Answer:
There will be 90 ways to reach Greenup from Charleston.
Step-by-step explanation:
Option C: 90 is correct.
Let's name all the ways and try to visualize the roads.
C = Charleston
M = Mattoon
T = Toledo
G = Greenup
Task = Charleston to Greenup. How many different ways to reach?
1 1
2 2 1
C 3 M 3 T 2 G
4 4 3
5 5
6
So, Refer to this above diagram.
If we Start from C then go to 1 and then go to M and then go to 1 and then go to T and then go to 1 and then go G.
If you notice, in this single possibility we have 3 ways: C to 1 to M, M to 1 to T, T to 1 to G.
It means we will have: 5 x 6 x 3 = 90 number of ways to reach greenup from Charleston.
The total number of ways to get from Charleston to Greenup is option C) 90.
To determine this, multiply the number of roads for each section:
Charleston to Mattoon: 5 roadsMattoon to Toledo: 6 roadsToledo to Greenup: 3 roadsThen, multiply the numbers of roads for all the sections: [tex]5 * 6 * 3 = 90[/tex].
W (t) models the daily water level (in cm) at a pond in Arizona, t days after the hottest day of the year. Here, t is entered in radians:
w(t) = 15 cos ((2pi / 365)t) + 43
What is the first time after the hottest day of the year that the water levels is 30 cm?
Answer:
152 days
Step-by-step explanation:
Given:
w(t) = 15 cos ((2π / 365)t) + 43
To find first time after the hottest day of the year that the water levels is 30 cm, substitute with w(t) = 30 and solve for t
30 = 15 cos ((2π / 365)t) + 43
30 - 43 = 15 cos ((2π / 365)t)
15 cos ((2π / 365)t) = -13
cos ((2π / 365)t) = -13/15
(2π / 365)t = cos⁻¹ (-13/15) = 150.07° ≈ (5/6) π
t = (365/2) * (5/6) ≈ 152 days
So, the first time after the hottest day of the year that the water levels is 30 cm is after 152 days
The water level reaches 30 cm approximately 125.3 days after the hottest day of the year. This was calculated by setting the given equation equal to 30 cm, isolating the variable, and using inverse cosine to solve in terms of radians.
Explanation:The given equation represents a cosine function, w(t) = 15cos(2π / 365)t + 43, which models the water level in a pond. Here, 15 is the amplitude, and 43 is the vertical shift, indicating the average water level is 43 cm. To find the first time after the hottest day of the year that the water level is 30 cm we first set w(t) equal to 30 and solve this for t:
30 = 15cos((2π / 365)t) + 43,
Subtract 43 from both sides to get:
-13 = 15cos((2π / 365)t),
Next, divide both sides by 15 to get:
-13/15 = cos((2π / 365)t),
Now, use the inverse cosine function, or arccos, to solve for the argument (2π / 365)t, which is in radians:
(2π / 365)t = arccos(-13/15).
Thus, t = (365 / 2π) * arccos(-13/15). This equation can be solved using a calculator that provides results in radians. The solution is approximately 125.3 days after the hottest day of the year.
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What is the volume of a cylinder, in cubic feet, with a height of 7 feet and a base
diameter of 18 feet? Round to the nearest tenths place
Answer:
1781.29
Sorry, no explanations
Answer:
V= 1781.3
Step-by-step explanation:
That’s the correct answer.
Sunil is solving the quadratic equation by completing the square. 6x2 + 24x + 5 = 0 6x2 + 24x = –5 What should Sunil do next? Isolate the variable x2. Isolate the constant. Factor 6 out of the variable terms. Subtract 24x from both sides of the equation.
Answer:
Factor 6 out of the variable terms.
Step-by-step explanation:
6x^2 + 24x + 5 = 0
6x^2 + 24x = –5
Factor out the 6 on the left hand side
6 (x^2 +4x) = -5
Answer:
FACTOR IS 6
Step-by-step explanation:
An artist wishes to make a painting in the shape of a golden rectangle, based on the theory that this shape is the most pleasing to
the average customer. If the canvas has an area of 108 in? what would be the dimensions of the canvas? Round to the nearest
inch.
a 17 x 11
C 9 x 12
b. 11 x 12
d. 6 x 10
Please select the best answer from the choices provided
Mark this and return
Save and Exit
Next
Submit
The dimensions of the canvas would be approximately 11 inches by 7 inches.
Explanation:To determine the dimensions of the canvas, we need to find the side lengths of the golden rectangle. A golden rectangle is a rectangle in which the length is approximately 1.618 times the width. The formula for the area of a rectangle is length multiplied by width. Given that the area of the canvas is 108 square inches, we can set up the equation: length x width = 108. Using the golden ratio, we can express the length in terms of the width as length = 1.618 x width.
Substituting this expression for length in the equation, we get (1.618 x width) x width = 108. Solving for the width, we find width ≈ 6.68 inches. Rounding this to the nearest inch, the width is 7 inches. Substituting this value back into the expression for length gives us length ≈ 11.31 inches, which rounds to 11 inches.
Therefore, the dimensions of the canvas are approximately 11 inches by 7 inches. The correct answer choice is a. 17 x 11.
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Model the following problem with a quadratic equation. Then solve.
Find the length of a side of a square with an area of 108 ft2.
Answer:
10.3923
Step-by-step explanation:
Answer:
6sqrt3
Step-by-step explanation:
To find the area of a square, we simply square the length of its side!
We can represent the length of the side by x; therefore, the area of the square would be x squared, or x^{2}.
Then, we solve!
x^{2} = 108, so we find the square root of 108.
108 = 2^2 * 3^3
So sqrt{2*2*3*3*3}
We can take the 2^2 and 3^2 out of the square root, so outside, it becomes 2 * 3, or 6.
The 3 is still inside the square root, leaving us with 6sqrt3.
Hope that helps!
To take a taxi it costs $3.00 plus an additional $2.00 per mile traveled. You spent exactly $20 on a taxi which includes the $1 tip you left. How many miles did you travel?
Answer:
8 Miles
Step-by-step explanation:
Start by creating an equation based off what you know. To start we know it costs $3 just to get a ride + $2 for ever mile we travel (represent this using x)+ the $1 tip we left=$20.
3+2x+1=20
Now you add the like terms together(3+1)
2x+4=20 Subtract the 4 from both sides.
-4 -4
2x=16 Now you just divide each side by 2
_ _
2 2
x=8
Don't forget your label (miles)
does any one know exponential equations?
Answer:
yes it is when you have in exponent you have to solve for example
3+2[tex]x^{2}[/tex]= 3+2x2=7
Please please please mark me brainliest
Step-by-step explanation:
Answer:Exponential functions follow all the rules of functions. However, because they also make up their own unique family, they have their own subset of rules. The following list outlines some basic rules that apply to exponential functions
Step-by-step explanation:The parent exponential function f(x) = bx always has a horizontal asymptote at y = 0, except when b = 1. You can’t raise a positive number to any power and get 0 or a negative number.
This rule is true because you can raise a positive number to any power. However, the range of exponential functions reflects that all exponential functions have horizontal asymptotes. All parent exponential functions (except when b = 1) have ranges greater than 0, or
The order of operations still governs how you act on the function. When the idea of a vertical transformation applies to an exponential function, most people take the order of operations and throw it out the window. Avoid this mistake.
You can’t multiply before you deal with the exponent.
You can’t have a base that’s negative. For example, y = (–2)x isn’t an equation you have to worry about graphing in pre-calculus. If you’re asked to graph y = –2x, don’t fret. You read this as “the opposite of 2 to the x,” which means that (remember the order of operations) you raise 2 to the power first and then multiply by –1. This simple change flips the graph upside down and changes its range to
A number with a negative exponent is the reciprocal of the number to the corresponding positive exponent. For instance, y = 2–3 doesn’t equal (–2)3 or –23. Raising any number to a negative power takes the reciprocal of the number to the positive power
When you multiply monomials with exponents, you add the exponents. F
When you have multiple factors inside parentheses raised to a power, you raise every single term to that power. For instance, (4x3y5)2 isn’t 4x3y10; it’s 16x6y10.
When graphing an exponential function, remember that the graph of an exponential function whose base number is greater than 1 always increases (or rises) as it moves to the right; as the graph moves to the left, it always approaches 0 but never actually get there. For example, f(x) = 2x is an exponential function, as is
The table shows the x and y values of these exponential functions. These parent functions illustrate that, as long as the exponent is positive, the graph of an exponential function whose base is greater than 1 increases as x increases — an example of exponential growth — whereas the graph of an exponential function whose base is between 0 and 1 decreases towards the x-axis as x increases — an example of exponential decay.
The graph of an exponential function who base numbers is fractions between 0 and 1 always rise to the left and approach 0 to the right. This rule holds true until you start to transform the parent graphs.
Determine the slope of the line that passes though the points (2,-5) and (4,3).
Answer: slope = 2
Step-by-step explanation:
The formula for calculating slope is given as :
[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1} }[/tex]
[tex]x_{1}=2[/tex]
[tex]x_{2}=4[/tex]
[tex]y_{1}=-5[/tex]
[tex]y_{2}=3[/tex]
substituting into the formula , we have :
[tex]m = \frac{3-(-5)}{4-2}[/tex]
[tex]m = \frac{8}{2}[/tex]
[tex]m = 2[/tex]
Therefore : slope = 2
Conor earns $9 an hour for yard work.He raked leaves 1 afternoon and earned $29.25. How many hours did he rake leaves? How much money does he get each minute?
Answer:
29.25 divided by 9 is 3.25 so this is equavilent to 3 hours and 15 minutes
he makes 0.15 per minute 9 divided by 60 is 0.15
How do u do this? Pls help me!!
Answer:
8.6 but im not sure.
Step-by-step explanation:
5 squared + 7 squared = 74 square root = 8.6
We have to find what "x" is greater than and less than.
(7-5)<x<(5+7) = 2 < x < 12
To be able to form a triangle, the sides can't be too small or big.
To find "x", use the formula above.
If you wish to show that two triangles are similar, which statement(s) is correct? You may choose more than one correct answer.
It is enough to show that all three pairs of corresponding sides are in the same ratio.
It is not enough to have information about only sides or only angles.
It is enough to show that two pairs of corresponding angles are congruent.
It is enough to show that two pairs of corresponding sides are in the same ratio.
It is enough to show that one pair of corresponding angles is congruent.
Answer:
It is enough to show that all three pairs of corresponding sides are in the same ratio.
It is enough to show that two pairs of corresponding angles are congruent.
Step-by-step explanation:
If you know that the corresponding sides have the same ratio, then both triangles will be similar (SSS Similarity)
If 2 corresponding angles are congruent, you know the 3rd one is too (Triangle Angle Sum) which makes the triangles similar (AA Similarity)
At store #1 for $625 you can buy 25 pair of shoes. At store #2 you can buy 33 pairs of shoes for 800. Which store has the best deal on shoes? How do you know?
Answer:
store #2 is the better deal
Step-by-step explanation:
In store #1 you need to take the total cost $625 and divide it by 25 to get your pere item cost
625/ 25 = 25
In store #2 do the same
800/ 33 = 24.24
so store two is the better deal as per item cost is lower
A bag contains 8 blue marbles, 15 red marbles, 10 yellow marbles, and 3 brown marbles. If a marble is randomly selected, what is the probability that it will be BROWN? Please select one answer. I REALLY NEED HELP!!!!!
Answer:
1/12
Step-by-step explanation:
8 blue marbles
15 red marbles
10 yellow marbles
3 brown marbles
So let's add them up
8+15+10+3
=36
Probability of picking brown marbles
3/36
Divide both by 3
1/12
So the probability of picking brown is 1/12
I. There is a gap in the Potato Chips group
II. There is a gap in the Tortilla Chips group
III. The range is greater for the Potato Chips group
Which of the statements are true?
A) I only
B) II only
C) I and II
D) III only
Answer:
C) I and II
There is a gap in the Potato Chips group for the stem "14" and the Tortilla Chips group for the stem "12"
Answer:
its c
Step-by-step explanation:
i got it right on usatestprep
need help asap 30 POINTS A digital camera memory card is one fourth full. The card is two thirds full when 375 more pictures have been taken How many pictures are on the memory card when it is five sixths full?
1/4=3/12
2/3=8/12
5/12=375
375/5=75
1/12=75
75*12=900
10/12=5/6
5/6=750
Answer:
750 add and divide and stuff
Organize the given volumes of cubes as either a perfect cube or not-perfect cube.
900m3
Perfect cubes
Not-perfect cubes
9m
8m3
343m
1,000m
300m
Answer:
343m3,8m3,1000m3 for Perfect squares
300m3,9m3,900m3 for Not-perfect squares
Step-by-step explanation:
Did an assignment on edge
Answer: answer in the picture
Step-by-step explanation:
I need help like ASAP
I need assistance on this question
Answer:
The solution is (1,2) plz give branliest
Step-by-step explanation:
The solution is where the point intersect
In the coordinate plane, when you graph a positive 210 degree angle you go
counter-clockwise and end up in the 2nd quadrant.
clockwise and end up in the 2nd quadrant
counter-clockwise and end up in the 3rd quadrant
clockwise and end up in the 3rd quadrant
Answer:
clockwise and end up in the 3rd quadrant
Step-by-step explanation:
That's how you're supposed to graph angles. Also, 180<210<270, which are the parameters for the 3rd quadrant
In the coordinate plane, when you graph a positive 210 degrees angle you go option (C) counter-clockwise and end up in the 3rd quadrant
What is Coordinate plane?A coordinate plane is a tool used for graphing points, lines, and other objects. It functions like a map that follows directions from one point to another.
What is angle?A figure which is formed by two rays or lines that shares a common endpoint is called an angle
Given,
We have to plot a positive 210 degree angle
So the movement will be in counter clockwise direction and angle 210 degrees in the third quadrant
Therefore when you graph positive 210 degrees you go in counterclockwise direction and end up in the 3rd quadrant
Hence, In the coordinate plane, when you graph a positive 210 degrees angle you go option (C) counter-clockwise and end up in the 3rd quadrant
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What is the value of x
It depends on your Divisor, Product, or Value. There is just not a gaven value for X or X=0
Which statements are true about y Less-than-or-equal-to 8 and its graph? Check all that apply.
y = 0 is part of the solution set.
y = 8 is part of the solution set.
y = 10 is part of the solution set.
There is an open circle on the graph at 8.
There is a closed circle on the graph at 8.
The arrow on the graph points left.
The arrow on the graph points right.
When the inequality sign is </> (less than/greater than), the dot is an open circle.
When the inequality sign is ≤/≥ (less than or equal to/greater than or equal to), the dot is a closed circle.
y = number that is a solution/makes the inequality true
y ≤ 8 (y is any number less than or equal to 8)
#1: y = 0 is part of the solution set.
Yes because if you substitute/plug in 0 into "y" in the inequality, since y = 0:
0 ≤ 8 0 is less than 8.
#2: y = 8 is part of the solution set.
Yes because if you plug it into the inequality:
8 ≤ 8 8 is equal to 8
#3: y = 10 is part of the solution set.
No because if you plug it into the inequality:
10 ≤ 8 10 is not less than or equal to 8
#4: There is an open circle on the graph at 8.
No because the inequality sign is ≤, so there should be a closed circle on 8.
#5: There is a closed circle on the graph at 8.
Yes because the inequality sign is ≤
#6: The arrow on the graph points left.
Yes because if the arrow is pointing left then the numbers are decreasing, and y is any number less than or equal to 8.
#7: The arrow on the graph points right.
No because if the arrow is point right then the numbers are increasing, but y is not a number greater than 8.
Your answer is the 1st, 2nd, 5th, and 6th option
To solve the problem first we need to understand the Inequality Signs.
Inequality SignIn an inequality sign there is a dot(circle) present, but whether the circle is open or closed depends, upon the inequality sign.
If the inequality sign is less than(<) or greater than(>), the dot is an open circle.
whereas, if the inequality sign is less than or equal to (≤) and greater than or equal to(≥), the dot is a closed circle.
The correct options are A, B, E, and F.
ExplanationGiven statements to us,
A.) y = 0 is part of the solution set.
B.) y = 8 is part of the solution set.
C.) y = 10 is part of the solution set.
D.) There is an open circle on the graph at 8.
E.) There is a closed circle on the graph at 8.
F.) The arrow on the graph points left.
G.) The arrow on the graph points right.
Solutions
We know that the number line is always decreasing number or negative towards the left while positive towards the right.
Therefore, y≤8 means, y is true for any value less than and equal to 8, which will give a closed circle on the graph, and the arrow will be pointing toward the left.
Now looking at the options we have,
A.) y = 0 is part of the solution set.
The statement is true as the y value is less than 8.
B.) y = 8 is part of the solution set.
The statement is true as the y value is equal to 8.
C.) y = 10 is part of the solution set.
The statement is false as the y value is greater than 8.
D.) There is an open circle on the graph at 8.
The statement is false as the inequality sign given is less than or equal to (≤).
E.) There is a closed circle on the graph at 8.
The statement is true as the inequality sign given is less than or equal to (≤).
F.) The arrow on the graph points left.
The statement is true as the value of y is always on the decreasing side, the number line is always decreasing the number or negative towards the left while positive towards the right.
G.) The arrow on the graph points right.
The statement is false as the value of y is always on the decreasing side, the number line is always decreasing the number or negative towards the left while positive towards the right.
Hence, the correct options are A, B, E, and F.
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The chance that Rachel will win a prize is 21 over 50. Write this probability as a decimal and as a percent.
Answer:
.42 or 42%
Step-by-step explanation:
21/50 is equal to .42 which is the decimal answer. To get percent multiply the decimal by 100, and you get 42%.
Answer:
42%
0.42
Step-by-step explanation:
21/50 x2 = 42/100
what is the slope of the line that passes through points (-1,5) and (2,3)
Answer:
-2/3
Step-by-step explanation:
The slope of a line can be found using the formula change in y coordinate divided by change in x coordinate (rise over run). SO, first you find the difference in y: 3-5 which is equal to -2, then divide it by change in x (2--1 / 2+1 = 3), giving an answer of -2/3.
What is the volume of a cylinder with base radius 3 and height 6?
Either enter an exact answer in terms of or use 3.14 for and enter your answer as a decimal.
cubic units
Answer:
the volume of the cylinder is about 169.646
Step-by-step explanation:
V= 3.14 r^2 h = 3.14 × 3^2 × 6 = 169.646
Name the types of angles shown.
J
Check all that apply.
I
A. straight angle
B. right angle
O
c. complementary angles
D. supplementary angles
Answer:
All except complementary angle.
Step-by-step explanation:
Complementary angles equal 90 degrees.
Answer:
all is correct
Step-by-step explanation:
because a right angle, complementary angle and 90% angle are the same thing and a supplementary angle and straight angle are 180% so all answers are correct
A triangular prism. The rectangular sides are 8 inches by 4 inches, 8 inches by 5 inches, and 8 inches by 3 inches. The triangular sides have a base of 4 inches and height of 3 inches.
The area of each triangular base is:
A = 1/2(b)(h) A = 1/2(4)(3)
A = in.2
There are two bases, so total base area is in.2.
The lateral area is:
A = 8(4) + 8(3) + 8(5)
A = in.2
The total surface area is in.2.
Answer:
A of each triangular base = 6 in²
A of both bases = 12 in²
Lateral A = 96 in²
Surface area = 108 in²
Step-by-step explanation:
Area of each triangular base
1/2(3)(4) = 1/2(12) = 6
Area of both bases
6*2 = 12
Lateral Area
(8)(3) + (8)(4) + (8)(5)
24 + 32 + 40
96
Total Surface area
96 + 12 = 108 in²
Wednesday's temperature was 30° cooler than Monday's temperature, t. Write an
expression for Wednesday's temperature.
Answer:
W=t-30
Step-by-step explanation:
If t is Monday, and Wednesday is W, then T- 30 is saying 30 less then T
Can you answer this for me it’s hard, thanks!
Answer:
30[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
Please help! I’ll give 10 points.
Answer: 80m
Step-by-step explanation:
What I did was is 3/x=1.67/44.5
I set it up as a proportion, cross multiplied, and divided. you get around 79.9.... so I rounded up to 80. Hope that helped
Answer:
The buildings height was 64.23 (meters) to 2dp
Step-by-step explanation:
This is because the pole shadow = 44.3333% increase to get to 3ft
Seeing that 1.67 was the shadow and beside it the building shows 44.5 we just multiply it by the percentage and to not add one (1) to the decimal to add if not adding or showing what 44.33% becomes.
44.5 x 1.443333 =64.2283185 and sum (add) as its an increase = (44.5 + 19.72831 = 64.2283185) So 19.73 to 2dp is the difference without the 1 used and without being seen.
This is the hidden increase as we just say 44.33% of 44.5 ft But as we used the 1. to represent the x100.
We find 44.33% of 44.5 finds us the buildings exact measure to 2dp = 64.22m
Converted (= 210.72 feet to 2dp)
Hope this helps.
You estimate that there are 75 marbles in a jar. The actual amount is 82 marbles. Find the percent error
Answer:
Percent Error:: 12/36 = 33 1/3 %
Step-by-step explanation:
Final answer:
To find the percent error when estimating marbles in a jar, you subtract the estimated value from the actual value, divide by the actual value, and multiply by 100. In this case, the percent error is 8.54%.
Explanation:
To find the percent error, you first calculate the absolute error by subtracting the estimated value from the actual value. Then, divide the absolute error by the actual value and multiply by 100 to get the percent error.
Calculate absolute error: 82 (actual) - 75 (estimated) = 7
Percent error formula: (Absolute error / Actual value) x 100%
Percent error = (7 / 82) x 100% = 8.54%