Calculate the principal if the maturity value is $4,500 and the simple interest is $350.

Answer:

(0, 0) is a saddle point

(1, 1) is a local minimum

(-1, -1) is another point  of local minimum

Step-by-step explanation:

We first locate the critical points. In order to get the critical points we need to find the first derivatives and then set them to zero.

f(x, y) = x⁴ + y⁴ - 4 xy + 1  

Find the first derivatives wrt to x and y

[tex]f_{x}(x,y)[/tex] = 4x ³ - 4y  --> (1)

[tex]f_{y}(x,y)[/tex] = 4y³ - 4x  --> (2)

Solve (1) for y

4x ³ - 4y = 0

x ³ = y

y = x ³ ---> (3)

Solve (2) for x

4y³ - 4x = 0

4y³ = 4x

y³ = x

x = y³  ----> (4)

Plug  (3) into (2)

4y³ - 4x

4(x ³)³ - 4x = 0

4x⁹ - 4x = 0

4x (x ⁸ - 1) = 0

4x (x ⁴ - 1)(x⁴  + 1) = 0

4x (x ² - 1)(x ² + 1)(x ⁴ + 1) = 0

4x (x - 1)(x + 1)(x ² + 1)(x ⁴ + 1) = 0

So

x = 1 , -1 , 0

In order to find values of y, Plug each x value in (3)

For

x = 0

corresponding y value

y = x ³

y = 0 ³

y = 0

For

x = 1

y = x ³

y = 1 ³

y = 1

For

x = -1

y = x ³

y = (-1 )³

y = -1

Hence we get the critical points which are:

(0, 0)

(1, 1)  and

(-1, -1)

Now for each critical point, we have to compute D(x,y)

For a critical point (x,y), D computed as:

D(x, y) = [tex]f_{xx}[/tex] (x, y) - [tex]f_{yy}[/tex] (x, y) - ([tex]f_{xy}[/tex] (x, y))²

After computing D(x,y) check:

If D(x, y) > 0 and [tex]f_{xx}[/tex] (x, y) > 0:

f(x, y) is a local minimum.

If D(x, y) > 0 and  [tex]f_{xx}[/tex] (x, y) < 0:

f(x, y) is a local maximum.

If D(x, y) < 0:

then f(x, y) is a saddle point

Here first compute the second derivative in order to get  [tex]f_{xx}[/tex] ,  [tex]f_{yy}[/tex] and [tex]f_{xy}[/tex]

we have already computed:

[tex]f_{x}(x,y)[/tex] = 4x ³ - 4y  --> (1)

[tex]f_{y}(x,y)[/tex] = 4y³ - 4x  --> (2)

Now

[tex]f_{xx}(x,y)[/tex]  = 12x²

[tex]f_{yy}(x,y)[/tex]  = 12y²

[tex]f_{xy}(x,y)[/tex]  = -4

Compute D(x,y)

Critical Point (0, 0):

[tex]D(0, 0) = f_{xx} (0,0) f_{yy}(0,0)-(f_{xy}(0,0))^{2}[/tex]

Putting values of  [tex]f_{xx}(x,y)[/tex] , [tex]f_{yy}(x,y)[/tex] and [tex]f_{xy}(x,y)[/tex] in above equation:

D(0,0) = 12(0)² * 12(0)² - (-4)²

          = 0 * 0 -16

D(0,0) = -16

We know that if D < 0, the critical point f(x, y) is a saddle point.

D(0,0) < 0 because D(0,0) = -16

Hence (0, 0) is a saddle point

Compute D(x,y)

Critical Point (1, 1):

[tex]D(1, 1) = f_{xx} (1,1) f_{yy}(1,1)-(f_{xy}(1,1))^{2}[/tex]

Putting values of  [tex]f_{xx}(x,y)[/tex] , [tex]f_{yy}(x,y)[/tex] and [tex]f_{xy}(x,y)[/tex] in above equation:

D(1,1) = 12(1)² * 12(1)² - (-4)²

        = 12 * 12 - 16

D(1,1) = 128

We know that if D(x, y) > 0 and [tex]f_{xx}[/tex] (x, y) > 0 then f(x, y) is a local minimum.

D(1,1) > 0 because D(1,1) = 128

[tex]f_{xx}[/tex] (x, y) > 0 because  [tex]f_{xx}[/tex] (x, y) = 12

Hence (1,1) is the local minimum

Compute D(x,y)

Critical Point (-1, -1):

[tex]D(-1, -1) = f_{xx} (-1,-1) f_{yy}(-1,-1)-(f_{xy}(-1,-1))^{2}[/tex]

Putting values of  [tex]f_{xx}(x,y)[/tex] , [tex]f_{yy}(x,y)[/tex] and [tex]f_{xy}(x,y)[/tex] in above equation:

D(-1,-1) = 12(-1)² * 12(-1)² - (-4)²

          = 12 * 12 - 16

D(-1,-1) = 128

We know that if D(x, y) > 0 and [tex]f_{xx}[/tex] (x, y) > 0 then f(x, y) is a local minimum.

D(-1,-1) > 0 because D(-1,-1) = 128

[tex]f_{xx}[/tex] (x, y) > 0 because  [tex]f_{xx}[/tex] (x, y) = 12

Hence (-1,-1) is the local minimum

Answer: 0.47

Step-by-step explanation:

Given that

n = 100, probability of rolling 1 = 1/6

binomial approximation

np = 100 ( 1/6) = 16.667

standard deviation = √ 100 × 1/6 ×5/6 = 3.7627

P ( 9 ≤ X ≤ 16 )

= P ( 8.5 < X < 16.5 )

so,

= P ((8.5 - 16.6667) / 3.7627 < Z < (16.5 - 16.6667) / 3.7627

= P ( -2.17 < Z < -0.04 )

= 0.484 - 0.015

= 0.47

Therefore the approximate probability that you will roll between 9 and 16 ones is 0.47

Answer:

6214

Step-by-step explanation:

you round up 62 and 4 20 times and that is your answer but for give me if this answer wrong

Answer:

The best and most correct answer among the choices provided by the question is

The statement that points out his most serious omission is "What if the electric bill increases?".

Step-by-step explanation:

Answer:

-70[tex]\frac{73}{100}[/tex]

Hope It Help

Multiply by [tex]A^{-1}[/tex] on the right of both sides of [tex]A^3=I[/tex], then use the fact that matrix multiplication is associative.

If [tex]A^3=I[/tex], then

[tex]A^3A^{-1}=IA^{-1}[/tex]

[tex]A^2(AA^{-1})=A^{-1}[/tex]

[tex]A^2I=A^{-1}[/tex]

[tex]\implies A^2=A^{-1}[/tex]

Answer:

[tex] \boxed{\sf Amount \ of \ food \ each \ elephant \ receive = 510 \ pounds} [/tex]

Given:

Total amount of food = 3,570 pounds

Total number of elephants = 7

To Find:

Amount of food each elephant receive

Step-by-step explanation:

7 elephants receive = 3,570 pounds

[tex] \sf 1 \: elephant \: receive = \frac{3570}{7} \: pounds[/tex]

= 510 pounds

So,

Amount of food each elephant receive = 510 pounds

Answer:

The  correct option is   b

Step-by-step explanation:

From the question we are told that

   The  sample size is  [tex]n = 100[/tex]

    The  population  mean is  [tex]\mu = 2.5[/tex]

   The  sample  standard deviation is  [tex]\sigma = 0.2[/tex]

Generally the mean of the sampling distribution of sample means is mathematically represented as

       [tex]\mu_{\= x } = \mu[/tex]

=>    [tex]\mu_{\= x } = 2.5[/tex]

Answer:

Step-by-step explanation:

Given that:

The mean μ = 310

The standard deviation σ =  40

Using the empirical rule to determine the following :

a. About 95 % of organs will be between what weights?

At 95% data values lies within 2 standard deviations of mean.

Thus, the  required range is :

= μ ± 2σ

= ( 310 - 2 (40) ,  310 + 2(40) )  

= (230, 390)

b. What percentage of organs weighs between 270 grams and 350 grams

Here:

μ ± σ = (310 - 40,  310 + 40)

μ ± σ = (270, 350)

Using empirical rule, 68% data values is in the range within 1 standard deviation of mean. This implies that 68% data values lie between (270, 350).

c. What percentage of organs weighs less than 270 grams or more than 350 grams?

The complement theorem can be use to estimate the  percentage of organs that weighs less than 270 grams or more than 350 grams,

This can be illustrated as :

= 100 % - 68 %

= 32 %

d. What percentage of organs weighs between 230 grams and 430 grams?

Using the empirical rule:

The percentage of organs weighs between 230 grams and 430 grams is:

u - 2σ  and  u + 3σ respectively.

Answer:

Amount after 10 years is $1472.775

Step-by-step explanation:

Amy deposited $750 in a saving account that pays 6.75% Interest compounded monthly for 10 years.

Principal amount= $750

Rate of interest= 6.75%

Time= 10 years

Number of times compounded= 10*12

Number of times compounded= 120

A= p(1+r/n)^(nt)

A= 750(1+0.0675/120)^(120*10)

A= 750(1+0.0005625)^(1200)

A= 750(1.0005625)^(1200)

A= 750(1.9637)

A= 1472.775

Amount after 10 years is $1472.775

Answer: 0.08 yards

Step-by-step explanation: 1 centimeter equals to about  0.01 yards. You have to multiple 0.01 to 8 and it will give 0.08 yards.

Answer:

x = 0,087489064

Step-by-step explanation:

1 cm =  0.010936133 yards

8 cm = x

x = 8 cm x 0.010936133 yards/ 1 cm

x = 0,087489064

Unclear question. However, I inferred you want to know about hypotehsis test.

Step-by-step explanation:

Remember, any hypothesis test is divided into two types. They are:

Using this question example, here's the hypothesis statements ma sound:

Null hypothesis; There is a significant impact by the explanatory variables on engine overhaul time.

Alternate hypotheses; There is no impact by impact by the explanatory variables on engine overhaul time.

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{28.28 \: }}}}}[/tex]

Step-by-step explanation:

Given, diameter of a circle = 6

pi ( π ) = 22 / 7

Finding the radius of the circle

We know that the radius of a circle is just half of the diameter. So, 6 / 2 = 3

Finding the area of circle having radius of 3

[tex] \boxed{ \sf{area \: of \: circle = \pi \: {r}^{2} }}[/tex]

plug the values

⇒[tex] \sf{area \: of \: circle = \frac{22}{7} \times {3}^{2} }[/tex]

Evaluate the power

⇒[tex] \sf{area \: of \: circle = \frac{22}{7} \times 9}[/tex]

Calculate

⇒[tex] \sf{area \:of \: circle = 28.28 \: }[/tex]

Hope I helped!

Best regards! :D

Answer:

See the attachment for formatted formulas

Step-by-step explanation:

Let X11, X12, ……,X1n  and X21 , X22……., X2n be two small independent random samples from two normal populations with means u1 and u2  and the standard deviations σ1 and σ2 respectively. If σ1= σ2 (=σ) but unknown then the unbiased pooled or combined estimate of the common variance σ2 (the term variance means that each population has the same variance) is given by

Sp2  = ((n_1-1)  s_(1^2 )+ (n_2-1) s_2^2)/(n_1+n_2-2)

Where

S12 = 1/(n_1- 1) ∑▒〖 (X_1i- X`_1)〗^2  and

S22 = 1/(n_2- 1) ∑▒〖 (X_2j- X`_2)〗^2

The test statistic

t = ((X_1`-X_2`)- (μ_1- μ_2))/(√(s_p&1/n_1 )+ 1/n_2 )

Has t distribution with v= n1 + n2 – 2 degrees of freedom.

It is used as a test statistic for testing hypotheses about the difference between two population means.

The procedure for testing hypothesis H0: μ_1- μ_2= ∆_0 in case of small independent samples when σ_1= σ_2 is as follows.

H0: μ_1- μ_2= ∆_0  against the appropriate alternative.

t = ((X_1`-X_2`)- ∆_0  )/(√(s_p&1/n_1 )+ 1/n_2 )

Which has t distribution with v= n1 + n2 – 2 degrees of freedom.

Answer:

5.36910

Step-by-step explanation

whatever you see like 95 can round up to 100.

5.369095... you just round up 95 to 100.

5 decimal is 5.36910

The number 5.36909546581 which is needed to be rounded off up to 5 decimal places is 5.36910.

The decimal numeral system is the most widely used system for representing both integer and non-integer values. It is the Hindu-Arabic numeral system's expansion to non-integer numbers. The method of representing numbers in the decimal system is commonly referred to as decimal.

Given the number 5.36909546581 which is needed to be rounded off up to 5 decimal places. Therefore, if we look at the sixth place after the decimal it is equal to 5.

Thus, fifth place is needed to be rounded off to the next number.

Hence, the number 5.36909546581 which is needed to be rounded off up to 5 decimal places is 5.36910.

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Answer:

Length of square cut = 1.569 inches

Step-by-step explanation:

given data

Length of cardboard = 12 inches

Breadth of cardboard = 8 inches

solution

we will consider here side of the square = x

when we cutting out the square then there Length and breadth of candy box will be

Length of box = (12 - x - x)

Length of box = (12 - 2x) inches.

and

Breadth of box = (8 - x - x)

Breadth of box = (8 - 2x) inches.

and Height of candy box  wil be = x inches

so

Volume of a cuboid = L × b × h    .....................1

Volume of a cuboid = (12 - 2x) × (8 - 2x) × x

Volume of a cuboid = 96x - 40x² + 4x³

now we Differentiate with respect to x

V' = 96 - 80x + 12x²

and for maximum volume we put V' = 0

0 = 96 - 80x + 12x²

solve it we get

x = 5.097

x = 1.569

when x = 5.097 inches

Breadth of candy box = 8 - 10.194 = -2.194 inches

but we know breadth never be negative,

so we take

Length of square cut = 1.569 inches

Answer:

Each book costs $15 dollars

Step-by-step explanation

150-15=135

135/9=15

$15

Answer:

In the form of

Y= mx+c

Y= 1/2x +2

m = 1/2

Step-by-step explanation:

A linear equation in it's standard form is in the format

Y= mx+c

Where m is the slope and c is the y intercept

Let's use these two points to determine both the slope and the equation

(2, 3), (4,4)

Slope= (y2-y1)/(x2-x1)

Slope= (4-3)/(4-2)

Slope= 1/2

Equation of the linear function

(Y-y1)/(x-x1)= m

(Y-3)/(x-2)= 1/2

2(y-3) = x-2

2y -6 = x-2

2y= x-2+6

2y= x+4

Y= 1/2x +2

Answer:

Probability each player gets an ace, a $2 and a $3 = 0.0374

Step-by-step explanation:

The total number of ways to divide the card in triples among four players = 369600 ways

The total number of ways to share the cards such that no card is repeated in each triple = 13824 ways

Probability each player gets an ace, a $2 and a $3 = 13824/369600

Probability each player gets an ace a $2 and a $3 = 0.0374

Note: Further explanation is provided in the attachment.

Answer:

Here is the full question:

Find the sum of the convergent series by using a well-known function. (Round your answer to four decimal places.) Σ_(n=1)^∞ (-1)^n+1 1/7^n n

Step-by-step explanation:

Σ_(n=1)^∞ (-1)^n+1 1/7^n n

We will use the function In (1 + x)

We will now give a power series expansion of the function while it is centered at x=0

This will give us In (1 + x) = Σ_(n=1)^∞[tex](-1)^{n+1}[/tex][tex]\frac{x^{n} }{n}[/tex]

Note that x= 1/7

Now let us equate the two equations

Σ_(n=1)^∞[tex](-1)^{n+1}[/tex][tex]\frac{1}{7^{n}n }[/tex] = ㏑(1 + x)|[tex]_{x = \frac{1}{7} }[/tex] = ㏑[tex]\frac{8}{7}[/tex]

Sum of the series will give ㏑[tex]\frac{8}{7}[/tex]

Answer:

C) 13

Step-by-step explanation:

A on the number line is about -5 and B is 8. Act as if there wasn't a negative sign in front of the 5. Add the two numbers together the get the distance.

Answer:

the standard deviation for the number of restaurants specializing in seafood is 0.8944

Step-by-step explanation:

Given that :

Sum total number N of top restaurants in Chicago = 20

Four of the restaurants specialize in seafood,

then , the probability that a randomly selected restaurant from the top 20 in the list will specialize in seafood will be  p = 4/20

p = 0.2

sample size n = 5

Assuming X to be the random variable that follows a Binomial distribution that represent the number of restaurants specializing in seafood.

Then: [tex]X \sim Binomial (n,p)[/tex]

where;

n = 5  and p = 0.2

The standard deviation σ  can be determined by using the formula:

[tex]\sigma = \sqrt{np(1-p)}[/tex]

[tex]\sigma = \sqrt{5\times 0.2(1-0.2)}[/tex]

[tex]\sigma = \sqrt{1.0(0.8)}[/tex]

[tex]\sigma = \sqrt{0.8}[/tex]

σ = 0.894427191

σ [tex]\simeq[/tex] 0.8944

Answer:

64,186,300 square miles

I'm sorry if I misunderstood.

Good luck mate! :)

Please add Brainliest if you'd like, not that it matters.

Remember to try your best every day!

Answer:

the ratio will be 132 to 89

The ratio is 132 : 89.

A comparison of two quantities by division is called a ratio and the equality of two ratios is called proportion. A ratio can be written in different forms like x : y or x/y and is commonly read as, x is to y.

Ratio is the comparison of two quantities which is obtained by dividing the first quantity by the other. If a and b are two quantities of the same kind and with the same units, such that b is not equal to 0, then the quotient a/b is called the ratio between a and b. Ratios are expressed using the symbol of the colon (:). This means that ratio a/b has no unit and it can be written as a : b

Given:

Boys= 132

girls= 89

adults= 14

So,

the ratio of number of boys to number of girls is

= 132/89

=132 : 89

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Answer:

a

Step-by-step explanation:

Replace x with each value and solve :

2 x 2^1 = 2 x 2 = 4

2 x 2^2 = 2 x 4 = 8

2x 2^3 = 2 x 8 = 16

2x 2^4 = 2 x 16 = 32

2 x 2^5 = 2 x 32 = 64

Now mark two points on the graph: (1,4) and (2,8) and draw a straight line though both points

The image is not rotated correctly...

Answer:

Q#2 y;; 4  8  16  32  64

Q#3 given below;

Step-by-step explanation:

Step-by-step explanation:

A proper noun is a specific name for a particular person, place, or thing.

The Internet is a communication network that gained popularity in the 1990s.