Answer:
[tex]a_n=27 \cdot (\frac{1}{3})^{n-1}[/tex].
Step-by-step explanation:
This is a geometric sequence that means there is a common ratio. That means there is a number you can multiply over and over to get the next term.
The first term is 27.
The second term is (1/3)(27)=9.
The third term is (1/3)(9)=3.
So the common ratio is 1/3.
That means you can keep multiplying by 1/3 to find the next term in the sequence.
The explicit form for a geometric sequence is [tex]a_n=a_1 \cdot r^{n-1}[/tex] where [tex]a_1[/tex] is the first term and [tex]r[/tex] is the common ratio.
We are given [tex]a_1=27[/tex] and [tex]r=\frac{1}{3}[/tex].
So the explicit form for the given sequence is [tex]a_n=27 \cdot (\frac{1}{3})^{n-1}[/tex].
Answer:
Its b on edge 2021
Step-by-step explanation:
just did it
which of these quadrilateral types must have congruent diagonals. a. rectangle, square, rhombus b.square, rhombus c.rectangle, square d.parallelogram, rectangle, square, rhombus
Rectangles and squares always have congruent diagonals due to their geometrical properties, making option c (rectangle, square) the correct answer.
The question asks which of the given sets of quadrilaterals must have congruent diagonals. The key to answering this question is understanding the properties of each kind of quadrilateral mentioned. Rectangles and squares always have congruent diagonals because their diagonals bisect each other and are of equal length due to the right angles at the corners of the shapes.
A rhombus, while having diagonals that bisect each other at right angles, does not necessarily have congruent diagonals because the angles between adjacent sides do not guarantee equal lengths of diagonals. As such, the correct answer is c.rectangle, square, where both of these shapes must have diagonals of equal length due to their geometrical properties.
How would you explain this ?
Answer:
Step-by-step explanation:
The first thing you have to do is look at the mother curve. That curve is y = 1/x
It becomes undefined at x = 0 (I will show both curves below).
That is not what has been given. The graph you have been given becomes undefined at x = - 1 , so the equation of the curve (so far) y = 1/(x + 1)
Now we have to worry about the y intercept. When x = 0, y = 4. That can be accomplished in two ways
A. y = 4/(x + 1) or
B. y = 2/(x + 1) + 2 or
C. y = 1/(x + 1) + 3
All three of these will give a value of y = 4 when x = 0. But you have 1 problem left. What happens as x goes to say 5.
The value of A will give y = 4/(5 + 1)=4/6 = 2/3. Which does not work.
The value of C will give y = 1/(5 + 1) + 3 which gives 3 1/5 which also does not work.
Only B works. y = 2/(5+1) + 2 = 2/6 + 2 = 2 1/3 which is a little above the horizontal asymptote.
Red: y = 1/x
Blue: y = 2/(x + 1) + 2
The value at the end is never going to change. y will always be just a bit
106 + (147x + 92)= what
Given
106 + (147x + 92)
Combine like terms
106 + 92 = 198
Simplify
147x + 198
Answer
147x + 198
106 + (147x + 92) = what
To solve this expression, you need to apply the distributive property, which states that a(b + c) = ab + ac.
Therefore, 106 + (147x + 92) = 106 + 147x + 92, which simplifies to 239 + 147x.
two perpendicular Lines intersect at the origin. If the slope of the First line is -1/2, What is the equation Of The second Line?
Answer: y=2x
Step-by-step explanation: A perpendicular line is the opposite reciprocal of the slope. The opposite reciprocal of -1/2 is 2.
The equation of the second line is y=2x
Two taps A and B can fill a cistern in 20 and 30 minif both are opend simultaneously how long will it take to fill the cistern
Answer:
it would take roughly 6 and a half minutes i think
If the length width and height of a cube all quadruple what happened to the volume of the cube
Answer:
if the length, width and height of a cube quadruple, then the volume of the cube will be multiplied by 64.
Step-by-step explanation:
Given a cube of width W, height H and length L, the volume of the cube will be: Volume = W*H*L
If all the three parameters quadruple, then:
New Width = 4W
New Height = 4H
New Length = 4L
New Volume = 4W*4H*4L = 64WHL
Therefore, if the length, width and height of a cube quadruple, then the volume of the cube will be multiplied by 64.
Answer:
Volume will be multiplied by 64.
Step-by-step explanation:
We are to find the effect of quadrupling the length, width and height of a cube on its volume.
Since the length, width and height of a cube are all of the same dimension, let us represent it was a variable [tex] S [/tex].
[tex] V o l u m e = S ^ 3 [/tex]
[tex]New Volume = (4S)^3 =64S^3[/tex]
Therefore, if the length width and height of a cube all are quadrupled, the volume will be 64 times.
How many months are in ¾ of a year
Answer:
9
Step-by-step explanation:
Answer:
9 months
Step-by-step explanation:
There are 12 months in a year
Multiply 12 months by 3/4
12 *3/4
36/4
9
There are 9 months in 3/4 of a year
what is the value of y
Answer:
A
Step-by-step explanation:
since you know the measure of the angle that isn't a is 50, because 180 - 130 = 50, and since the sum of all the angles in the triangle has to be 180, y = 130/2 which equals 65
Which can be the first step in finding the equation of the line that passes through the points 5,-4 and -1,8 in slope-intercept form?
The first step in finding the equation of the line would be to find the slope of the points.
The slope-intercept form of a line is given by:
[tex]\[ y = mx + b \][/tex]
where:
- [tex]\( m \)[/tex] is the slope of the line, and
- [tex]\( b \)[/tex] is the y-intercept.
To find the equation of the line that passes through the points (5, -4) and (-1, 8) in slope-intercept form, you need to follow these steps:
1. Find the slope [tex](\( m \))[/tex]:
The slope [tex](\( m \))[/tex] is given by the formula:
[tex]\[ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} \][/tex]
Pick two points, let's say (x1, y1) = (5, -4) and (x2, y2) = (-1, 8), and substitute them into the formula to find [tex]\( m \)[/tex].
[tex]\[ m = \frac{{8 - (-4)}}{{-1 - 5}} \][/tex]
Simplify the expression to find [tex]\( m \)[/tex].
2. Use the slope and one of the points to find the y-intercept [tex](\( b \))[/tex]:
Substitute the slope [tex](\( m \))[/tex] and one of the points (let's use (5, -4)) into the slope-intercept form equation and solve for [tex]\( b \)[/tex].
[tex]\[ -4 = m \cdot 5 + b \][/tex]
Substitute the value of [tex]\( m \)[/tex] that you found in step 1 and solve for [tex]\( b \)[/tex].
3. Write the equation in slope-intercept form:
Once you have the values of [tex]\( m \) and \( b \)[/tex], substitute them into the slope-intercept form equation.
[tex]\[ y = mx + b \][/tex]
Write the final equation.
By following these steps, you can find the equation of the line passing through the given points in slope-intercept form.
To find the equation of the line passing through (5,-4) and (-1,8), calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1), which results in a slope of -2.
Explanation:The first step in finding the equation of the line that passes through the points (5,-4) and (-1,8) in slope-intercept form is to calculate the slope (m) of the line. The slope of a line is determined by the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. In this case, we would use the following calculation:
Let Point 1 be (5, -4) and Point 2 be (-1, 8).The slope m = (8 - (-4)) / (-1 - 5)m = (8 + 4) / (-1 - 5)m = 12 / -6m = -2
With the slope, you can then use the point-slope form or directly the slope-intercept form (y = mx + b) to find the equation, using either of the two points to solve for b, the y-intercept.
simplify the following fraction (5/9x3/5)+6/7
Answer:
1 4/21
Step-by-step explanation:
(5/9*3/5)+6/7
The 5's cancel
(3/9)+6/7
Cancel a 3 in the numerator and a 3 in the denominator
1/3 + 6/7
We need to get a common denominator of 21
1/3 *7/7 + 6/7 *3/3
7/21 + 18/21
25/21
This is an improper fraction
21 goes into 25 1 time with 4 left over
1 4/21
Answer: [tex]\frac{25}{21}[/tex]
Step-by-step explanation:
The first step is to make the multiplication of the fractions inside the parentheses. To do this, you must multiply the numerator of the first fraction by de numerator of the second fraction and the denominator of the first fraction by the denominator of the second fraction:
[tex](\frac{5}{9}*\frac{3}{5})+\frac{6}{7}=\frac{15}{45}+\frac{6}{7}[/tex]
Now you can reduce the fraction [tex]\frac{15}{45}[/tex]:
[tex]=\frac{1}{3}+\frac{6}{7}[/tex]
And make the corresponding addition: in this case the Least Common Denominator (LCD) will be the multiplication of the denominators. Divide each denominator by the LCD and multiply this quotient by the corresponding numerator and then add the products. Therefore you get:
[tex]=\frac{7+18}{21}=\frac{25}{21}[/tex]
f(x)=3.7-2x
g(x) = 0.25x-5
What is f(x) + g(x)
A) h(x)=3.95x-7
B) h(x)=8.7-2.25x
C) h(x)=-1.3-1.75x
D) h(x)=3.95-7x
Answer:
C) h(x)=-1.3-1.75x
Step-by-step explanation:
f(x)=3.7-2x
g(x) = 0.25x-5
f(x) + g(x) =3.7-2x + 0.25x-5
Combine like terms
= -1.75x - 1.3
Answer:
The answer is C.) h(x)=-1.3-1.75x
Step-by-step explanation:
Suppose that there are two types of tickets to a show: advance and same-day. The combined cost of one advance ticket and one same-day ticket is $35. For
one performance, 35 advance tickets and 30 same-day tickets were sold. The total amount paid for the tickets was $1125. What was the price of each kind of
ticket?
Answer:
Advance=15$
Same-day=20$
Step-by-step explanation:
Advance=15 Same-day=20
15*35=525
20*30=600
525+600=1125
Which of the following is rational?
3•π
2/3 +9.26
45 + 36
14.3+5.78765239
Let's consider each of the options and evaluate whether the given number is rational or not. Remember, a rational number is any number that can be expressed as the quotient or fraction of two integers (where the denominator is not zero).
1. **3•π**: This number is not rational because π (pi) is an irrational number. An irrational number is a number that cannot be expressed as a simple fraction - its decimal goes on forever without repeating. When you multiply an irrational number by an integer (in this case 3), the result is still irrational.
2. **2/3 + 9.26**: To determine if this sum is rational, we can evaluate each addend. The fraction 2/3 is clearly rational, as it is already expressed as a quotient of two integers. The decimal 9.26 can be expressed as a fraction because it is a terminating decimal; in fraction form, it is \( \frac{926}{100} \) which simplifies to \( \frac{463}{50} \) when reduced to lowest terms. The sum of two rational numbers is also rational (since both can be written as fractions, and the sum of two fractions is a fraction), so this number is indeed rational.
3. **45 + 36**: Both 45 and 36 are integers and the sum of two integers is also an integer. Integers are a subset of rational numbers, because they can be expressed as a fraction with a denominator of 1 (e.g., \( \frac{45}{1} + \frac{36}{1} \)). Thus, this number is rational.
4. **14.3 + 5.78765239**: The number 14.3 is a terminating decimal and can be represented as a fraction (\( \frac{143}{10} \)). However, 5.78765239 is given without any indication that it is a repeating or terminating decimal. If it is a non-repeating and non-terminating decimal, then it cannot be expressed as a fraction and would be considered irrational. Without further information, we cannot determine if this number is rational or not. Therefore, we can neither confirm nor deny that the sum is rational.
Given these considerations, the rational option from the given choices is **45 + 36**.
A certain ferry moves up and down a river between Town A and B. It takes the ferry two hours to travel to Town A and only an hour and thirty minutes to return to Town B. If the current is 5mph how far apart are the two cities?
Answer:
the Answer is 60 miles.
Step-by-step explanation:
The current of the river is towards city B; hence, the reason the ferry moves faster from town A to B than when coming back from town B to A. The distance between both towns is 60m.
Let
[tex]s \to[/tex] speed in still water
[tex]d \to[/tex] distance between both cities
The given parameters are:
[tex]t_{AB} =2[/tex] -- from A to B
[tex]t_{BA} =1.5[/tex] -- from B to A
[tex]s_c = 5mph[/tex] -- speed of the current
Speed is calculated as:
[tex]Speed = \frac{Distance}{Time}[/tex]
The speed (s) from town A to town B is:
[tex]s = s_c + \frac{d}{t_{AB}}[/tex] --- i.e. speed of the current + speed in still water from A to B
[tex]s = 5 + \frac{d}{2}[/tex]
Multiply through by 2
[tex]2s = 10 + d[/tex]
Make d the subject
[tex]d = 2s - 10[/tex]
The speed (s) from town B to town Ais:
[tex]s = -s_c + \frac{d}{t_{BA}}[/tex] --- i.e speed in still water from B to A - . speed of the current
[tex]s = -5 + \frac{d}{1.5}[/tex]
Multiply through by 1.5
[tex]1.5s = -7.5 + d[/tex]
Make d the subject
[tex]d = 1.5s + 7.5[/tex]
So, we have:
[tex]d = 1.5s + 7.5[/tex] and [tex]d = 2s - 10[/tex]
Equate both values of d
[tex]2s - 10 = 1.5s + 7.5[/tex]
Collect like terms
[tex]2s - 1.5s= 10 + 7.5[/tex]
[tex]0.5s= 17.5[/tex]
Divide both sides by 0.5
[tex]s = 35[/tex]
Substitute [tex]s = 35[/tex] in [tex]d = 1.5s + 7.5[/tex] to calculate distance (d)
[tex]d =1.5 *35 + 7.5[/tex]
[tex]d =52.5 + 7.5[/tex]
[tex]d =60[/tex]
The distance between town A and B is 60m.
Read more about speed at
https://brainly.com/question/14750228
A patient received 84 mL per hour of normal saline solution. How many liters did the patient receive in 24-hour period?
Answer:
2.106 liters
Step-by-step explanation:
24 * 84 mL = 2016 mL = 2.106 L
Answer: 84*24=2016
You multiply 84 by 24 to get 2016.
!!PLEASE HELP I WILL MARK YOU BRAINLIEST!!!
In this unit you have learned about several different ways to solve quadratic equations. How do you determine which method to use when you’re trying to solve a quadratic equation?
Answer:
You will use this formula x= -b +
[tex] x = - b + \sqrt{ { \: - 4ac}^{?} } [/tex]
Step-by-step explanation:
4n
[tex] {?}^{?} [/tex]
so you want to do n to the second power minus and minus 39 equals 0 so you using the quadratic formula
-4(w+2)+6w=
Can someone ease help me with this
Answer:
2w -8
Step-by-step explanation:
-4(w+2)+6w
Distribute the -4
-4w -8 +6w
Combine like terms
-4w +6w -8
2w -8
Answer:
Step-by-step explanation:
-4w-8+6w=0
8+2w=0
2w= -8
w= -4
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Write a real-world problem in which you would solve the equation a+12=30.
Answer:
Brian has 12 apples. How many more apples does he need to have 30 apples in all?
Step-by-step explanation:
In this case "a" is the number of apples he needs to have 30 in all, and adding that to 12 results in the equation a + 12 = 30.
Hope this helps!
Complete the solution of the equation. Find
the value of y when x equals -2.
-9x - 3y = 6
Answer:
y=4
Step-by-step explanation:
-9x - 3y = 6
Let x =-2
-9(-2) -3y =6
18 -3y =6
Subtract 18 from each side
18-18-3y = 6-18
-3y = -12
Divide each side by -3
-3y/-3 =-12/-3
y=4
Segment XY is dilated through point M with a scale factor of 2. Which segment shows the correct result of the dilation?
1. AE
2. BF
3. CG
4. DH
Answer:
4.DH
Step-by-step explanation:
let's assume the point P to be the point that X will be after it is dilated.
we know that after dilation the length of PM should be two two times the length of XY
PM = 2.XY ===>[tex]\frac{PM}{XY}[/tex] = 2
and from proportionality theorem we now that:
[tex]\frac{PM}{XY}[/tex] = [tex]\frac{MX}{MP}[/tex] = 2
So we know XY should be half the size of MP and we can see the only line matching is DH thus the answer is DH
Which sequence is modeled by the graph below?
coordinate plane showing the points 1, 6; 2, 0.6; and 3, 0.06
Answer:
[tex]\large\boxed{a_n=6\left(\dfrac{1}{10}\right)^{n-1}}[/tex]
Step-by-step explanation:
Check:
[tex]n=1\\\\a_1=6\left(\dfrac{1}{10}\right)^{1-1}=6\left(\dfrac{1}{10}\right)^0=6(1)=6\qquad\bold{CORRECT}\ (1,\ 6)\\\\n=2\\\\a_2=6\left(\dfrac{1}{10}\right)^{2-1}=6\left(\dfrac{1}{10}\right)^1=6\left(\dfrac{1}{10}\right)=\dfrac{6}{10}=0.6\qquad\bold{CORRECT}\ (2,\ 0.6)\\\\n=3\\\\a_3=6\left(\dfrac{1}{10}\right)^{3-1}=6\left(\dfrac{1}{10}\right)^2=6\left(\dfrac{1}{100}\right)=\dfrac{6}{100}=0.06\qquad\bold{CORRECT}\ (3,\ 0.06)[/tex]
Answer:
[tex]a_n=6\left(\frac{1}{10}\right)^{n-1}[/tex]
Option 3 is correct
Step-by-step explanation:
The coordinates are (1,6) (2,0.6) and (3,0.06)
If we make table of given coordinate:
x : 1 2 3
y : 6 0.6 0.06
[tex]a_1=6,a_2=0.6,a_3=0.06[/tex]
Ratio of the sequence:
[tex]r=\dfrac{a_2}{a_1}=\dfrac{0.6}{6}=0.1[/tex]
Formula of geometric sequence:
[tex]a_n=ar^{n-1}[/tex]
[tex]a_n=6\cdot 0.1^{n-1}[/tex]
[tex]a_n=6\left(\frac{1}{10}\right)^{n-1}[/tex]
Hence, The sequence model by [tex]a_n=6\left(\frac{1}{10}\right)^{n-1}[/tex]
Find the least positive angle measurement that is coterminal with –100°.
Answer:
260 degrees is coterminal with -100 degrees.
Step-by-step explanation:
So a full rotation about a circle is 360 degrees.
So if we do 360+(-100) we get 260.
They will share the same terminal ray because if we go 100 clockwise from the initial ray that will be an angle coming counterclockwise 260 from the initial ray.
100+260=360.
Answer:
260°
Step-by-step explanation:
Co terminal angles are angle ± 360°n where n = 0, 1, 2, 3, ....
The least positive = - 100° + 360° = 260°
#11 Mrs Owen ordered 500 chicken wings to be shared equally among 250 guests invited to her wedding anniversary party. However the turnout was less than expected and every guest ate one more chicken wing than originally planned. If there were 92 chicken wings left after the party, how many people attended Mrs. Owen’s party?
#12 The total number of cherries on a plate, in a cup and in a bowl is 780. The plate contains 145 cherries. The number of cherries in the bowl is 4 times the total number of cherries on the plate and in the cup. How many cherries are in the cup?
Answer:
11: 136 people
12: 55 Cherries
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Conner's work is correct. To combine and make it simple, you Multiply:
(3^5+9)+(6^8+10) which will equal 3^14 6^18.
But Jane's work, instead of adding, Jane multiplies. So, Conner is correct.
Hope that helped!
What is the maximum of f(x) = sin(x)?
Answer:
Sinx= 1(maximum value)
Step-by-step explanation:
Answer:
The maximum is 1
Step-by-step explanation:
-1<_sin(x)<_1
Range of sin(x)= [-1,1]
sin(x)= 1
Evaluate 2g – 4, if the value of g = 5.
Answer:
6
Step-by-step explanation:
imputing 5 into g which makes the equation: 2(5) - 4
2(5) - 4
10 - 4
6
Answer:
6
Step-by-step explanation:
2(5)-4
2*5 is 10
10 subtracted by 4 is 6
Hope this helps ^-^
Cathy uses 3/4 teaspoon of vanilla in a batch of cookies. How many teaspoons are needed for 8 batches of cookies
A single card is drawn from a deck of 52 cards, find the following
probabilities:
a. result is a queen
b. result is a queen result is a face card
c. result is a heart
d. result is a heart | result is a red card
e. result is a heart result is a black card
f. result is a heart result is not a diamond
Answer:
a. 1/13
b. 1/78
c. 1/4
d. 1/12
e. 1/6
f. 1/4
Step-by-step explanation:
First, lets write some basic data
There are total 52 cards.26 cards are red and 26 cards are blackOut of 26 red cards; 13 cards are of diamond and 13 cards are of heartOut of 26 black cards; 13 cards are of spade and 13 cards are of clubsIn spade, clubs, heart and diamond there is one card of ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, King, Queen, Jacka. result is a queen
Each set has one queen; 1 of spade, 1 of clubs, 1 of heart, 1 of heart
There are total 4 queens
Total number of cards is 52
Probability = Number of favourable outcomes/total number of outcomes
Probability = 4/52
Probability = 1/13
b. result is a queen result is a face card
From my understanding, this question is result is a queen given that result is a face card.
Queen: 4 cards
Face card means King, Queen and Jack
Each set has one King, one Queen and one Jack
There are total 4 sets
Therefore, there are 4 Kings, 4 Queens and 4 Jacks
Face cards: 12-4 (because 4 queens have already been taken out) = 8
Total number of cards: 52-4 (because 4 queens have already been taken out) = 48
Probability (A|B) = P(A) * P(A|B)
P(A) = result is a queen = 4/52 = 1/13
P(A|B) = result is a face card = 8/48 = 1/6
Probability (A|B) = P(A) * P(A|B)
Probability (A|B) = 1/13 * 1/6
Probability (A|B) = 1/78 or 0.01282
c. result is a heart
Out of the 52 cards, there are 26 red cards and out of the 26 red cards, there are 13 cards of heart
Heart = 13 cards
Total number of cards = 52 cards
Probability = Number of favourable outcomes/total number of outcomes
Probability = 13/52
Probability = 1/4
d. result is a heart | result is a red card
Result is a heart = P(A) = 13/52 = 1/4
Result is a red card=26/52 Total number of red cards is 26 but 13 cards (heart) are already taken out so 13 will be subtracted from the numerator and denominator
= 13/39 = 1/3
Result is a heart given that result is a red card P(A|B) = 1/3
Probability (A|B) = P(A) * P(A|B)
Probability (A|B) = 1/4 * 1/3
Probability (A|B) = 1/12
e. result is a heart result is a black card
Result is a heart = P(A) = 13/52 = 1/4
Result is a black card=26/52 Total number of cards is 52 but 13 cards (heart) are already taken out so 13 will be subtracted from the denominator
= 26/39 = 2/3
Result is a heart given that result is a black card P(A|B) = 2/3
Probability (A|B) = P(A) * P(A|B)
Probability (A|B) = 1/4 * 2/3 = 1/6
f. result is a heart result is not a diamond
Result is a heart = P(A) = 13/52 = 1/4
Result is not a diamond = there are 13 diamonds in a deck so cards that are not diamond are 52-13 = 39
Total cards = 52 - 13 (because hearts are already taken out) = 39
= 39/39 = 1
Probability (A|B) = P(A) * P(A|B)
Probability (A|B) = 1/4 * 1 = 1/4
!!
The probabilities of the given result in each subpart for deck of 52 cards can be given as following:
a. 1/13
b. 1/3
c. 1/4
d. 1/2
e. 0
f. 1/3
Following are the basics points need to know to solve this question:
There are total 52 cards.26 cards are red and 26 cards are black.Out of 26 red cards; 13 cards are of diamond and 13 cards are of heart.Out of 26 black cards; 13 cards are of spade and 13 cards are of clubs.In spade, clubs, heart and diamond there is one card of ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, King, Queen, Jack.a. Probability that the result is a queen
There are 4 queens in a standard deck of 52 cards. So the probability:
[tex]P(Queen) = \frac{ Number \ of \ Queens }{Total \ Cards} = \frac{4}{52} = \frac{1}{13}[/tex]
b. Probability that the result is a queen given the result is a face card
There are 12 face cards in a deck (3 face cards each for 4 suits: Jack, Queen, King). So, conditional probability:
[tex]P(Queen | Face Card) = \frac{ Number \ of \ Queens }{Total \ Face \ Cards} = \frac{4}{12} = \frac{1}{3}[/tex]
c. Probability that the result is a heart
There are 13 hearts in a deck. So the probability:
[tex]P(Heart) = \frac{ Number \ of \ Hearts }{Total \ Cards} = \frac{13}{52} = \frac{1}{4}[/tex]
d. Probability that the result is a heart given the result is a red card
Red cards consist of hearts and diamonds. There are 26 red cards, and half of them are hearts. So, conditional probability:
[tex]P(Heart | Red \ Card) = \frac{ Number \ of \ Hearts }{Number \ of \ Red \ Hearts} = \frac{13}{26} = \frac{1}{2}[/tex]
e. Probability that the result is a heart given the result is a black card
Black cards consist of spades and clubs. There are no hearts in black cards. So:
[tex]P(Heart | Black \ Card) = 0[/tex]
f. Probability that the result is a heart given the result is not a diamond
If the card drawn is not a diamond, it must be either a heart, club, or spade. There are 39 such cards. So:
[tex]P(Heart |Not \ a \ Diamond) = \frac{ Number \ of \ Hearts }{Number \ of \ Non-Diamond \ Cards} = \frac{13}{39} = \frac{1}{3}[/tex]
two less than a number divided by four
Answer:
=x/4 - 2 (the third choice.
Step-by-step explanation:
Letting the number be x, the phrase two less than a number divided by four is expressed using the following steps:
We first take the the number x then divide by four then subtract 2.
The expression becomes:
(x/4) - 2
To solve an algebraic expression such as the one you described – "two less than a number divided by four" – you can follow these steps:
1. Start by identifying the variable, which is typically represented by "x." In this case, "a number" will be our variable "x."
2. The phrase "two less than" indicates a subtraction of two from a certain value. In algebraic terms, "two less than x" would be written as "x - 2."
3. Finally, the phrase "divided by four" tells us to take our result from step 2 and divide it by 4. So, we place the expression "(x - 2)" over 4, indicating division.
Putting it all together, the algebraic expression that represents the phrase "two less than a number divided by four" is:
(x - 2) / 4
To evaluate this expression for a particular value of x, you would substitute the value of x into the expression and then perform the calculation.
For example, if x is 10, you would evaluate the expression as:
(10 - 2) / 4
= 8 / 4
= 2
So, when x is 10, the value of the expression "two less than a number divided by four" is 2.
please help meeeeeeeee!
The velocity v at time t of an object travelling in a straight line is given by v = t - 3. Determine the distance it travels from t = 0 and t = 4.
Answer:
5
Step-by-step explanation:
To solve with calculus, distance is the integral of speed:
d = ∫ |v| dt
d = ∫₀⁴ |t − 3| dt
d = -∫₀³ (t − 3) dt + ∫₃⁴ (t − 3) dt
d = ∫₀³ (3 − t) dt + ∫₃⁴ (t − 3) dt
d = (3t − ½ t²) |₀³ + (½ t² − 3t) |₃⁴
d = [ (9 − 9/2 ) − (0 − 0) ] + [ (8 − 12) − (9/2 − 9) ]
d = 9/2 + 1/2
d = 5
You can also find this geometrically. Graph y = |x − 3|, then find the area under the curve. You will find it's the area of two triangles.
d = ½ (3)(3) + ½ (1)(1)
d = 5
It's important to note that distance is not the same thing as displacement. Displacement is the difference between where you start and where you stop. Distance is length of the path you take.