Answer:
1/128
Step-by-step explanation:
The probability of tossing a head is 1/2.
Each toss is an independent event.
We toss 7 times and get a head each time.
1/2 * 1/2* 1/2* 1/2* 1/2* 1/2* 1/2
1/128
41 and 51 are two side lengths of a right triangle. The three sides form a Pythagorean triple. Find the value of the third side, x. State whether it is the hyp or a leg.
1. How many telephones per 100 inhabitants did Bermuda have?
2. In 2005, the population of Luxembourg was 470,000. How many telephones were in use in Luxembourg?
Please help with two questions!!!
In Bermuda, there are a total of 90 telephones for each 100 people. Also there are a total of 3,76,000 telephones in use in Luxembourg according to simple calculations.
Here, they given that a telephone symbol is equal to 5 telephones.
Then according to the given diagram,
1. There are:
= (5 + 5 + 5 + 3) 5 telephones
= ( 18 ) 5 telephones
= 90 telephones.
Therefore, there are a total of 90 telephones for each 100 people.
2. In 2005, the population of Luxembourg was 470,000.
According to the given diagram, there are 80 telephones available for every 100 people.
For 4,70,000:
100 -------------- 80
4,70,000 ------ (x)
After cross multiplication,
x * 100 = 80 * 470000
x = 8 * 47000
x = 3,76,000
Therefore, there are total of 3,76,000 telephones in use in Luxembourg.
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A capital is invested, at simple interest, at the rate of 4% per month. How long, at least, should it be applied, so that it is possible to redeem triple the amount applied? * 1 point a) 15 months b) 30 months c) 35 months d) 50 months.
The amount of time needed for this capital to triple would be 50 months, the letter "d" being correct. We arrive at this result using simple interest.
Simple interestSimple interest is a type of financial calculation that is used to calculate the amount of interest on borrowed or invested capital for a given period of time.
In order to find the amount of time required for the principal to be equal to three times the redemption, we have to note that the amount will be equal to three times the principal, using this information in the formula. Calculating, we have:
M = C * (1 + i * t)
3C = C * (1 + 0.04t)
3 = 1 + 0.04t
0.04t = 3 - 1
0.04t = 2
t = 2/0.04
t = 50
What is the measure of
Answer:
∠w = 50°
∠y = 130°
Step-by-step explanation:
Angles ∠w and ∠y are supplementary angles, which means their sum is 180.
4x + 6 + 12x - 2 = 180
Add like terms16x + 4 = 180
Subtract 4 from both sides16x = 176
Divide both sides by 16x = 11
To find the angle measures replace x with 11
∠w = 4x + 6
∠w = 4*11 + 6
∠w = 50°
Now, ∠y
∠y = 12x - 2
∠y = 12*11 - 2
∠y = 130°
Help with math problems
The inequality can be solved to get 2 > x, and the graph on the number line can be seen in the image at the end.
How to solve the inequality?Here we have an inequality and we want to sole it, to do so, we just need to isolate the variable in the inequality.
Here we have:
10 > 5x
To isolate the variable we can divide both sides of the inequality by 5, then we will get:
10/5 > 5x/5
2 > x
So x is the set of all values smaller than 2.
That is the inequality solved, to graph this, drawn an open circle at x = 2 and a line that goes to the left. The graph is the one you can see in the image below.
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Watch help video
Given circle E with diameter CD and radius EA. AB is tangent to E at A. If
EC = 3 and EA = 3, solve for AC. Round your answer to the nearest tenth if
necessary. If the answer cannot be determined, click "Cannot be determined."
C
A
B
The circle E with diameter CD and radius EA having the length of AC is approximately 4.2 units.
What is Pythagoras' Theorem?
In a right-angled triangle, the square of the hypotenuse side equals the sum of the squares of the other two sides.
Since EA is a radius of circle E, and AB is tangent to E at A, we know that AB is perpendicular to EA. Thus, triangle EAB is a right triangle.
Let x be the length of AC. Then, by the Pythagorean Theorem in triangle EAC, we have:
[tex]AC^{2} = EA^{2} +EC^{2}[/tex]
[tex]AC^{2} = 3^{2} + 3^{2}[/tex]
[tex]AC^{2} = 18[/tex]
AC ≈ 4.2 (rounded to the nearest tenth)
Therefore, the length of AC is approximately 4.2 units.
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The circumference of a circle is 81.64 miles. What is the circle's radius?
Use 3.14 for л.
The radius of the circle with given circumference is 13.
What is circumference?
In mathematics, the circumference of any shape determines the path or boundary that surrounds it. In other words, the perimeter, also referred to as the circumference, helps determine how lengthy the outline of a shape is.
We are given that the circumference of a circle is 81.64 miles.
We know that circumference of a circle is given by 2πr.
So, using this we get
⇒ C = 2πr
⇒ 81.64 = 2 * 3.14 * r
⇒ 81.64 = 6.28 * r
⇒ r = 13
Hence, the radius of the circle with given circumference is 13.
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Use the information given below to find tan(a + B)
cos a = 3/5, with a in quadrant IV
tan B = 4/3, with B in quadrant I I I
Give the exact answer, not a decimal approximation.
tan(a + B) = ?
let's bear in mind that on the III Quadrant, sine and cosine are both negative, whilst on the IV Quadrant, sine is negative and cosine is positive, that said
[tex]\cos(\alpha )=\cfrac{\stackrel{adjacent}{3}}{\underset{hypotenuse}{5}}\hspace{5em}\textit{let's find the \underline{opposite side}} \\\\\\ \begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{5}\\ a=\stackrel{adjacent}{3}\\ o=opposite \end{cases} \\\\\\ o=\pm \sqrt{ 5^2 - 3^2} \implies o=\pm \sqrt{ 16 }\implies o=\pm 4\implies \stackrel{IV~Quadrant }{o=-4} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\tan(\beta )=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{3}}\implies \tan(\beta )=\cfrac{\stackrel{opposite}{-4}}{\underset{adjacent}{-3}} \\\\[-0.35em] ~\dotfill\\\\ \tan(\alpha + \beta) = \cfrac{\tan(\alpha)+ \tan(\beta)}{1- \tan(\alpha)\tan(\beta)} \\\\\\ \tan(\alpha + \beta)\implies \cfrac{ ~~\frac{-4}{3}~~ + ~~\frac{-4}{-3} ~~ }{1-\left( \frac{-4}{3} \right)\left( \frac{-4}{-3} \right)}\implies \cfrac{0}{1-\left( \frac{-4}{3} \right)\left( \frac{-4}{-3} \right)}\implies \text{\LARGE 0}[/tex]
A wire 2.5 meters long was cut in a ratio of 1:4, find the measure of the longer part of the wire after cutting?
The wire can be divided into five equal parts, where one portion is one-fifth of the total length and the other four parts are four-fifths of the total length. the measure of the longer part of the wire after cutting is 2 meters.
What is the measure of the longer part of the wire?If the wire was cut in a ratio of 1:4, then the total length of the wire can be divided into 5 parts, where one part is 1/5 of the total length, and four parts are 4/5 of the total length. Let's call the length of one part "x".
So, the total length of the wire is:
[tex]5x = 2.5[/tex] meters
To find the length of the longer part of the wire, we need to find how many parts are in the longer portion. Since the wire was cut in a 1:4 ratio, the longer portion has four parts.
Therefore, the length of the longer part of the wire is:
[tex]4x = 4/5 \times 2.5 meters = 2 meters[/tex]
Therefore, the measure of the longer part of the wire after cutting is 2 meters.
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The average overseas trip cost 2708 per visitor. If we assume a normal distribution with a standard deviation of 405 what is the probability that the cost for a randomly selected trip is more than 3000? If we elect a random sample of 30 overseas trips and find the mean of the sample, what is the probability that the mean is greater than 3000
Randomly selected trip: 24.5% chance > $3000. Sample mean of 30 trips: very small chance > $3000.
Utilizing z-score recipe:
z = (x - μ)/σ
where x is the worth we're keen on, μ is the mean, and σ is the standard deviation.For the primary inquiry:
z = (3000 - 2708)/405 = 0.69
Utilizing a standard typical circulation table or number cruncher, we can track down that the likelihood of getting a z-score more prominent than 0.69 is around 0.245. Consequently, the likelihood that the expense for a haphazardly chosen trip is more than 3000 is around 0.245 or 24.5%.
For the subsequent inquiry:
The example size (n) = 30, and the standard deviation (σ) = 405/sqrt(30) = 74.02 (approx.)
z = (3000 - 2708)/74.02 = 3.94
Utilizing a standard typical dissemination table or number cruncher, we can track down that the likelihood of getting a z-score more prominent than 3.94 is tiny, near 0. Consequently, the likelihood that the mean expense of an example of 30 abroad excursions is more noteworthy than 3000 is tiny.
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The probability that the mean is greater than 3000 is 24.5%
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur.
Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
Given that, the average overseas trip cost 2708 per visitor, assuming a normal distribution with a standard deviation of 405 what is the probability that the cost for a randomly selected trip is more than 3000
z-score:
z = (x - μ)/σ
where μ is the mean, and σ is the standard deviation.
So,
z = (3000 - 2708)/405 = 0.69
Z-score 0.69 = 0.245.
Thus, the likelihood that the expense of the chosen trip is more than 3000 is around 0.245 or 24.5%.
The sample size (n) = 30, and the standard deviation (σ) = 405/√(30) = 74.02 (approx.)
z = (3000 - 2708)/74.02 = 3.94
z-score 3.94 = 0.
Thus, the likelihood that the mean expense of an example of 30 abroad excursions is more noteworthy than 3000 is tiny.
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Please help me!!!
Suppose the proportion p of a school’s students who oppose a change to the school’s dress code is 73%. Nicole surveys a random sample of 56 students to find the percent of students who oppose the change. What are the values of p that she is likely to obtain?
Express the trig ratios as fractions in simplest terms.
cOS K =
sin L=
cos K and sin L
Therefore, cos(K) = √(17)/9, sin(L) = 8/9, and cos(K) and sin(L) together are (√(17)/9, 8/9) are trigonometric ratios as fractions in simplest terms.
Trigonometric Ratios of Particular Angles: What Are They?It is possible to calculate trigonometric ratios for various orientations. However, we memories the trigonometric ratios of a few particular angles, such as 0°, 30°, 45°, 60°, and 90°, to make computations easier. The numbers of the ratios at these angles can be found in the trigonometric ratios table.
The Pythagorean formula can be applied to the illustration to determine the length of the third side:
c²= a²+ b²
c²= 8² + √(17)²
c²= 64 + 17
c² = 81
c = 9
We can now calculate the trigonometry ratios of angles K and L:
cos(K) = adjacent/hypotenuse = √(17)/9
sin(L) = opposite/hypotenuse = 8/9
Using the same hypotenuse number of 9, we can calculate both cos(K) and sin(L) as follows:
cos(K) = adjacent/hypotenuse = √(17)/9
sin(L) = opposite/hypotenuse = 8/9
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Match each expression to its equivalent expression.
Answer: top two goes together, middle left goes to bottom right, bottom left goes to middle right
Step-by-step explanation:
Substitute x for an easy number like 2 and solve.
x - 2/3 - 1/2x = 1/2x - 2/3
x - 1/2 - 3/4x = 1/4x- 1/2
1/3x - 3/4 - 2/3x = -1/3x - 3/4
PLEAS HELP!
Which best describes why it is helpful to know the slant height of a pyramid to find its surface area?
Responses
1)Knowing the slant height helps because it represents the height of the triangle that makes up the base. So, the slant height helps you to find the area of the base.
2)Knowing the slant height helps because it represents the height of the rectangle that makes up each lateral face. So, the slant height helps you to find the area of each lateral face.
3)Knowing the slant height helps because it represents the height of the triangle that makes up two of the lateral faces. So, the slant height helps you to find the area of those two lateral faces.
4)Knowing the slant height helps because it represents the height of the triangle that makes up each lateral face. So, the slant height helps you to find the area of each lateral face.
Therefore, knowing the slant height is important in calculating the lateral area of the pyramid, which is one component of the total surface area.
by the question.
Option 2 is the correct response. Knowing the slant height is helpful because it represents the height of the rectangle that makes up each lateral face of the pyramid. The lateral faces are made up of triangles and rectangles, and the slant height is used to find the height of these rectangles.
Knowing the slant height helps because it represents the height of the rectangle that makes up each lateral face. So, the slant height helps you to find the area of each lateral face. The formula for the lateral area of a pyramid involves the slant height, the perimeter of the base, and the apothem (the distance from the center of the base to the midpoint of a side). Once you know the lateral area, you can add it to the area of the base to find the total surface area of the pyramid.
The slant height of a pyramid is the height of each triangular lateral face, which is an essential component in calculating the lateral surface area of a pyramid. Knowing the slant height is used in the formula for finding the lateral area of a pyramid, which is the sum of the areas of all the triangular lateral faces. Additionally, the base area of the pyramid is also needed to find the total surface area of the pyramid. So, knowing the slant h
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Im stuck on these questions I need help
Answer:
Step-by-step explanation:
modal weight: the weight that appear most often
4.5 kg appears 3 times
6-sided polygon: even though it is an irregular polygon, the interior angles still add up to (6 - 2)180 = 720
therefore, angle f = 720 - 576 = 144 (the sum of a+b+c+d+e is very blurry in the image, it looks like 576--please double check that!)
modal score: read this right off the graph. The score with the highest frequency is the modal score: 14 (meaning, 9 contestants got this score)
Determine the perimeter of the composite figure.
The perimeter of the figure is approximately 63.6 meters, since the lengths of all the sides add up to the figure's perimeter.
What is perimeter?Perimeter is the total length of the boundary of a closed 2-dimensional shape. In other words, it is the distance around the edge of a shape. The perimeter is usually measured in units such as meters, centimeters, feet, or inches depending on the measurement system used. The perimeter can be calculated by adding up the lengths of all the sides of the shape.
Since opposite sides of a parallelogram are equal in length, the length of the straight side of the first parallelogram is:
Length of first parallelogram = 9m
Similarly, the length of the straight side of the second parallelogram is:
Length of second parallelogram = 11m
Now, let's find the length of the straight side of the semicircle segment. We are given that the other side of each parallelogram gets half of the diameter, which is 17m. Therefore, the length of the straight side of the semicircle segment is:
Length of semicircle segment = 17m / 2 = 8.5m
The lengths of all the sides add up to the figure's perimeter. Let's use P to represent the perimeter. Then:
P = 2 (parallelogram length) + semicircle length
When we replace the values we discovered earlier, we obtain:
P = 2(9m + 11m) + π(17m)/2
= 38m + 8.5πm
≈ 63.6m (using π ≈ 3.14)
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I have a barn that is a regular hexagon, as shown. Each side of the barn is 100 feet long. I tether my burro to point A with a 150 foot rope. Find the area of the region in which my burro can graze. Round your answer to nearest foot squared.
The area of the region in which the burro can graze will be 833 pi square feet.
What is the value of the area?Each interior vertex angle of a regular hexagon is (n - 2)·180°/n = (6 - 2)·180°o/6 = 120°
I'll break up the area into three sections.
There is one major section, going 150' along one side in a circular arc to 150' along the adjacent side.
Since the interior angle is 120°, the exterior angle will be 240°.
The area of this section will be: (240°/360°)·pi·radius2 = (2/3)·pi·1502 = 15,000 pi
Then, on each end, around the corner of the barn, the goat can go in a circular arc with radius = 50'.
This angle will be 60°, or one-sixth or a circle.
The area of each section will be (1/6)·pi·502 = 416 2/3 pi
Total area: 15,000 pi + 416 2/3 pi + 416 2/3 pi = 833 1/3 pi square feet.
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The bookstore has 27 chapter books, 9 comic books, and 30 picture books. The shop sold
one-third of the books. How many books were sold?
Answer:
22
Step-by-step explanation:
first you would add all books from the book store to get 66
Then you would divide that by 3 to get
66÷3=22
Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.
Y=38(1.09)^x
The exponential equation represents a growth, and the rate of increase is 9%.
Is it a growth or a decay?The general exponential equation is written as:
y = A*(1 + r)^x
Where A is the intial value, and r is the rate of growth or decay, depending of the sign of it (positive is growth, negative is decay).
Here we have:
y = 38*(1.09)^x
We can rewrite this as:
y = 38*(1 + 0.09)^x
So we can see that r is positive, thus, we have a growth, and the percentage rate of increase is 100% times r, or:
100%*0.09 = 9%
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A seed company planted a floral mosaic of a national flag. The perimeter of the flag is 2,120 ft Determine the flag's width and length if the length is 400 ft greater than the width.
The flag's width is and the length is what?
PLEASE HURRY
Answer:
Step-by-step explanation:
Let's assume that the width of the flag is "w" ft.
According to the problem, the length of the flag is 400 ft greater than the width, which means it can be expressed as:
length = w + 400
Now, we know that the perimeter of the flag is 2,120ft. The perimeter of a rectangle is given by:
perimeter = 2(length + width)
Substituting the values, we get:
2120 = 2[(w+400) + w]
2120 = 2[2w + 400]
2120 = 4w + 800
4w = 1320
w = 330
Hence, the width of the flag is 330ft.
From our equation for the length, we have:
length = w + 400
length = 330 + 400
length = 730
Therefore, the length of the flag is 730ft.
16 Triangle ABC is translated to triangle A'B'C' by
the following motion rule.
(x, y)(x+2y-5)
-8 -6
G
A. (4,-4)
B. (2,-5)
C. (0.6)
D. (-2.5)
N
8
6
B
-2
S
-6
-8
2
What will be the coordinates of A'?
6 8
Answer:
To find the coordinates of A' after the translation, we need to apply the motion rule to the coordinates of A:
(x, y) → (x + 2y - 5, y - 6)
Substituting the coordinates of point A, which is (4, -4), into this motion rule, we get:
A' = (4 + 2(-4) - 5, -4 - 6) = (-3, -10)
Therefore, the coordinates of A' after the translation are (-3, -10).
If the diameter of a circle is
30
30 centimeters, what is the radius of the circle?
Answer:
15 centimeters
Step-by-step explanation:
radius is half of the circles diameter
bob had 2 apples and he ate 1 how many does he have now?
Answer: He has one left
Step-by-step explanation: 2-1=1
I need help with my homework
The table that represents the function for a lawn being mowed more quickly than by Killian's rate is given as follows:
Second table.
How to obtain the average rate of change?The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function. Hence we must identify the change in the output, the change in the input, and then divide then to obtain the average rate of change.
Killian can cut grass at a rate of 1000 square feet each 10 minutes, hence his average rate of change is given as follows:
1000/10 = 100 square feet per minute.
For the second table, in 7 minutes, 1100 square feet of lawn is mowed, hence the rate is given as follows:
1100/7 = 157 square feet per minute.
It is more quickly than Killian's as the rate of change is greater.
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100 Points!!! Algebra question, multiple choice. Only looking for an answer to #8. Find the maximum value of f(x,y)=3x+y for the feasible region. Photo attached. Thank you!
Answer:
+4
Step-by-step explanation:
F(x,y) = 3x+y and y <= -2x+ 4 sub in for 'y'
= 3x + (-2x+4)
= x + 4
If you look at the graph for y <= - 2x+4 ( see below)
you will see that the domain (x values ) can only go from 0 to 4 and the max value is +4 ( rememeber too that y is restricted to >= 0 as is x )
Marissa ate 4 hot dogs every 16 hours. At that rate, how many would she eat in 12 hours?
Answer: 3
Step-by-step explanation:
Answer: 3
Step-by-step explanation:
16/4=unit rate =4
1 in 4 hour
3 for 12 hours
A carpenter attaches a brace to a rectangular picture frame. If the dimensions of the picture frame are 30 inches by 40 inches, what is the length of the
brace?
The brace measures 50 inches in length.
What is Pythagoras's Theorem?The Pythagorean Theorem states that the squares on the hypotenuse of a right triangle, which is the side opposite the right angle, equals the sum of the squares on the legs of the triangle, a2 + b2 = c2.
The other two sides of the picture frame are its length and width. We thus have:
Length of the hypotenuse (brace)² = Length² of the picture frame + Width² of the picture frame
Let's enter the picture frame's specified dimensions:
Length of the brace² = 30² + 40²
Length of the brace² = 900 + 1600
Length of the brace² = 2500
Taking the square root of both sides, we get:
Length of the brace = √(2500)
Length of the brace = 50
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A ladder leans against the side of a house. The angle of elevation of the ladder is 69 when the bottom of the ladder is 8ft from the side of the house. How high is the top of the ladder from the ground? Round your answer to the nearest tenth.
Answer:
20.8
Step-by-step explanation:
Let h be the height of the ladder. We know that the distance BC is 8 ft, and the angle of elevation BAC is 69 degrees. Therefore, we have:
tan(69) = h/8
Multiplying both sides by 8, we get:
8*tan(69) = h
Using a calculator, we get:
h ≈ 20.8 ft
Therefore, the height of the top of the ladder from the ground is approximately 20.8 feet.
11) m/EFG=132°, m/CFG=x+111,
and m/EFC=x+23. Find mLEFC.
Find the value of X!!
The angle made by one chord and tangent of the circle is 32.5 degrees.
What is the Alternate Segment Theorem?
The Alternate Segment Theorem is a theorem in geometry that relates the angles formed by a line that is tangent to a circle and a chord of that circle. The theorem states that the angle formed by a tangent and a chord of a circle is equal to the angle that is subtended by the chord in the opposite segment of the circle
In a circle, the angle formed by a chord and a tangent that intersect at a point on the circle is equal to half the measure of the arc intercepted by the chord.
Therefore, if the arc intercepted by the chord is 65 degrees, then the angle formed by the chord and the tangent is half of 65 degrees, which is:
65 degrees / 2 = 32.5 degrees
So, the angle X made by the chord and the tangent is 32.5 degrees.
Therefore, the angle made by one chord and tangent of the circle is 32.5 degrees.
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[tex]x^{0}[/tex] has a value of [tex]27.5[/tex] degrees.
What are types and value?Values are the benchmarks or ideals by which we judge the acts, traits, possessions, or circumstances of others. Values that are embraced by many include those of beauty, honesty, fairness, harmony, and charity. When considering values, it might be helpful to categorise them into one of three categories: Personal values are those that an individual upholds.
What are the two major categories of value?Values come in two varieties. They serve as either terminal or auxiliary values for Rokeach. Terminal values always are end-states whereas qualities are always forms of conduct. Individuals think that acting in line with cognitive factors and reaching terminal values are always related.
We find the value of [tex]x^{0}[/tex]
[tex]Angle P = 1/2 (mAC-AB)[/tex]
[tex]x^{0}=\frac{1}{2} (120^{0}- 65^{0} )[/tex]
[tex]x^{0} =\frac{1}{2}*55^{0}[/tex]
Therefore, [tex]x^{0}= 27.5^{0}[/tex]
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