Instructions: For the following sequence, state the common ratio, identify which is the explicit form and which is the recursive form of the rule.
Given that the series is 1, 3, 9, 27, ............
The common ratio will be
[tex]Common\text{ ratio=}\frac{2nd\text{ term}}{1st\text{ term}}=\frac{3}{1}=3[/tex]So the common ratio is 3.
The explicit formula uses starting term and the recursive formula uses the previous term.
As
[tex]\begin{gathered} Explicit\text{ form} \\ a_n=3^{n-1} \\ Recursive\text{ form} \\ a_n=a_{n-1}\times3 \end{gathered}[/tex]These are the required forms.
Suzanne's salary grew from $40,000 in 2000 to $56,000 in 2021. during the same time period, Mike's salary grew form $38,000 to $53,000. Whose salary grew more in absolute change? In percentage change?
Absolute change (AC) refers to the simple difference in the indicator over two periods. that is
[tex]\begin{gathered} \text{AC (Suzanne)=56000-40000} \\ \text{AC (Suzanne)=16000} \end{gathered}[/tex]and, for Mike:
[tex]\begin{gathered} \text{AC (Mike)=53000-3}8000 \\ \text{AC (Mike)=1}5000 \end{gathered}[/tex]Whose salary grew more in absolute change? Suzanne's salary.
The relative change (RC) express the absolute change as a pencentage of the value of the indicator in the earlier period:
[tex]RC=\frac{value\text{ 2nd period - value 1st period}}{\text{value 1st period}}\times100[/tex]For Suzanne, we have
[tex]\begin{gathered} RC(\text{Suzzane)}=\frac{56000-40000}{56000}\cdot100 \\ RC(\text{Suzzane)}=\frac{16000}{56000}\cdot100 \\ RC(\text{Suzzane)}=0.286\cdot100 \\ RC(\text{Suzzane)}=28.6 \end{gathered}[/tex]and for Mike, we have
[tex]\begin{gathered} RC(\text{Mike)}=\frac{53000-28000}{53000}\cdot100 \\ RC(\text{Mike)}=\frac{15000}{53000}\cdot100 \\ RC(\text{Mike)}=0.283\cdot100 \\ RC(\text{Mike)}=28.3 \end{gathered}[/tex]In percentage change? For Suzanne is 28.6% and for Mike 28.3%
Answer: Mike's salary grew from $ 38,000 to $ 53,000.
Step-by-step explanation:
Suppose that the function f is defined, for all real numbers, as follows.
f(x)= {5x-4 if x≤1
-x+4 if x>1
Graph the function f. Then determine whether or not the function is continuous.
Answer:
F(x)
Step-by-step explanation:
hope it helps
Given the function [tex]f(x) = \left \{ {{5x-4, \ \ \ x\leq 1} \atop {-x+4, \ \ \ \ \ x > 1}} \right.[/tex], the function is not continuous at x = 1.
A function is said to be continuous if it can be drawn without picking up the pencil. Otherwise, a function is said to be discontinuous.
Given function,
[tex]f(x) = \left \{ {{5x-4, \ \ \ x\leq 1} \atop {-x+4, \ \ \ \ \ x > 1}} \right.[/tex]
We need to check the continuity of the function f(x) at x = 1. At all other points, it is continuous.
f(x) at x = 1 : 5x - 4 = 5*1 - 4 = 5 - 4 = 1
f(x) at x < 1 : 5x - 4 = 5*1 - 4 = 5 - 4 = 1
f(x) at x > 1 : -x + 4 = -1 + 4 = 3
Since, f(x) at x < 1 ≠ f(x) at x > 1, therefore, f(x) is not continuous at x = 1.
The same is also visible from the graph attached below. There is a disruption at x = 1, the graph is not a smooth line.
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Social Security is 6.2% of the first $97,500. Medicare is 1.45% of all income.
The state tax is 2% of gross pay, and the local tax is 1.5% of gross pay.
7.) Orville Staples is a painter who earns $30,000.00 a year. He is single and claims 3 allowances. Weekly deductions include $34.50 for medical insurance and union dues of $15.00.
Please calculate Federal Income Tax, Social Security Tax, Medicare Tax, State Tax & Local tax. Please show work.
The deductions for the taxes are given as follows:
Federal Income Tax: $4,626.27.Social Security Tax: $1,860.Medicare Tax: $435.State Tax: $600.Local Tax: $450.What are his deductions?To calculate the taxes, we have to consider his gross pay, which is given in the text as follows:
Gross pay = $30,000.
The Federal Income Tax for people in his income range is of $1,027.50 plus 12% of the amount over $10,275, hence:
Federal Income Tax = 1027.50 + 0.12 x (30000 - 10.275) = $4,626.27.
The Social Security tax is of 6.2% of his salary, hence:
Social Security Tax = 0.062 x 30000 = $1,860.
The Medicare tax is of 1.45% of his salary, hence:
Medicare Tax = 0.0145 x 30000 = $435.
The State Tax is of 2% os his salary, hence:
State Tax = 0.02 x 30000 = $600.
The Local Tax is of 1.5% of his salary, hence:
Local Tax = 0.015 x 30000 = $450.
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A basketball player scores 14, 16, 20, 5, 22, 30, 16, and 28 points during a
tournament. Make a box-and-whisker plot for the points scored by the player.
The diagram attached shows the box-and-whisker plot for the points scored by the player.
How to Make a Box-and-whisker Plot for a Data Set?A box-and-whisker plot displays the maximum and minimum data values, the upper and lower quartiles, and the median of the data. They are called the five-number summary.
Given the data for the number of points scored by a basketball player is: 14, 16, 20, 5, 22, 30, 16, and 28, the five-number summary for the data would therefore be:
Minimum: smallest data point, which is 5.First Quartile: center of the first part of the data set when ordered, which is 15.Median: The middle data point, which is 18.Third Quartile: center of the second part of the data set, which is, 25Maximum: this represents the highest data point, which is, 30The box-and-whisker plot is shown below.
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if h(x, y) moves 12 units to the left and 4 units up. what is the rule that describes this translation .
Answer:
(x,y) -> (x-12, y+4)
Step-by-step explanation:
(x,y) -> (x-12, y+4)
Write a cosine function that has an amplitude of 3, a midline of 5 and a period of 3/4. .
A cosine function is said to have an amplitude of 3, a midline of 5, and a period of 3/4.
It is required to write the cosine function.
Recall that the standard form of a cosine function is:
[tex]y=a\cos(bx+c)+d[/tex]Where a is the amplitude, 2π/b is the period, c is the horizontal shift, and d is the midline or vertical shift.
Equate the given period to 2π/b and solve for b:
[tex]\begin{gathered} \frac{2\pi}{b}=\frac{3}{4} \\ \Rightarrow3b=8\pi \\ \Rightarrow\frac{3b}{3}=\frac{8\pi}{3} \\ \Rightarrow b=\frac{8\pi}{3} \end{gathered}[/tex]Hence, substitute a=3, b=8π/3, and d=5 into the standard form of the cosine function:
[tex]y=3\cos(\frac{8\pi}{3}x+c)+5[/tex]Since it is not given that the cosine function has a horizontal shift, substitute c=0 to get the required function:
[tex]y=3\cos(\frac{8\pi}{3}x)+5[/tex]The function is y=3cos((8π/3) x)+5.
This is a Statistics question. Please Help
Considering the normally distributed variable, the proportion/percentage are given as follows:
a) Proportion of serves faster than 121 mph: 0.16.
b) Percentage of serves between 109 and 133 mph: 84%.
Normal DistributionThe z-score of a measure X of a variable that has mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by the following equation:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure represented by X is above or below the mean of the distribution, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X in the distribution.As stated in the problem, the mean and the standard deviation of the serve speeds are given as follows:
[tex]\mu = 115, \sigma = 6[/tex]
The proportion of serves faster than 121 mph is one subtracted by the p-value of Z when X = 121, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (121 - 115)/6
Z = 1
Z = 1 has a p-value of 0.8413.
1 - 0.8413 = 0.1587, which is the desired proportion.
The proportion of serve speeds between 109 and 133 mph is the p-value of Z when X = 133 subtracted by the p-value of Z when X = 109, hence:
X = 133:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (133 - 115)/6
Z = 3
Z = 3 has a p-value of 0.9987.
X = 109:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (109 - 115)/6
Z = -1
Z = -1 has a p-value of 0.1587.
0.9987 - 0.1587 = 0.84, hence the percentage is of 84%.
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what is 42/100 of x over 35?
The value of x in 42/100 of x over 35 based on the computation is 14.7.
How to calculate the fraction?It should be noted that a fraction simply means a number that's not a whole number.
Based on the information, we want to calculate 42/100 × x/35. This will be illustrated thus:
= 42/100 × x/35.
Cross multiply
(100 × x) = (42 × 35)
100x = 1470
Divide through by 100
100x / 100 = 1470 / 100
x = 14.7
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A pizza is taken out of an oven and placed on a counter. The temperature, T, in degrees Fahrenheit, of the pizza after m minutes is modeled by the function Which graph represents the model?
The graph of the exponential function that represents the temperature of the pizza after m minutes is given at the end of the answer.
Which model represents the temperature of the pizza?The model that represents the temperature of the pizza m minutes after it is taken out of the oven and placed on the counter is given by:
[tex]T(m) = 72 + 200e^{-0.0445m}[/tex]
The number e is the Euler number, and the function is the exponential function translated 72 units up, hence the minimum value that the pizza obtains is of 72 degrees Fahrenheit.
Due to the negative exponent, the temperature is decaying over time, but it never gets less than 72 ºF.
The time cannot be negative, hence the domain of the graph is given as follows:
m ≥ 0.
Then, considering this, the graph of the function is given at the end of the answer.
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Answer:
Step-by-step explanation:
a
HELP PLSSSSSSSSSSSSS
Answer:
the volume of the toy house is 66cm3
I need help on what the question is asking. Can you help me solve it step by step?
Given:
The total number of tamiliies is N = 30.
The objective is to find the mean number of gallons of milk consumed by 30 families.
Explanation:
The total number of milk consumed consumed by 30 families can be calculated as,
[tex]\begin{gathered} T=(8\times3)+(9\times2)+(13\times5) \\ =24+18+65 \\ =107 \end{gathered}[/tex]To find mean:
The mean number of gallons of milk can be calculated as,
[tex]M=\frac{T}{N}[/tex]On plugging the obtained values in the above equation,
[tex]\begin{gathered} M=\frac{107}{30} \\ =3.56666\ldots\text{.} \\ =3.6 \end{gathered}[/tex]Hence, the mean number of milk consumed by 30 families is 3.6 gallons.
How do I write this in function notation part b
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given details
Total rice bought is 75kg
Each week, he used 4.5kg, this means in w weeks, he will use:
[tex]4.5\times w=4.5w[/tex]STEP 2: Get the remaining kilograms of rice after w weeks
This will be gotten by using the function below:
[tex]75-4.5w[/tex]Hence, the function will be gotten as:
[tex]r(w)=75-4.5w[/tex]on the unit circle., in standard position an angle of which measure is coterminal with an angle that measures 3pi/5 radians
Coterminal angles are angles with the same terminal sides.
[tex]\theta\rightarrow\theta+2\pi\rightarrow\theta-2\pi[/tex]For the given angle, the coterminal angles are;
[tex]\begin{gathered} \theta=\frac{3\pi}{5} \\ \theta+2\pi=\frac{3\pi}{5}+2\pi=\frac{3\pi}{5}+\frac{10\pi}{5}=\frac{13\pi}{5} \\ \theta-2\pi=\frac{3\pi}{5}-2\pi=\frac{3\pi}{5}-\frac{10\pi}{5}=-\frac{7\pi}{5} \\ \theta+2(2\pi)=\frac{3\pi}{5}+4\pi=\frac{3\pi}{5}+\frac{20\pi}{5}=\frac{23\pi}{5} \end{gathered}[/tex]From the given answer choices, the coterminal angle is;
[tex]\frac{23\pi}{5}[/tex]13) y = 4x - 3 -8x + 6y = 14
Replacing y in the second equation
[tex]\begin{gathered} -8x+6(4x-3)=14_{} \\ -8x+24x-18=14 \\ 16x=14+18 \\ 16x=32 \\ x=\frac{32}{16} \\ x=2 \end{gathered}[/tex]Then
[tex]\begin{gathered} y=4(2)-3 \\ y=8-3 \\ y=5 \end{gathered}[/tex]Just checking our answer
[tex]-8(2)+6(5)=-16+30=14[/tex]So the correct answer is x=2 and y=5
Finding a difference quotient for a linear or quadratic function
Given the function
[tex]f(x)=-2x^2-3x+6[/tex]We are to look for the difference quotient:
[tex]\frac{f(x+h)-f(x)}{h}[/tex]Get f(x + h)
[tex]\begin{gathered} f(x+h)=-2(x+h)^2-3(x+h)+6 \\ f(x+h)=-2(x^2+2xh+h^2)-3x-3h+6 \\ f(x+h)=-2x^2-4xh-2h^2-3x-3h+6 \\ \end{gathered}[/tex]Given f(x) expressed as:
[tex]f(x)=-2x^2-3x+6[/tex]Substitute both functions into the difference quotient;
[tex]\begin{gathered} \frac{-2x^2-4xh-2h^2-3x-3h+6-(-2x^2-3x+6)}{h} \\ \frac{-\cancel{2x^2}-4xh-2h^2-\cancel{3x}-3h+\cancel{6}+\cancel{2x^2}+\cancel{3x}-\cancel{6}}{h} \\ \frac{-4xh-2h^2-3h}{h} \end{gathered}[/tex]Factor out "h" from the result to have
[tex]\begin{gathered} \frac{\cancel{h}(-4x-2h-3)}{\cancel{h}} \\ -4x-2h-3 \end{gathered}[/tex]This shows that the simplified form of the expression is -4x - 2h - 3
I need help with this question please?
[tex]t=100 \left(1-\frac{V}{50} \right)^2\\\\\frac{t}{100}=\left(1-\frac{V}{50} \right)^2[/tex]
Since time is positive, we take the positive square root.
[tex]\frac{\sqrt{t}}{10}=1-\frac{V}{50}\\\\\frac{\sqrt{t}}{10}-1=-\frac{V}{50}\\\\50-5\sqrt{t}=V\\\\\therefore f^{-1}(V)=\boxed{50-5\sqrt{V}}[/tex]
The area of a large plantation is eleven and seven hundredths kilometers. The length of the plantation is one tenth kilometers. How many kilometers is the width of the plantations?
The width of the plantation is 110. 7 kilometers
How to determine the width of the plantationIt is important to note that the formula for calculating the area of a rectangle is expressed as;
Area, A = lw
Where;
A represents the area of the rectanglel is the length of the rectanglew is the width the rectangleGiven that;
The value of the area of the large plantation is eleven and seven hundredths kilometers.
This is expressed as;
Area = 11. 07 kilometers
The value of the length is one tenth kilometers.
This is expressed as;
Length = 1/10 kilometers = 0. 1 kilometers
Now, substitute the values into the formula to determine the width
11. 07 = 0. 1w
Divide both sides by the coefficient of w, w have;
11.07/0.1 = 0.1w/0.1
Find the quotient
w = 110. 7 kilometers
Hence, the value is 110. 7 kilometers
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How many ounces of yogurt does the carton hold? (Hint: 1 ounce equals 1.805 in.³) round to the nearest tenth as needed
The carton holds 8.9 ounces of yoghurt
Explanation:The upper diameter, D = 2 in
R = D/2
R = 2/2
The upper radius, R = 1 inch
[tex]\begin{gathered} \text{The lower diameter, d= 2}\frac{7}{16}\text{ in = }2.4375 \\ \text{The lower radius, r = }\frac{d}{2}=\text{ }\frac{2.4375}{2}in\text{ = }1.22\text{ in} \end{gathered}[/tex]The height, h = 3 in
The volume of the cone frustrum is:
[tex]\begin{gathered} V=\frac{1}{3}\pi h(R^2+r^2+Rr) \\ V=\frac{1}{3}\times3.142\times3(1^2+1.22^2_{}+1.22(1)) \\ V=3.142(3.7084)) \\ V=11.65in^3 \end{gathered}[/tex]1.805 in.³ = 1 ounce
11.65in.³ = 11.65/1.805 ounce
11.65in.³ = 6.5 ounces
The carton holds 6.5 ounces of yoghurt
Suppose a person's score on a personality test that is normally distributed with a mean of 50 and a standard deviation of 10. If you
were to pick a person completely at random, what is the probability that you would pick someone with a score on this test higher than 70?
Answer:
2.28%
Step-by-step explanation:
P(X > 70) = 1 - Ф((70 - 50)/10) = 0.0228 = 2.28%
what is the result of processing the set of numbers in a domain called
Answer:
the output
Step-by-step explanation:
output
A client of Susan's has asked her to create a new wood floor for his living room. The design will be created by laying wood strips in different directions, as shown on the coordinate grid. Determine whether Quadrilateral can best be described as a trapezoid, a rhombus, a rectangle, or a square. Explain your reasoning.
Answer: Where's the graph
Step-by-step explanation:
Simplify −3(x+4)+5x Write your answer in factored form
Answer:-3x - 12 + 5x
Step-by-step explanation:
NEED HELP ASAP‼️‼️‼️‼️‼️‼️‼️‼️‼️
simplify 3xy³ + x²y⁵ over xy²
PLEASE SEND QUICK DUE IN 10-15 MINUTES ‼️‼️‼️
Answer:
[tex]4xy^3[/tex]
Step-by-step explanation:
3xy^3 + x^2y^5/xy^2
WILL MARK BRAINLIEST PLS HELP
⇒For m=2 and n=-3 in the equation 3m-4n In the place of m plug in 2 and in the place of n plug in -3 and simplify.
[tex]=3(2)-4(-3)\\=6+12\\=18[/tex]
Option C is the answer.
many of these boxes do you need to buy?you need to buy 40 packsExample 2.At a restaurant one day. 60 sandwiches were sold in all, some on rye bread and 28 onwhite bread. The number of sandwiches sold on try bread was twice the number soldthe day before. How many sandwiches on rye bread were sold the day before"?
rye bread sandwiches + white bread sandwiches = total number of sandwiches
rye bread sandwiches + 28 = 60
rye bread sandwiches = 60 - 28
rye bread sandwiches = 32
This number, 32, is twice the day before, that is, the day before was half of 32 sandwiches, which is 32/2 = 16.
The day before, 16 sandwiches on rye bread were sold.
jerry had 3409 pieces of marble he swallowed 1290 then is mom brought his 3456 more. How much does jerry have?
Answer: 5575 Marbles
Step-by-step explanation:
This can be solved simply by subtracting and adding.
3409-1290=2119
2119+3456=5575
Question 7Simplity 663x - 5) + (2x - 1). Show each step on a separate line and tell what you did in that step. Write your answer in factored form.
The expression is given as
[tex]6(3x-5)+5(2x-1)[/tex]STEP 1
Expand the first parenthesis by multiplying all the terms there by 6.
[tex]18x-30+5(2x-1)[/tex]STEP 2
Expand the second parenthesis by multiplying all the terms there by 5.
[tex]18x-30+10x-5[/tex]STEP 3
Collect the like terms.
[tex]18x+10x-30-5[/tex]STEP 4
Perform the arithmetic operations (addition and subtraction) to get the final answer.
[tex]28x-35[/tex]The final answer is 28x - 35
URGENT Please help!!!!!!
Divide 6.1 x 1020 by 3.2 x 105. Express your answer in scientific notation.
The value of the division of the expression will be; 19.52 x 10^{25}.
How does scientific notations work?The number is written in the form [tex]a \times 10^b[/tex] where we have [tex]1 \leq a < 10[/tex]
The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10.
Scientific notations have some of the profits; Better readability due to compact representation that value in terms of power of 10 is known, which helps in easy comparison of quantities differing by a large value.
Given the expression as 6.1 x [tex]10^{20}[/tex] by 3.2 x 10⁵
We have to divide the expression
( 6.1 x [tex]10^{20}[/tex] ) / (3.2 x 10⁵)
= 19.52 x [tex]10^{20 + 5}[/tex]
= 19.52 x [tex]10^{25}[/tex]
Therefore, the value of the division of the expression will be; 19.52 x [tex]10^{25}[/tex].
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mr. Smith took out a 54200 car loan at 10.2% compounded annually what would the interest be after 4 years
The compounded loan means that in the first year the 10.2% of interest is add to the initial 54200 and that value generate the next year the 10.2%
then in the first year the interest will be:
You use a rule of three:
[tex]\text{1st}=\frac{54200\cdot10.2}{100}=5528.4[/tex]As the first year the interest is 5528.4
To the second year that sum is added to the 54200 to get the interest:
[tex]54200+5528.4=59728.4[/tex][tex]2nd=\frac{59728.4\cdot10.2}{100}=6092.3[/tex]Third year:
[tex]59728.4+6092.3=60820.7[/tex][tex]3rd=\frac{60820.7\cdot10.2}{100}=6203.7[/tex]Fourth year:
[tex]60820.7+6203.7=67024.4[/tex][tex]4th=\frac{67024.4\cdot10.2}{100}=6836.5[/tex]After 4 years:
[tex]67024.4+6836.5=73860.9[/tex][tex]=\frac{73860.9\cdot10.2}{100}=7533.8[/tex]After 4 years the interest will be: 7533.8