The percentage of people between the ages of 21 and 34 who prefer football are: 25%
What is a random sample?A random sample is a subset of a larger population that is chosen so that every person or thing has an equal chance of being chosen.
To find the percentage, we need to find the number of people between 21 and 34 who prefer football and divide by the total number of people in that age range:
Number of people between 21 and 34 who prefer football: 9
Total number of people between 21 and 34 are: 36
So the percentage of people between the ages of 21 and 34 who prefer football are:
⇒ (9 / 36) x 100%
⇒ 25%
Rounding to the nearest whole number, the answer is 25%
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Complete figure-
Last week, Kristen spent 4 hours gardening over a period of 7 days. She spent the same amount of time gardening each day.About how much time did she spend gardening each day last week?
A.less than 1 hour
B.between 1 and 2 hours
C.between 2 and 3 hours
D.between 4 and 7 hours
We can see that the choice falls within the range of (A) less than 1 hour. Therefore, the answer is (A), Kristen spends less than 1 hour .
What does "unitary method" mean?Finding the value of a single unit using the unitary technique allows us to determine the value of the necessary number of units based on this value.
To find out approximately how much time Kristen spent gardening each day, we can divide the total time she spent gardening by the number of days she gardened.
Total time = 4 hours
Number of days = 7
So, Kristen spent approximately 4/7 = 0.57 hours or about 34 minutes each day gardening.
Since the answer choices are in ranges, we can see that this falls within the range of (A) less than 1 hour. Therefore, the answer is (A).
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please help me with this pentomino question.
a. There are twelve unique pentominos possible in all.
b. In total, only 6 pentominos have the refection symmetry.
What is a pentomino?
A pentomino is an order 5 polyomino, or a plane polygon formed of 5 identical squares joined edge to edge. This is just linked with a certain arrangement of squares.
a. There are twelve unique pentominos possible in all which on reflection and rotation can create multiple more pentominos.
b. In total, 6 pentominos have refection symmetry which means that now the total pentominos are 18 of which 6 have reflection symmetry.
Hence, the required solution has been obtained.
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Find the amount accumulated after
investing a principle P for t years and an
interest rate compounded twice a year.
P = $100 r = 3% t= 5 k = 2
Hint: A = P(1 + E)kt
A = $[?]
After five years of investing $100 at a 3% annual interest rate compounded twice, the total amount is $116.18.
What is principle?
The whole sum borrowed (or invested), exclusive of interest and dividends.
What is compound interest?
The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.
The formula for the amount A accumulated after investing a principle P for t years at an annual interest rate r compounded k times per year is:
A = P * [tex](1 + r/k)^{(k*t)}[/tex]
Substituting the given values into this formula, we have:
A = $100 *[tex](1 + 0.03/2)^(2*5)[/tex]
A = $100 * [tex](1 + 0.015)^{10}[/tex]
A = $100 * 1.161834...
A = $116.18 (rounded to the nearest cent)
Therefore, the amount accumulated after investing a principle of $100 for 5 years at an interest rate of 3% compounded twice a year is $116.18.
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Given F(x) = 4x - 8 and g(x) = -3x + 1, what is (f - g)(x)?
A) 7x-9
B) 7x - 7
C) x-9
D) x - 7
Therefore, the answer is (A) 7x-9 when it is given that function F(x) = 4x - 8 and g(x) = -3x + 1.
What is function?In mathematics, a function is a relationship between two sets of values, where each input (or domain element) is associated with a unique output (or range element). In other words, a function is a rule or a process that takes an input (or inputs) and produces a corresponding output. Functions can be expressed using various mathematical notations, such as algebraic formulas, graphs, tables, or even verbal descriptions. They are widely used in many fields of mathematics, science, engineering, economics, and computer science, to model and solve problems that involve relationships between variables or quantities.
Here,
To find (f - g)(x), we need to subtract g(x) from f(x), so we get:
(f - g)(x) = f(x) - g(x)
Substituting the given functions, we get:
(f - g)(x) = (4x - 8) - (-3x + 1)
Simplifying the expression by distributing the negative sign, we get:
(f - g)(x) = 4x - 8 + 3x - 1
Combining like terms, we get:
(f - g)(x) = 7x - 9
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The count in a bateria culture was initially 300, and after 35 minutes the population had increased to 1600. Find the doubling period. Find the population after 70 minutes. When will the population reach 10000?
What are answers to these questions?
1. f is concave up on the intervals = ?
2. f is concave down on the intervals = ?
3. The inflection points occur at x = ?
f(x) is concave up on the interval (-∞, √(6/7)) U (√(6/7), ∞),f(x) is concave down on the interval (-√(6/7), √(6/7)) ,The inflection points occur at x = -√(6/7) and x = √(6/7).
What is inflection Point?An inflection point is a point on a curve where the concavity changes, from concave up to concave down or vice versa, indicating a change in the curvature of the curve.
According to the given information:
To determine the intervals where f(x) is concave up or down, we need to find the second derivative of f(x) and determine its sign.
First, we find the first derivative of f(x):
f'(x) = (14x)/(7x²+6)²
Then, we find the second derivative of f(x):
f''(x) = [28(7x²+6)²- 28x(7x²+6)(4x)] / (7x²+6)^4
Simplifying the expression, we get:
f''(x) = 28(42x² - 72) / (7x^2+6)³
To determine where f(x) is concave up or down, we need to find the intervals where f''(x) is positive or negative, respectively.
Setting f''(x) = 0, we get:
42x² - 72 = 0
Solving for x, we get:
x = ±√(6/7)
These are the possible inflection points of f(x). To determine if they are inflection points, we need to check the sign of f''(x) on both sides of each point.
We can use a sign chart to determine the sign of f''(x) on each interval.
Intervals where f''(x) > 0 are where f(x) is concave up, and intervals where f''(x) < 0 are where f(x) is concave down.
Here is the sign chart for f''(x):
x | -∞ | -√(6/7) | √(6/7) | ∞
f''(x)| - | + | - | +
From the sign chart, we can see that:
a) f(x) is concave up on the interval (-∞, √(6/7)) U (√(6/7), ∞).
b) f(x) is concave down on the interval (-sqrt(6/7), √(6/7)).
c) The inflection points occur at x = -√(6/7) and x = √(6/7).
Therefore, the open intervals where f(x) is concave up are (-∞, -√(6/7)) and (√(6/7), ∞), and the open interval where f(x) is concave down is (-√(6/7), √(6/7)). The inflection points occur at x = -√(6/7) and x = √(6/7).
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The f(x) is concave up on the interval (-∞, √(6/7)) U (√(6/7), ∞),f(x) is concave down on the interval (-√(6/7), √(6/7)) ,The inflection points occur at x = -√(6/7) and x = √(6/7).
What is inflection Point?
An inflection point is a point on a curve where the concavity changes, from concave up to concave down or vice versa, indicating a change in the curvature of the curve.
According to the given information:
To determine the intervals where f(x) is concave up or down, we need to find the second derivative of f(x) and determine its sign.
First, we find the first derivative of f(x):
f'(x) = (14x)/(7x²+6)²
Then, we find the second derivative of f(x):
f''(x) = [28(7x²+6)²- 28x(7x²+6)(4x)] / (7x²+6)^4
Simplifying the expression, we get:
f''(x) = 28(4x² - 72) / (7x^2+6)³
To determine where f(x) is concave up or down, we need to find the intervals where f''(x) is positive or negative, respectively.
Setting f''(x) = 0, we get:
42x² - 72 = 0
Solving for x, we get:
x = ±√(6/7)
These are the possible inflection points of f(x). To determine if they are inflection points, we need to check the sign of f''(x) on both sides of each point.
We can use a sign chart to determine the sign of f''(x) on each interval.
Intervals where f''(x) > 0 are where f(x) is concave up, and intervals where f''(x) < 0 are where f(x) is concave down.
Here is the sign chart for f''(x):
x | -∞ | -√(6/7) | √(6/7) | ∞
f''(x)| - | + | - | +
From the sign chart, we can see that:
a) f(x) is concave up on the interval (-∞, √(6/7)) U (√(6/7), ∞).
b) f(x) is concave down on the interval (-sqrt(6/7), √(6/7)).
c) The inflection points occur at x = -√(6/7) and x = √(6/7).
Therefore, the open intervals where f(x) is concave up are (-∞, -√(6/7)) and (√(6/7), ∞), and the open interval where f(x) is concave down is (-√(6/7), √(6/7)). The inflection points occur at x = -√(6/7) and x = √(6/7).
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How many years will it take $6,000 invested at 8% interest to earn $1,680?
Answer:
We can use the formula for simple interest to solve this problem:
I = Prt
where I is the amount of interest earned, P is the principal (the initial amount invested), r is the annual interest rate (as a decimal), and t is the time (in years).
In this problem, we know that P = $6,000, r = 0.08, and I = $1,680. We want to find t, the time required to earn $1,680 in interest.
Substituting these values into the formula, we get:
$1,680 = $6,000 x 0.08 x t
Simplifying and solving for t, we get:
t = $1,680 / ($6,000 x 0.08) = 3.5 years
Therefore, it will take 3.5 years for $6,000 invested at 8% interest to earn $1,680 in interest.
in triangle rst r=6 s=10 and t=14.find the measure of the largest angle to the nearest degree and the length of the altitude from S to the three significant digits .Write your answers in the answer box provided below.
Measure of angle ∠R = 55° , Measure of ∠S = x+10 =55+10 = 65°, Measure of ∠T = x+5= 55 + 5 =60°
What is a triangle?Recall that a triangle is a three-sided polygon that consists of three edges and three vertices.
Since we have given that RST is a triangle,
Angle S is 10° greater than angle R and
angle T us 5° less than Angle S
Let the measure of ∠R be 'x'.
Let the measure of ∠S be 'x+10'
Let the measure of ∠T be 'x+10-5'='x+5'
As we know that "Sum of all angles in triangle is 180°.
So, it becomes,
∠R + ∠S + ∠T =180°
x + x + 10 + x + 5 = 180
3x +15 = 180
3x = 180-15
3x = 165
x = 165/3
x =55
So, Measure of ∠R = 55°
Measure of ∠S = x+10 =55+10 = 65°
Measure of ∠T = x+5= 55 + 5 =60°
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consider a collection of enveloped consisting of 2 red, 1 blue, 2 green envelopes, and 2 yellow envelopes. If two envelopes are selected at random, with replacement, determine the probability that at least one envelope is a yellow envelope.
Can I get a detailed answer so that I can use it to study?
Answer:
The probability of picking a yellow envelope is 2/7
Step-by-step explanation:
red envelope =2
blue " " =1
green " "=2
yellow " " =2
Total envelope =2+1+2+2=7
Probability thay at least one envelope will be yellow
P=number of yellow envelope/Total envelope
P=2/7
I need helppp!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
The distance formula is
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
x1 is a,
x2 is 0,
y1 is 0 and
y2 is b. Fitting those into the formula where they belong:
[tex]d=\sqrt{(0-a)^2+(b-0)^2}[/tex] and
[tex]d=\sqrt{(-a)^2+(b)^2}[/tex]
Since a negative squared is a positive, then
[tex]d=\sqrt{a^2+b^2}[/tex]
which is the second choice down.
Find the length of the triangle.
The length of the unknown side of the triangle is __________
Answer:
The answer is 2√10
Step-by-step explanation:
Hyp²=opp²+adj²
let hyp be x
x²=6²+2²
x²=36+4
x²=40
square root both sides
√x²=√40
x=2√10
An eraser is 2 1/2 inches long. How long are 10 erasers places end to end?
Answer:
25 inches
Step-by-step explanation:
We Know
An eraser is 2 1/2 inches long.
2 1/2 = 5/2 = 2.5 inches long
How long are 10 erasers placed end to end?
We Take
2.5 x 10 = 25 inches
So, it is long 25 inches.
A company’s cereal boxes advertise that 9.65 ounces of cereal are contained in each box. In fact, the amount of cereal in a box follows an approximately normal distribution with mean μ = 9.70 ounces and standard deviation σ = 0.03 ounce. Let x-bar be the sample mean amount of cereal in 5 randomly selected boxes.
Shape: Approximately normal because the population distribution is approximately normal
Center: μ x-bar = 9.70 ounces.
Variability: σ x-bar = 0.013 ounces.
(b) What is the probability that the mean amount of cereal x-bar in 5 randomly selected boxes is at most 9.65?
Round your answer to 5 decimal places.
The probability that the mean amount of cereal x-bar in 5 randomly selected boxes is at most 9.65 is 0.0001.
How to calculate the probabilityProbability 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.
Mean μ=9.70
Sample size=n=5
standard deviation=σ = 0.03
Now in order to use the table we have to to figure out z value.
z=(x-μ)/σ
z=(9.65-9.70)/0.0134
z=-3.73
From the probability index tables, so P(z≤-3.73)=0.0001
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for ouls salt 1/4 (8x+12) = 19
Answer:
x = 8
Step-by-step explanation:
1/4 (8x + 12) = 19
Distribution property
1/4 x 8= 2
1/4 x 12= 3
2x + 3 = 19
19 - 3= 16
2x= 16
16/2 = 8
X= 8
PLEASE HELP DUE TODAY ASAP
im pretty sure the answer is B Please tell me if im correct ASAP!
Question 3(Multiple Choice Worth 1 points)
(08.07 LC)
The function g(x) is shown on the graph.
The graph shows an upward opening parabola with a vertex at negative 4 comma 3, a point at negative 6 comma 7, and a point at negative 2 comma 7.
What is the equation of g(x) in vertex form?
g(x) = (x − 4)2 − 3
g(x) = (x − 4)2 + 3
g(x) = (x + 4)2 − 3
g(x) = (x + 4)2 + 3
Step-by-step explanation:
Vertex at -4,3 would result in vertex form of parabola
g(x) = (x+4)^2 + 3
7. A group of students wants to demonstrate that sunlight provides the energy for plants to grow. What is
the control group for the experiment?
A. Some plants will receive less water
B. Some plants will receive fertilizer
C. Some plants will receive no sunlight
D. Some plants will receive no water
I
The control group for the experiment would be option C: some plants will receive no sunlight.
What is control group for experiment ?The control group in an experiment is the group that does not receive the treatment or intervention being tested, so that the effects of the treatment can be compared to a baseline or reference point. In this experiment, the treatment being tested is the provision of sunlight as an energy source for plant growth.
Therefore, the control group should not receive sunlight, so that the effects of sunlight can be compared to the baseline of plant growth without sunlight.
Therefore, the control group for the experiment would be option C: some plants will receive no sunlight.
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Test the following hypotheses by using the given sample information and α = .01. Assume the populations are normally distributed.
H0 : σ2 =σ2 Ha:σ2 >σ2 1212
n1 =10, n2 =11, s2 =562, s2 =1013 12
Since the calculated F-value of 0.555 is less than the critical value of 4.025, we fail to reject the null hypothesis.
What is null hypothesis?A null hypothesis is a statement that establishes the equality of two expressions and frequently includes variables, constants, and mathematical operations.
The equal sign (=) is used to denote the space between the two sides, which are referred to as the left-hand side (LHS) and the right-hand side (RHS).
To test the given hypothesis, we will use the F-test for two variances.
The null and alternative hypotheses are:
H0: σ1² = σ2² (no difference in population variances)
Ha: σ1² > σ2² (population variance of first group is greater than that of second group)
The test statistic is calculated as:
F = s1² / s2²
Where s1² and s2² are the sample variances of the two groups.
The degrees of freedom for the F-distribution are df1 = n1 - 1 and df2 = n2 - 1.
Using the given sample information, we have:
n1 = 10, n2 = 11
s1² = 562, s2² = 1013
Therefore, the test statistic is:
F = s1² / s2² = 562 / 1013 = 0.555
The degrees of freedom are df1 = 9 and df2 = 10.
Using a significance level of α = 0.01 and the F-distribution tables or a calculator, the critical value for the right-tailed test with df1 = 9 and df2 = 10 is 4.025.
Since the calculated F-value of 0.555 is less than the critical value of 4.025, we fail to reject the null hypothesis. There is not enough evidence to conclude that the population variance of the first group is greater than that of the second group at a significance level of α = 0.01.
We can conclude that there is not enough evidence to support the claim that σ1² > σ2².
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please help fill these in..
Examining the curve the information obtained are
vertex (3, 13)
axis of symmetry: x = 13
y intercept: (0, 5)
maximum
Domain (-∞, ∞)
Range (-∞, 12]
What is a parabolic curveA parabolic curve, also known as a parabola, is a symmetrical U-shaped curve. It is defined by a mathematical equation of the form
y = ax^2 + bx + c,
where a, b, and c are constants, and x and y are the coordinates of points on the curve.
The graph of a parabolic curve is smooth and continuous, with no sharp corners or discontinuities.
The vertex is at the peak of the curve and the coordinates is (3, 13) where the axis of symmetry is where the curve is divided into two equal parts. This is represented by the equation x = 3
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please help 20 points
Factorize the following polynomials:
1) 54x²+42x³ - 30x4
Which of these is a simplified form of the equation 6Y +4 equals 8+ 2Y plus 2Y
the simplified form of the equation 6Y + 4 = 8 + 2Y + 2Y is Y = 2.
How to solve the question ?
To simplify the equation 6Y + 4 = 8 + 2Y + 2Y, we can combine like terms. Like terms are terms that have the same variable and the same exponent. In this case, we have two terms with Y as the variable, so we can combine them.
First, let's add the 2Y terms on the right side of the equation: 6Y + 4 = 8 + 4Y
Next, we can subtract 4Y from both sides of the equation to isolate the variable on one side: 6Y - 4Y + 4 = 8
Simplifying further, we can combine the Y terms: 2Y + 4 = 8
Finally, we can subtract 4 from both sides to isolate the variable: 2Y = 4
And we can solve for Y by dividing both sides by 2: Y = 2
Therefore, the simplified form of the equation 6Y + 4 = 8 + 2Y + 2Y is Y = 2.
In summary, to simplify an equation, we want to combine like terms and isolate the variable on one side of the equation. Once we have the variable on one side, we can solve for its value.
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find the height of the building when x = 3m, y = 6m, and d = 6m
Answer:
To find the height of the building, we can use the following formula:
height = y(d-x)/x
Substituting the given values, we get:
height = 6(6-3)/3
height = 6(3)/3
height = 6 meters
Therefore, the height of the building is 6 meters.
Look at the equations below. Find a pair of
equations whose lines are perpendicular.
Click on the correct answer.
y = x +6;y = −6x + 4
y = 5x-4; y = 5x +5
y = -5x + 6; y = -10x + 4
1
y=-x-4; y = −5x+5
The equations of line that are perpendicular to each other are:
A: y = (1/6)x + 6; y = -6x + 4
How to find perpendicular equations?The general formula for the equation of a line in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
Now, for two equations to be perpendicular, it means that their slope must be negative reciprocals of each other. Thus:
Looking at the equations, we can say the only ones that have slopes that are negative reciprocals of each other is option A.
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What kind of angle is
∠mah?
What is the value of x?
What is the measure of
∠mat ?
What is the measure of
∠tah ?
So according to the given figure ∠mah is right angle(90°), The value of x is 17, ∠mat is 38° and ∠tah is equal to 52°.
What is the source of this answer and define a graph?(A) ∠mah is right angle(90°) [GIVEN IN THE FIGURE]
(B) (2x+4)+(3x+1) = 90
5x+5 = 90
x= 17
(C) 2x+4 = 2×17 + 4 = 38°
(D) 3X + 1 = 3 × 17 + 1 = 52°
A graph is a visual representation or diagram that displays facts or values in an organised manner in mathematics. The points on a graph are typically used to depict the relationships between two or more things.
A graph in discrete mathematics is made up of vertices, which are groups of points, and edges, which are the connections between those vertices. There are numerous different types of graphs besides linked and disconnected graphs, weighted graphs, bipartite graphs, directed and undirected graphs, and simple graphs.
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KPI Payouts are: Prepaid Ring-out Only: $ 1.00 Prepaid Activation: $ 2.00 Accessories: 1.5 Equipment Protection: $ 1.00 You can make $ and ring it out at the POS. % when you activate a prepaid device with equipment protection
If no accessories are sold, $3 will be paid out. In the event that accessories are sold, the compensation is $2.00 plus $1.00 plus 1.5 percent of their worth.
Based on the information given, the KPI payouts are:
$1.00 for each Prepaid Ring-out Only
$2.00 for each Prepaid Activation
1.5% of the value of each Accessories sale
$1.00 for each Equipment Protection sale
We need to know the values of the prepaid activation and equipment protection in order to compute the payment for activating a prepaid device with equipment protection. Assume that the equipment protection is worth $Y and the prepaid activation is worth $X.
The following would be the total payment for activating a prepaid device with equipment protection:
Payout = $2.00 (for activation) + $1.00 (for equipment protection) + 1.5% (of the value of accessories sold)
If no accessories are sold, the payout would be:
Payout = $2.00 + $1.00
= $3.00
If accessories worth $Z are also sold, the payout would be:
Payout = $2.00 + $1.00 + 1.5% of $Z
= $2.00 + $1.00 + 0.015Z
So the payout for activating a prepaid device with equipment protection depends on the value of the accessories sold.
Therefore, If no accessories are sold, the payout is $3.00. If accessories are sold, the payout is $2.00 + $1.00 + 1.5% of the value of the accessories sold.
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PLEASE HELP!!!!
A parabola can be drawn given a focus of (0,7) and a directrix of y=−7. Write the equation of the parabola in any form.
Answer:
y = 1/28(x²)
Step-by-step explanation:
Not totally sure about this, but here's what I think is the answer:
focus (0,7)
directrix y = -7
Always a good idea to plot the point (0,7) and the line y = -7 so you can visualize what the parabola looks like.
From the graph, you can see that p = 7 (halfway between the focus and the directrix).
The vertex of this parabola is (0,0), which are your (h, k) values. You can see that from the graph. The parabola opens UP.
4p(y-k) = (x-h)² → 4p(y-0) = (x-0)²
4py = x²
y = x²/4p = x²/4(7) = x²/28
y = 1/28(x²)
sorry if this isn't the right answer, but I tried (I'm not a paid expert, just a fellow student trying to learn math)!
answer 1-7 and 11-14 please answers do not need to be accurate but should be realistic thank you
highschool geometry no need for explanation
1. The ratio for sin x in the trigonometry will be 12/13.
The ratio for cos x in the trigonometry will be 5/13.
The ratio for tan x in the trigonometry will be 12/5
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used extensively in various fields, including physics, engineering, and astronomy.
The three primary functions in trigonometry are sine, cosine, and tangent. These functions relate the ratios of the sides of a right triangle to its angles.
The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.
Trigonometry also involves inverse functions, such as the arcsine, arccosine, and arctangent. These functions are used to find the angle whose sine, cosine, or tangent is a given value.
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The five number summary of a dataset was found to be:
45, 52, 56, 63, 66
An observation is considered an outlier if it is below:
An observation is considered an outlier if it is above:
An observation is considered an outlier if it is below 35.5 or above 79.5 in this dataset.
Identifying the outliers in the summaryTo determine the outliers in a dataset using the five-number summary, we need to calculate the interquartile range (IQR), which is the difference between the third quartile (Q3) and the first quartile (Q1).
IQR = Q3 - Q1
Where
Q1 = 52
Q3 = 63
So, we have
IQR = 63 - 52
IQR = 11
An observation is considered an outlier if it is:
Below Q1 - 1.5 × IQR
Above Q3 + 1.5 × IQR
Substituting the values, we get:
Below 52 - 1.5 × 11 = 35.5
Above 63 + 1.5 × 11 = 79.5
Therefore, an observation is considered an outlier if it is below 35.5 or above 79.5 in this dataset.
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Has the marrying age of a man changed over the years? The United States Bureau of the Census takes a formal count of everyone in the U.S. every 10 years and has provided the following data that gives the median age of an American man at the time of his first marriage.
What does a rate of change of zero mean in this situation?
a.
The median age of a man at the time of his first marriage is, on the average, constant.
b.
The median age of a man at the time of his first marriage is, on the average, decreasing.
c.
The median age of a man at the time of his first marriage is, on the average, increasing.
d.
The rate of change cannot be zero in this situation.
ITs not D so dont say it if you dont know the answer dont reply i put up this post for those who need to get the answer because all other post are wrong.
For the given data the general trend is neither continuously rising nor falling. thus, the correct answer is option a: The median age of a man at the time of his first marriage is, on the average, constant.
How to calculate rate of change of mean?We can compute the rates of change by deducting the current year's median age from the prior year's median age. A result of zero denotes no change, a result of zero denotes no decline, and a result of one denotes an increase.
[tex]\text{Rate of Change} = Median\; Age (current \;year) - Median \;Age (previous \;year)[/tex]
[tex]1910-1920: 24.6 - 25.1 = -0.5\\1920-1930: 24.3 - 24.6 = -0.3\\1930-1940: 24.3 - 24.3 = 0\\1940-1950: 22.8 - 24.3 = -1.5\\1950-1960: 22.8 - 22.8 = 0\\1960-1970: 23.2 - 22.8 = 0.4\\1970-1980: 24.7 - 23.2 = 1.5\\1980-1990: 26.1 - 24.7 = 1.4\\1990-2000: 26.8 - 26.1 = 0.7\\[/tex]
The rates of change, as we can see, alternate between positive and negative values, but the general trend is neither continuously rising nor falling. Several times, the rate of change is zero, showing that, generally speaking, the median age of a man at the time of his first marriage is holding steady through time.
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taylor has enough money to buy either 90 granola bars or 78 pop tarts. After returning from the atore, taylor has no money, 75 granola bars and p pop tarts
Using equations, we can find that the number of pop tarts that Taylor has with him, p = 13.
Define equations?An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. as in 3x + 5 = 15, for example. There are many different types of equations, including linear, quadratic, cubic, and others.
Let the cost of one granola bar = x.
Let the cost of one pop tart = y.
Now, assume Taylor had money, m.
So, as per the question:
90x = m
⇒ x = m/90
78y = m
⇒ y = m/78
75x + py = m
Substituting the values of x and y:
⇒ 75 × m/90 + p × m/78 = m
⇒ 75m/90 + pm/78 = m
⇒ (5850m + 90pm) / 7020 = m
⇒ 5850m + 90pm = 7020m
⇒ 90pm = 7020m - 5850m
⇒ 90pm = 1170m
⇒ p = 1170m/90m
⇒ p = 13.
Therefore, the number of pop tarts, p = 13.
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