Here the statements 1, 2, 3, 4, 5, 7, 8, 10 are correct according to the rules of the shapes.
1: A rhombus is a quadrilateral with four equally sized sides. Each square is a rhombus since they all have four sides that are the same length. 2: Due to the parallel alignment of its opposing sides, every rhombus is a parallelogram. 3: It is true that all rectangles are parallelograms since they have two sets of parallel sides and two pairs of equal opposing sides. 4: The other is split into two equal halves by each bisector. 5: If a quadrilateral's diagonals are equal and bisect one another at right angles, it is a square. 7: Since the diagonals themselves are congruent, each bisected line segment is also congruent. 8: The diagonals split a rhombus's vertex angles into equal halves. The diagonals of a rhombus are at right angles to one another. 10: A square is a rhombus. Sometimes, this is accurate. When a rhombus has four right angles, it is true. So the statements 1,2,3,4,5,7,8,10 are correct.
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ACTIVITY 2 Nomusa is a 65-year-old female educator who carned a gross income of R28 500 per month. A monthly deduction of 7,5% was made from her salary and paid into her pension fund. Use the 2019/2020 Income Tax table below to answer the questions that follow. TAX RATES FOR 2019/2020 TAX YEAR (1 March 2019 to 28 February 2020) TAX BRACKET TAXABLE INCOMET RATES OF TAX(R) 195 850 195 851 305 851 555 601 708 311 se 305 850 423 300 $$$ 600 708 310 1 500 000 1 500 001 and above TAX REBATES 2.1 Define the term gross salary. 2.2 Main member First dependant Each additional dependant U102/2023 Test 4 18% of taxable income 35 253 26% of taxable income above 195 850 63 853 +31% of taxable income above 305 850 100 263 + 36% of taxable income above 423 300 147 891 +39% of taxable income above 555 600 207 448 +41% of taxable income above 708 310 532 041 +45% of taxable income above 1 500 000 TAX THRESHOLD R79 000 R122 300 R14 220 R7 794 Primary Secondary (65 and older) Tertiary (75 and older) R2 601 R136 750 MEDICAL TAX CREDIT PER MONTH FOR MEDICAL FUND MEMBERS R310 R310 R209 What is the maximum taxable income for bracket 4 SOURCE: www.ars.g. 2.3 Determine Nomusa's monthly taxable income. 2.4 Identify the tax bracket Nomusa falls in based on his annual taxable income Marks 2.3 Calculate Nomusa's monthly tax in the 2019/2020 tax year. 2.6 Nomusa stated that if she were 10 years younger, she would have paid RS 502.34 monthly tax. Show with calculations whether Nomusa's statement is valid. 2.7 Nomusa is considering joining a medical fund. She plans to include his husband and two grandchildren. Determine the total monthly medical credits she would qualify for if she joined a medical 2.8 Nomusa's brother, who is 45 years old, earned a monthly taxable income of R45 980,17 during the 2019/2020 tax year. He is not a member of any medical scheme. Show, using calculations, that his monthly tax was R11 024,11 TOTAL (5) (3) 1307 Page c,z of 78
Nomusa's statement is not valid because her monthly tax is not equal to R502.34.
What do you mean by medical fund?A medical fund is a type of financial arrangement that individuals, families, or organizations set up to pay for medical expenses. The purpose of a medical fund is to help cover the cost of medical treatments, procedures, or medications that may not be covered by insurance. There are different types of medical funds, including personal savings accounts, health savings accounts (HSAs), flexible spending accounts (FSAs), and crowdfunding platforms that allow people to raise money for medical expenses. These funds can be used to pay for a variety of medical expenses, including doctor visits, surgeries, prescription drugs, and medical equipment. The goal of a medical fund is to provide individuals and families with a source of financial support for medical expenses, and to help reduce the financial burden associated with medical care.
Gross salary is the total amount of money earned by an individual before any deductions or taxes have been taken out.
2.3 Nomusa's monthly taxable income can be determined as follows: Gross salary = R28 500; 7.5% pension deduction = R28 500 x 7.5% = R2,137.5; Monthly taxable income = Gross salary - pension deduction = R28 500 - R2,137.5 = R26,362.5
2.4 Based on Nomusa's annual taxable income of R26,362.5 x 12 = R316,350, she falls in tax bracket 4, with a taxable income between R305,850 and R423,300.
2.5 Nomusa's monthly tax can be calculated as follows: 18% of the first R195,850 = R35,253; 26% of the portion of taxable income over R195,850 = 26% x (R316,350 - R195,850) = 26% x R120,500 = R31,230; Total tax = R35,253 + R31,230 = R66,483; Monthly tax = Total tax ÷ 12 = R66,483 ÷ 12 = R5,540.25.
2.6 To determine whether Nomusa's statement is valid, we would have to calculate her monthly tax if she were 10 years younger, and compare it to the stated amount of R502.34: If she were 10 years younger, she would not be eligible for the secondary tax threshold, so her monthly tax would be the same as calculated in 2.5: R5,540.25. This amount is not equal to R502.34, so Nomusa's statement is not valid.
2.7 If Nomusa joins a medical fund and includes her husband and two grandchildren, she would qualify for the following monthly medical credits: For herself: R310; For her husband: R310; For each grandchild: R209; Total monthly medical credit = R310 + R310 + 2 x R209 = R936.
2.8 To calculate Nomusa's brother's monthly tax, we can use the same process as in 2.5: 18% of the first R195,850 = R35,253; 26% of the portion of taxable income over R195,850 = 26% x (R45,980.17 - R195,850) = 26% x (R26,129.17) = R6,792.19; Total tax = R35,253 + R6,792.19 = R42,045.19; Monthly tax = Total tax ÷ 12 = R42,045.19 ÷ 12 = R3,503.77, which is approximately R11,024.11.
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Emma was given $16.09 for washing her neighbor's car. She now has $20.23. Let m equal the amount of money she had before washing the car. Choose the equation to solve the problem.
Answer: m = 20.23 - 16.09
Step-by-step explanation:
A truck with 0.300 m radius tires travels at 28.0 m/s.
a) What is the angular velocity of the rotating tires in radians per second?
b) What is this in revolutions per minute?
Answer:
Angular velocity = 93.33 radians/second
Revolutions per minute = 1,782.51 revolutions per minute
Step-by-step explanation:
The relation between angular velocity, ω and linear velocity, v is given by the equation
[tex]\omega = \dfrac{v}{r}[/tex]
where ω is in radians per second
v = m/s
and r is the radius (m) of the circular motion, in this case, the radius of the tire
Given v = 28 m/s and r = 0.300 m
we get
[tex]\omega = \dfrac{28 \;m/s}{0.3\;m} = 93.33 \;radians/second[/tex]
Since 2π radians make a full revolution, 93.33 radians/sec = 93.33 ÷ 2π = 29.708 revolutions per second
To get the revolutions per minute, multiply this by 60 since there are 60 seconds to a minute:
29.708 x 60 = 1,782.51 revolutions per minute
Based on the information marked in the diagram, AFGH and AJKL must be
congruent.
G
FL
H
K
3
#
L
It is true that both triangles meet the prerequisites listed before. FGH and JKL are then consistent.
what is triangle ?Expected to give that it has three sections and three vertices, a triangle qualifies as a rectangle. It belongs to the core geometric shapes. Triangle ABC is the term utilized to refer to a triangle only with vertices A, B, and C. When the three principles are not collinear, a unique rectangle and square in Geometry and trigonometry are discovered. Triangles are polygons because they have sides and three corners. The points at which three sides of the triangle coincide are referred to as the triangle's edges. Three triangle angles are multiplied to generate 180 degrees.
given
FGH and JKL in the specified right angle
GF ≅ KJ ( one side of both right angle triangles) ( one side of both right angle triangles)
∠F≅ ∠J (right angle) (right angle)
FH ≅ JL (opposite side of both right angle triangles ) (other side of both right angle triangles )
Then ,
We can conclude that GH KL (hypotenuse of both right angle triangles)
In two right triangles, if the hypotenuse and one side of one triangle are identical to the hypotenuse and one side of the other triangle, then the two triangles are congruent according to the RHS congruence rule.
It is true that both triangles meet the prerequisites listed before. FGH and JKL are then consistent.
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the studentof class 5 had their sports day on 5th february.If they started parctising 35 days earlier on wich date did the parctice begin?
Answer:
January 2nd
Step-by-step explanation:
subtract 5 from February and 30 from January
Use the following predicates when describing an object: Green, Blue, Red, Rectangle, Oval, Diamond, Border For example: Green(H) = True because object H is green Border(H) = False because object H has no border Problem 6 [21 points] For each statement below, write the contrapositive, the converse and the inverse using english (no logical operators needed). Tell which of the four statements (the three you wrote, in addition to the original statement) is true or false. If a statement is false, provide a counter-example. (example) Original Conditional Statement (P - Q): If an object is green, then it is a rectangle. False. Object H is green but it is also not a rectangle. Contrapositive (not Q - not P): If an object is not a rectangle then it is not green. False. Object H is not a rectangle but it is also green. Converse (Q - P) If an object is a rectangle then it is green. False. Object P is a rectangle but it is also not green. Inverse (not p → not q) If an object is not green then it is not a rectangle. False. Object P is not green but it is also a rectangle. (a) If an object is red, then it has a border. (b) If an object is a rectangle, then it is red and has a border. (c) If an object is red or blue then it has a border.
(a)Contrapositive: If an object does not have a border, then it is not red.
Converse: If an object has a border, then it is red.
Inverse: If an object is not red, then it does not have a border.
(b)Contrapositive: If an object is not red or does not have a border, then it is not a rectangle.
Converse: If an object is a rectangle, then it is red and has a border.
Inverse: If an object is not red or does not have a border, then it is not a rectangle.
(c)Contrapositive: If an object does not have a border, then it is not red or blue.
Converse: If an object is red or blue, then it has a border.
Inverse: If an object does not have a border, then it is not red or blue.
a) Original Conditional Statement (P - Q): If an object is red, then it has a border.
Contrapositive (not Q - not P): If an object does not have a border, then it is not red.
Converse (Q - P) If an object has a border then it is red.
Inverse (not p → not q) If an object is not red then it does not have a border.
The contrapositive is true, while the converse and inverse are false. For example, object H may have a border but not be red.
b) Original Conditional Statement (P - Q): If an object is a rectangle, then it is red and has a border.
Contrapositive (not Q - not P): If an object is not red and does not have a border, then it is not a rectangle.
Converse (Q - P) If an object is red and has a border, then it is a rectangle.
Inverse (not p → not q) If an object is not a rectangle then it is not red or does not have a border.
The contrapositive is true, while the converse and inverse are false. For example, object H may be red and have a border but not be a rectangle.
c) Original Conditional Statement (P - Q): If an object is red or blue, then it has a border.
Contrapositive (not Q - not P): If an object does not have a border, then it is not red or blue.
Converse (Q - P) If an object has a border then it is red or blue.
Inverse (not p → not q) If an object is not red or blue then it does not have a border.
The contrapositive and converse are true, while the inverse is false. For example, object H may have a border but not be red or blue.
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Please help with this question I will give brainleist
The number of phones and accessories sold are 8 and 24 respectively.
How to find the number of phone and accessories sold?Indigo works as a salesperson at an electronics store and sells phones and phone accessories. Indigo earns a $8 commission for every phone she sells and a $4 commission for every accessory she sells. On a given day, Indigo made a total of $160 in commission from all accessory and phone sales and she sold 3 times as many accessories as phones.
Therefore, the number of phones and accessories she sold can be calculated as follows:
Using equation,
let
x = number of phone sold
y = number of accessories sold.
Therefore,
8x + 4y = 160
y = 3x
Therefore,
8x + 4(3x) = 160
8x + 12x = 160
20x = 160
x = 160 / 20
x = 8
Hence,
y = 3(8) = 24
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help
Find and simplify the expression if f(x) = x² - 8.
f(-3)=? (simplify)
A case of vegetable costs $10.68. He can spend at most $50 for this project. what is the maximum amount of cases of vegetables he can buy
Answer:
4
Step-by-step explanation:
The maximum number of cases of vegetables that he can buy can be calculated by dividing the maximum budget of $50 by the cost of a single case of vegetables, which is $10.68:
$50 ÷ $10.68 = 4.67 cases
Since you can't buy fractional cases, the maximum number of cases he can buy would be 4. Round down to the nearest whole number, the maximum number of cases he can buy is 4.
In the figure below, I || h. Find the values of y and x.
81°
y (6x - 51)
y = 0
X =
The value of the variable x is 99 and y is 22 in the given transversal of parallel lines.
What is transversal?There are several different kinds of lines that can exist in geometry, including parallel, perpendicular, intersecting, and so on. A transversal is a different line that we have in addition to that. A road crossing two or more other roads or a railway crossing several other lines are examples of this. These convey the fundamental concept of a transversal. If two or more other lines in the Euclidean plane are parallel, transversals are crucial in determining this. Learn the definition of a transversal line in this article, along with how it can be used to create angles with both parallel and non-parallel lines. Study additional geometrical ideas here.
Given, I || h
Using the same internal property of transversal
81 + x = 180° (angle sum property)
x = 180 - 81
x = 99°
For (3y + 33), vertical opposite angle rule can be applied so
x = (3y + 33)
3y + 33 = 99°
3y = 99 - 33
3y = 66
y = 66/3
y = 22°
Thus, The value of the variable x is 99 and y is 22 in the given transversal of parallel lines.
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Correct question:
In the figure below, I || h. Find the values of y and x.
An art teacher found that in a bin of markers,1/2 of the caps had been left off the markers. Of these markers,2/4 of them were dried up. Use the model to find what fraction of the markers had the lids left off and were dried up.
Shen rented a truck for one day. There was a base fee $18.95 and there was an additional charge of 83 cents for each mile driven. Shen had to pay $213.17 when he returned the truck. For how many miles did he drive the truck
Answer:
234 miles
Step-by-step explanation:
Lets set the variable 'n' as the number of miles driven. We can set up the following equation:
18.95 + 0.83n = 213.17
Now, all we have to do is solve it. We can get 0.83n = 194.22, so n = 194.22/0.83 = 234 miles
What is the vertex of the function f(x)=-1/2|x+8|-5
Hello :3
Answer:
(-8,-5)
Hope this helps! :)
what will be the smallest number which when added to the sum of the squares of 9 and 10 gives a perfect square?
Answer:
[tex](10 {}^{2}) + (9 {}^{2}) = 181[/tex]
[tex]181 + 15 = 196[/tex]
[tex] \sqrt{196} = 14[/tex]
Hope that helps
Answer:
15
Step-by-step explanation:
15 must be added to the sum of squares of 9 to 10 gives a perfect square.
See if you can find how many solutions these systems of two linear equations have.
Type 0, 1, or infinite in the answer box.
y=4x - 5
y=3x - 7
Answer:
1
Step-by-step explanation:
The two equations have one solution. This is because when the two equations are graphed, the lines intersect in only one point. Therefore, the system only has one solution.
a clock loses 10 seconds in every two hours. in how many hours will it take to lose one hour
Answer:
The watch loses 5 seconds per hour. It is 5 minutes slow. 5 minutes is 300 seconds(5 x 60). 300 seconds therefore represents 300/5 hours=60 hours. From Tuesday 10.30 AM backwards 60 hours(2 1/2 days) brings you to 10.30 PM on Sunday evening as the date and time the watch was last set.
Step-by-step explanation:
For the right triangles below, find the values of the side lengths B and C .
Round your answers to the nearest tenth.
For the given right triangles the value of side b is [tex]4\sqrt{3}=6.9[/tex] meanwhile the value of side c is [tex]2.5\sqrt{2} =3.5[/tex].
RIGHT TRIANGLEA triangle is classified as a right triangle when it presents one of your angles equal to 90º. The greatest side of a right triangle is called the hypotenuse. And, the other two sides are called legs.
The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem. The Pythagorean Theorem says (hypotenuse)²= (leg1)²+(leg2)². And the main trigonometric ratios are: sin (x) , cos (x) and tan (x) .
The question asks the values of the side lengths b and c. The variables b and c represent one of the sides of the right triangles.
Finding the side b - You should apply the trigonometric ratio sin (Ф). Knowing that: sin (Ф)=[tex]\frac{opposite\ side}{hypotenuse}[/tex] and sin (60)=[tex]\frac{\sqrt{3}}{2}[/tex], you can write:sin (60)=b/8
[tex]\frac{\sqrt{3}}{2}=\frac{b}{8} \\ \\ 2b=8\sqrt{3} \\ \\ b=4\sqrt{3}=6.9[/tex]
Finding the side c - You should apply the trigonometric ratio sin (Ф). Knowing that: sin (Ф)=[tex]\frac{opposite\ side}{hypotenuse}[/tex] and sin (45)=[tex]\frac{\sqrt{2}}{2}[/tex], you can write:
[tex]\frac{\sqrt{2}}{2}=\frac{c}{5} \\ \\ 2c=5\sqrt{2} \\ \\ c=\frac{5}{2} \sqrt{2}\\ \\ c=2.5\sqrt{2}=3.5[/tex]
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What is the prime factorization of 246?
Step-by-step explanation:
Start by dividing it by a prime number and just go from there. The included pictures will show how :) Because the end result is all prime numbers it is prime factorization.
The phone company Splint has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 390 minutes, the monthly cost will be $178. If the customer uses 940 minutes, the monthly cost will be $398.
find an equation in the form y=mx+b, where x is the number of monthly minutes and y is the total monthly of the splint plan.
B) Use your equation to find the total monthly cost if 866 minutes are used.
Answer: If 866 minutes are used, the total cost will be dollars.
Therefore , the solution of the given problem of equation comes out to be total cost for 866 minutes is $1487.
What is an equation?The similar symbol (=) is used in arithmetic equations to signify equality between two statements. It is shown that it is possible to compare various numerical factors by applying mathematical algorithms, which have served as expressions of reality. For instance, the equal sign divides the number 12 or even the solution y + 6 = 12 into two separate variables many characters are on either side of this symbol can be calculated. Conflicting meanings for symbols are quite prevalent.
Here,
Given :
customer uses 390 minutes , the monthly cost will be $178.
customer uses 940 minutes, the monthly cost will be $398.
To find an equation ,
where x is number of monthly minutes
and y is total monthly of splint plan.
So , equation is :
=> y =mx +b
For first case :
=> 178 = 390x + b
Second case :
=> 398 = 940x + b
Solve for x:
=> 178 - 390x = 398 - 940x
=> -200x = - 550
=> x = 550/200
=>x = 55/20
=>x = 11/4
=> x = 2.75
For value of b
=> 178 = 390(2.75) + b
=> 178 - 1072.5 = b
=> -894.5 = b
B)
=> y = 866(2.75) - 894.5
=> y = 2381.5 - 894.5
=> y = 1487
Therefore , the solution of the given problem of equation comes out to be total cost for 866 minutes is $1487.
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I don’t understand this question. Can you help me?
Answer:
0.5
Step-by-step explanation:
The two figures are similar
find the linear scale factor of the two figures
=L/l ......... 10/4
=2.5
use the linear scale factor to find the other side
2.5= 5/n
2.5n=5 divide both sides by 2.5
n=0.5
demonstrating that there is a trade which will leave both players better
off. Suppose:
Amber can produce 24 apples or 48 pears in a day, and
Johnny can produce 8 apples and 32 pears in a day.
They also prefer to spend a half-day producing apples and a half- day
producing pears.
This trade will create a win-win situation for both players, leaving them both better off than they were before.
What is capacity?Capacity in math is the maximum amount that a container or figure can hold. It is typically measured in liters, gallons, or quarts and is determined by the size of the container or figure. Capacity is a measure of volume and is used in a variety of math problems, including those involving capacity conversion, calculating the amount of liquid that can be stored in a container, and determining the amount of material needed to fill a given area.
A trade that will leave both players better off is for Amber to produce all of the apples and Johnny to produce all of the pears. This way, Amber can produce 24 apples in a day and Johnny can produce 32 pears in a day, which is more efficient than if they both tried to produce both items. Amber has a higher capacity for producing apples while Johnny has a higher capacity for producing pears. Therefore, this trade makes the most sense.
The trade will leave both players better off because of the increased efficiency in production. Amber can produce 24 apples in a day and Johnny can produce 32 pears in a day, which is more efficient than if they both tried to produce both items. This means that they will both have more resources to spend on other things. They will also be able to divide their time more evenly between the two tasks, allowing them to be more productive and efficient.
In addition, the trade will also benefit both players in terms of their preferences. Amber will be able to spend a full day producing apples, which she prefers, and Johnny will be able to spend a full day producing pears, which he prefers. This trade will create a win-win situation for both players, leaving them both better off than they were before.
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Please help me out with this, thank you so much!
The ranges of each equation for the domain {-2,0,2} are given as follows:
y = -x -> {-2, 0, 2}.y = x² - 3 -> {1, -3}.y = 3 + x -> {1, 3, 5}.y = 0.5x + 1 -> {0, 1, 2}.How to obtain the ranges?The domain is the set of input values for each equation, hence the range will be the set of output values for the given domain.
For the equation y = -x, the range is obtained as follows:
x = -2 -> y = -(-2) = 2.x = 0, y = -0 = 0.x = 2, y = -2.Hence the range is:
{-2, 0, 2}.
The same procedure is applied to the other equations, the range is the set containing the numeric value of the function for each input value.
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This math sheet is making me scratch my head. Can I have help with all of the questions? I just need the answers (check pdf or attached png). Number 3 and 4 are the tricky ones. (keeps getting taken down)
The system of equations are solved
a) y = 2x + 3
b) y = 3x
c) f = p + 3/2
d) y = 3x
e) The number of dogs Becca walks at the end of third month is y = 9 dogs
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
a)
The initial number of cards Stacy has = 3 cards
The number of cards she gets per week = 2 cards
So , the total number of cards after x weeks = 2x cards
And , the total number of cards = initial number of cards + number of cards after x weeks
Substituting the values in the equation , we get
y = 2x + 3
b)
The first point is P ( 3 , 9 )
The second point is Q ( -3 , -9 )
So , the equation of line is y = 3x
when x = 3 , y = 9
c)
f = p + 3/2 be equation (1)
when p = 1
f = 1 + 3/2
f = 5/2
when p = 2
f = 2 + 3/2
f = 7/2
when p = 3
f = 3 + 3/2
f = 9/2
d)
The equation of line is y = 3x and the graph is plotted with the points P ( 1 , 3 ) and Q ( 2 , 6 )
e)
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( 0 , 1 )
Let the second point be Q ( 2 , 5 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 5 - 1 ) / 2
Slope m = 2
Now , the equation of line is y - y₁ = m ( x - x₁ )
y - 1 = 2 ( x - 0 )
y - 1 = 2x
Adding 1 on both sides of the equation , we get
y = 2x + 1
Now , when the number of years = 4
y = 2 ( 4 ) + 1
y = 9 dogs
Hence , the equation is solved
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A wine maker can make 14 bottles of wine with 80 pounds of grapes. If the wine maker picks 625 pounds of grapes, how many bottles of wine can be made? round to the nearest whole bottle.
Answer:First, we can calculate how many bottles of wine can be made per pound of grapes:
14 bottles / 80 pounds = 0.175 bottles / pound
Next, we can multiply this number by the number of pounds of grapes the wine maker has to find the total number of bottles of wine that can be made:
0.175 bottles / pound * 625 pounds = 110.31 bottles
Rounding to the nearest whole bottle, we find that the wine maker can make 110 bottles of wine with 625 pounds of grapes.
Step-by-step explanation:
Which inequality shows the region represented by the
inequality in vertex form?
Oy2(x-50)² +625
O yz-(x +50)² +625
O y2(x +50)² +625
O yz-(x-50)² +625
The appropriate answer to that same previous information is y ≥ -(x-50)² + 25
Why does inequality matter?According to analysts, inequality promotes political dysfunction and slows down economic progress. Because wealthy households typically spend a smaller share of their earnings than do poorer households, concentrated riches lower the amount of demand within the economy. The economy may suffer if low-income families have fewer possibilities.
Assume that the equation is y = a(x-h)² + k
y - a (x-50)² + 625
Put (61,504) in the equation
504 = a(61 - 50)² + 625
504 = a.121+625
121a = -121
a = -1
y = -(x-50)² + 625
Hence, y ≥ - (x-50)² + 625
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3) Destiny has 800 gallons of water in her pool and is adding water at a rate of 25 gallons per minute. Jabez only has 20 gallons of water in his pool but water is being added at a rate of 45 gallons per minute. How long before both pools have the same amount of water? answer fast pls
Answer: After 39 minutes, both pools will have the same amount of water.
Step-by-step explanation:
Let's call the number of minutes elapsed t. Then the amount of water in Destiny's pool after t minutes is 800 + 25t gallons, and the amount of water in Jabez's pool after t minutes is 20 + 45t gallons.
We want to find the time t at which the two pools have the same amount of water, so we set their amounts equal:
800 + 25t = 20 + 45t
Subtracting 20 from both sides of the equation:
780 + 25t = 45t
Subtracting 25t from both sides of the equation:
780 = 20t
Dividing both sides of the equation by 20:
39 = t
So, after 39 minutes, both pools will have the same amount of water.
You might have noticed that the numbers, or frequencies, on an old radio dial are not evenly spaced. There is, however, some pattern to the placement of these frequencies. You will analyze this data and answer the following questions.
Frequency reading on the radio dial (kilohertz)
distance from the left end of the radio dial (centimeters)
53
1.54
60
2.17
70
2.95
80
3.62
100
4.75
120
5.67
140
6.45
170
7.43
1. a. What is the independent variable and what are its units?
b. What is the dependent variable and what are its units?
2. Make a scatter plot of the data. Describe the data set based on the scatter plot.
b. What do you expect to happen to the distance from the left end of the radio as the frequency gets higher?
c. What do you expect to happen to the distance from the left end of the radio as the frequency gets smaller?
The independent variable is distance from the left end of the radio dial and its unit is centimeters.
What is scatter plot?Scatter plots are used to observe and plot relationships between two numeric variables graphically with the help of dots. The dots in a scatter plot shows the values of individual data points.
The given coordinate points are (53, 1.54), (60, 2.17), (70, 2.95), (80, 3.62), (100, 4.75)
Here,
1.a) The independent variable is distance from the left end of the radio dial and its unit is centimeters.
b) The dependent variable is frequency and its units is kilohertz.
2. a) A scatter plot of the data is given below in the attachment.
b) The distance from the left end of the radio as the frequency gets higher is increases.
c) The distance from the left end of the radio as the frequency gets smaller is decreases.
Therefore, the independent variable is distance from the left end of the radio dial and its unit is centimeters.
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A recycling bin is in the shape of a rectangular box. Find the height of the box if its length is 15 ft, its width is 9 ft, and its surface area is 606 ft squared (In the figure, Assume that the given surface area includes that of the top lid of the box.)
convert to slope intercept form
: x- 2y=-6
Answer:
x-2y =6
x-2y =6
= 6-2y=x=4
S(t) = 3.1 ln(t) + 22 billion dollars (2 ≤ t ≤ 12),
where t is the year since 2000.† What was the total spent in 2010 (t = 10)? (Round your answer to the nearest whole number.)
How fast was it increasing? (Round your answer to three decimal places.)
The total spent in 2006 is nearly 28 billion dollars.
What is Logarithm function ?A logarithmic function is a function of the form. which is read “ y equals the log of x, base b” or “ y equals the log, base b, of x.” In both forms, x > 0 and b > 0, b ≠ 1. There are no restrictions on y.
here, we have,
The total spent on research and development by the federal government in the United States given by function,
S(t) = 3.1 ln(t) + 22
To find total spent in 2006.
We have to substitute t=6 in given function.
S(6) = 3.1 ln(6) + 22
= 5.5 + 22
=27.5
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