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Dax borrowed Nu 5000 from the bank to buy a computer. she paid the money back at the end of 1 year.she was charged 12 percent simple interest for the year. what amount did Dax pay in interest.how much did Dax have to pay back
Answer:
Interest = Nu 600
Amount = Nu 5600
Step-by-step explanation:
P = Nu 5000
R = 12%
T = 1
[tex]Interest = \frac{PRT}{100} = \frac{5000 \times 12 \times 1}{100} = Nu \ 600[/tex]
[tex]Amount = P + Interest = 5000 + 60 0 = Nu \ 5600[/tex]
Select the statements that describe exponential growth.
a. Exponential growth is common in many circumstances throughout nature.
b. Exponential growth is the rapid and unrestricted increase of a population.
c. Exponential growth is population growth limited by natural resources in the environment.
d. Exponential growth occurs when populations level off and stop growing.
e. Exponential growth occurs when a population increases at a fixed percentage of every generation.
Answer:
the answer is B
Step-by-step explanation:
cause exponensial means like a crazy amount very quickly
9514 1404 393
Answer:
e. Exponential growth occurs when a population increases at a fixed percentage of every generation.
Step-by-step explanation:
Exponential growth occurs when the amount of increase is proportional to the population. That is, the increase is a fixed percentage of the population in any given time period (generation).
__
Many populations appear to have exponential growth when resources are effectively unlimited. The growth can be rapid, but isn't always. At some point, the population generally finds a limit to its growth, which then ceases to be exponential.
A function describing population growth that is jointly proportional to population and available resources is called a logistic function. It has an exponential component, but is not an exponential function.
why do you think that increasing the number of people in a sample creates a normal curve?
Answer:
Increasing the number of people allows more variety and diversity, which makes the sample more accurate.
Find the mean, variance, and standard deviation of the following probability
distribution then interpret the computed values. Write your answer in your answer
sheets.
The number of computers sold per day at a local computer store, along with its
corresponding probabilities, is shown in the table below.
Number of Computer Sold X
Probability P(x)
0
0.1
2
0.2
5
0.3
7
0.2
9
0.2
Answer:
5.1 ; 8.29 ; 2.879
Step-by-step explanation:
Given :
Number of Computer Sold X
Probability P(x)
0
0.1
2
0.2
5
0.3
7
0.2
9
0.2
Mean = E(X) = Σ(x*p(x)
E(X) = (0*0.1) + (2*0.2) + (5*0.3) + (7*0.2) + (9*0.2)
E(X) = 5.1
Variance, Var(X) = Σx²p(x) − E(X)²
Var(X) = [(0^2*0.1) + (2^2*0.2) + (5^2*0.3) + (7^2*0.2) + (9^2*0.2)] - 5.1^2
Var(X) = 34.3 - 26.01 = 8.29
Standard deviation ; Std(X) = √Var(X) = √8.29 = 2.879
Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. f(x,y)= e^xy; X^3+y^3=16
Answer:
f(x,y) = [tex]e^{xy}[/tex] is maximum at x = 2 and y = 2 and f(2,2) = [tex]e^{4}[/tex]
Step-by-step explanation:
Since f(x,y) = [tex]e^{xy}[/tex] and x³ + y³ = 16, Ф(x,y) = x³ + y³ - 16
df/dx = y[tex]e^{xy}[/tex], df/dy = x[tex]e^{xy}[/tex], dФ/dx = 3x² and dФ/dy = 3y²
From the method of Lagrange multipliers,
df/dx = λdΦ/dx and df/dy = λdΦ/dy
y[tex]e^{xy}[/tex] = 3λx² (1) and x[tex]e^{xy}[/tex] = 3λy² (2)
multiplying (1) by x and (2) by y, we have
xy[tex]e^{xy}[/tex] = 3λx³ (4) and xy[tex]e^{xy}[/tex] = 3λy³ (5)
So, 3λx³ = 3λy³
⇒ x = y
Substituting x = y into the constraint equation, we have
x³ + y³ = 16
x³ + x³ = 16
2x³ = 16
x³ = 16/2
x³ = 8
x = ∛8
x = 2 ⇒ y = 2, since x = y
So, f(x,y) = f(2,2) = [tex]e^{2 X2}[/tex] = [tex]e^{4}[/tex]
We need to determine if this is a maximum or minimum point by considering other points that fit into the constraint equation.
Since x³ + y³ = 16 when x = 0, y is maximum when y = 0, x = maximum
So, 0³ + y³ = 16
y³ = 16
y = ∛16
Also, when y = 0, x = maximum
So, x³ + 0³ = 16
x³ = 16
x = ∛16
and f(0,∛16) = [tex]e^{0X\sqrt[3]{16} } = e^{0} = 1[/tex].
Also, f(∛16, 0) = [tex]e^{\sqrt[3]{16}X0 } = e^{0} = 1[/tex].
Since f(0,∛16) = f(∛16, 0) = 1 < f(2,2) = [tex]e^{4}[/tex]
f(2,2) is a maximum point
A tepee is designed to have a diameter of 10 ft and a volume of 393 ft. At
what height, h, should the support poles cross to assemble the tepee
correctly? Use 3.14 for 1 and round your answer to the nearest foot.
Answer:
15 ft.
Step-by-step explanation:
The tepee is a cone and its volume
= 1/3 pi r^2 h where r = radius and h = height.
The radius r = 1/2 * 10 = 5 ft.
So we have the equation:
393 = 1/3*3.14* 5^2 * h
h = 393 / (1/3*3.14*25)
= 15.02 ft.
A certain radioactive isotope is a by-product of some nuclear reactors. Due to an explosion, a nuclear reactor experiences a massive leak of this radioactive isotope. Fortunately, the isotope has a very short half-life of 13 days. Estimate the percentage of the original amount of the isotope released by the explosion that remains 6 days after the explosion.
Answer:
[tex]\frac{N}{N_o} = 0.726 = 72.6\%[/tex]
Step-by-step explanation:
The following formula can be utilized for this question:
[tex]N = N_o (\frac{1}{2})^{\frac{t}{t_{1/2}} } \\\\\frac{N}{N_o} = (\frac{1}{2})^{\frac{t}{t_{1/2}} } \\\\[/tex]
where,
[tex]\frac{N}{N_o}[/tex] = ratio of the remaining amount to the original amount = ?
t = tme passed = 6 days
[tex]t_{1/2}[/tex] = half-life = 13 days
Therefore,
[tex]\frac{N}{N_o} = (\frac{1}{2} )^{\frac{6\ days}{13\ days} }\\\\[/tex]
[tex]\frac{N}{N_o} = 0.726 = 72.6\%[/tex]
No link please
Ergent
Using matrix method solve
the following simulaneous equatin
2x+3y=9
3x-1y=3
Step-by-step explanation:
here are the matrices you were looking for
8x – 3y = 1
–2x + 3y = 11
Solve a Linear System by Elimination
The average age of Iowa residents is 37 years. Amy believes that the average age in her hometown in Iowa is not equal to this average and decided to sample 30 citizens in her neighborhood.Using the alternative hypothesis that µ ≠ 531, Amy found a t-test statistic of 1.311.What is the p-value of the test statistic?
Answer:
The p-value of the test is 0.2.
Step-by-step explanation:
Using the alternative hypothesis that µ ≠ 531, Amy found a t-test statistic of 1.311.
Alternative hypothesis means that e have a two-tailed hypothesis test.
Sample 30 citizens. Amy found a t-test statistic of 1.311.What is the p-value of the test statistic?
Thus, we have a two-tailed test with 30 - 1 = 29 degrees of freedom and t = 1.311. So, using a t-distribution calculator, the p-value of the test is 0.2.
The Madison Cosmetics Company has developed a new women's facial cleanser that they believe is superior to those currently on the market in the $5 - $10 range. They wish to test the cleanser against the two current best-sellers.
A. Identify a potential problem with using a completely randomized experimental design to test the cleanser. Explain.
B. The company executives decide to design and carry out a block design experiment to test the new cleanser against its competition. Choose an appropriate blocking scheme for the experiment and justify your choice.
C. Should the company put a control group into the experiment? Why or why not?
D. Could the experiment be a double-blind experiment? Explain.
Answer:
a. there could be a problem of high error
b. randomized block design can remove the issue of heterogeneity
c. yes they should
d, yes it could
Step-by-step explanation:
a. if their is a lack of homogeneity among the sample population, then the results that would be obtained are going to be with increased experimental error.
b. given the number of treatment, the randomized block design technique can be done. This would then remove the issue of heterogeneity. It also gives more information and the results from the test are easier. Even in the presence of missing data, the missing plot technique can be employed.
c. when a control group is used, it makes easier the examination of the market research in a more effective way.
d. Yes it could be a double blind one. This would help to take away the problem of bias.
PLEASE HELP WILL MARK YOU!
It says:state whay additional information is required in order to know that the triangles are congruent for the reason given
This is pt.1
Step-by-step explanation:
12) ASA - we need the second angle.
13) We need the side and second angle.
14) We need second side. First side we know is equal since both triangles share it.
How do I solve this and answer?
Step-by-step explanation:
at first solve first triangle with Pythagorean solving witch it c²=a²+b²
you have to change a bit so it will be c²-b²=a²
you start with 8 and 10 triangle and then you get line which is in the middle and yo udo just the same with triangle 8 and the solved side and you get x in the second triangle you have to use c²-a²=b²
A man at ground level measures the angle of elevation to the top of the building to
be 87°. If at this point, he is 20 meters away from the building, what is the height of
the building?
Answer:
The bulding is 381,623 meters high.
Step-by-step explanation:
To dertermine the height of the bulding I would use tanα = rectangulair side / closest rectangulair side.
19,08 = the height/ 20m.
<=> 19,08.20m= the height = 381,623 m
ABCD is a kite, so AC DB and DE = EB. Calculate the length of AC, to the nearest tenth of a centimeter.
9514 1404 393
Answer:
AC ≈ 6.8 cm
Step-by-step explanation:
For legs a and b of a right triangle with hypotenuse c, the Pythagorean theorem tells us ...
a = √(c² -b²)
Using this relation, we can find legs CE and AE.
CE = √(3² -2²) = √5
AE = √(5² -2²) = √21
AC is the sum of these two lengths:
AC = AE +EC = √21 +√5
AC ≈ 6.8 cm
Which choice shows the coordinates of C'if the trapezoid is reflected across the y-axis?
Answer:
The coordinate of C is (5, 3). The trapezoid is reflected across the y-axis. When it is reflected over y-axis only the sign of the x coordinate change and y coordinate remains the same. Hope this will helpful.
Caroline is going to invest in an account paying an interest rate of 5.2% compounded continuously. How much would Caroline need to invest, to the nearest dollar, for the value of the account to reach $940 in 6 years?
Answer:
688
Step-by-step explanation:
For delta math
Use algebra to solve 3x+4 = 1/x
The exact solutions are x=
Х
Answer:
Ignore the A before the ±, it wouldn't let me type it correctly.
[tex]x=\frac{2±\sqrt{7} }{3}[/tex]
Step-by-step explanation:
3x + 4 = 1 ÷ x
3x + 4 - 4 = 1 ÷ x - 4
3x = 1 ÷ x - 4
[tex]3x=\frac{1}{x} +\frac{x(-4)}{x}[/tex]
[tex]3x=\frac{1+x(-4)}{x}[/tex]
[tex]3x=\frac{1-4x}{x}[/tex]
[tex]x(3x)=x(\frac{1-4x}{x})[/tex]
x · 3x = - 4x + 1
3x² = - 4x + 1
3x² - (- 4x + 1) = 0
3x² + 4x - 1 = 0
Ignore the A before the ±, it wouldn't let me type it correctly.
[tex]x=\frac{-b±\sqrt{b^{2}-4ac } }{2a}[/tex]
a = 3
b = 4
c = - 1
[tex]x=\frac{-4±\sqrt{4^{2}-4((3)(-1)) } }{2(3)}[/tex]
[tex]x=\frac{-4±\sqrt{16-4((3)(-1)) } }{2(3)}[/tex]
[tex]x=\frac{-4±\sqrt{16+12 } }{2(3)}[/tex]
[tex]x=\frac{-4±\sqrt{28 } }{2(3)}[/tex]
[tex]x=\frac{-4±\sqrt{(2)(14) } }{2(3)}[/tex]
[tex]x=\frac{-4±\sqrt{(2)(2)(7) } }{2(3)}[/tex]
[tex]x=\frac{-4±\sqrt{2 } \sqrt{2}\sqrt{7} }{2(3)}[/tex]
[tex]x=\frac{-4±2\sqrt{7} }{2(3)}[/tex]
[tex]x=\frac{-4±2\sqrt{7} }{6}[/tex]
Two separate equations
[tex]x=\frac{-4+2\sqrt{7} }{6}[/tex]
[tex]x=\frac{2+\sqrt{7} }{3}[/tex]
[tex]x=\frac{-4-2\sqrt{7} }{6}[/tex]
[tex]x=\frac{2-\sqrt{7} }{3}[/tex]
247 1372 as a number
Answer:
Do you mean in words?
Step-by-step explanation:
then it is
Two million,four hundred and seventy one thousand,three hundred and seventy two.
4.27cm rounded to the nearest cm
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]4.27\text{cm} \approx\boxed{4\text{cm}}[/tex]
»»————- ★ ————-««
Here’s why:
We would locate the whole number and look at the number to the right. In this case, we would look at the '2' in the tenths place.Since it is less than or equal to 4, we would round down.⸻⸻⸻⸻
Recall the Rounding Rules:
If the digit to the right is less than or equal to 4, we round down.If the digit is greater than or equal to 5, we round up.⸻⸻⸻⸻
[tex]\underline{4.27cm}\\\\\rightarrow2\leq 4\\\\\boxed{4.27cm \approx 4cm}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
The curve y=9-6/x and the line y+x=8 intersect at two points. Find the coordinates of the two points
Answer: (2,6) (-3,11)
Step-by-step explanation:
At the intersection, y=9- 6/x and y+x = 8 are equal to each other
y + x = 8 is the same as y=8-x
Sub this into y = 9 - 6/x
8 - x = 9 - 6/x
Multiply everything by x:
8x - x^2 = 9x - 6
x^2 + x - 6 = 0
(x-2)(x+3) = 0
x = 2 (so y = 9 - 6/x so y = 9 - 6/2 =6)
x = -3 (so y = 9-6/x so y = 9-6/-3 = 11)
The coordinates of two points will be ; (2,6) and (-3,11).
It is given that the curve y = 9 - (6 / x) and line y + x = 8.
Find the coordinates of two points.
What is the general equation of line ?
General equation is given by ; y = mx + c.
At the intersection,
y = 9 - 6/x ----------- (Equation 1)
and y + x = 8 are equal to each other.
y + x = 8 can be written as y = 8-x.
Substitute this into Equation 1.
8 - x = 9 - ( 6/x )
Multiply both sides by x ;
8x - [tex]x^{2}[/tex] = 9x - 6
[tex]x^{2}[/tex] + x - 6 = 0
This can be written as ;
(x-2) (x+3) = 0
So we get values of x ;
i.e., x = 2 , -3
For , x = 2
y = 9 - 6/x
⇒ y = 9 - (6/2)
⇒ y = 6
For , x = - 3
⇒ y = 9 - (6/x)
⇒ y = 9 - (6/ -3)
⇒ y = 11
Thus , the coordinates of two points will be ; (2, 6) and (-3,11).
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plz answer if you know it....
Sales tax is charged on the subtotal (amount before tax).
First, find the subtotal by adding up all of the amounts.
4(675) + 2(110) + 5(41) + 6(135) + 230(2.50)
2700 + 220 + 205 + 810 + 575
Total = 4510
Next, we need to find 7% of 4510. That number is the sales tax.
0.07 x 4510 = 315.70
Sales Tax = $315.70
Total Amount (with tax) = $4825.70
Hope this helps!! :)
tell whether or not the measurements below form a triangle:
1. 4, 5, 10
2. 12, 26, 20
3. 2, 3, 5
Answer:
Below.
Step-by-step explanation:
If the sum of any 2 sides are less than or equal to the third side then there's no triangle
1. N0 because 4 + 5 < 10
2. YES
3. NO because 2 + 3 = 5.
Answer:
Step-by-step explanation:
1 . 4,5,10 : this measurement does not form a triangle because the sum of two sides is not greater than the third side (longest side)
4 + 5 > 10
9 > 10 (this is not satisfied)
2. 12,26,20 :this measurement forms a triangle beacuse the sum of two sides is greater than the third side
12 + 26 > 20
38 > 20
3 .
2,3,4 : this measurement does not form a triangle because the sum of two sides is not greater than the third side.
2 + 3 > 5
5 > 5 (this is not satisfied)
I need the answer plzzzzzz
Answer:
answer is 0 in the ones column
identify the population and the sample for the situation
A televised cooking program wants to know
what type of cuisine its viewers want to see on an upcoming episode. While on air, the program asked its viewers to vote online. Of the 3 million people watching the show, 0.2 million vote.
Answer:
The population of this problem would be the 3 million viewers and the sample would be the 0.2 million that voted.
hope this helps!
Please help me
Thank you.
Answer:
(8, -1)
General Formulas and Concepts:
Algebra I
Reading a coordinate planeCoordinates (x, y)Solving systems of equations by graphingStep-by-step explanation:
Where the 2 lines intersect is the solution to the systems of equations. The systems of equations intersect at (8, -1).
When a factory operates from 6 AM to 6 PM, its total fuel consumption varies according to the formula f(t)=0.9t^3−0.6t^0.5+10, where t is the time in hours after 6 AM and f(t) is the number of barrels of fuel oil. Step 1 of 3 : How much fuel is consumed by 11 AM? Round your answer to 2 decimal places.
Step-by-step explanation:
the answer is in the image above
The amount of oil consumed in 5 hours is 120.5 barrels.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given is an equation, of fuel consumption in a factory from 6 am to 6 pm,
The equation =
f(t) = 0.9t³-0.6[tex]t^{0.5}[/tex]+10
where t is the time in hours after 6 am and f(t) is the number of barrels of fuel oil.
We need to find the how much oil is consumed by 11 am,
So, the hours between 11 am to 6 am = 11-6 = 5 hours
So, we need to find the oil consumption in 5 hours, so for the same put t = 5, in the equation,
f(5) = 0.9(5)³-0.6[tex](5)^{0.5[/tex]+10
= 112.5-2+10
= 120.5
Hence, the amount of oil consumed in 5 hours is 120.5 barrels.
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Help please i will mark brainlist !!!!
Answer:
You need to add the numbers up
0.4 +0.2+0.1=0.7
1-0.7=0.3
Ans=0.3
When choosing a four-number PIN.
(personal identification number)
how many different PINS are possible?
(The choice of digits 0-9 are available for each number.)
Answer:
10,000 different PINS are possible
Step-by-step explanation:
Fundamental counting principle:
States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.
In this question:
Four each digit on the PIN, there are 10 possible outcomes. The digits are independent. So, by the fundamental counting principle:
[tex]T = 10^4 = 10000[/tex]
10,000 different PINS are possible
Write an equation for the line parallel to y = -7x + 15 that passes through the point P(9,-6).
Answer:
y = -7x + 57
Step-by-step explanation:
If the line is parallel, it will have the same slope. So, this line will also have a slope of -7.
Use y = mx + b, plug in the slope and given point, and solve for b:
y = mx + b
-6 = -7(9) + b
-6 = -63 + b
57 = b
Plug in the slope and y intercept into y = mx + b:
y = mx + b
y = -7x + 57
So, the equation is y = -7x + 57