If you invest Php 150,000 in a savings account that pays 5.3% simple interest, you will earn Php 79,500 in interest after a decade. The new balance in your account will be Php 229,500.
To calculate the interest earned, we can use the formula for simple interest: Interest = Principal x Rate x Time.
Given:
Principal (P) = Php 150,000
Rate (R) = 5.3% = 0.053 (expressed as a decimal)
Time (T) = 10 years
Substituting these values into the formula, we have:
Interest = 150,000 x 0.053 x 10
= 79,500
Therefore, you will earn Php 79,500 in interest after a decade.
To find the new balance, we add the interest earned to the principal:
New Balance = Principal + Interest
= 150,000 + 79,500
= 229,500
Thus, the new balance in your account after a decade will be Php 229,500.
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The population of a bacteria culture quadriples every 30 minutes. If the culture started with 8 cells, how many cells will be in the culture after 3 hours?
Using an exponential function, it is found that there will be 32,768 bacteria after 3 hours.
What is an exponential function?An exponential function is modeled by:
[tex]y = ab^x[/tex]
In which:
a is the initial value.b is the rate of change.x is the number of time periods.For this problem, the parameters are:
a = 8, b = 4.
3 hours is 6 periods of 30 minutes, hence the amount is:
[tex]y = 8 \times 4^6 = 32768[/tex]
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You draw a red marble out of a bag and give it your friend. You draw another marble out of the bag. Are the events independent? Explain.
The events are not independent
How to determine the type of events?Say that there are n marbles in the bag
When the first red marble is drawn, the number of marbles in the bags becomes n - 1
This means that the first red marble has changed the probability of drawing the second red marble
This represents a dependent event
Hence, the events are not independent
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(-1,-2) or (1,0) ????
Answer:
(-1,-2)
Step-by-step explanation:
See attached graph.
If the class sizes in a school from 18 to 24 what is the range?
Answer:
18 students
Step-by-step explanation:
Answer:
the range between 18 and 24 is 6
Step-by-step explanation:
24-18=6
If sinx + sin^2x = 1 then, show that cos^12x + 3cos^10x + 3cos^8x + cos^6x = 1
This can be proved by using identities of trigonometry.
Prove that cos¹²x + 3cos¹⁰x + 3cos⁸x + cos⁶x = 1:Given that,
sin x + sin²x = 1 ⇒ sin x = 1 - sin²x
⇒ sin x = cos²x (∵sin²x + cos²x = 1)
We have to prove that,
cos¹²x + 3cos¹⁰x + 3cos⁸x + cos⁶x = 1
LHS = cos¹²x + 3cos¹⁰x + 3cos⁸x + cos⁶x
= sin⁶x + 3sin⁵x + 3sin⁴ + sin³x
= (sin²x)³ + 3(sin²x)²sin x + 3(sin²x) (sin x)² + (sin x)³
= (sin²x + sin x)³ (∵(a+b)³ = a³ + 3a²b + 3 ab² + b³)
= 1³ = 1 = RHS
LHS = RHS
Hence the equation is proved since both sides of the equation are equal.
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Divide 24x2y + 8xy2 + 8xy by -4xy.
What is the quotient?
The quotient of 24x2y + 8xy2 + 8xy and -4xy is -6x - 2y - 2
How to determine the quotient?The statement is given as:
Divide 24x2y + 8xy2 + 8xy by -4xy
The quotient is represented as:
Quotient = (24x^2y + 8xy^2 + 8xy)/(-4xy)
Factor out -4xy
Quotient = (-4xy)(-6x - 2y - 2)/(-4xy)
Evaluate the quotient
Quotient = -6x - 2y - 2
Hence, the quotient of 24x2y + 8xy2 + 8xy and -4xy is -6x - 2y - 2
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Write down two irrational numbers with a sum of 4
Answer:
π & 4-π
Step-by-step explanation:
Taking, a = π & b = 4-π ,a + b = π + 4 - π = 4What can you say about the continuous function that generated the following table of values?
table
x y
0.125 -3
0.5 -1
2 1
8 3
64 6
A.not enough information to answer the question
B. the function has more than one x-intercept
C.the function has exactly one x-intercept
D.the function has no x-intercept
Option C. The function that has the table here has exactly one x-intercept.
How to find the interceptAs the signs of the functions are changing, we can see that there is a crossing to the x axis.
This tells us that the zero value that we see is the x intercept and there is no other x intercept in the question.
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If AB is the midsegment of ∆XYZ, then find AB and x.
Answer:
AB = 17, x = 6
Step-by-step explanation:
3x - 1 = 34 / 2
3x - 1 = 17
3x = 18
x = 6
AB = 17
x = 6
Quick algebra 1 question for 50 points!
Only answer if you know the answer, quick shout-out to Dinofish32, tysm for the help!
Answer:
b. -x + y = 0
Step-by-step explanation:
Direct variation:
Direct variation means "y varies directly as x”:
[tex]y \propto x \implies y=kx[/tex]
where k is the (non-zero) constant of variation.
To determine which of the given equations represents a direct variation, isolate y for each and compare with the direct variation equation.
Equation a
[tex]y=\dfrac{4}{3}x-2[/tex]
This is not a direct variation equation as there is an addition of -2.
Equation b
[tex]-x+y=0[/tex]
[tex]\implies y=x[/tex]
This is a direct variation equation where the constant of variation is 1.
Equation c
[tex]xy=8[/tex]
[tex]\implies y=\dfrac{8}{x}[/tex]
This is not a direct variation equation as y is inversely proportional to x.
Equation d
[tex]y=14[/tex]
This equation does not include the variable x, and so is therefore not a direct variation equation.
If y varies inversely with x then the line must be linear and increasing
And the y intercept must be 0 in y=mx+c
#1
y=4/3x-2c=-2
Not direct#2
y=xYes
#3
y=8/xNo
#4
y=14Parallel to x axis no direct variation
find the sum of the average monthly rainfall. this is on i ready okay so please help.
Based on the average monthly rainfall amounts as shown in the graph, the sum of the average monthly rainfall 11/12 inches.
What is the sum of the average monthly rainfall?The average can be found by adding up the monthly rainfall and dividing by 12 months.
Solving gives:
= (1/8 + 1/8 + 1/8 + 2/8+ 2/8 + 5/8 + 7/8 + 9/8 + 13/8 + 15/8 + 16/8 + 16/8) / 12
= (88/8) / 12
= 11/12 inches
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A right cylinder and an oblique cylinder have the same radius and the same height. How do the volumes of the two
cylinders compare?
A. The volumes are the same, based on Cavalieri's principle.
B. The volumes are not the same, because Cavalieri's principle does not apply to oblique solids.
C. The volumes are not the same, because the two solids do not have the same cross-sectional
area at every level parallel to the bases.
D. The volumes are not the same, because an oblique solid has less volume thanits corresponding
right solid with the same height.
Answer:
A. The volumes are the same, based on Cavalieri's principle.
Step-by-step explanation:
Cavalieri's principle tells us the volumes of solids will be identical if their cross sectional areas are identical at every height.
ApplicationA right cylinder and an oblique cylinder of the same height and radius will both have circular cross sections of the given radius at any height. Since the radius is the same, the area of the circle is the same. Hence the requirements of Cavalieri's principle are met, and the cylinders have the same volume.
Terrence’s car contains 8 gallons of fuel. He plans to drive the car m miles using the fuel currently in the car. If the car can drive 20 miles per gallon of fuel, which inequality gives the possible values of m?
The correct option is A. m ≤ (8)(20)
The inequality which gives the possible values of 'm' is m ≤ (8)(20).
What is inequality?A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.
An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.
According to the question;
Terrence's car contains 8 gallons of fuel.
Terrence can drive the car 'm' miles using the fuel currently in the car.
The car can drive 20 miles per gallon of fuel,(which is maximum fuel capacity of the car to drive).
Then,
The total miles 'm' covered by the car is 8×20 which is maximum capacity of the car to travel.
Thus, total miles covered by the car are less than the maximum value which is given by the inequality-
m ≤ (8)(20)
Therefore, the inequality which gives the possible values of 'm' is m ≤ (8)(20).
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The complete question is-
Terrence's car contains 8 gallons of fuel. He plans to drive the car 'm' miles using the fuel currently in the car. If the car can drive 20 miles per gallon of fuel, which inequality gives the possible values of 'm'?
answer choices
A. m ≤ (8)(20)
B. m ≥ (8)(20)
C. 8 ≤ 20m
D. 8 ≥ 20 m
Y is inversely proportional to the square of x. If Y = 2 when x = 8, then Y = , when x is_______.
The value of x when y =2 is 8
How to solve for x?The inverse proportion to the square of x represented as:
k = yx^2
Where
k represents the constant of proportion
When y = 2, x = 8.
So, we have:
k =2 * 8^2
k =128
Substitute k = 128 in k = yx^2
So, we have:
yx^2 = 128
When y = 2, we have:
2x^2 = 128
Divide by 2
x^2 = 64
Take the square roots
x = 8
Hence, the value of x when y =2 is 8
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How many ways can 8 people stand in a line if Alice and Bob refuse to stand next to each other.
Answer:
there are 6 people that need to sit down so let's see how we can fill those seeds we will start while finding seats for Alice and bob they can't sit next to each other so will remove one of the seeds them both in the remaining 5 then at a seat between them to ensure that they are not next to each other they are 5 ways to choose seat and 4 ways from those that we make giving 20 ways to seats
Step-by-step explanation:
once a lies and verb are ct we can arrange the remaining people in 4 is equal to 24 west in each other four seats for the total of 20 into 24 4 80 ways to seat everyone
PLEASE ANSWER ASAP
What is the solution to the following system of equations?
Answer:
(-3, 1)
Step-by-step explanation:
the easiest thing to do is look at the graph and find the point where the two lines intersect
Find the measure of each numbered angle.
Answer:
m∠1 = 51°
m∠2 = 16°
Step-by-step explanation:
First ,check the attached photo.
=================
In the right triangle ABC :
m∠1 = 90 - 39
= 51°
……………………
In the right triangle ABD :
m∠2 = 90 - 74
= 16°
Answer:
• ∠ 1 = 51°
• ∠ 2 = 16°
Step-by-step explanation:
• ∠ 1, the 39° angle, and the right angle marked in red are angles of a triangle.
∴ ∠ 1 + 90° + 39° = 180° [Angles in a triangle add up to 180°]
⇒ ∠ 1 = 180° - 90° - 39°
⇒ ∠ 1 = 51°
• The small triangle on the top-left of the image consists of ∠ 2, a right-angle (marked in red) and a 74° angle.
∴ ∠ 2 + 90° + 74° = 180° [Angles in a triangle add up to 180°]
⇒ ∠ 2 = 180° - 90° - 74°
⇒ ∠ 2 = 16°
To calculate accurate ____________________ (vital/hospital) statistics rates to represent the entire United States, the quotient is multiplied by an appropriate factor such as 1,000 or 100,000 to represent the larger population.
To calculate accurate vital statistics rates to represent the entire United States, the quotient is multiplied by an appropriate factor such as 1,000 or 100,000 to represent the larger population.
What are vital statistics?The term "vital statistics" refers to the collection of data on live births, deaths, migration, fetal deaths, marriages, and divorces. Civil registration, an administrative system used by governments to record vital events that occur in their populations, is the most prevalent method of gathering information on these events. Efforts to increase the quality of vital statistics will thus be inextricably linked to the growth of countries' civil registration systems. Since the nineteenth century, civil registration has followed the practice of churches keeping such records. To compute accurate vital statistics rates for the full United States, multiply the quotient by a suitable factor, such as 1,000 or 100,000 to represent the greater population.As it is given in the description itself, to compute accurate vital statistics rates for the full United States, multiply the quotient by a suitable factor, such as 1,000 or 100,000 to represent the greater population.
Therefore, to calculate accurate vital statistics rates to represent the entire United States, the quotient is multiplied by an appropriate factor such as 1,000 or 100,000 to represent the larger population.
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May someone please explain to me how exponents can be used to represent fractions between 0 and 1???
The fraction m/n that lies between 0 and 1 is equivalent to the real number m · n⁻¹, where m, n > 0 and m < n.
How can rational numbers between 0 and 1 be represented in terms of exponents?
By algebra, we know that fractions, a kind of rational numbers, are real numbers of the form m/n, where m and n are integers and n ≠ 0.
In addition, the operator "/" means division, an operator derived from the existence of multiplicative inverse and fundamental operation of multiplication in the real field.
Thus, the rational number m/n is equivalent to the number m · n⁻¹. If the rational number is between 0 and 1, then m, n > 0 and m < n.
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Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.
The number will represent a number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
Inequality expressionInequality are expressions not separated by an equal sign. Given the inequality expression:
3(8 – 4x) < 6(x – 5)
Expand
24 - 12x < 6x - 30
Collect the like terms
-12x-6x < -30 - 24
-18x <-54
x > 3
Hence the number will represent a number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
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Can somebody please help me I have exam tomorrowwww
Answer:
3x²y (2x²-3y²+ 4y)
Step-by-step explanation:
Factor the expression 6x^4y-9x²y³+12x²y².
First, check if there is a GCF. The GCF is 3x²y.
3x²y (2x²-3y²+ 4y).
This equation cannot be factored further. Therefore, the answer is
3x²y (2x²-3y²+ 4y).
Hope this helps!
Answer:
3x²y(-3y²+4y+2)
Step-by-step explanation:
6x⁴y-9x²y³+12x²y²
solution:
first common
3x²y(2x²-3y²+4y)
3x²y(-3y²+4y+2)
Solve for x.
A. 5
B.7
OC. 6
OD. 8
3
X
5
4
Answer:
6
Step-by-step explanation:
[tex]5(5+3)=4(x+4) \\ \\ 40=4(x+4) \\ \\ 10=x+4 \\ \\ x=6[/tex]
Use the following function rule to find h(w–5). Simplify your answer.
h(y)=y²–y–5
h(w–5)=
The value of the function is h(w - 5) = w^2 - 11w +25
How to determine the function?The function is given as:
h(y) = y^2 - y - 5
Substitute w - 5 for y
h(w - 5) = (w - 5)^2 - (w - 5) - 5
Expand the equation
h(w - 5) = w^2 - 10w + 25 - w + 5 - 5
Evaluate the like terms
h(w - 5) = w^2 - 11w +25
Hence, the value of the function is h(w - 5) = w^2 - 11w +25
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The equation 4x2 8x 15 = 0 is being rewritten in vertex form. fill in the missing step. given 4x2 8x 15 = 0 step 1 4(x2 2x ___) 15 ___ = 0 step 2 ✔ step 3 4(x 1)2 11 = 0 4(x2 2x 1) 15 − 4 = 0 4(x2 2x 1) 15 − 1 = 0 4(x2 2x 2) 15 − 2 = 0 4(x2 2x 4) 15 − 4 = 0
Answer:
a) is the correct answer
43. Consider the equation 4(x-8)+y=9(x-2)
[Part 1]
Find an expression for y of the form ax+b expression for y such that the equation has infinitely many solutions. Is there more than one such solution? Explain your reasoning using complete sentences.
[Part 2]
Find an expression for y of the form ax+b expression for y such that the equation has no real solutions. Is there more than one such solution? Explain your reasoning using complete sentences.
The expression of the equation 4(x - 8) + y = 9(x - 2) in slope intercept form is; y = 5x + 14
How to write an equation in Slope Intercept form?We want to express 4(x - 8) + y = 9(x - 2) in slope intercept form of y = mx + b.
Let us expand the equation to get;
4x - 32 + y = 9x - 18
Isolate y to get;
y = 9x - 4x - 18 + 32
y = 5x + 14
Thus;
Slope = 5
y - intercept = 14
x - intercept = -2.8
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Im the diagram shown JKL~ MNP. Find MP and PN.
Answer: [tex]MP=10, PN=6[/tex]
Step-by-step explanation:
Corresponding sides of similar triangles are proportional, so:
[tex]\\\\frac{MP}{5}=\frac{8}{4}\\\\MP=10\\\\\frac{PN}{3}=\frac{8}{4}\\\\PN=6[/tex]
The number of goldfish in a tank is 22, and the volume of the tank is 56 cubic feet. what is the density of the tank? 0.34 goldfish per cubic foot 0.39 goldfish per cubic foot 1.41 goldfish per cubic foot 2.55 goldfish per cubic foot
Option B is correct. 0.39 goldfish per cubic feet is the density of the tank given that there are 22 goldfishes and volume of the tank is 56 cubic feet. This can be obtained by using the formula of density.
Calculate the density of tank:Given that there are 22 goldfishes,
mass of tank = 22 goldfishes
volume of tank = 56 cubic feet
Density = mass/volume= 22/56
= 0.39 goldfish per cubic feet
Hence 0.39 goldfish per cubic feet is the density of the tank given that there are 22 goldfishes and volume of the tank is 56 cubic feet.
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Answer: 0.39 goldfish
Step-by-step explanation:
find the distance formula
Answer:
d=(x^2-x^1)+(y^2-y^1)^2
Answer:
[tex]\mathfrak{Distance \: between \: two \:points}[/tex]
The distance between two points [tex]A(x_1,y_1)[/tex] and [tex]B(x_2,y_2)[/tex] is given by the formula,
[tex]AB= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2 }[/tex]
Proof: Let X'OX and YOY' be the x-axis and y-axis respectively. Then, O is the origin.
Let[tex]A(x_1,y_1) [/tex] and [tex]B(x_2,y_2)[/tex]
be the given points.
Draw AL perpendicular to OX, BM perpendicular to OX and AN perpendicular to BM
Now,[tex]OL=x_1,OM=x_2,AL=y_1 \: and \: BM=y_2[/tex]
[tex] \therefore{AN=LM=(OM-OL)=(x_2-x_1)}[/tex]
[tex] \: \: \: BN=(BM-NM)=(BM-AL)=(y_2-y_1)[/tex]
In right angled triangle [tex] \triangle \: ANB[/tex],by Pythagorean theorem,
We have,
[tex] \: \: \: AB^2=AN^2+BN^2[/tex]
[tex]or,AB^2=(x_2-x_1)^2+(y_2-y_1)^2[/tex]
[tex] \therefore \: AB= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} [/tex]
Thus ,the distance between the points A(x_1,y_1) and B(x_2,y_2) is given by,
[tex] \implies \boxed{AB= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} }[/tex]
A map's numerical coordinates are in kilometres. Town A is at (16.3, 2.9) and town B is at
(4.5, 6.3). A road is to be constructed on a direct line between the two towns. Each town is
responsible for the construction up to the mid-point at a cost of $150 000 for each kilometre.
Determine the cost for each town.
Answer:
$92,250 per town
Step-by-step explanation:
See attached image.
The two towns may be connected with a straight line, the road, that can be made into the hypotenuse of a right triangle. The twio sides are calculated from the coordinates and shown in the image. Then use the phythagorean theorem to calculate the hypotenuse. The towns are 12.3 km apart. The total road cost would be:
($150,000/km)(12.3 km) = $1,845,000, or $92,250 per town.
solve for r as a percentage f(7000)=20000(1-r)^10
The value of r in the exponential decay function 7000 = 20000(1-r)^10 is 10%
How to solve for r as a percentage?The equation is given as:
7000 = 20000(1-r)^10
The above equation is an exponential decay function.
So, we have:
7000 = 20000(1-r)^10
Divide both sides of the equation by 20000
0.35 = (1-r)^10
Take the 10th root of both sides
0.35^(1/10) = 1 - r
Evaluate the exponent
0.9 = 1 - r
Add r to both sides
0.9 + r = 1
Subtract 0.9 from both sides
r = 1 - 0.9
Evaluate
r = 0.1
Express as percentage
r = 10%
Hence, the value of r in the exponential decay function 7000 = 20000(1-r)^10 is 10%
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