we have that
cubic root of 77,975=42.722
but remember that
rounded to three significant digits
so
42.7
a grocery store is offering a promotion where a customer receives $0.20 discount per selected sale items, and Paulo has a coupon where he receives $0.10 off regularly priced items. Before applying the discounts the cost of Paulo's sale items was $58..18 and the cost of Paulo's regularly priced items was $ 41.34. After applying the discounts, Paulo spent $92.32 on both the sale items and regularly priced items. if Paulo bought 6 more sale items than regularly priced items, how many items did he buy in all?
SOLUTION
Define a parameter
[tex]\begin{gathered} Sales\text{ item=X} \\ \operatorname{Re}gular\text{ items =y} \end{gathered}[/tex]Since Paulo have 6 more items, we have
[tex]\begin{gathered} y+6 \\ \text{and } \\ x-6 \end{gathered}[/tex]Then the equation becomes
[tex]undefined[/tex]
Which of the following logarithmic equations is equivalent to the exponentialequation below?8* -512A. log, 512 -B. 1096128 - XC. log, * - 512O D.log, 512 - 8
Answer:
To find the eqivalent exponential equation to the following equation
[tex]8^x=512[/tex]we have that,
A mathematical notation of expressing a quantity as a number raised to the power of another number is called the exponential form and it is also called as exponential notation. According to the exponentiation, a quantity is split as factors on the basis of a number.
From the definition of exponential function, we have
[tex]a^x=y\text{ if and only if }\log _ay=x[/tex]For the given equation we get,
[tex]\log _{10}512=x[/tex]Answer is: option A:
[tex]\log _{10}512=x[/tex]What is the y-value of the absolute maximum of the function in the graph shown
The absolute maximum of the function in the given graph is found at the highest peak.
Therefore, the absolute maximum is found at (0, 7).
The x-value of the absolute maximum is 0 while the y-value of the absolute maximum is 7.
write a function rule for the table. answer please. i give good ratings only
Step 1:
From the table, the input or independent variable is x and the dependent variable is y.
Step 2:
From the table, to get the output, you multiply the input by 2.
When input is x = -3, the output y = -6, therefore. y = 2x = 2x(-3) = -6
When input is x = -2, the output y = -4, therefore. y = 2x = 2x(-2) = -4
When input is x = -1, the output y = -2, therefore. y = 2x = 2x(-1) = -2
When input is x = 0, the output y = 0, therefore. y = 2x = 2x(0) = 0
Ste 3: Final answer
The rule of the function is: y = 2x
f(x) = 2x Option D is the correct answer
Which of the following is thegraph of(x + 3)2 + (y + 1)2 = 9 ?AB22-2022-24
The equation above is an equation of a circle
The equation can be written as follow.
[tex]\begin{gathered} (x+3)^2+(y+1)^2=3^2 \\ \text{Next compare with } \\ (x-a)^2+(y-b)^2=r^2 \\ r\text{ is the radius and ( a, b ) is the center.} \end{gathered}[/tex]Therefore,
Radius r = 3 and center = (-3, -1)
Six angles of a convex octagon is congruent. Each of the two remaining angles is 20 degrees more than one of the other six angles. Find the measure of EACH angle.
Determine the sum of angles of octagon.
[tex]\begin{gathered} S=(n-2)\times180 \\ =(8-2)\times180 \\ =6\cdot180 \\ =1080 \end{gathered}[/tex]Let measure of each angle of six congurent angle be x.
Then measure of each of other two remaining angle is (x + 20).
Determine the value of x by using the sum of angles of octagon.
[tex]\begin{gathered} x+x+x+x+x+x+x+20+x+20=1080 \\ 8x=1080-40 \\ x=\frac{1040}{8} \\ =130 \end{gathered}[/tex]So measure of each angle of six congurent angle is 130 degree.
Determine the measure of two remaining angles.
[tex]\begin{gathered} x+20=130+20 \\ =150 \end{gathered}[/tex]Thus measure of angles of octagone are,
Six angle measure 130 degree each and two angle measure 150 degree each.
[tex]130,130,130,130,130,130,150,150[/tex]On a recent day, 8 euros were worth $9 and 40 euros were worth $45. Enter an equation of the formy = kx to show the relationship between the number of euros and the value in dollars. Let y be the valuein dollars and x be the number of euros.The equation is y =
The equation between number of euro and number of dollars will be in the form y = kx.
y is the value in dollars and x is the value in euros.
From the information given,
8 euro = 9 dollar
dividing by '8' we can say:
8/8 euro = 9/8 dollars
1 euro = 9/8 dollar
This is the value for k.
Thus, we have:
[tex]y=\frac{9}{8}x[/tex]We were given 8 euro = 9 dollar and 40 euro = 45 dollars. Let's see if they are correct using our equation:
[tex]\begin{gathered} y=\frac{9}{8}\times8 \\ y=9 \\ \text{Correct!} \\ y=\frac{9}{8}\times40 \\ y=45 \\ \text{Correct!} \end{gathered}[/tex]Thus the correct relationship is:
[tex]y=\frac{9}{8}x[/tex]Ricardo is considering 2 monthly plans a dog walking service offers. Plan 1 charges $3 per walk plus $10 for grooming at the end of each month.Plan 2 charges $5 per walk and then offers free grooming at the end of each walk. After answering the question, you also need to explain what did you do to solve the problem.
PART A:
Based on the given information, if w is the number of walks the cost of plan1 and plan2 can modeled as follow:
Plan1 cost:
10 + 3w
Plan2 cost:
5w
The equation wich allows one to determine the number of walks w at which the cost for both plans is the same is:
10 + 3w = 5w
PART B:
Solve the equation for partA as follow:
10 + 3w = 5w subtract 3w both sides and simplify
10 = 5w - 3w
10 = 2w divide by 2 both sides
10/2 = w
5 = w
w = 5
Hence, you can conclude that for 5 walks the cost of both plans A and B is the same.
Calculate the sum of the first 8 terms of the arithmetic sequence in which a8=-1 and the common difference is d=-8
In the arithmetic sequence, the nth term is
[tex]a_n=a+(n-1)d[/tex]a is the first term
d is the common difference
n is the position of the number
Since a(8) = -1
Then n = 8
Since the common difference is -8, then
d = -8
Substitute them in the rule to find the first term a
[tex]\begin{gathered} -1=a+(8-1)(-8) \\ -1=a+(7)(-8) \\ -1=a-56 \end{gathered}[/tex]Add 56 to each side
[tex]\begin{gathered} -1+56=a-56+56 \\ 55=a \end{gathered}[/tex]The first term is 55
The rule of the sum of the nth term is
[tex]S_n=\frac{n}{2}\lbrack a+l\rbrack[/tex]l is the last term
Since we need the sum of 8 terms, then
a = 55
l = a(8) = -1
n = 8
[tex]\begin{gathered} S_8=\frac{8}{2}\lbrack55+(-1)\rbrack \\ S_8=4\lbrack54\rbrack \\ S_8=216 \end{gathered}[/tex]The sum of the first 8 terms is 216
The answer is A
Transform BC according to (x,y) (x-4, y-1). Sketch and write coordinates for B'C.
The coordinates of B are:
B = (-1 , -1)
And the coordinates of C are:
C = (-6 , 2)
Using the transformation:
B' = (-1 - 4, -1 - 1) = (-5, -2)
C' = (-6 - 4, 2 - 1) = (-10 , 1)
Circle R has a diameter ST with endpoints at S(4,5) and T (-2,-3).
Given
[tex]\begin{gathered} S(4,5) \\ T(-2,-3) \end{gathered}[/tex]Solution
Diameter is 10
Radius is 5
The Circumference
[tex]\begin{gathered} =2\pi r \\ \\ =2\times\pi\times5 \\ =10\pi \\ =31.42 \\ \end{gathered}[/tex]The area of the circle
[tex]\begin{gathered} =\pi r^2 \\ =\pi\times5^2 \\ =25\pi \\ =78.54 \end{gathered}[/tex]Solve for x1/2x - 2 = 5
Answer:
x = 14
Explanation:
The given expression is
[tex]\frac{1}{2}x-2=5[/tex]To solve for x, we first need to add 2 to both sides
[tex]\begin{gathered} \frac{1}{2}x-2+2=5+2 \\ \\ \frac{1}{2}x=7 \end{gathered}[/tex]Then, we can multiply both sides by 2
[tex]\begin{gathered} 2\cdot\frac{1}{2}x=2\cdot7 \\ \\ x=14 \end{gathered}[/tex]Therefore, the answer is
x = 14
r - 12 = -5This is a two step problem in I need help , can you help me
We have the equation:
[tex]r-12=-5[/tex]In the equation above, the variable is r, and we want to find the solution, so we have to isolate r:
[tex]\begin{gathered} r-12=-5 \\ r=-5+12 \\ r=7 \end{gathered}[/tex]The starting line for a race in Douglas is 9 kilometers from the finish line. On a map of the course, the starting and finish lines are 3 centimeters apart. What scale does the map use?Write your answer as a decimal or whole number.1 centimeter =
In this problem, we have that
distance on a map is 3 cm
distance in the actual is 9 km
the scale of the map is
3 cm/9 km
simplify
1 cm/3 km
therefore
the answer is
1 cm : 3 kmhow do this problem and what would be the answer?
We were given that:
[tex]\begin{gathered} f(x)=4x+3 \\ g(x)=2x \end{gathered}[/tex]Graph the following function on a coordinate graph.take a number (x), quadruple it , and subtract 2.
First, we have to write the function in the form:
y= mx+b
take a number x. quadruple it (multiply by 4) and subtract 2:
4x-2
So, the function is:
y=4x-2
The graph crosses the y-axis at y=-2 ( y-intercept) and has a slope of 4
Write a proof. Given: WX = ZY WX || ZY, Prove: (triangle)WXZ (triangle)YZX
Reasons:
1. Given
2. Given
3. Alternate interior angles
4. Reflexive property of equality
5. SAS
solve problems 1/2÷ 2=
Solve:
[tex]\frac{1}{2}\div2[/tex]Suppose we have 1 half of an orange:
So, slide the orange into two pieces::
Then, 1/2÷2=1/4.
answer answer your answer by filling in the blank boxes
We are given the following 2x2 matrix
[tex]A=\begin{bmatrix}{-3} & {-2} \\ {4} & {8}\end{bmatrix}[/tex]We are asked to find the inverse of matrix A.
Recall that the inverse of a 2x2 matrix is given by
[tex]A^{-1}=\frac{1}{ad-bc}\times\begin{bmatrix}{d} & {-b} \\ {-c} & {a}\end{bmatrix}[/tex]Where
a = -3
b = -2
c = 4
d = 8
Let us substitute these values into the above equation
[tex]A^{-1}=\frac{1}{(-3)(8)-(-2)(4)}\times\begin{bmatrix}{8} & {-(-2)} \\ {-(4)} & {-3}\end{bmatrix}[/tex]Now simplify
[tex]\begin{gathered} A^{-1}=\frac{1}{-24+8}\times\begin{bmatrix}{8} & {2} \\ {-4} & {-3}\end{bmatrix} \\ A^{-1}=\frac{1}{-16}\times\begin{bmatrix}{8} & {2} \\ {-4} & {-3}\end{bmatrix} \\ A^{-1}=\begin{bmatrix}{\frac{8}{-16}} & {\frac{2}{-16}} \\ {\frac{-4}{-16}} & {\frac{-3}{-16}}\end{bmatrix} \\ A^{-1}=\begin{bmatrix}{-\frac{1}{2}} & {-\frac{1}{8}} \\ {\frac{1}{4}} & {\frac{3}{16}}\end{bmatrix} \end{gathered}[/tex]Therefore, the inverse of the matrix A is
[tex]A^{-1}=\begin{bmatrix}{-\frac{1}{2}} & {-\frac{1}{8}} \\ {\frac{1}{4}} & {\frac{3}{16}}\end{bmatrix}[/tex]What the distance from the given point to the vertical axis. (9, 8)? Units
Given the point:
(x, y) ==> (9, 8)
Let's find the distance from the point to the vertical axis of the graph.
The vertical axis of a graph is the y-axis.
Hence, the distance from any pointy to the vertical axis is the unit of the x-coordinate of the point.
From the given point, we have:
x-coordinate = 9
y-coordinate = 8
The x-coordinate of the point is 9.
Therefore, the distance from the given point (9, 8) to the vertical axis (y-axis) is 9 units
ANSWER:
9 units
James invests a total of $26,500 in two accts. paying 10% and 2% annual interest, respectively. How much was invested in each account if after one year the total interest was $1970?
Answer:
account 1 investment: 18,000
account 2 investment: 8,500
Explanation:
Let us call A0 and B0 the principle amount in each account, then we know that
[tex]A_0+B_0=26,500[/tex]Furthermore, the simple interest earned on account A0, for example, is
[tex]I=A_0(1+r_At)-A_0=A_0r_At[/tex]where A0 ( 1+ rt) is the account balance after time t on simple interest. If we subtract the initial balance from the final, we would get the total interest earned. The expression above finds exactly just that ( the interest earned).
Now the interest earned on account B0 is
[tex]I=B_0(1+rt)-B_0=B_0+B_0rt-B_0=B_0r_Bt[/tex][tex]\Rightarrow I=B_0r_Bt[/tex]Now we know that the total interest earned is $1970, therefore,
[tex]B_0r_Bt+A_0r_At=1970[/tex]putting in rA = 10% = 0.10 , rB = 2% = 0.02, and t = 1 gives us the system:
[tex]\begin{gathered} A_0+B_0=26,500 \\ 0.10A_0+0.02B_0=1970 \end{gathered}[/tex]Now, this is a system of equations with unknowns A0 and B0.
We multiply the first equation by 0.10 t0 get:
[tex]\begin{gathered} 0.10A_0+0.10B_0=0.10\cdot26,500 \\ 0.10A_0+0.02B_0=1970 \end{gathered}[/tex]subtracting the second equation from the first gives
[tex]0.10A_0-0.10A_0+0.10B_0-0.02B_0=(0.10\cdot26,500)-1970[/tex][tex]0.08B_0=(0.10\cdot26,500)-1970[/tex][tex]0.08B_0=680[/tex]finally, dividing both sides by 0.08 gives
[tex]B_0=\frac{680}{0.08}[/tex][tex]\boxed{B_0=8500}[/tex]which is our answer!
Now that we have the value of B0, we now find the value of A0 from the following equation:
[tex]A_0+B_0=26,500[/tex]putting in b0 = 8500 gives
[tex]A_0+8500=26,500[/tex]finally, subtracting 8500 from both sides gives
[tex]\boxed{A_0=18,000.}[/tex]which is our answer!
Hence, the amount invested in the accounts was 8,500 and 18,000.
The graph of y = f(x) is shown in the xy-plane below.
Let's put more details in the given graph,
We will generate the equation of the graph based on the following form:
[tex]\text{ f(x) = a(x - h)}^2\text{ + k}[/tex]We get,
[tex]\text{ f(x) = a(x - h)}^2\text{ + k}[/tex][tex]\text{ f(x) = a(x - 1)}^2\text{ + }(-9)[/tex][tex]\text{ f(x) = a(x - 1)}^2\text{ }-9[/tex]Let's find a, use f(-2) = 0.
[tex]f\mleft(-2\mright)=0[/tex][tex]\text{ 0 = a\lbrack(-2) - 1\rbrack}^2\text{ - 9}[/tex][tex]\text{ 0 = a(-2 - 1)}^2\text{ - 9}[/tex][tex]\text{ 0 + 9 = a(-3)}^2\text{ - 9 + 9}[/tex][tex]\text{ 9 = 9a}[/tex][tex]\text{ }\frac{\text{9}}{9}\text{ = }\frac{\text{9a}}{9}[/tex][tex]\text{ a = 1}[/tex]Let's now complete the equation.
[tex]\text{ f(x) = a(x - 1)}^2\text{ }-9[/tex][tex]\text{ f(x) = (1)(x - 1)}^2\text{ }-9\text{ = (x - 1)}^2\text{ }-9\text{ }[/tex][tex]\text{ f(x) = x}^2\text{ - 2x + 1 - 9}[/tex][tex]\text{ f(x) = x}^2\text{ - 2x - 8}[/tex]Therefore, the answer is letter A.
Fill in the blanks with the word bank at the bottom
1. The average squared distance from each value from the mean is Variance
2. The middle value is Median
3. The average is Mean
4. Values that describe the centre data Measures of central tendency
5. The most repeated value is Mode
6. A value that describes how spread out a data is, is Measure of variation
7. The average distance of each value to the mean is Mean Absolute Deviation (MAD)
8. Square root of the variance is the Standard deviation
The Cookie Factory wants to sell chocolate chip and peanut butter cookies in combination packages of 6-12cookies. At least three of each type of cookie should be in each package. The cost of making a chocolatechip cookie is 19 cents, and the selling price is 44 cents each. The cost of making a peanut butter cookie is13 cents, and the selling price is 39 cents. How many of each type of cookie should be in each package tomaximize the profit?A. 3 chocolate chip and 3 peanut butter B. 3 chocolate chip and 9 peanut butterC. 9 chocolate chip and 3 peanut butter D. 0 chocolate chip and 12 peanut butter
Let the number of chocolate chip cookies sold=x
Let the number of peanut butter cookie sold =y
The cost of making a chocolate chip cookie is 19 cents, and the selling price is 44 cents each.
Therefore, the profit made on chocolate chip cookie
=44-19
=25 cents
=$0.25
The cost of making a peanut butter cookie is 13 cents, and the selling price is 39 cents.
Therefore, the profit made on peanut butter cookie
=39-13
=26 cents
=$0.26
Therefore, the profit made when x cookies and y cookies are sold will be:
P(x,y)=0.25x+0.26y
To determine how many of each type of cookie should be in each package to maximize the profit, we use the coordinates of the feasible region (which are given in the options).
Option A: x=3, y=3
P(x,y)=0.25(3)+0.26(3)=$1.53
Option B: x=3, y=9
P(x,y)=0.25(3)+0.26(9)=$3.09
Option C: x=9, y=3
P(x,y)=0.25(9)+0.26(3)=$3.03
Option D: x=0, y=12
P(x,y)=0.25(0)+0.26(12)=$3.12
Since the point (0,12) gives the highest value, 0 chocolate chip and 12 peanut butter cookies should be in each package to maximize the profit.
what the area of square 6/7 yd and 6/7
The area of a square is it's length times it's width. Since in a square the length and the width are the same, the area is just the size of it's sides squared:
[tex]A=\text{side}^{2}[/tex]This square have sides of 6/7 yd, so the area is:
[tex]A=(\frac{6}{7}yd)^{2}=\frac{6^2}{7^{2}}yd^{2}[/tex][tex]A=\frac{36}{49}yd^{2}[/tex]According to the graph below, what is the approximate temperature at an elevation of 3000 mete
We have a graph that relates elevation (in the x-axis) with temperature (in the y-axis).
As we have points for elevations between 500 m and 2250 m, we have to extrapolate for an elevation of 3000 m.
We will extrapolate grpahically and get:
The extrapolation give us, for an elevation of 3000 m, a temperature of approximately 3 °C.
Answer: For an elevation of 3000 m, we estimate a temperature of 3 °C.
Please help me by telling me the correct order please this is for my study guide
Okay, here we have this:
Considering the provided information, we are going to organize the steps correctly, so we obtain the following:
Step 1. Isolate the term with variables on one side of the equation and arrange them in descending order.
Step 2. Divide by the coefficient of squared term if that coefficient is not 1.
Step 3. Complete the square by taking half of the 1st degree term and adding its square.
Step 4. Express one side of the equation as the square of binomial.
Step 5. Use the principle of square root.
Step 6. Solve for the variable.
5. Solve the system of linear equations. 2x + 6y = -3 2x + y = 0 A. (0, 2) B. (9,7) C. no solution D. infinitely many solutions licorutions
EXPLANATION
Given the system of equations:
(1) 2x + 6y = -3
(2) 2x + 6y = 0
Subtract 6y from both sides:
2x + 6y - 6y = -3 - 6y
Simplify:
2x = -3 - 6y
Divide both sides by 2:
[tex]\frac{2x}{2}=-\frac{3}{2}-\frac{6y}{2}[/tex]Simplify:
[tex]x=\frac{-3-6y}{2}[/tex]Substitute:
[tex]x=\frac{-3-6y}{2}[/tex][tex]2\cdot\frac{-3-6y}{2}+6y\text{ = 0}[/tex]Simplifying:
[tex]-3-6y+6y=0[/tex]Adding like terms:
[tex]-3=0[/tex]-3=0 is false, therefore the system of equations has no solutions.
The answer is the option C.
I need help with this, please help if you can.
Let's put more details in the given figure:
Step 1: Let's first find x.
The total measure of a circle is 360°.
We get,
[tex]\text{ Arc LM + Arc MJ + Arc JR + x = 360}\degree[/tex][tex]\text{ 100}\degree\text{ + 72}\degree\text{ + 140}\degree\text{ + x = 360}\degree[/tex][tex]\text{ 312}\degree\text{ + x = 360}\degree[/tex][tex]\text{ x = 360}\degree\text{ - 312}\degree[/tex][tex]\text{ x = 48}\degree[/tex]
Step 2: Let's now find ∠K.
[tex]\text{ m\angle K = }\frac{1}{2}(Arc\text{ ML - x\rparen}[/tex][tex]\text{ = }\frac{1}{2}(72\text{ + 48\rparen = }\frac{1}{2}(120\degree)[/tex][tex]\text{ m\angle K = 60}\degree[/tex]Therefore, the measure of ∠K is 60°
A rectangular garden plot has an area of 250 square ft. which of the following are possible dimensions for the plot? - 20 ft X 20 ft- 25 ft X 10 ft - 125 ft by 2ft - 5 ft X 50 ft
Given:
A rectangular garden plot has an area of 250 square ft.
Required:
To choose the possible dimensions for the plot.
Explanation:
We know that the area of rectangle is,
[tex]A=l\times w[/tex]Now, consider the option (1)
[tex]\begin{gathered} 20ft\times20ft \\ =400\text{ sqr}ft \end{gathered}[/tex]Option(2):
[tex]\begin{gathered} 25ft\times10ft \\ =250sqrft \end{gathered}[/tex]Option(3):
[tex]\begin{gathered} 125ft\times2ft \\ =250sqrft \end{gathered}[/tex]Option(4):
[tex]\begin{gathered} 5ft\times50ft \\ =250sqrft \end{gathered}[/tex]Final Answer:
The possible dimension for the plot are,
- 25 ft X 10 ft
- 125 ft by 2ft
- 5 ft X 50 ft
s