if the number of shoppers increases by 20% daily and 671 shoppers had visited over 4 days then let the num ber of shoppers on the first day be x
The numebr of shopperes the next day will be
= x(100 + 20)%
= 1.2x
teh number of shoppers the day after
= 1.2x(100 + 20)%
= 1.44x
the next day, the number
= 1.44x (100 + 20)%
= 1.728x
Given that the total number of people that have shopped after 4 days is 671 then
x + 1.2x + 1.44x + 1.728x = 671
5.368x = 671
x = 671/5.368
= 125
if the number of shoppers increases by 20% daily and 671 shoppers had visited over 4 days then let the num ber of shoppers on the first day be x
The numebr of shopperes the next day will be
= x(100 + 20)%
= 1.2x
teh number of shoppers the day after
= 1.2x(100 + 20)%
= 1.44x
the next day, the number
= 1.44x (100 + 20)%
= 1.728x
Given that the total number of people that have shopped after 4 days is 671 then
x + 1.2x + 1.44x + 1.728x = 671
5.368x = 671
x = 671/5.368
= 125
Miss Taylor drove 30 miles in March she drove 9 times as many miles in May as she did in March she drove 2 times as many miles in April as she did in May how many miles did Miss Taylor Drive in April.
then we use the statement to solve
Miss Taylor drove 30 miles in March
[tex]March=30[/tex]she drove 9 times as many miles in May as she did in March
[tex]\begin{gathered} May=9\text{March} \\ May=9\times30=270 \end{gathered}[/tex]she drove 2 times as many miles in April as she did in May
[tex]\begin{gathered} April=2May \\ April=2\times270=540 \end{gathered}[/tex]Taylor Drove 540 Miles in April
Could you help me with this problem?There are 7 acts in a talent show.A comedian, a guitarist, a magician, a pianist, a singer, a violinist, and a whistler.A talent show host randomly schedules the 7 acts.Compute the probability of each of the following events.Event A: The magician is first, the comedian is second, and the whistler is third.Event B: The first three acts are the guitarist, the pianist, and the singer, in any order.Write your answers as fractions in simplest form.
EXPLANATION
For the event B, the order of the first 3 acts doesn't matter.
So, the number of acts taken from the seven acts when the order doesn't matter is calculated using combinations.
[tex]C(m,n)=\frac{m!}{n!(m-n)!}[/tex][tex]C(7,3)=\frac{7!}{3!(7-3)!}=\frac{7!}{3!4!}[/tex]Computing the factorials:
[tex]C(7,3)=\frac{5040}{6\cdot24}=\frac{5040}{144}=35[/tex]Hence, the number of ways the three acts could be given are 1:C(7,3)
Therefore, the probability of the event B is:
[tex]P(B)=\frac{1}{35}[/tex]For the event A, the order matters, so the difference between combinations and permutations is ordering. When the order matters we need to use permutations.
The number of ways in which four acts can be scheculed when the order matters is:
[tex]P(m,n)=\frac{m!}{(m-n)!}[/tex][tex]P(m,n)=\frac{7!}{(7-3)!}=\frac{5040}{24}=210[/tex]The number of ways the magician is first, the comedian is second and the whistler is third are 1:P(7,4)
Therefore, the probability of the event A is.
[tex]P(A)=\frac{1}{210}[/tex]Which expression would be easier to simplify if you used the associativeproperty to change the grouping?
In option A, if expression is simplify with out using associative property then addition of 4/9 and -2/9 is easy, as compare to addition 6 and 4/9. So no need to apply associateive property to option A.
In option B, 60 and 40 can be easily add as compare to 40 and -27 so this expression do not need to apply associative property.
In option C, the expression is easier to simplify if 5/2 and -1/2 is added, which is possible if associative is apply to the expression.
[tex]\begin{gathered} (2+\frac{5}{2})+(-\frac{1}{2})=2+(\frac{5}{2}-\frac{1}{2}) \\ =2+(\frac{5-1}{2}) \\ =2+2 \\ =4 \end{gathered}[/tex]Thus option C use associative property to make the simplification easier.
Answer: Option C.
Solve the inequality. Express your answer using set notation or interval notation. Graph the solution set.
Answer:
(D) {xIx ≥ 5} or [5, ∞)
Explanation:
Given inequality: 5x - 11 ≥ 9 + x
By collecting the like terms, we have
5x - x ≥ 9 + 11
4x ≥ 20
Divide bothsides by 4
4x/4 ≥ 20/4
x ≥ 5
In set notation, we have {5, ∞}
The graph of the solution set is
Approximate 14 plus cube root of 81 to the nearest tenth.
15.8
17.9
18.0
18.3
The Approximation of 14 plus cube root of 81 to the nearest tenth is 18.0
How can the terms be simplified?The concept that will be used to solve this is finding cube root of 81 which same thing as [tex]81^{\frac{1}{3} }[/tex].
Firstly we will need to find the cube root of 81, which can be expressed as this: [tex]\sqrt[3]{81}[/tex] and this can be calculated as 4.33.
This implies that the cube root of 81 will now be 4.33.
Then we can proceed to the simplification that was asked from the question which is 14 plus cube root of 81 and this can be expressed as ( 14) + (4.33) = 18.33
Then we were told to express in the the nearest tenth which is 18.0
Therefore, the third option is correct.
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Correctz is jointly proportional to x and y. If z = 115 when x = 8 and y = 3, find z when x = 5 and y = 2. (Round off your answer to the nearest hundredth.)
When we have a number that is jointly proportional to two other numebrs, the formula is:
[tex]a=kcb[/tex]This means "a is jointly proportional to c and b with a factor of k"
Then, we need to find the factor k.
In this case z is jointly proportional to x² and y³
This is:
[tex]z=kx^2y^3[/tex]Then, we know that z = 115 when x = 8 and y = 3. We can write:
[tex]115=k\cdot8^2\cdot3^3[/tex]And solve:
[tex]\begin{gathered} 115=k\cdot64\cdot27 \\ 115=k\cdot1728 \\ k=\frac{115}{1728} \end{gathered}[/tex]NOw we can use k to find the value of z when x = 5 and y = 2
[tex]z=\frac{115}{1728}\cdot5^2\cdot2^3=\frac{115}{1728}\cdot25\cdot8=\frac{2875}{216}\approx13.31[/tex]To the nearest hundreth, the value of z when x = 5 and y = 2 is 13.31
a blu ray player costs $80.99 in the store. what would your total cost be if the sales tax is 5.5%
ANSWER:
$ 85.44
STEP-BY-STEP EXPLANATION:
We have the value after tax, we must calculate the sum between the original value and the value equivalent to the established percentage, therefore, we calculate it like this:
[tex]\begin{gathered} p=80.99+80.99\cdot\frac{5.5}{100} \\ p=80.99+4.45 \\ p=\text{ \$85.44} \end{gathered}[/tex]The final price is $ 85.44
What is the image point of (1,−3) after a translation right 2 units and up 2 units?
For this problem we have the following point given:
[tex]P=(1,-3)[/tex]And we want to determine the image point after a translation of 2 units to the right and upward. So then we just need to do the following:
[tex]I=(1+2,-3+2)[/tex]And after do the math we got:
[tex]I=(3,-1)[/tex]And the final answer for this case would be I=(3,-1)
May I please get help with this. I need help with finding the original and final points on the figure and also finding out where I should put my reflection?
Answer:
Step-by-step explanation:
The rule for a reflection over the y-axis is represented by the following equation:
[tex](x,y)\rightarrow(-x,y)_{}[/tex]Therefore, for the given figure and given point:
The side of a square lot is (5×-3) meters. How many meters of fencing materials are needed to enclose the square lot?
The length of the fencing will be the perimeter of the given square with side (5x - 3) thus (20x - 12) meters will be the fencing length.
What is a square?A square is a geometrical figure in which we have four sides each side must be equal and the angle between two adjacent sides must be 90 degrees.
As per the given,
Side of square = 5x - 3
The fencing around the square will cover the complete perimeter of the square.
Since the perimeter of the square = 4 × side
Therefore,
Length of fencing = 4 × (5x - 3)
Length of fencing = 20x - 12
Hence "The length of the fencing will be the perimeter of the given square with side (5x - 3) thus (20x - 12) meters will be the fencing length".
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Coronado co. sells product p-14 at a price of $52 a unit. the per unit cost data are direct materials $16, direct labour $12, and overhead $12 (75% variable) Coronado has no excess capacity to accept a special order for 38,700 units at a discount of 25% from the regular price. Selling costs associated with this order would be $3 per unit. Indicate the net income/loss
The net loss from accepting the special order at a discount of 25% from the regular price, without the existence of excess capacity is $38,700.
How is the net loss determined?Since Coronado Co. lacks the excess capacity for special orders, it implies that it will incur fixed costs per unit of the special order in addition to the variable costs.
Therefore, the company will incur a per unit cost of $40 ($16 + $12 + $9 + $3) while generating a revenue of $39 per unit.
This results in a loss of $1 per unit.
Selling price per unit = $52
Unit Costs:
Direct Materials = $16
Direct Labor = $12
Variable Overhead = $9 (75% of $12)
Total variable cost per unit = $37
Fixed Overhead = $3 (25% of $12)
Special order price per unit = $39 ($52 x 1 - 75%)
Contribution margin per unit = $2 ($39 - $37)
Total contribution margin = $77,400 ($2 x 38,700)
Fixed Overhead without excess capacity = $116,100 ($3 x 38,700)
Net loss = $38,700 ($77,400 - $116,100)
Thus, without excess capacity, it is inadvisable for Coronado to accept the special order at a total loss of $38,700.
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Question is stated in picture. The figure is a triangular piece of cloth
Answer:
Alternative D - 8 sin(35°)
Step-by-step explanation:
Sin(x) is defined as:
[tex]\begin{gathered} \sin (x)=\frac{\text{Opposite side}}{Hypotenuse\text{ }} \\ \end{gathered}[/tex]In this exercise,
BC is the opposite side to 35°
AC is the hypotenuse and measures 8 in
Then:
[tex]\begin{gathered} \sin (35\degree)=\frac{BC}{8} \\ \sin (35\degree)\cdot8=BC \\ BC=8\sin (35\degree) \end{gathered}[/tex]Which answer choice shows 3.002 written in expanded form?A) 3 + 0.2B) 3 + 0.02C) 3 + 0.002D) 3+ 0.0002
SOLUTION
We want to know which answer choice shows 3.002 written in expanded form
To do this let us subtract 3.002 from 3, we have
We got 0.002
So the expanded form is
[tex]3+0.002[/tex]Hence the correct answer is option C
I need help for problem number 9. On the right side of the paper.
Constant of variation ( k ):
• y = 2/3
,• x = 1/4
[tex]k=\frac{y}{x}=\frac{\frac{2}{3}}{\frac{1}{4}}=\frac{8}{3}[/tex]k = 8/3
Based on k we can find the value of y when x =3/4 as follows:
[tex]\begin{gathered} k=\frac{y}{x} \\ y=k\cdot x \\ y=\frac{8}{3}\cdot\frac{3}{4}=2 \end{gathered}[/tex]Answer:
• k = 8/3
,• When ,x, = ,3/4,,, y = 2
Which of the following is a factor of the polynomial Step By Step Explanation Please
Use the quadratic formula.
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Where a = 3, b = -31, and c = -60.
[tex]x=\frac{-(-31)\pm\sqrt[]{(-31)^2-4(3)(-60)}}{2(3)}[/tex]Solve to find both solutions.
[tex]x=\frac{31\pm\sqrt[]{961+720}}{6}=\frac{31\pm\sqrt[]{1681}}{6}=\frac{31\pm41}{6}[/tex]Rewrite the expression as two.
[tex]\begin{gathered} x_1=\frac{31+41}{6}=\frac{72}{6}=12 \\ x_2=\frac{31-41}{6}=\frac{-10}{6}=-\frac{5}{3} \end{gathered}[/tex]Once we have the solutions, we express them as factors. To do that, we have to move the constant to the right side of each equation.
[tex]\begin{gathered} x=12\to(x-12) \\ x=-\frac{5}{3}\to(3x+5)_{} \end{gathered}[/tex]As can observe, the factor of the polynomial is (x-12).
Therefore, the answer is d.Write the trig equation needed to solve for X. Then solve for X. Round answers to the nearest tenth.
In order to solve for x, we need to use the tangent relation of the angle 48°.
The tangent relation is equal to the length of the opposite leg to the angle over the length of the adjacent leg to the angle.
So we have:
[tex]\begin{gathered} \tan (48\degree)=\frac{x}{17} \\ 1.1106=\frac{x}{17} \\ x=1.1106\cdot17 \\ x=18.88 \end{gathered}[/tex]Rounding to the nearest tenth, we have x = 18.9.
Help solving rational equations by cancelling denominator
Find the value of f(-9).
The function f(-9) is the -x value, find where the line is in the -y direction at -x = -9. The line crosses -y = -3 at -x = -9.
What is meant by the graph?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.
In discrete mathematics, a graph is made up of vertices—a collection of points—and edges—the lines connecting those vertices. In addition to linked and disconnected graphs, weighted graphs, bipartite graphs, directed and undirected graphs, and simple graphs, there are many other forms of graphs. A graph is a diagram that depicts the connections between two or more objects.
The function f(-9) is the -x value, find where the line is in the -y direction at -x = -9. The line crosses -y = -3 at -x = -9.
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60 went into a machine and 72 came out.What percent increase did this machine use?
From this question, we can deduce he following:
Original value = 60
New value = 72
Let's find the percentage increase.
To find the percentage increase, apply the formula below:
[tex]\text{ Percent increase = }\frac{New\text{ value - old value}}{old\text{ value}}\ast100[/tex]Thus, we have:
[tex]\begin{gathered} \text{Percent increase = }\frac{72-60}{60}\ast100 \\ \\ \text{Percent increase = }\frac{12}{60}\ast100 \\ \\ \text{Percent increase = }0.2\ast100 \\ \\ \text{Percent increase = 20 \%} \end{gathered}[/tex]Therefore, the percent increase is 20%.
ANSWER:
20%
In the lab, Deandre has two solutions that contain alcohol and is mixing them with each other. Solution A is 10% alcohol and Solution B is 60% alcohol. He uses200 milliliters of Solution A. How many milliliters of Solution B does he use, if the resulting mixture is a 40% alcohol solution?
The percentage of alcohol of a solution i is given by the quotient:
[tex]p_i=\frac{v_i}{V_i},_{}[/tex]where v_i is the volume of alcohol in the solution i and V_i is the volume of the solution i.
From the statement of the problem we know that:
1) Solution A has 10% of alcohol, i.e.
[tex]p_A=\frac{v_A_{}}{V_A}=0.1.\Rightarrow v_A=0.1\cdot V_A.[/tex]2) Solution B has 60% of alcohol, i.e.
[tex]p_B=\frac{v_B}{V_B}=0.6\Rightarrow v_B=0.6\cdot V_B.[/tex]3) The volume of solution A is V_A = 200ml.
4) The resulting mixture must have a percentage of 40% of alcohol, so we have that:
[tex]p_M=\frac{v_M}{V_M}=0.4.[/tex]5) The volume of the mixture v_M is equal to the sum of the volumes of alcohol in each solution:
[tex]v_M=v_A+v_{B\text{.}}_{}[/tex]6) The volume of the mixtureVv_M is equal to the sum of the volumes of each solution:
[tex]V_M=V_A+V_B\text{.}[/tex]7) Replacing 5) and 6) in 4) we have:
[tex]\frac{v_A+v_B}{V_A+V_B_{}}=0.4_{}\text{.}[/tex]8) Replacing 1) and 2) in 7) we have:
[tex]\frac{0.1\cdot V_B+0.6\cdot V_B}{V_A+V_B}=0.4_{}\text{.}[/tex]9) Replacing 3) in 8) we have:
[tex]\frac{0.1\cdot200ml_{}+0.6\cdot V_B}{200ml_{}+V_B}=0.4_{}\text{.}[/tex]Now we solve the last equation for V_B:
[tex]\begin{gathered} \frac{0.1\cdot200ml+0.6\cdot V_B}{200ml_{}+V_B}=0.4_{}, \\ \frac{20ml+0.6\cdot V_B}{200ml_{}+V_B}=0.4_{}, \\ 20ml+0.6\cdot V_B=0.4_{}\cdot(200ml+V_B), \\ 20ml+0.6\cdot V_B=80ml+0.4\cdot V_B, \\ 0.6\cdot V_B-0.4\cdot V_B=80ml-20ml, \\ 0.2\cdot V_B=60ml, \\ V_B=\frac{60}{0.2}\cdot ml=300ml. \end{gathered}[/tex]We must use 300ml of Solution B to have a 40% alcohol solution as the resulting mixture.
Answer: 300ml of Solution B.
Please help meSolve using A=PertThe half life gets me each time.
Solve the following system of equations using the elimination method. Give the final answer in (x,y) form.
Anisha used the substitution method to solve the system of equations.
She is missing the value of y.
To find it we plut the value of x in the first equation, then:
[tex]y=4-5=-1[/tex]Therefore the solution is (4,-1)
Determine the solution to the system of equations using substitution. (1 pt)2:+ y=6y = -6(2,6)(2,-6)(4, -2)(-2,4)
2x + y = 6 (1)
y = x - 6 (2)
Substituting y in equation (1)
2x + x - 6 = 6
3x - 6 = 6 Isolating 3x
3x = 6 + 6
3x = 12 Isolating x
x = 12/3 = 4
If x is 4 , then y is equal to -2 ( from equation (2) y)
How to find postulate
Note that if plane N and plane M intersects each other in two points (say A and B) it follows that they intersects each other in the line that contains A and B. So they cannot intersect exactly in only two points. Postulate number 10
Use the distributive property to simplify 10 - 5( -3-7m) completely .
Simplify the expression by using the distributive property.
[tex]\begin{gathered} 10-5(-3-7m)=10+(-5)\cdot(-3)+(-5)\cdot(-7m) \\ =10+15+35m \\ =25+35m \end{gathered}[/tex]So answer is 25 + 35m.
$75 dinner, 6.25% tax, 18% tip please show work.You have to find the total cost
According the the information given in the exercise, you know that the cost of the dinner was:
[tex]d=_{}$75$[/tex]Where "d" is the cost of the dinner in dollars.
Convert from percentages to decimal numbers by dividing them by 100:
1. 6.25% tax in decimal for:
[tex]\begin{gathered} tax=\frac{6.25}{100} \\ tax=0.0625 \\ \end{gathered}[/tex]2. 18% tip in decimal form:
[tex]\begin{gathered} tip=\frac{18}{100} \\ \\ tip=0.18 \end{gathered}[/tex]To find the amount in dollars of the tax and the the amount in dollars of the tip, multiply "d" by the decimals found above.
Knowing the above, let be "t" the total cost in dollars.
This is:
[tex]\begin{gathered} t=d+0.0625d+0.18d \\ t=75+(0.0625)(75)+(0.18)(75) \\ t=93.1875 \end{gathered}[/tex]Therefore the answer is: The total cost is $93.1875
8.
What is the measure of angle x in the figure?
40°
A 69°
B 71°
C 109°
D 111°
Answer:
C 109
Step-by-step explanation:
First add all the known angles inside the triangle first to get 109°
Then since all angles in a triangle add to 180°
you take away 109 from 180 so
180-109 which equals 71
Then since all angles on a straight line add up to 180°
you take 71 from 180 so
180-71 = 109
so x = 109°
# 3 symbols of inequalities and the coordinate system...hello I'm a 7th grader can u please help me with my math summer package and explain it in a way that a 7th grader can understand it
Given: A grocery store is located at the origin (0,0). Madison lives 3 blocks west of the grocery store, and Gavin lives 5 blocks west of the grocery store.
Required: To determine the coordinates of Madison's house and Gavin's house and the distance between the grocery store and madison's and Gavin's house. Also, write inequalities for the distance.
Explanation: Let the graph represents the directions as follows-
Then, the direction west lies on the negative x-axis. So, according to the question, Madison lives 3 blocks west of the grocery store, and Gavin lives 5 blocks west of the grocery store. This can be represented as follows-
Here, M represents Madison's house, and G represents Gavin's house. Now the distance from the grocery store to Madison's house is 3 blocks and to Gavin's house is 5 blocks.
Gavin lives at a greater distance from the store. Let d(M) represent the distance of Madison's house from the store and d(G) represent the distance of Gavin's house from the store. Then-
[tex]\begin{gathered} 0Final Answer: Coordinates of Madison's house=(0,-3).Coordinate of Gavin's house=(0,-5)
Distance from the grocery store to Madison's house=3 unit blocks.
Distance from the grocery store to Gavin's house=5 unit blocks.
Inequalities are-
[tex]\begin{gathered} 0\lt d(M))\leqslant3 \\ 0\lt d(G))\leqslant5 \end{gathered}[/tex]Problem 14.f(2)(a) Determine the equations of the perpendicular bisectors througheach side of the triangle.C(4,6)B(7,3)A(2,2)I
The product of the slopes of the perpendicular lines is -1, which means if the slope of one of them is m, then the slope of the perpendicular line is -1/m
In triangle ABC
The perpendicular bisector of the side BC is drawn from the opposite vertex A
Then to find it find the slope of BC and reciprocal it and change its sign to get its slope and find the midpoint of BC to use it in the equation of the perpendicular bisector
Since B = (7, 3) and C = (4, 6)
Let us find the slope of BC, using the rule of the slope
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Let (x1, y1) = (7, 3) and (x2, y2) = (4, 6)
[tex]\begin{gathered} m_{BC}=\frac{6-3}{4-7} \\ m_{BC}=\frac{3}{-3} \\ m_{BC}=-1 \end{gathered}[/tex]Now to find the slope of the perpendicular line to BC reciprocal it and change its sign
Since the reciprocal of 1 is 1 and the opposite of negative is positive, then
Then the slope of the perpendicular line is 1
Now, let us find the mid-point of BC
The rule of the midpoint is
[tex]M=(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]Then the mid-point of BC is
[tex]\begin{gathered} M_{BC}=(\frac{7+4}{2},\frac{3+6}{2}) \\ M_{BC}=(\frac{11}{2},\frac{9}{2}) \\ M_{BC}=(5.5,4.5) \end{gathered}[/tex]Now we can form the equation of the perpendicular bisector of BC using its slope 1 and the point (5.5, 4.5)
The form of the equation using a point and a slope is
[tex]y-y1=m(x-x1)[/tex]m is the slope and (x1, y1) is a point on the line
Since m = 1 and (x1, y1) = (5.5, 4.5), then
[tex]\begin{gathered} m=1,x1=5.5,y1=4.5 \\ y-4.5=1(x-5.5) \\ y-4.5=x-5.5 \end{gathered}[/tex]Add 4.5 to both sides
[tex]\begin{gathered} y-4.5+4.5=x-5.5+4.5 \\ y=x-1 \end{gathered}[/tex]The equation of the perpendicular bisector of BC is
[tex]y=x-1[/tex]We will do the same to AB and AC
A company needs to take 10 sample sensor readings if the sensor collects data at 1/3 of a sample per second how long will it take the company to take all 10 samples
Given:
Sample space = 10
Rate = 1/3 per second