215 divided by 32 with remainder

The line

\((x,y,z)=(11,-8,4)+t(3,-1,1)\)

runs in the direction of its tangent vector; we can get it by taking its derivative:

\(\vec T=\dfrac{\mathrm d}{\mathrm dt}\left[(11,-8,4)+t(3,-1,1)\right]=(3,-1,1)\)

Any line that runs perpendicular to this line will have a tangent vector that is orthogonal to \(\vec T\) above. So construct some vector \(\vec v\) that satisfies this.

\(\vec v=(x,y,z)\)

\(\vec v\cdot\vec T=(x,y,z)\cdot(3,-1,1)=3x-y+z=0\)

Suppose \(z=0\); then \(3x=y\), and we can pick any two values that satisfy this condition. For instance,

\(\vec v=(1,3,0)\)

And of course,

(1, 3, 0) • (3, -1, 1) = 3 - 3 + 0 = 0

so \(\vec v\) and \(\vec T\) are indeed orthogonal.

Now, the line running in the direction of \(\vec v\) and passing through the origin can be obtained by scaling

\((x,y,z)=(4,5,5)+t(1,3,0)\)

More generally, if you have a direction/tangent vector \(\vec v\) and some point \(\vec p\), the line through \(\vec p\) is given by

\((x,y,z)=\vec p+t\vec v\)

Testing the hypothesis using the z-distribution, it is found that since the p-value of the test is of 0.0262 < 0.05, it can be concluded that the new booklet is effective.

At the null hypothesis, we test if there has been no improvement, that is, the time is still of 3 hours. Hence:

\(H_0: \mu = 3\)

At the alternative hypothesis, we test if there has been improvement, that is, the time is of less than 3 hours. Thus:

\(H_1: \mu < 3\)

We have the standard deviation for the population, thus, the z-distribution is used. The test statistic is given by:

\(z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}\)

The parameters are:

In this problem, the values of the parameters are: \(\mu = 3, \sigma = 0.2, \overline{x} = 2.9, n = 15\).

Then, the value of the test statistic is:

\(z = \frac{2.9 - 3}{\frac{0.2}{\sqrt{15}}}\)

\(z = -1.94\)

The p-value of the test is the probability of finding a sample mean of 2.9 hours or less, which is the p-value of z = -1.94.

Looking at the z-table, z = -1.94 has a p-value of 0.0262.

Since the p-value of the test is of 0.0262 < 0.05, it can be concluded that the new booklet is effective.

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Answer: 165 miles

Step-by-step explanation: In order to figure out the answer, you must do 55 x 3 because he drove for 3 hours at 55 mph so you could break it up and go 50 x 3 to equal 150 and 5 x 3 to equal 15 and add those to get 165.

Answer:

The answer is 165miles

Step-by-step explanation:

\(distance = speed \times time\)

d=55×3

d=165 miles

Answer:

Given:

Area of the sector (A) = 104π/9 square inches

Central angle (θ) = 65 degrees

The formula for the area of a sector of a circle is:

A = (θ/360) * π * r^2

We can rearrange this formula to solve for the radius (r):

r^2 = (A * 360) / (θ * π)

Plugging in the given values:

r^2 = (104π/9 * 360) / (65 * π)

r^2 = (104 * 40) / 9

r^2 = 4160 / 9

r^2 ≈ 462.22

Taking the square root of both sides:

r ≈ √462.22

r ≈ 21.49

Therefore, the radius of the circle is approximately 21.49 inches.

Answer: 8 inches

Step-by-step explanation:

Answer:

a. quotient refers to division

Answer:

-6y^3+7y^2-2

Step-by-step explanation:

(-2y^3+2y^2-9)+(-4y^3+5y^2+7)

-2y^3-4y^3+2y^2+5y^2-9+7

-6y^3+7y^2-2

Step-by-step explanation:

if you can put a vertical line through it and it only touches the line once it's a function

Answer:

Step-by-step explanation:

The cost of a phone has lowered by 19% to $319.14 from its original $394 pricing.

In arithmetic, a percentile is a number or statistic that is given as a fraction of 100. Occasionally, the acronyms "pct.," "pct," nor "pc" are also used. But it is broadly classified into the following by the cent sign, "%." The % amount has no characteristics. Percentages are essentially integers when the denominator is 100. Use the percent sign (%) to indicate that a number is a percentage by placing it close to it. For instance, you score a 75% if you properly answer 75 so out 25 pages on a test (75/100). Divide the money by the whole and multiply the results by 100 you compute percentages. The formula for calculating the percentage is (value/total) x 100%.

given

Put this together using the conditions given: 319.14 / (1- 19%)

Determine the total or difference: 319.14 / 0.81

Diminish the fraction: 394

Response: 394

The cost of a phone has lowered by 19% to $319.14 from its original $394 pricing.

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Answer:

We can use the formula for compound interest to solve this problem. The formula is:

A = P * (1 + r/n)^(n*t)

where:

A = the amount of money after t years

P = the principal amount (the initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case, P = $5000, r = 0.03, n = 12 (since the interest is compounded monthly), and t = 10. Plugging these values into the formula, we get:

A = 5000 * (1 + 0.03/12)^(12*10)

A = 5000 * (1.0025)^120

A ≈ $6,621.36

So the investment will be worth approximately $6,621.36 after 10 years.

Answer:

44in²

Step-by-step explanation:

3 × 4 =12

4 × 8 = 32

12 + 32 = 44

good luck, i hope this helps :)

Answer: 44 \(in^{2}\)

Step-by-step explanation:

(Make this into two shapes. I made a horizontal line. You can label them as shape/rectangle A & shape/rectangle B)

Area of rectangle= L×W

Shape A area=  3×4= 12\(in^{2}\)

Shape B area= 8×4= 32\(in^{2}\)

TOTAL Area= 32\(in^{2}\)+12

=44\(in^{2}\\\)

Answer:

the answer is neither

Step-by-step explanation:

Answer:

56-123x+78 = -235

Step-by-step explanation:

too lazy for a diss.

56-123(3)+78

56-369+78

-313+78

-235

(could be wrong)

Answer:

-235

Step-by-step explanation:

56 - 123(3) =

56 - 369 = -313

-313 + 78 = -235

MEH SORRY AGAIN

Answer:

The answer is 2700 m

Answer:

1440 I hope this helps you

Answer:

1

Step-by-step explanation:

One is the starting term

1, 2, 4, 8, 16, 32, 64, 128, 256,

Answer:$69.08

Step-by-step explanation:

9.8 per hours

time and a half for hours worked over 40

48 hours - 40 hours = 8 hours over 40

9.8 + (9.8/2 ) = 14.7 per hour over 40

Gross earning: (9.80 x 40 ) + ( 14.7 x 8 ) = 392+117.6 = $509.6

Sorry but I don't see anything but your words...

What am I supposed to be answering?

Answer:

Nv5 my dude

Step-by-step explanation:

The computed mean expenses of the XYZ Corporation based on the given information are 9,911.22.

The mean refers to the average value.

The mean is computed as the quotient that results from dividing the total value of the data set by the number of items in the set.

Name                      Total Sales      Total Expenses

Quezon City            14,950.00             4,933.50

Caloocan City         18,290.00             6,035.70

Marikina City          37,200.00           12,276.00

Cebu City                18,900.00            6,237.00

Davao City             45,000.00          14,850.00

Mandaluyong City 23,000.00           7,590.00

Cavite                     22,000.00          7,260.00

Laguna                    21,000.00          6,930.00

Manila                    66,000.00         21,780.00

Iloilo                       34,000.00          11,220.00

Total                                                  99,112.20

Mean Expenses = 9,911.22 (99,112.20 ÷ 10)

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Answer:

The speed of the plane in the still air is 420 miles/hour

The speed of the wind 60 miles/hour

Step-by-step explanation:

Let the speed of the plane with the wind be v

Let the speed of the plane against the wind be u

Now, speed = distance/time

With the wind,

v = (1440 miles)/(3 hours) = 480 miles/hour

v = 480 miles/hour

Against the wind,

u = (1440 miles)/(4 hours) = 360 miles/hour

u = 360 miles/hour

Now, let the speed of plane be p, and speed of wind be w,

Now, with the wind, the speed is 480 mph,

so,

speed of plane + speed of wind = 480 mph

p + w = 480  (i)

and against the wind, the speed is 360 mph,

so,

speed of plane - speed of wind = 360mph

p-w = 360 (ii)

adding equations (i) and (ii), we get,

p+w + p-w = 480 + 360

2p = 840

p = 840/2

p = 420 miles/hour

Then, the speed of the wind will be,

p + w = 480,

420 + w = 480

w = 480 - 420

w = 60 miles/hour

The speed of the plane in still air is calculated to be 420 mph, and the speed of the wind is calculated to be 60 mph by solving the two simultaneous equations obtained from the time, rate, and distance relationship.

This problem is about the rate, time, and distance relationships. The rate at which the airplane travels in still air is r (unaffected by wind), and the speed of the wind is w. When the plane flies with the wind, it is 'assisted' and therefore travels faster - at a speed of (r + w); against the wind, it travels slower - at a speed of (r - w).

From the problem, we know that:

By solving these two equations, we get the following:

Adding these two gives 2r = 840 => r = 420 mph (the speed of the plane in still air), and subtracting gives 2w = 120 => w = 60 mph (the speed of the wind).

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Answer:

i think it is 212.8

Step-by-step explanation:

Answer: it’s 212.8

Step-by-step explanation:

2.  The value of 87.5 percent of 104 is 91.

3. The value of 20.8 is 32% of65.

What is percentage?

A percentage in mathematics is a number or ratio that may be stated as a fraction of 100.In determining a percentage of a number, we should first divide it by 100 before multiply the outcome by 100. As a result, the proportion refers to a part per 100. The word "percent" refers to a fraction of one hundred. The letter "%" stands for it.

Assume that x% of 104 is 91.

Therefore,

x% of 104 = 91

(x/100) × 104 = 91

Multiply both sides by 100:

104x = 9100

Divide both sides by 104

x = 9100/104

x = 87.5

Assume that 32% of y is 20.8.

Therefore,

32% of y = 20.8

(32/100) × y = 20.8

Multiply both sides by 100:

32y = 2080

Divide both sides by 32

y = 2080/32

x = 65

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Answer:

When a 3D figure is cut to create a cross-section parallel to the base, the direction of the perpendicular is vertical. This means that the cross-section will be perpendicular to the base and will have a vertical orientation.

Answer:

To solve the equation:

2/3x - 1/5x = x - 1

First, we need to find a common denominator for 2/3 and 1/5, which is 15. So we can rewrite the equation as:

(10/15)x - (3/15)x = 15/15 x - 1

Simplifying the left side:

(7/15)x = 15/15 x - 1

Multiplying both sides by 15:

7x = 15x - 15

Subtracting 7x from both sides:

-8x = -15

Dividing both sides by -8:

x = 15/8 or 1.875

Therefore, the solution to the equation is x = 1.875.

Answer:

Step-by-step explanation:

base area=41.57 in²

height=9 in

volume=41.57×9=374.13 in³

Answer:

\(5x-y+7z-38=0\)

or

\(5x-y+7z=38\)

Step-by-step explanation:

Given vector equation:

\(\textbf{r} = \textbf{i} - 5\textbf{j} + 4\textbf{k} + \lambda(3\textbf{i} + \textbf{j} - 2\textbf{k}) + \mu(-\textbf{i} + 2\textbf{j} + \textbf{k})\)

The vector 3i + j - 2k is perpendicular to n.

The vector -i + 2j + k is perpendicular to n.

\(\textsf{So}\;\;\textbf{n}=\left|\begin{array}{ccc}\textbf{i}&\textbf{j}&\textbf{k}\\3&1&-2\\-1&2&1\end{array}\right|\)

        \(=\textbf{i}\left|\begin{array}{rr}1&-2\\2&1\end{array}\right|-\textbf{j}\left|\begin{array}{rr}3&-2\\-1&1\end{array}\right|+\textbf{k}\left|\begin{array}{rr}3&1\\-1&2\end{array}\right|\)

        \(=\textbf{i}(1 \cdot 1 - (-2) \cdot 2)-\textbf{j}(3 \cdot 1-(-2) \cdot (-1))+\textbf{k}(3 \cdot 2-1 \cdot (-1))\)

        \(=\textbf{i}(1 +4)-\textbf{j}(3-2)+\textbf{k}(6+1)\)

        \(=5\textbf{i}-\textbf{j}+7\textbf{k}\)

So the equation of the plane written in Cartesian form is:

\(5x-y+7z+d=0\)

Substituting (1, -5, 4) gives:

\(5(1)-(-5)+7(4)+d=0\)

\(5+5+28+d=0\)

\(38+d=0\)

\(d=-38\)

Therefore, the given vector equation in Cartesian form is:

\(5x-y+7z-38=0\)

or

\(5x-y+7z=38\)

Answer:All equal

Step-by-step explanation:

Using the formula of compound interest, the number of years is 7.6 years

Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from simple interest, where interest is not added to the principal while calculating the interest during the next period.

The formula of compound interest is given as;

\(A = P(1 + \frac{r}{n} )^n^t\)

But in this case, the interest was compounded continuously

\(A = Pe^r^t\)

Substituting the values into the formula;

\(7450 = 5500e^(^0^.^0^5^2^5 ^* ^t^)\)

Solving for t;

t = 7.6 years

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