The area of the rectangle is d. 54 square units.
What is rectangle?A rectangle is a closed two-dimensional geometry with four sides, four corners, and four right angles (90°). A rectangle's opposite sides are equal and parallel. Because a rectangle is a 2-D form, it has two dimensions: length and width. The length of the rectangle is the longer side, while the width is the shorter side.
The rectangle has two pairs of parallel sides, so its area can be calculated by multiplying the length of one pair of parallel sides by the length of the other pair of parallel sides.
From the given points, we can see that the length of one pair of parallel sides of the rectangle is:
4 - (-5) = 9 units
And the length of the other pair of parallel sides of the rectangle is:
2 - (-4) = 6 units
Therefore, the area of the rectangle is:
9 units × 6 units = 54 square units.
So the area of the rectangle is d. 54 square units.
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Question 3
A group of 5 people went to the movies and spent $44 on food and drink. The total amount spent, including
tickets, was $98.50.
What was the price, in dollars, of one ticket?
Answer:
One ticket cost $10.90.
Step-by-step explanation:
The total spent was $98.50--food, drinks, admission--everything.
$44.00 was for food and drinks.
We can take the 44 away from the total.
98.50 - 44.00
= 54.50
They spent 54.50 on 5 tickets to get in. Divide to find the cost of one tickets. This assumes that all 5 tickets were the same price.
54.50 ÷ 5 = 10.90
The price of one ticket was $10.90
To make this look like algebra class...
let x = the price of one ticket
5x = the price of 5 tickets
5x + 44 = 98.50
subtract 44
5x = 54.50
divide by 5
x = 10.90
please help with 21 pleaseeeeee i need it
A simultaneous equation is a system of two or more equations that are to be solved together to find the values of the unknown variables.
What is a simultaneous equation?The unknown variables in each equation are related to each other and their values must satisfy all the equations in the system.
Given that;
x + y = 50
3x + 5y = 174
x = 50 - y
Substitute (3) into (2)
3(50 - y) + 5y = 174
150 - 3y + 5y = 174
150 + 2y = 174
2y = 174 - 150
y = 24/2
y = 12
Thus;
x + 12 = 50
x = 50 - 12
x = 38
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trigonometry problems pls help
Answer:
1) x = 4.721559618
2) x = 38.69059499
3) x = 56.44269024
4) x = 13.50132272
Step-by-step explanation:
We have to use the term SOHCAHTOA which stands for:
sin(Ø) = opposite / hypotenuse
cos(Ø) = adjacent / hypotenuse
tan(Ø) = opposite/adjacent.
Key:
Ø = angle
1. we use tan because we know the adjacent side length and we need to work out the opposite side length
so we do tan(34) = x/7
now we need to get x on its own. so we do tan(34)*7 = x
type into the calculator tan(34)*7
= 4.721559618
2. we use cos because we know the adjacent side length and we need to work out the hypotenuse length.
so we have to do cos(17) = 37/x
now we get x on its own. we do x*cos(17) = 37
then x = 37 / cos(17)
x = 38.69059499
3. we use sin because we know the hypotenuse length and opposite length.
sin(x) = 10/12
get x on its own.
x = sin^-1(10/12)
x = 56.44269024
4. we use cos because we know the adjacent side length and we need to work out the hypotenuse length.
cos (61) = 8/x
get x on its own.
x*cos(61) = 8
x = 8/cos(61)
x = 16.50132272
What is the answer to this question?
No, a continuous function function f(x) exits in (0 , 2 ) .
What does continuous function mean?
In mathematics, a continuous function is a function without discontinuities, i.e. without unexpected changes in value.
A function is continuous if it can be guaranteed for arbitrarily small changes by limiting the changes in the input to be small enough.
A function f(x) such that
f(0) = 10, f(2) = 2
f'(x) ≤ 1 ∀ in (0,2)
If f'(x) ≤ 0
then f(x) decreasing on (0, 2 )
But her f'(x) ≤ 1
So, f(x) is not continuous (0, 2 )
So, No continuous function f(x) exits in (0 , 2 ) .
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the grades fall from an Algebra Midterm were as follows: ( 60, 64, 75, 7, 83, 86, 91, 95, 98, 100) A) how many grades fall within one standard deviation of the mean? b) how many grades fall within 2 standard deviations of the mean? c) how many grades have a z-score less than 0.3?
a) There are 5 grades within one standard deviation of the mean.
b) All of the grades fall within two standard deviations of the mean.
c) There are 4 grades with a z-score less than 0.3.
What is standard deviation?The standard deviation is the square root of the variance.
We need to first calculate the mean and standard deviation of the grades.
Step 1: Calculate the mean
Mean = (60 + 64 + 75 + 77 + 83 + 86 + 91 + 95 + 98 + 100) / 10
= 811 / 10
= 81.1
Step 2: Calculate the standard deviation
s = √ {Σ(xi - x)²} / (N - 1)
where xi is the individual grade, x is the mean, and N is the total number of grades.
SD = √ {(60 - 81.1)² + (64 - 81.1)² + ... + (100 - 81.1)²} / 9
SD = √ [9746.9] / 9
SD = 10.78
Step 3: Use the mean and standard deviation to answer the questions.
A) One standard deviation from the mean in either direction would be:
81.1 - 10.78 = 70.32
81.1 + 10.78 = 91.88
So, the grades that fall within one standard deviation of the mean are:
(75, 77, 83, 86, 91)
There are 5 grades within one standard deviation of the mean.
B) Two standard deviations from the mean in either direction would be:
81.1 - 2(10.78) = 59.54
81.1 + 2(10.78) = 102.66
So, the grades that fall within two standard deviations of the mean are:
(60, 64, 75, 77, 83, 86, 91, 95, 98, 100)
All of the grades fall within two standard deviations of the mean.
C) To calculate the z-score for each grade, we use the formula:
z = (x - μ) / σ ; where x is the individual grade, μ is the mean, and σ is the standard deviation.
For a z-score to be less than 0.3, we need to find the grades that satisfy:
(x - μ) / σ < 0.3
Rearranging this inequality, we get:
x < μ + 0.3σ
Substituting the values for μ and σ, we get:
x < 84.86
So, the grades that have a z-score less than 0.3 are (60, 64, 75, 77)
There are 4 grades with a z-score less than 0.3.
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Answer in absolute and relative terms; If you were 60 inches three years ago and are now 69 inches, how much have you grown?
Answer:
In absolute terms, you have grown 9 inches (69 - 60).
In relative terms, your growth can be expressed as a percentage increase. To calculate this, we can use the formula:
(relative increase) = (absolute increase / original value) x 100%
Using the values given in the problem, we can plug in and solve:
(relative increase) = (9 / 60) x 100%
(relative increase) = 0.15 x 100%
(relative increase) = 15%
So in relative terms, you have grown 15% since you were 60 inches tall three years ago.
A sponsor created this box and whisker plot to show the ages of the 120 people seated in the first five rows at the concert. What was the median age of the 120 people sitting in the first five rows
The median age of the 120 people seated in the first five rows of the concert was 31.
What is value?Value is an important concept in economics and business. It is the worth of goods, services, or assets that is determined by the market or by an individual. It can be measured in terms of money, time, or effort. Value is also used to describe a person’s sense of worth or importance. Values can be seen as the principles, standards, or goals that guide an individual’s actions and decisions. Ultimately, value is subjective and is held by each person and can change over time.
The box and whisker plot provided by the sponsor shows the ages of the 120 people seated in the first five rows of the concert. The box and whisker plot shows a minimum value of 18, a maximum value of 45, a median of 31, a first quartile of 24, and a third quartile of 37. This indicates that 50% of the 120 people in the first five rows had an age of 31 or below, and 50% of the 120 people had an age of 37 or above. The median age of the 120 people seated in the first five rows of the concert was 31.
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Which quadratic regression equation best fits the data set
x1|-2 -1.5 -0.5 0 0.5 1.5 2
y1| 4 0.5 -3.5 -4 -3.5 0.5 4
y=2x2^+0x-4 or y=2x2^-4
y=-4x2^+0x+2 or y=-4x2^+2
y=x2x2^-4x+0 or y=2x2^-4x
The quadratic regression equation best fits the data set is:
[tex]y=-4x^2+0x+2\ or\ y=-4x^2+2[/tex]
What is quadratic regression ?
Quadratic regression is a statistical method used to determine the relationship between a dependent variable and one or more independent variables.
Given data set:
x1|-2 -1.5 -0.5 0 0.5 1.5 2
y1| 4 0.5 -3.5 -4 -3.5 0.5 4
To determine which quadratic regression equation best fits the data set, we need to calculate the regression equation that has the smallest sum of squared residuals.
Using a calculator or regression software, we can find that the quadratic regression equation that best fits the data set is:
[tex]y = -4x^2 + 0x + 2[/tex]
Therefore, the answer is:
[tex]y=-4x^2+0x+2\ or\ y=-4x^2+2[/tex]
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PLEASE help 1-4 pls and thank you
The arithmetic or geometric sequences, common difference (d) or the common ratio (r) include:
Arithmetic: d = 2, an = 2n, Terms: 2, 4, 6, 8, 10, 12Geometric: r = 0.5, a1 = 8, an = 8(0.5)^(n-1), Terms: 8, 4, 2, 1, 0.5, 0.25Arithmetic: d = 1.5, a1 = 7, an = 1.5n + 5.5, Terms: 7, 8.5, 10, 11.5, 13, 14.5Geometric: r = 4, a1 = 5, an = 5(4)^(n-1), Terms: 5, 20, 80, 320, 1280, 5120What is a geometric sequence?A geometric sequence is a sequence of numbers in which each term after the first is obtained by multiplying the preceding term by a fixed number, which is called the common ratio (r). In other words, a geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by the same number.
For example, the sequence 2, 4, 8, 16, 32 is a geometric sequence with a common ratio of 2. To get each term in the sequence, you multiply the preceding term by 2. So, 2 x 2 = 4, 4 x 2 = 8, and so on.
The explicit formula for a geometric sequence is: an = a1 × r^(n-1), where a1 is the first term, r is the common ratio, and n is the term number.
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Image transcribed:
For the following problems:
Determine whether the sequence is arithmetic or geometric. ⚫ Find the common difference (d) or the common ratio (r).
Write the explicit formula for the sequence.
Find the next 3 terms of the sequence.
1) 2,4,6,...
Arithmetic or Geometric
OR r =
an=
Terms:
2) 8,4,2
Arithmetic or Geometric
d=
OR r =
1
e
an=
Terms:
3) 7,8.5, 10, 11.5
4) 5, 20, 80, 320,
Arithmetic or Geometric
Arithmetic or Geometric
d=
d =
OR r =
an
Terms:
OR r=
an=
Terms:
4. Factors that influence a hypothesis test with the t statistic
Suppose you conduct a hypothesis test about a population mean when the standard deviation is unknown by calculating a t statistic and determining whether to reject the null hypothesis. Assume that your t statistic is a positive value and that you will reject the null hypothesis when t is very large. For each of the potential changes to the components of your study design or the results listed below, determine the change to the t statistic, and then select “Increases,” “Decreases,” or “Stays the same” from the dropdown menu in the right-hand column.
Change in Study Design or Results
The t statistic
A switch from using a one-tailed test to a two-tailed test
An increase in the sample standard deviation (s)
A decrease in the significance level (such as using α = .01 instead of α = .05)
A decrease in the sample size (n)
The t statistic: Stays the same
A switch from using a one-tailed test to a two-tailed test: Increases
An increase in the sample standard deviation (s): Decreases
A decrease in the significance level (such as using α = .01 instead of α = .05): Increases
A decrease in the sample size (n): Decreases
What is the t statistic?The t statistic: Stays the same
The t statistic itself is calculated based on the sample mean, the population mean, and the sample standard deviation.
Therefore, changing the study design or results in ways that do not affect these values will not change the t statistic.
A switch from using a one-tailed test to a two-tailed test: Increases.
An increase in the sample standard deviation (s): Decreases
A decrease in the significance level (such as using α = .01 instead of α = .05): Increases
A decrease in the sample size (n): Decreases
As the sample size decreases, the standard error of the mean increases, meaning that there is more variability in the sample means. Therefore, the t statistic will be smaller, making it less likely to reject the null hypothesis.
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A 2-column table with 7 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2, 3. The second column is labeled f of x with entries 15, 0, 3, 0, negative 3, 0, 15.
Predict which statements are true about the intervals of the continuous function. Check all that apply.
f(x) > 0 over the interval (−, 3).
f(x) ≤ 0 over the interval [0, 2].
f(x) < 0 over the interval (−1, 1).
f(x) > 0 over the interval (–2, 0).
f(x) ≥ 0 over the interval [2, ).
The time periods that satisfy the requirement include:
(B) f(x)<=0 over the interval [0,2]
(D) f(x)>0 over the interval (-2,0)
(E) f(x)>=0 over the interval [2,∞)
In the given situation:
The table containing values for x and f(x)
Let's examine the table and determine whether each choice satisfies f(x) or not.
Look at the values of x between -3 and 3, there are both positive and negative values for f(x).
Then, f(x)>0 is false over the interval (-∞,3)
The values of f(x) are 0 and negative between 0 and 2.
Then, f(x)<=0 over the interval [0,2]
F(x) values are both positive and negative over the range (-1, 1).
f(x)<0 is false over the interval (-1,1)
In the interval (-2,0), the f(x) is positive.
f(x)>0 over the interval (-2,0)
When divided by [2, ∞], f(x) is positive.
f(x)>=0 over the interval [2,∞)
Therefore, the time periods that satisfy the requirement include:
(B) f(x)<=0 over the interval [0,2]
(D) f(x)>0 over the interval (-2,0)
(E) f(x)>=0 over the interval [2,∞)
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Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
The correct equations are for:
[tex]x^{2}[/tex] – 4 = 0
4[tex]x^{2}[/tex] = 16
What is an equation?An equation is a mathematical statement that indicates that two expressions are equal. An equation consists of two sides: the left-hand side (LHS) and the right-hand side (RHS), connected by an equal sign (=). The LHS and RHS can be made up of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.
What are mathematical operations?Mathematical operations are procedures or actions that are used to manipulate or calculate numbers, variables, or other mathematical entities. These operations are the basic building blocks of mathematics and are used in a wide range of mathematical applications.
According to the given informationThe equations that are true for x = –2 and x = 2 are:
1) [tex]x^{2}[/tex] – 4 = 0 (when x = -2, this equation becomes ([tex]-2^{2})[/tex] - 4 = 0, which is true; when x = 2, this equation becomes [tex]2^{2}[/tex] - 4 = 0, which is also true)
2) 4[tex]x^{2}[/tex]= 16 (when x = -2, this equation becomes 4[tex]-2^{2}[/tex] = 16, which is true; when x = 2, this equation becomes 4[tex](2^{2})[/tex] = 16, which is also true)
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24x -27 -15 +18 -21x + 27
Answer:
3x + 3
Step-by-step explanation:
The given expression is 24x - 27 - 15 + 18 - 21x + 27.
To simplify this expression, we can combine like terms. Like terms are terms that have the same variable(s) and exponent(s). In this expression, we have two terms that have x: 24x and -21x. These terms can be combined by subtracting 21x from 24x to get 3x.
The other terms without any variables are -27, -15, 18, and 27. We can combine these terms by adding them together to get 3.
Therefore, the simplified expression is 3x + 3.
Answer:
3x+3
Step-by-stepStep-by-step explanation:
Combine like terms:
(24x+(−21x))+(−27+(−15)+18+27)
3x+3
Pls help. ASAp. Im confused
Jermaine is riding his bicycle across his state. At times, Jermaine stops and explores the local scenery or attractions. At other times, especially on the open road, Jermaine likes to travel at a constant speed.
Jermaine decides to travel at a constant speed and travels 50 miles in 5 hours.
Graph the line that represents the relationship between the time, in hours, that Jermaine rides his bicycle, and the distance, in miles, that he travels based on the given data.
The equation of the graph is y = 10x and the visual representation of the graph is given in the picture.
Graphing the line:To graph, the line that represents the relationship between the time Jermaine rides his bicycle and the distance he travels use the slope-intercept form of a linear equation.
This form of the equation is used to represent a straight line on a graph, where the slope represents the rate of change of the dependent variable with respect to the independent variable, and the y-intercept represents the initial value of the dependent variable when the independent variable is 0.
Here we have
Jermaine decides to travel at a constant speed and travels 50 miles in 5 hours.
To graph the line that represents the relationship between the time and the distance he travels, we can use the formula for the slope-intercept form of a linear equation:
y = mx + b
We know that Jermaine travels 50 miles in 5 hours
Slope (m) = (change in y) / (change in x) = (50 - 0) / (5 - 0) = 10
This tells us that for every 1 hour that Jermaine rides his bicycle, he travels 10 miles.
Hence, the equation of the line y = 10x + b
Take x = 0 and y = 0 [ Since the line passes through (0, 0)
=> 0 = 10(0) + b
=> b = 0
This tells us that the y-intercept of the line is 0.
Hence, the equation of the line, y = 10x
Now draw the graph of y = 10x as shown below
Therefore,
The equation of the graph is y = 10x and the visual representation of the graph is given in the picture.
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An office manager needs to cover the front face of a rectangular box with a label for shipping. The vertices of the face are (–5, 8), (3, 8), (–5, –4), and (3, –4). What is the area, in square inches, of the label needed to cover the face of the box?
96 in2
48 in2
40 in2
20 in2
The area of rectangle is 96in2 which is option A.
Area of rectangle calculation.
To find the area of the rectangular face, we need to find the length and width of the rectangle, and then multiply them together.
The length of the rectangle is the distance between the points (-5,8) and (3,8), which is 8 - (-4) = 12 inches.
The width of the rectangle is the distance between the points (-5,8) and (-5,-4), which is 3 - (-5) = 8 inches.
Therefore, the area of the rectangular face is 12 x 8 = 96 square inches.
So the answer is 96 in².
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Imani was curious if there was a relationship between one hand being longer than the other and one foot being longer than the other for students at her school. She measured the hands and feet of
100
100100 randomly selected students. Here is a summary of the data and the results from a chi-square test:
The most appropriate conclusion is: A) This is convincing evidence of an association between longer hand and longer foot.
What is chi-square test?The chi-square test is a statistical test used to determine whether there is a significant association between two categorical variables. It is used to compare observed frequencies of data to the expected frequencies to determine if they differ significantly. The test is based on the principle of comparing the difference between the observed frequencies and the expected frequencies, and then determining if this difference is statistically significant.
Here,
At the 0.05 significance level, with a chi-square statistic of 11.942 and 4 degrees of freedom, the P-value is 0.018.
Since the P-value is less than the significance level, we reject the null hypothesis of no association and conclude that there is evidence of an association between longer hand and longer foot.
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Complete question:
Imani was curious if there was a relationship between one hand being longer than the other and one foot being longer than the other for 100 randomly selected students. Here is a summary of the data and the results from a chi-square test:
A clothing business finds there is a linear relationship between the number of shirts (n) it can sell and the price (p) it can charge per shirt. In particular, historical data shows that 1,000 shirts can be sold at a price of $30, while 3,000 shirts can be sold at a price of $5. Find a linear equation in the form p(n)=mn+b that gives the price (p) they can charge for n shirts.
The form p = -n/250 + 34 is a linear equation that gives the price (p) they can charge for n shirts.
In mathematics, what exactly is a linear equation?An algebraic equation of the form y=mx+b is a linear equation. m is the slant and b is the y-capture. A "linear equation in two variables" with y and x as variables is sometimes referred to as the one above. A linear equation is one in which a variable is raised to its first power. One example of a one variable is ax+b = 0. x is a variable and an and b are genuine numbers.
Given that the relationship is linear and the equation has the form: Let n be the number of shirts and p be the price of a shirt. p = mn + b
Consequently we will view as m first. Let us express the two values of p and two of n as cartesian coordinates: 1000, 30) (3000 , 22)
(p₂ - p₁) = m(n₂ - n₁)
(22 - 30) = m(3000 - 1000)
m = 22 - 30/3000 - 1000
m = -8/2000
= -1/250
So the equation becomes:
p = -n/250 + b
Now to find b, :
30 = -1000/250 + b
b = - 4 = 30
b = 34
Now the equation becomes:
p = -n/250 + 34
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Can u explain this to me ?
the volume of the square pyramid is 50 cubic units. The volume of a square pyramid can be calculated using the formula:
Volume = (1/3) x Base Area x Height
what is square pyramid ?
A square pyramid is a three-dimensional geometric shape that has a square as its base and four triangular faces that meet at a common point called the apex. The triangular faces of the pyramid slope upwards and meet at the apex, which is directly above the center of the square base.
In the given question,
The volume of a square pyramid can be calculated using the formula:
Volume = (1/3) x Base Area x Height
where the base area is the area of the square at the base of the pyramid.
In this case, the side of the square base is given as 5, and the height of the pyramid is given as 6. To find the base area, we can use the formula for the area of a square:
Base Area = side²
Base Area = 5²
Base Area = 25
Now, we can plug in the given values into the formula for volume and simplify:
Volume = (1/3) x Base Area x Height
Volume = (1/3) x 25 x 6
Volume = (1/3) x 150
Volume = 50
Therefore, the volume of the square pyramid is 50 cubic units.
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Help please
Condense to a single logarithm is possible
In(6x^9)-In(x^2)
The expression can be condensed to a single logarithm as: In(6x^9) - In(x^2) = In(6x^7)
Condensing to a single logarithm is possibleWe can use the quotient rule of logarithms, which states that:
log(base a)(b) - log(base a)(c) = log(base a)(b/c)
Using this rule, we can simplify the expression as:
In(6x^9) - In(x^2) = In(6x^9/x^2)
Now, we can simplify the expression inside the logarithm by dividing 6x^9 by x^2:
In(6x^9/x^2) = In(6x^7)
Therefore, the expression can be condensed to a single logarithm as: In(6x^9) - In(x^2) = In(6x^7)
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Drag the tiles to the correct boxes. Not all tiles will be used.
What are the domain and the range of function f?
f(x) = x - 6 / x^2 - 3x - 18
range ---> ??
domain ---> ??
The Domain: (-∞, -3) ∪ (-3, 6) ∪ (6, ∞) and Range: (-∞, 0) ∪ (0, ∞).
What is domain?
The domain of a function refers to the set of all possible input values (also known as the independent variable) for which the function is defined.
According to question:
In this case, the denominator of the function is a quadratic expression, and we know that dividing by zero is undefined. Therefore, we need to find the values of x that make the denominator equal to zero, and exclude those values from the domain.
To find the values that make the denominator equal to zero, we can factor it as follows:
x² - 3x - 18 = 0
(x - 6)(x + 3) = 0
So, the denominator is equal to zero when x = 6 or x = -3. Therefore, the domain of the function is all real numbers except x = 6 and x = -3.
Domain: (-∞, -3) ∪ (-3, 6) ∪ (6, ∞)
The range of a function consists of all possible output values of the function, given the domain of the function.
To find the range of this function, we need to analyze the behavior of the function as x approaches positive or negative infinity.
As x approaches positive infinity, both the numerator and denominator of the function approach positive infinity. Therefore, the function approaches zero.
As x approaches negative infinity, both the numerator and denominator of the function approach negative infinity. Therefore, the function approaches zero.
Since the function approaches zero as x approaches positive or negative infinity, we can say that the range of the function is all real numbers except zero.
Range: (-∞, 0) ∪ (0, ∞).
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URGENT !
What effect does replacing x with - 4 have on the graph for the function f( x)?
f(x)= |x-6| +2
A. The graph is shifted 4 units up.
B. The graph is shifted 4 units right.
C. The graph is shifted 4 units left.
D.The graph is shifted 4 units down.
Answer: D
Step-by-step explanation:
In a scale drawing, the length of a rectangular room is 6 inches, and the width is 3 inches. The actual length of the room is 18 feet. a. What is the scale of the drawing? b. In a new scale drawing of the same room, the length of the room measures 4 inches. What is the scale of the new drawing? Explain. Question content area bottom Part 1 a. The scale of the drawing is 1 in. enter your response here ft. (Type an integer or a decimal.) Part 2 b. The scale is 1 in. = enter your response here ft. In the new scale drawing, a length of 4 inches represents an actual length of enter your response here feet. So, a length of 1 inch represents an actual length of enter your response here feet. (Type integers or decimals.) Enter your answer in each of the answer boxes.
a) The scale of the drawing is 1 inch represents 216 inches or 1 inch represents 18 feet. b) The scale of the new drawing is 1 inch represents 72 inches or 1 inch represents 6 feet.
What is ratio?A ratio is a comparison between two quantities, often expressed as a fraction. It represents the relative size of two or more values, and can be used to compare, scale, or measure different quantities.
According to question:a. To find the scale of the drawing, we can use the ratio of the length in the drawing to the actual length.
The length in the drawing is 6 inches and the actual length is 18 feet, which is equivalent to 216 inches (since 1 foot = 12 inches).
So the scale of the drawing is:
1 inch in the drawing = 216 inches in reality
Therefore, the scale is:
1 inch : 216 inches
Simplifying this ratio, we get:
1 : 216
Therefore, the scale of the drawing is 1 inch represents 216 inches or 1 inch represents 18 feet.
b. In the new scale drawing, the length of the room is 4 inches. We need to find the scale of this new drawing.
Let x be the scale of the new drawing, such that:
1 inch in the new drawing = x feet in reality
We can set up the proportion:
6 inches in the old drawing : 18 feet in reality = 4 inches in the new drawing : y feet in reality
Simplifying this proportion, we get:
6 : 18 = 4 : y/x
Dividing both sides by 2, we get:
3 : 9 = 2 : y/x
Cross-multiplying, we get:
3x = 18
Dividing both sides by 3, we get:
x = 6
Therefore, the scale of the new drawing is:
1 inch in the new drawing = 6 feet in reality
Simplifying this ratio, we get:
1 : 72
Therefore, the scale of the new drawing is 1 inch represents 72 inches or 1 inch represents 6 feet.
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Convert the complex number z = 9i to polar form.
Answer:
Step-by-step explanation:
Can someone please help me with this? Thank you!
part a .
the probability of winning the lottery when the order of the five numbers does not matter is 1
part b.
the probability of winning the lottery when the order of the five numbers does matter is 1
How do we calculate?(a) When the order of the five numbers does not matter, we are dealing with combinations.
The probability of winning can be found as shown:
Number of ways to select 5 numbers out of 20 = 20 C 5 = (20!)/(5!15!) = 15,504
Total number of possible combinations of 5 numbers out of 20 = 20 C 5 = 15,504
So, the probability of winning is:
P = Number of ways to win / Total number of possible combinations
P = 15,504 / 15,504
P = 1/1
P = 1
(b) When the order of the five numbers does matter, we are dealing with permutations.
The probability of winning is:
Number of ways to select and order 5 numbers out of 20 = 20 P 5 = 20! / (20-5)! = 3,584,000
Total number of possible permutations of 5 numbers out of 20 = 20 P 5 = 20! / (20-5)! = 3,584,000
The probability of winning is:
P = Number of ways to win / Total number of possible permutations
P = 3,584,000 / 3,584,000
P = 1/1
P = 1
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someone please help me i rally need help
The equation which shows the cost of the admission tickets with tax inclusive is 4x + 25 = 175.
The cost is therefore $ 37.50.
How to calculate the cost of the tickets ?As each admission ticket is the same price, the total cost of 4 tickets can be written as 4x.
Given that the price of parking and four entry tickets is $175.00, we can write:
4x + $25.00 = $175.00
We may find x by simplifying the problem as follows:
4x = $175.00 - $25.00
4x = $150.00
x = $37.50
Therefore, the cost, in dollars, of each admission ticket, including tax, is $37.50.
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MODELING REAL LIFE A Study investigated land use in Florida. The results are shown in the circle graph. Find each indicated arc measure. Developed: 14.9% Other Rural: 7,2% H
a. mAC: b. mAE: c. mGDH: d. mBHC: Florida Land Use B Forest: 35.2% Water: 8.5% C G F Federal: 10.4% D E Cropland: 7,1% Pasture: 10.1% Range: 6.6%
a. The arc measure of mAC is approximately 0.936 radians.
b. The arc measure of mAE is approximately 0.446 radians.
c. The arc measure of mGDH is approximately 0.936 radians.
d. The arc measure of mBHC is approximately 1.566 radians.
What is Arc?In mathematics and geometry, an arc is a segment of a curve or a portion of the circumference of a circle. More specifically, an arc is defined as the set of points on a curve that are located between two endpoints, which adrive-thru re typically referred to as the arc's "start point" and "end point".
For example, consider a circle with center O and radius r. An arc on this circle could be defined as the set of points on the circle that lie between two points A and B, where A and B are two distinct points on the circle. The arc would be denoted as "arc AB" or "arc BA", and it would be measured in units of length or degrees, depending on the context.
Arcs are commonly used in geometry and trigonometry to calculate angles, distances, and areas. They are also used in many other fields, including physics, engineering, and computer graphics.
Arc Length = (Angle Measure / 360) x (2πr)
where r is the radius of the circle. Since the circle graph does not provide the value of the radius, we can assume it to be 1 unit.
a. mAC represents the arc measure of the Developed category. According to the graph, the percentage of land used for developed purposes is 14.9%. To find the arc measure, we can use the formula:
Arc Length = (Angle Measure / 360) x (2πr)
Arc Length for Developed = (14.9 / 100) x (2π x 1)
Arc Length for Developed = 0.149 x 2π
Arc Length for Developed ≈ 0.936 radians
Therefore, the arc measure of ArC is approximately 0.936 radians.
b. mAE represents the arc measure of the Cropland category. According to the graph, the percentage of land used for cropland purposes is 7.1%. To find the arc measure, we can use the same formula:
Arc Length for Cropland = (7.1 / 100) x (2π x 1)
Arc Length for Cropland = 0.071 x 2π
Arc Length for Cropland ≈ 0.446 radians
Therefore, the arc measure of mAE is approximately 0.446 radians.
c. mGDH represents the arc measure of the Water and Federal categories combined. According to the graph, the percentage of land used for water purposes is 8.5%, and the percentage of land used for federal purposes is 10.4%. Therefore, the combined percentage is:
Combined Percentage = 8.5 + 10.4 = 18.9%
To find the arc measure, we can again use the same formula:
Arc Length for Water and Federal = (18.9 / 100) x (2π x 1)
Arc Length for Water and Federal = 0.189 x 2π
Arc Length for Water and Federal ≈ 1.187 radians
Therefore, the arc measure of mGDH is approximately 1.187 radians.
d. mBHC represents the arc measure of the Other Rural, Pasture, and Range categories combined. According to the graph, the percentages of land used for these categories are:
Other Rural: 7.2%
Pasture: 10.1%
Range: 6.6%
Therefore, the combined percentage is:
Combined Percentage = 7.2 + 10.1 + 6.6 = 24.9%
To find the arc measure, we can once again use the same formula:
Arc Length for Other Rural, Pasture, and Range = (24.9 / 100) x (2π x 1)
Arc Length for Other Rural, Pasture, and Range = 0.249 x 2π
Arc Length for Other Rural, Pasture, and Range ≈ 1.566 radians
Therefore, the arc measure of mBHC is approximately 1.566 radians.
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A sports writer wants to see if a football filled with helium travels farther, on average, than a football filled with air. 14 footballs were filled with helium to the recommend pressure and 12 footballs were filled with air to the recommended pressure. The mean yardage for the helium filled footballs was 281 yards with a standard deviation of 3 yards. The mean yardage for the air filled footballs was 233 yards with a standard deviation of 4 yards.
Construct a 80% confidence interval for the mean difference in yardage for the two types of footballs. Assume the populations are normal with equal variances. Round your answers to three decimal places, and use four decimal places for any interim calculations.
We are 80% confident that the interval ( , )contains the true mean difference in yardage between the two types of footballs
we can say with 80% confidence that the true mean difference in yardage between the two types of footballs is between 46.224 and 49.776 yards.
How to solve the question ?
To construct the confidence interval for the mean difference in yardage between the two types of footballs, we first need to calculate the pooled standard deviation and the standard error of the mean difference. Since the sample sizes are large and the populations are assumed to be normal with equal variances, we can use the following formulas:
Pooled standard deviation:
s_p = √[((n1-1)*s₁² + (n2-1)*s₁²)/(n₁+n₂-2)]
s_p = √[((14-1)*3² + (12-1)*4²)/(14+12-2)]
s_p = 3.517
Standard error of the mean difference:
SE = s_p√(1/n₁ + 1/n₂)
SE = 3.517√(1/14 + 1/12)
SE = 1.416
Next, we can calculate the margin of error by multiplying the standard error by the t-value for the 80% confidence level with degrees of freedom equal to n1+n2-2=24. Using a t-table or calculator, we find that the t-value is 1.329.
Margin of error:
ME = tSE
ME = 1.3291.416
ME = 1.776
Finally, we can construct the confidence interval by adding and subtracting the margin of error from the sample mean difference in yardage.
Confidence interval:
(281-233) +/- ME
48 +/- 1.776
(46.224, 49.776)
Therefore, we can say with 80% confidence that the true mean difference in yardage between the two types of footballs is between 46.224 and 49.776 yards. This means that, on average, the football filled with helium travels 46.224 to 49.776 yards farther than the football filled with air.
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TimeRyte is a company that manufactures highly accurate stopwatches for sporting events. The company has two manufacturing facilities, one on the east cost and one on the west coast. Some stopwatches are assembled with components manufactured at the east coast facility, some are assembled with components manufactured at the west coast facility, and some are assembled with components manufactured at both facilities. TimeRyte have recently started a new advertising campaign that claims their stopwatches are accurate to a thousandth of a second 98% of the time. An independent research company is investigating the reliability of TimeRyte's stopwatches and the honesty of their claim. Their testing revealed that stopwatches assembled with components from the east coast facility are accurate to one thousandth of a second 96% of the time, stop watches assembled with components from the west cost are accurate to one thousandth of a second 99% of the time, and that stopwatches assembled with components from both facilities are accurate to the thousandth of a second 98% of the time. This a fair and honest ad campaign because .
The ad campaign by TimeRyte claiming that their stopwatches are accurate to a thousandth of a second 98% of the time is fair and honest based on the information provided. The independent research company's findings support this claim.
According to the research, stopwatches assembled with components from the east coast facility are accurate to a thousandth of a second 96% of the time. This implies that the assembly process at the east coast facility may introduce a slight deviation from the claimed accuracy.
Stopwatches assembled with components from the west coast facility, on the other hand, are accurate to a thousandth of a second 99% of the time. This suggests that the assembly process at the west coast facility is more reliable in achieving the claimed accuracy.
Stopwatches assembled with components from both facilities, which accounts for some of the products, are accurate to a thousandth of a second 98% of the time. This suggests that the combined efforts of both facilities maintain the claimed accuracy.
Considering the overall findings and the accuracy percentages provided, it can be concluded that the ad campaign's claim of 98% accuracy to a thousandth of a second is fair and honest, given the performance of the stopwatches across different assembly scenarios.
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PLS HELP ME
PLS SHOW YOUR WORKING OUT
Answer:
Step-by-step explanation:
it is really easy
