In fraction, June is 9/8 as old as David.
What is a fraction?
A fraction is a portion of a whole or, more broadly, any number of equal pieces. In ordinary English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters. A common, vulgar, or simple fraction has a numerator above a line and a non-zero denominator below (or after) that line. Numerators and denominators are also employed in uncommon fractions such as compound fractions, complex fractions, and mixed numerals.
The required fraction is (3/4) x (3/2) = 9/8
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If p(a|b) =0.40, p(b) = 0.74, and p(a) = 0.42, are the events a and b independent?
The set of items that exist as part of both sets A and B exists at the intersection of the two sets.
If p(a|b) =0.40, p(b) = 0.74, and p(a) = 0.42, then P(A∩B) is 0.46.
What is Probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
It exists given that the Probability of two independent event A and B exists given by P(A) and P(B).
The intersection of event A and B is given by P( A∩B).
The group of items that are part of both sets A and B is the intersection of the two sets. A ∩ B represent the intersection. The symbol "∩" can be used to represent the intersection of sets.
The collection of all outcomes that are components of both sets A and B is known as the intersection of events A and B (abbreviated AB).
Given: P(a|b) = 0.40
P(A) = 1 - 0.40 = 0.6
P(B) = 1 - 0.74 = 0.26
P(A∪B) = P(A) + P(B) − P(A∩B)
substitute the values in the above equation, we get
0.40 = 0.6 + 0.26 - P(A∩B)
- P(A∩B) = 0.40 - 0.6 - 0.26
P(A∩B) = 0.46
Therefore, the independent events of A and B exists 0.46.
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A zoo orders food in bulk for its animals. They order enough fresh fruit to last 10 days, enough fresh vegetables for 7 days, and enough dried insects for 5 days. If they last ordered fresh fruit, fresh vegetables, and dried insects on January 1, in how many days will they need to order all three items on the same day?
50 days
65 days
35 days
70 days
Answer ASAP thanks :)
50 points
Answer: 70 days
Step-by-step explanation:
If eyeglasses with diverging lens are used (power = -1.16 dp),what is the far distance?
According to the given statement The total far distance = 88.2cm
Where does lens formula came from?A lens equation, sometimes known as a lens formula, is an equation that connects focal length, image distance, as well as object distance. . where v is the distance between the picture and the lens, u is the object distance, and f is the focal length
What is the lens's power?A lens's power is defined as both the reciprocal of its focal length. It is symbolized by that the letter P. P=1f gives the power P of something like a lens with a focal length of f (in m). The SI unit of lens power is a 'diopter.'
According to the given data:P = -1.16
The expression of the focal length is represented as:
f = 1/p
p is the power.
so,
f = 1/-1.16
= -0.862
= -86.2 cm
the expression for the lens formula is:
1/f = 1/v - 1/u
1/(-86.2) = 1/v - 0
v = -86.2
The total distance is represent as:
d = v + s
so,
d = 86.2 + 2
= 88.2 cm
The total far distance = 88.2cm.
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Each year a certain amount of money is deposited in an account which pays an
annual interest rate of r so that at the end of each year the balance in the account is
multiplied by a growth factor of x = 1 + r. $500 is deposited at the start of the first
year, an additional $200 is deposited at the start of the next year, and $600 at the
start of the following year.
The expression at the end of the third year would be: 500x³ + 200x² + 600x
How to find the polynomial expressionWe have the rate at x = 1 + r
This is the rate of the interest that is earned per year.
In the first year.
initial deposit = $500
deposit at the end of the year = 500 * x = 500x
In the second year
The initial balance = 500x + 200
The balance at the end of the year = (500x + 200)x
= 500x² + 200x
In the third year
Initial balance = 500x² + 200x + 600
Then the year end balance would be (500x² + 200x + 600)x
= 500x³ + 200x² + 600x
Hence the expression that can be used to show the polynomial is given as 500x³ + 200x² + 600x
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Two trains leave towns 978 miles apart at the same time and travel toward each other. one train travels 21 miles per hour faster than the other. if they meet in 6 hours what is the rate of each train?
If two trains leave towns 978 miles apart at the same time and travel toward each other and one train travels 21 miles per hour faster than the other and if they meet in 6 hours, then the rate of the faster and slower train will be 92mph and 71 mph respectively.
To determine the rate or speed of each train, an algebraic expression can be used.
As one train travels 21 miles per hour faster than the other, consider x to be the speed of the train that travels slower. In this case, an algebraic expression can be given as,
6x + 6(x + 21) = 978
Here, (x + 21) represents the speed of the faster train
6x + 6x + 126 = 978
12x = 978 - 126
12x = 852
x = 852 ÷ 12
x = 71
x + 21 = 71 + 21 = 92
Hence, the rate of the faster train is 92 miles per hour and the rate of the slower train is 71 miles per hour.
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234.8−38.94 helppppp
Answer:
195.86
Step-by-step explanation:
Answer: 195.86. Yw.
Step-by-step explanation: Pls add me Brainliest >3
PLEASE HELP Word problem involving average rate of change
Answer:
(a): 26.1
(b): 27.9
Please see below for the steps.
Step-by-step explanation:
(a):
Use points (0,0) and (3, 78.3)
Use slope formula. The slope formula is also used to find average rate of change (just so you know).
y2-y1/x2-x1
78.3-0/3-0=78.3/3=26.1
Answer for (a) is 26.1
(b):
Use points (4, 147.6) and (9, 287.1)
Use slope formula.
y2-y1/x2-x1
287.1-147.6/9-4=139.5/5=27.9
The answer for (b) is 27.9
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if CD is the bisector of AB and AD=13 units,what is DB?how many units does DB have
Answer: DB=6.5 units
Step-by-step explanation:
DB=BD
AB+BD=AD
AB=BD ==> Bisectors divide a segment into two equal parts
BD+BD=13
2*BD=13
BD=13/2
BD=
DB=6.5 units
Point A is chosen at random on BE- . Find the probability of the following event.
P(A is on CE-)
The probability of the event P(A is on [tex]\bar{CE}[/tex]) is 21/26.
Probability:
Probability defines the possibility of the event across the total event.
Given,
Point A is chosen at random on [tex]\bar{BE}[/tex].
Here we need to find the the probability of the following event.
P(A is on [tex]\bar{CE}[/tex]).
Let us consider the following image, in order to solve this.
Based on the image we have identified that the probability of the event P(A is on [tex]\bar{CE}[/tex]) is calculated by dividing the length of CE by the length of BE.
So, the probability of the event P(A is on [tex]\bar{CE}[/tex]) is,
P(A is on [tex]\bar{CE}[/tex]) = (length of CE) / (length of BE)
Then, length of CE is calculated by adding the distance,
=> CD + DE
=> 12 + 9
=> 21
Now,
Apply the values then we get,
P(A is on [tex]\bar{CE}[/tex]) = 21 / ( 5 + 12 + 9)
P(A is on [tex]\bar{CE}[/tex]) = 21 / 26
Therefore, the probability of the event P(A is on [tex]\bar{CE}[/tex]) is 21/26.
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Find the value of x if A C=4 x-3, D C=2 x+9, m∠ E C A=15 x+2, and EC is a median of ΔAED. Is EC also an altitude of Δ A E D ? Explain.
If AC = 4x - 3, DC = 2x + 9, m ∠ ECA = 15x + 2, and EC is a median of ΔAED then EC is not an altitude of ΔAED because of m ∠ ECA = 92.
What is meant by the altitude of a triangle?
In geometry, an altitude is a line that passes through two very specific points on a triangle: a triangle's vertex, or corner, and its opposite side at a right, or 90-degree, angle. The base is the opposite side. Triangles have three vertices and three opposite sides in common.
Given: AC = DC
4x - 3 = 2x + 9
4x - 2x - 3 = 2x - 2x + 9
simplifying the above equation, we get
2x - 3 = 9
2x - 3 + 3 = 9+3
2 x = 12
x = 6
Substitute the value of x in m ∠ ECA, then we get
m ∠ ECA = 15x + 2
= 15(6) + 2
m ∠ ECA = 92
EC is not an altitude of ΔAED because of m ∠ ECA = 92.
Therefore, EC is not an altitude of ΔAED.
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Anna is watching a space shuttle launch 6 miles from Cape Canaveral in Florida. When the angle of elevation from her viewing point to the shuttle is 80°C , how high is the shuttle, if it is going straight up?
The shuttle is 34.03 miles high.
In this question,
Anna is watching a space shuttle launch 6 miles from Cape Canaveral in Florida.
The angle of elevation from her viewing point to the shuttle is 80°
If the space shuttle is going straight up, we need to how high the shuttle is.
Let x be the unknown value.
Consider tangent of angle 80°
So, tan(80°) = x/6
⇒ x = 6 × tan(80°)
⇒ x = 6 × 5.6713
⇒ x = 34.03 miles
Therefore, the shuttle is 34.03 miles high.
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Write the equation of each line in slope-intercept form and identify the slope.
4 x+6 y=12
The equation of the line 4x + 6y = 12 expressed in slope-intercept form is y = -2/3 x + 2 with a slope equal to -2/3.
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The slope-intercept form of the equation of a line is given by the formula:
y = mx + b
where m is the slope of the line
b is the y- intercept
Given the equation of the line 4x + 6y = 12, which is in standard form, transform it into slope-intercept form by isolating the variable y in one side.
4x + 6y = 12
6y = -4x + 12
Dividing both sides by 6,
y = -4/6 x + 2
y = -2/3 x + 2
Hence, the equation of the line in slope-intercept form is y = -2/3 x + 2 where the slope, m, is equal to -2/3.
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Arianna takes $40 spending money out of her checking account every week. What is the change this causes in the number of dollars in her account after 5 weeks
.
.
A) $405
B) -$45
C) -$200
Answer:
C.)-200
Step-by-step explanation:
Each week if you take away $40 for 5 weeks, you would take away $220. -40*5=200.
3 base x +34 base x - 40 base x = 0
On solving for x, we get x = -1
What is base of a number?
A number base is the number of digits or combination of digits that a system of counting uses to represent numbers. Decimal system is the most commonly used number system with base 10.
Given is the following expression -
3 base x + 34 base x - 40 base x = 0
The given expression can be solved by converting the above expression in decimal form. Therefore -
3 base x in decimal = (3 x⁰) base 10 = 3
34 base x in decimal = (3 x¹ + 4 x⁰) base 10 = 3x + 4
40 base x = (4 x¹ + 0 x⁰) base 10 = 4x
Substituting the decimal values in the expression given -
3 + (3x + 4) + 4x = 0
7x + 7 = 0
7x = -7
x = - 1
Therefore, on solving for x, we get x = -1
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Solve each formula for the indicated variable. s = (1/2)gt² , for g
The solution of the given formula s = (1/2)gt² for the indicated variable g is g = 2s/t².
According to the given question.
We have a formula.
s = (1/2)gt²
Since, we have to solve this given formula s = (1/2)gt² for the variable g.
Which means we have to write separate variable g to one side from the other variables which are in the given formual s = (1/2)gt² .
Thereofre, the solution of the given formula for the variable g is given by
s = (1/2)gt²
⇒ 2s = gt² (multipling both the sides by 2)
⇒2s/t² = g (dividing both the sides by t²)
⇒ g = 2s/t²
Hence, the solution of the given formula s = (1/2)gt² for the indicated variable g is g = 2s/t².
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Evaluate each expression for x=5 .
3(x²-4) + 7(x - 2)
Answer:Substitute the value of the variable into the equation and simplify.
84
Step-by-step explanation:
Solve the problem. Show your work. Responses will be graded using the short-response scoring rubric given at the beginning of the lesson.
A passing boat is 310 feet from the base of a lighthouse. The angle of depression from the top of the lighthouse is 24°. What is the height of the lighthouse to the nearest tenth of a foot?
The height of the lighthouse to the nearest tenth of a foot is 137.8 feet.
This is a question of heights and distances.
It is given in the question that the passing boat is 310 feet from the base of a lighthouse. Also, the angle of depression from the top of the lighthouse is 24°.
We have to find the height of the lighthouse to the nearest tenth of a foot.
As you can see in the figure, using trigonometry we can write,
cot 24 = 310/Height of the lighthouse
Hence,
Height of the lighthouse = 310/cot 24
We know that,
cot 24 ≈ 2.25
Hence,
Height of the lighthouse = 310/2.25 ≈ 137.77778 ≈ 137.8 feet.
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Find the 32 nd term of each sequence. -9,-8.7,-8.4, ...........
The 32th term of the arithmetic sequence AP is estimated to be 0.3.
What is meant by arithmetic sequence AP?In math, an arithmetic progression (AP) is a list or sequence of numbers in which each term is obtained by adding a finite number to the term before it.
The fixed number is known as the arithmetic progression's common difference written by 'd'The common difference of AP is 'd': d = a2 - a1 = a3 - a2 = a4 - a3 =...... = a - an-1.nth term of an AP: an = a + (n - 1) dThe sum of n terms of an AP's is Sn = n/2(2a+(n-1)d) = n/2(a + l), where l is the final term of the AP.Now for the answer to the question;
The numbers in the given sequence are-
-9,-8.7,-8.4, ...........
There are 32 terms with in series for that we need to find the 32nd number.
Let's say the first term is 'a₁' = -9.
Let 'a₂' = -8.7 be the second term.
Let 'a₃' = -8.4 be the third term.
The common difference between two consecutive terms that are equal of an AP is 'd.'
d = a₂ - a₁
Substitute the values in the preceding equation; the 32nd term is
d = -8.7 - (-9)
d = -8.7 + 9
d = 0.3
Now calculated using the nth term formula.
nth term of an AP: an = a + (n - 1) dTotal number of terms is; n = 32First term is a = -9common difference d = 0.3Substitute all of the values in the formula now.
a₃₂ = a + (n - 1) d
a₃₂ = -9 + (32 - 1)(0.3)
a₃₂ = -9 + 9.6 - 0.3
a₃₂ = 0.3
As a result, the arithmetic sequence's 32nd term is estimated to be 0.3.
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HELP WITH INEQUALITY PROBLEM PLEASE!!!
Answer:
A. s+7726>=12,600
Step-by-step explanation:
s is the number of steps left to reach her goal of at least 12,600 steps.
7726 is the number of steps already taken.
12,600 is her goal.
s+7726>=12,600
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HELP ME WITH MY HOMEWORK!!!
The sum of -21.8 and a number is positive. Identify a possible value for that number. Explain your reasoning.
Answer:
21.9 is a possible value
Step-by-step explanation:
I just wrote the equation below have a very small but positive value on the right side and solved for x
x - 21.8 = 0.1
x = 21.9
limit x tends to 0 (x cot 2x)
Step-by-step explanation:
[tex] = \lim \limits_{x \to0}x \cot(2x) [/tex]
[tex] = \lim \limits_{x \to0} \frac{x}{ \tan(2x) } [/tex]
[tex] = \lim \limits_{x \to0} \frac{x}{ \tan(2x) } \times \frac{2x}{2x} [/tex]
[tex] = \lim \limits_{x \to0} \frac{2x}{ \tan(2x) } \times \lim \limits_{x \to0} \frac{x}{2x} [/tex]
[tex] = \lim \limits_{u \to0} \frac{u}{ \tan(u) } \times \frac{1}{2} [/tex]
[tex] = \frac{1}{2} [/tex]
On Monday, 222 students went on a trip to then zoo. All 4 buses were filled and 6 students had to travel in cars. Write an equation where x is the number of students on each bus. How many students were on the bus
Step-by-step explanation:
222-6=216
216÷4=54
so 54 students per bus
Answer:
54 students
Step-by-step explanation:
222 - 6 (students that had to travel in cars) = 216
216 / 4 (4 buses) = x
x = number of students on each bus
216 / 4 = 54
x = 54
54 students on each bus
216 students rode the bus, 6 students rode in cars
Bag with 4 marbles. Two red and two blue. Draw the balls one at a time, but before it comes out, try to predict the color. If correct, you get a dollar. If you play optimally, what is the expected value of the game?
The situation can be solved by determining the probability of the selecting a certain color marble.
Probability is the ratio of a favorable outcome x to the total number of outcomes n of an event. In the give case, if the prediction is correct, you get a dollar.
Probability=x/n
On the first draw, the chance that predicted color is drawn is:
Probability=2/4=1/2
Amount you may get is ½*1=1/2
On the second draw, the chance the color with two left balls is predicted and come out:
Probability=2/3
Amount you may get is 2/3*1=2/3
On the third draw, you predicted a color with no same color balls left:
Probability=1/3
Amount you may get is 1/3*1=1/3
Or you predicted a color with two different color balls left
Probability=2/3*1/2=2/6=1/3
Amount you may get is 1/3*1=1/3
On the fourth draw, the probability of correct predicted ball is 1
Amount you may get is 1=1
If you played the game optimally, summing up the amount=1/2+2/3+1/3+1/3+1=17/6≈2.88
Hence, by playing the game optimally, the expected value of the game is $2.88.
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Read the question. Then write the letter of the correct answer on your paper.For f(x)= 2x 3 find f(1/4) a. -3/2 b. -2 c. 2(1/2) d. -7/2
The value is 3/2 (a)
The given function is , f(x)= 2x 3 where x = value of this function .
Here , we will put the value 1/4 ( here x = 1/4 ) into the given function. if , f(1/4) = 2 . 1/4 . 3 = 3/2
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linda is twice the age of vera. tanya is 4 less than 4 times the age of linda. their total age is 2 more than nine times the age of vera. how old is tanya?
If linda is twice the age of vera. tanya is 4 less than 4 times the age of linda. their total age is 2 more than nine times the age of vera. tanya is 20 years old.
Total ageLet Vera's age be v
Let Linda's age be 2v
Let Tanya's age be 8v- 4
Let the total age be 9v + 2
Hence,
v + 2v + 8v- 4 = 9v + 2
11v - 4 = 9v + 2
Collect like terms
2v = 6
Divide both side by 2v
v=6/3
v = 3
So,
Tanya's age = 8v - 4
Tanya's age= 8(3) - 4
Tanya's age=24-4
Tanya's age = 20 years
Therefore if linda is twice the age of vera. tanya is 4 less than 4 times the age of linda. their total age is 2 more than nine times the age of vera. tanya is 20 years old.
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Which graph represents exponential decay?
Answer:
The graph of g(x) shows exponential decay, while the graph of f(x) shows exponential growth. What you need in your answer: The graphs are reflections of each other over the y-axis. The g(x) function represents exponential decay.
Graph f(x) = 46(0.75). What is the constant percent rate of change of f(x) with respect to x? Does the graph represent growth or decay?
O 75% growth
O 75% decay
O25% growth
O 25% decay
The constant percent rate of change of f(x) with respect to x is (d) 25% decay
What is the constant percent rate of change of f(x) with respect to x?The function is given as
f(x) = 46(0.75)^x
The above function is an exponential function
The growth/decay factor is
b = 0.75
The constant rate is then calculated as
Rate = 1 - b
This is because b is less than 1 (i.e. an exponential decay)
So, we have
Rate = 1 - 0.75
Evaluate
Rate = 25%
Hence, the constant percent rate of change of f(x) with respect to x is (d) 25% decay
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Answer: D
Hope this helps :)
The table shows the number and type of books that Sarah owns. Find the probability.
A randomly chosen title is a print or audio book.
Answer:
hi
Step-by-step explanation:
Answer:
FITNESS Laura wants to go to a fitness class
tomorrow. She can choose a 5:00 or a 7:30 class and
spin or water aerobics. Represent the sample space
for the situation by making an organized list, a table,
and a tree diagram.
Step-by-step explanation:
Does anyone can help me ? exercices 3 and 4
3) a) The domain of the rational function is x ≥ 1.
b) The domain of the rational function is all the real numbers except x = 3 and x = - 4.
4) a) The root of the rational function is 6.
b) The roots of the rational function are 4 and 1.
How to determine the domain and the roots of a rational function
Rational functions are algebraic expressions of the form P(x) / Q(x), where P(x) is the numerator and Q(x) is the denominator. 3) The domain of rational functions are the x-values that comprises P(x) except all values such that Q(x) = 0. Then, we proceed to find the domain of each function:
Case 1
The domain of P(x) = √(x - 1) is x ≥ 1 and the indetermination values of Q(x) = 2 · x is x = 0. Then, the domain of the rational function is x ≥ 1.
Case 2
The domain of P(x) = 3 is all the real numbers and the indetermination values of Q(x) = (x - 3) · (x + 4) are x = 3 and x = - 4. Then, the domain of the rational function is all the real numbers except x = 3 and x = - 4.
4) The roots of a function are all the values at which the function is evaluated such that is equal to zero.
Case 1
1 - 2 / (x - 4) = 0
[(x - 4) - 2] / (x - 4) = 0
x - 6 = 0
x = 6
The root of the rational function is 6.
Case 2
(x² - 5 · x + 4) / 5 = 0
x² - 5 · x + 4 = 0
(x - 4) · (x + 1) = 0
The roots of the rational function are 4 and 1.
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ASAP NEED>...............
