Answer:
Explanation:
Zak jogs from his house to a lake. He then jogs 5 laps around the lake at a constant speed. The table shows thetotal amount of time, in minutes, Zak has been jogging after completing x laps.Which equation represents the time, m, in minutes, Zak has been jogging after completing x laps?A m = 12x + 5B m = 5x + 12C m = 24x + 5D m = 5x + 24
We are given Zak's laps jogged along with the minutes elapsed.
If the equation of a line is:
m = kx + b
Where m is the number of minutes.
k is the slope of the line
x is the Laps
b is the y-intercept (or where the line crosses the y-axis)
In order to get the equation of the relationship between Laps (x) and Minutes (m),
we need to calculate the slope k and intercept b.
The formulas for doing these are given below:
[tex]\begin{gathered} m=\frac{\sum(x_i-X)(y_i-Y)}{(x_i-X)^2} \\ \text{where,} \\ x_i=\text{data points of Laps x} \\ X=\text{ Average of the Laps x} \\ y_i=\text{data points of Minutes m} \\ Y=\text{Average of Minutes m} \end{gathered}[/tex]The formula for intercept (b) is;
[tex]b=Y-kX[/tex]where Y and X are the averages of m and x values from the table.
[tex]\begin{gathered} Y=\frac{\sum m}{n}\text{ (n is the number of data values of Y)} \\ Y=\frac{17+41+65}{3} \\ \\ Y=41 \\ \\ X=\frac{\sum x}{n}\text{ (n is the number of data values of X)} \\ X=\frac{1+3+5}{3} \\ \\ X=3 \end{gathered}[/tex]In order to be tidy and quick, a table is used to solve.
This table is shown in the image below:
Therefore, we can now calculate slope (m):
[tex]\begin{gathered} m=\frac{\sum(x_i-X)(y_i-Y)}{(x_i-X)^2} \\ \\ m=\frac{\mleft(-24\mright)\mleft(-2\mright)+0\mleft(0\mright)+\mleft(24\mright)\mleft(2\mright)}{4+0+4} \\ m=\frac{96}{8} \\ \\ m=12 \end{gathered}[/tex]Now that we have slope (k) = 12, we can get the intercept b
[tex]\begin{gathered} b=Y-kX \\ Y=41-12(3) \\ Y=41-36 \\ Y=5 \end{gathered}[/tex]Therefore, the equation is:
m = 12x + 5
A planner at Barnes and Noble originally cost $10. During the weekend, the planner went on sale for $9. What is the price markdown (percent of change)?
new cost = $9
original cost = $10
Substitute the value into the formula;
[tex]\text{percentage change =}\frac{10-9}{10}\times100^{}[/tex]
= 1/10 x 100%
= 10%
Simplity 24 ÷ (-2)(3) + 7
Nashia, this is the solution:
24 ÷ (-2)(3) + 7
• We use ,PEMDAS, for the order of operations, as follows:
Step 1: Solve the parenthesis
24 ÷ -6 + 7
Step 2: We solve the division
-4 + 7
Step 3: We solve the addition
3
The result is 3
Suppose Latoya borrows$4000.00 at an interest rate of 18% compounded each year.Assume that no payments are made on the loan.Find the amount owed at the end of 1 year.Find the amount owed at the end of 2 years.
Answer:
[tex]\begin{gathered} A=\text{ \$4,720 at the end of 1 year} \\ A=\text{ \$5,570 at the end of 2 year} \end{gathered}[/tex]Step-by-step explanation:
The compound interest is represented by the following equation:
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ where, \\ P=\text{ principal borrowed} \\ r=\text{ rate} \\ n=\text{ number of times compounded per time ''t''} \\ t=\text{ time in years} \end{gathered}[/tex]Therefore, if Latoya borrows $4000 at an interest rate of 18% compounded each year;
[tex]\begin{gathered} A=4000(1+\frac{0.18}{1})^1 \\ A=\text{ \$4,720 at the end of 1 year} \end{gathered}[/tex]Now, at the end of 2 years:
[tex]\begin{gathered} A=4000(1+\frac{0.18}{2})^2 \\ A=\text{ \$5,569.6 at the end of 2 year} \end{gathered}[/tex]Factors of 12: 1. 2. 3. 4. 6. 12 Factors of 20: 1, 2, 4, 5, 10, 20 • Which numbers are common factors of 12 and 20? Choose ALL that apply. 1 2 3 6 10 12 20
The common factors are; 1,2,4
Yoshi has played in 6 basketball games so far this season. Her points in each game aredisplayed in the table below.GamePoints181234562420142224What is the median of Yoshi's points per game?O 21None of the other answers are correctO 221920
Let us revise how to find the median
At first you must arrange the numbers from small to big
Let us do that
14, 18, 20, 22, 24, 24
We have 6 numbers we need to find the middle one because the median means middle number in a set of data
But there are 6 numbers the middle numbers are 20 and 22
So the median will be the average of the two number
[tex]\text{Median}=\frac{20+22}{2}=\frac{42}{2}=21[/tex]There is a very important note for the median
If the number of data is even the median will be the average of the middle two numbers as our question, but if the number of data is odd then the median will be the middle number.
The answer is the first choice
The radius of a circle is 11ft. Find its area in terms of pi
Answer: A≈380.13ft²
Step-by-step explanation:
A train leaves Little Rock, Arkansas, and travels north at 90 kilometers per
hour. Another train leaves at the same time and travels south at 60 kilometers
per hour. How long will it take before they are 300 kilometers apart?
Answer: 240 ft to be sure
Step-by-step explanation:
John's bank account was overdrawn. The status of his account was − $162. He did not realize the problem and wrote another check for $78. The bank charged him a $24 fee for being overdrawn.What was the new status of John's account at this point?
The initial status of John's bank account was -$162.
After he wrote a check for $78 and being charged in $24 for being overdrawn, the new status is - 162 - 78 - 24 = -$264
If 3m+5=27, then the value of m is
Answer:
m=7 1/3 in mixed number or 22/3 in improper fraction
Step-by-step explanation:
3m+5=27 is your equation
You will have to subtract 5 on both sides and you will be left with
3m=22
After that you will divide three on both sides
Therefore the answer is m=7 1/3 or 22/3
Determine whether each pair of polygons is similar. OPTIONSSimilar, sides are proportional and angles are corresponding Similar, sides are proportional and angles are congruent Not similar, sides are not proportional and angles are congruent Not similar, sides are proportional and angles are not congruent
From the figure it can be observed that angles of both figure are equal to 90 degrees. So angles are congurent of polygons are conurent to each other.
Determine the ratio of corresponding sides of two polygon.
[tex]\frac{3}{4}[/tex]And
[tex]\frac{6}{9}=\frac{2}{3}[/tex]As sides of the polygons are not proportional to each other. So figure are not similar.
Thus correct option is,
Not similar, sides are not proportional and angles are congruent .
Find the square of each number. (Do not add extra spaces in your response.)
1.) 7 =
2.) 21 =
3.) -3 =
4.) 45 =
5.) 2.7 =
6.) −14=
7.) -5.7 =
8.) 25=
someone help me thanks! it's on pythagoras theorem btw
Answer:
y = 3
Step-by-step explanation:
Pythag theorem : ( only applies to RIGHT triangles)
Hypotenuse ^2 = leg1 ^2 + leg 2^2
(7y-1)^2 = (5y-3)^2 + (5y+1)^2
49 y^2 - 14y +1 = 25y^2 -30 y + 9 + 25y^2 + 10y + 1
-y^2 + 6y -9 = 0
or y^2 -6y + 9 = 0 solve by factoring or using Quadratic Formula
( y -3)(y-3) = 0 shows y = 3
The cost per student of a ski trip varies inversely as the number of students who attend. It will cost each student $250 if 24 students attend. How many students would have to attend to get the cost down to $200?
ANSWER
30 students
EXPLANATION
The cost per student varies inversely as the number of students.
Inverse proportion is written as:
[tex]\begin{gathered} y\propto\frac{1}{x} \\ y=\frac{k}{x} \\ \text{where k = constant of proportionality} \end{gathered}[/tex]Let the cost per student be y.
Let the number of students be x.
It will cost each student $250 if 24 students attend. This means that:
[tex]\begin{gathered} 250=\frac{k}{24} \\ \Rightarrow k=250\cdot24 \\ k=6000 \end{gathered}[/tex]If the cost is down to $200, it means that y is now $200.
That is:
[tex]\begin{gathered} 200=\frac{6000}{x} \\ \Rightarrow x=\frac{6000}{200} \\ x=30\text{ students} \end{gathered}[/tex]Therefore, 30 students could attend.
Our school district is sending two teachers to a 3-day training session on innovative teaching
strategies. Expenses per person: registration, $275; supplies, $40; breakfast, $8; lunch $15;
and dinner $20. Total transportation cost for the two people is $120. If our district has
budgeted $1,500 for the 2 to attend the training session, what is the most they can each pay
for their hotel per person per night?
Answer: Approximately $117.33
Step-by-step explanation:
1. Add all the Expenses per person to get $338
2. Multiply these expenses by 2 for each person to get $676
3. Add $120 for Transportation to get $796
4. Multiply the people going by the amount of days they are staying to get 6
5. Subtract the total expenses by the budget to get $704
7. Divide the answer of step 4 by the remaking budget to get the final answer of approximately $117.33
What is the total volume of all four gum balls?
What is x?
-2 + 3x = 5x - 8
Answer:
x = 3
Step-by-step explanation:
-2 + 3x = 5x - 8
add 8 to both sides:
-2 + 3x + 8 = 5x - 8 + 8
6 + 3x = 5x
subtract 3x from both sides:
6 + 3x - 3x = 5x - 3x
6 = 2x
divide both sides by 2:
6/2 = 2x/2
x = 3
check: when x = 3
-2 + 3(3) = 5(3) - 8
-2 + 9 = 15 - 8
7 = 7
Answer:
X = 3
Step-by-step explanation:
-2 + 3x = 5x - 8
+8 Because -8 is lower then -2 we start by doing the opposite and +8 to -2
6 + 3x = 5x
-3x Because now we have to do the opposite on the variable too.
6 = 2x
/2 Because you have to divide the integer by the variable
x = 3
If D = t +9t2 and C = t - t - 8, find an expression that equals D - 3C in standard form?
we have
[tex]\begin{gathered} D-3C=t+9t^2-3(t-t-8)=t+9t^2-3(-8) \\ =t+9t^2+24 \end{gathered}[/tex]in standard form
[tex]9t^2+t+24[/tex]3. Is there another method to determine this value besides a calculator? What are the pros and cons to using the nCr function on yourgraphing calculator in comparison to the other method(s) you mentioned?
Given:
The expression is:
[tex]_{12}C_5[/tex]Find-:
The value of the expression
Explanation-:
The formula of:
[tex]_nC_r[/tex]Combination formula:
[tex]_nC_r=\frac{n!}{(n-r)!r!}[/tex]The given expression is:
[tex]\begin{gathered} n=12 \\ \\ r=5 \end{gathered}[/tex]So, the value is:
[tex]\begin{gathered} _{12}C_5=\frac{12!}{(12-5)!5!} \\ \\ =\frac{12\times11\times10\times9\times8\times7!}{7!\times5!} \\ \\ =\frac{12\times11\times10\times9\times8}{5!} \\ \\ =\frac{12\times11\times10\times9\times8}{5\times4\times3\times2\times1} \\ \\ =792 \end{gathered}[/tex]The value is 792.
(Laws of Exponents with Integer Exponents LC) Create an equivalent expression for 9−7 • 95.
The expression 9⁻⁷ • 9⁵ when simplified is 9⁻²
How to evaluate the expression?The expression is given as
9−7 • 95.
Rewrite properly
9⁻⁷ • 9⁵
The base of the above expression are the same
i.e. Base = 9
This means that we can apply the law of indices
When the law of indices is applied, we have the following equation:
9⁻⁷ • 9⁵ = 9⁻⁷ ⁺ ⁵
Evaluate the sum in the above equation
So, we have
9⁻⁷ • 9⁵ = 9⁻²
Hence, the simplified expression of the expression given as 9⁻⁷ • 9⁵ is 9⁻²
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URGENT PLEASE HELL SOLVE FOR X . idc if you don’t show work
hello I need on this hw question please thank you
Given:
The given equation is,
[tex]3x-19+(?)x=-5x-19[/tex]Required:
To find the missing value.
Answer:
The given equation is,
[tex]\begin{gathered} 3x-19+(?)x=-5x-19 \\ \end{gathered}[/tex]By putting (-8) in place of (?) in the given equation, we get,
[tex]\begin{gathered} 3x-19+(-8)x=-5x-19 \\ \Rightarrow3x-19-8x=-5x-19 \\ \Rightarrow-5x-19=-5x-19 \\ \Rightarrow-19=-19 \end{gathered}[/tex]This shows that the given equation has infinitely many solutions.
Final Answer:
The missing value is -8.
What is the equation for a line transforming from y= x with a slope 5/6?
The equation of the transformed function is y' = 5/6x
How to determine the equation of the transformed function?From the question, we have the following equation that can be used in our computation:
y = x
Also, we have the slope of the linear function to be
Slope = 5/6
This can be rewritten as:
m = 5/6
When the function is transformed, we have the following representation:
y' = m * y
Substitute the known values in the above equation
y' = 5/6 * x
Evaluate
y' = 5/6x
Hence, the equation is y' = 5/6x
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convert each fraction to its equivalent using the least common denominator 3/7 , 3/4
The least common denominator of 3/7 and 3/4 is 7*4=28, therefore:
[tex]\begin{gathered} \frac{3}{7}=\frac{3\cdot4}{7\cdot4}=\frac{12}{28}, \\ \frac{3}{4}=\frac{3\cdot7}{4\cdot7}=\frac{21}{28}. \end{gathered}[/tex]Answer:
3/7, option e.
3/4, option c.
For a right triangle ABC, you are told that cos A=X and sun A=y. Which option gives an expression that is equivalent to tan A? X/ x2+y2. X/y. Y/X. Y/x2+y2
For a right triangle ABC, the expression that is equivalent to tan A is y/x.
What is defined as the trigonometric functions?Trigonometric functions, also recognized as circular functions, are simply functions of a triangle's angle. These trig functions define the relationship between both the angles as well as sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions. The sine, cosine, as well as tangent angles are the primary categorization of trigonometric functions. The primary functions can be used to derive the three functions cotangent, secant, and cosecant.For the given question,
In a right triangle ABC.
The cosine and sin functions are defined as;
cos A=X and sin A=y.
Then, we know that tan A function can be written in the form in the form of cos A and sin A as,
tan A = sin A/ cos A
Put the values,
tan A = y/x
Thus, the expression that is equivalent to tan A is y/x.
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Use the information to find and compare ∆y and dy (Round your answers to three decimal places.)
y=4x^3 x=2 ∆x=dx=0.1
The values of derivatives Δy and dy are given as 0.48 and 4.8
The values of Δy and dy will be calculated using the formula Δy = f(x + Δx) - f(x) and dy = f'(x)dx. For calculating the values, we put the values which are given in the question that is
Δy = f(x + Δx) - f(x)
Δy = f(2 + 0.1) - f(2)
Δy = f(2.01) - f(2)
Δy = 4(2.01)³ - 4(2)³
Δy = 32.48 - 32
Δy = 0.48
Now, we have f(x) = 4x³, so we have f'(x) = 12x²
Now, dy = f'(x)dx
dy = 12x²dx
dy = 12(2)²(0.1)
dy = 4.8
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What’s the equation passing threw the points? And is parallel to the line 3x+y=3
The parallel line 3x + y =3, can be write on y-intercept form:
Solve for y the equation:
3x + y = 3
y = 3 -3x
Now, two lines are parallel when they have the same slope. In this case for line y= 3 -3x, the slope is the number with the x.
Therefore, the slope is -3.
Use the slope intercept-form using slope=m=3 and the point (1,-7):
[tex]y-y_1=m(x-x_1)[/tex]Replace these values and solve for y:
[tex]y-(-7)=-3(x-1)[/tex][tex]y+7=-3x+3[/tex]Solving for x:
[tex]y=3x+3-7[/tex]The equation that passes through the point (1,-7) and is parallel to the line3x + y =3 is :
[tex]y=-3x-4[/tex]700 tickets were sold for a game for a total of $900.00 If adult tickets sold for $2.00 and children's tickets sold for $1.00 how many of each kind of ticket were sold?
Let x be the number of adult tickets and let y be the number of children.
We know that in total there were sold 700 tickets, that means:
[tex]x+y=700[/tex]Now we know that each adult ticket was $2 and the children's tickets was $1, and that the total was $900, this means that:
[tex]2x+y=900[/tex]Then we have the following system of equations:
[tex]\begin{gathered} x+y=700 \\ 2x+y=900 \end{gathered}[/tex]To solve it we substract the second equation from the first one, then we have:
[tex]\begin{gathered} x+y-2x-y=700-900 \\ -x=-200 \\ x=200 \end{gathered}[/tex]Now that we have the value of x we plug it in the first equation to find y:
[tex]\begin{gathered} 200+y=700 \\ y=700-200 \\ y=500 \end{gathered}[/tex]Therefore, there were 200 adult's tickets and 500 children's tickets sold.
What is 13^c^11?
O A. 91
OB. 105
C. 78
D. 120
78
1) Since we have a Combination, we can write out the following formula:
[tex]_{13}C_{11}=\frac{13!}{11!(13-11)!}=\frac{13\times12\times11!}{11!\text{ 2!}}=\frac{13\times12}{2}=78[/tex]Note that we canceled 11! on the numerator by the factorial of 11! on the denominator. And notice this is only possible when the order does not matter.
2) Hence, the answer is 78 because there are 78 combinations of 13 choosing 11.
f(x) = 2x2 + 6x - 4 9(2) = 573 – 6x2 – 3 Find (f +9)(2). O A. (f +g)(x) = -523 + 8x2 + 6x – 1 O B. (f +9)(x) = 5x3 + 2x2 – 7 O C. (f+g)(x) =1723 – 7 O D. (f + g)(x) = 5x3 - 4x2 + 6x - 7
Answer:
The function (f+g)(x) is:
[tex](f+g)(x)=5x^3-4x^2+6x-7[/tex]Explanation:
Given the functions;
[tex]\begin{gathered} f(x)=2x^2+6x-4 \\ g(x)=5x^3-6x^2-3 \end{gathered}[/tex]We want to find the function (f+g)(x);
[tex]\begin{gathered} (f+g)(x)=f(x)+g(x) \\ (f+g)(x)=(2x^2+6x-4)+(5x^3-6x^2-3) \\ (f+g)(x)=5x^3+2x^2-6x^2+6x-4-3 \\ (f+g)(x)=5x^3-4x^2+6x-7 \end{gathered}[/tex]Therefore, the function (f+g)(x) is:
[tex](f+g)(x)=5x^3-4x^2+6x-7[/tex]