If the discount is one fourth off, it means the discount is 1/4 = 25% of the original price, so the final price will be 75% or 3/4 of the original price.
In order to find the original price, we just need to divide the final price by 3/4, this way we "remove" the discount.
For example, if the sale price is $75, the original price would be:
[tex]\text{original price}=\frac{75}{\frac{3}{4}}=75\cdot\frac{4}{3}=25\cdot4=100[/tex]So for a sale price of $75, the original price would be $100.
In general, for a discount of x%, the original price (given the sale price) can be calculated as:
[tex]\text{original price}=\frac{\text{sale price}}{1-\frac{x}{100}}[/tex]Find the values of sin 0, cos 0, and tan e for the given right triangle. Give the exact values.sin 0=cos 0=tan 0=87
We can use the definition:
[tex]\begin{gathered} \sin \theta=\frac{\text{opposite }}{\text{hypotenuse}} \\ \\ \cos \theta=\frac{\text{adjcent}}{\text{hypotenuse}} \\ \\ \tan \theta=\frac{\text{opposite}}{\text{adjacent}} \end{gathered}[/tex]Looking at the figure we can see the values:
But we don't have the hypotenuse value, we must use the Pythagorean theorem to find it
[tex]\begin{gathered} \text{hypotenuse = }\sqrt[]{7^2+8^2} \\ \\ \text{hypotenuse = }\sqrt[]{113} \end{gathered}[/tex]Now we have the hypotenuse we can find all values
[tex]\begin{gathered} \sin \theta=\frac{\text{opposite }}{\text{hypotenuse}}=\frac{8}{\sqrt[]{113}} \\ \\ \cos \theta=\frac{\text{adjcent}}{\text{hypotenuse}}=\frac{7}{\sqrt[]{113}} \\ \\ \tan \theta=\frac{\text{opposite}}{\text{adjacent}}=\frac{8}{7} \end{gathered}[/tex]A swim team consists of 5 boys and 5 girls. A relay team of 4 swimmers is chosen at random from the team members. What is the probability that 3 boys are selected for the relay team given that the first selection was a girl? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
In order to find the probability start the construction of the possible relay team, if the team is made by any 4 swimmers then
[tex]10\cdot9\cdot8\cdot7=5040[/tex]if the first member is a girl and the other three needs to be boys, the number of possibilities are
[tex]1\cdot5\cdot4\cdot3=60[/tex]then, divide in order to find the probability
[tex]\frac{60}{5040}=\frac{1}{84}[/tex]Mr. Garcia gave his students a biology test last week.Here are the test scores for each of the fifteen students.Test scores938398899791838692908884858291(b) Construct a histogram for the data.(a) Complete the grouped frequency distribution forthe data. (Note that the class width is 5.)FrequencyTest scores7-6+79 to 835+84 to 88Frequency0.0043+89 to 932+1194 to 980-79 1083941 98844 to 58 89 to 93Test scoresx5?
Test scores: 93 83 98 89 97 91 83 86 92 90 88 84 85 82 91
organizing the data: 82,83,83,84,85,86,88,89,90,91,91,92,93,97,98
(a) Complete the grouped frequency distribution for the data.
79 to 83 -> 3
84 to 88 -> 4
89 to 93 -> 6
94 to 98 -> 2
(b) Construct a histogram for the data.
the histogram can be constructed using the information obtained in point (a)
The length of a rectangle is 9 inches more than the width. The perimeter is 34 inches. Find the length I need both length and the width of the rectangle
The perimeter is the sum of the side lengths of a polygon. Now, let it be:
• l,: the length of the rectangle
,• w,: the width of the rectangle
Considering the information given and the previous definition, we can write and solve the following system of equations.
[tex]\begin{cases}l=9+w\Rightarrow\text{ Equation 1} \\ l+w+l+w=34\Rightarrow\text{ Equation 2}\end{cases}[/tex]We can use the substitution method to solve the system of equations.
Step 1: We combine like terms in Equation 2.
[tex]\begin{cases}l=9+w\Rightarrow\text{ Equation 1} \\ 2l+2w=34\Rightarrow\text{ Equation 2}\end{cases}[/tex]Step 2: We substitute the value of l from Equation 1 into Equation 2.
[tex]\begin{gathered} 2l+2w=34 \\ 2(9+w)+2w=34 \end{gathered}[/tex]Step 3: We solve for w the resulting equation.
[tex]\begin{gathered} \text{ Apply the distributive property on the left side} \\ 2\cdot9+2\cdot w+2w=34 \\ 18+2w+2w=34 \\ \text{ Add similar terms} \\ 18+4w=34 \\ \text{ Subtract 18 from both sides} \\ 18+4w-18=34-18 \\ 4w=16 \\ \text{ Divide by 4 from both sides} \\ \frac{4w}{4}=\frac{16}{4} \\ w=4 \end{gathered}[/tex]Step 4: We replace the value of w in Equation 1.
[tex]\begin{gathered} \begin{equation*} l=9+w \end{equation*} \\ l=9+4 \\ l=13 \end{gathered}[/tex]Thus, the solution of the system of equations is:
[tex]\begin{gathered} l=13 \\ w=4 \end{gathered}[/tex]AnswerThe length of the rectangle is 13 inches, and the width of the rectangle is 4 inches.
good night I will send a picture of work
In the form of the equation
S = m D + b
S represented on the y-axis
D represented on the x-axis
The independent is x
The dependent is y
Then D is the independent
S is the dependent
let us find the correct answer
Which of the following tools did the Greeks limit themselves to in their
The Greeks limited themselves to using only compass and ruler in their formal geometric constructions.
Answer: Options B and D.
The chart below shows how many newspapers each person stacked. Which operation would be used to find the total number of newspapers Diane stacked?
Answer:
Where's the chart?
Step-by-step explanation:
please help this is very difficult
Answer:
x=-6. y=6. xy=-36
x=-2. y=-3. xy=6
x=1. y=2. xy=2
2x 5x+6 please simplify
Answer:
Step-by-step explanation:
Maybe
2x times 11x
The ratio of sand to gravel 4 to 9
Since we are told there are 4 parts of sand for every 9 of gravel, the ratio of sand to gravel is 4/9.
Sara’s dogsMorning: 39, 21, 12, 27, 23, 19, 31, 36, 25Afternoon: 15, 51, 8, 16, 43, 34, 27, 11, 8, 39Comparing the morning and afternoon groups Create frequency tables to represent the morning and afternoon dogs as two sets of data. Group the weights into classes that range 10 pounds.
Answer;
Medain for morning is 25
Median for evening is 21.5
Explanation;
Here, we want to create frequency tables for each of the given groups
We start with the morning group
The frequency table for it is as follows;
Now, we proceed to the afternoon group
We have this as follows;
Lastly, we will want to get the median value of both groups
To do this, we need to re-arrange the values in the data set in ascending or descending order
For the purpose of this solution, we shall be using the ascending order mode. Then from here, we pick out the middle value
For the morning group, we have;
12, 19,21, 23,25,27,31,36,39
Since the numbers are 9, the middle number will be the 5th number since it leaves equal spread of values on the left and right
Thus, we have the median value as 25
The afternoon set, we have it as;
8,8,11,15,16,27,34,39,43,51
We proceed to choose the mid 5th values comig from both ends
We have this as;
We have these values as; 16 and 27
We add these and divide by 2
We have this as;
[tex]\frac{16+27}{2}\text{ = 21.5}[/tex]
I can't solve them 15 here and 15 on another post
6. Measure of angle 1 is 60 degrees because it congruent to angle 4 because they are opposed by the vertex
7. Measure of angle 3 is equal to 180 - angle 1 - angle 2 = 180 - 60 - 40 = 80 because these three angles sum 180 degrees
8. Measure of angle 5 is 40 degrees because it congruent to angle 2 because they are opposed by the vertex
9. Measure of angle 6 is equal to angle 3, because they are congruent, so it measures 80 degrees
10. Mesure of angle 7 is equal to the sum of angles 1 and 2 because they are congruent, so measure of angle 7 is 100
11. 80
12. 60
13. 120
14. 60
15. 120
What is the y-intercept of the line that passes through the point (4,-9) with a slope of -1/2
Answer:
The y-intercept b for the derived equation is;
[tex]b=-7[/tex]Explanation:
Given that the line passes through the point (4,-9) and has a slope of -1/2;
[tex]\begin{gathered} \text{slope m=-}\frac{1}{2} \\ \text{ point (4,-9)} \end{gathered}[/tex]Applying the point-slope form of linear equation;
[tex]y-y_1=m(x-x_1)[/tex]substituting the slope and the given point;
[tex]\begin{gathered} y-(-9)=-\frac{1}{2}(x-4) \\ y+9=-\frac{1}{2}x+\frac{4}{2} \\ y+9=-\frac{x}{2}+2 \\ y=-\frac{x}{2}+2-9 \\ y=-\frac{x}{2}-7 \end{gathered}[/tex]Comparing it to the slope intercept form of linear equation;
[tex]y=mx+b[/tex]where;
m = slope
and b = y-intercept
Therefore, the y-intercept b for the derived equation is;
[tex]b=-7[/tex]Which expression represents the area of the rectangle below in square units
Area of rectangle is given by:-
[tex]\begin{gathered} l\times b \\ =(3x+2)\times2x \\ =6x^2+4x \end{gathered}[/tex]So the correct answer is
[tex]6x^2+4x[/tex]can someone please help me find the value of x?
Since we have a right triangle, we can relate the angle 28 with x and side 34 by meand of the sine function, that is,
[tex]\sin 28=\frac{34}{x}[/tex]where x is the hypotenuse. By moving x to the left hand side, we have
[tex]x\cdot\sin 28=34[/tex]and by moving sin28 to the right hand side, we get
[tex]x=\frac{34}{\sin 28}[/tex]since sin28=0.4694, we have
[tex]x=\frac{34}{0.4694}[/tex]then, x is given by
[tex]x=72.42[/tex]by rounding down, the answer is option D: x=72.4
Two rectangles overlap, as shown below. Find the area of the overlapping region (which is shaded) if AB = BE = 2 and AD = ED = 4.
The area of the overlapping region is of: 6.25 units squared.
Area of a rectangleThe area of a rectangle of length l and width w is given by the multiplication of the dimensions, as follows:
A = lw.
The dimensions of the right triangle as follows:
Leg x.Leg 2.Hence the remaining leg on the overlapping region is:
4 - x, as AD = 4.
By symmetry, the other dimension of the overlapping region is also of:
4 - x.
Being also the hypotenuse of the right triangles.
The value of x can be found applying the Pythagorean Theorem as follows:
x² + 2² = (4 - x)²
x² + 4 = 16 - 8x + x²
8x = 12
x = 1.5.
Then the two dimensions of the shaded region are:
4 - 1.5 = 2.5.
Meaning that the area is of:
A = 2.5 x 2.5 = 6.25 units squared.
Missing information
The figure is missing and is given by the image at the end of the answer.
More can be learned about the area of a rectangle at https://brainly.com/question/10489198
#SPJ1
what do I do to compute the exact average of the fractions, in decimal form?
Average is computed as follows:
[tex]\begin{gathered} \text{Avg=}\frac{\text{ sum of terms}}{\text{ number of terms}} \\ \text{Avg}=\frac{5+0.2+2}{3} \\ \text{Avg}=\frac{7.2}{3} \\ Avg=2.4 \end{gathered}[/tex]Find the restricted values of x for the following rational expression. If there are no restricted values of x, Indicate "No Restrictions".
−5r – 8/x² + 4
The restricted values of x for the following rational expression.
x = 0
x = -3/4
What are restriction value?Restricted values are those values in a rational expression that bring the denominator to zero. When referring to "Market Value," the term "restricted value" denotes the property's value under the assumption that it is subject to a temporary governmental or private limit on rentals and tenant income levels. The denominator's real numbers that have a value of 0 are not included in the domain. The word "restrictions" refers to these values. Similar to how fractions are simplified, rational expressions can be too. Cancel the common factors after factoring the numerator and denominator. Place a zero as the denominator. Put the equation to rest. The restricted values are the answer or answers.
Rational expressions should first be multiplied, and then the numerator and denominator should be factored. Next, common factors should be cancelled. Notify yourself of the domain's limitations.
−5x– 8/x² + 4 = 0
- 5x - 8/[tex]x^{2}[/tex] = -4
x = 0
x = -3/4
To know more about restriction value ,visit:
brainly.com/question/28122593
#SPJ13
Write an equation of a line in slope-intercept form that has a slope of -3 and goes through the point (0, 3) O y = 3x - 1 O y = 3x + 2 O y = 3x O y = -3x + 3
ANSWER
y = -3x + 3
EXPLANATION
We want to write the equation in slope-intercept form, which is the form:
y = mx + c
where m = slope; c = intercept
To do that, we have to use the point-slope method:
y - y1 = m(x - x1)
where (x1, y1) = point the line goes through
From the question:
m = -3
(x1, y1) = (0, 3)
So, we have that:
y - 3 = -3(x - 0)
y - 3 = -3x
=> y = -3x + 3
That is the equation of the line in slope-intercept form.
how much must be deposited at the beginning of every six months in account that pays 6% compounded semi-annually so that account will contain 21,000 at the end of three years
The formula for Final Amount, A after compounding for n period of times is given by
[tex]A=p(1+\frac{r}{100})^n[/tex]Where A = amount
p= principal
r = rate (in %)
n = number of compounding periods
From the question.
A=21,000, p = ?, r=6, n = 3 x 2 = 6
[tex]\begin{gathered} 21000=p(1+\frac{6}{100})6 \\ \\ 21000=p(1+0.06)^6 \\ 21000=p(1.06)6 \\ 21000=p(1.41852) \\ 21000=1.41852p \\ p=\frac{21000}{1.41852} \\ p=14,804.17 \end{gathered}[/tex]The amount that must be deposited at the beginning is 14,804.17
Are the triangles congruent using AAS?
True
False
A truck rental is $25 plus $.35/mi. Find out how many miles Ken traveled if his bill was $51.95.
So,
We could write the following equation, where "x" is the number of miles travelled.
[tex]0.35x+25=51.95[/tex]If we solve this equation, the first thing we're going to do is to let all "x terms" in a side of the equation and all the numbers in the other side. If "25" is summing in a side, it will change its sign when we pass it to the other side. Like this:
[tex]0.35x=51.95-25[/tex]Now, we substract the numbers above and get:
[tex]0.35x=26.95[/tex]Now, if 0.35 is multiplying "x", we are going to pass this number to divide the amount in the other side:
[tex]x=\frac{26.95}{0.35}=77[/tex]Therefore, Ken travelled 77 miles.
A salaried employee receives an annual salary of $40000. there are 26 pay periods during the year. during the current pay period, She receives a bonus of $200 what is her gross pay for this pay period ?A. $1,938.46B. $1,738.46C. $1,538.46D. $1,338.46
ANSWER:
C. $1,538.46
STEP-BY-STEP EXPLANATION:
To understand the question we must take into account that it is the gross payment, which is the payment received by the employee agreed with the company, without taking into account deductions or bonuses.
Therefore, we calculate it with the total payment divided by the amount of payments, like this:
[tex]\begin{gathered} p=\frac{40000}{26} \\ \\ p=\text{ \$}1538.46 \end{gathered}[/tex]So the correct answer is C. $1,538.46
Supposed g is a one-to-one function with the following valuesg(-7)= -6g(11)= -1
Given:
The function g(x) is one-one.
[tex]g(-7)=-6[/tex][tex]g(11)=-1[/tex]Required:
We need to find the values of the inverse image of the function g(x).
Explanation:
Recall that the image of distinct elements of the function is distinct.
There exist an inverse of g(x) since g(x) is one to one.
The inverse image of the given can be written as follows.
Consider the equation
[tex]g(-7)=-6[/tex][tex]g^{-1}g(-7)=g^{-1}(-6)[/tex][tex]g^{-1}(-6)=-7[/tex][tex]g(11)=-1[/tex][tex]g^{-1}g(11)=g^{-1}(-1)[/tex][tex]g^{-1}(-1)=11[/tex]Final answer:
[tex]g^{-1}(-6)=-7[/tex][tex]g^{-1}(-1)=11[/tex]1. Which of the following would be considered a statistical question? (1) Who was the highest paid athlete in 2020? (2) How much does a gallon of gasoline cost? (3) How many people voted for president in 2016?(4) What are the different types of maple trees?
Looking at the sentences, we have that (1), (2) and (3) are questions that require just one specific answer (For (1) it's a name of a person, for (2) it's a value and for (3) it's also a single value).
But in sentence (4), there are more than one type of maple tree, so we can answer with each type of maple tree, stating the percentage of each type for example.
So the sentence that would be considered a statistical question is (4).
Find the distance and the midpoint for each set of points given
Given,
The coordinates of the points are (2,6) and (7, 2).
Required:
The distance between the points and the midpoint of the points.
The distance between two points is calculated as,
[tex]\begin{gathered} Distance\text{ =}\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ =\sqrt{(7-2)^2+(2-6)^2} \\ =\sqrt{5^2+4^2} \\ =\sqrt{25+16} \\ =\sqrt{41} \\ =6.4 \end{gathered}[/tex]Hence, the distance between the points is 6.4
The midpoint is calculated as,
[tex]\begin{gathered} Midpoint=(\frac{2+7}{2},\frac{6+2}{2}) \\ =\frac{9}{2},\frac{8}{2} \\ =(4.5,4) \end{gathered}[/tex]Hence, the midpoint is (4.5,4).
use the above diagram to answer the following questions.
Remember that the sum of the interior angles is 180. Then, we have the following equation:
[tex]55^{\circ}+65^{\circ}\text{ + }\angle M\text{ = 180}[/tex]This is equivalent to:
[tex]120^{\circ}\text{ + }\angle M=180^{\circ}[/tex]solve for M-angle:
[tex]\text{ }\angle M=180^{\circ}-\text{ 120}^{\circ}=60^{\circ}[/tex]Then, te correct answer is :
[tex]\text{ }\angle M^{}=60^{\circ}[/tex]72bz +96b2h + 90xbz + 120xbh +
Factoring
Factor the expression:
[tex]72b^2z+96b^2h+90xbz+120xbh[/tex]Divide the expression into two halves:
[tex](72b^2z+96b^2h)+(90xbz+120xbh)[/tex]Factor b^2 from the first group and xb from the second group:
[tex]b^2(72z+96h)+xb(90z+120h)[/tex]Now find the greatest common multiple of 72 and 96:
72= 2*2*2*3*3
96=2*2*2*2*2*2*3
Now we take the common factors with their least number of repetitions:
GCF=2*2*2*3=24
Now we find the GCF of 90 and 120:
90=2*3*3*5
120=2*2*2*3*5
GCF=2*3*5=30
Taking the GCF of each group:
[tex]\begin{gathered} b^224(3z+4h)+xb30(3z+4h) \\ =24b^2(3z+4h)+30xb(3z+4h) \end{gathered}[/tex]Now we finally take out 3z+4h from both groups:
[tex]\mleft(3z+4h\mright)(24b^2+30xb)[/tex]This last expression can be further factored by taking out 6b from both terms:
[tex]6b(3z+4h)(4b+5x)[/tex]This is the final expression factored as much as possible
Calculate the net price and trade discount (use net price equivalent rate and single equivalent discount rate) for the following: Sony Hd flat-screen list price: 899 chain discount: 5/4 net price: Trade discount
The net price and trade discount for the good is.539.4 and 359.6 respectively.
How to calculate the net price?From the information given, tuw.Sony Hd flat-screen list price is 899 and has a discount: 5/4 net price:
The net price will be:
= List price × (1 - Discount rate)
= 899 × (1 - 40%)
= 899 × 60%
= 899 × 0.6
= 539.4
The trade discount will be:
= List price - Net price
= 899 - 539.4
= 359.6
Learn more about discount on:
brainly.com/question/7459025
#SPJ1
Complete question:
Calculate the net price and trade discount (use net price equivalent rate and single equivalent discount rate) for the following: Sony Hd flat-screen list price: 899 chain discount: 5/4 net price and discount 40%
Can you help me with my math homework?"There are 600 seats in the auditorium. This is 112 less than the number of seats in the gymnasium. How many seats are in the gymnasium? Let s= the number of seats in the gymnasium"
According to the problem, there are 600 seats in the auditorium.
112 less than the number of seats in the gymnasium.
So, to find the number of seats in the gymnasium, we just have to add 122 and 600 because the auditorium has 112 seats less.
[tex]s=600+112=712[/tex]Hence, there are 712 seats in the gymnasium.