Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
At West Painting, they get about three calls a day asking for an estimate of the cost for having the interior of a house painted. To write up an estimate for the cost of a job, they need to know how much paint a job will take. If they average painting of a room with of a gallon of paint, then they can paint, on average,
rooms per gallon.

Answer:

[tex]\huge\boxed{\sf 14\ ft}[/tex]

Step-by-step explanation:

Yard sticks = 4

12-inch rulers = 2

All are placed end to end.

We know that,

1 yard = 3 feet

4 yards = 3 × 4 feet

4 yards = 12 feet

We know that:

1 inch = 0.083 feet

24 inch = 0.083 × 24 feet

24 inch = 2 feet

= 4 yardsticks + 2 12-inch rules

= 12 ft + 2 ft

= 14 ft

[tex]\rule[225]{225}{2}[/tex]

Given the parameterization

[tex]\vec r(u,v) = u\cos(v) \, \vec\imath + u\sin(v) \,\vec\jmath + v \,\vec k[/tex]

take the normal vector to be

[tex]\vec n = \dfrac{\partial\vec r}{\partial u} \times \dfrac{\partial \vec r}{\partial v} = \sin(v) \,\vec\imath - \cos(v) \,\vec\jmath - u \,\vec k[/tex]

(The order of partial derivatives in the cross product doesn't matter since this a scalar line integral.)

Compute the magnitude of the normal vector.

[tex]\|\vec n\| = \sqrt{\sin^2(v) + (-\cos(v))^2 + (-u)^2} = \sqrt{1+u^2}[/tex]

so that the area element reduces to

[tex]dS = \|\vec n\| \, du\,du = \sqrt{1+u^2}\,du\,du[/tex]

Evaluate the integrand at [tex]\vec r[/tex] to get

[tex]\sqrt{1 + (u\cos(v))^2 + (u\sin(v))^2} = \sqrt{1 + u^2}[/tex]

The surface integral reduces to

[tex]\displaystyle \iint_S \sqrt{1+x^2+y^2} \, dS = \int_0^{2\pi} \int_0^1 (1+u^2) \, du \, dv = 2\pi \int_0^1 (1+u^2) \, du = \boxed{\frac{8\pi}3}[/tex]

Answer:

6.25 litres

Step-by-step explanation:

ratio 1:4

25/4 = 6.25

4 * 6.25 = 25

1 * 6.25 = 6.25

= 6.25 litres of concentrate

Answer:

6.25 litres of juice concentrate

The length of the base is 40 meters

We have:

Area= 160 square meters

Height = 4 meters

The area is calculated using:

Area = Base * Height

So, we have:

160 = Base * 4

Divide both sides by 4

Base = 40

Hence, the length of the base is 40 meters

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Answer:

45.5%

Step-by-step explanation:

The increase in population was 45.5%

Answer:

  16x² +48x +36

Step-by-step explanation:

A perfect square trinomial is of the form ...

  (a +b)² = a² +2ab +b²

We want to match this form.

__

Comparing the known terms, we see ...

  16x² = a²   ⇒   a = 4x

  36 = b²   ⇒   b = 6

The missing term is the linear term:

  2ab = 2(4x)(6) = 48x

  ? = 48

Using the normal approximation to the binomial, it is found that the probabilities are given as follows:

a) 0.0055 = 0.55%.

b) 0.2296 = 22.96%.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters of the binomial distribution are given as follows:

n = 150, p = 0.889.

Hence the mean and the standard deviation of the approximation are:

Item a:

Using continuity correction, the probability is P(123.5 < X < 124.5), which is the p-value of Z when X = 124.5 subtracted by the p-value of Z when X = 123.5, hence:

X = 124.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{124.5 - 133.35}{3.8473}[/tex]

Z = -2.3

Z = -2.3 has a p-value of 0.0107.

X = 123.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{123.5 - 133.35}{3.8473}[/tex]

Z = -2.56

Z = -2.56 has a p-value of 0.0052.

Hence the probability is 0.0107 - 0.0052 = 0.0055 = 0.55%.

Item b:

The probability is P(112.5 < X < 130.5), which is the p-value of Z when X = 130.5 subtracted by the p-value of Z when X = 112.5, hence:

X = 130.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{130.5 - 133.35}{3.8473}[/tex]

Z = -0.74

Z = -0.74 has a p-value of 0.2296.

X = 112.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{112.5 - 133.35}{3.8473}[/tex]

Z = -5.42

Z = -5.42 has a p-value of 0.

Hence the probability is 0.2296 - 0 = 0.2296 = 22.96%.

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The correct answer is Option c which is the cubic expression is 4x³ − 3x² − 2x + 11

The correct question is as given below:-

Need help ASAP. Choose the expression that represents a cubic expression.

a. 2x + 11

b . −3x² − 2x + 11

c . 4x³ − 3x² − 2x + 11

d . 5x⁴ + 4x³ − 3x² − 2x + 11

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The polynomial having a degree of three is called the cubic polynomial which means that the maximum power of the polynomial will be three and the solutions will also be three.

Here in the option, we can see that the maximum power of the polynomial is three and it will have a maximum of three solutions.

The third-degree expression will be:-

E = 4x³ − 3x² − 2x + 11

Therefore the correct answer is Option c which is the cubic expression is 4x³ − 3x² − 2x + 11

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Answer:

D

Step-by-step explanation:

The rate of change of radius at radius 6cm is 0.79 cm/sec.

The rate of change of a function is simply the derivative of the function with respect to the changing parameter in the function i.e. variable in the function.

So for calculating the rate of change of radius, we calculate the rate of volume change as volume is the function of radius.

As we know volume of the cylinder is given by V=πr²h

where r is the radius and h is the height of the cyclinder.

Given that rate of change of volume = 563 cm/sec

⇒ dV/dt =563 cm/sec

⇒ d(πr²h)/dt =563

taking πh outside the derivative as π and h is constant term

⇒ πh dr²/dt =563

⇒ πh (dr²/dr)(dr/dt)= 563 (applying chain rule dy/dx = (dy/du)(du/dx))

⇒ πh(2r)(dr/dt) =563

⇒dr/dt= 563/(2πhr)

given height of the cylinder h= 19cm

rate of change of radius at radius r =6cm= dr/dt= 563/(2πhr)= 563/(2*π*19*6)= 0.79 cm/sec

Therefore rate of change of radius at radius 6cm is 0.79 cm/sec.

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Answer:

It is solved on a graph

Step-by-step explanation:

A quadratic graphical solution.

Answer:

y = 5x + 11

Step-by-step explanation:

We are given that a line passes through (-2, 1) and also it contains a slope of 5

We want to write the equation of this line in slope-intercept form

Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y axis

As we are already given the slope, we can immediately substitute it into the formula

Replace m with 5 in y=mx+b:

y = 5x +  b

Now we need to find b

As the equation passes through the point (-2, 1), we can use its values to help solve for b.

Substitute -2 as x and 1 as y:

1 = 5(-2) + b

Multiply

1 = -10 + b

Add 10 to both sides

11 = b

Substitute 11 as b in the equation

y = 5x + 11

Topic: finding the equation of the line

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5%3×4+14-15 answers thes questions

Answer :

Points at (1, 3) and (3, 3) and (2, 1)

Explanation:

The original graph (dashed) is an absolute value function meaning f(x) = |x|

Given: y = 2f(x - 2) + 1

f(x - 2) means you plug in x - 2 for x in f(x) function

the new graph equation is: y = 2|x - 2| + 1

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Visual:

Answer:

A = 60 ft²

Step-by-step explanation:

the area (A) of the shaded sector is calculated as

A = area of circle × fraction of circle

   = 90 × [tex]\frac{240}{360}[/tex]

   = 90 × [tex]\frac{2}{3}[/tex]

    = 30 × 2

    = 60 ft²

Answer:

58.83 ft^2

Step-by-step explanation:

Finding the radius:

A = πr^2

90 = πr^2

90/π = r^2

28.6 = r^2

5.3 = r

Using the area of a sector of a circle formula:

θ/360 x πr^2

240/360 x π(5.3)^2

= 58.83 ft^2

Answer:

50

Step-by-step explanation:

Fractions are division problems. :) You have to complete that first to solve the equation (PEMDAS).

48/6 = 8

42 + 8 = 50

The graph of the function is y = arcsec(x).

Answer:

4 (2a ⋅ 5) = (4 ⋅ 2a) ⋅ 5

Step-by-step explanation:

Since we have given that

Measure of revolution = 360°

Now, the measure of [tex]\frac{3}{4}[/tex] of revolution.

So, it becomes,

[tex]\frac{3}{4}[/tex]×360

= 3 × 90

= 270

Hence, the measure of 3/4 of revolution is 270°.

Hope this helped and have a good day

Answer:

2-4i/5

Step-by-step explanation:

[tex]\frac{2i}{i-2} *\frac{i+2}{i+2}\\=\frac{2i(i+2)}{i^2-4}\\= \frac{2i(i+2)}{-1-4}\\ =\frac{2i(i+2)}{-5} \\ = \frac{-2 + 4i}{-5}\\ =( 2 - 4i )/ 5[/tex]

Answer:

[tex]\frac{2i}{i-2}=\frac{2-4i}{5}[/tex]

Step-by-step explanation:

Part (a)

Decreasing means that as x increases, y decreases.

So the intervals are [tex](-8, -4), (0, 5), (9, \infty)[/tex]

Part (b)

A local minimum is where the function changes from decreasing to increasing.

So, the local minima are at [tex]x=-4, 5[/tex]

Part (c)

The function is approaching negative infinity as x approaches both positive and negative infinity, so the leading coefficient is negative

Part (d)

The degree is given by the number of roots (including multiplicity).

From the graph, we see there is a single root at x = -6, a single root at x = -1, a single root at x = 1, a single root between x=6 and x=8, and a single root at around x = 10.

Thus, there are a minimum of 5 roots for the graph (there could be more outside of the given section)

However, since the graph has the same end behavior in both directions, the degree must be even.

So, the possible answers are any even number that is at least 6

Answer:

As the x-values go to positive infinity, the function's

values go to negative infinity.

Step-by-step explanation:

upon viewing the graph you will notice that the function in blue will appear to go down (negative) as you follow the x to the right, in the positive direction.

Making your answer to be as the x goes to positive inf (right) the values of the function go to negative inf (down).

The total interest accrued is $2,407.41 if you invested $7,000 into a money market account for 10 years at an annual interest rate of 3%.

An investment is a payment made to acquire the securities of other firms with the intention of making a profit.

We are assuming the interest will be compounded annually

[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]

Where A = Final amount

          P = Principal amount

          r  = annual rate of interest

          n = how many times interest is compounded per year

          t = How long the money is deposited or borrowed (in years)

We have:

P = $7000

r = 3% = 0.03

t = 10 years

n = 1

[tex]\rm A = 7000(1+\dfrac{0.03}{1})^{1\times10}[/tex]

After calculating:

A = $9407.41

I = A - P = 9407.41 - 7000 = $2,407.41

Thus, the total interest accrued is $2,407.41 if you invested $7,000 into a money market account for 10 years at an annual interest rate of 3%.

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If she arrives by boat;

The distance she needs to row = Lake diameter

Distance = Lake diameter = 2 x Radius

Boat distance = 2 x 2 miles = 4 miles

So;

When moving on foot

The distance that needs to be moved D = Half of the circle circle

∴ D = π × Radius

The distance that needs to be moved D = π × 2 miles = 2π Miles

Arc length = Radius × θ

String length = radius x 2 x sin (θ / 2)

0 ≤ θ ≤ π, 0 ≤ sin (θ / 2) ≤ 1

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Answer:

91 degrees

Step-by-step explanation:

Sum of angles in a quadrilateral: 360 degrees

87, 89, 91, 93 are four consecutive odd numbers that add up to 360

third angle is 91 degrees

Answer:

[tex]x = \frac{y - 1150}{5} [/tex]

Step-by-step explanation:

[tex]y - 1150 = 5x \\ \frac{y - 1150}{5} = x \\ x = \frac{y - 1150}{5} [/tex]

Answer:

as ABC = 3* DEF

AB = 5

DE = 15 = 5*3

AC = 3

DF = 9 = 3*3

BC = 4

EF = 12 = 4 * 3

Explanation:

Equation: x + 1 = 9

Solving Steps:

x + 1 = 9                 (subtract both sides by 1)

x + 1 - 1 = 9 - 1        (simplify the following)

x = 8

Then check for solution:

x + 1 = 9

                         [insert x = 8]

8 + 1 = 9

9  =  9

As both sides are equal, the statement is true.

[tex]\large\underline{ \cal{SOLUTION:}}[/tex]

[tex] \large \bold{x + 1 = 9}[/tex]

[tex] \large \bold{x = 9 - 1}[/tex]

[tex] \large \bold{x = \red{8}}[/tex]

[tex] \: [/tex]

[tex]\large\underline{ \cal{CHECKING:}}[/tex]

[tex] \large{ \bold{ \underline{ \red{8} }+ 1 = 9}}[/tex]

[tex] \large \bold{-N} \frak{unx-}[/tex]

Answer:

he should check

3x and x

1/4 and 0.5

-m and 8m

-xy2 and 2xy2

Step-by-step explanation:

Answer:

The answer is A B C D H

Step-by-step explanation:

She did 21 question correctly.

Let number of correct answers : x

Let number of wrong answer : y

Given, Total question wrote : 30

So,  

      x + y = 30          (i) - equation

Got 8 point on each correct answer, total point : 8*x

Got -2 point on each wrong answer, total point : (-2)*y

Total point she score was : 150          (given)

so, our next equation is

                                      8*x - 2*y = 150       (ii) - equation

                                      y = 30 - x            [from (i) - equation]

put in (ii) - equation, we get

                                    8*x - 2*(30 - x) = 150

                                    8*x - 60 + 2*x = 150

                                    10*x = 210

                                       x = 21

Therefor, only 21 answers are correct.

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