Use a larger confidence level would produce a new confidence interval with larger width (larger margin of error) based on these same data.
How do you calculate the population proportion's 95% confidence interval?
We must determine p′ and q′ in order to construct the confidence interval. p′ = 0.842 is the sample percentage; this is the point estimate of the population proportion.
Since CL = 0.95 is the requested confidence level, the calculation is as follows: = 1 - CL = 1 - 0.95 = 0.05 ( 2) ( 2) = 0.025.
What does confidence interval mean?
When you conduct your experiment again or resample the population in the same way, you may anticipate your estimate to fall inside a specific range of values a certain proportion of the time. This is known as the confidence interval.
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What type equation is this is it a rational ?
Answer:
A rational equation is an equation containing at least one fraction whose numerator and denominator are polynomials, \frac{P(x)}{Q(x)}. Q(x)P(x). These fractions may be on one or both sides of the equation.
X=
6±√(-6)²-4(1)(1)
___________
2(1)
The zeroes of the quadratic equation are [tex]{\displaystyle x= {3-2{\sqrt {2}}}[/tex] and [tex]{\displaystyle x={3+2{\sqrt {2}}}[/tex] for the given quadratic equation.
What is quadratic equation?A second-degree algebraic equation known as a quadratic equation can be found in mathematics (having one or more variables raised to the second power). Ancient Babylonian cuneiform texts from the time of Hammurabi demonstrate a knowledge of how to solve quadratic equations, but it seems that ancient Egyptian mathematicians were not familiar with this technique.
They have played a significant role in the physics of accelerated motion, such as free fall in a vacuum, ever since Galileo's time. The general quadratic equation in one variable is written as ax2 + bx + c = 0, where a, b, and c are arbitrary constants (or parameters) and an is not equal to 0.
Given to solve the quadratic equation
[tex]{\displaystyle x={\frac {6\pm {\sqrt {(-6)^{2}-4(1)(1)}}}{2(1)}}}[/tex]
[tex]{\displaystyle x={\frac {6\pm {\sqrt {36-4}}}{2}}}[/tex]
[tex]{\displaystyle x={\frac {6\pm {\sqrt {32}}}{2}}}[/tex]
[tex]{\displaystyle x={\frac {6-4{\sqrt {2}}}{2}}}[/tex]
[tex]{\displaystyle x= {3-2{\sqrt {2}}}[/tex]
x = 0.171573
[tex]{\displaystyle x={\frac {6+4{\sqrt {2}}}{2}}}[/tex]
[tex]{\displaystyle x={3+2{\sqrt {2}}}[/tex]
x = 5.828427
Thus, the zeroes of the quadratic equation are [tex]{\displaystyle x= {3-2{\sqrt {2}}}[/tex] and [tex]{\displaystyle x={3+2{\sqrt {2}}}[/tex] for the given quadratic equation.
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if we mark off a distance t along the unit circle, starting at (1, 0) and moving in a counterclockwise direction, we arrive at the ---select--- point determined by t
If we mark off a distance t along the unit circle, starting at (1, 0) and moving in a counterclockwise direction, we arrive at the terminal point determined by t.
What is a terminal point?
The ray that has been rotated around the origin to form an angle with the stationary ray that is the initial side of the angle is the ray that has reached its terminal point. The most typical acute-angle measurements are represented by the sine and cosine values.
The coordinates of the terminal point come from the coordinates of the reference point (positive or negative depending on the quadrant.)
We know that a unit circle is the circle of radius 1 which is centered at the origin in the xy-plane.
General equation of a unit circle is: x^2+ y^2 = 1
Starting at the point (1,0),
If t≥0, then, t is the distance along the unit circle in clockwise direction
If t<0, then mod t is the distance along the unit circle in clockwise direction.
Here, role="math" , localid="1648202152711"t is a real number by which a point P(x,y) is generated. This point is known as the terminal point which is determined by the real number t.
Hence, if we mark off a distance t along the unit circle, starting at (1, 0) and moving in a counterclockwise direction, we arrive at the terminal point determined by t.
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The percentage of battery remaining, y, on a tablet's battery after x hours can be represented by the given graph.
coordinate grid with the x axis labeled time in hours and the y axis labeled percent of battery remaining, with a line that passes through the points 0 comma 40 and 4 comma 0
What is the meaning of the y-intercept in the context of the problem?
After 40 hours, the tablet will have 0 percent of battery left.
The tablet will not have any battery remaining after 4 hours.
The tablet starts with 40 percent of battery remaining.
The tablet loses 4 percent of battery every hour.
The meaning of the y-intercept of the linear function is given as follows:
The tablet starts with 40 percent of battery remaining.
How to interpret the y-intercept of a linear function?The two most important features of a linear function are the slope and the intercept, and their meaning is explained as follows:
Slope: rate of change of the output variable relative to the input variable.Intercept: value assumed by the output variable when the input variable assumes a value of zero.When x = 0, y = 40, hence the intercept of this function is of 40, representing the initial value of 40 of the percentage of battery remaining.
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are y-1/7x-2 & x-7y=4 parallel perpendicular intersecting but not perpendicular
y-1/7x-2 & x-7y=4 are intersecting but not parallel or perpendicular lines.
Two lines are parallel if they have the same slope (or no slope at all), and two lines are perpendicular if the product of their slopes is -1. To determine if lines are parallel or perpendicular, you can find their slopes and check if they are equal or if the product of their slopes is -1.
The first line y-1/7x-2 can be rewritten in slope-intercept form y = mx + b as y = 1/7x + 2
The second line x-7y=4 can be rewritten in slope-intercept form y = mx + b as y = x/7 - 4/7
The slopes of the two lines are 1/7 and -1/7 respectively. The product of the slopes of two lines is 1/49 which is not -1, that means that the two lines are not perpendicular. Also, the slopes are not equal, which means that the lines are not parallel.
Therefore, the two lines y-1/7x-2 & x-7y=4 are intersecting but not parallel or perpendicular lines.
suppose you take a random sample of size 25 from a population with mean of 120 and a standard deviation of 15. your sample has a mean of 115 and a standard deviation of 13.8. which of the following has a mean of 120 and a standard deviation of 3?
3 has a mean of 120 and a standard deviation of 3.
Describe standard deviation using an example?
The dispersion of the data around the mean value is measured by the standard deviation. It might be helpful when comparing data sets that may have the same mean but a different range.
The means of the two numbers 15, 15, 15, 14, 16, and 2, 7, 14, 22, 30 are the same, for instance. The second is, however, obviously more dispersed.
mean of sample means = true mean = 120
std dev of sample mean = true std / sqrt(n)
= 15/5 = 3
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Ivan must choose a number between 55 and 101 that is a multiple of 4, 10, and 20. Write all the numbers that he could choose. If there is more than one number, separate them with commas.
Using the LCM, the numbers that Ivan could choose between 55 and 101 which are multiples of 4, 10, and 20 are 60, 80, and 100.
What is a multiple of numbers?A multiple of numbers is the lowest common multiple (lcm) of two or more numbers.
The LCM shows the numbers into which the given numbers can divide without a remainder. The result is always an even integer.
Between 55 and 101, we know that 4, 10, and 20 can each divide 60, 80, and 100 without leaving a remainder.
For example, when 4 divides 60, 80, and 100, we have 15, 20, and 25.
When 10 divides 60, 80, and 100, we have 6, 8, and 10.
Lastly, when 20 divides 60, 80, and 100, we have 3, 4, and 5.
Thus, Ivan can choose 60, 80, and 100, which are between 55 and 101 as the multiples of 4, 10, and 20.
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assume that the int variables x, y, z, and low have been properly declared and initialized. the code segment below is intended to print the sum of the greatest two of the three values but does not work in some cases. if(x > y
A function named "sum three(x, y, z)" that accepts three integer arguments and returns their sum is defined in the aforementioned code.
The function first determines whether any two or three of the three integers (x, y, and z) are equal and if so, it assigns 0 to the variable "sum".
If not, the variable "sum" is set to the sum of the three integers.
It then gives the value of "sum" back.
The function is finally run four times with various inputs, printing the sum of the inputs each time.
def sum_three(x, y, z):
if x == y or y == z or x==z:
sum = 0
else:
sum = x + y + z
return sum
print(sum_three(2, 1, 2))
print(sum_three(3, 2, 2))
print(sum_three(2, 2, 2))
print(sum_three(1, 2, 3))
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V
Let sets A and B be defined as follows.
A={c, d, e, f, g}
B is the set of integers greater than -5 and less than 4
(a) Find the cardinalities of A and B.
n(A) = 5
n(B) = [
Answer:
n(A) = 5
n(B) = 8
Step-by-step explanation:
Cardinality of a set is the number of elements in that set
A has 5 elements so n(A) = 5
The set of integers >- 5 but less than 4 is
B: {- 4, - 3, - 2, - 1, 0, 1, 2, 3}
There are 8 elements in set B so n(B) = 8
In a city library, the mean number of pages in a novel is 525 with a standard deviation of 200.
Furthermore, 30% of the novels have fewer than 400 pages. Suppose that you randomly select 50 nov from the library.
What is the probability that at least 20 of the novels have fewer than 400 pages?
The probability that at least 20 of the novels have fewer than 400 pages is 1 - 0.2266 = 0.7734 or 77.34%.
What is the normal distribution and the cumulative distribution?
The normal distribution, also known as the Gaussian distribution or bell curve, is a probability distribution that describes the distribution of a continuous random variable.
The cumulative distribution function (CDF) is a function that gives the probability that a random variable is less than or equal to a certain value
To solve this problem, we can use the normal distribution and the cumulative distribution function (CDF) of a normal distribution. The normal distribution is a probability distribution that describes how many novels have a certain number of pages.
The mean number of pages in a novel is given as 525 and the standard deviation is 200. We know that 30% of the novels have fewer than 400 pages, which corresponds to a z-score of (400 - 525) / 200 = -0.75.
We can use the cumulative distribution function (CDF) to find the probability that at least 20 of the novels have fewer than 400 pages. The CDF of a normal distribution gives the probability that a random variable is less than or equal to a certain value.
The probability that at least 20 of the novels have fewer than 400 pages is the same as the probability that at most 30 of the novels have more than 400 pages. Using a standard normal table or software, we can find the probability that a standard normal random variable is less than -0.75 as P(X< -0.75) = 0.2266, this is the probability that less than 30 novels have more than 400 pages.
Hence, the probability that at least 20 of the novels have fewer than 400 pages is 1 - 0.2266 = 0.7734 or 77.34%.
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A bag of Starburst candies can be considered an SRS of the whole population of Starburst candies; Since there are 4 flavors. the probability that each Starburst is cherry flavor IS % 0.25. Each bag of Starburst contains 200 candies Suppose we buy = one bag of Starburst X v the number of cherry Ilavor Starburst candies in the pag 1. Is this binomial distribution? 2. What is n? What is p? 3. What is the mean of X? Interpret: 4. What is the standard deviation of X?_ Interpret 5. What is the probability of getting exactly 60 cherry filavored starburst?
6. What is the probability of getting at most 60 cherry flavored starburst
1. Yes, this is a binomial distribution.
2. n = 200, p = 0.25.
3. The mean of X is 50. This means that we can expect to get 50 cherry flavored Starburst candies on average.
4. The standard deviation of X is 7.07. This means that the number of cherry flavored candies is likely to be close to the mean of 50, but it could vary by up to 7.07 in either direction.
5. The probability of getting exactly 60 cherry flavored Starburst is 0.108.
6. The probability of getting at most 60 cherry flavored Starburst is 0.619.
A bag of Starburst candies can be considered an SRS of the whole population of Starburst candies since there are 4 flavors. The probability that each Starburst is cherry flavor is 0.25. Since we are buying one bag of Starburst, the number of cherry flavored candies in the bag can be represented by a binomial distribution with n = 200 and p = 0.25. This means that the mean of X (the number of cherry flavored candies) is 50. The standard deviation of X is 7.07, which means that the number of cherry flavored candies is likely to be close to the mean of 50, but could vary by up to 7.07 in either direction. The probability of getting exactly 60 cherry flavored Starburst is 0.108, and the probability of getting at most 60 cherry flavored Starburst is 0.619.
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At a college, 51% of the students are woken, 25% are business majors…
15. What is the probability that a randomly selected student will either be a woman or a business major?
The probability that a randomly selected student will either be a woman or a business major will be 76%.
How to calculate the probability?Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.
In this case, at the college, 51% of the students are women, 25% are business major, the probability that a randomly selected student will either be a woman or a business major will be:
= 25% + 51%
= 76%
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Use a right triangle to write the following expression as an algebraic expression. Assume that x is positive and that the given inverse trigonometric function is defined for the expression in X. cos (sin - 15x) Identify the right triangle that can be used to simplify the given expression. Choose the correct answer below.
The expression cos (sin - 15x) is a composition of two trigonometric functions, cosine and sine. To simplify this expression, we can use the identity cos (a - b) = cos a cos b + sin a sin b.
To use this identity, we need to identify a right triangle that relates the two trigonometric functions in the expression. One such triangle is the one that relates the sine and cosine functions, known as the "sine-cosine triangle".
This triangle relates the sine and cosine functions through the following identities:
sin a = y/r
cos a = x/r
Where a is the angle opposite to the side of length y, x is the side opposite to angle a and r is the hypotenuse of the triangle.
We can use these identities to write the given expression as:
cos (sin - 15x) = cos (y/r - 15x) = cos y/r cos(-15x) - sin y/r sin(-15x)
This is by using the identity cos (a-b) = cos a cos b - sin a sin b
The expression cos (sin - 15x) can be written as cos y/r cos(-15x) - sin y/r sin(-15x)
It's important to note that this simplified expression is still not in its final form as we have no information about the value of y and r, this is only possible if we have a specific angle or triangle that we are working with.
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Find the area of the figure.
Answer:
A = 30 yd²
Step-by-step explanation:
the figure is a trapezium whose area (A) is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂)
where h is the perpendicular height between bases b₁ and b₂
here h = 5 , b₁ = 8 , b₂ = 4 , then
A = [tex]\frac{1}{2}[/tex] × 5 × (8 + 4) = 2.5 × 12 = 30 yd²
the measure of angle a is 5 times the measure of its supplement. what is the measure of each angle? enter your answers in the boxes.
The measure of an angle which is 5 times its supplement is 150.
Supplementary Angles. When the sum of the measures of two angles is 180 then the angles are called supplementary angles. When two angles are supplementary, each angle is said to be the supplement of the other.
thus, x and y two angle which sum is 180 then x and y supplement to each other.
According to the problem,
The measure of an angle which is 5 times its supplement.
Supplementary angles means , sum of angles is 180.
⟹x=5(180 −x)
⟹x=5×180 −5x
⟹6x=5×180
⟹x=5×30
=150
Hence, x=150
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The function f is defined by the following rule
f(x)=2x+1
Complete the function table
Function Table:
x f(x)
0 1
1 3
2 5
3 7
4 9
5 11
6 13
7 15
8 17
9 19
And so on, f(x) will always be 2x + 1.
Unit 3 Cumulative Assessment
What is the height, x, in the triangle below?
5
X
O A 2√5
OB. 5
O C. 5√2
OD. 10
10
The height, x, in the triangle is 0 units.
What to find perpendicular distance?
Perpendicular distance is a measure of the distance between a point and a line. It is the shortest distance between the point and the line, and it is always perpendicular to the line. The perpendicular distance is also known as the "altitude" or "height" in geometry.
In the triangle, the side OB is 5 units and the side OC is 5√2 units. The height, x, is the perpendicular distance from the vertex O to the line segment OB.
Using the Pythagorean theorem, we can find the value of x:
x^2 + (5)^2 = (5√2)^2
x^2 = (5√2)^2 - (5)^2
x^2 = 25 - 25
x^2 = 0
x = 0
Therefore, the height, x, in the triangle is 0 units.
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Super is a ride-sharing company. The Chief of Operations wants the revenue (output value) to be seven times the cost of service operations (input cost). Suppose that each regular car earns a value of $1500 per month and premium cars earn $2500 per unit per month. The monthly cost of operating a regular car is $100 per month and $500 per premium car. Super currently has 19 regular cars. How many premium cars do they need to achieve a productivity ratio of 7? (Enter your response rounded to whole number.)
Super would need 2 premium cars to achieve a productivity ratio of 7.
How to find the productivity ratio?Let's call the number of premium cars "x".
The total revenue from the regular cars would be $1500 * 19 = $28,500 per month.
The total revenue from the premium cars would be $2500 * x.
The total cost of the regular cars would be $100 * 19 = $1900 per month.
The total cost of the premium cars would be $500 * x.
The Chief of Operations wants the revenue to be 7 times the cost of service operations, so we can write the following equation:
($28,500 + $2500x) / ($1900 + $500x) = 7
Expanding and simplifying the equation, we get:
$2500x + $28,500 = 7($1900 + $500x)
$2500x + $28,500 = $13,300 + 7$500x
$11,200 = 6$500x
$11,200 / $6,500 = x
x = 1.723
Rounding up, Super would need 2 premium cars to achieve a productivity ratio of 7.
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PLEASE THIS IS DUE SOON!!!!
QUESTION DOWN BELOW
The data are reported with a mean and standard deviation of 3 and 1.72, respectively.
What is the standard deviation?The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
Given a histogram and we need to find the values of the Mean and standard deviation.
For mean:
Step 1: Multiply the category (number) by the height of each bar in our histogram (how many of each number we have).
Step 2: To obtain the total of our data, add each of the goods determined in Step 1 together.
Step 3: To determine our mean, divide this amount by the total of the bars' heights.
Multiply each category by its respective height.
1* 60 = 60
2 * 30 = 60
3*10 = 30
4 * 30 = 120
5 * 60 = 300
Add the products from Step 1 together.
Adding these products together, we get: 60 + 60 + 30 + 120 + 300
Sum = 570
Divide this sum by the sum of the heights of the categories.
The sum of the heights of the categories will tell us how many individual pieces of data we have. In this case, this is:
60 + 30 + 10 + 30 +60
Sum of frequency = 190
So, we need to divide the sum of the products in Step 2 by the sum of the heights given above to get our mean.
Mean = 570 /190
Mean = 3
Therefore, the Mean and standard deviation of the given data are 3 and 1.72 respectively.
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Popcorn at a concession stand comes in two different-sized containers. The dimensions of the small container with a diameter of 4 in. are shown below.
A popcorn container shaped like a cylinder is shown. A dashed line across the top of the container is labeled four inches. The height of the container is labeled four and five tenths inches.
The large container of popcorn has the same height as the small container, but its diameter is 1.5 times greater. How do the volumes of the two containers of popcorn compare? Use 3.14 for π.
Select the answers from the drop-down lists to correctly complete each sentence.
The volume of the large container of popcorn is _______ in.^3
OPTIONS FOR BLANK :
A) 56.52
B) 84.78
C)127.17
D) 169.56
This is ______ times the volume of the small container.
OPTIONS FOR THIS BLANK :
A) 2.88
B) 2.25
C) 1.8
D) 1.5
The volume of the large container of popcorn is 56.52 in³
This is 2.25 times the volume of the small container.
How to determine how the volumes of the two containers of popcorn compare?The volume of a cylinder is given by the formula:
V = πr²h
where r and h represent the radius and height respectively
Volume of small container = 3.14 × 2² × 4.5 = 56.52 in³
For large container:
diameter = 1.5 × 4 = 6 in and radius = 3 in
Volume of large container = 3.14 × 3² × 4.5 = 127.17 in³
Volume of large container/Volume of small container = 127.17/56.52 = 2.25
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I just need the answer and an explanation as to why it is that answer please and thank you
Triangles that are congruent have the same size and form.Triangle HGK is congruent to triangle KHJ.
What do congruent and similar mean? Triangles that are congruent have the same size and form.Three pairs of matching sides are equivalent in two triangles according to the Side-Side-Side (SSS) Theorem.Side-Angle-Side (SAS) Theorem: Two triangles have two pairs of matching sides and two pairs of corresponding angles that are congruent.The triangles are congruent if their included sides are congruent and two of their angles match two of the other triangle's angles. Using labels: Triangle HGK is congruent to triangle KHJ if in triangles HGK and KHJ, angle H = angle G, angle H = angle J, and angle HG = HK and GK = KJTo learn more about congruent refer to:
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Triangle HGK is congruent to triangle KHJ if in triangles HGK and KHJ, angle H = angle G, angle H = angle J, and angle HG = HK and GK = KJ
What do congruent and similar mean?Triangles that are congruent have the same size and form.
Three pairs of matching sides are equivalent in two triangles according to the Side-Side-Side (SSS) Theorem.
Side-Angle-Side (SAS) Theorem: Two triangles have two pairs of matching sides and two pairs of corresponding angles that are congruent.
The triangles are congruent if their included sides are congruent and two of their angles match two of the other triangle's angles. Using labels:
Triangle HGK is congruent to triangle KHJ if in triangles HGK and KHJ, angle H = angle G, angle H = angle J, and angle
HG = HK and GK = KJ
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A store sells oranges and apples. Oranges cost $1.00 each and apples cost $2.00 each. In the first sale of the day, 15 fruits were sold in total, and the price was $25. How many of each type of frust was sold?
A store sells 5 oranges and 10 apples.
What is the cost amount?
The cost of an asset to you often serves as its basis. The cost is the sum that you pay for it using money, debt, other goods, or services. Sales tax and other purchase-related costs are included in the price.
Here, we have
Given: A store sells oranges and apples. Oranges cost $1.00 each and apples cost $2.00 each. In the first sale of the day, 15 fruits were sold in total, and the price was $25.
We have to determine how many of each type of fruit were sold.
We, let the oranges be x.
let the apples be y.
x + y = 15...(1)
1x + 2y = 25...(2)
We subtract equation(2) from equation(1), we get
y = 10
Now we put the value of y in equation (1) and we get
x + 10 = 15
x= 5
Hence, a store sells 5 oranges and 10 apples.
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given a n percent chance of something happening, find the probability of it happening at least n times out of k
P(at least n times) = 1 - (1 - p)^k, where p is the probability of the event happening and k is the number of trials.
The probability of an event happening at least n times out of k trials can be calculated using the formula P(at least n times) = 1 - (1 - p)^k. Here, p is the probability of the event happening, and k is the number of trials. The formula is based on the principle that the probability of an event happening at least n times is equal to one minus the probability of it happening less than n times. The probability of it happening less than n times is calculated by taking the probability of the event happening once, and then multiplying it by itself k times. This is because each trial is independent, and the probability of the event happening for each trial is the same. The result of this multiplication is then subtracted from one, which gives us the probability of it happening at least n times out of k trials
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Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
The equations that are equivalent are:
2 + x = 5
x + 1 = 4
-5 + x = -2
How to Determine Equivalent Equations?If any two or more equations are equivalent, they would have the same value when evaluated.
To find which equations are equivalent, solve to find the value of x in each given equation.
A. 2 + x = 5
x = 5 - 2
x = 3
B. x + 1 = 4
x = 4 - 1
x = 3
C. 9 + x = 6
x = 6 - 9
x = -3
D. x + (-4) = 7
x = 7 + 4
x = 11
E. -5 + x = -2
x = -2 + 5
x = 3
The equivalent equations are:
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Please help me will mark u as brainliest
Answer:
-9,-6,6,12
Step-by-step explanation:
The number of bacteria in a culture is modeled by
Answer:
Bacteria Growth The number N of bacteria in culture is modeled by N= 250e^kt where t is the time in hours. If N = 280 when t= 10, estimate the time required for the population to double in size.
Step-by-step explanation:
(◔‿◔)(◔‿◔)(◔‿◔)
16w) 3 4 Write your answer in the form A or A B , where A and B are constants or variable expressions that have no variables in common. All exponents in your answer should be positive. Submit
The required expression is 4w4w² or Aw.Bw².
What is an expression?One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.
Given:
An expression,
16w³.
To write an answer in the form A or AB, where A and B are constants or variable expressions that have no variables in common:
16w³,
= 4w 4w²
Where A = 4 and B = 4.
So, 16w³ = Aw.Bw².
Therefore, the expression is 4w4w² or Aw.Bw².
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The lengths of the two sides of a right triangle containing the right angle differ by 2 cm. If the area of the triangle is 24cm 2
, find the perimeter of the triangle.
The perimeter of the triangle is 28 cm. The perimeter of the triangle containing the right angle with two sides that differ by 2 cm is 28 cm. This can be determined by using the Pythagorean Theorem to solve for the length of the sides.
Let the two sides of the right triangle be x and x+2
Apply the Pythagorean Theorem:
(x)^2 + (x + 2)^2 = 24
x^2 + x^2 + 4x + 4 = 24
2x^2 + 4x = 20
2x(x + 2) = 20
x(x + 2) = 10
x = 5 and x + 2 = 7
Therefore the perimeter of the triangle is 5 + 7 + 7 = 19 cm.
The perimeter of the triangle is 28 cm.
The perimeter of the triangle containing the right angle with two sides that differ by 2 cm is 28 cm. This can be determined by using the Pythagorean Theorem to solve for the b of the sides. The equation 2x(x + 2) = 20 can be used to solve for x, which is equal to 5. Therefore, the two sides of the triangle are 5 cm and 7 cm. Adding these lengths together, the perimeter of the triangle is 5 + 7 + 7 = 28 cm.
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List all the vertices, edges, and faces in the figure below.
The vertices are A, B, C, D, E, F. The edges are AB, BC, CA, ED, DF, FE, BD, CF, and AE and the faces are DBCF, DEAB, EFCA, EDF, and ABC.
What are vertices, edges, and faces?The three-dimensional shape's vertices are the points at which the edges converge. Edges are the lines where two faces converge, while faces are flat surfaces.
Vertices are the locations where the sides of a polyhedron constructed of line segments connect.
According to the definition given above, the vertices are A, B, C, D, E, and F.
Line segments from which the formation of a polyhedron takes place are known as edges.
Hence in the given figure, AB, BC, CA, ED, DF, FE, BD, CF, and AE are the edges.
Two-dimensional surfaces in a three-dimensional figure are known as faces.
In the given prism, DBCF, DEAB, EFCA, EDF, and ABC are the faces of the prism.
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−4≤−2(y−1)<2
Step 2 of 2 : Graph the solution set.
Answer:
draw a line between an empty point at 0 and a filled point at 3
Step-by-step explanation:
To graph this inequality we first want to isolate the y variable to make it a bit easier to deal with. This is a compound inequality and when isolating the y variable instead of just doing an operation on both sides, we do it to all sides which follows the same principle of maintaining equality.
We start with the original inequality:
[tex]-4 \le -2(y-1) < 2[/tex]
From here we divide by -2 on all sides, but since we're dividing by a negative we would flip the way the inequality is pointing so we get:
[tex]2\ge y-1 > -1[/tex]
From here we add 1 to all sides.
[tex]3 \ge y > 0[/tex]
Although generally we would write this as:
[tex]0 < y \le 3[/tex]
Now to graph this we would draw a hole on the number line at the point zero, and a filled point on the number line at 3, since 3 is included (since less than or equal to 3) and then just connect the two points. I'll include an image that demonstrates this.
