What rate of interest, to the nearest tenth of a percent, compounded quarterly is needed for an investment of $1600 to grow to $2400 in 11 years
Answers
Compound interest is the interest earned on the principal and the interest previously accumulated. It is given by
[tex]A=P(1+r/n)^{nt}[/tex]
where P = Principal, r = annual rate of interest, n = the number of times interest is compounded per year & t = time in years.
The given principal is $1600 for 11 years & amount is $2400 compounded quarterly.
To find the rate of interest compounded quarterly for 11 years substitute the given values in the above formula i.e
[tex]2400=1600(1+r/4)^{11*4}[/tex]
r=3.70%.
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Related Questions
A college student takes the same number of credits each semester. They had 19 credits when they started, and after 6 semesters, they had 67 credits. Which of these expresses the rate at which they is earning credits?
Answers
As per the given variables, the rate at which they earn credits is 8 credits per semester
Total number of credits = 19
Total number of semesters = 6
Credits after six semesters = 67
Calculating the change in credits -
Change in credits -
Credits after six semesters - Inital credits
= 67 - 19
= 48 credits
Total time = 6 semesters
Calculating the change in credits over the six semesters and dividing by the total time to get the pace at which the college student is acquiring credits.
Therefore, the rate at which the college student is earning credits is:
Rate = Change in credits / Total time
= 48 credits / 6 semesters
= 8 credits per semester
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For two programs at a university, the type of student for two majors is as follows. find the probability a student is a graduate student, given they are a history major.
Answers
The probability that a student is a graduate student given they are a history major is approximately 0.16.
What is probability?The likelihood or chance that an event will occur is quantified by probability. A number between 0 and 1, where 0 denotes that the occurrence is impossible and 1, denotes that the event is certain, is generally used to express it.
According to question:We are given the following information:
Total number of students who are history major: 463
Total number of graduate students: 261
Number of graduate students who are history major: 73
We can use the formula for conditional probability to find the probability that a student is a graduate student given that they are a history major:
P(graduate | history) = P(graduate and history)/P(history)
P(graduate | history) = 73/463
P(graduate | history) ≈ 0.1575 (rounded to the nearest hundredth)
Therefore, the probability that a student is a graduate student given they are a history major is approximately 0.16.
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An equilateral triangle is shown inside a square inside a regular pentagon inside a regular hexagon. Write an expression for the exact area of each shaded region in the figure. Then find the approximate area of the entire shaded region, rounded to the nearest whole unit.
Answers
An expression for the exact area of each shaded region in the figure include the following:
Shaded area = area of the regular hexagon - area of the regular pentagon + area of the square - area of the equilateral triangle.
How to calculate the area of a regular polygon?In Mathematics and Geometry, the area of a regular polygon can be calculated by using the following formula:
Area of a regular polygon = (n × s × a)/2
Where:
n is the number of sides.s is the side length.a is the apothem.Based on the diagram (see attachment), the area of the first shaded region is given by;
Area of first shaded region = Area regular hexagon - Area regular pentagon
For the area of the second shaded region, we have;
Area of second shaded region = Area of a square - Area of the equilateral triangle
Therefore, the total area of all of the shaded regions is given by;
Total shaded area = {area of the regular hexagon - area of the regular pentagon} + area of the square - {area of the equilateral triangle}.
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A rainwater collection system uses a cylindrical storage tank with a diameter of 50 cm and a height of 80 cm what is the total volume of water in cubic centimeters that can be collected
Answers
Answer:
157,000
Step-by-step explanation:
π r² h
PLEASE HELP! Showing all work, solve for x and why and round to nearest tenth
Answers
Answer:
x = 7.9 (nearest tenth)
y = 24.6° (nearest tenth)
Step-by-step explanation:
Pythagoras Theorem explains the relationship between the three sides of a right triangle. The square of the hypotenuse (longest side) is equal to the sum of the squares of the legs of a right triangle.
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
As we have been given the lengths of both legs of the right triangle, we can use Pythagoras Theorem to find the length of the hypotenuse, x:
[tex]\begin{aligned}3.2^2+7^2&=x^2\\10.24+49&=x^2\\59.24&=x^2\\x^2&=59.24\\x&=\sqrt{59.24}\\x&=7.6967525...\\x&=7.9\; \sf (nearest\;tenth)\end{aligned}[/tex]
Therefore, x = 7.9.
[tex]\hrulefill[/tex]
The tangent ratio is a trigonometric ratio that relates the angle of a right triangle to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
[tex]\boxed{\begin{minipage}{7 cm}\underline{Tangent trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\end{minipage}}[/tex]
As we have been given the lengths of the sides that are opposite and adjacent angle y, we can use the tangent trigonometric ratio to find the measure of angle y:
[tex]\begin{aligned}\tan(y)&=\dfrac{3.2}{7}\\y&=\tan^{-1}\left(\dfrac{3.2}{7}\right)\\y&=\vphantom{\dfrac12}24.5671713...^{\circ}\\y&=24.6^{\circ}\;\sf (nearest\;tenth)\end{aligned}[/tex]
Therefore, y = 24.6°.
what is the value for 43.7 x 0.25
Answers
Answer:
43.7 x 0.25 is 10.925
Step-by-step explanation:
To multiply decimals, we can use the following steps:
1. Multiply the numbers as if they were whole numbers, ignoring the decimal points.
2. Count the total number of decimal places in the factors being multiplied. This will be the number of decimal places in the product.
3. Place the decimal point in the product so that it has the same number of decimal places as the total counted in step 2.
Using these steps, we can find the product of 43.7 and 0.25 as follows:
1. 437 x 25 = 10925
2. There are two decimal places in 43.7 and two decimal places in 0.25, so there are a total of four decimal places in the factors being multiplied.
3. Place the decimal point in the product so that it has four decimal places: 10.925
Therefore, the value of 43.7 x 0.25 is 10.925.
= 437/40
= 10(whole number)37/40
= 10.925
Spelled result in words is four hundred thirty-seven fortieths (or ten and thirty-seven fortieths).
How do we solve fractions step by step?
1.) Conversion a decimal number to a fraction: 0.25 = 25/100 = 1/4
a) Write down the decimal 0.25 divided by 1: 0.25 = 0.25/1
b) Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)
0.25/1
= 2.5/10
= 25/100
Note: 25/100 is called a decimal fraction.
c) Simplify and reduce the fraction
25/100
= 1 * 25/4 * 25
= 1 * 25/4 * 25
= 1/4
2.) Conversion a decimal number to a fraction: 43.7 = 437/10 = 437/10
a) Write down the decimal 43.7 divided by 1: 43.7 = 43.7/1
b) Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)
43.7/1. = 437/10
Note: 437/10 is called a decimal fraction.
c) Simplify and reduce the fraction
437/10 = 437 * 1/10 * 1= 437 * 1/10 * 1
3.)Multiple: 0.25 * 43.7 = 1 · 437/4 · 10
= 437/40
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(437, 40) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - one quarter multiplied by four hundred thirty-seven tenths is four hundred thirty-seven fortieths.
Navid earns a basic wage of $10.25 an hour. He works for 40 hours a week. He earns 20% more than his basic wage when he works overtime. Navid wants to earn at least $500 this week. Calculate the total number of hours he needs to work. Give your answer to the nearest hour.
Answers
$10.25/hour x 40 hours = $410
To earn at least $500, Navid needs to earn an additional $90 ($500 - $410).
To earn 20% more than his basic wage, Navid would earn:
$10.25/hour x 1.2 = $12.30/hour for each overtime hour
So, Navid needs to work:
$90 ÷ ($12.30/hour - $10.25/hour) = 47.4 hours
Since Navid cannot work a fraction of an hour, he needs to work 48 hours to earn at least $500.
Therefore, Navid needs to work for a total of 40 hours + 8 hours of overtime, which is 48 hours in total (rounded up to the nearest hour).
The ratio of two numbers is 7 to 3 and the sum of their squares is 232. Find the numbers.
Answers
We know that (7x)^2 + (3x)^2 = 232.
Expanding this equation, we get 58x^2 = 232.
Dividing both sides by 58, we get x^2 = 4.
Therefore, x = +/- 2.
Plugging this value of x into the expression for the two numbers, we get that the numbers are 14 and 6, or -14 and -6.
x/y = 7/3
We can use this information to solve for one of the variables in terms of the other. For example, we can solve for y in terms of x:
y = (3/7) x
Now we know that one of the numbers is equal to (3/7) times the other. We also know that the sum of their squares is 232, so we can write:
x^2 + y^2 = 232
Substituting y = (3/7) x, we get:
x^2 + (3/7)^2 x^2 = 232
Simplifying, we get:
(1 + (3/7)^2) x^2 = 232
(1 + 9/49) x^2 = 232
(58/49) x^2 = 232
x^2 = (232 * 49) / 58
x^2 = 196
Taking the square root of both sides, we get:
x = 14
Now we can use the equation y = (3/7) x to find y:
y = (3/7) * 14 = 6
Therefore, the two numbers are 14 and 6.
Line g has an equation of y = 2x + 1. Line h includes the point (-5, 2) and is perpendicular
to line g. What is the equation of line h?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified
proper fractions, improper fractions, or integers.
Submit
Answers
Slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept. Line g’s equation is already in the correct form. If line g has a slope m=ab, then line h perpendicular to it will have a slope m⊥=−ba.
2/1 = 2, so the reciprocal is 1/2. It will also be negative to become: y= (-1/2)x + b.
We want to find the y-intercept, b.
Plug in the coordinate that line h passes through (-5,2) for the (x,y) values in the equation.
2 = (-1/2)(-5) + b
2 = 5/2 + b
Subtract 5/2 from both sides:
Note that 2 is equal to 4/2, which makes it easier to deal with.
(4/2) - (5/2) = b
Simplify:
-1/2 = b.
Put all values into line h’s equation, and y = (-1/2)x - 1/2.
On a scale drawing of a soccer field, 0.5 cm equals 8 m.
If the drawing has dimensions 6.5 cm X 3.25 cm, what is the actual length of the soccer field, in meters?
Answers
[tex]\sf Length\, of\,the\,field=\boxed{\sf 104(m)}}.[/tex]
Step-by-step explanation:1. Create a conversion factor.A conversion factor is just a fraction that contains an equivalence. We make the numerator be the unit we want to have as a result and the denominator is the current unit that we have.
The problem states that 0.5 cm equals 8 m, and we want to convert from cm to m, therefore, a conversion factor for this problem is:
[tex]\sf \dfrac{8(m)}{0.5(cm)}[/tex]
2. Use the conversion factor to convert each unit,To use the conversion factor, just multiply each measure by the fraction:
[tex]\sf 6.5(cm) \dfrac{8(m)}{0.5(cm)}[/tex]
Here the centimeters (cm) cancel out each other and the ending answer is expressed in meters:
[tex]\sf 6.5(cm) \dfrac{8(m)}{0.5(cm)}=\boxed{\sf 104(m)}.[/tex]
For the other measure:
[tex]\sf 3.25(cm) \dfrac{8(m)}{0.5(cm)}=\boxed{\sf 52(m)}.[/tex]
So a soccer field, as you may already know, is always longer than it is wide, therefore, the greatest measure (104m) should be the length of the field.
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Enter your answer, rounded to the nearest tenth, in the box.
Answers
Answer:
[tex]f(0) = 6.2 \sqrt{4.5} + 18 = 31.2[/tex]
Factor by grouping. Then supply the term that is missing below. 4mn+3m+8n+6=(m+2)(?+3)
Answers
Answer:
4mn + 3m + 8n + 6 = (m + 2)(4n + 3)
The missing term is 4n.
Factor the expression. x^2-14x-32
Answers
Answer:
[tex](x-2)(x+16)[/tex]
Step-by-step explanation:
Use graphing calculator and find the x-intercepts.
Starting from rest, an object travels at a constant speed of 150 cm/s (centimeters per second) along a straight line. If d is the total distance in cm that the object has traveled at time t seconds, then which of the following gives the equation expressing d as a function of t, and the total distance d in meters that the object has traveled at time t = 2 seconds?
Answers
The equation expressing d as a function of t can be found by using the formula for distance traveled with constant speed:
d = vt
where d is the distance, v is the constant speed, and t is the time elapsed.
In this case, the speed is 150 cm/s, so the equation is:
d = 150t
To find the total distance traveled in meters at t = 2 seconds, we need to first find the total distance traveled in centimeters at t = 2 seconds:
d = 150t
d = 150(2)
d = 300 cm
To convert to meters, we divide by 100:
d = 300/100
d = 3 meters
Therefore, at t = 2 seconds, the object has traveled a total distance of 3 meters.
The perimeter of the quadrilateral is 34 centimeters. Find the length of each side.
x+8
x +4
2x - 2
x²-2x
Answers
Answer: x=4, sides = 12, 8, 6, 8
Step-by-step explain
Perimeter means the sum of all sides of a shape, in this example there are four sides add the sides and set it equal to 34.
X+8+x+4+2x-2+x²-2x=34
x²+2x+10=34
x²+2x-24
(x-4)(x+6)
x=4, x=-6
x can not be -6 because then the x+4 side would be -2, therefore it is extraneous and x=4 is the correct answer.
Now to find side lengths just plug in 4 for x
4+8=12
4+4=8
2*4-2=6
4*4-2*4=8
Find the volume of the cone shown. Use 3.14 for pi. Round your answer to the nearest hundredth.
Answers
Answer: 100.48 cubic feet
Step-by-step explanation:
NEED HELP ASAP PLS AND THX PIC IS ATTACHED
Answers
The trigonometry functions when evaluated are shown below
Evaluating the trigonometry functionsIn trigonometry, sine (sin), cosine (cos), and tangent (tan) are three basic functions that relate angles to the sides of a right triangle.
They are defined as follows:
sin A = opposite side/hypotenuse.
cos A = adjacent side/hypotenuse.
tan A = opposite side/adjacent side.
So, we have
Figure 1
sin A = 6/9cos A = √5/3tan A = 6/√5Figure 2
sin A = √2/2cos A = √2/2tan A = 1Figure 3
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Write the standard form of the following polynomial.
(2x-3)²-3(x-2)(x+4)-7
X² ? X+ ?
Answers
(2x-3)²-3(x-2)(x+4)-7
= (2x-3)(2x-3) - 3(x²+2x-8) - 7
= 4x² - 12x + 9 - 3x² - 6x + 24 - 7
= x² - 18x + 26
Therefore, the standard form of the polynomial is x² - 18x + 26.
Santiago is going to see a movie and is taking his 3 kids. Each movie ticket costs $15 and there are an assortment of snacks available to purchase for $4.50 each. How much total money would Santiago have to pay for his family if he were to buy 6 snacks for everybody to share? How much would Santiago have to pay if he bought x snacks for everybody to share?
Answers
Answer:
25$ if the tickets were involved it would be 70$
Santiago would have to pay $87 in total if he bought 6 snacks for everyone to share. The cost increases to $60 + 4.5*x when a variable number of snacks, represented by x, are bought.
Explanation:The topic of this question is
Mathematics
, specifically about using multiplication and addition in problem-solving.
Firstly, Santiago is going to see a movie with his 3 kids. Therefore, he needs to buy 4 tickets. If each ticket costs $15, then the total cost for movie tickets will be 4 * 15 = $60.
Secondly, if Santiago buys 6 snacks for everybody to share with each snack costing $4.50, the total cost for snacks will be 6 * 4.5 = $27. The total money Santiago would have to pay for his family would then be the sum of the costs of the tickets and snacks, which is 60 + 27 = $87.
Regarding the case when Santiago bought x snacks for everybody to share, the total cost would become 60 + 4.5*x. This formula gives the total cost based on the given number of snacks.
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Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning in the situation.
United States Birth Rate (per 1000)
Birth Rate
A graph titled United States Birth Rate (per 1000) has year on the x-axis and birthrate on the y-axis. Points trend in a negative line.
Year
Source: National Center for Health Statistics, U.S. Dept. of Health and Human Services
a.
no correlation
b.
positive correlation; as time passes, the birth rate increases.
c.
positive correlation; as time passes, the birth rate decreases.
d.
negative correlation; as time passes, the birth rate decreases.
Answers
A negative correlation may be seen on the graph. The birth rate declines over time. This indicates that the number of births per 1000 persons in the US has been declining over time.
1. A rectangular block of wood has dimensions 24 cm by 9 cm by 7 cm. It is cut up into children's bricks. Each brick is a cube of side 3 cm.
(a) Find the largest number of bricks that can be cut from the block.
(b) Find the volume of wood that is left.
Answers
The dimensions of the rectangular block indicates;
(a) The largest number of bricks that can be cut from the block is 48 bricks
(b) The volume of the wood left is 216 cm³
What is the volume of a rectangular block?The volume of the rectangular block is the product of the length, L, width, W, and height, H.
1. The dimensions of the rectangular block indicates that the block volume is; V = 24 cm × 9 cm × 7 cm = 1,512 cm³
The largest number of bricks that have side lengths of 3 cm that can be cut from the block is therefore;
Number of cubes; (24)/3 × (9)/3 × (7)/3 ⇒ 8 × 3 × 2 = 48
48 cube bricks can be cut from the block(b) The volume of wood left = 1512 - 48 × 3 × 3 × 3 = 216
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if 3x+2y=36 and (5y)/(3x)=5, what is the value of x+y?
Answers
Answer:
16
Step-by-step explanation:
5y/3x = 5
3x = 5y/5
3x = y
3x + 2y = 36
y + 2y = 36
3y = 36
y = 36/3
y = 12
3x = y
3x = 12
x = 12/3
x = 4
x + y
= 4 + 12
= 16
x + y = 16
 Cooper can purchase a item for $45.00, Which store has the best buy?
A. Store 1: 25% off coupon
B. Store 2: $15 dollars off
C. Store 3: 10% off
I’ll give brainly please help me
Answers
Need help with this question. Been stuck on this for 20 mins.
Answers
Answer:
see below
Step-by-step explanation:
The Reason for #1 is literally GIVEN to you.
Statement #2: Since the Base Angles of an isosceles triangle are congruent, this statement should be ∠CAB≅∠CBA.
Reason #3: Notice that the statement repeats itself (AB=AB). This demonstrates the REFLEXIVE property.
Reason #4: (Clue) Note which items have been Given or Proven congruent and use it as the triangle congruence property. It helps to actually mark them. Your choices are SSS, SAS, ASA, and AAS.
Reason #5: (Clue) Since the triangles of which AM and BN are of part are now proven congruent, these Corresponding Parts are Congruent as well.
2raised to power m-3 = 1
Answers
Answer:
m = 3
Step-by-step explanation:
Given:
[tex]2^{m-3}[/tex] = 1
Take the logarithm of both sides (logarithm of 1 is 0):
m - 3 = 0
Add 3 to both sides:
m - 3 + 3 = 0 + 3
m = 3
Hence, m = 3.
Logarithm is the power to which a number must be raised in order to get some other number. For example:
The base ten logarithm of 100 is 2, because ten raised to the power of two is 100: log 100 = 2. Meaning [tex]10^{2}[/tex] = 100.PLS HELP IM FAILING ALGEBRA
Answers
Casey is going to wear a gray sportscoat and is trying to decide what tie he should wear to work. In his closet, he has 29 ties, 15 of which he feels go well with the sport coat. If Casey selects one tie at random, determine the probability and the odds of the tie going well or not going well with the sport coat.
Answers
The probability of Casey selecting a tie that goes well with the sport coat is 0.517.
The probability of Casey selecting a tie that does not go well with the sport coat is 0.483
What are the probability and the odds of the tie going well or not going well with the sport coat?The probability of Casey selecting a tie that goes well with the sport coat is:
P(goes well) = 15/29
P(goes well) ≈ 0.517
The probability of Casey selecting a tie that does not go well with the sport coat is:
P(does not go well) = 1 - P(goes well)
P(does not go well) = 1 - 15/29 = 14/29
P(does not go well) ≈ 0.483
The odds in favor of the tie going well with the sport coat are:
P(goes well) : P(does not go well) = 15/29 : 14/29
P(goes well) : P(does not go well) = 15:14
The odds against the tie going well with the sport coat are:
P(does not go well) : P(goes well) = 14/29 : 15/29
P(does not go well) : P(goes well) = 14:15
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the line is parellel to graph of 2x-3y=7 and contains the point (-3,-3)
Answers
The equation of the line parallel to the graph of 2x - 3y = 7 and containing the point (-3,-3) is y = (2/3)x - 1.
What is the equation of the parallel line?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the equation of the graph: 2x - 3y = 7.
First, we need to rearrange the given equation into slope-intercept form (y = mx + b) by solving for y:
2x - 3y = 7
-3y = -2x + 7
y = (2/3)x - 7/3
The slope of the given line is 2/3.
Hence, any line parallel to it will also have a slope of 2/3.
Using the point-slope form, we determine the equation of the line that passes through (-3,-3) and has a slope of 2/3:
y - y1 = m(x - x1)
y - (-3) = (2/3)(x - (-3))
y + 3 = (2/3)x + 2
y = (2/3)x - 1
Therefore, the equation of the line is y = (2/3)x - 1.
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I need help with the answer to the photo provieded
Answers
Answer:
26
Step-by-step explanation:
Evaluate the following expression.
If x=12,y=8, and z=6.
X2y-2z over 4
Answers
The value of the expression "(x²y - 2z)/4", when x = 12 , y = 8 and z = 6, is (c) 285.
An "Expression" is defined as a combination of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation, which are written using mathematical symbols and follow certain rules.
We have to evaluate the expression : (x²y - 2z)/4, if x = 12 , y = 8 and z = 6,
To evaluate , we substitute x = 12 , y = 8 and z = 6, in the expression,
So, We have,
⇒ (12² × 8 - 2×6)/4,
⇒ (144 × 8 - 12)/4,
⇒ (144 × 8 - 12)/4,
⇒ (1152 - 12)/4,
⇒ 1140/4,
⇒ 285,
Therefore, the value of the given expression, when x=12, y=8, and z=6, is 285, the correct option is (c).
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