Answer:
10 years
Step-by-step explanation:
Simple interest formula:
AV=PV(1+it)
13200=8000(1+.065t)
1.65=1+.065x
.65=.065x
10=x
if n=200 and x=70, construct a 99onfidence interval estimate for the population proportion.
A 99% confidence interval estimate for a population proportion can be calculated using the formula: CI = p ± z*√(p(1-p)/n). Given a sample size of 200 and a sample proportion of 0.35, the 99% confidence interval estimate for the population proportion is approximately (0.271, 0.429).
To construct a 99% confidence interval estimate for the population proportion, we can use the following formula:
CI = p ± z*√(p(1-p)/n)
where p is the sample proportion (x/n), z* is the critical value for a 99% confidence interval (2.576), and n is the sample size.
Substituting the given values, we get:
CI = 70/200 ± 2.576*√[(70/200)(1-70/200)/200]
= 0.35 ± 0.079
Therefore, the 99% confidence interval estimate for the population proportion is (0.271, 0.429). This means that we are 99% confident that the true population proportion falls within this interval.
To construct a 99% confidence interval estimate for the population proportion, we'll use the formula:
CI = p ± Z * √(p(1-p)/n)
Here, n = 200, x = 70, and Z is the Z-score for a 99% confidence interval, which is 2.576.
First, we calculate the sample proportion (p):
p = x/n = 70/200 = 0.35
Next, we'll plug these values into the formula:
CI = 0.35 ± 2.576 * √(0.35(1-0.35)/200)
CI = 0.35 ± 2.576 * √(0.2275/200)
CI = 0.35 ± 2.576 * 0.034
Now, calculate the margin of error:
Margin of error = 2.576 * 0.034 ≈ 0.0876
Finally, construct the confidence interval:
Lower limit = 0.35 - 0.0876 ≈ 0.2624
Upper limit = 0.35 + 0.0876 ≈ 0.4376
So, the 99% confidence interval estimate for the population proportion is approximately (0.2624, 0.4376).
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x^2-x-6 factorising plplplp
The factors of the given expression, x²-x-6, are (x+2)(x-3)
What are expressions?A mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Given is an expression, x²-x-6, we need to factorize it,
x²-x-6,
Splitting the middle term by the multiples of 6,
2-3 = -1 and 2×3 = 6
x²-x-6
= x²-3x+2x-6
= x(x-3)+2(x-3)
= (x+2)(x-3)
Hence, the factors of the given expression, x²-x-6, are (x+2)(x-3)
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The endpoints of GH are G(-3,0) and G(7, -8) Find the coordinates of the midpoint M
Answer:
(2,-4)
Step-by-step explanation:
WILL GIVE BRAINLIEST!!!!!!!!!!!
Answer:
[tex)63^{\circ}\)
Step-by-step explanation:
\(m\angle EHF+27^{\circ}=90^{\circ} \implies m\angle EHF=63^{\circ}\)
Answer:
Since this is a 90 degrees right angle, and FHG is 27 degrees, we can subtract. 90 - 27 is 63.
Line EHF is 63 degrees
Step-by-step explanation:
A bag contains 8 apples and 6 oranges. You randomly draw a piece of fruit from the bag, eat it, and than randomly draw another. What is the probability you draw and eat an apple than draw an orange?
Answer:
\(probability \ of\ choosing\ apple\ first = \frac{8}{14}\\\\probability\ of\ choosing\ orange\ second = \frac{6}{13}\\\\probability \ of \ choosing \ apple \ and \then \ orange = \frac{8}{14} \times\frac{6}{13} = \frac{24}{91}\)
if 3x+5/x-=16, what is x?
Answer:
x=5, x= 1/3
Step-by-step explanation:
Answer :
\(x = \frac{1}{3} \\ x = 5\)
Given that y varies jointly as x and z, and y = 13 when x = 5
andz=8, find the following:
a. y when x= 4 and z=10
b. x when y= 20 and z = 12
c. z when x=6 and y=15
Step-by-step explanation:
y=kxz
13=k x 5 x 8
13= 40k
K=13/40
a. y=13/40 x 4 x 10
y=13/40 x 40
y=13
b. 20=13/40 x x x 12
20=13/40 x 12x
20=156x
40
20 x 40=156x
800=156x
X=800
156
X=200
39
X=5 5/39
C. 15=13/40 x 6 x z
15=78z
40
15x40=78z
600=78z
Z=600
78
Z=100
3
Z=7 9/13
Jak starts to save at age 40 for a vacation home that he wants to buy for his 50th birthday. He will contribute $1000 each quarter to an account, which earns 2.1% interest, compounded annually. What is the future value of the investment, rounded to the nearest dollar, when jak is ready to purchase the vacation home?
Answer:
\(P=\$40840\)
Step-by-step explanation:\(I=840\)
From the question we are told that:
Time interval \(t=50-40=>10years\)
Annual contribution \(X= 4*1000=>\$4000\)
Annual interest rate \(r=2.1\%\)
Generally the 10 years interest I is mathematically given by
\(I=X*t*r\)
\(I=4000*0.021*10\)
\(I=840\)
Generally the equation for the future value of the investment \(P\) is mathematically given by
\(P=X*t+840\)
\(P=(4000*10)+840\)
\(P=\$40840\)
Michelle brought $26 with him to the Freeport Carnival. She wants to buy a pretzel for $4.50 and then spend the remaining money on rides. The cost of each ride is $1.25. Write an inequality that can be used to solve for r, the number of rides Michelle can go on. Use the inequality to determine the maximum number of rides he can go on?
Answer:
26=1.25x+4.50 17 rides
Step-by-step explanation:
26=1.25+4.50 26-4.50= 21.50 After buying the pretzel Michelle has $21.50 left. 21.50 divided by 1.25 = 17.2 But since you can't ride .2 of a ride, it is rounded to 17 rides.
A girl that is 4 feet tall casts a shadow that is 2 feet long. Find the height of a boy that casts a 3-foot shadow.
A. 6.5 feet
B. 6 feet
C. 5.5 feet
D. 4.5 feet
Answer:
B. 6 feet
Step-by-step explanation:
4 ÷ 2 = 2
6 ÷ 2 = 3
Answer:
The answer is B,6.
Step-by-step explanation:
Hope this helps. :)
If i got it right, can you mark me Brainliest.
Lydia bought a shirt at 20% off its retail price of $40. She paid 5% tax on the price after the discount. How much did Lydia pay for the shirt?
make sure to look at the photo :) i hope you have a good day
Answer:
$33.60
Step-by-step explanation:
Original price of shirt: $40
Percent discount: 20%
Amount of discount: 20% of $40 = 0.2 × $40 = $8
Price after discount: $40 - $8 = $32
Percent of tax: 5%
Amount of tax: 5% of $32 = 0.05 × $32 = $1.60
Total paid after discount and tax: $32 + $1.60 = $33.60
Answer: Lydia paid the amount of 33.60 dollar
Step-by-step explanation:
Retail price of shirt = 40 dollar
Discount = 20%
Discount value:
=20% of 40 dollar [ 20/100 * 40 ⇒ 1/5 * 40 ⇒ 40/5 = 8 ]
= 8 dollar [ discount value]
Price of shirt after discount :
= 40 - 8
= 32 dollar
As she paid 5% discount on the discounted price ( 32 dollar )
So, 5% of 32 = 1.6 dollar [ 5/ 100 * 32 ⇒ 1/20 * 32 ⇒ 32/20 = 1.6]
Amount to pay = 32( price after discount) + 1.6 ( Tax)
= 33.60 dollar
A chemist wishes to make a 10% acid solution. she has a 4% acid solution and a solution that is 28% acid. how many liters of each should she use if she needs 5 liters of the 10% solution?
The chemist should use 3.75 liters of the 4% acid solution and 1.25 liters of the 28% acid solution to make 5 liters of a 10% acid solution.
Let's denote the volume of the 4% acid solution as x and the volume of the 28% acid solution as y, both in liters.
To make a 10% acid solution, we need to mix the two solutions in such a way that the resulting mixture has a total volume of 5 liters, and the concentration of acid in the mixture is 10%.
Since we want 5 liters of the final mixture, we can write the following equation based on the conservation of volume:
x + y = 5
The total amount of acid in the final mixture should be 10% of the total volume of the mixture, so we can write the following equation:
0.04x + 0.28y = 0.1(5)
On simplifying:
0.04x + 0.28y = 0.5
From the first equation:
y = 5 - x
Substituting into second equation:
0.04x + 0.28(5 - x) = 0.5
Simplifying and solving for x:
0.04x + 1.4 - 0.28x = 0.5
-0.24x = -0.9
x = 3.75
Using first equation,
x + y = 5
3.75 + y = 5
y = 1.25
Therefore, she needs to use 3.75 liters of the 4% acid solution and 1.25 liters of the 28% acid solution to make 5 liters of a 10% acid solution.
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how to determine the end behavior of a rational function
By analyzing the degrees and leading coefficients, you can determine how the rational function behaves at the extreme ends of the x-axis.
To determine the end behavior of a rational function, you need to examine the degrees of the numerator and denominator polynomials. The end behavior refers to how the function behaves as the input (x-values) approaches positive or negative infinity.
Here are the steps to determine the end behavior of a rational function:
1. Identify the highest power of x in the numerator and denominator. Let's call them n and m, respectively.
2. If n < m, the degree of the denominator is greater than the numerator. In this case, the function's end behavior is determined by the degree of the denominator.
- If m is even, the function approaches the horizontal axis (y = 0) as x approaches both positive and negative infinity.
- If m is odd, the function approaches opposite infinities: positive infinity as x approaches negative infinity and negative infinity as x approaches positive infinity.
3. If n = m, the degree of the numerator is equal to the denominator. In this case, the leading coefficients of the numerator and denominator determine the end behavior.
- The function approaches the ratio of the leading coefficients as x approaches both positive and negative infinity.
4. If n > m, the degree of the numerator is greater than the denominator. In this case, the function's end behavior is determined by the degree of the numerator.
- If n is even, the function approaches positive infinity as x approaches both positive and negative infinity.
- If n is odd, the function approaches opposite infinities: positive infinity as x approaches positive infinity and negative infinity as x approaches negative infinity.
By analyzing the degrees and leading coefficients, you can determine how the rational function behaves at the extreme ends of the x-axis.
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personnel director interviewing 9 senior engineers for four job openings has scheduled seven interviews for the first day and two for the second day of interviewing. assume that the candidates are interviewed in a random order. (a) what is the probability that x of the top four candidates are interviewed on the first day? h(n; 2, 4, 9) h(x; 7, 4, 9) h(x; 2, 9, 4) h(n; 7, 9, 4) correct: your answer is correct. (b) how many of the top four candidates can be expected to be interviewed on the first day? (round your answer to two decimal places.)
The probability is h(x; 7, 4, 9) = [x(4 - x)] / 126 and the number of top four candidates that can be expected to be interviewed on the first day is 3.11.
(a) The probability that x of the top four candidates are interviewed on the first day is given by the hypergeometric probability distribution function, which is h(x; 7, 4, 9). The values of n, m, and k are 9, 4, and 7, respectively. Therefore, the probability is:
h(x; 7, 4, 9) = [mCx * (n - m)C(k - x)] / nCk= [4C x * 5C(7-x)] / 9C7= [4!/(x!(4-x)!) * 5!/(7-x)!] / 9!/(7!2!) [n!/(n - k)!k!]
On simplification, we get: h(x; 7, 4, 9) = [x(4 - x)] / 126
The probability that x of the top four candidates are interviewed on the first day is h(x; 7, 4, 9) = [x(4 - x)] / 126
(b) The expected number of the top four candidates to be interviewed on the first day is given by the mean of the hypergeometric probability distribution function, which is np. Therefore, the expected number of candidates is: np = 7(4/9) = 3.11 (rounded to two decimal places)
Hence, the number of top four candidates that can be expected to be interviewed on the first day is 3.11.
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PLEASE HELP QUICK!!!!
Bernie borrowed b books from his friend Grant's collection of 29 books. What does the expression 29 - b represent?
If MK = 10 m, find the length of MKL. Round to the nearest hundredth.
K
52
L
N
M
m
arc MKL =
Length of MKL is 15.71 m.
If MK = 10 m, find the length of MKL. Round to the nearest hundredth.
The radius of the circle is MK = 10 m.The central angle of arc MKL is 52 degrees.The ratio of the arc length to the circumference of the circle is equal to the ratio of the central angle to 360 degrees.Therefore, the arc length of MKL is equal to (52 degrees / 360 degrees) * 2 * pi * 10 m = 15.7079 m.Rounding to the nearest hundredth, the length of MKL is 15.71 m.Learn more about arc length.
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Describe and correct the error in setting up the trigonometric function.
The value of side length w is 13.75 .
Given right angled triangle,
Perpendicular = w
Hypotenuse = 17
Angle of triangle = 54°
So,
According to the trigonometric ratios,
tanФ = p/b
cosФ = b/h
sinФ = p/h
By using sinФ,
sinФ = p/h
sin 54° = w/ 17
0.809 = w/17
w = 13.75 .
Thus after correction w will be 13.75
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Oil flows back and forth between a small and large tank. When oil is moving into the large tank, the flow rate is positive. When oil is moving into the small tank, the flow rate is negative.
The large tank begins with 600 gallons of oil. The flow rate is recorded as –4 gallons per minute. After a period of 32 minutes, how much oil has been moved and to which tank?
into the
tank.
After the 32 minutes, how much oil is in the large tank?
gallons
Answer:
MY GOD...
C,B,A!
Step-by-step explanation:
PLS HELP
Translate this phrase into an algebraic expression. 19 increased by twice Chau's height Use the variable c to represent Chau's height.
Answer:
19 + 2c
Step-by-step explanation:
19 is increasing two times Chau's height, (c), which gives you 19 plus twice c, (2c).
need help fast what is the equation
The equation is 128 + 2x = 180.
What are corresponding angles?The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.
Corresponding angles are equal.
We have,
The sum of the same-side interior angles between two parallel lines is supplementary
This means,
128 + 2x = 180
2x = 180 - 128
2x = 52
x = 26
Thus,
The value of x is 26.
The equation is 128 + 2x = 180.
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PLEASE HELPP!!!!!!!!!!!!
Answer:
yes it is rotated
Step-by-step explanation:
since it was already dilated (widened), it was the rotated to create the way that it is now
What is the length of the line?
Answer:
5 units
Step-by-step explanation:
Use Pythagorean Theorem
x = 4 units y = 3 units
4^2 + 3^2 = L^2
16 + 9 = L^2
L = 5
Answer:
5 units
Step-by-step explanation:
By the Pythagorean theorem:
c² = a² + b²
c = length of the line
a = 4
b = 3
Then:
c² = 4² + 3²
c² = 16 + 9
c² = 25
√c² = √25
c = 5
Does this expression x2+y2=1 satisfy the DE dy/dx +x/y =0
we can conclude that the expression x² + y² = 1 satisfies the differential equation dy/dx + x/y = 0.
To determine if the expression x² + y² = 1 satisfies the given differential equation dy/dx + x/y = 0, we can follow these steps:
Given: x² + y² = 1
We need to find the derivative of x² + y² = 1 with respect to x. We can use implicit differentiation for this purpose.
Differentiating the expression with respect to x, we get:
2x + 2y(dy/dx) = 0
Now, we can solve for dy/dx:
dy/dx = -(2x)/(2y) = -(x/y)
Substituting this value of dy/dx into the given differential equation dy/dx + x/y = 0, we have:
-(x/y) + x/y = 0
The equation simplifies to 0 = 0, which is a true statement.
Therefore, we can conclude that the expression x² + y² = 1 satisfies the differential equation dy/dx + x/y = 0.
Hence, the given expression satisfies the given differential equation.
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______ as a type of sales promotion is beneficial because they can encourage consumers to try out a product at reduced risk, but they can be detrimental because they reduce perception of value for the product or service.
Free samples or product trials as a type of sales promotion can be both beneficial and detrimental. They encourage consumers to try a product at reduced risk, but they can also reduce the perception of value for the product or service.
Offering free samples or product trials is a common sales promotion strategy to attract customers and encourage them to try a product or service. This approach has several benefits. Firstly, it lowers the perceived risk for consumers as they can experience the product without making a financial commitment upfront. This can be especially effective for new or unfamiliar products, as it allows potential customers to test the product's quality and functionality.
However, there can be drawbacks to this sales promotion technique. Providing free samples or trials can create the perception that the product or service has less value or is of lower quality. Consumers may develop a mindset of expecting free or discounted offerings, and it can undermine the willingness to pay the full price in the future. Additionally, if the free samples or trials are not managed effectively, it may attract individuals who are not genuinely interested in the product, leading to wastage of resources and potentially diluting the brand image.
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Round 7.12568 to the nearest thousandth
Answer:
The answer is 0
Step-by-step explanation:
find the inverse of f(x)=x^3-8
Answer:
Step-by-step explanation:
Eparture time of a car is 0540 hours and it traveled for 45 minutes before it reached its destination. At what time did the car arrived at its destination : *
Answer:
The time at which the car arrives at its destination is 0625 hours or 6: 25 am or 25 minutes past 6.
Step-by-step explanation:
Departure time = 0540 Hours means 5: 40 am or 40 minutes past 5 in the morning.
Now add 45 mins
Hours : Minutes
5: 40
+ 45
5 : 85
But 1 hour contains 60 minutes so 85 - 60 gives 25 minutes . those 60 minutes = 1 hour are carried over the hours and added .
Hours : Minutes
1
5: 40
+ 45
6 : 25
The time at which the car arrives at its destination is 0625 hours or 6: 25 am or 25 minutes past 6 in the morning.
The distance between point (-3,6) and another point is 10. What are the possible
coordinates of the other point?
Answer:
The distance between point A(-3,6) and another point is 10.
=> That point belongs to the circle with center A and radius 10.
=> The coordinate (x, y) of that point satisfies the equation of circle:
(x - -3)^2 + (y - 6)^2 = 10^2
or
(x + 3)^2 + (y - 6)^2 = 100
Hope this helps!
Question:
Victoria took a test and got 80% of the questions right. She answered 20 questions correctly. How many questions were on the test?
Options:
20
22
25
28
Answer: 25
Step-by-step explanation:
80/ 100 = 0.8
20/? = 0.8
= 20/0.8 = 25
What is the slope-intercept form of the following equation? −6x−2y=−18
Answer:
y = -3x + 9
Step-by-step explanation:
−6x − 2y = −18
+6x +6x
------------------------
-2y = -18 + 6x
/-2 /-2
-------------------------
y = 9 - 3x
y = -3x + 9 ---> this is your slope-intercept form