Bob has taken out a loan of $15,000 for a term of 48 months (4 years) at an interest rate of 6.5%. Using the amortization table provided, what will be his total finance
charge over the course of his loan?
Monthly Payment per $1,000 of Principal
Rate 1 Year 2 Years 3 Years 4 Years 5 Years
6.5% $86.30 $44.55 $30.65 $23.71 $19.57
7.0% $86.53 $44.77
$30.88
$23.95
$19.80
7.5% $86.76 $45.00
$31.11
$24.18
$20.04
8.0% $86.99 $45.23
$31.34
$24.41
$20.28
8.5% $87.22 $45.46
$24.65
$24.65
$20.52
9.0% $87.45 $45.68
$31.80
$24.89
$20.76
A.
$355.65
O
B.
$975.00
C.
$1,682.40
D.
$2,071.20
E. $17,071.20
Reset
Next
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Answer:
D. $2071.20
Step-by-step explanation:
The table tells you that Bob's monthly payment on a 4-year loan at 6.5% will be $23.71 per thousand borrowed. The sum of those 48 payments is ...
48 × $23.71 = $1138.08
That means, Bob pays $138.08 in total finance charge for each $1000 he borrows. He is borrowing 15 times $1000, so his total finance charge will be ...
finance charge = 15 × $138.08 = $2071.20 . . . matches choice D
How to work out the medium in maths
Answer:
To find the median you cross off the first few numbers and the last few until you get to the middle then when you get the middle number that will be your median
Step-by-step explanation:
Answer:
Below.
Step-by-step explanation:
It's the middle value of a list of numbers arranged in order.
For example the median of the list 1 2 3 4 5 is 3.
If there are an even number of values, the median is the mean of the middle two. For example:
1 3 4 5 7 9:
The middle 2 numbers are 4 and 5 so
the median is (4 + 5) / 2 = 4.5
Chantal is driving on a highway at a steady speed. She drives 55 miles every hour. Let d be the total distance in miles and let h be the number of hours.
Write an equation that represents the situation. I'll give out the brainliest if you get it right.
Answer:
[tex] d = 55h [/tex]
Step-by-step explanation:
We are given that Chantal drives at a constant speed of 55 miles per hour.
If, d represents the total distance in miles, and
h represents number of hours, the following equation can be used to express the given situation:
[tex] d = 55h [/tex]
For every hour, a distance of 55 miles is covered.
Thus, if h = 1, [tex] d = 55(1) = 55 miles [/tex]
If h = 2, [tex] d = 55(2) = 110 miles [/tex].
Therefore, [tex] d = 55h [/tex] , is an ideal equation that represents the situation given in the question above.
Finding which number supports the idea that the rational numbers are dense in the real numbers.
Answer:A terminating decimal between -3.14 and -3.15.
Step-by-step explanation:
A natural number includes non-negative numbers like 5, 203, and 18476.
It is encapsulated by integers, which include negative numbers like -29, -4, and -198.
Integers are further encapsulated by rational numbers, which includes terminating decimals like 3.14, 1.495, and 9.47283.
By showing a terminating decimal between -3.14 and -3.15, you are showing that rational numbers include integers (because integers include negative numbers.
A ship travels due north for 100 miles from point C to point A. From point A the ship travels to point B at 60° east of north. From point B, the ship returns to point C heading 45° west of south. What approximate distance did the ship travel from point A to point B? How far does it travel in total?
Answer:
AandB=80miles
Total=240miles
Step-by-step explanation:
Draw the figure first indicating the figures then find the distance each degrees then find the total
The distance ship travels from A to B is 273.2 miles and total distance covered by ship is 707.82 miles.
What is laws of sines?The law of sines specifies how many sides there are in a triangle and how their individual sine angles are equal. The sine law, sine rule, and sine formula are additional names for the sine law.
The side or unknown angle of an oblique triangle is found using the law of sine. Any triangle that is not a right triangle is referred to as an oblique triangle. At least two angles and their corresponding side measurements should be used at once for the sine law to function.
Given distance from C to A = 100 miles north
From B to A ship travels 60° east of north,
and From B to C 45° west of south,
the figure for problem is attached,
from figure we can calculate the angles of A, B and C
so ∠A makes supplementary with 60°
∠A + 60° = 180°
∠A = 120°
for ∠B we need to draw an imaginary perpendicular on the line extending from A, we get
∠B + 45° + 30° = 90° (30° is angle of imaginary right triangle)
∠B = 90 - 75 = 15°
and ∠C can be found by,
∠A + ∠B + ∠C = 180°
∠C = 180 - 15 - 120
∠C = 45°
now use sine formula for triangles,
sinA/a = sinB/b = sinC/c
where A, B and C are angles of triangle and a, b and c are length of opposite side of angle A, B and C respectively.
a = BC, b = AC, and c = AB
so
sinA/BC = sinB/AC = sinC/AB
we have AC = 100 miles
substitute the values
sinC/AB = sinB/AC
sin(45)/AB = sin(15)/100
AB = 100/(√2sin(15))
AB = 100/0.3659
AB = 273.298 miles
and sinA/BC = sinB/AC
BC = AC sinA/sinB
BC = 100(sin 120/sin15)
BC = 100(0.866/0.2588)
BC = 100 x 3.3462
BC = 334.62 miles
total distance = AB + BC + AC
total distance = 334.62 + 273.2 + 100
total distance = 707.82 miles
Hence the distance from A to B is 273.2 miles and total distance is 707.82 miles.
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kinda confused buttttt anyone know this?
Answer:
Hey there!
The overlapping part is the product.
Thus, the product is 1/8.
Hope this helps :)
Which of the following is an example of the difference of two squares?
A x2−9
B x3−9
C (x+9)2
D (x−9)2
I know the answer is either A or B i might be wrong tho pls help im not sure.
Answer:
1) What does it mean when a polynomial equation is in standard form?
All terms are on one side of the equation, and zero is on the other side.
2) When factoring 6x2−7x−20 by grouping, how should the middle term be rewritten?
It should be written as 8x−15x.
3) Is the given equation a quadratic equation? Explain.
x(x−6)=−5
The equation is a quadratic equation because there is an x2-term.
4) Which of the following factored forms given below represent the correct factorization of the trinomial x2+10x+16?
(2+x)(8+x)
5) Which of the following is an example of the difference of two squares?
x2−9
Step-by-step explanation:
I hope this helps you out ☺
A binomial whose first term and second term can be squared, and has a subtraction sign between both squared terms represents the difference of two squares, an example of the difference of two squares is:
A. [tex]x^2 - 9[/tex]
Recall:
Difference of two squares is when you have a binomial that is expressed as [tex]x^2 - y^2[/tex].The first and second term of the binomial will have an exponential of 2 wile the subtraction sign will be in the middle.Thus, from the options given, option A: [tex]x^2 - 9[/tex] is an example of a binomial that is the difference of two squares.
This is why:9 can be expressed as [tex]3^2[/tex].
In summary, a binomial whose first term and second term can be squared, and has a subtraction sign between both squared terms represents the difference of two squares, an example of the difference of two squares is:
A. [tex]x^2 - 9[/tex]
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Dena uses 7.4 pints of white paint and blue paint to paint her bedroom walls. 2/5 of this amount is white paint, and the rest is blue paint. How many pints of blue paint did she use yo paint her bedroom walls
Answer:
4.44 pints
Step-by-step explanation:
7.4 times 3/5
If 2x3 – 4x2 + kx + 10 is divided by (x + 2), the remainder is 4. Find the value of k using remainder theorem. Please help :)
The polynomial remainder theorem states that the remainder of the division of a polynomial [tex]P(x)[/tex] by [tex]x-a[/tex] is equal to [tex]P(a)[/tex].
Therefore
[tex]P(-2)=4\\2\cdot(-2)^3 - 4\cdot(-2)^2 + k\cdot(-2) + 10=4\\-16-16-2k=-6\\-2k=26\\k=-13[/tex]
Please answer this question now
Answer:
Approximately 439.6 square millimeters.
Step-by-step explanation:
The formula for the surface area of a cone is the following:
[tex]A=\pi r^2+\pi r l[/tex]
Where, r is the radius and l is the slant height.
The radius is 7 and the slant height is 13. We also use 3.14 for π Thus:
[tex]A=(3.14)(7)^2+(3.14)(7)(13)\\\text{Use a Calculator}\\A\approx 439.6[/tex]
Answer:
292.77
Step-by-step explanation:
πr(r+[tex]\sqrt{h2+r2}[/tex])
13 x 2 = 26
7 x 2 = 14
26 + 14 = 40
[tex]\sqrt{40}[/tex] = 6.32
7 + 6.32 = 13.32
3.14 x 7 = 21.98
21.98 x 13.32 =
292.77
30 PTS!! Can someone PLEASE rephrase this? The compass and straightedge is more important in constructing geometric structures than other drawing tools such as rulers and protractors. Because steps taken with a compass and straightedge cannot be seen at first glance and this situation become a problem for students.
Answer:
Step-by-step explanation:
This study investigated three mathematics teachers' construction process of geometric structures using compass and straightedge. The teacher-student-tool interaction was analysed. The study consists of the use of a compass and straightedge by the teachers, the ideas of the teachers about their use, and the observations regarding the learning process during the construction of the geometric structures. A semi-structured interview was conducted with the teachers about the importance of the use of a compass and straightedge to construct geometric structures. It was found that teachers taught compass and straightedge constructions in a rote manner where learning is little more than steps in a process. The study concludes with some suggestions for the use of a compass and straightedge in mathematics classes based on the research results. SUMMARY Purpose and significance: For more than 2,000 years, the way in which geometric structures could be constructed with the help of compasses and straightedges has caught the attention of mathematicians. Nowadays, mathematics curriculums place an emphasis on the use of the compass and straightedge. The compass and straightedge is more important in constructing geometric structures than other drawing tools such as rulers and protractors. Because steps taken with a compass and straightedge cannot be seen at first glance and this situation become a problem for students. However, 'doing compass and straightedge construction early in the course helps students to understand properties of figures'
Jonas needs a cell phone. He has a choice between two companies with the following monthly billing policies. Each company’s monthly billing policy has an initial operating fee and charge per text message. Sprint charges $29.95 monthly plus .15 cents per text, AT&T charges $4.95 monthly plus .39 cents per text. Create equations for the two cell phone plans.
Answer:
Since both companies have a different plan, two equations are created to determine which company Jonas should choose with respect to the number of messages sent.
Step-by-step explanation:
- Sprint = $ 29.95 * X (0.15)
- AT & T = $ 4.95 * X (0.39)
One dollar equals 100 cents, so 0.15 cents equals $ 0.0015 dollars.
- Sprint = $ 29.95 * X (0.0015)
- AT & T = $ 4.95 * X (0.0039)
Si Jonas envía 500 mensajes de texto el valor mensual de cada empresa sería de:
- Sprint = $ 29.95 * 500 (0.0015) = 22.46 dollar per month.
- AT & T = $ 4.95 * 500 (0.0039) = 9.65 dollar per month.
The company Jonas should choose is AT&T.
AT&T also charges a little more per number of text messages, but since the phone's value is so low it would take thousands of text messages to compare to Sprint's monthly value.
I need help answering these two questions
Answer:
Step-by-step explanation:
1. Area=3b*b=300 inches^2
3b^2=300
:3 :3
b^2=100
b=V100inches ^2
b=10 inches
2. Area=4b*3b
so 12b^2=4800
:12 :12
b^2=400
b=V400
b=20 inches
For a quadratic function y = ax² + bx + c, suppose the constants a, b, and c are consecutive terms of a geometric sequence. Show that the function does not cut the x axis.
Hello, because of the geometric sequence we can say that:
[tex]\alpha = \dfrac{b}{a}=\dfrac{c}{b}\\\\\dfrac{c}{a}=\dfrac{c*b}{a*b}=\dfrac{c}{b}\dfrac{b}{a}=\alpha^2\\\\\text{So the equation becomes.}\\\\ax^2+bx+c=0<=>x^2+\dfrac{b}{a}x+\dfrac{c}{a}=0\\\\<=>x^2+\alpha x+ \alpha^2=0\\\\\Delta=b^2-4ac = \alpha^2-4\alpha^2=-3\alpha^2 < 0[/tex]
So there is no real root, so the function does not cut the x axis.
Thank you
For the given quadratic function, the x-axis is not cut by the function because there is no true root.
What is a quadratic function?To determine values for various parameters, quadratic functions are employed in a variety of scientific and engineering disciplines. A parabola is used to graphically illustrate them. The orientation of the curve is defined by the highest degree factor.
As per provided data in question,
α = b/a = c/b
c/a = (c × b)/(a × b) = (c/b) (b/a) = α²
For the equation,
ax² + bx + c = 0
x² + b/a(x) + c/a = 0
⇒ x² + ax + α² =0
Δ = b² - 4 ac = α² - 4α²
Δ = -3α² < 0, which means that no real root is there.
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SP=2x+3, and LN=5x−14. Find SP.
Answer:
43
Step-by-step explanation:
Using Thales theorem:
● SP/LN = RP /RN
Notice that RN = 2×RP
● SP/LN = RP/2RP
● SP /LN = 1/2
● SP / (5x-14) = 0.5
● (2x+3)/(5x-14) = 0.5
● 2x+3 = 0.5(5x-14)
● 2x+3 = 2.5x -7
Add 7 to both sides
● 2x+3+7 = 2.5x-7+7
● 2x+10 = 2.5x
Sustract 2x brom both sides
● 2x+10-2x = 2.5x-2x
● 10 = 0.5x
Multiply both sides by 2
● 10×2 = 0.5x×2
● 20 = x
Replace x with 20 in Sp expression:
● SP = 2x+3
● SP = 2×20+3
● SP = 43
PLS ANSWER BRAINLIST AND A THANK YOU WILL BE GIVEN!!!!
Answer:
[tex]\huge\boxed{Option \ D}[/tex]
Step-by-step explanation:
4x + 5x = 180 [They are angles on a "straight" line so they will add up to 180 degrees)
Answer:
D
Step-by-step explanation:
The sum of angles that are formed on a straight line is 180.
4x + 5x = 180
Am I doing this right if not please help me
Answer:
Step-by-step explanation:
For the m it would just be -3 because the equation for slope intercept form is y=mx+b
What are the lower quartile, upper quartile, and median for this box and
whisker plot?
A) LQ = 22 UQ = 10 Median = 18.5
B) LQ = 10 UQ = 22 Median = 18
C) LQ = 10 UQ = 22 Median = 18.5
D) LQ = 10 UQ = 22 Median = 19
Answer:
C
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
The lower quartile range is shown by the bottom of the box which is at 10.
The median is shown in the middle line, which is closer to 18 than 18.5.
The upper quartile range in the end of the box, which is at 22!
(You can also look at the picture attached if that helps.)
Please help!
Suppose that [tex]\alpha[/tex] is inversely proportional to [tex]\beta[/tex]. If [tex]\alpha=4[/tex] when [tex]\beta=9[/tex], find [tex]\alpha[/tex] when [tex]\beta=-72[/tex]
Answer:
The answer is
[tex] \alpha = - \frac{1}{2} [/tex]Step-by-step explanation:
From the question
[tex]\alpha[/tex] is inversely proportional to [tex]\beta[/tex] is written as
[tex] \alpha = \frac{k}{ \beta } [/tex]where k is the constant of proportionality
When
[tex]\alpha[/tex] = 4[tex]\beta[/tex] = 9Substituting the values into the formula
we have
[tex]4 = \frac{k}{9} [/tex]
cross multiply
k = 4 × 9
k = 36
So the formula for the variation is
[tex] \alpha = \frac{36}{ \beta } [/tex]
when
[tex]\beta[/tex] = - 72
That's
[tex] \alpha = \frac{36}{ - 72} [/tex]
Simplify
We have the final answer as
[tex] \alpha = - \frac{ 1}{2} [/tex]Hope this helps you
in exponential growth functions, the base of the exponent must be greater than 1. How would the function change if the base exponent were 1? How would the function change if the base of the exponent were between 0 and 1?
Answer:
GREAT QUESTION!!
Step-by-step explanation:
Bases of exponential functions CANNOT be 1.
It the base was between 0 and 1, .25 for example, then it would be exponential decay, because as x would increase y would decrease.
Just search up exponential decay to see what it looks like, or type in y=.25^x in google search bar.
if this helped, Please give brainly, I need it! Thank you!
Answer:
If the base of the exponent were 1, the function would remain constant. The graph would be a horizontal line. If the base of the exponent were less than 1, but greater than 0, the function would be decreasing.
Step-by-step explanation:
If the base were 1, the function would be constant.
If the base were 1, the graph would be a horizontal line.
If the base were between 0 and 1, the function would be decreasing.
Point B is on line segment AC. Given BC=9 and AB=11, determine the length AC.
Answer:
20
Step-by-step explanation:
If point B is on line segment AC, then we know for sure AB + BC = AC.
To understand this better, draw a line segment, then put a point anywhere on the line segment. There are two line segment divided by that point. If you combine those two line segments then you have your original figure.
So 11 + 9 = 20.
The subject is operations on rational expressions.
The instructions are add or subtract the following expressions. Remember to find a common denominator when necessary. Reduce all answers to lowest terms.
Answer:
[tex]\frac{2(x-1)(2x+9)}{(x-3)(x-2)}[/tex]
Step-by-step explanation:
[tex]\frac{4x}{(x-3)}+\frac{6}{(x+2)}[/tex]
= [tex]\frac{4x(x+2)}{(x-3)(x+2)}+\frac{6(x-3)}{(x+2)(x-3)}[/tex]
Now we have done the denominators of each term of the expression equal.
Further we add the terms,
[tex]\frac{4x(x+2)}{(x-3)(x+2)}+\frac{6(x-3)}{(x+2)(x-3)}[/tex]
= [tex]\frac{4x(x+2)+6(x-3)}{(x-3)(x+2)}[/tex]
= [tex]\frac{4x^{2}+8x+6x-18}{(x-3)(x+2)}[/tex]
= [tex]\frac{4x^{2}+14x-18}{(x-3)(x-2)}[/tex]
Now factorize the numerator of the fraction.
4x² + 14x - 18 = 2(2x² + 7x - 9)
= 2(2x² + 9x - 2x - 9)
= 2[x(2x + 9) - 1(2x + 9)]
= 2(x - 1)(2x + 9)
Therefore, [tex]\frac{2(x-1)(2x+9)}{(x-3)(x-2)}[/tex] will be the answer.
I don’t really understand this
Answer
pretty sure its a or c, sorry I cant be more specific
Step-by-step explanation:
please this urgent!!
Answer:
Step-by-step explanation:
1)First convert mixed fraction to improper fraction and them prime factorize
[tex]6\frac{1}{4} = \frac{25}{4}\\[/tex]
[tex]\sqrt{\frac{25}{4}}= \sqrt{\frac{5*5}{2*2}}= \frac{5}{2} = 2 \frac{1}{2} \\\\[/tex]
2)
[tex](2 \frac{1}{2}- 1 \frac{1}{2})*1 \frac{1}{7}=( \frac{5}{2}- \frac{3}{2})* \frac{8}{7}\\\\\\= \frac{2}{2}* \frac{8}{7}\\\\=1* \frac{8}{7}= \frac{8}{7}\\\\\\=1 \frac{1}{7}[/tex]
3) 0.00706 = 7.06 * [tex]10^{-3}[/tex]
4) 144 = 12 * 12
12 = 6*2
6 = 2*3
Prime factorization of 144 = 2 * 3 * 2 * 2 * 3 *2
= 2⁴ * 3²
5) To find LCM, prime factorize 96 & 144
96 = 2 * 2 * 2 * 2 * 2 * 3 = 2⁵ * 3
144 = 2⁴ * 3²
LCM = 2⁵ * 3² = 32 * 9 = 288
6) HCF
105 = 7 * 5 * 3
135 = 5 * 3* 3 * 3
180 = 5 * 3 * 3 * 2 * 2
HCF = 5 * 3 = 15
7) 24 = 3 * 2 * 2 * 2 = 3 * 2³
36 = 3 * 3 * 2 * 2 = 3² * 2²
40 = 5 * 2 * 2 * 2 = 5 * 2³
LCM = 5 * 2³ * 3² = 5 * 8 * 9 = 360
HCF = 2² = 4
Difference = 360 - 4 = 356
8) Multiply each digit of the binary number by the corresponding power of 2, solve the powers and add them all
1111 = 1 *2³ + 1*2² + 1*2¹ + 1*2° = 8 + 4 + 2 + 1 = 15
Ans: 15
9) 36₇ = 102₅
10) 6.9163 = 6.916
I knew only this much
hope it's helpful
:)
The product of 2 rational numbers is -16/9 . If one of the numbers is -4/3 find the other plz fast
Answer:
4/3
Step-by-step explanation:
let the other number be x.
-4/3 x=-16/9
x=-16/9×-3/4=4/3
Given that ∆MTW ≅ ∆CAD, which angles are corresponding parts of the congruent triangles? ∠W ≅ ∠C ∠W ≅ ∠D ∠W ≅ ∠A
Answer:
The Answer would be ∠W ≅ ∠C
Step-by-step explanation:
Only one that is congruent
The measure of the angle ∠TWM is congruent to the measure of the angle ∠ADC. Therefore, the correct option is B.
What are congruent triangles?Two triangles are said to be congruent if their corresponding sides and angles are equal.
A triangle is a three-sided polygon with three edges and three vertices in geometry.
Given that the triangle ∆MTW is congruent to the triangle ∆CAD.
So, we have
∠MTW ≅ ∠CAD
∠WMT ≅ ∠DCA
∠TWM ≅ ∠ADC
If two triangles are equivalent, the ratio of matching sides will stay constant.
The proportion of the point ∠TWM is harmonious with the proportion of the point ∠ADC.
Therefore, at that point, the right choice is B.
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What is the reflection image of
(5,−3)across the line
y=x
Answer: The Answer is (-5,-3)
hope so my answer is correct
Step-by-step explanation:
A trader buys tea for $1200 and sells it for $1500. Per sack of tea he makes a profit of $50. How many sacks of tea did he have?
Answer:
6 sacks
Step-by-step explanation:
Buying Price = $1200
Selling Price = $1500
Total profit = Selling price - Buying Price
= $1500 - $1200
= $300
Given that the profit on each sack of tea is $50
Number of Sacks of Tea = Total Profit ÷ profit per sack
= $300 ÷ 50
= 6 sacks
The number of sacks of tea he has is 6.
The first step is to determine the total profit earned by the trader. Profit is the selling price less the cost price.
Profit = selling price - cost price
$1500 - $1200 = $300
The second step is to divide the total profit by the profit made per sack of tea.
Number of sacks = $300 / $50 = 6
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Is a 118 supplementary or complementary?pls ASAP!!
Answer:
[tex]\huge\boxed{Supplementary \ Angle}[/tex]
Step-by-step explanation:
118 is a supplementary angle. It is not a complementary angle because complementary angles add up to 90 and 118 is greater than 90 degrees. So, 118 is a supplementary angle and it is an angle adding up to 180 degrees with any other angle measuring 62 degrees.
Answer:Supplementary
Step-by-step explanation:You should remember that complementary refers to any number from 0-90 and supplementary refers to any number from 90 onwards..
Hereby giving the answer as ''Supplementary''
Shane biked 1 mile less than three times the number of miles Lissette biked. Shane biked a total of 7 miles. Write an equation to determine how many miles Lissette biked.
7 = 3x − 1
x − 1 = 3(7)
x over seven = 3(1)
7 + 3x = 1
Answer
Equation : x + 1 + 3x = 7
Miles Lissette biked : 3/2 miles
Step-by-step explanation:
Step 1: Determine the total number of miles biked.
From my understanding. 7 miles is the total number of miles biked by both.
Step 2: Assume the values
Miles Lissette biked = x
Miles Shane biked = 1 + 3x
Step 3: Add miles biked by Lissette and Shane which will be equal to total miles.
Equation for miles Lissette biked: x + 1 + 3x = 7
4x + 1 = 7
x = 6/4
Step 4: Simplify
x = 6/4
x = 3/2
Therefore, the equation for miles Lissette biked is x + 1 + 3x = 7 and Lissete biked for 3/2 miles.
Hope it helped if yes mark me BRAINLIEST
Tysmm
Answer:
7 = 3x - 1
Step-by-step explanation:
Miles Shane biked = y
Miles Lissette biked = x
The equation is
(x ⋅ 3) - 1 = y
And we know y = 7, so
(x ⋅ 3) - 1 = 7
3x - 1 = 7
