7,40Divide. (If there is no remainder, then enter 0.)

7,402 ÷ 37​

======================================================

Explanation:

Vector u has magnitude 8 and direction 150 degrees.

So r = 8 and theta = 150

The polar form

r*(cos(theta)+i*sin(theta))

updates to

8*(cos(150)+i*sin(150))

---------------------

Use your calculator to evaluate that last expression to get it into a+bi form

8*(cos(150)+i*sin(150))

8*(-0.866025 + i*0.5)

-6.9282 + 4i

So this is the a+bi form of vector u. It's a rough approximation of it.

-----------------------

Repeat those steps for vector v

v = r*(cos(theta)+i*sin(theta))

v = 3*(cos(115)+i*sin(115))

v = 3*(-0.422618 + i*0.906308)

v = -1.267854 + 2.718924i

----------------------

We're converting each vector to a+bi form so that we can add the vectors.

The general idea is that if you want to add v = a+bi and w = c+di, then

v+w = (a+c)+(b+d)i

we simply add the corresponding real components together, and the imaginary components are added together as well.

-----------------------

Add up u and v

u+v = (-6.9282 + 4i) + (-1.267854 + 2.718924i)

u+v = (-6.9282 + -1.267854) + (4i + 2.718924i)

u+v = -8.196054 + 6.718924i

When rounding to four decimal places, the real and imaginary components are -8.1961 and 6.7189 respectively. These represent the x and y components of the vector.

So we can say vector u+v is approximately < -8.1961, 6.7189 >

Answer:

Step-by-step explanation:

volume of a cylinder=πr^2h

=π*5^2*15

=π*25*15

=375π cm^3

Volume of a cylinder = πr^2h

→ π × 5^2 × 15

→ π × 25 × 15

→ 375π cm^3

Answer:

.

Step-by-step explanation:

[tex]2 {x}^{2} - 5x - 3[/tex]

Answer:

Part A)

57.57 ; 5.757

Part B)

3% of 50 is 1.5.

300% of 50 is 150.

Together, they add to 151.5.

Step-by-step explanation:

To find something "of" something, we can multiply the two values.

A)

To find 101% of 57, we will multiply the two values. Hence:

[tex]101\%(57)=1.01(57)=57.57[/tex]

And 10% of that will be:

[tex]10\%(57.57)=0.1(57.57)=5.757[/tex]

B)

First, find 3% of 50:

[tex]3\%(50)=0.03(50)=1.5[/tex]

Next, we can find 300% of 50:

[tex]300\%(50) = 3(50)=150[/tex]

Finally, add:

[tex]\Rightarrow 1.5+150=151.5[/tex]

Answer:

for the lengths, just double the numbrrs

1.5 -> 3

2.5 -> 5

bc the scale factor is two (the upper edge is given)

the angles are just the same, no matter the zoom factor

There are two polygons where B is greater than A.

One side in polygon A has a length of 2.5 and the corresponding length in polygon B is 5.

So, the scale factor is

[tex]\dfrac{5}{2.5}=2[/tex]

So, the missing sides in polygon B are

[tex]1.5\times2=3[/tex]

[tex]2.5\times 2=5[/tex]

The angles in polygon A will be the same as B as all the sides of the polygon have changed according to the scale factor.

So, the missing sides in polygon B are 3 and 5, and the angles in polygon A are [tex]53^{\circ}[/tex] and [tex]82^{\circ}[/tex].

Learn more:

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Answer:

36

Step-by-step explanation:

Since there are 18 students in the class and they picked 660 strawberries, you divided 660 by 18, giving you a quotient of 36.6666667. Since the question asks for how many whole strawberries each student can have, the answer is 36.

Answer:

36

Step-by-step explanation:

Answer:

no solutions

Step-by-step explanation:

The lines are parallel and never intersect.  The solutions occur when the lines intersect, so there are no solutions

The system of equations which is graphed have no solution.

A system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables.

According to the given question.

We have a graph.

In the given graph the two lines are drawn,  which are parallel to each other. So, they don't have a common point.

Therefore, the system of equations which is graphed have no solution.

Find out more information about system of equations here:

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#SPJ2

Answer:

(2x -1)  (7xy+2)

Step-by-step explanation:

Rewrite the equation as follows:

(14x^2y - 7xy)   +  (4x -2)

Factor 7xy from the first term and 2 from the second term:

7xy(2x -1 ) + 2 ( 2x -1)

Factor (2x-1) from each term to get

(2x -1) ( 7xy + 2)

You can multiply this out to verify the answer.

Answer:

Step-by-step explanation:

We can do this the easy way and just set up an inequality and let the factoring do the work for us. The inequality will look like this:

[tex]-16t^2+112t>192[/tex] We will move the constant over and get

[tex]-16t^2+112t-192>0[/tex] and when you factor this you get that

3 < t < 4

Between 3 and 4 seconds is where the projectile reaches a height higher than 192 feet. With a little more work and some calculus you can find the max height to be 196 feet.

Answer:

its A

Step-by-step explanation:

got it right

Answer:

972 cm³

Step-by-step explanation:

the maximum volume is

⅓×18³= 972 cm³

Answer:

they are not equal

Step-by-step explanation:

13/4 hour is 3hour and 15 minutes

Answer:

The answer is 13.

Step-by-step explanation:

n ÷ 7

= 91 ÷ 7

=13

Answer:

[tex](a)\ k(r) = \ln(1+r)[/tex]

[tex](b)\ r(T_2) = 2^{1/T_2}-1[/tex]

[tex](c)\ T_2(k) = \frac{\ln(2)}{k}[/tex]

Step-by-step explanation:

Given

[tex]y(t) = y_0e^{kt}[/tex]

[tex]y(t) = y_0(1+r)^t[/tex]

[tex]y(t) = y_02^{t/T_2}[/tex]

Solving (a): k(r)

Equate [tex]y(t) = y_0e^{kt}[/tex] and [tex]y(t) = y_0(1+r)^t[/tex]

[tex]y_0e^{kt} = y_0(1+r)^t[/tex]

Cancel out common terms

[tex]e^{kt} = (1+r)^t[/tex]

Take ln of both sides

[tex]\ln(e^{kt}) = \ln((1+r)^t)[/tex]

Rewrite as:

[tex]kt\ln(e) = t\ln(1+r)[/tex]

Divide both sides by t

[tex]k = \ln(1+r)[/tex]

Hence:

[tex]k(r) = \ln(1+r)[/tex]

Solving (b): r(T2)

Equate [tex]y(t) = y_02^{t/T_2}[/tex] and [tex]y(t) = y_0(1+r)^t[/tex]

[tex]y_0(1+r)^t = y_02^{t/T_2}[/tex]

Cancel out common terms

[tex](1+r)^t = 2^{t/T_2}[/tex]

Take t th root of both sides

[tex](1+r)^{t*1/t} = 2^{t/T_2*1/t}[/tex]

[tex]1+r = 2^{1/T_2}[/tex]

Make r the subject

[tex]r = 2^{1/T_2}-1[/tex]

Hence:

[tex]r(T_2) = 2^{1/T_2}-1[/tex]

Solving (c): T2(k)

Equate [tex]y(t) = y_02^{t/T_2}[/tex] and [tex]y(t) = y_0e^{kt}[/tex]

[tex]y_02^{t/T_2} = y_0e^{kt}[/tex]

Cancel out common terms

[tex]2^{t/T_2} = e^{kt}[/tex]

Take ln of both sides

[tex]\ln(2^{t/T_2}) = \ln(e^{kt})[/tex]

Rewrite as:

[tex]\frac{t}{T_2} * \ln(2) = kt\ln(e)[/tex]

[tex]\frac{t}{T_2} * \ln(2) = kt*1[/tex]

[tex]\frac{t}{T_2} * \ln(2) = kt[/tex]

Divide both sides by t

[tex]\frac{1}{T_2} * \ln(2) = k[/tex]

Cross multiply

[tex]kT_2 = \ln(2)[/tex]

Make T2 the subject

[tex]T_2 = \frac{\ln(2)}{k}[/tex]

Hence:

[tex]T_2(k) = \frac{\ln(2)}{k}[/tex]

Answer:

[tex]ln( |1 + u| ) = 7t + \frac{ {t}^{2} }{2} + c[/tex]

Step-by-step explanation:

[tex]integral( \frac{1}{1 + u} )du = \\ integral(7 + t)dt[/tex]

[tex] ln( |1 + u| ) = 7t + \frac{ {t}^{2} }{2} + c[/tex]

Answer:

96√3 cm^2

Step-by-step explanation:

half base = 4 cm

height of each triangle = 4√3 cm

Area of each triangle

(8 * 4√3)/2 = 16√3 cm^2

area of the hexagonal = 16√3 * 6 = 96√3 cm^2

Answer:

f = 1.6

Step-by-step explanation:

Answer:

f = 8/5

Step-by-step explanation:

[tex]5 + 5f - 6 = 7\\5f - 1 = 7\\5f = 7 + 1 \\5f = 8\\\\f = \frac{8}{5}[/tex]

Answer:

depends on the size of the food

Step-by-step explanation:

Answer:

Step-by-step explanation:

115+94+107+2x=360 degree(sum of interior angles of four angles is always 360 degree)

316+2x=360

2x=360-316

x=44/2

x=22 degree

Answer:35457$

Step-by-step explanation:

qowiufrasjofjoqjOASIEJKDJF

IOVAJ

Answer: Brian ran 9 miles

Sonia ran 24 miles

Step-by-step explanation:

Let's Brian's distance be represented by x.

Since Sonia ran 6 miles more than twice as far as Brian. This will be:

= (2 × x) + 6

= 2x + 6

Therefore,

x + 2x+6 = 33

3x + 6 = 33

3x = 33 - 6.

3x = 27

x = 27/3

x = 9

Brian ran 9 miles

Sonia ran = 2x+6 = 2(9).+ 6 = 18+6 = 24 miles

9514 1404 393

Answer:

  $2398.20

Step-by-step explanation:

Perhaps you want the monthly payment. It is given by the amortization formula ...

  A = P(r/n)/(1 -(1 +r/n)^(-nt))

where P is the principal amount, r is the annual interest rate, n is the number of payments per year, t is the number of years.

Your monthly payment will use P = 400,000; r = 0.06, n = 12, t = 30.

  A = $400,000(0.06/12)/(1 -(1 +0.06/12)^(-12·30)) ≈ $2398.20

Answer:

H0: p1=p2   versus   Ha:p1≠p2

Step-by-step explanation:

Let p1 be the proportion experiencing the primary outcome with the treatment and p2 the proportion without the treatment.

We want to determine whether the proportion of persons having the treatment suffering the primary outcome of a fatal cardiovascular event is equal to the proportion of people  without the treatment suffering the primary outcome of a fatal cardiovascular event.

The hypothesis is based on the study under observation. The claim is set as the alternate hypothesis.

The null and alternate hypotheses are

H0: p1=p2   versus   Ha:p1≠p2

Both proportion ( with and without treatment ) are same

against the claim

Both proportion ( with and without treatment ) are  not the same .

Option which gives the answer

H0: p1=p2   versus   Ha:p1≠p2

is the best option.

Answer:

because in lowest term it's ratio is same

Step-by-step explanation:

hope you understand

Answer:

The ratios of 3:2, 6:4, and 9:6 are all equivalent because when you divide the numerator over the denominator, you get the same result for all of them. This means that if we took 3/2 and got 1.5, and took 6/4 and got 1.5 as an answer, and took 9/6 and got 1.5 as an answer as well, we would have the same answer for all of them. This is why (in my own words) the ratios are all equivalent.

Answer:

A

Step-by-step explanation:

The profit for selling x pairs of shoes is given by:

[tex]P(x)=-4x^2+32x-39[/tex]

And we want to determine the number of pairs that needs to be sold in order to maximize profit.

Since the function is a quadratic with a negative leading coefficient, the maximum profit will occur at its vertex point. The x-coordinate of the vertex of a quadratic is given by:

[tex]\displaystyle x=-\frac{b}{2a}[/tex]

In this case, a = -4, b = 32, and c = -39. Substitute and evaluate:

[tex]\displaystyle x=-\frac{(32)}{2(-4)}=\frac{32}{8}=4[/tex]

So, in order to maximize profit, only four pairs of sohoes should be sold.

Our answer is A.

Answer:

A

Step-by-step explanation:

Answer:

give brainllest if right

c

Step-by-step explanation:

Answer:

[tex]\frac{x^2}{36} + \frac{y^2}{100} = 1[/tex]

Step-by-step explanation:

Required

The equation of the ellipse

This is calculated as:

[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1[/tex]

Where:

[tex]b =6[/tex] ---- height

[tex]a = 0.5 * 20 =10[/tex] --- width

So:

[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1[/tex]

[tex]\frac{x^2}{6^2} + \frac{y^2}{10^2} = 1[/tex]

[tex]\frac{x^2}{36} + \frac{y^2}{100} = 1[/tex]

Answer:

{4, 4, 8, 13, 16}

Step-by-step explanation:

If we have a set of N numbers in order:

{x₁, x₂, ..., xₙ}

The median is the middle number of the set.

The mode is the value that is repeated more times in the set

The mean is computed as:

[tex]M = \frac{x_1 + x_2 + ... + x_n}{N}[/tex]

And the range is the difference between the largest value and the smallest value.

Here we want 5 positive integers, so we have something like:

{x₁, x₂, x₃, x₄, x₅}

We know that the median is 8.

Then the middle value, x₃, is equal to 8.

We also know that the mode is 4, then we can have the number 4 repeated two times, and because 4 is smaller than 8 and this must be in order, then we can have:

x₁ = x₂ = 4

Replacing these in the set we have:

{4, 4, 8, x₄, x₅}

Now we know that the range is 12, and this was the difference between the largest and smallest value.

We know that the smallest value is 4, and the largest value is x₅, then we will have:

x₅ - 4 = 12

x₅ = 12 + 4 = 16

Then our set is:

{4, 4, 8, x₄, 16}

Finally, we know that the mean is 9.

Remember that the equation for the mean is:

[tex]M = \frac{4 + 4 + 8 + x_4 + 16}{5}[/tex]

Then we need to solve:

[tex]9 = \frac{4 + 4 + 8 + x_4 + 16}{5}[/tex]

[tex]9*5 = 4 + 4 + 8 + x_4 + 16}[/tex]

[tex]45 = 32 + x_4[/tex]

[tex]45 - 32 = x_4 = 13[/tex]

Then the set of five positive integers is:

{4, 4, 8, 13, 16}