Answer:
x = 12, y = 60
Step-by-step explanation:
We have parallel lines, so alternate interior angles are congruent.
6x + 3 = 75
6x = 72
x = 12
The interior angles of a triangle add up to 180 degrees.
45 + 75 + y = 180
120 + y = 180
y = 60
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Find the product. Write your answer as a mixed number in simplest form.
5 × 2 =
=
Answer:
667/45 or 14 37/45
Step-by-step explanation:
you have to convert 5 4/5 x 2 5/9 then you multiply those numbers but simply them which would be 29/5 x 23/9 then you get 667/45 or 14 37/45 as an alternative form
hope this helps
A cyclist's speed is 1.5 times faster than a walker's speed. they simultaneously start at the same point and after 1.5 hours the distance between them is 12.5 miles. what are their speeds?
The speed of the walker is 16.67 miles per hour.
The speed of the cyclist is 25 miles per hour.
How to calculate the value?Let the speed of a walker = x
Biker's speed = 1.5x
Their relative speed will be:
= 1.5x - x = 0.5x
Distance between them = 12.5 miles
Time taken = 1.5 hours.
It should be noted that distance will be:
= Speed × Time
12.5 = 1.5 × 0.5x
Divide through to get x
12.5 = 0.75x
x = 16.67 miles per hour.
Speed of cyclist = 16.67 × 1.5 = 25 miles per hour.
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Paul is a carpenter and earns $21.50 per hour. Last week Paul worked 40 hours, what is
Paul's gross pay?
Answer: $860 this week.
Step-by-step explanation:
Paul worked 40 hours this week, and makes 21.50 dollars an hour. Gross pay means the amount of money paid before taxes.
So we don't need to calculate any taxes, which means all we need to do is multiply 21.50 by 40 hours, since he makes 21.50 an hour, and he worked 40 hours.
3x-5y=11 if x equals -1,0,1
Answer:
x = 5.33333333333
Step-by-step explanation:
3x-5=11
+5 +5
3x= 16
3 3
u need to separate the 3x
so u use the opposite operation on - 5
add +5 on both sides
-5 plus 5 cancel each other
add 11 to 5 and that is 16
bring them down and divide both by 3
and ur 3 cancel each other,
now divide 16 by 3
and u get x = 5.33333333333
(extra credit) suppose you have a well-balanced "super coin" with three sides or outcomes equally likely: head, middle, and tail. (the super coin is a die with opposite faces showing head, middle, and tail) you tossed this super coin two times.
Possible outcomes are Head, Middle, and Tail.
Since all outcomes are equally likely, the probability of each event is same, therefore
P(Head) = P(Middle) = P(Tail)
= 1/3
P(B|A) is 1/3
P(C|A) is 2/3
A and B are independent
A and C are not independent
Part a
Finding the sample space, S
S = { (HH), (HM), (HT), (MH), (MM), (MT), (TH), (TM), (TT) }
Part b
Finding P(B|A) and P(C|A):
n(B and A) = no. of outcomes in which the first toss is Middle and second toss is Tail = 1
n(A) = Total no. of events in which the first toss is Middle = 3
Therefore, P(B|A) = 1/3
n(C and A) = no. of outcomes in which the first toss is Middle and total no. of heads is zero = 2
n(A) = Total no. of events in which the first toss is Middle = 3
Therefore, P(C|A) = 2/3
Part c
Finding if A and B are independent, or if A and C are independent
Two events A and B are said to be independent when the occurrence of one event does not affect the occurrence of the other event and vice versa. In case of independent events,
P(A) = P(first toss is Middle) = 3/9 =1/3
P(B) = P(second toss is Tail) = 3/9 = 1/3
P(A and B) = P(first toss is Middle and second toss is Tail) = 1/9
P(A)*P(B) = (1/3)*(1/3)
= 1/9 = P(A and B)
Hence, we can say that events A and B are independent.
For A and C, we have,
P(A) = P(first toss is Middle) = 3/9
P(C) = P(total no. of Heads is 0) = 4/9
P(A and C) = P(first toss is Middle and total no. of heads is 0) = 2/9
P(A)*P(C) = (3/9)*(4/9)
= 4/27 P(A and C)
Hence, events A and C are not independent.
The question was incomplete, the complete question is:
(Extra Credit) Suppose you have a well-balanced "super coin" with three sides or outcomes equally likely: Head, Middle, and Tail. (the super coin is a die with opposite faces showing Head, Middle, and Tail) You tossed this super coin two times
a) Describe the sample space using the notation HM for example, if the results are Head first, and Middle second.
Let;
A = event the first toss is Middle,
B = event the second toss is Tail, and
C = event the total number of Heads is 0.
b) Find
P(B|A)
P(C|A)
c) Are A and B independent? YES, NO, Why?
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Mrs. Jenkins gave her class the function f(x)=(x-5)(x+1). Four students made a claim about the function. Each student's claim is below.
• Annie: The x-intercepts are (5,0) and (1,0)
•Jacob: The y-intercept is at (-5,0)
• Neil: The vertex is at (2, -9)
•Zoey: The midpoint between the x-intercepts is at (-2,0)
Which student's claim about the function is correct?
The only student with the correct claim about the given quadratic equation is; Neil: The vertex is at (2, -9)
How to identify the features of a quadratic function?We are given the quadratic function;
f(x) = (x - 5)(x + 1)
1) The x-intercepts of the quadratic function are simply the roots of the quadratic function. Now, the roots are at; (5, 0) and (-1, 0). Thus, Annie's claim is not correct.
2) The y-intercept is the point at which x = 0. Thus;
f(0) = (0 - 5)(0 + 1)
f(0) = -5
y-intercept is at; (0, -5)
Thus, Jacob is wrong.
3) The x-coordinate of the vertex is;
x = -b/2a
The equation is; x² - 4x - 5
Vertex = -(-4)/(2 * 1) = 2
y-coordinate is;
y = 2² - 4(2) - 5
y = -9
Thus, Jacob is correct
4) Zoey is incorrect because she didn't properly find the midpoint of the x-intercepts.
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Solve for x :
3x+2=11
Answer:
x = 3
Step-by-step explanation:
3x + 2 = 11
3x = 11 - 2
3x = 9
x = 9/3
x = 3
Answer:
Separate the x and the numbers on each side and solve.
3x + 2 = 11
3x = 9
x = 3
find the indicated probability. in one town, 72% of adults have health insurance. what is the probability that 7 adults selected at random from the town all have health insurance?
Model Real Life The Elephant
Building is 335 feet high. A real
Asian elephant is 12 feet tall. If
29 real elephants could stand on
top of each other, would they reach
the top of the building?
Answer:
Yes
Step-by-step explanation:
The Elephant Building is 335 feet high. A real Asian elephant is 12 feet tall. If 29 real elephants could stand on top of each other, would they reach the top of the building?
They are asking if 29 12' elephants are as tall as as a 335' building:
29 × 12' = 348' elephant stack
because 348' is taller than 335' building then yes, 29 staked elephant would reach and pass the top of a 335' building.
Bottled Drinking Water Americans drank an average of 23.2 gallons of bottled water per capita in 2004. If the standard deviation is 2.7 gallonvariable is normally distributed, find the following probabilities. Use a graphing calculator and round the answers to four decimal places.More than 25 gallons of bottled water.P (more than 25 gallons of botted water)
They tell us that it is distributed in a normal way, which means that the distribution has the following characteristics:
If teh standart deviation is 2.7 gallon and the avriabe is normal distributed we need to know the probability highlighted in the image above, when replacing in the formula with x greater than 25 we obtain:
[tex]P(x>25)=0.2525[/tex]Please answer the questions
The numeric values for the given functions are as follows:
1. g(-4) = -21.
2. f(-1) = 3.
How to find the numeric value of a function or of an expression?To find the numeric value of a function at input x = a, we replace each instance of the variable x in the function by the desired value of a.
For item 1, function g(x) is defined as follows:
g(x) = -x² - 5.
We want to find the numeric value at x = -4, hence the lone instance of x is replaced by -4 as is shown below:
g(-4) = -(-4)² - 5 = -16 - 5 = -21.
Hence g(-4) = -21 is the numeric value.
For item 2, the function f(x) is given as follows:
f(x) = -3(1 - x - 3x²).
To find the numeric value at x = -1, both instances of x have their values replaced by -1, hence the numeric value will be given as follows:
f(-1) = -3(1 - (-1) - 3(-1)²) = -3(1 + 1 - 3) = 3.
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If x [tex]\neq[/tex] 0, what is the value of (5x)^0?
Answer:
1
Step-by-step explanation:
from the rule of exponents
• [tex]a^{0}[/tex] = 1 , then
[tex](5x)^{0}[/tex] = 1
An 8 1/4 candle burnt down in 11 hours how far has it burn after 4 1/2 hours
Answer:
27/8 or 3⅜
Step-by-step explanation:
please rate as brainliest
Find the value of x when 6 - 3x = 5x - 10x + 4.
The value of x is
Answer:
-1
Step-by-step explanation:
First combine like terms on the right side (5x-10x) to get -5x +4
6-3x=-5x+4
then move the -5x over to get 2x because you would add the -5x to the -3x.
6+2x= 4
then subtract 6 on both sides.
2x=-2
to make your final answer -1.
What does the standard deviation measure?
Answer:
Standard deviation measures the dispersion of a dataset relative to its mean
Step-by-step explanation:
can someone help with the last problem
Answer:
Bro x =21
Step-by-step explanation:
X=21 and AM=14
As all the lines are same so all will be 7 and x will be 3 times 7 which is 21 and in the AM case there 7 is 2 times thus multiply 7 by 2 for 14
From a hot-air balloon, Nayeli measures a 35^{\circ} ∘ angle of depression to a landmark that’s 905 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground? Round your answer to the nearest tenth of a foot if necessary.
The balloon's vertical distance above the ground is equal to 633.7 feet
What is angle of depression?
The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line.
Given data ,
we have Angle of depression = 35°
Base distance D = 905 ft
Let the vertical distance be H
To calculate the vertical distance H of the balloon above the ground , we use the angle of depression and the base distance.
Therefore , using the trigonometric identities ,
sin = Opposite / Hypotenuse
cos = Adjacent / Hypotenuse
tan = Opposite / Adjacent
So , tan Ф = tan 35°
= H / D
tan 35°= H / 905
H = tan 35° x 905 ft
H = 0.7002075 x 905
H = 633.7 ft
Hence , vertical distance is equal to 633.7 ft
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The properties that characterize a square based pyramid that includes the faces,edges and vertices
Answer:
A square pyramid is composed of an eight-sided square base, four triangular sides, five vertices, and five vertices. This pyramid has a square base with a peak at the top. The fact that a square pyramid is a polyhedron was noted.
Step-by-step explanation:
The three-dimensional geometric shape of a square pyramid has a square base and four triangular sides that are joined at the vertex. Five facets make up its polyhedron shape (pentahedron). Four triangles joined at the vertex and a square base make up a square pyramid. Three sides, a square base, and a central vertex characterize the triangle side faces. The tallest point of the pyramid is known as its "apex." The base is represented by the bottom square. Faces are the three triangular vertices of the triangle. When viewed from the bottom up, a pentahedron is a five-sided, three-dimensional shape that resembles a square pyramid.
tienes una urna con "x" esferas. ¿cuales de la expresión algebraica de la extracción de 3 esferas?
porfaaaaa
Si definimos N como el nuevo número de esferas en la urna, entonces la expresión algebraica será:
N = x - 3.
¿Cual es la expresión algebraica para la extracción de 3 esferas?Sabemos que tenemos una urna con x esferas, donde x representa un numero entero.
Sabemos que 3 esferas se extraen de la urna, es decir, el número total de esferas en la urna decrese en 3 unidades.
Entonces podemos escribir la expresión algebraica como:
N = x - 3
Donde definimos N como el nuevo número de esferas en la urna.
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You use the equation M/5 - 26 = 2L- 1/2g to calculate the amount of money M in your account at the end of the month, where L is the number of lawns mowed and g is the number of gallons of gas used.
a. Solve the equation for M
Based on the given equation, the change of subject of the equation to M is given by M = 10L - 5/2g + 130
How to make M the subject of the formulaChanging the subject of formula of an equation is the working out of a particular variable from the list of variables in the formula. The variable is either denoted with letter or symbol.
M/5 - 26 = 2L- 1/2g
Where,
M = the amount of money in your account at the end of the monthL = number of lawns mowedg = number of gallons of gas used.M/5 - 26 = 2L- 1/2g
Add 26 to both sidesM/5 = 2L - 1/2g + 26
Cross productM = 5(2L - 1/2g + 26)
M = 10L - 5/2g + 130
Therefore, the solving for M in the equation will give M = 10L - 5/2g + 130
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can you please help me?
Answer:
Time since the person starts walking is the input
t represents the input
Step-by-step explanation:
A radioactive sample has a half-life of 12 hours. after hours, 4 milligrams of the sample remain. what is the initial amount of the radio-active substance?
After 18 hours the remaining quantity of the radioactive sample will be (A) 4.68 grams.
What are mathematical operations?An operation, also known as an "operand" or "argument," is a function in mathematics that converts zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands.Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are the operations that are most frequently studied.So, original radioactive substance = 3000 grams.
Half-life = 3 hoursSo, a number of half-lives in 18 hours:
18/3 = 6Then, after 18 hours:
1/(2)⁶ ⇒ 1/64 × 300 = 4.6875 gramsTherefore, after 18 hours the remaining quantity of the radioactive sample will be (A) 4.68 grams.
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The correct question is given below:
300 grams of a radioactive sample has a half-life of 3 hours. After 18 hours, the remaining quantity will be:
(A) 4.68 gm
(B) 2.34 gm
(C) 3.34 gm
(D) 9.37 gm
Find the 62nd term of the arithmetic sequence-27,-21,-15
Step-by-step explanation:
For Arithmetic Sequence
Tn = a + (n -- 1)d
Where Tn = the no of nth term
a = First number
n = nth term
d = common difference
a = --27, T2 = --21
d = second term -- first term
d = --27 -- (--21)
d = --27 + 21 = --6
a = --27, n = 62, d = --6, T62 = ?
Tn = a + (n -- 1)d
T62 = --27 + (62 -- 1)×--6
T62 = --27 + (61 × --6)
T62 = --27 + (--366)
T62 = --27 -- 366
T62 = --393
Find f (g (x)) for the functions f (x) = x+2 and g (x) = x²
Answer:
f(g(x) ) = x² + 2
Step-by-step explanation:
to find f(g(x) ) substitute x = g(x) into f(x)
f(g(x) )
= f(x²)
= x² + 2
Nicole went for a drive in her new car. She drove for 169.6 miles at a speed of 53 miles per hour. For how many hours did she drive?
169.6/53 = 3.2
about 3.2 hours
Answer:
3.2 hours
Step-by-step explanation:
169.6 ÷ 53 = 3.2
so, she drove 3.2 hours
8.
A ladder 3.5m long leaning against the wall of a house reaches
a height of 3.3m.
3.3m
wall
3.5m
(a) What angle does the ladder make with the ground? (3 marks)
Hence the angle theta is 70.5°
What is angle?
The space between two lines or surface that meet measured in degrees.
As per the given question a ladder 3.5 m long leaning against the wall of a house reaches a height of 3.3 m we have to find what ladder make the ground.
Sol-
Let the angle is theta
Length of the ladder is 3.5m
Height of the ladder is 3.3 m
Sin= 3.5/3.3
=0.942
Sin =sin 70.5°
Theta = 70.5°
Hence the angle is theta =70.5°
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The silo shown has a volume of 14,250 cubic feet. The top of the silo
is a hemisphere. And has a radius of 9. Find the height of the silo
Answer:
Step-by-step explanation:
Part A. The figure at the right is of 2 grain, storage silos. The diameter of each measures 24 feet and the height of the cylinder measures 51 feet. The height ...
-23x² + x² - 6x + 10 + 2x²
Step-by-step explanation:
what do you need to do ?
the only thing we can do here without any further information is simplification if the expression:
-23x² + x² - 6x + 10 + 2x²
now we group ask the terms of the same variable exponents :
-23x² + x² + 2x² - 6x + 10
-20x² -6x + 10
we could do
2×(-10x² - 3x + 5)
but I personally don't find this more simplified that the previous form.
5/8 divided by 2 1/10
Answer:
0.29761904761
Step-by-step explanation:
Brainlest, Please!
Answer:
25/84
Step-by-step explanation:
1. 2 1/10 is mixed number fraction so convert it into an improper fraction.
~ Multiply whole number and denominator and add the numerator of 1
~ Improper fraction: 21/10
2. So, new equation is (5/8) / (21/10)
3. Use the Keep, Change, Flip method:
~ Keep the 5/8
~ Change division to multiplication
~ Flip the improper fraction to 10/21
4. Solve the equation:
~ (5/8) x (10/21) = 50/ 168
5. Reduce fraction:
~ By 2
~ 25/84
A tennis ball machine fires balls a distance that is approximately normally distributed. The mean distance, μ, is unknown and the standard deviation is 1.2 feet. If 5% of balls go farther than 70 feet, find μ. (Round to 3 decimal places.)
The mean distance, μ, If 5% of balls go farther than 70 feet is; μ = 68.032
How to calculate the population mean?We know that the formula to find the z-score is;
z = (x' - μ)/σ
where;
z is z-score
x' is sample mean
μ is population mean
σ is standard deviation
We are given;
σ = standard deviation = 1.2
x' = sample mean = 70 ft
Now, the z-score that produces a p-value of 0.05 or 5% is; z = 1.64
Thus;
1.64 = (70 - μ)/1.2
μ = 70 - (1.64 * 1.2)
μ = 68.032
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