The distance between the guy and the wire attached is 14.42m
Pythagoras theoremThe square of the longest side is equal to the sum of the square of other two sides.
In order to determine the length of base of the tower, we will use the expression below:
b² = 28² - 24²
b² = 208
b = 14.42
Hence the distance between the guy and the wire attached is 14.42m
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Which of the following rational functions is graphed below?
Answer:
A
Step-by-step explanation:
If you were to substitute 2 or -3 into equation A, the denominator would be zero and you would have to divide by zero. Thus there are asymptotes for this function at -3 and 2, matching the graph
they’re 25 student’s 14 female and 11 male two students are selected at random to participate in a probability experiment. compute that
b) a male is selected then a female
c) a female selected then a male
d) two females are selected
e) no males are selected
The probabilities in each of the given categories are; A) 51.33%; B) 51.33% C) 30.33% D) 30.33%
How to find the Probability of Selection?The number of ways to select 2 out of 25 is; 25C2 = 25! / (23! * 2!)
= 25*24/2
= 300
(A) Probability of selecting 1 male and 1 female:
[(11C1) * (14C1)]/300 = [11!/(10! * 1!)] * [(14!/(12! * 2!))
= 51.33%
(B) Probability of selecting 1 female and 1 male:
[(14C1) * (11C1)]/300 = 51.33%
(C) Probability that 2 females are selected is;
(14C2)/300 = 30.33%
D) Probability that no males are selected is;
P(no males) = (11C0 * 14C2 )/300 = 30.33%
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lim f(x) 2^x-1/x. Find the limit of x as x approaches 0
The limit happens to be the derivative of [tex]2^x[/tex] at [tex]x=0[/tex]:
[tex]\displaystyle f'(c) = \lim_{x\to c}\frac{f(x)-f(c)}{x-c} \implies \lim_{x\to0} \frac{2^x - 1}x = (2^x)'\bigg|_{x=0} = \ln(2)\,2^x \bigg|_{x=0} = \boxed{\ln(2)}[/tex]
The current in a stream moves at a rate of 7 mph. If a boat travels 98 miles downstream in the same time that it takes to travel 49 miles upstream, what is the speed of the boat in still water?
The answer is x=21 the explanation is on the picture above I hope I helped
If the current in a stream moves at a rate of 7 mph. If a boat travels 98 miles downstream in the same time that it takes to travel 49 miles upstream then the speed of the boat in still water is 21 miles per hour.
What is speed?Speed is the distance covered by an object in a certain time period. It is also known as velocity. The formula of speed is as follows:
Speed=Distance/ Time.
How to calculate speed?We have been given that the speed of stream is 7miles per hour.
Let v be the speed of the boat, and t the time to travel
98=t*(7+v) (1)
49=t(v-7) (2)
(1)+(2) => 2tv=147
7t+(49+7t)=98
14t+49=98
14t=49
t=49/14
t=7/2
Put the value of t in equation 1 to get the value of v:
98=t(7+v)
98=7/2(7+v)
196/7=7+v
28=7+v
v=28-7
v=21
Hence if the current in a stream moves at a rate of 7 mph. If a boat travels 98 miles downstream in the same time that it takes to travel 49 miles upstream then the speed of the boat in still water is 21 miles per hour.
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For csc 330:
a) state value of the ratio exactly
b) find one equivalent expression
c) draw a diagram to illustarte.
The value of the ratio based on the angle illustrated is 1:12.
How to illustrate the information?From the information given, it should be noted that the angle in a circle is 360°. Therefore, the value of theta will be:
= 360° - 330°
= 30°
The equivalent expression based on the angle will be:
= 30/360
= 1/12
= 1:12
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The function f(x)=−4x+1 has a horizontal asymptote at?
The function has a horizontal asymptote at y = 1
How to determine the horizontal asymptote?The function is given as:
f(x) = -4/x + 1
Set the radicand to 0.
So, we have:
y = 0 + 1
Evaluate
y = 1
Hence, the function has a horizontal asymptote at y = 1
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In ΔABC, BC = 13, CA = 20 and AB = 19. Which statement about the angles of ΔABC must be true?
m∠B > m∠ A > m∠C
m∠C > m∠B > m∠A
m∠A > m∠B > m∠C
m∠C > m∠A > m∠B
m∠B > m∠C > m∠A
m∠A > m∠C > m∠B
Answer:
m∠B > m∠C > m∠A
Step-by-step explanation:
The angle opposite the largest side in a triangle is the largest, and the angle opposite the shortest side is the smallest.
14-yard fishing line is cut into two pieces. Three times the length of the longer piece is four times the length of the shorter piece. Find the length of each piece.
(Hint: Let x = smaller piece...)
Answer:
The small piece is 6 yards and the large piece is 8 yards.
Step-by-step explanation:
Let x = small
Let y = large
x + y = 14 3y = 4x
3y = 4x Divide both sides of the equation by 3 to solve for y
y = [tex]\frac{4}{3}[/tex] x Plug [tex]\frac{4}{3}[/tex] x in for y in the first equation above.
x + y = 14
x + [tex]\frac{4}{3}[/tex] x = 14 x and 1 x mean the same thing. Another name for 1 is [tex]\frac{3}{3}[/tex]
[tex]\frac{3}{3}[/tex]x + [tex]\frac{4}{3}[/tex]x = 14
[tex]\frac{7}{3}[/tex]x = 14 Multiple both sides by [tex]\frac{3}{7}[/tex] to solve for x
([tex]\frac{3}{7}[/tex])([tex]\frac{7}{3}[/tex]x) = 14([tex]\frac{3}{7}[/tex]) you can write 14 as [tex]\frac{14}{1}[/tex]([tex]\frac{3}{7}[/tex]) = [tex]\frac{42}{7}[/tex]= 6
x = 6
If x = 6, then y must be 8 because 6 + 8 = 14
A and B are independent events. P(A) = 0.60 and P(B) = 0.30.
What is P(A and B)?
A. 0
B. 0.18
C. 0.90
D. 0.018
Answer: 0.18
Step-by-step explanation:
The probability of the event P(A and B) is equal to 0.18.
The correct option is (C).
What is Probability?A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Probability has been introduced in Arithmetic to forecast how likely occurrences are to happen.
As per the given data:
We are given the probability of two events:
P(A) = 0.60 and P(B) = 0.30
We are also given that A and B are independent events.
To find the probability of P(A and B):
The term and is equivalent to the term intersection.
P(A and B) = P(A∩B)
For any 2 independent events A and B the probability P(A∩B) is given by:
= P(A) × P(B)
By substituting the given values in the question
= 0.60 × 0.30
= 0.18
The probability of the event P(A and B) is equal to 0.18.
Hence, The probability of the event P(A and B) is equal to 0.18.
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Calculate the following ratios, correct to 3 decimal places. a. sin 58 = b. cos 26 = c. tan 63=.
Answer: sin(58) = 0.848, cos(26) = 0.898, and tan(63) = 1.962
Step-by-step explanation:
Prove that (- 1 + i)^7 = -8(1 + i)
Convert [tex]-1+i[/tex] to polar form.
[tex]z = -1 + i \implies \begin{cases}|z| = \sqrt{(-1)^2 + 1^2} = \sqrt2 \\\\ \arg(z) = \pi + \tan^{-1}\left(\dfrac1{-1}\right) = \dfrac{3\pi}4 \end{cases}[/tex]
By de Moivre's theorem,
[tex]\left(-1+i\right)^7 = \left(\sqrt2 \, e^{i\,\frac{3\pi}4}\right)^7 \\\\ ~~~~~~~~ = \left(\sqrt2\right)^7 e^{i\,\frac{21\pi}4} \\\\ ~~~~~~~~ = 8\sqrt2 \, e^{-i\,\frac{3\pi}4} \\\\ ~~~~~~~~ = 8\sqrt2 \left(\cos\left(\dfrac{3\pi}4\right) - i \sin\left(\dfrac{3\pi}4\right)\right) \\\\ ~~~~~~~~ = 8\sqrt2 \left(-\dfrac1{\sqrt2} - \dfrac1{\sqrt2}\,i\right) \\\\ ~~~~~~~~ = -8 (1 + i)[/tex]
QED
56m² = ____________ GCF =
68m² = ____________ GCF =
The greatest common factor of the expression is 4m⁴.
What is GCF?GCF simply means the greatest common factor.
The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share.
Hence,
56m⁵
68m⁴
The greatest common factor of the expression is the largest positive expression that divides evenly into all numbers with zero .
Hence, the greatest common factor is 4m⁴
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find x and y
can someone pls solve
Answer:
x = 65°y = 105°
Step-by-step explanation:
According to the picture, the angles with measure of 65° and x are included between two parallel pairs of lines.
It makes them equal:
x = 65°y is the exterior angle of the triangle with two remote interior angles with measure of 40° and 65°.
As per definition of the exterior angle its measure is same as the sum of remote interior angles:
y = 65° + 40° = 105°Kylie has a modern quarter with a mass of 5.623 g and an older silver quarter with a mass of 6.24 g What is the combined mass of the quarters?
Answer:
11.863 g
Step-by-step explanation:
5.623 g + 6.24 g = 11.863 g
I cant figure this one out pls help
The value of x from the given expression is -2
Slope of a lineThe formula for calculating the slope of a line is expressed as:
Slope = y2-y1/x2-x1
Given the following parameters
m = 1
(x1, y1) = (0, 2)
(x2, y2) = (x, 0)
Substitute
1 = x-0/0-2
1 = x/-2
x = -2
Hence the value of x from the given expression is -2
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1
Select the correct answer from each drop-down menu.
Ray and Terry work in the same office. They sit across from each other at fixed desks that are separated by a partition, or a short dividing wall,
exactly halfway between them. The distance between the end of each desk and the partition is 35 inches. For both Ray and Terry, the top of the
partition is at an angle of elevation of 30° with respect to the end of the desk. This scenario can be modeled by the given diagram.
Ray has the incorrect reasoning because he incorrectly select the sine function when he should have utilized the tangent.
How to find the height of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees.
The height of the ray can be found using trigonometric ratios.
Therefore,
tan 30 = opposite / adjacent
where
opposite side = height
adjacent side = 35 inches
Therefore,
tan 30° = height / 35
cross multiply
height = 35 tan 30°
height = 20.2072594216
height = 20.21 inches
Therefore, Ray has the incorrect reasoning because he incorrectly select the sine function when he should have utilized the tangent.
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Answer:
1. Ray
2. Sine
3. Tangent
Step-by-step explanation:
Plato/Edmentum
120 increased by d percent and increased by 25 percent. what is the result?
Using proportions, the expression for the final amount is:
150(1+d).
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
For this problem, we have that:
The increase of d% is equivalent to a multiplication by (1 + d).The increase of 25% is equivalent to a multiplication by 1.25.Hence the equivalent expression is:
120 x 1.25 x (1 + d) = 150(1+d).
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find the value of x and y
Consider the equation x+4=−2x+19. Let f(x)=x+4and g(x)=−2x+19. The graph of each function is shown. Coordinate plane with the graphs of two lines. The horizontal x axis labeled from negative three to nine in increments of one. The vertical y axis labeled from negative two to nineteen. The line f of x passes through ordered pairs zero comma four and two comma six. The line g of x passes through the ordered pairs zero comma nineteen and one comma seventeen. At what point do the graphs intersect? Enter your answer in the box.
The point of intersection of both graphs will have the coordinate (5, 9).
What is the Point of Intersection of the Graph?
We are given the functions;
f(x) = x + 4
g(x) = -2x + 19
Now, the point of intersection of both graphs is when both functions are equal which is at f(x) = g(x). Thus;
x + 4 = -2x + 19
x + 2x = 19 - 4
3x = 15
x = 15/3
x = 5
Thus;
f(x) = 5 + 4 = 9
g(x) = -2(5) + 19 = 9
Thus, the point of intersection of both graphs will have the coordinate (5, 9)
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What is the solution (1/4)x+1=32
[tex] \frac{1}{4} x + 1 = 32 \\ \frac{1}{4} x = 32 - 1 \\ \frac{1}{4} x = 31 \\ x = 31 \times 4 = 124[/tex]
The answer is 124.
(1/4)x + 1 = 32(1/4)x = 31x = 31(4)x = 124Assignment
Slide the green dot from 0 to plot the number at the correct
location.
Plot-1.
-6 -5 4 -3 -2 -1 0 1
2
3 4
5
+
6
Use the interactive number line to find each sum to
complete the table.
A
1
-1
-4
-6
B
2
-2
1
-3
A + B
3
R
S
T
From the number line, the values which completes the sum in the table are:
R = -3.S = -3.T = -9.What is a number line?A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.
How to find each sum?From the table of values (see attachment), the values on the number line are represented as follows:
a + b = a + b
R = -1 - 2
R = -3.
a + b = a + b
S = -4 + 1
S = -3.
a + b = a + b
T = -6 - 3
T = -9.
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A 8 gram sample of a substance that's a by-product of fireworks has a k-value of 0.1027. Find the substance's half-life, in days. Round your answer to the nearest tenth
The substance's half - life is 7 days
How to determine the half-life
The formula for finding the half - life is given as;
Half - life = [tex]\frac{0. 693}{k}[/tex]
The k value given is 0.1027
Half - life = [tex]\frac{0. 693}{0.1027}[/tex]
Half - life = 6. 75
Half - life = 7 days in the nearest tenth
Thus, the substance's half - life is 7 days
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Pls help me I'm stuck
The measure of the angle BAM is approximately 40.894°.
What is the angle withing a rectangle?
In this problem we proceed to draw the figure representing the entire figure and labeling all known lengths, both from statement and derived from Pythagorean theorem. Since the angle BAM is part of a right triangle, then we can apply the following trigonometric function:
[tex]\tan \theta = \frac{BM}{AB}[/tex]
[tex]\tan \theta = \frac{\frac{\sqrt{3}}{2}\cdot x }{x}[/tex]
[tex]\tan \theta = \frac{\sqrt{3}}{2}[/tex]
θ ≈ 40.894°
The measure of the angle BAM is approximately 40.894°.
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In 2012, the population of a city was 6.38million. The exponential growth rate was 2.38% per year.
a) Find the exponential growth function.
b) Estimate the population of the city in 2018.
c) When will the population of the city be 9million?
d) Find the doubling time.
Question content area bottom
Part 1
a) The exponential growth function is P(t)
enter your response here, where t is in terms of the number of years since 2012 and P(t) is the population in millions.
The exponential growth function is P(t) = 6.38 million x (1.0238^t).
The population of the city in 2018 is 7.35 million.
The year the population would be 9 million is 14.46 years.
The doubling time is 29.12 years.
What is the exponential growth function?FV = P (1 + r)^n
FV = Future populationP = Present populationR = rate of growthN = number of years6.38 million x (1.0238^t)
Population in 2018 = 6.38 million x (1.0238^6) = 7.35 million
Number of years when population would be 9 million : (In FV / PV) / r
(In 9 / 6.38) / 0.0238 = 14.46 years
Doubling time = In 2 / 0.0238 = 29.12 years
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Does this represent a proportional relationship
Answer:
D.
Step-by-step explanation:
the suggested relation can be described as y=15x. Then the correct answer is D) Yes, the points are on the line that passes through the origin.
equivalent expressions to 7^3*7^x
Find the critical value (t-value) that form the boundaries of the critical region for a two-tailed test with a = 0.05 for a sample size of n1 =11 & n2 =8
Using a calculator, the critical value for the t-distribution with a confidence level of 95% and 17 df is of Tc = 2.1098.
How to find the critical value of the t-distribution?It is found using a calculator, with two inputs, which are given by:
The confidence level.The number of degrees of freedom, which is one less than the sample size.In this problem, the inputs are given as follows:
Confidence level of 95%, as 1 - 0.05 = 0.95.17 degrees of freedom, as there are two samples, one with 11 - 1 = 10 df, and the other with 8 - 1 = 7 df, hence the total df is 10 + 7 = 17.Hence, using a calculator, the critical value for the t-distribution with a confidence level of 95% and 17 df, using the stated two-tailed test, is of Tc = 2.1098.
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a cylinder and a cone have the same radius and height. The volume of the cylinder is 534ft3 . what volume of the cone?
Answer: 178 ft^3
Step-by-step explanation:
A cylinder has the formula V=pi radius ^2 height
A cone has the formula V= 1/3 pi radius ^2 height
So 1/3 of the volume of the cylinder is the volume of a cone
1/3 of 534 = 178 ft^3
just need b1 and b2
brainliest to whoever answers
50 points
Step-by-step explanation:
b1) Any line parallel to the x-axis is horizontal. If we look at the graph of a horizontal line, we see that for any x-value you give, the y-value will be the same. In this case, the y-value is -1. Hence, the equation for the line is [tex]y=-1[/tex], as y will be -1 no matter the x.
The gradient for a horizontal line is 0, as the "rise" of the function is 0. If we use the formula [tex]\frac{rise}{run}[/tex], we would have 0 on the top, which makes the whole fraction 0.
b2) Any line parallel to the y-axis is vertical. If we look at the graph of a vertical line, we see that for any y-value, the x-value will be the same. In this case, the x-value is -1. Hence, the equation for the line is [tex]x=-1[/tex], as x will be -1 no matter the y.
The gradient for a vertical line is undefined, as the "run" of the function is 0. If we use the formula [tex]\frac{rise}{run}[/tex], we would be dividing by 0, which is undefined.
John is twice as old as Peter. In 8 years, John's age will be 2 more than the sum of their present ages. How old is John now?
Answer:12
Step-by-step explanation:
Peter's age = x
John's age = y
y=2x
after 8 years = y+8=y+x+2
=(y-y)+8-2=x
=6=x
y=2(6)=12