Answer:
The principal amount invested is $4395.93 .
Step-by-step explanation:
Given as :
The Amount that saved for future = A = $5,000
The bank applied rate of interest = r = 4.3% compounded monthly
The time period of loan = t = 3 years
Let the principal amount invested = $p
Now, From monthly Compound Interest method
Amount = principal × [tex](1+\dfrac{\textrm rate}{12\times 100})^{12\times time}[/tex]
Or, A = p × [tex](1+\dfrac{\textrm r}{12\times 100})^{12\times t}[/tex]
Or, $5000 = p × [tex](1+\dfrac{\textrm 4.3}{12\times 100})^{12\times 3}[/tex]
Or, $5000 = p × [tex](1.003583)^{36}[/tex]
Or, $5000 = p × 1.137414
∴ p = [tex]\dfrac{5000}{1.137414}[/tex]
i.e p = $4395.93
So, The principal amount invested = p = $4395.93
Hence, The principal amount invested is $4395.93 . Answer
If u (x) = negative 2 x squared and v (x) = StartFraction 1 Over x EndFraction, what is the range of (u circle v) (x)?
(one-third, 0)
(3, infinity)
(negative infinity, 3)
(negative infinity, positive infinity)
The range of (u circle v) (x) is (negative infinity, 0).
Explanation:To find the range of (u circle v) (x), we need to substitute v(x) into u(x), which means replacing x in u(x) with v(x).
u(x) = -2x²
So, (u circle v) (x) = -2(v(x))² = -2(1/x)² = -2/x²
The range of (u circle v) (x) is (negative infinity, 0) because as x approaches 0 from the right, (-2/x²) approaches negative infinity, and as x approaches 0 from the left, (-2/x²) approaches positive infinity.
A local flower shop is selling $1 raffle tickets and is donating all proceeds to the children's hospital. They sold 5,500 tickets and plan to give away 20 flower arrangements valued at $70 and 20 gift certificates valued at $25. Find the expected value of purchasing a raffle ticket.
Round to the nearest cent. Do not round until the final calculation.
The expected value of purchasing a raffle ticket is -0.647.
What is the Expected Value of a Probability & Statistical Analysis?The expected value is derived in probability analysis by the multiplication of each of the potential possibilities by the likelihood that each result will occur and then adding all of those values together.
Using the formula below, we can calculate the expected value as follows:
[tex]\mathbf{ E(X)= \sum^{n}_{i=1}X_i P(X_i)}[/tex]
However, the probability (Pr) of each event can be categorized as follows:
Pr (to win a flower arrangement ) [tex]\mathbf{=\dfrac{20}{5500}}[/tex]Pr (to gift a certificate) [tex]\mathbf{=\dfrac{20}{5500}}[/tex]Pr (no win) ) [tex]\mathbf{=\dfrac{5500 - 20 - 20}{5500}=\dfrac{5460}{5500}}[/tex]Thus;
[tex]\mathbf{E(X) = 70(\dfrac{20}{5500} \times 25 ((\dfrac{20}{5500} )- 1(\dfrac{5460}{5500} )}[/tex]
[tex]\mathbf{E(X) =-0.647}[/tex]
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A car travels at 30 1/5 miles in 2/3 of an hour. What is the average speed in miles per hour of the car
Answer:
Adverage of 20 mph
30 1/5 = 30.2
2/3 = .6667
30.2 x .6667 = 20.13
Answer:
45.3 miles/hour
Step-by-step explanation:
the information we have is:
distance:
[tex]d=30\frac{1}{5}miles=30.2miles[/tex]
time:
[tex]t=\frac{2}{3} hour[/tex]
the formula for the average speed is:
[tex]v=\frac{distance}{time} =\frac{d}{t}[/tex]
substituting all the known values we get:
[tex]v=\frac{30.2miles}{2/3hour} =\frac{3(30.2miles)}{2hour}= 45.3miles/hour[/tex]
the average speed in miles per hour is: 45.3
Estimate a 10% tip on a bill of $143.17 by first rounding the bill amount to the nearest ten dollars.
Estimated tip: $il
x
6
?
Answer:
Step-by-step explanation:
143.17
round the bill to the nearest $ 10..
that would make it $ 140
a 10% tip......its the same thing as multiplying by 0.1
and when u multiply any number by 0.1 ur actually starting at the decimal ( or the end of the number) and move one space to the left.
examples :
10% of 245 = 24.5
10% of 5010 = 501
10% of 76 = 7.6
10% of 88.5 = 8.85 .....if there is a decimal, start at the decimal
so.....10% of 140
start at the end of the number and move 1 space to the left...
ur answer is 14 <==
A lender wil verity and carefully consider your income before approving you for a loan because
a they need to be sure you will be able to pay the loan back
b government restrictons reoeam u salary to be approved for a dan
C. loan applicants with higher salaries are generally more trustworthy than other applicants
d. they need to be sure you make at least the minimum payment for the loan you applied for
Please select the best answer from the choices provided
Answer:
A
Step-by-step explanation:
2. What are the next two terms of the following sequence?-2,4,-8, 16, ...
A. -32, 64 D . 32, – 64
B. -32, 64
C. 32, 64
Answer:
(A.B.)-32, 64Step-by-step explanation:
[tex]-2\\(-2)(-2)=4\\(-2)(4)=-8\\(-2)(-8)=16\\-----------------\\(-2)(16)=-32\\(-2)(-32)=64\\\vdots[/tex]
Each next term is created by multiplying the previous term by (-2).
Answer:
It's the geometric sequence so the following numbers are:
-32,64
d= -2(multiplication number)
Answer: i did not fully understand,since there are two similar answer options(it's wether A or B)
Good luck!
Intelligent Muslim,
From Uzbekistan.
What is the remainder R when the polynomial p(x) is divided by (x - 2)? Is (x - 2) a factor of p(x)?
p(x) = -4x4 + 6x3 + 8x2 - 6x - 4
Answer:
The answer can be calculated by doing the following steps;
Step-by-step explanation:
The Reminder is 0 and (x -2) is the factor of polynomial p(x).
What is polynomials?Polynomials are mathematical articulations that comprise of factors and coefficients. In other cases, variables are referred to as indeterminates. We can perform math activities like expansion, deduction, increase, and furthermore sure number types for polynomial articulations yet not division by factor.
Given polynomials p(x) = -4x⁴ + 6x³ + 8x² - 6x - 4
to divide by (x - 2)
We choose long division and look for what will multiply with (x-2) to make the polynomial
(x - 2)(-4x³) = -4x⁴ + 8x³
We subtract this from the original -4x⁴ + 6x³ + 8x² - 6x - 4 - (-4x⁴ + 8x³)
this leaves -2x³ + 8x² - 6x - 4
repeat the same process
(x - 2)(-2x²) = -2x³ + 4x²
subtract this from -2x³ + 8x² - 6x - 4 we get
-2x³ + 8x² - 6x - 4 - (-2x³ + 4x²) = 4x² - 6x - 4
again repeat the process
(x - 2)(4x) = 4x² - 8x
subtract this from 4x² - 6x - 4 we get
4x² - 6x - 4 - (4x² - 8x) = 2x - 4
repeat again
(x - 2)(2) = 2x - 4
subtract this from 2x - 4 we get
2x - 4 - (2x - 4) = 0
Hence the reminder of polynomials p(x) = -4x⁴ + 6x³ + 8x² - 6x - 4 is 0 and (x - 2) is factor of p(x).
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perfect cube
.
[tex]7.4[/tex]
Answer:
405.224
Step-by-step explanation:
Which polynomial is factored completely?
121x2 + 36y2
(4x + 4)(x + 1)
2x(x2-4
3x4 – 151° +12
Answer:
121x2 + 36y2
Step-by-step explanation:
= (4x + 4)(x + 1)
= 4(x + 1)(x + 1)
= 4(x + 1)2 and is hence the fully factored form
not sure bout the rest though...... it may have mistakes in the question forms.
Polynomials given to us can be factored except 121x² + 36y²,
so we can say that 121x² + 36y² is factored completely.
What do we mean by factorization of a polynomial?Factorization of a polynomial is the method by which we write the given polynomial as a product of two or more factors, which when multiplied gives back the same Polynomial.
How do we solve the given question?
We will analyze all the given polynomial.
121x² + 36y², cannot be factored further(4x + 4)(x + 1) = 4(x+1)(x+1) = 4(x+1)², factored further2x(x²-4) = 2x(x+2)(x-2), factored furtherCannot be determined∴ After checking all the options, we can say that 121x² + 36y² was completely factored.
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If someone makes $200,000 per year, receives a paycheck monthly and pays 25.6% in income tax, how much is deducted from each paycheck for income tax?
$4266.67 is deducted every month for income tax.
Step-by-step explanation:
Given,
Amount earned per year = $200,000
Income tax = 25.6%
Amount of income tax = 25.6% of amount earned
Amount of income tax = [tex]\frac{25.6}{100}*200000 = \frac{5120000}{100}[/tex]
Amount of income tax = $51200
As this amount is yearly, therefore, we will divide it by 12 to find monthly amount.
Income tax deducted per month = [tex]\frac{51200}{12}=\$4266.67[/tex]
$4266.67 is deducted every month for income tax.
Keywords: income tax, percentage
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Which graph represents the solution to the given system ? Y=- 6X - 2Y +2=- 6X
Answer: The graph is attached.
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
Given the first equation:
[tex]y=- 6x - 2[/tex]
You can identify that:
[tex]m=-6\\b=-2[/tex]
By definition, the line intersects the x-axis when [tex]y=0[/tex]. Then, subsituting this value into the equation and solving for "x", you get that the x-intercept is:
[tex]0=- 6x - 2\\\\2=-6x\\\\x=-\frac{1}{3}\\\\x=-0.333[/tex]
Now you can graph it.
Solve for "y" from the second equation:
[tex]y +2=- 6x\\\\y=-6x-2[/tex]
You can identify that:
[tex]m=-6\\b=-2[/tex]
Notice that the slopes and the y-intercepts of the first line and the second line are equal; this means that they are exactly the same line and the System of equations has Infinitely many solutions.
See the graph attached.
A group of friends bought 7 tickets to a dog show for $30 each. How much did they spend on the tickets?
Answer:
$210
Step-by-step explanation:
1 ticket= 30
7 tickets = 7*30=$210
dori left her house at 12:00 pm and walked at 50 steps per minute and malory left her house at 12:20 and walked 90 steps per minute what time did malory catch up to dori?
Final answer:
Malory catches up to Dori 25 minutes after starting her walk. Since Malory started at 12:20 pm, she catches up to Dori at 12:45 pm by walking at a faster pace.
Explanation:
To determine what time Malory caught up to Dori, we can set up an equation based on the distance each has traveled. Since distance equals speed multiplied by time, and steps per minute can be considered as speed, we need to find a point at which they have both covered the same distance.
Dori started walking at 12:00 pm and Malory started at 12:20 pm, so Malory starts walking 20 minutes later. We'll use t to represent the time in minutes that Malory has been walking when she catches up to Dori.
Thus, Dori has been walking for t + 20 minutes by the time Malory catches up.
We set up the following equation to find t:
Dori's distance = Malory's distance
50 steps/minute × (t + 20) = 90 steps/minute × t
Solving for t gives us:
50t + 1000 = 90t
1000 = 40t
t = 25 minutes
Therefore, Malory catches up to Dori 25 minutes after Malory started walking. Since Malory started walking at 12:20 pm, we add 25 minutes to this time to find out the catch up time is 12:45 pm.
(-3)/-6
what is the value?
-2
2
1/2
-1/2
｡☆✼★ ━━━━━━━━━━━━━━ ☾
The negatives cancel each other out
Thus, your answer is C. 1/2
Have A Nice Day ❤
Stay Brainly! ヅ
- Ally ✧
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Answer: 1/2
Step-by-step explanation: When dividing integers, if the signs are the same, the quotient is positive. So a negative divided by a negative always equals a positive. In this problem -3 ÷ -6 is 0.5.
However, there is no 0.5 on the list so we need to write the decimal as a fraction.
To write the decimal 0.5 as a fraction, we use the place value chart. 0.5 means 0 units and 5 tenths which can be written as the fraction 5/10.
Notice however that 5/10 is not in lowest terms so we need to divide the numerator and denominator by the greatest common factor of 5 and 10 which is 5 to get the equivalent fraction 1/2.
Evaluate Ic2 + b2l, given a = 5, b = -3, and c= -2.
Answer:
Ic² + b²l = 13 units.
Step-by-step explanation:
We have to evaluate the expression Ic² + b²l with unknowns b and c and having the values of b and c respectively - 3 and - 2.
Now, Ic² + b²l
= I(- 2)² + (- 3)²l {Putting the values of b and c}
= I4 + 9l
= I13l
= 13 units.
Therefore, Ic² + b²l = 13 units. (Answer)
If f(x) = 4x+5 what is f(-3)
In this question, you're solving the given function.
In this case, you would plug in "-3" to the x variable, then solve.
Solve:
f(x) =4(-3) + 5
f(x) = -12 + 5
f(x) = - 7
When you're done solving, your answer should be -7.
Answer:
f(x) = - 7
Answer:
-7
Step-by-step explanation:
f(x) = 4 x + 5
f(-3) = 4 (-3) + 5
f(-3) = -12 + 5
f(-3) = -7
29.5 divided by four
Which function is the inverse of y = 2x+5/2?
Answer:
y=1/2x-5/4
Step-by-step explanation:
y=2x+5/2
x=2y+5/2
2y=x-5/2
y=1/2x-(5/2)/2
y=1/2x-(5/2)(1/2)
y=1/2x-5/4
Solve for x when m LKM=90
Answer:
x= -15
Step-by-step explanation:
3x+10=2x-5
3(-15)+10=2(-15)-5
-45+10=-30-5
-35=-35
Each side of the angle is equal, that's how i knew the two were supposed to be equal. <3 Hope this helps!
(I found the picture.)
Answer:
17
Step-by-step explanation:
L 3x + 10 5875 =90 2x - 5 x=_17 5 5 - x =17 Use the image to answer questions 6-7. 125 Given that Xll Y use the figure below to answer questions 8 - 11. -40-40 normal Unit 2: Equations & Exponents Directions: 1. Solve each problem.
You have 4/6 cup of cocoa in your cupboard. A recipe for cookies calls for
2/5 cup of cocoa. How much cocoa would you have left if you made the cookies?
Answer:
4/15 cocoa would be left if we made cookies
Step-by-step explanation:
4/6- 2/5
= 4(5)- 2(6)/30
= 20-12/30
=8/30
=4/15
After making the cookies using 2/5 cup of cocoa from the initial 4/6 cup, you would subtract 12/30 cup from 20/30 cup to find that you would have 4/15 cup of cocoa left.
Explanation:To determine how much cocoa you would have left after making the cookies using 4/6 cup of cocoa and using 2/5 cup for the recipe, you would need to subtract the amount used from the initial amount. To perform the subtraction, you first need to have the quantities expressed with a common denominator. The least common denominator for 6 and 5 is 30.
Convert 4/6 cup to an equivalent fraction with a denominator of 30: (4 × 5) / (6 × 5) = 20/30 cup.
Convert 2/5 cup to an equivalent fraction with a denominator of 30: (2 × 6) / (5 × 6) = 12/30 cup.
Now you can subtract the amount of cocoa used for the cookies from the total amount you have:
Remaining cocoa = Initial amount - Amount used = 20/30 cup - 12/30 cup.
Remaining cocoa = (20 - 12) / 30 = 8/30 cup of cocoa.
To simplify this, divide both the numerator and denominator by their greatest common divisor, which is 2:
Remaining cocoa = 4/15 cup. So you would have 4/15 cup of cocoa left after making the cookies.
The average test score of RSM students in September increased by 10%. In October it increased by another 15%. By what percent did the average score on the test increase during the two months? PLEASE HELP I NEED THE ANSWER QUICK
Answer:
26.5%
Step-by-step explanation:
Increasing Percentages
When sequential percentages increasing are computed, each increase applies to the previous result, instead of the first quantity. That is why sometimes the final results may be confusing. For example, increasing 10% and then 15% will not be the same as increasing a total of 25%.
The average test scores of RSM students first increased by 10%. It means that some quantity C increased by
[tex]10C/100=0.1C[/tex]
Now the average test scores are
[tex]C+0.1C=1.1C[/tex]
A new increasing occurred by 15%, and the previous quantity must be multiplied by 1.15, so the final average test scores are
[tex]1.15(1.1C)=1.265C[/tex]
It means that the total increasing was [tex]100(1.265-1)=26.5\%[/tex]
Answer:
26.5%
Step-by-step explanation:
IM SMART! :D
1. Will is 30 years old and works for a company that matches his 401(k) contribution up to 3%. The interest rate for
his 401(k) is 7.13%. If he puts away 9% of his $41,000 salary every year, how much would he have saved in 10
years? Round your answer to the nearest cent.
Oooo
$52,835.72
$56,602.91
$68,395.76
$73, 272.37
Answer:
C. $68,395.76
Step-by-step explanation:
ED2020
Final answer:
Will would have saved approximately $9,420.12 in 10 years by contributing 9% of his $41,000 salary annually, with a 3% employer match and a 7.13% interest rate.
Explanation:
To calculate how much Will would have saved in 10 years, we need to consider both his salary contribution and the employer's matching contribution. Will saves 9% of his $41,000 salary every year, which comes out to $3,690. The employer matches his contribution up to 3%, so the employer would contribute an additional $1,230 (3% of $41,000) every year.
To calculate the total savings after 10 years, we can use the formula for compound interest: A = P(1 + r/n)^(nt). In this case, the principal P is the total annual contributions, the interest rate r is 7.13%, and n is the number of times interest is compounded per year, which we will assume to be once per year.
Using the formula, we can calculate:
A = ($3,690 + $1,230)(1 + 0.0713/1)^(1*10)
A = $5,920 * 1.0713^10
A = $9,420.123296
Rounding to the nearest cent, Will would have saved approximately $9,420.12 in 10 years.
I need this please 64 points!
Answer:
None. Wanda's work is correct.
Step-by-step explanation:
The first is correct.
Answer:
Wanda converted the percent to a decimal incorrectly. It should be 0.73
Step-by-step explanation:
It has to be move two decimal place.
Find the solution to the following system of equations:
y+2x=3
y-4x=10
Answer:
x=-7/6, y=16/3. (-7/6, 16/3).
Step-by-step explanation:
y+2x=3
y-4x=10
-----------
y=4x+10
4x+10+2x=3
6x+10=3
6x=3-10
6x=-7
x=-7/6
y+2(-7/6)=3
y-14/6=3
y=3+14/6
y=18/6+14/6
y=32/6=16/3
Rachel hikes at a steady rate from a ranger station to a campground that is 20 mi away. After 2 h, she is 13 mi from the campground. After 4 h, she is 6 mi from the campground. A graph shows her distance y from the campground, in miles, after x hours. What is the slope of the graph, and what does it represent?
From 2 hours to 4 hours she traveled 7 miles.
7 miles / 2 hours = 3.5 miles per hour.
The slope is 3.5 , which is 3.5 miles per hour, which is how fast she is walking.
How many integers have a square root that is greater than 10 and less than 11?
Answer:
20
Step-by-step explanation:
We know that 10² = 100, so all integers above 100 have a square root greater than 10. Similarly, 11² = 121, so all integers below 121 have a square root less than 11. So, we want the integers from 101 through 120, inclusive. There are integers from through (just as there are 20 integers from 1 through 20).
Marla will paint 48 pots . She plans to paint 9 pots each week . Draw an array to find how many weeks it will take Marla to paint all of the pots . Explain
Answer:
The number of weeks Marla will take to paint all the pots is 5 weeks and 3 days .
Step-by-step explanation:
Given as :
The number of pots Marla will paint = 48 pots
The number of pots she plans to paint each week = 9 pots
Let The number of weeks Marla needs to paints all pots = n weeks
Now, According to question
The number of weeks = [tex]\dfrac{number of pots Marla will paints}{\textrm The number of pots Marla will paints each week}[/tex]
Or , n = [tex]\dfrac{48}{9}[/tex]
∴ n = 5.3
So The number of weeks = n = 5 weeks and 3 days
Hence The number of weeks Marla will take to paint all the pots is 5 weeks and 3 days . Answer
anything’s appreciated :)
Answer:
See explanation
Step-by-step explanation:
An inscribed angle is the angle with vertex and two endpoints lying on the circle.
1) This option shows an inscribed angle, because vertex A and endpoints B ans C lie on the circle.
2) This option doesn't show an inscribed angle, because vertex K doesn't lie on the circle.
3) This option shows an inscribed angle, because vertex X and endpoints V ans W lie on the circle.
4) This option doesn't show an inscribed angle, because vertex M doesn't lie on the circle.
5) Angle CAB is inscribed angle subtended on the arc BC with measure of 80°, so its measure is 40° (half of the measure of arc BC)
6) Angle WXV is inscribed in the circle and subtended on the arc WV. Hence, the measure of the arc WV is twice the measure of angle VXW and is equal to 84°.
Options 7) and 8) are not visible.
State weather the equation represents exponential growth, exponential decay or neither, 30 POINTS EASY
Answer:
Exponential Decay
Step-by-step explanation:
It's exponential growth when your base value is > 1. Example:
1.3ˣ, 2ˣ, 7ˣ, 999ˣ
It's exponential decay when the base value is < 1. Example:
0.9ˣ, 0.45ˣ, (1/2)ˣ, 0.79ˣ, .999ˣ
It's neither when the base value = 1. Example:
1ˣ
What exponential expression is equal to 2 to the negative 5th power • 2 to the 8th power ?
Answer:
2^3
Step-by-step explanation:
2^-5×2^8=2^(-5+8)
= 2^3
Answer:
2³
Step-by-step explanation:
Written in numerical form:
2⁻⁵ · 2⁸
Since both exponents have the same base, one of the exponent rules apply. When multiplying exponents with the same base, you add the exponents.
xᵃ · xᵇ = xᵃ⁺ᵇ
2⁻⁵ · 2⁸
= 2⁽⁻⁵⁾ ⁺ ⁸
= 2³ Simplified exponent form
= 8 Most simplified form