Find the sum of the first 50 terms of the sequence below.
An = 3n + 2
Answer:
3925
Step-by-step explanation:
this arithmetic sequence the first term is : A1 = 3(1)+2=5
and common difference is r = 3
the sum of the first 50 terms is : S50 = 50/2(A1 + A50)
A50 = 3(50)+2 = 152
S50 = 50/2(5 + 152)= 3925
The height of the Empire State Building is 318.00 meters. If a stone is dropped from the top of the building, what is the stone's velocity just before it strikes the ground?
The surface area of two similar solids are 340yd^2 and 1,158yd^2. The volume of the larger solid is 1,712yd^2. What is the volume of the smaller solid? ...?
Find the linear approximation of f(x)=lnx at x=1 and use it to estimate ln1.38.
L(x)= ?
ln1.38 approximately = ? ...?
Fernando purchased 1 pound of dried cranberries and 4 pounds of almonds to make a trail mix. Cranberries cost $4 per pound and almonds cost $5 per pound. What is the price per pound of the trail mix?
What is the difference? -2/15 -(-9/15)
a.-11/15
b. -7/15
c. 7/15
d. 11/15
What is 20 + 10? (Nobody answer this)
What is 1036.50 rounded the the nearest whole number?
Using the properties of equality to solve the equation -2b + 7 = -13, you would _____.
add 13 and then divide by -2
add 13 and then add 2
subtract 7 and then add 2
subtract 7 and then divide by -2
To solve the equation, firstly subtract 7 from both sides, converting the equation into -2b = -20. Then divide both sides by -2 to find the value of b, which is 10.
Explanation:To use the properties of equality to solve the given equation, -2b + 7 = -13, follow these steps:
First, isolate the term containing the variable b on one side of the equation. This is done by subtracting 7 from both sides of the equation. The equation becomes -2b = -20.Next, to find the value of the variable b, divide both sides of the equation by -2. So, the final equation becomes b = 10.Learn more about Properties of Equality here:https://brainly.com/question/10617252
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Use the Laplace transform to solve the given initial value problem. y' + 6y = e^4t ; y(0)=2 ...?
The Laplace transform method is applied to solve the differential equation y' + 6y = e^4t with the initial condition y(0)=2. After transforming, simplifying, and solving for Y(s), we use inverse Laplace transform to find the solution y(t) in the time domain.
Explanation:Laplace transform is a powerful tool in the field of mathematics used for solving differential equations. To solve the given initial value problem y' + 6y = e^4t ; y(0)=2, we can start by taking the Laplace transform of both sides of the equation.
The Laplace transform of y' is sY(s) - y(0) and the Laplace transform of y is Y(s). Therefore, the Laplace transform of y' + 6y gives sY(s) - y(0) + 6Y(s). Given that y(0)=2, this simplifies to sY(s) + 6Y(s) - 2.
On the right-hand side, the Laplace transform of e^4t is 1/(s-4). Thus, we have the equation sY(s) + 6Y(s) - 2 = 1/(s-4).
By solving for Y(s), we can find the inverse Laplace transform to get the solution y(t) in the time domain.
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Three interior angles of a quadrilateral measure 55°, 117°, and 120°. What is the measure of the fourth interior angle?
68°
78°
88°
98°
The measure of the fourth interior angle of the given quadrilateral is: B. 68°
What is the Sum of a Quadrilateral?The sum of all the interior angles of a quadrilateral equals 360 degrees.
The given interior angles of the quadrilateral are: 55°, 117°, and 120°
The measure of the fourth interior angle = 360 - 55 - 117 - 120
The measure of the fourth interior angle = 68 degrees.
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If f(x) = 8, what is f(x) when x = 10? 4 9 13 36
If f(x) = 8, then f(x) when x = 10 is also 8, because the function's value is constant for all x.
Explanation:If the function f(x) is defined as f(x) = 8 for all values of x, then regardless of the value we substitute for x, the function's output remains constant at 8. So when x = 10, the value of f(x) is still 8. This is an example of a horizontal line on a graph where the y-value does not change regardless of the x-value. In terms of probability, if we're dealing with a continuous probability distribution where f(x) is a constant, then to find P(0 < x < a), we would simply evaluate the integral of f(x) over the interval from 0 to a. However, given that in this case f(x) is not a probability density function and is a constant value, P(x) would not be applicable.
4(x+3)=20
Help? Solve the equation
1735/1000 is what in decimal form
how are the integers and rational numbers different? ...?
Is the ordered pair a solution to the system of linear equations?
Select Yes or No.
Ordered pair: (−2,2)(−2,2)
System of equations:
−7x+2y=0
6x+6y=0
What is the average rate of change of the function f(x)=2(3)^x from x = 2 to x = 4?
The average rate of change of the given function will be 72.
What is the average rate of change of the function?It quantifies how much the function changed per unit on average throughout that time interval. The slope of the straight line connecting the interval's ends on the function's graph is used to calculate it.
The given function is f(x)=2(3)ˣ and the interval is x ∈ [2,4].
The formula to calculate the average rate of change is (f(b)-f(a))/(b-a).
Here, a = 2 and b = 4
So,f (2) = 2.3² = 18
Now,f (4) = 2.3⁴ = 162
The average rate of change = (162 - 18)/(4 - 2)
The average rate of change = 144/2
The average rate of change = 72
Therefore, the average rate of change of the given function will be 72.
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The average rate of change of the function f(x) = 2(3)ˣ from x = 2 to x = 4 is 72. This means the secant line that intersects the graph of the function at x = 2 and x = 4 has a slope of 72.
Step 1: Formula for Average Rate of Change
The average rate of change of a function f(x) over the interval [a, b] is calculated using the following formula:
Average rate of change = (f(b) - f(a)) / (b - a)
where:
f(b) is the function's value at the upper bound (x = 4 in this case).f(a) is the function's value at the lower bound (x = 2 in this case).b is the upper bound of the interval (x = 4).a is the lower bound of the interval (x = 2).Step 2: Find f(b) and f(a)
We are given the function f(x) = 2(3)ˣ . Let's find the function's values at x = 4 (upper bound) and x = 2 (lower bound):
f(4) = 2(3)⁴ = 2 × 81 = 162f(2) = 2(3)⁴ = 2 × 9 = 18Step 3: Calculate the Average Rate of Change
Now that we have f(b) and f(a), we can plug them into the formula along with the interval's bounds:
Average rate of change = (f(4) - f(2)) / (4 - 2)Average rate of change = (162 - 18) / (2)Average rate of change = 144 / 2Average rate of change = 72
Suppose that alpha and beta are int variables. The statement alpha = beta--; is equivalent to the statement(s) ____.
a. alpha = 1 - beta;
b. alpha = beta - 1;
c. beta = beta - 1;
alpha = beta;
d. alpha = beta;
beta = beta - 1
170 percent converted to a fraction equals: ...?
After finding the simplest form by dividing 100 the fraction equivalent to 170 percent we get 17/10.
A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the word percent means.
Here we have to convert:
170 percent into a fraction
Divide it by 100 to condert into fractions,
170/100
Divide both the numerator and denominator by 10
17/10
Since 17 and 10 are co-primes,
Therefore, it is in simplest form.
Hene,
The fraction 17/10 is equivalent to 170%.
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Eric bought 300 t-shirts, which were sold in packs of 12. How many packs did Eric buy?
A) 20
B) 25
C) 28
D) 30
Answer is B, 25, because 300 Divided 12 is 25 & 25x12=300.
Let p: The integer has one digit.
Let q: The integer is less than 10.
Which represents "The integer has one digit if and only if the integer is less than 10”?
p ∨ q
p ∧ q
p → q
p ↔ q
Answer:
p ↔ q
Step-by-step explanation:
Given :
Let p: The integer has one digit.
Let q: The integer is less than 10.
To Find:Which represents "The integer has one digit if and only if the integer is less than 10”?
Solution:
1. p ∧ q denotes “p and q”
2.p ∨ q denotes “p or q" (or both)
3.p → q denotes “if p then q”
4. Biconditional p ↔ q denotes “p if and only if q"
Thus Biconditional p ↔ q represents "The integer has one digit if and only if the integer is less than 10”
Hence Option D is correct p ↔ q
write an explicit formula for sequence
The Given Sequence is..
3,-6,12,-24..
Explain why all linear angle pairs must be supplementary, but all supplementary angles do not have to be linear pairs?
Final answer:
Linear angle pairs are always supplementary and formed by intersecting lines, while supplementary angles can be any two angles that add up to 180 degrees.
Explanation:
In mathematics, linear angle pairs are formed by two adjacent angles that add up to 180 degrees. This is known as supplementary angles. Linear angle pairs always occur when two lines intersect, creating opposite angles or a straight angle, such as in the case of a triangle.
On the other hand, supplementary angles do not have to be linear pairs. Supplementary angles are any two angles that add up to 180 degrees, regardless of their position or relation to each other. They can be adjacent angles, non-adjacent angles, or angles across parallel lines.
For example, two angles measuring 60 degrees and 120 degrees are supplementary angles but not a linear pair, since they are not adjacent to each other or formed by intersecting lines.
A population of 240 birds increases at a rate of 16% annually. Jemel writes an exponential function of the form f(x) = abx to represent the number of birds after x years. Which values should she use for a and b?
Answer:
Hence the values of a and b are given by:
a=240
and b=1.16.
Step-by-step explanation:
It is given that:
A population of 240 birds increases at a rate of 16% annually.
i.e. the initial population of birds is 240.
Also they are increasing at a rate of 16% =0.16.
Hence, it clearly implies that the growth is exponential and the function that represents the population of the birds after x years is given by:
[tex]f(x)=240\times (1+0.16)^x\\\\\\f(x)=240\times (1.16)^x[/tex]
Hence, on comparing our function with the exponential function:
[tex]f(x)=ab^x[/tex]
we have:
a=240
and b=1.16.
Jim earns $1,600 per month after taxes. He is working on his budget and has the first three categories finished.
Housing $576
Food $272
Transportation $320
Why will he have a problem with the rest of his budget?
He is budgeting too much for transportation.
He has used the highest recommended percentages to calculate the amounts for the three categories.
He is budgeting too much for housing.
He has used the lowest recommended percentages to calculate the amounts for the three categories.
B.
He has used the highest recommended percentages to calculate the amounts for the three categories.
Write the number 7/10 as a decimal and describe the process
Simplify (4xy^-2)/(12x^(-1/3)y^-5) and Show work ...?
One more and I should be good, i'm pretty familar with this but i'd like to make sure,
Two brothers, Bill and Eric, are 4 years apart, and Bill is the older of the two. If the sum of the boys' ages is 28, how old is bill and how old is eric?
Both boys age is unknown, yet we can mark both with say,
x = Eric's age
y = Bills' age
There are many ways to solve this, but we DO know they're 4 years apart, so it'd have to be
x + y4 = ?,
actually that's off but you understand what i'm saying... Thanks!
Which of the following are equivalent to the function y = 4cos x - 2? Check all that apply.
A. y = -4cos x + 2
B. y = 4sin(x +π/2 ) - 2
C. y = 4sin(x - π/2) - 2
D. y = 4cos(-x) - 2 ...?
Out of the given options, B (y = 4sin(x +ext{ extpi}/2 ) - 2) and D (y = 4cos(-x) - 2) are equivalent to the function y = 4cos x - 2, due to trigonometric identities and properties.
To determine which of the given options are equivalent to the function y = 4cos x - 2, we need to look at trigonometric identities and properties of cosine and sine functions.
Option A: y = -4cos x + 2 is not equivalent since it represents a reflection in the x-axis followed by a vertical shift, which alters the original function's graph completely.Option B: y = 4sin(x +rac{ext{extpi}}{2}) - 2 is equivalent because of the co-function identity sin(x + rac{ext{ extpi}}{2}) = cos x, which makes the functions identical.Option C: y = 4sin(x - rac{ext{extpi}}{2}) - 2 is not equivalent because sin(x - rac{ext{extpi}}{2}) is not equal to cos x.Option D: y = 4cos(-x) - 2 is equivalent due to the even property of the cosine function, which states that cos(-x) = cos x.
a cinder block is sitting on a platform 20 high. lt weighs 79n. The block has_____ energy. calculate it.