Answer:
Results are below.
Step-by-step explanation:
1. First, we need to calculate the Future Value:
FV= {A*[(1+i)^n-1]}/i
A= quarterly deposit
n= 10*4= 40
i= 0.12/4= 0.03
FV= {4,000*[(1.03^40) - 1]} / 0.03
FV= $301,605.04
Now, the present value:
PV= FV/(1+i)^N
PV= 301,605.04/(1.03^40)
PV= $92,459.09
2. First, we need to calculate the value of the first year of college:
FV= PV*(1+i)^n
FV= 24,000*(1.04^3)
FV= $26,996.74
Now, the quarterly payments:
FV= {A*[(1+i)^n-1]}/i
A= quarterly deposit
Isolating A:
A= (FV*i)/{[(1+i)^n]-1}
i= 0.08/4= 0.02
n= 3*4= 12
A= (26,996.74*0.02) / [(1.02^12) - 1]
A= $2,012.87
Rafael earns $35 more per week than Andrew. If their weekly salaries total $715, what amount does each earn?
Answer:
Rafael earns $375
Andrew earns $340
Step-by-step explanation:
Here, we will set up a system of equations where r represents Rafael and a represents andrew.
r = a + 35
r + a = 715
Next, we substitute a + 35 for r in the second equation.
(a + 35) + a = 715 (combine like terms)
2a + 35 = 715 (subtract 35 from both sides)
2a = 680 (divide both sides by 2)
a = 340
To solve for r, we can plug 340 for a into either equation.
r = (340) + 35
r = 375
We can double check by plugging both values into the other equation.
375 + 340 = 715 (yes, it works!)
Brainliest, please :)
Graph the function f(x) = 2√x +3.
The graph is shown in the attached image.
Which function is graphed?
Answer: A
Step-by-step explanation:
The parabola has an open hole at x=3 and the line has a closed hole at x=3, so there should be [tex]x < 3[/tex] for the parabola and [tex]x \geq 3[/tex] for the line.
This eliminates all the options except for A.
According to the general equation for conditional probability, if P(AB) = and P(B) = 2, what is P(A/B)? 12 O A. 3/ О в. 4 O c. 2/ C. 5 O D. 9
Using conditional probability, it is found that:
[tex]P(A|B^\prime) = \frac{1}{3}[/tex]
What is Conditional Probability?Conditional probability is the probability of one event happening, considering a previous event. The formula is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which:
P(B|A) is the probability of event B happening, given that A happened.[tex]P(A \cap B)[/tex] is the probability of both A and B happening.P(A) is the probability of A happening.For this problem, we are given that:
[tex]P(B^\prime) = 1 - P(B) = 1 - \frac{1}{3} = \frac{2}{3}[/tex].[tex]P(A \cap B^\prime) = \frac{2}{9}[/tex]Then:
[tex]P(A|B^\prime) = \frac{P(A \cap B^\prime)}{P(B^\prime)}[/tex]
[tex]P(A|B^\prime) = \frac{\frac{2}{9}}{\frac{2}{3}}[/tex]
[tex]P(A|B^\prime) = \frac{1}{3}[/tex]
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Simplify (x + 5)2 using the square of a binomial formula.
x² + 10x + 25
x²-10X-25
x²-10x+25
x² + 10x - 25
Answer:
[tex]x^2 + 10x + 25[/tex]
Step-by-step explanation:
Hello!
Formula: [tex](a +b)^2 = a^2 + 2ab + b^2[/tex]
a = xb = 5Plug it into the formula and simplify.
Simplify[tex](a +b)^2 = a^2 + 2ab + b^2[/tex][tex](x +5)^2 = x^2 + 2(x)(5) + 5^2[/tex][tex](x +5)^2 = x^2 + 10x + 25[/tex]The answer is the first option: [tex]x^2 + 10x + 25[/tex].
Answer:
x^2-10x+25
Step-by-step explanation:
This is the correct answer
if a = { 1,2,3,...,10} and U={1,2,4,8} then find A'
Answer:
U-A empty
Step-by-step explanation:
all in a is in u in u is in a therfore empty is found on u but not in a
find the slope of this line.
Answer:
4/5
Step-by-step explanation:
SImply use slope formula. We see the graph has defined points at (5, 4), and (-5, -4).
m=(Y2-Y1)/(X2-X1)
(4-(-4))/(5-(-5))=8/10
Simplify 8/10
=4/5
3. A line with a slope of passes through the point (10,-5).
The equation of the line in slope intercept form
can be given by the formula y = mx + b
where m=
and b =
√x
The equation of the line is y = -3/2x + 10
How to determine the line equation?The given parameters are:
Slope, m = -3/2
Point, (x, y) = (10, -5)
The line equation is represented as
y = mx + b
Substitute the given parameters in the equation
-5 = -3/2 * 10 + b
This gives
-5 = -15 + b
Add 15 to both sides
b = 10
So, we have:
y = -3/2x + 10
Hence, the equation of the line is y = -3/2x + 10
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Proving a uadrilateral is a Parallelogram
Assignment Active
Determining Side Lengths in a Parallelogram
In quadrilateral ABCD, AD 1, BC.
3x+7
D
A
B
5x-9
What must the length of segment AD be for the
quadrilateral to be a parallelogram?
O 8 units
O 16 units
O 31 units
O 62 units
Answer:
31 units
Step-by-step explanation:
If a quadrilateral has a pair of sides that is both parallel and congruent, then the quadrilateral is a parallelogram.
Sides AD and BC are given as parallel.
If they are also congruent, then quadrilateral ABCD is a parallelogram.
3x + 7 = 5x - 9
-2x = -16
x = 8
AD = 3x + 7
AD = 3(8) + 7
AD = 31
Answer: 31 units
I need a good answer, with a good explanation.
Janie and Jasmine are playing three games at an arcade. Each of the games requires either 2, 3, or 4 tokens. The girls plan to play as many games as they can before running out of tokens.
Write an expression to represent the total number of tokens that Janie and Jasmine will need to play each of the three games at least once. Let m represent the number of games that require 2 tokens; n represent the number of games that require 3 tokens; p represent the number of games that require 4 tokens.
The expression to represent the information will be 2(2m + 3n + 4p)
How to illustrate the expression?From the information given, Janie and Jasmine are playing three games at an arcade. Each of the games requires either 2, 3, or 4 tokens.
There are m number of games required.
There are n number of games that require 3 token.
Therefore, the expression to represent the information will be:
= 2(2 × m) + 2(3 × n) + 2(4 × p)
= 2(2m + 3n + 4p)
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Answer:
The other person who answered is incorrect!! The real answer is 2m + 3n + 4p
Step-by-step explanation:
have a good besti!!!!
-leeknowishawt
D
C
63. If AD 20 centimeters, DC= 15 centimeters,
BC=7 centimeters, and AB = 24 centimeters,
what is the area of quadrilateral ABCD?
A. 66 sq cm
B.
B
117 sq cm
C. 234 sq cm
D.
468 sq cm
The area of the irregular quadrilateral ABCD is equal to 234 square centimeters. (Correct choice: C)
What is the area of the quadrilateral?
Herein we have a description of an irregular quadrilateral, whose area must be determined by adding the areas of minor quadrilaterals and triangles that are part of it. The area is now determined:
A = 0.5 · (24 cm) · (7 cm) + 0.5 · (15 cm) · (20 cm)
A = 234 cm²
The area of the irregular quadrilateral ABCD is equal to 234 square centimeters. (Correct choice: C)
Remark
The picture with the quadrilateral is missing and is included as attachment.
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Give the name (monomial,
binomial, trinomial etc.) and
degree of the polynomial.
3x4
Name? [?]
Degree? [ ]
Answer:
monopoly, order 1
Step-by-step explanation:
because the x has just power of one that is why is monopoly and in order 1
Please Help! Brainliest Available!!!!!
Using the z-distribution, the test statistic is:
c) -2.63.
What are the hypothesis tested?At the null hypothesis we test if the means are equal, equivalent to a subtraction of 0, hence:
[tex]H_0: \mu_D - \mu_C = 0[/tex]
At the alternative hypothesis, we test if they are different, hence:
[tex]H_1: \mu_D - \mu_C \neq 0[/tex]
What are the mean and the standard error for the distribution of differences?For each sample, they are given as follows:
[tex]\mu_D = 12, s_D = \frac{5.2}{\sqrt{73}} = 0.6086[/tex].[tex]\mu_C = 14, s_C = \frac{4.1}{\sqrt{81}} = 0.4556[/tex].For the distribution of differences, it is given by:
[tex]\overline{x} = \mu_D - \mu_C = 12 - 14 = -2[/tex].[tex]s = \sqrt{s_D^2 + s_C^2} = \sqrt{0.6086^2 + 0.4556^2} = 0.76[/tex]What is the test statistic?The test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{s}[/tex]
In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.
Hence:
[tex]z = \frac{\overline{x} - \mu}{s}[/tex]
[tex]z = \frac{-2 - 0}{0.76}[/tex]
z = -2.63.
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Explain the box and whisker plot in detail.
Based on the box and whisker plot shown above, we can infer and logically deduce that the number of lepilemures have a minimum at 0 but are well spread.
What is a box and whisker plot?A box and whisker plot is also referred to as boxplot and it can be defined as a type of chart that can be used to graphically represent the five-number summary of a data set with respect to locality, skewness, and spread. Also, the five-number summary include the following:
MinimumFirst quartileMedianThird quartileMaximumBy critically observing the box and whisker plot shown above, we can infer and logically deduce that the data (number of lepilemures) have a minimum at 0 but are well spread.
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When Billy's asked how old he is, he replies, "In two years I will be twice as old as I was five years ago." How old is he?
brainliest to whoever answers
Answer:
12 years old
Step-by-step explanation:
Set up the following equation:
x + 2 = 2(x - 5) (distribute the 2)
x + 2 = 2x - 10 (subtract 2 from both sides)
x = 2x - 12 (subtract 2x from both sides)
-x = -12 (multiply both sides by negative 1)
x = 12
Brainliest, please :)
Answer: 12
Step-by-step explanation:
Let's algebraically represent this situation. Say his current age is x. We can rephrase the sentence to say that in two years, his age is the same as twice his age 5 years ago.
The phrase "in two years" means when his age is 2 more than his current age, or x + 2.
The phrase "same as" represents equality. The expressions on both sides have the same value.
The phrase "twice his age 5 years ago" is his age minus 5, multiplied by 2. We can write this as 2*(x-5).
Now that we have "translated" the equation from words to numbers, let's put it all in one equation and solve:
[tex]x+2=2(x-5)[/tex]
[tex]x+2=2x-10[/tex] [Distributive Property]
[tex]x+2-2x-2=2x-10-2x-2[/tex] [Adding -2x-2 to both sides]
[tex]-x=-12[/tex] [Combining like terms and simplifying]
[tex]x=12[/tex] [Multiplying both sides by -1 to remove the negative]
Hence, Billy's age is 12.
Maths Trigonometry Question
40 Points!
Will give brainliest to whoever answers
The calculation of the trigonometry illustrates that:
sin 45° = 1/✓2
cos45/tan 45 =
cos 45 sin 45 = 1/2
How to illustrate the trigonometry?Opposite = 1
Adjacent = 1
Hypothenuse = ✓2
Tan 45 = opposite/adjacent = 1
Sin 45 = opposite/hypothenuse = 1/✓2
Cos 45 = adjacent/hypothenuse = 1/✓2
cos45/tan 45 = (1/✓2) / 1 = 1/✓2
Cos 45 sin 45 = 1/✓2 × 1/✓2 = 1/2
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Ray and Kelsey have summer internships at an engineering firm. As part of their internship, they get to assist in the planning of a brand new roller coaster. For this assignment, you help Ray and Kelsey as they tackle the math behind some simple curves in the coaster's track.
Part A
The first part of Ray and Kelsey's roller coaster is a curved pattern that can be represented by a polynomial function.
Ray and Kelsey are working to graph a third-degree polynomial function that represents the first pattern in the coaster plan. Ray says the third-degree polynomial has four intercepts. Kelsey argues the function can have as many as three zeros only. Is there a way for the both of them to be correct? Explain your answer.
Kelsey has a list of possible functions. Pick one of the g(x) functions below and then describe to Kelsey the key features of g(x), including the end behavior, y-intercept, and zeros.
g(x) = (x + 2)(x − 1)(x − 2)
g(x) = (x + 3)(x + 2)(x − 3)
g(x) = (x + 2)(x − 2)(x − 3)
g(x) = (x + 5)(x + 2)(x − 5)
g(x) = (x + 7)(x + 1)(x − 1)
Create a graph of the polynomial function you selected from Question 2.
From the information given about the polynomial function, It is correct to state that there is a way for both of them to be correct. See the explanation below and the attached for the graph related to the second question.
What is the explanation for the above?A polynomial could only have a number of zeros equal to its degree. A third degree polynomial can thus have three zeroes, but Ray claims the polynomial has four Intercepts.
While the words "zeroes" and "intercepts" are sometimes used interchangeably, a zero is officially an x-intercept. A function can also have a y-intercept, therefore a cubic can have four intercepts in total, albeit only three will be zeroes.
The zeros of g(x)= x3-x2-4x+4 are -2,2, and 1. End behavior, the Y- intercept, the axis of symmetry, and the vertex are other important characteristics of polynomial functions.
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Which choice is equivalent to the quotient shown here for acceptable values of x?
The expression [tex]\sqrt{\frac{5}{x-1} }[/tex] is equivalent to the given quotient.
Option A is correct.
When we divide one number by another, the result is a quotient. Although a quotient can be greater than the divisor, it will never be greater than the dividend.
In mathematics, the outcome of dividing a number by any divisor is known as the quotient. It refers to how many times the dividend contains the divisor.
After the division has been done, the quotient is obtained. This signifies that the quotient is the result of dividing a dividend by a divisor.
According to the question,
[tex]\sqrt{25(x-1)}[/tex] ÷ [tex]\sqrt{5(x-1)^{2} }[/tex] = 5[tex]\sqrt{x-1}[/tex] ÷ (x-1)[tex]\sqrt{5}[/tex]
= [tex]\sqrt{\frac{5}{x-1} }[/tex]
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A rectangular lot has a perimeter of 80 meters and a length of 25 meters. Find the
width of the lot.
Fence->
25m
Meters
W
Answer:
15m
Step-by-step explanation:
Let w be the width, l the length and p the perimeter.
We know, by definition, that p = 2w + 2l. We also know that p = 80m and l = 25m.
So we can re-write the perimeter formula as:
80 = 2w + 50
2w = 30
w = 15m
So we now know that the width is 15m.
Tanisha is signing up for a gym membership with a one-time fee to join and then a
monthly fee to remain a member. The monthly fee is $50 and the one-time joining
fee is $100. Make a table of values and then write an equation for C, in terms of t,
representing the total cost of the gym membership over t months.
Answer:
t=150
Step-by-step explanation:
50+100=150
50×12=600
Which of the following choices will simplify 5-3•2?
a vendor is thinking about changing the number of sweatshirts he brings to tan event. to make sure he doesn't run out, he plans to bring more of the size most likely to be sold. the table shows the number of sweatshirts of each size sold at the vendors last event and the number he had for sale. which size should he bring more of?
The sweatshirt size which the vendor should bring more of by virtue of that which is most likely to be sold is; Choice A; Extra-large.
Which sweatshirt size should the vendor bring more of?If follows from the task content that the
ratio of extralarge shirts sold relative to the quantity he had to sell is
= 99/108
= 11/12,
This is a ratio which is larger than any other shirt.
Consequently, the vendor must bring more of the X-large shirts to avoid running out of them.
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A sience teacher uses an overhead projector to display a diagram of a pulley sytem. the actual diagram is 6'' by 7.2''. The image projected onto the wall is 4' 2'' by 5'' what is the scale factor of the projection
Answer:
25/36, or .694444
Step-by-step explanation:
First, let's convert 6" to inches.
That gives us 72. After we convert 4'2" into inches, we get 50.
This means that the diagram goes from 72 inches wide to 50. Put this into a proportion to find the scale factor:
50/72 = 25/36 = .6944444
Find the point on the line y = 5x + 2 that is closest to the origin.
Answer: [tex]\left(-\frac{5}{13}, \frac{1}{13}\right)[/tex]
Step-by-step explanation:
The shortest distance from a point to a line is the perpendicular distance. The origin is essentially a point with coordinates (0,0); hence, we have to find the equation of the line that's both perpendicular to [tex]y=5x+2[/tex] and crosses the origin.
We can do this by recognizing that slope of a perpendicular line is the opposite reciprocal of the slope of the original line.
Opposite Reciprocal of 5: [tex]-\frac{1}{5}[/tex]
Now that we have the slope and the point, we can use the point-slope form to get the equation of the perpendicular.
Point-Slope Form: [tex]y-y_1=m(x-x_1)[/tex] (m is slope, [tex]x_1[/tex] and [tex]y_1[/tex] are the point's coordinates)
[tex]y-0=-\frac{1}{5}(x-0)\\y=-\frac{1}{5}x[/tex]
Since we need to find a point on the original line that's closest to the origin, we need to find the intersection of the line and its perpendicular. We can do this by setting both lines equal to each other and solving for x and y.
[tex]5x+2=-\frac{1}{5}x\\25x+10=-x\\26x=-10\\x=-\frac{10}{26}\\x=-\frac{5}{13}[/tex]
Substituting x in any of the equations will give us y. Here, I will put it in the equation [tex]y=-\frac{1}{5}x[/tex]
[tex]y=-\frac{1}{5}*-\frac{5}{13}\\y=\frac{5}{65}\\y=\frac{1}{13}[/tex]
The closest point to the origin on the line [tex]y=5x+2[/tex] is [tex]\left(-\frac{5}{13}, \frac{1}{13}\right)[/tex]
The point on the line y = 5x + 2 that is closest to the origin is (-5/13, 1/13).
What is the point slope form?The point slope form is used to find the equation of the straight line which is inclined at a given angle to the x-axis and passes through a given point.
The given equation of a line is y=5x+2 ------(I)
The shortest distance from a point to a line is the perpendicular distance. The origin is essentially a point with coordinates (0,0); hence, we have to find the equation of the line that's both perpendicular to y=5x+2 and crosses the origin.
We can do this by recognizing that slope of a perpendicular line is the opposite reciprocal of the slope of the original line.
So, slope of perpendicular line is -1/5
The equation of the point slope form is: (y - y1) = m(x - x1)
Now, substitute m=-1/5 and (x, y)=(0, 0), we get
y-0=-1/5 (x-0)
y=-1/5 x -----(II)
Equate equation (I) and (II), we get
5x+2=-1/5 x
⇒ -x=25x+10
⇒ -26x=10
⇒ x= -5/13
So, y=-1/5 x =1/13
Therefore, the point on the line y = 5x + 2 that is closest to the origin is (-5/13, 1/13).
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Which of the following are equations for the line shown below? Check all that
apply.
(-4,3)
(4,-5)
A. y=-x-1
B. y+ 5=-(x-4)
C. y-3 = -(x+4)
D. y=-x-9
Answer: A, B, C
Step-by-step explanation:
[tex]m=\frac{-5-3}{4-(-4)}=-1[/tex]
Substituting into point-slope form, we get [tex]y-3=-(x+4)[/tex] and [tex]y+5=-(x-4)[/tex]. Rearranging this into slope-intercept form,
[tex]y-3=-(x+4)\\\\y-3=-x-4\\\\y=-x+1[/tex]
¿cuál es el número que no pertenece a esta suceción 99,105111,117,123,129,135,141,147,153
No hay ninguno de los nimbers que no pertenezca a la secuencia.
¿Qué número no pertenece a la secuencia?
Sabemos que una secuencia tiene que ver con un arreglo de números en un orden definido. Todos los números en una secuencia deben tener la misma razón común o diferencia común.
Si miramos todos los números que están escritos en la secuencia, la diferencia común aquí es seis. Se sigue entonces que todos los números son parte de la sucesión y no hay ninguno de los números que no pertenezca a la sucesión.
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On a ΔABC, mΔA=80, mΔB=60
Find mΔC
The measure of angle C (m ∠C) is 40°
Calculating angles in a triangleFrom the question, we are to determine the measure of angle C (m ∠C)
In any given triangle, the sum of all the angles is 180°
Thus,
In ΔABC, the angles sum up to 180°
That is,
∠A + ∠B + ∠C = 180°
From the given information,
m ∠A = 80°, m ∠B = 60°
Thus,
80° + 60° + m ∠C = 180°
140° + m ∠C = 180°
m ∠C = 180° - 140°
m ∠C = 40°
Hence, the measure of angle C (m ∠C) is 40°
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Which point is the center of the Circle with the given equation.
(x + 5)2 + (y - 4)2 = 9
The center of the circle is (-5, 4)
How to determine the center of the circle?The circle equation is given as:
(x + 5)^2 + (y - 4)^2 = 9
A circle equation is represented as:
(x - a)^2 + (y - b)^2 = r^2
Where
Center = (a, b)
By comparing both equations, we have
(a, b) = (-5, 4)
Hence, the center of the circle is (-5, 4)
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An employee worked for 8 hours on 2 days, 6 hours on 1 day, and 4 hours on 2 day
What is the average number of hours the employee worked per day?
A.) 6.0
B.) 6.5
C.) 7.0
D.) 7.5
E.) 8.0
Answer:
A) 6.0
Step-by-step explanation:
First, total amount of hours, since average is sum of the numbers by how many numbers there is.
Day 1=8x2 hr
Day 2=6x1 hr
Day 3=4x2 hr
which is, 16+6+8=30
then divide 30 by how many days there is, which is 5 days.
30/5=6
5. A 12-ounce jar of jam costs $2.40. A 16-ounce jar costs $4.00. What is the
difference in the cost per ounce?
$
per ounce
The difference in the cost per ounce is $0.05 per ounce
Fractions and proportionFractions are written as the ratio of two integers
If a 12-ounce jar of jam costs $2.40, the cost per ounce will be:
Unit cost = 2.40/12
Unit cost = $0.2
Similarly, if a 16-ounce jar costs $4.00, the price of a ounce will be:
Unit cost = 4/16
Unit cost. =$0.25
difference = $0.25 - $0.2
difference = $0.05
Hence the difference in the cost per ounce is $0.05 per ounce
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