I think the sum is supposed to be
[tex]\displaystyle\sum_{n=1}^4\frac n{n!}=\sum_{n=1}^4\frac1{(n-1)!}[/tex]
since [tex]n!=n\cdot(n-1)![/tex]. Then
[tex]\displaystyle\sum_{n=1}^4\frac1{(n-1)!}=\frac1{0!}+\frac1{1!}+\frac1{2!}+\frac1{3!}[/tex]
and [tex]0!=1[/tex] by definition so that the sum has a value of [tex]\dfrac83[/tex].
In the figure, mAB = 45° and mCD = 23°. The diagram is not drawn to scale.
What is the value of x?
A. 34°
B. 56.5°
C. 22°
D. 68°
Answer:
Option A. [tex]x=34\°[/tex]
Step-by-step explanation:
we know that
The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.
[tex]x=\frac{1}{2}(arc\ CD+arc\ AB)[/tex]
substitute the values
[tex]x=\frac{1}{2}(23\°+45\°)[/tex]
[tex]x=34\°[/tex]
Which statement BEST describes how the graph of g(x)=−5x^2 compares to the graph off(x)=x^2? Question 11 options:
A)The graph of g(x) is a vertical stretch of f(x) by a factor of 5.
B) The graph of g(x) is a reflection of f(x) across the x-axis.
C)The graph of g(x) is a vertical compression of f(x) by a factor of 15 and reflection across the x-axis.
D) The graph of g(x) is a vertical stretch of f(x) by a factor of 5 and a reflection across the x-axis.
Answer:
D) The graph of g(x) is a vertical stretch of f(x) by a factor of 5 and a reflection across the x-axis
Step-by-step explanation:
I just did this and got it correct
true or false the angle
Answer:
Second option: False
Step-by-step explanation:
You need to use the following identity:
[tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]
Let be "x" the lenght of the buildings's shadow.
[tex]opposite=x[/tex] (Lenght of building's shadow)
You can observe in the figure that:
[tex]\alpha=75\°\\\\hypotenuse=50ft[/tex]
Substitute these values into [tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex] and solve for ""x":
[tex]sin(75\°)=\frac{x}{50}\\\\(50)(sin(75\°))=x\\\\x=48.29\°[/tex]
Therefore, the length of its shadow IS NOT 12.94 feet.
Evaluate 35.5 - 35.36.(round to the hundredths place)
A. 319.64
B.-0.14
C. 0.14
D.70.86
The answer is C. 0.14.
Determine whether the function is periodic. If it is periodic, find the period.
f(x) = 7 sin3 x
Answer:
The period is 2pi
Step-by-step explanation:
A function is said to be periodic if there exists a T for which f(x+T)=f(x). In this case, the function is f(x) =7sin^3(x).
The period of sin(x) = 2pi. Then, in this case, no matter if the sin is elevated to a power of three, the period will remain the same.
Let's prove it:
f(x) =7sin^3(0) = 0
f(0 + 2pi) = f( 2pi) = 7sin^3(2pi) = 0.
Then, there exists a T for which f(x+T)=f(x) and it's T=2pi.
Answer: a, 2pi
Step-by-step explanation:
right on edg
A wall map is 45 cm high and 27 cm wide. Ashley wants to proportionately shrink it so its height is 12 cm. How wide would it be then?
Answer:
[tex]x=7\frac{1}{5}\ cm[/tex]
Step-by-step explanation:
Let
x-------> the proportional wide
we know that
Using proportion
[tex]\frac{45}{27}=\frac{12}{x}\\ \\x=27*12/45\\ \\x= 7.2\ cm[/tex]
Convert to mixed number
[tex]7.2\ cm=7+0.2=7+\frac{2}{10}=7+\frac{1}{5}=7\frac{1}{5}\ cm[/tex]
Answer: [tex] x=\ 7\dfrac{1}{5}\ cm[/tex]
Step-by-step explanation:
If there is proportional relation between two variables x and y , then we have the following equation:
[tex]\dfrac{x_1}{y_1}=\dfrac{x_2}{y_2}[/tex]
Given: A wall map is 45 cm high and 27 cm wide.
Ashley wants to proportionately shrink it so its height is 12 cm.
Let x be the width of the shrunk map.
Then by using above formula we have,
[tex]\dfrac{x}{27}=\dfrac{12}{45}\\\\\Rightarrow\ x=27\times\dfrac{12}{45}\\\\\Rightarrow x=\ 7\dfrac{1}{5}\ cm[/tex]
Why are radicals simplified before adding and subtracting? Explain your reasoning by adding sqrt8 and sqrt32. Compare the process to multiplying and dividing.
yes, just yes. Trust me, the answer is yes.
Love you. Plz HLP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
i think quadratic or rational
Step-by-step explanation:
For accounting purposes, the value of assets (land, buildings, equipment) in a business are depreciated at a set rate per year. The value, V(t) of $393,000 worth of assets after t years, that depreciate at 15% per year, is given by the formula V(t) = Vo(b)t. What is the value of Vo and b, and when rounded to the nearest cent, what are the assets valued at after 7 years?
Vo = $393,000, b = 0.15, and the value after 7 years is $0.67
Vo = $393,000, b = 1.15, and the value after 7 years is $108,543.57
Vo = $393,000, b = 0.85, and the value after 7 years is $47,721.43
Vo = $393,000, b = 0.85, and the value after 7 years is $125,986.80
Answer:
So, option d is correct i.e,
V₀ = $393,000, b = 0.85, and the value after 7 years is $125,986.80
Step-by-step explanation:
The formula given is V(t)=V₀(b)^t
The value of V₀ (the actual worth) is:
V₀ = $393,000
The value of b is :
b= (1-15%) = (1-0.15) = 0.85
Value of assets after 7 years is:
t= 7, V₀ = $393,000, b=0.85
putting values in formula:
V(t) = Vo(b)^t.
V(7)= $393,000 * (0.85) ^ 7
V(7)= $393,000 * (0.320)
V(7)= $125986.80
So, option d is correct i.e,
Vo = $393,000, b = 0.85, and the value after 7 years is $125,986.80
Choose the correct function rule.
Sheryl charged $25 plus $0.60 per page to type the term paper.
A.) 0.60x+25
B.) 0.50x+75
Answer:
A is the right answer i do believe
.60 cents per x papers plus $25
Sheryl typed the term paper for $25 + $0.60 per page. If x is the cost of typing a term paper in dollars per page. 0.60x+25 is the equation. Option A is correct.
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
If x is the cost in $ per page to type the term paper. The equation is found as;
⇒0.60x+25
Hence, option A is correct.
To learn more, about equations, refer;
https://brainly.com/question/10413253
#SPJ2
A rectangle has an area of 30 scuare meters and a perimeter of 34 meters what are the dimensions of the rectangle?
Answer:
P = 34 = 2(l + w) | : 2 => l + w = 17 => w = 17 - l
A = 30 = l×w
30 = l(17 - l)
17l - l² - 30 = 0 | (-)
l² - 17l + 30 = 0
l² - 2l - 15l + 30 = 0
l(l - 2) - 15(l - 2) = 0
(l - 15)(l - 2) = 0
l - 15 = 0 => l₁ = 15 m => w₁ = 2 m
l - 2 = 0 => l₂ = 2 m => w₂ = 15 m
PLEASE HELPP also sorry the photo is sideways
Reflecting /\ (triangle) LMN across the horizontal line y = -1, we get its image /\ (triangle) L' M' N'. Suppose LL', MM', NN' intersect the line of reflection at S, T, and U as shown below.
[tex]\overline{LL'}, \ \overline{MM'} \ and \ \overline{NN'}[/tex] are each perpendicular to the line of reflection
This option is the only one that is correct. The line of reflection is [tex]y=-1[/tex]. When we talk about reflection, we are talking about reflecting across a line, or axis. Reflecting a shape means looking at the mirror image on the other side of the axis. So in this case, this mirror is the line of reflection. As you can see, these three segments [tex]\overline{LL'}, \ \overline{MM'} \ and \ \overline{NN'}[/tex] form a right angle at the point each segment intersects the line [tex]y=-1[/tex].
b) Find each lengthSince the line [tex]y=-1[/tex] is an axis that allows to get a mirror image, therefore it is true that:
[tex]\overline{LS}=\overline{L'S} \\ \\ \overline{MT}=\overline{M'T} \\ \\ \overline{NU}=\overline{N'U}[/tex]
To find those values [tex]\overline{LS}[/tex], count the number of units you get from the point S to L, which is 3 units. Do the same to find [tex]\overline{MT}[/tex] but from the point T to M, which is 6 units and finally, for [tex]\overline{NU}[/tex] but from the point U to N, which is 4 units. Therefore:
[tex]\overline{LS}=\overline{L'S}=3 \ units \\ \\ \overline{MT}=\overline{M'T}=6 \ units \\ \\ \overline{NU}=\overline{N'U}=4 \ units[/tex]
c) Correct StatementThe line of reflection is the perpendicular bisector of each segment joining a point and its image.
A bisector is the line dividing something into two equal parts. In this case, the line of reflection divides each segment into two equal parts and is perpendicular because this line form a right angle with each segment. As we demonstrated in a) each segment is perpendicular to the line of reflection, so the first statement is false. On the other hand, each side of the original triangle is not perpendicular to its image and this is obvious when taking a look at the figure. Finally, as we said the line of reflection is perpendicular to each of the mentioned segments, so they can't be parallel as established in the last statement.
Which type of deposit is paid in advance to protect landlords against nonpayment?
Answer:
Security deposits
Step-by-step explanation:
security deposits are the amount of money that the landlords are supposed to acquire from tenants in advance while renting out the property as to protect against non-payment.
At the natural time of expiry of the contract between the landlord and tenants the security deposits can be utilized by the landlords for following causes:
Non-payment of rent
Any damage to the rented property
Any other non-paid dues !
Jeremy and Caitlin collect baseball cards. The ratio of Jeremy's cards to Caitlin's cards was 9 to 3. After Jeremy gave 12 cards to Caitlin, they had an equal number of cards. How many cards did Caitlin and Jeremy have at first? Explain.
Caitlin will have 18 and Jeremy will have 6 at first because then 18-6=12 which is how many cards Caitlin have to Jeremy
The graphs of two trigonometric functions, f(x) = 4 cos (0 - 90°) and g(x) = 2 cos (0 - 90°) + 1, are shown below. The two functions are added together to get a new function A(x). What is the maximum value of A(x)?
6
1
7
5
ANSWER
7
EXPLANATION
The given functions are:
[tex]f(x) = 4 \cos( \theta - 90) [/tex]
and
[tex]f(x) = 2 \cos( \theta - 90) + 1[/tex]
From the question,
[tex]A(x)=f(x)+g(x)[/tex]
[tex]A(x)=4 \cos( \theta - 90) + 2 \cos( \theta - 90) + 1[/tex]
This simplifies to:
[tex]A(x)=6\cos( \theta - 90) + 1[/tex]
The maximum value is 6+1=7
What is the value for this expression? 2e-5
A.
0.0134
B.
296.826
C.
1.6375
D.
0.0034
Answer:
A. 0.0134
Step-by-step explanation:
This is a question that must be answered using a table or calculator. (Tables are not in general use these days.) See below for a calculator's output.
___
The answer would be 0.0135 if it were properly rounded.
Wahaj buys a pizza for rs 800.A week later,the same piza costs rs 900.When wahaj asks the manger for the reason ,he explain that the government has imposed a general sales tax on all resturants .What is the general sale tax percentage
Answer:
12.5%
Step-by-step explanation:
The price increased from 800 to 900. So what is the PERCENTAGE INCREASE??
The increase is 900 - 800 = 100
To find this in terms of original, we need to divide 100 by 800 and multiply by 100 to get the "percentage". Let's do it:
[tex]\frac{100}{800}*100=12.5[/tex]
So the increase is 12.5% and thus the general sales tax is 12.5%
Final answer:
The general sales tax percentage imposed on the pizza price is 12.5%, calculated by dividing the increase in price by the original price and multiplying by 100.
Explanation:
When Wahaj experienced an increase in price from rs 800 to rs 900 for the same pizza after a week, this is due to the imposition of a general sales tax by the government. To calculate the percentage rate of the sales tax, we can compare the two prices.
The original price of the pizza was rs 800. A week later, the price rose to rs 900. The difference between the two prices, which is rs 100, represents the amount of the sales tax added to the original price. The percentage rate of this sales tax can be calculated as follows:
Sales Tax Percentage = (Amount of Sales Tax / Original Price) x 100%
Using the figures we have: Sales Tax Percentage = (100 / 800) x 100% = 0.125 x 100% = 12.5%
Therefore, the general sales tax percentage imposed on the restaurant is 12.5%
you are standing next to a really big circular like you want to measure that amateur of the lake but you don't want to swim across with a measuring tape you decide to walk around the perimeter of the lake and measure it circumference and find that it's 400 by meters what is diameter of the lake
Answer:
The answer is actually 400m
Step-by-step explanation:
A number is chosen at random from the first 20 integers. Find the probability that the number is a multiple of 3.
Answer:
3/10
Step-by-step explanation:
Multiples of 3: 3,6,9,12,15,18
There are 6 in the numbers 1-20
P(multiple of 3) = number of "multiples of 3" / total
= 6/20
=3/10
Final answer:
The probability that a number chosen at random from the first 20 integers is a multiple of 3 is 3/10 or 30%.
Explanation:
The student is asking to find the probability that a number chosen at random from the first 20 integers is a multiple of 3. To solve this, we first identify the multiples of 3 within the first 20 integers. They are 3, 6, 9, 12, 15, and 18, a total of 6 numbers. The total number of possible outcomes when choosing one number from the first 20 integers is 20.
The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Therefore, the probability of choosing a multiple of 3 is 6/20, which simplifies to 3/10 or 0.3. This means there is a 30% chance of choosing a multiple of 3 from the first 20 integers.
1.)Find the volume of a cylinder that has a radius of 1/2 and a height of 1.
2.) What is the volume of a sphere with a diameter of 11ft? Round your answer to the nearest cubic foot.
2786 cubic feet
5572 cubic feet
8359 cubic feet
6193 cubic feet
3.) Find the volume of a cone that has a radius of 1/2 and a height of 1.
answer choices :
1/12pie
3/2pie
3/4pie
1/6pie
Answer:
a.V=1.57
b. 2786 cubic feet (696.9)
c. 1/12 pie
Step-by-step explanation:
a. I have that the volume of a cylinder can be expressed as [tex]V= \pi r^{2} h[/tex] what would be the base (the area of the circle) by the height, so [tex]V=\pi * (\frac{1}{2}) ^{2} *1 =\frac{\pi }{2} = 1.57[/tex]
b. The volume of a sphere is given by the formula [tex]V=\frac{4}{3} \pi r^{3}[/tex] as the diameter is twice the radius I have to
[tex]V= \frac{4}{3} \pi (\frac{d}{2} )^{3} =\frac{4}{3} \pi (5.5)^{3} = 696.9[/tex]cubic feet the nearest cubic foot be 2786 cubic feet
c. The volume of a cone is given by the formula [tex]V=\frac{1}{3} \pi r^{2} h[/tex] so [tex]V=\frac{1}{3} \pi r^{2} h=\frac{1}{3} \pi (\frac{1}{2} )^{2} *1=\frac{1}{3}\pi \frac{1}{4}=\frac{1}{12}\pi[/tex]
Please help
A toy rocket is fired into the air from a base that is 3 feet tall. The rocket's path can be modeled by the function, h(t) = −16t2+75t +3, where time (t) is represented in seconds and the height is h(t). At what time does the rocket hit the ground?
between 2 and 3 seconds
between 3 and 4 seconds
between 4 and 5 seconds
The rocket never hits the ground.
between 4 and 5 seconds is the correct answer
Compare each of the functions shown below:
Answer:
D. All three functions have the same rate of change.
Step-by-step explanation:
1. For the function f(x):
at [tex]x=\pi,[/tex] [tex]f(\pi)=0;[/tex]at [tex]x=\dfrac{3\pi }{2},[/tex] [tex]f\left(\dfrac{3\pi}{2}\right)=-4.[/tex]The rate of change is
[tex]\dfrac{f(\frac{3\pi}{2})-f(\pi)}{\frac{3\pi}{2}-\pi}=\dfrac{-4-0}{\frac{\pi}{2}}=-\dfrac{8}{\pi}.[/tex]
2. For the function g(x):
at [tex]x=\pi,[/tex] [tex]g(\pi)=0;[/tex]at [tex]x=\dfrac{3\pi }{2},[/tex] [tex]g\left(\dfrac{3\pi}{2}\right)=-4.[/tex]The rate of change is
[tex]\dfrac{g(\frac{3\pi}{2})-g(\pi)}{\frac{3\pi}{2}-\pi}=\dfrac{-4-0}{\frac{\pi}{2}}=-\dfrac{8}{\pi}.[/tex]
3. For the function h(x):
at [tex]x=\pi,[/tex] [tex]h(\pi)=4\cdot \sin \pi+2=2;[/tex]at [tex]x=\dfrac{3\pi }{2},[/tex] [tex]h\left(\dfrac{3\pi}{2}\right)=4\cdot \sin \frac{3\pi}{2}+2=-4+2=-2.[/tex]The rate of change is
[tex]\dfrac{h(\frac{3\pi}{2})-h(\pi)}{\frac{3\pi}{2}-\pi}=\dfrac{-2-2}{\frac{\pi}{2}}=-\dfrac{8}{\pi}.[/tex]
All three functions have the same rate of change.
Emily needs 5 cups of milk to make a vanilla milkshake. Should she buy a pint a quart or a gallon of milk. Explain your answer.
A pint has 2 cups, quart has 4, and gallon has 16 so she would need at least a gallon
Answer:
Gallon
Step-by-step explanation:
Because a pint has 2 cups and a quart has 4 but you need 5
Find the exact value of csc (-4pi/3)
1. 2sqrt3/3
2. sqrt3/2
3. -sqrt3/2
4. -2sqrt3/3
Answer:
option 1
2sqrt3/3
Step-by-step explanation:
Given in the question
csc(-4π/3)
we know that csc(x) = [tex]\frac{1}{sin(x)}[/tex] that means
[tex]csc(\frac{-4\pi}{3})=\frac{1}{sin(\frac{-4\pi}{3} )}[/tex]
sin(-4π/3) = [tex]\frac{\sqrt{3}}{2}[/tex]
so,
[tex]csc(\frac{-4\pi}{3})=\frac{1}{\frac{\sqrt{3}}{2} }[/tex]
[tex]\frac{1}{\sqrt{3}/2 }[/tex] = [tex]\frac{2}{\sqrt{3}}=\frac{2\sqrt{3}}{3}[/tex]
For the following pair of lines, identify the system by type.
A) consistent
B) equivalent
C) inconsistent
ANSWER
C) inconsistent
EXPLANATION
The given system is inconsistent.
The two lines are parallel and have distinct y-intercepts.
This means that the two lines will never meet.
Since the two lines have no points of intersection, it means the system of equations they represent has no solution.
Therefore the system is inconsistent.
The correct choice is C
Answer:
If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.
Step-by-step explanation:
Use the explicit formula an = a1 + (n - 1) • d to find the 350th term of the sequence below. 57, 66, 75, 84, 93, ... A. 3234 B. 3207 C. 3141 D. 3198
Answer:
D
Step-by-step explanation:
57+(350-1)*9
Answer:
D
Step-by-step explanation:
Each term goes up 9 from the term before it.
Givens
a1 = 57
d = 9
n = 350
an = ?
Formula
an = a1 + (n- 1)*d
Solution
An = 57 + (350 - 1)*9
An = 57 + 3141
An = 3198
D
Does this graph represent a function?
A. Yes, because each x-value has exactly one corresponding y-value
B. No, because some of the y-values are paired with two x-values
C. No, because there are no closed circles to show here the graph ends.
D. Yes, because it touches the y-axis exactly one time.
A function assigns the value of each element of one set to the other specific element of another set. The correct option is A.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
In the given graph each specific value of x from the x-axis is representing a value on the y-axis. Therefore, as per the definition of the function, it can be concluded that the given graph is a function because each x-value has exactly one corresponding y-value.
Learn more about Function:
https://brainly.com/question/5245372
#SPJ2
Dominique paints faces on annual carnival her goal this year is to earn $100 she spends $15 on supplies and we'll work for 2.5 hours how much will she need to earn in dollars per hour in order to reach your goal
Answer:
46
Step-by-step explanation:
Final answer:
Dominique needs to earn $34 per hour to reach her goal of $100, after accounting for her $15 expenses on supplies, for the 2.5 hours she will be working at the carnival.
Explanation:
To calculate how much Dominique needs to earn per hour to reach her goal of $100 after spending $15 on supplies, we first need to subtract the cost of supplies from her earnings goal:
$100 - $15 = $85
This leaves us with $85 that she needs to earn while working for 2.5 hours. By dividing $85 by the 2.5 hours, we can find out her required hourly earning rate.
So, the calculation will be $85 ÷ 2.5 hours = $34 per hour.
Therefore, Dominique will need to earn $34 per hour during her 2.5 hours of work to reach her goal of $100 after spending $15 on supplies.
find the height of the skyscraper in feet, correct to two decimal places.
Answer:
264.49Step-by-step explanation:
Look at the picture.
We must use the tangent.
[tex]tangent=\dfrac{opposite}{adjacent}[/tex]
We have:
[tex]opposite=h\\adjacent=1,500\ ft\\\\\tan10^o\approx0.1763[/tex]
Substitute:
[tex]\dfrac{h}{1,500\ ft}=0.1763[/tex] multiply both sides by 1,500 ft
[tex]h=264.45\ ft\to h\approx264.49\ ft[/tex]
1. Consider the following quadratic equation x^2 =4x -5. How many solutions does it have?
A The equation has one real solution.
B The equation has two real solutions.
C The equation has no real solutions
D The number of solutions can not be determined.
2. Consider the quadratic equation ax^2+bx+c where a,b, and c are rational numbers and the quadratic has two distinct zeros. If one is rational, what is true for the other zeros.
A) The other zero is rational.
B) The other zero could be rational or irrational.
C) The other zero is not a real number.
D) The other zero is rational.
Answer:
C) The equation has no real solutions A) The other zero is rational.D) The other zero is rational.
Step-by-step explanation:
1. The attached graph shows there are no values of x where the left side of the equation is equal to the right side of the equation. There are no real solutions.
If you rewrite the quadratic to standard form (by subtracting the right-side expression), you get ...
x^2 -4x +5 = 0
Using the hint, the discriminant is b^2-4ac = (-4)^2-4(1)(5) = 16 -20 = -4. It is negative, so both roots will be complex.
__
2. The (rational) number "b" is the opposite of the sum of the zeros. If one zero is rational, the other root must be. The difference of rational numbers is rational.
Choices A and D are identical, so both are correct. Perhaps a typo?
__
We can also consider the discriminant in problem 2. The roots of the quadratic are the sum (or difference) of -b and the square root of the discriminant, all divided by 2a. Any one root can only be rational if the square root is rational. In that case, the other root will be rational as well.