Match the function with its graph.
1) y= tan x
2) y= cot x
3) y= -tan x
4) y= -cot x
Answers
Answer:
Option a. 1C, 2A, 3B, 4D.
Step-by-step explanation:
1) We know that tan(x)=sin(x)/cos(x). If x=0, sin(x)=0 and cos(x)=1 then tan(x)=0. For that reason, we know that the graph passes through the point (0,0).
If x=45, then sin(45)= [tex]\frac{\sqrt{2}}{2}[/tex] and cos(45)=[tex]\frac{\sqrt{2}}{2}[/tex]. Thus tan(45)=1. The only graph that passes through the point (0,0) and is possitive when x=45 is the graph C.
2) We know that cot(x)=cos(x)/sin(x). If x=0, sin(x)=0 and cos(x)=1 then tan(x)=+∞. For that reason, we know that the graph has an asymptote in y=0, in other words, it never crosses the y-axis.
If x=45, then sin(45)= [tex]\frac{\sqrt{2}}{2}[/tex] and cos(45)=[tex]\frac{\sqrt{2}}{2}[/tex]. Thus cot(45)=1. The only graph that has an asymptote in y=0 and is possitive when x=45 is the graph A.
3) We know that -tan(x)=-sin(x)/cos(x). If x=0, sin(x)=0 and cos(x)=1 then -tan(x)=0. For that reason, we know that the graph passes through the point (0,0).
If x=45, then sin(45)= [tex]\frac{\sqrt{2}}{2}[/tex] and cos(45)=[tex]\frac{\sqrt{2}}{2}[/tex]. Thus -tan(45)=-1. The only graph that passes through the point (0,0) and is negative when x=45 is the graph B.
) We know that -cot(x)=-cos(x)/sin(x). If x=0, sin(x)=0 and cos(x)=1 then tan(x)=-∞. For that reason, we know that the graph has an asymptote in y=0, in other words, it never crosses the y-axis.
If x=45, then sin(45)= [tex]\frac{\sqrt{2}}{2}[/tex] and cos(45)=[tex]\frac{\sqrt{2}}{2}[/tex]. Thus -cot(45)=-1. The only graph that has an asymptote in y=0 and is negative when x=45 is the graph D.
The correct matches of the functions with their graphs are as follows: 1) y = tan(x) matches with graph C, 2) y = cot(x) matches with graph A, 3) y = -tan(x) matches with graph B, and 4) y = -cot(x) matches with graph D.
1) y = tan(x) matches with graph C:
- The tangent function has a period of π (180 degrees) and is undefined at odd multiples of π/2 (90 degrees). This is why it has vertical asymptotes at x = π/2, 3π/2, etc.
- The graph of y = tan(x) passes through (0, 0) because tan(0) = 0.
- It has a repeating pattern where it increases to positive infinity as it approaches the vertical asymptotes and decreases to negative infinity as it approaches the odd multiples of π/2.
2) y = cot(x) matches with graph A:
- The cotangent function is the reciprocal of the tangent function: cot(x) = 1/tan(x). It is undefined at even multiples of π/2 (0, π, 2π, etc.), which is why it has vertical asymptotes at x = 0, π, 2π, etc.
- The graph of y = cot(x) never crosses the y-axis, and it has an asymptote at y = 0.
- It has a repeating pattern where it approaches 0 as it approaches the vertical asymptotes.
3) y = -tan(x) matches with graph B:
- The negative tangent function, -tan(x), is the reflection of the positive tangent function y = tan(x) about the x-axis.
- The graph of y = -tan(x) passes through (0, 0) because -tan(0) = 0.
- It has a repeating pattern similar to the positive tangent but is reflected about the x-axis.
4) y = -cot(x) matches with graph D:
- The negative cotangent function, -cot(x), is the reflection of the positive cotangent function y = cot(x) about the x-axis.
- The graph of y = -cot(x) never crosses the y-axis, similar to the positive cotangent, and it has an asymptote at y = 0.
- It has a repeating pattern similar to the positive cotangent but is reflected about the x-axis.
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Related Questions
which of the following are sets of discrete check all that apply
A{-3,6,9,17,24}
B(-10,29]
C(1,99)
D{1,3,5,7,...}
E{5,8}
Answers
Answer:
C(1,99) and E(5,8)
Step-by-step explanation:
Discrete data are numerical values that are distinct and outstanding mostly assigned from surveys by counting e.t.c
Thus, these numerical values cannot be negative as we can not count negative values.
the data can only take known exact values so it is not continuous. From the given sets of data the sets that satisfy the given guidelines are C(1,99) and E(5,8)
A rectangle has vertices at (-1, 6), (-1, -2), (3, 6), and (3,-2). What is the area of the rectangle?
Answers
Answer:
32 units²
Step-by-step explanation:
From point 1 to point 2, the y values change by 8 units while the x values stay the same. This side of the rectangle has a length of 8
From point 1 to point 3, the x values change by 4 units while the y values stay the same. This side of the polygon has a length of 4
The area of the rectangle is 8x4 = 32 units²
Answer:
32 square units
Step-by-step explanation:
A rectangle has vertices at (-1, 6), (-1, -2), (3, 6), and (3,-2)
Area of a rectangle = length times width
LEts find the distance between (-1, 6) and (3, 6)
Apply distance formula
[tex]D= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]D= \sqrt{(3+1)^2+(6-6)^2}=\sqrt(16)= 4[/tex]
LEts find the distance between (-1, 6), (-1, -2)
[tex]D= \sqrt{(-1+1)^2+(-2-6)^2}=\sqrt(64)= 8[/tex]
Area of the rectangle = 4 times 8= 32 square units
A fish tank is 3/4 full. 2/3 of the water leak out. After the water leaks out, 10 gallons are left in the tank. How many gallons of water does the tank hold when full?
Answers
Capacity of the fish tank is 40 gallons
Fine the area. The figure is not drawn to scale.
Answers
Answer:
Step-by-step explanation:
Area = 7.6 × 3.7
Area = 28.12 cm²
I hope I helped you.
Answer:
[tex]28.12cm^2[/tex]
Step-by-step explanation:
The figure shown in the diagram is a parallelogram.
The area of a parallelogram is [tex]base \times height.[/tex].
The base of the parallelogram is 3.7cm
The height of the parallelogram is 7.6cm.
The area of the parallelogram
[tex]3.7\times 7.6=28.12cm^2[/tex]
The first choice is the correct answer
The probability of a type ii error is represented by the greek symbol, β.
a. True
b. False
Answers
The answer to your question is a. TRUE
Final answer:
The statement that the probability of a Type II error is represented by the Greek symbol β is true. The β symbol denotes the likelihood of failing to reject a false null hypothesis, while the power of a test (1-β) indicates the probability of accurately detecting a false null hypothesis.
Explanation:
The question is asking whether the statement 'The probability of a type ii error is represented by the greek symbol, β' is true or false. The correct answer is a. True. In statistics, a Type II error, which occurs when a false null hypothesis is not rejected, is indeed represented by the Greek letter β (beta). Therefore, the probability of committing a Type II error is denoted as β (beta). Conversely, a Type I error, symbolized by α (alpha), happens when the null hypothesis is incorrectly rejected. It is important to minimize both α and β as they represent the probabilities of these two types of errors. While α is often set by the researcher (commonly at 0.05), β is affected by factors such as effect size, sample size, and the chosen significance level α.
The power of a statistical test, defined as 1 - β, is the probability of correctly rejecting a false null hypothesis. A high statistical power is desirable as it indicates a lower chance of committing a Type II error. Estimating or calculating β directly can be complex, but understanding its role is crucial for interpreting the results of hypothesis testing.
A value of a plot of land has increased by 10% in the past year. The new value of the plot is $46,200. What was the value of the plot last year.
Answers
Answer:
42,000 dollars was the value of the plot last year
Step-by-step explanation:
[tex]x*\frac{110}{100}=46200\\110x=4620000\\x=\frac{4620000}{110} \\x=42000[/tex]
Consider the characteristics of the graph. Which statement DOES NOT describe the data set
Answers
Where are the statements ?
Answer: The data is skewed right.
Bobby gets 5.5% commission on the cost of each vehicle he sells. What is his commission if he sells a truck for $32,459 ?
$98.19
$1,785.25
$1,073.02
$3,245.90
Answers
The answer should be B: $1,785.25
Answer:
$1785.245
Step-by-step explanation:
Cost of truck = $32,459
We are given that Bobby gets 5.5% commission on the cost of each vehicle he sells.
So, Commission = [tex]\frac{5.5}{100} \times 32459[/tex]
Commission = [tex]1785.245[/tex]
Hence his commission if he sells a truck for $32,459 is $1785.245
One winter morning in Canada, the temperature at 8:00 was 1.5°C. From 8:00 to 11:00, the temperature increased by 0.7°C. From 11:00 to 2:00, it dropped 2.6°C, and from 2:00 to 5:00, it decreased by 0.9°C. What expression shows the temperature in °C at 5:00 p.M.?
Answers
Answer:
See below.
Step-by-step explanation:
Temperature at 5 pm = 1.5 + 0.7 - 2.6 - 0.9
(= -1.3 degrees C).
Answer:=1.5 + 0.7 - 2.6 - 0.9
Step-by-step explanation:
A salsa recipe uses green pepper onion and tomato in the extended ratio 2:5:9
Answers
Answer:
30
Step-by-step explanation:
cos 2x = ____
Check all that apply.
Answers
Answer:
see below
Step-by-step explanation:
The double angle formulas for trig functions are generally based on the sum of angle formulas, where the two angles are equal.
cos(a+b) = cos(a)cos(b) -sin(a)sin(b)
When a=b=x, then ...
cos(2x) = cos(x)² -sin(x)²
The Pythagorean identity can be used to substitute for either of the squares:
cos(2x) = (1 -sin(x)²) -sin(x)²
cos(2x) = 1 - 2sin(x)²
or
cos(2x) = cos(x)² -(1 -cos(x)²)
cos(2x) = 2cos(x)² - 1
The correct representations of the identity cos2x from the provided options are A (1 - 2sin²x), B (2sin²x - 1), and D (cos²x - sin²x). The Option C (sin²x - cos²x) is not correct. Therefore, option A,B and D are correct
Explanation:The question is asking for various forms of the identity cos2x, where x is an angle.
From the given options, A, B, and D are correct.
We know that cos2x can be represented in three possible ways: 1 - 2sin²x (Option A), 2cos²x - 1 (not provided in the options), and 2sin²x - 1 (Option B).
Thus, the correct options are A (1-2sin²x) and B (2sin²x - 1). Option D (cos²x - sin²x) is another equivalent form of cos2x based on the identity cos²x + sin²x = 1 (provided as Reference 7). Option C (sin²x - cos²x) is not a formula for cos2x so it's incorrect.
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The correct statement is written below:
cos2x=____. Check all that apply.
A. 1-2sin^2 x.
B. 2sin^2 x-1.
C. sin^2 x-cos^2 x.
D. cos^2 x-sin^2 x
(1CQ) Determine whether the series -8/5+32/25-128/125+... is convergent or divergent.
Answers
Answer:
The series is convergent answer ⇒ (a)
Step-by-step explanation:
* The series is -8/5 + 32/25 + -128/125 + ........
- It is a geometric series with:
- first term a = -8/5 and common ratio r = 32/25 ÷ -8/5 = -4/5
* The difference between the convergent and divergent
in the geometric series is :
- If the geometric series is given by sum = a + a r + a r² + a r³ + ...
* Where a is the first term and r is the common ratio
* If |r| < 1 then the following geometric series converges to a / (1 - r).
- Where a/1 - r is the sum to infinity
* The proof is:
∵ S = a(1 - r^n)/(1 - r) ⇒ when IrI < 1 and n very large number
∴ r^n approach to zero
∴ S = a(1 - 0)/(1 - r) = a/(1 - r)
∴ S∞ = a/1 - r
* If |r| ≥ 1 then the above geometric series diverges
∵ r = -4/5
∴ IrI = 4/5
∴ IrI < 1
∴ The series is convergent
The ratio of successive terms leads to a limit of 4/5, which is less than 1. Hence, the series is convergent.
Convergence or Divergence of a Series
To determine whether the series -8/5+32/25-128/125+... is convergent or divergent, we observe the series' structure and apply the ratio test. For a series ∑a_n, the ratio test considers the limit L = lim (n→∞) |a_(n+1) / a_n|.
Let's compute this for our series:
[tex]a_n = (-1)^{(n+1)} * 8 * (4/5)^{(n-1)}[/tex]
Compute [tex]a_(n+1): a_(n+1) = (-1)^{(n+2)} * 8 * (4/5)^n[/tex]
Calculate |a_(n+1) / a_n| = [tex]|(-1)^{(n+2)} * 8 * (4/5)^n / (-1)^{(n+1)} * 8 * (4/5)^{(n-1)}| = |(4/5)|[/tex]
The limit L = |(4/5)| = 4/5 which is less than 1.
Since L < 1, by the ratio test, the series -8/5+32/25-128/125+... is convergent.
One diagonal of a cube has length 12. Compute the surface area of the cube.
Answers
Answer:
The surface area of the cube is [tex]288\ units^{2}[/tex]
Step-by-step explanation:
we know that
The length of a diagonal of a cube is equal to
[tex]D=b\sqrt{3}[/tex]
where
b is the length side of a cube
In this problem we have
[tex]D=12\ units[/tex]
so
[tex]12=b\sqrt{3}[/tex]
solve for b
[tex]b=\frac{12}{\sqrt{3}}\ units[/tex]
Simplify
[tex]b=4\sqrt{3}\ units[/tex]
Find the surface area of the cube
The surface area of the cube is equal to
[tex]SA=6b^{2}[/tex]
substitute the value of b
[tex]SA=6(4\sqrt{3})^{2}=288\ units^{2}[/tex]
A rectangular room is 4 meters longer than it is wide, and its perimeter is 32 meters. Find the dimension of the room
Answers
Answer:
x=6
Step-by-step explanation:
2(x+4)+2x=32
2x+8+2x=32
4x+8=32
4x=24
x=6
The dimensions of the room are 6 meters in width and 10 meters in length.
The student's question pertains to finding the dimensions of a rectangular room based on given conditions: the room is 4 meters longer than it is wide and the perimeter is 32 meters. Let's denote the width of the room as w meters. Therefore, the length will be w + 4 meters. The perimeter of a rectangle is calculated by the formula
P = 2(length + width), which in this case is:
2(w + w + 4) = 32
4w + 8 = 32
4w = 32 - 8
4w = 24
w = 24 / 4
w = 6 meters
Now, since the length is 4 meters longer, it will be:
length = w + 4
length = 6 + 4 = 10 meters
Therefore, the dimensions of the room are 6 meters in width and 10 meters in length.
If (3, y) lies on the graph of y = -(2x), then y =
1/8
-6
-8
Answers
Answer:
The answer is -6.
Step-by-step explanation:
To find the value of y in (3, y), plug in 3 for x in y = -(2x) and solve for y.
y = -(2(3))
y = -6
y = -6, so the answer is -6.
Answer:
-8
Step-by-step explanation:
I think the equation you want is y=-(2^x) because if you meant what you put originally the first guy is right.
What you do is take 2^3 which equals 8 and then you have the negative left which gets you to -8. I probably explained this terribly and I am sorry.
Before 1918, approximately 60% of the wolves in a region were male, and 40% were female. However, cattle ranchers in this area have made a determined effort to exterminate wolves. From 1918 to the present, approximately 70% of wolves in the region are male, and 30% are female. Biologists suspect that male wolves are more likely than females to return to an area where the population has been greatly reduced. (Round your answers to three decimal places.) (a) Before 1918, in a random sample of 12 wolves spotted in the region, what is the probability that 9 or more were male? What is the probability that 9 or more were female? What is the probability that fewer than 6 were female? (b) For the period from 1918 to the present, in a random sample of 12 wolves spotted in the region, what is the probability that 9 or more were male? What is the probability that 9 or more were female? What is the probability that fewer than 6 were female?
Answers
Answer:
A) 0.2253, 0.0153; B) 0.4925, 0.0017
Step-by-step explanation:
This is a binomial distribution. This is because there are only two outcomes; each trial is independent of each other; and the outcomes are independent.
This means we use the formula
[tex]_nC_r\times p^r\times (1-p)^{n-r}[/tex]
For part A,
There are 12 wolves selected; this means n = 12. We want the probability that 9 or more are male; this makes r = 9, 10, 11 or 12. We will find each probability and add them together.
p, the probability of success, is 0.6 for the first question (males). This makes 1-p = 1-0.6 = 0.4. Together this gives us
[tex]_{12}C_9(0.6)^9(0.4)^3+_{12}C_{10}(0.6)^{10}(0.4)^2+_{12}C_{11}(0.6)^{11}(0.4)^1+_{12}C_{12}(0.6)^{12}(0.4)^0\\\\=220(0.6)^9(0.4)^3+66(0.6)^{10}(0.4)^2+12(0.6)^{11}(0.4)+1(0.6)^{12}(1)\\\\\\= 0.2253[/tex]
We now want the probability that 9 or more are female; this makes r = 9, 10, 11 or 12. p is now 0.4; this makes 1-p = 1-0.4 = 0.6. This gives us
[tex]_{12}C_9(0.4)^9(0.6)^3+_{12}C_{10}(0.4)^{10}(0.6)^2+_{12}C_{11}(0.4)^{11}(0.6)^1+_{12}C_{12}(0.4)^{12}(0.6)^0\\\\=220(0.4)^9(0.6)^3+66(0.4)^{10}(0.6)^2+12(0.4)^{11}(0.6)^1+1(0.4)^{12}(1)\\\\=0.0153[/tex]
For part B,
There are again 12 wolves selected, so n = 12. We want the probability in the first question that 9 or more are male; this makes r = 9, 10, 11 or 12. The probability of success is now 0.7, so 1-p = 1-0.7 = 0.3[tex]_{12}C_9(0.7)^9(0.3)^3+_{12}C_{10}(0.7)^{10}(0.3)^2+_{12}C_{11}(0.7)^{11}(0.3)^1+_{12}C_{12}(0.7)^{12}(0.3)^0\\\\=220(0.7)^9(0.3)^3+66(0.7)^{10}(0.3)^2+12(0.7)^{11}(0.3)^1+1(0.7)^{12}(0.3)^0\\\\= 0.4925[/tex]
For the second question, the probability of success is now 0.3 and 1-p = 1-0.3 = 0.7:
[tex]220(0.3)^9(0.7)^3+66(0.3)^{10}(0.7)^2+12(0.3)^{11}(0.7)^1+1(0.3)^{12}(0.7)^0\\\\=0.0017[/tex]
Probabilities are used to determine the outcomes of events.
Before 1918,
The probability of selecting 9 or more male wolves is 0.225The probability of selecting 9 or more female wolves is 0.015The probability of selecting lesser than 6 female wolves is 0.665Since 1918,
The probability of selecting 9 or more male wolves is 0.493The probability of selecting 9 or more female wolves is 0.002The probability of selecting lesser than 6 female wolves is 0.516The question is an illustration of binomial probability, where:
[tex]\mathbf{P(x) = ^nC_x \times p^x \times (1 - p)^{n -x}}[/tex]
(a i) Probability of selecting 9 or more wolves out of 12, before 1918
The given parameters are:
[tex]\mathbf{p = 0.60}[/tex] --- the probability of selecting a male wolf
So, we have:
[tex]\mathbf{P(x \ge 9) = P(9) + P(10) + P(11) + P(12)}[/tex]
Using [tex]\mathbf{P(x) = ^nC_x \times p^x \times (1 - p)^{n -x}}[/tex], we have:
[tex]\mathbf{P(x \ge 9) = ^{12}C_9 \times 0.6^9 \times (1 - 0.6)^{12-9} +..............+^{12}C_{12} \times 0.6^{12} \times (1 - 0.6)^{12-12} }[/tex]
[tex]\mathbf{P(x \ge 9) = 220 \times 0.00064497254 +..........+1 \times 0.00217678233}[/tex]
[tex]\mathbf{P(x \ge 9) =0.225 }[/tex]
(a ii) Probability of selecting 9 or more female wolves
The given parameters are:
[tex]\mathbf{p = 0.40}[/tex] --- the probability of selecting a female wolf
So, we have:
[tex]\mathbf{P(x \ge 9) = P(9) + P(10) + P(11) + P(12)}[/tex]
Using [tex]\mathbf{P(x) = ^nC_x \times p^x \times (1 - p)^{n -x}}[/tex], we have:
[tex]\mathbf{P(x \ge 9) = ^{12}C_9 \times 0.4^9 \times (1 - 0.4)^{12-9} +..............+^{12}C_{12} \times 0.4^{12} \times (1 - 0.4)^{12-12} }[/tex]
[tex]\mathbf{P(x \ge 9) = 220 \times 0.0000566231+..........+1 \times 0.00001677721}[/tex]
[tex]\mathbf{P(x \ge 9) =0.015 }[/tex]
(a ii) Probability of selecting fewer than 6 female wolves
The given parameters are:
[tex]\mathbf{p = 0.40}[/tex] --- the probability of selecting a female wolf
Using the complement rule, we have:
[tex]\mathbf{P(x < 6) = 1 - P(x \ge 6)}[/tex]
So, we have:
[tex]\mathbf{P(x < 6) = 1 - [P(6) + P(7) + P(8) + P(x \ge 9)]}[/tex]
Using [tex]\mathbf{P(x) = ^nC_x \times p^x \times (1 - p)^{n -x}}[/tex], we have:
[tex]\mathbf{P(x < 6) = 1 - [^{12}C_6 \times 0.4^6 \times 0.6^6 + ^{12}C_7 \times 0.4^7 \times 0.6^5 + ^{12}C_8 \times 0.4^8 \times 0.6^4 + P(x \ge 9)}[/tex][tex]\mathbf{P(x < 6) = 1 - [924 \times 0.00019110297 +........ + 0.0153]}[/tex]
[tex]\mathbf{P(x < 6) = 1 - [0.335]}[/tex]
[tex]\mathbf{P(x < 6) = 0.665}[/tex]
(b i) Probability of selecting 9 or more wolves out of 12, since 1918
The given parameters are:
[tex]\mathbf{p = 0.70}[/tex] --- the probability of selecting a male wolf
So, we have:
[tex]\mathbf{P(x \ge 9) = P(9) + P(10) + P(11) + P(12)}[/tex]
Using [tex]\mathbf{P(x) = ^nC_x \times p^x \times (1 - p)^{n -x}}[/tex], we have:
[tex]\mathbf{P(x \ge 9) = ^{12}C_9 \times 0.7^9 \times (1 - 0.7)^{12-9} +..............+^{12}C_{12} \times 0.7^{12} \times (1 - 0.7)^{12-12} }[/tex]
[tex]\mathbf{P(x \ge 9) = 220 \times 0.00108954738+..........+1 \times 0.0138412872}[/tex]
[tex]\mathbf{P(x \ge 9) =0.493 }[/tex]
(b ii) Probability of selecting 9 or more female wolves
The given parameters are:
[tex]\mathbf{p = 0.30}[/tex] --- the probability of selecting a female wolf
So, we have:
[tex]\mathbf{P(x \ge 9) = P(9) + P(10) + P(11) + P(12)}[/tex]
Using [tex]\mathbf{P(x) = ^nC_x \times p^x \times (1 - p)^{n -x}}[/tex], we have:
[tex]\mathbf{P(x \ge 9) = ^{12}C_9 \times 0.3^9 \times (1 - 0.3)^{12-9} +..............+^{12}C_{12} \times 0.3^{12} \times (1 - 0.3)^{12-12} }[/tex]
[tex]\mathbf{P(x \ge 9) = 220 \times 0.00000675126+..........+1 \times 5.31441e-7}[/tex]
[tex]\mathbf{P(x \ge 9) =0.002 }[/tex]
(b iii) Probability of selecting fewer than 6 female wolves
The given parameters are:
[tex]\mathbf{p = 0.40}[/tex] --- the probability of selecting a female wolf
Using the complement rule, we have:
[tex]\mathbf{P(x < 6) = 1 - P(x \ge 6)}[/tex]
So, we have:
[tex]\mathbf{P(x < 6) = 1 - [P(6) + P(7) + P(8) + P(x \ge 9)]}[/tex]
Using [tex]\mathbf{P(x) = ^nC_x \times p^x \times (1 - p)^{n -x}}[/tex], we have:
[tex]\mathbf{P(x < 6) = 1 - [^{12}C_6 \times 0.3^6 \times 0.7^6 + ^{12}C_7 \times 0.3^7 \times 0.7^5 + ^{12}C_8 \times 0.3^8 \times 0.7^4 + P(x \ge 9)}[/tex]
[tex]\mathbf{P(x < 6) = 1 - [924 \times 0.4^6 \times 0.7^6 + 792 \times 0.3^7 \times 0.7^5 + 495 \times 0.3^8 \times 0.7^4 + 0.002}[/tex]
[tex]\mathbf{P(x < 6) = 1 - [0.484]}[/tex]
[tex]\mathbf{P(x < 6) = 0.516}[/tex]
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Given that 81^-3/4 = 3^n fins the value of n
Please help!!
Answers
Answer:
3^-3
Step-by-step explanation:
So first 81^-3/4 is cubing 81, finding the forth root, and then putting it on the denominator. Doing this you get 1/27.
Now you think, how do I get 3 to equal 27?
3^1 = 3
3^2 = 9
3^3 = 27
From here you just put a negative in front of the power, 3^-3, which puts the 27 on the bottom of the fraction, leaving you with 1/27, which is what we were trying to get.
You've probably heard of Albert Einstein's formula regarding the speed of light: E = mc2. While this is an important formula that you will use throughout your academic career, it is not a formula you apply in your daily life. Describe some common or unique formulas that you use in your life. I DIDNT GET THE FULL ANSWER ON some unique formlas
Answers
Answer:
1. The Pythagoras theorem
Hypotenuse^2 = base^2 + perpendicular^2
2. Formula for calculating speed
Speed = Distance Time
3. Areas
Rectangle = length * width
Square = side^2
4. Profit and loss formulas
Step-by-step explanation:
Final answer:
Einstein's second postulate on the constant speed of light in a vacuum led to the famous equation [tex]E = mc^2,[/tex] demonstrating mass-energy equivalence. Although not commonly used in everyday life, other practical formulas impact daily activities such as finance, medicine, and cooking.
Explanation:
The second postulate upon which Albert Einstein based his theory of special relativity is related to the speed of light. This principle states that light travels at a constant speed of [tex]c = 3.00 imes 10^8 m/s[/tex] in a vacuum and does not depend on the frame of reference from which it is observed. This postulate led to one of the most renowned equations in physics, [tex]E = mc^2[/tex], which describes the relationship between energy (E), mass (m), and the speed of light (c). In this equation, E represents the energy equivalent of a certain mass (m) when it is converted into energy, revealing the profound concept that mass and energy are interchangeable.
While [tex]E = mc^2[/tex] is a groundbreaking equation in theoretical physics, it is not commonly applied in everyday situations. However, there are many other formulas that are routinely used in daily life. Examples include calculations for simple interest in finance, dose calculations in medicine, and recipes in cooking that require proportional adjustments. These formulas help us to navigate various practical aspects of our day-to-day activities.
Solve the following equations for x:
a. 3x=30
b. 12x=12
c. 1=x−3
d. −24=4x
Answers
a.
3x = 30
x = 30/3
x = 10
b.
12x = 12
x = 12/12
x = 1
c.
1 = x-3
x = 1+3
x = 4
d.
-24 = 4x
x = -24/4
x = -6
HOPE THIS WILL HELP YOU
In a game, if you roll a 6 on a 6-sided number cube, you lose a turn.
(a) What is the probability that you roll a 6? Explain your reasoning.
(b) What is the probability that you either roll a 6 or do not roll a 6? Explain your reasoning.
(c) What is the probability that you don’t roll a 6? Explain your reasoning.
Answers
a) There are 6 sides, one of them having 6 on it. Therefore, the chances is 1/6.
b) Rolling a six or not rolling a six is guaranteed, because there is no other option. The probability is 1.
c) There are 6 sides, five of them not having a 6. So, the probability is 5/6.
Graph. y−2=23(x+4) Use the Line Tool and select two points to graph the equation. Use the slope and the point provided in the equation.
Answers
The graph of the equation y − 2 = 2⁄3(x + 4) is a blue line that passes through the points (0, 2) and (3, 4).
To graph the equation `y − 2 = 2⁄3(x + 4)` using the Line Tool and selecting two points, we can use the following steps:
1. Find the slope and y-intercept of the line.
The equation is already in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 2⁄3 and the y-intercept is 2.
2. Find a point on the line.
The y-intercept is always a point on the line, so we can use the point (0, 2) as our first point.
3. Use the slope to find another point on the line.
The slope tells us how much to move up or down and how much to move to the right to find another point on the line. In this case, the slope is 2⁄3, so we need to move up 2 units and to the right 3 units from our first point. This gives us the point (3, 4).
4. Select the two points in the Line Tool and draw the line.
Once we have selected the two points, we can draw the line by clicking and dragging the mouse.
Step 1: Find the slope and y-intercept of the line.
The equation `y − 2 = 2⁄3(x + 4)` is already in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 2⁄3 and the y-intercept is 2.
Step 2: Find a point on the line.
The y-intercept is always a point on the line, so we can use the point (0, 2) as our first point.
Step 3: Use the slope to find another point on the line.
The slope tells us how much to move up or down and how much to move to the right to find another point on the line. In this case, the slope is 2⁄3, so we need to move up 2 units and to the right 3 units from our first point. This gives us the point (3, 4).
Step 4: Select the two points in the Line Tool and draw the line.
Once we have selected the two points, we can draw the line by clicking and dragging the mouse.
Here is a diagram of the graph:
[Image of a graph of the equation y − 2 = 2⁄3(x + 4)]
The blue line is the graph of the equation. The red point is the point (0, 2) and the green point is the point (3, 4).
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a beekeeper estimates that his population of bees will triple each year. currently he has 150 bees. write a function to represent the growth of the beekeepers population over time. use x to represent the number of bees
Answers
Answer:
[tex]x = 150 * 3^{y}[/tex]
Step-by-step explanation:
Let's start by creating the beginning of the data sample, knowing the population of bees triples each year.
Year 0 = 150
Year 1 = 450
Year 2 = 1350
Year 3 = 4050
Year 4 = 12150
If we look at the numbers, we see they are all divided by 150:
Year 0 = 150 / 150 = 1
Year 1 = 450 / 150 = 3
Year 2 = 1350 / 150 = 9
Year 3 = 4050 / 150 = 27
Year 4 = 12150 / 150 = 81
We then see the result of the division by 150 is in fact the table of multiplication by 3.
So, by inverting the operation, we can see the number of bees (x) for any given year starting from now is 150 times 3 at the power of the year (y).
Answer:
y=150(3)^x
Step-by-step explanation:
I had to do an assignment with the same question, this is the answer :)
Ms.Beard bought 10 acres of land she plans to divide the land into smaller slots that are each 1/20 of an acre how many smaller lots will she have
Answers
Answer:
200 smaller lots
Step-by-step explanation:
10 ÷ 1/20 = 200
The number of smaller lots should be 200
Given information:Ms.Beard bought 10 acres of land she plans to divide the land into smaller slots that are each 1/20 of an acre
Calculation of number of smaller lots:= 10 ÷ 1/20
= 200
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The principal randomly selected six students to take an aptitude test. Their scores were: 87.4 86.9 89.9 78.3 75.1 70.6 Determine a 90% confidence interval for the mean score for all students. Assume the population is normally distributed. Give the lower limit of the interval as your answer below. Round to two decimal places. (Hint from class: Note that you will need to calculate the sample mean (xbar) and sample standard deviation (s) for this sample data in order to find the confidence interval endpoints. In class I referred to the formula for that -- and erroneously gave the formula for the sample variance instead of the sample standard deviation. The sample standard deviation would be the square root of the sample variance. Formulas for both can be found on the Test formula sheets posted on iLearn among other places.)
Answers
Answer:
79.5688 < µ < 83.1646
Step-by-step explanation:
Sample mean is the sum of all scores, divided the the total number of test takers. In this case, the sample mean is:
(87.4 + 86.9 + 89.9 + 78.3 + 75.1 + 70.6)/6 = 488.2/2 = 81.3667
The sample standard deviation is the square root of the sample variance. See attached photo 1 for calculation of these values...
The sample standard deviation is 3.1856
We need to make a 90% confidence interval for this data. Since n < 30, we will use a t-value. The degrees of freedom is always one less than the sample size so on the t-distribution chart, look under the column for Area under the curve = 0.10, and the row for 5. The t-value you should see is t = 2.015
See attached photo 2 for the construction of the confidence interval
ABCD is a trapezoid. Find the value of x and y.
Answers
A = x = 110 degrees
B = 117 degrees
C = y = 63 degrees
D = 70 degrees
In a trapezoid, the two angles on the same side of the parallel lines are supplementary, meaning their measures add up to 180 degrees.
So, for angle A and angle D:
A + D = 180
x + 70 = 180
x = 180 - 70
x = 110
For angle B and angle C:
B + C = 180
117 + y = 180
y = 180 - 117
y = 63
Therefore, in the trapezoid ABCD:
A = x = 110 degrees
B = 117 degrees
C = y = 63 degrees
D = 70 degrees
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Jada is solving the equation shown below. -1/2 (x+4) = 6 Which is a possible first step to begin to simplify the equation? Check all that apply. Divide both sides of the equation by –2. Subtract 4 from both sides of the equation. Multiply both sides of the equation by –2. Distribute –2 over (x+4). Distribute -1/2 over (x=4). Multiply both sides of the equation by -1/2.
Answers
Answer:
Multiply both sides of the equation by -2
Distribute -1/2 over (x+4)
Step-by-step explanation:
we have
[tex]-\frac{1}{2}(x+4)=6[/tex]
Method 1
Multiply both sides of the equation by -2 ------> Step 1
[tex](x+4)=6*(-2)[/tex]
[tex](x+4)=-12[/tex]
Subtract 4 from both sides of the equation
[tex]x=-12-4=-16[/tex]
Method 2
Distribute -1/2 over (x+4)-------> Step 1
[tex]-\frac{1}{2}x-2=6[/tex]
Multiply both sides of the equation by -2
[tex]x+4=6(-2)[/tex]
[tex]x+4=-12[/tex]
Subtract 4 from both sides of the equation
[tex]x=-12-4=-16[/tex]
Answer:
⇒ Multiply both sides of the equation by -2
⇒ Distribute -1/2 over (x+4)
Those are the 2 answers.
A water balloon is 5 feet above the ground when Sally launches it into the air. Use the quadratic equation 0 = -t2 + 4t + 5 to find how much time, t, it takes for the water balloon to reach the ground.
Answers
Answer:
2-sqrt14/2, 2+sqrt13/2.
Step-by-step explanation:
What you do is you have to do the quadratic equation like it says in the problem.
x= −b± sqrtb^2 −4ac /2a .
a=-2, b=4, c=5.
x=-4±sqrt(4)^2-4(-2)(5)/2(-2).
x=-4±sqrt16+40/-4.
x=-4±2sqrt14/-2.
2-sqrt14/2, 2+sqrt13/2. is your answer once you have done everything.
Answer:
5 seconds
Step-by-step explanation:
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The table below shows function r, which represents the total cost of a field trip to the science museum, in dollars, if n students return permission slips to attend. Which function represents the situation?
A.
r(n) = 15n + 55
B.
r(n) = 55n + 15
C.
r(n) = 30n - 20
D.
r(n) = 5n + 45
Answers
The answer has to be A) r(n) = 15n +55, as when n=0, r(n)=55 so the equation must end with +55.
Answer:
A. [tex]r(n)=15*n+55[/tex]
Step-by-step explanation
Since the value of n is given in the table as 0,5,15,30 and 35.So we will put the value of n in the given option starting from A.
Now putting the value of n as 0 in option A
we get [tex]r(n)=15*n+55[/tex]
[tex]r(0)=15*0+55\\r(0)=55[/tex]
Now putting the value of n as 5 in option A
we get [tex]r(n)=15*n+55[/tex]
[tex]r(5)=15*5+55\\r(0)=130[/tex]
Now putting the value of n as 15 in option A
we get [tex]r(n)=15*n+55[/tex]
[tex]r(15)=15*15+55\\r(0)=280[/tex]
Now putting the value of n as 30 in option A
we get [tex]r(n)=15*n+55[/tex]
[tex]r(30)=15*30+55\\r(0)=505[/tex]
Now putting the value of n as 35 in option A
we get [tex]r(n)=15*n+55[/tex]
[tex]r(35)=15*35+55\\r(0)=580[/tex]
After seeing the results of each value we see that option A is matching with all the given values. So the correct answer is A.
Determine whether the value is a discrete random variable, continuous random variable, or not a random variable. a. The amount of snowfall in December in City A b. The number of bald eagles in a country c. The gender of college students d. The number of statistics students now reading a book e. The number of people with blood type A in a random sample of 18 people f. The number of points scored during a basketball game
Answers
Answer:
a) a continuous random variable; b) a discrete random variable; c) not a random variable; d) a discrete random variable; e) a discrete random variable; f) a discrete random variable
Step-by-step explanation:
A continuous random variable is one that can take multiple values between whole number values; for instance, fractions and decimals. Snowfall is a continuous random variable.
A discrete random variable is one that can only take whole number values. The number of bald eagles, the number of students reading a book, the number of people with blood type A, and the number of points scored in a basketball game are discrete random variables.
Gender of students is not a numerical value; this is not a random variable.
Here, we are required to determine whether the value a list of data sets are, discrete random variable, continuous random variable, or not a random variable.
Options B, D, E and F are examples of discrete random variable values.Option A is an example of a continuous random variable value.Option C is an example of a non-random variable value.First, it is important to know the characteristics of each type of value as follows;
A discrete random variable is one which usually (although not necessarily) are counts. The statement above means they may take on only a countable number of distinct values such as 0,1,2,3, and on. Put simply, they can take only a finite number of distinct values. Distinct in this case means whole number values. Examples are as follows;The number of bald eagles in a countryThe number of statistics students now reading a bookThe number of people with blood type A in a random sample of 18 peopleThe number of points scored during a basketball game
2. A continuous random variable is one which has an infinite number of possible values. This means that the value of a continuous variable is usually associated with fractions of whole numbers, i.e continuous random variables are used majorly for measurements such as length, height and so on. An example from the question above is;
The amount of snowfall in December in City3. A non-random variable is one whose values are definite. An example from above is;
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A bakery can make 30 donuts every 15 minutes. What is the unit rate at which the bakery makes donuts?
Answers
Answer:
Your answer is 2/1. 2 donuts every minute.
Step-by-step explanation: The rate you are given is 30 donuts every 30 minutes. This equals 30/15.
To make a unit rate, you must make the fraction have a ratio of x/1. You can simply do this by dividing and/or simplifying the equation 30/15.
The unit rate at which the bakery makes donuts is 2 donuts per minute. This is determined by dividing the total number of donuts (30) by the total time in minutes (15).
Explanation:The question is asking for the unit rate at which the bakery makes donuts. A unit rate is a ratio that compares the quantity of one thing to 1 of something else. In this case, we want to find how many donuts the bakery makes in 1 minute. Given that the bakery can make 30 donuts every 15 minutes, we divide 30 (donuts) by 15 (minutes) to find the unit rate. So, 30 donuts ÷ 15 minutes = 2 donuts per minute. Therefore, the unit rate at which the bakery makes donuts is 2 donuts per minute.
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