The simplified form of (5m² - 3)² is 25m⁴ - 30m² + 9.
Given is an expression (5m² - 3)², we need to simplify the expression,
To multiply the expression (5m² - 3)², we can use the formula for squaring a binomial:
(a - b)² = a² - 2ab + b²
In this case, a = 5m² and b = 3.
Substituting these values into the formula, we get:
(5m² - 3)² = (5m²)² - 2(5m²)(3) + (3)²
= 25m⁴ - 30m² + 9
Therefore, the simplified form of (5m² - 3)² is 25m⁴ - 30m² + 9.
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Question
Given the frequency table below, what is the relative frequency of the data value 8?
Value
4
5
6
7
8
Frequency
2
7
9
6
6
Answer:
2
3
5
5
7
13
14
17
21
31
52
Step-by-step explanation:
but I think the town & is the best. I am not coming out of my reward.. this will be the last one day.. this will not go on. I am not coming to the office until tomorrow as I'm working for, and if I don't get any of that, I'll break it up with a choice. I am a bit worried, so I was 165 2762
How to solve triangle inequalities?
Answer: The triangle inequality theorem describes the relationship between the three sides of a triangle. According to this theorem, for any triangle, the sum of lengths of two sides is always greater than the third side.
Your bank statement shows a balance of $683. Your checkbook register shows a balance of $462. You earned interest of $11 and had a service charge of $8. There are no outstanding deposits. What is the amount of outstanding checks?
Amount of outstanding checks is $218
Given,
Bank balance = $683
Check book register balance = $462
Interest earned = $11
Service charge = $8
Now,
Form the linear equation,
Bank balance = Check book register balance + Interest earned + Amount of outstanding check - Service charge
Substitute the data given in the question,
$683 = $462 + $11 + Amount of outstanding check - $8
Amount of outstanding check = $218
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a) Simplify p x q x 4
b) Simplify t x t x t
The expressions are simplified to;
a. 4pq
b. t³
What are algebraic expressions?Algebraic expressions are defined as expressions that are made up of terms, variables, coefficients, factors and constants.
These algebraic expressions are also made up of mathematical or arithmetic operations, such as;
AdditionMutiplicationDivisionBracketParenthesesSubtractionFrom the information given, we have that;
The expressions are;
1. p x q x 4
Multiply the terms, we have that;
4qp
2.t x t x t
Multiply the terms, we get;
t³
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Evaluate : 3² x (-2)³ x 5 Working out:
Answer: 180
Step-by-step explanation:
Use the order of operations: PEMDAS
Parenthesis
Exponents
Multiplication/Division
Addition/Subtraction
3² x (-2)³ x 5 >There is nothing to simplify within parenthesis
>Exponents are next in Order of Operations
(3)(3) x (-2)(-2) x 5 >This is the exponents expanded
9 x 4 x 5 >Multiply from left to right
36 x 5
180
Use the table below to find the percentage of data items in a normal distribution that lie a. below and b. above a z-score of 1.8.
z-score
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Percentile 53.98 57.93 61.79 65.54 69.15 72.57 75 80 78.81 81.59 84.13
z-score 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
Percentile 86.43 88.49 90.32 91.92 93.32 94.52 95.54 96.41 97.13 97.72
z-score
2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0
Percentile 98.21 98.61 98.93 99.18 99.38 99.53 99.65 99.74 99.81 99.87
1. The percentage of data items below a z-score of 1.8 is 96.41%.
2. The percentage of data items above a z-score of 1.8, is 3.59%.
How did we arrive at the percentage?To find these percentages, we can look up the z-score of 1.8 is located in the row labeled "1.8" and the column labeled "Percentile."
The value in this cell is 96.41. This means that 96.41% of the data items in the normal distribution table will have a z-score that is less than or equal to 1.8.
P(z = 1.8) = 96.41%.
To find the percentage above 1.8
100 - 96.41 = 3.59%.
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50 POINTS FOR ANSWER AND BRAINLIEST
mukti step equation
Answer:
The answer is 53
Step-by-step explanation:
50+48+59+39+58=294
360-294=106
106/2=53
Answer:
53
Step-by-step explanation:
The sum of exterior angles of any polygon is 360 degrees
x + x + 59 + 48 + 50 + 39 + 58 = 360
2x + 254 = 360
x = (360 - 254)/2 = 53
A man had a square window with sides equal to 1 metre in his house. He decided that it lets in too much light, so he boarded up half of it and still had a square window 1 metre high and 1 metre wide. How did he do that? (6) Total: 40 marks
The man rotated the window by 45 degrees and covered one of the diagonals, resulting in a smaller square window with sides measuring 1 meter.
The man achieved the transformation of his square window by dividing it into two equal halves and boarding up one of them.
Let's analyze the steps he took to accomplish this:
Initially, the man had a square window with sides measuring 1 meter
This means that the window had an area of 1 square meter (1m x 1m = 1m²).
To reduce the amount of light coming through the window, the man decided to board up half of it.
This implies that he covered one of the equal halves of the square window, while leaving the other half open.
By boarding up half of the window, he effectively blocked off half of the area of the square window.
Since the original window had an area of 1 square meter, boarding up half of it reduces the effective area to 1/2 square meter (1m² ÷ 2 = 1/2m²).
The remaining open half of the window still retains its square shape, with sides equal to 1 meter.
Therefore, the man ends up with a square window that measures 1 meter in height and 1 meter in width, but with an area of only 1/2 square meter.
In summary, the man achieved the transformation by boarding up half of the square window, effectively reducing its area to half of the original size while maintaining the same dimensions for the remaining open half. This manipulation allows him to control the amount of light entering his house while preserving the square shape of the window.
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can someone explain how to do this please?
Answer: 97 degrees
Step-by-step explanation: 180-83=97
wich expression is equivalent to x -5/3
Answer:
[tex] {x}^{ - \frac{5}{3} } = \frac{1}{ {x}^{ \frac{5}{3} } } = \frac{1}{ \sqrt[3]{ {x}^{5} } } [/tex]
MARKING AS BRAINLIST PLS HELP
The value of probability P (A or B) is,
⇒ P (A or B) = 45
We have to given that;
To find the probability that either event will occur.
Now, By given figure we get;
P (A) = 25 + 5
P (A) = 30
P (B) = 5 + 15
P (B) = 20
P (A and B) = 5
Since, The formula is,
⇒ P (A or B) = P (A) + P (B) - P (A and B)
Substitute all the values we get;
⇒ P (A or B) = 30 + 20 - 5
⇒ P (A or B) = 50 - 5
⇒ P (A or B) = 45
Therefore, The value of probability P (A or B) is,
⇒ P (A or B) = 45
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find the ordered pair
The ordered pair that is a solution of the system is (-3, -3), the second option.
Which ordered pair is a solution of the system of inequalities?There are two ways of finding this.
You can use your graph and identify which of the given pointes lies in the region where the two shaded areas intersect.
Another way, is replacing the values of the coordinate points in both inequalities and checking that both are true when evaluated in the point.
Here we will use the graph, because you already had it (and you can see a more precise graph in the image at the end).
We can see that the region os solutions is on the left side of the graph, and the only point that lies on there is (-3, -3)
So that point is the solution.
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How many paths are there from $A$ to $B,$ if you travel along the edges? You can travel along each edge at most once, but you can pass through the same point more than once. (You can pass through $B,$ as long as you end up at the point $B.$)
Answer:
9
Step-by-step explanation:
You don't need to pass through each edge once.
If we name the top vertex 1 and the bottom vertex 2 then here are the possible combinations:
A-1-B
A-B
A-2-B
A-1-B-A-2-B
A-2-B-A-1-B
A-B-1-A-2-B
A-B-2-A-1-B
A-1-B-2-A-B
A-2-B-1-A-B
Some people say 6 because they think you need to pass through all the edges. But the only restriction with travelling on the edges is you can't pass one twice. The point is read the wording and it becomes easy.
Hope this helps!
A car rental company charge $50 a day and 20 cents per mile for renting a car. Let y be the total rental charge (in dollar) for a car for one day and x be the miles driven. The equation for the relationship between x and y is y = 50 + 20x How much will a person pay who rents a car for one day and drives it 100miles
Answer:$2050.
Step-by-step explanation:
To find out how much a person will pay for renting a car for one day and driving it 100 miles using the given equation, you can substitute x = 100 into the equation y = 50 + 20x and solve for y:
y = 50 + 20x
y = 50 + 20(100)
y = 50 + 2000
y = 2050
Therefore, a person who rents a car for one day and drives it 100 miles will pay $2050.
how do i do this? i have test on it tomorrow
The measure of the angle ∠ADC is 36°.
Given that a circle T, the inscribed angle ∠ABC = 72°, we need to find the measure of the angle ∠ADC,
So, according to the inscribed angle theorem,
2 ∠ABC = arc AC
arc AC = 144°
Now, since the whole circumference is 360°,
So,
arc ADC = 360° - arc AC
arc ADC = 216°
So,
∠ADC = 1/2 [arc ADC - arc AC]
∠ADC = 1/2 [216° - 144°]
∠ADC = 36°
Hence the measure of the angle ∠ADC is 36°.
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Please Answer!
Given the following diagram, find the required measures.
Answer:
55°
Step-by-step explanation:
if angle 4 = 105°, then angle 3 must be 180 - 105 = 75° (angles in straight line add up to 180°).
angles in a triangle also add up to 180°.
so we expect angle 2 to be 180 - angle 6 - angle 3
= 180 - 50 - 75
= 55°.
an academy:
1. Explain the concept of conservation of energy and provide examples to illustrate its
application.
solve the simultaneous equations
2x + 5y = -4
The solution to the system of equations is x = 2 and y = -1.
To solve the system of equations:
2x - 5y = 9 ...(1)
3x + 4y = 2 ...(2)
Multiplying equation (1) by 4 and equation (2) by 5, we can eliminate the variable 'y':
8x - 20y = 36 ...(3)
15x + 20y = 10 ...(4)
Adding equation (3) and equation (4), the 'y' terms cancel out:
(8x - 20y) + (15x + 20y) = 36 + 10
23x = 46
Dividing both sides of the equation by 23, we find:
x = 2
Plugging the value of 'x'
2(2) - 5y = 9
4 - 5y = 9
Subtracting 4 from both sides of the equation:
-5y = 9 - 4
-5y = 5
y = -1
Therefore, the solution to the system of equations is x = 2 and y = -1.
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Tyshawn is trying to pick out an outfit for the first day of school. He can choose from 8 pairs of pants, 5 t-shirts, 4 sweaters or hoodies, and 2 pairs of shoes. How many different outfits does Tyshawn have to choose from?
Step-by-step explanation:
A LOT of different outfits !
8 x 5 x 4 x 2 = 320 outfit possibilities
A boy walks 1260m on a bearing of 120°. How far south is he from his starting point
The boy is 630 meters south from his starting point.
To determine how far south the boy is from his starting pointWe must take into account the southward component of his shift.
We can imagine a right-angled triangle where the hypotenuse represents the boy's total displacement of 1260 meters, the angle between the hypotenuse and the south direction is 120°, and the side next to the angle represents the southward displacement given that the boy walks 1260 meters on a bearing of 120°.
We can use trigonometric functions to calculate the displacement to the south. Since the adjacent side and hypotenuse of a right triangle are connected in this instance, we will use the cosine function.
cos(120°) = adjacent / hypotenuse
cos(120°) = adjacent / 1260
Solving for the adjacent side (southward displacement):
adjacent = cos(120°) * 1260
adjacent = (-0.5) * 1260
adjacent = -630
The negative sign indicates that the southward displacement is in the opposite direction or "south" relative to the starting point.
Therefore, the boy is 630 meters south from his starting point.
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Complete the table by identifying u and du for the integral.
can anyone help me
The required first answer u = [tex]x^{2}[/tex] + 1 and du = 2x and second answer u = tanx and du = [tex]sec^2 x[/tex] .
Given that if [tex]\int\limits {f(g(x)) g'(x)} \, dx[/tex] then u = g(x) and du = g'(x),
[tex]\int\limits {\frac{x}{\sqrt{x^2+1} } } \, dx[/tex] and [tex]\int\limits {tan^2 x sec^2 x} \, dx[/tex]
To find u and du by using the integral property
[tex]\int\limits {f(g(x)) g'(x)} \, dx = f(g(x))[/tex].
Consider [tex]\int\limits {\frac{x}{\sqrt{x^2+1} } } \, dx[/tex]
The above integral can be expressed as
[tex]\int\limits {\frac{x}{\sqrt{x^2+1} } } \, dx = \int\limits {\frac{1}{\sqrt{x^2+1} } } \,x dx[/tex]
That implies, u = g(x) = [tex]x^{2}[/tex] + 1.
Differentiating with respect to x gives,
du = g'(x)
du = d/dx( [tex]x^{2}[/tex] + 1 )
du = 2x + 0.
du = 2x.
Consider [tex]\int\limits {tan^2 x sec^2 x} \, dx[/tex]
The above integral can be expressed as
[tex]\int\limits {tan^2 x sec^2 x} \, dx = \int\limits {(tanx)^2 sec^2 x} \, dx[/tex]
That implies, u = g(x) = tanx.
Differentiating with respect to x gives,
du = g'(x)
du = d/dx( tanx )
du = [tex]sec^2 x[/tex].
du = [tex]sec^2 x[/tex].
Hence, the required first answer u = [tex]x^{2}[/tex] + 1 and du = 2x and second answer u = tanx and du = [tex]sec^2 x[/tex].
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AB is the line segment, M is the midpoint of AB. A is (-4,5) and M is (5, -1), what are the coordinates of B?
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-4}~,~\stackrel{y_1}{5})\qquad B(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x -4}{2}~~~ ,~~~ \cfrac{ y +5}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M} }{(5~~,~~-1)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x -4 }{2}=5\implies x-4=10\implies \boxed{x=14} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +5 }{2}=-1\implies y+5=-2\implies \boxed{y=-7}[/tex]
Two snails have shells that are similar in shape. The younger snail has a shell with a height of 3.9 centimeters and a volume of 3 cubic centimeters. The older snail has a shell with a volume of 10 cubic centimeters. Estimate the height of the older snail’s shell. Round your answer to the nearest tenth.
can someone pls answer this asap and show ur work
The estimated height of the older snail's shell is approximately 13 centimeters.
To estimate the height of the older snail's shell, we can use the concept of proportional relationships between the heights and volumes of the snail shells.
Let's denote the height of the older snail's shell as "h" (in centimeters). We can set up a proportion based on the relationship between the heights and volumes of the snail shells:
(height of younger snail) / (volume of younger snail) = (height of older snail) / (volume of older snail)
Substituting the given values:
3.9 / 3 = h / 10
To solve for "h," we can cross-multiply and then divide:
3 * h = 3.9 * 10
3h = 39
h = 39 / 3
h ≈ 13
The estimated height of the older snail's shell is approximately 13 centimeters.
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what is the GCF of 36+60
Answer:
The GCF (Greatest Common Factor) of two numbers is the largest number that divides both of them. In this case, the GCF of 36 and 60 is 12.
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Solve h(t) = -16t^2 + 16t + 480 where t is time and h is height and finding out how long it would take a ball to hit the ground.
Answer: Factor the problem
Step-by-step explanation:
Take out the common factor (-16), it will leave you with (t^2 - t - 30)
Factor (t - 6) (t + 5)
t - 6 = 0 or t + 5 = 0
t = 6 seconds
Assume that the probability density function of a continuous random variant X is
[tex]f(x)\left \{ {{0,5x, 0\ \textless \ x\ \textless \ 2} \atop {0, else}} \right.[/tex]
try to compute:
(1) E(2X)
(2) E(X^2)
The calculated values of the expected values are E(2x) = 8/3 and E(x²) = 2
How to calculate the expected valuesFrom the question, we have the following parameters that can be used in our computation:
f(x) = 0.5x, 0 < x < 2
The expected value of 2x is calculated as
E(2x) = ∫2x * f(x) dx
So, we have
E(2x) = ∫2x * 0.5x dx
Evaluate
E(2x) = ∫x² dx
Integrate the function
So, we have
E(2x) = x³/3
Using the boundaries, we have
E(2x) = (2 - 0)³/3
Evaluate
E(2x) = 8/3
The expected value of x² is calculated as
E(x²) = ∫x² * f(x) dx
So, we have
E(x²) = ∫x² * 0.5x dx
Evaluate
E(x²) = ∫0.5x³ dx
Integrate the function
So, we have
E(x²) = 0.5x⁴/4
Using the boundaries, we have
E(x²) = 0.5 * (2 - 0)⁴/4
Evaluate
E(x²) = 2
Hence, the expected values are E(2x) = 8/3 and E(x²) = 2
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Need help on finding g .
Evaluating the piecewise function we will get:
g(-1) = -2
g(2) = 0
g(3) = 1/2
How to evaluate the piecewise function?To evaluate the piecewise function we need to use the correct part depending on the domains.
g(-1), here x = -1, then we need to use the second part of the function:
g(-1) = -(-1 - 1)² + 2 = -4 + 2 = -2
For the second one x = 2, we use the last part:
g(2) = (1/2)*2 - 1 = 0
For the last one, we have x = 3, again we need to use the last part:
g(3) = (1/2)*3 - 1 = 3/2 - 2/2 = 1/2
These are the 3 values.
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According to the rational zero theorem, which is not possible zero of the function
(x)=2x^4-5x^3+10x^2-9
A. -9
B. -1/2
C. 1/3
D. 3
Answer:
C. 1/3
Step-by-step explanation:
You want to identify the rational number listed that cannot be a root of the given polynomial.
Rational root theoremPossible rational roots will be off the form ...
± (divisor of the constant) / (divisor of the leading coefficient)
ApplicationWhen the divisors are listed, this is ...
±{1, 3, 9}/{1, 2}
This shows you that 3 cannot be the denominator of any possible rational root.
1/3 is not a possible zero of the function
__
Additional comment
The list of possible roots is ±{1/2, 1, 3/2, 3, 9/2, 9}.
As it happens, neither of the two real roots is rational.
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Beridze Manufacturing expects to produce 2,400 units in January and 3,700 units in February. Beridze budgets $45 per unit for direct materials. The amount of indirect materials needed for production has been determined to be insignificant and will therefore not be considered in the calculation. The balance in the Raw Materials Inventory account (all direct materials) on January 1 is $39,150. Beridze desires the ending balance in Raw Materials Inventory to be 10% of the next month's direct materials needed for production. Desired ending balance for February is $50,200. What is the cost of budgeted purchases of direct materials needed for January?
Question content area bottom
Part 1
A.$ 108 comma 000
$108,000
B.$ 79 comma 650
$79,650
C.$ 124 comma 650
$124,650
D.$ 85 comma 500
A
Step-by-step explanation:
In 2020, the Ministry of Health, in a report on investment in infrastructure and equipment for health units (2007-2020), counted 2,074 health units (between new and improved). If the number of improved health units exceeds the new ones by 200, how many new and improved health units are shown in the report?
The number of new health units is 937, and the number of improved health units is 1,137.
The number of improved health units exceeds the new ones by 200. In other words, I = N + 200.
We also know that the total number of health units counted in the report is 2,074.
Therefore, we have the equation N + I = 2,074.
Substituting the value of I from the first equation into the second equation, we can solve for N:
N + N + 200 = 2,074
2N + 200 = 2,074
2N = 1,874
N = 937
Now, we can substitute the value of N back into the first equation to find I:
I = N + 200
I = 937 + 200
I = 1,137
Therefore, the number of new health units is 937, and the number of improved health units is 1,137.
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