Given Data:
The sale price of the jeans is: s=$30
The discount is: d=20%
The expression to calculate the original price is,
[tex]s=P\times\frac{d}{100}[/tex]Here P represents the original price.
[tex]\begin{gathered} 30=P\times\frac{20}{100} \\ P=30\times\frac{100}{20} \\ =30\times5 \\ P=150 \end{gathered}[/tex]Thus, the original price of the jeans is $150.
find the rate of the discount of a $12 99 novel on sale for $5.50
In order to find the rate of discount, calculate what is the associated percentage of 5.50 related to 12.99, just as follow:
(5.50/12.99)(100) = 42.34
5.50 is the 42.34% of 12.99.
Hence, the discount was 100% - 42.34% = 57.65%
Set A is the set of all whole numbers to 20. Set B is the set of all odd integers between 8 and 18. How many numbers do the two sets have in common?
ANSWER
5 numbers they have in common
EXPLANATION
Set A has all whole numbers to 20:
[tex]A\colon1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20[/tex]Set B has only odd integer between 8 and 18:
[tex]B\colon9,11,13,15,17[/tex]We can see that set B is inside set A, because it has whole numbers that are less than 20, so the amount of numbers they have in common is all of set B: 5 numbers.
I need a tutor for algebra
Answer:
0.40
Explanation:
From the question, we're given that;
* 8% of the members run only long-distance, so the probability that a member of the team will run only long-distance, P(A) = 8/100 = 0.08
* 12% compete only in non-running events, so the probability that a member will compete only in non-running events, P(B) = 12/100 = 0.12
* 32% are sprinters only, so the probability that a member is a sprinter only P(C) = 32/100 = 0.32
We're asked in the question to determine the probability that a randomly chosen team member runs only long-distance or competes only in sprint events, since these events cannot occur at the same time, we can use the below formula to solve as shown below;
[tex]P(\text{A or C) = P(A) + P(C)}[/tex]P(A or C) = 0.08 + 0.32 = 0.40
A boat travels 82 km on a 160 degree course. Find the distances it travel south and east, respectively
A boat travels 82 km on a 160-degree course. Find the distances it travels south and east, respectively
see the attached figure to better understand the problem
step 1
Find out the East's distance (dx)
we have that
cos(20)=dx/82
dx=82*cos(20)
dx=77.05 Kmstep 2
Find out the South's distance (dy)
sin(20)=dy/82
dy=82*sin(20)
dy=28.05 KmH.O.T. FOCUS ON HIGHER ORDER THINKING 20. Communicate Mathematical Ideas Explain how to graph the inequality 8≥ y.
Given the inequality:
8 ≥ y
Let's graph the inequality.
To graph the inequality, take the following steps:
Step 1.
Rewrite the inequality for y and slip the inequality.
[tex]y\le8[/tex]Step 2.
Draw a solid horizontal line at y = 8.
Since the y is less than or equal to 8, shade the region below the boundary line.
Thus, we have the graph of the inequality below:
Find the coordinates of the other endpoint of a segment with the given endpoint and Midpoint M.T(-8,-1)M(0,3)
If we have 2 endpoints (x1, y1) and (x2, y2), the coordinates of the midpoint will be:
[tex]\begin{gathered} x=\frac{x_1+x_2}{2} \\ y=\frac{y_1+y_2}{2} \end{gathered}[/tex]Now, we know the coordinates of one endpoint (x1, y1) equal to (-8, -1) and the midpoint (x, y) equal to (0,3), so we can replace those values and solve for x2 and y2.
Then, for the x-coordinate, we get:
[tex]\begin{gathered} 0=\frac{-8+x_2}{2} \\ 0\cdot2=-8+x_2 \\ 0=-8+x_2 \\ 0+8=-8+x_2+8 \\ 8=x_2 \end{gathered}[/tex]At the same way, for the y-coordinate, we get:
[tex]\begin{gathered} 3=\frac{-1+y_2}{2} \\ 3\cdot2=-1+y_2 \\ 6=-1+y_2 \\ 6+1=-1+y_2+1 \\ 7=y_2 \end{gathered}[/tex]Therefore, the coordinates of the other endpoint are (8, 7)
Answer: (8, 7)
A delivery company uses robot dogs to deliver packages in anoffice building. The graph shows how long a robot dog can operatetor each hour its battery is charged.Pickany two points on the line. Find the slope of the line betweenInesetwo points. Can you find another pair of points on the linehat gives you a different slope?
Given:
Let the two points from the graph are
[tex](1,30)\text{ and (}2,60)[/tex][tex]\begin{gathered} \text{Slope}=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{60-30}{2-1} \\ =30 \end{gathered}[/tex]No, its impossible to find the another pair of points to give a different slope.
Only one slope from a line.
Describe the two different methods shown for writing the complex expression in standard form. Which method do you prefer? Explain
The first method simlpy executes the distributive property of multiplication over addition, and the definition of the imaginary number, i.
The second method factored out 4i first then perform the operation on the terms left inside the parenthesis , then executes the distributive property of multiplication over addition and the definition of the imaginary number, i.
I prefer the first method . It's simple and straight forward,
The area of the triangle is 330 square feet.The height of the triangle is ___
Answer:
22 feet
Explanation:
The area of a triangle can be calculated using the following equation:
[tex]A=\frac{b\times h}{2}[/tex]Where b is the base and h is the height.
We know that the area is 330 square feet and the base is 30 ft, so we can replace these values to get:
[tex]330=\frac{30\times h}{2}[/tex]Now, we can solve the equation for h. First, multiply both sides by 2:
[tex]\begin{gathered} 2\times330=2\times\frac{30\times h}{2} \\ 660=30\times h \end{gathered}[/tex]Then, divide both sides by 30:
[tex]\begin{gathered} \frac{660}{30}=\frac{30\times h}{30} \\ 22=h \end{gathered}[/tex]Therefore, the height of the triangle is 22 feet.
Find the due date of a note dated October 24, 2018 for 2 months.
2 months after october 24th 2018 will be:
24th December 2018 which was a monday.
Add 3 days of grace period will give the due date to be 27th December 2018.
When 6 is subtracted from the 5 times of a number the sum becomes 9 find the number
Let that unknown number be x
⇒Mathematically this is written as
[tex]5(x)-6=9\\5x-6=9\\5x=9+6\\5x=15\\\frac{5x}{5} =\frac{15}{5} \\x=3[/tex]
This just means that the unknown number is 3
GOODLUCK!!
Answer:
nine plus six
= 15 ÷ five
answer Three
Question 19 of 25What are the more appropriate measures of center and spread for this dataset?000:oooo000000000Select two choices: one for the center and one for the spread.I A: Better measure of spread: interquartile range (IQR)O B. Better measure of center: medianI c. Better measure of spread: standard deviationD. Better measure of center: mean
Measures of center:
The mean is usually the better measure of center, however, this measure is greatly affected by extreme values (very low or very high values). If the data set is strongly skewed or has extreme values, the mean will be affected and won't reflect the true center of the said data set.
The median separates the data set in halves and is not affected by extreme values.
Given that this data set is strongly skewed to the left, the best measure of center will be the median.
Measures of dispersion:
The standard deviation is usually the most preferable measure of dispersion. But, one of
Find the perimeter and area of the polygon with given vertices
Let's begin by listing out the information given to us:
[tex]\begin{gathered} A(-3,3),B(-3,-1),C(4,-1),D(4,3) \\ AB=3-(-1)=3+1=4_{} \\ BC=|-3-4|=|-7|=7 \\ CD=|-1-3|=|-4|=4 \\ AD=|-3-4|=|-7|=7 \\ \\ Perimeter=2(l+w)=2(7+4)_{}=2(11)=22 \\ Perimeter=22unit \\ \\ Area=lw=7\cdot4=28unit^2 \\ Area=28unit^2 \end{gathered}[/tex]14.select the correct answerwhat is the sum of [tex]9.72 \times {10}^{8 \: and} 1.93 \times {10}^{7} [/tex]Answer options[tex]9.913 \times {10}^{7} [/tex][tex]9.913 \times 10 {}^{8} [/tex][tex]1.165 \times {10}^{8} [/tex][tex]1.165 \times {10}^{9} [/tex]
9.72 x 10⁸ + 1.93 x 10⁷
= 972 000000 + 193 00000
=991 300 000
= 9.913 x 10⁸
the length of the rectangle is two feet less than 3 times the width.if the area is 65ft^2.find the dimension.
Given:
The area of the rectangle, A=65ft^2.
Let l be the length of the rectangle and w be the width of the rectangle.
It is given that the length of the rectangle is two feet less than 3 times the width.
Hence, the expression for the length of the rectangle is,
[tex]l=3w-2\text{ ----(A)}[/tex]Now, the expression for the area of the rectangle can be written as,
[tex]\begin{gathered} A=\text{length}\times width \\ A=l\times w \\ A=(3w-2)\times w \\ A=3w^2-2w \end{gathered}[/tex]Since A=65ft^2, we get
[tex]\begin{gathered} 65=3w^2-2w \\ 3w^2-2w-65=0\text{ ---(1)} \end{gathered}[/tex]Equation (1) is similar to a quadratic equation given by,
[tex]aw^2+bw+c=0\text{ ---(2)}[/tex]Comparing equations (1) and (2), we get a=3, b=-2 and c=-65.
Using discriminant method, the solution of equation (1) is,
[tex]\begin{gathered} w=\frac{-b\pm\sqrt[]{^{}b^2-4ac}}{2a} \\ w=\frac{-(-2)\pm\sqrt[]{(-2)^2-4\times3\times(-65)}}{2\times3} \\ w=\frac{2\pm\sqrt[]{4^{}+780}}{2\times3} \\ w=\frac{2\pm\sqrt[]{784}}{6} \\ w=\frac{2\pm28}{6} \end{gathered}[/tex]Since w cannot be negative, we consider only the positive value for w. Hence,
[tex]\begin{gathered} w=\frac{2+28}{6} \\ w=\frac{30}{6} \\ w=5\text{ ft} \end{gathered}[/tex]Now, put w=5 in equation (A) to obtain the value of l.
[tex]\begin{gathered} l=3w-2 \\ =3\times5-2 \\ =15-2 \\ =13ft \end{gathered}[/tex]Therefore, the length of the rectangle is l=13 ft and the width is w=5 ft.
I need helps this is an assignment dealing with kites
In a kite, there is one pair of congurent angles. So
[tex]3x-22=x+52[/tex]Solve the equation for x.
[tex]\begin{gathered} 3x-22=x+52 \\ 3x-x=52+22 \\ x=\frac{74}{2} \\ =37 \end{gathered}[/tex]So value of x is 37.
Answer: 37
I need to write this equation that has a infinite number of solutions
2 (8x+4) -x =
Simplify the equation:
2(8x)+2(4) -x
16x +8 -x
15x +8
If both sides of the equation are equal o equivalent, there is an infinite number of solutions.
2 (8x+4) -x = 15x + 8
Find the slope of the line through the given points . If the slope of the line is undefined state so (13,1) and (1,4)
ANSWER:
A. The slope of the line is -1/4
STEP-BY-STEP EXPLANATION:
Given:
(13,1) and (1,4)
The slope can be calculated using the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]We substitute each value and calculate the slope:
[tex]m=\frac{1-4}{13-1}=\frac{-3}{12}=-\frac{1}{4}[/tex]Therefore, the correct answer would be:
A. The slope of the line is -1/4
Natural Logs Propertydo not include any spaces when trying to type in your answer if you have an exponent use ^
Given:
[tex]ln\mleft(e^{2x}\mright)+ln\mleft(e^x\mright)[/tex]To simplify:
Applying the log rule,
[tex]\log _c\mleft(a\mright)+\log _c\mleft(b\mright)=\log _c\mleft(ab\mright)[/tex]We get,
[tex]\begin{gathered} ln(e^{2x})+ln(e^x)=\ln (e^{2x}\cdot e^x) \\ =\ln (e^{3x}) \\ =3x(\ln e) \\ =3x(1) \\ =3x \end{gathered}[/tex]Hence, the answer is 3x.
1
P(7,-3); y=x+2
Write an equation for the line in point-slope form.
(Simplify your answer. Use integers or fractions for any numbers in the equation.)
The equation of line in point-slope form is Y + 3 = 1(X - 7).
What is point-slope form?
The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form.
(Y-Y1)=m(X-X1) is the point-slope form of the equation.
Here the given equation of line is y = x + 2 and the point is (X1, Y1) = (7, -3).
Compare this equation with y = mx + c, which is point slope form of the line.
Where, m is the slope and c is the y - intercept.
So, m = 1 and c = 2.
Now plug m = 1 and (x1, y1) = (7, -3) in the equation (Y-Y1)=m(X-X1),
(Y - (-3)) = 1(X - 7)
Y + 3 = 1(X - 7)
Therefore, the equation for the line y = x + 2 in point - slope form is Y + 3 = 1(X - 7).
To know more about the Point slope form, of the equation of line click on the link
https://brainly.com/question/24907633
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7. Flora has a square fountain. It is a square fountain and she wants to place a walkway around it. The square fountain measures 4 meters on each side. The walkway will be one meter wide around the fountain.. a. Find the area of the walkway. b. One bag of colored stones covers 1 square meter, how many bags of stones will be needed to cover the entire walkway around the fountain? C. A bag of colored stones cost $24.99. How much will it cost to fill in he walkway with colored stones?
Answer:
[tex]\begin{gathered} a)20m^2 \\ b)\text{ 20 bags of colored stones} \\ c)\text{ \$499.8} \end{gathered}[/tex]Step-by-step explanation:
Since the square fountain measures 4 meters on each side and the walkway will be one meter wide, let's make a diagram to see the situation:
Then, to calculate the area of the walkway (green shaded region)
[tex]\begin{gathered} A_{total}=b\cdot h \\ A_{total}=6\cdot6=36m^2 \\ A_{founta\in}=4\cdot4=16m^2 \end{gathered}[/tex][tex]\begin{gathered} A_{walkway}=A_{total}-A_{fountain} \\ A_{walkway}=36-16=20m^2 \end{gathered}[/tex]Now, how many colored stones will be needed if one bag covers 1 square meter:
There are 20 square meters on the walkway, then will be needed 20 bags of colored stones.
A bag of colored stones costs $24.99, then multiply 20 by $24.99:
[tex]20\cdot24.99=\text{ \$499.8}[/tex]Find the rate of change of each linear function 1. y = x - 7
Rate of change = 1
Explanations:The given linear function is:
y = x - 7
The rate of change of the function is gotten by finding the derivative (dy/dx) of the function
dy/dx = 1
The rate of change = 1
Persevere with Problems Analyze how the circumference of a circle would change if the diameter was doubled. Provide an example to support your explanation.
Circumference of a circle . Girth
Circumference C= π•D
Then if D'=2D
New Circumference C'= π•2D = 2•π•D
Circumference is doubled, if diameter is doubled
EXAMPLE
Suppose D= 5 cm
Then C= π•5 = 15.70
If D'= 2•5=10 cm
Then C'= π•10= 31.415
Now divide C'/C = 31.415/15.70 = 2.00
A triangle is graphed in this coordinate plane. what is the area of this triangle in square units A.9B.12C.18D.36
Answer
Option C is correct.
The area of the triangle = 18 square units
Explanation
The area of a triangle is given as
Area of the triangle = ½ × B × H
where
B = Base of the triangle = 6 units (From -3 t
Which of the following are solutions to the inequality below? Select all that apply.
The first step to solving this problem is to put the variable on one side. Thus, you must move 7 to the right side to make [tex]\frac{f}{25} \leq -3[/tex]
Next, you must multiply the 25 to the right side to isolate the variable
You get [tex]f \leq -75[/tex]
With this explained, the answer would be the second option (f=-75)
Hope this helped :)
3|x -1| > 9Group of answer choicesx> 4 or x < -2x > 4x < 4 or x > -2x > 7 or x < -5
Answer:
[tex]x\text{ > 4 or x < -2}[/tex]Explanation:
Here, we want to get the correct x values
We have this as follows:
[tex]\begin{gathered} 3|x-1|\text{ > 9} \\ =\text{ 3(x-1) > 9} \\ 3x-3\text{ > 9} \\ 3x\text{ > 9 + 3} \\ 3x\text{ > 12} \\ x\text{ > 12/3} \\ x\text{ > 4} \\ \\ OR \\ \\ -3(x-1)\text{ > 9} \\ -3x\text{ + 3 > 9} \\ -3x\text{ > 9-3} \\ -3x\text{ > 6} \\ x\text{ < 6/-3} \\ x\text{ < -2} \end{gathered}[/tex]A bag of tokens contains 55 red, 44 green, and 55 blue tokens. What is the probability that a randomly selected token is not red? Enter your answer as a fraction.
Explanation
In the bag of tokens, we are told 55 red, 44 green, and 55 blue tokens. Therefore, the total number of tokens in the bag is
[tex]55+44+55=154[/tex]Hence to find the probability that a randomly selected token is not red becomes;
[tex]Pr(not\text{ red black})=\frac{n(green)+n(blue)}{n(tokens)}=\frac{44+55}{154}=\frac{99}{154}=\frac{9}{14}[/tex]Answer: 9/14
determine the solution,if it exists,for each system of linear equation. Verify your solution on the coordinate plane. x + 3 = y 3x + 4y = 7
then
[tex]\begin{gathered} 3\mleft(y-3\mright)+4y=7 \\ 3y-9+4y=7 \\ 7y-9=7 \\ 7y-9+9=7+9 \\ 7y=16 \\ \frac{7y}{7}=\frac{16}{7} \\ y=\frac{16}{7} \end{gathered}[/tex]replacing in x
[tex]undefined[/tex]Which of the following shows the division problem down below
Question:
Solution:
Synthetic division is a quick method of dividing polynomials; it can be used when the divisor is of the form x-c. In synthetic division, we write only the essential parts of the long division. Notice that the long division of the given problem is written as:
thus, the synthetic division of the given problem would be:
Writing 6 instead of -6 allows us to add instead of subtracting. We can conclude that the correct answer is:
A.
To the nearest whole foot, how many feet would it be to walk diagonally across this field? A. 42B. 50C. 65D. None of the above
