Out of 58 cities, 26 have either a lake or a river, which simplifies to a fraction of 13/29 of the cities having one of these features.
Explanation:To find the fraction of 58 cities that have either a lake or a river running through them, we need to determine how many cities have at least one of these features. It is important to check if any city has both a lake and a river, but since the question does not provide this information, we will assume that there are no cities that have both. The question tells us that 3 cities have a lake and 23 have a river. We simply add these counts together to find the total number of cities with at least one water feature.
The calculation would be:
3 (cities with a lake) + 23 (cities with a river) = 26 (cities with a lake or a river)
To find the fraction of the 58 cities that have a lake or a river, we divide the number of cities with a water feature by the total number of cities:
26 (cities with a lake or a river) / 58 (total cities) = 13/29 (simplified fraction).
Final answer:
Of the 58 cities, 26 have either a lake or a river, which means the fraction of cities with a lake or a river is 26/58.
Explanation:
To determine what fraction of the 58 cities have a lake or a river running through them, we must consider that the question does not specify whether some cities might have both a lake and a river. Assuming that the cities with lakes and the cities with rivers do not overlap, we simply add the number of cities with each feature.
There are 3 cities with a lake and 23 with a river. To find the total number of cities with either a lake or a river, we add these two numbers together:
3 (cities with a lake) + 23 (cities with a river) = 26 (cities with a lake or a river).
Now, to find the fraction of the 58 cities that have a lake or a river, we divide the number of cities with water features by the total number of cities:
26 / 58 = fraction of cities with a lake or a river running through them.
The first 4 terms of a geometric sequence are 108, 36, 12, 4, ... What is the eighth term of the sequence?
Answer:
4/81
Step-by-step explanation:
Answer:
32
Step-by-step explanation:
hope it helps
Ten people at two local restaurants were randomly surveyed and asked to rate their experience, with “1” representing very poor and “10” representing very good. The data is shown in the dot plots. Find the mean for each set of data. Blue Terrace: Paradiso Grill:
Answer:
Blue Terrace: 6.1
Paradiso Grill: 6.3
Step-by-step explanation This is the right answer
Answer:
6.1 and 6.3
Step-by-step explanation:
what is the area of a circle if the diameter is 16 millimetres
Answer:
201.1 mm²
Step-by-step explanation:
given that the diameter is 16mm,
radius = diameter ÷ 2 = 16÷2 = 8 mm
area of a circle is given by
A = πr², where
π=3.142
r = radius = 8 mm
Substituting these into the equation,
A = πr²
= 3.142 (8)²
= 201.088 mm²
= 201.1 mm² (rounded to nearest tenth)
A ball is thrown vertically upward. After seconds, its height (in feet) is given by the function 56t - 16t^2 . What is the maximum height that the ball will reach?
Answer:
Therefore the maximum height that the reach is 49 feet after 1.75 seconds.
Step-by-step explanation:
Given that,
A ball is thrown vertically upward. After t seconds its height is given by the function
[tex]h=56t-16 t^2[/tex]
where h is height in feet.
Maximum value:
Given function f(x)= at²+bt+c.
Find the value [tex]-\frac{b}{2a}[/tex] Putting [tex]x= -\frac{b}{2a}[/tex] in the given function. The maximum value of the given function is [tex]f(-\frac{b}{2a})[/tex].Here a= -16 , b=56 and c=0
The ball attains its maximum height when [tex]t=-\frac{56}{2.(-16)}=1.75[/tex] s.
Putting the value of t in the given function
[tex]h=(56\times 1.75)-16(1.75)^2[/tex]
=49 feet
Therefore the maximum height that the reach is 49 feet after 1.75 seconds.
The maximum height the ball will reach is given by the vertex of the parabola represented by the equation 56t - 16t^2. This is reached at t = 1.75 seconds, giving a maximum height of 49 feet.
Explanation:The equation 56t - 16t^2 represents the trajectory of the ball thrown upwards over time. To identify the maximum height reached by the ball, we should look for the vertex of the parabola this equation graphically represents. This equation is a quadratic function given in the standard form at^2 + bt + c, where a = -16, b = 56, and c = 0. The time at which the maximum height is reached is found by the formula -b / (2.a). This yields t = -56 / (2 * -16) = 1.75 seconds. When substituted back into the equation, the maximum height (h) would be h = 56 * 1.75 - 16 * (1.75)^2 = 49 feet.
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if 3n is an odd number, which of the following is an even number?
(a) 3n-1
(b) 3n+2
(c) 3n-2
(d) 3n +2n
Answer:
Option (a).
Step-by-step explanation:
It is given that 3n is an odd number.
We need to find an even number from the given options.
Even numbers: Which are divisible by 2.
Odd numbers: Which are not divisible by 2.
We need know that the numbers are alternatively even and odd.
If we add or subtract 1 from an odd number, we always get an even number.
If we add or subtract 2 from an odd number, we always get an odd number.
3n is an odd number. So,
3n-1 is an odd number.
3n+2 is an even number.
3n+2 is an even number.
3n+2n is an even number because 2n is an even number and sum of two even numbers in always an even number.
Therefore, the correct option is (a).
What is the coefficient of x in the following expression?
1 - 10x + 4y
Evaluate the following expression for x = 15.
LaTeX: \frac{1}{5}1 5x - 12
Answer:
(1) The coefficient of x in this expression is -10.
(2) The value of the expression for x = 15 is -9.
Step-by-step explanation:
(1)
A coefficient is a numerical value that is placed before a variable or is multiplied by the variable in an algebraic equation.
For example, in the algebraic equation 4x² + 5y the coefficient of variable y is 5.
The expression given is:
1 - 10 x + 4 y
The coefficient of x in this expression is -10.
(2)
The expression provided is:
[tex]f(x)=\frac{1}{5}x - 12[/tex]
Compute the value of the expression for x = 15 as follows:
[tex]f(x)=\frac{1}{5}x - 12\\=(\frac{1}{5}\times 15) - 12\\=3-12\\=-9[/tex]
Thus, the value of the expression for x = 15 is -9.
Victor has already taken 4 pages of notes on his own, and he will take 2 pages during each hour of class. Write an equation that shows the relationship between the time in class h and the number of pages p.
Write your answer as an equation with p first, followed by an equals sign
Answer:
The answer is p = 4 + 2h .
Step-by-step explanation:
It is given that Victor has already taken 4 pages and he will take 2 pages per hour of class. So you have to make an equation of p in terms of h :
Let p be pages,
Let h be hours,
p = 4 + (2×h)
p = 4 + 2h
determine if the listed line is tangent to the circle
Answer:
SEG KL is not a tangent coz Pythagoras theorem doesn't apply hereSEG GH is not a tangent coz Pythagoras theorem doesn't apply hereSEG GF is not a tangent coz Pythagoras theorem doesn't apply hereSEG FG is not a tangent coz Pythagoras theorem doesn't apply hereSEG XY is a tangent Pythagoras theorem apply here 24²+7²=25²SEG XY is not a tangent coz Pythagoras theorem doesn't apply hereWhich statements are true? Check all that apply.
The radius of the cone is 9 units.
The height of the cone is 15 units.
The height of the cone is 12 units.
The volume of the cone is represented by the
expression 17(15)?(9).
The volume of the cone is represented by the
expression 1.9(9)2(12)
Answer: ACE
The radius of the cone is 9 units
The height of the cone is 12 units
The volume of the cone is represented by the expression 1/3 pie (9)2(12)
Step-by-step explanation:
The volume of a gas "V" varies inversely with the pressure "P" put on it. If the volume is 360cm³ under a pressure of 20 kgcm2, then what pressure is needed for it to have a volume of 480cm³?
Answer:
[tex]15\,\,kg/cm^2[/tex]
Step-by-step explanation:
Given:
The volume of a gas "V" varies inversely with the pressure "P" put on it.
Volume is 360 [tex]cm^3[/tex] under a pressure of 20 [tex]kg/cm^2[/tex]
To find:
pressure when volume is 480 [tex]cm^3[/tex]
Solution:
As of a gas "V" varies inversely with the pressure "P" put on it,
[tex]V=\frac{k}{P}[/tex]
Here, k is a constant
As volume is 360 [tex]cm^3[/tex] under a pressure of 20 [tex]kg/cm^2[/tex], put [tex]V=360\,,\,P=20[/tex]
[tex]360=\frac{k}{20}\\k=360\times 20\\=7200[/tex]
So,
[tex]V=\frac{7200}{P}[/tex]
Put [tex]V=480[/tex]
[tex]480=\frac{7200}{P}\\P=\frac{7200}{480}\\=15\,\,kg/cm^2[/tex]
Which are ways to decompose the composite figure into simpler shapes that you have area formulas for? Check all that apply
Answer:
A,B and C
Step-by-step explanation:
Answer
a,b,c are the correct answer
Step-by-step explanation:
hope it helps you my luvs
Circle A and circle B are similar. A. What is the similarity ratio of circle A to circle B? B. What is the circumference of each circle? Leave answers in terms of . C. What is the ratio of the Circumference of circle B to the Circumference of circle A? Simplify your ratio.
Answer: A) 5/2
B) 10pi for A and 4pi for B
C) 5/2
Step-by-step explanation:
Please find the attached file for the solution
Any jogs 1/3 of a mile in 1/5 of an hour while john takes 1/30 of an hour to jog 1/5 of an mile if they continued at this rate who would jog farther in one hour and by how much?
Answer:
At the end of one hour, John would be ahead of Anny by 4.33 miles
Step-by-step explanation:
In this question, we are to state who jogs Farther between these. 2 persons per hour.
Any jogs 1/3 of a mile in 1/5 of an hour, what this means that he jogs one-third of a mile in 1/5 * 60 in 12 minutes
John however jogs 1/5 miles in 1/30 of hour. This means he jugs one-fifth of a mile in 1/30 * 60 in 2 minutes
Let’s go back to Any
if Any jogs 1/3 in 12 minutes, then the whole lap will be completed in 36 minutes
Thus if he can jog 1 mile in 36 minutes, then in 60 minutes he would have jogged 1.67 miles
If he Jogs 1/5 in 2 minutes, this mean that the whole lap of 1 mile would be completed in 10 minutes
Thus if he can jug 1 mile in 10 minutes, then in 60 minutes, he will be able to jug a whopping 6 miles
This shows that John is actually faster than Any.
By how much distance? that would be 6 - 1.67 = 4.33 miles
The Intelligence Quotient (IQ) test scores for adults are normally distributed with a population mean of 100 and a population standard deviation of 15. What is the probability we could select a sample of 50 adults and find that the mean of this sample exceeds 104
Answer:
[tex] P( \bar X >104) = P(Z > \frac{104-100}{\frac{15}{\sqrt{50}}}) = P(Z>1.886)[/tex]
And we can use the complement rule and the normal standard distribution or excel and we got:
[tex] P(z>1.886) = 1-P(Z<1.886) = 1-0.970 = 0.03[/tex]
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the IQ of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(100,15)[/tex]
Where [tex]\mu=100[/tex] and [tex]\sigma=15[/tex]
We select a sample of n = 50 and we want to find the probability that:
[tex]P(\bar X >104)[/tex]
Since the distribution for X is normal then we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
And we can use the z score formula given by:
[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}} [/tex]
And using this formula we got:
[tex] P( \bar X >104) = P(Z > \frac{104-100}{\frac{15}{\sqrt{50}}}) = P(Z>1.886)[/tex]
And we can use the complement rule and the normal standard distribution or excel and we got:
[tex] P(z>1.886) = 1-P(Z<1.886) = 1-0.970 = 0.03[/tex]
From an upstairs window, I can see my neighbor’s fence. The angle of depression is 7 degrees. If my window is 15 ft off the ground, how far is my neighbor’s fence from my house?
Answer:
1.84ft
Step-by-step explanation:
From the figure attached,
AB = Height of the window = 15ft
Let the distance between the base of the housr and the fence 'C' = xft
If the angle of depression = 7°
Then angle of elevation of the top of the fence from the house = 7°
Now from right triangle ABC,
tan7° = x/15
x = tan7°×15
x = 0.1227×15
x = 1.84ft
Therefore, distance of the house from the fence is 1.84ft
what is the range for this set of data 38,17,55,40
a)2
B)38
C)39
D)72
Answer:
b.38
Step-by-step explanation:
1.
Solve the following inequalities:
- 4x >72
Answer:
x<18
Step-by-step explanation:
-4x>72 / divide both side ÷-4
x<-18
xe(-œ,-18)
An open-top box is to be made from a 70-centimeter by 96-centimeter piece of plastic by removing a square from each corner of the plastic and folding up the flaps on each side. What size square should be cut out of each corner to get a box with the maximum volume? Enter the area of the square and do not include any units in your answer. Enter an improper fraction if necessary.
Answer:
[tex]177 \frac{7}{9} cm^2[/tex]
Step-by-step explanation:
Length of the Plastic Sheet= 96cm
Width of the plastic Sheet =70cm
If a square of side x is cut from each corner of the plastic sheet to form the box.
Length of the box=96-2x
Width of the box=70-2x
Height of the box =x
Volume of the box = LWH
Volume=(96-2x)(70-2x)x
The maximum volume of the box is obtained at the point where the derivative is zero.
[tex]V=(96-2x)(70-2x)x\\V^{'}=4(x-42)(3x-40)[/tex]
Setting the derivative to 0.
[tex]4(x-42)(3x-40)=0\\x-42=0\: 3x-40=0\\x=42\:or\: x=\frac{40}{3}[/tex]
Since we are looking for the minimum value of x,
[tex]x=\frac{40}{3}\\\text{Area of the Square} = x^2\\=\frac{40}{3} X \frac{40}{3}\\=177 \frac{7}{9} cm^2[/tex]
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A teacher had 1 apple, he gave 1 to his student. How many apples does the teacher have and how much apples does his student have?
Answer:
Teacher has 0 . Student has 1 apple
Step-by-step explanation:
Find the profit function for the given marginal profit and initial condition. Marginal Profit Initial Condition dP dx = −20x + 290 P(5) = $670 P(x) =
Answer:
[tex]P(x) = -10x^2+290x-530[/tex]
Step-by-step explanation:
We are given the following in the question:
[tex]\dfrac{dP}{dx} = -20x + 290[/tex]
Initial condition:
[tex]P(5) = $670[/tex]
Solving the given differential equation, we get,
[tex]\dfrac{dP}{dx} = -20x + 290\\\\dP=(-20x + 290)dx\\\text{Integrating both sides}\\\\\displaystyle\int dP = \int (-20x + 290)dx\\\\P(x) = -20\dfrac{x^2}{2} + 290x + C\\\\\text{where C is constant of integration}\\P(x) = -10x^2+290x + C\\P(5) = 670\\670 = -10(5)^2+290(5) + C\\670 = 1200 + C\\\Rightarrow C = -530\\P(x) = -10x^2+290x-530[/tex]
is the required profit function.
To determine the profit function, integrate the given marginal profit function. After integration, apply the initial condition to find the integration constant. The final profit function is [tex]P(x) = -10x^2 + 290x - 60.[/tex]
Explanation:The subject matter of this question is calculus, specifically how to determine the profit function based from the given marginal profit and initial condition. To determine the profit function, you need to integrate the marginal profit function. The marginal profit is given as dP/dx = -20x + 290. When you integrate this, you will get [tex]P(x) = -10x^2 + 290x + C[/tex], where C is an integration constant that we determine using the initial condition P(5) = 670.
To do this, substitute 5 into x in the equation and set P(x) equal to[tex]670: 670 = -10*5^2 + 290*5 + C.[/tex] Solving for C, you will find that C equals -60. So the profit function is [tex]P(x) = -10x^2 + 290x - 60.[/tex]
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What is the domain of the function y = StartRoot x EndRoot?
Answer:
C
Step-by-step explanation:
0 is less than or equal to x is less than infinity. PERIODT.
The domain of the function y = √x will be [0, ∞).
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
The function is given below.
y = √x
The graph of the function is similar to the rightward parabola, the function is not defined for the negative value of x, because the function becomes imaginary.
For the domain of the function, the value of x should be greater than equal to zero.
Because the value under the square root should be greater than or equal to zero.
Then the domain of the function y = √x will be
x ≥ 0
Thus, the domain of the function y = √x will be [0, ∞).
The graph of the function is given below.
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Paddling with the current in a river, jake traveled 16 miles. Even though he paddled upstream for an hour longer than the amount of the time he paddled downstream jake could only travel 6 miles against the current. I'm still waterJake paddles at a rate of 5 mph. What is the speed of the current I the river
Answer: the rate of the current is 3 mph.
Step-by-step explanation:
Let x represent the rate of the current.
In still water, Jake paddles at a rate of 5 mph. Paddling with the current in a river, Jake traveled 16 miles. It means that the speed with which she travelled downstream (with the current) is (5 + x) mph
Time = distance/speed
Time spent in paddling downstream is
16/(5 + x)
While paddling upstream, it took an hour longer. The speed with which he paddled upstream is (5 - x) mph.
Jake could only travel 6 miles against the current. It means that the time spent in travelling upstream us
6/(5 - x)
Since it took 1 hour longer, then
6/(5 - x) = 16/(5 + x) + 1
Cross multiplying by (5 - x)(5 + x), it becomes
6(5 + x) = 16(5 - x) + 1(5 + x)(5 - x)
30 + 6x = 80 - 16x + 25 - 5x + 5x - x²
30 + 6x = - x² - 16x + 5x - 5x + 25 + 80
30 + 6x = - x² - 16x + 105
x² + 16x + 6x + 30 - 105 = 0
x² + 22x - 75 = 0
x² + 25x - 3x - 75 = 0
x(x + 25) - 3(x + 25) = 0
x - 3 = 0 or x + 25 = 0
x = 3 or x = - 25
Since x cannot be negative, then x = 3 mph
Answer: x=3
Step-by-step explanation:
Took test
"A passenger train traveled 100 miles in the same amount of time it took a freight train to travel 90 miles. The rate of the freight train was 10 miles per hour slower than the rate of the passenger train. Find the rate of the passenger train."
The rate of the passenger train is 100 miles per hour.
Given:
1. The passenger train traveled 100 miles in the same amount of time it took the freight train to travel 90 miles.
2. The rate of the freight train was 10 miles per hour slower than the rate of the passenger train.
We can set up equations based on the distances traveled and the rates:
1. For the passenger train:
[tex]\[ \text{Distance} = \text{Rate} \times \text{Time} \]\[ 100 = r_p \times \text{Time} \]2. For the freight train:\[ 90 = r_f \times \text{Time} \]Since we know that the rate of the freight train (\( r_f \)) is 10 miles per hour slower than the rate of the passenger train (\( r_p \)), we can express \( r_f \) in terms of \( r_p \):\[ r_f = r_p - 10 \][/tex]
Now, we need to find the time it took for both trains to travel their respective distances. Since the time is the same for both trains, we can equate the expressions for time:
[tex]\[ \text{Time} = \frac{\text{Distance}}{\text{Rate}} \]For both trains, time is the same, so:\[ \frac{100}{r_p} = \frac{90}{r_f} \]Substitute \( r_f = r_p - 10 \):\[ \frac{100}{r_p} = \frac{90}{r_p - 10} \]Now, let's solve for \( r_p \):\[ 100(r_p - 10) = 90r_p \]\[ 100r_p - 1000 = 90r_p \]\[ 10r_p = 1000 \]\[ r_p = \frac{1000}{10} \]\[ r_p = 100 \][/tex]
So, the rate of the passenger train is 100 miles per hour.
Tickets to the school play cost $4.00 for adults and $2.00 for students. If 85 people attend the show, and the receipts totaled $268, how many students attended the show?
Answer:I think it is 226
Step-by-step explanation:
85/2= 42.5 then 268 - 42.5= 225.5 then round it and you get 226
suppose the diameter is a circle 8 units what is the circumference in units
Answer:
C = 8π
Step-by-step explanation:
C = 2πr
C = 2π(8/2)
C = 2π × 4
C = 8π
Answer:
18.84 units
Step-by-step explanation:
diameter is 6 units so radius will be 3 units.
circumference = 2πr = 2×22/7×3
= 18.84 units
Mrs. Benton selects one student's work to display on a bulletin board each week. Each student's name is placed in a bag from which Mrs. Benton draws a name. What is the probability that an eighth grade student will NOT be selected? A) 3 /10 B) 2/ 5 C) 1 /2 D) 2/ 3
Answer:
1/2
Step-by-step explanation:
two-fifth of the students in a mixed school are boys. if there are 30 girl in the school how many are boys
Answer:
12
Step-by-step explanation:
One fifth of 30 would mean u divide 30 by 5 which equals 6. Since it's two fifths you would have 12.
Determine the value of the expression given below. 121 / 2÷(−1 3/8)
Answer:
-44
Step-by-step explanation:
A group of individuals were surveyed about their plans for vacation. There were 21 individuals who said they were going to the desert for vacation. How many individuals were surveyed in total? How many people are planning on going to the mountains for their vacation?
Answer:
140 individuals were surveyed
42 people are planning on going to the mountains
Step-by-step explanation:
The question is missing the information regarding the percentage of people who said that they were going to each of the possible destinations. After a quick google search I've found that, in the original question, 32% of individuals were going to the beach, 15% to the desert, 23% to major cities, and 30% to the mountains.
If 21 people said they were going to the desert, and that corresponds to 15% of the total number of people surveyed, the number of people surveyed is:
[tex]21=n*0.15\\n=140\ individuals[/tex]
140 individuals were surveyed
Since 30% responded "the mountains", the number of people planning on going to the mountains is:
[tex]m = 140*0.30\\m=42\ people[/tex]
42 people are planning on going to the mountains
f(4)= ______
-11
-2
1
30
if g(x) = 2, x = _______
0
2
5
30
Answer:
f(4) = -11
If g(x) = 2 then x = 0
Step-by-step explanation:
here it asks to determine graphically, so we need to use the provided graph:
f(4) = -11 ( just notice the y-coordinate of the point of x-coordination 4)
If g(x) = 2 then x = 0 (just notice the x-coordinate of the point of y-coordination 2)