add their powers.
Here a appeared twice a*a=a²
And c appeared twice that is c*c=c²
Combining the two exponents together we have that
a²+c²
In conclusion, the exponent of a*a*a*a is a²+c²
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12. A job pays $25.00 per day plus $5.00 for each additional hour worked. Let x represent the number of hours
worked and y represent the total amount paid.
a. Write an equation in slope-intercept form to represent the amount paid for one day. (3 points)
b. What is the amount paid for one day if you work an 8 hour shift? (2 points)
c. How many hours do you need to work to make $100 in a day? (2 points)
Answer:
Step-by-step explanation:
Calculating Average Weekly Pay for Uneven Work Hours Some professions like nurses & doctors in the healthcare industry might work longer shifts where they are on for 12 hours
which of the following is false? 0 / 1 point standard error measures the variability in means of samples of the same size taken from different populations. in order to reduce the standard error by half, sample size should be increased by a factor of 4. as the sample size increases, the variability of the sampling distribution decreases. standard error computed based on a sample standard deviation will always be lower than the standard deviation of that sample.
The correct option is: As the sample size increases, the variability of the sampling distribution decreases. is the FALSE statement.
Explain the term sampling distribution?The probability distribution of the a statistic that is acquired by repeated sampling of a particular population is called the sampling distribution.
It outlines a variety of potential possibilities for a statistic, including the mean or mode of a population's mean or mode of certain variable.How far distant the means of each sample set are from population mean and from each other will indicate how closely the sample mean resembles the population mean. As the sample size is increased, the sampling distribution's standard error is reduced.Thus, it is incorrect to say that as the sample size increases, the variability of the sampling distribution decreases.
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Esteban purchased an iphone 13 which are projected to decrease in value 20% each year. If Esteban purchased the iphone at $1000, which equation represents the value, V, over the course of years, t?
The equation with value V indicating the decrease in value of iPhone 13 with years t is V = [tex] {1000 (1 - 0.02)}^{t} [/tex].
The equation to be used for the calculation of decreased value is -
A = [tex] {P (1 - r)}^{t} [/tex]. In this formula, A is amount, P is principal, r is rate and t represents time. Based on the information in question, A will be replaced with V. So, the required formula will be -
V = [tex] {P (1 - r)}^{t} [/tex]
Now keeping the values in formula for numerical equation -
V = [tex] {1000 (1 - 0.02)}^{t} [/tex]
Since two values are unknown here, the equation can not be solved further.
Therefore, the required equation is V = [tex] {1000 (1 - 0.02)}^{t} [/tex].
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evaluate the iterated integral by converting to polar coordinates. a 0 0 6x2y dx dy − a2 − y2
The iterated integral by converting to polar coordinates [tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] is 7a^4/12.
In the given question, we have to evaluate the iterated integral by converting to polar coordinates.
The given integral is
[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex]
Let polar coordinate.
x = rcosθ, y = rsinθ, x^2 + y^2 = r^2
So dxdy = rdrdθ
r from 0 to a and θ from π/2 to π
Now the integral is
[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]\int_{\pi/2}^{\pi}\int_{0}^{a}7(r\cos\theta)^2(r\sin\theta)drd\theta[/tex]
[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]\int_{\pi/2}^{\pi}\int_{0}^{a}7(r^2\cos^2\theta)(r\sin\theta)drd\theta[/tex]
[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]7\int_{\pi/2}^{\pi}\int_{0}^{a}r^3\cos^2\theta\sin\theta drd\theta[/tex]
Now integrating the first integral
[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]7\int_{\pi/2}^{\pi}\left[\frac{r^4}{4}\right]_{0}^{a}\cos^2\theta\sin\theta d\theta[/tex]
[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]7\int_{\pi/2}^{\pi}\left[\frac{a^4}{4}-\frac{0^4}{4}\right]\cos^2\theta\sin\theta d\theta[/tex]
[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]\frac{7a^4}{4}\int_{\pi/2}^{\pi}\cos^2\theta\sin\theta d\theta[/tex]
Let cosθ = t
So -sinθ = dt/dθ
So sinθdθ = -dt
[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]-\frac{7a^4}{4}\int_{\pi/2}^{\pi}t^2dt[/tex]
[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]-\frac{7a^4}{4}\left[\frac{t^3}{3}\right]_{\pi/2}^{\pi}[/tex]
[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]-\frac{7a^4}{4}\left[\frac{\cos^3\theta}{3}\right]_{\pi/2}^{\pi}[/tex]
[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]-\frac{7a^4}{12}\left[\cos^3\pi-\cos^3(\pi/2)\right][/tex]
[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = -7a^4/12[(-1)^3 - 0]
[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = 7a^4/12
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The complete question is:
Evaluate the iterated integral by converting to polar coordinates.
[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex]
Based on the graph below, what are the new dilation vertices of triangle JKLM with vertices J(-6,2), K(-4,4), L(0,0) M(-2,-2): K= 5/2
The new dilation vertices of the rectangle are J'(-15, 5), K'(-10, 10) L'(0, 0) and M'(-5, -5).
What is the Dilation of the rectangle?
Dilation occurs when a polygon grows or shrinks while maintaining its overall shape. It's similar to zooming in or out on a camera. The polygon in the figure above is a rectangle JKLM. As you move the slider on the right, the transformed rectangle J'K'L'M' grows and shrinks but retains its shape.
We have,
Rectangle JKLM with vertices:
J(-6,2), K(-4,4), L(0,0) M(-2,-2): K= 5/2
New dilation vertices of the rectangle are:
J'(-15, 5), K'(-10, 10) L'(0, 0) and M'(-5, -5)
Hence, the new dilation vertices of the rectangle are J'(-15, 5), K'(-10, 10) L'(0, 0), and M'(-5, -5).
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E is the midpoint of DF¯¯¯¯¯¯¯¯. What are the coordinates of F?
Segment DF with midpoint E. The coordinates of point E are 1, negative 1. The coordinates of point D are 10, 7.
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ D(\stackrel{x_1}{10}~,~\stackrel{y_1}{7})\qquad F(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +10}{2}~~~ ,~~~ \cfrac{ y +7}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE E}}{(1~~,~~-1)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +10}{2}=1\implies x+10=2\implies \boxed{x=-8} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +7}{2}=-1\implies y+7=-2\implies \boxed{y=-9}[/tex]
Write a function in any form that would match the graph shown below.
The function that matches the graph is f(x) = (17/24)(x + 2)²(x + 6).
What is a graph?A graph is a diametrical representation of any function between the dependent and independent variables.
The graph is easy to understand the behavior of the graph.
As per the given graph,
The function is symmetric at x = -2 so it will be an even degree function as (x + 2)².
The function is not symmetric about x = -6 so it will have an odd degree as (x + 6)¹.
The function will be f(x) = C(x + 2)²(x + 6).
The constant will be C = 17/(2² × 6) = 17/24
Hence "The function that matches is f(x) = (17/24)(x + 2)²(x + 6)".
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A city has a 5% sales tax. A book costs $32.55 after tax. How much did it cost before tax?
Answer:
$31
Step-by-step explanation:
x=cost before tax
$32.55 = x + x * 5% ==> solve for x
$32.55 = x + x * 5/100
$32.55 = x + 5x/100
$32.55 = 100x/100 + 5x/100 ==> make common denominators
$32.55 = (100x+5x)/100
$32.55 = 105x/100 ==> simplify
100 * $32.55 = 100 * 105x/100 ==> multiply by 100 on both sides to remove
fractions
$3255 = 105x
x = $3255/105
x = $31
How tall is the table?
1- D
120 cm
90 cm
Answer:
Step-by-step explanation:
105 cm
the following set of ordered pairs defines a function. complete the following {(-26,10), (-30,10),(15,10),(10,10),(-9,10)} add one additional ordered pair to this set such that the set of the ordered pairs still define a function
Answer:
(0,10)
Step-by-step explanation:
You could put any ordered pair, as long as the y value is 10.
The equation of this function is
y = 10 It is a horizontal line going through. The y intercept is (0,10)
Given the function f(k)= 6k4 + 2k³ - 6, find the value of f(-4)
Answer: 1402
Step-by-step explanation:
Im assuming u mean [tex]6k^{4} +2k^{3} -6[/tex]
sub in the k value when k = -4
[tex]6(-4)^{4} +2(-4)^{3} -6[/tex]
1536−128−6=1402
According to the IRS, taxpayers calling the IRS in 2017 waited 13 minutes on average for an IRS telephone assister to answer. Do callers who use the IRS help line early in the day have a shorter wait? Suppose a sample of 50 callers who placed their calls to the IRS in the first 30 minutes that the line is open during the day have a mean waiting time of 11 minutes before an IRS telephone assister answers. Based on data from past years, you can assume that the standard deviation of waiting times is 8 minutes. Using these sample results, can you conclude that the waiting time for calls placed during the first 30 minutes the IRS help line is open each day is significantly less that the overall mean waiting time of 13 minutes? Use alpha=0.05
Establish the two hypotheses
Calculate the test statistic
Make a decision using the critical value approach
Make a decision using the p-value approach
P-value = 0.0384
As P-value < 0.05, reject the null hypothesis.
What is test statistic?
A statistic (a number obtained from the sample) used in statistical hypothesis testing is known as a test statistic. Usually, a hypothesis test is described in words.
A test statistic is a figure obtained from a statistical analysis. It explains how distant your observed data is from the null hypothesis, which states that there is no correlation between the variables or distinction between the sample groups.
The alternative and null hypotheses are listed below.
Lack of hypothesis H0: μ = 13
Ha: 13 Alternative Hypothesis
Statistical test, z = (xbar - mu)/(sigma/sqrt(n))
z = (11 - 13)/(8/sqrt(50))
z = -1.77
Region of Rejection
For α= 0.05, this is a left-tailed test.
Z has a critical value of -1.645.
Therefore, if z -1.645, reject H0 and accept the null hypothesis.
P-value Approach
P-value = 0.0384
As P-value < 0.05, reject the null hypothesis
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assume you wanted to save$2000 to buy a used car 18 months from now.How much money do you need to save every week to accomplish your goal
Answer: $28 per week
Step-by-step explanation:
1 month = 4 weeks
18 times 4 = 72 weeks
So you know you want to save 2000 to buy a car 72 weeks from now.
So take 2000 divided by 72 = $27.77 per week
So you need to save about $28 per week.
a small town has 3000 inhabitants. at 8 am, 240 people have heard a rumor. by noon half the town has heard it. at what time will 90% of the population have heard the rumor? (do not round k in your calculation. round your final answer to one decimal place.)
The time will 90% of the population have heard the rumor are by the time of 3:48 PM.
There are commonly 3 forms of populace pyramids made out of age-intercourse distributions-- expansive, constrictive and stationary.Population is described as all nationals gift in, or briefly absent from a country, and extraterrestrial beings completely settled in a country.
This indicator indicates the variety of humans that typically stay in an area. Growth prices are the yearly adjustments in populace as a result of births, deaths and internet migration at some stage in the year.3000–240=1260
1260 folks heard in four hours=315 folks consistent with hour
90% of populace= 3000 x 0.9= 2700 folks
2700–1500=1200 folks
1200/315=3.eight hours past midday or 3.forty eight pm.
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the distribution of salaries of teachers is approximately normal. which measure of central tendency would be the best measure to determine the location of the center of the distribution?
The best measure of central tendency to determine the center of the distribution of teacher salaries is the mean.
The mean is the average of all values in a set and is calculated by adding up all the values and dividing them by the number of values. This measure is particularly useful for data that follows a normal distribution, as teacher salaries are likely to do.
The mean is the most commonly used measure of central tendency and is a good indicator of the center of the data set. It is also relatively easy to calculate. So mean will be the measure of the central tendency to determine the center of the distribution of teacher salaries.
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A rubber ball is dropped from an initial height of 40 feet. The ball consistently rebounds to 80% of its previous height
Answer:
The ball travels (exactly) 75 feet.
Step-by-step explanation:
Assuming the balls comes to rest:
S = a1 / (1 - r)
Now a1 is the first bounce, 20 ft (10 feet up, 10 feet down.
r is 2/3
S = 20 (1 / (1 - 2/3)
S = 20 / (1/3)
S = 60
Yet that is only the bounce. The drop of 15 feet must be added.
What values x and y prove that triangles ABC ~= BAD?
By using congruency, it can be calculated that
x = 6, y = 5
What are congruent triangles?
Two triangles are said to be congruent if their corrosponding sides and corrosponding angles are same. There are different axioms of congruency. They are-
AAS axiom, SAS axiom, ASA axiom, SSS axiom, RHS axiom
It is given that [tex]\Delta[/tex] ABC [tex]\cong[/tex] [tex]\Delta[/tex] BAD
So [tex]\angle[/tex]CAB = [tex]\angle[/tex]ABD [Corrosponding parts of congruent triangles are congruent]
4y = 20
y = [tex]\frac{20}{4}\\[/tex]
y = 5
Also,
AC = BD [Corrosponding parts of congruent triangles are congruent]
5x - 3 = 3x + 9
5x - 3x = 9 + 3
2x = 12
x = [tex]\frac{12}{2}[/tex]
x = 6
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The 4th term of an AP i 6 if the um of the 8th and 9th term i -72, the common difference i
The 4th term of an AP is 6 if the um of the 8th and 9th term is -72, The 4th term of an AP is -18.
The sum of 8th and 9th term of an AP is given as -72.
We can use the formula for the sum of any n terms of an AP,
Sn = n/2[2a + (n-1)d]
Where,
a = first term
d = common difference
n = number of terms
Therefore,
-72 = 8/2[2a + (8-1)d]
-72 = 4[2a + 7d]
-18 = 2a + 7d
Subtracting 7d from both the sides,
-18 - 7d = 2a
Dividing both the sides by 2,
(-18 - 7d)/2 = a
a = -18/2 - (7d)/2
a = -9 - (7d)/2
For the 4th term of an AP,
a4 = a + (4-1)d
=-9 - (7d)/2 + 3d
=-9 + 6d
=-9
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