Given the repeating decimal 0.155...
We will convert it to a fraction as follows:
[tex]\begin{gathered} 0.1555.\ldots=0.1+0.055\ldots \\ \\ =\frac{1}{10}+\frac{5}{100-10} \\ \\ =\frac{1}{10}+\frac{5}{90}=\frac{9}{90}+\frac{5}{90}=\frac{14}{90}=\frac{7}{45} \end{gathered}[/tex]so, the answer will be:
[tex]0.1555\ldots=\frac{7}{45}[/tex]Al gets paid semimonthly. His gross pay for each pay period is $750.He has 18% withheld for taxes and 48 withheld for personal deductions.What is the amount of his annual net pay?a. $7,200b. $14,040c. $15,300d. $15,600
so given $750 as gross pay
18% withheld for taxes
48 withheld for personal term this also means 4%
18% = 0.18
4% = 0.04
so to get the annual net,
750 x (1 - 0.18 - 0.04) x 24
= 14040
=$14, 040
this makes option B the corect answer
how are the processes for converting 5/8 to decimal and to a percentage similar and how are the processes different
To convert 5 to a decimal, divide it by 8.
To convert a decimal to a percent, multiply it by 100.
What is decimal and percentage conversion?
To convert a percentage to a decimal, divide by 100. So 25% is 25/100, or 0.25. To convert a decimal to a percentage, multiply by 100 (just move the decimal point 2 places to the right) and give the % symbol.
Consider, the given fraction, 5/8
Divide 5 by 8 to change a decimal.
So, 5/8 = 0.625
Now to convert decimal 0.625 into a percent.
Multiply 0.625 by 100 to get 62.5%.
So, the conversion of fraction into decimal is 0.625 and the decimal into percent is 62.5%.
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Given the pattern -36, 12, -4, ...(a) Write an explicit formula for the pattern.(b) Write a recursive formula for the pattern.(c) Does the pattern converge or diverge? If it converges, to what value does it converge?(d) If you added the terms in this pattern, would the sum converge or diverge? If it converges, to what value does it converge?
Answer:
[tex]\begin{gathered} a)a_n=-36\cdot\frac{1}{3}^{n-1} \\ b)\text{ }a_n=\frac{1}{3}\cdot a_{n-1} \\ c)\text{ converges to -54} \\ d)\text{ s=-54} \end{gathered}[/tex]Step-by-step explanation:
The explicit and recursive formula for a geometric sequence is represented by the following:
[tex]\begin{gathered} \text{ Explicit formula:} \\ a_n=a_1\cdot r^{n-1} \\ \text{ Recursive formula:} \\ a_n=r\cdot a_{n-1} \\ \text{where,} \\ r=\text{ common ratio} \end{gathered}[/tex]The common ratio of the pattern is:
[tex]\begin{gathered} \frac{-12}{-36}=\frac{1}{3} \\ \frac{-4}{-12}=\frac{1}{3} \end{gathered}[/tex]Then, for the explicit formula:
[tex]a_n=-36\cdot\frac{1}{3}^{n-1}[/tex]Recursive formula:
[tex]a_n=\frac{1}{3}\cdot a_{n-1}[/tex]Now, to determine if the pattern converge or diverge:
[tex]\begin{gathered} \lvert r\rvert<1,\text{ the series converge to }\frac{a_1}{1-r} \\ \lvert r\rvert\ge1,\text{ the series diverges} \end{gathered}[/tex]Since the common ratio is less than 1, the series converges to:
[tex]\text{converges to }\frac{-36}{1-\frac{1}{3}}=-54[/tex]A sum of an infinite geometric series can be determined if it converges since this pattern converges, the sum would converge to;
[tex]\begin{gathered} S=\frac{a_1}{1-r} \\ S=\frac{-36}{1-\frac{1}{3}}=-54 \end{gathered}[/tex]m =Y2-71x2-x1Find the slope of the line that passesthrough these two points,(3, 1) (4,9)m = [?]
1) Since, we've got already two points. Let's plug them into the slope formula so that we can find how steep is the line between those two points:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{9-1}{4-3}=\frac{8}{1}=8[/tex]2) Thus, that's the slope.
Choose the correct table for the inverse of the relation below
GIVEN:
We are given a table of x and y values that defines a function.
Required;
To find the inverse of the relation as shown.
Step-by-step solution;
For a relation defined as an ordered pair in the form,
[tex](x,y)[/tex]then its inverse is a relation of the set of ordered pairs in the form;
[tex](y,x)[/tex]In other words, what we have is;
[tex]\begin{gathered} f(x)=(x,y) \\ \\ f^{-1}(x)=(y,x) \end{gathered}[/tex]The function given has the following ordered pairs;
[tex]\begin{gathered} For\text{ }f(x): \\ \\ (-4,-3),(-1,1),(1,2),(3,6) \end{gathered}[/tex]Therefore, the inverse would be;
[tex]\begin{gathered} For\text{ }f^{-1}(x): \\ \\ (-3,-4),(1,-1),(2,1),(6,3) \end{gathered}[/tex]ANSWER:
Therefore, option A is the correct answer
Suppose one-seventh of the employees of a certain company work in the Southeastern region. If the company employs 247 workers in that region, what is the total number of employees working for the company?How many total employees?
Given:
One-seventh of the employees of certain companies work in the Southeastern region. If the company employs 247 workers in that region,
Required:
Find the total number of employees.
Explanation:
Let the number of employees be x.
According to the question
[tex]\begin{gathered} \frac{1}{7}x=247 \\ x=247\times7 \\ x=1729 \end{gathered}[/tex]Final Answer:
The total number of employees working is 1729.
You want to know the number of minutes that you can use on your $45.00 phone card. The card company chargesyou $0.50 for the first minute and $0.05 for cach additional minute. Solve the formula $45.00 = $0.50 + $0.05mfor m. Justify each step with an algebraic property of equality.
To solve m:
1. Subtract 0.50 in both sides of the equation (subtraction property of equality):
[tex]\begin{gathered} 45.00-0.50=0.50-0.50+0.05m \\ 44.5=0.05m \end{gathered}[/tex]2. Divide both sides of the equation into 0.05 (Division property of equality):
[tex]\begin{gathered} \frac{44.5}{0.05}=\frac{0.05}{0.05}m \\ \\ 890=m \end{gathered}[/tex]3. Rewrite the equation (Symmetric property):
[tex]m=890[/tex]Then, you can use 890 minutes on your $45.00 phone card.Please show work for this !!
The midpoint of the given endpoints is (0,4).
From the graph:
points are (-4,4) and (4,0)
Midpoint = (x1+x2 / 2 , y1+y2 / 2)
= (-4+4 / 2 , 4 + 4 / 2)
= (0/2 , 8/2)
= (0,4)
Therefore the midpoint of the given endpoints is (0,4).
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Solve and graph the solution set. Indicate a scale. Please draw it clearly and understandably.
Answer:
x>=4
Explanation:
Given the inequality expression
[tex]4x-3\ge13[/tex]Add 3 to both sides of the inequality
[tex]\begin{gathered} 4x-3+3\ge13+3 \\ 4x\ge16 \end{gathered}[/tex]Divide both sides by 4
[tex]\begin{gathered} \frac{4x}{4}\ge\frac{16}{4} \\ x\ge4 \end{gathered}[/tex]Represent the solution on a number line;
Note that the circle was shaded because the inequality sign includes the equality sign and the arrow points to the positive side since it is a greater than sign.
What is Three subtracted from a number that equals 63
Explanation
To compute the answer, let us make the unknown number y
Thus
We can represent the given statement as
[tex]y-3=63[/tex]The next step will be to solve for y
[tex]\begin{gathered} add\text{ 3 to both sides} \\ \\ y-3+3=63+3 \\ y=66 \end{gathered}[/tex]Therefore, the number is 66
1. Select the equations that are true.In the figure shown, lines f and g are parallel.1. Circle all equations that are true.456A. mZ3+ m25 = 180 because they are a linear pair.B. m3 = m25 because they are alternate interior angles.C. m 3 = m_2 because they are vertical angles.D. m 2+ m24 = 180 because they are a linear pair.E. m24 = mZ5 because they are alternate interior anglesF. mZ1 = m28 because m25 = m28 are vertical anglesand mZ1 = m25 are corresponding anglesG. m27 = m_3 because they are corresponding angles.
As shown at the graph:
Use a table of values with at least 5 values to graph the following function:
A function take an input and produce a unique output.
[tex]y=2^x[/tex]y is the output
x is the input
[tex]\begin{gathered} x=1y=2^x=2^1\text{ = 2} \\ x=2y=2^{2\text{ = 4}} \\ x=3y=2^3\text{ = 8} \\ x=4y=2^4\text{ = 16} \\ x=5y=x^5\text{ = 32} \end{gathered}[/tex]How many pairwise comparisons are needed to learn the outcome of an election involving n=15 candidates ?
Remember that
The formula for the number of independent pairwise comparisons is k(k-1)/2, where k is the number of conditions
In this problem
k=15
substitute
15(15-1)/2=105
therefore
The answer is 105The function C(x) = 300x + 180 gives the cost for a college to offer x sections of an introductory class in CPR (cardiopulmonary resuscitation). The function R(x) = 390x gives the amount of revenue the college brings in when offering x sections of CPR. Find the point where the cost equals the revenue by graphing each function on the same coordinate system. (x, y) =
Cost = Revenue
Then
300x + 180 = 390x
x= (390-300)/180= 180/90 = 2
Now graph both functions
Determine which if any of given ordered pairs satisfy the system of linear equations
Solution:
The equations are given below as
[tex]\begin{gathered} x+3y-z=-11-----(1) \\ 2x-y+2z=11------(2) \\ 3x+2y+3z=6------(3) \end{gathered}[/tex]Step 1:
Make x the subject of the formula from equation (1)
[tex]\begin{gathered} x+3y-z=-11 \\ x=-11-3y+z-----(4) \end{gathered}[/tex]Step 2:
Substitute equation (4) in equations (2) and (3)
[tex]\begin{gathered} 2x-y+2z=11 \\ 2(-11-3y+z)-y+2z=11 \\ -22-6y+2z-y+2z=11 \\ -7y+4z=11+22 \\ -7y+4z=33-----(5) \\ \\ 3x+2y+3z=6 \\ 3(-11-3y+z)+2y+3z=6 \\ -33-9y+3z+2y+3z=6 \\ -7y+6z=6+33 \\ -7y+6z=39------(6) \end{gathered}[/tex]Step 3:
Substract equation 5 from 6
[tex]\begin{gathered} -7y-(-7y)+4z-6z=33-39 \\ -2z=-6 \\ z=3 \end{gathered}[/tex]Step 4:
Substitute the value of z=3 in equation (4)
[tex]\begin{gathered} -7y+4z=33 \\ -7y+4(3)=33 \\ -7y+12=33 \\ -7y=33-12 \\ -7y=21 \\ y=-3 \end{gathered}[/tex]Step 4:
Substitute y=-3, z= 3 in equation (4)
[tex]\begin{gathered} \begin{equation*} x=-11-3y+z \end{equation*} \\ x=-11-3(-3)+3 \\ x=-11+9+3 \\ x=1 \end{gathered}[/tex]Hence,
The final answer is
[tex]\Rightarrow(1,-3,3)[/tex]ONLY THE ORDERED PAIR ( 1, -3, 3) satisfies the system of linear equations
OPTION B is the right answer
43. For the first art project, 15 students will equally share a 50-pound packageof clay. Later, each student will be given an additional 2 pounds of clay forthe second project.Which equation could be used to find p, the total number of pounds ofclay used per student?Bp = (50 - 15) - 2p = 15 + (50 = 2)p = (50 = 15) - 2p = 2 + (50 - 15)
The equation that could be used to find the total number of pounds of clay used per student is:
p = 2 + 50/15
Explanation:The equation that could be used to find the total number of pounds of clay used per student is:
p = 2 + 50/15
This shows the addition of the extra 2 pounds of clay for the second project with the 50 pounds of clay shared by all 15 students
Angles K and M are vertical angles. K’s measurement is 72 degrees. What is the measure of M ?
If two angles are vertical and congruent, the angle is the same:
[tex]\begin{gathered} K=M \\ M=72 \end{gathered}[/tex]The measure of M is 72°
Please HelpWhich of the following is a continuous random variable?A. X= number of incoming flights at the local airportB. T=winning time in the man's 100 meter dash at the 2016 OlympicsC. P=number of points scored by Stephen curry in a game D.H=The number of hats sold on Tuesday
A continuous random variable must be a variable that can take decimal values.
In this case, the number of incoming flights at the local airport can not take decimal values, because you can not say 3 and a half flights.
In a basketball game you can not score half point, it means this variable can neither take decimal values.
You can not sell 5 and a quarter hats, it means this variable can not take decimal values.
The only variable that meets this condition is the winning time in the man's 100 meter dash at the 2016 Olympics.
The correct answer is B.
if planet 1 is 32.7 million miles farther from the sun than planet 2, then planet 3 is 26.5 million miles farther from the sun than planet 1. when the toal of distnaces for these three planets from the sun is 190.0 million miles, how far away from thesun is planet 2?
The distance between planet 2 and sun is of 32.7 million miles.
Let the distance between planet 2 and sun = x
Distance between planet 1 and sun = 32.7 + x
Distance between planet 3 and sun = (32.7 + x) + 26.5
= 59.2 + x
According to question,
Distance between planet 1 and sun + distance between planet 2 and sun + Distance between planet 3 and sun = 190
(32.7 + x) + x + (59.2 + x) = 190
3x + 91.9 = 190
3x = 190 - 91.9
3x = 98.1
x = 98.1 / 3
x = 32.7
Hence, Distance between planet 2 and sun is 32.7 million miles.
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Charlie is flying a kite one afternoon and steps on the end of the string to have hishands free to take a picture. The string is 135 feet long and forms a 68-degree anglewith the ground. How high is his kite at this time? Round to the nearest foot, andenter the number only.AV
The string of the kite, ground and hieght of the kite makes the right angle triangle.
The hypotenuse side of triangle is 135 feet long.
Determine the height of the kite by usng the trigonometry.
[tex]\begin{gathered} \sin 68=\frac{h}{135} \\ h=0.9272\cdot135 \\ =125.172 \\ \approx125 \end{gathered}[/tex]So answer is 125 feet.
You need a 50% alcohol solution. On hand, you have a 300 mL of a 40% alcohol mixture. You also
have 80% alcohol mixture. How much of the 80% mixture will you need to add to obtain the desired
solution?
You will need
—————————mL of the 80% solution
You will need 100 mL of the 80% solution and solve the question by using percentage concept.
What is the percentage?
A percentage is a number or ratio that can be expressed as a fraction of 100.
Assume that x mL of 80% solution is needed.
The amount of alcohol in 300 mL of a 40% alcohol mixture is
300 mL × 40% = 300 × (40/100) = 120 ml.
The amount of alcohol in 300 mL of a 40% alcohol mixture is
300 mL - 120 mL = 180 mL.
The amount of alcohol in x mL of a 80% alcohol mixture is
x mL × 80% = x × (80/100) = (8x)/10 ml.
The amount of alcohol in x mL of a 80% alcohol mixture is
x - (8x)/10 ml = (2x)/10 mL.
Total amount of alcohol is 120 + (8x)/10 mL
Total amount of water is 180 + (2x)/10 mL
The meaning of 50% alcohol solution is the amount of alcohol and water is equal.
120 + (8x)/10 = 180 + (2x)/10
(8x)/(10)- (2x)/10 = 180 -120
(6x)/(10) = 60
x = 100
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what is this 3+12c-4c
what is this 3+12c-4c
step 1
combine like terms
3+(12c-4c)
answer is
3+8ca hot air balloon decrease its altitude by 3/8 ft each for two seconds what was the total change in altitude
The rate of change is the decrease in altitude per change in two seconds
[tex]\begin{gathered} \frac{3}{8}\text{ divided by 2} \\ \frac{3}{8}\text{ x}\frac{1}{2} \\ \Rightarrow\frac{3}{16}ft\text{ per second} \end{gathered}[/tex]If the initial altitude is y ft
Vijay inherited some money from his grandfather and put it in a bank account that earns 6% interest compounded annually. After 3 years, Vijay had $4,000.00 in the bank account. How much interest did he earn? Round your answer to the nearest cent.
We have in this question a case of Annual Compound Interest. The formula for this case is as follows:
[tex]A=P(1+r)^n_{}_{}[/tex]Where:
A = accrued amount.
P = Principal (starting amount).
r = interest rate.
n = number of years.
We have from the question:
r = 6%
n = 3 years.
P = $4,000.00
A = it is the unknown amount.
We can determine A to then find the interest he earned. Thus, we can proceed as follows:
[tex]A=4000(1+0.06)^3\Rightarrow A=4000(1.06)^3\Rightarrow A=4764.064[/tex]This previous amount is the accrued amount (the starting amount plus the interest after 3 years annually compounded).
Therefore, the amount Vijay earned in interests (after 3 years) is:
[tex]4764.064-4000=764.064[/tex]And, rounding this amount to the nearest cent, we have that, finally, the earned interest (after 3 years) is $764.06.
4х - Зу = 4 2х + 4 y = 3*solving system by elimination*
Answer
x = (25/22)
y = (2/11)
Explanation
4х - Зу = 4
2х + 4y = 3
We are asked to solve the system of equations by elimination
To do that, we will multiply the first equation by 1 and the second equation by 2
(4х - Зу = 4) × 1
(2х + 4y = 3) × 2
4x - 3y = 4
4x + 8y = 6
Subtract equation 1 from equation 2
4x + 8y = 6
- (4x - 3y = 4)
4x - 4x + 8y + 3y = 6 - 4
0 + 11y = 2
11y = 2
Divide both sides by 11
(11y/11) = (2/11)
y = (2/11)
Using one of the equations, we can solve for x
2x + 4y = 3
2x + 4(2/11) = 3
2x + (8/11) = 3
2x = 3 - (8/11)
2x = (33/11) - (8/11)
2x = (25/11)
x = (25/22)
Hope this Helps!!!
Estimate the quotient using compatible numbers.61.32 divided by 11.7 =
Answer:
5
Explanation:
Given the quotient:
[tex]61.32\div11.7[/tex]First, we estimate each of the numbers:
[tex]\begin{gathered} 61.32\approx60\text{ (to the nearest tens)} \\ 11.7\approx12\text{ (to the nearest whole number)} \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} 61.32\div11.7\approx60\div12 \\ =5 \end{gathered}[/tex]In the early afternoon, a tree casts a shadow that is 2 feet long. A 4.2-foot-tall boy standing nextto the tree casts a shadow that is 0.7 feet long. How tall is the tree?
In this drawing, the traingle on the left, has the height of the tree (T) and the size of the shadow 2 feet
The tringle on the right, has the height of the boy, 4.2 feet and the shadow is 0.7 feet
The angle a is the angle with respect to the sun light
The triangles are congruent, because therefore the proportion of their sides is equal, so we can write:
T/2 = 4.2/0.7
Solving for T:
T = 2(4.2/0.7) = 12
T = 12
Answer:
The tree is 12 feet tall
Sasha drew a scale drawing of a restaurant. A countertop in the restaurant, which is 5 feet long in real life, is 10 inches long in the drawing. What scale factor does the drawing use?Simplify your answer and write it as a ratio, using a colon.
Answer:
Explanations:
Based on the given information, we are told that Sasha drew a scale drawing of a restaurant. If the countertop in the restaurant is 5 feet long in real life and 10 inches long in the drawing, this shows that the drawing of the building was reduced.
To deetermine the scale factor, we will
Each week, Tasha saves 60% of the money she earns babysitting and spends the rest. This week she earned $20.00. How much more money did she save than spend this week?
Answer:
$4.00 more saved than spent
Step-by-step explanation:
Given that Tasha saves 60% of her earnings and that she earned $20.00 this week, we need to find the amount she saved and subtract this amount and the amount she earned.
Letting A represent the amount Tasha saves and e represent her earnings, we can find how much she saved using
A(e) = 0.60e
A(20) = 0.60 * 20 = 12
Since she only earned $20.00, we can find the amount she spent by subtracting 12 from 20:
20 - 12 = 8
Finally, we can find how much more she saved than spent this week by subtracting 8 from 12:
12 - 8 = $4.00
Tyee has 10 1/4 yards of ribbon to make bows. Each bow is made from a piece of ribbon that is 3/5 yard long. What is the maximum number of complete bows Tyee can make?
Given:
Tyee has 10 1/4 yards of ribbon to make bows.
The length of each bow = 3/5 yards
We will find the maximum number of bows by divided the total length by the length of one bow.
so, the number of bows will be as follows:
[tex]10\frac{1}{4}\div\frac{3}{5}=\frac{41}{4}\div\frac{3}{5}=\frac{41}{4}\times\frac{5}{3}=\frac{205}{12}=17\frac{1}{12}[/tex]The number of bows will be an integer number
so, the answer will be:
The maximum number of complete bows = 17