what is the probability of rolling a 6 and then a 2 from one die in that order?
and
how many different ways are there to roll 3 dice??
*PLEASE ANSWER ASAP*
Answer:
1/36 and 216
Step-by-step explanation:
The probability of rolling a 6 or a 2 on either piece of dice is 1/6. Therefore, 1/6x1/6= 1/36.
When rolling three dice, we also need to consider the fact that there is a 1/6 chance of rolling any number. 6x6x6= 216.
What is the solution to this equation? -2x + 15 = 30
After simplifying we get, the solution to the equation as -2x + 15 = 30 is x = -7.5.
To solve the equation -2x + 15 = 30, we need to isolate the variable x on one side of the equation. We can do this by performing the same operation on both sides of the equation to maintain its balance.
First, we will subtract 15 from both sides of the equation to get:
-2x + 15 - 15 = 30 - 15
Simplifying the left-hand side and the right-hand side of the equation, we obtain:
-2x = 15
Next, we will divide both sides of the equation by -2 to isolate x:
-2x/-2 = 15/-2
Simplifying, we get:
x = -7.5
Therefore, the solution to the equation -2x + 15 = 30 is x = -7.5.
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Find the following for each equation:
The rate of change?
State whether the y-values are increasing,
decreasing, or neither as x increases.
Give the y-intercept.
List the coordinates of two points that lie on the
graph of the equation.
a. y = 1.5x
b. y = −3x + 10
c. y = −2x + 6
d. y = 2x + 5
a) Rate of change: 1.5
b) Rate of change: -3
c) Rate of change: -2
d) Rate of change: 2, other values are calculated below.
Define the term equation?When two sides of a balance scale are equal, the equation will remain true.
a. y = 1.5x
Rate of change: 1.5 (which means that for every increase of 1 in x, y increases by 1.5)
Y-values increase as x increases
Y-intercept: 0 (the point where the line crosses the y-axis)
Two points: (0,0) and (2,3)
b. y = -3x + 10
Rate of change: -3 (which means that for every increase of 1 in x, y decreases by 3)
Y-values decrease as x increases
Y-intercept: 10
Two points: (0,10) and (3,1)
c. y = -2x + 6
Rate of change: -2 (which means that for every increase of 1 in x, y decreases by 2)
Y-values decrease as x increases
Y-intercept: 6
Two points: (0,6) and (3,0)
d. y = 2x + 5
Rate of change: 2 (which means that for every increase of 1 in x, y increases by 2)
Y-values increase as x increases
Y-intercept: 5
Two points: (0,5) and (3,11)
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If the triangles shown at the right are similar,
what is the value of x?
Answer:
28.235
Step-by-step explanation:
10/34 = x/96
960= 34x
960/34= x
x= 28.235
[tex]4/7 + 3/4 + 1/8[/tex]
Fraction
Therefore , the solution of the given problem of fraction comes out to be 81/56 is the result of adding the three decimals.
A fraction is what?Any combination of like-sized pieces or portions can represent a whole. Standard English defines "quantity" as "a portion" of a particular measure. 8, 3/4. Wholes also include fractions. In mathematics, numerals are expressed by the ratio of quotient to ratio. Every one of these fractions of integers are simple fractions. The fraction contains a fraction, but the fraction's remainder is a challenging fraction. because the values, 4.91, and numerators of real fractions can vary.
Here,
We must identify a common denominator in order to combine these fractions. Finding the denominators' least common multiple (LCM), in this instance 56, is one way to accomplish this.
=> 4/7 + 3/4 + 1/8 = (4/7) * (8/8) + (3/4) * (14/14) + (1/8) * (7/7)
=> 32/56 + 42/56 + 7/56
=> (32 + 42 + 7)/56
=> 81/56
Therefore, 81/56 is the result of adding the three decimals. The ultimate solution is this fraction because it cannot be further condensed.
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Kelly's taxable income is $50,000. Approximately what percent of her taxable income is her tax? Round to one tenth of a percent.
Approximately 24.1% of Kelly's taxable income is her tax.
What is percent?
Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.
To determine what percent of Kelly's taxable income is her tax, we need to calculate her tax liability first.
Assuming that Kelly files as a single taxpayer with no dependents and takes the standard deduction, her taxable income of $50,000 falls into the 22% tax bracket for the year 2021.
Using the IRS tax tables for 2021, Kelly's tax liability would be approximately:
$9950 + (0.22 * ($50,000 - $40,525)) = $9950 + $2095.50 = $12045.50
Therefore, Kelly's tax liability is approximately $12,045.50.
To calculate what percent of her taxable income is her tax, we can divide her tax liability by her taxable income and multiply by 100:
($12,045.50 / $50,000) * 100 = 24.09%)
Therefore, approximately 24.1% of Kelly's taxable income is her tax. Rounded to one tenth of a percent, this is 24.1%.
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Shefali goes to a farmers’ market every Saturday. Two Saturdays ago, Shefali purchased 3 apples and 4 oranges for a total of $3.47 . Last Saturday, she purchased 1 2 12 oranges, but no apples, and spent $6.36 . Today, she only has one $10 bill. Given that none of the prices have changed over the last 3 weeks, what is the maximum number of apples she can purchase today?
The maximum number οf apples she can purchase is 15.
Let's start by finding the cοst οf οne apple and οne οrange using the infοrmatiοn frοm twο Saturdays agο:
3a + 4ο = 3.47, where "a" is the cοst οf οne apple and "ο" is the cοst οf οne οrange.
We can simplify this equatiοn by dividing bοth sides by 3: a + 4/3 ο = 1.1567
Nοw, let's use the infοrmatiοn frοm last Saturday:
12ο = 6.36
ο = 0.53
We can substitute this value οf "ο" intο οur simplified equatiοn tο find the cοst οf οne apple:
a + 4/3(0.53) = 1.1567
a = 0.63
Sο, οne apple cοsts $0.63 and οne οrange cοsts $0.53.
If Shefali has οne $10 bill and she wants tο buy the maximum number οf apples, she can spend at mοst $10 οn apples. Let "n" be the number οf apples she can buy:
0.63n ≤ 10
n ≤ 15.87
Since Shefali can't buy a fractiοnal part οf an apple, the maximum number οf apples she can purchase is 15.
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Which is an example of a survey involving quantitative data?
The number of cavities each person has had is an example of a survey involving quantitative data.
Quantitative data is any data that can be expressed in numerical terms and can be measured or counted. It includes variables such as counts, amounts, measurements, or ratings. In the given options, the number of cavities each person has had is a numerical variable that can be counted and analyzed statistically, making it an example of quantitative data. Other options, such as favorite food or color of the walls, are qualitative data, which is non-numerical and cannot be measured in numerical terms.
Quantitative data is commonly used in surveys, experiments, and statistical analyses to study patterns and relationships between variables. It allows for precise measurements, comparisons, and statistical modeling. Examples of quantitative data include age, height, weight, temperature, test scores, sales figures, and population counts. By contrast, qualitative data is often used to explore attitudes, beliefs, perceptions, or opinions, and is typically recorded as text or verbal data. Examples of qualitative data include interviews, open-ended survey questions, observations, and focus group discussions.
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The complete question is:
Which survey uses quantitative data, as an example?
each person individual's preferred food.
how many cavities each individual has had.
the color of each person's bedroom's walls.
the type of car each individual person owns.
Nachelle can text 63 words in 6 minutes. At this rate, how many minutes would it take her to text 147 words? pls help this will save my grade
Answer:
14 minutes
Step-by-step explanation:
We take
63 / 6 = 10.5 words per minute
So, Nachelle can text 10.5 words per minute.
At this rate, how many minutes would it take her to text 147 words?
We take
147 / 10.5 = 14 minutes
So, at this rate, it would take her 14 minutes to text 147 words.
PLEASE SHOW WORK!!!!!!!!!
He needed to save $15 over the remaining 2 weeks. This means she needed to save an average of $7.50 per week to reach her goal.
What distinguishes the weighted mean from the arithmetic mean?Both the arithmetic mean and the weighted mean may be used to determine the average of a group of integers. The sum of all the numbers in the group divided by the entire amount of numbers in the set yields the arithmetic mean. Regardless of significance or relevance, it gives each integer in the set the same amount of weight. On the other hand, the weighted mean gives the integers in the set distinct weights based on their significance or relevance. This indicates that certain numbers in the set provide a greater weighted mean contribution than others.
Given that, Bobbi's goal was to save an average of $7.00 per week.
Thus the amount saved is:
12 x $7 = $84.
He saved $5 for 11 weeks thus,
11 x $5 = $55.
Then in the 12th week the amount saved is:
$29 - $14 = $15.
Hence, she needed to save $15 over the remaining 2 weeks. This means she needed to save an average of $7.50 per week to reach her goal.
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4.02 Lesson check ! (2)
The given sequence -1, -2, -6, -24 is not arithmetic.
How to determine if the sequence is arithmetic?An arithmetic sequence is a sequence where the difference between any pair of consecutive terms is a constant knowed as the common difference, and if d is that common difference, we can write the recursive formula as:
f(n) = f(n - 1) + d
Here we have the sequence:
-1, -2, -6, -24
Taking the differences we will get:
-2 - (-1) = -1
-6 - (-2) = -4
-24 - (-6) = -18
The differences are different, thus, this is not an arithmetic sequence.
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In how many ways can 6 people be seated in a row of 9 chairs
There are 60,480 ways to seat 6 people in a row of 9 chairs using the multiplication principle of counting.
There are 9 choices for the first person, 8 choices for the second person (since one chair is already taken), 7 choices for the third person, and so on. Therefore, the total number of ways 6 people can be seated in a row of 9 chairs is:
[tex]9 * 8 * 7 * 6 * 5 * 4 = 60,480[/tex]
So there are 60,480 ways to seat 6 people in a row of 9 chairs.
To count the number of ways 6 people can be seated in a row of 9 chairs, we can use the multiplication principle of counting.
First, we consider the number of choices for the first person. Since there are 9 chairs and the order in which the people are seated matters, there are 9 choices for the first person. Once the first person is seated, there are 8 chairs remaining for the second person to choose from, since one chair is already taken. Therefore, there are 8 choices for the second person. Continuing in this way, there are 7 choices for the third person, 6 choices for the fourth person, 5 choices for the fifth person, and 4 choices for the sixth person.
To find the total number of ways to seat 6 people in a row of 9 chairs, we multiply the number of choices at each step together. Hence, the total number of ways is:
[tex]9 * 8 * 7 * 6 * 5 * 4 = 60,480[/tex]
So there are 60,480 ways to seat 6 people in a row of 9 chairs.
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The complete question is:
How many different arrangements are possible for 6 persons to sit in a row of 9 chairs?
a) 6720
b) 60480
c) 30
d) 346
When his first child was born, a father put $3000 in a savings account that pays 4% annual interest, compounded quarterly. How much will be in the account on the child's 18th birthday? Answer rounded to the whole number
Answer:
$6141
Step-by-step explanation:
We can use the formula for compound interest to find the amount in the account after 18 years:
A = P(1 + r/n)^(nt)
Where:
A = the amount in the account after 18 years
P = the principal amount (initial deposit) = $3000
r = the annual interest rate = 4% = 0.04
n = the number of times the interest is compounded per year = 4 (quarterly)
t = the time in years = 18
Plugging in these values, we get:
A = 3000(1 + 4%/4)^(4*18)
A = 3000(1.01)^72
A = 3000*2047
A = 6141
Rounding to the nearest whole number, we get:
A = $6141
Therefore, there will be $6141 in the account on the child's 18th birthday.
A markoting surviry is concluctod in when students are to tasto two diflorbet brands of soff drink. Their task is io corrocily idontify the brand tastod. A random sample of 190 students is taken. Assume that the stutents thove no ability to distingush betwoen the two brands. Comploto (a) through (d) below a. What is the probability that the sample will have between 50% and 55% of the identifications correct? (Round to four decimal places as needed.) b. The probability is 90 os that the sample percentage is contained within what symmetrical limits of the population percentage? Identify the limits of the population percentage. The lower limit is The upper limit is (Round to four decimal places as needed.) There is a 90% probability that the sample percentage will be contained within % symmetrically around the population percentage. (Round to the one decimal place as needed.) c. What is the probability that the sample percentage of correct A marketing survoy es conducted in which students are to taste two dilinrent brands of soft drink. Their task is to correctly identify the brand tasted. A tandom sample of 190 students e taken. Assume that the students have no ability to distinguish botween the two brands. Complete (a) through (d) beiow c. What is the probability that the sample percentage of correct identifications is greater than 65% ? (Round to four decimal places as needed.) d. Which is more likely to occur-more than 62% correct identifications in a sample of 190 or more than 56% correct identifications in a sample of 1,000? Explain.
a. The probability that the sample will have between 50% and 55% of the identifications correct is 0.2058.
b. The lower limit of the population percentage is 45% and the upper limit is 55%. There is a 90% probability that the sample percentage will be contained within 10% symmetrically around the population percentage.
c. The probability that the sample percentage of correct identifications is greater than 65% is 0.0432.
d. It is more likely to have more than 62% correct identifications in a sample of 190 than more than 56% correct identifications in a sample of 1,000. This is due to the larger sample size in the second case, which makes it less likely for the sample to deviate from the population percentage.
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The Given is m ………………..
Where T is the subject of the formula, the expression becomes, T = N²SL/M². (Option B)
What is the explanation for the above response?
To make T the subject of the formula M = N√(SL/T), we need to isolate T on one side of the equation by performing mathematical operations in a way that cancels out all other variables.
Here's how we can do that:
Square both sides of the equation to eliminate the square root:
M² = N²SL/T
Multiply both sides of the equation by T to get rid of the denominator on the right-hand side:
M²T = N²SL
Divide both sides of the equation by M² to isolate T on one side:
T = N²SL/M²
Therefore, the formula for T in terms of the other variables is:
T = N²SL/M².
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Full Question:
Although part of your question is missing, you might be referring to this full question:
Given M = N√(SL/T), make T the subject of the formula.
A. NSL/M
B. N²SL/M²
C. N²SL/M
D. NSL/M²
How do you convert between exponential and logarithmic form?
Plsss I needdd this answer asp
Applying the power rules, it was found that the equivalent expressions are: [tex]6^{(x+7)}*(2)^{5x}[/tex] and [tex](2)^{5x+1}*6^{(x+6)}*3[/tex].
Power RulesThe main power rules are presented below.
Multiplication with the same base: you should repeat the base and add the exponents.Division with the same base: you should repeat the base and subtract the exponents.Power. For this rule, you should repeat the base and multiply the exponents.Exponent negative - For this rule, you should write the reciprocal number with the exponent positive.Zero Exponent. When you have an exponent equal to zero, the result must be 1.For solving this question, you should apply the power rules and check the options are equivalent to the given expression [tex]6*(36)^{\frac{x}{2}+3}*(2)^{5x}[/tex].
From the power rules, you can simplify the given expression, as shown below.
[tex]6*(36)^{\frac{x}{2}+3}*(2)^{5x}=6*(6^2)^{\frac{x}{2}+3}*(2)^{5x}\\ \\ 6*(36)^{\frac{x}{2}+3}*(2)^{5x}=6*(6)^{x+6}*(2)^{5x}\\ \\ 6*(36)^{\frac{x}{2}+3}*(2)^{5x}=6*6^x*6^6*(2)^{5x}\\ \\ 6*(36)^{\frac{x}{2}+3}*(2)^{5x}=6^{(x+7)}*(2)^{5x}[/tex]
Then, you should find an expression equivalent to [tex]6^{(x+7)}*(2)^{5x}[/tex].
Option 1 - [tex]6^{(x+7)}*(2)^{5x}[/tex]This expression is exactly the result of the simplification done in the expression given [tex]6*(36)^{\frac{x}{2}+3}*(2)^{5x}[/tex].
It is equivalent to [tex]6^{(x+7)}*(2)^{5x}[/tex].
Option 2- [tex]6^{(2x+6)}*(2)^{5x}[/tex]The expression [tex]6^{(2x+6)}*(2)^{5x}[/tex] is not equivalent to [tex]6*(36)^{\frac{x}{2}+3}*(2)^{5x}[/tex].
Option 3- [tex](2)^{5x+1}*6^{(x+6)}*3[/tex][tex](2)^{5x+1}*6^{(x+6)}*3= 2^{5x}*2^1*6^x*6^6*3\\ \\ (2)^{5x+1}*6^{(x+6)}*3= 2^{5x}*6^x*6^6*6\\ \\ (2)^{5x+1}*6^{(x+6)}*3= 2^{5x}*6^x*6^7\\ \\ (2)^{5x+1}*6^{(x+6)}*3= 2^{5x}*6^{x+7}[/tex]
The expression [tex](2)^{5x+1}*6^{(x+6)}*3[/tex] is equivalent to [tex]6*(36)^{\frac{x}{2}+3}*(2)^{5x}[/tex].
Option 4- [tex]32^x*(216)^{\frac{x}{2}+3}[/tex][tex]32^x*(216)^{\frac{x}{2}+3} =2^{5x}*(6^3)^{\frac{x}{2}+3}\\ \\ 32^x*(216)^{\frac{x}{2}+3} =2^{5x}*(6^\frac{3x}{2} )*6^9}\\ \\[/tex]
The expression [tex]32^x*(216)^{\frac{x}{2}+3}[/tex] is not equivalent to [tex]6*(36)^{\frac{x}{2}+3}*(2)^{5x}[/tex].
Option 5- [tex]32^x*(6)^{\frac{x}{2}+4}[/tex][tex]32^x*(6)^{\frac{x}{2}+4}=2^{5x}*6^{\frac{x}{2} }*6^4[/tex]
The expression [tex]32^x*(6)^{\frac{x}{2}+4}[/tex] is not equivalent to [tex]6*(36)^{\frac{x}{2}+3}*(2)^{5x}[/tex].
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What is the inequality shown?
find the value of the question mark in the equation below (image)
Answer:
x = 12? = 12Step-by-step explanation:
Given equation,
→ 0.48 = ?/25
Let's change the symbol into x,
→ 0.48 = x/25
Now we have to,
→ Find the required value of x.
Then the value of x will be,
→ 0.48 = x/25
→ x/25 = 0.48
→ x = 0.48 × 25
→ [ x = 12 ]
Hence, the value of x is 12.
1x+9/2-5x-6/3=4x-3/3
Answer:
5.33333
Step-by-step explanation:
Given:
[tex]x + \frac{9}{2} - 5x - \frac{6}{3} = 4x - \frac{-3}{3}[/tex]
Make the denominators Equal
[tex]\frac{6x + 27-30x-12}{6} = \frac{24 + 6}{6}[/tex]
[tex]\frac{-24x + 15}{6} = \frac{24x+6}{6}[/tex]
Cross- Multiply :
[tex]6(-24x + 15) = 6(24x + 6)[/tex]
[tex]-144x + 90 = 144x + 36[/tex]
[tex]90 - 36 = 144x + 144x[/tex]
[tex]54 = 288x[/tex]
[tex]x = \frac{288}{54} = 5.3333[/tex]
Hope it helps.
If sin theta = 4/9, then what is the value of sin(pi - theta)
Sin(pi - theta) has a value of 4/9. sin(pi - theta) is equal to sin for any value of theta (theta). sin(pi - theta) has a value of 4/9.
We may calculate the value of sin(pi - theta) using the trigonometric identity sin(pi - theta) = sin(pi)cos(theta) - cos(pi)sin(theta):
Pi minus theta equals sin (pi)
cos(pi)sin - cos(theta) (theta)
We may simplify the expression to: since sin(pi) = 0 and cos(pi) = -1
0*cos(theta) - (-1)*sin = sin(pi - theta) (theta)
Pi minus theta equals sin (theta)
The value of sin(theta) can now be substituted to obtain:
Theta = 4/9 sin(pi - theta)
Hence, sin(pi - theta) has a value of 4/9.
The value of theta determines the value of sin(pi - theta). In terms of the trigonometric functions of theta, there is a generic formula to get sin(pi - theta): Pi minus theta equals sin (pi)
cos(pi)sin - cos(theta) (theta)
We may simplify the expression to: since sin(pi) = 0 and cos(pi) = -1
0*cos(theta) - (-1)*sin = sin(pi - theta) (theta)
Pi minus theta equals sin (theta)
Hence, sin(pi - theta) is equal to sin for any value of theta (theta).
Hence, sin(pi - theta) has a value of 4/9.
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If f(x)=4x+8 and g(x) = square root x+4, what is (f °g)(12)
For given functions f(x) and g(x), the value of (f °g)(12) is 24.
What exactly is a function?
In mathematics, a function is a rule that assigns to each input value (also called the argument) exactly one output value. The input values are typically drawn from a specific set, called the domain of the function, and the output values are drawn from another set, called the range of the function.
Now,
To find (f °g)(12), we need to first evaluate g(12) and then use the result to evaluate f(g(12)).
g(x) = √(x+4), so g(12) = √(12+4) = √16 = 4.
f(x) = 4x+8, so f(g(12)) = f(4) = 4(4) + 8 = 16 + 8 = 24.
Therefore,
The value of (f ° g)(12) = f(g(12)) = 24.
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I NEED HELP! pleaseeee!
The length of the rectangle is 63 cm and the Breadth of the rectangle is 12 cm, for this, we have to know something about rectangles.
What is a rectangle?Rectangle, It is a plane shape, as opposed to a square, with four(4) straight sides and four(4) right angles, particularly one(1) with uneven neighboring sides.
Square, A square is a regular quadrilateral in Euclidean geometry, which means that it has four(4) equal(same) sides and four(4) equal angles. It can alternatively be explained as a rectangle with two(2) neighboring sides that are of equal(same) length.
Given, Perimeter = 150 cm, Length, l = 5b+3 , Breadth = b
150 = 2(5b + 3 + b)
150 = 2(6b +3)
6b +3 = 75
6b = 72
b = 12 cm, So l = 63 cm (By putting the b value in the l equation
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pls aswer!!!
and give simple workingout
The n-ary rule for linear sequences is 7n - 1. The given sequence is an arithmetic sequence.
What is Arithmetic Progression?
Any two consecutive integers in a sequence are in "arithmetic progression" (AP) if their difference is constant.
The formula is given by Tn = a + (n - 1) d. where,
a, first term = 6 n, number of terms
d, binomial tolerance = 13 - 6 = 7
So substitute the value into the equations. It will be as follows.
Tn = a + (n - 1)d
= 6 + (n - 1)7
= 6 + 7n - 7
= 7n - 1
So the n term of this sequence is 7n - 1.
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Charlie has 1. 56 pounds of meat. He uses 0. 26 pound of meat to make one hamburger. How many hamburgers can Charlie make with the meat he has?
Charlie can make 6 hamburger form 1.56 pounds of meat if each uses 0.26 pounds.
The number of hamburger made by 0.26 pounds meat = 1
So, the number of hamburger possible from 1.56 pounds of meat = total amount of meat/amount of meat in one hamburger
Now, keep the values in formula to find the required answer
Number of hamburger = 1.56/0.26
Performing division on Right Hand Side of the equation to find the possible number of hamburger
Number of hamburger = 6
The 6 hamburger can be made from the meat.
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ronsapa ar
9. Two distinct lines, l and m, are each perpendicular to the same line n.
Explain why & and m are parallel lines. (Lesson 1-6)
When two distinct lines, l and m, are each perpendicular to the same line n, it means that the two lines have the same angle of rotation in relation to n.
What is angle?An angle is a figure formed by two lines or rays diverging from a common point. It is measured in degrees, with a full circle representing 360 degrees. Angles are used to describe the direction and orientation of objects, as well as to measure the size of an area or the relationship between two lines. Angles are an important part of mathematics, used in problems such as geometry, trigonometry and calculus.
This angle is equal to 90 degrees, meaning that the two lines are parallel to one another.
Parallel lines are lines that never intersect and are always the same distance apart. This is the case for l and m because both lines are perpendicular to the same line n and, thus, have the same angle. Therefore, the two lines are parallel to one another, meaning that they will never cross and will always remain the same distance apart.
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The temperature at 6 A.M. was -5°F. By noon it was 17°F. What was the temperature range
those 6 hours?
Answer:
-5≤y≤17
Step-by-step explanation:
Answer: -5 to 17 degrees
Step-by-step explanation:
2x+3y=4
2x=7y+24
can you help me solve this problem
Therefore , the solution of the given problem of equation comes out to be the system of equations has an answer of x = 5 and y = -2.
How are equations used?Mathematical formulas frequently use the same variable letter to try to enforce harmony among two assertions. Many academic numbers are shown to be equal using mathematical expression, also known as assertions. In this case, instead of splitting 12 into two parts, the normalise adds b + 6 using the example of y + 6. It is possible to determine the link number between each sign portion and the line length.
Here,
One of the solutions for a single variable should be solved in terms of the other.
We can find x from the first solution by solving in terms of y:
=> 2x + 3y = 4
=> 2x = 4 - 3y
=> x = (4 - 3y)/2
Solve for the other variable by substituting the formula for the variable from step 1 into the other equation.
Change x in the second expression to (4 - 3y)/2:
=> 2x = 7y + 24
=> 2((4 - 3y)/2) = 7y + 24
=> 4 - 3y = 7y + 24
=> -10y = 20
=> y = -2
Solve for the other variable by substituting the value of the variable from step 2 into one of the initial formulae.
When the first solution is used:
=> 2x + 3y = 4
=> 2x + 3(-2) = 4
=> 2x - 6 = 4
=> 2x = 10
=> x = 5
As a result, the system of equations has an answer of x = 5 and y = -2.
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The backyard of a new home is shaped like a trapezoid with a height of 46 ft and bases of 90 ft and 112ft. What is the cost of putting sod on the yard, if the landscaper charges $ 0.25 per square foot for sod?
The cost of putting sod on the yard is $1161.5
What exactly is a trapezoid?A trapezoid is a polygon that has just one pair of parallel sides. The two extra sides of a trapezoid, known as the legs, are not parallel.
The price is calculated by multiplying the area in square feet by the price per square foot.
The formula for a trapezoid's area is
A = (1/2)([tex]b_{1}[/tex] + [tex]b_{2}[/tex])h.
where h represents height and [tex]b_{1}[/tex] and [tex]b_{2}[/tex] represent base lengths.
The area is
A = (1/2)(90 ft + 112 ft)(46 ft)
= 4646 [tex]ft^{2}[/tex]
when the supplied information is filled in.
Given that each square foot costs $0.25,
the price for this many square feet (4646[tex]ft^{2}[/tex] ) is $0.25/[tex]ft^{2}[/tex] × $989.23.
The cost of sodding the backyard will be $1161.5 according to the landscaper.
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What is the general form and explanation of Gaussian Function in Statistical Method?
Thank you
The Gaussian Function in statistical method is defined as follows:
f(x) = (1 / σ√(2π)) e^(-0.5((x-μ)/σ)²)
In which the parameters are listed as follows:
μ is the mean of the distributionσ is the standard deviation of the distributione is the mathematical constant approximately equal to 2.71828π is the mathematical constant approximately equal to 3.14159x is the variable of the function.What is the Gaussian Function?The Gaussian function is a widely used probability density function in statistics, also known as the normal distribution or bell curve, and has the equation defined at the beginning of the answer.
The curve is symmetrical around the mean (μ) of the distribution. The standard deviation (σ) of the distribution determines the width of the curve, with smaller standard deviations resulting in narrower curves and larger standard deviations resulting in wider curves.
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