Therefore , the solution of the given problem of equation comes out to be spot A's coordinates are (80,-20).
Equation: What is it?In mathematical formulas, it is common to use the same variable term to guarantee agreement between two claims. Mathematical assertions, also known as equations expression, are employed to convey the equality of numerous academic figures. In this case, the normalise method adds b + 6 using the data of y + 6 rather than splitting 12 into two parts.
Here,
Let (a,b) represent the location of point A. Consequently, the inclination of the line through (0,0) and (a,b) is
=> m = (b - 0) / (a - 0) Equals b / a
This line being parallel to the initial road gives us:
=> m = -1/4
Therefore:
=> b / a = -1/4
=> b = -a/4
=> √[(a - 0)² + (-a/4 - 0)²] = √(17a²/16)
From (a,-a/4) to (85,0), the distance is:
=> √[(85 - a)² + (0 - (-a/4))²] = √[(85 - a)² + (a/4)²]
These two separations are equal, so we can put them at the same value and find a:
=> √[(85 - a)² + (a/4)²] = √(17a²/16)
When we square both edges, we obtain:
=> (85 - a)² + (a/4)² = 17a²/16
=> 16(85 - a)² + a² = 17a²
=> 16(7225 - 170a + a²) + a² = 17a²
=> 115600 - 2720a + 17a² + a² = 17a²
=> 18a² - 2720a + 115600 = 0
=> 9a² - 1360a + 57800 = 0
=> a = (1360 ± √(1360² - 4957800)) / (2*9)
=> a = (1360 ± √(307600)) / 18
=> a = (1360 ± 560) / 18
=> a = 80 or a = 40/9
Point A's y-coordinate is:
=> b = -a/4 = -80/4 = -20
Consequently, spot A's coordinates are (80,-20).
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The City of Dire Dewa started calendar year 2013 with General Fund cash of Br. 50,000 and fund balance (unassigned) of Br. 50,000. The Dire Dewa council approved the following General Fund budget for 2013:Estimated RevenuesProperty taxes …………………………………..Br.850,000Licenses and fees ………………………………….70,000Investment income …………………………………5,000 ……….. Br.925,000AppropriationsSalaries ………………………………… Br.800,000Utilities ……………………………………50,000Equipment …………………………………85,000……………….. 935,000Budgeted Decrease in Fund Balance …………………………… Br.10,000The following transactions and events occurred in 2013:i. Recorded the approved budget for the year.ii. Levied property taxes of Br.850,000. (The council assumed all property taxes would be collected in time to pay the year’s expenditures.)iii. Collected property taxes in the amount of Br.840,000 and licenses and fees of Br.70,000.iv. Invested Br.50,000 of available cash in a CD. Later in the year, redeemed the CD in full with interest of Br.2,000.v. Ordered police sedans for Br.80,000.vi. Received police sedans (with some extra bells and whistles) and an invoice for Br.82,000. (The Police chief liked the bells and whistles and approved the invoice for Br.82,000.) The invoice was subsequently paid. (Note: Record this purchase as capital outlay expenditure.)vii. Paid salaries of Br.770,000 and utility bills of Br.45,000.viii. During the last few days in December, Dire Dewar employees earned Br.25,000, which will be paid at the end of the pay period in early January 2014. Also, Dire Dewar received a utility bill for Br.4,000 for December 2013, which will be paid in January 2014.Use the preceding information to do the following:a. Prepare journal entries to record the foregoing transactions and events. b. Prepare a statement of revenues, expenditures, and changes in fund balance. c.Prepare balance sheet.
Answer:
Step-by-step explanation:
a. Journal Entries:
i. Budget Approval:
Debit: Appropriations - Salaries - Br. 800,000
Debit: Appropriations - Utilities - Br. 50,000
Debit: Appropriations - Equipment - Br. 85,000
Credit: Estimated Revenues - Property Taxes - Br. 850,000
Credit: Estimated Revenues - Licenses and Fees - Br. 70,000
Credit: Estimated Revenues - Investment Income - Br. 5,000
ii. Property Tax Levy:
Debit: Property Taxes Receivable - Br. 850,000
Credit: Property Taxes Revenue - Br. 850,000
iii. Collection of Revenues:
Debit: Cash - Br. 910,000
Credit: Property Taxes Receivable - Br. 840,000
Credit: Licenses and Fees Revenue - Br. 70,000
iv. Investment in CD:
Debit: Cash - Br. 50,000
Credit: Investments - Br. 50,000
v. Purchase of Police Sedans:
Debit: Equipment - Br. 80,000
Credit: Cash - Br. 80,000
vi. Payment for Police Sedans:
Debit: Equipment - Br. 2,000
Credit: Cash - Br. 82,000
vii. Payment of Salaries and Utility Bills:
Debit: Salaries Expense - Br. 770,000
Debit: Utilities Expense - Br. 45,000
Credit: Cash - Br. 815,000
b. Statement of Revenues, Expenditures, and Changes in Fund Balance:
Revenues:
Property Taxes Revenue - Br. 850,000
Licenses and Fees Revenue - Br. 70,000
Investment Income - Br. 2,000
Total Revenues - Br. 922,000
Expenditures:
Salaries Expense - Br. 800,000
Utilities Expense - Br. 50,000
Capital Outlay - Br. 82,000
Total Expenditures - Br. 932,000
Net Change in Fund Balance:
Revenues - Expenditures - Br. 10,000
Fund Balance:
Beginning Fund Balance - Br. 50,000
Net Change in Fund Balance - Br. 10,000
Ending Fund Balance - Br. 40,000
c. Balance Sheet:
Assets:
Cash - Br. 58,000
Investments - Br. 50,000
Property Taxes Receivable - Br. 10,000
Equipment - Br. 85,000
Total Assets - Br. 203,000
Liabilities:
None
Fund Balance:
Unassigned - Br. 40,000
Total Liabilities and Fund Balance - Br. 203,000
Lol please help me , cant get this right!!!
Kiran says that -2 < -5 . do you agree with Kiran?b explain or shoe your reasoning
No, Kiran is incorrect. -2 is actually greater than -5, so the correct statement is -5 < -2.
What is number line?A number line is an image of numbers plotted on a straight line, either horizontally or vertically. We can compare numbers and execute simple arithmetic operations on them easily by writing the numbers down on a number line. The starting point of a number line is often regarded as zero (0). The numbers to the left of zero are all negative whereas the numbers on the right of zero are all positive. As a result, we may argue that on a number line, the value of numbers grows as we approach towards the right. The numbers on the right are thus greater than the ones on the left, according to this statement.
No, Kiran is incorrect. -2 is actually greater than -5, so the correct statement is -5 < -2.
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Bailey works at an athletic store. He earns $90 per day plus an 11% commission on his sales. On Thursday, Bailey has $500 in sides. How much money does Bailey earn on Thursday, including his commission
Answer:
Bailey earned approximately $499.99 on Thursday, including his commission
Step-by-step explanation:
Bailey's earnings on Thursday consist of his base pay plus his commission. His base pay is $90, and his commission is 11% of his sales.
Let's call Bailey's sales on Thursday "S". Then his commission is 0.11S.
We know that Bailey's total earnings on Thursday were $500. So we can write an equation:
$90 + 0.11S = 500$
To solve for S, we can subtract $90$ from both sides of the equation:
$0.11S = 410$
Then we can divide both sides by $0.11$:
$S = 3,727.27$
So Bailey's sales on Thursday were $3,727.27.
To find Bailey's total earnings, we can add his base pay and commission:
$90 + 0.11(3,727.27) \approx 499.99$
So Bailey earned approximately $499.99 on Thursday, including his commission.
NEED AWNSER ASAPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPIdentify the formula used to find total surface area, then calculate total surface area. Select the appropriate choices.
Formula:
Total Surface Area:
The total surface area of the triangular prism is 556 unit²
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators such as addition, subtraction, exponent, multiplication and division.
The total surface area is the sum of each face area of the triangular prism. Hence:
Total surface area = [(1/2) * 8 * 17] + [(1/2) * 8 * 17] + (10 * 17) + (10 * 14) + (10 * 11) = 556 unit²
The total surface area is 556 unit²
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HELPP PLSS The following tree diagram represents the possibilities of two spins on a fair spinner
A. What are the number of outcomes in the sample space?
B. How many favorable outcomes for spinning the same color twice in a row?
C. How many favorable outcomes for spinning blue?
Therefore , the solution of the given problem of probability comes out to be rotating blue has two positive results.
What precisely is probability?Each of the procedure's criteria-based methods have as their main objective determining the likelihood that a statement is accurate or that an event will take place. Any number from zero to one, where 0 typically represents percentage and 1 typically reflects degree of certainty, can be used to symbolize chance. A probability illustration shows the likelihood that a particular occurrence will occur.
Here,
A. The number of potential outcomes for each spin can be multiplied to determine the number of outcomes in the sample space. Since there are two potential outcomes for each spin in this scenario, there are a total of:
=> 2 x 2 = 4
There are four potential outcomes in the sample space as a result.
B. There are two of these branches: blue-blue and red-red. Therefore, spinning the same hue twice in a row has two positive results.
C. Counting the number of branches that lead to blue on either spin will allow us to determine how many good outcomes there are for spinning blue. These stems come in two varieties: blue-red and blue-blue. Therefore, rotating blue has two positive results.
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The points C(-8, -9), D(-2,-2), E(0, 7), and F(-6, 0) form rhombus CDEF.
Plot the points then click the "Graph Quadrilateral" button. Then find the area of the
rhombus.
Answer:
The area of the rhombus CDEF is 32 units squared.
Step-by-step explanation:
The area of the rhombus CDEF is 24 square units. This can be determined by using the formula for finding the area of a rhombus which is A = 1/2 × d1 × d2 where d1 and d2 are the lengths of the diagonals of the rhombus. In this case, d1 is the distance from C to E and d2 is the distance from D to F. Calculating the lengths of the diagonals gives d1 = 8.9 and d2 = 8. Therefore, the area of the rhombus is 24 square units.
f(x) = 2x^(2)-3x+6 find the value of f(-2)
Answer:
We can find the value of f(-2) by substituting -2 for x in the given function:
f(-2) = 2(-2)^(2) - 3(-2) + 6
= 2(4) + 6 + 6
= 8 + 12
= 20
Therefore, f(-2) = 20.
Step-by-step explanation:
Answer:
F(-2)=20
Step-by-step explanation:
You have to Substitute The X’s in your question with -2
This gives you: 2(-2)^2-3(-2)+6
2(-2)^2=2(4)=8 (Remember, A negative times a negative is a positive!)
-3(-2)=6
This leaves us with 8+6+6 which is equivalent to 20.
The answer to question 18 and 19
The circumference of the circle is 150.768 units.
The area of the circle is 1809.216 units squared.
How to find the area and circumference of a circle?The area and circumference of a circle can be found as follows:
Let's find the circumference of the circle as follows:
circumference of a circle = 2πr
where
r = radiusTherefore,
circumference of a circle = 2πr
r = 24 units
π = 3.141
Hence,
circumference of the circle = 2 × 3.141 × 24
circumference of the circle = 150.768 units
Let's find the area of the circle as follows:
area of the circle = πr²
area of the circle = 3.141 × 24²
area of the circle = 1809.216 units squared
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Find the value of x and please show work
After addressing the issue at hand, we can state that As a result, x equals triangle 180 degrees.
What precisely is a triangle?A polygon is a triangle with four or more sections. It is rectangular in shape. The edges of a triangle ABC are A, B, and C. Euclidean geometry yields a single plane and cube when the sides are not collinear. A polygon is formed when a triangle has three components and three angles. The corners of a triangle are the points at which the three edges meet. Triangle sides add up to 180 degrees.A polygon is a triangle with four or more sections. It is rectangular in shape. The edges of a triangle ABC are A, B, and C. Euclidean geometry yields a single plane and cube when the sides are not collinear. A polygon is formed when a triangle has three components and three angles. The corners of a triangle are the points at which the three edges meet. Triangle sides add up to 180 degrees.
To calculate x, we must use the fact that the sum of a triangle's interior angles is 180 degrees.
First, determine the size of angle B. Angle A is 60 degrees, and angle C is 75 degrees. So,
angle B = 180 minus angle A A - angle C angle B = 180 - 60 - 75 angle B = 45
D = 360 minus angle angle A angle B angle C angle D = 360° - 60° - 45° - 75° D is equal to 180 degrees.
angle E stands for angle. D\sangle E is equal to 180 degrees.
As a result, the value of x is:
x = the angle 180 degrees = E x
As a result, x equals 180 degrees.
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Benny purchased $400,000 of Peach Corporation face value bonds for $320,000 on November 13, 2020. The bonds had been issued with $80,000 of original issue discount (OID), because Peach was in financial difficulty in 2020. On December 3, 2021, Benny sold the bonds for $283,000 after amortizing $1,000 of the original issue discount.
What are the nature and amount of Benny's gain or loss?
Benny has a $fill in the blank 1
long-term capital loss
from the sale of the bonds.
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Please help me with this math!
Pythagorean theorem: This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as a^2 + b^2 = c^2, where a and b are the lengths of the other two sides, and c is the length of the hypotenuse.
12² + 12² = x²
288= x²
x =16.98 = 17
Colin's mom had a long day at work. "I feel like I drank 3 gallons of coffee today!" she joked. If she really drank that much coffee, how many times would she have filled her 12-fluid-ounce mug?
If Colin's mom really drank 3 gallons of coffee, she would have filled her 12-fluid-ounce mug 32 times.
What is multiplication ?
Multiplication is a mathematical operation that involves combining groups of equal sizes to find a total quantity. It is represented by the symbol "×" or "⋅" and involves two or more factors. The result of a multiplication operation is called the product.
1 gallon is equal to 128 fluid ounces, so 3 gallons is equal to 3 x 128 = 384 fluid ounces.
To find out how many times Colin's mom would have filled her 12-fluid-ounce mug, we divide the total amount of coffee by the size of the mug:
384 fluid ounces ÷ 12 fluid ounces/mug = 32 mugs
Therefore, if Colin's mom really drank 3 gallons of coffee, she would have filled her 12-fluid-ounce mug 32 times.
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Please help will mark Brainly
The quadratic function on the graph is:
y = (-4/9)*(x - 3)^2 + 6
How to find the quadratic equation?Here we can see that we have a quadratic equation, remember that if the vertex is (h, k) and the leading coefficient is a, then we can write this as:
f(x) = a*(x - h)^2 + k
Here we can see that the vertex is at (3, 6), then we can write:
f(x) = a*(x - 3)^2 + 6
And we can see that the y-intercept is (0, 2), then we can write:
2 =a*(0 - 3)^2 + 6
2 = a*9 + 6
2 - 6 = a*9
-4/9 = a
Then the function is:
y = (-4/9)*(x - 3)^2 + 6
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Write 762 in the base seven system
762 base 10 to base 7 is 2136 base 7
What are Base Numbers?
Base Numbers are the number of units, or numbers, we use in our counting system. The most common base number is ten because the digits 0-9 are used in the number system.
And it is a base-7 number system we would only use seven different digits, like 0-6.
How to determine this
By dividing the number 762 base 10 in base 7 until it can no more be divided in base 7.
First divide 762 /7 = 108 remainder 6
108/7 = 15 remainder 3
15/7 = 2 remainder 1
2/7 = 0 remainder 2
Where the remainders arranged in descending is the base system.
So, by arranging from the bottom
= 2136 base 7
Therefore, 762 base 10 is 2136 base 7
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Find the value of p in this proportion show work below answer here P=
The value οf p that satisfies the prοpοrtiοn is 16.
What is a prοpοrtiοn in math?Prοpοrtiοn is explained majοrly based οn ratiο and fractiοns. A fractiοn, represented in the fοrm οf a/b, while ratiο a:b, then a prοpοrtiοn states that twο ratiοs are equal. Here, a and b are any twο integers. The ratiο and prοpοrtiοn are key fοundatiοns tο understand the variοus cοncepts in mathematics as well as in science.
Prοpοrtiοn finds applicatiοn in sοlving many daily life prοblems such as in business while dealing with transactiοns οr while cοοking, etc. It establishes a relatiοn between twο οr mοre quantities and thus helps in their cοmparisοn.
Tο sοlve fοr p in the prοpοrtiοn:
10/p = 5/8
We can crοss-multiply tο οbtain:
5p = 80
Dividing bοth sides by 5, we get:
p = 16
Therefοre, the value οf p that satisfies the prοpοrtiοn is 16.
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1
Select the correct answer.
Over which interval of the domain is function h decreasing?
x < 1
(22,
√x + 3,
z ≥ 1
h(x) =
O A.
O B.
O C.
O D. (-∞0, ∞0)
(1, 00)
(-∞0, 1)
The function is increasing only.
Twο statement for this graph are true -
O The functiοn is increasing οn the interval (-∞, 0).
O The functiοn is increasing οn the interval (0, ∞).
What is the dοmain οf functiοn?A functiοn's parameters are a grοup οf values that can be plugged intο the dοmain οf the functiοn. This set οf data cοntains the x values fοr a functiοn like f. (x).
The term "range" refers tο the set οf numbers that the functiοn cοnsiders tο be valid. The functiοn οutputs this string οf values in respοnse tο the insertiοn οf an x value.
The functiοn h(x) = 3x is a linear functiοn (straight line) with a slοpe οf 3, and a y-intercept οf 0. The cοnstant, pοsitive slοpe means that h(x) will increase οver the interval (-∞, ∞).
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The complete question is -
Given the function h(x)=3x, which statement is true about h(x)?
O The function is decreasing on the interval (-∞, 0).
O The function is increasing on the interval (-∞, 0).
O The function is decreasing on the interval (0, ∞).
O The function is increasing on the interval (0, ∞).
Describe a situation that could be represented by the expression `4-2.27`.
Answer:
I had 4 dollars, but I spent 2.27 on my new pencil.
Step-by-step explanation:
You need to create a situation where you have 4 of 'blank' and you take away 2.27 of 'blank' to answer this question.
A recipe for whole-grain bread calls for 1 oz of rye flour for every 4 oz of whole-wheat flour. How many ounces of each kind of flour should be used to make a loaf of bread weighing
37 oz?
Therefore, we need 7.4 ounces of rye flour and 29.6 ounces of whole-wheat flour to make a loaf of bread weighing 37 ounces, according to the recipe.
What is equation?An equation is a mathematical statement that shows the equality of two expressions, usually with an equal sign "=" in between them. An equation can contain variables, constants, and operators. The variables are represented by letters and can take on different values, while constants are fixed values that do not change. Operators include mathematical symbols like plus, minus, multiplication, and division, as well as exponents and logarithms.
Here,
Let's first assign variables to represent the amounts of rye and whole-wheat flour we need to use:
Let x be the number of ounces of rye flour.
Let y be the number of ounces of whole-wheat flour.
We know from the recipe that we need to use 1 oz of rye flour for every 4 oz of whole-wheat flour. This can be expressed as:
x = y/4 (equation 1)
We also know that the total weight of the loaf of bread should be 37 oz. This means that:
x + y = 37 (equation 2)
Now we can use equation 1 to substitute for x in equation 2:
y/4 + y = 37
Multiplying both sides by 4 to eliminate the fraction, we get:
y + 4y = 148
5y = 148
y = 29.6
So we need 29.6 ounces of whole-wheat flour. Using equation 1 to find x:
x = y/4 = 29.6/4 = 7.4
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I will mark you brainiest!
Which quadrilaterals have all of the properties of a parallelogram?
A) rhombus,kite, and trapezoid
B) rhombus, rectangle, and square
C) rhombus, kite, and square
D) Rhombus trapezoid, and rectangle
Answer:
The correct answer is B) rhombus, rectangle, and square.
A parallelogram is defined as a quadrilateral with two pairs of parallel sides. A rhombus, a rectangle, and a square are all special cases of parallelograms with additional properties.
A rhombus is a parallelogram with all sides equal in length.
A rectangle is a parallelogram with four right angles.
A square is a parallelogram with four equal sides and four right angles.
A kite and a trapezoid are not parallelograms since they do not have two pairs of parallel sides. While a trapezoid has one pair of parallel sides, a kite has no parallel sides.
The following data represent the number of grams of fat in breakfast meals offered at a local fast food restaurant. (a) Construct an ordered stem-and-leaf plot and (b) describe the shape of the distribution.
The stem and leaf plot for the data given is obtained as -
Stem Leaf
0 3 3 3 5 6
1 2 2 3 3 3 4 5 9
2 2 2 2 3 3
3 7 7 9
4 3
What is stem and leaf plot?
A stem and leaf plot, also known as a stem and leaf diagram, is a way to arrange data so that it is simple to see how frequently various sorts of values occur. It is a graph that displays ordered numerical data. A stem and a leaf are divided into each piece of data.
The data is given that represents the number of grams of fat in breakfast meals offered at a local fast food restaurant.
According to the data, the stem and leaf plot is -
Stem Leaf
0 3 3 3 5 6
1 2 2 3 3 3 4 5 9
2 2 2 2 3 3
3 7 7 9
4 3
The stem contains the first digits of the number, and the leaf plot contains the second digits of the number.
Therefore, the stem and leaf plot is obtained.
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The value of 'x' in the equation log(x-3) = 5 is A. 33 B. 32. C. 35. D. 34
Therefore , the solution of the given problem of equation comes out to be x = 100,003 is the value of x that fulfils the equation log(x-3) = 5.
What is an equation?It is standard practise in mathematical formulas to employ a single variable term to ensure agreement between competing claims. Equations, which are mathematical statements, are used to demonstrate the equality of many academic expression numbers. Instead of dividing 12 into 2 parts in this instance, the normalise technique adds b + 6 to use the data from
y + 6.
Here,
By utilising the characteristics of logarithms, we can find x.
Beginning with the expression provided:
=> log(x-3) = 5
It can be rewritten in exponential form as follows:
=> 10^5 = x - 3
When we simplify this solution, we obtain:
=> x = 10^5 + 3
We can calculate that 105 = 100,000 by using a calculator, so:
=> x = 100,000 + 3 = 100,003
As a result, x = 100,003 is the value of x that fulfils the equation
log(x-3) = 5.
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Downloading 30 songs from a music website costs £45. How much does it cost to download 15 songs? How much does it cost to download 45 songs?
Answer:
Download 15 songs cost £22.50
Download 45 songs cost £67.50
Step-by-step explanation:
We know
Downloading 30 songs from a music website costs £45.
45 / 30 = £1.5 for 1 song
Download 1 song = £1.50
How much does it cost to download 15 songs?
1.5 x 15 = £22.50
How much does it cost to download 45 songs?
1.5 x 45 = £67.50
So,
Download 15 songs cost £22.50
Download 45 songs cost £67.50
If the base is 7.5 cm and the height is 12.2cm and the width is 4.5cm what’s the area of the parallelogra?
Answer:
The formula gives the area of a parallelogram:
Area = base x height
Substituting the given values, we get:
Area = 7.5 cm x 12.2 cm
Area = 91.5 cm^2
Therefore, the area of the parallelogram is 91.5 square centimeters.
Step-by-step explanation:
Answer:
91.5 sq cm
Step-by-step explanation:
A=bh=7.5·12.2=91.5
Which is the smallest ratio?
2
3 to 4, 3, 10:12, 2 to 1
O 3 to 4
O 10:12
O2 to 1
Comparing the three in their simplest form we have the smallest ratio as 3 to 4.
What is a ratio and how does it apply to math and daily life?A mathematical phrase that compares two values is called a ratio. It is written as the product of the division of two different quantities. As in 2:1 or 2/1, ratios are frequently expressed as a fraction or with a colon.
Mathematicians employ ratios in many different contexts, such as arithmetic, algebra, and geometry. They are used to compare amounts, identify equivalent values, and resolve proportional and rate-of-change issues.
Convert the ratios in their simplest form:
3 to 4 can be simplified by dividing both terms by their greatest common factor, which is 1. Therefore, 3 to 4 is already in its simplest form.
10 to 12 can be simplified by dividing both terms by their greatest common factor, which is 2. So, 10 to 12 simplifies to 5 to 6.
2 to 1 is already in its simplest form.
Thus, comparing the three we have the smallest ratio as 3 to 4.
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Construct a polynomial function with the started properties. Third-degree, with zeros of −3 , − 1 , and 2 , and passes through the point (3,5)
Step 1: Convert zeros to factors of the polynomial.
If "k" is a zero, then (x-k) is a factor of the polynomial.
The allows us to convert zeros of -3, -1, and 2 into the factors (x+3)(x+1)(x-2).
So right now we have y= (x+3)(x+1)(x-2), but there's a missing piece, the leading coefficient of "a", so really we currently have
y = a · (x+3)(x+1)(x-2)
This is where the point (3,5) comes in. We need to substitute x=3 and y=5 into the equation above to find a.
5 = a · (3+3)(3+1)(3-2)
5 = a · (6)(4)(1)
5 = a · 24
5/24 = a
That's the full function:
f(x) = 5/24 (x+3)(x+1)(x-2)
Answer:
[tex]f(x)=\dfrac{5}{24}x^3+\dfrac{5}{12}x^2-\dfrac{25}{24}x-\dfrac{5}{4}[/tex]
Step-by-step explanation:
The zeros of a polynomial f(x) are the values of x which satisfy f(x) = 0.
If the polynomial function is degree 3 with 3 zeros, in factored form it can be written as f(x) = k(x - r₁)(x - r₂)(x - r₃) where r are the zeros and k ≠ 0.
Substitute the given zeros -3, -1 and 2 into the formula:
[tex]\implies f(x)=k(x-(-3))(x-(-1))(x-2)[/tex]
[tex]\implies f(x)=k(x+3)(x+1)(x-2)[/tex]
To find the value of k, substitute the given point (3, 5) into the function:
[tex]\begin{aligned}\implies f(3)&=5\\k(3+3)(3+1)(3-2)&=5\\k(6)(4)(1)&=5\\24k&=5\\k&=\dfrac{5}{24}\end{aligned}[/tex]
Therefore, the factored form of the polynomial function is:
[tex]\implies f(x)=\dfrac{5}{24}(x+3)(x+1)(x-2)[/tex]
To write in standard form, expand and distribute:
[tex]\implies f(x)=\dfrac{5}{24}(x^2+4x+3)(x-2)[/tex]
[tex]\implies f(x)=\dfrac{5}{24}(x^3+2x^2-5x-6)[/tex]
[tex]\implies f(x)=\dfrac{5}{24}x^3+\dfrac{10}{24}x^2-\dfrac{25}{24}x-\dfrac{30}{24}[/tex]
[tex]\implies f(x)=\dfrac{5}{24}x^3+\dfrac{5}{12}x^2-\dfrac{25}{24}x-\dfrac{5}{4}[/tex]
The population of American IQ scores are normally distributed with a mean of 101 and a standard deviation of 17. If a random sample of 416 American IQ scores are selected, what sample average score would be the 33rd percentile for all such sample averages?
In the given problem, using central limit theorem, the sample average score that corresponds to the 33rd percentile of all such sample averages is 100.66.
How to Calculate the Average?To solve this problem, we need to use the central limit theorem, which states that the distribution of sample averages is approximately normal, regardless of the distribution of the population, as long as the sample size is sufficiently large.
The mean of the sample means is equal to the population mean, which is 101. The standard deviation of the sample means, also known as the standard error of the mean, is equal to the population standard deviation divided by the square root of the sample size. In this case, the standard error of the mean is:
SE = 17 / sqrt(416) = 0.831
To find the sample average score that corresponds to the 33rd percentile of all such sample averages, we need to find the z-score that corresponds to the 33rd percentile and then use it to calculate the sample average score.
The z-score corresponding to the 33rd percentile is given by:
z = invNorm(0.33) = -0.439
where "invNorm" is the inverse normal distribution function.
We can use the formula for the z-score of a sample mean:
z = (x - μ) / SE
Rearranging this formula, we get:
x = z * SE + μ
Substituting the values we have, we get:
x = -0.439 * 0.831 + 101 = 100.66
Therefore, the sample average score that corresponds to the 33rd percentile of all such sample averages is 100.66.
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Divide 42 apples in the ratio 3:4
Answer:
18:24
Step-by-step explanation:
We know
For every 7 apples, we divided to 3:4
To get from 7 to 42, we time 6. So, we take the ratio times 6 and get 18:24
Find the parametric equation of
X=4sin(5t)
Y=-48sin^2(5t)+8sin(5t)-3
The parametric equations for the curve are X = 4 sin(5t), Y = -48 sin²(5t) + 8 sin(5t) + 45
Describe Parametric Equation?A parametric equation is a set of equations that express the coordinates of a point as functions of one or more parameters. These equations define a curve or a surface in a space and are commonly used in mathematics, physics, engineering, and computer graphics to model and analyze various phenomena.
Parametric equations can be useful in many applications, such as modeling the motion of particles, designing curves and surfaces, and creating computer animations. They also allow for the visualization of complex shapes and curves that may be difficult to describe using traditional equations.
To find the parametric equation of the given curve, we need to express the coordinates x and y in terms of a parameter t. We can use the trigonometric identities to simplify the given equations and get:
X = 4 sin(5t)
Y = -48 sin²(5t) + 8 sin(5t) - 3
Let's start with Y. We can use the identity sin²(θ) + cos²(θ) = 1 to rewrite -48 sin²(5t) as -48 (1 - cos²(5t)) = -48 cos²(5t) + 48. Substituting this into the equation for Y, we get:
Y = -48 cos²(5t) + 8 sin(5t) - 3
Now, we can use another trigonometric identity, sin²(θ) + cos²(θ) = 1, to rewrite cos²(5t) as 1 - sin²(5t). Substituting this into the equation for Y, we get:
Y = -48 (1 - sin²(5t)) + 8 sin(5t) - 3
Y = -48 sin²(5t) + 8 sin(5t) + 45
So, the parametric equations for the curve are:
X = 4 sin(5t)
Y = -48 sin²(5t) + 8 sin(5t) + 45
This is the final answer.
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The weights for newborn babies is approximately normally distributed with a mean of 5.8 pounds and a standard deviation of 2.1 pounds.
Consider a group of 1100 newborn babies:
1. How many would you expect to weigh between 4 and 7 pounds?
2. How many would you expect to weigh less than 6 pounds?
3. How many would you expect to weigh more than 5 pounds?
4. How many would you expect to weigh between 5.8 and 10 pounds
Answer:
Step-by-step explanation:
To find the number of newborn babies weighing between 4 and 7 pounds, we need to calculate the z-scores for these two weights and use the normal distribution table.
For 4 pounds: z = (4 - 5.8) / 2.1 = -0.857
For 7 pounds: z = (7 - 5.8) / 2.1 = 0.571
Using the normal distribution table, the area between z = -0.857 and z = 0.571 is 0.5418.
So, the expected number of newborn babies weighing between 4 and 7 pounds is:
0.5418 x 1100 = 596 (rounded to the nearest whole number)
To find the number of newborn babies weighing less than 6 pounds, we need to calculate the z-score for 6 pounds and use the normal distribution table.
z = (6 - 5.8) / 2.1 = 0.095
Using the normal distribution table, the area to the left of z = 0.095 is 0.5375.
So, the expected number of newborn babies weighing less than 6 pounds is:
0.5375 x 1100 = 591 (rounded to the nearest whole number)
To find the number of newborn babies weighing more than 5 pounds, we need to calculate the z-score for 5 pounds and use the normal distribution table.
z = (5 - 5.8) / 2.1 = -0.381
Using the normal distribution table, the area to the right of z = -0.381 is 0.6499.
So, the expected number of newborn babies weighing more than 5 pounds is:
0.6499 x 1100 = 715 (rounded to the nearest whole number)
To find the number of newborn babies weighing between 5.8 and 10 pounds, we need to calculate the z-scores for these two weights and use the normal distribution table.
For 5.8 pounds: z = (5.8 - 5.8) / 2.1 = 0
For 10 pounds: z = (10 - 5.8) / 2.1 = 1.905
Using the normal distribution table, the area between z = 0 and z = 1.905 is 0.4713.
So, the expected number of newborn babies weighing between 5.8 and 10 pounds is:
0.4713 x 1100 = 518 (rounded to the nearest whole number)