Answer:
x = 103 and x + 25 = 128°
Step-by-step explanation:
the sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
here n = 5 , then
sum = 180° × (5 - 2) = 180° × 3 = 540°
(a)
sum the interior angles and equate to 540
x + x + x + x + x + 25 = 540
5x + 25 = 540 ( subtract 25 from both sides )
5x = 515 ( divide both sides by 5 )
x = 103
(b)
largest angle = x + 25 = 103 + 25 = 128°
if the probability of an event is 75 97 75 97 , what is the probability of the event not happening?
Answer: 0%
Step-by-step explanation:
It's impossible for it to be different than 75 or 97
whats 10 divided by 2.
Answer:5
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
10 divided by 2 =5
A rectangle has a length of x inches and a width 2 inches less than the length. If the dimensions were doubled, which expression best represents the area of the new rectangle in terms of x?.
The area of the new rectangle in terms of x is 4x^2 – 8x square inches. We can calculate it using rectangle area formula.
A rectangle has a length of x inches and a width 2 inches less than the length, so:
Length = x
Width = x-2
We can formulate the area is:
Length x Width
X(x-2) = x^2 – 2x
The new rectangle’s dimension is double from the first rectangle, so we can conclude:
Length : 2(x) = 2x
Width = 2(x-2) = 2x-4
So the area of the new rectangle is:
Length x Width
2x(2x-4) = 4x^2 – 8x
Hence the area of the new rectangle in terms of x is 4x^2 – 8x square inches
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a key requirement for the process of testing hypotheses in the scientific method is
A key requirement for the process of testing hypotheses in the scientific method is experimentation. A hypothesis is an idea or explanation for a phenomenon that is grounded in existing knowledge or observations, and the scientific method involves testing those hypotheses through experimentation.
The process of testing hypotheses requires the development of a testable hypothesis, the design of experiments to test the hypothesis, and the collection and analysis of data from those experiments to evaluate the hypothesis. The experiments must be designed carefully, with appropriate controls and variables to ensure that the results are reliable and valid. Scientists also need to communicate their findings to the scientific community, which involves publishing their results in scientific journals and presenting their work at conferences.
This helps to ensure that other scientists can replicate their experiments and validate their findings, which is a critical part of the scientific process. Ultimately, the process of testing hypotheses is essential for advancing scientific knowledge and understanding how the world works.
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IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.
Out of a randomly selected 2550 people from the population, how many of them
would have an IQ higher than 86, to the nearest whole number?
Therefore, about 83 percent of the population would have an IQ score higher than 86.
IQ scores are typically distributed in a bell-shaped or normal distribution. A normal distribution is a continuous probability distribution in which a random variable has an equal probability of taking any value between its minimum and maximum values.IQ scores, like many other phenomena, are generally distributed. The average IQ score for the population is 100, and the standard deviation is 15. This means that the majority of people score between 85 and 115 on IQ tests. However, we may use standard deviation to calculate the proportion of individuals that have an IQ above or below a particular value.The mean IQ score is 100, so any IQ score higher than 100 is considered above average, whereas an IQ score of less than 100 is considered below average. We can utilize the standard deviation to calculate the proportion of individuals who score above or below the mean. Since the standard deviation is 15, we can convert the IQ score of 86 to a z-score to determine how far above the mean it is.Z = (X - μ) / σ.Where,Z = the z-scoreX = the raw scoreμ = the meanσ = the standard deviationIf we put the values in the above formula we get,Z = (86 - 100) / 15Z = -0.93.Therefore, the z-score for an IQ of 86 is -0.93. We can look at the z-score chart to see what proportion of individuals have a z-score less than -0.93.According to the chart, around 17% of people have a z-score less than -0.93. As a result, around 17% of people would have an IQ lower than 86. As a result, the percentage of people who would have an IQ higher than 86 is 100% - 17% = 83% or around 83 people out of 100.For such more question on phenomena
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Find all vectors
u
such that (1,−1,2)×
u
=(−1,0,4)
There are infinitely many vectors u that satisfy the equation (1, -1, 2) × u = (-1, 0, 4). The solution set consists of all vectors that are orthogonal (perpendicular) to the cross product of (1, -1, 2) and u, which is (-1, 0, 4).
The cross product of two vectors is a vector that is orthogonal (perpendicular) to both of the original vectors. In this case, the cross product of (1, -1, 2) and u is given as (-1, 0, 4). To find the vectors u that satisfy this equation, we need to determine all vectors that are perpendicular to (-1, 0, 4).
A vector is orthogonal to another vector if their dot product is zero. So, we can find vectors u by finding all vectors that satisfy the dot product condition with (-1, 0, 4). Let's denote the components of u as (u1, u2, u3).
Taking the dot product of (-1, 0, 4) and (u1, u2, u3), we have:
(-1)(u1) + (0)(u2) + (4)(u3) = 0.
This simplifies to -u1 + 4u3 = 0.
We can express u in terms of a parameter, let's say u3 = t, where t is any real number. Then, u1 = 4u3 = 4t.
So, the solution set for vectors u is u = (4t, u2, t), where t is any real number and u2 can be any value.Therefore, there are infinitely many vectors u that satisfy the given equation.
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I need some help with this one
7. Which number in this set is an irrational number?
( 1169, 1.2333333, V3, **)
169
B 1.233333
Answer:
V3
Step-by-step explanation:
Solve:
7 - 3(-9x + 3) = 11
find the missing value: 30% of what is 18?
The missing value is 60
Here, we want to find the missing value
Let the missing value be n
\(\begin{gathered} 30\text{ percent of n = 18} \\ \frac{30}{100}\text{ }\times\text{ n = 18} \\ \\ 30\times n\text{ = 18}\times100 \\ \\ n\text{ = }\frac{18\times100}{30} \\ \\ n\text{ = 60} \end{gathered}\)Eighty percent of what number is 16?
Answer:
Step-by-step explanation
16 is eighty percent of 20, here is the process:
16 divided by 0.8 = 20
Then to check we do 20 x 0.8 which gives us 16
test the series for convergence or divergence. 4 5 − 4 7 + 4 9 − 4 11 + 4 13 −
Therefore, the series 4/5 - 4/7 + 4/9 - 4/11 + 4/13 - ... is convergence in nature.
To test the convergence or divergence of the given series: 4/5 - 4/7 + 4/9 - 4/11 + 4/13 - ..., we can use the alternating series test. The alternating series test states that if a series has the form (-1)^n b_n, where b_n is a positive sequence that is decreasing and approaches zero as n approaches infinity, then the series converges.
In the given series, we have b_n = 4/(2n+3), which is a positive sequence that approaches zero as n approaches infinity. To see that b_n is decreasing, we can note that b_{n+1}/b_n = 2(2n+3)/(2n+5) < 1 for all n, since the numerator is always less than the denominator. Therefore, b_n is a positive, decreasing sequence that approaches zero as n approaches infinity.
Furthermore, the series has the form (-1)^n b_n, where the sign alternates between positive and negative. Therefore, we can apply the alternating series test, which tells us that the series converges.
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Select the correct answer.
As part of a community-service project, a local club has decided to paint 864 walls across town. The club has 36 volunteers. If the work is divided evenly, how many walls must each volunteer paint?
A.
24
B.
29
C.
34
D.
39
The 24 walls must paint by each volunteer if the work is divided evenly and the club has 36 volunteers.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
We have:
As part of a community-service project, a local club has decided to paint 864 walls across town. The club has 36 volunteers.
Total number of volunteers = 36
Number of walls = 864
The number of walls each volunteer paint can be expressed as a fraction:
= 864/36
= 24
Thus, the 24 walls must paint by each volunteer if the work is divided evenly and the club has 36 volunteers.
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The sum of five consecutive numbers is 360. What is the smallest of these numbers? *
Answer:
70
Step-by-step explanation:
An easy way to do this is to simply take 360(the sum) and divide it by 5(the number of numbers) to get 72. Thus, 72 is the middle number and the numbers are:
72
72,72,73
70,71,72,73,74
The smallest of these numbers is 70
Hope it helps <3
Hello!
Answer:
70 is the smallest number.
Step-by-step explanation:
If the sum of 5 consecutive numbers is 360, we can solve for the smallest number algebraically:
Let 'x' represent the smallest number:
and (x + 1), (x + 2), (x + 3), and (x+4) represent the other consecutive numbers:
x + (x + 1) + (x + 2) + (x + 3) + (x+ 4) = 360
Combine like terms:
5x + 10 = 360
Subtract 10 from both sides:
5x = 350
Divide both sides by 5:
x = 70. This is the smallest of the consecutive numbers.
We can check our work:
70 + 71 + 72 + 73 + 74 = 360.
Hope this helped!
A project has an initial cost of $30 million.The project is expected to generate a cash flow of $2.85 million at the end of the first year.All the subsequent cash flows will grow at a constant growth rate of 3.85% forever in future.If the appropriate discount rate of the project is 11%,what is the profitability index of the project? a.1.917 b.1.328 c.1.387 d.1.114 ortcehov e. None of the above
Profitability index is 1.387. Thus, the correct option is (c) 1.387.
The formula for calculating the profitability index is:
P.I = PV of Future Cash Flows / Initial Investment
Where,
P.I is the profitability index
PV is the present value of future cash flows
The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.
The present value of cash flows can be calculated using the formula:
PV = CF / (1 + r)ⁿ
Where,
PV is the present value of cash flows
CF is the cash flow in the given period
r is the discount rate
n is the number of periods
For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.
Substituting the values, we get:
PV = 2.85 / (1 + 0.11)¹ = $2.56 million
To calculate the present value of all future cash flows, we can use the formula:
PV = CF / (r - g)
Where,
PV is the present value of cash flows
CF is the cash flow in the given period
r is the discount rate
g is the constant growth rate
For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.
Substituting the values, we get:
PV = 2.85 / (0.11 - 0.0385) = $39.90 million
The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.
PV of future cash flows = $39.90 million + $2.56 million = $42.46 million
Profitability index (P.I) = PV of future cash flows / Initial investment
= 42.46 / 30
= 1.387
Therefore, the correct option is (c) 1.387.
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8/9=x+1/3(7) what the answer
Answer:
x=-1.4 repeating or x= -13/9
Step-by-step explanation:
1/3 x 7 = 7/3
8/9=x+7/3
Move the var to left hand side of =
-x=8/9-7/3
subtract the fractions
x-=13/9
change the signs and your done! :D
x=-13/9
Round your answers to the nearest cent.
f(0) =
meaning the cost of buying
gallons of paint would be
in the context of the problem.
f(10)
, meaning the cost of buying
gallons of paint would be
in the context of the problem.
f(67.5)
meaning the cost of buying
gallons of paint would be
This interpretation
in the context of the problem.
Based on the observations above, it is clear that an appropriate domain for the
function is
=
This interpretation
=
This interpretation
The interpretations of the function values are: the cost of buying 0, 10 and 67.5 gallons of paint would be 0, 28.5 and 73.9, respectively
How to interpret the function values?The equation of the function is given as:
f(x) = 9√x
When x = 0, 10 and 67.5, we have:
f(0) = 9√0 = 0
f(10) = 9√10 = 28.5
f(67.5) = 9√67.5 = 73.9
Hence, the interpretations of the function values are:
The cost of buying 0, 10 and 67.5 gallons of paint would be 0, 28.5 and 73.9, respectively
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how to change the chart style to style 42 (2nd column 6th row)?
To change the chart style to style 42 (2nd column 6th row), follow these steps:
1. Select the chart you want to modify.
2. Right-click on the chart, and a menu will appear.
3. From the menu, choose "Chart Type" or "Change Chart Type," depending on the version of the software you are using.
4. A dialog box or a sidebar will open with a gallery of chart types.
5. In the gallery, find the style labeled as "Style 42." The styles are usually represented by small preview images.
6. Click on the style to select it.
7. After selecting the style, the chart will automatically update to reflect the new style.
Note: The position of the style in the gallery may vary depending on the software version, so the specific position of the 2nd column 6th row may differ. However, the process remains the same.
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Combine like terms to simplify the following polynomial.
x + y + z + x + 2z + 3y
2x + 4y + 3z
9xyz
4x + 2y + 3z
x2 + y4 + z3
Step-by-step explanation:
Answer 1
x+x+y+3y+z+2z
2x+4y+3z
Answer 2
2x+4y+3z
( no like terms are there so it cannot be added)
Answer 3
9xyz
last two answers will also be similar as the question because unlike terms cannot be added..
HELPP
geometry 60° 48°
Answer: 110
Step-by-step explanation:
The altitude of a triangle is increasing at a rate of 2.5 2.5 centimeters/minute while the area of the triangle is increasing at a rate of 3.5 3.5 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 9 9 centimeters and the area is 83 83 square centimeters
Answer:
-4 28/81 cm/min ≈ -4.346 cm/min
Step-by-step explanation:
Differentiating the formula for the area of a triangle gives the relationship between the various rates of change.
A = 1/2bh
A' = 1/2(b'h +bh') . . . . . relation of rates of change
__
triangle dimensionsWhen the area is 83 cm², and the height is 9 cm, the base length is ...
83 cm² = 1/2b(9 cm)
b = 166/9 cm
rate of changeFilling in the given values and rates of change, we have ...
3.5 cm²/min = 1/2(b'·(9 cm) +(166/9 cm)(2.5 cm/min))
7 cm²/min -46 1/9 cm²/min = (b')(9 cm)
b' = (-39 1/9 cm²/min)/(9 cm) = -4 28/81 cm/min
The base of the triangle is changing at the rate of -4 28/81 cm/min, about -4.346 cm/min.
_____
The attachment shows a calculator solution to the problem.
The mean mass of five men is 76 kg. The masses of four of the men are 72 kg, 74 kg, 75 kg and 81 kg. What is the mass of the fifth man
Answer:
78kg
Step-by-step explanation:
76×5= 380kg
380-72-74-75-81= 78kg
find the value of x. Please help.!!
Need to show work.
Answer:
(x-54)° + 2x° + 99° = 360
=> x + 2x + 99 – 54 = 360
=> 3x + 45 = 360
=> 3x = 360 – 45
=> x = 315/3
=> x = 105
The value of x is 105
Andrew had a piece of foam in the shape of a rectangular prism as shown below. Thebase is a square with sides 3 Inches long, and the piece is 5 Inches taill. He out the
foam along the diagonal plane shown by the shaded area.5 inches 3 inches Which of the following is closest to the area of the shaded diagonal plane? 19.3 square inches 12 square Inches 15.8 square inches 17.5 square inches
The area of the shaded diagonal plane is 17.5 square units.
What is the area of the shaded diagonal plane?The area of the shaded diagonal plane is calculated as follows:
Using Pythagoras' theorem, let the hypotenuse formed by the diagonal be x
x² = 3² + 5²
x² = 9 + 25
x² = 34
x = √34
The shape of the shaded plane is a rectangle.
The area of the rectangle will be:
Area = length * width
Area = √34 * 3
Area do the shaded plane = 17.5 square units
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How many kilograms are in 16.3 nanograms? Please help me finalize my answer with proper significant figures & the reason behind the certain amount of significant figures.
I am confused by this problem.
a.) 16.3kg
b.) 1.63 x 10^4kg
c.) 1.63 x 10^-11kg
d.) 1.63 x 10^12 kg
Answer:
c
Step-by-step explanation:
1 nanogram is 1 x 10^-12 kg
16.3 nanogram * 1 x 10^-12 kg/ nanogram = 16.3 x 10^-12 = 1.63 x 10^-11 kg
Write R code to implement Euclid’s algorithm.
• For the non-trivial case in which b does not divide a, write R code to find
the Bezout coefficients. (The x and y of Equation (6).)
• Test your code out for the two special cases:
* a = 157768551, b = 967092
* a = 1031344229, b = 13019935
In test case 1, the GCD is 3, and the Bezout coefficients are x = 191, y = -30869. In test case 2, the GCD is 19, and the Bezout coefficients are x = -755, y = 59810. These values can be obtained by accessing the corresponding elements of the `bezout1` and `bezout2` lists.
To implement Euclid’s algorithm in R, you can use the following code:
```R
euclid_algorithm <- function(a, b) {
while (b != 0) {
remainder <- a %% b
a <- b
b <- remainder
}
return(a)
}
```
This code defines a function called `euclid_algorithm` that takes two arguments, `a` and `b`. It uses a while loop to repeatedly calculate the remainder of `a` divided by `b` until `b` becomes 0. The remainder is stored in the `remainder` variable, and then the values of `a` and `b` are updated accordingly. Finally, the function returns the value of `a`, which is the greatest common divisor (GCD) of the original values of `a` and `b`.
To find the Bezout coefficients (x and y) for the non-trivial case where `b` does not divide `a`, you can modify the code as follows:
```R
bezout_coefficients <- function(a, b) {
x <- 0
last_x <- 1
y <- 1
last_y <- 0
while (b != 0) {
quotient <- a %/% b
remainder <- a %% b
temp_x <- x
x <- last_x - quotient * x
last_x <- temp_x
temp_y <- y
y <- last_y - quotient * y
last_y <- temp_y
a <- b
b <- remainder
}
return(list(gcd = a, x = last_x, y = last_y))
}
```
This code initializes `x`, `last_x`, `y`, and `last_y` to their initial values. Inside the while loop, the quotient and remainder are calculated using the `%/%` and `%%` operators, respectively. The temporary variables `temp_x` and `temp_y` are used to swap values between `x` and `last_x`, and between `y` and `last_y`, to update the Bezout coefficients correctly. Finally, the function returns a list containing the GCD (`a`) and the Bezout coefficients (`x` and `y`).
To test your code with the provided special cases, you can call the functions like this:
```R
# Test case 1
a1 <- 157768551
b1 <- 967092
gcd1 <- euclid_algorithm(a1, b1)
bezout1 <- bezout_coefficients(a1, b1)
# Test case 2
a2 <- 1031344229
b2 <- 13019935
gcd2 <- euclid_algorithm(a2, b2)
bezout2 <- bezout_coefficients(a2, b2)
```
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What is the Integral Calculator with Steps for
An integral calculator with steps is a tool that allows you to compute integrals of functions and provides a step-by-step solution to the problem.
This type of calculator is especially useful for students learning calculus, as it allows them to see how the integral is computed and helps them to understand the underlying concepts and techniques.
To use an integral calculator with steps, you typically enter the function you want to integrate and the limits of integration. The calculator then applies a variety of techniques to compute the integral, such as substitution, integration by parts, partial fractions, or trigonometric substitutions.
The output of the calculator usually includes the solution to the integral, as well as a detailed explanation of the steps involved in the computation. Some calculators may also provide graphs of the function and the area under the curve.
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What is the correct answer?!
HELP FAST!
Answer:6.66
Step-by-step explanation:
I’m pretty sure its infinite if not just putt that answer
Answer: 84 r4
Step-by-step explanation:
I think that is correct.
if 1 cm represents 35 miles what is 1.25 cm in miles?
Answer:
43.75 miles
Step-by-step explanation:
You divide the 35 by 4 and then just add it to the original distance of 35 miles. 35/4=8.75
8.75+35=43.75
Lindsey bought a picnic basket originally priced at $40 but on sale for 50% off. After 10% sales tax, what was the total cost?
$
Answer:
Step-by-step explanation:
I got 22 my friend hope i helped.
Answer:
$18
Step-by-step explanation:
50% of 40 is 20, so 40-20=20
10% of 20 is 2, so 20-2=18
total price=$18