Using distributive property, the equivalent expression is 45 - 16x
What is the equivalent expression?To find the equivalent expression of 13 - 8(2x - 4), we need to simplify the expression using the distributive property and then combine like terms.
First, we distribute the -8 to the terms inside the parentheses:
13 - 8(2x - 4) = 13 - 16x + 32
Next, we combine the constant terms:
13 - 16x + 32 = 45 - 16x
Therefore, the equivalent expression of 13 - 8(2x - 4) is 45 - 16x.
Overall, finding the equivalent expression of an algebraic expression can help simplify calculations and make solving equations easier.
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During a single day at the radio station WMZH, the probability that a particular song is played is 1/6. What is the probability that this song will be played on exactly 6 days out of 7 days? Round your answer to the nearest thousandth.
Around 0.000125 or 0.0125% of the time, the song will be played exactly six out of seven days.
Every day represents a trial in this binomial probability issue, and there are only two potential results:
either the music is played (a success), or it is not (failure). We're looking for the likelihood that exactly 6 out of 7 trials will be successful.
The likelihood of success (performing the song) is 1/6, while the likelihood of failure (not playing the song) is 1 - 1/6 = 5/6, on any given day.
We can use the binomial probability formula to find the probability of exactly 6 successes in 7 trials:
P(6 successes) = (7 choose 6) * (1/6)⁶ * (5/6)¹
where (7 choose 6) is the number of ways to choose 6 days out of 7 to play the song, and is calculated as:
(7 choose 6) = 7! / (6! * 1!) = 7
Plugging in the values, we get:
P(6 successes) = 7 * (1/6)⁶ * (5/6)¹
P(6 successes) ≈0.00012502
Therefore, the probability that the song will be played on exactly 6 days out of 7 is approximately 0.000125 or 0.0125%.
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given Q= 100K^0.5 L^0.5 w=50 r=40 show how to determine the amount of labor and capital that the firm should use in order to minimize the cost of producing 1,118 units of output. what is the minimum cost?
In this exercise we have to use the knowledge of function to write the minimum production cost, so we have to:
\(K=13.975\)
Thus writing the function that corresponds to this will be:
\(MPK = Q'(K) = 50L^{0.5}/K^{0.5} = 25\\MPL = Q'(L) = 50K^{0.5}/L^{0.5} = 100\)
Now calculating the minimum production cost we have:
\(MPK/r = MPL/w\\MPK/40 = 100/50\\MPK =80\\MPK = 50L^{0.5}/K^{0.5} = 80\\K=(1.118/80)= 13.975\)
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Find the measure of angle x in the figure below: A triangle is shown. At the top vertex of the triangle is a horizontal line aligned to the base of the triangle. The angle formed between the horizontal line and the left edge of the triangle is shown as 56 degrees, the angle formed between the horizontal line and the right edge of the triangle is shown as 51 degrees. The angle at the top vertex of the triangle is labeled as y, and the interior angle on the right is labeled as 72 degrees. The interior angle on the left is labeled as x.
Answer:
\(x=35^\circ\)
Step-by-step explanation:
From the diagram which I have drawn and attached below:
\(56^\circ+y+51^\circ=180^\circ$ (Sum of Angles on a Straight Line)\\y=180^\circ-(56^\circ+51^\circ)\\y=73^\circ\)
Next, in the triangle, the sum of the three interior angles:
\(y+x+72^\circ=180^\circ\\$Since y=73^\circ\\73^\circ+x+72^\circ=180^\circ\\x=180^\circ-(73^\circ+72^\circ)\\x=35^\circ\)
The value of angle x is 35 degrees.
Which statement about both quadrilaterals is true?
Answer:
the second statement: The corresponding angles of quadrilaterals ABCD and A'B'C'D' are congruent.
What is the probability of rolling a six on a fair die?
Answer: 1/6
Step-by-step explanation: To find the probability of rolling a six,
let's use our ratio for the probability of an event.
number of favorable outcomes / total number of outcomes
Since only one side of a die has a six on on it, the number of favorable
outcomes for rolling a six is 1 and since there are six sides to a die and it's
equally likely that the die will landy on any of these sides, the total number
of outcomes is 6.
So the probability of rolling a six is 1/6.
What is the shortest distance Jill can travel is she leaves her house, goes to City Hall, to the Post Office, and then returns home?
A. 9 miles
B. 16 miles
C. 38 miles
D. 48 miles
Can you post an image of the map?
Answer:
i believe that the answer is 38 please trust me
Amanda went to the Farmer’s market with her family. She had $5.00 to spend and decided she wanted to spend it on peaches. Each peach cost 68 cents. How many peaches could she buy ?
Army
2. A group of armed forces personnel were surveyed. The branch of service was recorded in the chart below.
Branch of Service Number of Members
165
Navy
135
Marine Corps
60
Air Force
130
Coast Guard
10
What would the degree measure for the sector for the Navy be in a circle graph?
43.20
97.20
93.60
118.80
Answer:
97.2°
Step-by-step explanation:
yw
The degree measure for the sector for the Navy be in a circle graph is 118.80.
What is angle of a sector ?"The angle of the sector is 360°, area of the sector, i.e. the Whole circle = πr2. When the Angle is 1°, area of sector = πr2/360° So, when the angle is θ, area of sector, OPAQ, is defined as; A = (θ/360°) × πr2."
Given here,
Navy = 165 members
Total members = 495
So, navy percentage in the circle is \(\165*495/ 100 = 27.27\)
And, angle of the sector of Navy is = \(27.27*360/100\) = 118.80
Hence, option D is correct.
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Erica solved the equation −5x − 25 = 78; her work is shown below. Identify the error and where it was made. −5x − 25 = 78
Step 1: −5x − 25 − 25 = 78 − 25
Step 2: −5x = 53
Step 3: negative five times x over negative five = fifty-three over negative five Step 4: x = negative fifty-three over five
(A.) Step 1: She should have added 25 to each side.
(B.)Step 1: She should have divided both sides by −5.
(C.)Step 3: She should have divided both sides by −5.
(D.)Step 3: She should have multiplied both sides by −5.
Answer:
A
Step-by-step explanation:
She should have added 25 to each side in order to cancel it out.
Answer:
A
Step-by-step explanation:
she should have added 25 to both
A puzzle has 1080 pieces. How many pieces are 80% of the puzzle?
Answer:
864
Step-by-step explanation:
80/100 simplified is 4/5
so you do 4/5 of 1080
which is 1080 divided by 5 that is 216
and then 216 x 4 which is 864
Complete the table. Answer should be T or F.
P Q
T F P V Q P ^ Q P -> Q -P -Q -P V -Q -P -> Q -P -> -Q P <-> Q
F T P V Q P ^ Q P -> Q -P -Q -P V -Q -P -> Q -P -> -Q P <-> Q
P Q P V Q P ^ Q P -> Q -P -Q -P V -Q -P -> Q -P -> -Q P <-> Q
T T T T T F F F F F T T
F T T F F T T T T T F F
P F T F F T T T T T F F
-P T T F F T T T T T F F
-Q T T T T F T F F F T T
-P V -Q T T F F T T T T T F
-P -> Q T T F F T T T T T F
-P -> -Q T T F F T T T T T F
P <-> Q T T T T F T T T T F
Here is a more detailed explanation of how I filled out the table:
P | Q : This column is simply the truth value of P and Q. If P and Q are both true, then the entry in this column is T. If P is true and Q is false, then the entry in this column is F. If P is false and Q is true, then the entry in this column is F. And if P and Q are both false, then the entry in this column is T.
P V Q : This column is the truth value of P or Q. If P is true, then the entry in this column is T. If Q is true, then the entry in this column is T. And if P and Q are both false, then the entry in this column is F.
P ^ Q : This column is the truth value of P and Q. If P and Q are both true, then the entry in this column is T. And if P and Q are both false, then the entry in this column is F.
P -> Q : This column is the truth value of P implies Q. If P is true and Q is false, then the entry in this column is F. And if P is false or Q is true, then the entry in this column is T.
-P : This column is the negation of P. If P is true, then the entry in this column is F. And if P is false, then the entry in this column is T.
-Q : This column is the negation of Q. If Q is true, then the entry in this column is F. And if Q is false, then the entry in this column is T.
-P V -Q : This column is the truth value of not P or not Q. If P and Q are both true, then the entry in this column is F. If P and Q are both false, then the entry in this column is T. And if P or Q is true, then the entry in this column is T.
-P -> Q : This column is the truth value of not P implies Q. If P is true and Q is false, then the entry in this column is T. And if P is false or Q is true, then the entry in this column is F.
-P -> -Q : This column is the truth value of not P implies not Q. If P and Q are both true, then the entry in this column is T. If P is false or Q is false, then the entry in this column is T. And if P is true and Q is true, then the entry in this column is F.
P <-> Q : This column is the truth value of P if and only if Q. If P and Q are both true or P and Q are both false, then the entry in this column is T. And if P and Q have different truth values, then the entry in this column is F.
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In circle O, secants ADB and AEC are drawn from external point A
such that points D, B, E, and C are on circle O. If AD = 8, AE = 6,
and EC is 12 more than BD, the length of BD is
(1) 6
(2) 22
(3) 36
(4) 48
The length of BD is 22.
In the given scenario, let's consider the following information.
AD = 8
AE = 6
EC is 12 more than BD.
To find the length of BD, we can utilize the Intercepted Arcs Theorem, which states that when two secants intersect outside a circle, the measure of an intercepted arc formed by those secants is equal to half the difference of the measures of the intercepted angles.
From the given information, we know that AD = 8 and AE = 6.
Since these are the lengths of the secants, we can use them to calculate the intercepted arcs.
First, let's find the intercepted arc corresponding to AD:
Intercepted Arc ADB = 2 \(\times\) AD = 2 \(\times\) 8 = 16
Similarly, we can find the intercepted arc corresponding to AE:
Intercepted Arc AEC = 2 \(\times\) AE = 2 \(\times\) 6 = 12
Now, we know that EC is 12 more than BD.
Let's assume the length of BD as x.
BD + 12 = EC
Now, let's consider the intercepted arcs theorem:
Intercepted Arc ADB - Intercepted Arc AEC = Intercepted Angle B - Intercepted Angle C
16 - 12 = Angle B - Angle C
4 = Angle B - Angle C.
Since Angle B and Angle C are vertical angles, they are congruent:
Angle B = Angle C.
Therefore, we can say:
4 = Angle B - Angle B
4 = 0
However, we have reached an inconsistency here.
The equation does not hold true, indicating that the given information is not consistent or there may be an error in the problem statement.
As a result, we cannot determine the length of BD based on the given information.
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FASTEST GETS MOST POINTS
a tuxedo rental service charges $150 flat fee for a suit plus $50 per additinal day. The total cost of the tuxedo is $300. How many days was the tuxedo rental for?
The tuxedo was rented for 4 days.
Let's start by assigning variables to the unknowns. Let "x" be the number of additional days rented, and "d" be the total number of days rented (including the first day).
From the given information, we know that the flat fee for the rental is $150, so the cost of the additional days is the total cost minus the flat fee, which is $300 - $150 = $150. We also know that the cost for each additional day is $50. Therefore, we can set up the equation:
$150 + $50x = $300
Subtracting $150 from both sides, we get:
$50x = $150
Dividing both sides by $50, we get:
x = 3
So the tuxedo was rented for 3 additional days, making the total number of days rented:
d = 1 + 3 = 4
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Jackie has a box of mixed spring flower bulbs
containing 12 daffodils, 10 hyacinths, and 14
tulips. Jackie reaches into the box, randomly
chooses a bulb, plants it, then chooses
another, and plants it. What is the probability
that the first bulb Jackie plants is a daffodil
and the second is a hyacinth?
The probability that the first plant is daffodil and the second plant is hyacinth is 2/21
Let the number of flowers be denoted as ,
Number of daffodils, D = 12
Number of hyacinths, H = 10
Number of tulips, T = 14
Total number of flowers = 12 + 10 + 14 = 36
The probability is given as = (Number of favorable outcomes)/(Total number of outcomes)
Thus, the probability of planting daffodils, P(D) = 12/36 = 1/3
The probability of planting hyacinth, P(H) = 10/35 = 2/7
We have to find the probability that the first plant was daffodils and the second was hyacinth, that is,
Probability = P(D) * P(H)
= 1/3 * 2/7
= 2/21
Hence the probability that the first plant is daffodil and the second plant is hyacinth is 2/21
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O.5% as a fraction and decimal
Answer: As a fraction: 1/2
As a decimal: 0.005
Step-by-step explanation:
FRACTION:
To figure out how to write 0.5% as a fraction, all you need to know is that 0.5 = to a half, or 1/2 because 0.5 is half of 1.
DECIMAL:
0.5% as a decimal form is 0.005 because it is 1000 times less than 1, so you move the 0 3 times right.
Angie bought 312 pounds of apples to make a pie. There are 16 ounces in one pound. How many ounces of apples did she buy?
please help me thank you so much
Answer:
1)
7+9-15 = add 7 and 9, then subtract 15
2)
15-(7+9) = The sum of 7 and 9 subtracted from 15
3)
15-(7+9) = subtract 7 from 15, then add 9
Step-by-step explanation:
Learn BODMAS. The order of how to do equations. A simple tutorial on yt should be sufficient
-
CDEF maps to JKLM with the transformations (x,y) → (8x, 8y) → (x - 4, y - 4). What is
the value of EF/LM? Use fractions for your answer if necessary.
The ratio of the sides EF/LM after the transformation is 1/8
Transformation
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.
Dilation is the increase or decrease in size of a figure by a factor while translation is the movement of a point up, down, left or right.
Given the tansformation:
(x,y) → (8x, 8y) → (x - 4, y - 4). This means a dilation of CDEF by 8 and translated 4 units down and 4 units left.Hence:
LM = 8 * EF
EF/LM = 1/8
The ratio of the sides EF/LM after the transformation is 1/8
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5x^2 - 6x - 28 = 0
please help me do this
Answer:
x= 3 5 + 1 5 √149 or x= 3 5 + −1 5 √149
20 points for this question
Answer:
107
Step-by-step explanation:
3, 7, 11, 15, 19,
23, 27, 31, 35,
39, 43, 47, 51,
55, 59, 63, 67,
71, 75, 79, 83,
87, 91, 95, 99,
103, 107
32nd term is 107
Solve for x. Round to the nearest tenth, if necessary
Using the tangent ratio, the value of x in the right triangle shown is calculated to the nearest tenth as: 2.6 units.
How to Find the Value of x Using the Tangent Ratio?The tangent ratio is part of the trigonometry ratios that is applied when solving a right triangle, and it is expressed as:
tan ∅ = length of the opposite side / length of the adjacent side.
We are given the following information from the image above:
Reference angle (∅) = 43 degrees
length of the opposite side = x
length of the adjacent side = 2.8
Plug in the values:
tan 43 = x/2.8
2.8 * tan 43 = x
x = 2.6 [to the nearest tenth]
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Mrs. Helms's class can be divided into equal groups of 5 students or groups of 6
students. Which of the following is a possible size of her class?
Answer:
30
Step-by-step explanation:
5 times 6 equals 30
The common ratio in a geometric series is 4 44 and the first term is 3 33. Find the sum of the first 8 88 terms in the series.
The sum of the first 8 terms in the given geometric series is 65,535.
A geometric series is a sequence of numbers in which each term after the first is obtained by multiplying the previous term by a fixed non-zero constant called the common ratio.
In this case, the common ratio is 4, and the first term is 3. So, the first 8 terms of the series are:
3, 12, 48, 192, 768, 3072, 12288, 49152
To find the sum of the first 8 terms, we can use the formula for the sum of a finite geometric series:
S = a(1 - r^n) / (1 - r)
where S is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.
Plugging in the given values, we get:
S = 3(1 - 4^8) / (1 - 4)
Simplifying the expression, we get:
S = 65,535
Therefore, the sum of the first 8 terms in the given geometric series is 65,535.
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--The question is incomplete, answering to the question below--
"The common ratio in a geometric series is 4 and the first term is 3. Find the sum of the first 8 terms in the series."
the sum of four number is 20500.three of the numbers are 2341.578 and 10690.What is the fourth number?
Answer:
5216.844
Step-by-step explanation:
Let x be the fourth number.
We know that the sum of the four numbers is 20500:
2341.578 + 10690 + x + 2341.578 = 20500
Simplifying and solving for x:
x = 20500 - 2341.578 - 10690 - 2341.578
x = 5216.844
please help!
find the value of x
Answer:
24°
Step-by-step explanation:
\(180 - (94 + 41) = 45\)
\(180 - (111 + 45) = 24\)
Write an algebraic expression for
the verbal expression:
"5 times the sum of a squared and
b minus 3 times the sum of
a and b".
Answer:
"5 times the sum of a squared and b minus 3 times the sum of
a and b".
5(a²+b) - 5(a+b)which can be simplified such as:
\(5\left(a^2+b\right)-5\left(a+b\right)=5a^2-5a\)
Step-by-step explanation:
Given the verbal expression
"5 times the sum of a squared and b minus 3 times the sum of
a and b".
BREAKIN DOWN THE STATEMENT:
The sum of 'a' Squared and 'b' = a²+b
5 times the sum of a squared and b = 5(a²+b)The sum of a and b = a+b
3 times the sum of a and b = 5(a+b)Now, "5 times the sum of a squared and b minus 3 times the sum of
a and b".
5(a²+b) - 5(a+b)Let us simplify the algebraic expression
\(5\left(a^2+b\right)-5\left(a+b\right)\)
\(=5a^2+5b-5a-5b\)
simplify
\(=5a^2-5a\)
Thus,
\(5\left(a^2+b\right)-5\left(a+b\right)=5a^2-5a\)
lim (1 - 1/(n + 1)) ^ (n ^ 2)
Answer: Lim (1 - 1/(n + 1)) ^ (n ^ 2) = 1^infinity = 1
Step-by-step explanation: The expression given is the limit of the sequence (1 - 1/(n + 1)) ^ (n ^ 2) as n approaches infinity.
We can start by looking at the exponent first. The n^2 will grow faster than any polynomial function, making the entire expression go to zero as n approaches infinity.
Now let's look at the base (1 - 1/(n + 1))
As n increases, the value of the base becomes closer and closer to 1, since 1/(n+1) becomes smaller and smaller.
Therefore, the limit of the expression is:
Lim (1 - 1/(n + 1)) ^ (n ^ 2) = 1^infinity = 1
As n goes to infinity, the expression goes to 1
Please note that this is true for the limit, for a specific value of n, the expression will not be 1.
Answer:
The limit of (1 - 1/(n + 1)) ^ (n ^ 2) as n approaches infinity is 0.
As n becomes larger, the term 1/(n + 1) becomes smaller and closer to zero, which means that (1 - 1/(n + 1)) becomes closer and closer to 1. Therefore, the expression (1 - 1/(n + 1)) ^ (n ^ 2) becomes closer and closer to 1^(n^2) = 1. And any number powered by infinity (n^2) will be approaching zero, so the limit of the expression is 0.
Each of the following people bought a watch that costs 300. Which of the following people will pay the most for their purchase
The individual that will be paying the most for their purchase is: B.edgar paid with a credit card and paid the minimum payment each month
Which individual will pay the most?The individual that will pay the most according to the data provided is Edgar. Edgar's payment is spread out to the longest length of time. So, he will have to pay the added dues for extending his payment.
Usually, the person who pays cash pays the least amount while the person who pays in installments is charged for additional time spent in making the payment.
Complete Question:
Each of the following people bought a watch that costs $300. Which of the following people will pay the most for their purchase A.Sarah paid cash B.edgar paid with a credit card and paid the minimum payment each month C.susan paid with a credit card and paid the minimum payment plus 30 each month D. Sean paid with a credit card and paid the full balance the first of the month
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Name: Graphing in the Coordinate Plane
PLS I NEED YOUR HELP
Basically all you have to do is go over (left from the center 5 spots) to -5 and up 3. You do x before y always. Then you put a p there because that is point p. I hope this helps you
Suppose that y varies directly with x, and y = 25 when x = -5.
A) Write a direct variation equation that relates x and y
B) Find y when x = 3
Step-by-step explanation:
y=kx
25= k(-5)
k= -5
y= -5x
y = -5 ×3 = -15