On average, the number of miles the athlete ran per day is; 18/5 or 3.6 miles per day
How to calculate the average distance?We are given;
Number of days the athletes ran = 3¹/₂ days = 7/2 days
Total distance ran in the given time = 12³/₅ miles = 63/5 miles
Now, the average distance will simply be given by the expression;
Average Distance = Total Distance/Number of days of running
Now, let us convert the fractions to improper fraction for easy division. Thus, we have;
Number of days the athletes ran = 7/2 days
Total distance ran in the given time = 63/5 miles
Thus;
Average Distance = (63/5)/(7/2)
Average distance = 63/5 * 2/7 = 18/5 = 3.6 miles per day
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(x-2)^2, how do i do this, I'm confused and need help
Answer:
Step-by-step explanation:
DONT distribute the exponent
Instead, expand it to (x-2)*(x-2)
Multiply the First terms, Outer terms, Inner terms, then Last terms (FOIL)
Writing it out: (x*x) + (x*-2) + (-2*x) + (-2*-2)
Simplify: x^2 - 2x - 2x + 4
Answer: x^2 - 4x + 4
Estimate 93% of 149.
Answer:
Convert 93% to decimal and round. "Of" means to multiply.
93% = 0.93 ≈ 0.9
0.9 × 150(estimate) ≈ 135
Thus, the estimate is 135
Hope this helps!
8
The price of a share of stock started the day at $19.
During the day it went down $13, up $1, down $14, and up $4.
Which integer represents the price of a share at the end of the day?
Answer: $
Answer:
$ - 2
Step-by-step explanation:
$19 - $13 + 2 - $14 + 4 = - $2
What are the coordinates of G after it is translated LEFT 4 UNITS AND UP 3 UNITS?
this is a text
Answer:
The coordinates of G' after being translated is (-8,6)
Step-by-step explanation:
Find the original coordinates of G by looking at the graph. In this case it's (-4,3). Translate the changes: When you go to the left you are subtracting the x-axis from the original x-axis and when you go up you are adding the y-axis from the original y-axis so it would be -4 -4 is -8 and 3 + 3 is 6 so the new coordinates are (-8,6)Think About the Process At a little-known vacation spot, taxi fares are a bargain. A 63 mile taxi ride takes 81 minutes and costs $.56.70 You want to find the cost of a 31 - minute taxi ride. What unit price do you need?
The unit price that is going to be needed for the 31 minute ride would be 21.4 dollars.
How to solve for the amount that would be needed for a 31 minute rideWe have the fare for 81 minutes to be $56. 70
Then we are to find the amount that would be needed for 31 minutes.
In order to get this value we would have to cross multiply
such that we would have
81 minutes = $56.70
31 minutes = ?
then 56 * 31 = 1736
1736 / 81
= 21.4 dollars.
Hence we would conclude that the unit price that is going to be needed for the 31 minute ride would be 21.4 dollars.
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how do you find the area of a circle
Answer: A=(pi)r^2
Step-by-step explanation:
multiply pi (3.14) times the radius to the power of 2.
Round to the nearest hundredth, if necessary. Complete the statement. 30.9mm = in
The complete statement is 30.9mm = 1. 21 in
What is conversion of units?Conversion of units is simply the conversion between different units of measurement for a particular quantity.
Given the statement;
30.9mm = in
It is important to note that;
25. 4 millimeters = 1 inch
Then;
30. 9 millimeters = x inches
Cross multiply
x × 25. 4 = 30. 9 × 1
To make 'x' the subject
Divide both sides by 25. 4, we have;
x = 30. 9/ 25. 4
x = 1. 21 Inches
Thus, the complete statement is 30.9mm = 1. 21 in
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hello who help me with this? i think that's no complicated
Using the sine ratio, the value of x is: A. 26°.
How to Apply the Sine Ratio?Sine ratio is:
Sin ∅ = opposite side length / hypotenuse length of a right angle.
Given the following:
Reference angle (∅) = x
Opposite side length = 11
Hypotenuse side length = 25
Plug in the values
Sin x = 11/25
x = sin^(-1)(11/25)
x ≈ 26°
Thus, using the sine ratio, the value of x is: A. 26°
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Please help! The Great Wall of China built in the 7th century BCE, is about 1 x 10^4 miles long. The Panama Canal, built two thousand years later, is about 5 x 10^1 miles long. Write your answer in standard form.
The Great Wall of China is about what times long as the Panama Canal?
The number of times that the Great Wall of China is as long as the Panama Canal will be 2 × 10².
How to calculate the standard form?It should be noted that the Great Wall of China built in the 7th century BCE, is about 1 x 10⁴ miles long and the Panama Canal, built two thousand years later, is about 5 x 10^1 miles long.
Therefore, the number of times that the Great Wall of China is as long as the Panama Canal will be:
= 1 × 10⁴ / 5 × 10¹
= 2 × 10²
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What is the simplified form of 2+i / 2-i ?
(A) -1 (B) 3+4i/3 (C) 5+4i/5 (D) 3+4 i/ 5
The simplified form of (2 + i)/(2 - i) is (3 + 4i)/5
A Simple Form or simplified form can be defined as When a fraction's numerator and denominator share only one common factor, it is said to be in its simplest form.
Consider the given complex number(2 + i)/(2 - i)
Multiply both numerator and denominator with the complex number (2 + i), and we get
{(2 + i) × (2 + i)} / {(2 + i) × (2 - i)}= {(2 + i) × (2 + i)} / (2² - i²)
(using the formula (x + y)(x - y) = x² - y²)= {(2 + i) × (2 + i)} / (4 - (-1))= {(2 + i) × (2 + i)} / (4 + 1)= {(2 + i) × (2 + i)} / 5= (2² + 2i + 2i + i²)/5= (4 + 4i + (-1))/5= (3 + 4i)/5
Therefore, the simplified form of (2 + i)/(2 - i) is (3 + 4i)/5.
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Solve for y and calculate the ACB. Using the picture below. Show all work
Applying the linear pair postulate:
y = 30
m<ACB = 160°
What is the Linear Pair Postulate?According to the linear pair postulate, the sum of two adjacent angles that form a linear pair is equal to 180 degrees.
Given the following:
m<ACB = (4y + 40)°
m<DCE = (y - 10)°
Angles ACB and DCE are a linear pair. Therefore:
m<ACB + m<DCE = 180°
Substitute
(4y + 40) + (y - 10) = 180
Solve for y
4y + 40 + y - 10 = 180
Combine like terms
5y + 30 = 180
Subtract 30 from both sides
5y + 30 - 30 = 180 - 30
5y = 150
Divide both sides by 5
5y/5 = 150/5
y = 30
Find m<ACB:
m<ACB = (4y + 40)°
Plug in the value of y
m<ACB = 4(30) + 40
m<ACB = 120 + 40
m<ACB = 160°
Thus, applying the linear pair postulate:
y = 30
m<ACB = 160°
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What expression is not equivalent to 12x^4/4x^16
The expression equivalent to [tex]\frac{12x^{4} }{4x^{16} }[/tex] is 3[tex]x^{-12}[/tex] or 3[tex]x^{4-16}[/tex].that is option C) is correct.
According to the question the expression that we have been given to us is :
[tex]\frac{12x^{4} }{4x^{16} }[/tex]
Note that we know the property of exponent which states that if teh exponents with same base and different power are divided then the powers are subtracted. That is,
[tex]\frac{x^{m} }{x^{n} } = x^{m-n}[/tex] (1)
Now using this rule we will evaluate the equation given that is
= [tex]\frac{12}{4} * \frac{x^{4} }{x^{16} } \\\\[/tex]
First we will divide 12/4 which gives 3 then we will apply the property of exponent to the exponent function which gives,
= 3 [tex]x^{4-16}[/tex]
= 3 [tex]x^{-12}[/tex]
Hence the expression equivalent to [tex]\frac{12x^{4} }{4x^{16} }[/tex] is 3[tex]x^{-12}[/tex]or 3[tex]x^{4-16}[/tex] that is option C) is correct.
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One edge that is parallel to line segment FG is line segment ___.
Answer:
BC.
Step-by-step explanation:
Answer:
Line segment BC.
Step-by-step explanation:
Parallel lines are always the same distance apart at least. In this instance, FG and BC are parallel.
Renting a roller rink for your birthday costs $150 plus $8 per person. The total charge
for your party was $294. Translate this information into an equation using a to
represent the number of guests at your party.
Answer:
294 - 150 divided by 8 = A
Step-by-step explanation:
So, we already know, that we have $294 as our total. If we subtract $150, we get $144. The final step would be to divide it by $8 and that would be 18. There is 18 guests at the party.
Hope it helped!
Seamus sees a good helmet that is 195 and on a 35% off discount. What is the original price?
The original price of the helmet is 300.
What is percent?In mathematics, a percent is a number or ratio expressed as a fraction of 100. It is often denoted using percentage sign "%".
Now it is given that,
Price of helmet = 195
Discount on helmet = 35% = 0.35
Let the original price be x.
Now since Price of helmet = 195
Thus, Original price = x - 0.35x = 0.65x
Hence we get
0.65x = 195
Dividing both the side by 0.65 we get
x = 195/0.65
Solving we get
x = 300
this is the required original price of the helmet.
Thus, the original price of the helmet is 300.
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BC = 8, AC = 3x - 8 and AB = 2x - 7
The length of AC and AB is 19 and 11.
What is length?It is the measurement of something from end to end or along its longest side or a measurement of a particular part of something:
We have,
BC = 8
AC = 3x - 8
AB = 2x - 7
We can make the line as:
A______B______C
We can write as:
AC = AB + BC
3x - 8 = 2x - 7 + 8
Simplify all the like terms together.
3x - 2x = 8 - 7 + 8
x = 16 - 7
x = 9
Now,
AC = 3x - 8 = 3 x 9 - 8 = 27 - 8 = 19
AB = 2x - 7 = 2 x 9 - 7 = 18 - 7 = 11
Thus the length of AC and AB is 19 and 11.
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The complete question is:
AC = 3x - 8, BC = 2x + 7, and AB = 8. Find AC and AB.
Write each equation in logarithmic form.
(1/3)³ = 1/27
The logarithmic form of the equation is [tex]log_{\frac{1}{3} }(\frac{1}{27}) =3[/tex] .
In mathematics, the logarithmic function is the inverse of power. Then the function is given as f(x) = log x The logarithm base is a. This can be read as the logarithmic base a of x. The two most common bases used in logarithmic functions are base 10 and base e. The logarithm function has several properties that allow the logarithm to be simplified when the input is in the form of products, quotients, or values raised to powers.We have given an equation [tex](\frac{1}{3})^3 =\frac{1}{27}[/tex] .
Taking log on both sides , we get
[tex]log(\frac{1}{3})^3 =log(\frac{1}{27})[/tex] ..(1)
Applying the property of logarithm which is given by [tex]log_ab=bloga[/tex] in equation (1) ,we get
[tex]3log(\frac{1}{3}) =log(\frac{1}{27})[/tex]
On rearranging the above equation , we get
[tex]\frac{log(\frac{1}{27})}{log(\frac{1}{3})} =3[/tex] ..(2)
Applying the property of logarithm which is given by [tex]log_xy=\frac{log_ay}{log_ax}[/tex]\
[tex]\frac{log(\frac{1}{27})}{log(\frac{1}{3})}[/tex] can be written as [tex]log_{\frac{1}{3} }\frac{1}{27}[/tex] using property
Putting in equation (2) , we get
[tex]log_{\frac{1}{3} }(\frac{1}{27}) =3[/tex]
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Find the midpoint,M of CD
Answer:
The midpoint is (-1, 3)
Step-by-step explanation:
Given M = [tex]\sf \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} \right)[/tex]
[tex]M=\left(\frac{2+(-4)}{2}, \frac{5+1}{2} \right)\\M=(-1, 3)[/tex]
answer both please i will give brainliest
Answer: The first one is 15 and the second one is 1.
Step-by-step explanation: I plugged in -4 where x is so the equation was (-4)^2-1 which equals 15.For other one i did the same thing except with the 2 so the equation was 3(2)-5 which equals 1.
Factorise 3(a-b)(3r-T)+9(b-a)(2t-5s)
The factorization of the given expression 3(a-b)(3r-T)+9(b-a)(2t-5s) will be equal to 3(a-b){[3r-T]-392t-5s]}.
What is an expression?Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Given expression is 3(a-b)(3r-T)+9(b-a)(2t-5s) the factorization will be done as below:-
E = 3(a-b)(3r-T)+9(b-a)(2t-5s)
E = 3(a-b)(3r-T)- 9(a-b)(2t-5s)
E = 3(a-b){[3r-T]-392t-5s]}.
Therefore, the factorization of the given expression 3(a-b)(3r-T)+9(b-a)(2t-5s) will be equal to 3(a-b){[3r-T]-392t-5s]}.
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A group of friends wants to go to the amusement park. they have no more than $155 to spend on parking and admission. parking is $6.25, and tickets cost $20.50 per person, including tax. what is the maximum number of people who can go to the amusement park?
The maximum number of people who can go to the amusement park is 7 based on tickets cost of $20.50 per person
What is the total cost function for the amusement park?
The total cost is made up of cost of admission and parking and the tickets cost per person, which means that the total cost can be modeled as shown below based on the fact the number of persons that can attend is x
total cost=6.25+20.50x
total cost=155
155=6.25+20.50x
155-6.25=20.50x
148.75=20.50x
x=148.75/20.50
x=7(rounded to the nearest whole number)
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If you can fit 19 people in a 5ft x 5ft square, how many people would fit along a parade route, 10ft deep on each side of the street and one mile long?
There are 40128 peoples in the parade route by proportion.
According to the given question.
You can fit 19 people in a 5ft x 5ft square.
Here we need to find the number of peoples in the 10ft x 1 mile parade.
Since, we have to convert miles into feet then,
1 mile = 5280 feet
We know that the parade route is in the form of rectangle.
Also, the process of proportion reasoning involves understanding the multiplicative relationships between rational quantities.
Now we will find the number of peoples by proportions,
Let us consider the number of people in the rectangle as x.
Therefore,
19/25 = x/5280
⇒ (19/25)(5280) = x
⇒ x = 40128
Hence, there are 40128 peoples in the parade route by proportion.
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Let g(x) = -x² + 4. What is the value of g at x = -3 and x = 1 ?
A. g(−3) = −5, g(1) = 3
B. g(-3) = 13, g(1) = 3
C. g(-3) = -5, g(1)=5
D. g(-3) = 13, g(1) = 5
Answer:3) Find the domain of each, express answers in interval notation x+1 a) f(x) = 3x +2 b) f(x)=. 5 x² - 4x-12 x+1 for x < -2 ... 1 a) g(x) = f(x+10) b) g(x)
Step-by-step explanation:
If QR = 5x, RS = x + 3, and QS = 9, what is QR?
The value of QR is 5
What is a line segment?A line segment can be defined as the part of a straight line bounded by two different end points, and also contains every point on the line between its endpoints.
From the information given, the line QS has segments, line QR , RS and QS with R and the midpoint between Q and S
Given the points;
QR = 5xRS = x + 3 QS = 9We have that;
QR + RS = QS
substitute the values
5x + x + 3 = 9
collect like terms
6x = 9 - 3
6x = 6
Make 'x' the subject
x = 6/ 6
x = 1
But QR = 5x = 5(1) = 5
Thus, the value of QR is 5
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The complete question;
If R is the midpoint of QS and QR = 5x, RS = x + 3, and QS = 9, what is QR?
Let g(x)=3 x+2 and f(x)= x-2 / 3 . Find each value.
f(g(1))
The value for f(g(1)) = 1
What are the domain of the function f(g(1))?Given:
g(x) =3 x+2 and f(x)= x-2 / 3
f(x) = x-2 / 3
substitute x =1 into the function f(x). Then:
f(1) = 1-2 / 3
f(1) = -1/3
Now, the next step is to substitute f(1) into the function g(x)
g(x) = 3 x+2
g(f(1)) = 3 (-1/3)+2
g(f(1)) = 1
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(5 * 10^-2) (4 * 10^-3), write in scientific notation.
Answer:
[tex]2 \times 10^{-4}[/tex]
Step-by-step explanation:
[tex]5 \times 10^{-2} \times 4 \times 10^{-3} \\\to 20 \times 10^{-2 + -3} \\\to 2 \times 10 \times 10^{-5} \\\to 2 \times 10^{1 + -5} \\\to 2 \times 10^{-4}[/tex]
[tex] \large \bf \implies{2 \times {10}^{ - 4} }[/tex]
Step-by-step explanation :[tex] \bf(5 \times {10}^{ - 2} )(4 \times {10}^{ - 3} )[/tex]
Step 1) : Rewrite the expression
[tex] \bf \longrightarrow(5 \times 4) \times( {10}^{ - 2} \times {10}^{ - 3} )[/tex]
Step 2) : Calculate the product or quotient
[tex] \bf \longrightarrow20 \times ( {10}^{ - 2} \times {10}^{ - 3} )[/tex]
Step 3) : Simplify using exponent rule with same base
[tex] \bf {a}^{n} . \: {a}^{m} = {a}^{n + m} [/tex]
[tex] \bf \longrightarrow20 \times {10}^{ - 2 - 3} [/tex]
Step 4) : Calculate the sum or difference
[tex] \bf \longrightarrow20 \times {10}^{ - 5} [/tex]
Step 5) : Express the number in scientific notation
[tex] \bf \longrightarrow2 \times {10}^{ - 4} [/tex]
Please help me please help me please
Answer: (2,-2 )
Step-by-step explanation: That's where U is located on the Graph.
A die is rolled 200 times with the following results.
What is the theoretical probability of the given event?
P(3)
Answer:
You didn’t add the data chart. But I’ll try my best to help.
Step-by-step explanation:
If it landed on the same time multiple times than you will most likely land the same time again.
Which linear inequality is represented by the graph?
O y>_1/3x-4
Oy<_1/3x-4
Oy<_1/3x+4
Oy>_1/3x+4
answer is y ≤ [tex]\frac{1}{3}x (-4)[/tex]
Given that,
Area of shaded inequality below solid line is positive
and y-intercept of the solid line is equal to - 4
therefore,
The inequality must be
y ≤ [tex]\frac{1}{3}x (-4)[/tex]
In Mathematics, inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in Maths. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠). The different types of inequalities in Maths are polynomial inequality, rational inequality, absolute value inequality.
A system of linear inequalities in two variables includes at least two linear inequalities in the identical variables. When we solve linear inequality then we get an ordered pair. So basically, in a system, the solution to all inequalities and the graph of the linear inequality is the graph displaying all solutions of the system. Let us see an example to understand it.
the Linear inequality: 2x – y >1, x – 2y < – 1
The symbols ‘<‘ and ‘>’ express the strict inequalities and the symbols ‘≤’ and ‘≥’ denote slack inequalities. A linear inequality seems exactly like a linear equation but there is a change in the symbol that relates two expressions.
here is given step to easily find the value of inequality:
Step 1: The inequality is already in the form that we want. That is, the variable y y is isolated on the left side of the inequality.
Step 2: Change inequality to equality. Therefore, y > x + 1y>x+1 becomes y = x + 1y=x+1.
Step 3: Now graph the y = x + 1y=x+1. Use the method that you prefer when graphing a line. In addition, since the original inequality is strictly greater than symbol, \Large{>}>, we will graph the boundary line as a dotted line.
Step 4: The original inequality is y > x + 1y>x+1. The greater than symbol implies that we are going to shade the top area or region.
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Currently i am paying $60.00 a month for my service. i would like to upgrade to the $80.00 service package because my new employer offers a 20% discount with your company. what would be the cost difference compared to what i am paying now if i upgraded?" employee: "with your discount you would only pay __________ a month more for the upgraded plan."
Employee: "with your discount you would only pay $4.00 a month more for the upgraded plan."
What is the discounted cost per month with new upgraded version and employer's 20% discount?
The new price before considering the employer's discount is $80.00, which means that by deducting 20% of the new price, the employee is left to pay $64.00 every month and excess of that over the current monthly payment is $4.00 as shown explicitly below:
new upgraded price=$80.00
new upgraded after discount of 20%=$80*(1-20%)
new upgraded after discount of 20%=$64.00
The extra amount payable every month=new upgraded after discount of 20%-current charge
current monthly charge=$60.00
The extra amount payable every month=$64.00-$60.00
The extra amount payable every month(cost difference)=$4.00
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