The balance of an account is given as follows:
[tex]B = \frac{P\left(\left(1 + \frac{r}{n}\right)^{nt}-1\right)}{\frac{r}{n}}[/tex]
The meaning of each parameter is given as follows:
P is the periodic payment.r is the interest rate.n is the number of yearly compoundings.t is the time in years.The payments in this problem are given as follows:
$90 -> your friend.0.5 x $90 = $45 -> Company.For the balance over 20 years, the values of the parameters are given as follows:
P = 135, r = 0.035, n = 12, t = 20.
Then the balance is given as follows:
[tex]B = \frac{P\left(\left(1 + \frac{r}{n}\right)^{nt}-1\right)}{\frac{r}{n}}[/tex]
[tex]B = \frac{135\left(\left(1 + \frac{0.035}{12}\right)^{12 \times 20}-1\right)}{\frac{0.035}{12}}[/tex]
B = $93,113.
The contributed amounts are given as follows:
Friend: 90 x 12 x 20 = $21,600.Company: 45 x 12 x 20 = $10,800.Hence the accrued interest is of:
93,113 - (21,600 + 10,800) = $60,713.
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Dasan is participating in a traditional cornstalk archery competition hosted by the Chickasaw
Nation. He is using a custom bow and arrow, handmade by a Chickasaw bowmaker. The quadratic
expression below represents the height of an arrow, in feet, a seconds after Dasan launches it
toward the cornstalks.
What is the linear term of the quadratic expression?
-16x² +50x+4
The algebraic systems of equations that contain one linear equation and one quadratic equation are known as linear and quadratic equations.
What Is the Linear Expression?If each term is a constant or a variable raised to the first power, an algebraic statement is referred to as a linear expression. That is to say, no exponent can be greater than 1.A variable raised to the first power is referred to as x, whereas a variable raised to the second power is referred to as x2.Five is an illustration of a constant.Keep in mind that the coefficients put in front of the variables have no real meaning. Let's take a look at a few instances of these polynomials, which are merely expressions with two or more terms.In a linear formulation,
-16x² +50x+4
-2(8x² - 25x - 2)
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12. The hourly temperatures at Eppley Airfield Airport in Omaha, Nebraska, in May 2014 are approximately normally distributed with a mean of 64.4˚F and a standard deviation of 12.2 ˚F. The z-score of the lowest temperature is −2.49. What is the lowest temperature? Round your result to the one’s place.
The lowest temperature with a z score of of -2.49 is 24.0 ˚F
How to find the temperature with a z score of -2.49Z scores, measures the amount of standard deviation sample X is from mean. the formula is below
z = (X - μ) / σ
Definition of variables
mean, μ = 4.4˚F
standard deviation, σ = 12.2 ˚F
X = lowest temperature
z = -2.49
substituting into the formula
-2.49 = (X - μ) / σ
-2.49 = (X - 64.4) / 12.2
-2.49 * 12.2 = X - 64.4
-30.378 + 64.4 = X
X = 34.022
X = 34.0 (to one decimal place)
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Which congruence theorem can be used to prove that the triangles are congruent AAS SSS SAS HL?
Side-Angle-Side (SAS) Rule prove the congruency of the triangle
What is a triangle ?
A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
Triangles can be divided into three sorts based on the lengths of their sides, and they are: Scalene. Isosceles. Equilateral.
The Side-Angle-Side rule is used to demonstrate whether a set of triangles is congruent. According to the SAS rule, two sides and the included angle of one triangle must equal two sides and the included angle of another triangle in order for the two triangles to be considered congruent.
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The width of a rectangular slab of concrete is 10m less than the length. The area is 24 m ^2
The width and the length of the slab are 2 meters and 12 meters, respectively
How to determine the dimensions of the slab?From the question, we have the following parameters that can be used in our computation:
Width of a rectangular slab of concrete = 10m less than the length.
Area = 24 m²
These parameters can be represented as
Width = Length - 10
Area = Length * Width
So, we have
w = l - 10
A = lw
Also, we have
A = 24
Substitute w = l - 10 in A = lw
A = l(l - 10)
So, we have
l(l - 10) = 24
Expand
l² - 10l = 24
This gives
l² - 10l - 24 = 0
Expand
l² + 2l - 12l - 24 = 0
Factorize
(l + 2)(l - 12) = 0
So, we have
l = -2 and l = 12
The length cannot be negative
So, we have
l = 12
Recall that
w = l - 10
So, we have
w = 12 - 10
Evaluate
w = 2
Hence, the dimensions are 2 meters and 12 meters, respectively
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Possible question
The width of a rectangular slab of concrete is 10m less than the length. The area is 24 m ^2
Compute the dimensions of the slab
The prices of two radios are in the ratio x : y
When the prices are both increased by £20, the ratio becomes 5:2
When the prices are both reduced by £5, the ratio becomes 5:1
Express the ratio x : y in its lowest terms.
Prices of two ratios in the ratio is 4 : 1.
What do you mean by ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Ratios can be classified into two types. One is part to part ratio and the other is part to whole ratio. The part-to-part ratio denotes how two distinct entities or groups are related.
For example, the ratio of boys to girls in a class is 12: 15, whereas, the part-to-whole ratio denotes the relationship between a specific group to a whole.
For example, out of every 10 people, 5 of them like to read books. Therefore, the part to the whole ratio is 5: 10, which means every 5 people from 10 people like to read books.
Let us assume price of radios are x and y
According to the question
[tex]\frac{x + 20}{y+20} =\frac{5}{2}\\2x+40=5y+100\\2x-5y=60[/tex]-------------------------- eq(1)
and
[tex]\frac{x-5}{y-5} =\frac{5}{1}\\5y-x = 20[/tex]
5y-x = 20
multiplying this equation by 2
we get
10y-2x = 40 ------------------ eq(2)
adding eq 1 and 2
we get
5y=100
y=20
solving further we get x=80
Thus the ratio is 4 : 1.
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What is always true about an isosceles triangle?
In an isosceles triangle, two angles and two sides are always equal.
What do we mean by an isosceles triangle?In geometry, an isosceles triangle is one with at least two sides of equal length.
It can be defined as having exactly two equal-length sides or as having at least two equal-length sides, with the equilateral triangle being an exception to the second definition.
Isosceles Triangle: A triangle is referred to as being isosceles if any of its two sides is equal.
if the triangle has X, Y, and Z as its three sides.
The triangle is isosceles when X = Y, X = Z, or Y = Z.
Scalene triangles are recognized as triangles without equal sides.
Therefore, in an isosceles triangle, two angles and two sides are always equal.
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Multiply and write a fraction or mixed numbers in its simplest form
2/5 x 6/7
25/24 as a decimal rounded to the nearest tenth
Answer:
1.0
Step-by-step explanation:
Hope this helps! :)
The solution is, 1.0 when 25/24 as a decimal rounded to the nearest tenth .
What is round off?Rounding off means a number is made simpler by keeping its value intact but closer to the next number. It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc.
here, we have,
given that, 25/24
now, we have to rounded to the nearest tenth
as decimal, so, we have to divide 25 by 24
i.e. 25/24 = 1.041
we get, 1.041 => 1.0
so, it is 1.0 a decimal rounded to the nearest tenth
Hence, The solution is, 1.0 when 25/24 as a decimal rounded to the nearest tenth .
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A radio is bought at 550 and sold at a profit of 35. What is the selling price?
The selling price of the radio with a cost price of 550 and sold at a profit of 35 is 585.
What is selling price?The selling price is how much a buyer pays for a product or service.
To calculate the selling price of the radio, we use the formula below.
Formula:
S.P = C.P+Profit............ Equation 1Where:
S.P = Selling Price of the radioC.P = Cost price of the radioFrom the question,
Given:
C.P = 550Profit = 35Substitute these values into equation 1
S.P = 550+35S.P = 585.Hence, the selling price of the radio is 585.
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Find the equation of the line that passes through the point (3, 28) and has slope 11. Simplify your equation to the following form.
=11+____
Answer:
y=11x-5
Step-by-step explanation:
y=mx+b
28=11(3)+b
28=33+b
b=-5
y=11x-5
Mia is 1.65 meters tall. At 3 p.m., she measures the length of a tree's shadow to be
26.45 meters. She stands 21.4 meters away from the tree, so that the tip of her
shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest
hundredth of a meter.
The height of the tree to the nearest hundredth of a meter is 8.64 meters
What are equivalent ratios?"Two or more ratios that reflect the same relation or comparison of numbers are known as equivalent ratios," according to the definition of the equivalent ratio in mathematics. The idea of corresponding fractions is comparable. The term "proportion" also refers to the equivalence of two ratios. Even if the values of the antecedent and the consequent are different, if we simplify them, we will still arrive at the same value.
How to solve?
Mia's height=1.65 m
Tree's equivalent height=26.45m
Mia's height w.r.t. the tree's shadow=26.45-21.40 =5.05m
Ratio of the equivalent height w.r.t original height=5.05:1.65 =3.06
Tree's original height= tree's equivalent height: ratio of Mia's height
= 26.45:3.06 =8.64m
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Explore
A 100-unit-long line is split in half.
Half of the line is used to form one large circle.
The other half forms two identical smaller circles.
Which is larger?
The larger circle is, half of the line is used to form one large circle.
What is split in half?
To split or cause to split, especially violently, by cleaving into distinct pieces, typically into two nearly equal ones.
To split into a lesser number of things neatly or equally. The mirror collapsed and broke into three almost identical pieces.
Here, a 100-unit-long line is split in half.
That means a line is divided into two equal part with length 50 unit each.
Also, half of the line is used to form one large circle. The other half forms two identical smaller circles.
From this we can see that half of the line is used to form one large circle is always a lager circle.
And other half forms two identical smaller circles are the smaller circles.
Hence, the larger circle is, half of the line is used to form one large circle.
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What should be the remainder of the polynomial function for the divisor to be a factor?
Answer:
zero
Step-by-step explanation:
You want to know the remainder of the polynomial function for the divisor to be a factor?
DivisionA divisor is a factor of the dividend in any division problem if and only if the remainder is zero (0).
The divisor will be a factor of a polynomial function if division of the function by that divisor has a remainder of zero.
4x+8y-3z=1 -5x-2y+6z=-6 9x+3y-10z=10
What is LCD and how do I do it in math??
Answer:
LCD is the abbreviation for Least Common Denominator.
Step-by-step explanation:
To find the LCD of two numbers, you list out the multiples of each number. Then you look for the smallest multiple of both numbers and there you have it!
For example, if we had to find the LCD of 4 and 3, we'll first list out the multiples of both.
4: 4, 8, 12, 16, 20, ...
3: 3, 6, 9, 12, 15, ...
The first least multiple we found in those two numbers is 12.
Therefore, the LCD would be 12.
for a fishing trip, debra is going to choose lures to put in her tackle box. she has 4 lures that are jigs and 9 that are spinnerbaits. In how many waits can she choose 6 lures if more than 4 must be spinnerbaits?
Answer:
1680
Step-by-step explanation:
2. A standard package of pencils contains 24
pencils.
# of
packages
# of
pencils
127
?
1
?
3
?
4
?
6
1
2
?
Answer:
12, 24,72,96,156
Step-by-step explanation:
1/2 package would be 1/2 of 24 which is 12
21 x 24 = 24
3 x 24 = 72
4 x 24 = 72
We know that 3 packages is 72 so 6 packages is double that at 144. We also know that have a package is 12. so 144 + 12 = 156
Answer:
1/2 package = 1/2 of 24 = 12 pencils
1 package = 24 pencils
3 packages = 24*3 = 72 pencils
4 packages = 24*4 = 96 pencils
6 1/2 packages = 24*6.5 = 156
Step-by-step explanation:
1 package = 24 pencils
1/2 package = 1/2 of 24 = 12 pencils
1 package = 24 pencils
3 packages = 24*3 = 72 pencils
4 packages = 24*4 = 96 pencils
6 1/2 packages = 24*6.5 = 156
What are the coordinates of B′ after the pentagon is rotated 90° about the origin?
Assuming that the rotation is anticlockwise (as it is not defined) the coordinates of B after the rotation are (-5, 1), so the correct option is C.
What are the coordinates of B' after the rotation?If the pentagon is rotated 90°, then all the vertices are also rotated 90° about the origin.
Here we don't know if the rotation is clockwise or anticlockwise, so we assume it is anticlockwise, as this is the standard rotation.
The orignal coordiates of point B are (1, 5)
This is on the first quadrant, a rotation of 90° anticlockwise will:
Interchange the x-value and the y-value.Add a negative sign to the new x-value.So we will go from a point (x, y) to (-y, x)
Then the new coordinates of B' are (-5, 1)
Thus, the correct option is C.
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Journee and her brother were arguing over who was responsible for the dishes. Journee explained to her brother that she had washed the dishes the last three nights
Her brother replied, "Sure, but that's just because you're a nerd with nothing better to do." Which logical fallacy has Journee's brother used?
O Ad hominem
Oad populum
Answer: Ad Hominum
Step-by-step explanation:
It just attacks the person.
What theorem states that if the two legs of one right triangle are congruent to two legs of another right triangle then the two right triangles are congruent?
The hypotenuse leg theorem states that two right triangles are congruent if the hypotenuse and one leg of one right triangle are congruent to the other right triangle's hypotenuse and leg side.
What is the hypotenuse leg theorem?
The hypotenuse leg theorem states that two right triangles are congruent if the hypotenuse and one leg of one right triangle are congruent to the other right triangle's hypotenuse and leg side.
The HL Postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.
Hypotenuse-Leg (HL) for Right Triangles. There is one case where SSA is valid, and that is when the angles are right angles. In words, if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the triangles are congruent.
Hence, if the hypotenuse leg theorem states that two right triangles are congruent if the hypotenuse and one leg of one right triangle are congruent to the other right triangle's hypotenuse and leg side.
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graph the exponential function y52x
The graph of exponential function y = 5.2^x
exponential function in the form y = ab^x + c
Exponential function:
An exponential function is a mathematical function of the following form: f ( x ) = a^x. where x is also a variable, and a is a constant called the base of the function.
where
a is the initial y - intercept.
b is the constant ratio.
c is the horizontal asymptote.
So, in this problem, we have:
constant ratio = 2
y-intercept at y = 5
horizontal asymptote at y = 0
The graph is in the image uploaded.
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Question 10(Multiple Choice Worth 1 points) (03.01 MC) Simplify 7√3-4√6 +√48 - √54 11√6-7√12 11√3-7√6 -3√9 4√9 PLEASE HELP QUICK 65 POINTS
Answer: [tex]11\sqrt{3}-7\sqrt{6}[/tex]
Step-by-step explanation:
[tex]7\sqrt{3}-4\sqrt{6}+\sqrt{48}-\sqrt{54}\\\\=7\sqrt{3}-4\sqrt{6}+\sqrt{16 \cdot 3}-\sqrt{9 \cdot 6}\\\\=7\sqrt{3}-4\sqrt{6}+\sqrt{16}\sqrt{3}-\sqrt{9}\sqrt{6}\\\\=7\sqrt{3}-4\sqrt{6}+4\sqrt{3}-3\sqrt{6}\\\\=11\sqrt{3}-7\sqrt{6}[/tex]
Digitalis is a technology company that makes high-end computer processors. Their newest processor, the luteA, is going to be sold directly to the public. The processor is to be sold for $2800 , making Digitalis a profit of $452 . Unfortunately there was a manufacturing flaw, and some of these luteA processors are defective and cannot be repaired. On these defective processors, Digitalis is going to give the customer a full refund. Suppose that for each luteA there is an 12% chance that it is defective and an 88% chance that it is not defective. If Digitalis knows it will sell many of these processors, should it expect to make or lose money from selling them? How much?
The correct option regarding the expected profit of the company is given as follows:
Dugitalis can expected to make money from selling these processors.
In the long run, they should expect to make $116 on each processor sold.
How to obtain the expected value of a discrete probability distribution?The expected value of a discrete probability distribution is given by the sum of each outcome multiplied by it's respective probability.
The distribution of profits in this problem is given as follows:
P(X = 452) = 0.88 -> non-defective processors sold.P(X = -2348) = 0.12 -> defective processors.For the second probability, we have the number 2348, which is the cost of manufacturing each processor, as 2800 - 452 = $2,348.
Then the expected profit over time is given as follows:
E(X) = 0.88 x 452 - 2348 x 0.12 = $116.
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Finding the multiplier to give a final amount after a percentage increase or decrease
With percent increase or decrease situations, you have to consider the starting point as being 100%. So if the account increased by 27%, it's now 100% + 27% or 127% of it's original value.
As a decimal, 127% = 1.27. So 1.27 is your multiplier in this example.
And 1.27 • 7600 = 9652, which is the ending balance.
This gets the same result as finding 27% of 7600 and adding it back on to 7600, but does it more efficiently.
how many solutions are there to this nonlinear system
There is only one solution to the nonlinear system.
What is Nonlinear system?
A nonlinear system is a system in which the change of the output is not proportional to the change of the input.
The solutions of a nonlinear system of equations are in the form of x and y values and these are the points at which the graphs intersect. Such systems have no solution, or one or more solutions.
So, here function 1 is a parabola and function 2 is a straight line. The parabola is touching the straight line at one point only, so this has one solution.
Hence the answer is there is only one solution to the nonlinear system.
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Please help will mark Brainly
Answer:
is
Step-by-step explanation:
The domain of g is identical to the domain of f.
They both have the same slope which means they have the same domain.
Answer:
is NOT
Step-by-step explanation:
the equation of g(x) is not the same as f(x)
so, g(x) and f(x) are NOT identical (aka not the same)
*domain is different by looking at b-value
3. The number of pupils in Team A to the number of pupils in Team B is in the ratio 7:6. If 45 pupils are transferred from Team A to Team B, the ratio will become 2: 3. How many pupils are there in each team?
Answers:
Team A = 175 people
Team B = 150 people
This is before the 45 students transfer from A to B.
===========================================================
Explanation:
x = number of people in team A
y = number of people in team B
These counts are before the 45 pupils transfer from A to B.
The counts are in ratio 7:6, which means,
x/y = 7/6
6x = 7y
x = 7y/6
If we subtract 45 people from team A, we have x-45 people left. Those 45 people go to team B to have y+45 pupils there.
The quantities x-45 and y+45 are in ratio 2:3, so,
(x-45)/(y+45) = 2/3
3(x-45) = 2(y+45)
3x-135 = 2y+90
3(7y/6)-135 = 2y+90 .... plug in x = 7y/6
21y/6 - 135 = 2y+90
6*( 21y/6 - 135 ) = 6*(2y+90)
21y-810 = 12y+540
21y-12y = 540+810
9y = 1350
y = 1350/9
y = 150
x = 7y/6
x = 7(150)/6
x = 175
We have 175 people on team A, and 150 people on team B.
This is before the 45 students transfer from A to B.
-------------------
Check:
x/y = 175/150 = (7*25)/(6*50) = 7/6
This shows x and y are in ratio 7:6 to match the instructions.
x-45 = 175-45 = 130
y+45 = 150+45 = 195
(x-45)/(y+45) = 130/195 = (2*65)/(3*65) = 2/3
And we have the updated counts in the ratio 2:3, which matches the stated info in the instructions. The answers are fully confirmed.
What are the 3 medians of a triangle?
The 3 medians of triangle are the line segments that connects a vertex to the midpoint of the opposite side.
A triangle is a three-sided polygon with three vertices and three sides that enclose three angles.It can be an acute-angled, obtuse-angled, or right-angled triangle depending on the angles measured. The sum of a triangle's interior angles is 180 degrees.
Median of a Triangle:-
A median of triangle is a line segment that connects a vertex to the midpoint of the opposite side. AD in the diagram is the median that divides BC into two equal halves, DB = DC.Each triangle has three medians, one at each vertex. The triangle ABC's three medians are AE, BF, and CD.Whatever the shape of the triangle, the three medians always meet at a single point.The triangle's centroid is the point where the three medians intersect. The centroid of the triangle ABC is at point O.Each median of a triangle divides it into two smaller triangles of equal area.In fact, the three medians divide the triangle into six equal-area triangles.Thus, the median of triangle line segment that connects a vertex to the midpoint of the opposite side.
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If l 1m, then <1 is a right angle
Right angle is an angle of 90 degrees while complementary angles add up to 90 degrees.
What are complementary angles and right angles?When the sum of two angles is 90°, then the angles are known as complementary angles.
A right angle is an angle of 90°.
Perpendicular lines are lines that intersect at a 90° angle. Perpendicular lines forms a right angle.
The complementary angle theorem states, "If two angles are complementary to the same angle, then they are congruent to each other".
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(a)In a certain board game, players spin a spinner to determine how many spaces they advance. The odds in favor of advancing five spaces are 3/10. Find the probability of advancing five spaces.
(b)Ravi has a box of candies with different flavors. He will randomly choose one piece of candy. The probability that he chooses a strawberry-flavored piece is 6/19. What are the odds against him choosing a strawberry-flavored piece?
The probability of advancing five spaces is 0.2307.
Given that, the odds in favor of advancing five spaces are 3/10.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
The probability of advancing five spaces can be obtained as:
P =Odds/1+Odds
= [tex]\frac{\frac{3}{10} }{1+\frac{3}{10} }[/tex]
= [tex]\frac{\frac{3}{10} }{\frac{13}{10} }[/tex]
= 3/13
= 0.2307
Therefore, the probability of advancing five spaces is 0.2307.
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