ANSWER
6
EXPLANATION
The given equation is:
[tex] \frac{1}{3} (12x - 24) = 16[/tex]
Multiply through by 3.
12x-24=16×3
12x-24=48
Group similar terms:
12x=48+24
12x=72
Divide both sides by 12
x=6
The answer is 6.hope this helps. please add brainlist
If an equation is an identity, then how many solutions does it have?
Identities have INFINITE solutions.
Hope I could help! :)
Answer:
Infinite solution
Step-by-step explanation:
We are given an equation is identity
We have to find that how many solutions equation have
Identity equation:Identity equation is that true equation in which no matter what value is substitute for variable .It is always true statement.
Suppose that we have an identity equation
[tex]x=x[/tex]
[tex]x-x=0[/tex]
[tex]0=0[/tex]
If this type of condition is obtained then we have infinite solutions.
So, if an equation is identity then the equation have infinite solutions.
A rectangle is 17 inches long and 7 inches wide. Find its area,
112 square inches
0
59 aquare inches
©
119 square inches
24 square inches
119 square inches long
Answer:
119
Step-by-step explanation:
(✿◠‿◠)
How many different sandwiches with one meat, one cheese, and one type of bread can be made if there are 3 choices of meat, 2 choices of cheese, and 4 choices of bread?
Answer:
24
Step-by-step explanation:
⇒The question is on probability, to be specific its about counting principal
⇒You need to understand the counting rule where we multiply events together to get the total number of outcomes .
⇒In general if we have an event t and another event s the total outcome for the events is given by t×s
⇒In this question you multiply the number of ways we can make the different sandwiches
Given
meat=3 choices
cheese=2 choices
bread=4 choices
Outcomes= 3×2×4=24
The total number of sandwiches that can be made = 24
There are 24 different sandwiches that can be made with 3 choices of meat, 2 choices of cheese, and 4 choices of bread.
Explanation:The subject of this question is related to combinatorics, a topic in mathematics. The question asks, 'How many different sandwiches with one meat, one cheese, and one type of bread can be made if there are 3 choices of meat, 2 choices of cheese, and 4 choices of bread?'.
To find the answer, you would use the fundamental principle of counting which states that if there are n ways to do one thing and m ways to do another thing, then there are n * m total ways to perform both actions. In this case, we multiply the number of options together:
There are 3 choices for the meat.There are 2 choices for the cheese.There are 4 choices for the bread.Hence, the total number of different sandwiches that can be made is given by 3 (choices of meat) * 2 (choices of cheese) * 4 (choices of bread), which equals 24 different sandwiches.
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A roll of fabric was 120 inches long. A customer bought 2 feet of the fabric.
How many feet of fabric were remaining?
(Hint: 1 foot = 12 inches)
OA. 12
OB. 7
OC. 118
OD.8
the correct answer is OB. 7.
Someone plz help me with this
Answer:
Step-by-step explanation:
Which choice is equivalent to the expression below? square root of negative 20
Answer:
B
Step-by-step explanation:
The expression can be written as
[tex]\sqrt{-20}[/tex]
The - can be taken out from under the radicand and a 2 can be factored out of the expression to leave you with the expression
[tex]2i\sqrt{5}[/tex]
Answer:
Correct option is:
B
Step-by-step explanation:
We have to find a expression which is similar to:
[tex]\sqrt{-20}[/tex]
Now we start solving
[tex]\sqrt{-20}[/tex] could also be written as:
[tex]\sqrt{-2\times 2\times 5}[/tex]
When we take - sign out of the square root it becomes i
i.e. [tex]\sqrt{-1}=i[/tex]
And there are two 2's inside the square root when we take square root it becomes 2
Hence, [tex]\sqrt{-20}=2i\sqrt{5}[/tex]
Hence, Correct option is:
B
A tourist has planned a trip to cover the distance of 640 miles, driving at some constant speed. However, when he already covered a quarter of the distance, he took a rest for 1.2 hours. Then, in order to arrive at the destination on time, he increased the speed by 20 mph. How long, actually, the trip lasted?
Answer:
The trip lasted for a total of 8 hours.
Step-by-step explanation:
Distance planned = S = 640 miles
Constant speed = V
Thus the time to be taken would be = T = V/S
We have an equation 640 = VT ----- eq (a)
Time For First Quarter = T/4
speed = V
Distance = 640/4 = 160
After first quarter, there is a rest of 1.2 hours and to complete his trip on time, he increased the velocity by 20 mph.
So, the remaining distance = 640 - 160 = 480 miles.
Speed = V + 20 mph
Time remaining = [(T-T/4) - 1.2] = 3T/4 - 1.2 hours
We have an equation for remaining distance s = vt
=> 480 = (V+20)(3T/4 - 1.2) ----- eq (b)
using eq (a), we have V = 640/T. Putting it in eq (b), we have:
[tex]480 = (\frac{640}{T} + 20)(3\frac{T}{4} - 1.2)\\480 = 480 - \frac{768}{T} + 15T - 24\\=> 15T - \frac{768}{T} -24 = 0\\=> 15T^{2} - 24T - 768 = 0\\[/tex]
Solving the equation, we get T = 8 or T = -32/5(which is not possible.
So, the right answer is T = 8 hours
ABC or d? I really need help and CANNOT get this wrong
Answer:
1.A. X6Y5
Step-by-step explanation:
Remove the Parenthesis calculate the product#2 I have no clue on that one.
So sorry but I simply forgot to answer your questions.
The answer to question 1 is A.
The answer to question 2 is D.
Which of the following is a feature of a credit card?
A: more flexibility
B: purchases are automatically deducted
C: requires a linked bank account
D: similar to cash
Credit cards offer more flexibility compared to other payment methods.
The correct answer is
A: more flexibility.
A: more flexibility - Credit cards provide users with the flexibility to make purchases without needing to have the full amount of money upfront. Instead, they can borrow funds up to a certain limit, known as the credit limit, and repay them later, often with interest. This flexibility allows cardholders to manage their cash flow more effectively and make purchases even when they may not have sufficient funds available in their bank account.
B: purchases are automatically deducted - This feature describes a debit card rather than a credit card. With a debit card, purchases are automatically deducted from the linked bank account at the time of the transaction, meaning that the cardholder needs to have sufficient funds available in their account to cover the purchase.
C: requires a linked bank account - While credit cards may require applicants to have a bank account for verification purposes, they do not necessarily need to be linked to a specific bank account for transactions to be processed. Credit cards operate on a revolving line of credit extended by the issuer, allowing cardholders to borrow money up to a certain limit regardless of their bank account balances.
D: similar to cash - Credit cards are not similar to cash. Unlike cash, which involves immediate payment and does not incur any interest charges, credit cards allow users to defer payment for purchases and may accrue interest if the balance is not paid in full by the due date. Additionally, credit cards offer various benefits such as rewards, cashback, and purchase protection, which are not typically associated with cash transactions.
Therefore the correct option is A: more flexibility
Complete question
Which of the following is a feature of a credit card?
A: more flexibility
B: purchases are automatically deducted
C: requires a linked bank account
D: similar to cash
21/35 in simplest form.
The answer would be 0.6 if you divide 21/35.
Answer:
[tex]\frac{3}{5}[/tex]
Step-by-step explanation:
To simplify divide the numerator/denominator by the highest common factor of 21 and 35, that is 7
[tex]\frac{21}{35}[/tex] = [tex]\frac{3}{5}[/tex] ← in simplest form
the diameter of a bicycle wheel is 0.7 meters. find the number of complete revolutions made by the wheel if the bicycle travels 440 meters. use 22/7 as an approximation for [tex]\pi[/tex]
Final answer:
To calculate the number of complete revolutions a bicycle wheel makes after traveling 440 meters, we find the wheel's circumference using its diameter and then divide the travel distance by the circumference. With a diameter of 0.7 meters and using 22/7 as an approximation for π, the wheel's circumference is 2.2 meters. The wheel makes 200 complete revolutions to cover 440 meters.
Explanation:
Finding the Number of Complete Revolutions
To find the number of complete revolutions made by a bicycle wheel when the bicycle travels a certain distance, we firstly need to calculate the circumference of the wheel. The circumference 'C' of a circle can be found using the formula C = πd, where π (Pi) is a constant (approximately 22/7 or 3.14) and 'd' is the diameter of the circle. In this case, we are given that the diameter of the bicycle wheel is 0.7 meters.
Using the approximation for π of 22/7 and the given diameter, the circumference is: C = π × d = (22/7) × 0.7 meters = 2.2 meters.
To find the number of complete revolutions 'N', we divide the total distance the bicycle travels by the circumference of the wheel: N = total distance / circumference = 440 meters / 2.2 meters. So, the number of complete revolutions the wheel makes is 200.
Find the volume of the cone with the given dimensions: r = 9 m, h = 13 m
[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=9\\ h=13 \end{cases}\implies V=\cfrac{\pi (9)^2(13)}{3} \\\\\\ V=351\pi \implies V\approx 1102.70[/tex]
Sarah Saver writes a $40 check which is returned by her bank with additional charges. If the company she wrote the check to, Johnson Plumbing, also charges $25 for returned checks, which of the following represents the amount Sarah must have to balance her debts?
Answer: $65 dollars to johnson plumbing
Step-by-step explanation:
she would owe johnson plumbing 40 for the check plus the returned check fee of 25
$40 + $25 = $65 to johnson plumbing
plus whatever her bank charged ( i did not see that amount listed)
Final answer:
Sarah Saver must have enough money to cover the original $40 check, the $25 fee from Johnson Plumbing, and any additional bank charges. The expression representing the total amount needed is $40 + $25 + B, where B represents the bank's charges.
Explanation:
The student is asking about the total amount Sarah Saver must have to balance her debts after writing a $40 check that was returned with additional charges and a $25 fee for the returned check from the company. To find the total amount Sarah owes, you need to sum the amount of the check and the additional fees charged by her bank and Johnson Plumbing.
Add the original check amount: $40.
Add the fee charged by Johnson Plumbing for the returned check: $25.
Add any additional charges by her bank (the question doesn't specify an amount, so let's denote this amount as B).
The total amount Sarah needs to settle her debts will be $40 + $25 + B.
Therefore, without knowing the specific bank charges, we cannot provide a numerical answer, but the expression $40 + $25 + B represents the total amount Sarah needs to cover her debts, with B being the additional bank charges.
what’s the MAD of 7 20 9 35 12 15 7 10 20 25
Answer:
Population size:10
Mean (μ): 16
Mean Absolute Deviation (MAD): 7.2
Step-by-step explanation:
Mean absolute deviation (MAD) Mean absolute deviation (MAD) of a data set is the average distance between each data value and the mean. ... Mean absolute deviation helps us get a sense of how "spread out" the values in a data set are.
Solve for the variable x in the following equation. x2 = 121 x =±
Answer:
x = ±11
Step-by-step explanation:
x^2 = 121
Take the square root of each side
sqrt(x^2) = sqrt(121)
x = ±11
The ratio of Alex’s toy cars to Jim’s toy cars is 8:3. How many toy cars do they have altogether, if Alex has 40 more cars than Jim.
[tex]\bf \cfrac{\textit{Alex's cars}}{\textit{Jim's cars}}=\cfrac{8}{3}\qquad \qquad \cfrac{\stackrel{\textit{40 more than \underline{j}}}{j+40}}{j}=\cfrac{8}{3}\implies 3j+120=8j \\\\\\ 120=5j\implies \cfrac{120}{5}=j\implies 24=j \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{Jim}}{j = 24}\qquad \qquad \stackrel{\textit{Alex}}{24+40\implies 64}\qquad \qquad \stackrel{\textit{altogether}}{24+64\implies 88}[/tex]
The total number of cars that Alex and Jim have altogether is 84 cars.
What is a ratio?A ratio is a quantitative relationship between two different numbers that express the number of times in which a number is divisible within the other number. Sometimes ratios can be expressed in fraction form.
From the given information:
The ratio of Alex to Jim's toy is 8 : 3If Alex has more toys than Jim, i.e Jim = x and Alex = x + 40.Then, we can express them in fraction form as:
[tex]\mathbf{\dfrac{8}{3} = \dfrac{x +40}{x}}[/tex]
8x = 3(x +40)
8x = 3x + 120
8x = 3x = 120
5x = 120
x = 120/5
x = 24
Jim = x = 24 cars
Alex = x + 40 = 24 + 40 = 64 cars.
The total number of cars they have altogether is 24+64 = 84 cars.
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Help me
Check it for me
Answer:
£270
Step-by-step explanation:
Works 7.5 hours per shift and there are 5 shifts in a week, hence
hours worked per week = 7.5 × 5 = 37.5
Pay per hour = £7.20, thus
Earnings for a week = 37.5 × 7.20 = £270
What is the value of z in the equation 2(4z − 9 − 7) = 166 − 46?
Answer:
z = 19
Step-by-step explanation:
Given
2(4z - 9 - 7) = 166 - 46 ← simplify both sides
2(4z - 16) = 120 ← distribute parenthesis on left side
8z - 32 = 120 ( add 32 to both sides )
8z = 152 ( divide both sides by 8 )
z = 19
Answer:
z = 19.
Step-by-step explanation:
2(4z − 9 − 7) = 166 − 46
2(4z − 9 − 7) = 120
Divide both sides by 2:
4z − 9 − 7 = 60
4z = 76
z = 19.
Find all solutions of the equation in the interval [0, 2 pi) 2 cos0-1=0
Answer:
θ = π/3, 5π/3
Step-by-step explanation:
2 cos θ - 1 = 0
2 cos θ = 1
cos θ = 1/2
θ = π/3, 5π/3
ANSWER
EXPLANATION
The given trigonometric equation is:
[tex]2 \cos( \theta) - 1 = 0[/tex]
[tex] \implies \: 2 \cos( \theta) = 1[/tex]
[tex]\implies \: \cos( \theta) = \frac{1}{2} [/tex]
The cosine ratio is positive in the first and fourth quadrants.
In the first quadrant,
[tex]\theta = \cos ^{ - 1} ( \frac{1}{2}) [/tex]
[tex]\theta = \frac{\pi}{3} [/tex]
In the fourth quadrant,
[tex]\theta =2 \pi - \cos ^{ - 1} ( \frac{1}{2}) [/tex]
[tex]\theta =2 \pi - \frac{\pi}{3} [/tex]
[tex]\theta = \frac{5\pi}{3} [/tex]
Therefore on the interval, [0,2π] the solution to the given trigonometric equation is:
[tex]\theta = \frac{\pi}{3} \: and \: \frac{5\pi}{3} [/tex]
what is x in 25-3x=40
Step 1: Subtract 25 to both sides. This will cancel 25 on the left side and bring it over to the right
(25 - 25) - 3x = 40 - 25
(0) - 3x = 15
-3x = 15
Step 2: Isolate x by dividing -3 to both sides (the opposite of multiplication is division).
-3x ÷ (-3) = 15 ÷ (-3)
x = -5
Check:
25 - 3(-5) = 40
25 + 15 = 40
40 = 40 ....................................Correct!
Hope this helped!
The value of x in this equation is -5.
What is an equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation in algebra.
Equation given in the question:
25 - 3x = 40
25 - 40 = 3x
-15 = 3x
x = -5
The value of x in this equation is -5.
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When Joe got out of bed, it was 58 in his room. He turned on the heater, and the temperature warmed up to 67 in five minutes. How many degrees per minute did the temperature rise?
Answer: 1.8
Step-by-step explanation:
Answer:
1.8
Step-by-step explanation:
(67 degrees - 58 degrees) / 5 minutes
1.8 degrees per minute
Select all the correct answers.
An architect is designing a swimming pool with a base in the shape of a right triangle. According to the architect, the pool’s depth should be 6 feet less than its length, x, and its width should be 8 feet less than its length. The volume of water in the pool cannot exceed 1,680 cubic feet. Which statements about the pool are true?
The water level in the pool cannot exceed 14 feet.
The water level in the pool cannot exceed 20 feet.
The inequality x3 − 14x2 + 48x − 1,680 ≥ 0 can be used to find pool’s length.
The inequality x3 − 14x2 + 48x − 1,680 ≤ 0 can be used to find pool’s length.
The inequality x3 − 14x2 + 48x − 3,360 ≤ 0 can be used to find pool’s length.
Answer:
The inequality x3 − 14x2 + 48x − 1,680 ≤ 0 can be used to find pool’s length.
⇒The water level in the pool cannot exceed 14 feet.
Step-by-step explanation:
The question is on inequalities
Given;
Length= x ft
depth= x-6 ft
Width= x-8 ft
volume ≤ 1680 ft³
Forming the inequality to find length x of the pool
Volume= base area × depth
base area × depth ≤ volume
x(x-8) × (x-6) = 1680
(x²-8x )(x-6) = 1680
x(x²-8x) -6 (x²-8x)=1680
x³-8x²-6x²+48x=1680
x³-14x²+48x=1680
x³-14x²+48x-1680 ≤ 0
⇒The water level in the pool cannot exceed 14 feet...why?
taking the value of x at maximum to be 17 according to the graph, then maximum depth will be;
d=x-6 = 17-6=11 ft
⇒11 ft is less than 14ft
Rewrite as a simplified fraction.
__
0.612 = ?
Final answer:
To convert the decimal 0.612 to a fraction, express it as 612/1000 and then divide both the numerator and the denominator by their greatest common divisor, which is 4, to get the simplified fraction 153/250.
Explanation:
To rewrite 0.612 as a simplified fraction, one can first recognize that it's equivalent to 612/1000. After realizing that, we can simplify the fraction by finding the greatest common divisor (GCD) of both the numerator and the denominator. In this case, the GCD of 612 and 1000 is 4. Hence, we can divide both numerator and denominator by 4 to simplify the fraction.
Dividing both 612 and 1000 by 4, we obtain 153/250. So, 0.612 as a simplified fraction is 153/250.
Evaluate 4 · 1 + 6 · 16 + 0
a) 8
b) 0
c) 100
d) 185
4+96=100 when you follow PEMDAS
Answer:
c) 100
Step-by-step explanation:
We want to evaluate
[tex]4\times1+6\times 16+0[/tex]
We use the order of operations, PEDMAS to solve this problem.
The first step here is to multiply to get:
[tex]4+96+0[/tex]
We now add to obtain:
[tex]100[/tex]
The correct answer is C) 100
Shelly invested $1,000 at a rate of 5% interest per year. Which equation models the value of the investment, V, after t years?
Answer:
Step-by-step explanation:
You don't say whether this is compound interest or simple interest.
I will assume it's compounding that interests you.
The appropriate formula is
A = P(1 + r)^t, where r is the interest rate as a decimal fraction, t is the time in years, and P is the original amount. Thus:
A = $1000·(1 + 0.05)^t, or A = $1000·(1.05)^t
Please note: There were apparently possible answer choices. Next time, please be sure to list such choices. Thank you.
Final answer:
The equation modeling the value of an investment, V, after t years, for an initial investment of $1,000 at a 5% annual interest rate is V = 1000(1 + 0.05)^t, incorporating the principles of compounding interest.
Explanation:
The question asks about the equation modeling the value of an investment, V, after t years, given an initial investment of $1,000 at a 5% annual interest rate. Using the formula for the future value of a single sum, V = P(1 + r)^t, where P is the principal amount ($1,000), r is the annual interest rate (5% or 0.05), and t is the number of years, we can determine that the equation modeling the value of the investment is V = 1000(1 + 0.05)^t. This formula is applied to calculate the future value of the investment, taking into account the compounding interest over a period t years.
Help me please will give 14 points
First, set up a proportional fraction.
[tex]\frac{5 sec}{30 gallons}[/tex] = [tex]\frac{x sec}{1gallon}[/tex]
Cross multiply
5 * 1 = 5
30 * x = 30x
So,
30x = 5
Divide 5 by 30
x = 5 / 30
x = 1 / 6 or 0.17
Do the same thing to find for 17 gallons.
30x = 85
x = 85 / 30
x = 17 / 6 or 2.8
Suppose you deal three cards from a regular deck of 52 cards. What is the probability that they will all be jacks?
Answer:
Probability of getting three jacks = [tex] \frac { 3 } { 5 2 } [/tex]
Step-by-step explanation:
It is given that you deal three cards from a regular deck which contains 52 cards.
We are to find the probability of getting all three Jack cards.
We know that there are a total of 4 jacks in a regular deck of 52 cards.
Therefore, the probability of getting three jacks = [tex] \frac { 3 } { 5 2 } [/tex]
3 chances of jacks out of 52 cards
multiply (a-2)(2a^2-5a-2)
Distribute sum groups
a(2a^2 - 5a - 2) - 2(2a^2 - 5a - 2)
Expand
2a^3 - 5a^2 - 2a - (4a^2 - 10a - 4)
Simplify brackets
2a^3 - 5a^2 - 2a - 4a^2 + 10a + 4
Collect like terms
2a^3 + (-5a^2 - 4a^2) + (- 2a + 10a) + 4
Simplify
= 2a^3 - 9a^2 + 8a + 4
need helpppppp thank you!!
Answer:
I would say 50%
Step-by-step explanation:
The answer is 50%. Hope that helps!
Find f(t – 3) for f(x) = 4x^2 – 8x + 4.
Question 11 options:
A. 4t^2 – 32t + 64
B. 64
C. 4t^2 – 32t – 64
D. 4t^2 + 32t + 64
Answer:
A. 4t² - 32t + 64Step-by-step explanation:
Instead of x put (t - 3) in the equation of the function f(x) = 4x² - 8x + 4:
f(t - 3) = 4(t - 3)² - 8(t - 3) + 4
use (a - b)² = a² - 2ab + b² and the distributive property a(b + c) = ab + ac
f(t - 3) = 4(t² - (2)(t)(3) + 3²) + (-8)(t) + (-8)(-3) + 4
f(t - 3) = 4(t² - 6t + 9) - 8t + 24 + 4
f(t - 3) = (4)(t²) + (4)(-6t) + (4)(9) - 8t + 28
f(t - 3) = 4t² - 24t + 36 - 8t + 28
f(t - 3) = 4t² + (-24t - 8t) + (36 + 28)
f(t - 3) = 4t² - 32t + 64