Answer:
The Amount initially deposited is $37046.64
Step-by-step explanation:
A = p (1+r/n)^(nt)
A= final amount= $5000
P = principal amount=
r = rate = 0.05
n = number of times compounded
= 6*12
= 48
t = years= 6
A = p (1+r/n)^(nt)
50000 = p (1+0.05/48)^(48*6)
50000= p(1.001041667)^288
50000= p (1.34965)
50000/1.34965= p
37046.64 = p
The Amount initially deposited is $37046.64
Transformation of exponential functions need help ASAP
Answer:
These are vertical transformations because the parent function is being translated up and down which are vertical directions.
How many square feet of outdoor carpet will we need for this hole?
Answer:
9.
Step-by-step explanation:
You would have to find the area of the triangle which is 1/2(bh) which would give you 9. So you would 9 feet of outdoor carpet. Which is actually already given to you as the area inside the triangle.
Answer:
9
Step-by-step explanation:
I finally got it!
Evaluate. Write your answer as a fraction or whole number without exponents. 9^–3 =
Answer:
[tex]\frac{1}{9^3}[/tex] or [tex]\frac{1}{729}[/tex]
Step-by-step explanation:
When we have an exponent that is a negative, it is the same thing as 1 over the positive exponent. So, we move 9^-3 into 1/9^3 and then we evaluate the exponent to get our answer.
What would be the slope of the positions (3,3) and (4,5)
Answer:
m = 2
Step-by-step explanation:
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Simply plug our coordinates into the slope formula and solve for m:
m = (5 - 3)/(4 - 3)
m = 2/1
m = 2
Answer:
2Step-by-step explanation:
Let the points be A and B
A( 3 , 3 ) -----> ( x1 , y1 )
B(4 , 5 ) ------>( x2 , y2 )
Now,
finding the slope,
Slope =[tex] \frac{y2 - y1}{x2 - x1} [/tex]
[tex] = \frac{5 - 3}{4 - 3} [/tex]
[tex] = \frac{2}{1} [/tex]
[tex] = 2[/tex]
Hope this helps...
Good luck on your assignment..
BRAINLIEST ANSWER WINS! A satellite is to be put into an elliptical orbit around a moon as shown below. A vertical ellipse is shown surrounding a spherical object labeled, moon. The moon is a sphere with radius of 1000 km. Determine an equation for the ellipse if the distance of the satellite from the surface of the moon varies from 953 km to 466 km.
Answer:
D. x²/1953² + y²/ 1466² = 1
Step-by-step explanation:
==>Given:
Radius of spherical moon = 1000km
Distance of satellite from moon surface = 953km to 466km
==>Required:
Derived equation of ellipse
==>Solution:
The formula for driving an equation of ellipse is given as:
x²/a² + y²/b² = 1
Where,
a = length of the semi-major axis, while,
b = length of the semi-major axis
Since we are told that the satellite distance to the surface of the moon varies from 953km to 466km, values of a and b is calculated by summing each length to the radius of the moon as follows:
a = radius of moon + the larger distance of the satellite = 1000+953 = 1,953km
b = radius of moon + the smaller distance of the satellite = 1000+466 = 1,466km
Thus, the equation of the ellipse would be:
x²/1953² + y²/ 1466² = 1
I NEED HELP PLEASE ASAP!!!
Answer:
see below
Step-by-step explanation:
There are a couple of ways to go about this.
The general form of a conic equation is ...
Ax^2 +Bxy +Cy^2 +Dx +Ey +F = 0
For AC > 0, this is the equation of an ellipse or circle. (AC < 0, hyperbola; AC = 0, parabola)
So, from the coefficients of the given equation, AC = 2·5 = 10, you know the equation is of an ellipse.
__
The rotation matrix for Cartesian coordinates tells you ...
x = x'·cos(θ) +y'·sin(θ)
y = -x'·sin(θ) +y'·cos(θ)
For θ = 45° the values of these trig functions are all (√2)/2. That is, there is no way to get coefficients in the rotated equation that involve √3. This eliminates choice 2.
The only remaining viable choice is choice 4.
__
If you like, you can substitute for x and y using the above relations. You will find that the result differs from any of the answer choices. The rotated figure will have the equation ...
[tex]5x^2-6xy+9y^2+10\sqrt{2}x+2\sqrt{2}y-80=0[/tex]
For example, the x and y terms become ...
[tex]6x-4y=6(x'\cos{(45^{\circ})}+y'\sin{(45^{\circ})})-4(-x'\sin{(45^{\circ})}+y'\cos{(45^{\circ})})\\\\=10x'\dfrac{\sqrt{2}}{2}+2y'\dfrac{\sqrt{2}}{2}\\\\\text{Multiplying this by 2 gives $\dots$}\\\\10x'\sqrt{2}+2y'\sqrt{2}[/tex]
Note that this is not the 10√2x' -10√2y' shown in choice 4.
__
Another way to look at this is to look at the angle of rotation relative to alignment with the x- and y-axes. That angle α is given by ...
cot(2α) = (A -C)/B
For the original ellipse, the rotation angle is ...
α = arccot((2 -5)/2)/2 ≈ -16.85°
For the transformed ellipse of choice 4, the rotation angle is ...
α = arccot((9 -5)/6)/2 ≈ 28.15°
This is 45° more*, as it should be, indicating choice 4 is the better of the offered choices.
__
If you do the angle calculation for the 2nd answer choice, you will find it has no relation to a 45° rotation of the original ellipse.
_____
* While the computed rotation angle is as expected, the fact that the x^2 and y^2 coefficients have been swapped means that the long and short axes of the ellipse have been swapped. That is, the long axis of the ellipse has been rotated 45° in the wrong direction by the equation given in the answer choices. The second attachment shows the original ellipse (red), the properly rotated ellipse (dashed red) and the ellipse of choice 4 (blue).
PLZ HELP !!!!! The graph represents the transformation called a ____. Rotation Translation Reflection
The graph represents a rotation transformation
Write a number with 2 decimal places, that is bigger than 4 and 1/5 but smaller than 4.25?
Answer: 4 wholes and 1/5 is 4.20 and you need something greater than that but less than 4.25 which still has only 2 decimals.
The height of the triangle is
The base of the triangle is
The area of the triangle is
Answer:
The height of triangle is 12cm.
The base of triangle is 25 cm.
The area of triangle is 150cm².
Step-by-step explanation:
Given that the area of triangle is Area = 1/2×base×height. So you have to substitute the values into the formula :
[tex]area = \frac{1}{2} \times base \times height[/tex]
[tex]let \: base = 25 \\ let \: height = 12[/tex]
[tex]area = \frac{1}{2} \times 25 \times 12[/tex]
[tex]area = \frac{1}{2} \times 300[/tex]
[tex]area = 150 \: {cm}^{2} [/tex]
of the digital video recorders (DVRs) in an inventory are known to be defective. What is the probability you randomly select a DVR that is not defective? The probability is nothing.
Full question:
Eighteen of 50 digital video recorders (DVRs) in an inventory are known to be defective. What is the probability you randomly select an item that is not defective?
Answer:
16/25
Step-by-step explanation:
Probability is the likelihood of an event happening and it is calculated as the number of favourable outcomes divided by the total number of possible outcomes. From the above we can calculate probability of finding a DVR that is not defective by adding up number of DVRS that are not defective in the DVRS(favourable outcomes) and dividing it by the total number of DVRS(total number of possible outcomes).
Non defective dvrs=total number of dvrs-defective dvrs=50-18=32
So probability here=non defective dvrs/total number of dvrs
=32/50=16/25
please simplify this
Answer:
(√77) / 22
Step-by-step explanation:
To rationalize the fraction we must multiply the entire fraction by √11 / √11. Note that the 2 is not important because it's not a radical. This gives us √77 / 22.
Help!!! Type SSS, SAS, ASA,
AAS, or HL to justify
why the two larger
triangles are congruent.
DB = CA
its congruent by HL or RHSaxiom
Answer:
HL
Step-by-step explanation:
[tex] In\: right \triangle 's DAB \: \&\: CBA\\
\angle DAB \cong \angle CBA... (each 90\degree) \\ hypotenuse \: DB \cong hypotenuse \: CA. (given) \\
side AB \cong side BA.. (common) \\
\therefore \triangle DAB \cong \triangle CBA.. (By \: RHS\: or \: HL \: Postulate) [/tex]
What is 4 2/3 ÷ 1 1/5
Answer:
3 8/9
Step-by-step explanation:
1.) Convert each fraction from a mixed number to a improper fraction (to do that multiply the denominator with the whole number then add the numerator, the improper fraction denominator will remain the same as the mixed number denominator):
14/3 ÷ 6/5
2.) Solve
a. To divide the fractions, Flip the reciprocal, and multiply the fractions
14/3 x 5/6
b. Check if you can reduce the numbers, which you can 14 and 6 can be both divided by 2:
7/3x5/3
c. Multiply fractions (simply by multiplying across):
35/9
3.) Simplify numbers into mixed fraction (or decimal):
3 8/9
Identify the parent function that can be used to graph the function/(x) = 471-3.
a. f(x) = x
c. f(x) = x
b. f(x) - [x]
d. f(x) -11
write the number name for 6782163 in international system
Answer:
Six Million Seven Hundred Eighty Two Thousand one hundred sixty three
Step-by-step explanation:
Hope it helps...Pls Mark as Brainliest!!
Answer:
Six Million Seven Hundred Eighty Two Thousand One Hundred and Sixty Three.
Step-by-step explanation:
6, 782, 163
In a certain college, 33% of the physics majors belong to ethnic minorities. Find the probability of the event from a random sample of 10 students who are physics majors.
Answer:
The probability that no more than 6 students belong to a ethnic minority is 0.9815.
Step-by-step explanation:
The question is incomplete:
In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the physics majors, what is the probability that no more than 6 belong to an ethnic minority?
We can model this with a random variable, with sample size n=10 and probability of success p=0.33.
The probability that k answers are guessed right in the sample is:
[tex]P(x=k)=\dbinom{n}{k}p^k(1-p)^{n-k}=\dbinom{10}{k}\cdot0.33^k\cdot0.67^{10-k}[/tex]
We have to calculate the probability that 6 or less students belong to a ethnic minority. This can be calculated as:
[tex]P(x\leq6)=P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)+P(x=5)+P(x=6)\\\\\\[/tex]
[tex]P(x=0)=\dbinom{10}{0}\cdot0.33^{0}\cdot0.67^{10}=1\cdot1\cdot0.0182=0.0182\\\\\\P(x=1)=\dbinom{10}{1}\cdot0.33^{1}\cdot0.67^{9}=10\cdot0.33\cdot0.0272=0.0898\\\\\\P(x=2)=\dbinom{10}{2}\cdot0.33^{2}\cdot0.67^{8}=45\cdot0.1089\cdot0.0406=0.1990\\\\\\P(x=3)=\dbinom{10}{3}\cdot0.33^{3}\cdot0.67^{7}=120\cdot0.0359\cdot0.0606=0.2614\\\\\\[/tex]
[tex]P(x=4)=\dbinom{10}{4}\cdot0.33^{4}\cdot0.67^{6}=210\cdot0.0119\cdot0.0905=0.2253\\\\\\P(x=5)=\dbinom{10}{5}\cdot0.33^{5}\cdot0.67^{5}=252\cdot0.0039\cdot0.135=0.1332\\\\\\P(x=6)=\dbinom{10}{6}\cdot0.33^{6}\cdot0.67^{4}=210\cdot0.0013\cdot0.2015=0.0547\\\\\\\\\\\\[/tex]
[tex]P(x\leq6)=0.0182+0.0898+0.1990+0.2614+0.2253+0.1332+0.0547\\\\\\P(x\leq6)=0.9815[/tex]
The probability that 6 or less students belong to a ethnic minority is 0.9815.
Does this table represent a function? Why or why not?
х
y
0
4
7
8
5
5
8
8
10
9
A. No, because two of the y-values are the same.
B. Yes, because there are two x-values that are the same,
C. Yes, because every x-value corresponds to exactly one y-value.
D. No, because one x-value corresponds to two different y-values.
Answer:
no because one x value corresponds to two different y values
The average college major requires 34 credit hours to complete, with a standard deviation of 3 hours. A college's academic advisors conduct a study to see how many credit hours a sample size of 50 students will need to take to complete their majors. They calculate:μx= μ = 34and σx= μ /√n =34/√50=4.81What did they do wrong?
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
The average college major requires 34 credit hours to complete, with a standard deviation of 3 hours. A college's academic advisors conduct a study to see how many credit hours a sample size of 50 students will need to take to complete their majors.
They calculate:
μx = μ = 34
σx = μ/√n = 34/√50 = 4.81
What did they do wrong?
Answer:
The sample mean will be the same as the population mean
μx = μ = 34
Whereas the standard deviation of the sample would be
σx = σ/√n
σx = 3/√50
σx = 0.424
Therefore, the college's academic advisors wrongly calculated the standard deviation of the sampling distribution.
Step-by-step explanation:
From the given information we know that,
The population mean is
μ = 34 credit hours
The population standard deviation is
σ = 34 credit hours
The college's academic advisors take a sample size of 50 students so
sample size = n = 50
Since the sample size is quite large then according to the central limit theorem,
The sample mean will be the same as the population mean
μx = μ = 34
Whereas the standard deviation of the sample would be
σx = σ/√n
σx = 3/√50
σx = 0.424
Therefore, the college's academic advisors wrongly calculated the standard deviation of the sampling distribution.
520 after a 30% increase
Answer:
676
Step-by-step explanation:
Convert the percentage to a decimal.
30% = 0.3
Multiply the number by the decimal.
520 × 0.3 = 156
Add this number by the number given.
520 + 156 = 676
Alexandra has 36 coins valued at $6.00 she has only nickels and quarters which equation can be used to solve for the number of nickels n
Answer
I will give you some hints and yea
Step-by-step explanation:
first try to figure out how much the quarters are you can first guess for example there were 8 quarters and ?nickels and work your way up and then you will get closer and closer to your answer
Answer:
0.05n + 0.25(36 – n) = 6
Step-by-step explanation:
Solve for w. 5w + 9z = 2z + 3w
Answer:
w = -7z/2
Step-by-step explanation:
Our goal is to isolate w
1. subtract 3w from both sides to get 2w+9z = 2z
2. Subtract 9z from both sides to get 2w = -7z
3. Divide both sides by 2 to get w = -7z/2
We cannot simplify further, so this is our answer.
18 points please help pic inserted
Answer:
1). [tex]\text{log}_4(5x^2+2)=\text{log}_4(x + 8)[/tex]
2). log(x - 1) + log5x = 2
3). ln(x + 5) = ln(x - 1) + ln(x + 1)
4). [tex]e^{x^2}=e^{4x+5}[/tex]
Step-by-step explanation:
1). ln(x + 5) = ln(x - 1) + ln(x + 1)
ln(x + 5) = ln(x - 1)(x + 1) [Since ln(a×b) = ln a + lnb]
(x + 5) = (x- 1)(x + 1)
x + 5 = x² - 1
x² - x - 6 = 0
x² - 3x + 2x - 6 = 0
x(x - 3) + 2(x - 3) = 0
(x + 2)(x - 3 ) = 0
x = -2, 3
But x = -2 is an extraneous solution.
Therefore, x = 3 is the only solution.
2). [tex]e^{x^2}=e^{4x+5}[/tex]
x² = 4x +5
x² - 4x - 5 = 0
x² - 5x + x - 5 = 0
x(x - 5) + 1(x - 5) = 0
(x + 1)(x - 5) = 0
x = -1, 5
Therefore, solution set is (-1, 5)
3). [tex]\text{log}_4(5x^2+2)=\text{log}_4(x + 8)[/tex]
5x² + 2 = (x + 8)
5x² - x - 6 = 0
5x² - 6x + 5x - 6 = 0
x(5x - 6) + 1(5x - 6) = 0
(x + 1)(5x - 6) = 0
x = -1, [tex]\frac{6}{5}[/tex]
4). log(x - 1) + log5x = 2
log(x - 1)(5x) = 2
5x(x - 1) = 10² [if loga = b, [tex]a=10^{b}[/tex]]
5x² - 5x - 100 = 0
x² - x - 20 = 0
x² - 5x + 4x - 20 = 0
x(x - 5) + 4(x - 5) =0
(x - 5)(x + 4) = 0
x = -4, 5
But x = -4 is an extraneous solution.
Therefore, x = 5 is the only solution.
Evaluate the following:
Answer:
csc∅ = 25/7
sec∅ = 25/24
cot∅ = 24/7
Step-by-step explanation:
Cosecant (csc) is 1/sin∅ or hypotenuse over opposite
Secant (sec) is 1/cos∅ or hypotenuse over adjacent
Cotangent (cot) is 1/tan∅ or adjacent over opposite
Micah mixed 5 ounces of yellow paint with 11 ounces of blue paint. What is the ratio of blue paint to the total amount of paint that Micah used? Write the ratio using a colon and no spaces.
Answer: 11:16
Step-by-step explanation: 11 ounces of blue paint: the total number ounces of paint (adding blue and yellow)
Answer:
5:16
Step-by-step explanation:
The amount of blue paint is 5 oz
The total amount of paint is 16 oz
Make these numbers a ratio of blue to total
What is the equation of the given line in the point slope -form ?
Answer:
see below
Step-by-step explanation:
We are given two points (3,4) and (0,1)
so we can find the slope
m = ( y2-y1)/(x2-x1)
= (1-4)/(0-3)
= -3/-3
= 1
The point slope form is
( y-y1) = m(x-x1)
y - (4) = 1 (x-3)
y - (4) = (x-3)
or using the other point
y - 1 = 1( x-0)
y - 1 = x
I paid twice as much by not waiting for a sale and not ordering on line. Which ofthe following statements is also true?
(a) I paid 200% more than I could have online and on sale.
(b) I paid 100% of what I could have online and on sale.
(c) I paid 200% of what I could have online and on sale.
(d) I paid 3 times what I could have online and on sale.
Answer:
(c) I paid 200% of what I could have online and on sale.
Step-by-step explanation:
The multiplier for a increase of a% is 1 + a/100.
In this question:
You paid twice, which means that the multiplier is 2. So
a is the increase, as a percent.
[tex]1 + \frac{a}{100} = 2[/tex]
[tex]\frac{a}{100} = 1[/tex]
[tex]a = 100[/tex]
You had an increase of 100% on the price. Since the original amount was 100% you paid 100 + 100 = 200%(100% more, 2 times) of what you could have paid.
So the correct answer is:
(c) I paid 200% of what I could have online and on sale.
A random sample of 32 salespersons with a degree had an average weekly sale of $3599 last year, while 35 salespersons without a college degree averaged $3311 in weekly sales. The standard deviations were $468 and $642 respectively.
Required:
Is there evidence at the 5% level to support the retailer's belief?
Answer:
There is enough evidence to support the claim that the average sales are significantly greater for salespersons with a college degree than for salespersons without it.
Step-by-step explanation:
The question is incomplete:
"A national computer retailer believes that the average sales are greater for salespersons with a college degree. A random sample of 32 salespersons with a degree had an average weekly sale of $3599 last year, while 35 salespersons without a college degree averaged $3311 in weekly sales. The standard deviations were $468 and $642 respectively.
Required:
Is there evidence at the 5% level to support the retailer's belief?"
This is a hypothesis test for the difference between populations means.
The claim is that the average sales are significantly greater for salespersons with a college degree than for salespersons without it.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2> 0[/tex]
The significance level is 0.05.
The sample 1 (college degree), of size n1=32 has a mean of 3599 and a standard deviation of 468.
The sample 2 (non-college degree), of size n2=35 has a mean of 3311 and a standard deviation of 642.
The difference between sample means is Md=288.
[tex]M_d=M_1-M_2=3599-3311=288[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{468^2}{32}+\dfrac{642^2}{35}}\\\\\\s_{M_d}=\sqrt{6844.5+11776.114}=\sqrt{18620.614}=136.4574[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{288-0}{136.4574}=\dfrac{288}{136.4574}=2.11[/tex]
The degrees of freedom for this test are:
[tex]df=n_1+n_2-2=32+35-2=65[/tex]
This test is a right-tailed test, with 65 degrees of freedom and t=2.11, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t>2.11)=0.019[/tex]
As the P-value (0.019) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the average sales are significantly greater for salespersons with a college degree than for salespersons without it.
Can somebody help me with this question
Answer: [tex]x^{2} + 8x[/tex]
Step-by-step explanation:
In a triangle A = 1/2bh.
Thus, multiply 1/2 * 2x * (x+8)
x(x+8)
[tex]x^{2} + 8x[/tex]
Robert uses a wheelbarrow to haul wood from the back yard to his neighbor's house located 9 meters away. If he takes two breaks evenly when pushing the wheelbarrow to its destination, at which distance will he reach his first break?
Robert has 36 pieces to take, but can only take 9 each time. What distance in meters will he travel to move all the wood?
Answer:
3 meters
63 meters
Step-by-step explanation:
In order for his two breaks to occur after even distances, simply divide his total path in three:
[tex]B = \frac{9}{3}\\ B=3\ meters[/tex]
He will reach his first break after 3 meters.
If he can only take 9 pieces at a time the number of trips required is:
[tex]n=\frac{36}{9}\\ n=4[/tex]
Note that he will have to back to the back yard for the first three trips (traveling back the 9 meters path). The total distance traveled is:
[tex]d= 3*(9+9)+9\\d=63\ meters[/tex]
He will travel 63 meters.
What is the answer? X=
Answer:
5
Step-by-step explanation:
[tex] \because \triangle ACB \cong \triangle DCE... (given) \\
\therefore \angle A \cong \angle D... (c.a.c.t)\\
\therefore m\angle A = m\angle D\\
\therefore 50\degree = 10x\\\\
\therefore x = \frac{50\degree}{10}\\\\
\huge \orange {\boxed {\therefore x = 5\degree}} [/tex]