We have 4⁶ = 4096 and 4⁷ = 16,384, which is to say that the given sum only contains the first six powers of 4.
Now,
[tex]\displaystyle 1+2+3+\cdots+5000 = \sum_{k=1}^{5000}k[/tex]
and you subtract the sum of the first six powers of 4 to get the sum S that you want,
[tex]\displaystyle S = \boxed{\sum_{k=1}^{5000}k - \sum_{k=1}^64^k}[/tex]
I need you guy’s help answer thanks so much
Find the measure of x. X=8, x=7, x=9, x=11
Answer:
[tex]\frac{135}{15} =\frac{15(x+2)}{15}[/tex]
[tex]9=x+2[/tex]
[tex]x=7[/tex]
OAmalOHopeO
Find COS Instructions: Find the value of the trigonometric ratio. Make sure to simplify the If needed
Answer:
Sin A = 15 / 17
Step-by-step explanation:
Given a right angled triangle, we are to obtain the Sin of the angle A ;
Using trigonometry, the sin of the angle A, Sin A is the ratio of the angle opposite A to the hypotenus of the right angle triangle.
Hence. Sin A = opposite / hypotenus
Opposite = 15 ; hypotenus = 17
Sin A = 15 / 17
2. What is the number 643,581 rounded off
to the thousands place?
(1) 640,000
(2) 643,000
(3) 643,600
(4) 644,000
(5) 644,600
Answer:
(4) 644,000
Step-by-step explanation:
643,581
The 3 is in the thousands place
We look at the hundreds place
5
It is 5 or greater so we round the thousands place up 1
644000
Please help me with this on the picture
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Answer:
(-5, 4)
Step-by-step explanation:
The inside corner moves from (2, -2) to (-3, 2). That is 5 is subtracted from the x-coordinate, and 4 is added to the y-coordinate. (x, y) ⇒ (x -5, y +4)
The translation vector can be written horizontally as (-5, 4), or vertically as ...
[tex]\displaystyle\binom{-5}{4}[/tex]
find the missing side lengths
this is a special triangle so v = 17
u = 17√2
Answer:
v = 17
u = 17[tex]\sqrt{2}[/tex]
Step-by-step explanation:
If v = 17 (it is because it is a right triangle, so the pythagorean theorum works, and triangles are 180 degrees, so 180 - 90 = 90, so the other two angles are 45 degrees, meaning that v is the same length as 17.) then
17 ^ 2 = u ^2
289 = u^2
17 root to 2
I want to know how to solve this equation
Answer:
B
Step-by-step explanation:
5³.5^×
simply means
5³×5^×
using indices rule,
multiplication is addition
5 is common
so 5(³+×)
hence 5^3+×
Find the remainder when f(x) = –2x3 + x2 - 4x + 1 is divided by x + 3.
Answer:
Step-by-step explanation:
The remainder when f(x) is divided by x + 3 would be 76.
What is remainder theorem for polynomials?If there is a polynomial p(x), and a constant number 'a', then
[tex]\dfrac{p(x)}{(x-a)} = g(x) + p(a)[/tex]
where g(x) is a factor of p(x).
We have been given a function;
[tex]f(x) = -2x^3 + x^2 - 4x + 1[/tex]
We need to find the remainder when f(x) is divided by x + 3.
So, Let p(x) = x + 3
p(x) = 0
x + 3 = 0
x = -3
Substitute in the given function f(x);
[tex]f(x) = -2x^3 + x^2 - 4x + 1\\\\f(-3) = -2(-3)^3 + (-3)^2 - 4(-3) + 1\\\\f(-3) = 54 + 9 + 12 + 1\\\\f(-3) = 76[/tex]
Thus, the remainder when f(x) is divided by x + 3 would be 76.
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Which of the answer choices has matrix multiplication defined?
Answer:
AB
Step-by-step explanation:
For the multiplication of two matrices to be defined then the number of columns of the first matrix must be equal to the number of rows of the second matrix. For example, 2*3 and 3*2 matrices can be multiplied since the number of columns of the first matrix must be equal to the number of rows of the second matrix.
Matrix A = 2*2
Matrix B = 2*3
Matrix C = 3*3
Matrix D = 1 * 3
From the matrices given, we can see that the matrices that can be multiplied together are AB and BC since the number of columns of the first matrix must be equal to the number of rows of the second matrix. Hence the correct option is AB
Help me please thanks guys
Answer:
B, D, F
Step-by-step explanation:
In a rational exponent, the numerator is an exponent, and the denominator becomes the index of the root.
[tex]a^{\frac{m}{n}} = \sqrt[n] {a^m}[/tex]
Answer: B, D, F
Solve 3 - 5(a - 4) any one who can answer in the next 3 mins plz answer
Answer:
[tex]3-5\left(a-4\right)[/tex]
[tex]-5(a-4)=-5a+20[/tex]
[tex]=3-5a+20[/tex]
[tex]=-5a+23[/tex]
OAmalOHopeO
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\text{3 - 5(a - 4)}\\\\\huge\text{\underline{\underline{DISTRUBUTE -5 within the parentheses}}}\\\\\large\text{3 - 5(a) - 5(-4)}\\\large\text{= 3 - 5a + 20}\\\\\huge\text{\underline{\underline{COMBINE the LIKE TERMS}}}\\\large\text{-5a + (3 + 20)}\\\large\text{= \bf -5a + 23}\\\\\\\boxed{\boxed{\huge\text{Therefore, your answer is: \bf -5a + 23}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!} \\\\\\\frak{Amphitrite1040:)}[/tex]
an international company has 27,100 employees in one country. if this represents 18.4% of the company's employees, how many employees does it have in total? round to nearest whole number
How many numbers multiple of 3 are in the range [2,2000]?
Answer: so there are 666 multiples of 3 between 2 and 2000.
Step-by-step explanation:
the smallest number = 3 which is 3*1. The largest number is = 1998 = 3*666
multiples of 3 between {2,2000} = 666-1+1 = 666
Four spinners are spun. Spinner 1 has outcomes Spinner 2 has outcomes Spinner 3 has outcomes Spinner 4 has outcomes The outcomes for each spinner are equally likely. is the sum of the numbers that come up on the spinners. What is the expected value of
Complete Question
Four spinners are spun. Spinner 1 has outcomes {1,2,3,4,5,6,7,8} Spinner 2 has outcomes {1,2,3,4,5,6} Spinner 3 has outcomes {1,2,3,4,5,6} Spinner 4 has outcomes {1,2,3,4,5} The outcomes for each spinner are equally likely. S is the sum of the numbers that come up on the spinners. What is the expected value of S?
Answer:
[tex]E(s)=14.5[/tex]
Step-by-step explanation:
From the question we are told that:
Spinner 1 ={1,2,3,4,5,6,7,8}
Spinner 2= {1,2,3,4,5,6}
Spinner 3 = {1,2,3,4,5,6}
Spinner 4 {1,2,3,4,5}
Generally the equation for expected outcome is mathematically given by
[tex]E(s)=\sum P(x).x[/tex]
Where
[tex]x=\frac{n(n+1)}{2}[/tex]
For Spinner 1
[tex]E(s_1)=\sum \frac{1}{8}*\frac{8(8+1)}{2}[/tex]
[tex]E(s_1)=4.5[/tex]
For Spinner 2
[tex]E(s_2)=\sum \frac{1}{6}*\frac{6(6+1)}{2}[/tex]
[tex]E(s_2)=3.5[/tex]
For Spinner 3
[tex]E(s_2)=E(s_3)[/tex]
For Spinner 3
[tex]E(s_4)=\sum \frac{1}{6}*\frac{6(6+1)}{2}[/tex]
[tex]E(s_4)=3[/tex]
Therefore The Expected Value
[tex]E(s)=\sum E(s 1..4)[/tex]
[tex]E(s)=4.5+2(3.5)+3[/tex]
[tex]E(s)=14.5[/tex]
PLZ ANSWER QUESTION IN PICTURE
Answer: [tex](\frac{2}{5},0) ; (0,2)[/tex]
Step-by-step explanation:
(to find the x-intercept, plug in 0 for y)
(to find the y-intercept, plug in 0 for x)
[tex]0=-5x+2\\5x=2\\x=\frac{2}{5}\\(\frac{2}{5},0)\\y=-5(0)+2\\y=2 \\(0,2)[/tex]
Help me this question
Answer:
(a) 218.6 N
(b) 97.14 N
Step-by-step explanation:
When the system is in equilibrium, the net torque on the system is zero.
AC = 1.5 m, CD = 2.3 m, DB = 5 - 1.5 - 2.3 = 1.2 m
Let the centre of gravity of plank is at G.
AG = 2.5 m, CG = 2.5 - 1.5 = 1 m, GB = 2.5 m
(a) Let the reaction at C is R and at D is R'.
R + R' = 29 x 9.8 = 284.2 N ... (1)
Take the torque about C.
29 x 9.8 x CG = R' x GD
29 x 9.8 x 1 = R' x 1.3
R' = 218.6 N
(b) Take the torque about D.
6 x 9.8 x AD = R x CD
6 x 9.8 x (1.5 + 2.3) = R x 2.3
R = 97.14 N
According to government data, the probability than an adult never had the flu is 19%. You randomly select 70 adults and ask if he or she ever had the flu. Decide whether you can use the normal distribution to approximate the binomial distribution, If so, find the mean and standard deviation, If not, explain why. Round to the nearest hundredth when necessary.
Answer:
Since [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], the normal distribution can be used to approximate the binomial distribution.
The mean is 13.3 and the standard deviation is 3.28.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex], if [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex].
The probability than an adult never had the flu is 19%.
This means that [tex]p = 0.19[/tex]
You randomly select 70 adults and ask if he or she ever had the flu.
This means that [tex]n = 70[/tex]
Decide whether you can use the normal distribution to approximate the binomial distribution
[tex]np = 70*0.19 = 13.3 \geq 10[/tex]
[tex]n(1-p) = 70*0.81 = 56.7 \geq 10[/tex]
Since [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], the normal distribution can be used to approximate the binomial distribution.
Mean:
[tex]\mu = E(X) = np = 70*0.19 = 13.3[/tex]
Standard deviation:
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{70*0.19*0.81} = 3.28[/tex]
The mean is 13.3 and the standard deviation is 3.28.
Please help me to find this answer
Answer:
Look in Step by Step Explanation
Step-by-step explanation:
3)SOHCAHTOA
tan=opposite/adjacent
tan(20)=x/83
83tan(20)=x
x=30.209
2) SOHCAHTOA
Tangent=opposite/adjacent
Tan(62)=x/8
8tan(62)=x
x=15.04
3)SOHCAHTOA
Sin=opposite/hypotonouse
sin(25)=30/x
x=30/sin(25)
x=70.986
Yooooo HELPPP
with this question plz
Answer:
Step-by-step explanation:
(x-2)(x+4)=x^2+4x-2x-8=0=> x =2, x=0
Answer:
A
Step-by-step explanation:
In an experiment, you choose to have two randomly assigned groups. In one, you take measurements both pretest and posttest; with the second, a posttest-only measure. This describes which task of conducting an experiment
Answer:
The answer is "Specific treatment levels".
Step-by-step explanation:
When we experimenting with 'level' which is related to the quantity or magnitude of treatment. For this part of an experiment or study, a group or individual is exposed to a specified set of circumstances. For example: If four categories are exposed to different doses of a given drug, then each dose reflects a level of a treatment factor in the model.
A manufacturer knows that their items have a normally distributed length, with a mean of 18.2 inches, and standard deviation of 3.9 inches. If 2 items are chosen at random, what is the probability that their mean length is less than 21.9 inches
Answer:
0.9099 = 90.99% probability that their mean length is less than 21.9 inches.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 18.2 inches, and standard deviation of 3.9 inches.
This means that [tex]\mu = 18.2, \sigma = 3.9[/tex]
2 itens:
This means that [tex]n = 2, s = \frac{3.9}{\sqrt{2}}[/tex]
What is the probability that their mean length is less than 21.9 inches?
This is the p-value of Z when X = 21.9. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{21.9 - 18.2}{\frac{3.9}{\sqrt{2}}}[/tex]
[tex]Z = 1.34[/tex]
[tex]Z = 1.34[/tex] has a p-value of 0.9099.
0.9099 = 90.99% probability that their mean length is less than 21.9 inches.
A person on the top of a tall building looks through his binoculars at his friend that is 300 ft away from the building on the ground. If the angle of depression from the person on the building is 30°, how tall is the building?
Answer:
520 feets
Step-by-step explanation:
The height of the building, h can be obtuined using trigonometry ;
From the attached diagram, opposite side = 300 feets ; height, h = adjacent side
Hence,
Tan θ = opposite / Adjacent
Tan 30° = 300 / height
0.5773502 = 300 / height
Height = 300 / 0.5773502
Height = 519.615
Height = 520 feets
Write a quadratic equation with integer coefficients having the given numbers as solutions.
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Answer:
x² -22 = 0
Step-by-step explanation:
The roots are opposites, so the equation is pretty simple.
x = ±√22
x² = 22 . . . . . square both sides
x² -22 = 0 . . . . your quadratic equation in standard form
WILL MARK BRAINLIEST PLEASE SHOW WORK :)
Answer:
(1). A = 18 cm² ; (2). TR = 18 units
Step-by-step explanation:
If sin(x) = 1 and cos(x) = 0, what is cot(x)?
0
1
undefined
Answer:
It's 0
Edge said it's 0
The value of the ratio of the cos(x) and the sin(x) is 0.
Trigonometric ratios are mathematical functions that relate the angles of a right triangle to the ratios of the lengths of its sides. These ratios are fundamental in trigonometry and have applications in various fields, such as physics, engineering, and navigation.
Trigonometry is a branch of mathematics that deals with the relationships and properties of angles and triangles. It explores the ratios between the sides of a triangle and the angles within that triangle. The word "trigonometry" is derived from two Greek words: "trigonal," meaning "triangle," and "metron," meaning "measure."
The value of the sin(x) is 1. The value of cos(x) is 0.
The formula for the cot(x) is written below:
cot(x) = cos(x) / sin(x)
cot(x) = 0 / 1
cot(x) = 0
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Dưới đây là bảng CĐKT gần đây nhất của VNA:
ĐVT: tỷ đồng
TÀI SẢN
NGUỒN VỐN
Tài sản lưu động
Tài sản cố định
Tổng tài sản
11.30
21.35
32.65
Nợ ngắn hạn (NH)
Nợ dài hạn
Vốn cổ phần ưu đãi
Vốn cổ phần thường
Tổng nguồn vốn
10.69
9.46
2.50
10.00
32.65
Biết: Nợ NH không chịu bất kỳ khoản phí nào, chi phí trung bình nợ NH sau thuế là 5.5%;
Chi phí nợ dài hạn trước thuế là 11.5%;
Tỷ suất sinh lời cần thiết trên vốn cổ phần ưu đãi là 13.5%; hệ số beta = 1,25
Tỷ suất lợi nhuận cho rủi ro thị trường là 8%; tỷ lệ lãi suất trái phiếu cũng 8%
Thuế TNDN là 32%.
Yêu cầu:
Tính chi phí vốn của mỗi nguồn nợ ngắn hạn, nợ dài hạn, vốn cổ phần ưu đãi, vốn cổ phần phổ thông?
Tính chi phí bình quân gia quyền vốn WACC của VNA?
I need this please pleaseeee nowww
Answer:
y = 3x - 5
Step-by-step explanation:
Slope = 3
x-intercept (what the value of y is when its 0) = -5 so y = 3x - 5
Answer:
y = 3x - 5
Step-by-step explanation:
Find the slope of the line between (0,−5)(0,-5) and (3,4)(3,4) using m=y2−y1x2−x1m=y2-y1x2-x1, which is the change of yy over the change of xx.
m=3m=3
Use the slope 33 and a given point (0,−5)(0,-5) to substitute for x1x1 and y1y1 in the point-slope form y−y1=m(x−x1)y-y1=m(x-x1), which is derived from the slope equation m=y2−y1x2−x1m=y2-y1x2-x1.
y−(−5)=3⋅(x−(0))y-(-5)=3⋅(x-(0))
Simplify the equation and keep it in point-slope form.
y+5=3⋅(x+0)
Add xx and 00.
y+5=3xy+5=3x
Subtract 55 from both sides of the equation.
y=3x−5
Let f(x) = e ^3x/5x − 2. Find f'(0).
Answer:
Step-by-step explanation:
Our friend asking what the actual function is has a point. I completed this under the assumption that what we have is:
[tex]f(x)=\frac{e^{3x}}{5x-2}[/tex] and used the quotient rule to find the derivative, as follows:
[tex]f'(x)=\frac{e^{3x}(5)-[(5x-2)(3e^{3x})]}{(5x-2)^2}[/tex] and simplifying a bit:
[tex]f'(x)=\frac{5e^{3x}-[15xe^{3x}-6e^{3x}]}{(5x-2)^2}[/tex]and a bit more to:
[tex]f'(x)=\frac{5e^{3x}-15xe^{3x}+6e^{3x}}{(5x-2)^2}[/tex] and combining like terms:
[tex]f'(x)=\frac{11e^{3x}-15xe^{3x}}{(5x-2)^2}[/tex] and factor out the GFC in the numerator to get:
[tex]f'(x)=\frac{e^{3x}(11-15x)}{(5x-2)^2}[/tex] That's the derivative simplified. If we want f'(0), we sub in 0's for the x's in there and get the value of the derivative at x = 0:
[tex]f'(0)=\frac{e^0(11-15(0))}{(5(0)-2)^2}[/tex] which simplifies to
[tex]f'(0)=\frac{11}{4}[/tex] which translates to
The slope of the function is 11/4 at the point (0, -1/2)
what expression is equivalent to (-7²-x-5)-(3x²+x)
Answer:
-3x² - 2x - 54
Step-by-step explanation:
(-7²-x-5)-(3x²+x)
-7² - x - 5 - 3x² - x
-49 - x - 5 - 3x² - x
-3x² - x - x - 49 - 5
-3x² - 2x - 54
The average mileage per gallon for cars built since 1940 approximates to the following curve 0.0075*t^2-.2672*t+14.8 where t is year -1940.
Answer the following questions:
What is the expected MPG in 2025?
How about 2050?
Is this a valid function?
Is there a top end to MPG?
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Answer:
46.3 in 202576.2 in 2050Step-by-step explanation:
The attached shows the predicted mileage for cars built in 2025 to be 46.3 mpg, 76.2 mpg for cars built in 2050.
__
No doubt, the function is valid over the time period used to derive it. It may or may not be valid for predicting MPG beyond that period.
Virtually any function that predicts future increases without bound will turn out to be unreliable at some point. In this universe, there are always limits to growth.
