The rate of change is 3.
The initial value is 6.
Step - by - Step Explanation
What to find?
• Rate of change.
,• Initial value.
Given:
y = 3x + 6
The rate of change is also the same as the slope.
To find the slope of the gien equation, compare the equation with y=mx + b.
Where m is the slope (rate of change).
Comparing the two equations, m = 3
Hence, the rate of change is 3.
The initial value also known as the y-intercept, is the value of y at x=0.
y = 3(0) + 6
y = 6
Hence, the initial value is 6.
5. (20 x 5 + 10) - (8 × 8 - 4)=
a. 58
b. 50
c. 40
Answer:
b. 50
Step-by-step explanation:
20 x 5 + 10 = 110
8 × 8 - 4 = 60
110 - 60 = 50
Answer:
b. 50
Step-by-step explanation:
(20x5+10)- (8x8-4)
(100+10) - (64-4)
110 - 60
equals 50
Which one of the following angle measurements is the largest?
We have
[tex]\pi\approx3.14\text{ radians}[/tex]and
[tex]\pi=180^0[/tex]From these,
[tex]2\text{ radians<3 radians<}\pi<200^o[/tex]The largest measurement is 200 degrees. Thus, option B is correct.
A box contains 4 red balls and 6 green balls. If a ball is drawn at random, then find the probability that the ball is red.1/102/104/106/10
To calculate the probability of event A, divide the number of outcomes favorable to A by the total number of possible outcomes.
[tex]P(A)=\frac{favourable\text{ outcomes}}{total\text{ outcomes}}[/tex]so
Step 1
a)let
[tex]\begin{gathered} favourable\text{ outcomes=red balls = 4 \lparen there are 4 red balls\rparen=4} \\ total\text{ outcomes= total balls= 4 red+6 green=10 balls=10} \end{gathered}[/tex]b) now, replace in the formula and simplify
.
[tex]P(A)=\frac{4}{10}=\frac{2}{5}[/tex]therefore, the answer is
[tex]\frac{4}{10}[/tex]I hope this helps you
A glass aquarium is in the form of a rectangular parallelepiped with dimensions 50cm by 100cm, and its depth is 30cm.How many liters of water will it hold?
Hello! To find the number of liters of water, we have to calculate the volume of the parallelepiped:
The formula of the volume is:
[tex]\begin{gathered} \text{Volume = a}\times\text{ b }\times\text{c} \\ \text{Volume = 50}\times\text{100}\times\text{30} \\ \text{Volume = }150,000\operatorname{cm}^3 \end{gathered}[/tex]Now that we know the volume, we have to convert cm³ to liters.
For this, we must remember:
1cm³ = 0.001 liter
Multiplying by rule of three, we will obtain:
[tex]\begin{gathered} 1\cdot x\text{ = 150,000 }\cdot\text{ 0.001} \\ x\text{ = 150 liters} \end{gathered}[/tex]I think is the average of the highest point and the lowest one, what's the midline of the graph?
The Midline of a Sinusoid
A sinusoid is a periodic function which parent expression is:
f(x) = A. sin (wt)
Where A is the amplitude and w is the angular frequency
The sine function has a maximum value of A and a minimum value of -A.
The midline can be found as the average value of the maximum and the minimum value.
For the parent function explained above, the midline is:
[tex]M=\frac{\text{Mx}+Mn}{2}[/tex]Since Mx and Mn are, respectively A and -A, the midline is zero.
The graph shown in the image has a maximum of Mx=1 and a minimum of Mn=-5.
Thus, the midline is:
[tex]M=\frac{\text{1}-5}{2}=-\frac{4}{2}=-2[/tex]The midline of the graph is y=-2
A shop, had a sale.
(a) In the sale, normal prices were reduced by 15%.
The normal price of a chair was reduced in the sale by $24.
Work out the normal price of the chair.
Answer:
$160
Step-by-step explanation:
A shop, had a sale. In the sale, normal prices were reduced by 15%. The normal price of a chair was reduced in the sale by $24. Work out the normal price of the chair.
if 15% of normal price equals $24 then:
24/15% or 24/0.15 = $160 normal price
CHECK:
$160 * 0.15 = $24
Answer:
$160
Step-by-step explanation:
We want to know the price of the chair
So:
24 / 0.15 = 160$
or
24 / 15% = 160
complete the following: 1. Find the locus of points whose: (a) ordinate saquare decressed by the square of the abscissa is the sum of the coordinates
P(x,y) is the coordinate point of the locus
ordinate is y
abscissa is x
Following the sentence we have
ordinate square y^2
decreased means subtract
square of the abscissa x^2
is means equal
the sum of the coordinates x+y
[tex]y^2-x^2=x+y[/tex]can u help me w this i got it incorrect and can’t figure out why
1) We can see here a case in which there are two secant lines coming from a single point over that circle.
2) So, we can write out the following relation
[tex]\begin{gathered} PA\cdot PB=PC\cdot PD \\ 4(4+x)=5(5+7) \\ 16+4x=25+35 \\ 16+4x=60 \\ 16-16+4x=60-16 \\ 4x=44 \\ \frac{4x}{4}=\frac{44}{4} \\ x=11 \end{gathered}[/tex]The function h(x) is a transformed function of f(x) = |x|. The transformation is as follows: 1 units vertical shift up, 4 units horizontal shift left.a). Write the transformed equation, h(x).b). Graph f(x) and h(x) on the same coordinate plane. Be sure to label the functions f(x) and h(x). This must be graphed by hand or by using the tools in Word.
To transform a function 1 unit up, we add 1 outside of the function
h(x) = |x| +1
shifting it 4 units to the left, we will add 4 units from x inside
h(x) = |x+4| +1
The transformed function is
h(x) = |x+4| +1
Find the simple interest. Principal Time in Months Rate 1 $11.800 21% 4 The simple interest is $ (Round to the nearest cent.)
we use the formula
Where Cn is the final amount= co the initial amount, n the number of months and i the rate dividing between 100
transform the mixed number
[tex]2\frac{1}{4}=2.25[/tex]now, replace
[tex]\begin{gathered} Cn=11,800(1+(4)\times(\frac{2.25}{100})) \\ \\ Cn=11,800(1.09) \\ \\ Cn=12862 \end{gathered}[/tex]the solution is 12,862
Find the probability of at least 2 girls in 6 births. Assume that male and female births are equally likely and that the births are independent events.0.6560.1090.2340.891
We need to use Binomial Probability.
Of 6 births, we want to find the probability of at least 2 of them being girls.
To solve this, we need to find:
Probability of exactly 2 girls
Probability of exactly 3 girls
Probability of exactly 4 girls
Probability of exactly 5 girls
Probability of exactly 6 girls
If we add all these probabilities, we get the probability of at least 2 girls.
To find the probabilities, we can use the formula:
[tex]_nC_r\cdot p^r(1-p)^{n-r}[/tex]Where:
n is the number of trials (in this case, the number of total births)
r is the number of girls we want to find the probability
p is the probability of the event occurring
[tex]_nC_r\text{ }is\text{ }the\text{ }combinatoric\text{ }"n\text{ }choose\text{ }r"[/tex]The formula for "n choose r" is:
[tex]_nC_r=\frac{n!}{r!(n-r)!}[/tex]Then, let's find the probability of exactly 2 girls:
The probability of the event occurring is:
[tex]P(girl)=\frac{1}{2}[/tex]Because there is a 50% probability of being a girl or a boy.
let's find "6 choose 2":
[tex]_6C_2=\frac{6!}{2!(6-2)!}=\frac{720}{2\cdot24}=15[/tex]Now we can find the probability of exactly 2 girls:
[tex]Exactly\text{ }2\text{ }girls=15\cdot(\frac{1}{2})^2(1-\frac{1}{2})^{6-2}=15\cdot\frac{1}{4}\cdot(\frac{1}{2})^4=\frac{15}{4}\cdot\frac{1}{16}=\frac{15}{64}[/tex]We need to repeat these calculations for exactly 3, 4, 5, and 6 girls:
Exactly 3 girls:
let's find "6 choose 3":
[tex]_6C_3=\frac{6!}{3!(6-3)!}=\frac{720}{6\cdot6}=20[/tex]Thus:
[tex]Exactly\text{ }3\text{ }girls=20\cdot(\frac{1}{2})^3(1-\frac{1}{2})^{6-3}=20\cdot\frac{1}{8}\cdot\frac{1}{8}=\frac{5}{16}[/tex]Exactly 4 girls:
"6 choose 4":
[tex]_6C_4=\frac{6!}{4!(6-4)!}=\frac{720}{24\cdot2}=15[/tex]Thus:
[tex]Exactly\text{ }4\text{ }girls=15\cdot(\frac{1}{2})^4(1-\frac{1}{2})^{6-4}=15\cdot\frac{1}{16}\cdot\frac{1}{4}=\frac{15}{64}[/tex]Exactly 5 girls:
"6 choose 5"
[tex]_6C_5=\frac{6!}{5!(6-5)!}=\frac{720}{120}=6[/tex]Thus:
[tex]Exactly\text{ }5\text{ }girls=6\cdot(\frac{1}{2})^5(1-\frac{1}{2})^{6-5}=6\cdot\frac{1}{32}\cdot\frac{1}{2}=\frac{3}{32}[/tex]Exactly 6 girls:
"6 choose 6"
[tex]_6C_6=\frac{6!}{6!(6-6)!}=\frac{720}{720\cdot0!}=\frac{720}{720}=1[/tex]Thus:
[tex]Exactly\text{ }6\text{ }girls=1\cdot(\frac{1}{2})^6(1-\frac{1}{2})^{6-6}=\frac{1}{64}\cdot(\frac{1}{2})^0=\frac{1}{64}[/tex]now, to find the answer we need to add these 5 values:
[tex]\frac{15}{64}+\frac{5}{16}+\frac{15}{64}+\frac{3}{32}+\frac{1}{64}=\frac{57}{64}=0.890625[/tex]To the nearest tenth, the probability of at least 3 girls is 0.891, thus, the last option is the correct one.
Madeline is a salesperson who sells computers at an electronics store. She makes a base pay of $80 each day and then is paid a $20 commission for every computer sale she makes. Make a table of values and then write an equation for P, in terms of x, representing Madeline's total pay on a day on which she sells x computers.
I need the Equation.
The linear equation that gives the values of P in terms of x which is Madeline's total pay on a given day is; P + 20·x + 80
What is an equation in mathematics?An equation consists of two expressions that are joined by an equal to sign to complete a mathematical statement.
The given parameters are:
Madeline's daily base pay = $80
Madeline's commission for each computer sold = $20
The given table of values is presented as follows:
Daily pay, in Dollars, P; [tex]{}[/tex] 80, 100, 120, 140
Number of computers sold, x; [tex]{}[/tex] 0, 1, 2, 3
From the above table of values, given that the independent variable, x, is increasing at a constant rate, and that the first difference is constant, we have that the relationship is a linear relationship, that has an equation of the form; P = m·x + c
Where:
m = The slope
c = The y-intercept
The slope which gives the ratio of the rise to the run of the graph is given by the equation; [tex]m = \dfrac{100-80}{1-0} =20[/tex]
The equation in point and slope form is therefore: P - 80 = 20·(x - 0) = 20·x
P - 80 = 20·x
P = 20·x + 80
Learn more about writing linear equations here:
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f(n) = -11 + 22(n - 1)Complete the recursive formula of f(n).f(1) = f(n) = f(n - 1) +
F(n) = -11 + 22(n-1)
[tex]\begin{gathered} f(1)\text{ implies that n=1} \\ F(1)\text{ = -11+22(1-1)} \\ f(1)=-11 \end{gathered}[/tex]Hence F(1) = -11
[tex]\begin{gathered} f(n-1)\text{ implies n=n-1} \\ f(n-1)=-11\text{ +22(n-1-1)} \\ f(n-1)=-11+22(n-2)_{} \\ =\text{ -11+22n-44} \\ f(n-1)=22n-55 \end{gathered}[/tex][tex]\begin{gathered} f(n)=\text{ -11+22(n-1)} \\ =-11+22n-22 \\ 22n-33 \\ \end{gathered}[/tex]
let An = F(n) -F(n-1)
[tex]\begin{gathered} 22n-33\text{ - (22n-55)} \\ 22n\text{ - 33-22n+55} \\ =-33+55 \\ =22 \end{gathered}[/tex]Hence F(n)= f(n-1) +22
11. The table lists postage for letters weighing as much as 3 oz. You want to mail a letter that weighs 1.7 oz.Graph the step function. How much will you pay in postage?Weight Less ThanPrice1 oz422 oz66903 Oz
In the table says that every letter that weighs less that 1 oz. have a price of 42, in the graphic we represented that in this part:
Following the data in the table as above we got the final graphic.
And for the question:
If you have a letter that weighs 1.7 oz. it will be more than 1 oz. but less than 2 oz. so you will pay 66, as we can see in the following graphic:
plot the graph f on the graphf(x)=|1/2x-2|
• We will determine the domain, range and x ;y intercept then plot the graph
1. The domain is given by :
[tex]\begin{gathered} \text{Domain = }x<0\text{ = (-}\infty\text{ },\text{ 0) } \\ \text{ x >0 = ( 0 },\infty)\text{ } \\ \text{ =(-}\infty;0)\text{ U ( 0 ;}\infty) \end{gathered}[/tex]2. Range is given by :
[tex]\begin{gathered} \text{Range = f(x) }\ge0\text{ } \\ \text{ =}\lbrack0;\infty) \end{gathered}[/tex]3. x - and y -intercept :
[tex]x\text{ - intercept = ( }\frac{1}{4};\text{ 0) }[/tex]4. asymptote :
[tex]\begin{gathered} \text{vertical : }x\text{ = 0 } \\ \text{horizontal : y = 2 } \end{gathered}[/tex]Now that we have the necessary points to plot the f(x) = | 1/2x -2 | , the graph will look as follows :Farrah borrows $18,000 to purchase a new car. The annual interest rate for the 60-month loan is 4.3%.If she makes all the monthly payments, what is the total amount of interest she will pay on the loan?
SOLUTION:
Step 1:
In this question, we are given the following:
Principal = $ 18,000
Time = 60 month = 60/ 12 = 5 years
Interest = 4. 3%
Step 2:
The total amount she will pay at the end of the 5 -year period is given as follows:
[tex]\begin{gathered} A\text{ = P ( 1 + }\frac{R}{100})^t \\ A\text{ = 18000 ( 1 + }\frac{4.3}{100})^5 \\ \end{gathered}[/tex][tex]\begin{gathered} A\text{ = 22,217. 4416} \\ A\text{ }\approx\text{ }22,217.44\text{ dollars} \end{gathered}[/tex]Step 3:
Now, we have that the amount = 22, 217. 44 dollars.
And the Principal = 18,000 dollars
If she makes all the monthly payments,
Then, the total amount of interest she will pay on the loan is:
[tex]22,\text{ 217. 44 - 18,000 = 4,217. 44 dollars}[/tex]CONCLUSION:
The total amount of interest she will pay on the loan = 4, 217. 44 dollars.
A pile of cards contains eight cards, numbered 1 through 8. What is the probability of NOT choosing the 6?
The probability of NOT choosing the 6 is 7/8.
What is the probability?Probability is used to calculate the likelihood that a random event would happen. The chances that the random event happens is a probability value that lies between 0 and 1. The more likely it is that the event occurs, the closer the probability value would be to 1. If it is equally likely for the event to occur or not to occur, the probability value would be 0.50.
The probability of NOT choosing the 6 = number of cards that are not 6 / total number of card
Cards that do not have a value of 6 = 1, 2, 3, 4, 5, 7, 8
Total is 7
The probability of NOT choosing the 6 = 7 / 8
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Find the length and width of a rectangle with the following information belowArea = 2x^2 + 3x Perimeter = 6x + 6
Length: L
Width: W
The area of a rectangle is:
[tex]A=L\cdot W[/tex]The perimeter of a rectangle is:
[tex]P=2W+2L[/tex]Given information:
[tex]\begin{gathered} A=2x^2+3x \\ \\ P=6x+6 \end{gathered}[/tex][tex]\begin{gathered} L\cdot W=2x^2+3x \\ 2W+2L=6x+6 \end{gathered}[/tex]Solve L in the second equation (Perimeter):
[tex]undefined[/tex]ifvx varies directly as y and x =36 when y=6 find x when y=9
Answer:
54
Step-by-step explanation:
Hello!
A direct variation can be expressed as [tex]y = ax[/tex], where a is multiplied.
As you can see, x is 6 times greater than y, proving that when y is 6, x is 36 (6*6 = 36).
Therefore, we can say that if y is 9, we can multiply the value by 6 to find the x-value:
x = 6 * 9x = 54So the value of x is 54.
5. Which of the following expressions isequivalent to the expression below?2 394Х4AC29;woltON Alw94B+D1M
A) 9 cups of berries to 12 cups of juice
Explanation
to figure out this, we need to find the original ratio and then compare
Step 1
find the ratio:
ratio cups of berries to cups of juices
[tex]\text{ratio}=\frac{3\text{ cups of berries}}{4\text{ cups of juices}}=\frac{3}{4}[/tex]hence, the rario is 3/4
Step 2
now, check the ratio of every option
a)9 cups of berries to 12 cups of juice
[tex]\begin{gathered} \text{ratio}_a=\frac{9\text{ cups of berries}}{12\text{ cups of juice}}=\frac{3}{4} \\ \text{ratio}_a=\frac{3}{4} \end{gathered}[/tex]b) 12 cups of berries to 9 cups of juice
[tex]\text{ratio}_b=\frac{12\text{ cups of berries}}{9\text{ cups of juice}}=\frac{4}{3}[/tex]c) 6 cups of berries to 15 cups of juice
[tex]\text{ratio}_c=\frac{6\text{ cups of berries }}{15\text{ cups of juice}}=\frac{6}{15}=\frac{2}{5}[/tex]d) 15 cups of berries to 10 cups of juice
[tex]\text{ratio}_d=\frac{15\text{ cups of berries }}{10\text{ cups of juice}}=\frac{15}{10}=\frac{3}{2}[/tex]therefore, the option that haas the same ratio is a) 3/4
I hope this helps you
Tommy paid $8.25 for three pounds of gummy candy.Tommy created a graph from the data on his chart. Is his graph correct? Why or Why not?
Notice that the relationship between the number of pounds of gummy candy and the number of dollars that that number of pounds costs is a function because there cannot be two prices for the same number of pounds.
Now, notice that the graph that Tommy creates does not represent a function because it fails the vertical line test at x=3.
Also, from the given table we get that (4,11) is a point of the graph.
Then the graph that Tommy creates is not correct.
Answer: No, because the graph does not represent a function and the point (4,11) is not part of the graph.
Imagine you are four years old. A rich aunt wants to provide for your future. She hasoffered to do one of two things.Option 1: She would give you $1000.50 a year until you are twenty-one.Option 2: She would give you $1 this year, $2 next year, and so on, doubling the amounteach year until you were 21.If you only received money for ten years, which option would give you the most money?
Given the situation to model the arithmetic and the geometric sequences.
Imagine you are four years old. A rich aunt wants to provide for your future. She has offered to do one of two things.
Option 1: She would give you $1000.50 a year until you are twenty-one.
This option represents the arithmetic sequence
The first term = a = 1000.50
The common difference = d = 1000.50
The general formula will be as follows:
[tex]\begin{gathered} a_n=a+d(n-1) \\ a_n=1000.50+1000.50(n-1) \\ \end{gathered}[/tex]Simplify the expression:
[tex]a_n=1000.50n[/tex]Option 2: She would give you $1 this year, $2 next year, and so on, doubling the amount each year until you were 21.
This option represents the geometric sequence
The first term = a = 1
The common ratio = r = 2/1 = 2
The general formula will be as follows:
[tex]\begin{gathered} a_n=a\cdot r^{n-1} \\ a_n=1\cdot2^{n-1} \end{gathered}[/tex]Now, we will compare the options:
The first term of both options is when you are four years old that n = 1
you only received money for ten years so, n = 10
So, substitute with n = 10 into both formulas:
[tex]\begin{gathered} Option1\rightarrow a_{10}=1000.50(10)=10005 \\ Option2\rightarrow a_{10}=1\cdot2^{10-1}=2^9=512 \end{gathered}[/tex]So, the answer will be:
For ten years, the option that gives the most money = Option 1
A sphere has a radius that is 2.94 centimeters long. Find the volume of the sphere. Round to the nearest tenth.
The volume of a sphere is given as
[tex]V=\frac{4}{3}\pi r^3^{}[/tex]Where r = 2.94 cm
π = 3.14
Substituting values,
[tex]\begin{gathered} V=\frac{4}{3}\times3.14\times2.94^3=1.33\times3.14\times25.41 \\ V=106.12 \end{gathered}[/tex]The volume to the nearest tenth is 106.1 cubic centimeters.
can someone please help me find the mesauser of the following?
Answer:
The measure of the given arcs are;
[tex]undefined[/tex]Given the figure in the attached image.
we want to find the measure of the given arcs.
For arc ED.
The measure of arc ED is equal to the measure of arc AB;
[tex]\begin{gathered} ED=AB=\measuredangle AOB=50^{\circ} \\ ED=50^{\circ} \end{gathered}[/tex]To get the measure of BC, we can see that AB, BC, and CD will sum up to 180 degrees.
[tex]\begin{gathered} AB+BC+CD=180^{\circ} \\ 50^{\circ}+BC+40^{\circ}=180^{\circ} \\ BC=180^0-(50^{\circ}+40^{\circ}) \\ BC=90^{\circ} \end{gathered}[/tex]To get arc BED;
[tex]\begin{gathered} \text{BED}=BE+ED \\ \text{BED}=180+50 \\ \text{BED}=230^{\circ} \end{gathered}[/tex]....................
Answer:
oop
Step-by-step explanation:
oh
Find the length of AC
The rule of the length of an arc is
[tex]L=\frac{x}{360}\times2\pi\text{ r}[/tex]Where L is the length of the arc
x is the central angle subtended by the arc
r is the radius of the circle
∵ BC = r
∵ BC = 16 ft
∴ r = 16
∵ < ABC is a central angle subtended by the arc AC
∴ ∵ < ABC = 51 degrees
∴ x = 51
→ Substitute the values of x and r in the rule above to find The length of arc AC
[tex]\begin{gathered} AC=\frac{51}{360}\times2\times3.14\times16 \\ AC=14.23466667 \end{gathered}[/tex]→ Round it to 2 decimal places
∴ AC arc = 14.23 ft
find distance between 2 points A(-1,-7), B(-8,7)
To calculate the length between A and B you have to draw them in the cartesian system and link them with a line, then using that line as hypothenuse, draw a right triangle, whose base will be paralel to the x-axis and its height will be paralel to the y-axis.
Using the coordinates calculate the length of the base and height of the triangle:
Base= XA-XB= (-1)-(-8)=7
Height= YB-YA=7-(-7)=14
Now you have to apply pythagoras theorem you can calculate the length of the hypotenuse:
[tex]\begin{gathered} a^2+b^2=c^2 \\ c^2=7^2+14^2 \\ c^2=245 \\ c=\sqrt{245}=15.65 \end{gathered}[/tex]The distance between poins A and B is 15.65
can you help with this question please
We need to give the steps for proving the corresponding angles theorem for parallel lines crossed by a transverse line.
Westart with the
p || q as Given info
Next we use that
< 1 = <7 due to internal alternate angles among parallel lines
< 7 = <5 due to angles opposed by vertex
<1 = <5 due to transitive property <1 = <7 = <5
how do I know which picture goes with the correct equation
If B is between A and C, but B is not midpoint, then the graph would be
The equation would be
[tex]AC=AB+BC[/tex]On the other hand, if B is between A and C, and B is a midpoint, the graph would be
The equation would be
[tex]AB=BC[/tex]Find the value of x so that f(x) = 7.YA6f4200246XX =
The blue line in the graph indicates the function f(x).
The values in the y-axis are the value of the function, that is, the value of f(x) for a given value of x. The x-axis indicates what value of x generates the value in the y-axis.
So, if we want to find the value of x that gives us f(x) = 7, we need to find where is the value '7' in the y-axis, then we draw an horizontal line from this value toward the line of the function (blue line).
This horizontal line will intersect the function in a certain point. This point is where the function has the value 7.
Now, to find the value of x of this point, we draw a vertical line from this point downwards, until it intersects the x-axis.
This way, looking at the image, we can see that the value of x that gives us f(x) = 7 is the value x = 5.