The exponential model for the data is: [tex]y = 693(1.5)^x[/tex]
When the cost is of $6000, the weight is of approximately 5.3 carats.
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.From the table, the rate of change is given by:
b = 4980/3210 = 3210/2140 = 2140/1430 = 1.5.
When x = 1, y = 1040, hence the initial value is found as follows:
1.5a = 1040.
a = 1040/1.5
a = 693.
So the model is:
[tex]y = 693(1.5)^x[/tex]
When the cost is of $6000, the weight is found as follows:
[tex]693(1.5)^x = 6000[/tex]
[tex](1.5)^x = \frac{6000}{693}[/tex]
[tex]1.5^x = 8.658[/tex]
[tex]\log{1.5^x} = \log{8.658}[/tex]
x log(1.5) = log(8.658)
x = log(8.658)/log(1.5)
x = 5.3
When the cost is of $6000, the weight is of approximately 5.3 carats.
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Information about a play took up 1/3 of the pages in the program. Information about the actors took up 1/4 of the remaining pages. Information about the director, the producer, and the designer took up 2 pages, the same number of pages devoted to the actors. How many pages were there in the program? help pls
Answer: 4
Step-by-step explanation:
x - (1/3)x - (1/6)x = 2
(6x - 2x - x)/6 = 2
3x/6 = 2
x=4
Prove the following relations.
Cos²A + cos²A.cot²A=cot²A
(1-sin²A)(1+cot²A)=cot²A
Step-by-step explanation:
Let's solve for the first one,
[tex]R.H.S. = Cos²A + cos²A.cot²A[/tex]
Step 1- Take Cos²A common,
[tex] = Cos²A( 1+ cot²A)[/tex]
[tex] \small \sf \: Now \: we \: know \: that \\ \small (1 + Cot^{2} \theta = Cosec^{2} \theta)[/tex]
Step 2 - Substituting above value in step 1,
[tex] = Cos^{2} A(Cosec^2A)[/tex]
[tex] \small \sf \: We \: know \: that \: Cosec \theta= \frac{1}{Sin \theta} [/tex]
Step 3 - Substitute Cosec²A with 1/Sin²A
[tex] = \frac{Cos^2A}{Sin^2A} [/tex]
[tex] \small \sf \: Now \: the \: basic \: trigonometric \: function \: is \\ \small \frac{Cos\theta}{Sin \theta} = Cot\theta[/tex]
Step 4 - Replacing the product of step 3 with above function,
[tex] = {Cot}^{2} A[/tex]
Hence proved,
[tex]R.H.S = L.H.S[/tex]
﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌
Now let's prove the second relation,
[tex](1-sin²A)(1+cot²A)=cot²A[/tex]
Let's solve for R.H.S.,
[tex]R.H.S.= (1-sin^{2} A)(1+cot^{2} A)[/tex]
As I told above,
[tex]\small(1+cot^{2} \theta) = cosec^{2} \theta[/tex]
Another important relation is,
[tex] \small sin^2\theta + cos^2\theta= 1 \: or \: \\ \small cos^2\theta = 1 - sin^2\theta[/tex]
Replacing both the above brackets with this relation we get,
[tex] = Cos^2A \cdot Cosec^2A [/tex]
Now follow the step 3 and step 4 of first question and you will get,
[tex]R.H.S. = L.H.S.[/tex]
﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌
Some important trigonometric relations that you must learn,
[tex]Sin^2\theta + Cos^2\theta = 1 \\ 1 + Cot^2\theta = Cosec^2\theta \\ 1+Tan^2\theta = Sec^2\theta[/tex]
[tex] \small\sf \: Thanks \: for \: joining \: brainly \: community! [/tex]
Directions: Find the missing side of each triangle. Round your answers to the nearest tenth if necessary.
Answer:
1) 13m, 2) 10ft, 3) 11.4ft, 4) 12.7m
Step-by-step explanation:
Since all of these triangles are right triangles, we can use the Pythagorean Theorem: a^2+b^2 = c^2
1) 5^2+12^2 = c^2 = 25+144 = c^2 = 169 = c^2 = 13 = c
2) 6^2+8^2 = c^2 = 36+64 = c^2 = 100 = c^2 = 10 = c
3) 5^2+10.3^2 = c^2 = 25+106.09 = c^2 = 131.09 = c^2 = 11.4494541 = 11.4 = c
4) 8.6^2+9.4^2 = c^2 = 73.96+88.36 = c^2 = 162.32 = c^2 = 12.7404866 = 12.7 = c
a chef uses 5 2/5 pounds of ground beef to make a hamburger and 2 1/4 pounds of ground beef to make meatloaf. the ground beef comes in 1/2 pound packages. how many packages of ground beef are needed to make hamburgers and meatloaf?
Answer:
16 packages
Step-by-step explanation:
5 2/5 + 2 1/4 Use the common denominator of 20
5 8/20 + 2 5/20
7 13/20
I know that I will need 14 packages for the 7 pounds. For the fraction part, 10/20 would be half, so I would need to buy a half pound for that, but I need 13/20 which would be more than a half pound, so I will need to buy 2 more pounds for the fraction part.
14 + 2 = 16
For a certain company, the cost function for producing x items is C(x)=40x+150 and the revenue function for selling x items is r(x)=-0.5(x-120)^2+7200. The maximum capacity of the company is 170 items.
No, we are unable to produce an endless amount in a given space. because the function is at its highest point when x is equal to 70, and its highest point of output is 2300.
We are unable to produce zero items in one day.
Maximum available output = 2300
The graph of the function is quadratic (parabolic), and the point at which it reaches its highest value, denoted by the vertex x = 70,
What is the maximum capacity of a company?Generally, The greatest level of production that a firm is able to maintain in order to provide its goods or services is referred to as its capacity. Capacity may refer to a manufacturing process, the distribution of human resources, technological thresholds, or any one of a number of other related ideas, depending on the sort of company being discussed.
In conclusion, No, we are unable to produce an endless amount in a given space. because the function is at its highest point when x is equal to 70, and its highest point of output is 2300.
We are unable to produce zero items in one day.
Maximum available output = 2300
The graph of the function is quadratic (parabolic), and the point at which it reaches its highest value, denoted by the vertex x = 70,
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Mrs. Smith has a total of 28 kids in her class. There are 5 more boys than there are girls. Write a system of equations to model this.
Answer:
x+(x+5)=28
Step-by-step explanation:
girls(g)should be equal to x
boys(b) will therefore be x+5
x+(x+5)=28
if a rectangular piece of metal has 27.75 square inches what is the length and width?
The maximum area of a rectangular piece of metal with perimeter of 27.75 in² has length of 6.9375 in and width of 6.9375 in.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the length and y represent the width. hence:
Perimeter = 2(x + y)
27.75 = 2(x + y)
y = 13.875 - x
Area (A) = xy
A = x(13.875 - x)
A = 13.875x - x²
Maximum area is at A' = 0, hence:
A' = 13.875 - 2x
13.875 - 2x = 0
x = 6.9375
y = 6.9375
The maximum area of a rectangular piece of metal with perimeter of 27.75 in² has length of 6.9375 in and width of 6.9375 in.
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Admission into an amusement park for 4 children
and 2 adults is $116.90. For 6 children and 3 adults,
the admission is $175.35. Assuming a different price
for children and adults, what is the price of the child's
ticket and the price of the adult ticket?
Answer:
A child ticket costs $16.50 and an adult ticket costs $25.45.
It is found that the child ticket costs $16.50 and an adult ticket costs $25.45.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given that 4 children and 2 adults are $116.90. For 6 children and 3 adults, the admission is $175.35.
Assuming a different price for children and adults,
Let the children are x and the adult is y.
Therefore,
4x + 2y = 116.90
6x + 3y = 175.35
Hence, the child ticket costs $16.50 and an adult ticket costs $25.45.
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40 points
The table shows the heights of students in a group.
Student Height (in inches)
A 45
B 48
C 49
D 40
E 53
What is the mean height of the students in the group?
47 inches
49 inches
51 inches
53 inches
Answer:
Step-by-step explanation:
answer: 47
add the heights then divide by 5
what is 4.685 in expanded form
Answer:
4*1/1000+6*100+8*10+5*1
Step-by-step explanation:
The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 39 ounces and a standard deviation of 5 ounces.
Use the Standard Deviation Rule, also known as the Empirical Rule.
Suggestion: sketch the distribution in order to answer these questions.
The answer to these questions are
Option A: This is in the attachmentOption B : 24 and 54Option C: 97.59%Option D: 84.13%
How to find the point where the distribution lies at 99.7%. The data is 3 sd from mean
Hence
39 - 3*(5) = 24
39 + 3*(5) = 54
The widget lies between 24 and 54
c. P(29.0 < x < 54.0)
= 29 - 39 / 5 and 54 - 39 / 5
= -2.0 and 3.0
We have to find P(Z < 3.0) - P(Z < -2.0)
= 0.9987 - 0.0228
= 97.59%
d. x = 44
= 44 - 39/ 5
= 1
We are to find P(z < 1.0) = 84.13%
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Question: 2 Based on the mass of lactose of 0.28 grams in 1 mL of skim milk, calculate the percent composition of lactose in skim milk.
Considering the definition of mass volume percent, the percent composition of lactose in skim milk is 28%.
Mass volume percentThe concentration of solutions is the amount of solute contained in a given amount of solvent or solution. In other words, the relationship between the amount of solute and the amount of solvent is called concentration.
Mass volume percent (% m/V) is a measure of concentration that indicates the number of grams of solute in each 100 mL of solution.
In other words, mass-volume percent is an intensive property that is defined as the mass of solute (in grams) that there are in 100 mL of solution and it is calculated by applying the following equation:
[tex]Mass volume percent=\frac{mass solute (grams)}{volume solution (mL)}x100[/tex]
This is, mass volume percent is defined as the ratio of the mass of solute that is present in a solution, relative to the volume of the solution, as a whole.
Percent composition of lactose in skim milkIn this case, you know:
mass solute= 0.28 gramsvolume solution= 1 mLReplacing in the definition of mass volume percent:
[tex]Mass volume percent=\frac{0.28 grams}{1 mL}x100[/tex]
Solving:
mass volume percent= 28 %
Finally, the percent composition of lactose in skim milk is 28%.
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Find a z-score for a data value of 19 if the mean of a set of data is 37 and the standard deviation is 8.6.
The z-score for a data value of 19 if the mean of a set of data is 37 and the standard deviation is 8.6 is -2.09
How to determine the z-score of the data value?From the question, the given parameters about the distribution are
Mean value of the set of data = 37
Standard deviation value of the set of data = 8.6
The actual data value = 19
The z-score of the data value is calculated using the following formula
z = (x - mean value)/standard deviation
Substitute the given parameters in the above equation
z = (19 - 37)/8.6
Evaluate the difference of 19 and 37
z = -18/8.6
Evaluate the quotient of -18 and 8.6
z = -2.09
Hence, the z-score for a data value of 19 if the mean of a set of data is 37 and the standard deviation is 8.6 is -2.09
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z=2cispi/3 in rectangular form
The conversion of "z = 2(cos(π/3))" in polar form to rectangular form is equal to 1.
What is a polar coordinate?A polar coordinate can be defined as a two-dimensional coordinate system, wherein each point on a plane is typically determined by a distance (r) from the pole (origin) and an angle (θ) from a reference direction (polar axis).
How to transform polar coordinates to rectangular coordinates?In geometry, the relationship between a polar coordinate (r, θ) and a rectangular coordinate (x, y) based on the conversion rules is given by the following polar functions:
a = rcos(θ) ....equation 1.
b = rsin(θ) ....equation 2.
Where:
θ is the angle.r is the radius of a circle.Note: The exact value of cos(π/3) is equal to ½.
Substituting the given parameters into the formula, we have;
z = 2(½)
z = 2/2
z = 1.
In conclusion, we can logically deduce that the conversion of "z = 2(cos(π/3))" in polar form to rectangular form is equal to 1.
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Complete Question:
Convert z = 2(cos(π/3)) in rectangular form
Which of the following inequalities represents the number line below?
Answer:
x ≤ 4
Step-by-step explanation:
the solid dot at 4 indicates that x can equal 4
the arrow points to the left indicating values less than 4 , then
x ≤ 4
Consider the equation V=6h where V is the volume (in cubic centimeters) of a box with a variable height h in centimeters and a fixed base of area 6cm2.
The volume (in cubic centimeters) of a box) given the fixed base area of 6cm² and height of 6 cm is 36 cm³.
VolumeV = 6h
Where,
V = volume (in cubic centimeters) of a boxh = height in centimeters andIf the height = 6 cm
Fixed base area = 6 cm²
V = 6h
= 6 cm² × 6 cm
V = 36 cm³
Therefore, the volume of the box given the fixed base area of 6cm² and height of 6 cm is 36 cm³.
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Find the area between the following curves.
y=x^3-x^2+x+8 ; y=5x^2-7x+8
Find where the two curves meet.
[tex]x^3 - x^2 + x + 8 = 5x^2 - 7x + 8 \\\\ \implies x^3 - 6x^2 + 8x = 0 \\\\ \implies x (x-2) (x - 4)= 0 \implies x=0, x=2, x=4[/tex]
The area between the curves is
[tex]\displaystyle \int_0^4 \left|\left(x^3-x^2+x+8\right) - \left(5x^2 - 7x + 8\right)\right| \, dx = \int_0^4 \left|x(x-2)(x-4)\right| \, dx[/tex]
When [tex]x[/tex] is between 0 and 2, [tex]x(x-2)(x-4)[/tex] is positive; when [tex]x[/tex] is between 2 and 4, [tex]x(x-2)(x-4)[/tex] is negative. So we split the integral at [tex]x=2[/tex] to get
[tex]\displaystyle \int_0^2 x(x-2)(x-4) \, dx - \int_2^4 x(x-2)(x-4)\,dx[/tex]
In the second integral, substitute [tex]y=x-2[/tex] to get
[tex]\displaystyle \int_0^2 x(x-2)(x-4) \, dx - \int_0^2 (y+2)y(y-2)\,dy[/tex]
[tex]\displaystyle \int_0^2 x(x-2) \bigg((x-4) - (x+2)\bigg) \, dx[/tex]
[tex]\displaystyle -6 \int_0^2 x(x-2) \, dx[/tex]
[tex]\displaystyle 6 \int_0^2 \left(2x - x^2\right) \, dx[/tex]
[tex]\displaystyle 6 \left(x^2 - \frac13x^3\right)\bigg|_0^2 = \boxed{8}[/tex]
Find the value of 8!
Hey there!
8!
= 8(7)(6)(5)(4)(3)(2)(1)
= 56(6)(5)(4)(3)(2)(1)
= 336(5)(4)(3)(2)(1)
= 1,680(4)(3)(2)(1)
= 6,720(3)(2)(1)
= 20,160(2)(1)
= 40,320(1)
= 40,320
Therefore, your answer should be:
40,320
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
can someone give the exact answer for all the blanks
Considering the given function, we have that:
f(a) = 4 - 2a + 6a²f(a + h) = 6a² + 12ah + 6h² - 2a - 2h + 4.[f(a + h) - f(a)]/h = 12a + 6h - 2.What is the function for this problem?The function is:
f(x) = 4 - 2x + 6x².
When x = a, we have that:
f(a) = 4 - 2a + 6a².
When x = a + h, we have that:
f(a + h) = 4 - 2(a + h) + 6(a + h)² = 6a² + 12ah + 6h² - 2a - 2h + 4.
For the fraction, we have that:
[f(a + h) - f(a)]/h = [6a² + 12ah + 6h² - 2a - 2h + 4 - 4 + 2a - 6a²]/h = [12ah + 6h² - 2h]/h = h(12a + 6h - 2)/h
Hence:
[f(a + h) - f(a)]/h = 12a + 6h - 2.
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Will mark brainliest
a. The area on [0, 10] is that of a trapezoid with bases 5 and 15 and height 10, so
[tex]\displaystyle \int_0^{10} f(x) \, dx = \frac{5+15}2\cdot10 = \boxed{100}[/tex]
b. By linearity of the definite integral, we have
[tex]\displaystyle \int_0^{25} f(x)\,dx = \int_0^{10} f(x)\,dx + \int_{10}^{25} f(x)\,dx[/tex]
and the area on [10, 25] is another trapezoid with bases 15 and 7.5 and height 15, so that
[tex]\displaystyle \int_{10}^{25} f(x)\,dx = \frac{15+7.5}2\cdot15 = 168.75[/tex]
Then the total area on [0, 25] is
[tex]\displaystyle \int_0^{25} f(x)\,dx = \boxed{268.75}[/tex]
c. The area on [25, 35] is that of a triangle with base 10 and height 15. However, [tex]f(x)<0[/tex] on this interval, so we multiply this area by -1 to get
[tex]\displaystyle \int_{25}^{35} f(x)\,dx = -\frac{10\cdot15}2 = \boxed{-75}[/tex]
d. The area on [15, 25] is the same as the area on [25, 35] because it's another triangle with the same dimensions. But the area on [15, 25] lies above the horizontal axis, so
[tex]\displaystyle \int_{15}^{25} f(x)\,dx = \int_{15}^{25} f(x)\,dx + \int_{25}^{35} f(x)\,dx = \boxed{0}[/tex]
e. The plot of [tex]|f(x)|[/tex] lies above the horizontal axis. We know the area on [15, 25] is the same as the area on [25, 35], but now both areas are positive, so
[tex]\displaystyle \int_{15}^{35} |f(x)| \, dx = \int_{15}^{25} f(x)\,dx - \int_{25}^{35} f(x)\,dx = 2 \int_{15}^{25} f(x)\,dx = \boxed{150}[/tex]
f. Changing the order of the limits in the integral swaps the sign of the overall integral, so
[tex]\displaystyle \int_{10}^0 f(x)\,dx = -\int_0^{10} f(x)\,dx = \boxed{-100}[/tex]
The Mogul Runners ski club planned a trip to Park City. Of the total number of club members, 11 signed up to go. If this is 25% of the club, how many members does the ski club have?
Answer: 44
Step-by-step explanation: Since 11 members are equal to 25% of the club, 11 members is 1/4 of the club because 25% = 1/4. There are four-fourths in a whole so 11x4 = 44 members. The ski club has 44 members.
A backyard pool has a concrete walkway around it that is 5' wide on all sides the total area of the pool and the walkway is 950' at the length of the pool is 8' longer than the width find the dimensions of the pool
The dimensions of the pool would give a quadratic equation x² + 28x - 770 = 0
How to determine the dimension
For the pool, we have that;
Let the width = x feet
Length = (x+8) feet
The pool alongside the walkway gives;
Width = x + 5 + 5 = (x + 10) feet
Length = x + 8 + 5 + 5 = (x + 18) feet
Total area of the pool with walkway = 950 square feet
Note that formula for area is given as
Area = length * width = 950
Equate the length and width
(x+18) × (x + 10) = 950
Using the FOIL method, we have;
(x × x )+ (x × 10) + (18 × x) + (18 × 10) = 950
x² + 10x + 18x + 180 -950 = 0
collect like terms
x² + 28x - 770 = 0
Thus, the dimensions of the pool would give a quadratic equation x² + 28x - 770 = 0
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Find the area of the trapezoid 19 12.6 29.2 14.5
Answer:
303.66 in²
Option 4 is the correct answer
What is the sum of 3x^3-2x+8,2x^2+5x,and x^3+2x^2-3x-3
Answer:
4x³ + 4x² + 5
Step-by-step explanation:
3x³ - 2x + 8 + 2x² + 5x + x³ + 2x² - 3x - 3.
4x³ - 2x + 8 + 2x² + 5x + 2x² - 3x - 3
4x³ + 4x² - 2x + 8 + 5x - 3x - 3
4x³ + 4x² + 8 - 3
4x³ + 4x² + 5
We will start with a string which is pulled tight enough to vibrate at 288 Hertz when
plucked. Let the length of the string be 1 unit. We can find additional nice sounding
notes by using a string of a smaller length with the same amount of tension. To find
the string lengths, we need to use fractions whose numerators are powers of 2 and
whose denominators are powers of 3 (which are larger than ½, but smaller than 1).
The first few fractions are given below. Determine the remaining fractions:
The series of fractions is 1, 2/3, 8/9, 16/27, 64/81, 128/243, 512/729, 2048/2187, 4096/6516, 16384/19683, 32768/59049, 131072/177147.
The string lengths are fractions whose numerators are powers of 2 and denominators are powers of 3, and the fractions are larger than 1/2 but smaller than 1.
Some powers of 2 are:
2⁰ = 1, 2¹ = 2, 2² = 4, 2³ = 8, 2⁴ = 16, 2⁵ = 32, 2⁶ = 64, 2⁷ = 128, 2⁸ = 256, 2⁹ = 512, 2¹⁰ = 1024, 2¹¹ = 2048, 2¹² = 4096, 2¹³ = 8192, 2¹⁴ = 16384, 2¹⁵ = 32768, 2¹⁶ = 65536, and 2¹⁷ = 131072.
Some powers of 3 are:
3⁰ = 1, 3¹ = 3, 3² = 9, 3³ = 27, 3⁴ = 81, 3⁵ = 243, 3⁶ = 729, 3⁷ = 2187, 2⁸ = 6561, 3⁹ = 19683, 3¹⁰ = 59049, and 3¹¹ = 177147.
The fractions, for which the numerator is a power of 2, the denominator is a power of 3, and the value is between 1/2 and 1 are:
2/3, 8/9, 16/27, 64/81, 128/243, 512/729, 2048/2187, 4096/6516, 16384/19683, 32768/59049, 131072/177147.
Thus, the series of fractions is 1, 2/3, 8/9, 16/27, 64/81, 128/243, 512/729, 2048/2187, 4096/6516, 16384/19683, 32768/59049, 131072/177147.
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Pls help me with this calculus question
Answer:
5
Step-by-step explanation:
Gradient (slope) of the curve can be found by deriving a curve function.
In this scenario, the given function is a polynomial function which we can use Power Rules to derive it.
Power Rules
[tex]\displaystyle{y=ax^n \to y' = nax^{n-1}}[/tex]
Thus, using the power rules, we will have:
[tex]\displaystyle{y'=3x^2-4x+5}[/tex]
Note that deriving a constant will always result in 0.
Then the problem gives us that we want to find the slope or gradient at where the curve crosses y-axis.
The curve crosses y-axis at x = 0 only. Therefore, we substitute x = 0 in a derived function.
[tex]\displaystyle{y'(0) = 3(0)^2-4(0)+5}\\\\\displaystyle{y'(0) = 5}[/tex]
Therefore, the slope at the point where a curve crosses y-axis will be 5.
Karsten is preparing his will. He wants to leave the same amount of money to his two daughters. His elder daughter is careful with money, but the younger daughter spends it carelessly, so he decides to give them the money in different ways. How much must his estate pay his younger daughter each month over 20 years, so that the accumulated present value will be equal to the $50000 cash his elder daughter will receive upon his death? Assume that the younger daughters inheritance earns 6%/a compounded monthly
The amount that Karsten's estate should pay his younger daughter each month over 20 years so that the accumulated present value will be equal to $50,000 is $358.22.
How to calculate periodic payments?The monthly payments out of the present value of $50,000 can be computed using an online finance calculator.
The periodic payment represents the equal amount that can be paid to the daughter monthly so that it equals the PV of $50,000 of the estate share.
Data and Calculations:N (# of periods) = 240
I/Y (Interest per year) = 6%
PV (Present Value) = $50,000
FV (Future Value) = $0
Results:
Monthly Payment = $358.22
Sum of all periodic payments = $85,971.73 ($358.22 x 2400
Total Interest = $35,971.73
Thus, Karsten's younger daughter can be paid $358.22 to equal the accumulated present value of $50,000.
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Given: m space measured angle space C space equals space 76, a = 20, and b = 13. What is the length of c to the nearest tenth?
Based on the given parameters, the length of c is 8.0 units
How to determine the side length of c?The given parameters are
Angle c = 76 degrees
Side a = 20
Side b = 13
The length of c is then calculated using the following law of sines
c^2 = a^2 + b^2 - 2absin(C)
Substitute the known values in the above equation
So, we have
c^2 = 20^2 + 13^2 - 2 * 20 * 13 * sin(76)
Express 20^2 as 400
c^2 = 400 + 13^2 - 2 * 20 * 13 * sin(76)
Express 13^2 as 169
c^2 = 400 + 169 - 2 * 20 * 13 * sin(76)
Evaluate the product and sin(76)
c^2 = 400 + 169 - 520 * 0.9703
Evaluate the product
c^2 = 400 + 169 - 504.55
Evaluate the exponents
c^2 = 400 + 169 - 504.55
So, we have
c^2 = 64.45
Evaluate the square root
c = 8.0
Hence, the length of c is 8.0 units
Read more about law of sines at:
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cos 90 - 2sin45 + 2tan180
Answer:
- [tex]\sqrt{2}[/tex]
Step-by-step explanation:
cos90° - 2sin45° + 2tan180°
= 0 - ( 2 × [tex]\frac{\sqrt{2} }{2}[/tex] ) + 2(0)
= 0 - [tex]\sqrt{2}[/tex] + 0
= - [tex]\sqrt{2}[/tex]
PLEASE HELP ME QUICK
In the diagram, points D and E are marked by drawing arcs of equal size centered at B such that the arcs intersect BA and BC
Then, intersecting arcs of equal size are drawn centered at points D and E. Point P is located at the intersection of these arcs.
Based on this construction, m∠ABP is ANSWER ° and m∠ABC is ANSWER°
Answer:
m∠ABP is 32°,m∠ABC is 64°.Step-by-step explanation:
According to the construction we have:
BD = BEPD = PEBP - is common side of triangles BPD and BPEIt gives us:
ΔPBD ≅ ΔPBEThen, corresponding angles of congruent triangles are congruent:
∠DBP ≅ ∠EBPSo,
∠ABP ≅ ∠CBP ⇒ m∠ABP = 32°Then,
m∠ABC = m∠ABP + m∠CBP = 32° + 32° = 64°