An item is regularly priced at $35.
Cost price of item = $35
Lena bought it on sale for 20% off the regular price
i.e. 20% of 35 is off in the item of cost $35
So, The amount Leena will paid = $35- 20% of 35
[tex]\begin{gathered} \text{Amount L}eena\text{ will pay =}35-20\text{ \%of35} \\ \text{Amount L}eena\text{ will pay}=35-\frac{20\times35}{100} \\ \text{Amount L}eena\text{ will pay}=35-7 \\ \text{Amount L}eena\text{ will pay}=28\text{ dollars} \end{gathered}[/tex]So, Leena will pay $28
Answer: $28
!!!!!!!???!??!???!!!???!!??!
!!!!!!!???!??!???!!!???!!??! is equal to 111111222122211122211221
PLS HELP Quadrilateral ABCD is located at A(-2, 2), B(-2, 4), C(2, 4), and D(2, 2). The quadrilateral is then transformed using the rule (x + 7, y - 1) to form the imagecoordinates of A', B', C', and D'? Describe what characteristics you would find if the corresponding vertices were connected with line segments
Given:
The coordinates of Quadrilateral ABCD is A(-2, 2), B(-2, 4), C(2, 4), and D(2, 2).
The quadrilateral is transformed with the rule,
[tex](x,y)\rightarrow\mleft(x+7,y-1\mright)[/tex]It becomes,
[tex]\begin{gathered} A\mleft(-2,2\mright)\rightarrow A^{\prime}\mleft(-2+7,2-1\mright)=A^{\prime}(5,1) \\ B\mleft(-2,4\mright)\rightarrow B^{\prime}(-2+7,4-1)=B^{\prime}(5,3) \\ C\mleft(2,4\mright)\rightarrow C^{\prime}(2+7,4-1)=C^{\prime}(9,3) \\ D(2,2)\rightarrow D^{\prime}(2+7,2-1)=D^{\prime}(9,1) \end{gathered}[/tex]Now, join the corresponding vertices of both the quadrilateral with the line segment.
After joining the vertices of the quadrilateral ABCD and A'B'C'D'. it gives the 3-dimensional shape- a rectangular prism.
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
How much should be invested now at an interest rate of 7% per year, compounded continuously, to have 2000 dollars in three years? Do not round intermediate computations, and round your answer to the nearest cent
Answer:
The amount that should be invested is $1621.16
Explanation:
The formula for continuous compound interest is:
[tex]A=Pe^{rt}[/tex]Where:
A is the amount of money after t years
P is the invested amount (what we want to find, in this case)
r is the rate of compounding in decimal
t i the amount of time compounding, in years
Then, in this case:
A = $2000
r = 0.07 (to convert percentage to decimal, we divide by 100: 7% / 100 = 0.07)
t = 3 years
Then:
[tex]2000=Pe^{0.07\cdot3}[/tex][tex]2000=Pe^{0.21}[/tex][tex]P=\frac{2000}{e^{0.21}}\approx1621.16849[/tex]To the nearest cent, P = $1621.16
Pic attached of problem. Answer must be with proper number of significant figures
Answer:
1310 cubic feet per minute
Explanation:
Let x represent the value in cubic feet per minute
Note that;
1 cubic meter per second = 2118.87997 cubic feet per minute
Given 0.618 cubic meter per second, to be able to solve for x, we'll go ahead and set the proportions as seen below;
[tex]\frac{1\text{ cubic meter per second}}{0.618\text{ cubic meter per second}}=\frac{2118.87997\text{ cubic f}eet\text{ per minute}}{x\text{ cubic f}eet\text{ per minute}}[/tex]Let's go ahead and cross-multiply;
[tex]\begin{gathered} x=2118.87997\times0.618 \\ x=1309.46782146cfm \\ x=1310\text{cfm (to 3 significant figures)} \end{gathered}[/tex]-87, -70, -27, -36,...a(n)= 17n - 10432nd term
We have the arithmetic progression given by
[tex]a_n=17n-104[/tex]if n = 1 we have the first term, n = 2 the second one and, so on, to find the 32nd term we just do n = 32, therefore
[tex]\begin{gathered} a_{32}=17\cdot32-104 \\ \\ a_{32}=544-104 \\ \\ a_{32}=440 \end{gathered}[/tex]The 32nd term is 440.
check the image I got y=-xsqrt3/3 but I want to double check
Answer:
To convert the polar equation to a rectangular equation .
Given polar equation is,
[tex]\theta=\frac{11\pi}{6}[/tex]we know the convertion of polar coordinates (r,theta) to rectangular equation as,
[tex]\begin{gathered} x=r\cos \theta \\ y=r\sin \theta \end{gathered}[/tex]we get,
[tex]\theta=\frac{11\pi}{6}=(2\pi-\frac{\pi}{6})[/tex]Substitute this in the above equation we get,
[tex]\begin{gathered} x=r\cos (2\pi-\frac{\pi}{6}) \\ \\ y=r\sin (2\pi-\frac{\pi}{6}) \end{gathered}[/tex]Solving we get,
[tex]\begin{gathered} x=r\cos (\frac{\pi}{6}) \\ \\ y=-r\sin (\frac{\pi}{6}) \end{gathered}[/tex]we get,
[tex]x=r(\frac{\sqrt[]{3}}{2})[/tex][tex]y=-r(\frac{1}{2})[/tex]Substitute r=-2y in x we get,
[tex]x=-2y(\frac{\sqrt[]{3}}{2})[/tex][tex]y=-\frac{x}{\sqrt[]{3}}[/tex][tex]y=-\frac{\sqrt[]{3}x}{3}[/tex]The required rectangular form of the given plar equation is,
[tex]y=-\frac{\sqrt[]{3}x}{3}[/tex]Identify the domain and range of the relation. Is the relation a function? Why or why not?
{(-3, 1), (0, 2), (1, 5), (2, 4), (2, 1)}
Domain: {-3, 0, 1, 2}
Range: {1, 2, 4, 5}
The relation is not a function because one of its x-values has two corresponding y-values.
What is the Domain and Range of a Relation?All the set of values of x in a relation are referred to as the range of a relation, while all the set of values of y in a relation are called the domain of the relation.
How to Determine if a Relation is a Function?If each of the x-values in a relation all have only one possible corresponding y-value, then the relation is a function.
Given the relation, {(-3, 1), (0, 2), (1, 5), (2, 4), (2, 1)}:
The domain is: {-3, 0, 1, 2}
The range is: {1, 2, 4, 5}
The relation has two y-values, 4 and 1, that corresponds to the x-value, 2. Therefore, it is not a function.
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The given relation is not a function because its x-values have two corresponding y-values. Domain: {-3, 0, 1, 2} and Range: {1, 2, 4, 5}
What is the Domain and Range of a Relation?The domain of a function is the set of all the possible input values that are valid for the given function.
The range of a function is the set of all the possible output values that are valid for the given function.
Given the relation as {(-3, 1), (0, 2), (1, 5), (2, 4), (2, 1)}
Therefore,
The domain will be: {-3, 0, 1, 2}
The range will be: {1, 2, 4, 5}
The relation has two y-values, 4 and 1, which corresponds to the x-value, 2.
The given relation is not a function because its x-values have two corresponding y-values. Domain: {-3, 0, 1, 2} and Range: {1, 2, 4, 5}
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个HS: Math II North Carolina High School Math II [M] (Prescripti8. Which statement is true?O OIf two figures are congruent, then they have the same shape but nOIf two figures are congruent, then they are similar.OIf two figures are similar, then they are congruent.OIf two figures are similar, then corresponding sides must be congru
For two triangles to be similar, it is enough if two angles of one triangle are equal to two angles of the other triangle.
If two figures are congruent, the corresponding sides must be equal and also the corresponding sides.
Therefore, the answer is:
If two figures are congruent, then they are similar
Betsy has $400 in a personal bank account, and then withdraws $14 perweek. Carlos has $25 in a personal bank account, and then deposits $61earned from babysitting each week. After how many weeks will they have thesame amount of money in the bank?
Given:
Betsy has $400 in a personal bank account, and then withdraws $14 per
week.
Carlos has $25 in a personal bank account, and then deposits $61
earned from babysitting each week.
Required:
The same amount will they have in the bank after how many week.
Explanation:
After 5 weeks Betsy will have $330 in her account.
Since
[tex]\begin{gathered} 14\times5=70 \\ \Rightarrow400-70=330 \end{gathered}[/tex]After 5 weeks Carlos will have $330 in her account.
Since
[tex]\begin{gathered} 61\times5=305 \\ \Rightarrow305+25=330 \end{gathered}[/tex]Hence, after 5 weeks they will have the same amount of money $330 in the bank.
Final Answer:
After 5 weeks they will have the same amount of money $330 in the bank.
Aldo gets paid biweekly. His gross pay for each pay period is $850.He has 16% withheld for taxes and 7% withheld for personal deductionsWhat is the amount of his annual net pay?a. $8,160b. $17,340c. $17,017d. $17,680
First, we compute the 16% of $850 and the 7% of $850:
[tex]\begin{gathered} 850(0.16)=136 \\ 850(0.07)=59.5 \end{gathered}[/tex]Then, after deductions, Aldo gets paid $850-$136-$59.5=$654.5 biweekly. Therefore, since he gets paid biweekly we multiply $654.5 per 26 and get that Aldo earns $17017 per year.
Answer: Option C.
I need help with my math
Answer:
The fourth choice: y+3 = 1(x+2); y= x-1
Explanation:
The point slope form of a linear equation is
[tex]y-y_0=m(x-x_0)[/tex]where (x0,y0) is a point on the line and m is the slope.
Now we first calculate the slope.
[tex]m=\frac{3-(-3)}{4-(-2)}=\frac{6}{6}=1[/tex]therefore, we have
[tex]y-y_0=1(x-x_0)[/tex]Now we use (x0, y0) = (-2, -3) and get
[tex]y-(-3)_{}=1(x-(-2))[/tex][tex]\boxed{y+3=1\mleft(x+2\mright)}[/tex]which is our equation in point-slope form.
Now, we convert the equation above into the slope-intercept form.
Subtracting 3 from both sides gives
[tex]y+3-3=x+2-3[/tex][tex]\boxed{y=x-1}[/tex]which is the equation in slope-intercept form.
Hence, the answer to the question is
[tex]y+3=1(x+2);y=x-1[/tex]which is the fourth option.
A teacher determines the linear equation y=12x + 40 best models the number of points a student should earn on a test, y, if the student studies for x hours. Which statement is true
Given the equation:
y = 12x + 40
Where x represents the number of hours and y represents the number of points the student should earn.
To find the correct statement substitute the number of hours and points given for x and y respectively. If the left hand side of the equation equals the right hand side then the statement is the true.
We have:
1. A student who studies for 3 hours should earn about 76 points.
x = 3
y = 76
Substitute 3 for x and 76 for y.
y = 12x + 40
76 = 12(3) + 40
76 = 36 + 40
76 = 76
This statement is true.
2.
A rectangular garden has a walkway around it. The area of the garden is 2(4.5x +1.5). Thecombined area of the garden and the walkway is 3.5(8x + 4). Find the area of the walkway aroundthe garden as the sum of two terms.The area of the walkway around the garden is(Simplify your answer. Use integers or decimals for any numbers in the expression.)
In this case, we'll have to carry out several steps to find the solution.
Step 01:
DataL
garden area = 2(4.5x +1.5)
garden + walkway area = 3.5(8x + 4)
walkway area = ?
Step 02:
walkway area:
walkway area = 3.5(8x + 4) - 2(4.5x +1.5)
= 28x + 14 - 9x - 3
= 19x + 11
The answer is:
The area of the walkway around the garden is 19x + 11
21/x=48/96. 70/b=20/80. 50/20=x/72
In summary, the respective values of the unknown variables in the equations are 42, 280, and 1800.
An unsharpened, round pencil is in the shape of a right circular cylinder. For one such pencil, the radius is 4.6 mm and the length is 167.7 mm. Find the volume of the pencil. Round your answer to the nearest whole number. Do not type the units in the space below. (Be sure to use the pi button on your calculator to do the calculation.)
The volume of the cylindrical pencil to the nearest whole number is 11149cubic millimeters
What is a cylinder?A cylinder is a 3-D shape consisting of two circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder.
The volume of a cylinder is πr^2h
r is the radius, h is the height or length of the cylinder
putting the values of r and h in the formula and π=3.142
V= 3.142×4.6×4.6×167.7
there the volume of the cylindrical pencil is 11149cubic millimeters ( nearest whole number)
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37. The average height of American adult males is 177 cm, with a standard deviation of 7.4 cm. Meanwhile, the average height of Indian males is 165 cm, with a standard deviation of 6.7 cm. Which is taller relative to his nationality, a 173-cm American man or a 150-cm Indian man? The American man The Indian man
ANSWER
The American man
EXPLANATION
To find the man that is taller relative to his nationality, we have to find the z-score of both men. The z-score represents how far away from the mean that a data value is.
To find the z-score, apply the formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]where x = data value; μ = mean; σ = standard deviation
For the American man, the z-score is:
[tex]\begin{gathered} z=\frac{173-177}{7.4} \\ z=\frac{-4}{7.4} \\ z=-0.541 \end{gathered}[/tex]For the Indian man, the z-score is:
[tex]\begin{gathered} z=\frac{150-165}{6.7} \\ z=\frac{-15}{6.7} \\ z=-2.239 \end{gathered}[/tex]We see that the American man has a height with a z-score higher than that of the Indian man.
This means that the American man is taller than the Indian man relative to their nationalities.
What kind of polyhedron can be assembled from this net?
It could be assembled a rectangular prism
and
solve. 45÷n=5 problem
Which system of linear equations could be used to determine the price of each book
Answer:
Let the price of the maths book be m and price of the novel book be n
Given that,
Total cost of the books is $54
The price of math book is $8 more than 3 times the price of novel book.
we get,
The system of equation as,
[tex]\begin{gathered} m+n=54 \\ m=8+3n \end{gathered}[/tex]Hence the system of equation to determine the price of the maths and novel book is,
[tex]\begin{gathered} m+n=54 \\ m=8+3n \end{gathered}[/tex]each expression below.Click on "Undefined" as needed.6 = 0Í00Undefined=x 6?
It is required to find:
[tex]\frac{4}{0}[/tex]Note that any number divided by zero is undefined.
This implies that division 4/0 is undefined.
The same goes for:
[tex]6\div0[/tex]The correct answer is undefined for both divisions.
Write the equation of the function in the graph.. Please show all of your work so i can understand
The vertex form of a parabola is:
[tex]y=a(x-h)^2+k[/tex]where (h, k) is the vertex of the parabola and a is some constant.
From the graph, the vertex is located at (1, 4), that is, h = 1 and k = 4.
Substituting with these values and the point (0, 3), we get:
[tex]\begin{gathered} 3=a(0-1)^2+4 \\ 3-4=a(-1)^2 \\ -1=a\cdot1 \\ -\frac{1}{1}=a \\ -1=a \end{gathered}[/tex]Then, the equation of the function is:
[tex]\begin{gathered} y=-1(x-1)^2+4 \\ y=-(x-1)^2+4 \end{gathered}[/tex]The r value of -0.89 suggests that the independent variable ________, the dependent _________
We have that a correlation coefficient shows us how related is the dependent variable to the behavior of the independent variable.
MagnitudA correlation coefficient of ±1 means that the dependent variable moves as the independent variables moves too.
0 means that the dependent variable can move or not no matter how the independent variable changes.
As ±0.89 is near to ±1, we can say that in this case dependent and independent variable are related.
SignWhen the coeffitcient of correlation is negative it means that if the independent variable goes up, the dependent goes down, and visceversa.
In this case, while one decreases the other increases.
Answer: as the independent value increases, the dependent value decreases.
(1.2 x 10^7)(2.2 x 10^-3)
The value of the expression is:
2.64 x 10² or 26400
Step - by - Step Explanation
From the question;
(1.2 x 10⁷ )(2.2 x 10⁻³)
To sim plify the expression above, we will multiply the decimal part and then apply indices to the exponent.
That is;
[tex]1.2\times2.2\times10^{7-3}[/tex][tex]=2.64\times10^2[/tex]Or
=26400
Which subsets of numbers does belong to?
Natural numbers are just counting numbers. It doesn't include a negative number. Integers include both positive and negative whole numbers. rational numbers are fractions that can be expressed as two integers. We can have - 8/1 = - 8
Finally, real numbers is any positive or negative number. It includes integers and rational numbers. Therefore, the subset that contains - 8 would be
real, rational and integer numbers
I need help with this problem it says to find the area of each shaded sector and round to the hundredth place
Answer:
1330.81 square feet
Explanation:
In the circle, there are two unshaded sectors with central angles 26° and 90°.
The sum of the central angles = 360°.
Therefore, the sum of the central angle of the shaded sectors will be:
[tex]360\degree-(26\degree+90\degree)=244\degree[/tex]The area of a sector is calculated using the formula:
[tex]A=\frac{\theta}{360\degree}\times\pi r^2\text{ where }\begin{cases}Central\; Angle,\theta=244\degree \\ Radius,r,HK=25ft\end{cases}[/tex]Substitute the values into the formula:
[tex]\begin{gathered} A=\frac{244}{360}\times\pi\times25^2 \\ =1330.8136 \\ \approx1330.81\; ft^2 \end{gathered}[/tex]The area of the shaded sector is 1330.81 square feet (rounded to the hundredth place).
Jason assembles bicycles for the Comer Bike Shop.He can assemble three racing bikes in five hours but itonly takes two hours to assemble six beach cruisers.Match each type of bicycle to the graph that representsthe average number of hours needed to assemble it. (2.)
we have that
He can assemble three racing bikes in five hours-----> ordered pair (5,3)
takes two hours to assemble six beach cruisers -----> ordered pair (2,6)
therefore
the graph of racing bikes is the graph at the left -----> y=(3/5)x
the graph of beach cruisers is the graph at the right-----> y=3x
What is the product of 8i and 4i
The product of given complex number that is 8i and 4i will be -32 by the properties of complex number that states i*i will be -1 and 8*4 will be 32.
What is complex number?Every complex number can be expressed in the form a + bi, where a and b are real numbers. A complex number is an element of a number system that extends the real numbers with a specific element denoted I also known as the imaginary unit, and satisfying the equation i²=-1.
What are the property of complex number?Commutative, Associative, Distributive Properties: All complex numbers are commutative and associative under addition and multiplication, and multiplication distributes over addition.
Here,
The product of 8i*4i=-32
as 8*4=32
and i²=-1
32*-1=-32
Due to the properties of complex numbers, which state that i*i will be -1 and 8*4 will be 32, the product of the given complex number, which is 8i and 4i, will be -32.
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“John is buying carpet for his house. He pays $1.30 per square foot for the first 1000 square feet. He pays $1.00 peradditional square foot after 1000 square feet.Part A: Write an equation for the total price when John buys less than 1000 square feet of carpet. Let c representthe amount of carpet needed in square feet, and p represent the total price in dollars.Enter vour equation in the first response boxPart B: John calculates that the total price will be $1500. How many square feet of carpet will he buy?Place your answer in the second response box”
EXPLANATION:
Given:
We are told that John pays $1.30 per square foot for the first 1000 square feet of carpet he buys. Then he pays $1.00 per additional square foot after the first 1000 square feet.
Required:
We are required to write an equation to represent the total price when he buys less than 1000 square feet.
Step-by-step solution;
Take note that he pays $1.30 per square foot for the first 1000 square feet. The amount spent, that is the price would be represented by p while, c would represent the amount of carpet to be bought.
Hence, for buying less than 1000 square feet;
[tex]p=1.30c[/tex]Next we note that John calculates that the total price would be $1500.
If John pays the amount of $1.30 for the first 1000 square feet, then he would have paid;
[tex]p=1.30(1000)[/tex][tex]p=1300[/tex]However, we are told that John calculates a total of $1500. This simply means that he will buy more than 1000 square feet of carpet.
He is going to spend an extra $200 (that is 1500 minus 1300). The cost of any extra foot after the first 1000 is $1.00. That means;
[tex]Extra\text{ }carpet=\frac{200}{1.00}[/tex][tex]Extra\text{ }carpet=200ft^2[/tex]That means John would be paying the sum of $1500 to buy 1,200 square feet of carpet.
ANSWER:
[tex]\begin{gathered} Part\text{ }A: \\ p=1.30c \end{gathered}[/tex][tex]\begin{gathered} Part\text{ }B: \\ 1200ft^2 \end{gathered}[/tex]Enter the explicit and recursive equations for the sequence 2, -4, -10, -16 Please HELP
The explicit and recursive forms of the arithmetic sequence are f(n) = 2 - 6 · (n - 1) and f(n) = f(n - 1) - 6, f(1) = 2, respectively.
How to derive equations for the elements of an arithmetic sequence
In this problem we need to find the explicit and recursive equations for an arithmetic sequence, whose definitions are described below:
Explicit form
f(n) = a + r · (n - 1)
Recursive form
f(n) = f(n - 1) + r, f(1) = a
Where:
a - First element of the sequence.r - Common difference.n - Index of the n-th element of the sequence.If we know that a = 2, r = - 6, then the explicit and recursive forms of the sequence are:
Explicit form
f(n) = 2 - 6 · (n - 1)
Recursive form
f(n) = f(n - 1) - 6, f(1) = 2
The first four elements of the sequence generated by the formulas are 2, - 4, - 10, - 16.
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