Substitution refers to the process of replacing one group with another. We can say that it refers to replacing a variable with another given value.
For example, given that x = 17, we can substitute the value of 17 in for x and evaluate the obtained expression to get the value of x.
We can name the expression: F (x) = 17 + 3x - 4.
here , let's say x = 2
then , F (x) = 17 + 6 + 2 = 25
The algebraic method which is used for solving simultaneous linear equations is known as the substitution method. The value of one variable from one equation is substituted in the second equation, as the name implies.
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Edwin graphs the relationship of the gallons of milk he buys in terms of dollars.
Sam buys milk from a different shop. He writes an equation for the amount he spends on milk, p = 3.4g, where p is the cost and g is the gallons of milk bought. Who buys milk at a lower rate, and what is the price?
Using a proportional relationship, it is found that Sam buys milk at a lower rate, of $3.4 per gallon.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
Researching the problem on the internet, Edwin's graph goes through (2,7), hence the price is:
p = (7/2)g = 3.5g.
3.5 > 3.4, hence Sam buys milk at a lower rate, of $3.4 per gallon.
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How could the relationship of the data be classified? (1 point)
(see photo)
A fairly strong positive correlation
A fairly weak positive correlation
A fairly strong negative correlation
A fairly weak negative correlation
The relationship of the data can be classified as a fairly strong positive correlation.
What is positive correlation?
Correlation is a statistical measure used to measure the relationship that exists between two variables.
Positive correlation is when two variables move in the same direction. If one variable increases, the other variable also increases. When there is a positive correlation, the graph of the variables is upward sloping
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Do you do boblox if so send me a request my acc is ravenonperks.
One day, eleven babies are born at a hospital. assuming each baby has an equal chance of being a boy or girl, what is the probability that at most nine of the eleven babies are girls?
The probability of having, at most, 9 girls, is 0.9515
How to get the probability?The probability that a random baby is a girl is:
p = 0.5
And the probability that a random baby is a boy is:
q = 0.5
Then the probability that, at most, 9 out of 11 babys are girls, is given by:
1 - p(10) - p(11)
Where P(10) is the probability that 10 of the babies are girls and p(11) is the probability that the 11 babies are girls.
p(10) = C(11, 10)*(0.5)^10*(0.5)^1 = C(11, 9)*(0.5)^11
Where C(11, 10) is the combinations of 10 elements that we can make with a set of 11 elements, such that:
C(11, 10)= 11!/(11 - 10)!*10! = 11
Replacing that, we get:
P = 11*(0.5)^11 = 0.0054
p(11) = C(11, 11)*0.5^11 = 1*0.5^11 = 0.0005
Then the probability is:
P = 1 - 0.0054 - 0.0005 = 0.9515
The probability of having, at most, 9 girls, is 0.9515
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What is the probability that a random sample of 12 students will have a mean reading rate of more than 95 wpm
The probability that a random sample of 12 students will have a mean reading rate of more than 95 wpm is 0.0418.
There are several sorts of mean in arithmetic, in particular in statistics. each implies serves to summarize a given institution of information, often to better recognize the general fee of a given record set.
They imply (aka the mathematics mean, extraordinary from the geometric imply) of a dataset is the sum of all values divided with the aid of the entire variety of values. it is the maximum commonly used a degree of crucial tendency and is regularly referred to as the “average.”
Common can truely be described as the sum of all of the numbers divided by means of the entire quantity of values. An average is described as the mathematical common of the set of or more statistics values. common is commonly described as implying or arithmetic mean. mean is really a method of describing the average of the sample.
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If a = √3-√11 and b = 1 /a, then find a² - b²
If [tex]b=\frac1a[/tex], then by rationalizing the denominator we can rewrite
[tex]b = \dfrac1{\sqrt3-\sqrt{11}} \times \dfrac{\sqrt3+\sqrt{11}}{\sqrt3+\sqrt{11}} = \dfrac{\sqrt3+\sqrt{11}}{\left(\sqrt3\right)^2-\left(\sqrt{11}\right)^2} = -\dfrac{\sqrt3+\sqrt{11}}8[/tex]
Now,
[tex]a^2 - b^2 = (a-b) (a+b)[/tex]
and
[tex]a - b = \sqrt3 - \sqrt{11} + \dfrac{\sqrt3 + \sqrt{11}}8 = \dfrac{9\sqrt3 - 7\sqrt{11}}8[/tex]
[tex]a + b = \sqrt3 - \sqrt{11} - \dfrac{\sqrt3 + \sqrt{11}}8 = \dfrac{7\sqrt3 - 9\sqrt{11}}8[/tex]
[tex]\implies a^2 - b^2 = \dfrac{\left(9\sqrt3 - 7\sqrt{11}\right) \left(7\sqrt3 - 9\sqrt{11}\right)}{64} = \boxed{\dfrac{441 - 65\sqrt{33}}{32}}[/tex]
Triangle A B C. Side A B is 4, B C is 5, A C is 3. Triangle A prime B prime C prime.
If the scale factor for the dilation shown is 3, which is the length of B'C'?
5/3
8
12
15
Answer:
The correct answer is 15.
Step-by-step explanation:
We are given that the original sides BC is 5. To find the length of B'C' we take the side of BC and multiply it by the scale factor.
5 (original BC) x 5 (the given scale factor) = 15
Answer:
15
Step-by-step explanation:
correct on edge 2023
TRUE OR FALSE: No matter the population distribution from which a sample of size n is taken, we can use the normal distribution to approximate the distribution of the sample mean as long as n is large enough.
Answer:
true
Step-by-step explanation:
mean we show up the distribution
PLEASE HELP ME I NEED HELP I'LL GIVE YOU BRAINLEST PLEASE I BEG YOU NICELY.
Can some one help me with this. This isn't school work this is math that I am doing at home on prodigy the app. I will mark you brainlest if you get this correct. Also look at both of the pictures one of them has a hint for you.
The perimeter of a rectangle is the sum of its side lengths.
A rectangle is special in that sides opposite one another have equal length. So if [tex]x[/tex] is the length of the horizontal sides, the total perimeter of the rectangle is
[tex]4\,\mathrm{cm} + 4\,\mathrm{cm} + x\,\mathrm{cm} + x\,\mathrm{cm} = (8+2x)\,\mathrm{cm}[/tex]
We're given the perimeter is actually 18 cm, so
[tex]8+2x = 18[/tex]
Solve for [tex]x[/tex].
[tex](8 + 2x) - 8 = 18 - 8[/tex]
[tex]2x = 10[/tex]
[tex]\dfrac12 \cdot 2x = \dfrac12 \cdot 10[/tex]
[tex]\boxed{x = 5}[/tex]
A roll of aluminum for you measure 76.2 m long by 304 m wide what is the length in millimeters
Answer:
76,200 mm
Step-by-step explanation:
1 meter = 1000 mm, by definition. Make that a conversion factor:
(1 meter)/(1000 mm), or (1000 mm)/(1 meter). Both are equal to 1, since 1 meter = 1000 mm. We can multiply anything by 1, so take the original measurement of length of 76.2 meters, and multiply it by (1000 mm)/(1 meter).
(76.2 meters)*((1000 mm)/(1 meter)) = 76,200 mm. The meters cancels, leaving just mm, the desired unit.
The perimeter of square JKLM is 48 units.
Square J K L M is shown. The length of J K is x + 3.
What is the value of x?
6
9
12
15
Answer:
9
(Correct On Edgen)
Quick algebra 1 question only for 5 points :(
I would give more but people have been stealing my 100 point questions :(
Only answer if you know the answer, quick shout-out to Dinofish32, tysm for the help!
[tex]x = y + 5 \\ y = x - 5[/tex]
2)[tex]x = \frac{3}{8} y \\ y = \frac{8}{3}x [/tex]
3)[tex]x = - y - 2 \\ y = - 2 - x[/tex]
4)[tex]x = 6y + 1 \\ 6y = x - 1 \\ y = \frac{x - 1}{6} [/tex]
5)[tex]x = y - 11 \\ y = x + 11[/tex]
6)[tex]x = 8y \\ y = \frac{x}{8} [/tex]
7)[tex]x = \frac{ - 1}{3} y \\ y = - 3x[/tex]
[tex]basically \: flip \: x \: and \: y \: then \: solve \: for \: y[/tex]
Which monomials are perfect squares? Select three options.
6x2
9x8
17x9
25x12
36x16
Answer: B, D, E
Step-by-step explanation:
Complete this sequence.
30, 21, 12, 3, [?], [ ]
Answer:
-6, -15
Step-by-step explanation:
Each term is 9 less than the previous term.
Two fishing boats leave the same dock at the same time. One boat heads northeast and is travelling at a speed of 15 km/h while the other is travelling northwest at 18 km/h. After 45 minutes, the boats are 14.0 km apart. Assuming that both boats are travelling in straight paths, what is the angle between their paths to the nearest degree?
The angle between their paths to the nearest degree is 68⁰.
Displacement of each boats after 45 minutes
first displacement, a = 15 km/h x (45/60)
first displacement, a = 11.25 km
second displacement, b = 18 km/h x (45/60)
b = 13.5 km
Angle between their paths to the nearest degreec² = a² + b² - 2ab(cosθ)
2ab(cosθ) = a² + b² - c²
cosθ = (a² + b² - c²)/(2ab)
cosθ = (11.25² + 13.5² - 14²) / (2 x 11.25 x 13.5)
cosθ = 0.371
θ = arc cos(0.371)
θ = 68.22 ⁰
Thus, the angle between their paths to the nearest degree is 68⁰.
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l=10m,b=8m,h=5m
Please answer
Step-by-step explanation:
we have given
l=10m
b=8m
h=5m
volume =?
area=?
volume =l*b*h
= 10*8*5
=400
area=2(lb+lh+bh)
=2(10*8+10*5+8*5)
=2(80+50+40)
=2(170)
=340
hope this is helpful please make me brainliest
Solve for x when [tex]x^{yz} =y^{2}[/tex]
The value of x in x^yz = y^2 is [tex]x = \sqrt[yz]{y^2}[/tex]
How to solve for x?The equation is given as:
x^yz = y^2
Rewrite the equation properly as follows
[tex]x^{yz} = y^2[/tex]
Take the yz root of both sides
[tex]\sqrt[yz]{x^{yz}} = \sqrt[yz]{y^2}[/tex]
Apply the law of indices
[tex]x^{\frac{yz}{yz}} = \sqrt[yz]{y^2}[/tex]
Divide yz by yz
[tex]x = \sqrt[yz]{y^2}[/tex]
Hence, the value of x in x^yz = y^2 is [tex]x = \sqrt[yz]{y^2}[/tex]
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Answer:
e
Step-by-step explanation:
Using euler's identity we can see that e^ipi=-1 and considering that i=y and i^2=-1 we can conclude that x=e
The graph of the function f(x) = -(x+6)(x + 2) is shown below. 46 £ Mark this and return 6+ 4 2 1-2- 4 2 ++ 4 6 X Which statement about the function is true? The function is increasing for all real values of x where O The function is increasing for all real values of x where -6 < x < -2. O The function is decreasing for all real values of x where x -2. O The function is decreasing for all real values of x where X
The correct statements regarding the behavior of a quadratic function are:
The function in increasing for all real values of x where -6 < x < -2.The function is decreasing for all real values of x where x < -6 or x > -2.When is a quadratic function increasing or decreasing?A quadratic function with roots [tex]x_1[/tex] and [tex]x_2[/tex] is defined by:
[tex]y = a(x - x_1)(x - x_2)[/tex]
In which a is the leading coefficient.
The coefficient influences the behavior, as follows:
If a < 0, the function is increasing between the roots, and decreasing otherwise.If a > 0, the function is decreasing between the roots, and increasing otherwise.In this problem, the function is:
f(x) = -(x + 6)(x + 2).
The roots are x = -6 and x = -2, and the leading coefficient is of a = -1 < 0, hence:
The function in increasing for all real values of x where -6 < x < -2.The function is decreasing for all real values of x where x < -6 or x > -2.More can be learned about quadratic functions at https://brainly.com/question/24737967
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help me I need help now!!
what help? how can i help you?
Picture vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
Answer:
pretzel: 2
hotdog: 3
Step-by-step explanation:
Let h be the hotdog price and p the pretzel price.
We know that:
h + p = 5
and
2h + 3p = 12
We can solve this system of equations:
h = 5-p
2(5-p) + 3p = 12
So the second eq. becomes:
10 - 2p + 3p = 12
10 + p = 12
p = 2
Sub in the first:
h = 5 - p = 5-2 = 3
So p = 2, h = 3
Answer: $3 / hot dog
Step-by-step explanation:
Given information:
1 hot dog + 1 pretzel = $5
2 hot dogs + 3 pretzels = $12
Set variables:
Let x be the price per hot dog
Let y be the price per pretzel
Set system of equations:
x + y = 5
2x + 3y = 12
Multiply the first equation by 3:
3x + 3y = 15
2x + 3y = 12
Subtract the second equation from the first equation (Elimination):
(3x + 3y) - (2x + 3y) = 15 - 12
3x + 3y - 2x - 3y = 3
(3y - 3y) + 3x - 2x = 3
0 + x = 3
[tex]\boxed{x=3}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
what is the temperature in Celsius? (LOOK AT PIC)
Answer:
21
Step-by-step explanation:
(69.8-32)×(5/9)=21
In a bag of 10 marbles, there are 4 blue, 3 red, 2 green,
and 1 yellow. What is the probability that you draw one
marble that is blue, replace it, and draw another marble
that is red?
Enter your answer as a fraction in lowest terms. Do not add
spaces to your answer. (EX: 1/2)
Answer: 1/8
Step-by-step explanation:
There are 3 pieces of glass that are cracked. if a rock is thrown by a lawn mower hits the window, what is the probability, that the rock hits a piece of glass that is cracked?
The chance or chance that the lawn mower will hit a chunk of glass that is already cracked is calculated with the aid of dividing the variety of glasses that are cracked by way of the full quantity of glasses. on this item, the unknown may be calculated through . The solution is, therefore, 0.20.
Opportunity is a measure of the chance of an event to arise. Many occasions cannot be predicted with overall reality. We are able to are expecting only the danger of an event to arise i.e. how likely they're to manifest, using it.
The possibility is the branch of arithmetic regarding numerical descriptions of how in all likelihood an occasion is to arise, or how possibly it's miles that a proposition is actual. The possibility of an occasion various between 0 and 1, where, roughly talking, 0 indicates the impossibility of the event and 1 shows reality.
The probability of an event can be calculated by possibility components via surely dividing the favorable range of effects through the full range of possible outcomes.
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While traveling to Europe, Phelan exchanged 250 US dollars for euros. He spent 150 euros on his trip. After returning to the United States he converts his money back to US dollars. How much of the original 250 US dollars does Phelan now have? Round to the nearest cent.
The computation shows that the amount will be 44.70 Dollars.
How to illustrate the information?The options are missing: Here are the missing options:
A. 44.70 US dollars
B. 73.06 US dollars
C. 136.87 US dollars
D. 140.41 US dollars
For solving this question first we will convert the USD to euros.
The conversion rate we have is:
1 euro = 1.3687 USD
250/1.3687 = 182.655 euros
Now we will subtract it from what he has spent:
= 182.655 - 150
= 32.655 euros
Now we will again convert it back to USD. This will be:
32.655 euros * 1.3687 = 44,695 us dollars
Therefore, the answer is 44.70.
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A surveyor measures the angle of elevation of the top of a mountain from a point at
sea level as 20◦. She then travels 1000 m along a road that slopes uniformly uphill
towards the mountain. From this point, which is 100 m above sea level, she measures
the angle of elevation as 23◦. Find the height of the mountain above sea level, correct to
the nearest metre.
(use sin rule/ cos rule)
The height of the mountain from a point a sea level is approximately 1496.650 meters.
What is the height of mountain from sea level?
First, we construct the geometric diagram of the situation and find all needed angles and sides to determine the height of the mountain. First, we determine the missing side x by the law of sines:
Law of sines
1000 m/sin 3° = x/sin 14.261°
x ≈ 4706.886 m
Now we determine the height of the mountain by trigonometric functions:
h = 100 m + (4706.886 m) · sin 17.261°
h ≈ 1496.650 m
The height of the mountain from a point a sea level is approximately 1496.650 meters.
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Please help with the bonus! Thank you:)
a. The function that models the situation is F(t) = 48(1.08)ˣ
b. The price of the stock 6 years from now is $76.17
c. Find the graph in the attachment
d. I receive a dividend of $0.026.
a. Write a function f(t) that models the situation.Since the stock price increases at a rate of 8% every year, and is initially $48, it follows exponential growth.
So, the current price [tex]F(t) = A(1 + r)^{t}[/tex] where
A = price at current moment = $48, r = rate of growth = 8% = 0.08 and t = number of yearsSo, [tex]F(t) = A(1 + r)^{t}[/tex]
[tex]F(t) = 48(1 + 0.08)^{t} \\= 48(1.08)^{t}[/tex]
So, the function that models the situation is F(t) = 48(1.08)ˣ
b. Determine the price of the stock 6 years from now?The price of the stock 6 years from now is gotten when t = 6.
So,
[tex]F(t) = 48(1.08)^{t} \\= 48(1.08)^{6} \\= 48(1.5869)\\= 76.17[/tex]
So, the price of the stock 6 years from now is $76.17
c. Sketch a graph of the price of the function vs time in yearsFind the graph in the attachment
d. BonusSince every quarter, the company pays a dividend of 1.5 %, the rate per year would be r = 1.5 % ÷ 1/4 year = 1.5 % × 4 = 6 % per year.
Since they pay at a rate, r = 6 % = 0.06 of the stock price, F(t) as dividend.
After n years, the dividend is D = (r)ⁿF(t)
= (0.06)ⁿF(t)
So, [tex]D = (0.06)^{t}F(t) \\= (0.06)^{t}[4.8(1.08)^{t}][/tex]
So, after 3 years when t = 3,
[tex]D = (0.06)^{t}[4.8(1.08)^{t}]\\D = (0.06)^{3}[4.8(1.08)^{3}]\\D = 0.000216 \times 48 \times 1.2597\\D = 0.013[/tex]
Since there are 3 shares, the total dividend would be D' = 3D
= 3 × 0.013
= 0.026
So, i receive a dividend of $0.026
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Two fishing boats leave the same dock at the same time. One boat heads northeast and is travelling at a speed of 15 km/h while the other is travelling northwest at 18 km/h. After 45 minutes, the boats are 14.0 km apart. Assuming that both boats are travelling in straight paths, what is the angle between their paths to the nearest degree?
The boat speeds of 15 km/h and 18 km/h, directions, and the time of travel of 45 minutes gives the angle between their paths as approximately 68°.
How can the angle between the paths of the boats be found?The given parameters are;
Direction of the first boat = Northeast
Speed of the first boat = 15 km/h
Direction of the second boat = Northwest
Speed of the second boat = 18 km/h
Distance between the boats after 45 minutes = 14.0 km.
45 minutes = 0.75 × 1 hour
Distance traveled by the first boat in 45 minutes, d1, is therefore;
d1 = 15 km/h × 0.75 hr = 11.25 km
For the second boat, we have;
d2 = 18 km/h × 0.75 hr = 13.5 km
Using cosine rule, we have;
14² = 11.25² + 13.5² - 2 × 11.25 × 13.5 × cos(A)
Where A is the angle between the paths of the two boats.
Which gives;
[tex]cos(A) = \frac{361}{972} [/tex]
[tex] A= \mathbf{ arccos\left(\frac{361}{972} \right) }\approx 68^\circ [/tex]
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Select the correct answer. which equation is correctly rewritten to solve for x?
The rewritten equation for the given equation is [tex]x=\frac{h+g}{-f}[/tex]. So, option C is correct.
How to rewrite an equation?A linear equation given in the form ax + b = c can be rewritten to solve for x as below:
ax + b = c
⇒ ax = c - b
∴ x = (c - b)/a
So, here the basic operations such as addition, subtraction, multiplication, and division are used on both sides to rewrite the given equation for solving x.
Calculation:Given equation is -fx - g = h
Step 1: Adding 'g' on both sides
-fx - g + g = h + g
⇒ -fx = h + g
Step 2: Dividing by '-f' on both sides
-fx = h + g
⇒ -fx/-f = (h + g)/-f
∴ x = (h + g)/-f
Therefore, the rewritten equation to solve for x is x = (h + g)/-f.
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Disclaimer: The given question was incomplete in the portal. Here is the complete question.
Question: Select the correct answer. which equation is correctly rewritten to solve for x?
Equation: -fx = h + g
A. x = (g - h)/f
B. x = (h - g)/-f
C. x = (h + g)/-f
D. x = (h + g)/f
Can someone help me on these problems and show work please !
Answer:
1. 3 terms; degree 5
2. 2 terms; degree 3
3. 9mn³ + 14mn²
4. 9a^4b^3
Step-by-step explanation:
Problems 1 - 2:
Each product of a number and variables is a term. The number may be 1, so it is not written. Also, a term may not have a variable.
The degree of a term is the sum of the exponents of all the variables of the term. A plain variable, such as x has an exponent of 1 which is not written but must be added to determine the degree.
The degree of the polynomial is the same as the degree of the term with the highest degree.
1.
3 terms
degree 5
2.
2 terms
degree 3
Problems 3 - 4:
Combine like terms. Like terms have the same variables and exponents.
3.
6mn³ - mn² + 3mn³ + 15mn² =
= 6mn³ + 3mn³ - mn² + 15mn²
= 9mn³ + 14mn²
4.
a^4b^3 + 8a^4b^3 =
= 1a^4b^3 + 8a^4b^3
= 9a^4b^3
triangle properties help