The given information:
% mark up = 40
Reduced = $144
Markdown = ?
The formula for percentage markup is given as
[tex]\text{ \%markup }=\frac{markup}{actual\text{ price}}\times100[/tex]Let the actual price be x
Hence,
Reduced price = 60% of actual price
[tex]60\text{\% of x = 144}[/tex]Solving for x
[tex]\begin{gathered} \frac{60x}{100}=144 \\ x=\frac{144\times100}{60} \\ x=240 \end{gathered}[/tex]Therefore, actual price = $240
Inserting these values into the %markup formula gives
[tex]40=\frac{\text{markup}}{240}\times100[/tex]Solve for markup
[tex]\begin{gathered} 40=\frac{100\times\text{markup}}{240} \\ 40\times240=100\times\text{markup} \\ \text{markup}=\frac{40\times240}{100} \\ \text{markup}=96 \end{gathered}[/tex]Threefore, markup = $96
Find the x- and y-intercepts for the following equation. Then use the intercepts to graph the equation.
4x + 2y = 8
Answer:
Step-by-step explanation:
x int=2
y int=4
graph 2,0 and 0,4 as two points
Rectangle WXYZ has vertices located at W(−6, 4), X(−6,−1), Y(2,−1), and Z(2, 4) on a coordinate plane. It is translated 4 units right and 2 units down to produce rectangle W'X'Y'Z'. What is the location of the vertices of the transformed rectangle?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Rectangle WXYZ
W(−6, 4)
X(−6,−1)
Y(2,−1)
Z(2, 4)
Step 02:
Translated
4 units right ===> x + 4
2 units down ===> y - 2
W' (−6+4, 4 -2) = W' (-2, 2)
X' (−6+4,−1 - 2) = X' (-2,-3)
Y' (2+4,−1-2) = Y' (6,-3)
Z' (2+4, 4-2) = Z' (6, 2)
The answer is:
W' (-2, 2)
X' (-2,-3)
Y' (6,-3)
Z' (6, 2)
Given an example to show a quadratic that does not factor into binomial • binomial.
An example of the required quadratic equation is x(x+1)
What is an equation?
An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. The word equation and its cognates in various languages may have somewhat different definitions; for example, in French, an équation is defined as including one or more variables, but in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign. Solving an equation with variables entails finding which variables' values make the equality true. The variables for which the equation must be solved are also known as unknowns, and the values of the unknowns that fulfill the equality are known as equation solutions. Identity equations and conditional equations are the two types of equations.
An example of the required quadratic equation is x(x+1)
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The formula Total cost=C+Shipping cost+Installation is used to find the total cost of a business asset. The formula can be written in symbols as T=C+S+I. Solve the formula for I, the Installation cost of the asset.
Formulas
The formula for the Total Cost is given as:
T = C + S + I
Where C is the shipping cost, I is t
-1.5(x - 2) = 6. What is X equaled to
Answer:
x-2=6÷(-1.5)
x-2=-4
x=-4-2
x=-6
compare and contrast the graphs y=2x+1 with the domain {1,2,3,4} and y=2x+1 with the domain of all real numbers
Comparison of both the graphs y=2x+1 with domain {1,2,3,4} and set of all real numbers is :
Slope =2 , y-intercept =1 and x-intercept = -1/2 is same.
Contrast is range is different:
Range = { 3, 5, 7, 9} for domain {1,2,3,4}
Range = set of all real numbers for domain all real numbers.
As given in the question,
Given function for the graphs are:
y =2x+1
Different domains
Domain ={1,2,3,4}
Domain =All real numbers
Compare with y=mx +c
Slope m =2
For y-intercept put x=0
y=2(0) +1
=1
For x-intercept put y=0
0 =2x+1
⇒x=-1/2
Contrast:
For domain ={1,2,3,4}
Range is :
y = 2(1)+1
=3
y=2(2)+1
=5
y=2(3) +1
=7
y=2(4)+1
=9
Range ={ 3, 5, 7,9}
For domain= all real numbers
Range = set of all real numbers
Therefore, comparison of both the graphs y=2x+1 with domain {1,2,3,4} and set of all real numbers is :
Slope =2 , y-intercept =1 and x-intercept = -1/2 is same.
Contrast is range is different:
Range = { 3, 5, 7, 9} for domain {1,2,3,4}
Range = set of all real numbers for domain all real numbers.
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the value of square root (8/64)³
The expression is
[tex]\begin{gathered} (\sqrt[]{\frac{8}{64}})^3 \\ By\text{ simplifying, we have} \\ (\sqrt[]{\frac{1}{8}})^3 \\ =\text{ (}\frac{1}{8})^{\frac{3}{2}} \\ 0.0442 \end{gathered}[/tex]A container built for transatlantic shipping is constructed in the shape of a right rectangular prism. Its dimensions are 9.5 ft by 5.5 ft by 9 ft. The container is entirely full. If, on average, its contents weigh 0.99 pounds per cubic foot, and, on average, the contents are worth $4.37 per pound, find the value of the container’s contents. Round your answer to the nearest cent.
step 1
Find out the volume of the rectangular container
[tex]V=L\cdot W\cdot H[/tex]Substitute given values
[tex]\begin{gathered} V=9.5\cdot5.5\cdot9 \\ V=470.25\text{ ft3} \end{gathered}[/tex]step 2
Find out the weight of the container
Multiply the volume by the density of 0.99 pounds per cubic foot
0.99*470.25=465.5475 pounds
step 3
Multiply the weight by the factor of $4.37 per pound
so
4.37*465.5475=$2,034.44
therefore
The answer is $2,034.44Find the probability and odds of winning the two-number bet (split) in roulette. Then find expected value of a $1 bet in roulette for the two-number bet.P.S Might not have enough information
We have to find the probaiblity of winning a split bet in roulette.
Then, we will have 2 numbers that will make us wind the bet out of 37 numbers that make the sample space.
We can then calculate the probability of winning the split bet as the quotient between the number of success outcomes (2) and the number of possible otucomes (37):
[tex]P(w)=\frac{2}{37}\approx0.054[/tex]We can transform this into the odds of winning by taking into account that if 2 are the success outcomes, then 37-2 = 35 are the failure outcomes.
Then, the odds of winning are 2:35.
We now have to calculate the expected value for a $1 bet.
We know the probabilities of winning and losing, but we don't know the value or prize for winning.
The payout for a split bet is 17:1, meaning that winning a split bet of $1 has a prize of $17.
Then, we can use this to calculate the expected value as:
[tex]\begin{gathered} E(x)=P(w)*w+P(l)*l \\ E(x)=\frac{2}{37}*17+\frac{35}{37}*0 \\ E(x)=\frac{34}{37} \\ E(x)\approx0.9189 \end{gathered}[/tex]This means that is expected to win $0.9189 per $1 split bet.
Answer:
Probability of winning: 2/37 ≈ 0.054
Odds of winning: 2:35
Expected value of $1 split bet (17:1 payout): $0.9189
when the occurrence of one event precludes the occurrence of the other the events are said to be what
Answer:
Mutually Exclusive.
Explanation:
When the occurrence of one event prevents or affects the occurrence of the other, the events are said to be Mutually Exclusive.
A. Side a is 24 inches longand side bis 21 inches longB. Side a is 63 inches long and side bis 54 inches long.C. Side a is 18 inches long and side bis 15 inches long.D. Side a is 7 inches long and side bis 6 inches long.
Since both drawings are similar and have a scale factor, we can say that all sides keep the same scamle factor, if the scale drawing is in a proportion of 3:1 means that all of its sides is 3 times the real objects sides.
write this as equations
[tex]\begin{gathered} 3\cdot a=21in \\ 3\cdot b=18in \end{gathered}[/tex]to find the respetive values for a and b we divide the sides by 3
[tex]\begin{gathered} a=\frac{21in}{3}=7in \\ b=\frac{18in}{3}=6in \end{gathered}[/tex]The correct answer is D.
What is the slope of the line that passes through the points (6,-10) and (3,-13)? Write in simplist form
Use the slope formula to find the slope of a line that goes through two points:
[tex]\begin{gathered} \text{Coordinates of two points}\rightarrow\text{ }(x_1,y_1),(x_2,y_2) \\ \text{Slope of a line through those points}\rightarrow m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]Substitute the coordinates (6,-10) and (3,-13) into the slope formula:
[tex]\begin{gathered} m=\frac{(-13)-(-10)}{(3)-(6)} \\ =\frac{-13+10}{3-6} \\ =\frac{-3}{-3} \\ =1 \end{gathered}[/tex]Therefore, the slope of a line that passes through those points, is 1.
of a sample of 200 students surveyed,38 students said the soccer was their favorite sport what percent of the students in the sample prefer soccer 19% 38%40%76%
Out of 200 students surveyed, 38 said that soccer was their favorite sport.
The total number of students surveyed represents 100% of the sample, to determine which percentage does 38 represent, you can use cross multiplication:
200 students____100%
38 students _____ x%
Both relationships are at the same ratio so that:
[tex]\frac{100}{200}=\frac{x}{38}[/tex]To determine the percentage multiply both sides by 38:
[tex]\begin{gathered} 38\cdot\frac{100}{200}=38\cdot\frac{x}{38} \\ 19=x \end{gathered}[/tex]The percentage of students surveyed that like soccer is 19%
Find the slope of the line?Ordered pairs (-4, 1) and (1, -2)
The slope of the line is:
[tex]m=-\frac{3}{5}[/tex]To find the slope of a line with two points, P and Q, the formula is:
[tex]\begin{gathered} P=(x_p,y_p);Q=(x_q,y_q) \\ m=\frac{y_p-y_q}{x_p-x_q} \end{gathered}[/tex]Then if P = (-4, 1) and Q = (1, -2)
We can replace inthe formula:
[tex]m=\frac{1-(-2)}{-4-1}=-\frac{3}{5}[/tex]- Polynomial Functions -For each function, state the vertex; whether the vertex is a maximum or minimum point; the equation of the axis of symmetry and whether the function's graph is steeper than, flatter than, or the same shape as the graph of f(x)=x²
EXPLANATION
Given the function f(x) = (x-6)^2 + 1
[tex]\mathrm{The\: vertex\: of\: an\: up-down\: facing\: parabola\: of\: the\: form}\: y=ax^2+bx+c\: \mathrm{is}\: x_v=-\frac{b}{2a}[/tex]Expanding (x-6)^2 + 1 by applying the Perfect Square Formula:
[tex]=x^2-12x+37[/tex][tex]\mathrm{The\: parabola\: params\: are\colon}[/tex][tex]a=1,\: b=-12,\: c=37[/tex][tex]x_v=-\frac{b}{2a}[/tex][tex]x_v=-\frac{\left(-12\right)}{2\cdot\:1}[/tex][tex]\mathrm{Simplify}[/tex][tex]x_v=6[/tex][tex]y_v=6^2-12\cdot\: 6+37[/tex]Simplify:
[tex]y_v=1[/tex][tex]\mathrm{Therefore\: the\: parabola\: vertex\: is}[/tex][tex]\mleft(6,\: 1\mright)[/tex][tex]\mathrm{If}\: a<0,\: \mathrm{then\: the\: vertex\: is\: a\: maximum\: value}[/tex][tex]\mathrm{If}\: a>0,\: \mathrm{then\: the\: vertex\: is\: a\: minimum\: value}[/tex][tex]a=1[/tex][tex]\mathrm{Minimum}\mleft(6,\: 1\mright)[/tex][tex]\mathrm{For\: a\: parabola\: in\: standard\: form}\: y=ax^2+bx+c\: \mathrm{the\: axis\: of\: symmetry\: is\: the\: vertical\: line\: that\: goes\: through\: the\: vertex}\: x=\frac{-b}{2a}[/tex]Expanding (x-6)^2 + 1 by applying the Perfect Square Formula:
[tex]y=x^2-12x+37[/tex][tex]\mathrm{Axis\: of\: Symmetry\: for}\: y=ax^2+bx+c\: \mathrm{is}\: x=\frac{-b}{2a}[/tex][tex]a=1,\: b=-12[/tex][tex]x=\frac{-\left(-12\right)}{2\cdot\:1}[/tex][tex]\mathrm{Refine}[/tex]Axis of simmetry : x=6
The quadratic function has the same shape than the parent function y=x^2 because there is NOT a coefficient within x.
Divide 8 A) 3 B) 0) 7 16 D) 7. 32
Answer
3(1/2) or (7/2) or 3.5
Step-by-step Explanation
The question wants us to divide (7/8) by (1/4).
[tex]\frac{7}{8}\div\frac{1}{4}[/tex]The first step to solving division when it comes to fractions is to change the division sign to multiplication sign, which changes the fraction after the division sign to its inverse.
That is, in changing ÷ into ×, (1/4) changes to (4/1)
So,
[tex]\begin{gathered} \frac{7}{8}\div\frac{1}{4} \\ =\frac{7}{8}\times\frac{4}{1} \\ =\frac{28}{8} \\ =\frac{7}{2} \\ =3\frac{1}{2} \end{gathered}[/tex]Hope this Help!!!
QUESTION IS IN IMAGE!!! DONT NEED TO SHOW WORK JUST NEED ANSWER!!!!!
Since P is the center of the circle, then the segments PS and PQ are both radii of the circle and have the same measure. Then, the triangle PQS is an isosceles triangle, then, the measures of the angles PQS and QSP must be the same.
Since the sum of the internal angles of a triangle must be equal to 180º, then:
[tex]\begin{gathered} m\angle PQS+m\angle QSP+m\angle SPQ=180º \\ \Rightarrow m\angle PQS+m\angle PQS+113º=180º \\ \Rightarrow2m\angle PQS=180º-113º \\ \Rightarrow2m\angle PQS=67º \\ \Rightarrow m\angle PQS=\frac{67º}{2} \\ \Rightarrow m\angle PQS=33.5º \end{gathered}[/tex]The measure of RQS is the same as the measure of PQS.
Therefore, the answer is:
[tex]m\angle RQS=33.5º[/tex]Why would a person pay property taxes?
translate the inequality into a sentence. ten subtracted from the product of 9 and a number is at most -17. use x for unknown number
How does the graph of f(x) = (x + 7)^3 − 8 compare to the parent function g(x) = x^3
The ways in which the graph of f(x) = (x + 7)^3 − 8 compare to the parent function g(x) = x^3 are as follows:
Shifted 7 units to the left.Shifted 8 units down. What is a translation?In Mathematics, the translation a geometric figure to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image while translating a geometric figure down simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.
In Geometry, g(x + 7) simply means shifting a graph 7 units to the left while subtracting 8 from the function simply means moving the graph down.
In this context, we can reasonably infer and logically deduce that the parent function g(x) was shifted 7 units to the left and 8 units down.
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My Marjorie made for rates and 6 hours and 6 wreaths and 9 hours what is the constant of proportionality
The constant of proportionality is computed as follows:
[tex]k=\frac{\text{number of wreaths}}{\text{ number of hours}}[/tex]Assuming that 6 wreaths correspond to 9 hours, the constant of proportionality is:
[tex]k=\frac{6\text{ wreaths}}{9\text{ hours}}=\frac{2}{3}\frac{wreath}{hour}[/tex]The sides of triangle ABC are: AB = 6 cm,BC = 12 cm, AC = 10cm. K, M and P arethe midpoints of the sides AB, BC and AC respectivelyare the midpoints of the sides and the midpoints of the sides. Calculate the perimeter of KMP.
Answer: By inspecting the triangle we can come up with the following relationships, using the proportionality:
[tex]\begin{gathered} \frac{12}{10}=\frac{6}{x}\rightarrow(1) \\ \frac{12}{6}=\frac{6}{y}\rightarrow(2) \\ \frac{6}{12}=\frac{3}{z}\rightarrow(3) \end{gathered}[/tex]Solving the three equations, (1) (2) and (3) gives the answer for x,y,z which are the three sides of the smaller triangle, the steps are as follows:
[tex]\begin{gathered} x=KM=5 \\ y=MP=3 \\ z=KP=6 \end{gathered}[/tex]Therefore the perimeter is as follows:
[tex]\begin{gathered} P=x+y+x=5+3+6=14 \\ P_{(KMP)}=14 \end{gathered}[/tex]A rectangle has an area ofx² + 9x + 14Find the expressions that represent the dimensions of the rectangle.O (x - 2) and (x - 7)O (x + 3) and (x + 6)(x + 2) and (x + 7)O (x + 1) and (x + 14)
x² + 9x + 14
The area of a rectangle is the product of the length and the width.
Factorizing the expression
x² + 9x + 14 = x² + 7x + 2x + 14
= x(x + 7) + 2(x + 7)
= (x + 7)(x + 2)
Hence the dimensions are (x + 2) and (x + 7)
Translate into a number sentence7. Four less than seven is greater than zero
In order to translate the words into a number sentence, first let's translate each word or expression separately:
Four less than seven: "7 - 4"
Is greater than: ">"
Zero: "0"
Therefore the number sentence will be:
[tex]7-4>0[/tex]James types 50 words per minute. He spends 20 minutes typing his homework. What is the domain of this situation?
Answer:
You answer is B, from 0 to 20 and including 0 and 20.
Step-by-step explanation:
John sells plain cakes for $8 and decorated cakes for $12. On a particular day, John started with a total of 100 cakes, and sold all but 4. His sales that day totaled $800.He sold ___plain cakes and ____decorated cakes that day.
INFORMATION:
We know that:
- John sells plain cakes for $8 and decorated cakes for $12.
- On a particular day, John started with a total of 100 cakes, and sold all but 4.
- His sales that day totaled $800.
And we must find the number of plain cakes and decorated cakes that he sold that day.
STEP BY STEP EXPLANATION:
To find them, we can represent the situation using a system of equations
[tex]\begin{cases}x+y={100-4...(1)} \\ 8x+12y={800...(2)}\end{cases}[/tex]Where, x represents the number of plain cakes that he sold and y represents the number of decorated cakes that he sold.
Now, we must solve the system:
1. We must multiply the equation (1) by -8
[tex]\begin{gathered} -8(x+y)=-8(100-4) \\ -8x-8y=-768...(3) \end{gathered}[/tex]2. We must add equations (2) and (3)
[tex]\begin{gathered} 8x+12y=800 \\ -8x-8y=-768 \\ ---------- \\ 0x+4y=32 \\ \text{ Simplifying, } \\ 4y=32...(4) \end{gathered}[/tex]3. We must solve equation (4) for y
[tex]\begin{gathered} 4y=32 \\ y=\frac{32}{4} \\ y=8 \end{gathered}[/tex]4. We must replace the value of y in equation (1) and then solve it for x
[tex]\begin{gathered} x+8=100-4 \\ x=100-4-8 \\ x=88 \end{gathered}[/tex]So, we found that x = 88 and y = 8.
Finally, John sold 88 plain cakes and 8 decorated cakes.
ANSWER:
He sold 88 plain cakes and 8 decorated cakes that day.
Fill in the blank with a number to make the expression of perfect square.x^2-18x t
Answer:
[tex]81[/tex]Explanation:
Here, we want to write a figure that would make the given expression a perfect square
As a perfect square, we mean that:
[tex]ax^2+bx+c=(x+d)(x+d)=(x+d)^2[/tex]In this case, what we have to do is to divide the coefficient of x by 2, square it and write it
The coefficient of x is the number before x (we must consider its sign however)
Thus, we have the coefficient in this case as -18
Dividing this by 2 and squaring, we have:
[tex]\frac{-18}{2}=(-9)^2\text{ = 81}[/tex]Thus, we have:
[tex]x^2-18x+81=(x-9)(x-9)=(x-9)^2[/tex]
having trouble solving quadratic equations using factoring, examples are fine
Let's solve the quadratic equation using factorization:
x²-9x -22= 0
In order to solve using this method, we should beforehand factorize the polynomial:
The middle number is -9 and the last number is -22.
Factoring means we want something like
(x+_)(x+_)
Which numbers go in the blanks? Let's think about two numbers that add up to -9 and multiply together to -22...
These numbers will be -11 and 2:
-11 +2= 9
-11*2= -22
So the factorization is:
(x+2)*(x-11) = 0
That means:
x + 2 =0
and
x - 11 = 0
Solving the equations:
x= -2
x= 11
S= {-2, 11}
Is y-x+wz=5 linear? And not, why and if so, can you put it in slope intercept form?
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of this kind of equation is given by:
[tex]Ax+By=C[/tex]For the equation:
[tex]y-x+wz=5[/tex]We can conclude is not a linear equation since there is a product between two variables.
A game uses a single 6-sided die. To play the game, the die is rolled one time, with the following results: Even number = lose $91 or 3 = win $25 = win $12What is the expected value of the game?
The expected value of the game is $1.83.
