Answer:
a. The initial amount of money that was left in this savings account was of 5000.
b. Decrease of 2% each year.
Step-by-step explanation:
Exponential function:
An exponential function, with an initial value of A(0), and a decay rate of r, as a decimal, is given by:
[tex]A(t) = A(0)(1-r)^t[/tex]
In this question, we have:
[tex]y = 5000*(0.98)^x[/tex]
a. What was the initial amount of money that was left in this savings account?
This is y(0) = 5000
The initial amount of money that was left in this savings account was of 5000.
b. What is the percent of change each year in this savings account?
First as a decimal.
1 - r = 0.98
r = 1 - 0.98
r = 0.02
So a decrease of 2% each year.
Find the roots of the equation below.
x2 - 6x + 12 = 0
-3 ± √3
3 ± √3
-3 ± i√3
3 ± i√3
Answer:
[tex]\displaystyle x = 3 \pm i\sqrt{3}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
FactoringStandard Form: ax² + bx + c = 0Quadratic Formula: [tex]\displaystyle x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]Algebra II
Imaginary Numbers: √-1 = iStep-by-step explanation:
Step 1: Define
x² - 6x + 12 = 0
Step 2: Identify Variables
Compare the quadratic to standard form.
x² - 6x + 12 = 0 ↔ ax² + bx + c = 0
a = 1, b = -6, c = 12
Step 3: Find Roots
Substitute in variables [Quadratic Formula]: [tex]\displaystyle x=\frac{-(-6)\pm\sqrt{(-6)^2-4(1)(12)}}{2(1)}[/tex][Quadratic Formula] Simplify: [tex]\displaystyle x=\frac{6\pm\sqrt{(-6)^2-4(1)(12)}}{2(1)}[/tex][Quadratic Formula] [√Radical] Evaluate exponents: [tex]\displaystyle x=\frac{6\pm\sqrt{36-4(1)(12)}}{2(1)}[/tex][Quadratic Formula] [√Radical] Multiply: [tex]\displaystyle x=\frac{6\pm\sqrt{36-48}}{2(1)}[/tex][Quadratic Formula] [√Radical] Subtract: [tex]\displaystyle x=\frac{6\pm\sqrt{-12}}{2(1)}[/tex][Quadratic Formula] [√Radical] Factor: [tex]\displaystyle x=\frac{6\pm \sqrt{-1} \cdot \sqrt{12}}{2(1)}[/tex][Quadratic Formula] [√Radicals] Simplify: [tex]\displaystyle x=\frac{6 \pm 2i\sqrt{3}}{2(1)}[/tex][Quadratic Formula] [Fraction - Denominator] Multiply: [tex]\displaystyle x=\frac{6 \pm 2i\sqrt{3}}{2}[/tex][Quadratic Formula] [Fraction - Numerator] Factor: [tex]\displaystyle x=\frac{2(3 \pm i\sqrt{3})}{2}[/tex][Quadratic Formula] [Fraction] Divide: [tex]\displaystyle x = 3 \pm i\sqrt{3}[/tex]PLEASE HELP MEEEEEE I need help quickly
Answer:
60
Step-by-step explanation:
There are sixty students.
15% = 9
------------------
100% = x
Cross muliply.
900
------
15x
Divide 15x by 15, and 900 by 15.
Answer is 60.
I hope this helps!
Brainliest would be awesome!
A garden table and a bench cost $793 combined. The garden table costs $43 more than the bench. What is the cost of the bench?
Answer:
The bench costs $375
Step-by-step explanation:
t + b = 793
t = b+43
(b+43) + b = 793
2b + 43 = 793
2b = 750
b = 375
The bench costs $375
Help me. Will give brainliest.
Answer:
63
Step-by-step explanation:
WHAT IS THE PRUDTUCT OF 7\9 AND 6 A. 1 4/9 B. 3 7\9 C. 4 2\3 D. 7 5\7
Answer:
C.
Step-by-step explanation:
A credit card company wanted to estimate the proportion of its customers who pay their credit card minimum balance on time. The company sampled 500 records and constructed a confidence interval for the true proportion of customers who pay their credit card minimum balance on time. The resulting 95 percent confidence interval was (0.765, 0.835). Which of the following is a true statement regarding the value of the point estimate and margin of error of the percentage of customers who pay their credit card minimum balance on time?
a. The point estimate is 0.765 and the margin of error is 0.07.
b. The point estimate is 0.765 and the margin of error is 0.835.
c. The point estimate is 0.80 and the margin of error is 0.035.
d. The point estimate is 0.80 and the margin of error is 0.07.
e. The point estimate could be any number within the interval and the margin of error is 0.035.
Answer: c. The point estimate is 0.80 and the margin of error is 0.035.
Step-by-step explanation:
Given: The 95 percent confidence interval was (0.765, 0.835).
Confidence interval = Point estimate ± Margin of error.
I.e. Point estimate + Margin of error = 0.835 (i)
Point estimate - Margin of error = 0.765 (ii)
Add (i) and (ii), we get
2 (Point estimate)= 1.60
⇒ Point estimate = 0.80
Put this in (i), we get
0.80+Margin of error = 0.835
⇒ Margin of error = 0.835 -0.80
⇒ Margin of error = 0.035
Hence, the correct statement is:
c. The point estimate is 0.80 and the margin of error is 0.035.
What is the reverse of subtract 849
what's the correct choice please help
Year. 2006. 2007. 2011 . 2012. 2013
CPI. 201.6. 207.342. 224.939. 229.594 232.957
Suppose you bought a house in 2013 for $90,000. Use the table above to calculate the 2006 value adjusted for inflation. which is the correct answer below
$90,314
$91,398
$103,999
$77,886
Answer:
$77,886
Step-by-step explanation:
We solve this question by proportions, using a rule of three.
The table states that:
$201.6 in 2006 is worth $232.957 in 2013.
We want to find:
The value of $90,000 in 2013 in 2006:
$201.6 - $232.957
x - $90000
Applying cross multiplication
[tex]232957x = 201.6*90000[/tex]
[tex]x = \frac{201.6*90000}{232957}[/tex]
[tex]x = 77886[/tex]
$77,886 is the answer
Find the distance travelled by a vehicle in 10 seconds when it travels at the uniform speed of 72kmh
Answer:
If the initial velocity being is a straight line, and the final velocity being 0 km/hr, or o m/s, then:
v(final) = v(initial) + at
0 = 72 Km/h + (-=a * 10 s)
- a * 10 s = 72 km/hr * hr/3600s * 1000m/km = 20m/s
a = - (20 m/s) / (10 s)
a = - 2 m/s^2
That’s 2 m/s^2.
Step-by-step explanation:
Please give thanks to all my answers and please mark as brilliant and please follow me
Step-by-step explanation:
Formula : distance=speed×time
time.= 10s = 10÷60÷60= 1/360h
speed = 72km/h
distance = 72×1/360 = 0.2km
In a store the number of dogs is 12 times greater than 3 times of cats. If there are 21 dogs in the store, how many cats are in the store?
Answer:
If you really meant that the number of dogs is 12 greater than 3 times the number of cats then:
3 cats
Step-by-step explanation:
21= number of dogs
c = number of cats
21 = 12 + (3c)
3c = 9
c = 3
how do I solve the question 3/4+1/2
Answer: 1 1/4
Step-by-step explanation:
Mrs. Wilson bought 2 boxes of candy for the party. After filling the pinata and the candy dish, she had ⅚ of a box left. If she split the remaining candy into 10 goodie bags, how much of a box of candy did she put in each bag?
Answer:
Mrs Wilson put 1/12 of the box of candy in each goodie bag
Step-by-step explanation:
5/6 is kinda hard to divide into 10 pieces left like it is, so we turn 5/6 into 10/12 (they're both the same)
Then from here, it's easy
10/12 and 10 goodie bags
So 1/12 goes into each one
Penny is the manager of a nursery for pre-school children.
She knows that the ratio of the number of adults to the number of children must be 1 : 8
Penny has 56 children at the nursery.
Work out the number of adults Penny needs for 56 children?
Show your wor
Answer:
9
Step-by-step explanation:
on a nice day there are 90% of children playing outside during recess. if there are 150 children how many of them are playing outside
Answer:
150.9 ?
Step-by-step explanation:
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA POINTS*..
IM GIVING 40 POINTS !! DONT SKIP :((.
Answer:
y = 10 x = 4
Step-by-step explanation:
Answer:
y = 10x - 30
Step-by-step explanation:
x = 5
5 x 10 = 50
50 - 30 = 20
y = 20
x = 6
6 x 10 = 60
60 - 30 = 30
y = 30
x = 7
7 x 10 = 70
70 - 30 = 40
y = 40
x = 8
8 x 10 = 80
80 - 30 = 50
y = 50
If it takes 30 apples to fill 2 boxes, how many apples are needed to fill 3 boxes?
Answer: 45 apples will be needed to fill 3 boxes
Step-by-step explanation: If there are an even amount of apples in each box, 15 times 2 is 30. So if there are 15 apples in each box, 15 times 3 is 45.
Answer:45 apples
Step-by-step explanation:
Since 15 apples are needed to fill 1 box, 45 apples are needed to fill 3 bboxes
Evaluate the expression when x-=12.5 and y=6 12x-3y^2
Answer:
Step-by-step explanation:
Expresión x--12.5*y-612*x-3*y-2 = 9.5*y-611.0*x-2.0
If x = y and y = Z, which statement must be true?
Answer:
Step-by-step explanation:
that means that x=z transitive prop of equality
if my answer helps please mark as brainliest
If one face of a cube has an area of 6 in2, what is the total surface area of the cube?
Answer:
216..................
Determine m ASAP please help!!
Answer:
m=52
Step-by-step explanation:
ABC and FBE are congruent and we know that ABC is 52
90-38=52
so FBE is also 52
Hope this helps ^-^
I need help please quickly!!
Answer:
37.68
Step-by-step explanation:
A= 3.14 x 4 x 4 = 50.24
50.24 ÷ 4 = 12.56
12.56 x 3 = 37.68
Find the solutions of each equation on the interval [0, 2π)
Answer/Step-by-step explanation:
Factor this. GCF=2
2(2cos2x+cos x-1)=0
2(2cos x -1)(cos x+1)=0 Set each factor equal to zero and solve
2cos x -1=0 Add 1 to both sides
2cos x =1 Divide by 2
cos x =1/2
x=π/3
x=5π/3
cos x+1=0 Subtract 1 from both sides
cos x=-1
x = π
During a test period, an experimental group of 10 vehicles using an 85 percent ethanol-gasoline mixture showed mean CO2 emissions of 240 pounds per 100 miles, with a standard deviation of 20 pounds. A control group of 14 vehicles using regular gasoline showed mean CO2 emissions of 252 pounds per 100 miles with a standard deviation of 15 pounds. A quick comparison of the sample variances suggests that the population variances are:
a. probably equal.
b. probably unequal.
c. incomparable.
Answer:
Probably unequal ( B )
Step-by-step explanation:
experimental group = 10
using 85% ethanol gasoline
mean = 240 pounds per 100 miles
standard deviation = 20 pounds
control group = 14 vehicles
using regular gasoline
mean = 252 pounds per 100 miles
standard deviation = 15 pounds
comparing the sample variance of each group shows that they are probably unequal using the equation below
Variance for a sample set of data = ∑ ( x - X ) ^2 / n - 1
where n = number of events
X = mean value
x = value of events
suppose that rectangle ABCD is dilated to A'B'C'D using the origin as the center and a mangnitude of 2. What are the coordinates of C'?
Answer:
-8,-8
Step-by-step explanation:
Hope u get it right! :D
9(5x) need help asap
Answer:
45x happy to help ya :)
Step-by-step explanation:
chase travel 192 miles in 16 hours on his inline skates .What is his unit rate in milees per hour
Answers
a 1 mph
b 0.083
c 12 mph
d 24 mph
The equation h(t) = -16t^2? + 32t + 128 models the path of a ball thrown in the air from the top of a building. After how many seconds does the ball reach its maximum
height?
Answer:
1 second
Step-by-step explanation:
The number of seconds for the ball to reach the maximum height is t = 1 s
What is a function rule?The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.
A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given data ,
Let the function be represented as A
Now , the value of A is
f ( x ) = -16t² + 32t + 128
The function h(t) gives the height of the ball at time t. The maximum height occurs at the vertex of the parabolic path, which is given by the formula:
t = -b / (2a)
where a = -16 and b = 32 are the coefficients of the quadratic term and the linear term, respectively.
Substituting these values into the formula, we get:
t = -32 / (2(-16)) = 1
Therefore, the ball reaches its maximum height after 1 second
Hence , the function is solved
To learn more about function rule click :
https://brainly.com/question/3760195
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Solve the following for c: 10c + 12 = - 48
Answer:
c = -6
Step-by-step explanation:
10c + 12 = -48
subtract 12 from both sides
10c = -60
divide by 10 on both sides
c = -6
Answer:
C = -6
Step-by-step explanation:
10c + 12 = - 48
-12 -12
10c = -60
/10 /10
c = -6
Juries should have the same racial distribution as the surrounding communities. According to the U.S. Census Bureau, 18% of residents in Minneapolis, Minnesota, are African Americans. Suppose a local court will randomly sample 100 state residents and will then observe the proportion in the sample who are African American. How likely is the resulting sample proportion to be between 0.066 and 0.294 (i.e., 6.6% to 29.4% African American)
Answer:
0.997 = 99.7% probability that the resulting sample proportion to be between 0.066 and 0.294
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
18% of residents in Minneapolis, Minnesota, are African Americans. Suppose a local court will randomly sample 100 state residents and will then observe the proportion in the sample who are African American.
This means that [tex]p = 0.18, n = 100[/tex]
So, by the Central Limit Theorem:
[tex]\mu = 0.18, s = \sqrt{\frac{0.18*0.82}{100}} = 0.0384[/tex]
How likely is the resulting sample proportion to be between 0.066 and 0.294?
This is the pvalue of Z when X = 0.294 subtracted by the pvalue of Z when X = 0.066. So
X = 0.294
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.294 - 0.18}{0.0384}[/tex]
[tex]Z = 2.97[/tex]
[tex]Z = 2.97[/tex] has a pvalue of 0.9985
X = 0.066
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.066 - 0.18}{0.0384}[/tex]
[tex]Z = -2.97[/tex]
[tex]Z = -2.97[/tex] has a pvalue of 0.0015
0.9985 - 0.0015 = 0.997
0.997 = 99.7% probability that the resulting sample proportion to be between 0.066 and 0.294
Graham Sugar Company has 900 pounds of sugar to package. Each bag of sugar holds two and four-tenths pounds. How many bags are needed?
Answer:
375 bags
Step-by-step explanation:
900/2.4=375 bags
