To determine how many triangles are represented by the angles a=120 degrees, a=250 degrees, and b=195 degrees, we need to use the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
First, we need to determine which angle corresponds to which side. Let's assume that angle a is opposite to the longest side, and angle b is opposite to the shortest side. Therefore, we have: a = 250 degrees (longest side) a = 120 degrees b = 195 degrees (shortest side) Next, we need to use the triangle inequality theorem to determine which combinations of sides can form a triangle. For any two sides a and b, the third side c must satisfy the following condition: c < a + b Using this condition, we can determine the valid combinations of sides: - a + b > c: This is always true, since a and b are the longest and shortest sides, respectively. - a + c > b: This is true for all values of c, since a is the longest side. - b + c > a: This is true only when c > a - b.
Substituting the given values, we get: c > a - b c > 250 - 195 c > 55 Therefore, any side c that is greater than 55 can form a triangle with sides a and b. We can use this condition to count the number of valid triangles: - If c = 56, then we have one triangle. - If c = 57, then we have two triangles (c can be either adjacent side). - If c = 58, then we have three triangles (c can be any of the three sides). Continuing this pattern, we can count the number of triangles for each value of c: c = 56: 1 triangle c = 57: 2 triangles c = 58: 3 triangles c = 59: 4 triangles c = 60: 5 triangles c = 61: 6 triangles c = 62: 7 triangles c = 63: 8 triangles c = 64: 9 triangles c = 65: 10 triangles c = 66: 11 triangles c = 67: 12 triangles c = 68: 13 triangles c = 69: 14 triangles c = 70: 15 triangles c > 70: 16 triangles (since all three sides can form a triangle) Therefore, there are 16 possible triangles that can be formed with the given angles and side lengths.
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Shawn wrote down the activities for his day on Saturday. In which situation will his activity result in a final value of zero?
1 point
A. Shawn places four quarters in a jar of quarters which contains four quarters.
B. In the morning, Shawn added six hard candies to a jar which contained four hard candies. By the end of the day he ate ten candies from this jar.
C. Shawn starts out on the ground and then climbs ten feet on a ladder.
D. Shawn travels east ten feet and then travels south ten feet
The situation in which Shawn's activity will result in a final value of zero is Shawn travels east ten feet and then travels south ten feet. The correct option is D.
This is because when Shawn travels east ten feet, he moves horizontally to the right of his starting point. When he travels south ten feet after that, he moves vertically downwards from his previous position, cancelling out the horizontal movement he made earlier.
The displacement caused by Shawn's movement in the east direction is equal in magnitude but opposite in direction to the displacement caused by his movement in the south direction.
The net displacement of Shawn's movement is zero, and he ends up back at his starting point. Options A, B, and C do not involve any movements that result in a net displacement of zero.
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Suppose you want to represent a triangle with sides of 12 feet, 15 feet, and 18 feet on a drawing where 1 Inch - 3 feet How long should the sides of the triangle be in inches? 12 feet should be inches. 15 feet should be 18 feet should be inches.
In linear equation, The sides of the triangle on the drawing should be 6 inches, 8 inches, and 9 inches.
What in mathematics is a linear equation?
An algebraic equation B. y=mx+b (where m is the slope and b is the y-intercept) containing simple constants and first-order (linear) components, such as the following, is called a linear equation.
The above is sometimes called a "linear equation in two variables" where x and y are variables. Equations in which the variable is power 1 are called linear equations. axe+b = 0 is a one-variable example where a and b are real numbers and x is a variable.
A triangle with sides 12 feet, 16 feet, and 18 feet on a drawing where 1 inch = 2 feet.
Then, 1 feet of original triangle = 1/2 inch on drawing.
Now, the sides of the triangle on the drawing are
12 feet = 1/2 * 12 = 6 in
12 feet = 1/2 * 16 = 8 in
12 feet = 1/2 * 18 = 9 in
Hence, the sides of the triangle on the drawing should be 6 inches, 8 inches, and 9 inches..
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Jamie jogged x km. Anabel jogged 1/4 less than Jamie. Choose the equation that best represents the situation. A
y = 3/4x
b
x = 4/3y
c
y = 1/4x
d
x = 1/4y
The equation that best represents the situation is y = 3/4x. The correct answer is A.
The given problem involves two people, Jamie and Anabel, who jogged a certain distance. Let's say Jamie jogged x km. Anabel jogged 1/4 less than Jamie, which means she jogged 3/4 of x km (since 1 - 1/4 = 3/4).
To represent this situation in an equation, we need to find the relationship between the distance jogged by Jamie and the distance jogged by Anabel. Since Anabel jogged 3/4 of the distance jogged by Jamie, we can write:
distance jogged by Anabel = 3/4(distance jogged by Jamie)
Using the given variable x for the distance jogged by Jamie, we can rewrite the equation as:
distance jogged by Anabel = 3/4x
And since the question is asking for an equation that best represents the situation, the correct answer is:
Cy = 3/4x
Therefore, Cy = 3/4x is the equation that best represents the situation where Jamie jogged x km and Anabel jogged 1/4 less than Jamie. The correct answer is A.
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Jocelyn is considering taking out one of the two following loans. loan h is a three-year loan with a principal of $5,650 and an interest rate of 12.24%, compounded monthly. loan i is a four-year loan with a principal of $6,830 and an interest rate of 10.97%, compounded monthly. which loan will have the smaller monthly payment, and how much smaller will it be? round all dollar values to the nearest cent. a. loan h's monthly payment will be $42.46 smaller than loan i's. b. loan h's monthly payment will be $140.79 smaller than loan i's. c. loan i's monthly payment will be $11.88 smaller than loan h's. d. loan i's monthly payment will be $26.98 smaller than loan h's.
Loan H's monthly payment will be $42.46 smaller than loan I's (rounded to the nearest cent). The correct option is a.
To determine which loan will have the smaller monthly payment, we need to calculate the monthly payments for both loans using the given information.
For loan H, the monthly interest rate is 12.24%/12 = 1.02%, and the number of payments is 3 years x 12 months/year = 36. Using the formula for the monthly payment on a loan with monthly compounding, we have:
P = (r(PV))/(1 - (1+r[tex])^{(-n)})[/tex]
where P is the monthly payment, r is the monthly interest rate, PV is the principal value of the loan, and n is the total number of payments.
Plugging in the values given for loan H, we get:
P = (0.0102 x $5,650) / (1 - (1+0.0102)⁻³⁶) = $186.25
For loan I, the monthly interest rate is 10.97%/12 = 0.9142%, and the number of payments is 4 years x 12 months/year = 48. Using the same formula as above, we have:
P = (0.009142 x $6,830) / (1 - (1+0.009142)⁻⁴⁸) = $227.04
Therefore, the monthly payment for loan H is $186.25 and the monthly payment for loan I is $227.04.
To find the difference between the monthly payments, we subtract the monthly payment for loan H from the monthly payment for loan I:
$227.04 - $186.25 = $40.79
Therefore, the answer is (a) loan H's monthly payment will be $42.46 smaller than loan I's (rounded to the nearest cent).
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What is the difference in credit score between those over the age of 55 and those between 18-24 years old?
According to recent studies, there is a notable difference in credit scores between those over the age of 55 and those between the ages of 18-24.
On average, individuals over the age of 55 tend to have higher credit scores than those in the 18-24 age range. This is primarily due to the fact that older individuals have had more time to establish and build their credit history, whereas younger individuals are just starting out and may not have had the opportunity to establish credit yet.
Additionally, older individuals tend to have more stable financial situations and may have less debt compared to younger individuals who may be dealing with student loans or other types of debt.
However, it's important to note that credit scores can vary greatly between individuals, regardless of age, and there are many factors that contribute to credit score, such as payment history, credit utilization, and length of credit history.
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Determine the missing length in each right triangle using the Pythagorean theorem. Round the answer to the nearest tenth, if necessary
The evaluated missing length in right triangle by using the Pythagorean theorem is 9 yards under the condition given the triangle is a right triangle.
The Pythagoras theorem projects that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides,
It is given to us that in a right triangle,
Hypotenuse = 15 yd
Perpendicular = 12 yd
Therefore, applying Pythagoras theorem;
Base² = 15² - 12²
Base² = 225 - 144
Base² = 81
Base = √81
Base = 9 yards
Hence, The missing length present in the right triangle by applying the Pythagorean theorem is,
9 yards
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The complete question is
Determine the missing length in each right triangle using the Pythagorean theorem. Round the answer to the nearest tenth, if necessary
A binomial experiment has the given number of trials n and the given success probability p.
n=10, p=0. 2
(a) Determine the probability P (2 or fewer). Round the answer to at least three decimal places.
P(2 or fewer)
The probability P(2 or fewer) is 0.678.
To find the probability of 2 or fewer successes in a binomial experiment with 10 trials and a success probability of 0.2, we can use the binomial probability formula:
P(2 or fewer) = P(0) + P(1) + P(2)
where P(0), P(1), and P(2) represent the probabilities of getting 0, 1, or 2 successes, respectively.
P(0) = (10 choose 0) * 0.2^0 * 0.8^10 = 0.1074
P(1) = (10 choose 1) * 0.2^1 * 0.8^9 = 0.2684
P(2) = (10 choose 2) * 0.2^2 * 0.8^8 = 0.3020
Therefore,
P(2 or fewer) = 0.1074 + 0.2684 + 0.3020 = 0.6778
Rounded to at least three decimal places, the probability P(2 or fewer) is 0.678.
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Can you find continuous function & so that when an = f(n) we have SIGMA an = ∫ f(x)dx
[tex]SIGMA an = 1 + 2 + 3 + ... + n = n(n+1)/2 = ∫_1^n f(x)dx = ∫ f(x)dx[/tex]
f(x) = x is indeed a continuous function that satisfies the given condition.
Yes, we can find a continuous function f(x) such that when an = f(n), we have SIGMA an = ∫ f(x)dx.
One such function is f(x) = x.
To see why this works, let's consider a few terms of the series SIGMA an.
When n = 1, we have a1 = f(1) = 1, so the series starts with 1.
When n = 2, we have a2 = f(2) = 2, so the series becomes 1 + 2. When n = 3, we have a3 = f(3) = 3, so the series
becomes 1 + 2 + 3. And so on.
Notice that this series is just the sum of the first n positive integers, which we know is equal to n(n+1)/2.
But if we take the derivative of f(x) = x, we get f'(x) = 1, which means that the integral of f(x) from 1 to n is just n.
So we have:
[tex]∫ f(x)dx = ∫ xdx = 1/2 x^2 + C[/tex]
[tex]∫_1^n f(x)dx = (1/2 n^2 + C) - (1/2 (1)^2 + C) = 1/2 n^2 - 1/2[/tex]
And therefore:
[tex]SIGMA an = 1 + 2 + 3 + ... + n = n(n+1)/2 = ∫_1^n f(x)dx = ∫ f(x)dx[/tex]
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Height of 10th grade boys is normally distributed with a mean of 63. 5 in. And a standard deviation of 2. 9 in. The area greater than the z-score is the probability that a randomly selected 14-year old boy exceeds 70 in. What is the probability that a randomly selected 10th grade boy exceeds 70 in. ?Use your standard normal table.
Heights for 16-year-old boys are normally distributed with a mean of 68. 3 in. And a standard deviation of 2. 9 in. Find the z-score associated with the 96th percentile. Find the height of a 16-year-old boy in the 96th percentile. State your answer to the nearest inch
The probability that a randomly selected 10th grade boy exceeds 70 in is approximately 0.0127 or 1.27%.
The height of a 16-year-old boy in the 96th percentile is approximately 73 inches.
For the first question, we need to find the z-score for a height of 70 inches using the formula:
z = (x - μ) / σ
where x is the height of 70 inches, μ is the mean of 63.5 inches, and σ is the standard deviation of 2.9 inches.
z = (70 - 63.5) / 2.9 = 2.241
Using a standard normal table, we can find the area to the right of this z-score, which represents the probability that a randomly selected 10th grade boy exceeds 70 inches. The area to the right of 2.24 is 0.0127. Therefore, the probability is approximately 0.0127 or 1.27%.
For the second question, we need to find the z-score associated with the 96th percentile using a standard normal table. The 96th percentile is the point below which 96% of the data falls and above which 4% of the data falls. This corresponds to a z-score of approximately 1.75.
To find the height of a 16-year-old boy in the 96th percentile, we can use the formula:
x = μ + z * σ
where x is the height we want to find, μ is the mean of 68.3 inches, σ is the standard deviation of 2.9 inches, and z is the z-score we just found.
x = 68.3 + 1.75 * 2.9 = 73.28
Therefore, the height of a 16-year-old boy in the 96th percentile is approximately 73 inches.
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Misty needs 216 square inches of metal
to make a yield sign. If the height of the sign is 18 inches,
how long is the top edge of the sign?
24 inches
12 inches
198 inches
22 inches
pls give explanation not just the awnser
The answer is 96 inches, which is equivalent to 8 feet.
Find out the length of the top edge of the yeild sign ?To find the length of the top edge of the yield sign, we need to use the formula for the area of a trapezoid:
A = (b1 + b2)h/2
where A is the area of the trapezoid, h is the height, b1, and b2 are the lengths of the two parallel bases of the trapezoid.
In this case, we are given the area of the sign (216 square inches) and the height (18 inches), but we don't know the length of either base. However, we do know that the shape of a yield sign is that of a regular octagon, which means it has eight equal sides and eight equal angles.
If we draw a line from the top of the sign to the midpoint of one of the sides, we will form a right triangle with the height of the sign as one leg, half the length of the top edge as the other leg, and the length of one of the sides as the hypotenuse. We can use the Pythagorean theorem to find the length of the side:
a^2 + b^2 = c^2
where a is the height of the sign (18 inches), b is half the length of the top edge (what we are trying to find), and c is the length of one of the sides.
Since the sign has eight sides, we can divide the total area by 8 to get the area of one of the eight triangles that make up the sign. We can then use this area to find the length of one of the sides:
A = (bh)/2
216 sq. in. = (bh)/2
432 sq. in. = bh
Since the sign is a regular octagon, each of the eight triangles has the same base (the side of the octagon) and height (half the length of the top edge), so we can use this equation to solve for b:
432 sq. in. = b(18 in.)/2
b = 48 in.
Now we know that half the length of the top edge is 48 inches, so the full length of the top edge is:
2(48 in.) = 96 in.
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The value of a professional basketball player's autograph rose 40% in the last year. It is now worth $350.00. What was it worth a year ago? A. $260.00 B. $250.00 C. $270.00 D. $230.00
Answer: B
Step-by-step explanation: 250 x 140% = 350
If P (6, 1), find the image
of P under the following rotation.
180° counterclockwise about the
origin
([?],
Enter the number that belongs in
the green box,
The image of point P (6, 1) under a 180° counterclockwise rotation about the origin is (-6, -1).
To find the image of point P (6, 1) under a 180° counterclockwise rotation about the origin, we can use the rotation formula for 2D coordinates.
The formula for rotating a point (x, y) counterclockwise by θ degrees about the origin is:
x' = x [tex]\times[/tex] cos(θ) - y [tex]\times[/tex] sin(θ)
y' = x [tex]\times[/tex] sin(θ) + y [tex]\times[/tex] cos(θ)
In this case, θ is 180°.
So, let's substitute the values of x and y from point P into the rotation formula:
x' = 6 [tex]\times[/tex] cos(180°) - 1 [tex]\times[/tex] sin(180°)
y' = 6 [tex]\times[/tex] sin(180°) + 1 [tex]\times[/tex] cos(180°)
Now, let's simplify these equations using the trigonometric values for 180°:
[tex]x' = 6 \times (-1) - 1 \times 0[/tex]
[tex]y' = 6 \times 0 + 1 \times (-1)[/tex]
Simplifying further:
x' = -6
y' = -1
Therefore, the image of point P (6, 1) under a 180° counterclockwise rotation about the origin is (-6, -1).
Please note that the rotation formula assumes angles are measured in radians.
However, for simplicity, we used degrees in this explanation.
The trigonometric functions (cos and sin) can be evaluated in radians using their corresponding values for 180°.
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the length of a shadow of building is 12m. The distance from the top of the building to the tip of shadow is 20m. Find the height of the building. if necessary, round your answer to the nearest tenth.
The height of the building is 16 meters.
What is right triangle?
A right triangle is a type of triangle that has one of its angles measuring 90 degrees (π/2 radians). The side which is opposite to the right angle is the hypotenuse, while the other two sides are called the legs.
We can solve this problem using the Pythagorean theorem, which relates the sides of a right triangle. Let h be the height of the building. Then we can draw a right triangle with one leg of length h and the other leg of length 12m, representing the height and length of the shadow, respectively. The hypotenuse of this triangle is the distance from the top of the building to the tip of the shadow, which is 20m. So we have:
h² + 12² = 20²
Simplifying and solving for h, we get:
h² = 20² - 12²
h² = 256
h = sqrt(256)
h = 16
Therefore, the height of the building is 16 meters.
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2. Assume that a cell is a sphere with radius 10 or 0. 001 centimeter, and that a cell's density is 1. 1 grams per cubic centimeter. A. Koalas weigh 6 kilograms on average. How many cells are in the average koala?
The number of cells found in an average Koala is 1.30 x 10¹², under the condition that a cell is a sphere with radius 10 or 0. 001 centimeter.
Then the volume of a sphere with radius 10 cm is considered to be 4/3π(10)³ cubic cm that is approximately 4,188.79 cubic cm.
The evaluated volume of a sphere with radius 0.001 cm is 4/3π(0.001)³ cubic cm that is approximately 0.00000419 cubic cm.
Then the evaluated mass of a single cell is found by applying the formula
mass = density x volume
In case of larger cell, the mass will be
mass = 1.1 g/cm³ x 4,188.79 cubic cm
= 4,607.67 grams
In case of smaller cell, the mass will be
mass = 1.1 g/cm³ x 0.00000419 cubic cm
= 0.00000461 grams
As koalas measure an average of 6 kilograms or 6,000 grams², we can evaluate the number of cells in an average koala using division of the weight of the koala by the mass of a single cell
In case of larger cells
number of cells = weight of koala / mass of single cell
number of cells = 6,000 grams / 4,607.67 grams
≈ 1.30 x 10⁶ cells
For smaller cells:
number of cells = weight of koala / mass of single cell
number of cells = 6,000 grams / 0.00000461 grams
≈ 1.30 x 10¹² cells
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⁶
Express tan H as a fraction in simplest terms.
F
H
28
7
G
Answer:
4 or [tex]\frac{4}{1}[/tex]
Step-by-step explanation:
To solve this we need to remember SOH-CAH-TOA. With SOH being Sine, CAH being Cosine, and TOA being Tangent. In the last term (TOA), the O means opposite and the A is adjacent. This means the segment opposite of angle H you have to divide that by the segment adjacent to H.
In this case, the opposite is 28 and the adjacent is 7. So we have to do [tex]\frac{28}{7}[/tex]. This is tan(H). Now we have to simplify this. Now we get our tangent of H to be [tex]\frac{4}{1}[/tex] or 4. So 4/1 or 4 is our answer
QUESTION IN PHOTO I MARK BRAINLIEST
The value of measure of arc QI is,
⇒ m QI = 94°
We have to given that;
⇒ m YS = 180°
⇒ m ∠QBI = 137°
Hence, We can formulate;
⇒ m ∠QBI = 1/2 (m YS + m QI)
⇒ 137 = 1/2 (180 + m QI)
⇒ 274 = 180 + m QI
⇒ m QI = 274 - 180
⇒ m QI = 94°
Thus, The value of measure of arc QI is,
⇒ m QI = 94°
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Choose the function table that matches the given rule. Output = Input – 3 (1 point) Input Output –2 –5 1 –2 6 3 Input Output 2 –1 –2 3 0 –6 Input Output 5 2 2 –5 0 9 Input Output 6 3 –6 –3 5 0
The function table that matches the given rule output = input - 3 is
Input = -2, 1, 6 and output = -5, -2, 3
A) first function table
Output = Input - 3
Value of input:- -2
Putting the value of the input
Output = -2 -3
The value of output we get
Output = -5
Value of input:- 1
Putting the value of the input
Output = 1 -3
The value of output we get
Output = -2
Value of input:- 6
Putting the value of the input
Output = 6 -3
The value of output we get
Output = 3
Hence function table A is correct match
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HELP ON MATH ASAPPP I NEED TO PASS
I think it might be C
solve the initial value problem. f '(x) = 5 x2 − x2 5 , f(1) = 0
We can start by integrating both sides of the differential equation to obtain:
∫f '(x) dx = ∫([tex]5x^2 - x^2/5[/tex]) dx
f(x) = (5/3)[tex]x^3[/tex] - (1/15) [tex]x^5[/tex] + C
where C is the constant of integration.
To find the value of C, we can use the initial condition f(1) = 0:
f(1) = (5/3)[tex](1)^3[/tex] - (1/15) [tex](1)^5[/tex] + C = 0
Simplifying this equation gives:
C = (1/15) - (5/3)
C = -2/9
Therefore, the solution to the initial value problem f '(x) = 5[tex]x^2[/tex] − [tex]x^2[/tex]/5 , f(1) = 0 is:
f(x) = (5/3) [tex]x^3[/tex] - (1/15) [tex]x^5[/tex] - (2/9)
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Mara putting together pieces of string for an art project. She has a piece of string that is 30 inches, a piece that is 22 inches, and a piece that is 20 inches. Once she puts together the pieces, what will be the total length in feet?
Step 1 - What will be the total length of the string in inches?
Step 2 - How many feet is this equal to? (Inches -> Feet)
2. A water jug holds 300 ounces of water. The football team has 2 water jugs. How many cups of water will both water jugs hold altogether?
Step 1 - How many ounces do both water jugs hold?
Step 2 - How many cups is this equal to? (Ounces -> Cups
Please help me if you help me and explain all the answer I will give you brainiest!!!
The total length of the string in feet is 6 feet, and the combined capacity of both water jugs in cups is 75 cups.
What is the total length of the string, and how many cups of water can the two water jugs hold altogether?Step 1: To find the total length of the string in inches, Mara needs to add the lengths of the three pieces of string:
30 inches + 22 inches + 20 inches = 72 inches
So the total length of the string in inches is 72 inches.
Step 2: To convert inches to feet, we need to divide the number of inches by 12 (since there are 12 inches in a foot):
72 inches ÷ 12 = 6 feet
Therefore, once Mara puts together the three pieces of string, the total length will be 6 feet.
Step 1: To find out how many ounces of water both water jugs hold altogether, we need to add the capacity of the two jugs:
300 ounces + 300 ounces = 600 ounces
So both water jugs together can hold 600 ounces of water.
Step 2: To convert ounces to cups, we need to divide the number of ounces by 8 (since there are 8 ounces in a cup):
600 ounces ÷ 8 = 75 cups
Therefore, both water jugs together can hold 75 cups of water.
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A function f(x) = 3x^² dominates g(x) = x^2. O True O False
The given statement "A function f(x) = 3x² dominates g(x) = x²" is True as it grows faster than the other function.
To show that f(x) dominates g(x), we need to prove that there exists a constant c such that f(x) > c * g(x) for all x > 0.
Let's consider c = 3. Then, for all x > 0, we have:
[tex]f(x) = 3x^2 > 3x^2/1 = 3x^2 * 1 > x^2 * 3 = g(x) * 3[/tex]
A function dominates another function when it grows faster than the other function. In this case, f(x) = 3x² and g(x) = x². Since f(x) has a higher coefficient (3) than g(x) (1) for the x² term, it grows faster than g(x) as x increases.
Therefore, we have shown that f(x) > 3g(x) for all x > 0, which means that f(x) dominates g(x).
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Read and imagine what is happening in this problem. Hannah mixed 6. 83 lb of pretzels with 3. 57 lb of popcorn. After filling up 6 bags that were the same size with the mixture, she had 0. 35 lb left.
Hannah mixed 6.83 lb of pretzels with 3.57 lb of popcorn to make 10.4 lb of mixture. She then filled up 6 bags with an average of 1.68 lb of mixture per bag, leaving her with 0.35 lb of mixture left over.
In this problem, Hannah mixed 6.83 lb of pretzels with 3.57 lb of popcorn. This means that she had a total of 10.4 lb of mixture. She then filled up 6 bags that were the same size with the mixture, which means that each bag had approximately 1.73 lb of mixture (10.4 lb / 6 bags).
After filling up all 6 bags, Hannah had 0.35 lb of the mixture left over. This means that she used a total of 10.05 lb of mixture for the bags (10.4 lb - 0.35 lb).
To find out how much mixture was used per bag, we can divide the total amount of mixture used (10.05 lb) by the number of bags (6). This gives us an average of approximately 1.68 lb per bag.
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Rate of Change of Production Costs The daily total cost C(x) incurred by Trappee and Sons for producing x cases of TexaPep hot sauce is given by the following function. C(x) = 0.000002x^3 + 4x + 300 Calculate the following for h = 1, 0.1, 0.01, 0.001, and 0.0001. (Round your answers to four decimal places.)
C(100+h) – C(100)/h
The instantaneous rate of change of cost with respect to x when x = 100 is 4.
We can begin by calculating C(100+h) and C(100):
C(100+h) = 0.000002(100+h)^3 + 4(100+h) + 300
C(100+h) = 0.000002(1,000,000 + 300h^2 + 30h^2 + h^3) + 400 + 4h + 300
C(100+h) = 0.000002h^3 + 0.0006h^2 + 4h + 700
C(100) = 0.000002(100)^3 + 4(100) + 300
C(100) = 2 + 400 + 300
C(100) = 702
Therefore,
C(100+h) - C(100) = (0.000002h^3 + 0.0006h^2 + 4h + 700) - 702
C(100+h) - C(100) = 0.000002h^3 + 0.0006h^2 + 4h - 2
Now, we can find the rate of change of cost with respect to x by dividing this expression by h and taking the limit as h approaches 0:
(C(100+h) - C(100))/h = (0.000002h^3 + 0.0006h^2 + 4h - 2)/h
(C(100+h) - C(100))/h = 0.000002h^2 + 0.0006h + 4 - (2/h)
As h approaches 0, the term 2/h approaches infinity, which means the rate of change of cost with respect to x is undefined. However, we can calculate the limit of the expression as h approaches 0 from the left and from the right to see if it has a finite value:
limit (h->0+) ((C(100+h) - C(100))/h) = 4
limit (h->0-) ((C(100+h) - C(100))/h) = 4
Since the left and right limits are equal, the overall limit exists and equals 4. Therefore, the instantaneous rate of change of cost with respect to x when x = 100 is 4.
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Question 2(Multiple Choice Worth 4 points) (05.03 MC) Solve the system of equations using elimination. 2x + 3y = -8 3x+y=2 O(-4,0) (2,-4) (5.-6) (8-8)
Answer:
(2,-4)
Step-by-step explanation:
In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.
2x+3y=−8,3x+y=2
To make 2x and 3x equal, multiply all terms on each side of the first equation by 3 and all terms on each side of the second by 2. Then simplify
6x+9y=−24,6x+2y=4
Add 6x to −6x. Terms 6x and −6x cancel out, leaving an equation with only one variable that can be solved, add 9y to −2y, add −24 to −4, and divide both sides by 7.
y=−4
Substitute −4 for y in 3x+y=2. Because the resulting equation contains only one variable, you can solve for x directly. Add 4 to both sides of the equation and divide both sides by 3.
x=2
By comparison a car with one of the worst car depreciations is a BMW 7 series. In 5 years it losses 72.6% of its value. If brand new the car costs $86,000, how much will the car be worth in 8 years?
The value of the car after 8 years is given as follows:
$10,836.76.
How to define an exponential function?An exponential function has the definition presented as follows:
[tex]y = ab^\frac{x}{n}[/tex]
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.n is the time needed for the rate of change.The parameter values for this problem are given as follows:
a = 86000, n = 5, b = 1 - 0.726 = 0.274.
Hence the function for the value of the car after x years is given as follows:
[tex]y = ab^\frac{x}{n}[/tex]
[tex]y = 86000(0.274)^\frac{x}{5}[/tex]
The value of the car after 8 years is then given as follows:
[tex]y = 86000(0.274)^\frac{8}{5}[/tex]
y = $10,836.76.
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Amanda wants to add 6732 and 4975 how can Amanda use mental math to add the numbers is Amanda answer correct explain
she can add each number one by one , and whenever she needs to carry numbers over. She can add them to the already existing numbers. she cna check with a calculator
Ao
Del
5. An archway has vertical sides 10 feet high. The top of an archway can
be modeled by the quadratic function f(x) = -0. 5x2 + 10 where x is the
horizontal distance, in feet, along the archway. How far apart are the
walls of the archway? Round your answer to the nearest tenth of a foot.
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
293
The walls of the archway are approximately 8.9 apart.
Find out the distance between the walls of the archway?To find the distance between the walls of the archway, we need to find the horizontal distance where the function f(x) intersects the x-axis. This is because the archway's walls are vertical, and their distance apart is the same as the horizontal distance between the points where the archway meets them.
To find the x-intercepts of the function f(x) = -0.5x^2 + 10, we need to set f(x) = 0 and solve for x:
0 = -0.5x^2 + 10
0.5x^2 = 10
x^2 = 20
x = ±√20
Since the archway is a physical object, we can discard the negative value for x, which means the archway meets the walls at x = √20 feet.
To find the distance between the walls of the archway, we can double this value:
2√20 ≈ 8.94
Then it's concluded that the walls of the archway are approximately 8.9 feet apart.
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There is a line through the origin that divides the region bounded by the parabola y = 2x − 7 x^2 and the x-axis into two regions with equal area. What is the slope of that line?
The slope of the line that divides the region into two equal parts is 8/7.
How to find the slope of that line?We begin by finding the x-coordinates of the points where the parabola intersects the x-axis. Setting y = 0, we get:
[tex]2x - 7x^2 = 0[/tex]
x(2 − 7x) = 0
x = 0 or x = 2/7
Thus, the parabola intersects the x-axis at x = 0 and x = 2/7.
We want to find the slope of the line through the origin that divides the region bounded by the parabola and the x-axis into two regions with equal area.
Let's call this slope m.
We know that the area under the parabola from x = 0 to x = 2/7 is:
A = ∫[0,2/7] (2x − 7[tex]x^2[/tex]) dx
A = [[tex]x^2[/tex] − (7/3)[tex]x^3[/tex]] from 0 to 2/7
A = (4/21)
Since we want the line to divide this area into two equal parts, the area to the left of the line must be (2/21).
Let's call the x-intercept of the line h. Then the equation of the line is y = mx, and the area to the left of the line is:
(1/2)h(mx) = (1/2)mhx
We want this to be equal to (2/21), so we can solve for h:
(1/2)mhx = (2/21)
h = (4/21m)
The x-coordinate of the point of intersection of the line and the parabola is given by:
2x − 7[tex]x^2[/tex] = mx
Simplifying, we get:
[tex]7x^2 - (2 + m)x = 0[/tex]
Using the quadratic formula, we get:
[tex]x = [(2 + m) \pm \sqrt((2 + m)^2 - 4(7)(0))]/(2(7))[/tex]
x = [(2 + m) ± √(4 + 4m + [tex]m^2[/tex])]/14
x = [(2 + m) ± (2 + m)]/14
x = 1/7 or x = −(2/7)
Since we want the line to pass through the origin, we must choose x = 1/7, and we can solve for m:
[tex]2(1/7) - 7(1/7)^2 = m(1/7)[/tex]
m = 8/7
Therefore, the slope of the line that divides the region into two equal parts is 8/7.
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A pet boarder keeps a dog-to-cat ratio of 5:2. If the boarder has room for 98 animals then how many of them can be dogs
The pet boarder can accommodate 70 dogs.
To determine the number of dogsLet's calculate how many dogs and cats the pet boarding facility can hold using the ratio of dogs to cats, which is 5:2.
First, we can figure out how many parts there are in the ratio: 5 + 2 = 7.
This indicates that there are 7 equal components in the ratio, 5 of which are dogs and 2 of which are cats.
We need to multiply the result by the number of dog components (5) after dividing the total number of parts (7) into the 98 available locations to get the number of dogs:
Number of dogs = (5 / 7) * 98
Number of dogs = 70
Therefore, the pet boarder can accommodate 70 dogs.
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SOMEONE HELP PLS, giving brainlist to anyone who answers!!!
Answer: $532,000
Step-by-step explanation:
If the company is making $140,000 and they get 20% each year, we just multiply it by 20%, or 0.20, and get $28,000. So, we would multiply that by 14, the years the company operated, and then add it to the original $140,000.
28,000 x 14 = 392,000
392,000 + 140,000 = 532,000
So, over the course of 14 years, the company made a profit of $532,000.