Answer:
Simple interest is calculated by multiplying the principal (the initial amount of money deposited), the interest rate, and the number of years the money is on deposit.
To find out how much interest Diane will be paid in the first 2 years, we need to calculate the total interest earned over that time period.
First, we find the interest rate by multiplying the annual interest rate of 5% by .01 (to convert the percentage to decimal form)
0.05 * .01 = 0.05
Next, we find the total interest earned by multiplying the principal (400), the interest rate (0.05), and the number of years (2)
400 x 0.05 x 2 = 40
So, in the first 2 years, Diane will be paid $40 in interest on her deposit of $400.
Answer:
in total, Diane will be paid $20 + $40 = $60 in interest over the first 2 years.
Step-by-step explanation:
Simple interest is calculated as:
I = Prt
where:
I = Interest
P = Principal (initial amount deposited)
r = Interest rate (expressed as a decimal)
t = Time (in years)
So in this case, with a principal of $400 and an interest rate of 5% (or 0.05 as a decimal), the interest paid in the first year would be:
I = $400 * 0.05 * 1 = $20
And in the second year, it would be:
I = $400 * 0.05 * 2 = $40
So in total, Diane will be paid $20 + $40 = $60 in interest over the first 2 years.
Due to the installation of a muffler, the noise level of an engine decreased from 88 to 72 decibels. Find the percent decrease in the intensity of the noise as a result of the installation of the muffler given the following information:
The number of decibels [tex]\beta[/tex] of a sound with an intensity of [tex]I[/tex] watts per square meter is given by [tex]\beta = 10\log\left(\dfrac{I}{I_0}\right)[/tex].
[tex]I_0[/tex] is an intensity of [tex]10^{-12}[/tex] watts per square meter, corresponding roughly to the faintest sound that can be heard by the human ear.
Answer:
97.5% decrease
Step-by-step explanation:
You want the percentage change in noise intensity when it is reduced from 88 to 72 dB.
Intensity ratioThe intensity can be found by solving the given equation for I:
[tex]\beta_1=10\log\left(\dfrac{I_1}{I_0}\right)\\\\10^{\beta_1/10}=\dfrac{I_1}{I_0}\\\\I_1=I_0\cdot10^{\beta_1/10}[/tex]
Similarly, the reduced intensity is ...
[tex]I_2=I_0\cdot10^{\beta_2/10}[/tex]
Percent changeThe percentage change is found from ...
percentage change = (I₂/I₁ -1) × 100%
Using the above expressions for I₁ and I₂, this becomes ...
[tex]\text{\% change}=\left(\dfrac{I_0\cdot10^{\beta_2/10}}{I_0\cdot10^{\beta_1/10}}-1\right)\times100\%\\\\=(10^{(\beta_2-\beta_1)/10}-1)\times100\%=(10^{(72-88)/10}-1)\times100\%\\\\=(10^{-1.6}-1)\times100\% \approx -0.975\times100\% =\boxed{ -97.5\%}[/tex]
The noise intensity decreased by about 97.5%.
__
Additional comment
It can be useful to remember that log(2) ≈ 0.30103. That is, a reduction of 3 dB is a reduction by a factor of 2. Hence 16 db is a factor of about 40.
Answer:
97.49% (2 d.p.)
Step-by-step explanation:
Given equation:
[tex]\beta=10 \log\left(\dfrac{I}{I_0}\right)[/tex]
Divide both sides by 10:
[tex]\implies \dfrac{\beta}{10}= \log\left(\dfrac{I}{I_0}\right)[/tex]
Switch sides:
[tex]\implies \log\left(\dfrac{I}{I_0}\right)=\dfrac{\beta}{10}[/tex]
[tex]\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b[/tex]
[tex]\implies 10^{\frac{\beta}{10}}=\dfrac{I}{I_0}[/tex]
Multiply both sides by I₀:
[tex]\implies I=I_010^{\frac{\beta}{10}}\\[/tex]
Substitute the given value of I₀:
[tex]\implies I=10^{-12} \cdot 10^{\frac{\beta}{10}}\\[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies I=10^{\left(\frac{\beta}{10}-12\right)}\\[/tex]
Therefore, the value of I when β = 88 dB is:
[tex]\implies I=10^{\left(\frac{88}{10}-12\right)}\\[/tex]
[tex]\implies I=10^{-3.2}[/tex]
And the value of I when β = 72 dB is:
[tex]\implies I=10^{\left(\frac{72}{10}-12\right)}\\[/tex]
[tex]\implies I=10^{-4.8}[/tex]
Percent Decrease formula
[tex]\sf Percent\:decrease=\dfrac{original\:value-new\:value}{original\:value} \times 100[/tex]
Therefore, the percent decrease is:
[tex]\implies \dfrac{10^{-3.2}-10^{-4.8}}{10^{-3.2}} \times 100[/tex]
[tex]\implies 97.4881135...\%[/tex]
[tex]\implies 97.49\%\; \sf (2\; d.p.)[/tex]
Jackie obtains a 30-year 4/2 ARM at 5% with a 4/7 cap structure in the amount of $313,500. What is the monthly payment during the initial period? (3 points)
$1,832. 69
$1,496. 70
$1,682. 94
$870. 83
The monthly payment during the initial period is about $1,682.94
The type of loan Jackie obtains is an Adjustable Rate Mortgage, ARM, loan, which is a 4/2 ARM
The introductory interest rate of 5% is fixed for the first 4 years, and will be adjusted every 2 years after the first four years.
Let us assume that m represents the initial monthly payment.
[tex]M=\frac{P.(\frac{r}{12} ).(1+\frac{r}{12} )^n}{(1+\frac{r}{12} )^n - 1}[/tex]
where, M is the monthly payment during the initial period
P is the amount on loan
r is the interest rate = 5% = 0.05
n is period = 30 × 12 = 360
Here, P = $313,500
r = 5%
r = 0.05
n = 30 × 12
n = 360
Substituting these values in the above formula we get,
[tex]M=\frac{313500\times (\frac{0.05}{12} ).(1+\frac{0.05}{12} )^{360}}{(1+\frac{0.05}{12} )^{360} - 1}[/tex]
M ≈ 1,682.94
Therefore, the monthly payment is about $1,682.94
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The options for X are:
a. -3
b. 3
c. 0
d. 2/3
[tex]4y-\cfrac{1}{2}=\cfrac{x}{3}-\cfrac{5}{2}\implies 4\stackrel{y}{\left( -\cfrac{1}{2} \right)}-\cfrac{1}{2}=\cfrac{x}{3}-\cfrac{5}{2}\implies -2-\cfrac{1}{2}=\cfrac{x}{3}-\cfrac{5}{2} \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{6}}{6\left( -2-\cfrac{1}{2} \right)=6\left( \cfrac{x}{3}-\cfrac{5}{2} \right)}\implies -12-3=2x-15 \\\\\\ -12-3+15=2x\implies 0=2x\implies \cfrac{0}{2}=x\implies \boxed{0=x}[/tex]
A rectangular piece of metal is 9 in. longer than it is wide, Squares with sides 4 in. long are cut from the four corners, and the flaps are folded upward to form an open box. Which equation indicates that the volume of the box is 56 in.³?
Choose the correct answer below.
OA (x+1)(x-8)=56
OB. x(x +9)(4)=56
OC. (x+1)(x-8)(4)=56
OD. x(x +9)=56
OC (x+1)(x-8)(4)=56 indicates that the volume of the box is 56 in³ because it takes into account the length of the sides after the four corners were cut off, and the height of the box which is 4 in. The equation can be written as (length of sides)(width of sides)(height) = volume.
What is a volume?A volume is a three-dimensional space that contains a specific amount of material, which is commonly measured in liters, cubic meters, or gallons. It is frequently used to calculate the capacity of containers like tanks, bottles, and barrels. Volume may also refer to the quantity of space occupied by an item, such as the volume of a room or the volume of a sphere.
In the given question, OC is the correct answer: (x+1)(x-8)(4)=56. This equation reveals that the volume of the box is 56 [tex]in^{3}[/tex] because it considers the length of the sides after the four corners were taken off, which are (x+1) and (x-8), as well as the height of the box, which is 4 in. The formula is (length of sides)(width of sides)(height) Equals volume. As a result, the equation (x+1)(x-8)(4) = 56 reveals that the box's volume is 56 [tex]in^{3}[/tex].
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(8x³ + 6x - 5)/(x + 1)
The quotient for the given expression is 8x^2-8x+14 and the remainder is -19. The solution has been obtained using the method of long division of polynomial.
What is polynomial long division?
A formula for dividing one polynomial by another of the same degree or lower is known as a long division polynomial. Like with long division of numbers, the components of long division of polynomials include the divisor, quotient, dividend, and remainder.
Using Polynomial Long Division,
Dividing : 8x^3 + 6x - 5 ("Dividend")
By : x+1 ("Divisor")
Dividend 8x^3 + 0x^2 + 6x - 5
- divisor * 8x^2 8x^3 + 8x^2
Remainder - 8x^2 + 6x - 5
- divisor * (-8x) - 8x^2 - 8x
Remainder 14x - 5
- divisor * 14 14x + 14
Remainder - 19
Quotient : 8x^2-8x+14
Remainder: -19
Hence, the quotient for the given expression is 8x^2-8x+14 and the remainder is -19.
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Lila knows that 3/16 means ""3 divided by 16. "" She uses this to find the decimal equivalent for 316
Lila finds out the decimal equivalent of 3 divided by 16 is equal to 0.1875.
Lila knows that 3/16 means "3 divided by 16."
To find the decimal equivalent for 3/16, she would divide 3 by 16 using a calculator or long division. This would give her a decimal answer of 0.1875.
It's important to note that 3/16 is a fraction, which represents a ratio of two numbers, the numerator, and the denominator. The decimal equivalent is simply another way to represent the same value but in decimal form.
Lila understands that to convert fractions to decimals, she can divide the numerator by the denominator. And to convert decimals to fractions, she can write the decimal as a fraction with the denominator as a power of 10.
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Point B has coordinates (2,1). The x-coordinate of point A is −3. The distance between point A and point B is 13 units. What are the possible coordinates of point A
How do I proof quadrilaterals?
Step-by-step explanation:
1. MN || LO - ( PARALLEL LINES ) .
2. <NMO = <LOM - ( GIVEN ) .
3. <MLO = <ONM - ( REFLEXIVE PROPERTY ) .
4. ..... - ( AAA S-C ) .
Rocky has 7 bottles of water. he will buy more bottles of water from the store. the store has 8 cases in stock and each case contains 24 bottles of water. the store will not sell partial cases. the function that models the number of bottles of water rocky will have after his purchase is , where c is the number of cases of water he buys. what is the practical domain of the function?
Answer:
{1, 2, 3, 4, 5, 6, 7, 8}
Step-by-step explanation:
In this problem, we use the variable c to represent the independent quantity. This means that the domain is all possible values for c. Since the store only has 8 cases of water, the domain cannot be any number larger than 8. Since the store only sells complete cases, not partial cases, of water, the domain cannot be a fraction or decimal number. This means that the practical domain, or domain that makes sense for the problem situation, is {1, 2, 3, 4, 5, 6, 7, 8}.
Mr. Grant needs at least 55 paintbrushes for his art classes. He has 25 paintbrushes already and will buy more paintbrushes in packages of 6. Which inequality can be used to find how many packages of paintbrushes, p, Mr. Grant needs to buy in order to have at least 55 paintbrushes?
The packages of paintbrushes, p, that Mr. Grant needs to buy in order to have at least 55 paintbrushes will be at least 5 packages.
How to calculate the inequality?Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.
In this case, Grant has 25 paintbrushes already and will buy more paintbrushes in packages of 6.
The inequality to illustrate this will be:
25 + 6p ≥ 55
where P = packages of paintbrushes
Collect the like terms
6p ≥ 55 - 25
6p ≥ 30.
Divide
p ≥ 30 / 6
p ≥ 5
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What is the distance between points (4, 36) and (13, -4) on a coordinate plane?
What percent of the youths surveyed prefer reading electronic books? Round your answer to the nearest tenth of a percent.
Answer: 54% of youths surveyed prefer reading electronic books.
Step-by-step explanation: 74 divided by 100 = 0.74. Divide 40 by 0.74 and you get 54.05%. Round that to 54% and you have your answer.
HI IM STUCK PLEASE HELP,TEST QUESTION & LIMITED TIME!
Question- Write the standard form equation of a circle given the center of (-7, -15) and an area of A = π. Show all work for your calculations using the equation editor.
The equation of the circle with center (-7, -15) and area π is
(x + 7)² + (y + 15)² = 1.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2πr.
The area of a circle is πr².
We have,
Centre of the circle = (-7, -15)
The equation of a circle is r² = (x - h)² + (y - k)²
Where (h, k) is the center of the circle.
Now,
h = -7
k = -15
The equation of a circle.
r² = (x + 7)² + (y + 15)² _____(1)
Now,
Area = πr²
πr² = π
r² = 1 _____(2)
Now,
From (1) and (2),
(x + 7)² + (y + 15)² = 1
Thus,
The equation of the circle is (x + 7)² + (y + 15)² = 1.
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Find the balance in the account after the given period. $7,700 deposit earning 3.9% compounded monthly, after 4 years.
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$7700\\ r=rate\to 3.9\%\to \frac{3.9}{100}\dotfill &0.039\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &4 \end{cases} \\\\\\ A = 7700\left(1+\frac{0.039}{12}\right)^{12\cdot 4}\implies A=7700(1.00325)^{48} \implies A \approx 8997.69[/tex]
Ali runs each lap in minutes. He will run at least minutes today. What are the possible numbers of laps he will run today? Use for the number of laps he will run today. Write your answer as an inequality solved for .
The possible minutes Ali will run today can be represented by the inequality x ≥ 66.
What is Linear Inequalities?Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.
Given that,
Minutes taken to complete one lap = 6 minutes
Also, he will run at least 11 laps today.
This means that Ali will run laps greater than or equal to 11 laps.
Let x be the number of minutes taken by Ali today.
x ≥ 6 × 11
x ≥ 66
Hence Ali runs 11 laps in at least 66 minutes.
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The complete question is as follows :
Ali runs each lap in 6 minutes. He will run at least 11 laps today. What are the possible numbers of minutes he will run today?
What is the perimeter of 6(1/2x + 5)
Answer: The perimeter of a rectangle is the sum of the lengths of all four sides. If one of the sides is 6(1/2x + 5), then we can find the perimeter by multiplying that by 2.
Perimeter = 2*6(1/2x + 5)
Perimeter = 12(1/2x + 5)
To simplify the expression, we can distribute the 12:
Perimeter = 121/2x + 125
Perimeter = 6x + 60
So the perimeter of 6(1/2x + 5) is 6x + 60.
Step-by-step explanation:
You spend $100 on gifts for your family and friends. You buy 40 gifts altogether.
Some gifts were $2 and the rest were $4.
I bought 30 gifts costing $2 each and 10 gifts costing $4 each for my family.
What is an equation?An equation is an expression showing the relationship between numbers and variables.
Let x represent the number of gifts costing $2 and y represent those costing $4
You spend $100 on gifts for your family and friends. Hence:
2x + 4y = 100 (1)
You buy 40 gifts altogether, hence:
x + y = 40 (2)
From both equations:
x = 30, y = 10
A total of 40 gifts was bought
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Assume your walking rate is 1. 4 meters per second.
How long would it take you to walk 500 meters?
If the rate of walking is 1. 4 meters per second, then 357.14 sec would take you to walk 500 meters.
We can calculate speed, distance or time using the formula s = d/t, distance equals speed times time. The Speed Distance Time formula can solve for the unknown sdt value given two known values.
Time can be entered or solved in units of seconds (s), minutes (min), hours (hr), or hours and minutes and seconds (hh: mm: ss).
We have,
The rate of walking is 1. 4 meters per second.
The distance to cover is 500 meters.
Now, we know the formula
Speed = Distance/Time
⇒Time = Distance/Speed
⇒Time = 500/1.4
⇒Time = 357.14 sec
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The tread of a tire is the part that contacts
the road. Find the surface area of the tread
of a tire with a diameter of 32 inches. Round
your answer to the tenths place.
Answer:
That is correct. The probability of rolling a 2 and a 5 when rolling two dice is 1 in 36, which is considered likely.
Answer:
not enough information
Step-by-step explanation:
The tire is shaped like a cylinder. The tread of a tire is the lateral surface of a cylinder. We know the diameter of the cylinder, 32 inches, but we are not given the width of the tire which is the height of the cylinder, so we cannot calculate the area.
Answer: not enough information
HELP ME ASAPPPPP please make it right because i’m in so much trouble rn.
Please only answer problem number 44 from the picture. fill-in-the-blanks using each of the numbers 027 exactly once, so that the percent, decimal, in fraction below are ordered from least to greatest. Justify your answer.
By using each of the numbers 0 - 7 exactly once, so that the percent, decimal, in fraction below are ordered from least to greatest are,
⇒ 20.3% , 4.56, and 9/1
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Here, We have to use each of the numbers 0 - 7 exactly once.
Hence, The percent, decimal, in fraction below are ordered from least to greatest are,
⇒ 20.3% = 0.203
⇒ 4.56
⇒ 9/1 = 9
Thus, By using each of the numbers 0 - 7 exactly once, so that the percent, decimal, in fraction below are ordered from least to greatest are,
⇒ 20.3% , 4.56, and 9/1
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A high school class conducts a survey where students are asked about their eye color and whether or not they wear glasses. The two-way table below shows the results of the survey as relative frequencies.
based on the results of the survey, what is the possibility, rounded to the nearest tenth, that a students eye color is brown given that the student wears glasses?
A ) 33.3%
B ) 42.9%
C ) 60.0%
D ) 50.0%
According to the information in the graph, it can be inferred that the percentage of students who have brown eyes among the group that wears glasses is equivalent to 42.9% (option B).
How to calculate the percentage of students who have brown eyes in the group that wears glasses?To calculate the percentage of students who have brown eyes in the group that wears glasses we must perform the following mathematical operation.
We must add all the values of the group that wears glasses
0.04 + 0.08 + 0.12 + 0.04 = 0.280.28 = 100%0.12 = X= 42.85%According to the previous operation, the result must be approximated to 42.9% and the correct option would be B.
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3, 18, 18, 5, 2, 17, 30, 9, 38, 17, 12
Key: 30 = 30
Here is the stem and leaf plot:
Stem Leaf
0 2, 3, 5, 9
1 2, 7, 7,, 8, 8
2
3 0, 8
What is a stem and leaf plot?A stem-and-leaf plot is a table that is used to display a dataset. A stem-and-leaf plot divides a number into a stem and a leaf.
The stem is the first number in the digit. In this question, the stem is the tens digit. The leaf is the last number. In this question, the leaf is the units digit. For example in the number 18, 1 would be the stem and 8 would be the leaf.
Here is the complete question:
Create a stem and plot diagram using the dataset provided: 3, 18, 18, 5, 2, 17, 30, 9, 38, 17, 12
Key: 30 = 30
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Henry and Jessica skipping rocks across the surface of a pond for every nine rocks at Henry throws he got five of them to skip across the pond for every twelve rocks
Jessica throws she got seven of them to skip across the pond who gets more rocks to skip across the surface of the pond
Jessica gets more rocks to skip across the surface of the pond than Henry.
To determine who gets more rocks to skip across the surface of the pond, we will take the ratio of rocks that skip to rocks that are thrown for each person.
For Henry, the ratio is 5 rocks that skip to 9 rocks thrown i.e 5/9.
For Jessica, the ratio is 7 rocks that skip to 12 rocks thrown i.e 7/12.
Now to compare the ratios, we need to convert them into like fractions. We will do this by making the denominations of both the fractions same.
We will multiply the numerator and denominator of Henry's ratio by 12 to get -
5/9 x 12/12 = 60/108
Also, we will multiply the numerator and denominator of Jessica's ratio by 9 to get -
7/12 x 9/9 = 63/108
Comparing the numerators we get 60<63.
This implies that 60/108 < 63/108.
Therefore, Jessica gets more rocks to skip across the surface of the pond.
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The complete question is -
Henry and Jessica skipping rocks across the surface of a pond. For every nine rocks Henry throws he got five of them to skip across the pond. For every twelve rocks
Jessica throws she got seven of them to skip across the pond. Who gets more rocks to skip across the surface of the pond?
Find the 9th term of the arithmetic sequence -5x + 2,
-11x - 3,-17x -8,...
Answer: An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. We can call this constant difference "d".
In this sequence, we can see that the difference between consecutive terms is -6x - 5.
The 9th term of an arithmetic sequence can be found by using the formula:
a_n = a_1 + (n-1)d
Where a_n is the nth term of the sequence, a_1 is the first term of the sequence and d is the common difference.
Given the sequence -5x + 2, -11x - 3, -17x -8, ...
The 9th term is:
-5x + 2 + (9-1) (-6x-5) = -5x + 2 - 48x - 40 = -53x -38
Therefore the 9th term of the arithmetic sequence is -53x -38.
Step-by-step explanation:
Which the correct solution of the equation 1/2a + 2/3b = 50, when b=30
According to the given formula, the value of a is:
60
If b=30 then 1/2a+2/3b=50
How do you find the value of a in the given equation?First, replace the 30 in b.
1/2a+2/3(30)=50
According to the order of operations, we must first multiply 2/3 by 30. yes:
2/3 times 30 is equal to 20.
2/3 times 30/1. 3 is 10 times 30, so 2 times 10 = 20. Now it looks like this:
1/2a+20=50
20 and 50 are similar terms, so I'll put those two together. Move the positive 20 to the other side where the 50 is. 20 has moved to the other side, so it changes sign and becomes negative.
yes:
1/2a=50-20
50-20 = 30
1/2a=30
Multiply each side by 2, because only 2 makes the variable 1a.
1/2a × 2 = 1a
30 times 2 = 60, so:
1a=60, which is also a=60. So a perfect simplification is a= 60
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Cynthia buys a shirt for $46 at her favorite store. There is a 7% sales tax on all items in the store. How much tax will she have to pay?
Answer: $3.22 tax
Step-by-step explanation:
7/100 x 46 = $3.22
Answer:3.22$
Step-by-step explanation:3.22$ in the USA
Convert 1.2% to a decimal
Answer: I think its .012
hope this helps
Answer:
0.012
Step-by-step explanation:
Find the measure of the indicated angle.
The measure of the indicated angle is 33 degrees
How to determine the value of the angleIt is important to note the properties of a triangle
The properties of a triangle are given as;
A triangle has three sides and also three anglesThe sum of the angles in a triangle is 180 degreesThe sum of the exterior angles of a triangle always add up to 360 degreesThe sum of consecutive interior and exterior angle of a triangle is supplementary, that is, they sum up to 180 degreesFrom the diagram shown, we have;
57° + K + 90° = 180°
Collect like terms, we get;
K = 180° - 147°
Subtract the numbers
K = 33°
Hence, the value is 33°
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Find the volume of the conical paper cup.
(Radius 3 cm)
(Height 8 cm)
A. 24 cm
O B. 72 7 cm3
C. 64 7 cm3
D. 8 TT cm3
[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=8 \end{cases}\implies V=\cfrac{\pi (3)^2(8)}{3}\implies V=24\pi ~cm^3[/tex]