The equation expressing the statement is A = k/r, where k is the constant of proportionality. Given that r = 3 and A = 7, the constant of proportionality can be found by rearranging the equation to k = A × r and substituting the given values to calculate: k = 7 × 3 = 21.
The statement "A varies inversely as r" can be expressed mathematically as an equation: A = k/r, where k is the constant of proportionality. This equation states that A is proportional to 1/r, meaning that as r increases, A decreases, and as r decreases, A increases. To find k, we can rearrange the equation to k = A × r and substitute the given values. In this case, if r = 3 and A = 7, then k = 7 × 3 = 21. Therefore, the constant of proportionality is 21. This equation can be used to determine the values of A, given a value of r, or the values of r, given a value of A. For example, if r = 4, then A = k/4 = 21/4 = 5.25. Conversely, if A = 10, then r = k/A = 21/10 = 2.1. This equation can be used to determine the values of A and r for any given situation.
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Find the area, apothem and each side of this figure. Round your answers to the nearest tenth.
Each side of the given figure measures 2yd and the area of the polygon is A = 8 + 8√2 square units, and apothem is 8 + 8√2 units.
What is octagon?A polygon is a closed, two-dimensional (2-D) figure formed of segments of straight lines. The octagon is an 8-sided polygon in geometry. An octagon is referred to as a regular octagon if all of its sides and angles have equal lengths. In other words, an ordinary octagon has congruent sides. In a standard octagon, the inside angle is 135 degrees, and the outer angle is 45 degrees. A preset set of formulas known as the "octagon formula" can be used to calculate the area and perimeter of a regular octagon.
Given that the perimeter of the octagon is 16yd.
The perimeter is the sum of all the segments or boundaries. So, the perimeter of the octagon is:
P = 8s
16 = 8s
s= 2yd.
The area of a regular octagon is given as:
A = 2a²(1 + √2)
A = 2(2)²(1 + √2)
A = 8 + 8√2
The apothem is given by:
A = 1/2 (s)(a)
8 + 8√2 = 1/2 (2)(a)
a = 8 + 8√2
Hence, each side of the given figure measures 2yd and the area of the polygon is A = 8 + 8√2 square units, and apothem is 8 + 8√2 units.
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MARBLES Jerod has a bag of 20 marbles containing 12 red, 6 green, and 2 blue marbles. What is the probability that Jerod selects two green marbles at random from the bag
Answer:
Step-by-step explanation:
Total marbles = 0
Number of green marbles = 6
so,
Probability of getting 2 green marbles = 2/20 = 1/10
The probability that Jerod selects two green marbles at random from the bag is 1/10
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
We are given that Jerod has a bag of 20 marbles containing 12 red, 6 green, and 2 blue marbles.
Total marbles = 0
Number of green marbles = 6
Therefore,
Probability of getting 2 green marbles ;
= 2/20 = 1/10
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If four loaves of bread costs $8, a loaf of bread and a bag of oranges costs $8, and a loaf of bread, two bags of oranges and a basket of apples costs $19, what is the cost of a basket of apples?
Trey bought five times the number of cookies as Gerald. Gerald has 8 less than the number of cookies as Trey. How many cookies do they each have?
Answer: Let's call the number of cookies Trey has "x".
Gerald has 8 less cookies than Trey, so he has x - 8 cookies.
Trey bought five times the number of cookies as Gerald, so he has 5 * (x - 8) = 5x - 40 cookies.
Combining these two equations, we have:
x + (x - 8) = 5x - 40
Simplifying, we get:
2x - 8 = 5x - 40
Solving for x, we find:
3x = 32
And finally, x = 10.
So Trey has 10 cookies and Gerald has 2 cookies.
Step-by-step explanation:
I’m having a hard time can somebody help please
The capacity required for a kitchen size, given the additional BTU recommended, is A. 10, 000 BTUs.
How to find the capacity ?The area of the kitchen would be:
= Length x Width
= 16 x 10
= 160 ft ²
At this capacity, it means that the recommended capacity would be over 5, 000 BTUs which is for 150 ft² kitchens.
The next recommended capacity is 6, 000 BTUs and with a kitchen requiring 4, 000 BTUs over the capacity, the BTUs is :
= 6, 000 + 4, 000
= 10, 000 BTUs
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A farmer places beehives containing bees in her orchard to pollinate the plants. The table
below shows the ratio of the number of beehives to the number of acres in the orchard.
BEEHIVES PER ACRE:
Number of beehives:
3 9 12 18
Number of acres:
8 24 32 ?
If the bees pollinate the plants at a constant rate, how many acres will be pollinated by the
bees in 18 beehives?
A. 38
B. 40
C. 44
D. 48
The number of acres that will be pollinated by the bees in 18 beehives is given as follows:
D. 48.
What is a proportional relationship?A proportional relationship is defined as follows:
y = kx.
In which k is the constant of proportionality.
The variables for this problem are given as follows:
x: number of beehives.y: number of acres.From the table, the constant is obtained as follows:
3k = 8
k = 8/3.
Hence the equation is of:
y = 8x/3.
The number of acres that will be pollinated by 18 beehives is then given as follows:
y = 8(18)/3
y = 48 acres.
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Answer: D. 48.
Step-by-step explanation:
because the table shows 3k = 8k = 8/3. y = 8x/3. So then it turns into y = 8(18)/3 = y = 48 acres.
who knows how to solve this?
The profit was maximum when the current price raised by $2 then the profit falls in further increase of price.
What Does the axis of graph tells?The axis graph displays the point where two real number lines—one vertical and one horizontal (X axis)—intersect (Y axis). The X axis is referred to as the data set's independent variable, while the Y axis is referred to as the data set's dependent variable.
Given:
We have the Graph in which X- axis shows increase in price over the current value of Milkshake and, Y- axis shows Weekly profit Earned.
From the graph we can see that when the amount increased by $2 that gave the maximum profit.
After that it rising the money in prices leads to falls in profit.
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A sample of n = 9 scores is selected from a parent population with μ = 50 and σ = 12. The probability of obtaining a
sample mean greater than 46 is p = 0.8413.
The statement that the probability of obtaining a sample mean greater than 46 is: p = 0.8413.
How to find the probability from a z-score?The parameters given are;
Sample size; n = 9
Population mean; μ = 50
Population standard deviation; σ = 12
Sample mean; x' = 46
Formula for the z-score here is;
z = (x' - μ)/(σ/√n)
z = (46 - 50)/(12/√9)
z = -4/4
z = -1
From p-value from z-score calculator, we have;
p-value = 0.8413
Thus, the statement is true
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what is the equation of a line when a y-intercept of -3 and a slope of -4/5
Answer:
y= -4/5x -3
Step-by-step explanation:
-6xy if x=-2 y=3
Help
Answer: 8
Step-by-step explanation:
1. There are 40 students in Mr. Jackson's math club. All the students are between the ages of 15 and 18, inclusive. The table shows how many students in the club are each age.
Part A:
Complete table becomes:
Age (x) Probability (p) (x × p)
15 9/40 = 0.225 3.375
16 12/40=0.30 4.8
17 8/40=0.20 3.4
18 11/40=0.275 4.95
....................................................................................................
Total 1.00 16.525
Part B:
Mean becomes: 16.525
What is probability?The area of mathematics known as probability deals with numerical representations of how likely it is for an event to happen or for a claim to be true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty. Fundamentally, probability is a discipline of mathematics that uses computations to foretell the potential outcomes of a certain occurrence. It provides you the power to forecast the outcomes of future occurrences, which makes it seem cool.
Part A:
Age (x) Probability (p) (x × p)
15 9/40 = 0.225 3.375
16 12/40=0.30 4.8
17 8/40=0.20 3.4
18 11/40=0.275 4.95
....................................................................................................
Total 1.00 16.525
Part B:
mean (μ) = ∑⁴(i = 1) xi pi
mean (μ) = 16.525
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How do I Solve for x
Answer:
Step-by-step explanation:
Assuming the sides are equal:
-3x - 6 = 4x + 15
-3x - 6 -15 = 4x + 15 - 15
-3x - 21 = 4x
-3x + 3x - 21 = 4x + 3x
-21 = 7x
-21/7 = 7x /7
-3 = x
Given: AB = 3, BC = 6, CA = 4
GH = 30, HJ = 20, JG = 15
Complete the similarity statement if the triangles constructed with the side lengths given above are similar
triangle ABC ~ triangle _______
Answer:
triangle ABC ~ triangle GHJ
Step-by-step explanation:
The similarity statement compares the two triangles based on their corresponding sides. If two triangles have proportional corresponding sides, then they are similar.
In this case, triangle ABC and triangle GHJ have corresponding sides that are proportional. Specifically, side AB is half the length of side GH, side BC is three-fifths the length of side HJ, and side AC is two-fifths the length of side GJ. Therefore, by the definition of similarity, triangle ABC is similar to triangle GHJ.
The quotient of a number d and 5 is 14
Write the word sentence as an equation.
Answer:
D=5=14 I hope this helps
Step-by-step explanation:
Please help due tonight
Answer:
[tex]x=16\sqrt{30}; \ y=16\sqrt{10}.[/tex]
Step-by-step explanation:
1. if the angles in the given triangle are 30°-60°-90°, then
[tex]2. \ x=32\sqrt{10} *cos[30 к]; \ = > \ x=32\sqrt{10} *\frac{\sqrt{3}}{2} =16\sqrt{30};[/tex]
[tex]3. \ y=0.5*32\sqrt{10}=16\sqrt{10};[/tex]
4. finally, x=16√[30]; y=16√[10].
50^2 - 40 x 6 + 19 - 2 = 2279 - 2 -- are the equations balanced?
Answer:
No, the equations are not balanced.
Step-by-step explanation:
Let's solve 50² - 40 × 6 + 19 - 2.
According to the PEMDAS rule, you will start with exponents as we have no parentheses.50² = 2500.The equation is now 2500 - 40 × 6 + 19 - 2.
2. 40 × 6 = 240.
The equation is now 2500 - 240 + 19 - 2.
3. 240 + 19 = 259.
The equation is now 2500 - 259 - 2.
4. 2500 - 259 = 2241.
The equation is now 2241 - 2.
5. 2241 - 2 = 2.
50² - 40 × 6 + 19 - 2 = 2241.
Now, lets solve 2279 - 2.
2279 - 2 = 22772241 ≠ 2277. In addition, 2241 is not equal to 2277, meaning that the equations are not balanced.
Caitlin, a client of yours since you opened your practice, has become very intrigued by investing in the stock market. She has interest-bearing securities and dividend-paying stocks. She also owns U.S. Securities. She is considering selling $500,000 in stocks. She does not know if she should sell the additional stock for a loss to help offset the stock sale of $500,000. Caitlin called you to ask what tax consequences the interest and dividends will have along with the stock sale. What tax advice would you offer to Caitlin in planning for this situation?
a. Her AGI is under the assumption she sells all of the stock now after receiving $1,000 dividends from the stock. is $34500.
b. The computation under the assumption she sells only half of the stock this year and also receives $1,000 in dividends from the stock is $21000.
What is a stock?All of the shares used to divide ownership of a corporation or company constitute stock in the financial world. A single share of stock represents a fractional ownership interest in the company based on the total number of shares.
Compute her AGI under the assumption she sells all of the stock now after receiving $1,000 dividends from the stock.
This will be the addition of the taxable pension, half of the social security benefits, stock gain, and the dividend received. This will be:
= $10000 + ($7000 × 50%) + $20000 + $1000
= $10000 + $3500 + $20000 + $1000.
= $34500
The computation is under the assumption she sells only half of the stock this year and also receives $1,000 in dividends from the stock.
= $10000 + $10000 + $1000
= $21000
The correct question is given below.
Lucia is a 69-year-old single individual who receives a taxable pension of $10,000 per year and Social Security benefits of $7,000. Lucia is considering the possibility of selling stock she has owned for years and using the funds to purchase a summer home. She will realize a gain of $20,000 when she sells the stock, which has been paying $1,000 of dividends each year. Lucia says her brother recommended that she sell half the stock this year and half next year because selling all of the stock at once would affect the tax treatment of her Social Security benefits.
a) Computer her AGI under the assumption she sells all of the stock now after receiving $1,000 dividends from the stock.
b) Repeat the computation under the assumption she sells only half of the stock this year and also receives $1,000 in dividends from the stock.
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solve the equation -2²-2x²+2x+1=0
Answer:
Step-by-step explanation:
Quadratic X €
Evaluate -20
Answer:
[tex]x=\frac{1}{2} \pm \frac{i\sqrt{5}}{2}[/tex]
Step-by-step explanation:
Lets solve for [tex]x[/tex] in
[tex]-2^2-2x^2+2x+1=0[/tex]
Evaluate [tex]2^2[/tex]
[tex]-4-2x^2+2x+1=0[/tex]
Add [tex]-4[/tex] and [tex]1[/tex].
[tex]-2x^2+2x-3=0[/tex]
Divide both sides of the equation by [tex]-2[/tex].
[tex]x^2-x+\frac{3}{2}=0[/tex]
Now the equation is in standard form.
[tex]ax^2+bx+c=0[/tex]
We can solve this quadratic by completing the square.
Subtract [tex]\frac{3}{2}[/tex] from both sides of the equation.
[tex]x^2-x=-\frac{3}{2}[/tex]
Take one half of the coefficient of [tex]x[/tex] and square it, then add it to both sides.
Add [tex]\frac{1}{4}[/tex] to both sides.
[tex]x^2-x+\frac{1}{4} =-\frac{3}{2}+\frac{1}{4}[/tex]
[tex]x^2-x+\frac{1}{4} =-\frac{5}{4}[/tex]
The left hand side is a perfect trinomial square.
Factor the left hand side by writing it as a square.
[tex]\left(x-\frac{1}{2}\right)^2 =-\frac{5}{4}[/tex]
Take the square root of both sides to eliminate the exponent.
[tex]x-\frac{1}{2} =\pm\sqrt{-\frac{5}{4}}[/tex]
Rewrite [tex]\frac{5}{4}[/tex] as [tex]\left(\frac{i}{2} \right)^2 *5[/tex]
[tex]x-\frac{1}{2} =\pm\sqrt{\left(\frac{i}{2} \right)^2 *5}[/tex]
Pull terms out from under the radical.
[tex]x-\frac{1}{2} =\pm \frac{i}{2} \sqrt{5}[/tex]
Combine [tex]\frac{i}{2}[/tex] and [tex]\sqrt5[/tex].
[tex]x-\frac{1}{2} =\pm \frac{i\sqrt{5}}{2}[/tex]
Add [tex]\frac{1}{2}[/tex] to both sides of the equation.
[tex]x=\frac{1}{2} \pm \frac{i\sqrt{5}}{2}[/tex]
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it takes 25 people 90 days to do a job. how many people can do that job in 15 days?!
Answer:
25people =90days
? =15days
cross multiply
25×15÷90
=375÷90
=4.16666666
approximately =4.2
150 people needed to complete the work in 15 days.
Given that 25 people take 90 days to do a job.
Relation between number of people and number of days needed to complete a work when work quantity is fixed is inversely proportional.
That is, if number of people is less then the work needs more time and vice versa.
To complete a job in 90 days the number of people required is = 25
To complete that same job in 1 days the number of people needed is = 25 * 90 = 2250
To complete the same job in 15 days the number of people needed is = 2250/15 = 150.
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Sam counted 14 blinks in 20 seconds. How many times does Sam blink in a day if we assume he sleeps for eight hours.
Answer:
35280 blinks
Step-by-step explanation:
1 day = 24 hours
24 - 8 = 16 hours
1 hour = 3600 seconds
16 hours = 50400 seconds
Now we have to find how many blink in 1 second
14 divided by 20 = 0.7 blink in 1 second
Now we take
0.7 times 50400 = 35280 blinks
So, Sam blink 35280 times a day
1
Unless otherwise informed, report all answers in standard notation to 3 significant figures.
1 point
How many Gg/hr are there in 8.34 x 10^6 ton/wk?
There are 0.0496 Gg/hr in 8.34 x 10^6 tons/week
How to determine the number of Gg/hr in ton/wk?To convert from tons/week to Gg/hr:
you need to divide the number of tons by the number of hours in a week and then multiply by 1 Gg/ton.
There are 168 hours in a week, so:
8.34 x 10^6 ton/wk / 168 hrs/week = 49642.85 ton/hr
And 1 Gg = 1,000,000 ton, so:
49642.85 ton/hr * 1 Gg/1,000,000 ton = 0.0496 Gg/hr
So, 8.34 x 10^6 tons/week is equivalent to 0.0496 Gg/hr.
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EQUATION OF A STRAIGHT LINE!!
Answer:
Below
Step-by-step explanation:
y - y1 = m ( x - x1 ) is point slope form of a line m = slope
For point ( -1,3) :
y-3 = 3 (x- -1)
y -3 = 3x + 3 add 3 to both sides
y = 3x + 6 The underlined equations are the same line just different forms....you'll need to pick the one you need
Next time, the rabbit from the previous problem started at 10 where on the number line can he be after the same three jumps?
This is the previous problem: A rabbit started at point 0 and made 3 jumps a jump of 4 units then a jump of 2 units and then a jump of 1 unit we do not know the direction of either jump where on the line could the rabbit be.
After the 3 jumps a jump of 4 units then a jump of 2 units and then a jump of 1 unit is at 20 on number line.
What is number line?A number line is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally or vertically.
A rabbit started at point 0 and made 3 jumps a jump of 4 units then a jump of 2 units and then a jump of 1 unit we do not know the direction of either jump where on the line could the rabbit be.
Now, Rabbit is at 10 on number line
If rabbit made same jumps, rabbit will be at
10+3+4+2+1
= 20
Therefore, after the 3 jumps a jump of 4 units then a jump of 2 units and then a jump of 1 unit is at 20 on number line.
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Q1. If the facility treats 16,000,000 liters of water per day, and 25,000 milligrams of ozone is used for processing the water, what is the ratio of ozone used to the total amount of water treated per day?
Answer:
The ratio of ozone used to the total amount of water treated per day can be calculated as follows:
Ozone used = 25,000 mg
Amount of water treated = 16,000,000 liters = 16,000,000 x 1000 ml = 16,000,000 x 1000 x 1000 mg = 16,000,000,000,000 mg
Ratio of ozone used to water treated = 25,000 / 16,000,000,000,000 = 1.5625 x 10^-11
So, the ratio of ozone used to the total amount of water treated per day is approximately 1.5625 x 10^-11.
[tex]15.625*10^{-4}[/tex] miligrams of ozone / liter of water.
Step-by-step explanation:1. Identify the data.16,000,000 liters of water
25,000 milligrams of ozone
2. Create the ratio of ozone.A ratio is basically telling how much of one thing corresponds to a unit of another thing. Hence, let's express this as a division in the following fashion:
[tex]\frac{25,000}{16,000,000} =\\ \\\frac{0.0015625}{1} =\\ \\\frac{15.625*10^{-4} }{1}[/tex]
3. Express as a ratio of units.[tex]15.625*10^{-4}[/tex] miligrams of ozone / liter of water.
Jacob just bought a new pair of basketball shoes. He expects the shoes to last for two hundred twenty-five games. He plays two games a week. Define a unit for the time Jacob has been using his new pair of basketball shoes. Enter a variable for the time Jacob has been using his new pair of basketball shoes and use this variable to write an expression for the number of games remaining for the shoes.
The expression for the time of the number of games remaining for shoes will be T = 225 - 2W.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Jacob just bought a new pair of basketball shoes. He expects the shoes to last for two hundred twenty-five games. He plays two games a week.
The expression for the life of the shoes will be written as:-
T = 225 - 2W
Here, T is the time and W is the number of weeks.
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j=JUST HELP MY FAMILY IS MAD partition and shade to show
5 over 7
.
The partition and shade to show 5/7 is added as an attachment
How to make the diagramFrom the question, we have the following parameters that can be used in our computation:
partition and shade to show 5/7
To do this, we can make use of a tape diagram
Such that the size of each partition is equal
Using the above as a guide, we have the following:
5/7 implies that we create 7 partitions and shade 5 sections
Next, we make the tape diagram (see attachment)
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a cone has a volume of 8 pi cubic inches what is the radius of the cone?
Answer:
[tex]r = \sqrt{\frac{24}{h}}[/tex] inches
Step-by-step explanation:
Volume of a cone = [tex]\frac{1}{3} \pi r^{3}h[/tex]
where: r = radius of cone
h = perpendicular height of the cone
Provided volume of cone = 8π cubic inches
[tex]8\pi = \frac{1}{3}\pi r^{2} h[/tex]
Cross multiplication is applied and 'r' is isolated:
[tex]3(8\pi ) = \pi r^{2} h[/tex]
[tex]24\pi =\pi r^{2} h[/tex]
[tex]r^{2} h = \frac{24\pi}{\pi}[/tex]
[tex]\pi[/tex] in the numerator and denominator cancel each other out completely:
[tex]r^{2} h = 24[/tex]
[tex]r^{2} = \frac{24}{h}[/tex]
Taking the square root on both sides of the equation in order to get rid of the square:
[tex]r = \sqrt{\frac{24}{h}}[/tex] inches
kenia wants to buy a $75.00 skateboard. She has 25.00 saved so far. she mows lawns to make extra money and earns 20.00 for each lawn she mows. Which inequality can be used to determine the number of lawns, x, she needs to mow to have enough money to buy the skateboard
Step-by-step explanation:
75.00 - 25.00 = 50.00
50.00 / 20.00 = 2.50
So, she needs to mow 2.5 lawns or more to have enough money to buy the skateboard.
The inequality can be expressed as:
20.00 * x >= 50.00
x >= 2.50
So, the inequality "x >= 2.50" can be used to determine the number of lawns she needs to mow to have enough money to buy the skateboard.
What is the slope of the line through (3, 9) and (x, y) for y = x² and x = 2.97? x = 3.001? x = 3 + h? What happens to this last slope when h is very small (close to 0)? Sketch the graph of y = x² for x near 3.
When h is very small, then the slope would be equal to 6
How to solve for the slopeWe have
m = y2 - y1 / x2 - x1
where 2.97² - 3² / 2.97 - 3
we would have
-0.1791 / -0.03
m = 5.97
We have to do the same for x = 3.001
3.001² - 3² / 3.001 - 3
m = 6.001
finally we have to solve for x = 3 + h
m = [tex]\frac{(3 + h)^2-(3)^2}{3+h-3}[/tex]
m = [tex]\frac{9+h^2+6h-9}{h}[/tex]
m = [tex](\frac{h}{h})*(\frac{h+6}{1} )[/tex]
m = h + 6
if h is close to 0 then m = 6
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I NEED HELP ASAP MATH O