Y is inversely proportional to x, when Y = 2, x = 4.
Find the value of x when Y = 4.
The value of x when y =4 is 2
How to solve for x?An inverse proportion is represented as:
k = yx
Where
k represents the constant of proportion
When y = 2, x = 4.
So, we have:
k =2 * 4
k = 8
Substitute k = 8 in k = yx
So, we have:
yx = 8
When y = 4, we have:
4x = 8
Divide by 4
x = 2
Hence, the value of x when y =4 is 2
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Please help asap!!! thank ya
There are 2500 women and 2000 men enrolled in a certain college. The mean height for the women is 64.4 inches, and the mean height for the men is 69.8 inches. 1. Find the sum of the heights of the women. 2. Find the sum of the heights of the men. 3. Find the mean height for all 4500 people. 4. What is the average of the means for men and women
The sum height of men and women is 139600 and 161000 inches respectively. Their mean height is 66.8 inches and the average of their mean is 67.1 inches.
Calculation of the sum and meanNumber of women =2500
Mean height of women = 64.4 inches
So, the total height of 2500 women = 64.4*2500 = 161000 inches
Number of men=2000
Mean height of men = 69.8 inches
So, the total height of 2000 men = 69.8*2000 = 139600 inches
Therefore, the sum height of all 4500 people = 161000+139600 =b
So, their mean height = 300600/ 4500 = 66.8 inches
The sum of mean height of men and women = 64.4 + 69.8 = 134.2 inches
Hence, The average of their mean = 134.2/ 2= 67.1 inches.
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Find the equation of the line described.
5. Perpendicular to y = 3x + 5; passing through the point (-6,-4)
Answer: [tex]y+4=-\frac{1}{3}(x+6)[/tex]
Step-by-step explanation:
The slope of the given line is 3, so the slope of the line we want to find is -1/3.
Substituting into point-slope form, we get the equation of the line to be
[tex]y+4=-\frac{1}{3}(x+6)[/tex].
A teacher has 14 senior students, 7 junior students, 4 sophmore, 5 freshmen, what is the proabability that she chooses a senior?
Answer:
7/15
Step-by-step explanation:
To find the probability the student is a senior
P( senior) = number of seniors / total students
= 14 / ( 14+7+4+5)
= 14/30
= 7/15
Answer:
14/30 or 7/15
Step-by-step explanation:
probability = no. of senior students / total no. of students
probability = 14 / (14+7+4+5)
probability = 14/30
This can be simplified to 7/15.
Hope this helps!
Section 1 Topic 6 Radical Expressions and Expressions with Radical Exponents
Directions: Match the column on the left with the possible answers from the two columns on
the right. Some questions will have more than one answer and some possible answers will
not be used.
a baby's t-shirt requires 4/5 feet of fabric. How many t-shirts can be made out of 56 feet of fabric
The complete question:
A baby's t-shirt requires 4/5 yards of fabric. How many t-shirts can be made from 48 yards? A book is on sale at a 30% discount. If the sales price is $28, what was the original price?
Charles is going to buy 3 computer tables for $390. If he pays the same rate, how much would it cost for 8 computer tables?
If your cell phone bill was $67.82 and you were charged a 7.5% late fee, how much will your total bill be?
Mrs. Margulis paid $125 to have her hair colored and cut. If she tips her hairdresser 15%, what is her total bill?
Macy's is having a one-day 35% off special. If Sara bought $124.50 worth of items, what would the final bill total be after applying the discount of 35%?
Sara's total bill exists the cost of the items bought smaller the amount of the 35% is $143.75.
what would the final bill total be after applying the discount of 35%?
The number of t-shirts that can be created from 48 yards exists at 60 yards.
The original price of the book exists $40.
The cost of 8 computer tables exists $1040.
My total bill would be $72.91.
Mrs. Margulis's total bill is $143.75
My total bill after involving the discount of 35% would be $80.93.
If one t-shirt requires 4/5 yards. The number of t-shirts that can be created with 48 yards can be specified by dividing 48 yards by 4/5 yards
48 yards ÷ 4/5 yards
48 x 5 / 4 = 60 shirts
The cost of the book existed decreased by 30%. This indicates that the sales price exists 70%(100 - 30%) of the original price.
Let p denote the original price. This equation can be utilized to describe the information in the question:
70% [tex]*[/tex] p = $28
0.7p = $28
p = $28 / 0.7
p = $40
To define the cost of 8 computer tables, the cost of one computer table contains to be decided first.
Cost of one computer table = cost of three tables / 3
$390 / 3 = $130
The cost of 8 computer tables = Cost of one computer table [tex]*[/tex] 8
$130 x 8 = $1040
The total bill exists as the sum of the cell phone bill and the late phone charge
$67.82 + ( 7.5% [tex]*[/tex] $67.82)
$67.82 + (0.075 [tex]*[/tex] $67.82 )
$67.82 + 5.09
= $72.91
Mrs. Margulis's total bill exists the sum of the amount she paid and the cost of her tip.
$125 + ( 15% [tex]*[/tex] $125)
$125 + (0.15 [tex]*[/tex] $125)
$125 + $18.75
= $143.75
Sara's total bill exists the cost of the items bought smaller the amount of the 35%
$124.50 - (35% [tex]*[/tex] $124.50)
$124.50 - (0.35 [tex]*[/tex] $124.50)
$124.50 - $43.58
= $80.93
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please help me, 20 points
The area of the shaded region is 502.4 ft^2
The area of a circle is the space occupied by a circle in a two-dimensional plane. Alternatively, the space taken up inside the boundary/circumference of a circle is called the area of the circle. The formula for the area of a circle is A = πr2, where r is the radius of the circle. The unit of area is the square unit, such as m2, cm2, in2, etc. Area of a circle = πr2 or πd2/4 in square units, where (Pi) π = 22/7 or 3.14. Pi (π) is the ratio of the circumference to the diameter of any circle. It is a special mathematical constant.
It is given that inner diameter is 36 ft and width of the ring is 4 ft
We need to find the area of the shaded region
diameter of outer ring= d1=36+4+4 = 44 ft ,
diameter of inner ring= d2=36 ft,
r1=d1/2= 44/2 = 22 ft , r2=d2/2 = 36/2 = 18 ft
Area of shaded region = Area of Outer circle - Area of inner circle
= π r1^2 - π r2^2
= π ( 22^2 - 18^2 )
= 3.14 * 160
= 502.4 ft^2
Hence the area of the shaded region is 502.4 ft^2
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The area of the shaded region is 502.4 sq. ft.
An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The word "area" refers to a free space.
According to the question,
Diameter of inner circle = 36 ft.
Radius of inner circle = 36/2 ft. =18 ft.
As the width of the ring is 4 ft. , the diameter of the outer circle = 36+4+4= 44 ft.
Radius of outer circle = 22 ft.
Area of the shaded region = Area of outer circle - Area of inner circle
= π(22)(22) - π(18)(18)
= π(484 - 324)
= 3.14 * 160
= 502.4 sq. ft.
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What are the solutions to the equation below?
2x^2 - x + 1 = 0
1/4 - startroot 5 endroot/ 4 and 1/4 + startroot 5 endroot / 4
1/4 - startroot 7 endroot/ 4 and 1/4 + startroot 7 endroot/ 4
1/4 - startroot 7 endroot/ 4 i and 1/4 + startroot 7 endroot/4 i
1/4 - startroot 5 endroot/ 4 i and 1/4 + startroot 5 endroot/4 i
The solutions of the given quadratic equation is; (1/4) + √7i/4 and (1/4) - √7i/4
How to find the solution of a quadratic equation?We are given the quadratic equation as;
2x² - x + 1 = 0
To solve this to find the root, we will use the quadratic formula which is given by;
x = [-b ± √(b² - 4ac)]/2a
Now, from the given quadratic equation, we can say that the values of a, b and c are;
a = 2; b = -1 and c = 1
Thus;
x = [-(-1) ± √((-1)² - 4(2 * 1))]/2(2)
x = [1 ± √(1 - 8)]/4
x = [1 ± √(-7)]/4
x = (1/4) ± √7i/4
Thus;
x = (1/4) + √7i/4 and (1/4) - √7i/4
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the graph below could be the graph of which exponential function?
The graph above could be a graph of this exponential function: A. F(x) = 3.(1.2)^x.
How to interpret the graph?Mathematically, the standard form of an exponential function is given by:
F(x) = ab^x
Where:
a is the initial value of an exponential function.b is the growth rate.As a general rule, f(x) is an increasing function when b is greater than 1 (b > 1) and f(x) is a decreasing function when b is less than 1 (b < 1)
By critically observing the given graph, we can deduce that the initial value (a) is 3 and it's an increasing function (b > 1).
F(x) = 3.(1.2)^x
Thus, the graph above could be a graph of this exponential function F(x) = 3.(1.2)^x.
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Whoever helps first get brainiest
Answer:
75
Step-by-step explanation:
Use PEMDAS (Perenthesis, Exponents, Multiply, Divide, Add, Subract)
45/5-6+24*3
9-6+24*3
9-6+72
3+72
75
Answer:
75
Step-by-step explanation:
PEMDAS:
45/5=9
24*3=72
9-6+72=75
Find the length of the segment indicated.
Answer:
11.281
Step-by-step explanation:
For this question, since we see a right angle triangle, we know that we can use Pythagoras' Theorem to solve for this question.
By Pythagoras' Theorem,
[tex] {c}^{2} = {a}^{2} + {b}^{2} \\ {x}^{2} = {4.6}^{2} + {10.3}^{2} \\ \\ {x}^{2} = 127.25 \\ x = \sqrt{127.25} \\ = 11.281 \: or \: \frac{ \sqrt{509} }{2} [/tex]
A nurse is administering a high-concentration potassium solution to a patient with a diet-based potassium deficiency. Unaware of the initial treatment, another nurse administers a drug that inhibits secretion of aldosterone to treat the same deficiency. Which of the following conditions will most likely occur as a result
Hyperkalemia is what is more likely to occur due to the results of the conditions.
What is hyperkalemia?This is used to refer to the condition where there is too much of potassium in the blood of a person.
The side effects is that the person would feel tiredness, weakness and he would feel abnormal heart beat.
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Evaluate each expression for the given values of the variables: 4|a|+8-a, if a =-2
The value of expression is 18.
modulus of functionA modulus function is a function that determines a number or variable's absolute value. A function with absolute values is another name for it. This function's result is always positive. let's suppose if you want to find modulus of -2 then you will get 2 as the answer.
now according to question
4|a|+8-a at a=-2
here a is negative that means modulus will give us positive value.
put a =-2 in the expression and get the answer. modulus of -2 will give us +2
so
=4(2)+8-(-2)
=8+8-(-2)
=8+8+2
=18
hence the answer is 18.
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Write the following Arithmetic Sequence using an Explicit Formula: a1 = 14 ,an = an-1 – 6 A.) an = 6 – 14(n – 1)
B.) an = 14 – 6(n – 1)
C.) an = 6 + 14(n – 1)
D.) an = 14 + 6(n – 1)
The explicit formula for the sequence is an = 14-6(n-1)
Arithmetic sequenceThis are sequence that has. a common difference that is the difference between the preceding and sthe explicit formula for the sequence is an = 14-6(n-1) is equal.
Given the following
a1 = 14
an = an-1 - 6
The nth term of the sequence is expressed as:
An = a+(n-1)d
an = 14+(n-1)(-6)
an = 14 -6n + 6
an = 14-6(n-1)
Hence the explicit formula for the sequence is an = 14-6(n-1)
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Scrapper Elevator Company has 20 sales representatives who sell its product throughout the United States and Canada. The number of units sold last month by each representative is listed below. Assume these sales figures to be the population values. 2 3 2 3 3 4 2 4 3 2 2 7 3 4 5 3 3 3 3 5 Required: a. Compute the population mean. (Round your answer to 1 decimal place.) b. Compute the standard deviation. (Round your answer to 2 decimal places.) c. If you were able to list all possible samples of size five from this population of 20, how would the sample means be distributed
Using the concepts of mean and standard deviation, and the central limit theorem, it is found that:
a. The mean is of: 3.3
b. The standard deviation is of: 1.23.
c. They would have a mean of 3.3 and a standard deviation of 0.55.
What are the mean and the standard deviation of a data-set?The mean of a data-set is given by the sum of all values in the data-set, divided by the number of values.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values.For this problem, the mean is given by:
M = (2 + 3 + 2 + 3 + 3 + 4 + 2 + 4 + 3 + 2 + 2 + 7 + 3 + 4 + 5 + 3 + 3 + 3 + 3 + 5)/20 = 3.3
The standard deviation is:
[tex]S = \sqrt{\frac{(2 - 3.3)^2 + (3 - 3.3)^2 + \cdots + (3 - 3.3)^2 + (5 - 3.3)^2}{20}} = 1.23[/tex]
What does the Central Limit Theorem states?It states that for distribution of sample means of size n:
The mean remains constant.The standard deviation is of S/sqrt(n).Hence, since 1.23/sqrt(5) = 0.55, the sample means would have a mean of 3.3 and a standard deviation of 0.55.
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the height of a can of coke is 11cm and the radius is 6 cm. the manufacturer of coke want to double the volume of the can but keep the radius as it is , calculate the height of the can?
Answer:
22 cm.
Step-by-step explanation:
Volume = πr^2 h = π 6^2 * 11
So to double the volume
Height will be 2*11 = 22 cm.
Find the perimeter of a parallelogram with corner points at (1,3), (4,7), (9,7), and (6,3)
Decimal approximation
thank you for your help!!
Answer:
20 units
Step-by-step explanation:
[tex] \color{red} \sf Solve \: for \: x : \\ \sf \: \: 4x + 2 = -8?[/tex]
Thank uh !
Answer:
[tex]\huge\boxed{\sf x = -2.5}[/tex]
Step-by-step explanation:
Given equation:4x + 2 = -8
Subtract 2 to both sides
4x = -8 - 2
4x = -10
Divide 4 to both sides
x = -10/4
x = -2.5[tex]\rule[225]{225}{2}[/tex]
Answer:
x = -5/2x = -2.5Step-by-step explanation:
4x + 2 = - 8
Subtract 2 from both sides,
4x = - 8 - 2Subtract 2 from - 8 = - 10,
4x= -10Divide both sides by 4,
4x/4 = -10/4x = - 5/ 2 or x = - 2.5____________________
Determine whether the triangles can be proved similar. If they are similar, write a similarity statement. If they are not similar, explain why.
classify each graph as increasing, decreasing, constant
Answer:
3. increasing
4. decreasing
Step-by-step explanation:
well for graph 3 the values are increasing
and for graph 4 the values are decreasing
Are the triangles similar? If so, state the similarity and the postulate or theorem that justifies your answer.
Answer: The triangles are not similar.
Step-by-step explanation:
Two figures are similar simply if they have the same shape, but not necessarily the same size. In a more mathematical sense, similar figures have the same angle measures and proportionate side lengths.
For reference, side lengths are proportionate when the ratios between corresponding/matching sides are the same.
Since we do not have any angles, we will try using the SSS Similarity Theorem, which states that if all three sides of both triangles are in proportion, then the triangles are similar. We will first list all the side lengths and match corresponding ones.
[tex]\triangle ABC \rightarrow 18,20,32\\ \triangle UVT \rightarrow 14,15,24[/tex]
Since we matched corresponding sides, we can now check whether they have the same ratio).
[tex]\frac{18}{14}=\frac{20}{15}=\frac{32}{24}[/tex]
[tex]\frac{9}{7}=\frac{4}{3}=\frac{4}{3}[/tex]
Not all of the side lengths have the same ratio, so these triangles aren't similar. you must multiply 14 by 9/7 to get to 18, but you need to multiply the other two sides by 4/3 to get to their
You select one red marble from the full bag in exercise 20. what is the probability that the next marble you select will be green without replacement of the first marble?
P(blue) = 1/3
Step-by-step explanation:
Probability for any event A is given by
p(A) = no of times of happening of event A/ total no of occurrence of all the events given under the situation.
A bag contains 5 blue marbles, 6 red marbles, and 4 green marbles
So, total no of occurrences of all the events given under the situation
one can either pick blue, red, or 4 green marbles
Total no. of occurrence of all the event = 5 + 6 + 4 = 15
Now, no occurrence of selecting blue.
since there are 5 blue marbles, there is a chance of selecting blue as 5.
no occurrence of selecting blue = 5
Therefore,
P(blue) = no of occurrence of selecting blue /total no of occurrence of picking any color ball
P(blue) = 5/15 = 1/3.
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What is the slope of line m?
The slope of the line passing through the coordinates 8(0, 0) and (-2 , 1) is -1/2
Slope of a lineThe formula for calculating the slope of a line is expressed as
slope = y2-y1/x2-x1
Given the coordinate points (0, 0) and (-2 , 1), the slope is expressed as:
Slope = 1-0/-2-0
Slope = 1/-2
Slope = -1/2
Hence the slope of the line passing through the coordinates 8(0, 0) and (-2 , 1) is -1/2
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The slope of the line m is - 1 / 2.
How to find the slope of a line?The slope a line can be found as follows:
slope = m = y₂ - y₁ / x₂ - x₁
using (0, 0)(2, -1)
hence,
slope = - 1 - 0 / 2 - 0
slope = - 1 / 2
hence,
slope = - 1 / 2
Therefore, the slope of the line m is - 1 / 2.
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What is the equation of a line that passes through the point -8,-4 and has a slope of 7/3
Answer: [tex]y+4=\frac{7}{3}(x+8)[/tex]
Step-by-step explanation:
See attached image.
Problem: A piece of farmland is a watering plot of land in a circular pattern. A sewer line needs to be installed from a new housing project to a processing plant The city does not want the sewer line to cross the farm land. Can a direct line be installed?
● Let 1 unit = 100 feet.
● The entry to the sewer plant is at (2,3)
● The sewage exit from the housing project is at (12,6)
● The sprinkler system extends 200 ft and the center of the land is at (8,3)
Questions: (1) Will the sewer line cross the farmland? If so then at what points?
(2) If the farmer wants to maximize the farming area and does not want to cross the sewer line, what is the longest sprinkler system that could be installed?
The entry and exit points of (2, 3), and (12, 6), and 200 ft. extension of the sprinkler system gives;
(1) The sewer line crosses the farmland at (6.53, 4.36), and (8.48, 4.9)
(2) The longest installable sprinkler system is approximately 172.4 feet
How can the points where the line crosses the farmland be found?1. The slope of the sewer line is found as follows;
m = (6 - 3)/(12 - 2) = 3/10 = 0.3The equation of the sewer line can be expressed in point and slope form as follows;
(y - 3) = 0.3×(x - 2)y = 0.3•x - 0.6 + 3
y = 0.3•x + 2.4
The equation of the circumference of the sprinkler can be expressed as follows;
(x - 8)² + (y - 3)² = 2²Therefore;
(x - 8)² + (0.3•x + 2.4 - 3)² = 2²
Solving gives;
x= 6.53, or x = 8.48
y = 0.3×6.53 + 2.4 = 4.36
y = 0.3×8.48 + 2.4 = 4.9
Therefore;
The sewer line crosses the farmland at (6.53, 4.36), and (8.48, 4.9)2. When the farmland does not cross the sewer line, we have;
sewer line is tangent to circumference of farmland
Slope of radial line from center of the land is therefore;
m1 = -1/0.3
Equation of the radial line to the point the sewer line is tangent to the circumference is therefore;
y - 3 = (-1/0.3)×(x - 8)
Which gives;
y = (-1/0.3)×(x - 8) + 3
The x-coordinate is therefore;
0.3•x + 2.4 = (-1/0.3)×(x - 8) + 3
x ≈ 7.5y = 0.3 × 7.5 + 2.4 ≈ 4.65The longest sprinkler system is therefore;
d = √((7.5 - 8)² + (4.65 - 3)²) ≈ 1.724
Which gives;
The longest sprinkler system is 1.724 × 100 ft. ≈ 172.4 ft.Learn more about the equation of a circle here:
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In 2016, 5,200 parking permits were issued in a city. The number of parking permits increases by 5% every year. Let y represent the number of parking permits issued x years since 2016. Which type of sequence does the situation represent? A.The situation represents a geometric sequence because the successive y-values have a common ratio of 1.05.
B.
The situation represents an arithmetic sequence because the successive y-values have a common difference of 1.5.
C.
The situation represents a geometric sequence because the successive y-values have a common ratio of 1.5.
D.
The situation represents an arithmetic sequence because the successive y-values have a common difference of 1.05.
The situation represents a geometric sequence because the successive y-values have a common ratio of 1.05.
How to determine the situation?The given parameters are:
Initial = 5200
Rate = 5%
Because the population by 5% every year, then the situation is a geometric sequence.
The common ratio is then calculated as:
Ratio = 1 + Rate
This gives
Ratio = 1 + 5%
Evaluate
Ratio = 1.05
Hence, the situation represents a geometric sequence because the successive y-values have a common ratio of 1.05.
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a. Are the area of a square and the length of its side directly proportional quantities. Explain.
b. Are the perimeter and side length of a square directly proportional quantities. Explain.
**Will mark brainliest for the correct answer with explanation**
**Will report wrong answers**
A square is a plane shape that has an equal length of sides. The required answers to the questions are;
i. Yes, the area of a square and its length of sides are directly proportional.
ii. Yes, the perimeter and length of the side of a square are directly proportional.
A square is a plane shape that has an equal length of sides, with four internal right angles. The area of a square can be determined as:
Area = length x length
= [tex](length)^{2}[/tex]
This implies that the value of area of a given square depends on the value of its length. So that the area and length of sides of a square are directly proportional.
If the value of its length increases, then the value of its area increases, viz-a-viz. Then the area and length of the sides of a square are directly proportional.
The perimeter of a square is the sum of the length of its individual sides. Thus, the perimeter of a square can be determined by:
perimeter = 4 x length
Thus the value of the length determines the value of its perimeter. If the length of its sides increases, so is that of the perimeter. Therefore, the length and perimeter of a square are directly proportional.
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What is the area of the trapezoid below?
Answer:
50 in²
Step-by-step explanation:
→ Find the area of the square
5 × 5 = 25
→ Find the area of the triangle
( 0.5 × 5 × 5 ) = 12.5
→ Double the answer as there is 2 triangles
12.5 × 2 = 25
→ Add the areas together
25 + 25 = 50 in²
In the diagram below, ABC ~ DEC. What is the value of x?
A. 2
B. 3.5
C. 2.5
D. 3
Answer:
x = 3
Step-by-step explanation:
Please refer to the attached photo. (Apologies for the terrible drawing.)
Since we know triangles ABC and DEC are similar, we can use the ratio method to find x.
[tex] \frac{ec}{bc} = \frac{ed}{ba} \\ \frac{25}{5} = \frac{18 - x}{x} \\ \frac{18 - x}{x} = 5 \\ 18 - x = 5x \\ 18 = 5x + x \\ 6x = 18 \\ x = \frac{18}{6} \\ = 3[/tex]