Answer:
2. Open the bracket
Step-by-step explanation:
1. Given:
\(3(x + 2) = 12\)
2. Open the bracket, by multiplying 3 on every term in the bracket.
\( (3 \times x) + (3 \times 2) = 12 \\ 3x + 6 = 12\)
3.Subtraction Property of equality:
\(3x + 6 - 6 = 12 - 6\)
4. Simplify:
\(3x = 6\)
5. Divide property of equality:
\( \frac{3x}{3} = \frac{6}{3} \)
6. Simplify:
\(x = 2\)
Robert wants to use all the ingredients listed in the table at the right to make trail mix . How many 1/2 pound packages can he make?
Answer:
Robert can make 16 packages
What number is less than 500 but greater than 100, no even digits, not divisible by 3, but is divisible by 11?
Pls helllppp thank youuuuuu
Answer:
319
Step-by-step explanation:
...............///.......///
AB is the angle bisector find x
Answer:
x=9
Step-by-step explanation:
2(x-1)=3x-11
distribute the 2
subtract 2x from both sides and get -2=x-11
add 11 to both sides and get x=9
three cards are chosen at random from a standard -card deck. what is the probability that they are not all the same color? 3334
The probability that they are not all the same color is approximately 0.875. This can be calculated by taking the total number of possible combinations of three cards from a standard 52-card deck (52 x 51 x 50) and dividing it by the total number of possible outcomes (52 x 51 x 50 x 48 x 47 x 46).
1. Calculate total possible combinations of three cards from a standard 52-card deck:
52 x 51 x 50
= 13,200
2. Calculate total possible outcomes:
52 x 51 x 50 x 48 x 47 x 46
= 1,415,072
3. Divide total combinations by total outcomes:
13,200/1,415,072
= 0.0093 or 0.875 (rounded to the nearest thousandth)
The probability of not all three cards being the same color is 0.875. This can be calculated by dividing the total number of combinations of three cards from a standard 52-card deck by the total number of possible outcomes. This ratio is then rounded to the nearest thousandth for the final result.
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8.3 + x= 12.1
I will love you if you can help me!
Answer: x= 3.8
Step-by-step explanation:
21.1 - 8.3 = 3.8
x= 3.8
Answer:
X = 3.8
Explanation: 12.1 minus 8.3 equals the missing value
In a transportation problem, the activities correspond to the shipping lanes while the _______ of each activity is the quantity shipped.
In a transportation problem, the activities correspond to the shipping lanes while the supply of each activity is the quantity shipped.
In the transportation problem, activities are the shipping lanes that are taken to transport goods from sources to destinations.
The quantities to be shipped are known as supplies or availabilities. The transportation problem is a linear programming problem that is used to determine how to allocate resources to obtain a minimum cost or maximum profit.The transportation problem is one of the most widely used problems in linear programming. It is used to solve many real-world problems such as supply chain management, production planning, and logistics.
In the transportation problem, we are given a set of sources and a set of destinations. The supply and demand at each source and destination are also given. The objective is to minimize the total cost of transporting the goods from sources to destinations while satisfying the demand and supply constraints.
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Find the area and perimeter of each shape.
Answer:
perimeter=4l then multiply with how many square are there
then area = l²
multiple with how many square are there
A tour guide organizes vacation packages at a beachside town. There are 7 hotels, 5 cabins, 4 meal plans, 3 escape rooms, and 2 amusement parks. The tour guide chooses either a hotel or a cabin and then selects one of each of the remaining options. Find the total number of possible vacation packages.
Answer:
288
Step-by-step explanation:
288 was the answer.
The total number of possible vacation packages 288.
What is multiplication?The fundamental concept of repeatedly adding the same number is represented by the process of multiplication.
The number of ways to choose a hotel or a cabin is 7 + 5 = 12, and the number of ways to choose one of each of the remaining options is 4 x 3 x 2 = 24, since there are 4 meal plans, 3 escape rooms, and 2 amusement parks to choose from.
To find the total number of possible vacation packages, we can multiply these numbers:
Total number of possible vacation packages = 12 x 24
Total number of possible vacation packages = 288
Therefore, there are 288 possible vacation packages.
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Can someone help me please explain how to solve
Answer:
120 sq ft 1/2 x b x h
Step-by-step explanation:
What is the value of 3x^2 + 5x + 25, when x = 3
(3x^2 means 3x squared)
okay I bearly even know what a function is and this is practice I have a test monday!?
Answer:
A.
Step-by-step explanation:
A. because an input cannot have two outputs. However, two different inputs can have the same output.
What is the whole number for 15/4. If you have the answer please tell me.
Answer: 4
Step-by-step explanation:
Well 15/4 is 3.75 so to get the whole number you need to round up
.75 rounds up to .8 now round 3.8 well 3.8 rounded up is 4 there's your answer! :)
The value of the logarithmic function log 2 log 2 log 2 16 is equal to a. 0 b. 1 c. 2 d. 4
The value of the logarithmic function log 2 log 2 log 2 16 is equal to 4. To see why, we can simplify the expression by evaluating each logarithm one at a time:
log 2 16 = 4, since 2 to the fourth power is 16. log 2 (log 2 16) = log 2 4 = 2, since 2 to the second power is 4.log 2 (log 2 (log 2 16)) = log 2 2 = 1, since 2 to the first power is 2.Therefore, the overall value of the expression is 1+2+1=4.
The value of the logarithmic function log₂(log₂(log₂(16))) can be found by evaluating each log step by step.
1. First, find the value of log₂(16): log₂(16) = 4 (since 2^4 = 16)
2. Next, find the value of log₂(log₂(16)) which is log₂(4): log₂(4) = 2 (since 2^2 = 4)
3. Finally, find the value of log₂(log₂(log₂(16))): log₂(2) = 1 (since 2^1 = 2)
So, the value of the given logarithmic function is 1 (option b).
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Archie co. purchased a framing machine for $45,000 on january 1, 2018. the machine is expected to have a four-year life, with a residual value of $5,000 at the end of four years. using the sum-of-the-years-digits method, depreciation for 2018 and book value at december 31, 2018, would be:_________.
a) $18,000 and $27.000.
b) $16,000 and $29,000.
c) $16,000 and $24,000
d) $18,000 and $22,000
The accumulated depreciation is $16,000 and the book value at December 31, 2018, would be $29,000 ($45,000 - $16,000). Therefore, the correct answer is option C: $16,000 and $24,000.
Using the sum-of-the-years-digits method, depreciation for the first year (2018) is calculated as follows:
Step 1: Determine the total number of years of useful life of the machine. In this case, it is four years.
Step 2: Calculate the sum of the digits of the useful life of the machine. This is done by adding the digits 1 to 4, which gives a total of 10.
Step 3: Determine the fraction to be used in each year's depreciation. For the first year, the fraction is 4/10 or 40% (the remaining fractions for the next three years would be 3/10, 2/10, and 1/10 respectively).
Step 4: Calculate the depreciation expense for 2018 by multiplying the depreciable base (which is the cost of the machine minus the residual value) by the fraction for the first year. In this case, the depreciable base is $40,000 ($45,000 - $5,000) and the depreciation expense for 2018 is $16,000.
Step 5: Calculate the book value of the machine at the end of 2018 by subtracting the accumulated depreciation (which is the sum of the annual depreciation expenses) from the cost of the machine. In this case, the accumulated depreciation is $16,000 and the book value at December 31, 2018, would be $29,000 ($45,000 - $16,000).
Therefore, the correct answer is option C: $16,000 and $24,000.
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find the volume of the largest right circular cone that can be inscribed in a sphere of radius r.
The volume of the largest right circular cone that can be inscribed in a sphere of radius r is 8/27 (volume of sphere)
Let r serve as the foundation. the volume of the area, and radius x is the separation between the base and the sphere's center. Height h of the cone = R + x
∴ V= 1/3πr² h= π/ 3 (R² −x²)(R + x)
= π/3 (R² + R² x − Rx² −x² )
∴ dV/ dx = π /3 [R²−2Rx−3x² ]
d²V/ dx² = π/3 [−2R−6x]
For max or min V dV/dx =0
∴ R² −2Rx−3x² =0
⇒(R + x)(x−3x)=0
2) x=−R, x/3 but x = −R
When x= R/3 d² V/dx² <0 V is max only when x= R/3
∴ Max V= 1/3π(R² − R²/9 )(R+ R/3 )
= 32πR³/81
= 8/27 ( 4/3 πR³)
= 8/27 (volume of sphere)
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What is the slope of the line that passes through the points (-8,3)
and (-8, 2)? Write your answer in simplest form.
Answer:
Undifined
Step-by-step explanation:
A culture of bacteria has an initial population of 39000 bacteria and doubles every 9 hours. Using the formula P_t = P_0\cdot 2^{\frac{t}{d}}P t =P 0 ⋅2 d t , where P_tP t is the population after t hours, P_0P 0 is the initial population, t is the time in hours and d is the doubling time, what is the population of bacteria in the culture after 2 hours, to the nearest whole number?
Answer:
45495
Step-by-step explanation:
Answer:
10077
Step-by-step explanation:
A culture of bacteria has an initial population of 5400 bacteria and doubles every 10 hours. Using the formula P_t = P_0\cdot 2^{\frac{t}{d}}P
t
=P
0
⋅2
d
t
, where P_tP
t
is the population after t hours, P_0P
0
is the initial population, t is the time in hours and d is the doubling time, what is the population of bacteria in the culture after 9 hours, to the nearest whole number?
P_0=5400
P
0
=5400
The initial population
t=9
t=9
Time elapsed
d=10
d=10
The doubling time
P_t = P_0\cdot 2^{\frac{t}{d}}
P
t
=P
0
⋅2
d
t
P_t=5400\cdot 2^\frac{9}{10}
P
t
=5400⋅2
10
9
Plug in
P_t=10076.7563\approx10077
P
t
=10076.7563≈10077
Use parenthesis in the calculator for the exponent
solve for x. please help.
Answer:
x = 16
Step-by-step explanation:
adjacent angles in a parallelogram are supplementary
3x + 5 + 9x - 17 = 180
12x - 12 = 180
12x = 192
x = 16
If x is directly proportional to y, and x = 4.5 when y = 3, find
(i) an equation connecting x and y
(ii) the value of x when y = 6,
(iii) the value of y when x = 12.
Answer:
1. don't know what you want for the first one but..
2. x=9
3. y= 8
Step-by-step explanation:
x = 1.5y
ex y=2 x=2
Today is Derek's 25th birthday. Derek has been advised that he needs to have $2,176,097.00 in his retirement account the day he turns 65 . He estimates his retirement account will pay 8.00% interest. Assume he chooses not to deposit anything today. Rather he chooses to make annual deposits into the retirement account starting on his 27.00 th birthday and ending on his 65th birthday. How much must those deposits be? Answer format: Currency: Round to: 2 decimal places.
To accumulate $2,176,097.00 in his retirement account by age 65, Derek needs to make annual deposits of $5,000.00 starting on his 27th birthday and ending on his 65th birthday, assuming an 8.00% interest rate.
To determine the annual deposits Derek needs to make, we can use the future value of an ordinary annuity formula. First, we calculate the number of years between Derek's 25th and 65th birthdays, which is 65 - 25 = 40 years. Next, we calculate the future value of the retirement account using the given interest rate of 8.00%. Using the formula:
Future Value = Present Value * (1 + interest rate)^number of periods
In this case, the future value is $2,176,097.00, the interest rate is 8.00%, and the number of periods is 40. We can rearrange the formula to solve for the present value:Present Value = Future Value / (1 + interest rate)^number of periods
Substituting the values:Present Value = $2,176,097.00 / (1 + 0.08)^40 = $123,529.31 (rounded to 2 decimal places)
Now, we need to find the annual deposit amount. Since Derek starts making deposits on his 27th birthday and ends on his 65th birthday, he makes deposits for 65 - 27 = 38 years.Annual Deposit = Present Value / ((1 + interest rate)^number of periods - 1)Substituting the values:
Annual Deposit = $123,529.31 / ((1 + 0.08)^38 - 1) = $5,000.00 (rounded to 2 decimal places)Therefore, Derek must make annual deposits of $5,000.00 into his retirement account starting on his 27th birthday and ending on his 65th birthday to accumulate $2,176,097.00 by the time he turns 65.
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A mobile device that normally sells for $99.90 is
marked down 10%. What's the discount price?
$99.00
$89.99
$89.91
$89.90
Answer:
89.90 is the answerrrrrrrrrrr
Answer:
89.91
Step-by-step explanation:
You can do this with a calculator 99.90-10%
instantaneous velocity can be positive, negative, or zero.a. trueb. false
True. Instantaneous velocity is the rate of change of displacement at a specific instant in time and can be positive, negative, or zero.
Calculating instantaneous velocity involves dividing the displacement change by the time change. A car's instantaneous velocity, for instance, would be 5/3 metres per second if it travelled 5 metres in 3 seconds.The rate of change of displacement at a particular moment in time is known as the instantaneous velocity. It is the speed in an instant at a particular location, and it can be positive, negative, or zero. The change in displacement (delta x) is divided by the change in time to determine instantaneous velocity. A car's instantaneous velocity, for instance, would be 5/3 meters per second if it travelled 5 meters in 3 seconds.
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The height at time t (in seconds) of a mass, oscillating at the end of a spring, is s(t) = 300 + 16 sin t cm. Find the velocity and acceleration at t = pi/3 s. v(pi/3) = a(pi/3) =
The height at time t (in seconds) of a mass, oscillating at the end of a spring, is s(t) = 300 + 16 sin t cm. We have to find the velocity and acceleration at t = π/3 s.
Let's first find the velocity of the mass. The velocity of the mass is given by the derivative of the position of the mass with respect to time.t = π/3 s
s(t) = 300 + 16 sin t cm
Differentiating both sides of the above equation with respect to time
v(t) = s'(t) = 16 cos t cm/s
Now, let's substitute t = π/3 in the above equation,
v(π/3) = 16 cos (π/3) cm/s
v(π/3) = -8√3 cm/s
Now, let's find the acceleration of the mass. The acceleration of the mass is given by the derivative of the velocity of the mass with respect to time.t = π/3 s
v(t) = 16 cos t cm/s
Differentiating both sides of the above equation with respect to time
a(t) = v'(t) = -16 sin t cm/s²
Now, let's substitute t = π/3 in the above equation,
a(π/3) = -16 sin (π/3) cm/s²
a(π/3) = -8 cm/s²
Given, s(t) = 300 + 16 sin t cm, the height of the mass oscillating at the end of a spring. We need to find the velocity and acceleration of the mass at t = π/3 s.
Using the above concept, we can find the velocity and acceleration of the mass. Therefore, the velocity of the mass at t = π/3 s is v(π/3) = -8√3 cm/s, and the acceleration of the mass at t = π/3 s is a(π/3) = -8 cm/s².
At time t = π/3 s, the velocity of the mass is -8√3 cm/s, and the acceleration of the mass is -8 cm/s².
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How do i solve this question?
Answer & step-by-step explanation:
Which numbers are written in scientific notation check all that apply
Answer:
2.7 x 10⁻³
6.1 x 10⁵
9.582 x 10⁶
Step-by-step explanation:
The first digits part should be more or equal 1 and less 10
Answer:
Step-by-step explanation:
B c and d
i need help, i keep seeing 3,-1 as the answer but i don’t have that option
Given the expression:
\(x^2-2x-3=0\)We will rewrite the expression to be as the form (x - a)² = b
So, we need to make a complete square
\(x^2-2x=3\)The coefficient of x = -2
Half the coefficient = -1
Square it will give 1
So, add (1) to both sides of the equation
\(x^2-2x+1=3+1\)Factor the left side of the equation, it is a complete square
\((x-1)^2=4\)Compare the result to the given form.
So, the answer will be:
\(a=1,and,b=4\)Evaluate the expression when a=6 and b=4. b - 3a
-14 is the value of the expression b - 3a at a =6 and b = 4.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given an expression b - 3a
For this expression given,
a = 6 and b = 4
Thus the value of expression at given values
=> b - 3a
=> 4 - 3 * 6
=>4 - 18
=> -14
Therefore, the value of the expression b - 3a at a =6 and b = 4 is -14.
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What are the zeros of the function h (x) = x² + 3x - 8?
A
x = -8 and x = -2
OB
x= -8 and x = 2
cx = -2 and x = 8
OD x = 2 and x = 8
The following are the zeros for the function h (x) = x2 + 3x - 8: - x= -4 and x=2.
Describe functions.Given a collection of inputs X (domain) and a set of potential outputs Y (codomain), a function is more technically defined as a set of ordered pairings (x,y) where xX and yY with the caveat that there can only be one ordered pair with the same value of x. The function notation f:XY can be used to express that f is a function from X to Y.
The function's zero is a value of x that makes it equal to zero. In other words, the equation f(x) = 0 leads to a zero.
By putting h(x) equal to zero and figuring out x, we may determine the zeroes for the function h(x) = x2 + 3x - 8.
h(x) = x² + 3x - 8 = 0
We may factor the left side of the equation to find x:
x² + 3x - 8 = (x-2)(x+4) = 0
We set each factor to zero and solve for x to discover the zeroes:
x-2 = 0 or x+4 = 0
x = 2 or x = -4
Consequently, the function's zeros are x = 2 and x = -4.
So, A is the right response. x = -4 and x = 2
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The complete question is
What are the zeros of the function h (x) = x² + 3x - 8?
A. x = -4 and x = -2
B. x= -8 and x = 2
C. x = -2 and x = 8
D. x = 2 and x = 8
use the chain rule to find ∂z ∂s and ∂z ∂t . z = ln(5x 3y), x = s sin(t), y = t cos(s)
∂z/∂s = 3cos(t)/y, ∂z/∂t = 3s*cos(t)/y - sin(s)/x (using the chain rule to differentiate each term and substituting the given expressions for x and y)
To find ∂z/∂s and ∂z/∂t using the chain rule, we start by finding the partial derivatives of z with respect to x and y, and then apply the chain rule.
First, let's find ∂z/∂x and ∂z/∂y.
∂z/∂x = ∂/∂x [ln(5x^3y)]
= (1/5x^3y) ∂/∂x [5x^3y]
= (1/5x^3y) 15x^2y
= 3/y
∂z/∂y = ∂/∂y [ln(5x^3y)]
= (1/5x^3y) ∂/∂y [5x^3y]
= (1/5x^3y) 5x^3
= 1/x
Now, using the chain rule, we can find ∂z/∂s and ∂z/∂t.
∂z/∂s = (∂z/∂x) (∂x/∂s) + (∂z/∂y) (∂y/∂s)
= (3/y) (cos(t)) + (1/x) (0)
= 3cos(t)/y
∂z/∂t = (∂z/∂x) (∂x/∂t) + (∂z/∂y) (∂y/∂t)
= (3/y) * (scos(t)) + (1/x) (-sin(s))
= 3scos(t)/y - sin(s)/x
Therefore, ∂z/∂s = 3cos(t)/y and ∂z/∂t = 3s*cos(t)/y - sin(s)/x.
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When x is 1 what value of y makes the equation true? (Show work for credit)
y=-3x + 2.5
Answer:
-0.5
Step-by-step explanation:
y=-3x+2.5
y=-3 (1) +2.5
y=-3+2.5
y=-0.5
The solution is y = -0.5
The value of y from the equation when x = 1 is y = -0.5
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
y = -3x + 2.5 be equation (1)
On simplifying the equation , we get
when x = 1
Substitute the value of x in the equation , we get
y = -3 ( 1 ) + 2.5
y = -3 + 2.5
y = -0.5
Therefore , the value of y = -0.5
Hence , the value of the equation is y = -0.5
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