Answer:
Step-by-step explanation:
Question 1: Assumption: This is a 30-60-90 triangle.
Remember that the sides of a 30-60-90 triangle are in the ratio 1:√3:2
The side opposite the 90° angle is 16, so the side opposite the 30° angle is 16/2 = 8
x = 8 units.
:::::
Question 2: Assumption: This is an isosceles triangle.
Draw the altitude to the vertex angle and you get a 30-60-90 triangle.
The side opposite the 90° angle has length 22, so the side opposite the 30° angle has length 11.
x/2 = 11
x = 22 units
:::::
Question 3: Assumption: This is a 45-45-90 triangle.
The sides of a 45-45-90 triangle are in the ratio 1:1:√2
The sides opposite the 45° angles are 19 and x.
x = 19
:::::
Question 4: Assumption: This is an isosceles triangle.
x = 13 units
:::::
Question 5: Assumption: This is a right triangle.
sin(54°) = x/45
x = 45sin(54°) ≅ 36.4 units
:::::
Question 6: Assumption: This is a right triangle.
sin(35°) = z/23
z = 23sin(35°) ≅ 13.2 units
a scientist was interested in studying if students beliefs about illegal drug use changes as they go through college. the scientist randomly selected 104 students and asked them before they entered college if they thought that illegal drug use was wrong or o.k. four years later, the same 104 students were asked if thought that illegal drug use was wrong or o.k. the scientist decided to perform mcnemar's test. the data is below. what is the null hypothesis?
In this case, the scientist is studying if students' beliefs about illegal drug use change as they go through college. The null hypothesis (H0) for McNemar's test in this context would state that there is no significant change in students' beliefs about illegal drug use between the time they enter college and four years later. In other words, the proportion of students who change their beliefs about illegal drug use is not significantly different from the proportion who do not change their beliefs.
Null hypothesis (H0): There is no significant difference in students' beliefs about illegal drug use before and after going through college.
Find dx/dy by implicit differentiation x^2=x+y/x−y
Answer:
\({ \tt{ \frac{dy}{dx} ( {x}^{2}) = \frac{dy}{dx} ( \frac{x + y}{x - y}) }} \\ { \tt{2x = \frac{(x - y) \frac{dy}{dx} + (x + y) \frac{dy}{dx} }{ {(x - y)}^{2} } }} \\ { \tt{ \frac{dy}{dx}(2x) = 2x {(x - y)}^{2} }} \\ { \tt{ \frac{dy}{dx} = {(x - y)}^{2} }}\)
Which expression is equivalent to 12.8-3s+15.5+8s?
A. -2+5s
B. 5s+28.3
C. 33.3s
D. 27.3+5s
Answer:
5s + 28.3
Step-by-step explanation:
12.8 + 15.5 = 28.3.
-3s + 8s = 5s.
so 12.8-3s+15.5+8s = 5s + 28.3
If there is a discount of 40% on an article costing #7000, then the price after discount is
Answer:
The answer is # 4200Step-by-step explanation:
A discount of 40% was allowed on the price
To find the price after the discount first calculate the discount and subtract it from the original price
That's
\( \frac{40}{100} \times 7000\)
= 2800
So the price after the discount is
#7000 - #2800
Which is
# 4200Hope this helps you
I need help this question is so confusing!
The bearing of B from C is calculated to be 115 degrees
The bearing of D from B is calculated to be 213.65 degrees
How to find the bearingsThe bearing from B to C is worked using SOH CAH TOA
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
The direction of movements describes a right triangle of
opposite = 30 km
adjacent = 30 km
The bearing is calculated using tan, TOA let the angle be x
tan x = Opposite / Adjacent
tan x = 30 / 30
tan x = 1
x = arc tan 1
x = 45 degrees
The bearing is 90 + 45 = 115 degrees
The bearing of D from B
x = arc tan (45/30)
x = 56.31
90 - 56.31 = 33.65
180 + 33.65 = 213.65 degrees
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In anova, by dividing the mean square between groups by the mean square within groups, a(n) _____ statistic is computed.group of answer choices
In anova, by dividing the mean square between groups by the mean square within groups, a(n) Analysis of variance statistic is computed.
What is Analysis of variance ?
With the help of the statistical analysis approach known as ANOVA, apparent aggregate variability within a data set is explained by separating systematic components from random factors. Systematic influences, but not random ones, statistically affect the data set that is being presented.What are some instances where ANOVA has been applied?
An ANOVA demonstrates the link between the dependent variable and the level of the independent variable. For illustration: In order to determine whether there is a difference in the number of hours of sleep each night as your independent variable, you divide the groups into low, medium, and high social media use categories.Learn more about Analysis of variance
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Screenshot 2023-05-01 at 19.09.51
The circumference of the circle is given as follows: C = 109.9 in.
The relationship between the diameter of a circle and it's circumference is presented in this problem.
We have,
The circumference of a circle of radius r is given by the equation presented as follows:
C = 2πr
The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, while the diameter of the circle is the distance between two points on the circumference of the circle that pass through the center. Hence, the diameter’s length is twice the radius length.
The diameter is twice the radius, hence, for a circle with diameter 35 in, the radius is given as follows:
r = 0.5 x 35
r = 17.5 in.
Then the circumference of the circle is given as follows:
C = 2 x pi x 17.5
C = 109.9 in.
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Missing Information
The problem is incomplete, hence the relation between the diameter of a circle and it's circumference is presented.
i need help show work
ill mark brainliest
Answer:
The population will be 896 turtles 6 years later ⇒ B
Step-by-step explanation:
The exponential increasing formula is y = a\((1+r)^{x}\), where
y is the new valuea is the initial valuer is the rate of increase in decimalx is the time in years∵ There are 300 turtles
∴ a = 300
∵ The population of the turtles exponentially increases 20% each year
∴ r = 20%
→ Divide it by 100 to change it to decimal
∵ 20% = 20 ÷ 100 = 0.2
∴ r = 0.2
∵ The time is 6 years
∴ x = 6
→ Substitute these values in the exponential formula above
∵ y = 300\((1+0.2)^{6}\)
∴ y = 300\((1.2)^{6}\)
∴ y = 895.7952
→ Round it to the nearest whole number
∴ y = 896
∴ The population will be 896 turtles 6 years later
Which method can you use to prove that the triangles are congruent
Answer:
HL
Step-by-step explanation:
It's a right triangle.
Answer: HL
Step-by-step explanation: because they are right triangles
Please add a number line of you can!
Answer:
574
Step-by-step explanation:
You are considering investing in a security that will pay you $3,000 in 34 years. a. If the appropriate discount rate is 8 percent, what is the present value of this investment? b. Assume these investments sell for $773 in return for which you receive $3,000 in 34 years. What is the rate of return investors earn on this investment if they buy it for $773? a. If the appropriate discount rate is 8 percent, the present value of this investment is $ 219.13. (Round to the nearest cent.) b. The rate of return investors can earn on this investment if they buy it for $773 is %. (Round to two decimal places.)
In this scenario, we are considering an investment that will pay $3,000 in 34 years. We are given an appropriate discount rate of 8 percent. To determine the present value of this investment, we can use the present value formula. Additionally, we are provided with the information that the investment is being sold for $773, and we need to calculate the rate of return investors will earn on this investment.
a. Present value of the investment:
To calculate the present value of the investment, we use the present value formula:
Present Value = Future Value / (1 + Discount Rate)^n,
where Future Value is $3,000, the Discount Rate is 8 percent (0.08), and n is the number of years, which is 34 in this case.
Present Value = $3,000 / (1 + 0.08)^34 = $219.13
Therefore, the present value of the investment, considering an 8 percent discount rate, is $219.13.
b. Rate of return on the investment:
The rate of return on an investment is calculated using the formula:
Rate of Return = (Future Value - Purchase Price) / Purchase Price * 100,
where Future Value is $3,000 and the Purchase Price is $773.
Rate of Return = ($3,000 - $773) / $773 * 100 ≈ 288.46%
Therefore, the rate of return investors can earn on this investment, if they buy it for $773, is approximately 288.46%.
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With reference to the figure, sin X equals?
1.) 0.250
2.)0.447
3.)0.894
4.)1
Answer:
3.) 0.894
Step-by-step explanation:
✔️First, find BD using Pythagorean Theorem:
BD² = BC² - DC²
BC = 17.89
DC = 16
Plug in the values
BD² = 17.89² - 16²
BD² = 64.0521
BD = √64.0521
BD = 8.0 (nearest tenth)
✔️Next, find AD using the right triangle altitude theorem:
BD = √(AD*DC)
Plug in the values into the equation
8 = √(AD*16)
Square both sides
8² = AD*16
64 = AD*16
Divide both sides by 16
4 = AD
AD = 4
✔️Find AB using Pythagorean Theorem:
AB = √(BD² + AD²)
AB = √(8² + 4²)
AB = √(64 + 16)
AB = √(80)
AB = 8.9 (nearest tenth)
✔️Find sin x using trigonometric ratio formula:
Reference angle = x
Opposite side = BD = 8
Hypotenuse = AB = 8.944
Thus:
\( sin(x) = \frac{opp}{hyp} = \frac{8}{8.944} = 0.894 \) (nearest thousandth)
Answer:
Hey! The correct answer is the third option, I just took the test and it was correct
Step-by-step explanation:
3.) 0.894
ANSWER THIS RIGHT AND GET 60+ POINTS
Answer:
The cost of a adult is $8
The cost of a student is $4
System of equations I think is X=4..? or 2
Please prove by mathematical induction.
4) Prove that 3 ||n3 + 5n+6) for any integer n 20. n
To prove the statement that 3 divides (n³ + 5n + 6) for any integer n ≥ 20 using mathematical induction, we will show that the statement holds for the base case (n = 20) and then assume it holds for an arbitrary value of n and prove it for (n + 1).
Base case (n = 20):
Substitute n = 20 into the expression (n³ + 5n + 6):
(20³ + 5 * 20 + 6) = 9266
Since 9266 is divisible by 3 (9266 = 3 * 3088), the statement holds for the base case.
Inductive step:
Assume that the statement holds for an arbitrary value of n, denoted as k, i.e., 3 divides (k³ + 5k + 6).
Now we need to prove that the statement holds for (k + 1), i.e., 3 divides ((k + 1)³ + 5(k + 1) + 6).
Expand the expression ((k + 1)³ + 5(k + 1) + 6):
(k³ + 3k² + 3k + 1 + 5k + 5 + 6) = (k³ + 5k + 6) + (3k² + 3k + 6)
By the induction hypothesis, we know that (k³ + 5k + 6) is divisible by 3. Now we need to show that (3k² + 3k + 6) is also divisible by 3.
Factoring out 3 from (3k² + 3k + 6), we get: 3(k² + k + 2).
Since k² + k + 2 is an integer, we conclude that (3k² + 3k + 6) is divisible by 3.
Therefore, the statement holds for (k + 1).
By the principle of mathematical induction, we have shown that the statement "3 divides (n³ + 5n + 6)" holds for any integer n ≥ 20.
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A triangle has vertices at (1,3),(2,-3), and (-1,-1). What is the approximate perimeter of the triangle? A. 16 B: 14 C: 15 D: 10
Answer:
B 14
explanation:
i did the math
The perimeter of the given triangle is 14 units, so the correct option is B.
How to get the perimeter of the triangle?
The perimeter of the triangle will be equal to the sum between the distances between the given points.
Remember that the distance between two points is (x₁, y₁) and (x₂, y₂) is:
\(d = \sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}\)
For the pair of (1,3), (2,-3): the distance is:
\(d = \sqrt{(2 - 1)^2 + (-3 - 3)^2} = 6.08\)
For the pair (1, 3) , (-1, -1) the distance is:
\(d = \sqrt{(-1 - 1)^2 + (-1 - 3)^2} = 4.5\)
For the pair (2, -3) and (-1, -1) the distance is:
\(d = \sqrt{(2 - (-1))^2 + (-3 - (-1))^2} = 3.6\)
Then the total perimeter, rounded to the next whole number is:
6.08 + 4.5 + 3.6 = 14
So the correct option is B.
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If
CE
and
FH
are parallel lines and mCDB= 65°, what is mEDB?
Answer:
65° or 115°
Step-by-step explanation:
there is no picture but if
mEDB looks like mCDB then its 65°
but if they dont look alike then
180-65=115
straight line is 180°
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The weights of 11 1111 different babies are recorded on the line plot below. Each weight was rounded to the nearest 1 8 8 1 start fraction, 1, divided by, 8, end fraction pound. 6 6 6 4 8 6 8 4 7 7 7 4 8 7 8 4 8 8 8 4 8 8 8 4 9 9 9 4 8 9 8 4 10 10 A line plot labeled 6 to 10 with tick marks every one-eighth unit. Above the tick mark at six and six-eighths is one dot. Above the tick mark at seven and one-eighth is a column of three dots. Above the tick mark at seven and two-eighths is a column of two dots. Above the tick mark at eight and three-eighths there is a column of three dots. Above the tick mark at eight and four-eighths there is one dot. Above the tick mark at nine and two-eighths is one dot. What is the difference, in weight, between the two heaviest babies? pounds pounds start text, space, p, o, u, n, d, s, end text
Answer:
6/8
Step-by-step explanation:
Answer: The answer is 6/8 ☻
Step-by-step explanation: I took the quiz and got it corrected. ヾ(^▽^*)))
How does Dickinson's use of rhyme reflect her
interpretation of the traditional ballad form?
She follows the tradition of the ballad by
using perfect rhyme.
She uses rhyme in a variety of ways to
combine the ballad with her own style.
She avoids rhyme altogether to create a
more modern style.
She uses rhyme incorrectly because she
doesn't understand the ballad form.
Answer:
b on edge 2020
Step-by-step explanation:
URGENT I NEED HELP ASAP Which of the following steps were applied to AABC obtain AA'B'C'?
B
12
10
-6
8-
64
4
2-
-2
-2
र
8
10
A. Shifted 4 units right and 3 units up
B. Shifted 3 units right and 2 units up
C. Shifted 3 units right and 3 units up
D. Shifted 2 units right and 3 units up
T
B
2
C
C'
The steps to translate the triangle ABC to A'B'C' are Shifted 3 units right and 2 units up.
The correct option is (B).
What is Coordinate Geometry?By using graphs with curves and lines, coordinate geometry (also known as the analytic geometry) explains how geometry and algebra are related.
As per the given diagram:
We are given the diagram of two triangles drawn on a graph.
With the help of the graph, we can easily figure out the coordinates of each point of the triangle.
The steps to translate the triangle will be the same as that to translate any vertices of the triangle.
Let us consider A:
Coordinates of A = (2, 5)
Coordinates of A' = (5, 7)
For translating A to A':
3 units in +ve x direction. {right}
2 units in +ve y direction. {up}
Hence, The steps to translate the triangle ABC to A'B'C' are Shifted 3 units right and 2 units up.
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PLEASEE HELP!!! LOTS OF POINTS ARE ON THE LINE
Which point is located in Quadrant II?
A coordinate plane.
(–4, 5)
(–4, –5)
(4, –5)
(4, 5)
Answer:
(-4,5) is located on the 2nd quadrant
Answer:
(-4, 5)
Step-by-step explanation:
Quadrant II is at the top left. So, point (-4, 5) is located in Quadrant II.
Write an equation in point-slope form for the line that passes through (–2, 1) with a slope of 1/4. Giving brainliest!
Answer:
y=1/4x+1.5
Step-by-step explanation:
Slope is 1/4 and I figured out that the y-intercept point is 1.5y.
I am not exactly sure though
What is the value of SS for the following set of scores? Scores: 0, 1, 4,5
a. 18
b. 42
c. Cannot answer without knowing whether it is a sample or a population
d.7
For the scores the sum of squares SS is calculated to be
17What is sum of squares?A statistical measure of deviation from the mean is the sum of squares. Variance is another name for it.
The squared differences of each data point are added together to calculate it. The sum of squares is calculated by squaring the separation between each data point and the line of best fit, then adding the results.
The mean is calculated as follows
= (0 + 1 + 4 + 5) / 4
= 10 / 4
= 2.5
the variance
= (0 - 2.5)² + (1 - 2.5)² + (4 - 2.5)² + (5 - 2.5)²
= 6.25 + 2.25 + 2.25 + 6.25
= 17
the sum of squares is 17
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3. Find the slope of a line passing through the points (-15, 48) (-3,60) *
Answer:
slope (m) = 1
There are 4,500 cities on planet Purple. The planetary government takes a random sample of 350 cities and finds that the average number of complaints about feral cats from the sample was 3.4 ± 0.49. Which of the following is an estimate of the total number of feral cat complaints for planet Purple?
Between 1018.5 and 1361.5 complaints
Between 171.5 and 1190 complaints
Between 13,095 and 17,505 complaints
Between 2,205 and 15,300 complaints
Based on the margin of error, an estimate of the total number of feral cat complaints for planet Purple is A. Between 1018.5 and 1361.5 complaints.
What is the margin of error?The margin of error shows the statistical difference between the actual and projected or estimated results.
The margin of error gives the difference between the upper limit and the lower limit of the sample estimate.
With the margin of error, one establishes a level of confidence or the confidence interval in the sample results.
The total number of cities on planet Purple = 4,500
Random sample size = 350 cities
Average complaints = 3.4
Margin or error = ± 0.49
Upper limit = 1,361.5 [350 x (3.4 + 0.49)]
Lower limit = 1,081.5 [350 x (3.4 - 0.49)]
Thus, using the margin of error, an estimate of feral cat complaints hovers over Option A.
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Which of the following is true?
The statements that are true include the following:
B. Both graphs are exponential function.
C. Both graphs have exactly one asymptote.
What is an exponential function?In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:
\(f(x) = a(b)^x\)
Where:
a represents the initial value or y-intercept.x represents x-variable.b represents the rate of change, common ratio, decay rate, or growth rate.In Mathematics and Geometry, a horizontal asymptote is a horizontal line (y = b) where the graph of a function approaches the line as the input values (domain or independent value) approach negative infinity (-∞) to positive infinity (∞).
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wHaT is 3+3x+45??????????
Answer:
3x+48
add 3+45=48
Step-by-step explanation:
Hope this helps! Please consider marking brainliest! I hope you have an amazing day. Always remember, your smart and you got this! -Alycia :)
Answer:
3(x+16)
Step-by-step explanation:
45+3=48
3x/3=x
48/3=16
3(x+16)
Which expression is equivalent to 2x2−x+18?
A
2(x−12)2
B
2(x−14)2
C
2(x−18)2
D
2(x−116)2
As a result of answering the given question, we may state that When we expressions compare the finished square form\(2(x - 1/4)^2 + 143/8\) to the answer alternatives, we see that option \(D: 2(x - 1/16)`^2.\)
what is expression ?In mathematics, an expression is a set of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, division, exponentiation, and so on) that expresses a quantity or value. Expressions might be simple, like "3 + 4", or complex, like "(\(3x^2\) - 2) / (x + 1)". They may also include functions such as "sin(x)" or "log(y)". Expressions can be evaluated by substituting values for the variables and carrying out the mathematical operations in the given order. For instance, if x = 2, the formula "3x + 5" is 3(2) + 5 = 11. In mathematics, expressions are widely used to explain real-world situations, build equations, and simplify complex mathematical issues.
expression is equivalent -
\(2(x^2 - 1/2x) + 18\\2(x^2 - 1/2x + 1/16 - 1/16) + 18\\2((x - 1/4)^2 - 1/16) + 18\\2(x - 1/4)^2 - 1/8 + 18\\2(x - 1/4)^2 + 143/8\\\)
When we compare the finished square form\(2(x - 1/4)^2 + 143/8\) to the answer alternatives, we see that option \(D: 2(x - 1/16)`^2.\)
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Use synthetic division to evaluate f (x)= x^3+ 6x^2-2x - 12 when x = 3
The function value of given function at x = 3 is 63.
Synthetic division :The given function is,
\(f(x)=x^{3} +6x^{2} -2x-12\)
We have to calculate function value when \(x=3\).
\(f(3)=3^{3} +6*3^{2}-2(3)-12\\ \\f(3)=27+54-6-12\\\\f(3)=81-18\\\\f(3)=63\)
Thus, the function value of given function at x = 3 is 63.
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Match the vocabulary term to the correct definitions.
1. The _________ number in an exponential expression which tells how many times a factor is repeated exponent
2. When a__________ number increases at a constantly growing rate exponential decay
3. When a___________ number decreases at a constantly reducing rate exponential growth
superscript
Answer:
1. superscript number
2. exponential growth
3. exponential decay
Step-by-step explanation:
In an exponential expression, the exponent (superscript) number indicates how many times the factor (i.e., the base number) is repeated. For example, the expression 2ⁿ indicates that the base number (2) is repeated n times.
The exponential growth indicates how a specific quantity increases over time, thereby the curve drawing an exponential function. The exponential growth is produced when the rate of increase of a quantity in a given time is directly proportional to the quantity itself.
The exponential decay describes how a specific quantity proportionally decreases across time, thereby showing a percentage decrease rate over time.
Answer:
1. superscript number
2. exponential growth
3. exponential decay
Step-by-step explanation:
Q 35- The difference between two positive numbers is 20 and their ratio is 3:2. Find the product of the two numbers? A-400 B-800 C-900 D-1600
Answer: The product of the two numbers is 2400.
Step-by-step explanation: You multiply the numbers on the ratio with the difference first you multiply 2 with 20 then you multiply 3 with 20.