a.) Discount = 30%
Percent of the original price on sale = 100% - 30% = 70%
b.) Original price = $500
Discount = 30%
Dollar amount of the discount = $500 x (30% / 100%) = $500 x 0.30 = $150
c.) The sale price = $500 - (Discount Amount) = $500 - $150 = $350
The cost in dollars for removing p percent of pollutants from a river in Smith County is Find the cost of removing 20%Cost for removing 20%, in dollars is = _________Find the cost of removing half of the pollutants. Cost for removing half, in dollars is = __________ Find the cost of removing all but 5% of the pollutants. Cost for removing all but 5%, in dollars, is = _________
Given the cost of removing p percent of pollutant from a river is Smith County in dollars as
[tex]C(p)=\frac{71000p}{100-p}[/tex]To find the cost of removing the pollutant for a particular percentage, we will substitute the value of the pollutant in the cost formula above.
Thus, for p equal to 20%
[tex]\begin{gathered} C(20)=\frac{71000\times20}{100-20}=\frac{1420000}{80} \\ C(20)=\text{ \$}17,750 \end{gathered}[/tex]Hence, the cost of removing 20% of the pollutant is $17,750
The cost of removing half of the pollutants is equivalent to the cost of removing 50%, thus, p in percentage is 50%
[tex]\begin{gathered} C(50)=\frac{71000\times50}{100-50}=\frac{3550000}{50} \\ C(50)=\text{ \$}71,000 \end{gathered}[/tex]Hence, the cost of removing half of the pollutants is $71,000
The cost of removing all but 5% of the pollutant is equivalent to the cost of removing 95% of the pollutants. Hence, p is 95
[tex]\begin{gathered} C(95)=\frac{71000\times95}{100-95}=\frac{6745000}{5} \\ C(95)=\text{ \$}1,349,000 \end{gathered}[/tex]Hence, the cost of removing all but 5% of the pollutants is $1,349,000
Make a scatter plot of the data. Scale the x-axis by ones and the y-axis by twos.
Answer
Age of Car in years is represented as x
Avg. Miles per Gallon is represented as y
y = 0.97x + 1.214
Correlation Coefficient = 0.673
Explanation
Age of Car in years is represented as x
Avg. Miles per Gallon is represented as y
The datapoints are fed into a calculator and plotted with the datapoints also processed according to some formulas that'll be provided here
The first figure contains the data points and the regression data processed to be used to calaculate the required parameters.
The second attached image shows the plotted data and the line of best fit and the equation that best represents the relationship between the two parameters.
Then the last image shows the parameters used to calculate the equation of correlation and the correlation coefficient.
Hope this Helps!!!
What are the first two steps to graph y=4/5x + 3?
The function y=4/5x + 3 represents a linear equation.
Let's find some points.
Where x=1, then:
[tex]y=\frac{4}{5}x+3[/tex][tex]y=\frac{4}{5}(1)+3[/tex][tex]y=\frac{19}{5}[/tex]We find the point (1,19/5).
Where 19/5 = 3.8
Now, lest find the x-intercept and y-intercept.
To find the x-intercept, set y=0
[tex]0=\frac{4}{5}x+3[/tex]Solve for x:
[tex]-3=\frac{4}{5}x[/tex][tex]5\cdot-3=4x[/tex][tex]-15=4x[/tex]where
[tex]x=-\frac{15}{4}=-3.75[/tex]So, the x-intercept is the point (-15/4, 0)
To find the y-intercept, set x=0. Then:
[tex]y=\frac{4}{5}x+3[/tex][tex]y=\frac{4}{5}(0)+3[/tex][tex]y=3[/tex]So, the y-intercept is the point (0,3)
Use this information to graph the line.
Hence, the graph for y=4/5x + 3 is given by:
Find the principal which amounts to #5,000 at simple interestin 5 years at 2% per annum
To answer this we have to apply the simple interest formula:
I =P x r x t
Where:
I= interest
P= Principal
R= Interest rate ( in decimal form)
t = time (years)
Replacing with the values given:
Interest= I
Principal = ?
Interest rate = 2/100 =0.02
time= 5 years
I = P x 0.02 x 5
I= 0.1P
Amount= P+I
A = P+0.1P
5,000= P+0.1P
5,000= 1.1P
5,000/1.1 =P
4,545.45 =P
Fill in the gaps to factorise the expression.
2x^2+7x+3
The factorised form of the expression given in the task content is; 2x² + 7x + 3 is; (2x + 1) (x + 1).
Factorisation of quadratic expressions.It follows from the task content that the factorised form of the expression is to be determined.
On this note, the factorised form of the expression is as follows;
2x² + 6x + x + 3.
By grouping terms; we have;
(2x² + 6x) + (x + 3).
Factorise two terms each at as follows;
2x(x + 1) + 1(x+3)
(2x + 1) (x + 1)
Therefore, the factorised form of the expression; 2x² + 7x + 3 is; (2x + 1) (x + 1).
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A sprinkler rotates back and forth from point A to point B. The water reaches 8 meters from the base of the sprinkler.What is the length of the arc AB, rounded to the nearest tenth of a meter? Use 3.14 for [tex]\pi[/tex]
20.9m
1) Since we want to know the length of that arc, and the angle is written in degrees, let's use a formula to find this out:
[tex]\begin{gathered} l=\frac{\alpha}{360}\cdot2\pi R \\ l=\frac{150}{360}\cdot2(3.14)\cdot8 \\ l=20.93\approx20.9m \end{gathered}[/tex]2) Rounding off to the nearest tenth we have the length of this arc is 20.9, m
A consumer group feels that the average person spends less than 5 dollars each month on tooth care products. They decide to use hypothesis testing to see if they are right. Which of the following would be the alternative hypothesis?
The alternative hypothesis will be Ha : u < 5
What is an alternative hypothesis?An alternative hypothesis simply means the proposed explanation in the hypothesis test. It is used to demonstrate a particular condition.
In this case, the consumer group feels that the average person spends less than 5 dollars each month on tooth care products.
Therefore, the alternative hypothesis will be that the average is less than 5.
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Little help here please
Step-by-step explanation:
as the intersection angles of parallel lines with a third line are the same for both parallel lines (and then vice versa for the other pair of parallel lines), we have a lot of equal angles here.
not to forget : the sum of all angles around a single point on one side of a line is always 180°.
51 = (y + z)
(6z + 9y) = x
x + (x + z) = x + 51 = 180°
x = 129°
we have now
y + z = 51
9y + 6z = 129
so,
z = 51 - y
9y + 6(51 - y) = 129
9y + 306 - 6y = 129
3y = -177
y = -59
z = 51 - y = 51 - -59 = 51 + 59 = 110
the value of z that makes j and k parallel is 110.
2. Angela is arranging 32 pictures in a photo album. She wants to
have the same number of pictures in each row. How can she
arrange her pictures?
Angela can arrange pictures in 6 different ways; (1 x 32), (2 x 16), (4 x 8), (8 x 4), (16 x 2), (32 x 1).
Given,
Angela have 32 pictures with her.
She wants to arrange it in an album with equal number of pictures in each row.
We have to find the possible arrangements.
Here,
32 pictures.
Lets see the possibilities.
1 row = 32 pictures in a row2 rows = 32/2 = 16 pictures in each row4 rows = 32/4 = 8 pictures in each row8 rows = 32/8 = 4 pictures in each row16 rows = 32/16 = 2 pictures in each row32 rows = 1 picture in each row.That is,
Angela can arrange pictures in 6 different ways; (1 x 32), (2 x 16), (4 x 8), (8 x 4), (16 x 2), (32 x 1).
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Help me please I paid for the tutor Version of this app and it can’t fine me a tutor like I just paid 100 dollars for nothing
The Solution.
The function is increasing on the interval below:
[tex](-2.5,1)[/tex]The function is decreasing on the intervals below:
[tex](-\infty,-2.5)\cup(1,\infty)[/tex]Given the following piecewise function, determine the value of g(4) - 3g(3).
Piecewise Function
We are given the piecewise function shown in the figure.
We are required to calculate g(4) - 3g(3).
First, we calculate g(4). Since 4 is greater than 3, we use the second function:
[tex]g(4)=4^4+4^2+4-3=273[/tex]Now we need to calculate g(3). We use the same function because 3 is greater or equal to 3:
[tex]g(3)=3^4+3^2+3-3=90[/tex]Now we calculate:
g(4) - 3g(3) = 273 - 3*90 = 273 - 270 = 3
Answer: 3
I would like to ask for Some help on this equation please?
ABC is a right triangle
AB is perpendicular to BC
If 2 lines are perpendicular, the product of slopes is -1
m1 x m2 = -1
mAB x mBC = -1
mAB = -1 / mBC
mAB = -1 / (1/2)
mAB = -2
Compute the derivative of f(x) = x * sin(x) . Use the result to compute f^ prime ( pi 2 )
Solution
Step 1
f(x) = xsinx
Step 2
[tex]\begin{gathered} f(x)=x\sin\left(x\right) \\ \\ f^{\prime}(x)=\sin\left(x\right)+x\cos\left(x\right) \end{gathered}[/tex]Step 3
[tex]\begin{gathered} f^{\prime}(\frac{\pi}{2})=\sin\left(\frac{\pi}{2}\right)+\frac{\pi}{2}\cos\left(\frac{\pi}{2}\right) \\ \\ f^{\prime}(\frac{\pi}{2})=1 \end{gathered}[/tex]Final answer
A. 1
hey can anyone help me on this im failing school xd
slope of line is -3 for points (1,0) and (0,3)
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
From graph let us take two points (1, 0) and (0, 3)
x₁=1, x₂=0, y₁=0,y₂=3
Substitute these values in slope formula
m=3-0/0-1
m=3/-1
m=-3
Hence slope of line is -3.
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Find the volume of a cone. Round your answer to the nearest wholenumber.7 ft4 ft
Answer:
117 cubic feet
Explanation:
From the diagram:
• The radius of the cone, r = 4 ft
,• The perpendicular height, h = 7 ft
[tex]\text{Volume of a cone=}\frac{1}{3}\pi r^2h[/tex]Substitute the given values:
[tex]\begin{gathered} V=\frac{1}{3}\times\pi\times4^2\times7 \\ =117.2ft^3 \\ \approx117\; ft^3 \end{gathered}[/tex]The volume of a cone is 117 cubic feet (to the nearest whole number).
L Pretest: Unit 2Question 5 of 21Which of the following represents the factorization of the polynomial functiongraphed below? (Assume it has no constant factor.)55
1) The best way to tackle questions like this is to locate the x-intercepts. Since according to the options the leading coefficient is 1, we just need to locate the zeroes and plug them into the quadratic equation form, in its factored form.
2) So now, let's write out the factored form and plug the zeroes into them:
[tex]\begin{gathered} y=a(x-x_1)(x-x_2) \\ y=1(x-1)(x-3) \\ y=(x-1)(x-3) \end{gathered}[/tex]You and a friend are in school and are trying to figure out where to eat. You told her that you would like to go to your favorite pizza place that is 5 miles away from your home. Both of you know that your home is 10 miles away from school. Approximately how far is the pizza place from the school?The pizza place is between approximately 5 to 15 miles away from school.Not enough information to solve the problem.The pizza place is approximately less than 5 miles away from school.
Okay, here we have this:
Considering the provided information, we are going to identify approximately how far is the pizza place from the school, so we obtain the following:
Then from the given information we can identify that the pizzeria can be 5 miles in the same direction from the school or 5 miles in any other direction,
This means that in the best case the distance from the pizzeria to the school is 5 miles (if it is halfway), and in the worst case it is 15 miles (if it is in a completely opposite sense).
And in an average case it can be at an angle other than 180 degrees, with which the distance would be between 5 and 15 miles, therefore the correct answer is:
The pizza place is between approximately 5 to 15 miles away from school.
west high schools population is 250 students fewer than twice the population of east high school. the two schools have a total of 2858 students. how many students attend east high school?
From properties of linear equation, 1036 students attend east high school.
What is linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Let east high school have x students
West high school have 2x - 250
Total count of students from both the schools are 2858 students.
Then we get
x + 2x-250 = 2858
=> 3x - 250 = 2858
=> 3x = 2858 + 250
=> 3x = 3108
=> x = 3108/3
=> x = 1036
Therefore, 1036 students attend east high school.
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Which answer choice gives a correct version of this problem? -35 ÷ -7
A.) - (-35/-7) or B.) -35/7 or C.) 35/7 or D.) 35/-7
(Please note that I'm not looking for the total value rather I'm looking for what (-35 ÷ (-7) is as a fraction.)
2. If 25% of 80 is 10% of a number? What is number?
Given that 25% of 80 is 10% of a number.
We have to find the number.
Let the number be x. So, 25% of 80 is equal to 10% of x. Therefore,
[tex]\begin{gathered} \frac{10}{100}\times x=\frac{25}{100}\times80 \\ 10x=2000 \\ x=\frac{2000}{10} \\ x=200 \end{gathered}[/tex]Thus, the number is 200.
Make a tree diagram, Please complete number 18.Please be quick, I am in a hurry.
Explanation:
The question wants us to list out all the possible outcomes in question 18
From the question
We have a spinner that has 5 possible outcomes
[tex]\mleft\lbrace\text{Red, Orange, Green, Purple, Yellow}\mright\rbrace[/tex]The outcomes of flipping a coin are
[tex]\begin{gathered} \mleft\lbrace\text{Head, Tail}\mright\rbrace\text{ } \\ \text{which can be written as} \\ \mleft\lbrace H,T\mright\rbrace \end{gathered}[/tex]Thus, to get the possible outcomes, we will have
Which of the following sets of ordered pairs lies on the y-axis of a coordinate grid?
Solution
for this case the point that lies on the y axis need to satisfy that the x coordinate must be:
x= 0
then the best solution would be:
(0, -4)
please help I think I know how to do this it I am not sure it has a time limit and I'm sorry I need to andwer it quick I've been working on it for awhile so it took time off the time limit
we are given the following polynomial:
[tex]x^2+3-7x[/tex]The standard form of a polynomial is of the following form:
[tex]ax^n+bx^{n-1}+cx^{n-2}+\cdots+d[/tex]Rewriting the given polynomial we get:
[tex]x^2-7x+3[/tex]This is a trinomial because it has 3 terms.
Since the maximum exponent of the polynomial is 2, this is a quadratic polynomial.
Sketch the vectors u and w with angle θ between them and sketch the resultant.
Given:
Two vectors (u) and (w) and the angle between them θ
[tex]\begin{gathered} |u|=50 \\ |w|=12 \\ \theta=35\degree \end{gathered}[/tex]the sketch of the vectors will be as shown in the following figure:
As shown, the resultant vector is the blue line segment
The vector R has a magnitude = 60.22
And the angle between u and R = 5.56°
In triangle ABC, if AC = 17 cm, CB = 10 cm, AD = x cm, DB = y cm and AB = 21 cm, find the value of (x − y).
The value of (x-y) is 9 cm for the given triangle ABC.
According to the question,
We have the following information:
In triangle ABC, if AC = 17 cm, CB = 10 cm, AD = x cm, DB = y cm and AB = 21 cm.
So, we have:
x+y = 21 cm
y = (21-x) cm
Using Pythagoras theorem in right-angled triangle ADC and CDB:
[tex]AC^{2} = AD^{2} +CD^{2}[/tex] and [tex]BC^{2} = BD^{2}+CD^{2}[/tex]
Now, we have the equal values of [tex]CD^{2}[/tex]:
[tex]17^{2} -x^{2} = 10^{2} -y^{2}[/tex]
289 -[tex]x^{2}[/tex] = 100 - [tex](21-x)^{2}[/tex]
289 - [tex]x^{2}[/tex] = 100 - (441+[tex]x^{2}[/tex]-42x)
289-[tex]x^{2}[/tex] = 100 - 441-[tex]x^{2}[/tex] + 42x
289 = 100 -441+42x
42x-331 = 289
42x = 289+331
42x = 630
x = 630/42
x = 15 cm
y = 21-x
y = 21-15
y = 6 cm
Now, x-y = 15-6
x-y = 9 cm
Hence, the value of (x-y) is 9 cm.
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3. A square has sides of length 612 inches. Area of length times width.
What is the area of the square in square inches?
The area of the square in square inches is 374544 inches².
How to find the area of a square?A square is a quadrilateral with 4 sides equal to each other. Opposite sides of a square is parallel to each other.
Each angle of a square is 90 degrees.
Therefore,
area of square = l²
where
l = side lengthTherefore,
The square has a side length of 612 inches. The area of the square can be found as follows:
area of square = l²
l = 612 inches
Hence,
area of square = 612²
Therefore,
area of the square = 612 × 612
area of the square = 374544 inches²
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Which set can represent the side lengths of a right triangle?
The set that represents a right triangle has to satisfy Pythagorean's Theorem where the greatest side is the hypothenuse. Let's evaluate each of them until we get the right set.
[tex]\begin{gathered} 7^2=6^2+(\sqrt[]{21})^2 \\ 49=36+21 \\ 49=57 \end{gathered}[/tex][tex]\begin{gathered} (5\sqrt[]{3})^2=7^2+5^2 \\ 25\cdot3=49+25 \\ 75=74 \end{gathered}[/tex][tex]\begin{gathered} (2\sqrt[]{5})^2=4^2+2^2 \\ 4\cdot5=16+4 \\ 20=20 \end{gathered}[/tex]As you can observe, set B satisfies the theorem.
Hence, B is the answer.jamals lawn is shaped like a square with an area of 224.9ft2 .which measurement is closest to the side length of his lawn in feet
We use the formula for the area "A" of a square with equal sides of length "l":
[tex]A=l^2[/tex]Since we know the value of the area is:
[tex]A=224.9ft^2[/tex]We substitute that value into the formula for the area:
[tex]224.9ft^2=l^2[/tex]Next, we take the square root of both sides of the equation:
[tex]\sqrt[]{224.9ft^2}=\sqrt[]{l^2}[/tex]On the right side, the exponent and the square root will cancel, and we will get "l", and on the left side, we calculate the square root:
[tex]14.99ft=l[/tex]Which can be rounded to the closest value, that is 15 ft.
Answer: 15 feet
Maria jogs 5 laps of a football field that
is 100 m by 50 m. How far does she jog?
Answer:
1500 m
Step-by-step explanation:
given that the field is 100m by 50m we can find that the perimeter of the field is 300m. if she jogged 300m 5 times she would have jogged 1500m
Can you please help me find the area of the shaded triangle? Thank you :)
Area of shaded triangle = Area of triangle - area of circle
Area of triangle = 1/2 x base x height
Base= 16 yds
Height= 19 yds
Area of triangle = 1/2 x 16 x 19 = 8 x 19 =152 square yard
[tex]\begin{gathered} \text{Area of circle = }\pi\times r^2 \\ \pi=3.14 \\ r=5\text{yds} \\ \text{Area of circle = 3.14 }\times5^2=78.5yard^2 \end{gathered}[/tex]Area of shaded triangle = 152 - 78.5 =73.5 square yard