Answer: Use a point-slope equation to find the amount he will raise if he completes the walk.
Step-by-step explanation:
We can start by using the point-slope equation:
y - y1 = m(x - x1)
where y is the amount James raises, x is the number of miles he walks, m is the rate at which he raises money per mile, and (x1, y1) is a point on the line.
We know that James raises $15 extra for every mile he walks, so m = 15. We also know that he has received $600 in fixed pledges, which is the amount he would raise if he walked 0 miles. So (0, 600) is a point on the line.
Using this information, we can write the point-slope equation:
y - 600 = 15(x - 0)
Simplifying, we get:
y = 15x + 600
This equation tells us the amount James will raise, y, for any number of miles he walks, x. For example, if he completes the 6-mile walk, we can plug in x = 6 to find:
y = 15(6) + 600 = 690
Therefore, if James completes the walk, he will raise $690.
{Hope This Helps! :)}
the first term of an a.p is 14 and the sum of the first five terms and the first ten terms are equal inmagnitude but opposite in sign. the 3rd term of the ap is:
The first term of an A.P is 14 and the sum of the first five terms and the first ten terms are equal in magnitude but opposite in sign. The 3rd term of the A.P is 70/11.
The first term of an A.P is 14. Let the common difference be d. Then the second term of the A.P is given by 14 + d. Similarly, the third term of the A.P is given by 14 + 2d.
The third term of the A.P.Solution:
Sum of the first 5 terms of the A.P can be expressed as:
5/2 [2a + (5 - 1) d] = 5/2 [2(14) + 4d] = 35 + 10d
Sum of the first 10 terms of the A.P can be expressed as:
10/2 [2a + (10 - 1) d] = 10/2 [2(14) + 9d] = 70 + 45d
According to the question, the sum of the first five terms and the first ten terms are equal in magnitude but opposite in sign. It can be written as follows: 35 + 10d = - (70 + 45d)
Simplifying the above equation, we get:
55d = -105⇒ d = -105/55 = -21/11
Substituting the value of d in 14 + 2d, we get:
14 + 2d = 14 + 2(-21/11) = 14 - 42/11= 112/11 - 42/11= 70/11
Hence, the third term of the A.P is 70/11.
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WZ and XR are diameters. Find the measure of arc ZWX. (The figure is not drawn to scale. )
The measure of arc ZWX is 180 degrees.
Given that WZ and XR are diameters, we know that they are both perpendicular to chord WX. This creates four right angles at point X, and as a result, we have a rectangle formed by the four line segments.
Since WZ and XR are diameters, they each extend from one end of the rectangle to the other. This means that arc ZWX is actually a semicircle, with a measure of 180 degrees.
To see why this is the case, consider that a full circle has a measure of 360 degrees. Since arc ZWX spans exactly half of the circle, it must have a measure of half the circle, or 180 degrees.
In summary, the measure of arc ZWX is 180 degrees. This can be derived from the fact that WZ and XR are diameters, which create a rectangle and a semicircle in the process. While the figure may not be drawn to scale, the relationships between the different line segments and angles remain constant, allowing us to determine the measure of arc ZWX with confidence.
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Sophia spends a total of $6.30 on cheese. She buys 500g of Cheddar cheese and 200g of Stilton cheese. The cost of the Cheddar cheese is $9.20 for 1kg. Work out the cost of 1kg of the Stilton cheese
Answer:
The price would be 7.20
Step-by-step explanation:
20 points!! please help, will give brainliest
Answer:
(-0.8, 2.2)
Step-by-step explanation:
Where the two lines intersect is the solution to the System of Equations.
Answer:
the answer would be (-0.8, 2.2) since it hasn't hit -3 yet and if it were to be -1 it would be in the bottom left
multiple choice write a function rule for finding the amount of daily pay, p, in the following situation: a bus driver gets paid $100 each day plus $0.20 per kilometer, k. a. 100
The equation for finding amount of daily pay is bus-driver gets paid $100 each day plus $0.20 per kilometer, "k" is p = 100 + 0.20k.
The equation for finding the amount of daily pay, "p", in the given situation would be : p = 100 + 0.20k,
In this equation, "p" represents the total daily-pay, "100" is the fixed amount paid each day, and
"$0.20" is the rate per kilometer. "k" represents the number of kilometers driven on that day.
To calculate the daily pay, you add the fixed amount of $100 to the product of the rate per kilometer and the number of kilometers driven on that day.
Therefore, the required equation is p = 100 + 0.20k.
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The given question is incomplete, the complete question is
Write an equation for finding the amount of daily pay, p, in the following situation: A bus driver gets paid $100 each day plus $0.20 per kilometer, "k".
(b) A different circle has a circumference of 120 cm.
What is the radius of the circle?
You must show your working.
Answer:
r≈19.1cm
Step-by-step explanation:
Using the formula
C=2πr
Solving forr
r=C
2π=120
2·π≈19.09859cm
Hope this helps
I honestly have no clue what im saying here-
Answer:
the answer is lateral area
The vertex form of the equation of a parabola is y=2(x-3)^2+5. What is the standard form of the equation?
To convert the vertex form of a quadratic equation to standard form, we need to expand the squared term and simplify the expression.
Starting with the vertex form of the equation of a parabola:
y = 2(x - 3)^2 + 5
We can expand the squared term using the square of a binomial formula:
y = 2(x^2 - 6x + 9) + 5
Next, we distribute the coefficient 2:
y = 2x^2 - 12x + 18 + 5
Simplifying the constant terms:
y = 2x^2 - 12x + 23
This is the standard form of the equation of the parabola.
What polynomial has a graph that passes through the given points? (-4, 89), (-3, 7), (-1, -1), (1, -1), (4, 329).
Therefore, the polynomial that passes through the given points is: f(x) = 6 - 38x - 6x^2 + 4x^3 + 3x^4.
To find the polynomial that passes through the given points, we can use the method of interpolation. Since we have five points, we can use a fourth-degree polynomial to fit the data.
Let's assume that the polynomial is of the form:
f(x) = a0 + a1x + a2x^2 + a3x^3 + a4x^4
We can find the coefficients a0, a1, a2, a3, and a4 by substituting the given points into the equation and solving the resulting system of linear equations.
Substituting (-4, 89) into the equation, we get:
89 = a0 - 4a1 + 16a2 - 64a3 + 256a4
Substituting (-3, 7) into the equation, we get:
7 = a0 - 3a1 + 9a2 - 27a3 + 81a4
Substituting (-1, -1) into the equation, we get:
-1 = a0 - a1 + a2 - a3 + a4
Substituting (1, -1) into the equation, we get:
-1 = a0 + a1 + a2 + a3 + a4
Substituting (4, 329) into the equation, we get:
329 = a0 + 4a1 + 16a2 + 64a3 + 256a4
Now we have five linear equations with five unknowns, which we can solve using any method of linear algebra. One possible way is to use matrix inversion. After solving for the coefficients, we get:
a0 = 6
a1 = -38
a2 = -6
a3 = 4
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I’ll give BRAINLIEST to whoever’s right
Approximate the logarithm using the properties of logarithms, given log, 2≈ 0.3562, log, 3≈ 0.5646, and log, 5 ≈ 0.8271.(Round your answer to four decimal
places.)
logb (3b^4)
The approximated value of the logarithm expression is 0.5646 + 4log(b)
Approximating the logarithm expression using the logarithms propertyFrom the question, we have the following parameters that can be used in our computation:
log, 2≈ 0.3562,
log, 3≈ 0.5646, and
log, 5 ≈ 0.8271
Also, we have
logb (3b⁴)
Using the logarithms property, we have
logb (3b⁴) = logb (3) + log(b⁴)
This gives
logb (3b⁴) = logb (3) + 4log(b)
Substitute the known values in the above equation, so, we have the following representation
logb (3b⁴) = 0.5646 + 4log(b)
Hence, the approximated value is 0.5646 + 4log(b)
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Solve the application problem.
In one day a baker used 1/3
of a pound of flour, then 1/4
of a pound of flour, then 5/12
of a pound of flour. How much flour was used that day?
Answer:
1 cup
Step-by-step explanation:
What is a fraction?A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.
To solve for the total number of cups used, we need to first convert each fraction to have a common denominator.
What is a common denominator?A common denominator consists of two or more fractions that have the same denominator. This makes it easier to perform numeric equations, and to solve them.
As of now, each fraction looks like this:
[tex]\frac{1}{3} +\frac{1}{4} +\frac{5}{12}[/tex]Looking at each of the denominators, we can see that 12 is a multiple of both 4 and 3!
So, let's convert [tex]\frac{1}{3}[/tex].
3 can be multiplied by 4 to get 12.Now that we have the denominator, we need to multiply the numerator by the same amount, so it stays equivalent.
1 can be multiplied by 4 to get 4.[tex]\frac{1}{3} =\frac{4}{12}[/tex]Now let's convert [tex]\frac{1}{4}[/tex].
4 can be multiplied by 3 to get 12.
1 can be multiplied by 3 to get 3.
[tex]\frac{1}{4} =\frac{3}{12}[/tex]Now, each fraction looks like this:
[tex]\frac{4}{12}+ \frac{3}{12}+ \frac{5}{12}[/tex]Adding up the numerators:
4 + 3 + 5 = 12Adding that back on top of the denominator:
[tex]\frac{12}{12} = 1[/tex]So, [tex]\frac{4}{12}+ \frac{3}{12}+ \frac{5}{12} = \frac{12}{12}[/tex] or 1.
Therefore 1 cup of flour was used that day.
One popular activity that tourists participate in when they visit Alaska is panning for gold. A gift shop by the panning center sells blocks of clay. The packaging on the clay claims that one in five blocks contains gold. A frequent purchaser of this item believes that this is an overstatement. To investigate, he purchases a random sample of 50 blocks from the large display in the store and finds that 8 of the blocks contain gold.
Based on this sample, is there convincing evidence that the true proportion of blocks that contain gold is less than 0.20? Use = 0.10. Provide statistical evidence to support your answer.
There is convincing evidence to support the conclusion that the true proportion of blocks that contain gold is less than 0.20.
How to explain the hypothesisThe null hypothesis is that the true proportion of blocks that contain gold is equal to 0.20. The alternative hypothesis is that the true proportion of blocks that contain gold is less than 0.20.
The test statistic is calculated as follows:
z = (p - p₀) / √(p₀(1-p₀) / n)
The test statistic is equal to -2.00.
The p-value is calculated as follows:
p-value = 2 * P(Z < -2.00)
The p-value is equal to 0.0477.
Since the p-value is less than the significance level of 0.10, we reject the null hypothesis. Therefore, there is convincing evidence to support the conclusion that the true proportion of blocks that contain gold is less than 0.20.
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I need some help please, How can you map figure P onto figure Q?
Answer:
6 units right
Step-by-step explanation:
To translate figure P onto figure Q, just translate the figure 6 units to the right.
The probablity of selecting a particular color almond M&M (according to the website) from a bag of M&Ms is listed below. Let the probability of selecting a color be represented as Br= Brown, Y= Yellow, R= Red, Bl = Blue, O= Orange and G = Green. A probability distribution is listed below.
brown yellow red blue orange green
probability 0.1 0.2 0.1 0.2 0.2 0.2
Suppose that you randomly select one M&M. What is the P(R or Br)?
To find the probability of selecting either a Red or a Brown almond M&M, we need to add their respective probabilities. The probability of selecting either a red or brown almond M&M is 0.2 or 20%.
P(R or Br) = P(R) + P(Br)
From the table given, we know that the probability of selecting a Red almond M&M is 0.1 and the probability of selecting a Brown almond M&M is also 0.1. Therefore,
P(R or Br) = 0.1 + 0.1 = 0.2
So, the probability of selecting either a Red or a Brown almond M&M is 0.2 or 20%.
In summary, to find the probability of selecting either one event or another event, we add their probabilities together. In this case, the probability of selecting a Red or a Brown almond M&M is 0.2 or 20%.
To find the probability of selecting either a red (R) or brown (Br) almond M&M, you can simply add the individual probabilities for each color since they are mutually exclusive events (selecting one does not affect the other).
According to the given probability distribution, the probability of selecting a red M&M (R) is 0.1, and the probability of selecting a brown M&M (Br) is 0.1.
So, to find the probability of selecting either a red or brown M&M (P(R or Br)), you can use the formula:
P(R or Br) = P(R) + P(Br)
Plugging in the given probabilities:
P(R or Br) = 0.1 (for R) + 0.1 (for Br)
P(R or Br) = 0.2
So, the probability of selecting either a red or brown almond M&M is 0.2 or 20%.
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The length of a rectangle is $6cm$ less than three times its width. The perimeter of rectangle is. Find the dimensions using Cramer’s rule
To find the dimensions of the rectangle, we need to use Cramer's rule, which is a method for solving systems of linear equations.
Let's start by defining the variables:
Let x be the width of the rectangle in cm.
Let y be the length of the rectangle in cm.
According to the problem, we have two equations:
y = 3x - 6 (the length is 6cm less than three times the width)
2(x + y) = P (the perimeter of the rectangle is P)
We can rewrite the second equation as:
2x + 2y = P
To solve for x and y, we need to set up a matrix and apply Cramer's rule. The matrix is:
| 0 1 | | x | | -6 |
| 2 2 | x | y | = | P |
Using Cramer's rule, we can solve for x and y as follows:
x = (|-6 1| / |-2 1|) = 9
y = (|0 -6| / |-2 1|) = 12
Therefore, the width of the rectangle is 9 cm and the length of the rectangle is 12 cm.
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darwin's geometric ratio of increase pertains specifically to
Darwin's geometric ratio of increase pertains specifically to the growth rate of populations in biological organisms. According to Darwin's theory of evolution, populations have the potential to increase exponentially over time if certain conditions are met. The geometric ratio of increase, often denoted as "r" or the intrinsic rate of natural increase, represents the factor by which a population multiplies during each reproductive cycle or generation.
In the context of natural selection, individuals with higher reproductive rates (higher r-values) have a greater chance of passing on their genetic traits to the next generation. Over time, this can lead to significant population growth and evolutionary changes within a species. However, the geometric ratio of increase is limited by various factors, such as availability of resources, competition, predation, and environmental constraints, which can result in a balance between population growth and environmental carrying capacity.
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if log 7 equals a and log 8 equals b then log 224 equals
A: a + 5/3b
B: a + 4b
C: 4a + B
D: 4ab
E: none of the above
If log 7 equals a and log 8 equals b then log 224 equals: E: none of the above.
What is log?Simplify the expression for log (224) by using:
log (ab) = log (a) + log (b) and log (a/b) = log (a) - log (b):
So,
log (224) = log ( 7 × 8 × 4)
= log (7) + log (8) + log (4)
Since log(4) = 0 (since 4 = 2^2)
Simplify
log(224) = log (7) + log (8) + log (4)
= log 7 + log 8
= a + b
Therefore the correct option is E.
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It would take 1 person 70 days of work to
build a house extension.
2 people have been working for 7 days on
this house extension.
a) How many days would it have taken 1
person to do this amount of work?
b) How many days would it take 1 person to
finish building this house extension?
Answer:
a) It would have taken 1 person 14 days to do this amount of work.
b) It would take 1 person 56 days to finish building this house extension.
We know that 1 person can build a house extension in 70 days. This means that in 1 day, 1 person can do 1/70 of the work. In 7 days, 2 people can do 2 * 7 * 1/70 = 2/10 of the work. This means that 1 person can do 1/10 of the work in 7 days. To finish the remaining 8/10 of the work, 1 person would need 7 * 8 = 56 days.
Step-by-step explanation:
Please solve for all!!! I need help asap please and thank you.
The value of the measure of each sides indicated are:
x = 4x = 11x = 21.9x = 32.2x = 9.1x = 9.1x = 7.4x = 7.8How do i determine the measurement of the indicated side?The measurement of the indicated side can be obtain as illustrated below:
1. The value of x can be obtain as follow:
Angle (θ) = 20Adjacent = 11Opposite = x =?Tan θ = Opposite / Adjacent
Tan 20 = x / 11
Cross multiply
x = 11 × Tan 20
Value of x = 4
2. The value of x can be obtain as follow:
Angle (θ) = 27Opposite = 5Hypotenuse = x =?Sine θ = Opposite / Hypotenuse
Sine 27 = 5 / x
Cross multiply
x × Sine 27 = 5
Divide both sides by Sine 27
x = 5 / Sine 27
Value of x = 11
3. The value of x can be obtain as follow:
Angle (θ) = 27.2Opposite = 10Hypotenuse = x =?Sine θ = Opposite / Hypotenuse
Sine 27.2 = 10 / x
Cross multiply
x × Sine 27.2 = 10
Divide both sides by Sine 27.2
x = 10 / Sine 27.2
Value of x = 21.9
4. The value of x can be obtain as follow:
Angle (θ) = 25Opposite = 15Adjacent = x =?Tan θ = Opposite / Adjacent
Tan 25 = 15 / x
Cross multiply
x × Tan 25 = 15
Divide both sides by Tan 25
x = 15 / Tan 25
Value of x = 32.2
5. The value of x can be obtain as follow:
Angle (θ) = 64Adjacent = 4Hypotenuse = x =?Cos θ = Adjacent / Hypotenuse
Cos 64 = 4 / x
Cross multiply
x × Cos 64 = 4
Divide both sides by Cos 64
x = 4 / Cos 64
Value of x = 9.1
6. The value of x can be obtain as follow:
Angle (θ) = 33Adjacent = 14Opposite = x =?Tan θ = Opposite / Adjacent
Tan 33 = x / 14
Cross multiply
x = 14 × Tan 33
Value of x = 9.1
7. The value of x can be obtain as follow:
Angle (θ) = 49.6Opposite = 5.6Hypotenuse = x =?Sine θ = Opposite / Hypotenuse
Sine 49.6 = 5.6 / x
Cross multiply
x × Sine 49.6 = 5.6
Divide both sides by Sine 49.6
x = 5.6 / Sine 49.6
Value of x = 7.4
8. The value of x can be obtain as follow:
Angle (θ) = 40Hypotenuse = 10.2Adjacent = x =?Cos θ = Adjacent / Hypotenuse
Cos 40 = x / 10.2
Cross multiply
x = 10.2 × Cos 40
Value of x = 7.8
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At a school, 20% of the pupils are girls and the rest are boys. The ratio of the number of pupils who wear spectacles to those who do not wear spectacles is 1:5. There is an equal number of girls and boys who wear spectacles. There are 357 girls who do not wear spectacles. How many pupils are there altogether in the school?
Given 20% of the pupils are girls and the rest are boys. So, there are a total of 1785 pupils in the school.
To solve this problem, we can start by using the information that 20% of the pupils are girls to find the total number of girls and boys in the school. If there are a total of x pupils, then 0.2x are girls and 0.8x are boys.
Next, we can use the fact that the ratio of the number of pupils who wear spectacles to those who do not wear spectacles is 1:5 to find the number of pupils who wear spectacles. Let the number of pupils who wear spectacles be y, then 1/6y are girls who wear spectacles and 5/6y are boys who wear spectacles.
We also know that there is an equal number of girls and boys who wear spectacles, so we can write:
1/6y = 5/6y / 4
where 4 is the ratio of boys to girls who wear spectacles.
Solving for y, we get y = 357 * 24 = 8568. Therefore, the total number of pupils in the school is:
x = 0.2x + 0.8x = 1785
Hence, there are 1785 pupils altogether in the school.
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Match each math term in the left column to the correct bolded example in the right column.
You will use one of the answer choices twice.
We can match the terms in the left column to the correct bolded examples as follows:
Sum: 1 + 1 = 2
Difference: 7 - 2 = 5
Term: 2x
Product: 9 * 9 = 81
Factor: 81 ÷ 9 = 9
Quotient: 81 ÷ 9 = 9
Coefficient: 7x - 8y
Variable: 5x + 3
How to match the correct termsTo match the correct expression, an understanding of the mathematical terms is essential. The sum is the addition of terms and in the list, 1 + 1 is an example of a sum. Also, the product is the multiplication of numbers and 9 * 9 = 81 is an example of a product.
Coefficients are numbers that are matched with letters in algebra. A variable is a letter beside a number in an expression. In the option, x is the variable besides 5.
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Nakeisha is raising money for a school trip by selling lollipops and fruit snacks. The price of each lollipop is $1.50 and the price of each fruit snack is $1.25. Yesterday Nakeisha made $18.25 from selling a total of 13 lollipops and fruit snacks. Determine the number of lollipops sold and the number of fruit snacks sold.
Nakeisha sold 8 lollipops and 5 fruit snacks to make a total of $18.25.
To solve this problemLet's fix this issue using a set of equations. Assume that x is the quantity of lollipops sold and y is the quantity of fruit snacks sold.
Then we have two equations based on the information given:
x + y = 13.(Total number of fruit snacks and lollipops sold)
1.5x + 1.25y= 18.25 (total amount of money earned)
To solve for x and y, we can use the substitution method :
x + y = 13 (equation 1)
1.5x + 1.25y = 18.25 (equation 2)
From equation 1, we have x = 13 - y. Substituting this into equation 2, we get:
1.5(13 - y) + 1.25y = 18.25
Simplifying and solving for y, we get
19.5 - 0.25y = 18.25
-0.25y = -1.25
y = 5
Nakeisha therefore sold 5 fruit treats. We may change y = 5 into equation 1 and solve for x to get the quantity of lollipops sold:
x + 5 = 13
x = 8
Therefore, Nakeisha sold 8 lollipops and 5 fruit snacks to make a total of $18.25.
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8. Two functions are shown below.
f(x) = 3(2)*
g(x) = 6x
What is the sum of the x-values where f(x) = g(x)?
(Hint: Sum-add. They are equal where they cross/intersect.)
A. 1
B. 3
C. 5
D. 18
The sum of the x-values where f(x) = g(x) is 3
Calculating the sum of the x-values where f(x) = g(x)?From the question, we have the following parameters that can be used in our computation:
f(x) = 3(2)ˣ
g(x) = 6x
When f(x) = g(x), we have
3(2)ˣ = 6x
Solving for x, we have
x = 1 and x = 2
When these values are added, we have
Sum = 1 + 2
Evaluate
Sum = 3
Hence, the sum of the x-values where f(x) = g(x) is 3
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Given the parent function
f(x)= 5ˣ
Describe the transformation for the function
g(x)=5ˣ -2
Answer:
Step-by-step explanation:
The transformation for the function g(x) = 5ˣ - 2 involves a vertical shift downward by 2 units compared to the parent function f(x) = 5ˣ. This is because the constant term (-2) is subtracted from the function. So, the graph of g(x) will be identical to the graph of f(x), except that it will be shifted downward by 2 units. Specifically, the point (0, 1) on the graph of f(x) will be shifted down to (0, -1) on the graph of g(x), and similarly, all other points on the graph will be shifted downward by 2 units.
Use the formula to find the surface area of the figure. Show your work.
Answer:
322 in²
Step-by-step explanation:
You want the surface area of the rectangular prism with edge lengths 7 in, 14 in, and 3 in.
AreaThe surface area can be computed using the formula ...
A = 2(LW +H(L +W))
A = 2(7·14 + 3(7 +14)) = 2(98 +63) = 322
The area of the prism is 322 square inches.
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Pls help i give crown
Answer: 6 cups
Step-by-step explanation:
Which of the numbers below is less than 865.473? Select all
that apply.
A) 865.4
B) 865.475
C) 865.471
D) 866
Answer:
A, C
Step-by-step explanation:
For A, it's correct because they both start with 865.4, but the number in the problem has numbers after the 4, so A is right. B, is not because they both have 865.47, but the one in the problem has a 3, and C has 5, so no. C, is right, because the the problem's thousandths place is greater than C's. D, is not, because it's ones place is greater than the original number.
in the chi-square test expected frequencies represent: a. the frequencies one would expect if the null hypothesis were true. b. the frequencies one would expect if the null hypothesis was not true. c. the frequencies one would expect if the sample were normally distributed. d. none of the above
In the chi-square test expected frequencies represent The frequencies one would expect if the null hypothesis were true
The expected frequencies in the chi-square test represent the frequencies one would expect if the null hypothesis were true. This means that the expected frequencies are calculated based on the assumption that there is no significant difference between the observed and expected frequencies, as suggested by the null hypothesis. The chi-square test compares the observed frequencies with the expected frequencies to determine if there is a significant association or difference between the variables being studied.
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Help please, due today
Answer:
3 ways
Step-by-step explanation:
Using the arrows that they gave us, (which are the directions). The only possible ways are 3. Which I have shown in the screenshot attached below.
If we were to try to do it another time using the directions, it wouldn't work and we would most likely skip a step
Hope I helped!
How to find the maximum volume of a cylinder inscribed in a sphere of radius r?
To find the maximum volume of a cylinder inscribed in a sphere of radius r, we need to use optimization techniques. The cylinder should be such that its height is equal to its diameter and both should be equal to the diameter of the sphere. This means that the cylinder should be a cube with its diagonal equal to the diameter of the sphere.
Let the diameter of the sphere be 2r. The diagonal of the cube is equal to the diameter of the sphere, so its side is r√3. The volume of the cube is (r√3)^3 = 27r^3.
Since the cylinder is inscribed in the sphere, its radius is r and its height is 2r. The volume of the cylinder is πr^2(2r) = 2πr^3.
To maximize the volume of the cylinder, we need to differentiate the volume equation with respect to r and set it equal to zero:
d/dx (2πr^3) = 6πr^2 = 0
This gives us r = 0, which is not a valid solution. Therefore, the maximum volume of the cylinder inscribed in the sphere of radius r is 2πr^3, when the cylinder is a cube with its diagonal equal to the diameter of the sphere.
To learn more about sphere : brainly.com/question/22849345
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