The trip would be shorter by $\frac{1}{4}-\frac{15}{16} = \frac{1}{16}$ of a mile as per pythagorean theorem.
What is Pythagorean Theorem?The Pythagorean theorem is a fundamental concept in geometry that describes the relationship between the sides of a right triangle. A right triangle is a triangle that has one angle that measures exactly 90 degrees, which is also known as a right angle.
In the given question, to find out how much shorter your trip would be if you could fly like a bird, we first need to find out the total distance of your current trip.
You go 1 block south, which is $\frac{1}{16}$ of a mile.
You then go 1 block east, which is also $\frac{1}{16}$ of a mile.
You then go 5 blocks north, which is $5\cdot\frac{1}{16} = \frac{5}{16}$ of a mile.
Finally, you go 2 blocks east, which is $2\cdot\frac{1}{16} = \frac{1}{8}$ of a mile.
So the total distance of your trip is $\frac{1}{16}+\frac{1}{16}+\frac{5}{16}+\frac{1}{8}=\frac{1}{4}$ of a mile.
If you could fly like a bird, you could go directly from your house to the grocery store, which we can assume is a straight line. Let's call the distance between your house and the grocery store "x".
Using the Pythagorean theorem, we can see that $x² = (\frac{1}{16})²+ (\frac{1}{8}+5\cdot\frac{1}{16})²$, which simplifies to $x² \frac{225}{256}$.
So the distance you would have to travel if you could fly like a bird is $\sqrt{\frac{225}{256}} = \frac{15}{16}$ of a mile.
Therefore, your trip would be shorter by
$\frac{1}{4}-\frac{15}{16} = \frac{1}{16}$ of a mile if you could fly like a bird.
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An initial population of 385 quail increases at an annual rate of 30%. Write an exponential function to
model the quail population. What will the approximate population be after 5 years?
The exponential function that models the quail population is:
P(t) = P0 * (1 + r)^t
where:
P0 is the initial population (385)
r is the annual growth rate (30% or 0.3)
t is the time in years
Substituting the values, we get:
P(t) = 385 * (1 + 0.3)^t
Simplifying:
P(t) = 385 * 1.3^t
To find the approximate population after 5 years, we substitute t = 5:
P(5) = 385 * 1.3^5
P(5) = 385 * 3.277
P(5) = 1262.45
Therefore, the approximate population after 5 years is 1262 quail
y= 2x + 1 and - 4x + y = 9, solve the system of equations without graphing
After solving the given equations we know that the value of x and y are -4 and -7 respectively.
What are equations?
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
Ax+By=C is the usual form for two-variable linear equations.
A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y).
This form is also highly useful when solving systems involving two linear equations.
So, we have the equations:
y=2x+1 ...(1)
-4x+y=9 ...(2)
Now, substitute y=2x+1 in equation (2):
-4x+y=9
-4x+2x+1=9
-2x=8
x=-4
Now, insert x=-4 in equation (1):
y=2x+1
y=2(-4)+1
y=-8+1
y=-7
Therefore, after solving the given equations we know that the value of x and y are -4 and -7 respectively.
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a circle has a radius of $25.$ a circular sector, with an angle of $345.6^\circ$ at the center, is cut from the circle, and then rolled to form a cone. find the volume of the cone.
The volume of the cone is 97225.52 cubic units.
We have A circle that has a radius of 25.
A circular sector with an angle of 345.6° at the center is cut from the circle and then rolled to form a cone.
The volume of the cone = 1/3 πr²h
Where, r = radius of the base of the cone
h = height of the cone
The radius of the base of the cone = 25
Height of the cone: When the sector is rolled to form a cone, the sector's arc becomes the base's circumference. And the angle at the center of the sector becomes the cone's slant height (l).
Converting degree to radian: 1 radian = 180/π degree
1 degree = π/180 radian
345.6° = 345.6 × π/180
radian= 6.03 radian
Slant height (l) = rθ
l = 25 × 6.03
l = 150.75 units
Now, h² = l² - r² ⇒ 150.75² - 25² ⇒ 22100.5625
h = √(22100.5625) ⇒ 148.6625
The volume of the cone= 1/3 πr²h ⇒ 1/3 × π × 25² × 148.625 ⇒ 97225.52 cubic units
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a certain congressional committee consists of 13 senators and 9 representatives. how many ways can a subcommittee of 5 be formed if at least 2 of the members must be representatives?
Answer:
Step-by-step explanation:
The perimeter of a rectangle is 22 inches. The length of the rectangle is 6 inches THE EQUATION
If the perimeter of a rectangle is 22 inches, then the value of x is 1.
We can use the formula for the perimeter of a rectangle, which is:
[tex]$$P = 2l + 2w$$[/tex]
where P is the perimeter, l is the length, and w is the width.
We are given that the perimeter is 22 inches, so we can substitute P = 22 in the formula and w = 5:
[tex]$$22 = 2l + 2(5)$$[/tex]
Simplifying this equation, we get:
[tex]$$22 = 2l + 10$$[/tex]
[tex]$$2l = 12$$[/tex]
[tex]$$l = 6x$$[/tex]
So the length of the rectangle is 6x inches.
We can now substitute the values of l and w into the formula for the perimeter:
[tex]$$22 = 2(6x) + 2(5)$$[/tex]
Simplifying this equation, we get:
[tex]$$22 = 12x + 10$$[/tex]
[tex]$$12x = 12$$[/tex]
[tex]$$x = 1$$[/tex]
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Question:-
The perimeter of a rectangle is 22 inches. The width of the rectangle is 5 and the length is 2x. What is the value of x?
Please urgent need the work and answer
X=3.2
Y=6.1
Z=0.2
XZ +Y2
Answer: 12.84
Step-by-step explanation:
if x = 3.2 and y = 6.1 and Z = 0.2
then plug in the numbers
(3.2)(0.2) + (6.1)(2)
0.64 + 12.2 = 12.84
Any variable next to a number means multiplication.
if I was wrong lmk
I need to know………….
Answer:
the second one ( subtrracting 2)
Step-by-step explanation:
Is the following a right triangle?
A. Yes, using the slope formula we see that BC is perpendicular to AC.
B. Yes, using the distance formula we see that AC is congruent to BC
C. No, using the slope formula we see that BC is not perpendicular to AC
D. No, using the distance formula we see that AC is not congruent to BC
Yes, the triangle is a right triangle, the correct option is A.
Is the triangle a right triangle?We can see that the vertices of the triangle are at:
A = (6, 4)
B = (-6, 9)
C = (0, 0)
Then the lenghts of each of the sides is:
AC = √( (6 - 0)² + (4 - 0)²) = √52
BC = √( (-6 - 0)² + (9 - 0)²) = √117
AB = √( (6 + 6)² + (4 - 9)²) = 13
If this is a right triangle, then the pythagorean theorem must be true, so:
AB² = AC² + BC²
13² = √52² + √117²
169 = 52 + 117
169 = 169
This means that BC is perpendicular to AC.
So yes, it is a right triangle. The correct option is A.
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Select the correct answer.
Which function defines (f - g)(x)?
f (x)
+ 11
g(x)
=
=
5 + 2/1/20
x
A. (f
O c.
(ƒ − g)(x) = √√√² + 2/1 − 16
B. (f -
(ƒ −
g)(x) = √√√ − 2²/1 + 6
-
(f - g)(x)
=
OD. (f - g)(x) =
=
800
√3/3
-
+
2
x
+ 16
-
6
So, the correct option is (B) the function. [tex](f - g)(x)[/tex] is equal to the square root of[tex]x/8[/tex] minus [tex]2/x[/tex] plus 6.
What is function?A function is a rule or mapping that associates each input value from a set (called the domain) with a unique output value from another set (called the range or codomain).
For example, let's consider a function.[tex]f(x) = x^2[/tex]. Here, the domain of the function could be any set of real numbers, and the range would be the set of non-negative real numbers. For any given input value x, the function f(x) would return the output value. [tex]x^2.[/tex]
by the question.
The function (f - g) (x) is defined as the difference between f(x) and g(x) evaluated at x. Therefore:
[tex](f - g)(x) = f(x) - g(x)[/tex]
Substituting the given expressions for f(x) and g(x) into this formula, we get:
[tex](f - g)(x) = [\sqrt(x/8) + 11] - [5 + 2/x][/tex]
Simplifying this expression, we can combine like terms to get:
[tex](f - g)(x) = \sqrt(x/8) - 2/x + 6[/tex]
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on 12(Multiple Choice Worth 2 points)
(Laws of Exponents with Integer Exponents MC)
What is the value of
0-1
*((-))*₂
01
O-40,353,607
O 40,353,607
?
Answer:
-40353607 is the answer
1.2. Between which two integers does each of the following irrational numbers lie?
1.2.1. √8
1.2.2. √29
1.2.3 √37
We can see this by noticing that [tex]6^2 = 36 < 37 < 49 =[/tex] [tex]7^{2}[/tex]. Taking the square root of each expression, we get [tex]\sqrt36 < \sqrt37 < \sqrt49,[/tex] which simplifies to [tex]6 < \sqrt37 < 7[/tex].
What is square root?The square root of a number is a value that, when multiplied by itself, gives the original number. In mathematical notation, the square root of a number "x" is represented by the symbol "√x". For example, the square root of 25 is 5, because 5 multiplied by 5 equals 25.
Given by the question.
[tex]\sqrt29[/tex] lies between 5 and 6.
We can estimate this by recognizing that. [tex]5^2 = 25 < 29 < 36 =[/tex] [tex]6^{2}[/tex]. Taking the square root of each expression, we get √25 < √29 < √36, which simplifies to [tex]5 < \sqrt29 < 6[/tex].
[tex]\sqrt37[/tex]lies between 6 and 7.
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one gold nugget weighs 0.008 ounces. a second gold nugget weighs 0.8 ounces. how many times as much as the first nugget does the second nugget weigh? how many times as much as the second nugget does the first nugget weigh
Therefore , the solution of the given problem of unitary method comes out to be it weighs 0.01 times as much as the first nugget.
An unitary method is what?This common convenience, already-existing variables, or all important elements from the original Diocesan customizable survey that followed a particular event methodology can all be used to achieve the goal. If it does, there will be another chance to get in touch with the entity. If it doesn't, each of the crucial elements of a term proof outcome will surely be lost.
Here,
We can divide the weight of the second nugget by the weight of the first nugget to determine how many times as much the second nugget weights the first:
=> 0.8 oz / 0.008 oz = 100
The second piece is therefore 100 times heavier than the first.
We can divide the first nugget's weight by the second nugget's weight to determine how much the first nugget weights in relation to the second nugget:
=> 0.008 oz /0.8 oz = 0.01
In other terms, the second nugget weighs 100 times as much as the first nugget, or it weighs 0.01 times as much as the first nugget.
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Red hair (autosomal recessive) is found in approximately 4% of the people in Norway. if we assume that the Norwegian population is in Hardy-Weinberg equilibrium with respect to hair color: A) what are the frequencies of the red hair (r) and non-red hair (R) alleles? B) what is the frequency of heterozygotes? C) what is the proportion of matings that CAN NOT have a child with red hair?
The answer is: A) r=0.04; R=0.96 B) 8% C) 92.16%.
The Hardy-Weinberg equilibrium is a method for determining the frequency of certain genetic traits in a population. The following are the frequencies of the red hair (r) and non-red hair (R) alleles in the Norwegian population, according to the question: A) The total frequency of alleles is 1. If red hair (r) is found in approximately 4% of the people in Norway, then the frequency of the R allele must be 0.96 or 96%. R = 0.96 r = 0.04 B) The frequency of hetero zygotes in a population can be determined by multiplying the frequency of the R allele by the frequency of the r allele and then multiplying that number by 2.
Heterogeneous genotype = 2pq Here, p represents the frequency of the R allele, and q represents the frequency of the r allele. p = R = 0.96 q = r = 0.04 Therefore, 2pq = 2(0.96 x 0.04) = 0.077, or approximately 8%. C) In order for a child to have red hair, both parents must carry the r allele. If both parents are homozygous for the R allele, there is no chance that their child will have red hair. This means that the proportion of matings that cannot result in a child with red hair is (0.96 x 0.96) = 0.9216 or 92.16%.
Therefore, the answer is: A) r=0.04; R=0.96 B) 8% C) 92.16%.
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Find the linear approximation of the functionf(x)=4√81+x at a=0. Use it to approximate the numbers 4√81.02 and 4√80.99.
The linear approximation of the given function f(x) is 40.5.
As f(X) = 4√(81+x) so by L(x) = f(a) + f'(a)(x-a) where a=0 and f(x)=4√(81+x) Then f'(x) = (1/2)(81+x)^(-1/2) So, f'(a) = (1/2)(81)^(-1/2) = 1/18.
Thus, L(x) = f(0) + f'(0)(x-0)
L(x) = 4√(81) + (1/18)x
L(x) = 36 + (1/18)x
Now we are asked to approximate the values 4√81.02 and 4√80.99 by using the linear approximation we found above. Let's solve the problems. Approximation of 4√81.02.L(x) = 36 + (1/18)x Now x=81.02. Thus, L(81.02) = 36 + (1/18)81.02L(81.02) = 36 + 4.5L(81.02) = 40.5.
Thus, the linear approximation of 4√81.02 is 40.5. Approximation of 4√80.99.L(x) = 36 + (1/18)x Now x=80.99. Thus, L(80.99) = 36 + (1/18)80.99L(80.99) = 36 + 4.49444...L(80.99) = 40.49444... ≈ 40.5. Thus, the linear approximation of 4√80.99 is approximately 40.5.
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tomas has $1,000 to spend on a vacation. his plane ticket costs $348.25. if he stays 5.5 days at his destination, how much can he spend each day? write an inequality and then solve.
Tomas can spend at most $118.50 each day. The inequality equation is 5.5x ≤ 651.75.
Tomas has $1,000 to spend on a vacation. His plane ticket costs $348.25. If he stays 5.5 days at his destination, how much can he spend each day? Write an inequality and then solve.
Let x be the amount that Tomas can spend each day. Since Tomas has to pay for the plane ticket, he will have $1,000 − $348.25 = $651.75 left to spend on the rest of the vacation.
Then, since he is staying for 5.5 days, the total amount he can spend would be 5.5x dollars. The inequality that represents the problem is as follows:
5.5x ≤ 651.75
To solve for x, divide both sides by 5.5
5.5x/5.5 ≤ 651.75/5.5x ≤ 118.5
Therefore, Tomas can spend at most $118.50 each day.
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Answer:
The answer to this solution is 118.5 a day
Step-by-step explanation:
The original price is $1,000 for the ticket it costs $348.25 and Tomas is staying for 5.5 days so dividing 651.75 by 5.5 is the ANSWER 118.5
What is the slope-intercept form of the linear equation 4x + 2y = 24?
Drag and drop the appropriate number, symbol, or variable to each box.
Answer:
y = -2x + 12
Step-by-step explanation:
In order to put the equation in slope intercept form [tex]y=mx+b[/tex] we need to solve for y.
[tex]4x+2y=24[/tex]
Subtract 4x on both sides
[tex]2y=-4x+24[/tex]
Divide by 2
[tex]y=-2x+12[/tex]
6(2x-3)-2(2x+1) simplest form
Answer:
16x-20
Step-by-step explanation:
6(2x-3)-2(2x+1)
12x-18-4x+2
16x-20
the heights of adult men can be approximated as normal with a mean of 70 and standard eviation of 3 what is the probality man is shorter than
Question: The heights of adult men can be approximated as normal, with a mean of 70 and a standard deviation of 3, the probability that a man is shorter than 65 inches is approximately 0.0475 or 4.75%.
Let X be the height of an adult man, which follows a normal distribution with mean μ = 70 and standard deviation σ = 3. Then, we need to find the probability that a man is shorter than some height, say x₀. We can write this probability as P(X < x₀).To find P(X < x₀), we need to standardize the random variable X by subtracting the mean and dividing by the standard deviation. This yields a new random variable Z with a standard normal distribution. Mathematically, we can write this transformation as:Z = (X - μ) / σwhere Z is the standard normal variable.
Now, we can find P(X < x₀) as:P(X < x₀) = P((X - μ) / σ < (x₀ - μ) / σ) = P(Z < (x₀ - μ) / σ)Here, we use the fact that the probability of a standard normal variable being less than some value z is denoted as P(Z < z), which is available in standard normal tables.
Therefore, to find the probability that a man is shorter than some height x₀, we need to standardize the height x₀ using the mean μ = 70 and the standard deviation σ = 3, and then look up the corresponding probability from the standard normal table.In other words, the probability that a man is shorter than x₀ can be expressed as:P(X < x₀) = P(Z < (x₀ - 70) / 3)We can now use standard normal tables or software to find the probability P(Z < z) for any value z.
For example, if x₀ = 65 (i.e., we want to find the probability that a man is shorter than 65 inches), then we have:z = (65 - 70) / 3 = -1.67Using a standard normal table, we can find that P(Z < -1.67) = 0.0475. Therefore, the probability that a man is shorter than 65 inches is approximately 0.0475 or 4.75%. Thus, P(X < 65) = 0.0475 or 4.75%. Therefore, the probability that a man is shorter than 65 inches is approximately 0.0475 or 4.75%.
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c) R= {(x,y): Y is the area of triangle x 3 determine if the relation is function or not
You have given a relation R = {(x,y): y is the area of triangle x 3}. This means that for each value of x, which represents the base of a triangle, y is the area of that triangle with height 3.
What is the function?To find out if this relation is a function, we need to check if there are any repeated x-values with different y-values. If there are none, then it is a function.
One way to do this is to use the formula for the area of a triangle: A = (1/2)bh, where b is the base and h is the height. Using this formula, we can find the y-values for some x-values:
[tex]x | y| - 0 | 0 1 | (1/2) * 1 * 3 = 3/2 2 | (1/2) * 2 * 3 = 3 3 | (1/2) * 3 * 3 = 9/2 4 | (1/2) * 4 * 3 = 6[/tex]
Therefore, As you can see, there are no repeated x-values with different y-values, this relation R is a function.
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If the midpoint of 2 sides of a triangle are connected with a segment then
The Midpoint is the middle- point of the line member. The midpoint connecting two sides of a triangle is resemblant to the third side and half as long.
The midpoint is the middle of the line member. It's equidistant from both endpoints and is the centroid of the member and endpoints. Cut a member in two.
The midpoint theorem states that a line member drawn from the midpoint of two sides of a triangle is resemblant to the third side and half the length of the third side of the triangle.
The mean theorem helps us find the missing values for the sides of triangles. Connects the sides of a triangle with a line member drawn from the midpoints of two sides of the triangle.
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Question is in photo answer a through d please
The products written in scientific notation are:
a) [tex]5.88*10^9[/tex]
b) [tex]15*10^{12}\\[/tex]
c) [tex]8.4*10^{-10}[/tex]
d) [tex]42*10^{-7}[/tex]
How to take the products?The first product we need to solve is:
[tex](4.2*10^6)*(1.4*10^3)[/tex]
We can reorder that product into the one below:
[tex](4.2*1.4)*(10^6*10^3)[/tex]
The exponents in the right side are added, so we get:
[tex](4.2*1.4)*(10^6*10^3) = 5.88*10^{3 + 6} = 5.88*10^9[/tex]
Now let's do the same in the others.
b)
[tex](5*10^5)*(3*10^7)\\= 5*3*10^{5 + 7}\\= 15*10^{12}\\[/tex]
Now we need to write the first number between 0 and 10, then we can rewrite this as:
[tex]1.5*10^{13}[/tex]
c) Again doing the same thing.
[tex](4*10^{-3})*(2.1*10^{-7}})\\= 4*2.1*10^{-3 - 7}\\= 8.4*10^{-10}[/tex]
d) Finally, this last product is:
[tex](6*10^{-2})*(7*10^{-5}})\\= 6*7*10^{-2 - 5}\\= 42*10^{-7}[/tex]
Again we need to have a number between 0 and 10, so we can rewrite this as:
[tex]4.2*10^{-8}[/tex]
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I need the answer for number 3 step by step, please help!
Answer:
[tex]\frac{-1}{3}[/tex]
Step-by-step explanation:
Look at the red slope triangle that is drawn. If you start at the point on the left, you go down 1 unit and then to the right 3 units. This would be represented by -1/3. Down would be negative and going right would be positive. The slope is the rise over the run.
Helping in the name of Jesus.
Fractions Questions 2
Happy Halloween. Determine the sampling distribution of the mean when you choose any 2 pumpkins out of 4 with the following weight, 35% of children prefer pumpkin D, 30% prefer pumpkin B,I and 20% prefer pumpkin A. Consider sampling without replacement. Pumpkin A B C DWeight(lbs) 10 12 8 14 Question 2 The amount of a particular impurity in a batch of a certain chemical product is a random variable with mean value 4.0 g and standard deviation 1.5 g. If 50 batches are independently prepared, what is the (approximate) probability that the sample average amount of impurity X is between 3.5 and 3.8 g?
1) The standard deviation is 0.275
2) The approximate probability is 0.165
Sampling distribution: The sampling distribution is a probability distribution of a statistic determined from a larger number of samples. A statistic, such as a mean or a standard deviation, is a numerical quantity calculated from data and used to make inferences about the population's parameters.
For the first question, we can use the hypergeometric distribution to find the sampling distribution of the mean when we choose any 2 pumpkins out of 4.
Let X be the number of pumpkins preferred by the 2 children we sample. Then X follows a hypergeometric distribution with N = 4 (total number of pumpkins), n = 2 (number of pumpkins we choose), and K = {0, 1, 2} (possible number of pumpkins preferred).
The probability mass function of X is given by:
P(X = k) = (K choose k) * (N - K choose n - k) / (N choose n)
where (a choose b) is the binomial coefficient "a choose b".
Using this formula and the given weights, we can calculate the probabilities for k = 0, 1, and 2:
P(X = 0) = (2 choose 0) * (2 choose 2) / (4 choose 2) = 1/6
P(X = 1) = (2 choose 1) * (2 choose 1) / (4 choose 2) = 2/3
P(X = 2) = (2 choose 2) * (2 choose 0) / (4 choose 2) = 1/6
Now we can find the mean and standard deviation of the sampling distribution of the mean, which is approximately normal by the central limit theorem since the sample size is relatively small:
Mean = E(X) = n * (K/N) = 2 * [(00.2)+(10.3)+(2*0.35)] / 4 = 0.95
Standard deviation = sqrt(n * K/N * (1 - K/N) * (N - n)/(N - 1))
= sqrt(2 * 0.95 * (1 - 0.95) * 2/3)
= 0.275
For the second question, we can use the central limit theorem to approximate the sampling distribution of the sample mean. Since we have a large sample size (n = 50), the sample mean X follows an approximately normal distribution with mean μ = 4.0 g and standard deviation
σ/sqrt(n) = 1.5/sqrt(50) ≈ 0.212 g.
Then, we can calculate the z-scores for the lower and upper bounds of the interval:
z_1 = (3.5 - 4.0) / 0.212 ≈ -2.36
z_2 = (3.8 - 4.0) / 0.212 ≈ -0.94
Using a standard normal distribution table or calculator, we can find the probabilities corresponding to these z-scores:
P(Z < -2.36) ≈ 0.009
P(Z < -0.94) ≈ 0.174
Then, we can find the probability that X falls within the interval [3.5, 3.8] by taking the difference between these probabilities:
P(3.5 ≤ X ≤ 3.8) ≈ P(-2.36 ≤ Z ≤ -0.94) ≈ 0.174 - 0.009 ≈ 0.165
Therefore, the approximate probability that the sample average amount of impurity X is between 3.5 and 3.8 g is 0.165.
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The summaries of data from the balance sheet, income statement, and retained earnings statement for two corporations, Walco Corporation, and Gunther Enterprises, are presented below for 2017.
Determine the missing amounts. Assume all changes in stockholders equity are due to changes in retained earnings
Walco Corporation Gunther Enterprise
Beginning of year Total assets $100,000 $159,000
Total liabilities 73,000 $_____ (d)
Total stockholders' equity $_____ (a) 67,500
End of year Total assets $_____ (b) 190,000
Total liabilities 128,000 50,000
Total stockholders' equity 54,000 $_____ (e)
Changes during year in retained earnings Dividends $_____ (c) 4,900
Total revenues 219,000 $_____ (f)
Total expenses 167,000 79,000
The missing amounts for Walco Corporation and Gunther Enterprises assuming all changes in stockholders equity are due to changes in retained earnings are
(a) Walco Corporation Total Stockholders' Equity = $54,000
(b) Walco Corporation Total Assets = $182,000
(c) Walco Corporation Dividends = $47,100
(d) Gunther Enterprises Total Liabilities = $140,000
(e) Gunther Enterprises Total Stockholders' Equity = $91,500
(f) Gunther Enterprises Total Revenues = $135,100
A balance sheet is a financial statement that reports a company's assets, liabilities, and stockholder equity on a specific date. Assets are resources a company owns that have monetary value, liabilities are obligations that must be paid in the future, and stockholder equity is the difference between a company's assets and liabilities. To calculate the missing amounts, you need to subtract the beginning of year figures from the end of year figures.
a) Total liabilities + Total stockholders' equity = Total assets
Total liabilities + $54,000 = $100,000
Total liabilities = $46,000
(b) Total assets = Total liabilities + Total stockholders' equity
Total assets = $128,000 + $54,000
Total assets = $182,000
(c) Changes during year in retained earnings = Total revenues - Total expenses - Dividends
Changes during year in retained earnings = $219,000 - $167,000 - $4,900
Changes during year in retained earnings = $47,100
The missing values for Gunther Enterprises:
(d) Total liabilities + Total stockholders' equity = Total assets
$67,500 + $(e) = $159,000
$(e) = $91,500
(f) Changes during year in retained earnings = Total revenues - Total expenses - Dividends
Changes during year in retained earnings = $(f) - $79,000 - $4,900
Changes during year in retained earnings = $(f) - $83,900
Using the balance sheet equation, we can find the missing values:
(d) Total liabilities = Total assets - Total stockholders' equity
Total liabilities = $159,000 - $67,500
Total liabilities = $91,500
(e) Total stockholders' equity = Total assets - Total liabilities
Total stockholders' equity = $190,000 - $50,000
Total stockholders' equity = $140,000
(f) Changes during year in retained earnings = Total revenues - Total expenses - Dividends
Changes during year in retained earnings = $219,000 - $79,000 - $4,900
Changes during year in retained earnings = $135,100
Therefore, the missing amounts are:
(a) Walco Corporation Total Stockholders' Equity = $54,000
(b) Walco Corporation Total Assets = $182,000
(c) Walco Corporation Dividends = $47,100
(d) Gunther Enterprises Total Liabilities = $140,000
(e) Gunther Enterprises Total Stockholders' Equity = $91,500
(f) Gunther Enterprises Total Revenues = $135,100
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Let $f(x)=(x^2+6x+9)^{50}-4x+3$, and let $r_1,r_2,\ldots,r_{100}$ be the roots of $f(x)$. Compute $(r_1+3)^{100}+(r_2+3)^{100}+\cdots+(r_{100}+3)^{100}$. Can you please explain the solution?
The sum of (r_1+3)^100+(r_2+3)^100+...+(r_{100}+3)^100 is 4^100
We can start by applying the binomial theorem to expand the expression (r + 3)^100:
(r + 3)^100 = ∑(i=0)^100 (100 choose i) r^i 3^(100-i)
Using this expression, we can write each term in the desired sum as:
(r_k + 3)^100 = ∑(i=0)^100 (100 choose i) r_k^i 3^(100-i)
Therefore, the sum we want to compute can be written as:
∑(k=1)^100 (r_k + 3)^100 = ∑(k=1)^100 ∑(i=0)^100 (100 choose i) r_k^i 3^(100-i)
Now, let's focus on the coefficients of this expression. Notice that each coefficient is a sum of terms of the form (100 choose i) r_k^i 3^(100-i), which are the same for all k. Therefore, we can factor out these terms from the sum over k:
∑(k=1)^100 (r_k + 3)^100 = ∑(i=0)^100 (100 choose i) 3^(100-i) ∑(k=1)^100 r_k^i
But the sum ∑(k=1)^100 r_k^i is just the i-th power sum of the roots of f(x). Using Vieta's formulas, we know that the i-th power sum of the roots of a polynomial of degree n can be expressed in terms of its coefficients:
s_i = (-1)^i × a_{n-i}/a_n,
where s_i is the i-th power sum and a_i is the coefficient of x^i in the polynomial. Applying this formula to f(x), we get:
s_0 = 100, s_1 = -6, s_2 = 0, ..., s_{99} = 0, s_{100} = -4
Substituting these values into the expression we derived above, we get:
∑(k=1)^100 (r_k + 3)^100 = ∑(i=0)^100 (100 choose i) 3^(100-i) (-1)^i a_{50-i}/a_{50}
where a_{50-i} is the coefficient of x^{50-i} in f(x). Since f(x) is a polynomial of degree 100, its coefficient a_{50} is nonzero, so we can use it as a denominator to simplify the expression further:
∑(k=1)^100 (r_k + 3)^100 = ∑(i=0)^100 (100 choose i) 3^(100-i) (-1)^i a_{50-i}/a_{50}
= ∑(i=0)^50 (100 choose i) 3^(100-i) a_{50-i}/a_{50} - ∑(i=51)^100 (100 choose i) 3^(100-i) a_{50-i}/a_{50}
The first sum can be computed using the binomial theorem:
∑(i=0)^50 (100 choose i) 3^(100-i) a_{50-i}/a_{50} = (3+1)^{100} a_{50}/a_{50}
= 4^{100}
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Pls help ASAP
photo below
Answer:
its ED DC CE i think hope this help :D sorry if you get this wonge :(
Step-by-step explanation:
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This composite figure is created by placing a sector of a circle on a rectangle. What is the area of this composite figure? Show you work
Thus, the total area of composite figure (circle on a rectangle) is found as 29.91 m².
Explain about the sector of the circle?A sector is a portion of the circle that is formed by two distinct radii. somewhat of like a slice of pie or pizza. A line segment known as a chord connects two points on a circle. A unique kind of chord called the diameter passes through the circle's focal point.Area of sector of the circle = (Ф/360°) *π*r²
r is the radius = 5.5 m
π = 3.14
Area = (30/360°) *3.14 * 5.5²
Area = 7.91 m²
Area of rectangle = width × length
Area = 4 × 5.5 = 22 m²
Total area of composite figure = area of the circle's sector + area of the rectangle
Total area of composite figure = 7.91 m² + 22 m² = 29.91 m²
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Can someone please help me with this? I really need help on it
A system of linear inequalities that the graph represent include the following:
x ≥ 4.
y < -x - 2
y ≥ 3x + 3
y > x - 4
What is the slope-intercept form?In Mathematics, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represent the gradient, slope, or rate of change.x and y represent the data points.c represents the y-intercept or initial value.At data points (-3, 0) and (0, 3), the slope of this line can be calculated as follows;
Slope = (3 - 0)/(0 + 3) = 3/3 = 1
y-intercept = 3.
Therefore, a linear inequality that models the line is given by:
y ≥ 3x + 3
At data points (-2, 0) and (0, -2), the slope of this line can be calculated as follows;
Slope = (-2 - 0)/(0 + 2) = -2/2 = -1
y-intercept = -2.
Therefore, a linear inequality that models the line is given by:
y < -x - 2
At data points (4, 0) and (0, -4), the slope of this line can be calculated as follows;
Slope = (-4 - 0)/(0 - 4) = -4/-4 = 1
y-intercept = -4.
Therefore, a linear inequality that models the line is given by:
y > x - 4
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As a special end-of-year treat, Kyle is making chocolate-covered strawberries for his teachers. If he dips s strawberries in chocolate, each teacher will get s 4 chocolate-covered strawberries. Last night, Kyle dipped 16 strawberries in chocolate
Each teacher will get 4 chocolate-covered strawberries. If Kyle dipped s strawberries in chocolate, and there are four teachers, each of them will get s/4 chocolate-covered strawberries. we can calculate the strawberries through the method of division.
Since Kyle dipped 16 strawberries in chocolate, and there are four teachers, each teacher would get 16 divided by 4 to get a perfect answer.
16/4 = 4 chocolate-covered strawberries will be distributed to four teachers of Kyle.
Therefore, each teacher will get 4 chocolate-covered strawberries. We can calculate according to the different numbers of teachers if we know to divide the total number of strawberries with the number of the population of teachers.
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The correct question is
As a special end-of-year treat, Kyle is making chocolate-covered strawberries for his teachers. If he dips s strawberries in chocolate, each teacher will get s/4 chocolate-covered strawberries. Last night, Kyle dipped 16 strawberries in chocolate.
How many chocolate-covered strawberries will each teacher get?
Write your answer as a whole number or decimal.
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