Step-by-step explanation:
x + y = 17
x = 17 - y
xy = 20
(17 - y)y = 20
-y² + 17y = 20
-y² + 17y - 20 = 0
the general solution to such a quadratic equation
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
y = (-17 ± sqrt(17² - 4×-1×-20))/(2×-1) =
= (-17 ± sqrt(289 - 80))/-2 =
= (-17 ± sqrt(209))/-2
y1 = (-17 + sqrt(209))/-2 = 1.271583853...
y2 = (-17 - sqrt(209))/-2 = 15.72841615...
the 2 numbers are
1.271583853...
15.72841615...
a manufacturer knows that their items have a lengths that are skewed right, with a mean of 18.8 inches, and standard deviation of 6.2 inches. if 48 items are chosen at random, what is the probability that their mean length is greater than 20.1 inches?
The probability that their mean length is greater than 20.1 inches is 0.32.
Standard deviation:
The standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.
The given value are:
Mean = 18.8 inches
Standard deviation = 6.2 inches
We have to find the probability that their mean length is greater than 20.1 inches.
Variance of sample mean = 6.2 / 48
= 0.13
S.D of sample mean= [tex]\sqrt{0.13}[/tex]
= 0.36
Z score for the length of 20.1 is ( 20.1 - 18.8) / 0.36 = 0.468
The p-value for 0.468 in the standard normal table is 0.32.
Therefore 0.32 chance of the sample means is greater than 20.1 inches.
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Jace's company has 17 employees who work full time. The company has a number of very dedicated
clients, and last year they generated $2 million in revenue. What type of software should Jace use?
The type of software should Jace use will be "Entry level accounting system" as his company has 17 employees who work full time. The company has a number of very dedicated clients, and last year they generated $2 million in revenue.
What is entry level accounting system?Entry-level accounting includes typical accounting operations such as accounts payables and receivables, as well as basic financial reporting. These are, predictably, among the most affordable items; some sellers even provide an entry-level bundle for free for a brief time as a trial period. Entry-level accounting jobs are the initial level of accounting positions for people who are just starting out in their careers. Accounting Representative, Accounting Executive, Accounting Assistant, Accounting Associate, Entry-Level Accounting Clerk, Staff Accountant, and Bookkeeper are examples of entry-level occupations.
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Please help. ill give brainliest
Answer:
I believe the answer is number 2, which is 20 degrees.
Step-by-step explanation:
When I plugged that number in for x for both of them I got the numbers 81 and 99. Added them together ad they made 180 degrees. Which makes them supplementary.
Find the rate of change between the following points:
(2,-1)
(-6,-5)
The rate of change between (2,-1) and (-6,-5) is 1/2.
What is the rate of change?
The slope is the ratio of the rate of change between two points (also known as the "slope") to (the change in the x coordinate).
Let (x,y)=(2,-1), (m,n)=(-6,-5)
Rate of change=(n-y)/(m-x)=(-5-(-1))/(-6-2)=1/2.
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does this equal to 10 or 5 abit confused I’ll brainlist .
Write an expression to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term.
–4, –3, –2, –1, ...
Answer:
[tex]a_{n}[/tex] = n - 5
Step-by-step explanation:
there is a common difference between consecutive terms in the sequence, that is
- 3 - (- 4) = - 2 - (- 3) = - 1 - (- 2) = 1
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = - 4 and d = 1 , then
[tex]a_{n}[/tex] = - 4 + 1 (n - 1) = - 4 + n - 1 = n - 5
Mark and Janet together have 10 pairs of jeans.
Janet has 6 more pairs of jeans than John.
How many pairs of jeans does John have?
Answer:
John has 4 pair of jeans.
Hope this helps : )
Step-by-step explanation:
Together they 10, so if Janet has 6 more, we have to subtract.
10 - 6 = 4
Check:
6 + 4 = 10 ✔
shopper needs 48 hot dogs. The store sells identical hot dogs in 2 differently sized packages. They sell a six-pack of hot dogs for $2.10, and an eight-pack of hot dogs for $3.12.
The pack of hot dogs that the shopper should buy that would be cheaper is six - pack of hot dogs
How to find the pack to be bought?If the shopper decided to buy the six-pack of hot dogs for $2.10, their total cost to be able to get 48 hot dogs would be:
= Cost per six pack of hot dogs x ( Number of hot dogs needed / Number of hot dogs in pack)
=2.10 x (48 / 6)
= 2.10 x 8
= $16.80
The cost if the shopper wants the eight pack is:
= 3.12 x (48 / 8)
= $18.72
The shopper should pick the six - pack of hot dogs because it is cheaper.
The rest of the question is:
Which option would be cheaper to the shopper?
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Fig. 3.3 shows an equilateral triangle with the lengths of its sides given in terms of x and y. Find the values of x and y. A 4x cm B 3y cm C (x + y + 5) cm
The values of x and y are 3 and 4.
Given:
shows an equilateral triangle with the lengths of its sides given in terms of x and y.
A 4x cm B 3y cm C (x + y + 5) cm
In equilateral triangle all sides are equal:
4x = 3y = x+y+5
4x = 3y
4x - 3y = 0. ---------eq(1)
4x = x + y + 5
3x - y = 5. ----------eq(2)
solving eq 1 - eq 2*3 we get,
4x - 3y - 9x + 3y = 0 - 15
-5x = -15
x = 3
4x - 3y = 0
4*3 - 3y = 0
12 = 3y
y = 12/3
y = 4
Therefore The values of x and y are 3 and 4.
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a bank auditor claims that credit card balances are normally distributed, with a mean of $2870 and a standard deviation of $900. a) what is the probability that a randomly selected credit card holder has a credit card balance less than $2500? b) you randomly select 25 credit card holders. what is the probability that their mean credit card balance is less than $2500? c) compare the probabilities from a) and b).
(a) -0.255 is the probability that a randomly selected credit card holder has a credit card balance less than $2500. (b) You randomly select 25 credit card holders. 0.0228 is the probability that their mean credit card balance is less than $2500.
Let us pull out the critical elements
Population: Normally distributed with mean of 2870
population standard deviation = 900 standard deviation of the sample mean (standard error) is 900 / √25. or 180
As population sigma is known, we do not have apply any corrections
P(xbar < $2500) = ?
Since μ and σ are known (population mean and standard deviation) we can use a simple Z test.
Ztest = (2500-2870 )/ 180 or -370/180 = -2.055
As this is very close to -2 one can use the rule of thumb for probability within ± 2 sigma being 95.44% to get a close estimate. If the area between -2 and 2 sigma = .9544 then the area outside = .0456. Half of this (the amount under the curve LESS THAN -2) would be .0228
Using a calculator or computer for an exact answer we find (using a TI-83/86):
nmcdf(-9E6,2500,2870,180) = .0199
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If Eof= 26 and FOG= 38, then what is the measure of BOG? The diagram is not to scale.
If EOF = 26 and FOG= 38, then the measure of BOG would be 64 degrees.
What is a measure of angle?
An angle is measured in degrees, thus the term "degree measure." Because one complete revolution equals 360 degrees, it is divided into 360 parts. Each stage of the revolution represents a degree.
The given data:
A measure of EOF = 26 and a measure of FOG = 38.
Then we can say that OF is an angle bisector of angle EOG.
Then the measure of BOG = EOF + FOG
= 26 + 38
= 64 degrees.
Hence, If EOF = 26 and FOG= 38, then the measure of BOG would be 64 degrees.
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Please help me!!!!!!!!
Can anyone write equation of the graph?
The equation of given graph is y = |x - 3| + 5.
The graph of a absolute or modulus function is a V- shape graph. The function of absolute is f(x) = |x|. The general form of absolute function is f(x)=a |x - h| + k. Where (h,k) is the vertex of graph.
Here, we can see that graph is in the form of V shape, so the function will be absolute function. Now, we have to find the vertex of graph.
As seen from the graph the minimum point on the graph is located at the point (3, 5) and the value of a should be 1.
So, by putting the value of vertex in general equation we get the equation of the graph,
y = |x - 3| + 5
Therefore, the equation of given graph is y = |x - 3| + 5.
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If a+4/a = 4 then find the value of a^5-1/a^5
pls answer this one as quick as possible.
Value of [tex]a^5-\frac{1}{a^5}[/tex] is 31.97.
What do you mean by algebraic expression?
In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.
There are 3 main types of algebraic expressions which include:
Monomial Expression
Binomial Expression
Polynomial Expression
An algebraic expression which is having only one term is known as a monomial.
Given expression:
a + 4/a = 4
We need to simplify the above expression and will find the value of a.
[tex]a+\frac{4}{a}=4[/tex]
⇒ [tex]\frac{a^2+4}{a}=4[/tex]
⇒ [tex]a^{2}+4=4a[/tex]
⇒ [tex]a^2-4a+4=0[/tex]
⇒ [tex]a^2-2a-2a+4=0[/tex]
⇒ a(a-2) -2(a-2) = 0
⇒ (a-2)(a-2) = 0
⇒ a = 2
Now, substitute this value of a in expression , [tex]a^5-\frac{1}{a^5}[/tex]
[tex]2^5-\frac{1}{2^5}[/tex]
= 32 - 1/32
= [tex]\frac{1024-1}{32} =1023/32 = 31.97[/tex]
Therefore, value of [tex]a^5-\frac{1}{a^5}[/tex] is 31.97.
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A box is filled with black (B), white (W), red (R), green (G), and prink (P) phone cases. A phone case is selected at random. what is the sample space for this experiment? A) S={B,W,R,G,P} B) S={B,W,R} C) S={G,P} D) S={B,R,G,P}
HELP!! SOLVER GETS ALL MY POINTS
The accounting profit is $10,800 and economic profit is - $14,200.
What is percentage?Percentage is a part of the whole number. It is denoted by % sign.
1 %= 1/100.
Given that,
The saving of Sarah = $50,000
The interest on $25,000 Sarah withdrew at the rate of 4% = $1000
The interest on $30,000 Sarah borrowed at the rate of 4% = %1200
The amount paid for ingredients = $27,000
Total investment = 27,000+30,000+ 1000+1200 = $59,200
Revenue of Sarah = $70,000
Accounting profit of Sarah = $70,000 - $59,200 = $10,800
Economic profit of Sarah = $70,000 - ($59,200+$25,000)
= - $14,200
The accounting profit is $10,800 and economic profit is - $14,200.
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i^50
Answer this question, include your reasoning and steps.
Answer:
-1
Step-by-step explanation:
Given:
[tex]i^{50}[/tex]
Rewrite 50 as the product of 2 and 25:
[tex]\implies i^{(2 \cdot 25)}[/tex]
[tex]\textsf{Apply the exponent rule} \quad a^{bc}=(a^b)^c:[/tex]
[tex]\implies \left(i^2\right)^{25}[/tex]
Apply the imaginary number rule i² = -1 :
[tex]\implies \left(-1\right)^{25}[/tex]
[tex]\textsf{Apply the exponent rule} \quad (-a)^n=-a^n,\:\: \textsf{ if }n \textsf{ is odd}:[/tex]
[tex]\implies -1^{25}[/tex]
As 1²⁵ = 1 then:
[tex]\implies -1[/tex]
Answer:
(i)⁵⁰ = -1
Step-by-step explanation:
The problem is,
→ (i)⁵⁰
Formula we use,
→ i² = -1
Let's solve the problem,
→ (i)⁵⁰
→ (i²)²⁵
→ (-1)²⁵
→ -1
Hence, the answer is -1.
What is the remainder of the following division problem?
x StartLongDivisionSymbol x + 1 EndLongDivisionSymbol. minus x to get a remainder of 0 + 1 and a quotient of 1.
x
1
0
–1
The remainder of the division problem given by the image at the end of the answer is as follows:
How to obtain the remainder of a division problem?When a division does not result in an exact term, we have that the quotient is added to the remainder.
A long division problem is represented as follows:
q(x) + (r(x)/b(x))
In which the terms are listed as follows:
q(x) is the quotient.r(x) is the remainder.b(x) is the divisor.In this problem, the division is given as follows:
(x + 1)/x.
Separating the division into two terms, we have that:
(x + 1)/x = x/x + 1/x = 1 + 1/x.
Hence:
The quotient is of x.The remainder is of 1.Missing InformationThe division in this problem is:
(x + 1)/x.
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Answer: B. 1
Step-by-step explanation:
edge 2023
-16 > -4y solve for the inequality of y and simplify your answer as much as possible
The given inequality solved for y is y > 4
Solving linear inequalitiesFrom the question, we are to solve the given linear inequality.
To solve an inequality, we will solve for the variable in the inequality.
The given inequality is
-16 > -4y
The variable in the inequality is y.
Now, we will solve for y
-16 > -4y
Divide both sides by -4
-16/-4 > -4y/-4
4 < y
Thus,
y > 4
Hence, the solution is y > 4
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whats the equation of a line that passes through the points
(12,12) and (20,6)
A line passes through point (8, 4) and has a slope of - 3/4 Write an equation in Ax + By = C form for this line. Use integers for A, B, and C.
The equation of the line in the given form Ax + By = C is 3x + 4y = 40
How to determine the equation in the given form?The given parameters from the question are given as
Point = (8, 4)
Slope = -3/4
Start by representing the equation in the slope intercept form
This is calculated as
y = m(x - X) + Y
Where
m, Slope = -3/4
(X, Y), Point = (8, 4)
So, we have
y = -3/4(x - 8) + 4
Multiply through by 4
4y = -3(x - 8) + 16
Evaluate the like terms
4y = -3x + 24 + 16
This gives
3x + 4y = 24 + 16
Evaluate
3x + 4y = 40
Hence, the equation is 3x + 4y = 40
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Suppose that y varies directly with .x, and y=-8 when x=2.
(a) Write a direct variation equation that relates x and y.
Equation:
(b) Find y when x = 5.
OC
Answer:
y = -4x
b. y = -20.
Step-by-step explanation:
y = kx
-8 = 2k
k = -8/2
k = -4
y = -4x
y = kx
y = -4 × 5
y = -20
help meeeeeeeeeeeeeeeeee please
Answer:
I believe it's 4.5 seconds
Ben and Charlie had the same number of books at first. Ben gave away 16 of his books, Charlie gave away 28 books. The ratio of the number of books Ben had left to that of Charlie's is 3:1. How many books did each boy have at first.
The number of books each boy had based on the 3:1 ratio of the books remaining is 34 books
What is a ratio?A ratio is a quantitative expression of the relationship between two values that indicates the relative proportion of each amount.
The initial number of books Ben had = The initial number of books Charlie has
The number of books Ben gave away = 16 books
The number of books Charlie gave away = 28 books
The ratio of the number of books Ben and Charlie had left is 3:1
Let x represent the number of books each of them initially have. Representing the numbers as a ratio gives;
The number of books Ben had left = x - 16
The number of books Charlie had left = x - 28
[tex]\dfrac{x - 16}{(x - 16) + (x - 28)} = \dfrac{3}{3+1}[/tex]
Which gives; [tex]\dfrac{x - 16}{(2\cdot x - 44) } = \dfrac{3}{4}[/tex]
4 × (x - 16) = 3 × (2·x - 44)
6·x - 4·x = 3×44 - 4×16 = 68
2·x = 68
x = 68 ÷ 2 = 34
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Sophia earned $36 at her job when she worked for 4 hours. Fill out a table of equivalent ratios and plot the points on the coordinate axes provided.
The ratio when Sophia earned $36 at her job when she worked for 4 hours is 1:9.
What is ratio?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
From the information, Sophia earned $36 at her job when she worked for 4 hours.
The equivalent ratio to illustrate the information will be:
= 4 / 36
= 1/9
= 1:9
Note that the coordinates point weren't given in the question.
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Given that ABCD is a rectangle, where EC = 7x -3 and AE=4x + 8. Find DE.
The length of segment DE on the rectangle, considering the midpoint, is given as follows:
DE = 22.67.
What is the midpoint?The midpoint of a segment divides a segment into two segments of equal length, having half the length of the entire segment.
In this problem, the diagonal of the rectangle represented by segment AC has midpoint E, hence the measure of x is calculated as follows:
EC = AE.
The measures are as follows:
EC = 7x - 3.AE = 4x + 8.Hence:
7x - 3 = 4x + 8
7x - 4x = 8 + 3
3x = 11
x = 11/3.
Segment DE is also half of a diagonal, hence it's length is obtained with the numeric value of any segment EC or AE, as follows:
DE = EC = 7x - 3 = 7 x 11/3 - 3 = 77/3 - 9/3 = 68/3 = 22.67.
Missing InformationThe rectangle is given by the image at the end of the answer.
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In the graph below, find the coordinate of the image point. O is the origin and P is the point (4, 3). Ry and Rx are reflections around the x- and y- axes.
Complete the following:
HpHo : (3, 0) --- >
(3, 0)
(-5, -6)
(11, 6)
algebra solution for tiffany had $330 in her account in 1999 and the value has been growing exponentially at a constant rate. the value of the account reached $590 in the 2007. what is the value in 2009?
The value of the account in the year 2009 will be $682.
The acount's balance, in t years after 1999, can be modeled by the following equation.
In which A(t) is the amount after t years, P is the initial money deposited, and r is the rate of interest.
In which A(t) is the amount after t years, P is the initial money deposited, and r is the rate of interest.
$330 in an account in the year 1999This means that $590 in the year 20072007 is 8 years after 1999, so P(8) = 590.We use this to find r.Determine the value of the account, to the nearest dollar, in the year 2009.2009 is 10 years after 1999, so this is A(10).The value of the account in the year 2009 will be $682.learn more about solutions here:
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Do You UNDERSTA
D?
1.? ESSENTIAL QUESTION Why is identifying
the domain and range important when
defining a function?
In Linguistics 101, the ratio of the number of juniors to the number of seniors is $3:2$. When seven more juniors join the class, and two seniors drop the class, the ratio of the number of juniors to the number of seniors becomes $5:2$. How many students are in the class after these changes?
The number of students in the class after the changes here are 35.
What are ratios?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)
The question tells us that 7 more juniors have joined this class, while 2 seniors have dropped the class. Then the ratio would be 5 : 2 from the question.
This would give us the ratios as
[tex]\frac{3x+7}{2x-2} = \frac{5}{2}[/tex]From here we would have to cross multiply
2(3x + 7) = 5(2x - 2)
6x + 14 = 10x - 10
6x - 10x = -10 - 14
- 4x = -24
x = 6
Put the value of x in both equations
3x + 7 = 3 x 6 + 7
= 25
2x - 2 = 2 x 6 - 2 = 10
25 + 10 = 35
The number of students that are in the class is given as 25
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