6xs + ys
Explanations:The given expression is:
(6x + y)s
This can be simplified by simplying expanding the brackets
The equation then becomes:
6xs + ys
Answer:
6xs + ys
Step-by-step explanation:
What is the total population of the four cities shown in the table? Express your answer in scientific notation and in standard form.
Scientific notation is a way of writing large or small numbers that have many digits in a simplified form. The index of the base 10 exponents indicates the number of digits there are after the decimal dot.
The table shows the population of 4 cities of Texas, Houston, San Antonio, El Paso, and Corpus Christi.
To determine the total population of all cities you have to add them together, the first step is to express each given population in standard form:
Houston:
[tex]2.3\cdot10^6[/tex]This notation indicates that there are 6 digits after the decimal dot, the first one is 3 and the other five digits are zero. The positive index indicates that this number is greater than 1, so to write the number in the standard form you have to erase the decimal dot:
[tex]2.3\cdot10^6=2300000[/tex]San Antonio:
[tex]1.5\cdot10^6[/tex]The notation indicates that there are 6 digits after the decimal point, the first one is 5 and the other five digits are zero. The positive exponent indicates that this number is greater than 1, so you have to erase the decimal dot:
[tex]1.5\cdot10^6=1500000[/tex]El Paso:
This population is already given in the standard form
[tex]680000[/tex]Corpus Christi:
[tex]3.2\cdot10^5[/tex]This notation indicates that there are 5 digits after the decimal dot, the first one is 5 and the next four are zero. The exponent is positive, so as mentioned before, this number is greater than one, and to write it in the standard form you have to erase the decimal dot:
[tex]3.2\cdot10^5=320000[/tex]Now that all values are expressed in the standard form you can add them:
[tex]2300000+1500000+680000+320000=4800000[/tex]In the standard form, the total population of the four cities is 4,800,000 people
To express this value using scientific notation you have to write the decimal dot after the first digit and then count the number of digits after the decimal dot.
When you use scientific notation you have to write only the digits that are different than zero.
There are 6 digits after the decimal dot, so the exponent of the base 10 number will be 6, and the result expressed in scientific notation is:
[tex]4.8\cdot10^6\text{people}[/tex]If the cost of a car is $6,345.00, and the tax rate is 6%, how much is the total cost of the car?
Given:
Cost of Car is $6,345
Tax rate is 6%
[tex]\begin{gathered} \text{Tax Amount=6345}\times\frac{6}{100} \\ \text{Tax Amount= \$380.70} \end{gathered}[/tex][tex]\begin{gathered} \text{Total cost of the car =6345+380.70} \\ \text{Total cost of the car = \$6725.70} \end{gathered}[/tex]how can you obtain the points for the log below from its inverse?
Answer
Check Explanation
Explanation
The laws of logarithms will come in handy in helping to obtain the points for the log from its inverse.
Before we commence, the two laws of logarithms that we will be using is that
log₄ 4ᶜ = c (log₄ 4)
And
log₄ 4 = 1
So, no matter the value of inverse given, a simple mathematical evaluation will give the log points.
when x = 1
f(x) = log₄ x
f(1) = log₄ 1 = log₄ 4⁰ = 0 log₄ 4 = 0 × 1 = 0
when x = 4
f(x) = log₄ x
f(4) = log₄ 4 = log₄ 4¹ = 1 (log₄ 4) = 1 × 1 = 1
when x = 16
f(x) = log₄ x
f(16) = log₄ 16 = log₄ 4² = 2 (log₄ 4) = 2 × 1 = 2
when x = 64
f(x) = log₄ x
f(64) = log₄ 64 = log₄ 4³ = 3 (log₄ 4) = 3 × 1 = 3
Hope this Helps!!!
How is the input force different from the output force?
Responses
The input force is all of the energy applied to the situation, and the output force is the result.
The input force is all of the energy applied to the situation, and the output force is the result.
The input force is applied to the problem, and the output force is the movement that results.
The input force is applied to the problem, and the output force is the movement that results.
The output force is applied to the simple machine, and the input force is the force the simple machine applies to an object.
The output force is applied to the simple machine, and the input force is the force the simple machine applies to an object.
The input force is applied to the simple machine, and the output force is the force the simple machine applies to an object.
The input force is applied to the simple machine, and the output force is the force the simple machine applies to an object.
The input force different from the output force is D. The input force is applied to the simple machine, and the output force is the force the simple machine applies to an object."
What is a simple machine?A simple machine is a mechanical device that alters the magnitude or direction of a force. In general, they are the most basic systems that exploit mechanical advantage to multiply force.
A simple machine is a mechanical device that adjusts the direction or amplitude of a force. According to Newton's third law, if object A exerts a force on object B, object B will exert a force of same size and opposite direction on object A.
In that situation, the input force is done by object A, and the output force is done by object B as a reaction.
With this in mind, we can see that the proper answer is: "The input force is applied to the simple machine, and the output force is the force applied to an item."
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what is the slope of (12 -18) (-15 -18)
Answer:
m = 0
Step-by-step explanation:
[tex]m=\frac{-18-(-18)}{-15-12)} \\m=\frac{0}{-27} \\m= 0/-27 = 0\\m=0[/tex]
What is the solution to 4x-8=12 please explain
Given the equation 4x-8=12 you need to clear the value of x.
First step is to leave the value of x in one side of the equation and the integers in the other side, to do so you have to add 8 to both sides of the equation
[tex]\begin{gathered} 4x-8=12 \\ 4x-8+8=12+8 \\ 4x=20 \end{gathered}[/tex]Next you have to divide both terms of the equation by 4 to get the value of x
[tex]\begin{gathered} 4x=20 \\ \frac{4x}{4}=\frac{20}{4} \\ x=5 \end{gathered}[/tex]The value of x=5
Kuta Software - Infinite Precalculus Angles and Angle Measure Find the measure of each angle.
Explanation:
We are to draw the angle that is equivalent to 5pi/4
First we need to convert the radian value to degree
Since pi rad = 180degrees
5pi/4 = x
Cross multiply
pi * x = 5pi/4 * 180
x = 5/4 * 180
x = 5 * 45
x = 225 degrees
This can also be written as 225 = 180 + 45
225degrees = 180 + pi/4
Note that 180degrees is an angle on a straight line. Find the digaram attached
The remaining angle which is pi/4 is the reason for the angle extensionon for the angle extension
5pi/4 = x
Cross multiply
pi * x = 5pi/4 * 180
x =
In statistics, how do I find the p-value? I understand how to get the z-value. Please help! I am so confused. Thank you in advance!
SOLUTION:
Step 1:
In this question, we are meant to discuss the p-value.
1. The p-value is calculated using the sampling distribution of the test statistic under the null hypothesis, the sample data, and the type of test being done (lower-tailed test, upper-tailed test, or two-sided test).
2.
3. What is the p-value in statistics?
The p-value is a number, calculated from a statistical test, that describes how likely you are to have found a particular set of observations if the null hypothesis were true. P-values are used in hypothesis testing to help decide whether to reject the null hypothesis.
4. How do I know when the test is left-tailed, right-tailed, or two-tailed?
Left-tailed test: The critical region is in the extreme left region (tail) under the curve.
Right-tailed test: The critical region is in the extreme right region (tail) under the curve.
5. How do you know when to use a one - tailed or two - tailed test?
This is because a two-tailed test uses both the positive and negative tails of the distribution.
In other words, it tests for the possibility of positive or negative differences. A one-tailed test is appropriate if you only want to determine if there is a difference between groups in a specific direction.
6. The formulae that involves z-score:
7. The formulae that involves p -value and standard deviation:
Answer the statistical measures and create a box and whiskers plot for the following set of data.
Solution
The picture below is the solution to the problem
Brief explanantion
From the data given, It is obvious that:
Minimum = 2
Maximum =
The total number of the data is 3, so the number 7th term is the median
Thus,
Median = 8
To find Q1
[tex]\begin{gathered} Q_1=\frac{1}{4}(n+1)th\text{ term} \\ Q_1=\frac{1}{4}(13+1)=\frac{14}{4}=3.5 \end{gathered}[/tex]Q1 is between the third and fourth term
Therefore, Q1 is
[tex]Q_1=0.5(4)+0.5(6)=5[/tex]Similarly, to find Q3
[tex]\begin{gathered} Q_3=\frac{3}{4}(n+1)th\text{ term} \\ Q_3=\frac{3}{4}(13+1)=3\times\frac{14}{4}=3\times3.5=10.5 \end{gathered}[/tex]Q3 is between the tenth and the eleventh term
Therefore, Q3 is
[tex]Q_3=0.5(11)+0.5(11)=11[/tex]Find the exact length of the arc intercepted by a central angle on a circle of radius . Then round to the nearest tenth of a unit.
Given:
Angle subtended at the center = 135 degrees
radius (r) = 4 yd
Solution
The formula for the length (l) of an arc is given as:
[tex]\begin{gathered} l\text{ = }\frac{\phi}{360^0}\text{ }\times\text{ 2}\pi r \\ \text{where }\phi\text{ is the angle subtend}ed\text{ at the center} \end{gathered}[/tex]When we substitute the given parameters, we can find the length (l) of the arc:
[tex]\begin{gathered} l\text{ = }\frac{135}{360}\text{ }\times\text{ 2 }\times\text{ }\pi\text{ }\times\text{ 4} \\ =3\pi \\ \approx\text{ 9.4 yd (nearest tenth)} \end{gathered}[/tex]Answer: 9.4 yd or 3.0 pi
How do I know which score is the highest frequency? how do I figure the scores had a frequency of 2?
To determine the score which presents the highest frequency, we need to check the last column, the frequency one, and find the highest value among them. The score which is in the same row that this value will be the score with the highest frequency.
In the present problem, there are values of frequency equal to 1, 2, 3, and 4. The one with frequency 4 is the one with the highest frequency. (8th row). And the Score related to it is Score 8.Once we check the frequency column once again, we see that the 2nd, the 4th, and the 7th rows have a frequency equal to 2.
Checking the Scores of the related rows, we are able to say that the scores with frequency 2 are: 2, 4, and 7.Michael withdraws $40 from his checking account each day how long will it take him to withdraw $680
Solution
- The amount Michael withdraws every day is $40.
- The number of days it takes to withdraw $680 is given by:
[tex]\frac{\text{Total Amount Withdrawn}}{\text{Amount Withdrawn per day}}[/tex]- Using the formula above, we have:
[tex]\frac{\text{Total Amount Withdrawn}}{\text{Amount Withdrawn per day}}=\frac{680}{40}=17\text{ days}[/tex]Final Answer
The answer is 17 days
A triangle has two sides of length 13 and 17. What is the largest possible whole numberlength for the third side?
Given two sides of a triangle, x, and z, such that
[tex]x\le z[/tex]then the third side y must satisfy the following condition
[tex]z-xIn our case,x =13, and z = 17
Then, the third side y
lies in
17-13 < x < 17 +13
4 < x < 30
Hence the largest possible whole number of the third side is 29
How else can you write 6p in mathematic terms?
In mathematic terms, the expression 6p is written as 6 times p.
Mathematic terms
Mathematic terms means a single mathematical expression. The terms may be a single number, a single variable, several variables multiplied but never added or subtracted. Some of the terms contain variables with a number in front of them. Those number in front of a term is called a coefficient.
Given,
Here we have the expression 6p.
Now, we have to write it as a mathematic term.
While we looking into the expression 6p.
The only operation word in this expression is p which is multiplied with the constant that is the number 6.
So, in the verbal phrase it can be written as 6 times p.
Here p take any valid number in the real numbers.
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A coin is tossed nine times what is the probability of getting all tails express your answer as a simplified fraction or decimal rounded to four decimal places
The probability of getting a tail on each toss is:
[tex]\frac{1}{2}[/tex]Since there is only one way of getting all tails, it follows that the required probability is given by:
[tex](\frac{1}{2})^9\approx0.0020[/tex]Hence, the required probability is approximately 0.0020
a turtle swims 15 kilometers in 9 hours how long does it take the turtle to swim 18 kilometers?
Answer:
10.8 hours or 648 minutes
Step-by-step explanation:
1. Find a factor of 15 and 18 kilometers. A similar factor is 3.
2. Find how long it will take the turtle to swim 3 kilometers.
3. Divide 9 by 5 which is how long it takes to swim three hours. (Keep it in a fraction for now)
4.Multiply 9/5 by 6 to get 18 hours; which is 10.8 hours.
The percentage of students in the school that attended the talent show for the years 2008 to 2013 are shown.This Year, the school had a total of 360 students. How many students do you expect to attend the talent show this year? Explain.
Considering this year as the last year in the table which is 2013
[tex]\text{the total number of students in 2013=360}[/tex][tex]\text{The percentage of students attendance in 2013=95\%}[/tex]Therefore,
The number of students to attend this year's talent show will be calculated by
[tex]A\text{ttendance}=\text{percentage of students}\times total\text{ number of students}[/tex][tex]\begin{gathered} \text{Attendance}=95\text{ \%}\times360 \\ \text{Attendance}=\frac{95}{100}\times360 \\ \text{Attendance}=\frac{34200}{100} \\ \text{Attendance}=342\text{ students} \end{gathered}[/tex]Hence.
The attendance for this year is 342 students
If sin A = 3/5 and cos B = 20/29 and angles A and B are in Quadrant 1, find the valueof tan(A + B).
Our approach is to use SOHCAHTOA to derive values for sine and cosines of both A and B.
[tex]\begin{gathered} \sin A=\frac{3}{5},\text{ cosA=}\frac{\sqrt[]{5^2-3^2}}{5}=\frac{4}{5} \\ \cos B=\frac{20}{29},\text{ sinB=}\frac{\sqrt[]{29^2-20^2}}{29}=\frac{21}{29} \end{gathered}[/tex][tex]\begin{gathered} \tan (A+B)=\frac{\tan A+\tan B}{1-\text{tanAtanB}}\text{ WHERE} \\ \tan A=\frac{\sin A}{\cos A},\tan B=\frac{\sin B}{\cos B} \end{gathered}[/tex][tex]\begin{gathered} \tan (A+B)=\frac{\frac{\frac{3}{5}}{\frac{4}{5}}+\frac{\frac{21}{29}}{\frac{20}{29}}}{1-\frac{\frac{3}{5}}{\frac{4}{5}}\times\frac{\frac{21}{29}}{\frac{20}{29}}}=\frac{\frac{3}{4}+\frac{21}{20}}{1-\frac{3}{4}\times\frac{21}{20}}=\frac{\frac{9}{5}}{1-\frac{63}{80}}=\frac{\frac{9}{5}}{\frac{17}{80}} \\ \tan (A+B)=8.47 \end{gathered}[/tex]tan (A+B) = 8.47
5x^2+2x-3 and x+4 how do I find the area
You have a rectangle with the followinf expressions for its sides:
w: width = 5x² + 2x - 3
h: height = x + 4
In order to calculate the area of the rectangle, you use the following formula for the area:
A = w*h
By replacing w and h by the given algebraic expressions you have:
A = (5x² + 2x - 3)(x + 4) use distribution property
A = 5x²(x) + 5x²(4) + 2x(x) + 2x(4) - 3(x) - 3(4) simplify
A = 5x³ + 20x² + 2x² + 8x - 3x - 12 simplify similar terms
A = 5x³ + 22x² + 5x - 12
Hence, the total area of the figure is 5x³ + 22x² + 5x - 12
make a table of values then graph the following quadratic functions, label atleast 5 points
Given the function below:
[tex]f(x)=\frac{-4(x-3)^2}{9}+4[/tex]Substituting each value of x in the table in the function above, we get
[tex]\begin{gathered} f(0)=\frac{-4(0-3)^2}{9}+4\text{ = }\frac{-4(-3)^2}{9}+4 \\ \\ f(0)=\frac{-4\times9}{9}+4\text{ =-4+4 = 0} \end{gathered}[/tex][tex]f(1)=\frac{-4(1-3)^2}{9}+4\text{ =}\frac{-4\times4}{9}+4=\frac{-16}{9}+4=\frac{20}{9}[/tex][tex]f(6)=\frac{-4(6-3)^2}{9}+4\text{ = }\frac{-4(3^2)}{9}+4\text{ =-4+4 = 0}[/tex]Graph the linear equation.
x=-2/12/12
X=
Use the graphing tool to graph the linear equation.
Click to
enlarge
graph
3
10
8
6
2
d
4
6
8
40
The graph of (3, 2) is located 3 units to the right of the y-axis and 2 units above the x-axis, while the graphs of (-3, 2), (-3, -2) and (3, -2) are located 3 units to the left of the y-axis and 2 units below the x-axis, 3 units to the right of the y-axis, and 3 units to the bottom of the x-axis, respectively.
What is linear equations?The ordinate of the point is the distance from the x-axis that it is placed at, and the abscissa of the point is the distance from the y-axis that it is located at. An algebraic equation of the type known as a linear equation.
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a quadratic function has its vertex at the point (4,6) the function passes through the point (-5,-2) find the quadratic and linear coefficients and the constant term of the function The quadratic coefficient is_____The linear coefficient is_______the constant term is_____
We have to find the equation of the quadratic function.
We know the vertex, located in (4,6), and one point (-5,-2).
The x-coordinate of the vertex (4) is equal to -b/2a, being a the quadratic coefficient and b the linear coefficient.
Now, we have 2 points to define the 3 parameters, so one of the parameters is undefined.
[tex]y=ax^2+bx+c[/tex]We start with the vertex, that we know that is:
[tex]\begin{gathered} x=-\frac{b}{2a}=4 \\ -b=4\cdot2a=8a \\ b=-8a \end{gathered}[/tex]Then, we can write the equation as:
[tex]y=ax^2-8ax+c=a(x^2-8x)+c[/tex]If we replace the point (-5,-2) in the equation, we get:
[tex]\begin{gathered} -2=a((-5)^2-8\cdot(-5))+c \\ -2=a(25+40)+c \\ -2=65a+c \\ c=-2-65a \end{gathered}[/tex]We replace the vertex coordinates and get:
[tex]\begin{gathered} 6=a(4^2-8\cdot4)+c \\ 6=a(16-32)+(-2-65a) \\ 6=-16a-2-65a \\ 6=-81a-2 \\ 81a=-2-6 \\ a=-\frac{8}{81}\approx-0.01 \end{gathered}[/tex]Then, the linear coefficient b is:
[tex]b=-8a=-8\cdot(-\frac{8}{81})=\frac{64}{81}\approx0.79[/tex]And the constant term is:
[tex]c=-2-65a=-2-65\cdot(-\frac{8}{81})=-2+\frac{520}{81}=\frac{-162+520}{81}=\frac{358}{81}\approx4.42[/tex]The quadratic coefficient is a=-0.01
The linear coefficient is b=0.79
the constant term is c=4.42
Which of the following is a proportion?8/10=6/83/4=12/154/6=9/126/9=8/12
To be able to determine which among the choices is a proportion, you check if each side has the same common ratio.
A. 8/10 = 6/8
Ratio: 0.80 = 0.75 (Not Proportional)
B. 3/4 = 12/15
Ratio: 0.75 = 0.80 (Not Proportional)
C. 4/6 = 9/12
Ratio: 0.67 = 0.75 (Not Proportional)
D. 6/9 = 8/12
Ratio: 0.67 = 0.67 (Proportional)
Since the ratio of each side of letter D is equal, Letter D is the one that is in Proportion.
For each ordered pair, determine whether it is a solution to 7x - 4y = -5.(x,y)(-2,6) it is a solution yes or no(1,3) it is a solution yes or no(-3,4) it is a solution yes or no(4,2) it is a solution yes or no
If x=1, then:
[tex]\begin{gathered} 7(1)-4y=-5 \\ \Rightarrow-4y=-5-7=-12 \\ \Rightarrow y=\frac{-12}{-4}=3 \\ \\ y=3 \end{gathered}[/tex]therefore, a solution to the equation 7x-4y=-5 is (1,3)
Write a mathematical sentence that expresses the information given below. Use b as your variable name. If necessary:
type < = to mean
or > = to mean .
If you need to show multiplication, do not use the letter x. Use the asterisk ( * ) symbol instead, or simplify your answer.
Emily has 300 books. If Frank were to double the number of books that he now owns, he would still have fewer than Emily has.
The number of books owned by frank is represented as b < 150
What is inequality?Inequality represents the form of writing expressions where the left hand side of the expression is not exactly equal to the right hand side of the expression
How to represent the required expressionInformation gotten from the data include
Emily has 300 books
Frank were to double the number of books that he now owns, he would still have fewer than Emily has.
Let the number of books owned by frank be b and from the information we have that:
2b < 300
b < 150
hence the number of books owned by frank, b less than 150
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A small company produces baseball and racquetball by the function B(x)=-6x^2+2,556x-106,878. The profit made from the racquetball products can be represented by the function R(x)=-x^2+293x-16,770. If x is the total number of products made, which function best describes P(x), the profit the company makes from these two products?
profit made from the baseball products
[tex]B(x)=-6x^2+2556x-106878[/tex]Profit made from the racquetball products
[tex]R(x)=-x^2+293x-16770[/tex]Profit made from those 2 products is
[tex]\begin{gathered} P(x)=-6x^2-x^2+2556x+293x-106878-16770 \\ P(x)=-7x^2+2849x-123648 \end{gathered}[/tex]The Consumer Price Index (CPI), which measures the cost of a typical package of consumer goods, was 202.9 in 2011 and 233.2 in 2016. Let x=11 correspond to the year 2011 and estimate the CPI in 2013 and 2014. Assume that the data can be modeled by a straight line and that the trend continues indefinitely. Use two data points to find such a line and then estimate the requested quantities. Let y represent the CPI. The linear equation that best models the CPI is____ (Simplify your answer. Use integers or decimals for any numbers in the equation. Round to the nearest hundredth as needed.)
The first thing we have to identify in our problem are the variables
[tex]\begin{gathered} x\to\text{time} \\ y\to\text{CPI} \end{gathered}[/tex]Now we see the points (x,y) that gives us the problem
[tex]\begin{gathered} 2011\to(11,202.9) \\ 2016\to(16,233.2) \end{gathered}[/tex]Since behavior can be modeled by a straight line, we use the general equation of the straight line
[tex]y=mx+b[/tex]Where m is the slope of the line and b is the y-intercept.
Taking this into account and with the 2 points that they give us, we proceed to calculate the equation of the line starting with the slope:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{233.2-202.9}{16-11} \\ m=\frac{30.3}{5} \\ m=6.06 \end{gathered}[/tex][tex]\begin{gathered} y=6.06x+b \\ 202.9=6.06(11)+b \\ b=202.9-66.66 \\ b=136.24 \end{gathered}[/tex]The equation that models the behavior of the CPI is
[tex]y=6.06x+136.24[/tex]Now we calculate the CPI values for the years 2013 and 2014
[tex]\begin{gathered} 2013\to x=13 \\ y=6.06(13)+136.24 \\ y=78.78+136.24 \\ y=215.02 \end{gathered}[/tex][tex]\begin{gathered} 2014\to x=14 \\ y=6.06(14)+136.24 \\ y=84.84+136.24 \\ y=221.08 \end{gathered}[/tex]There is a 40% chance that it will be cloudy tomorrow.
If it is cloudy, there is a 79% chance that it will rain.
What is the probability that it will rain?
Answer:
3.16%
Step-by-step explanation:
a*(79/100)*40/100
3.16a/100
3.16%
Answer:
O. 316
Step-by-step explanation:
40/100 × 79/100 =0.316
cell phone company A charges a fee of $50 per month plus an additional $0.10 for every minute talked. cell phone company B computes its monthly charge by using the equation y=$0.05 + $75 where y is the total cost and X is the number of minutes talked.
We will first write A equation
Let x be the number of minutes
y = 0.10x + 50
Comparing the above with y=mx + b where m is the rate of change
m = 0.10
Company B
y = 0.05x + 75
comparing with y =mx + b
rate of change (m) = 0.05
Hence, company A has a higher rate of change at $0.10
the math club has 18 members and 50% are sixth graders.The science club has 25 members and 40% are sixth graders. The principal wants to know which club has more sixth graders.
The science club had more sixth graders.
How to calculate the value?The math club has 18 members and 50% are sixth graders. The number of sixth graders will be:
= Percentage × Number of members
= 50% × 18
= 0.5 × 18
= 9
The science club has 25 members and 40% are sixth graders. The number of sixth graders will be:
= Percentage × Number of members
= 40% × 25
= 0.4 × 25
= 10
Since 10 is more than 5, the science class has higher number.
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