Answers
The inequality for the given graph is y ≥ - 3x + 4.
What does a math inequality graph look like?The act of illustrating which area of the number line has values that would "satisfy" the specified inequality is known as graphing the inequality. Take a look at the first inequality, "x > -5." The values that may be used to substitute x in our inequality to produce a true statement can be shown on a graph of our inequality.
A graphed system of inequality problems on a coordinate plane. Each axis on the x and y axes scales by two. Between the coordinates zero, two, and three, zero, there is a solid line that represents an inequality. The area for the disparity that is shaded is below the line.
First of all, we saw from the graph that the line is not dotted. So, we will use the signs ≥ or ≤.
Now find the slope
From the graph, consider
(x₁, y₁) = (0, 4)
(x₂, y₂) = (1, 1)
So, slope = (y₂ - y₁) /(x₂ -x₁)
= (1 - 4)/(1 - 0)
= - 3
The y-intercept is given as
y = mx + b
4 = -3 (0) + b
b = 4
So, the equation is
y= - 3x + 4
From the graph, the shaded region is above the line. So, inequality will be
y ≥ - 3x + 4
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Related Questions
An animal shelter spends $5. 00 per day to care for each bird and $6. 50 per
day to care for each cat. Sarah noticed that the shelter spent $100. 50 caring
for birds and cats on Thursday. Sarah found a record showing that there were
a total of 18 birds and cats on Thursday. How many birds were at the shelter
on Thursday?
Answers
There were total 11 birds and 7 cats on Thursday.
Make the cats = 'x'
and the birds = 'y'
x + y = 18.......(1)
500x + 650y = 10000......(20
Multiply (1) by 50
500x + 500y = 9000.....(1)
500x + 650y = 10050.....(2)
Subtract (2) from (1)
.......150y = 1050
y = 1050/150
y=7
Substitute y =7 into (1)
x + 7 = 18.......(1)
x = 18 - 7
x = 11
11 birds and 7 cats were in on Thursday.
Hence we get the required answer.
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Write an equation in standar form for the line that passes through (5,0) and (0,6)
Answers
The an equation in standard form for the line that passes through (5,0) and (0,6) is 5y + 6x - 30 = 0
We need to write an equation in standard form for the line that passes through (5,0) and (0,6)
The formula for equation of line with two points is
y - y₁ = ((y₂ - y₁)/(x₂ - x₁))(x - x₁)
y - 0 = ((6 - 0)/(0 - 5))(x - 5)
y = 6/-5 (x - 5)
-5y = 6(x - 5)
-5y = 6x - 30
5y + 6x - 30 = 0
Therefore, the an equation in standard form for the line that passes through (5,0) and (0,6) is 5y + 6x - 30 = 0
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10 times 10+10y=-20 what is the value of the y-coordinate
Answers
The value of the y-coordinate as calculated from the equation 10+10y=-20 is -3
The given equation is 10+10y=-20
We will solve this linear equation by taking the y coordinate of the function.
Subtracting 10 from both sides of the equation:
or ,10+10y -10 = -20 -10
or, 10y = -30
Dividing both sides by 10 we get:
or, 10y ÷10 = -30 ÷ 10
or, y = -3
In mathematical formulas, the equals sign is used to indicate that two expressions are equal. It's possible that the definitions of words like "equation" or their cognates vary slightly between languages. For instance, an equation is defined as having one or more variables, whereas an equation is any well-formed formula that consists of two expressions connected by the equals sign.
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A tudent earned 48 out of 50 point on the lat tet, what percent correct did the tudent earn
Answers
Answer:
96%
Step-by-step explanation:
48 ÷ 50 × 100
Brady's father is paying $60 for a monthly gym membership. the gym is offering a special sale for 18% off the regular price. After the discount, a 10% maintence fee is charged. what does brady's father pay for the gym membership? explain.
Answers
============================================================
Explanation:
If his father saves 18%, then he pays the remaining 82% since 100-18 = 82.
The 82% then converts to 0.82 which is one of the multipliers we'll use to get the answer.
The other multiplier is 1.10 to represent an increase of 10%
The net multiplier is 0.82*1.10 = 0.902
Therefore, his father pays 0.902*60 = 54.12 dollars after the discount and maintenance fee are applied.
Is the area of a triangle always 180?.
Answers
The three interior angles of a triangle will always have a sum of 180.
What is are of triangle?The area of a triangle is defined as the total space occupied by the three sides of the triangle in a two-dimensional plane. The basic formula for the area of a triangle is half the product of the base and the height, or A = 1/2 × w × h. This formula applies to all types of triangles, including scalene, isosceles, and equilateral triangles. Recall that the base and height of a triangle are perpendicular to each other.The area of a triangle is the area enclosed by the sides of the triangle.The area of a triangle varies from triangle to triangle depending on the length of the sides and the interior angles. The area of a triangle is expressed in square units. B. m2, cm2, in2, etc.Hence, The three interior angles of a triangle will always have a sum of 180.
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What value of x will make AONM similar to ASRQ by the SAS similarity theorem?.
Answers
The value of x is 25 will make ΔONM similar to ΔSRQ by the SAS similarity theorem.
Given:
∠ONM is similar to ∠SRQ
From the figure
NM = 10
SR = 20
NO = 8
QR = x
SAS Similarity Theorem:
if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.
Both the triangles are similar by SAS if
NO/NM = SR/QR
substitute the values
8/10 = 20/x
cross multiplication
8x = 200
dividing both sides by 8
x = 25
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What is the solution to the system of equations y =- 5x 3 y 1?.
Answers
The solution to the system of equations y=-5x+3 and y=1 is given by coordinates (x,y)=(0.4,1)
Define the system of equations ?
System of equations, or simultaneous equations, in algebra, two or more equations to be solved together (i.e., the solution must satisfy all the equations in the system). For a system to have a unique solution, the number of equations must equal the number of unknowns.
What is a subsitution method ?
The substitution method is the algebraic method to solve simultaneous linear equations.
Given:
y=-5x+3
and
y=1
On subsituting y=1 ,we get
⇒[tex]y=-5x+3[/tex]
⇒[tex]1 = -5x+3[/tex]
⇒[tex](1-3)=(-5)x[/tex]
⇒[tex]-2=-5x[/tex]
⇒[tex]2=5x[/tex]
⇒[tex]5x=2[/tex]
⇒[tex]x=\frac{2}{5} =0.4[/tex]
Hence ,x=0.4 and y=1
So, the coordinates of (x,y) are (0.4,1)
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find the sum of the measures of the interior angles of a convex 27- gon
Answers
The sum of the measures of the interior angles of a convex 27-gon is 4,500°.
The angles located inside a polygon are referred to as its interior angles. The number of interior angles in a polygon is equal to the number of sides.
According to the polygon sum formula, the internal angles of any n-polygon add up to (n - 2)x180°.
=(27-2)×180°
=25×180°
=4,500°
Each side of a regular convex polygon must be the same length, and all interior angles must be equal and less than 180 degrees.
Therefore, the sum of the measures of the interior angles of a convex 27-gon is [tex]4500^{\circ}[/tex].
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8 All 66 students in a drama group take part in at least one of the four activities given below.
acting (4) dancing (D) singing (S) stage management (M)
Of these 66 students
11 take part in acting, dancing and singing
17 take part in acting and singing
14 take part in dancing and singing
16 take part in acting and dancing
33 take part in singing
37 take part in acting
29 take part in dancing
Any student who takes part in stage management does not take part in acting, dancing
or singing.
(a) Show all this information on the Venn diagram, giving the number of students in
each subset.
Answers
The Venn diagram of the 66 students in the drama group is illustrated below.
Venn Diagram:
Basically, a diagram representing mathematical or logical sets pictorially as circles or closed curves within an enclosing rectangle (the universal set), common elements of the sets being represented by intersections of the circles.
Given,
All 66 students in a drama group take part in at least one of the four activities given below. acting (4) dancing (D) singing (S) stage management (M) Of these 66 students 11 take part in acting, dancing and singing 17 take part in acting and singing 14 take part in dancing and singing 16 take part in acting and dancing 33 take part in singing 37 take part in acting 29 take part in dancing Any student who takes part in stage management does not take part in acting, dancing or singing.
Here we need to show all this information on the Venn diagram, giving the number of students in each subset.
While we looking into the given information,
Total number of students = 66
Here A refers acting, D refers dancing and S refers singing
=> All three activities count = 11
=> Acting and singing = 17
=> Dancing and singing = 14
=> Acting and dancing = 16
=> Singing = 33
=> Acting = 37
=> Dancing = 29
Based on these details we have drawn the following Venn diagram.
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Which point is on the graph of the equation y = -3x + 4?
(-3, 4)
(2, 2)
(1, 1)
(0, -4)
Answers
Answer:
(1,1)
Step-by-step explanation:
we fill in the equation for these points to see if they are on the line
(-3,4)
4=-3(-3)+4
4=-9+4
4=-5
Not on line
2=-3(2)+4
2=-6+4
2=-2
Not on line
1=-3(1)+4
1=-3+4
1=1
On the line
-4=-3(0)+4
-4=4
Not on line
Hopes this helps please mark brainliest
Keith wants to have a laptop case shipped to his office. Company A charges a $12 shipping fee and $1.50 per pound. Company B charges a $15 shipping fee and $1 per pound. For how many pounds is the cost of both shipping companies the same?
Answers
Six pounds is the cost of both shipping companies the same.
An equation is a mathematical statement created by joining two numerical or variable expressions with an equal sign.
How do you find the solution of an equation?An equation is a mathematical statement created by joining two numerical or variable expressions with an equal sign, as in 3x+5=11. A number that may be entered for the variable to produce a true number statement is the answer to an equation.
company A:
shipping fee is 12 and $1.50 per pound
Let p be the variable for the pounds of the package.
Liner Equation :
shipping fee = [tex]12+ 1.5p[/tex]
For company B :
shipping fee = 15 + p
if the cost of both shipping companies the same then,
12+1.5p = 15+p
ie. P = 6.
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if x/y= 70 then the value of x/2y is
Answers
Answer:
35
Step-by-step explanation:
if x/y is 70
then x/2y is half 70
so it's. 70÷2
x/2y=35
The value for x/2y is 1/140.
What is Proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
x/y= 70
So, for x/2y we have multiply the quantity y by 2.
Then x/2y= 1/70 x 1/2
x/2y = 1/140
Hence, the value for x/2y is 1/140.
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Ignacio buys three types of fish. He buys 12 guppies,
9 mollies, and 15 swordtails. He plans to divide the fish
between more than one fish tank. He wants to put
the same number of each type of fish into each tank.
How many tanks should Ignacio use? How many of
each type of fish will be in each tank? Show your work.
Answers
Ignacio should use 3 fish tanks, number of guppies in each tank is 4, number of mollies in each tank is 3 and number of swordtails in each tank is 5.
The largest positive integer that divides each of the two or more integers is referred to as the greatest common divisor. The greatest common divisor of two integers x and y is shown by the symbol gcd (x, y).
Ignacio purchases 15 swordtails, 12 guppies, and 9 mollies.
He desires to divide the fish across several tanks and to place an equal number of each variety of fish in each tank.
The gcd of 12,9 and 15 will be used for the number of fish tanks.
Factors of the numbers are
12= 2x 2 x 3
9=3 x 3
15= 5 x 3
The common factor among all the numbers is 3.
The gcd of 12, 9, and 15 is therefore 3. Ignacio must therefore utilize three fish tanks.
Each type of fish in each tank is,
number of fish of each kind/ gcd(12,9,15)
Number of guppies in each tank= 12/3=4
Number of mollies in each tank= 9/3=3
Number of swordtails in each tank= 15/3=5
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What is the sum of 1 triangle?.
Answers
The sum of the triangle angles is 180°.
What is area of triangle?The area of a triangle is defined as the total space occupied by the three sides of the triangle in a two-dimensional plane.The basic formula for the area of a triangle is half the product of the base and the height, or A = 1/2 × w × h.This formula applies to all types of triangles, including scalene, isosceles, and equilateral triangles. Recall that the base and height of a triangle are perpendicular to each other.The area of a triangle is the area enclosed by the sides of the triangle.The area of a triangle varies from triangle to triangle depending on the length of the sides and the interior angles. The area of a triangle is expressed in square units. B. m2, cm2, in2, etc.Hence, The sum of the triangle angles is 180°.
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Cuantos es 998563÷73
Answers
According to the division methods, the quotient is 2037 and the remainder is 433.
Division method:
Division is the method for dividing large numbers, which breaks the division problem into multiple steps following a sequence.
There are four parts in the division operation. They are quotient, remainder, divisor and the dividend.
Given,
Here we have the expression 998563÷73.
Now, we have to divide the numbers and then we have to find the quotient and the remainder for the numbers.
In order to do the division, we have to perform the following steps,
Take the first digit of the dividend from the left. And then check if this digit is greater than or equal to the divisor.Now, divide it by the divisor and write the answer on top as the quotient.Then subtract the result from the digit and write the difference below.Bring then next digit down of the dividend (if present) and repeat the same process until no further division process.Based on these steps we have divided the given number, then we get the quotient as 2037 and the remainder as 433.
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find the slope (0,-4) and (-6,-2)
Answers
m= (-4-(-2))/(-6–0)
m= -2/-6
m= 1/3
The slope is 1/3
Ahmed purchaed a telecope for tar gazing. The total purchae price wa $128. 50, which included $10. 28 in ale tax. What percentage of the purchae price wa ale tax? a. Set up a mathematical tatement to repreent the ituation. B. Cro-multiply and olve
Answers
The percentage of the purchase price of the sale tax is 8%
Given that,
Ahmed bought a telescope to look at the star. The final purchase price, which included the $10. 28 sales tax, was $128. 50.
To find : The sale tax's share of the purchase price
Let PP = $128
Sales Tax = $10.28
To calculate the percentage :
Divide the Tax with purchased price and multiply with 100
By doing so we have ,
10.28/128 = 0.080 * 100 = 8%
Therefore, The percentage of the purchase price of the sale tax is 8%
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What is the answer to this question?
Please help
Answers
The candy bar A contains 261 calories and candy bar B contains 254 amount of calories.
What are the linear equations in two variables?
A linear equation in two variables is one that is written in the form ax + by + c=0, where a, b, and c are real numbers and the coefficients of x and y, i.e. a and b, are not equal to zero. For example, 10x+4y = 3 and -x+5y = 2 are two-variable linear equations.
Let candy bar A contains 'x' calories and candy bar B contains 'y' amount of calories.
Then by using the given data, we can prepare the equations as
x + 2y = 769 -----(I)
2x + y = 776 -------(II)
Multiplying equation (II) by '2' and then taking subtraction, we get
-3x = -783
x = 261
Now put x = 261 in equation (I), we get
261 + 2y = 769
2y = 508
y = 254.
Hence, the candy bar A contains 261 calories and candy bar B contains 254 amount of calories.
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The grade of a road is the slope of a road. In the u. S. , grade is often expressed as a percent by finding the product 100(slope). Approximate the grade of a road that has a rise of 950 ft over 3 mi.
Answers
A road's grade can be thought of as its slope. In the US, grades are frequently reported as percentages by dividing the result by 100. (slope). A road with a rise of 950 feet over three miles is roughly 3% grade.
The slope or gradient of a line in mathematics is a numerical representation of the steepness and direction of the line. Slope is usually represented with the letter m; the rationale for this is unclear, although O'Brien (1844) stated the equation for a straight line as "y = mx + b," which is the first recorded use of the letter in English. It was also written as "y = mx + c" by Todhunter in 1888. The ratio of the "vertical change" to the "horizontal change" between (any) two distinct points on a line is used to calculate slope.
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What ate the steps for using a compass and straightedge to construct a square?.
Answers
The steps for using a compass and straightedge to construct a square is:
Given:
Let AB the length of one side given.
Steps:
a. Using your straightedge, draw a reference line, if one is not provided.
b. Copy the side of the square onto the reference line, starting at a point labeled A'.
c. Construct a perpendicular at point B' to the line through [tex]AB[/tex].
d. Place your compass point at B', and copy the side of the square onto the perpendicular B'G. Label the end of the segment copy as point C.
e. With your compass still set at a span representing AB, place the compass point at C and swing an arc to the left.
f. Holding this same span, place the compass point at A' and swing an arc intersecting with the previous arc. Label the point of intersection as D.
g. Connect points A' to D, D to C, and C to B' to form a square.
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The diameter of a circular pizza is 18 inches. What is the area of the pizza? Use 3.14 for π.
Answers
Answer: π * (18/2)^2
= 3.14 * 81
= 254.34 inches
Step-by-step explanation:
Formula of circle's area: πr^2, or 3.14 * radius to the power of 2
Since the radius is diameter divided by 2, the radius is 9
So, we can do 3.14 * 9 to the power of 2, which is 81.
So the formula is 3.14 * 81, and 254.32 inches.
Steven read a total of 21 books over 7 months. After belonging to the book club for 12 months, how many books will Steven have read in all? Solve using unit rates.
Answers
Answer:
36 books
Step-by-step explanation:
21 books / 7 months = 3 books per month
3 books per month × 12 months =
36 books
8400 dollars is placed in an account with an annual interest rate of 6.75%. to the nearest year, how long will it take for the account value to reach 27200 dollars?
Answers
It will take 18 years to reach an amount of $ 27200
What is Simple Interest?
Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.
Simple Interest = PRT / 100
where P = Principal
R = rate of interest
T = time period
Given data ,
The principal amount = $ 8400
Interest rate = 6.75 %
= 0.0675
Let the time period be = n
The Amount in n years = $ 27200
Now ,
The Amount is calculated by the formula ,
A = P ( R+1 )ⁿ
where n = time period
Substituting the values of A , P , and R , we get
27200 = 8400 x ( 1.0675 )ⁿ
Dividing by 8400 on both sides , we get
( 1.0675 )ⁿ = 68 / 21
Taking logarithm on both sides , we get
[tex]n=log_{1. 0625} \frac{68}{21}[/tex]
On solving the equation , we get
n ≈ 18 years
Hence , it will take 18 years to reach an account value of $ 27200
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Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g. A. g(0) = 2 B. g(-4) = -11 C. g(-13) = 20 D. g(7) = -1
Answers
The statement that could be true for function g is g(-13) = 20
The correct answer is an option (C)
In this question we have been given a function g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45
Also, g(0) = -2
g(-9) = 6,
We need to select the statement that could be true for g.
A. g(0) = 2
As we have been given g(0) = -2, above statement is false.
B. g(-4) = -11
the range of function is -5 ≤ g(x) ≤ 45 but -11 < -5
this means, above statement is false.
C. g(-13) = 20
here the values of x and g(x) fall within given intervals of domain and range
so, this statement is true.
D. g(7) = -1
since the domain of g is -20 ≤ x ≤ 5 but here x has value 7 which is false.
Therefore, the statement that could be true for function g is g(-13) = 20
The correct answer is an option (C)
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4) Find the surface area of the regular pyramid
Answers
The surface area of the regular pyramid is 131.15 cm.
Define surface area.The surface area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. The whole area of the surface of the specified solid item is referred to as surface area. We should add the areas of the surfaces to determine the object's surface area because the faces of three-dimensional objects are essentially 2D shapes.
Given,
Surface area = 1/2(a× b) + 3/2(b ×s)
Where b is a pyramid's side, a is a triangle's base height, and s is a pyramid's slant height.
Side = 6.1
Base = 7
Slant height = 12
Equating in formula:
1/2(6.1 × 7) + 3/2(6.1 × 12)
1/2(42.7) + 3/2(73.2)
21.35 + 109.8
131.15
The surface area of the regular pyramid is 131.15 cm.
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amy, beth, and jo listen to four different songs and discuss which ones they like. no song is liked by all three. furthermore, for each of the three pairs of the girls, there is at least one song liked by those girls but disliked by the third. in how many different ways is this possible?
Answers
There are 132 different ways this is possible(given situation).
What is probability ?Probability turned into added into arithmetic to are expecting the possibility of an occasion occurring. Probability essentially approach how in all likelihood it's miles that some thing will happen. This is the fundamental principle of possibility and is likewise utilized in possibility distributions to examine feasible consequences of random experiments.
Calculationlet[tex]$AB, BJ$, and $AJ$[/tex] denote a song that is liked by Amy and Beth (but not Jo), Beth and Jo (but not Amy), and Amy and Jo (but not Beth), respectively. Similarly, let[tex]$A, B, J,$ and $N$[/tex] denote a song that is liked by only Amy, only Beth, only Jo, and none of them, respectively. Since we know that there is at least[tex]$1\: AB, BJ$, and $AJ$[/tex], they must be[tex]$3$[/tex] songs out of the [tex]$4$[/tex] that Amy, Beth, and Jo listened to. The fourth song can be of any type
[tex]$N, A, B, J, AB, BJ$, and $AJ$ (there is no $ABJ$[/tex]
because no song is liked by all three, as stated in the problem.) Therefore, we must find the number of ways to rearrangeand a song [tex]$AB, BJ, AJ$,[/tex]from the se[tex]t $\{N, A, B, J, AB, BJ, AJ\}$.[/tex]
Case 1: Fourth song =[tex]$N, A, B, J$[/tex]
Note that in Case 1, all four of the choices for the fourth song are different from the first three songs.
Number of ways to rearrange =[tex]$(4!)$[/tex] rearrangements for each choice[tex]$*\: 4$ choices = $96$.[/tex]
Case 2: Fourth song =[tex]$AB, BJ, AJ$\\[/tex]
Note that in Case 2 all three of the choices for the fourth song repeat somewhere in the first three songs.
Number of ways to rearrange = [tex]$(4!/2!)$[/tex]rearrangements for each choice [tex]$*\: 3$ choices = $36$.[/tex]
[tex]$96 + 36 = \boxed{\textbf{(B)} \: 132}$.[/tex]
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Solve for X. 5 star + heart reward for best answer!! Please give step by step explanation.
-1 - 8/3(1/4x) = 2
Hint given: Change subtraction to addition of the opposite
Answers
Answer:
[tex]\sf x=-6[/tex]Step-by-step explanation:
[tex]\sf \cfrac{-1-8}{3\left(\cfrac{1}{4}x\right)}=2[/tex]
Simplify:-
[tex]\sf -\cfrac{12}{x}=2[/tex]Multiply both sides by x:-
[tex]\sf -\cfrac{12}{x}\;x=2x[/tex]Simplify:-
[tex]\sf -12=2x[/tex]Divide both sides by 2:-
[tex]\sf \cfrac{-12}{2}=\cfrac{2x}{2}[/tex]Simplify:-
[tex]\sf x=-6[/tex]______________________
Hope this helps!
Have a great day!
A survey by the national retail federation found that women spend on average r146. On a saturday lunch. Assume the standard deviation is r29. 44. Find the percentage of women who spend less than r190. 00 on a saturday lunch. Assume the variable is normally distributed.
Answers
The percent of women who spend less than R190 is 0.93 .
In the question ,
it is given that ,
A survey was conducted by National Retail Federation .
the average that a women spends = R146
So , μ = 146 .
The standard deviation is R29.44 .
So , σ = 29.44
we need to find the percent of women who spend less than R190 ,
that is
P(x < 190) = P(Z < (x-μ)/σ)
= P(Z < (190-146)/29.44)
= P(Z < 44/29.44)
= P(Z < 1.49457)
By using the "Standard Normal Distribution" table ,
we get
P(x<190) = 0.93
Therefore , The percent of women who spend less than R190 is 0.93 .
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Answer: wheres the question
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