Answer:
X=12,-4
Step-by-step explanation:
Set them equal to each other to get x^2=8x+48. Then move them both to the other side to get x^2-8x-48. Then factor the expression to get (x-12)(x+4). Set that to 0 to get x=12 and x=-4
A couple is looking for a mortgage to purchase a house for $256,000. If the bank requires a 5% down payment, what is the amount to be mortgaged?
$128000
$12800
$243200
$25600
What are the advantages of being paid a salary instead of an hourly rate? What are the disadvantages of being paid a salary instead of an hourly rate?
the advantages of being paid salary is u get it even if u work 1 hour and the disadvantage of getting paid hourly is u have to work for along time
I need help with my math
(1, -3)
1) Solving that system by the Substitution Method, we can write out:
I) x= 1
II) y= x-4
2) Plugging into the 2nd one the first equation:
y = x-4
y = 1 -4
y =-3
Since we already know the quantity of x, we can write out S={(1, -3)}
I have to find which line is perpendicular to the line given
Perpendicularity law
\(\begin{gathered} m_1m_2=-1 \\ -5m_2=-1 \\ m_2=\frac{1}{5} \\ y-y_1=m(x-x_1) \\ y-(-4)=\frac{1}{5}(x-10) \\ y+4=\frac{x}{5}-2 \\ y=\frac{1}{5}x-2-4 \\ y=\frac{1}{5}x-6 \end{gathered}\)what theorem can be used to prove these triangles are congruent?
Answer:
B. HL
Step-by-step explanation:
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qs 14-18 determining components of costs of goods manufactured
Cost of Goods Manufactured is an accounting term used to describe the total cost of producing and manufacturing goods. It includes all direct and indirect costs of production, including labor, materials, overhead, and other expenses. Below are the five components of the cost of goods manufactured.
Direct Materials: It includes the cost of raw materials used in manufacturing a product.
Direct Labor: It includes the wages paid to workers who directly worked on the production line or in manufacturing a product.
Factory Overhead: It includes all indirect costs of manufacturing a product such as depreciation on equipment, rent, insurance, utilities, etc. Work-in-Process
Inventory: It includes the cost of materials, labor, and overhead that has been incurred but has not yet been completed. Finished Goods Inventory: It includes the cost of goods that have been fully manufactured but have not yet been sold.
To calculate the cost of goods manufactured, the sum of all these five components is calculated. It helps manufacturers to determine the total cost of goods manufactured and the cost per unit of production. Cost of goods manufactured is essential in determining the pricing strategy for a product as it helps to ensure that the product is profitable.
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The teacher has listed 30 books as book report options. You must read 5. How many different sets of 5 books could you have chosen to read? (Stats question)
Answer:You can choose 6 different sets of 5 books to read.
Step-by-step explanation:All you need to do is do 30 divided by 5 and you get 6
Im pretty sure its permutation
The total quantity of icing sugar and brown sugar needed to make a cake is 700ML if Mary uses 150ML less icing sugar than brown sugar how much of each kind does she use
Mary needs 425 mL of brown sugar and 275 mL of icing sugar to make the cake.
How to determine how much of each kind she usesFrom the question, we have the following parameters that can be used in our computation:
Total = 700
Icing sugar = Brown sugar - 150
Using the variables, we have
x = Icing and y = Sugar
This means that
x + y = 700
x = y - 150
By substitution, we have
x + (x - 150) = 700
Evaluate the like terms
So, we ave
2x - 150 = 700
This gives
2x = 850
x = 425
Recall that
x + y = 700
So, we have
425 + y = 700
Evaluate
y = 275
Hence, Mary needs 425 mL of brown sugar to make the cake.
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Rahul recorded the grade-level and instrument of everyone in the middle school
School of Rock below.
Seventh Grade Students
Instrument # of Students
Guitar
Bass
Drums
Keyboard
9
9
11
9
Eighth Grade Students
Instrument # of Students
Guitar
Bass
Drums
Keyboard
14
10
10
13
Based on these results, express the probability that a seventh grader chosen at
random will play an instrument other than guitar as a decimal to the nearest
hundredth.
Answer:
Step-by-step explanation:
The total number of seventh-grade students who play an instrument is 9 + 9 + 11 + 9 = 38. The number of seventh-grade students who play an instrument other than guitar is 9 + 11 + 9 = 29. Therefore, the probability that a seventh grader chosen at random will play an instrument other than guitar is 29/38 ≈ 0.76 (rounded to the nearest hundredth).
Acme Metals buys a sheet metal press for $140,000. They estimate that it will be worth $96,250
in 5 years time.
a. Set up a linear model for this situation. Identify your variables and assumptions clearly.
b. If the model is correct, what is the machine worth after 2 years? How much value has it lost
after 3 years?
c. Evaluate your model. What is its largest possible domain of applicability?
The linear model for the situation is V = 140,000 - 28,000t, where V is the value of the machine after t years and t is the number of years since the machine was purchased. If the model is correct, the machine will be worth $112,000 after 2 years and will have lost $28,000 in value after 3 years. The model is valid for t ≥ 0, but it is not accurate for t < 0.
(a) The linear model can be set up as follows: V = mt + b, where V is the value of the machine after t years, m is the slope of the line, and b is the y-intercept.
We know that the machine is worth $140,000 when it is purchased (t = 0) and $96,250 in 5 years (t = 5), so we can use these points to find the slope and y-intercept of the line.
Substituting t = 0 and V = 140,000 into the equation gives us b = 140,000. Substituting t = 5 and V = 96,250 into the equation gives us m = -28,000.
Therefore, the linear model for the situation is:
V = 140,000 - 28,000t
(b) If the model is correct, the machine will be worth $112,000 after 2 years and will have lost $28,000 in value after 3 years.
To find the value of the machine after 2 years, we can substitute t = 2 into the equation:
V = 140,000 - 28,000 * 2 = 112,000
To find the amount of value the machine has lost after 3 years, we can substitute t = 3 into the equation:
V = 140,000 - 28,000 * 3 = 92,000
Therefore, the machine has lost $28,000 in value after 3 years.
(c) The model is valid for t ≥ 0, but it is not accurate for t < 0. This is because the model assumes that the value of the machine decreases linearly over time. However, it is possible that the value of the machine could decrease at a faster or slower rate than linear.
The largest possible domain of applicability for the model is 0 ≤ t ≤ ∞. This is because the model is valid for any value of t that is greater than or equal to 0. However, it is important to note that the model may not be accurate for values of t that are very large.
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a person rolls a standard six-sided die 6 6 times. in how many ways can he get 3 3 fives, 2 2 sixes, and 1 1 two?
The person can get 3 fives, 2 sixes, and 1 two in 336 ways.
To find the number of ways to roll 3 fives, 2 sixes, and 1 two in 6 rolls of a standard six-sided die, we can use the formula for combinations with repetition:
\(C(n + k - 1, k) = C(6 + 3 - 1, 3) * C(3 + 2 - 1, 2) * C(1 + 1 - 1, 1)\)
where n is the number of possible outcomes (in this case, 6), k is the number of choices to make (in this case, 3 for fives, 2 for sixes, and 1 for twos), and C(n + k - 1, k) represents the number of combinations with repetition.
Using this formula, we can calculate:
\(C(8, 3) * C(4, 2) * C(1, 1) = 56 * 6 * 1 = 336\)
Therefore, there are 336 ways to roll 3 fives, 2 sixes, and 1 two in 6 rolls of a standard six-sided die.
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I'll give brainiest to the first person to respond BUT only if the answer is correct
when operating under ifr with a vfr-on-top clearance, what altitude should be maintained?
When operating under Instrument Flight Rules (IFR) with a Visual Flight Rules (VFR) on-top clearance, the altitude to be maintained depends on the specific clearance and regulations in place.
Generally, when flying VFR-on-top, the pilot is authorized to operate in VFR conditions above a layer of clouds or other obscuring phenomena. In terms of altitude, the pilot is expected to maintain a cruising altitude appropriate for the direction of flight and comply with the relevant airspace regulations. This typically involves flying at the appropriate altitude for the specific airspace class, as defined by the Federal Aviation Regulations (FARs) or the applicable regulatory authority. It's important for pilots to review and understand the specific requirements and altitude restrictions outlined in their VFR-on-top clearance, as well as any additional instructions provided by air traffic control.
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A, B & C form a triangle where Z BAC = 90°
AB = 4.8 mm and CA = 6.6 mm.
Find the length of BC, giving your answer rounded
to 1 DP.
Answer:
BC = 8.2 mm
Step-by-step explanation:
This is a right triangle with BC as the hypotenuse
(BC)^2 = 4.8^2 + 6.6^2
(BC)^2 = 23.04 + 43.56
(BC)^2 = 66.6
Take the square root of both sides
BC = 8.1608823052
Rounded
BC = 8.2 mm
Water is being pumped into an inverted conical tank at a constant rate of 0.1 m/min. The tank has height 9 m and the radius at the top is 3 m. At what rate is the water level rising when the water is 4 m deep?
The water level in the inverted conical tank is rising at a rate of approximately 0.0136 m/min when the water depth is 4 m.
To find the rate at which the water level is rising in the inverted conical tank, we can use related rates and the concept of similar triangles. Let's denote the depth of the water in the tank as h.
We know that the rate of change of the volume of water in the tank is constant and given as 0.1 m³/min. Since the tank is in the shape of an inverted cone, we can relate the volume and height of the water using the formula V = (1/3)πr²h, where r is the radius of the cone at the corresponding height.
By differentiating this volume equation with respect to time, we can express the rate of change of the volume as dV/dt = (1/3)πr²(dh/dt).
Given the dimensions of the tank (height = 9 m, radius at the top = 3 m), we can determine the radius at a particular height using similar triangles. At a depth of 4 m, the radius can be found as (4/9) * 3 = 4/3 m.
Substituting the values into the equation, we have 0.1 = (1/3)π(4/3)²(dh/dt). Solving for dh/dt, we find that the water level is rising at a rate of approximately 0.0136 m/min when the water depth is 4 m.
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An object is moving with velocity (in ft/sec) v(t)=t2−1t−12
Find the displacement and total distance travelled from t=0 to t=6
To find the displacement and total distance traveled by the object from t=0 to t=6, we need to integrate the velocity function over the given time interval.
The displacement can be found by integrating the velocity function v(t) with respect to t over the interval [0, 6]. The integral of v(t) represents the net change in position of the object during this time interval.
The total distance traveled can be determined by considering the absolute value of the velocity function over the interval [0, 6]. This accounts for both the forward and backward movements of the object.
Now, let's calculate the displacement and total distance traveled using the given velocity function v(t) = t^2 - (1/t) - 12 over the interval [0, 6].
To find the displacement, we integrate the velocity function as follows:
Displacement = ∫[0,6] (t^2 - (1/t) - 12) dt.
To find the total distance traveled, we integrate the absolute value of the velocity function as follows:
Total distance = ∫[0,6] |t^2 - (1/t) - 12| dt.
By evaluating these integrals, we can determine the displacement and total distance traveled by the object from t=0 to t=6.
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2/3 + 1/5
4/5 + 1/2
5/7 + 1/3
1/4 -2/5
Answer:
A. 13/15
B. 13/10
C. 22/21
D. −3/20
Step-by-step explanation:
Just make the denominators equal to each other and solve. Ask your teacher for extra help
If you are trying to predict Y scores from X scores, X is referred to as the ______. a. predictor variable b. dependent variable c. nominal variable d. criterion variable
If you are trying to predict Y scores from X scores, X is referred to as the a. predictor variable. Therefore, option a. predictor variable is correct.
The predictor variable, also known as the independent variable or explanatory variable, is a variable that is used to explain the changes or variations in another variable. In this case, the predictor variable (X) is used to predict the value of the dependent variable (Y).
For example, if you are trying to predict the score of a student on a test (Y) based on the number of hours they study (X), then the number of hours studied is the predictor variable. The predictor variable is what you manipulate or control to see its effect on the dependent variable. In other words, the predictor variable is what you believe influences the outcome variable.
It is important to note that the predictor variable does not necessarily cause changes in the dependent variable. There may be other variables at play that can affect the outcome variable. Therefore, it is important to consider other potential confounding variables in your analysis.
In summary, when trying to predict Y scores from X scores, X is referred to as the predictor variable. It is the variable that is manipulated to explain the changes in the dependent variable, Y.
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3(2x) + 4y(5)
I’m LowKey struggling can someone help meh
Answer:
6x+20y
Step-by-step explanation:
Answer: 20y+3(2x)
Step-by-step explanation:
Multiply the numbers
3(2x)+4y ⋅ 5
3(2x)+20y
Rearrange terms
3(2x)+20y
20y+3(2x)
6. suppose that a brand of aa batteries reaches a significant milestone to their death on average after 7.36 hours, with standard deviation of 0.29 hours. assume that when this milestone occurs follows a normal distribution (a) calculate the probability that a battery does not reach this milestone in its first 8 hours of usage. (b) suppose that the company wants to sell a pack of n batteries of which (at least) 10 will last until after 7.5 hours of usage. if n12, what is the probability of this goal being met? (c) How many batteries n should be in the package in order for the probability to exceed 1%? Give the smallest number n which works.
The smallest number of batteries in the package for the probability to exceed 1% is a) 17. This can be calculated using the binomial distribution with parameters n=17 and b)p=0.2927 and number of batteries is c)4. (Where p is the probability from part a).
a) The probability that a battery does not reach the significant milestone after 8 hours of usage is 0.2927.
This can be calculated using the cumulative normal distribution function. The parameters are μ=7.36, σ=0.29, and x=8.
b) The probability that at least 10 batteries will last more than 7.5 hours is 0.7012.
This can be calculated using the binomial distribution with parameters n=12 and p=0.2927 (where p is the probability from part a).
c) The number of batteries should be in package is μ*4.2/7.5 = 4.
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A spring has a mass of 2 units, a damping constant of 6 units, and a spring constant of 30.5 units. If the spring is extended 2 units and then released with a velocity of 2 units answer the following.
a) Write the differential equation with the initial values.
b) Find the displacement at time t = 2
c) Find the velocity at time t = 2
d) What is the limit of x(t) as tend tends to infinity?
As t approaches infinity, the exponential term e^(-3t/2) approaches 0. Therefore, the limit of x(t) as t approaches infinity is 0, indicating that the displacement tends to zero as time goes to infinity.
a) The differential equation that represents the given spring is:
2(d²x/dt²) + 6(dx/dt) + 30.5x = 0,
with initial condition x(0) = 2 units.
b) To find the displacement at time t = 2, we need to solve the differential equation and substitute t = 2 into the solution. The general solution of the differential equation is:
x(t) = c₁e^(rt₁) + c₂e^(rt₂),
where r₁ and r₂ are the roots of the characteristic equation 2r² + 6r + 30.5 = 0.
Solving the characteristic equation, we find the roots to be complex: r₁ = (-3 + √(23)i)/2 and r₂ = (-3 - √(23)i)/2.
The complex roots indicate that the solution will involve oscillatory behavior. However, since the system is damped, the oscillations will decay over time.
Plugging in the initial condition x(0) = 2, we can find the values of c₁ and c₂ using the real part of the complex roots. The solution becomes:
x(t) = e^(-3t/2)(c₁cos((√(23)t)/2) + c₂sin((√(23)t)/2)),
where c₁ and c₂ are constants to be determined.
c) To find the velocity at time t = 2, we differentiate the displacement function with respect to time:
dx/dt = -3e^(-3t/2)(c₁cos((√(23)t)/2) + c₂sin((√(23)t)/2)) - (√(23)/2)e^(-3t/2)(c₁sin((√(23)t)/2) - c₂cos((√(23)t)/2)).
Substituting t = 2 into the expression above will give the velocity at time t = 2.
d) As t approaches infinity, the exponential term e^(-3t/2) approaches 0. Therefore, the limit of x(t) as t approaches infinity is 0, indicating that the displacement tends to zero as time goes to infinity.
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in the xyxyx y plane a line that has the equation y cy cy equals c for some constant ccc intersects a parabola at exactly one point if the parabola has the equation y x 2 5xy x 2 5xy equals minus x squared plus 5 x what is the value of ccc
The value of c can be found by solving the equation yc^2 = -x^2 + 5x.
What is square?Square is a two-dimensional shape with four equal sides and four equal angles of 90 degrees each. It is a regular polygon and is one of the most common shapes in mathematics. Squares can be found in nature, architecture, and art. They are used to divide and organize space, and are often used as a form of measurement in areas such as geometry, construction, and engineering.
After rearranging the equation, we can solve for c by using the quadratic formula. c = (x^2 - 5x)/(x^2). Therefore, the value of c is (x^2 - 5x)/(x^2).
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change this root into a power
HELLPPPPPP I DONT UNDER
Answer:
y=16
Step-by-step explanation:
Notice that the first equation was multiplied by 4, so you have to multiply the result by 4 to keep it as a true equation
james makes an acai bowl using 3/5 cup of almond milk for every 1 1/2 teaspoons of cashew butter. james wants to know the number of cups of almond milk per teaspoon of cashew butter he uses when making the bowl. How much almond milk does james use per teaspoon of cashew butter?
____ cup(s) of almond milk per teaspoon of cashew butter
Answer:
the answer its 2/5
Step-by-step explanation:
hes rite
The sun of the first 3 terms of an arithmetic sequence is 21 while their product is 315 determine these three terms?
Answer:
The terms of the sequence are x=5 and a=2:
\( x + (x + a) + (x + 2a) = 21 \) → \( 5 + (5 + 2) + (5 +2*2) = 21 \)
\( x*(x + a)*(x + 2a) = 315 \) → \( 5*(5 + 2)*(5 + 2*2) = 315 \)
Step-by-step explanation:
We can find the terms of the following sequence:
\( x + (x + a) + (x + 2a) = 21 \)
\( 3x + 3a = 21 \)
\( x + a = 7 \) (1)
The product of that sequence is:
\( x*(x + a)*(x + 2a) = 315 \) (2)
Solving equation (1) for x:
\( x = 7 - a \) (3)
And by entering (3) into (2):
\( (7 - a)*(7 - a + a)*(7 - a + 2a) = 315 \)
\( 7*(7^{2} - a^{2}) = 315 \)
\( 343 - 7a^{2} = 315 \)
\( a = 2 \)
Now, by entering "a" into equation (3):
\( x = 7 - 2 = 5 \)
Therefore, the terms of the sequence are x=5 and a=2.
I hope it helps you!
Question
The heights of five adults are 62, 72, 73, 69, and 71 inches. What is the average height, in inches, of the
five adults?
O 68.6
O 68.8
O 69.2
O 69.4
Answer:
69.4 inches
Step-by-step explanation:
62 + 72 + 73 + 69 + 71 = 347
347 / 5 = 69.4
Graph linear equations in slope-intercept form. Y = 2x + 1
Answer:
Here's how to graph it!
since the function is in a slope-intercept form we see both the slope, 2x, and the y-intercept, +1, present in the equation
First, start at the y-intercept. In this function, it is positive 1.
After you have placed your first point at ( 0, 1 ), begin with the slope. In this function, the slope is 2 or 2/1. This means you will go 2 points up and 1 point to the right.
Which set represents the zeros of the function f(x) = 7x2 – 28x + 21?
Answer:
change f(x) to 0 than 7*2x=14x
0=14x-28x+21
0=-14x+21
-21=-14x
x=3/2
Three is no less than a number x
.
Step-by-step explanation:
if three(3) is not less than x, this means it's more than x so it'll be 3+x