Answer:
The amount of dividend Giant Machinery can pay its shareholders this year = $136,250
The Dividend Payout ratio of the company = 54.50%
Ex-dividend price = $22.875
The current value of the firm's equity in total = $9196428.571
The current value of the firm's equity per share = $6.131
Step-by-step explanation:
Given that:
The Current Capital Structure = 65% equity and 35% debt.
The net income in the current year = $250,000
Also, the company is planning to launch a project that will requires an investment of $175,000 next year.
The current share price = $25/share
(a)
The first objective is to determine how much dividend Giant Machinery can pay its shareholders this year and what is dividend payout ratio of the company.
The amount of dividend Giant Machinery can pay its shareholders this year= Net profit - Investment amount × (percentage of equity)
= 250,000 - 175,000 × (65%)
= 250,000 - 113,750
= $136,250
The dividend payout ratio of the company.can be calculated as follows:
Dividend Payout ratio of the company [tex]= \mathbf{\dfrac{ total \ \ dividends}{total \ \ earning}}[/tex]
We all know that the net income in the current year is the Total Earning which is 250,000
Thus;
The Dividend Payout ratio of the company [tex]= \mathbf{\dfrac{ 136250}{250000}}[/tex]
The Dividend Payout ratio of the company = 0.545
The Dividend Payout ratio of the company = 54.50%
b).
If the company is paying a dividend of $2.50/share and tomorrow the stock will go ex-dividend.
Also, assuming:
the tax on dividend = 15%.
We are to calculate the ex-dividend price tomorrow morning.
To calculate the ex-dividend price tomorrow morning; we use the relation:
Ex-dividend price which is the result of the difference between the current price and dividend multiply by the difference between the 1 and the tax on the dividend
i.e
Ex-dividend pric = current price - Dividend × (1 - tax on dividend)
Given that :
The current share price = $25/share
Therefore;
Ex-dividend price = $25 - $2.5 × ( 1 - 15%)
Ex-dividend price = $25 - $2.5 × ( 1 - 0.15)
Ex-dividend price = $25 - $2.5 × 0.85
Ex-dividend price = $25 - $2.125
Ex-dividend price = $22.875
C)
From the information given in the part C of the question:
the company now plans to pays a total dividend of $2.5 million.= $ 2,500.000
Let say the year the dividend was paid was 0 year
and 7.5 million one year from now as a liquidating dividend.
So; the dividend paid in year 1 now = 7.5 million = $ 7,500,000
The required rate of return for shareholders is 12%
Outstanding share of the firm = 1.5 million = $1,500,000
We are to calculate the current value of the firm’s equity in total and per share if the firm has 1.5 million shares outstanding.
To start with the current value of the firm’s equity in total;
The current value of the firm's equity in total =[tex]\mathbf{amount \ of \ dividend \ paid \ in \ 0 \ year + \dfrac {amount \ of \ dividend \ paid \ in \ 1 \ year } { 1+required \ rate \ of \ return } }[/tex]= [tex]\mathbf{2,500,000 + \dfrac{7,500,000 }{1+ 0.12} }[/tex]
[tex]=\mathbf{2,500,000 + \dfrac{7,500,000 }{1.12} }[/tex]
= 2,500,000 + 6696428.571
= $ 9196428.571
The current value of the firm's equity per share =[tex]\mathbf{ \dfrac{ current \ value \ of \ the \ firm's \ equity \ in \ total}{ Outstanding \ share }}[/tex]
[tex]\mathbf{= \dfrac{9196428.571}{1500000}}[/tex]
= $6.130952381
≅ $6.131
The current value of the firm's equity per share = $6.131
find the product of 4025 multiply 5 by using properties
Answer:
Change 4020 to 4000 + 25.
Then use the distributive property.
4025 * 5 = (4000 + 25) * 5 = 4000 * 5 + 25 * 5 = 20,000 + 125 = 20,125
explain why the solution to the absolute value inequality |4x-9|>-12 is all real numbers
Answer:
Step-by-step explanation:
Hello,
by definition the absolute value is always positive
so |4x-9| >= 0
so the equation |4x-9| > -12 is always true
so all real numbers are solution of this equation
hope this helps
There are 748 identical plastic chips numbered 1 through 748 in a box. What is the probability of reaching into the box and randomly drawing the chip numbered 513? Express your answer as a simplified fraction or a decimal rounded to four decimal places.
Answer:
1/748 or about 0.0013
Step-by-step explanation:
Since there is an exactly equal probability of drawing any of the chips, the probability of drawing the one numbered 513 is:
[tex]\dfrac{1}{748}\approx 0.0013[/tex]
Hope this helps!
Last month Maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. Let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. If she hiked a total of 90 miles, which equation can be used to find the number of times Maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x
Answer:
(C)90 – 10y = 5x
Step-by-step explanation:
Given:
x = number of times she hiked the 5-mile trail
Then, total Distance covered on the 5-mile trail =5xy = number of times she hiked the 10-mile trail
Then, total Distance covered on the 10-mile trail =10yMaria hikes a total of 90 miles
Therefore, total distance hiked can be represented by the equation:
5x+10y=90
Subtract 10y from both sides, we have:
5x=90-10y
This is option C.
Answer:
C
Step-by-step explanation:
Fill in the blanks.
In a normal distribution, ____________ percent of the data are above the mean, and___________ percent of the data are below the mean. Similarly, _____________ percent of all data points are within 1 standard deviation of the mean, ___________percent of all data points are within 2 standard deviations of the mean, and___________ percent are within 3 standard deviations of the mean.
Answer:
In a normal distribution, 50 percent of the data are above the mean, and 50 percent of the data are below the mean. Similarly, 68 percent of of all data points are within 1 standard deviation of the mean, 95 percent of all data points are within 2 standard deviations of the mean, and 99.7 percent are within 3 standard deviations of the mean.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
Also:
The normal distribution is symmetric, which means that 50% of the data is above the mean and 50% is below.
Then:
In a normal distribution, 50 percent of the data are above the mean, and 50 percent of the data are below the mean. Similarly, 68 percent of of all data points are within 1 standard deviation of the mean, 95 percent of all data points are within 2 standard deviations of the mean, and 99.7 percent are within 3 standard deviations of the mean.
In a normal distribution, 50 percent of the data are above the mean, and 50 percent of the data are below the mean. Similarly, 68 percent of all data points are within 1 standard deviation of the mean, 95 percent of all data points are within 2 standard deviations of the mean, and 99.9 percent are within 3 standard deviations of the mean.
The normal distribution is a probability distribution that is important in many areas. It is, in fact, a family of distributions of the same form, each with different location and scale parameters: the mean and standard deviation respectively. The standard normal distribution is the normal distribution with mean equal to zero, and standard deviation equal to one. The shape of its probability density function is similar to that of a bell.
Learn more in https://brainly.com/question/12421652
Helen wants to buy 8 boxes of crayons at $1.94 per box for the day care center that she runs estimate the total cost of the crayons
Answer: $16
Step-by-step explanation:
1.94 * 8 = 15.52
$15.52 rounds up to $16
Suppose that the thickness of one typical page of a book printed by a certain publisher is a random variable with mean 0.1 mm and a standard deviation of 0.002 mm. A new book will be printed on 500 sheets of this paper. Approximate the probability that the
Answer:
The probability that the thicknesses at the entire book will be between 49.9 mm and 50.1 mm is 0.97.
Step-by-step explanation:
The complete question is:
Suppose that the thickness of one typical page of a book printed by a certain publisher is a random variable with mean 0.1 mm and a standard deviation of 0.002 mm Anew book will be printed on 500 sheets of this paper. Approximate the probability that the thicknesses at the entire book (excluding the cover pages) will be between 49.9 mm and 50.1 mm. Note: total thickness of the book is the sum of the individual thicknesses of the pages Do not round your numbers until rounding up to two. Round your final answer to the nearest hundredth, or two digits after decimal point.
Solution:
According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sum of values of X, i.e S, will be approximately normally distributed.
Then, the mean of the distribution of the sum of values of X is given by,
[tex]\mu_{S}=n\mu[/tex]
And the standard deviation of the distribution of the sum of values of X is given by,
[tex]\sigma_{S}=\sqrt{n}\sigma[/tex]
The information provided is:
[tex]n=500\\\mu=0.1\\\sigma=0.002[/tex]
As n = 500 > 30, the central limit theorem can be used to approximate the total thickness of the book.
So, the total thickness of the book (S) will follow N (50, 0.045²).
Compute the probability that the thicknesses at the entire book will be between 49.9 mm and 50.1 mm as follows:
[tex]P(49.9<S<50.1)=P(\frac{49.9-50}{0.045}<\frac{S-E(S)}{SD(S)}<\frac{50.1-50}{0.045})[/tex]
[tex]=P(-2.22<Z<2.22)\\\\=P (Z<2.22)-P(Z<-2.22)\\\\=0.98679-0.01321\\\\=0.97358\\\\\approx 0.97[/tex]
Thus, the probability that the thicknesses at the entire book will be between 49.9 mm and 50.1 mm is 0.97.
0.5(repeated)+0.1(repeated)-0.3(repeated)?
Answer:
[tex]\dfrac{1}{3}=0.\overline{3}[/tex]
Step-by-step explanation:
Since a single digit is repeated in each case, and since the repeat starts at the decimal point, the fraction corresponding to the repeated digit is that digit divided by 9.
[tex]0.\overline{5}+0.\overline{1}-0.\overline{3}=\dfrac{5}{9}+\dfrac{1}{9}-\dfrac{3}{9}=\dfrac{5+1-3}{9}=\dfrac{3}{9}\\\\=\boxed{\dfrac{1}{3}}[/tex]
_____
Comment on equivalents to repeating decimals
The number of 9s in the denominator equals the number of repeated digits.
0.2727(repeated) = 27/99 = 3/11 . . . . . 2 repeated digits
Find the length of a rectangle with a diagonal of 10 and a height of 8.
Answer:
The length of the rectangle is 6.
Step-by-step explanation:
Given: The diagonal of a rectangle is 10 and the height is 8.
Please understand, that a diagonal, divides the rectangle into two tringles.
To find the length of the rectangle, you can use Pythagoras on one of the right sided triangles, because the length of the triangle, is also the length of the rectangle!
EXTRA:
If you know the special 3 4 5 triangle, a so called Pythagorean Triple, then you can "see" the simularity between the numbers.
Instead of 5, a diagonal of 10 is given (factor of 2 bigger).
Instead of 4, the height of 8 is given (factor of 2 bigger). By scaling the Pythagorean Triple 3 4 5 by a factor of 2, you get the numbers 6 8 10. Could it be, that the number we need to find, is six?
Try to verify, by calculating the missing number (which is the length of the rectangle we are looking for).
a² + b² = c²
a = length (and is unknown)
b = height = 8
c = hypothenusa/diagonal = 10
Substitute the numbers given:
a² + 8² = 10²
Subtract 8² left and right of the = sign.
a² +8² -8² = 10² - 8²
a² + 0 = 100 - 64
a² = 36
a = + - √36
a = + - 6
EXTRA:
You can ignore the -√36 = -6 part of the solution, because a length of -6 has no meaning here.
a = 6
So, the length of the triangle is 6 and thus, the length of the rectangle is also 6.
The amount of saturated fat in a daily serving of a particular brand of breakfast cereal is normally distributed with mean 25 g and standard deviation 4 g.
a. Find the sampling distribution of the daily average saturated fat intake over a 30-day period (one month). Include the mean and standard deviation in your answer, as well as the name of the distribution.
b. What is the probability that the average daily saturated fat intake for the month was more than 27 g?
Answer:
a) [tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}}) [/tex]
And replacing we got:
[tex]\bar X \sim N(\mu=25, \frac{4}{\sqrt{30}}= 0.730) [/tex]
b) [tex] z =\frac{27-25}{\frac{4}{\sqrt{30}}}= 2.739[/tex]
And using the normal standard distribution table and the complement rule we got:
[tex] P(z>2.739) =1- P(z<2.739) = 1-0.997= 0.003[/tex]
Step-by-step explanation:
From the info given if we define the random variable X as "amount of saturated fat in a daily serving of a particular brand of breakfast cereal " we know that the distribution of X is given by:
[tex] X \sim N(\mu =25, \sigma =4)[/tex]
Part a
For this case the sample size would be n =30 and then the distribution for the sample mean would be given by:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}}) [/tex]
And replacing we got:
[tex]\bar X \sim N(\mu=25, \frac{4}{\sqrt{30}}= 0.730) [/tex]
Part b
We want to find this probability:
[tex] P(\bar X >27)[/tex]
And we can use the z score formula given by:
[tex] z=\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And replacing we got:
[tex] z =\frac{27-25}{\frac{4}{\sqrt{30}}}= 2.739[/tex]
And using the normal standard distribution table and the complement rule we got:
[tex] P(z>2.739) =1- P(z<2.739) = 1-0.997= 0.003[/tex]
The weight of an organ in adult males has a bell shaped distribution with a mean of 325 grams and a standard deviation of 50 grams. (A) about 99.7% of organs will be between what weights? (B) what percentage of organs weighs between 275 grams and 375? (C) what percentage of organs weighs between 275 grams and 425 grams?
Answer:
A)
The number of weights of an organ in adult males = 374.85
B)
The percentage of organs weighs between 275 grams and 375
P(275≤x≤375) = 0.6826 = 68%
C)
The percentage of organs weighs between 275 grams and 425
P(275≤x≤375) = 0.8185 = 82%
Step-by-step explanation:
A)
Step(i):-
Given mean of the normal distribution = 325 grams
Given standard deviation of the normal distribution = 50 grams
Given Z- score = 99.7% = 0.997
[tex]Z = \frac{x-mean}{S.D} = \frac{x-325}{50}[/tex]
[tex]0.997 = \frac{x-325}{50}[/tex]
Cross multiplication , we get
[tex]0.997 X 50= x-325[/tex]
x - 325 = 49.85
x = 325 + 49.85
x = 374.85
The number of weights of an organ in adult males = 374.85
Step(ii):-
B)
Let X₁ = 275 grams
[tex]Z_{1} = \frac{x_{1} -mean}{S.D} = \frac{275-325}{50} = -1[/tex]
Let X₂ = 375 grams
[tex]Z_{2} = \frac{x_{2} -mean}{S.D} = \frac{375-325}{50} = 1[/tex]
The probability of organs weighs between 275 grams and 375
P(275≤x≤375) = P(-1≤Z≤1)
= P(Z≤1)- P(Z≤-1)
= 0.5 + A(1) - ( 0.5 - A(-1))
= A(1) + A(-1)
= 2 A(1)
= 2 × 0.3413
= 0.6826
The percentage of organs weighs between 275 grams and 375
P(275≤x≤375) = 0.6826 = 68%
C)
Let X₁ = 275 grams
[tex]Z_{1} = \frac{x_{1} -mean}{S.D} = \frac{275-325}{50} = -1[/tex]
Let X₂ = 425 grams
[tex]Z_{2} = \frac{x_{2} -mean}{S.D} = \frac{425-325}{50} = 2[/tex]
The probability of organs weighs between 275 grams and 425
P(275≤x≤425) = P(-1≤Z≤2)
= P(Z≤2)- P(Z≤-1)
= 0.5 + A(2) - ( 0.5 - A(-1))
= A(2) + A(-1)
= A(2) + A(1) (∵A(-1) =A(1)
= 0.4772 + 0.3413
= 0.8185
The percentage of organs weighs between 275 grams and 425
P(275≤x≤375) = 0.8185 = 82%
A large school district notices that about 26% of its sophomore students fail Algebra I. An online education supplier suggests the district try its new technology software, which is designed to improve Algebra 1 skills and, thus, decrease the number of students who fail the course. The new technology software is quite expensive, so the company offers a free, one-year trial period to determine whether the Algebra 1 pass rate improves. If it works, the district will pay for continued use of the software. What would happen if the school district makes a Type I error
Answer:
In the case of a Type I error, the null hypothesis would be wrongly rejected and the school district will conclude that the new technology is effective when it is not.
They will start to pay for the software when in fact it does not improve Algebra 1 skills.
Step-by-step explanation:
A Type I error happens when a true null hypothesis is rejected.
The probability of a Type I error is equal to the significance level, as it is the probabilty of getting an sample result with low probability but only due to chance, as the null hypothesis is in fact true.
In this scenario, the null hypothesis would represent the claim that the new technology does not make significant improvement.
In the case of a Type I error, this null hypothesis would be wrongly rejected and the school district will conclude that the new technology is effective when it is not.
They will start to pay for the software when in fact it does not improve Algebra 1 skills.
100 POINTS!!!!! PlZ help Find all possible values of the digits Y, E, A, R if YYYY - EEE + AA - R = 1234, and different letters represent different digits.
Answer:
Y = 1, E = -1, A= 1, R = -1
Step-by-step explanation:
YYYY - EEE + AA - R = 1234
First we would break down the digits in the whole numbers into their place value (thousands, hundreds, tens and units).
YYYY = 1000Y + 100Y +10Y + Y
EEE = 100E + 10E + E
-EEE = -100E - 10E - E
AA = 10A + A
R = R
-R = -R
1234 = 1000+200+30+4
Let's equate each place value for each of the numbers.
Thousands: 1000Y = 1000
Y = 1000/1000 = 1
Hundreds: 100Y - 100E = 200
100(1) - 100E = 200
-100E = 200-100
-100E= 100
E = -1
-EEE = -E(111)
Tens: 10Y - 10E + 10A = 30
10(1) - 10(-1) + 10A = 30
20+ 10A = 30
A = 10/10
A= 1
Units: Y - E + A - R = 4
1 - (-1) + 1 - R = 4
3-R = 4
R = 3-4 = -1
YYYY - EEE + AA - R = 1234
1111 - (-111) + 11 - (-1) = 1111+111+11+1 = 1234
All possible values of the digits Y, E, A, R are Y = 1, E = -1, A= 1, R = -1
Answer:
Y=2
E=9
A=1
R=0
Step-by-step explanation:
Let's check our work.
2,222 - 999 + 11 - 0
1,223 + 11 - 0
1,234 - 0
1,234
Also previous answerer how can digits be negative?
A pound contains 9.4 cubic yards of water. What is
the volume of the water in cubic meters to the nearest
tenth?
A. 12.3
B. 8.6
C. 10.3
D. 7.2
Answer:
the answer is 7.2
Step-by-step explanation:
Please answer this correctly
Answer:
[tex]50\%, \: 40\%, \: 10\%[/tex]
Step-by-step explanation:
[tex]150:120:30[/tex]
[tex]5:4:1[/tex]
[tex]\frac{100}{5+4+1}[/tex]
[tex]=\frac{100}{10}[/tex]
[tex]=10[/tex]
[tex]5 \times 10:4\times 10:1\times 10[/tex]
[tex]50:40:10[/tex]
Answer:
Cupcakes: 50%
Cookies: 40%
Cakes: 10%
Step-by-step explanation:
150 + 120 + 30 = 300 (there are 300 baked goods)
150 out of 300 = 50%
120 out of 300 = 40%
30 out of 300 = 10%
Okay, I really want to eat this.
Hope it helps!
Question 6 of 25
2 Points
Which of the following would be a good name for the function that takes the
weight of a box and returns the energy needed to lift it?
A. Box(cost)
B. Weight(energy)
C. Weight(box)
D. Energy(weight)
Answer:
C
Step-by-step explanation:
because you need the energy of the box to lift it, as my old professor used to say " you can only push on somthing as much as it can push you back "
Answer:
D. energy(weight) is the correct answer
hope this helps
For the following parameterized curve, find the unit tangent vector T(t) at the given value of t. r(t) = < 8 t,10,3 sine 2 t >, for 0
Answer:
The tangent vector for [tex]t = 0[/tex] is:
[tex]\vec T (t) = \left \langle \frac{8}{10}, 0, \frac{6}{10} \right\rangle[/tex]
Step-by-step explanation:
The function to be used is [tex]\vec r(t) = \langle 8\cdot t, 10, 3\cdot \sin (2\cdot t)\rangle[/tex]
The unit tangent vector is the gradient of [tex]\vec r (t)[/tex] divided by its norm, that is:
[tex]\vec T (t) = \frac{\vec \nabla r (t)}{\|\vec \nabla r (t)\|}[/tex]
Where [tex]\vec \nabla[/tex] is the gradient operator, whose definition is:
[tex]\vec \nabla f (x_{1}, x_{2},...,x_{n}) = \left\langle \frac{\partial f}{\partial x_{1}}, \frac{\partial f}{\partial x_{2}},...,\frac{\partial f}{\partial x_{n}} \right\rangle[/tex]
The components of the gradient function of [tex]\vec r(t)[/tex] are, respectively:
[tex]\frac{\partial r}{\partial x_{1}} = 8[/tex], [tex]\frac{\partial r}{\partial x_{2}} = 0[/tex] and [tex]\frac{\partial r}{\partial x_{3}} = 6 \cdot \cos (2\cdot t)[/tex]
For [tex]t = 0[/tex]:
[tex]\frac{\partial r}{\partial x_{1}} = 8[/tex], [tex]\frac{\partial r}{\partial x_{2}} = 0[/tex] and [tex]\frac{\partial r}{\partial x_{3}} = 6[/tex]
The norm of the gradient function of [tex]\vec r (t)[/tex] is:
[tex]\| \vec \nabla r(t) \| = \sqrt{8^{2}+0^{2}+ [6\cdot \cos (2\cdot t)]^{2}}[/tex]
[tex]\| \vec \nabla r(t) \| = \sqrt{64 + 36\cdot \cos^{2} (2\cdot t)}[/tex]
For [tex]t = 0[/tex]:
[tex]\| \vec r(t) \| = 10[/tex]
The tangent vector for [tex]t = 0[/tex] is:
[tex]\vec T (t) = \left \langle \frac{8}{10}, 0, \frac{6}{10} \right\rangle[/tex]
Find the exact value of each of the following under the given conditions.
a. cosine left parenthesis alpha plus beta right parenthesis b. sine left parenthesis alpha plus beta right parenthesis c. tangent left parenthesis alpha plus beta right parenthesis
tangent alpha equals one half
, pi less than alpha less than StartFraction 3 pi Over 2 EndFraction
, and cosine beta equals three fifths
, StartFraction 3 pi Over 2 EndFraction less than beta less than 2 pi
Answer:
[tex](a)-\dfrac{11\sqrt{5}}{25} \\(b) -\dfrac{2\sqrt{5}}{25} \\(c)\dfrac{11}{2}[/tex]
Step-by-step explanation:
[tex]\tan \alpha =\dfrac12, \pi < \alpha< \dfrac{3 \pi}{2}[/tex]
Therefore:
[tex]\alpha$ is in Quadrant III[/tex]
Opposite = -1
Adjacent =-2
Using Pythagoras Theorem
[tex]Hypotenuse^2=Opposite^2+Adjacent^2\\=(-1)^2+(-2)^2=5\\Hypotenuse=\sqrt{5}[/tex]
Therefore:
[tex]\sin \alpha =-\dfrac{1}{\sqrt{5}}\\\cos \alpha =-\dfrac{2}{\sqrt{5}}[/tex]
Similarly
[tex]\cos \beta =\dfrac35, \dfrac{3 \pi}{2}<\beta<2\pi\\\beta $ is in Quadrant IV (x is negative, y is positive), therefore:\\Adjacent=$-3\\$Hypotenuse=5\\Opposite=4 (Using Pythagoras Theorem)[/tex]
[tex]\sin \beta =\dfrac{4}{5}\\\tan \beta =-\dfrac{4}{3}[/tex]
(a)
[tex]\cos(\alpha + \beta)=\cos\alpha\cos\beta-\sin \alpha\sin \beta\\[/tex]
[tex]=-\dfrac{2}{\sqrt{5}}\cdot \dfrac{3}{5}-(-\dfrac{1}{\sqrt{5}})(\dfrac{4}{5})\\=-\dfrac{2\sqrt{5}}{5}\cdot \dfrac{3}{5}+\dfrac{\sqrt{5}}{5}\cdot\dfrac{4}{5}\\=-\dfrac{2\sqrt{5}}{25}[/tex]
(b)
[tex]\sin(\alpha + \beta)=\sin\alpha\cos\beta+\cos \alpha\sin \beta[/tex]
[tex]\sin(\alpha + \beta)=\sin\alpha\cos\beta+\cos \alpha\sin \beta\\=-\dfrac{1}{\sqrt{5}}\cdot\dfrac35+(-\dfrac{2}{\sqrt{5}})(\dfrac{4}{5})\\=-\dfrac{\sqrt{5}}{5}\cdot\dfrac35-\dfrac{2\sqrt{5}}{5}\cdot\dfrac{4}{5}\\=-\dfrac{11\sqrt{5}}{25}[/tex]
(c)
[tex]\tan(\alpha + \beta)=\dfrac{\sin(\alpha + \beta)}{\sin(\alpha + \beta)}=-\dfrac{11\sqrt{5}}{25} \div -\dfrac{2\sqrt{5}}{25} =\dfrac{11}{2}[/tex]
WORK OUT THE VALUE of 19+7⌹2-5
Answer:
17.5
Step-by-step explanation:
Remember PEMDAS
step 1 : divide 7 by 2
7 ÷ 2 = 3.5
step 2 : rewrite the equation
19 + 3.5 - 5
step 3 : add 19 + 3.5
19 + 3.5 = 22.5
step 4 : subtract 22.5 - 5
22.5 - 5 = 17.5
Which number is a perfect cube?
O 25
O 36
O 125
O 300
Answer:
125
Step-by-step explanation:
[tex]25=5^2[/tex]
[tex]36=6^2[/tex]
[tex]125=5^3[/tex]
[tex]300=...[/tex]
A company makes concrete bricks shaped like rectangular prisms. Each brick is 13 inches long, 5 inches wide, and 4 inches tall. If they used 11,700 in^3 of concrete, how many bricks did they make?
Answer:
45 bricks
Step-by-step explanation:
First we need to find the volume of one brick. The bricks are rectangular prisms. The volume formula for rectangular prisms is:
V=l*w*h
The bricks are 13 inches long, 5 inches wide and 4 inches high.
l=13 inches
w=5 inches
h=4 inches
V= 13 inches * 5 inches * 4 inches
V=65 inches^2 * 4 inches
V=260 inches ^3
Each brick has a volume of 260 inches^3. We know they used a total of 11,700 inches^3 of concrete. The question asks us to find how many bricks they made. We must divide the volume of concrete used by the volume of one brick.
concrete volume / one brick volume
concrete volume= 11,700 in^3
one brick volume= 260 in^3
11,700 in^3 / 260 in^3
11,700/260
45
They made 45 bricks.
Identify the polygon that has vertices A(−10,−1), P(−7,3), E(−3,0), and X(−6,−4), and then find the perimeter and area of the polygon.
Answer:
square; perimeter 20 units; area 25 square units.
Step-by-step explanation:
As the attachment shows, each side of the polygon is the hypotenuse of a 3-4-5 right triangle, so has length 5 units. The perimeter is the sum of those lengths, 4×5 = 20; the area is the product of the lengths of adjacent sides, 5×5 = 25.
The figure is a square of side length 5 units.
The perimeter is 20 units; the area is 25 square units.
Suppose the speeds of vehicles traveling on a highway are normally distributed and have a known population standard deviation of 7 miles per hour and an unknown population mean. A random sample of 32 vehicles is taken and gives a sample mean of 64 miles per hour. Find the margin of error for the confidence interval for the population mean with a 98% confidence level.
Answer:
2.88
Step-by-step explanation:
Data provided in the question
[tex]\sigma[/tex] = Population standard deviation = 7 miles per hour
Random sample = n = 32 vehicles
Sample mean = [tex]\bar X[/tex] = 64 miles per hour
98% confidence level
Now based on the above information, the alpha is
= 1 - confidence level
= 1 - 0.98
= 0.02
For [tex]\alpha_1_2[/tex] = 0.01
[tex]Z \alpha_1_2[/tex] = 2.326
Now the margin of error is
[tex]= Z \alpha_1_2 \times \frac{\sigma}{\sqrt{n}}[/tex]
[tex]= 2.326 \times \frac{7}{\sqrt{32}}[/tex]
= 2.88
hence, the margin of error is 2.88
Answer:
2.879 (rounded 3 decimal places)
Step-by-step explanation:
How many of these equations have the solution
x
=
12
x
=
12
?
x
−
2
=
10
x
−
2
=
10
x
2
=
24
x
2
=
24
10
−
x
=
2
10
−
x
=
2
2x1=25
2x−1=25
Answer:
a)x−2=10
b) 2x=24
Two equations have have the solution
x = 12
Question:
How many of these equations have the solution x=12 ?
x−2=10
2x=24
10−x=2
2x−1=25
Step-by-step explanation:
To determine which of the above equations have x= 12, we would solve for x in each of the equations.
a) x−2=10
Collecting like terms
x = 10+2
x = 12
This equation has x= 12 as a solution
b) 2x =24
Divide through by coefficient of x which is 2
2x/2 = 24/2
x = 12
This equation has x= 12 as a solution
c) 10−x=2
Collecting like terms
10-2 - x = 0
8 - x = 0
x = 8
d) 2x−1=25
Collecting like terms
2x = 25+1
2x = 26
Divide through by coefficient of x which is 2
2x/2 = 26/2
x = 13
Note: that (b) x2 = 24 from the question isn't clear enough. I used 2x = 24.
If x2 = 24 means x² = 24
Then x = √24 = √(4×6)
x = 2√6
Then the number of equations that have the solution x = 12 would be 1. That is (a) x−2=10 only
Answer:
1/2x + 12 >10
Step-by-step explanation:
Can someone plz help me solved this problem I need help ASAP plz help me! Will mark you as brainiest!
Answer:
A = 1.02 P
Step-by-step explanation:
A = P + 0.02P
Formula in Factorized form
(Taking P common)
A = P(1+0.02) [The required factorized from]
Then,
A = 1.02 P
Help asap giving branlist!!
Answer:
the answer is right below the picture sir ;-;
Step-by-step explanation:
Assume A, B, P, and D are n times n matrices. Determine whether the following statements are true or false. Justify each answer.
A matrix A is diagonalizable if A has n eigenvectors.
The statement is false. A matrix is diagonalizable if and only if it has n -1 linearly independent eigenvectors.
The statement is true. A diagonalizable matrix must have more than one linearly independent eigenvector.
The statement is true. A diagonalizable matrix must have a minimum of n linearly independent eigenvectors.
The statement is false. A diagonalizable matrix must have n linearly independent eigenvectors.
If A is diagonalizable, then A has n distinct eigenvalues.
The statement is false. A diagonalizable matrix can have fewer than n eigenvalues and still have n linearly independent eigenvectors.
The statement is true. A diagonalizable matrix must have n distinct eigenvalues.
The statement is false. A diagonalizable matrix must have more than n eigenvalues.
The statement is true. A diagonalizable matrix must have exactly n eigenvalues.
If AP = PD, with D diagonal, then the nonzero columns of P must be eigenvectors of A.
The statement is true. AP = PD implies that the columns of the product PD are eigenvalues that correspond to the eigenvectors of A.
The statement is false. If P has a zero column, then it is not linearly independent and so A is not diagonalizable.
The statement is true. Let v be a nonzero column in P and let lambda be the corresponding diagonal element in D. Then AP = PD implies that Av = lambda v, which means that v is an eigenvector of A.
The statement is false. AP = PD cannot imply that A is diagonalizable, so the columns of P may not be eigenvectors of A.
Answer:
The correct answers are (1) Option d (2) option a (3) option a
Step-by-step explanation:
Solution
(1) Option (d) The statement is false. A diagonalizable matrix must have n linearly independent eigenvectors: what it implies is that a matrix is diagnostic if it has linearity independent vectors.
(2) Option (a) The statement is false. A diagonalizable matrix can have fewer than n eigenvalues and still have n linearly independent eigenvectors: what this implies is that a diagonalizable matrix can have repeated eigenvalues.
(3) option (a) The statement is true. AP = PD implies that the columns of the product PD are eigenvalues that correspond to the eigenvectors of A : this implies that P is an invertible matrix whose column vectors are the linearity independent vectors of A.
PLEASE HELP MEH RN!!!
Answer:
its 4x
Step-by-step explanation:
Answer:
4x
Step-by-step explanation:
Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n.
4 0 x3 sin(x) dx, n = 8
Answer:
trapezoidal rule: -7.28midpoint rule: -4.82Simpson's rule: -5.61Step-by-step explanation:
The interval from 0 to 4 is divided into 8 equal parts, so each has a width of 0.5 units. For the trapezoidal and Simpson's rules, the function is evaluated at each end of each interval, and those results are combined in the manner specified by the rule.
__
For the trapezoidal rule, the function values are taken as the "bases" of trapezoids, whose "height" is the interval width. The estimate of the integral is the sum of the areas of these trapezoids.
__
For the midpoint rule, the function is evaluated at the midpoint of each interval, and that value is multiplied by the interval width to form an estimate of the integral over the interval. In the spreadsheet, midpoints and their function values are listed separately from those used for the other rules. The midpoint area is the rectangle area described here.
__
For Simpson's rule, the function values at the ends of each interval are combined with weights of 1, 2, or 4 in a particular pattern. The sum of products is multiplied by 1/3 the interval width. In the spreadsheet, the weights are listed so the SUMPRODUCT function could be used to create the desired total.
We note the Simpson's rule estimate of the integral (-5.61) is very close, as the actual value rounds to -5.64.
___
A graph of the function and a computation of the integral is shown in the second attachment.
a personality test maybe given to assess what
Answer:
A personality test may be given to assess individual behavior patterns. A personality test may be given to assess individual behavior patterns. This answer has been confirmed as correct and helpful.
Step-by-step explanation:
hopes this helps
Answer:
Interests, values, skill set and basic personality
Step-by-step explanation:
Personality tests are mostly used as an assessment tool be HR managers and employers during the interview process. They can provide a potential employer with information about your interests, values, skill set and even basic personality, which can be very useful to help an employer make a decision about whether you are the best fit for a position.
I hope this helped. I am sorry if you get this wrong.