Answer:
Step-by-step explanation:
(15.4*102)*(2.8*10-4)
(1,570.8)*(28-4)
(1,570.8)*(24)
37,699.2
Among all rectangles that have a perimeter of 172
, find the dimensions of the one whose area is largest. Write your answers as fractions reduced to lowest terms.
Answer: 43x43 units 1849 units^2
The area of the parallelogram is 60 square millimeters.
What is the parallelogram's base, b?
The base of the parallelogram is 60.
How to find?
To find the base of a parallelogram, we need to know its area and height. The area of a parallelogram is given by the formula:
A = b × h
where A is the area, b is the base, and h is the height.
In this case, we are given that the area of the parallelogram is 60 square millimeters. We do not know the height of the parallelogram, so we cannot solve for the base directly.
However, we do know that the area of a parallelogram is equal to the product of its base and height. So, if we can find the height of the parallelogram, we can then use the formula to solve for the base.
To find the height, we can use the formula:
h = A / b
where A is the area and b is the base.
Substituting the given values, we get:
h = 60 / b
Now, we still do not know the value of the base, but we can use this expression for the height to set up an equation that relates the base and height of the parallelogram.
We know that the opposite sides of a parallelogram are parallel and have the same length, so the height of the parallelogram is perpendicular to the base. Therefore, we can draw a perpendicular line from the height to the base, dividing the parallelogram into two congruent triangles.
Each triangle has an area of A/2, and its base and height are b and h, respectively. Therefore, we can set up the following equation:
A/2 = bh/2
Substituting the expression for the height, we get:
A/2 = b(60/b)/2
Simplifying, we get:
A/2 = 30
Multiplying both sides by 2, we get:
A = 60 = bh
Now we have an equation that relates the base and area of the parallelogram. Substituting the given value for the area, we get:
60 = b × h
Substituting the expression for the height, we get:
60 = b × (60 / b)
Simplifying, we get:
60 = 60
This equation is always true, which means that any value of b that satisfies the condition for a parallelogram (i.e., opposite sides are parallel and have the same length) will work. Therefore, we cannot determine the value of the base without additional information.
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American women's heights are normally distributed with a mean of 63.6 inches and a standard deviaiton of 2.5 inches. What is the probaility of randomly selecting 150 women with a mean height greater than 64 inches?
0.9750
0.0250
0.5636
0.4364
2. Assume that the population of human body temperature has a mean of 98.6 as is commonly believed. Also assume that the population standard deviation is 0.62. If a sample size of n=106 is randomly selected find the probability of getting a mean temperature of 98.2 or lower.
0.00001
0.9999
0.2578
0.4800
Addressing issue hand, we state that As a result, the linear equation likelihood of obtaining a mean temperature of 98.2 or lower is 0.0030, or approximately 0.003. up to get together with.
What is a linear equation?In algebra, a linear equation refers to one with its form y=mx+b. B is the gradient, and m is the esta. The preceding clause is commonly referred to as a "linear function with two variables" so even though y and x are variables. Bivariate linear equations are linear equations with two variables. There are several linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation seems to have the structure y=mx+b, where m is the slope and b is the y-intercept, it is said to be linear. When a measurement seems to have the formula y=mx+b, both with m identifying its slope and b denoting the y-intercept, it is said to be linear.
z = (64 - 63.6) / (2.5 / sqrt(150)) = 1.7889
P(Z > 1.7889) = 1 - P(Z < 1.7889) = 1 - 0.9633 = 0.0367
As a result, the probability of selecting 150 women at random with a mean height greater than 64 inches is 0.0367, or approximately 0.037. As a result, the answer is (B) 0.0250.
(x - mu) / (sigma / sqrt(n)) = z
where x represents the sample mean, mu represents the population mean, sigma represents the population standard deviation, and n represents the sample size.
When we substitute the given values, we get:
z = (98.2 - 98.6) / (0.62 / sqrt(106)) = -2.7465
The probability of getting a z-score less than -2.7465 using a standard normal distribution table is 0.0030. As a result, the likelihood of obtaining a mean temperature of 98.2 or lower is 0.0030, or approximately 0.003. up to get together with.
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Help me on this one please.
Number 6 only.
Answer:
x=1.5
Step-by-step explanation:
Given parallelogram EFGH, where EF = 2x+15, HE = 6x+4 and the perimeter is 69, which is the value of GH?
Answer: The perimeter of a parallelogram is the sum of the lengths of all four sides. In this case, the perimeter is given as 69, so we can write:
EF + FG + GH + HE = 69
We know that opposite sides of a parallelogram are equal in length, so EF = GH and FG = HE. Substituting these into the equation above, we get:
2(EF) + 2(FG) = 69
2(GH) + 2(HE) = 69
Simplifying each equation:
2(2x+15) + 2(6x+4) = 69
4x + 30 + 12x + 8 = 69
16x + 38 = 69
16x = 31
x = 31/16
Substituting x into the equation for GH, we get:
GH = 2x+15
GH = 2(31/16) + 15
GH = 31/8 + 120/8
GH = 151/8
Therefore, the value of GH is 18.875 units.
Step-by-step explanation:
The volume of a liquid is 750 mL at a pressure of 1 atm. If the volume increases to 500 mL, what will be the new pressure? Use Boyle’s Law to find your answer.
a. 2.3 atmc. 1.5 atm
b. 5.6 atmd. 4 atm
Using Boyle's law, which is mathematically expressed as P1V1 = P2V2, the new pressure is calculated as: c. 1.5 atm
What is Boyle’s Law?Boyle's law states that the product of the pressure and volume of a gas is constant, assuming that the temperature remains constant. Mathematically, it can be expressed as:
P1V1 = P2V2
where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
Using the given values, we can set up the equation as follows:
1 atm × 750 mL = P2 × 500 mL
Simplifying this equation, we get:
750 atm·mL = 500 P2
Dividing both sides by 500 mL, we get:
P2 = 750 atm·mL / 500 mL
P2 = 1.5 atm
Therefore, the new pressure is 1.5 atm.
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A ladder leans against the wall of a
building. The ladder measures
71 inches and forms an angle of 64 with the ground. How far from
the ground, in inches, is the top of the ladder? How far from the
wall, in inches, is the base of the ladder? Round to two decimal
places as needed.
Answer:
63.81 inches
Step-by-step explanation:
A large corporation with monopolistic control in the marketplace has its average daily costs, in dollars, given by
C = 500/x + 200x + x².
The daily demand for x units of its product is given by p= 450,000-100x dollars.
Find the quantity that gives maximum profit.
units
Find the maximum profit.
What selling price should the corporation set for its product?
Answer:
The profit function can be expressed as:
Profit = Revenue - Cost
Revenue = Price x Quantity
Price = p = 450,000 - 100x
Quantity = x
Cost = C = 500/x + 200x + x²
Substituting these values, we get:
Profit = (450,000 - 100x) x - (500/x + 200x + x²)
Simplifying this expression, we get:
Profit = -x² + 450,000x - 500 - 200x² - x³
To find the quantity that gives maximum profit, we need to differentiate the profit function with respect to x and set it equal to zero:
d(Profit)/dx = -3x² + 450,000 - 400x - 500/x²
Setting this derivative equal to zero and solving for x, we get:
3x³ - 450,000x² + 400x³ + 500 = 0
This equation can be solved numerically to obtain:
x ≈ 98.9
To confirm that this is a maximum, we can check the second derivative of the profit function:
d²(Profit)/dx² = -6x + 800/x³
At x = 98.9, this evaluates to:
d²(Profit)/dx² ≈ -2.71
Since the second derivative is negative, the profit function has a maximum at x ≈ 98.9.
The maximum profit can be found by substituting this value of x into the profit function:
Profit ≈ $20,007,710
To find the selling price that maximizes profit, we can use the demand function:
p = 450,000 - 100x
At x = 98.9, this evaluates to:
p ≈ $35,110
Therefore, the corporation should sell its product for $35,110 to maximize profit.
Simplify the rational expression (X^2-x-72)/(x^2-64)
Answer:
[tex] \frac{x - 9}{x - 8} [/tex]
Step-by-step explanation:
[tex] \frac{(x - 9)(x + 8)}{(x + 8)(x - 8)} [/tex]
[tex] \frac{x - 9}{x - 8} [/tex]
[tex]\cfrac{x^2-x-72}{x^2-64}\implies \cfrac{(x+8)(x-9)}{x^2-8^2}\implies \cfrac{(x-9)~~\begin{matrix} (x+8) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} (x+8) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(x-8)}\implies \cfrac{x-9}{x-8}[/tex]
By applying SAS congruence rule, you want to establish that triangle PQR =~ triangle KLM. It is given that PQ = KL and RP = MK. What additional information is needed to establish the congruence?
Answer:
Step-by-step explanation:
To establish the congruence of two triangles using the SAS (Side-Angle-Side) congruence rule, we need to know that two corresponding sides and the included angle are congruent.
In the given information, PQ = KL and RP = MK, but we do not know the measure of any included angle between the corresponding sides. Therefore, we need to know at least one angle that is congruent in both triangles to apply the SAS congruence rule.
Without additional information about an included angle, we cannot establish the congruence of triangle PQR and triangle KLM using the SAS congruence rule.
g(x)=4x-(3x+7x/3) Find the slope and y=intercept. Express the intercept as an ordered pair. Simplify your answer.
Answer:
Slope: -(4/3)
Y-intercept: 0
Compute the voltage drop if the source voltage is 240V and the load voltage is 237V.
The voltage drop is the difference between the source voltage and the load voltage, which is 3V.
What is voltage drop?Voltage drop is the decrease of electric potential along the path of a current flowing in a circuit. Voltage drops in the internal resistance of the source, across conductors, across contacts, and across connectors are undesirable because some of the energy supplied is dissipated.
Voltage drop of the circuit conductors can be determined by multiplying the current of the circuit by the total resistance of the circuit conductors: VD = I x R.
The voltage drop can be calculated by subtracting the load voltage from the source voltage. In this case, the voltage drop is:
240V - 237V = 3V
Thus, the voltage drop is 3V.
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Evaluate the given expression and show the steps, please.
To find:-
[tex]\displaystyle \sum_{n=1}^{4} 2(3^{n - 1})[/tex]Answer:-
We need to evaluate,
[tex]\implies s_4=\displaystyle \sum_{n=1}^{4} 2(3^{n - 1})[/tex]
Substituting n = 1 , 2 , 3 and 4 in [tex] 2(3^{n - 1})[/tex] and then adding them , we have;
[tex]\implies s_4 = 2(3^{1-1}) + 2( 3^{2-1})+2(3^{3-1})+2(3^{4-1}) \\[/tex]
Take out 2 as common,
[tex]\implies s_4 = 2 [ 3^0 + 3^1 + 3^2 + 3^3]\\[/tex]
[tex]\implies s_4 = 2 [ 1 + 3 + 9 + 27 ] \\[/tex]
[tex]\implies s_4 = 2 ( 40) \\[/tex]
[tex]\implies \underline{\underline{ s_4 = 80}} \\[/tex]
Hence the required answer is 80 .
and we are done!
URGENT !
Wayne factored the following polynomial using the "Grouping" method. However, another student says they didn't get the same answer so there must be a mistake
somewhere.
State which step Wayne made his mistake (2 points) and what that STEP should have actually looked like (2 points).
Problem: 16x4 +24x³ +64x² +96x
Step 1: 4x (4x³ + 6x² + 16x + 24)
Step 2: 4x [2x² (2x+3)+8(2x+3)]
Step 3: 4x (2x² + 8) (2x + 3)
(PLEASE DO NOT SHOW HOW YOU WOULD SOLVE THIS. FIX WAYNE'S STEP! HE NEEDS HELP!)
Wayne's mistake is that he omitted the parentheses around the two factors of 2x² and 8.
What is parentheses?Parentheses, also known as round brackets, are punctuation marks that are used to contain related information within a sentence. They are most commonly used to set off additional information, such as a clarification or an example. Parentheses can also be used to indicate a digression from the main point of a sentence, or to indicate that something is not essential to the foundation of a statement. In addition, they can be used to indicate an interruption in a sentence, or to separate items in a list. Parentheses are also used to indicate a pause or an aside in dialogue.
The step should have been written as: 4x (2x² + (8)(2x+3)). This properly shows that 8 is being multiplied by the expression 2x+3, rather than being added to it.
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Which polynomial is prime? x2 – 36 x2 + 6 x2 – 7x + 12 x2 – x – 20
The prime polynomial, considering it's concept, is given as follows:
x² + 6.
What are prime polynomials?A polynomial is called a prime polynomial if cannot be factored into a product of two or more polynomials of lower degree with integer coefficients.
The most common way to factor a polynomial into polynomials of lower degree is according to the Factor Theorem, when the roots of polynomial are obtained, and then the linear factors generated from these roots are multiplied.
For this problem, the polynomial x² + 6 has no real roots, as x² = -6 means that the roots are complex, hence it is the prime polynomial in the context of the problem.
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Answer: B.
Step-by-step explanation:
trust me on that one lol.:p
i need help with number 7
Answer:20$ per foot
Step-by-step explanation: just multiply the first cost(400) by the first foot amount(20) 400/20=20
what does 1\4 divided by 1 3/5 equal and how do i work it out
Answer:
slimer 16 goofy butt fart gamer setup
Step-by-step explanation:
Find the median of these numbers: 2.9, 9.1, 5.2, 2.9, 8.7, 7.4
Answer: 6.3
Step-by-step explanation:
Answer:
4.45
Step-by-step explanation:
5.2 + 7.4 ÷ 2 = 8.9 ÷ 2 = 4.45
Correct me if im wrong! Thank you!UwU
Work out the circumstances of this circle. take π to be 3.142 and give your answer to 1 decimal place. Radius is 4cm
Answer:
Step-by-step explanation:
The formula for the circumference of a circle is:
C = 2πr
where C is the circumference, π is pi, and r is the radius.
Substituting the given value of π = 3.142 and r = 4 cm, we get:
C = 2 x 3.142 x 4
C = 25.136 cm
Therefore, the circumference of the circle is 25.1 cm (rounded to 1 decimal place).
( 3x - 2y = 4
|-6x + 4y = 7
what is the ordered pare
Step-by-step explanation:
To find the ordered pair, you can use the elimination method to solve for one variable in terms of the other, and then substitute into one of the equations to solve for the other variable. Here's how:
First, multiply the first equation by 2 to get:
6x - 4y = 8
Then, add the second equation to this one to eliminate y:
6x - 4y + (-6x + 4y) = 8 + 7
Simplifying and solving for x, we get:
0x + 0y = 15
0 = 15
This is a contradiction, which means the system of equations has no solution. In other words, there is no ordered pair of (x,y) that satisfies both equations simultaneously.