Answers
Related Questions
Each square below represents one whole.
(one square - all shaded in of 4)
(second square - 3 shaded in of 4)
What percent is represented by the shaded area?
Answers
Answer:
The percent being represented by the shaded area is \(175\%\)
Step-by-step explanation:
The percent being represented by the shaded area can be calculated as follows
The first step is to evaluate the left square
Since each square represents one whole, and since the left square is all shaded in of \(4\) then the percent being represented by the shaded area in the left square is
\(1=\frac{4}{4}=\frac{100}{100}=100\%\)
The percent being represented by the shaded area in the first or the left square is \(100\%\)
The second step is to evaluate the right square
Since the right or the second square is \(3\) shaded in of \(4\), then the fraction being represented by the shaded area in the second square is
\(\frac{3}{4}\)
The third step is to convert \(\frac{3}{4}\) into the percent form by the following equation
\(\frac{3}{4}=\frac{x}{100}\)
Where \(x\) is the percent value for the second square
Multiply both side by \(100\) to isolate \(x\)
\(\frac{3}{4}\times 100=\frac{x}{100}\times 100\)
Simplify the equation
\(\frac{300}{4}=x\)
Simplify the left side of the equation
\(75=x\)
Since the value of \(x\) is \(75\), then the percent being represented by the shaded area in the second square is \(75\%\)
The fourth step is to calculate the total percent being represented by the all shaded area
Since the total percent is the sum of the percent for the first square and the percent for the second square, then it follows
\(\text{Total percent}=100\%+75\%\)
Simplify the equation
\(\text{Total percent}=175\%\)
Hence the percent being represented by the shaded are is \(175\%\)
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what is(7x10^-6) (5x10^-6) in scientific notation?
Answers
Answer:
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive. So 3.5 times 10 to the power of -11
Can y’all plz help me for brainliest
Answers
the awnser is #3
k=96
Answer:96
Step-by-step explanation:
4 can go into 96 24 times
Addition and Subtraction Property
what is x + 5 + 7
Answers
Answer:
the answer to the equation is x + 12
Step-by-step explanation:
x + 5 + 7 = x + 12
x + 12
Answer:
x+12 it think im not sure
Step-by-step explanation:
add 5 and 7 which get 12
A researcher is investigating the effect of sleep deprivation on learning. She recruits 30 participants and randomly assigns half to a "no sleep" group and half to a "regular sleep" group. The "no sleep" group are required to stay up all night and report to a testing room at 2PM the following day. The "regular sleep" group are instructed to have a normal night's sleep and report to the testing room at 9AM the following day. Unfortunately, a water pipe broke outside the testing room window and there was noisy construction crew working the whole day of testing. Which of the following statements is true?
a. The study may be affected by a situational variable.
b. The construction noise may contribute to variability in test scores.
C. The study has a confounding variable. The groups differ in the time they are to report to the testing room.
d. All of these are true.
Answers
The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.
The statement that is true is: d. All of these are true.Explanation:A study may have various sources of variability, including participant selection, the setting in which the study is conducted, and the measure used. The following options are as follows:a. The study may be affected by a situational variable.b. The construction noise may contribute to variability in test scores.c. The study has a confounding variable. The groups differ in the time they are to report to the testing room.d. All of these are true.Therefore, all of these options are true. For example, the study may be affected by a situational variable if a natural disaster or other unforeseen event happens that causes the study to be disrupted. In this case, the study was disrupted by a noisy construction crew, which may have contributed to variability in test scores. The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.
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At Smith Mountain Lake Boat Rentals, it cost $25 per hour to rent a pontoon boat, plus a one-time charge for cleaning. The Bengal family rented a boat from 11 am - 6:30 pm and paid $226.50. If the Jones family rented a boat from 8 am- 1pm, how much did the pay?
Answers
Answer: $164
Step-by-step explanation:
25*7=175
175+12.5
226.50-187.50
5*25=125+39
Jones family payed $164
Find the value of x. Round to the nearest tenth. helpppp image included
Answers
Answer:
x = 21.7 (nearest tenth)
Step-by-step explanation:
Use trig ratio cos(β) = A/H
where β is the angle, A is the side adjacent to the angle and H is the hypotenuse
⇒ cos(37) = 17.3 / x
⇒ x cos(37) = 17.3
⇒ x = 17.3 ÷ cos(37)
⇒ x = 21.7 (nearest tenth)
\(\\ \tt\hookrightarrow sec37=x/17.3\)
\(\\ \tt\hookrightarrow x=17.3sec37\)
\(\\ \tt\hookrightarrow x=17.3(1.26)\)
\(\\ \tt\hookrightarrow x=21.7\)
It's approximate value
a farmer has 2,000 meters 2,000 meters of fencing and wants to use it to create a rectangular area for grazing. the area will be against a stream so that only three sides will need to be fenced. what is the maximum area that can be enclosed?
Answers
The maximum rectangular area that can be fenced can be
2499 sq meters.
What are the area and perimeter of a rectangle?We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.
We know for a quadrilateral, A square has the maximum area.
We also know That the product of two numbers is maximum when the difference between them is minimum.
Given, A farmer has 2,000 meters of fencing and wants to use it to create a rectangular area for grazing.
So, 2(l + b) = 2000.
l + b = 1000.
For a square, it would be 500 and 500, But to be a rectangle it can be 49 and 51.
Therefore, The maximum area would be,
= (51×49) sq meters.
= 2499 sq meters.
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Which pair of triangles can be proven congruent by SAS?
Answers
Answer:
i don't know
Step-by-step explanation:
i am lower grade srry
The quality control supervisor of a tire-manufacturing company selects 75 random tires to check their diameters. He finds that 3 tires have an incorrect diameter. How many tires out of 5,000 should the supervisor predict have incorrect diameters?
Answers
The supervisor should predict that 200 out of 5,000 tires will have incorrect diameters based on the sample of 75 tires that were checked.
If the quality control supervisor has randomly selected 75 tries to check their diameters and found that 3 of them have incorrect diameters, we can use this information to estimate the proportion of tires in the population that have incorrect diameters.
we can use the sample proportion, which is the number of tires in the manufacturing company sample with incorrect diameters divided by the total number of tires in the sample. In this case, the sample proportion is p = 3/75 = 0.04.
To estimate the number of tires out of 5,000 that should have incorrect diameters, we can multiply the population size by the estimated proportion. This gives:
Number of tires with incorrect diameters = 5,000 x 0.04 = 200
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Show that w is in the subspace of R4 spanned by V1, V2, and V3, where these vectors are defined as follows. 1 -4 -9 -4 6 3 5 W= -2 - 1 - 1 -2 4 11 -8 - 15 To show that w is in the subspace, express was a linear combination of V1, V2, and V3. Select the correct answer below and, if necessary, fill in any answer boxes to complete your choice. O A. The vector w is in the subspace spanned by V1, V2, and V3. It is given by the formula w= (v1+ 2+ 3. (Simplify your answers. Type integers or fractions.) B. The vector w is not in the subspace spanned by V1, V2, and V3.
Answers
To show that w is in the subspace of R4 spanned by V1, V2, and V3, we need to find constants c1, c2, and c3 such that:
w = c1V1 + c2V2 + c3V3
We can write this as a matrix equation:
| 1 -4 -9 -4 | | c1 | | -2 |
| 6 3 5 1 | x | c2 | = | -1 |
| 2 4 11 -8 | | c3 | | -1 |
| -15 7 22 -14 | | -2 |
We can solve this system of equations using row reduction:
| 1 -4 -9 -4 | | c1 | | -2 |
| 6 3 5 1 | x | c2 | = | -1 |
| 2 4 11 -8 | | c3 | | -1 |
| -15 7 22 -14 | | -2 |
R2 = R2 - 6R1
R3 = R3 - 2R1
R4 = R4 + 15R1
| 1 -4 -9 -4 | | c1 | | -2 |
| 0 27 59 25 | x | c2 | = | 11 |
| 0 12 29 -16 | | c3 | | 3 |
| 0 -23 67 -59 | | -32 |
R4 = R4 + 23R2
| 1 -4 -9 -4 | | c1 | | -2 |
| 0 27 59 25 | x | c2 | = | 11 |
| 0 12 29 -16 | | c3 | | 3 |
| 0 0 174 -294 | | 225 |
R3 = R3 - (12/27)R2
R4 = (1/174)R4
| 1 -4 -9 -4 | | c1 | | -2 |
| 0 27 59 25 | x | c2 | = | 11 |
| 0 0 -1 22/3 | | c3 | | -13/3 |
| 0 0 1 -98/87 | | 25/58 |
R1 = R1 + 4R3
R2 = R2 - 59R3
R4 = R4 + (98/87)R3
| 1 0 -13 -10/3 | | c1 | | 21/29 |
| 0 27 0 -2119/87 | x | c2 | = | 2238/87 |
| 0 0 1 -98/87 | | c3 | | 25/58 |
| 0 0 0 1390/2391 | | 1009/2391 |
R1 = R1 + (13/1390)R4
R2 = (1/27)R2
R3 = R3 + (98/1390)R4
| 1
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Determine whether each pair of expressions is equivalent. Explain your reasoning.
Answers
The answer is:
\(\large\textbf{They aren't equivalent.}}\)
In-depth explanation:
To determine the answer to this problem, we will use one of the exponent properties:
\(\sf{x^{-m}=\dfrac{1}{x^m}}\)
And
\(\sf{\dfrac{1}{x^{-m}}=x^m}\)
Now we apply this to the problem.
What is 4⁻³ equal to? Well according to the property, it's equal to:
\(\sf{4^{-3}=\dfrac{1}{4^3}}\)
And this question asks us if 4⁻³ is the same as 1/4⁻3.
Well according to the calculations performed above, they're not equivalent.
Which of the following statements is not true about chi-square distributions? The mean decreases as the degrees of freedom increase. OPG? < 0) = 0 O PU2 > 3) is larger for a chi-square distribution with df = 10 than for df = 1 There are an infinite number of chi-square distributions, depending on degrees of freedom. They are always skewed to the right Previous Only saved at 4:44pm
Answers
The statement "The mean decreases as the degrees of freedom increase" is not true about chi-square distributions.
Is it true that the mean of a chi-square distribution decreases as the degrees of freedom increase?In fact, the mean of a chi-square distribution is equal to its degrees of freedom. It does not decrease as the degrees of freedom increase.
The mean remains constant regardless of the degrees of freedom. This is an important characteristic of chi-square distributions.
Regarding the other statements:
The statement "OPG? < 0) = 0" is true. The probability of a chi-square random variable being less than zero is always zero, as chi-square values are non-negative.The statement "OPU2 > 3) is larger for a chi-square distribution with df = 10 than for df = 1" is true. As the degrees of freedom increase, the right-tail probability of a chi-square distribution also increases.The statement "There are an infinite number of chi-square distributions, depending on degrees of freedom" is true. The number of chi-square distributions is infinite because the degrees of freedom can take any positive integer value.The statement "They are always skewed to the right" is generally true. Chi-square distributions tend to be skewed to the right, especially when the degrees of freedom are small.In summary, the statement that is not true about chi-square distributions is that the mean decreases as the degrees of freedom increase.
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Add.
(6x³ + 3x² − 2) + (x³ - 5x² − 3)
Express the answer in standard form. (Please and thank you)
Answers
Answer:
\(\\\sf7x^3 - 2x^2 - 5\)
Step-by-step explanation:
\(\\\sf(6x^3 + 3x^2 - 2) + (x^3 - 5x^2 - 3)\)
Remove parenthesis.
6x^3 + 3x^2 - 2 + x^3 - 5x^2 - 3
Rearrange:
6x^3 + x^3 + 3x^2 - 5x^2 - 2 - 3
Combine like terms to get:
7x^3 - 2x^2 - 5----------------------------------------
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Hope this helps! :)
Answer:
7x³ - 2x² - 5
Step-by-step explanation:
(6x³ + 3x² - 2) + (x³ - 5x² - 3)
Remove the round brackets.
= 6x³ + 3x² - 2 + x³ - 5x² - 3
Put like terms together.
= 6x³ + x³ + 3x² - 5x² - 2 - 3
Do the operations.
= 7x³ - 2x² - 5
____________
hope this helps!
what is the effect of the graph of the function f(x)=x^2 when f(x) is changed to f(x+8)?
Answers
Answer:
Step-by-step explanation:
graph is translated left by 8 units
consider the 22-parallelepiped in ℝ4r4 defined by the vectors ⃗ 1=⎡⎣⎢⎢⎢⎢133−3⎤⎦⎥⎥⎥⎥and⃗ 2=⎡⎣⎢⎢⎢⎢021−3⎤⎦⎥⎥⎥⎥. v→1=[133−3]andv→2=[021−3]. what is the 22-volume (area) of this?
Answers
The 22-volume (area) of the parallelepiped defined by the vectors \(\(\vec{v_1} = [1, 3, 3, -3]\)\) and \(\(\vec{v_2} = [0, 2, 1, -3]\)\) in \(\(\mathbb{R}^4\)\) is 7.
The 22-volume of a parallelepiped in \(\(\mathbb{R}^4\)\) is calculated using the scalar triple product. Let \(\(\vec{v_1}\) and \(\vec{v_2}\)\) be two vectors defining the parallelepiped. The 22-volume (area) of the parallelepiped is given by the magnitude of the scalar triple product of \(\(\vec{v_1}\), \(\vec{v_2}\)\), and their cross product \(\(\vec{n}\)\) (normal vector to the parallelepiped), divided by the magnitude of \(\(\vec{n}\)\).
To calculate the scalar triple product, we find the cross product of \(\(\vec{v_1}\) and \(\vec{v_2}\)\):
\(\(\vec{n} = \vec{v_1} \times \vec{v_2}\).\)
Next, we calculate the scalar triple product:
\(\(V = |\vec{v_1} \cdot \vec{v_2} \times \vec{n}| / |\vec{n}|\).\)
In this case, the cross product \(\(\vec{n}\) of \(\vec{v_1}\) and \(\vec{v_2}\)\) is [-7, 3, -2, -2]. The scalar triple product is \(\(V = |(-1) \cdot (-2) \cdot (-2) \cdot (-2)| / |(-7, 3, -2, -2)| = 7\)\).
Therefore, the 22-volume (area) of the parallelepiped is 7.
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structures with closely packed planes allow more plastic deformation than those that are not closely packed.
Answers
The statement is generally true.
Why the given statement is true?In materials science, the close-packing of atoms in crystal structures can affect the mechanical properties of the material, such as its ductility and ability to undergo plastic deformation.
In general, structures with closely packed planes (i.e., structures with a higher atomic packing factor) are more likely to undergo plastic deformation because the closely packed planes allow for more slip planes for atoms to move along without disrupting the overall crystal structure.
This means that when a force is applied to the material, the planes can slide more easily past one another, leading to plastic deformation.
In contrast, structures that are not closely packed (i.e., structures with a lower atomic packing factor) have fewer slip planes and are less likely to undergo plastic deformation. Instead, they may experience brittle fracture or other types of failure when subjected to stress.
However, it is important to note that the relationship between atomic packing and plastic deformation is complex and depends on a variety of factors, including the type of crystal structure, the presence of defects or impurities in the material, and the conditions under which the material is being deformed.
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I need help with this won’t take too long
Answers
b) The power of the given problems is: Power = 30556 J/s
c) The Force is: 500 N
The power is: 625 J/s
What is the power required?Power is defined as the rate at which work is done. That is workdone over time taken.
b) The formula for power when given force and velocity is:
Power = Force * velocity
We are given:
Force = 1000 N
Velocity = 110 km/h = 30.556 m/s
Thus:
Power = 1000 * 30.556
= 30556 J/s
c) The formula for workdone is:
W = Force * distance
Thus:
Force = Work/distance
Force = 25000J/50 m
Force = 500 N
The power = wordkdone/time taken
= 25000/40
= 625 J/s
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7. One number is 6 times a first number. A third number is 100 more than the first number. If the sum of the three numbers is 692, find the 3 numbers?
Answers
Step-by-step explanation:
6A = B
100+A = C
A + B + C = 692
just replace B and C with A values
A + (6A) + (100 + A) = 692
8A = 592
A = 74
take A and put back into original relationships to find other numbers.
6A = B
6(74) = 444
100 + A = C
100 + (74) = 174
74 + 444 + 174 = 692
Juliet's monthly entertainment expenses are $275. 00 and account for 12% of her income. She would like to reduce her entertainment spending to 8% of her income. Calculate her new monthly entertainment buget
Answers
Using her monthly income, Juliet's new monthly entertainment budget is approximately $183.33.
What is her new monthly entertainment budget?To calculate Juliet's new monthly entertainment budget, we need to find her total monthly income and then calculate 8% of that amount.
Let's assume her current monthly entertainment expenses, $275.00, account for 12% of her income. We can set up the following equation:
275 = 0.12 * income
To find her total monthly income, we can divide both sides of the equation by 0.12:
income = 275 / 0.12
income ≈ 2291.67
Now that we know her total monthly income is approximately $2291.67, we can calculate her new monthly entertainment budget by taking 8% of her income:
new budget = 0.08 * income
new budget = 0.08 * 2291.67
new budget ≈ $183.33
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The cot for 10 ounce of organic blueberrie i $2. 70 which equation can be ued to determine x the cot, in dollar for 30 ounce of organic blueberrie?
Answers
If the cost for 10 ounce of organic blueberry is $2. 70, the cost of 30 ounce of organic blueberry is represented by the equation x = 20y + 2.70 where y is the cost in dollars for one ounce of organic blueberry.
As x is the cost in dollar for 30 ounce of organic blueberry. For y is the cost in dollars for one ounce of organic blueberry, then
x = 30y + c
where c is the fixed cost
We know for 10 ounce of organic blueberry it costs $2.70. That is
2.70 = 10y + c
c = 2.70 - 10y
So x = 30y + 2.70 - 10y
x = 20y + 2.70
-- The question is incomplete, the complete question is as follows--
"The cost for 10 ounce of organic blueberry is $2. 70 which equation can be used to determine x the cost in dollars, for 30 ounces of organic blueberries.?"
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what is the polynomial function axis for Degree 4 Zeros "-3," 4, 6
Answers
The equation of the polynomial is P(x) = (x - 4)(x - 6)(x + 3)²
What are polynomial expressions?Polynomial expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the polynomial equation?The given parameters are
Degree of polynomial = 4Zeros = -3, 4 and 6−3 is a zero of multiplicity 2The sum of multiplicities of the polynomial equation must be equal to the degree.
This means that the multiplicity of the zeros 4 and 6 is 1
The equation of the polynomial is then calculated as
P(x) = (x - zero)^ multiplicity
So, we have
P(x) = (x - (-3))² * (x - 4) * (x - 6)
This gives
P(x) = (x - 4)(x - 6)(x + 3)²
Hence, the equation is P(x) = (x - 4)(x - 6)(x + 3)²
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is 0.11 and the probability that the flight will be delayed is 0.14. The probability that it will not rain and the flight will leave on time is 0.76. What is the probability that the flight would be delayed when it is raining? Round your answer to the nearest thousandth.
Answers
Since probabilities cannot be negative, we can conclude that the given probabilities are inconsistent or there might be an error in the information provided. Please verify the values and provide correct probabilities so that we can accurately calculate P(B|A), the probability of the flight being delayed when it is raining.
Let's denote the events as follows:
A: It will rain
B: The flight will be delayed
We are given the following probabilities:
P(A) = 0.11 (probability of rain)
P(B) = 0.14 (probability of flight delay)
P(A'∩B') = 0.76 (probability of no rain and on-time departure)
We can use the probability formula to calculate the probability of the flight being delayed when it is raining, P(B|A), which is the probability of B given A.
We know that:
P(B|A) = P(A∩B) / P(A)
To find P(A∩B), we can use the formula:
P(A∩B) = P(A) - P(A'∩B')
Substituting the given values:
P(A∩B) = P(A) - P(A'∩B')
P(A∩B) = 0.11 - 0.76
P(A∩B) = -0.65
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12) Find the sum, S7, for the geometric series (1 + 5 + 25+ --- + 15625).
Answers
Answer:
Find the (r) between adjacent members
a2/a1=+25/5=5
a3/a2=+125/+25=5
a4/a3=+625/+125=5
a5/a4=+3125/+625=5
a6/a5=+15625/+3125=5
The ration (r) between every two adjacent members of the series is constant and equal to 5
General Form: a
n
=a
1
×r
n-1
This geometric series: a
n
=5×5
n-1
The nature of this series
Sum of finite geometric series members
sum of a geometric series
The sum of our particular series
a 1-rn = 5 1-56 = 5 1-15625 = 5 -15624 =5×3906=19530
1-r 1-5 -4 -4
Finding the n
th
element
a2 =a1×r2-1 =a1×r1 =5×51 =25
a3 =a1×r3-1 =a1×r2 =5×52 =125
a4 =a1×r4-1 =a1×r3 =5×53 =625
a5 =a1×r5-1 =a1×r4 =5×54 =3125
a6 =a1×r6-1 =a1×r5 =5×55 =15625
a7 =a1×r7-1 =a1×r6 =5×56 =78125
a8 =a1×r8-1 =a1×r7 =5×57 =390625
a9 =a1×r9-1 =a1×r8 =5×58 =1953125
a10 =a1×r10-1 =a1×r9 =5×59 =9765625
a11 =a1×r11-1 =a1×r10 =5×510 =48828125
a12 =a1×r12-1 =a1×r11 =5×511 =244140625
a13 =a1×r13-1 =a1×r12 =5×512 =1220703125
a14 =a1×r14-1 =a1×r13 =5×513 =6103515625
a15 =a1×r15-1 =a1×r14 =5×514 =30517578125
a16 =a1×r16-1 =a1×r15 =5×515 =152587890625
I need help asap!!
Triangle 1 is composed of line segments AB, BC, and CA.
Triangle 2 is composed of line segments DE, EF, and FD.
The triangles are similar with a scale of 5:2.
Select the true statement about the proportions of the sides.
Answers
Similar triangles that have a scale ratio other than 1 are not congruent triangles.
The true statement about the proportions of the sides is \(\frac{AC}{DF} = \frac 52\)
The scale ratio is given as: 5 : 2
And the corresponding sides are given as:
AB and DE.BC and EF.CA and FD.The above highlights mean that,
\(\frac{AC}{DF} = \frac{BC}{EF} = \frac{AB}{DE} = \frac 52\)
Hence, the true statement is \(\frac{AC}{DF} = \frac 52\)
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If y(x-1)=a then x=
1. y-z
2. z/y+4
3. y(z-1)
4. z(y-1)
5. 1-zy
Answers
Answer:
z/y+4
Step-by-step explanation:
The requried, none of the given equations matches this form. Therefore, none of the options is the correct answer.
How does simplification work?Applying math and algebraic principles, simplification entails removing pointless variables, factors, or operations from an expression. Getting an expression that is simpler to use, manipulate, or solve is the aim. An algebraic equation, for instance, could be made simpler by factoring, merging like terms, or employing the distributive property.
Here,
To solve for x in the equation y(x-1) = a, we need to isolate x by dividing both sides by y and adding 1 to both sides. Therefore, we get:
y(x-1) = a
x-1 = a/y
x = a/y + 1
Thus, None of the given options matches this form. Therefore, none of the options is the correct answer.
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Sum1 plz help with this
Answers
Answer:
ur answer is 8.06
Step-by-step explanation:
a² + b²= c²
4² + 7² = c²
16 + 49 = c²
65 sooo u do √65= 8.06
Solve for x.
2x = 15 + x
x = 15/2
X=-15/2
x= 15
x= -15
Answers
Answer:
That doesnt make sense you already figured out what x is
Step-by-step explanation:
Answer:
x = 15
Step-by-step explanation:
2x = 15 + x
x = 15 (subtraction property of equality and subtract x on both sides)
You want to open an account with $2,400. You can earn 3.8% interest each year, and you plan to leave this account for 7 years. How much more would the account be worth after 7 years by calculating interest compounded quarterly versus calculating simple interest? Do not round until the final answer. Round to the nearest cent.
Answers
The difference between calculating simple interest and compound interest would be $482.15.
We are given data:
Principal Amount= $2,400Interest rate= 3.8%Time period= 7 years
We need to determine the difference in interest gained through simple interest and compound interest over a 7-year period.
Solution:
Simple Interest:
Simple interest is calculated on the principal amount for the entire duration of the loan.
Simple Interest formula= P×r×t
Where, P= Principal amount r= rate of interest t= time in years
The amount at the end of 7 years with simple interest would be:
Simple Interest = P × r × t
Simple Interest = 2400 × 3.8% × 7
Simple Interest = 2400 × 0.038 × 7
Simple Interest = $638.40
Compound Interest:
Compound interest is calculated on the principal amount and accumulated interest over successive periods.
Compound interest formula= P (1 + r/n)^(n×t)
Where, P= Principal amount r= rate of interest n= number of compounding periods in a year t= time in years
The amount at the end of 7 years with compound interest would be:
Quarterly compounding periods= 4 Compound Interest= P (1 + r/n)^(n×t)
Compound Interest= 2400 (1 + 0.038/4)^(4 × 7)
Compound Interest= 2400 × (1.0095)^28
Compound Interest= $3,120.55
Difference in the amount for Simple Interest and Compound Interest = $3,120.55 − $2,638.40 = $482.15
Therefore, the difference between calculating simple interest and compound interest would be $482.15.
Learn more about Simple interest:
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Can tell me if it's correct? If it's wrong, can you tell me the correct answer and how to solve it?
Answers
Answer:
C is a right triangle
Step-by-step explanation:
To determine if the triangle is right use Pythagoras' identity
A
9.4² = 88.36
6.4² + 7.1² = 91.37
88.36 ≠ 91.37 , thus not a right triangle
B
8.4² = 70.56
5.2² + 6.3² = 66.73
70.56 ≠ 66.73 , thus not a right triangle
C
9.7² = 94.09
6.5² + 7.2² = 94.09
Thus C is a right triangle
D
8.4² = 70.56
5.1² + 7.3² = 79.3
70.56 ≠ 79.3 , thus not a right triangle
Answer:
Answer C is the correct one
Step-by-step explanation:
Remember that the Pythagorean Theorem applies only to right triangles. In Answer A, the legs of the triangle shown are 6.4 and 7.1; we apply the Pythagorean Theorem and check whether the length of the hypotenuse is indeed 9.4:
6.4² + 7.1² = 40.96 + 50.41 = 91.37.
Is √91.37 equal to 9.4? Not quite! For now, reject Answer A.
Answer B: 5.2² + 6.3² yields 66.73. Is this equal to 8.4²? No, it is not.
Reject Answer B.
Answer C: 7.2² + 6.5² = 94.09. Is this equal to 9.7²? YES. So Answer C is the correct one.