A truck enters a stretch of road that drops 4 meters
in elevation for every 100 meters along the length of
the road. The road is at 1,300 meters elevation where
the truck entered, and the truck is traveling at
16 meters per second along the road. What is the
elevation of the road, in meters, at the point where
the truck passes t seconds after entering the road?
Answers
Answer:
The elevation would lower in total 52 feet.
Step-by-step explanation:
Answer:
it would be 52 feet
Step-By-Step explanation
Related Questions
On a coordinate plane, 2 right triangles are shown. The first triangle has points A (negative 1, 3), B (negative 1, 1), C (3, 1). The second triangle has points A prime (2, negative 2), B prime (2, negative 4), C prime (6, negative 4). Which statements are true about triangle ABC and its translated image, A'B'C'? Select two options. The rule for the translation can be written as T–5, 3(x, y). The rule for the translation can be written as T3, –5(x, y). The rule for the translation can be written as (x, y) → (x + 3, y – 3). The rule for the translation can be written as (x, y) → (x – 3, y – 3). Triangle ABC has been translated 3 units to the right and 5 units down.
Answers
Answer:
B and EStep-by-step explanation:
Given
ΔABC ⇒ A(- 1, 3), B(- 1, 1), C(3, 1)ΔA'B'C' ⇒ A'(2, - 2), B'(2, - 4), C'(6, - 4)Comparing the coordinates of the corresponding vertices, we see the difference:
x → x + 3, y → y - 5It means the ΔABC has been translated 3 units right and 5 units down
Correct answer choices are B and E
Answer:
b,e
Step-by-step explanation:
just did it
Find the solution for a 2x2 matrix A:
[4 4
0 1] to the nth power = [ ]
Answers
Answer:
Step-by-step explanation:
Answer:
A^n = [4^n 4^n
0 1]
Step-by-step explanation:
To find the solution for the 2x2 matrix A:
[4 4
0 1] to the nth power = [ ]
We can use matrix multiplication to raise A to the nth power. Let's start with n = 1:
A^1 = [4 4
0 1]
Now, let's solve for A^2 by multiplying A^1 by A:
A^2 = A x A^1
= [4 4 [4 4
0 1] 0 1]
= [16 16
0 1]
Next, let's solve for A^3:
A^3 = A x A^2
= [4 4 [16 16
0 1] 0 1]
= [64 64
0 1]
We can see a pattern emerging:
A^1 = [4 4
0 1]
A^2 = [16 16
0 1]
A^3 = [64 64
0 1]
We can generalize this pattern as follows:
A^n = [4^n 4^n
0 1]
Therefore, the solution for the 2x2 matrix A raised to the nth power is:
A^n = [4^n 4^n
0 1]
Make a frequency table using five classes.
class 31-38 39-46 47-54 55-62 63-70
f
11
24
15
7
3
Then estimate the mean and sample standard deviation using the frequency table. (Round s to two decimal places.)
Answers
Answer: C
Step-by-step explanation:
(p^2n^1/2)^0
√ p^5n^4 equivalent to p^18n^6 √p?
Answers
The two expressions are not equivalent.
To simplify the expression (p^2n^1/2)^0 √ p^5n^4, we first need to understand the properties of exponents and radicals.
Recall that any number raised to the power of zero is equal to 1, so (p^2n^1/2)^0 = 1.
Next, we can simplify the radical term by multiplying the exponents inside and outside the radical:
√ p^5n^4 =
(p^5n^4)^(1/2)
= p^(5/2)n^(4/2)
= p^(5/2)n^2
Combining this result with the previous step, we have:
(p^2n^1/2)^0 √ p^5n^4
= 1 * p^(5/2)n^2
= p^(5/2)n^2
This is not equivalent to p^18n^6 √p. In fact, p^(5/2)n^2 cannot be simplified any further without additional information about the expression. ,
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An airline charges the following baggage fees: $25 for the first bag and $35 for the second. Suppose 54% of passengers have no checked luggage, 34% have only one piece of checked luggage and 12% have two pieces. We suppose a negligible portion of people check more than two bags.a) The average baggage-related revenue per passenger is: $(please round to the nearest cent)b) The standard deviation of baggage-related revenue is: $(please round to the nearest cent)c) About how much revenue should the airline expect for a flight of 120 passengers?(please round to the nearest dollar)
Answers
Answer:
(a) The average baggage-related revenue per passenger is $15.70.
(b) The standard deviation of baggage-related revenue is $19.95.
(c) The expected revenue for 120 passengers is $1,884.
Step-by-step explanation:
Let the random variable X represent the baggage-related revenue per passenger.
It is provided that the baggage fees is $25 for the first bag and $35 for the second.
The probability model is:
X : 0 25 60
P (X) : 0.54 0.34 0.12
(a)
Compute the average baggage-related revenue per passenger as follows:
\(E(X)=\sum {X\times P (X)}\)
\(=(0\times 0.54)+(25\times 0.34)+(60\times 0.12)\\\\=0+8.50+7.20\\\\=15.70\)
Thus, the average baggage-related revenue per passenger is $15.70.
(b)
Compute the standard deviation of baggage-related revenue as follows:
\(E (X^{2})=\sum X^{2}\times P(X)}\\\\=(0^{2}\times 0.54)+(25^{2}\times 0.34)+(60^{2}\times 0.12)\\\\=0+212.50+432\\\\=644.5\\\)
\(SD(X)=\sqrt{E(X^{2})-(E(X))^{2}}\)
\(=\sqrt{644.5-(15.7)^{2}}\\\\=19.950188\\\\\approx 19.95\)
Thus, the standard deviation of baggage-related revenue is $19.95.
(c)
Compute the expected revenue for 120 passengers as follows:
\(E(R)=n\times E(X)\)
\(=120\times 15.7\\\\=1884\)
Thus, the expected revenue for 120 passengers is $1,884.
find the area of the circle
Answers
The area of the circle based on the information illustrated is C. 28.26ft².
What will the area be?It should be noted that the area of a circle is given as:
= πr²
In this case, the radius is 3ft.
Therefore, the area will be:
= πr²
= 3.14 × 3²
= 3.14 × 9
= 28.26 ft²
In conclusion, the area of the circle is 28.26ft².
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Decimal’s I can’t understand it
Answers
Answer:
In Mathematics, the numbers can be classified into different types, namely real numbers, natural numbers, whole numbers, rational numbers, and so on. Decimal numbers are among them
Types of Decimal Numbers
Decimal Numbers may be of different kinds, namely
Recurring Decimal Numbers (Repeating or Non-Terminating Decimals)
Example-
3.125125 (Finite)
3.121212121212….. (Infinite)
Non-Recurring Decimal Numbers (Non Repeating or Terminating Decimals):
Example:
3.2376 (Finite)
3.137654….(Infinite)
Decimal Fraction- It represents the fraction whose denominator in powers of ten.
Example:
81.75 = 8175/100
32.425 = 32425/1000
Converting the Decimal Number into Decimal Fraction:
For the decimal point place “1” in the denominator and remove the decimal point.
“1” is followed by a number of zeros equal to the number of digits following the decimal point.
For Example:
8 1 . 7 5
↓ ↓ ↓
1 0 0
81.75 = 8175/100
8 represents the power of 101 that is the tenths position.
1 represents the power of 100 that is the units position.
7 represents the power of 10-1 that is the one-tenths position.
5 represents the power of 10-2 that is the one-hundredths position.
So that is how each digit is represented by a particular power of 10 in the decimal number.
DEF is a right triangle. If FE=8 and DE=6, find DF.
Answers
1) Since this is a right triangle, and no information about angles has been given. It is safe to say that we can use the Pythagorean Relation to figure out the length of that hypotenuse DF
2) So we can write it down:
\(\begin{gathered} a^2=b^2+c^2 \\ DF^2=DE^2+EF^2 \\ DF^2=6^2+8^2 \\ DF^2=36+64 \\ DF^2=100 \\ \sqrt[]{DF^2}=\sqrt[]{100} \\ DF=-10,10 \end{gathered}\)Since there are no negative lengths, we can state that the answer is:
\(DF=10\)Noel bought 4 T-shirts and 2 pairs of pants for $92. The cost of each pair of pants is $22.
If all the T-shirts cost the same amount, the cost of each T-shirt is $
Answers
Answer:
each shirt costs $12.
Step-by-step explanation:
Answer: T shirt cost 12 dollars
Step-by-step explanation: The equation is 4x+44=92. Subtract 44 from both sides it becomes 4x=48. Divide it by 4 on both sides and the answer is x=12.
Levy is painting a miniature model of a World War II tank. His figure uses a 1:72 scale and is 22.5 cm
long. How many centimeters long was the actual tank?
cm
Answers
Levy is painting a miniature model of a World War II tank. His figure uses a 1:72 scale and is 22.5 cm long. The actual tank is 1620 cm long.
To determine the length of the actual tank, we need to scale up the length of the miniature model using the given scale of 1:72.
Let's denote the length of the actual tank as "x".
According to the scale, 1 cm on the miniature model represents 72 cm on the actual tank.
So, we can set up the following proportion:
1 cm (miniature model) / 72 cm (actual tank) = 22.5 cm (miniature model) / x cm (actual tank)
Cross-multiplying and solving for x, we get:
x = (72 cm * 22.5 cm) / 1 cmx = 1620 cm
The actual tank is 1620 cm long.
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Use the pair of functions to find f(g(x)) and g(f(x)). Simplify your answers.
f(x)= 1= ² + 4
X-4
Answers
To find f(g(x)), we need to substitute g(x) into the function f(x). Given that g(x) = x - 4, we substitute it into f(x) as follows:
\(f(g(x)) = f(x - 4) = (x - 4)^2 + 4\)
To simplify this expression, we can expand the square:
\(f(g(x)) = (x - 4)(x - 4) + 4\\ = x^2 - 8x + 16 + 4\\ = x^2 - 8x + 20\)
Therefore, f(g(x)) simplifies to\(x^2 - 8x + 20.\)
Next, let's find g(f(x)). We substitute f(x) into the function g(x):
\(g(f(x)) = g(1/x^2 + 4) = 1/x^2 + 4 - 4\\ = 1/x^2\)
Hence, g(f(x)) simplifies to 1/x^2.
In summary, f(g(x)) simplifies to\(x^2 - 8x + 20\), and g(f(x)) simplifies to 1/x^2.
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If a firm has a production quota of 400=5x1^2+8x1x2+15x2^2, what combination of good x1 and x2 should the firm produce to minimize cost of C=x1^2+x2^2
Answers
The firm should produce good x₁ = 4 and x₂ = 8 to minimize cost of C = x₁² + x₂² .
What is Lagrange multipliers ?
Lagrange multipliers is a method used in optimization problems to find the maximum or minimum value of a function subject to one or more constraints. The method involves introducing a Lagrange multiplier, which is a scalar variable, to the objective function and the constraint(s). This forms the Lagrangian function, which is then optimized with respect to the original variables and the Lagrange multiplier.
To minimize the cost C = x₁² + x₂²
We can use the method of Lagrange multipliers to solve this problem. Let's define the Lagrangian function L as:
L(x₁, x₂, λ) = x₁²+ x₂² + λ(400 - 5x₁²- 8x₁x₂ - 15x₂²)
Taking partial derivatives of L with respect to x₁, x₂, and λ, we get:
∂L/∂x₁ = 2x₁ - 10λx₁ - 8λx₂ = 0
∂L/∂x₂ = 2x₂ - 30λx₂ - 8λx₁ = 0
∂L/∂λ = 400 - 5x₁² - 8x₁x₂ - 15x₂² = 0
Solving these equations simultaneously, we get:
x₁ = 4
x₂ = 8
λ = 1/20
Hence, the firm should produce a combination of x₁ = 4 and x₂ = 8 to minimize the cost of C = x₁² + x₂² while satisfying the production quota of 400.
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Help me thank you if you help
Answers
p = 48
Answer:
p = 48
Step-by-step explanation:
Step 1: Cross-multiply.
\(6 * p = 96 * 3\) \(6p = 288\)Step 2: Divide both sides by 6.
\(\frac{6p}{6} = \frac{288}{6}\) \(p = 48\)Therefore, p = 48!
Choose all options that apply. Which of the following are equal to 20%? | a) .25 b) 1/5 Oc) 1/10 d) .20
Answers
Answer:
b and d
Step-by-step explanation:
b because 1/5=20 out 100% and d because 20. and go to the left 2 spaces which I feel like you have 2 answers
Answer:
b, d
Step-by-step explanation:
0.25 x 100 = 25%
1/5 = 0.20 = 20%
1/10 = 0.10 = 10%
0.20 x 100 = 20%
the set of lowercase words of length 8 in which each distinct letter appears exactly twice (e.g., approora, yetiteyi, tunantau).
Answers
There are 12 lowercase words of length 8 in which each distinct letter appears exactly twice.
What are the Lowercase Words?To form a lowercase word of length 8 in which each distinct letter appears exactly twice, we can choose 4 distinct letters from the English alphabet and then arrange them in pairs in the word. The number of ways to choose 4 distinct letters from 26 is:
C(26, 4) = 26! / (4! * 22!) = 14,950
Once we have chosen 4 distinct letters, we can arrange them in pairs in the word in the following way:
Choose the first pair: we can choose any of the 4 letters, so there are 4 options.Choose the second pair: we can choose any of the remaining 3 letters, so there are 3 options.Arrange the pairs: there is only one way to arrange the pairs.Therefore, the total number of such words is:
4 * 3 * 1 = 12
Thus, there are 12 lowercase words of length 8 in which each distinct letter appears exactly twice. Here are all the possible words:
aabbccddaabbddccaaccbbddaaccddbbaaddbbccaaddccbbbbaaccddbbaaddccbbcc aaddbbdd aaccccdd aabbddcc aabbLearn more about lowercase words here: https://brainly.com/question/16397886
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Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.)
A). (tan(x) − 4)(9 sin^2(x) − 1) = 0
B). 3 sin(2x) − 4 sin(x) = 0
Answers
Answer:
Step-by-step explanation:
A)\((tanx-4)(9sin^2x-1)=0\\\\\\\)
\(9sin^2x-1=0\\\\sin^2x=\frac{1}{9} sinx=\frac{1}{3}\) or \(sinx=\frac{-1}{3}\)
OR \(tanx=4\\\)
B)
\(3sin2x=3.2.sinx.cosx\\\\6.sinx.cosx-4.sinx= 2sinx.(3cosx-2)=0\\\\3.cosx=2 cosx=\frac{2}{3}\)
Jessica plans to watch 3 movies each month. Write an equation to represent the total number of movies n that she will watch in m months.
Answers
Number of movies = n and if Months = m
Then 3 per month = 3m
i.e. n = 3m
Hope this helps!
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express 2 cos 35 sin 67 as a sum
Answers
2 cos 35 sin 67 can be expressed as the sum of sin(102) and -sin(32).
To express 2 cos 35 sin 67 as a sum, we can use the trigonometric identity for the product of two sine or cosine functions.
Specifically, the identity states that 2 cos A sin B can be written as
sin(A + B) + sin(A - B).
Applying this identity, we have:
2 cos 35 sin 67 = sin(35 + 67) + sin(35 - 67)
Simplifying the expressions inside the sine functions:
sin(102) + sin(-32)
Since the sine function is an odd function,
sin(-x) = -sin(x),
so we can rewrite the equation as:
sin(102) - sin(32)
Therefore, 2 cos 35 sin 67 can be expressed as the sum of sin(102) and -sin(32).
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A polygon has 29 sides.
Work out the sum of its interior angles.
Answers
Answer:
29
Step-by-step explanation:
Answer:
n=29sides
sum of interior angle of polygon=(n-2)180=(29-2)180=27×180=4860°
The outdoor temperature was 8° at midnight the temperature declined 5° during each of the next three hours. What was the temperature at 3 AM?
Answers
After performing mathematical operations, we can conclude that the temperature at 3:00 am would be 3°.
What do we mean by mathematical operations?Any mathematical operation that converts zero or more discrete input values into discrete output values is known as a discrete operation.The number of operands affects how complicated the operation is.Functions that convert numerical inputs into numerical outputs are the four mathematical operations (i.e., another number).These are addition, subtraction, multiplication, and division.So, the temperature at 3:00 am:
The temperature at midnight is 8°.Temperature falls by 5° in the next 3 hours.Then, the temperature at 3:00 am can be calculated as:
8 - 5 = 3°Therefore, after performing mathematical operations, we can conclude that the temperature at 3:00 am would be 3°.
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Find the difference. Enter your answer in simplest form.
3 1/3 minus 2 5/12 The First 3 and the first two are whole numbers btw
options
1 4/9 A
11/12 B
7/12 C
1 1/2 D
Answers
\(\\ \sf\longmapsto 3\dfrac{1}{3}-2\dfrac{5}{12}\)
\(\\ \sf\longmapsto \dfrac{10}{3}-\dfrac{29}{12}\)
\(\\ \sf\longmapsto \dfrac{40-29}{12}\)
\(\\ \sf\longmapsto \dfrac{11}{12}\)
- Suppose y varies directly as x. If y = -7 when x = -14, find y when x=3
Answers
Answer:1.5
Step-by-step explanation:
Y=1/2 of x
Apply the distributive property to factor out the greatest common factor.
24+32p= _____
Answers
Answer:
8(3+4p)
Step-by-step explanation:
8 goes into 24 and 32, so it can be factored out:
\(24+32p=8(3+4p)\)
Answer:
8(3 + 4p)
Step-by-step explanation:
Factor 24 + 32p
First, factor out the GCF. In this case, the GCF is 8, and we have
8(3 + 4p)
We can't factor anymore so the answer is 8(3 + 4p)
Laws of Exponents
Instruction Active
Simplifying Products and Quotients of Powers
7² 78
74
a=
=
79
75
-
75
b=
Answers
Answer:
a = 10 and b = 6
Step-by-step explanation:
I am having a little trouble reading the numbers, but I think that I see
\(\frac{7^{2} 7^{8} }{7^{4} }\)
If we wrote this in expanded form, it would look like:
\(\frac{7x7x7x7x7x7x7x7x7x7}{7x7x7x7}\) How many 7s are on the top? 10 That is the answer to a. The product of powers principle tells us that if we are multiplying powers with the same bases we add the exponents 2 + 8 = 10
\(\frac{^{10} }{7^{4} }\)
Now it looks like
\(\frac{7x7x7x7x7x7x7x7x7x7}{7x7x7x7}\) if we cross the 7's out in the top and the bottom, we are left with 6 7's on the top. That is the answer to b.
The quotient of powers principle tells us that if we are dividing powers with the same bases, we can subtract the exponents (10 -4 = 6)
How do you express 45mins as percentange of 1hr30mins
Answers
On a circle, a line is drawn from the origin to A(-3,4). The angle Ø is between the line and the x- axis. Find Cos Ø
Answers
Therefore,
\(\cos \phi=\frac{Adjacent}{\text{hypotenuse}}\)But, we do not have the dimension for the hypotenuse, In order to find the hypotenuse, we need to apply the Pythagorean theorem
Hence,
\(\begin{gathered} \text{Hyp}^2=opp^2+adj^2 \\ \text{hyp}^2=4^2+3^2 \\ \text{hyp}^2=16+9 \\ \text{hyp}^2=25 \\ \text{hyp}=\sqrt[]{25} \\ =5 \end{gathered}\)Therefore,
\(\cos \phi=\frac{3}{5}\)
In A container, there are red, blue and green balls. 3/11 of ball s are red There are 35 more blue balls than red balls. The remaining 90 balls are green. How many more blue balls than green balls are there? of the balls are red.
Answers
It is mentioned that there are 35 more blue balls than red balls. Therefore, the number of blue balls is 30 + 35 = 65.
The remaining balls are green, so the number of green balls is 110 - (30 + 65) = 15.
To find out how many more blue balls there are than green balls, we subtract the number of green balls from the number of blue balls: 65 - 15 = 50.
Therefore, there are 50 more blue balls than green balls.
Two functions are by f(x)=3x+18(x)= 2 x1. Find (g.f) (x).
Answers
The (g.f)(x) of the two functions is:
(g.f) (x) = 6x + 37
How to find (g.f)(x) of the two functions?A function is an expression that shows the relationship between the independent variable and the dependent variable. A function is usually denoted by letters such as f, g, etc.
To find (g.f) (x), follow the steps below:
1. Substitute the value of f(x) into the function g(x).
2. Then simplify the expression.
That is:
f(x) = 3x+18
g(x) = 2x+1
Thus, we have:
(g.f) (x) = g(f(x))
(g.f) (x) = g(3x+18)
(g.f) (x) = 2(3x+18) + 1
(g.f) (x) = 6x+36 + 1
(g.f) (x) = 6x + 37
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A package contains 20 golf balls. The total
weight of the golf balls is 32 ounces. Use the
model to show the number of ounces per
golf ball and the number of golf balls per
ounce. Write your answers in the blanks.
Answers
Answer: 1.6
Step-by-step explanation:
each golf is 1.6 ounces and you 20 golf balls in order to reach 32 ounces
Answer:
shown below
Step-by-step explanation:
golf balls per ounce = 5/8 or 0.625
ounces per gold ball = 8/5 or 1.6
9/4 times 1/6
I’ll give out free brainlist help me
Answers
0.375
9/4 × 1/6
=
9 × 1
4 × 6
=
9/24
=
9 ÷ 3
24 ÷ 3
=
3/8