The angle bisectors of the same side interior angles, formed by two parallel lines and a transversal, intersect at a 90-degree angle.
Explanation:In geometry, when you have two parallel lines intersected by a transversal, the same side interior angles are those which are in the same position on the two lines. If we bisect these angles (i.e., divide them in two equal parts), the angle bisectors will intersect forming an angle that is 90 degrees.
To understand why, note that the same-side interior angles are supplementary (i.e., they sum up to 180 degrees) because they are on the same side of the transversal. So, if we bisect these angles, each pair of congruent angles will add up to 90 degrees. When these bisectors intersect, they form four right angles. Therefore, the angle at the intersection of the bisectors is 90 degrees.
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suppose you deposit $25,000 in to a fund for which the annual interest rate is 5.3% compounded continuously. find the number of years it will take to double in value (round your answer to the nearest tenth of a year)
For a normal distribution, the proportion in the tail beyond z = 0.30 is p = 0.1179.
a. True
b. False
Using the normal distribution, it is found that the statement is False, thus the correct option is b.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.The area on the tail beyond z is the proportion that is above z, that is, 1 subtracted by the p-value of z.For this problem, z = 0.3 has a p-value of 0.6554.
1 - 0.6554 = 0.3446
The proportion in the tail beyond z = 0.30 is p = 0.3446, thus, the statement is False.
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A bus can carry 50 people per run. At least how many times does the bus have to run in order to transfer 25,000 people?
solve for x:
4/x-3 + 2/x^2-9 = 1/x+3
a. -17/3
b.13/3
c.19/3
d.-5
Can anyone help me Plot a parabola through the points? Cause i dont understand what to do
solve each inequality. Justify each step (y-) - 4 + 2y > 11
A person at ground level measures the angle of elevation to the top of a building to be 74 degrees. If at this point the person is 34 feet away from the base of the building, then how tall is the building? (Please round to the tenths place; please show work/steps and provide units with your answer) WILL GIVE BRAINIEST
to find the height of the building multiply the distance ( 34 feet) by the tangent of the angle(74)
34 * tan(74) = 118.57 feet
HELP!!! A pentagonal pyramid is sliced parallel to its base. what shape does it make?
He for got his pin code. 20% of his pin code was 246.8. What was his pin code?
Engineers are designing a box-shaped aquarium with a square bottom and an open top. The aquarium must hold 256 ft^3 of water. What dimensions should they use to create an acceptable aquarium with the least amount of glass?
To solve the problem we must know about the volume and the surface area of cuboids.
The length of the aquarium is 4, and the width of the aquarium is 8.
Given to us
The aquarium must hold 256 ft^3 of water.We know that the base of the aquarium should be a square, therefore, the length and the breadth of the aquarium will be the same.
Volume of the AquariumLength x breadth x height = 256 ft³
Length x Length x height = 256 ft³
Length ² x height = 256 ft³
[tex]L^2\times H = 256\\\\H = \dfrac{256}{L^2}[/tex]
Surface Area of the AquariumSurface Area of the Aquarium
= Area of the base + (4 x Area of the 4 sides)
[tex]= L^2 + 4(L\times H)[/tex]
Substituting the value of H,
[tex]= L^2 + 4L(\dfrac{256}{L^2})[/tex]
Length of the AquariumLet the surface area be a function of L, therefore,
[tex]f(L) = L^2 + 4L(\dfrac{256}{L^2})[/tex]
Differentiating the function to get the minimum,
[tex]f(L) = L^2 + 4L(\dfrac{256}{L^2})\\\\f(L) = L^2 + (\dfrac{1024}{L})\\\\f'(L) = 2L - (\dfrac{1024}{L^2})[/tex]
Equating against zero,
[tex]2L - (\dfrac{1024}{L^2}) = 0\\\\\dfrac{2L^3-1024}{L^2} = 0\\\\2L^3-1024 = 0\\\\L = 8[/tex]
Substituting the value of L,
[tex]H = \dfrac{256}{L^2}\\\\H = \dfrac{256}{8^2}\\\\H = 4[/tex]
But this way the area will be more, therefore, replace the value of L with 8,
L = 4
H = 8
Hence, the length of the aquarium is 4, and the width of the aquarium is 8.
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An m-bit password is required to access a system. a hacker systematically works through all possible m-bit patterns. let x be the number of patterns tested until the correct password is found. find the conditional pmf of x given that the password has not been found after k tries
Final answer:
The conditional pmf of x, the number of patterns tested until the correct m-bit password is found, given that the password has not been found after k tries, is uniformly distributed with 1/(2^m - k) for x = k+1, k+2, ..., 2^m.
Explanation:
The question deals with the topic of probability and specifically centers around the concept of a conditional probability mass function (pmf). Given that an m-bit password is systematically being guessed by a hacker and has not been found after k attempts, we need to find the conditional pmf of x, where x is the number of patterns tested until the password is found.
Since the password has not been guessed within the first k tries, the conditional probability is based on the remaining 2m - k possibilities. The distribution of x will be uniform because each subsequent attempt has an equal probability of being correct. The conditional pmf of x given that the password was not found after k tries is 1/(2m - k) for x = k+1, k+2, ..., 2m.
A bicycle went 120 miles in 5 hours. A motorcycle is three times as fast as the bicycle. Find the speed of motorcycle.
Answer:
Step-by-step explanation:
120 x 5 = 600
The motorcycle is 3 times as fast.
600 x 3 = 1800
What expression is equivalent to x^2+2x-24/3x+18
The equivalent expression to [tex]x^2 + 2x - 24 / (3x + 18([/tex] is (x - 4) / 3, after factoring and simplifying the common terms.
The question is asking for an expression equivalent to [tex]x^2 + 2x - 24 / (3x + 18[/tex].
This expression can be factored and simplified.
First, notice that the quadratic expression in the numerator can be factored into (x + 6)(x - 4).
Similarly, the denominator can be factored as 3(x + 6). After factoring, we have:
= (x + 6)(x - 4) / 3(x + 6)
We can now simplify the expression by canceling out the common factor of (x + 6):
= (x + 6)(x - 4) / 3(x + 6) = (x - 4) / 3
So the equivalent expression is (x - 4) / 3.
A relation is plotted as a linear function on the coordinate plane starting at point E at
(0, 27)
and ending at point F at
(5, −8).
What is the rate of change for the linear function and what is its initial value?
The rate of change and the initial value are given as -5 and 27 respectively.
How to represent a straight line on a graph?To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.
Given that,
The points for the given linear function are given as (0, 27) and (5, -8) respectively.
The rate of change is equivalent to the slope of the straight line and is given as,
(-8 - 27)/(5 - 0) = -35/7 = -5
Now, the equation of the function can be written as,
(y - 27)/(x - 0) = -5
=> y - 27 = -5x
=> y = -5x + 27
The initial value is given at x = 0 as below,
y = -5 × 0 + 27
= 27
Hence, the rate of change for the function is -5 and its initial value is 27.
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the slope of the line that passes through the points (-6,w) and (-10,4) is 1/8. what is the value of w
The value of 'w' using the given slope is [tex]\frac{9}{2}[/tex]
Given :
the slope of the line that passes through the points (-6,w) and (-10,4) is 1/8
apply slope formula
[tex]slope =\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values given in the points and make it equal to 1/8
[tex]slope =\frac{4-w}{-10+6}=\frac{1}{8} \\\frac{4-w}{-4}=\frac{1}{8}\\(4-w)(8)=-4(1)\\32-8w=-4\\-8w=-4-32\\-8=-36[/tex]
Divide both sides by -8
[tex]w=\frac{-36}{-8} =\frac{9}{2}[/tex]
The value of 'w' is [tex]\frac{9}{2}[/tex]
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17 ÷ 4520= what is the product
The student's question is related to dividing 17 by 4520. This is performed by a straight division resulting in a small decimal quotient, not a product. The calculation is best done using a calculator and rounding to the proper number of significant figures.
The equation given, 17 by 4520, is asking for the result of dividing 17 by 4520. To compute this, we simply perform the division, recognizing that since 4520 is much larger than 17, the answer will be a very small decimal value. The term 'product' in the student's question seems to be a mistake, as they are likely referring to the quotient obtained from the division.
When attempting to perform the computation mentally and simplify the process, one might attempt to find numbers that are more easily divisible or apply scientific notation to simplify calculations, much like re-expressing numbers to make them more manageable. However, for this division, no mental math trick simplifies it effectively, and using a calculator might be the best option.
When going through this process, it is also important to consider significant figures when giving the final answer, rounding as necessary based on the precision of the data provided.
Determine the intercepts of the line. 7x-5=4y-6/7x−5=4y−6
Answer:
x.(-1/7,0)
y.(0,1/4)
Step-by-step explanation:
What are the solutions of 2x2 + 8x = −26
What is cos θ if sec θ = 2?
Answer:
the value of cos θ is [tex]\frac{1}{2}[/tex].
Step-by-step explanation:
Since, [tex] cos\theta=\frac{1}{sec\theta}[/tex]
we are given with sec θ = 2
To find the value of cos θ , we use this fact [tex] cos\theta=\frac{1}{sec\theta}[/tex]
put sec θ = 2 in [tex] cos\theta=\frac{1}{sec\theta}[/tex]
[tex] cos\theta=\frac{1}{2}[/tex]
Therefore, the value of cos θ is [tex]\frac{1}{2}[/tex].
The temperature, t, in Burrtown starts at 32°F at midnight, when h = 0. For the next few hours, the temperature drops 2 degrees every hour.Which equation represents the temperature, t, at hour h?
Answer: We find the equation that represents the temperature (t) at hour (t) using the slope-intercept form and it is:
t = -2 h + 32
Solution:
The temperature, t, in Burrtown starts at 32°F at midnight, when h = 0. This represents the y-interception of the right line, when h=0 hours, t=32 °F:
Point=(h,t)→Point=(0,32)=(0,b)→b=32
For the next few hours, the temperature drops 2 degrees every hour. This represents the slope of the line (m): m=-2, negative because the temperature drops.
Slope-Intercept form:
y=mx+b; y=t, m=-2, x=h, b=32
Replacing the values:
t=-2h+32
Answer:
t=-2h+32
Step-by-step explanation:
The length of a rectangle is one unit shorter than one-sixth of the width, x. Which expression represents the perimeter of the rectangle? 7/3x−2 1/3x−4 1/3x−2 7/3x−8
Answer: [tex]\dfrac{7}{3}x-2[/tex]
Step-by-step explanation:
Let x be the width of the rectangle , then the length of the rectangle will be :_
Length = [tex]\dfrac{1}{6}x-1[/tex]
We know that the perimeter of a rectangle is given by :-
[tex]P=2(l+w)[/tex]
Substitute the value of length and width we get,
[tex]P=2(\dfrac{1}{6}x-1+x)[/tex]
Combine like terms, we get
[tex]P=2(\dfrac{1+6}{6}x-1)\\\\\Rightarrow\ P=2(\dfrac{7}{6}x-1)\\\\\Rightarrow\ P=2\times\dfrac{7}{6}x-2\times1\\\\\Rightarrow\ P=\dfrac{7}{3}x-2[/tex]
Hence, the expression represents the perimeter of the rectangle : [tex]\dfrac{7}{3}x-2[/tex]
The Mississippi River is about 4,000 kilometers long. An M&M is about 1 centimeter long. There are 100 centimeters in a meter, and 1,000 meters in a kilometer. Estimate how many M&Ms it would take to measure the length of the Mississippi River
To measure the approximately 4,000 km long Mississippi River with M&Ms, we will need about 400,000,000 M&Ms, as there are 100 cm in a meter and 1,000 m in a km.
The question involves estimating the length of the Mississippi River using the size of M&Ms as a unit of measurement. Since the river is about 4,000 kilometers long and the standard unit of length in the SI system is the meter, we need to convert kilometers to centimeters to match the size of an M&M, which is about 1 centimeter long. There are 100 centimeters in a meter, and 1,000 meters in a kilometer. Therefore, we have:
Convert kilometers to meters: 4,000 km x 1,000 m/km = 4,000,000 m.Convert meters to centimeters: 4,000,000 m x 100 cm/m = 400,000,000 cm.Now, since each M&M is 1 centimeter, the number of M&Ms needed to measure the length of the Mississippi River is equal to the total number of centimeters:
400,000,000 M&Ms would be required to measure the approximate length of the Mississippi River.
What happens to the arrangement of water molecules as ice melts?
A. Molecules gain enough energy to escape as vapor.
B. Molecules release enough energy to escape as vapor.
C. Molecules release enough energy to move from their fixed positions.
D. Molecules gain enough energy to move from their fixed positions.
hich sentence is a run-on sentence?
A.
Dogs and hamsters are both fun pets, they relate to people in different ways.
B.
Dogs enjoy human contact; they love to fetch and chase.
C.
My hamster likes to run in his wheel, and he does not like to be held.
D.
When I try to pick up my hamster, he looks for a place to hide.
The perimeter of a rectangle is 42 cm. The longer side has length of 7 cm more than the shorter side. Find the length of longer side
calculate the cost of fuel. 40 L at 65.7cents/L
Find the equation of the ellipse with the following properties. The ellipse with x-intercepts (2, 0) and (-2, 0); y-intercepts (0, 4) and (0, -4).
a pail hold 6 3/4 gallon of water. how much is this in cups
The required, there are 108 cups of water in the pail as a pail hold 6 3/4 gallon of water.
What is a unit of measurement?Unit of measurement is defined as every entity having its measures in dimensions, weight, and time. Such as for length we have a meter, for liquid we have liters, and so on.
Here,
To convert 6 3/4 gallons to cups, we can use the fact that there are 16 cups in one gallon.
So, we can start by multiplying 6 (the number of whole gallons) by 16 to get the number of cups in those gallons:
6 gallons × 16 cups/gallon = 96 cups
Next, we need to convert the 3/4 of a gallon to cups. To do this, we can multiply the fraction by the number of cups in one gallon:
3/4 gallon × 16 cups/gallon = 12 cups
So, the total amount of water in the pail is:
96 cups + 12 cups = 108 cups
Therefore, there are 108 cups of water in the pail.
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A recipe makes 6 2/3 cups the serving size is 5/6 cup how many servings does the recipe make
The recipe can make serving 8 cups.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
Here, given that,
A recipe makes 6 2/3 cups
=20/3 cups
And, the serving size is 5/6 cup
So, the recipe can make serving = 20/3÷ 5/6 cups
=20/3 × 6/5 cups
=8 cups
Hence, the recipe can make serving 8 cups.
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Which expression shows the result of applying the distributive property to 3(2x−6) ?
A. 2x−18
B. 6x−18
C. 6x−6
D. 5x−3
Answer:
b
Step-by-step explanation: