[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$132.90\\ P=\textit{original amount deposited}\dotfill & \$6000\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ t=years \end{cases} \\\\\\ 132.90 = (6000)(0.055)(t)\implies \cfrac{132.90}{(6000)(0.055)}=t\implies \cfrac{443}{1100}=t \\\\\\ \stackrel{\textit{converting that to days}}{\cfrac{443}{1100}\cdot 365} ~~ \approx ~~ 147~days[/tex]
now, if we move back from August 14th by 147 days backwards, that'd put us on March 20th.
1)y-6=12 7)8t=42 porfavor alguien me ayuda con esto
2)-5+k=1 para quien no lo sepa,la cosa es encontrar el valor de
3)-2g=-14 8)-9+z=18 la letra que sale ay
4)y_4=12 9)7+w=14
5)12+u=-12 10)13_5=12
6)f-7=10 11)D_2=-10
The solution to the following equations is given below;
Equationy - 6 = 12
y = 12 + 6
y = 18
-5 + k = 1
k = 1 + 5
k = 6
-2g = -14
g = -14/-2
g = 7
y - 4 = 12
y = 12 + 4
y = 16
12 + u = -12
u = -12 - 12
u = -24
f - 7 = 10
f = 10 + 7
f = 17
8t = 42
t = 42/8
t = 5.25
-9 + z = 18
z = 18 + 9
z = 27
7 + w = 14
w = 14 - 7
w = 7
13 - 5 = 12
8 ≠ 12
D - 2 = -10
D = -10 + 2
D = -8
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For the following geometric sequence find the explicit formula.
(12, -6, 3, ...]
Answer: [tex]a_n=12(-\frac{1}{2})^{n-1}[/tex]
Step-by-step explanation:
Let's first find the common ratio this sequence. To get to the next term, we divide by 2 and we alternate signs. Hence, the common ratio is [tex]-\frac{1}{2}[/tex].
We can now use the formula [tex]a_n=a_1(r)^{n-1}[/tex] to get the formula, where [tex]a_1[/tex] is the first term and r is the common ratio.
[tex]a_n=a_1(r)^{n-1}\\a_n=12(-\frac{1}{2})^{n-1}[/tex]
Classify each number below as an integer or not.
Using it's concept, the integer numbers in the data-set are given as follows:
6/1, -14, 56/7.
The other numbers, -74.48 and 3/17, are not integers.
What are integer numbers?Integer numbers are numbers that have no decimal part. They can be represented by pure numbers, either negative or positive, or also fractions that result in an exact division.
In this problem, we have that:
The division of 6 by 1 has a exact result of 6, hence 6/1 is an integer.The division of 56 by 7 has a exact result of 8, hence 56/7 is an integer.-14 is a pure number with no decimal part, hence it is an integer.-74.48 has a decimal part, hence it is not an integer.3/17 is not an exact division, hence it is not an integer.More can be learned about integer numbers at https://brainly.com/question/17405059
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find r^-1 (x)
r(x) = 2/3 (4x -5)
Answer:
Step-by-step explanation:
Let r(y)=x.
[tex]x=\frac{2}{3}(4y-5)\\\\\frac{3}[2}x=4y-5\\\\\frac{3}{2}x+5=4y\\\\y=\frac{3}{8}x+\frac{5}{4}\\\\r^{-1}(x)=\frac{3}{8}x+\frac{5}{4}[/tex]
Quadratic equations…….
Step-by-step explanation:
Greetings !Completing the square is a method that is used for converting a quadratic expression of the form ax² + bx + c to the vertex form a(x - h)² + k. The most common application of completing the square is in solving a quadratic equation.
It's useCompleting the Square is a technique which can be used to find maximum or minimum values of quadratic functions. We can also use this technique to change or simplify the form of algebraic expressions. We can use it for solving quadratic equations.
Example:[tex]x {}^{2} + 6 = - 2 \\ x {}^{2} + 6x + 9 = 7 \\ (x + 3) {}^{2} = 7[/tex]
A balloon has a circumference of 28 in use the circumference to approximate the surface area of the ballon to the nearest square inch
The surface area of the balloon is 249 in².
What is the surface area of the balloon ?A balloon has the shape of a sphere. The distance round the sphere is equal to the circumference of the sphere.
Circumference of the sphere = 2πr
Where:
r = radius π = pi = 22 / 7Radius - circumference / 2π
28 / ( 2 x 22/7) = 4.45 inches
Surface area of a sphere = 4πr²
4 x 22/7 x 4.45² = 249 in²
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Please help!!!!! Two copies of the same Rational Function are shown below.
On the graph below draw the Horizontal Asymptote and write the equation for the horizontal asymptote underneath.
The equation for the horizontal asymptote will be y = -2.
How to illustrate the information?Since the degree of the numerator and denominator of f(x) is the same both being 1, therefore horizontal asymptote exists and is given by:
y = Leading coefficient of numerator of f(x) / Leading coefficient of denominator of f(x)
= y = -2/1
= y = -2
The vertical asymptote will be f(x) = -2x / (x + 3). To find the vertical asymptote we will equate the denominator of f(x) = 0
= x + 3 = 0
= x = -3
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In a study of 250,178 cell phone users,it was found that 81 developed cancer of the brain or nervous system. Assuming that cell phones have no effect, there is 0.000412 probability of a person developing cancer of the brain or nervous system. We therefore expect about 104 cases of such cancer in a group of 250,178 people.Estimate the probability of 81 or fewer cases of such cancer in a group of 250,178. What do these results suggest about media reports that all cell phone cause cancer of the brain or nervous system?
P(x≤81)=[tex]P(x\leq 81)\\What do these results suggest about media reports?[/tex]
Using the normal distribution, the probability is given as follows:
P(x≤81) = 0.0158.
Since this probability is very small, less than 0.05, it suggest that the media reports overstated the proportion of cellphone users that developed cancer.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].For this problem, the proportion and the sample size are given by:
p = 0.000412, n = 250178
Hence the mean and the standard deviation for the approximation are given by:
[tex]\mu = np = 250178 \times 0.000412 = 103.1[/tex].[tex]\sigma = \sqrt{np(1-p)} = \sqrt{250178 \times 0.000412 \times (1 - 0.000412)} = 10.15[/tex]The probability that x is of 81 or less than the p-value of Z when X = 81.5, accounting for continuity correction, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{81.5 - 103.1}{10.15}[/tex]
Z = -2.13
Z = -2.13 has a p-value of 0.0158.
Hence:
P(x≤81) = 0.0158.
Since this probability is very small, less than 0.05, it suggest that the media reports overstated the proportion of cellphone users that developed cancer.
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Please separate your final answer.
One second later, the distance between the two stones will change in a speed of 6.86 m/s
What is distance ?Distance can be defined as the length of change of position. When an object change from one position to another, the length between the points or position is known as distance.
If a dropped stone has a distance d = 4.9t²
Let us assumed that the time taken = 3 seconds
The distance d = 4.9 × 3² = 44.1 m
If another stone is dropped one second later, then the time t = 4 s
The distance = 4.9 × 4² = 78.4 m
One second later, the time = 5 seconds
The speed of change in distance = ( 78.4 - 44.1 )/ 5
The speed of change in distance = 34.3 / 5
The speed of change in distance = 6.86 m/s
Therefore, one second later, the distance between the two stones will change in 6.86 m/s
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Buns,cost 40p each. Cakes cost 55p each. I spend exactly £4.35 on buns and cakes.
How many of each did I buy?
Someone pls help me, I’m so stuck lol
By solving a linear equation, we conclude that you bought 4 buns and 5 cakes.
How many of each did I buy?
We will define the two variables:
x = number of buns bought.y = number of cakes bought.We know that you spent exactly £4.35, then we only need to solve the linear equation:
x*0.40 + y*0.55 = 4.35
We need to solve that equation for x and y, such that the values of x and y can only be positive whole numbers.
We can rewrite the equation as:
y*0.55 = 4.35 - x*0.40
y = (4.35 - x*0.40)/0.55
Now we only need to evaluate it in different values of x, and see for which value of x, the outcome y is also a whole number.
We will see that for x = 4, we have:
y = (4.35 - 4*0.40)/0.55 = 5
So you bought 4 buns and 5 cakes.
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40p + 55p = 95p
435p ÷ 95p = 4.57...
So, the sum of the two pairs can go into £4.35 four times.
That meant if I increase the buns & cakes four times, it will help me get closer to the sum of £4.35 & work out which was extra
(40 x 4 = 160) & (55 x 4 = 220)
160 + 220= 380p or £3.80
Adding them up I get 380 pence & that's 55p short to getting to the sum of 435p or £4.35
(435-380=55p)
Thus, the extra is the cake, meaning you bought 4 buns and 5 cakes.
Hope this helps!
3x - 2(2x - 5) = 2(x + 3) - 8
Answer:
x = 4
Step-by-step explanation:
Hello!
We can solve for x by expanding the parentheses and isolating x.
Solve for x3x - 2(2x - 5) = 2(x + 3)-83x - 4x + 10 = 2x + 6 - 8-x + 10 = 2x - 210 = 3x - 212 = 3xx = 4The value of x is 4.
Quadrilateral WXYZ has coordinates W(−3, 2), X(1, 3), Y(2, −2), and Z(−1, −2). What are the coordinates of the vertices of D2(WXYZ)?
the coordinates of the vertices of D2(WXYZ) are;
W' ( 2, 3)
X' ( 3, -1)
Y' ( -2, -2)
Z'(−1, −2)
How to determine the coordinatesIt is important to note that the general formula for finding the transformation of the coordinates is;
M ( h, k) = M' ( k, -h)
Where
h is the first coordinatesk is the second coordinatesFor the quadrilateral WXYZ we have to find the transformed coordinates
For W, we have
W(−3, 2)
h = -3
k = 2
Substitute the values
W' ( 2, 3)
For X,
X(1, 3)
h = 1
k = 3
Substitute the values
X' ( 3, -1)
For Y
Y(2, −2)
h = 2
k = -2
Substitute the values
Y' ( -2, -2)
For Z
Z(−1, −2)
h = -1
k = -2
Z'(−1, −2)
Thus, the coordinates of the vertices of D2(WXYZ) are;
W' ( 2, 3)
X' ( 3, -1)
Y' ( -2, -2)
Z'(−1, −2)
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Use a table of values to graph the function ƒ(x) = |x + 2| – 1. Select the correct graph below.
△ABC has vertices A(-2, 0), B(0,8), and C(4,2). Find the coordinates of the point of congruency of the altitudes (H)
Based on the calculations, the coordinates of the point of congruency of the altitudes (H) are (-160/11, 40/11).
What is a triangle?A triangle can be defined as a two-dimensional geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.
What is a slope?A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.
How to determine a slope?Mathematically, the slope of a straight line can be calculated by using this formula;
[tex]Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Assuming the following parameters for triangle ABC:
Let AM be the altitudes on BC.Let BN be the altitudes on CA.Let CL be the altitudes on AB.For the slope of BC, we have:
Slope of BC = (2 - 8)/(4 - 0)
Slope of BC = -6/4
Slope of BC = -3/2.
For the slope of CA, we have:
Slope of CA = (2 - 0)/(4 - (-2))
Slope of CA = 2/6
Slope of CA = 1/3.
For the slope of AB, we have:
Slope of AB = (8 - 0)/(0 - (-2))
Slope of AB = 8/2
Slope of AB = 4.
Note: The point of concurrency of three altitudes in a triangle is referred to as orthocenter.
Since side AB is perpendicular to side QC, we have:
m₁ × m₂ = -1
Slope of AB × Slope of QC = -1
Slope of QC = (k - 4)/(h - 2)
4 × (k - 4)/(h - 2) = -1
(4k - 16)/(h - 2) = -1
4k - 16 = -h + 2
4k + h = 18 .......equation 1.
Similarly, we have the following:
Slope of BC × Slope of AH = -1
-3/2 × (k)/(h + 2) = -1
3k/(2h + 4) = 1
3k = 2h + 4
3k - 2h = 4 .......equation 2.
Solving eqn. 1 and eqn. 2 simultaneously, we have:
8k + 2h = 36
3k - 2h = 4
11k = 40
k = 40/11.
For the value of h, we have:
h = -4k
h = -4 × (40/11)
h = -160/11
Therefore, the coordinates of the point of congruency of the altitudes (H) are (-160/11, 40/11).
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Por favor ayuda con este ejercicio
Answer:
-
-
+
+
Step-by-step explanation:
Consider the quadratic equation x2 + 2x - 35 = 0. Solve by factoring and using the zero-product property.
What are solutions to quadratic equations called? Show your work.
Answer:
x = -7
x = 5
Step-by-step explanation:
The standard form of quadratic equations is
Ax^2 + Bx + C = 0
The factors need to multiply together to be C and add together to be B.
The two numbers that will multiply together to be -35 and add together to be 2 are -5 & 7.
The factor pairs are (x+7)(x-5). Zero product property means we set each of those factor pairs = 0 and solve.
x + 7 = 0
-7 -7 Subtract 7 from each side to solve
x = -7
x - 5 = 0
+5 +5 Add 5 to each side to solve
x = 5
To solve the equation, factor x²+2x−35 use the formula x² +(a + b) x + ab = (x + a)(x + b). To find a and b, set up a system to be solved.
a + b = 2
ab = −35
Since ab is negative, a and b have opposite signs. Since a+b is positive, the positive number has a greater absolute value than the negative. Show all pairs of integers whose product is −35.
−1.35−5.7Calculate the sum of each pair.
−1 + 35 = 34−5 + 7 = 2The solution is the pair that gives sum 2.
a = −5b = 7Rewrite the factored expression (x + a)(x + b) with the values obtained.
(x − 5)(x + 7)To find solutions to equations, solve x−5=0 and x+7=0.
x = 5x = −7What are the solutions of quadratic equations called?The "solutions" of a Quadratic Equation are the values where the equation equals zero. They are also called "roots", or even "zeros".
ヘ( ^o^)ノ＼(^_^ )If you want to learn more about mathematics, I share this link to complement your learning:
https://brainly.com/question/16413695How do you compute this? 4(-2, 3) - 2(6, -7)
Step-by-step explanation:
Factor out two from the expression. The answer should be 2(2*(-2, 3)-(6, -7))
Find the value of x.
Answer:
17
Step-by-step explanation:
i think its the right answer
We are driving to Las Vegas. The sign says that it is one hundred forty-five miles to Las Vegas.
How many kilometers is it to Las Vegas?
Answer:
233.35488 km (Rounded to 233 km)
Step-by-step explanation:
If you convert miles to kilometers then you would use this conversion factor:
1 mile = 1.609344 km (or 1.61 km)
so in this case,
145 mile = 1.609344 km x 145
145 mile = 233.35488 km
I could also round it to 233 km.
Since your on a trip... i hope u enjoy ur journey to Las Vegas!
The new director of special events at a large university has decided to completely revamp graduation ceremonies. Toward that end, a PERT chart of the major activities has been developed. The chart has five paths with expected completion times and variances as shown in the table. Graduation day is 16 weeks from now. Use Table B and Table B1. Path Expected Duration (weeks) Variance A 10 1.21 B 8 2.00 C 12 1.00 D 15 2.89 E 14 1.44 Click here for the Excel Data File Assuming the project begins now, what is the probability that the project will be completed before: (Round your z-value to 2 decimal places and all intermediate probabilities to 4 decimal places. Round your final answers to 4 decimal places.) a. Graduation time? b. The end of week 15? c. The end of week 13?
The probability that the project will be completed before the graduation time is 0.6873.
What is probability?It should be noted that probability simply means the likelihood of the occurence of an event.
From the table attached, it can be seen that the probability that the project will be completed before the graduation time is 0.6873.
Also, the probability that the project will be completed before the end of week 15 will be 0.3983.
Lastly, the probability that the project will be completed before the end of week 13 will be 0.0203.
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Find the equation of the line parallel to y equals 1 half x plus 2 that passes through the point (4, 5) in slope-intercept form.
Answer: [tex]y=\frac{1}{2}x+3[/tex]
Step-by-step explanation:
We can solve this by using the point-slope form, which can help get the equation of a line given the slope of the line and a point on the line. Slope-intercept form is the form [tex]y=mx+b[/tex], and we can convert from point-slope form to this with simple algebra.
The point-slope form is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope of the line, and [tex](x_1,y_1)[/tex] is the point.
We know that the line is parallel to [tex]y=\frac{1}{2}x+2[/tex], which means it will have the same slope. The slope of this line is [tex]\frac{1}{2}[/tex], so the slope of any line parallel to it will also be [tex]\frac{1}{2}[/tex].
[tex]y-5=\frac{1}{2}(x-4)\\y-5=\frac{1}{2}x-2\\y=\frac{1}{2}x+3[/tex]
3 digit passcode using only digits 3 & 9
Answer:
339
Step-by-step explanation:
Find the equation of the line that passes through point (6, 1) with the x-intercept of 2.
[tex]y = \frac{ - 1}{4} x + \frac{1}{2} [/tex]
On a coordinate plane, a circle has center (0, 0) and radius 4. A parabola opens down and goes through (3, 0), has vertex (0, 2) and goes through (negative 3, 0). Everything above the parabola and inside of the circle is shaded. Which system has the solution set shown? x squared + y squared greater-than-or-equal-to 16 and y greater-than-or-equal-to negative one-fourth x squared + 2 x squared + y squared greater-than-or-equal-to 16 and y less-than-or-equal-to negative one-fourth x squared + 2 x squared + y squared less-than-or-equal-to 16 and y greater-than-or-equal-to negative one-fourth x squared + 2 x squared + y squared less-than-or-equal-to 16 and y less-than-or-equal-to negative one-fourth x squared + 2
The inequality system that has the solution set shown will be C. x squared + y squared less-than-or-equal-to 16 and y greater-than-or-equal-to negative one-fourth x squared + 2.
How to illustrate the information?It should be noted that inequalities are simply used to compare two expressions that are unequal.
It can be seen that the solution set that's illustrated is:
x² + y² <= 16
-1/4x² + 2 <= y
Therefore, the inequality system that has the solution set shown will be option C.
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You decide that you want to purchase a Tesla SUV. You borrow $95,000 for the purchase. You
agree to repay the loan by paying equal monthly payments of $1,200 until the balance is paid off. If
you're being charged 6% per year, compounded monthly, how long will it take you to pay off the
loan?
Answer:
8.5 years
Step-by-step explanation:
It will take 102 more payments
8.5 years
Interest will be $26,239
It would take approximately 15 years to pay back the loan of 95000 which is compounding monthly and the rate of interest is 6%.
What is compound interest?Compound interest is basically the interest which is calculated on the primcipal with addition to aggregate interest. The formula of sum after compounding is as under:
S=P[tex](1+r/n)^{nt}[/tex] in which P is principal amount, r is rate per annum, n is number of times of compounding and t is time period.
How to calculate time?We have been given that the amount of loan is $95000, installment is $1200 , rate of interest is 6% and it is compounded monthly.
First of all we have to find the effective rate=6%/12=0.005.
The future value of 95000 at a rate of 6% compunded monthly should be equal to the amount of all installments. So,
95000[tex](1+0.005)^{12n}[/tex]=12*1200*n
95000[tex]1.005^{12n}[/tex]=14400n
[tex]1.005^{12n}[/tex]=14400n/95000
[tex]1.005^{12n}[/tex]=0.1515n
We have to make graph of this to find the value of n which after graphing will come approx 15.
Hence it would take 15 years to pay back loan amount.
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What is in simplest form?
A.
B.
C.
D.
Answer:
C. 8√3
Step-by-step explanation:
* = multiply or times
To find √192 in its simplest form we need to divide it by a square number like 64.
192/64 = 3
√192 = √64 * √3 = 8√3
A cyclist covers a distance of 900m in 4min 30sec. what is the speed in km/h of the cyclist?
Answer:
12km/h
Step-by-step explanation:
s=d/t
900m is 0.9km and 4min and 30sec is 0.075h
0.9/0.075=12 which gives us 12km/h
Answer:
Step-by-step explanation:
4 min 30 seconds = 270 seconds
900m = 270 seconds
100m = 30 seconds
1000m= 300 seconds (5min)
12,000m=3600seconds (60min)
Answer = 12km/h
Crane Manufacturing management is considering overhauling their existing line, which currently has both a book value and a salvage value of $0. It would cost $280,000 to overhaul the existing line, but this expenditure would extend its useful life to five years. The line would have a $0 salvage value at the end of five years. The overhaul outlay would be capitalized and depreciated using MACRS over three years. The tax rate is 35 percent, the opportunity cost of capital is 12 percent. The NPV of the new production line is $-360,000.
Since the cost of the renovation or overhauling of the existing line would be recovered in Year 4 and the NPV of the new production line is $-360,000, Crane Manufacturing should renovate.
What is the difference between renovation and replacement?Renovation restores an old asset to a better state. Replacement rids the old in preference for a new asset.
When the two investment options are weighed, a better choice can be arrived at.
Data and Calculations:MACRS - Three Years Depreciation:Year 1 = $93,324 ($280,000 x 33.33%)
Year 2 = $124,460 ($280,000 x 44.45%)
Year 3 = $41,468 ($280,000 x 14.81%)
Year 4 = $20,748 ($280,000 x 7.41%)
Total cost = $280,000
NPV of new production line = $-360,000
Thus, based on the cost recovery of the old production line and the negative NPV of the new production line, Crane Manufacturing should renovate.
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Question Completion:Should Crane replace or renovate the existing line?
How many values are in the range?
0 to 50
Let a be an even integer number, b be an odd integer number and c be an integer number.
Which of the following statements is NOT true?
a.
If a+b=c, then c is odd integer.
b.
If b+b=c, then c is even integer.
c.
If b×b=c, then c is even integer.
d.
If a×b=c, then c is even integer.
The false statement is given by:
c. If b×b=c, then c is even integer.
When is the addition of two integers even or odd?It both numbers are even or both are odd, the addition is even.It one number is even and the other is odd, the addition is odd.When is the multiplication of two integers even or odd?It at least one of the numbers is even, the multiplication is even.If the two numbers are odd, the multiplication is odd.Hence, since b is odd, b x b = c is odd, hence statement c is false.
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