The 70th term of an arithmetic sequence is 115.5 and the common difference is 1.5 the first term of the sequence 12.
Common distinctionFormula\sa {n}=a {1}+(n-1) The nth term in the series is d a n.
The first term present in the sequence is a 1.
d is the common distinction between the terms.
an = a1 + (n-1)d
⇒ a1 = an - (n-1)d
= a70 - (70-1) (1.5)
= 115.5 - 69 (1.5)
= 12
What in mathematics is an arithmetic sequence?The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive terms is always two, so the sequence 3, 5, 7, 9... is arithmetic.
How can an arithmetic sequence be found?The formula for an arithmetic sequence is given as an=a1+(n1)d, where n is a general term, a1 a 1 is the initial term, and d is the common difference. To find the general word in the series, do this.
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Assume that 600 births are randomly selected and 309 of the births are girls. Use subjective judgment to describe the
number of girls as significantly high, significantly low, or neither significantly low nor significantly high.
Choose the correct answer below.
A. The number of girls is significantly low.
B. The number of girls is neither significantly low nor significantly high.
C. The number of girls is significantly high.
D. It is impossible to make a judgment with the given information.
Option b. The number of girls is neither significantly low nor significantly high.
How is the subjective judgement given?
Total number of births selected= 600
Half of the total number = 300
Number of girls = 309
As we can see, the number of girls is slightly higher than the half and not significantly higher . Therefore I can subjectively describe and conclude that the number 309 is neither significantly low nor significantly high. The total population of boys and girls are almost similar.What is subjective judgement ?
Subjective judgement is something that is based more on the individual's thoughts and feelings than on actual facts. The dominating eigenvector of a matrix of paired comparisons is a widely used technique for quantifying subjective judgement .To learn more about population, refer:
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What is the unit rate for the situation represented in the table?
Hours 3 5 7 9
Wages $35.25 $58.75 $82.25 $105.75
a $7.05/hour
b $2/hour
c $11.75/hour
d $16.45/hour
Answer:
c $11.75/hour
Step-by-step explanation:
You want the unit rate represented by the table of (hours, wages) = (3, $35.25), (5, $58.75), ....
Unit rateThe unit rate of dollars per hour is found by dividing dollars by hours:
$35.25/(3 hour) = $11.75/hour
You can check the other table values to see if they represent the same unit rate. (They do.)
f(x)=-3x^2+3x, find f(f)x))
The value of the composite function f(f(x)) is -3(-3x^2 + 3x)^2 + 3(-3x^2 + 3x)
How to determine the composite function?The functions are given as
f(x) = -3x^2 + 3x
The definition of the composite function is given as
f(f(x))
This composite function is calculated using the following composite function formula
f(f(x))= (f o f)(x)
Substitute the known values in the above equation
So, we have the following equation
f(f(x)) = -3f(x)^2 + 3f(x)
So, we have
f(f(x)) = -3(-3x^2 + 3x)^2 + 3(-3x^2 + 3x)
Hence, the composite function is f(f(x)) = -3(-3x^2 + 3x)^2 + 3(-3x^2 + 3x)
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Review and evaluate the following: By the given y = 2x + 1 ÷ x, what is the value of y when: 1. x=0 2. x = 1 3. x = 2.5 4.x = 1/3 5. x=a
ANSWER
[tex]\begin{gathered} 1)\text{ Undefined} \\ \\ 2)\text{ }3 \\ \\ 3)\text{ }2.4 \\ \\ 4)\text{ }5 \\ \\ 5)\text{ }2+\frac{1}{a} \end{gathered}[/tex]EXPLANATION
We want to find the value of y:
[tex]y=\frac{2x+1}{x}[/tex]for the values of x.
To do this, for each value of x, substitute the values of x into the equation and simplify.
1. x = 0:
[tex]\begin{gathered} y=\frac{2x+1}{x} \\ \\ y=\frac{2(0)+1}{0}=\frac{0+1}{0}=\frac{1}{0} \\ \\ y=\text{ Undefined} \end{gathered}[/tex]The value of y is undefined for x = 0 since any value divided by 0 is undefined.
2. x = 1:
[tex]\begin{gathered} y=\frac{2(1)+1}{1}=\frac{2+1}{1} \\ \\ y=\frac{3}{1} \\ \\ y=3 \end{gathered}[/tex]3. x = 2.5:
[tex]\begin{gathered} y=\frac{2(2.5)+1}{2.5}=\frac{5+1}{2.5} \\ \\ y=\frac{6}{2.5} \\ \\ y=2.4 \end{gathered}[/tex]4. x = 1/3:
[tex]\begin{gathered} y=\frac{2(\frac{1}{3})+1}{\frac{1}{3}}=\frac{\frac{2}{3}+1}{\frac{1}{3}} \\ \\ y=\frac{\frac{5}{3}}{\frac{1}{3}}=\frac{5}{3}*\frac{3}{1} \\ \\ y=5 \end{gathered}[/tex]5. x = a:
[tex]\begin{gathered} y=\frac{2(a)+1}{a}=\frac{2a+1}{a} \\ \\ y=2+\frac{1}{a} \end{gathered}[/tex]That is the answer.
Can u please help me solve this problem
Given that the initial point of vector "u" is:
[tex](4,8)[/tex]And the terminal point:
[tex](-12,14)[/tex]You need to find the Component Form of the vector with this formula:
[tex]u=\langle x_2-x_2,y_2-y_1\rangle[/tex]In this case:
[tex]\begin{gathered} x_2=-12 \\ x_1=4 \\ y_2=14 \\ y_1=8 \end{gathered}[/tex]Then, you get:
[tex]u=\langle-12-4,14-8\rangle=\langle-16,6\rangle[/tex]Find the Magnitude using this formula:
[tex]||u||=\sqrt{x^2+y^2}[/tex]In this case:
[tex]\begin{gathered} x=-16 \\ y=6 \end{gathered}[/tex]Therefore, by substituting values and evaluating, you get:
[tex]||u||=\sqrt{(-16)^2+(6)^2}\approx17.088[/tex]In order to find the direction of the vector "u", you need to use this formula:
[tex]\theta=tan^{-1}(\frac{y}{x})[/tex]Then, when you substitute the values of "x" and "y" into the formula and evaluate, you get:
[tex]\theta=tan^{-1}(\frac{6}{16})\approx20.556°[/tex]Hence, the answer is:
Apples are 99 cents a pound and pears are $1.25 a pound. Write an expression thatrepresents the total cost, in dollars, of a pounds of apples and p pounds of pears.
Answer
$(0.99 + 1.25p)
Explanation
Note: 100 cents = $1
Apples cost $(99/100) = $0.99 a pound
Pears cost $1.25 a pound
Since 1 pound of pears cost $1.25,
∴ p pounds of pears will cost $1.25p
Now total cost in $ of a pound of apples and p pound of pears = $(0.99 + 1.25p)
Hence, the expression that represents the total cost is $(0.99 + 1.25p)
Resting body temperatures are normally distributed with an average of 98.25 degreesFahrenheit and a standard deviation of 0.73 degrees Fahrenheit. A nurse examines 40 patients in one hour. What is the probability the average temperature of the 40 patients is between 98.0 degrees Fahrenheit and 98.50 degrees Fahrenheit? (Round to the hundredths)A)0.97B)0.11542313C)0.99D)Sample size is not larger than 40 so we cannot compute probability
Resting body temperatures are normally distributed with an average of 98.25 degrees
Fahrenheit and a standard deviation of 0.73 degrees Fahrenheit. A nurse examines 40 patients in one hour. What is the probability the average temperature of the 40 patients is between 98.0 degrees Fahrenheit and 98.50 degrees Fahrenheit? (Round to the hundredths)
A)0.97
B)0.11542313
C)0.99
D)Sample size is not larger than 40 so we cannot compute probability
step 1
Find the z-scores
For x=98.0 degrees
z=(98-98.25)/0.73 --------> z=-0.3425
For x=98.50
z=(98.50-98.25)/0.73 ------> z=0.3425
using a Z-score Calculator
we have that
P=0.26803
step 2
we have that
Can anyone help me with this problem please and thank you !
Answer:
d = 7
For step by step explaintion I am so sorry but I don't rember enough of my geometry class to properly explain this, but triangles BDC and ABD are congruent (I swear I can prove this if I dig up my old notes but I really do not feel like doing that) so these 2 equations (sides) are equal. So we just solve for d!
6d + 3 = 10d - 25
(we all know how to solve something this simple so I won't bore you with the details of inverse operations and such)
d = 7
Given that log 2 = a and log 3 = b, express the following in terms of a and b:
a) log 72
Answer:
Step-by-step explanation:
=a, log 3 = b Log 2 log 1.5= log 23/20 год 1.5 = = log 3-log 2 b-a The other terms log 1.2 log 0.24, log 0.5, log 0.836 cannot be expressed only. of in terms a or bor both. [Answer: Log 1.5 Option A
Answer:
[tex]\log 72=3a+2b[/tex]
Step-by-step explanation:
Given:
[tex]\log 2 = a[/tex][tex]\log 3 = b[/tex]Rewrite 72 as a product of 2s and 3s.
[tex]\implies 72 = 2 \times 2 \times 2 \times 3 \times 3[/tex]
[tex]\implies 72=2^3 \times 3^2[/tex]
Therefore:
[tex]\implies \log 72=\log(2^3 \times 3^2)[/tex]
[tex]\textsf{Apply the log product law}: \quad \log xy=\log x + \log y[/tex]
[tex]\implies \log 72=\log(2^3)+\log(3^2)[/tex]
[tex]\textsf{Apply the log power law}: \quad \log x^n=n\log x[/tex]
[tex]\implies \log 72=3\log2+2\log3[/tex]
Substitute the given values of log 2 and log 3:
[tex]\implies \log 72=3a+2b[/tex]
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Which value must be added to the expression x² - 8x to make it a perfect-square trinomial?
04
O-16
O-4
O 16
Answer: 16
Step-by-step explanation:
The standard form of a perfect square trinomial is:
[tex](x-a)^{2} = x^{2}-2ax+a^{2}[/tex]
Put the equation into standard form:
[tex]x^{2} -8x+c[/tex]
Compare to to the form of a perfect square trinomial:
[tex]-8x=-2ax\\\frac{-8x}{-2x}=a\\a=4[/tex]
Plug a back into the equation to get c:
[tex]c=a^{2}=4^{2}\\c=16[/tex]
Putting everything back together gives you:
[tex](x-4)^{2} = x^{2}-8x+16[/tex]
The required, we need to add 16 to the expression x² - 8x to make it a perfect square trinomial. Option D is correct.
A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the monomial, binomial, and trinomial, etc. ax+b is a polynomial.
To make the expression x² - 8x a perfect-square trinomial, we need to add the square of half of the coefficient of x to the expression.
The coefficient of x is -8, so half of it is -4. The square of -4 is 16.
Therefore, we need to add 16 to the expression x² - 8x to make it a perfect square trinomial.
Answer: 16.
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1.)Based on the average.how many people will usethe ramp each week? Setup ratio.2.) What will the surface areaof the ramp be? Writeequation & solve. Roundto the nearest hundredth.3.) What percentage of thepeople do not need theramp?4.) How high will the ramp be9 feet from the front walk?Draw a diagram & solve.5.) How high will the ramp be6 feet fromthe front walk?Draw a diagram & solve.Please help with these questions.thank you.
1)
Let:
N = Total people every week = 207
r = People which needs a ramp = 1:9 = 1/9
So:
[tex]N\cdot r=207\cdot\frac{1}{9}=23[/tex]Answer: 23 people
2)
[tex]\begin{gathered} SA=b\cdot h+pw \\ _{\text{ }}where\colon \\ b=18ft \\ h=4ft \\ p=b+h+l \\ l=\sqrt[]{h^2+b^2} \\ l=\sqrt[]{340} \\ w=4.75ft \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} SA=72+192.09 \\ SA=264.09ft^2 \end{gathered}[/tex]3)
The percentage of the people that don't need the ramp will be given by:
[tex]1-r=1-\frac{1}{9}=\frac{8}{9}\approx0.89[/tex]Answer: Approximately 89%
4)
[tex]\begin{gathered} h=\sqrt[]{(\sqrt[]{340})^2-9^2} \\ h=\sqrt[]{259} \\ h\approx16.09ft \end{gathered}[/tex]5)
[tex]\begin{gathered} h=\sqrt[]{(\sqrt[]{340})^2-6^2} \\ h=\sqrt[]{340} \\ h\approx17.44ft \end{gathered}[/tex]There are 4 corners at an intersection. A pole at each corner holds 2 traffic light, 1 streetlight, and 2 crosswalk light. How many lights are at the intersection in all ?
Using multiplication we calculate that there are 56 lights in the cross-section.
When two integers are multiplied together in mathematics, the result is a product, or an expression that describes the factors to be multiplied.
The commutative law of multiplication states that the outcome is unaffected by the sequence in which real or complex numbers are multiplied. For instance, the sum of 6 and 5 is 30. (the outcome of multiplication). Usually, the order of the factors determines the outcome of a multiplication of matrices or the constituents of other associative algebras. For instance, multiplication in general and in matrices are non-commutative operations in other algebras.There are many other kinds of products in mathematics: in addition to multiplying just numbers, polynomials, or matrices, one may also define products on a wide range of algebraic expressionsTotal number of lights in each pole = 2 + 1 + 2 = 5 lights
There are 4 corners
Total number of poles = 5 × 4 = 20
So by multiplication we get there are 20 lights in the intersection.
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Write the equation of the line that is parallel
to y = x-7 and passes through the point
(-3, 1)
Equation parallel to y = x+4,
How do you write an equation for a parallel line?Equations that are parallel have the same slope.The standard equation of an equation is written through slope intercept form, which is
y = mx + b
where m is your slope and b is the y intercept
So, in the equation provided, 1 is the slope.
To write an equation when given a slope and points, you use point slope form, which is
y −y1 =m(x−x1)
y1 is the y in the set of points you are given, same with x1
So,
y1 =1 and x1= -3
As stated before, m is the slope, and the slope is given as 1
Plug in the numbers into the equation
y −1 =1 (x+3)
y= x +4 ;
And there you have a equation parallel to
y=x +4
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11. At Outdoor Adventures Clothing Company, all items are marked up to maximize
profit. Life preservers cost $25 to buy from the manufacturer. They sell for $35. What
is the percent increase on life preservers, to the nearest whole percent?
Using the percentages formula, we conclude that the percentage increase in life preserves is 40%.
What is the percentage?A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" is also used, the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement. By dividing the value by the total value and multiplying the result by 100, one can determine the percentage. The percentage calculation formula is (value/total value)100%.So, the percentage increase in life preserves:
Formula: (selling value - cost)/cost ×100Now, substitute the values in the formula as follows:
(selling value - cost)/cost ×100(35 - 25)/25×10010/25×1000.4×10040%Therefore, using the percentages formula, we conclude that the percentage increase in life preserves is 40%.
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How do i solve this problem?
The function exists a Power function. The power of function is 3 and the constant variation is - 1/3
What is meant by Power function?Any function where y = x n, where n is any real constant integer, is referred to be a power function. In reality, many of our parent functions, including linear and quadratic functions, are power functions. A few other power functions are y = x³, y = 1/x, and y = x squared.
A parameter function used in statistical testing that represents the likelihood of rejecting the null hypothesis for a given value of the parameter, assuming that value is true.
Therefore, the power of function is 3 and the constant variation is - 1/3.
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How to find the range of data. 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26
Answer:
22
Step-by-step explanation:
To find the rage, you subtract the smallest number from the largest number in the set of numbers.
So...
26 - 4 = 22
What is a formula for the nth term of the given sequence 15,24,33
Answer:
87
Step-by-step explanation:
the whole sequence would be 15, 24, 33, 42, 51, 60, 69, 78, 87
in 2018, the population of los Angeles county, California, was 10,137,915. if los Angeles County covers 4,751 square miles, what's the average population density in the county?
The average population density in the county is:
10,137,915 people / 4,751 square miles = 2133.84 people / square mile
Rounding to nearest integer, we have: 2134 people / square mile
What is answer????????
Answer is 6
9 - 6 = 3
The difference of a number and 9 means to subtract said number from 9.
Solve the system of equations
-2x - 6y + 8z = 14
3x + 2y - z = 4
2x - y + 2z = 10
Indira finds that on a typical day, 4 out of every 5 students at her school eat a
cafeteria lunch. The rest of the students bring their lunch from home. Indira's
school has 495 students. On a typical day, how many students at her school bring
their lunch from home? Show your work.
By using fractions, we can conclude that 99 students bring their lunch from home.
What is a fraction?Consider a collection of items from which some of their components have been stolen. A fraction is a name given to the portion that was taken. The denominator is the bottom portion of the fraction, and the numerator is the upper portion.So, the Fraction of students eating a cafeteria lunch at her school = 4/5
A fraction of students bring their lunch from home:
1 / 4/55/4/51/5495 students attend her school in total.
Several students bring their lunch from home, including:
1/5 × 49599Therefore, by using fractions, we can conclude that 99 students bring their lunch from home.
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Para resolver una operación matemática ¿por qué es importante
primero conocer los signos y los números?
Answer:
para hacer la repuesta xd
Four friends have $525 that they want to share equally. To start, they divide the money so that each friend gets a $100 bill. What is the most useful next step?
If four friends have $525 that they want to share equally and they divide the money so that each friend gets a $100 bill, then next step will be divide the remaining money so that each friend gets a $31.25
Total money the have = $525
they divide the money so that each friend gets a $100 bill
The amount of money they split equally = 4×100
= $400
Remaining money = 525-400
= $125
Split the remaining money into 4 = 125/4
= $31.25
Hence, If four friends have $525 that they want to share equally and they divide the money so that each friend gets a $100 bill, then next step will be divide the remaining money equally so that each friend gets a $31.25
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Question 8 of 15
Triangle ABC with vertices A(-1, 2), B(-1, -2), and C(-4,-2) is dilated by a scale factor of 2 to form triangle A'B'C'.
у
A
C
4321
-4-3-2-10 이 1234
1
OHN 3 +
B
+2+
-3+
Submit Test
-4-
What is the length, in units, of side A'B'?
units
2223 Math Grade 8 IA1
X
The formula that most accurately captures the dilatation that Triangle ABC underwent to produce A'B'C will be:
(x, y) → (1/2x, 1/2y)
Detailed explanation?
A triangle's vertices are given.
A(-2, -4) (-2, -4)
B(2, -4) (2, -4)
C(-8, -4) (-8, -4)
The vertices of an image triangle should be after the dilatation
A' (-1, -2) (-1, -2)
B '(1, -2) (1, -2)
C' (-4, -2) (-4, -2)
If we look attentively, we can see that the vertices of the image triangle, A'B'C', make up half of the original triangle ABC.
For example, (x, y) (1/2x, 1/2y)
verification
A(-2, -4) → A'(-2/2, -4/2) = A'(-1, -2) (-1, -2)
B(2, -4) → B'(2/2, -4/2) = B'(1, -2) (1, -2)
C(-8, -4) → C'(-8/2, -4/2) = C'(-4, -2) (-4, -2)
As a result, it is confirmed, and we come to the conclusion that the rule that best captures the dilatation that Triangle ABC underwent to form A'B'C' will be:
(x, y) → (1/2x, 1/2y)
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Harry just deposited $1500 into a savings account giving 6% interest compounded monthly. How much will be in the account after 10 years and 20 years ?
Compound Interest
It occurs when the interest is reinvested rather than paying it out.
When it happens interest in the next period is then earned on the principal sum plus previously accumulated interest.
The formula is:
[tex]{\displaystyle A=P\mleft(1+{\frac{r}{n}}\mright)^{nt}}[/tex]Where:
A=final amount
P=initial principal balance
r=interest rate
n=number of times interest applied per time period
t=number of time periods elapsed
Harry deposited an initial amount of P = $1500.
The savings account gives r = 6% = 0.06 interest
Since the interest is compounded monthly, n = 12 (there are 12 months in a year)
The time is t = 10 years.
Now we apply the formula:
[tex]\begin{gathered} {\displaystyle A=1500(1+{\frac{0.06}{12}})^{12\cdot10}} \\ \text{Calculating:} \\ {\displaystyle A=1500(1+0.005)^{120}} \end{gathered}[/tex]Using a calculator:
A = $2729.095
Rounding to two decimals,
A = $2729.10
Harry will have $2729.10 in his account after 10 years
Now for t = 20 years:
[tex]{\displaystyle A=1500(1+{\frac{0.06}{12}})^{12\cdot20}}[/tex]Calculating again:
A = $4965.31
Harry will have $4965.31 in his account after 20 years
Sarah is working towards paying off the rest of her student loan. The graph models the amount owed, in dollars, for x months. What does the slope represent?
The slope of the graph that models the amount Sarah owed after a given number of x months, represents the monthly payment Sarah makes to repay the loan
What is a monthly payment on a loan?Monthly payment on a loan is the payment made each month within the period specified in the loan, to repay the loan and the interest on the loan.
The given parameters of the graph are;
Information on the graph = The amount owed for a number of x months
Taking the y–axis (Vertical axis) of the graph as specifying the amount owed given in Dollars, and the x–axis as the number of months of payment, we have;
[tex] \displaystyle{Slope = \frac{\Delta y}{\Delta x}} [/tex]
Where;
∆y = Change in the amount Sarah owes
∆x = Change in the time
Which gives;
[tex] \displaystyle{Slope = \frac{Change\: in\: the\: amount \:owed}{Change\: in\: time }}[/tex]
Whereby the graph is a straight line graph, we have;
The slope = Constant
Therefore, the change in the amount owed over a given time frame such a month, is constant
Which gives;
The slope represents the amount by which the Sarah's student loan changes each month, which is equivalent to and therefore;
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A coffee shop currently sells 440 lattes a day at $2.50 each. They recently tried raising the by price by $0.25 a latte, and found that they sold 60 less lattes a day.
a). Assume that the number of lattes they sell in a day, N, is linearly related to the sale price, p (in dollars). Find an equation for N as a function of p.
N(p)= (blank)
b). Revenue (the amount of money the store brings in before costs) can be found by multiplying the cost per cup times the number of cups sold. Again using p as the sales price, use your equation from above to write an equation for the revenue, R as a function of p.
R(p)= (blank)
c). The store wants to maximize their revenue (make as much money as possible). Find the value of p that will maximize the revenue (round to the nearest cent).
p= (blank) which will give a maximum revenue of $ (blank)
Show your work!
Explain your answer!
No incorrect answer!
No nonsense answers!
No spam answers!
Thanks!
Using linear function concepts, it is found that:
a) The amount of lattes sold function is: N(p) = -240p + 1040.
b) The revenue function is: R(p) = -240p² + 1040p.
c) The revenue is maximized when p = $2.17.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).For this problem, we have a linear function with the points having the following format:
(price, lattes sold).
Hence two points are given as follows:
(2.50, 440), (2.75, 380).
The slope is given by change in y divided by change in x, hence:
m = -60/0.25 = -240.
Then:
N(p) = -240p + b.
When p = 2.50, N(p) = 440, hence we solve for b as follows:
440 = -240(2.5) + b
b = 1040.
Thus the function is:
N(p) = -240p + 1040.
The revenue function is:
R(p) = pN(p)
Hence:
R(p) = p(-240p + 1040)
R(p) = -240p² + 1040p.
Which is a concave down quadratic function, with a = -240 and b = 1040. A concave down quadratic function is maximized when:
p = -b/2a
Hence:
p = -1040/2(-240) = $2.17.
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Find the equation of the line that passes through (-1,5) and (0,1)
We have to find the equation of the line that passes through the points (-1,5) and (0,1). We will write the equation in the slope-intercept form, which is given by:
[tex]y=mx+b[/tex]Where m represents the slope of the function, and b the y-intercept. We will find the slope, and then the y-intercept.
1. Finding the slope
For finding the slope we will use the formula:
[tex]m=\frac{y_2-y_1_{}}{x_2-x_1}[/tex]where (x₁,y₁) and (x₂,y₂) are two points that passes through the line. In this case, the points (-1,5) and (0,1).
Replacing, we obtain:
[tex]m=\frac{1-5}{0-(-1)}=\frac{-4}{1}=-4[/tex]Thus, the slope is -4.
2. Finding the y-intercept
For doing this step, we want to know the value of the function when x equals zero. But, as we have that the line passes through (0,1), this means that this value will be 1. This is, the y-intercept is 1.
3. Putting all together
Now, we just have to put the values obtained in the slope-intercept form:
[tex]\begin{gathered} y=mx+b \\ y=-4x+1 \end{gathered}[/tex]And this means that the equation of the line that passes through (-1,5) and (0,1) is y=-4x+1.
A flower bed is in the shape of a triangle with one side twice the length of the shortest side and the third side is 21 feet
more than the length of the shortest side. Find the dimensions if the perimeter is 121 feet.
What is the length of the shortest side?
The length of the shortest side is
Answer: 25 ft
Step-by-step explanation:
Let the shortest side be s. Then, the other two sides are 2s and s+21.
[tex]s+2s+s+21=121\\\\4s+21=121\\\\4s=100\\\\s=25[/tex]
If X - N(-3,4), find the probability that x is between -6 and 6. Round to 3 decimal places.
The probability that x is between -6 and 6 is 18.84%.
What is defined by the term normal distribution?The symmetry of the normal distribution is well known. This means that the distribution is just not skewed. We can easily calculate probabilities using this distribution; all we need are the z scores. The Standard Normal Distribution would be a probability distribution with known and constant parameters. That really is, the parameters remain unchanged.For the given question;
The probability of x should line between -6 and 6.
The formula for calculating the z-score is;
z = (x - μ)/σ
μ = mean (-3)
σ = standard deviation (4)
Put the values in the formula.
For x = -6
z = (-6 - (-3))/4
z = -3/4
z = -0.75
Now, x = 6
z = (-6 - 3)/4
z = -9/4
z = -2.25
P(-6 < x < 6) = P(-0.75 < x < -2.25)
Find the probability using negative z score.
P(-6 < x < 6) = 0.197 - 0.0122
P(-6 < x < 6) = 0.1848
P(-6 < x < 6) = 18.84%
Thus, the probability that x is between -6 and 6 is 18.84%.
To know more about normal distribution, here
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