To find the solution we can use the rule of three:
[tex]\begin{gathered} 60\rightarrow100 \\ 69\rightarrow x \end{gathered}[/tex]then:
[tex]\begin{gathered} x=\frac{69\cdot100}{60} \\ x=115 \end{gathered}[/tex]This means that 69 is 115% of 60.
Therefore 69 is 15% more than 60.
Is (4,-3) a solution to the following system of equations?X - y = 42x + y = 5
No, (4, -3) is not a solution to the system of equations
Explanation:If (4, -3) is a solution to the given system of equations, then
for x = 4, and y = -3, both of the equations are satisfied.
x - y = 4 - (-3)
= 4 + 3
= 7
This is not 4, so the first equation is not satisfied
2x + y = 2(4) + (-3)
= 8 - 3
= 5
This equation is satisfied
It is sufficient to conclude that (4, -3) is not a solution to the system of equations since it doesn't satisfy the first equation
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.Find the side of a square whose diagonal is of the given measure.Given = ft.
see the figure below to better understand the problem
In the given square ABCD
Apply the Pythagorean Theoren in the right triangle BDC
[tex]\begin{gathered} D^2=a^2+a^2 \\ D^2=2a^2 \\ we\text{ have} \\ D=12\sqrt{10}\text{ ft} \end{gathered}[/tex]Substitute given value
[tex]\begin{gathered} (12\sqrt{10})^2=2a^2 \\ 144(10)=2a^2 \\ 2a^2=1,440 \\ a^2=720 \\ a=\sqrt{720}\text{ ft} \end{gathered}[/tex]Simplify
[tex]a=12\sqrt{5}\text{ ft}[/tex]Zach puts $1000 into a savings account earning 5% compound interest for 5 years. How much
interest has Zach earned at the end of the the 5 years?
$_______
Do not enter the dollar sign as part of your answer
The amount of interest Zach earn in 5 years given the principal and interest rate compounded for 5 years is 276.3
What is the amount of interest Zach earned?A = P(1 + r/n)^nt
Where,
A = principal + interestPrincipal, P = $1000Interest rate, r = 5% = 0.05Time, t = 5 yearsNumber of periods, n = 1A = P(1 + r/n)^nt
= 1000(1 + 0.05/1) ^(1×5)
= 1000(1 + 0.05) ^5
= 1000(1.05)^5
= 1000(1.2762815625)
= 1,276.2815625
Approximately,
1,276.3
Hence,
A = principal + interest
1, 276.3 = 1000 + interest
1276.3 - 1000 = interest
Interest = 276.3
Therefore, the amount of interest earned in 5 years is 276.3
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i need help simplifying 1/3(3n+9)
Answer:
n+3
Explanation:
Given the expression:
[tex]\frac{1}{3}(3n+9)[/tex]To simplify, we first open the bracket.
[tex]=\frac{1}{3}(3n)+\frac{1}{3}(9)[/tex]We can then divide common factors:
[tex]\begin{gathered} =\frac{3n}{3}+\frac{9}{3} \\ =n+3 \end{gathered}[/tex]The simplified form is: n+3
What does the constant 1.6 reveal about the rate of change of the quantity?
The form of the exponential growth/decay function is
[tex]f(x)=a(1\pm r)^x[/tex]a is the initial amount
r is the rate of growth/decay per x years
We use + with growth and - with decay
Since the given function is
[tex]f(t)=2700(1.6)^{7t}[/tex]Where t is time per week
Compare the two functions
[tex]\begin{gathered} a=2700 \\ (1+r)=1.6 \\ x=7t \end{gathered}[/tex]Since 1.6 is greater than 1, then
The function is growth
Equate 1.6 by (1 + r) to find r
[tex]\begin{gathered} 1+r=1.6 \\ \\ 1-1+r=1.6-1 \\ \\ r=0.6 \end{gathered}[/tex]Change it to percent by multiplying it by 100%
[tex]\begin{gathered} r=0.6\times100\text{ \%} \\ \\ r=60\text{ \%} \end{gathered}[/tex]Since x = 7t then the time is every 7 weeks
The answer is
The function is growing exponentially at a rate of 60% every 7 weeks
Part B: select the box or boxes under the coordinate pairs the represent solutions for the system.
The given system of inequalities is
[tex]\begin{gathered} y>\frac{3}{2}x-2 \\ y\leq-3x-4 \end{gathered}[/tex]The area of the solution is the area shaded by the 2 colors
Let us check the points
(-2, -5) it lies on the red dashed line
Since the line is dashed, then the points lie on it do not belong to the solution, then
(-2, -5) does not belong to the solution
(-2, -5) is not a solution
(-2, 2) it lies on the blue line
Since the line is solid, then the points that lie on it belong to the solution, then
(-2, 2) is a solution
(0, -4) it is out of the area of both colors, then
(0, -4) is not a solution
(-3, -1) it lies in the area of the common colors, then
(-3, -1) is a solution
(-1, 4) it is out the area of both colors, then
(-1, 4) is not a solution
(-20, 15) is in the area of the common colors, then
(-20, 15) is a solution
(15, 20) it is out the area of both colors, then
(15, 20) is not a solution
Then the solutions of the system are:
(-2, 2), (-3, -1), (-20, 15)
Kevin and Randy have a jar containing 67 coins all of which are either quarters or nickels. The total value of the coins in the jar $12.75 ... how many of each type of coin do they have?
Answer:
47quarters and 20 nickel
Explanation:
Let the number of quarters be x
Let the number of nickels be y
If there are 67 coins in the jar, then;
x + y = 67 ....1
1 quarter = 0.25x
1 nickel = 0.05y
If the total value of the coins in the jar is $12.75, then;
0.25x + 0.05y = 12.75 ....2
Multiply through by 100
25x + 5y = 1275 ....2
Solve 1 and 2 simultaneously
x + y = 67 ....1 * 25
25x + 5y = 1275 ....2 * 1
Using Elimination method
________________________
25x + 25y = 1,675
25x + 5y = 1275
Subtract
25y - 5y = 1675 - 1275
20y = 400
y = 400/20
y = 20
Substitute y = 20 into equation 1;
From 1; x + y = 67
x + 20 = 67
x = 67 - 20
x = 47
This means there are 47quarters and 20 nickel.
4) P(A) = 0.55 P(B) = 0.25 P(A and B) = ? *a.0.2b.0.21c.0.3d.0.1375
Since P (A and B) = P(A) · P(B)
Since P(A) = 0.55 and P(B) = 0.25, then
P(A and B) = 0.55 x 0.25
P(A and B) = 0.1375
The answer is d
[the ending was select all that apply ] can somebody help me with this with an explanation on how to do it?
Answer: the goal is to isolate the variable so the answer is 12
Step-by-step explanation:
I need to solve each system by graphing. so pls help! This is Algebra 1
Given the system of inequalities:
2x + 3y < -6
-2x + 3y < 6
Let's solve the system by graphing.
To graph, rewrite the inequalities in slope-intercept form:
y = mx + b
Inequality 1:'
Subtract 2x from both sides:
2x - 2x + 3y < -2x - 6
3y < -2x - 6
Divide all terms by 3:
[tex]\begin{gathered} \frac{3y}{3}<-\frac{2x}{3}-\frac{6}{3} \\ \\ y<-\frac{2}{3}x-2 \end{gathered}[/tex]Inequality 2:
Add 2x to both sides:
-2x + 2x + 3y < 2x + 6
3y < 2x + 6
Divde all terms by 3:
[tex]\begin{gathered} \frac{3y}{3}<\frac{2x}{3}+\frac{6}{2} \\ \\ y<\frac{2}{3}x+2 \end{gathered}[/tex]Now, let's plot 3 points from each inequlality and connect using a straight edge.
Inequality 1:
When x = -3
Substitute -3 for x and solve for y:
[tex]\begin{gathered} y<-\frac{2}{3}(-3)-2 \\ \\ y<2-2 \\ \\ y<0 \end{gathered}[/tex]When x = 0:
[tex]\begin{gathered} y<-\frac{2}{3}(0)-2 \\ \\ y<-2 \end{gathered}[/tex]When x = 3:
[tex]\begin{gathered} y<-\frac{2}{3}(3)-2 \\ \\ y<-2-2 \\ \\ y<-4 \end{gathered}[/tex]From inequality 1, we have the points:
(x, y) ==> (-3, 0), (0, -2), (3, -4)
For inequlity 2:
When x = -3:
[tex]\begin{gathered} y<\frac{2}{3}(-3)+2 \\ \\ y<-2+2 \\ \\ y<0 \end{gathered}[/tex]When x = 0:
[tex]undefined[/tex]The sum of two consecutive integers is 17. Which equations could be used to find the twoconsecutive integers? Select all that are correct.A.X+X+1=17B.X+x=17C.2x=17D.2x+2=17E.X+X+2=17F.2x+1=17
hello
the answer to the question is option A
to solve a problem like this, let x represent the first number
x + (x + 1) = 17
x = first number
x + 1 = successive number
Each table represents a proportional relationship. For each, find theconstant of proportionality, k, and write an equation that represents therelationship. Write k as a simplified proper or improper fraction and use thegiven variables.
**For the first table:
*We determine the value of k, as follows:
[tex]30=k(18)\Rightarrow k=\frac{5}{3}[/tex]The equation that represents the table is:
[tex]f=\frac{5}{3}d[/tex]**For the second table:
*We determine the value of k, as follows:
[tex]18=k(30)\Rightarrow k=\frac{3}{5}[/tex]The equation that represents the table is:
[tex]d=\frac{3}{5}f[/tex]Find the coordinates of the midpoint between (8, 1) and (0, - 9). F. (4, -5) G. (4, -4) H. (8, -5) J. (8, -8)
(4, -4)
ExplanationIn order to find the midpoint between two points we have to obtain the midpoint horizontally and vertically.
In this case, we have:
Choose the expression that is equal to 28.3A. 3³+27.2-6.8+2⁴-3.1B. 3³+27.2-(6.8+2⁴-3.1)C. [3³+(27.2-6.8)]+2⁴-3.1D. 3³+27.2-(6.8+2⁴)-3.1
solution
For this case we can solve each case and we have:
A) 27 +27.2 -6.8 +16 -3.1= 60.3
B) 27 +27.2 -(6.8 +16 -3.1)= 54.2- 19.7= 34.5
C) 27 + 20.4 +16 -3.1= 30.1
D) 27 +27.2 - 22-8 -3.1= 28.3
then the correct solution for this case would be:
D)
Jessica borrowed $1,450 for three months at an annual rate of 8.75%under a single-payment plan. How much interest must she pay?a. $0.30b. $31.72c. $4,893.75d. $108.75
Given:
Principal amount (P)= $1450
Rate (R) = 8.75%
Time (T)= 3 months
The interest is given by the formula,
[tex]\begin{gathered} I=\frac{P\times R\times T}{100\times12} \\ =\frac{1450\times8.75\times3}{100\times12} \\ =31.71875 \end{gathered}[/tex]=O GRAPHINGFinding the next terms of an arithmetic sequence with integersThe first three terms of an arithmetic sequence are as follows.-5, -8, -11Find the next two terms of this sequence.5.-8.-11.008 OBx 6
Solution:
Given the first three terms of an arithmetic sequence as;
[tex]-5,-8,-11[/tex]An arithmetic sequence is a sequence with a common difference d, The common difference is the difference between two consecutive terms. Where;
[tex]\begin{gathered} d=a_2-a_1 \\ \text{Where;} \\ a_2=\text{ second term;} \\ a_1=\text{first term} \end{gathered}[/tex]Thus;
[tex]\begin{gathered} d=-8-(-5) \\ d=-8+5 \\ d=-3 \end{gathered}[/tex]Also, the next term of the sequence can be known by adding the common difference to the previous term.
Hence, the next two terms are;
[tex]\begin{gathered} =-11+(-3) \\ =-11-3 \\ =-14 \\ \text{and } \\ =-14+(-3) \\ =-14-3 \\ =-17 \end{gathered}[/tex]FINAL ANSWER:
[tex]-14,-17[/tex]3, -9, 27, -81,..... common difference/ratiod = 3r = 9r = -3 d = 12
To find the common ratio we divide the terms by the previous one. In this case we have:
[tex]-\frac{9}{3}=-3[/tex][tex]\frac{27}{-9}=-3[/tex][tex]-\frac{81}{27}=-3[/tex]Therefore, the common ratio is r=-3.
Are the graphs of the equations parallel, perpendicular, or neither? y= 2x +6 and y= 1/2x +3
Given the equations:
[tex]\begin{gathered} y=2x+6 \\ y=\frac{1}{2}x+3 \end{gathered}[/tex]The equation has the form of slope - intercept form which is like:
[tex]y=m\cdot x+b[/tex]Where m is the slope and b is y- intercept
So,
The slope of the first equation = 2
The slope of the second equation = 1/2
The graphs of the equations are parallel when the slopes are equal
The graphs of the equations are perpendicular when the product of the slopes = -1
so,
the slopes are not equal
The product of the slopes = 2 * 1/2 = 1
So, the graphs of the equations are neither parallel nor perpendicular.
Harold cut 18 1/2 inches off a rope that was 60 inches long. How is the length of the remaining rope written in decimals?
Substract 18 1/2 from 60 to determine the length of remaining rope.
[tex]\begin{gathered} 60-18\frac{1}{2}=60-\frac{37}{2} \\ =\frac{120-37}{2} \\ =\frac{83}{2} \\ =41.5 \end{gathered}[/tex]So length of remaining rope is 41.5 inches.
find the mean the median the mode range and standard invitation of each data set that is obtained after adding the given content to each value (number 1)
Answers:
Mean = 43.7
Median = 44.5
Mode = doesn't exist
Standard deviation = 4.78
Explanation:
First, we need to add the constant to each value, so the new data is:
33 + 11 = 44
38 + 11 = 49
29 + 11 = 40
35 + 11 = 46
27 + 11 = 38
34 + 11 = 45
36 + 11 = 47
28 + 11 = 39
41 + 11 = 52
26 + 11 = 37
Now, we can organize the data from least to greatest as:
37 38 39 40 44 45 46 47 49 52
Then, the mean is the sum of all the numbers divided by 10, because there are 10 values in the data. So, the mean is:
[tex]\begin{gathered} \operatorname{mean}=\frac{37+38+39+40+44+45+46+47+49+52}{10} \\ \operatorname{mean}=43.7 \end{gathered}[/tex]The median is the value that is located in the middle position of the organized data. Since there are 10 values, the values in the middle are the numbers 44 and 45, so the median can be calculated as:
[tex]\operatorname{median}=\frac{44+45}{2}=44.5[/tex]The mode is the value that appears more times in the data. Since all the values appear just one time, the mode doesn't exist.
To calculate the standard deviation, we will calculate first the variance.
The variance is the sum of the squared difference between each value and the mean, and then we divided by the number of values. So, the variance is equal to:
[tex]\begin{gathered} (37-43.7)^2+(38-43.7)^2+(39-43.7)^2+(40-43.7)^2+ \\ (44-43.7)^2+(45-43.7)^2+(46-43.7)^2+(47-43.7)^2+ \\ (49-43.7)^2+(52-43.7)^2=228.1 \end{gathered}[/tex][tex]\text{Variance}=\frac{228.1}{10}=22.81[/tex]Finally, the standard deviation is the square root of the variance, so the standard deviation is:
[tex]\text{standard deviation =}\sqrt[]{22.81}=4.78[/tex]Which inequality is represented by the graph
The inequality 4x - 2y < 12 is represented by the attached graph. which is the answer would be an option (B).
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
As per option (B),
4x - 2y < 12
We can see that the x-intercept is (0, -6), and the y-intercept is (2.5, 0) in the given graph which is determined by substituting the value of x and y is equal to 0 in the equation 4x - 2y = 12.
The inequality 4x - 2y < 12 is represented by the attached graph.
Hence, the answer would be option (B).
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it's late but I need help
Data:
X = weight of the puppy at thefirst visit
Runner A averages 5 miles per hour, and Runner B averages 6 miles per hour. At these rates, how much longer does it take Runner A than Runner B to run 15
miles?
1 hour
Shour
2.5 hours
1.5 hours
3 hours
If Runner A averages 5 miles per hour, and Runner B averages 6 miles per hour. At these rates, then it took 3 hours for runner A.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Runner A averages 5 miles per hour, and
Runner B averages 6 miles per hour.
The time required for A to complete 15 miles is
15/5=Time
3 hrs
Hence Runner A needs 3 hours to run 15 miles.
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From a window 100ft above the ground in building A, the top and bottom of building B are sighted so that the angles are 70 degrees and 30 degrees respectively. Find the height of building B?
Given:-
From a window 100ft above the ground in building A, the top and bottom of building B are sighted so that the angles are 70 degrees and 30 degrees respectively.
To find:-
The height of building B.
So now, the image of the given data is,
So now we find the value of PS. so we get,
[tex]\begin{gathered} \tan \text{ 30=}\frac{100}{PS} \\ \frac{1}{\sqrt[]{3}}=\frac{100}{PS} \\ PS=100\sqrt[]{3} \end{gathered}[/tex]So now we find the height of QS,
[tex]\begin{gathered} \tan \text{ 70=}\frac{QS}{PS} \\ 2.7474=\frac{QS}{100\sqrt[]{3}} \\ QS=100\sqrt[]{3}\times2.7474 \\ QS=475.84 \end{gathered}[/tex]So the total height is,
[tex]100+475.84=575.84[/tex]So the height of building B is 575.84
Yoko, Austin, and Bob have a total of $57 in their wallets. Austin has $7 less than Yoko. Bob has 2 times what Yoko has. How much does each have?
Yoko has $16 money, Austin has $9 and Bob has $32.
According to the question,
We have the following information:
Yoko, Austin, and Bob have a total of $57 in their wallets. Austin has $7 less than Yoko. Bob has 2 times what Yoko has.
Now, let's take the money Yoko has to be $x.
So, we have the following expressions for the money Austin and Bob have:
Austin = $(x-7)
Bob = $(2x)
Now, we have the following expression by adding them:
x+x-7+2x = 57
4x-7 = 57
4x = 57+7
4x = 64
x = 64/4
x = $16
Now, the money Austin has:
16-7
$9
Money Bob has:
2*16
$32
Hence, Yoko has $16 money, Austin has $9 and Bob has $32.
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Simplify: (3x-8)+(4x-17)
Answer:
7x-25
Explanation:
Given the expression:
[tex]\mleft(3x-8\mright)+\mleft(4x-17\mright)[/tex]First, we open the brackets
[tex]=3x-8+4x-17[/tex]Next, we rearrange bringing like terms together.
[tex]\begin{gathered} =3x+4x-8-17 \\ =7x-25 \end{gathered}[/tex]help me with this question please
So,
From the graph, we can clearly state that:
In 2 mins, there were 0 calls.
In 3 mins, there was 1 call.
In 4 mins, there were 4 calls.
In 5 mins, there were 6 calls.
In 6 mins, there were 4 calls.
Then, the number of calls that were answered to in 6 mins or less were 0+1+4+6+4 = 15
neeed double chedking on this
The area will be the area of the blue part minus the area of the white part:
9(8)-5(3)=72-15= 57 square centimeters
which point is located at (0,8)
The point (0, 8) simply means the x axis is 0 while the y axis is 8. The answer is C.
which choice is equivalent to the quotient below? sqrt 7/8* sqrt7/187/16/121/23/47/12
We can apply the following properties of radicals:
[tex]\begin{gathered} \sqrt[n]{ab}=\sqrt[n]{a}\cdot\sqrt[n]{b}\Rightarrow\text{ Product property} \\ \sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}\Rightarrow\text{ Quotient property} \end{gathered}[/tex]Then, we have:
[tex]\begin{gathered} \text{ Apply the product property} \\ \sqrt[]{\frac{7}{8}}\cdot\sqrt[]{\frac{7}{18}}=\sqrt[]{\frac{7}{8}\cdot\frac{7}{18}} \\ \sqrt[]{\frac{7}{8}}\cdot\sqrt[]{\frac{7}{18}}=\sqrt[]{\frac{7\cdot7}{8\cdot18}} \\ \sqrt[]{\frac{7}{8}}\cdot\sqrt[]{\frac{7}{18}}=\sqrt[]{\frac{49}{144}} \\ \text{ Apply the quotient property} \\ \sqrt[]{\frac{7}{8}}\cdot\sqrt[]{\frac{7}{18}}=\frac{\sqrt[]{49}}{\sqrt[]{144}} \\ \sqrt[]{\frac{7}{8}}\cdot\sqrt[]{\frac{7}{18}}=\frac{7}{12} \end{gathered}[/tex]Therefore, the choice that is equivalent to the given product is:
[tex]\frac{7}{12}[/tex]