Translate into an equation: The cost of V ounces at $2 per ounce equals $56.

The value of the expression when simplified is -13

It is important to note:

PEDMAS is a mathematical acronym that representing;

Also, we should note that absolute value of a number is the non-negative value of that number. It s the value of a number irrespective of its direction from zero.

It is denoted with the symbol '| |'

Given the expression;

|2-5|-(12 ÷4-1)^2

Solve the bracket

|-3| - (12 /3)^2

Solve further

|-3| - 4^2

Find the absolute value

3 - 4^2

Find the square

3 - 16

-13

The value is - 13

Thus, the value of the expression when simplified is -13

Learn more about PEDMAS here:

https://brainly.com/question/345677

#SPJ1

Answer:

Volume = 10a³ + 91a² + 54a - 792

Step-by-step explanation:

In the absence of answer choices, let's find the expression for the volume.

Given: Volume = length×width×height

V = lwh

length =(2a + 11)

width =(5a – 12)

height= (a + 6)

V =  (2a + 11)(5a – 12) (a + 6)

Expand the first two brackets using distributive property

V = (10a² -24a +55a - 132)(a + 6)

Collect like terms

V = (10a² + 31a -132)(a + 6)

Expand the two brackets using distributive property

V = 10a³ + 31a² - 132a + 60a² + 186a - 792

Collect like terms

V = 10a³ + 91a² + 54a - 792

The expression that represents the volume of the box = 10a³ + 91a² + 54a - 792

Answer:

Volume = 10a³ + 91a² + 54a - 792

Step-by-step explanation:

Answer:

2x^4−11x^3+7x^2+5x−3

Step-by-step explanation:

The  ^  means exponent

Answer:

Rounded to two decimals the regression curve is:

[tex]y=-0.70\,x^2+2.37\,x+11.96[/tex]

Step-by-step explanation:

The objective of this problem is to have you use a calculator and enter the data in to separate lists: one containing the x-values, and the other the correspondent y-values (following the same order).

Once the data is entered, you need to access the regression tool and request a quadratic form of regression.

You should get and image and resulting function as shown in the attached image.

Answer:

Rounded to two decimals the regression curve is:

Step-by-step explanation:

Answer:

3.025

Step-by-step explanation:

3.4-1/2(0.75)

3.4-0.375

3.025

Answer:

more info is needed

Step-by-step explanation:

Answer:

Step-by-step explanation:

5x(x + 3) + 6(x + 3)

The final answer is

( 5x + 6 ) ( x + 3 )

Hope this helps you

Answer:

Step-by-step explanation:

Let x represent the number of friends that Monica asked to a charity raffle ticket. If all but 4 of her friends bought a ticket, it means that only 4 of her friends did not buy the charity raffle ticket. Thus, the number of her friends that bought the charity raffle ticket is

x - 4

If each ticket costs $3 and the total amount that was raised is $18, then algebraic expression representing the number of friends that Monica asked is

3(x - 4) = 18

3x - 12 = 18

3x = 18 + 12 = 30

x = 30/3 = 10

Monica asked 10 friends

Answer:

y=6x+18

Step-by-step explanation:

Answer:

y = 6x - 30

Step-by-step explanation:

The slope is 6.

Use the formula for the equation of a line.

y = mx + b

Where m is the slope, and b is the y-intercept.

y = 6x + b

The point is given (4, -6)

                               (x , y)

Put x as 4, y as -6.

-6 = 6(4) + b

-6 = 24 + b

-6 - 24 = b

-30 = b

The y-intercept is -30.

The equation of the line is y = 6x - 30.

Answer:

c. Not significant at .055

Step-by-step explanation:

When a pair of dice is rolled, we have 6²=36 possible outcomes. Only 2 of these outcomes have a total score of 11:

Then, we can calculate the probability of getting 11 as the quotient between the successs outcomes and the total outcomes.

Then, the probability of getting 11 is:

[tex]P=\dfrac{X}{N}=\dfrac{2}{36}=0.055[/tex]

This probability is not equal or less than 0.05, so it is not significant at 0.055.

Answer:

Step-by-step explanation:

This problem bothers on permutation

Given the letters LEARN

The total alphabets are 5 in numbers

Since there are no repeating letters, and there are 5 total letters, there are 5!=5*4*3*2*1=  120 ways to arrange them

Answer:

a) 26.33 kg/d and 29.67 kg/d

b) 94.5%

Step-by-step explanation:

a. Find a 99% confidence interval for the true mean milk production.

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 2.575*\frac{2.25}{\sqrt{12}} = 1.67[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 28 - 1.67 = 26.33 kg/d

The upper end of the interval is the sample mean added to M. So it is 28 + 1.67 = 29.67 kg/d

The 99% confidence interval for the true mean milk production is between 26.33 kg/d and 29.67 kg/d

b. If the farms want the confidence interval to be no wider than ± 1.25 kg/d, what level of confidence would they need to use?

We need to find z initially, when M = 1.25.

[tex]M = z*\frac{2.25}{\sqrt{12}} = 1.67[/tex]

[tex]1.25 = z*\frac{2.25}{\sqrt{12}} = 1.67[/tex]

[tex]2.25z = 1.25\sqrt{12}[/tex]

[tex]z = \frac{1.25\sqrt{12}}{2.25}[/tex]

[tex]z = 1.92[/tex]

When [tex]z = 1.92[/tex], it has a pvalue of 0.9725.

1 - 2*(1 - 0.9725) = 0.945

So we should use a confidence level of 94.5%.

Answer:

(n- 2/3)²

Step-by-step explanation:

We have:

It can be put as:

Here we consider n = a and -2/3 = b, then

Now we add 4/9 to a given binomial to make it perfect square:

So, added 4/9 and got a perfect square (n- 2/3)²

Answer:

x = -3/2

Step-by-step explanation:

0 = 4x² + 12x + 9

4x² + 12x + 9 = 0

(2x + 3)² = 0

2x + 3 = 0

2x = -3

x = -3/2

Hope this helps! :)

Answer:

Range = [- 2.5, 0.5] = [ - 5/2, 1/2]

Step-by-step explanation:

Smallest value of cos α = - 1,

largest value of cos α = 1.

When cos 4x = - 1,  y=3/2cos4x-1 = 3/2*(-1) - 1 = - 5/2 = - 2 1/2 = - 2.5

When cos 4x = 1,  y=3/2cos4x-1 = 3/2*1 - 1 = 1/2 = 0.5

Range = [- 2.5, 0.5] = [ - 5/2, 1/2]

Expand everything in the limit:

[tex]\displaystyle\lim_{h\to0}\frac{(-7+h)^2-49}h=\lim_{h\to0}\frac{(49-14h+h^2)-49}h=\lim_{h\to0}\frac{h^2-14h}h[/tex]

We have [tex]h[/tex] approaching 0, and in particular [tex]h\neq0[/tex], so we can cancel a factor in the numerator and denominator:

[tex]\displaystyle\lim_{h\to0}\frac{h^2-14h}h=\lim_{h\to0}(h-14)=\boxed{-14}[/tex]

Alternatively, if you already know about derivatives, consider the function [tex]f(x)=x^2[/tex], whose derivative is [tex]f'(x)=2x[/tex].

Using the limit definition, we have

[tex]f'(x)=\displaystyle\lim_{h\to0}\frac{f(x+h)-f(x)}h=\lim_{h\to0}\frac{(x+h)^2-x^2}h[/tex]

which is exactly the original limit with [tex]x=-7[/tex]. The derivative is [tex]2x[/tex], so the value of the limit is, again, -14.

Answer:

48.3 cm²

Step-by-step explanation:

Let A be the area of the yellow region

A= the area of the square - the area of the quarter square

A= 15²-(15²*π)/4= 48.28≈ 48.3 cm²

Answer:

Key Feature: - decreasing, As x approaches -(infinite), y approaches (infinite), As x approaches (infinite), y approaches a constant.

Not a Key feature: increasing, As x approaches (infinite) y approaches (infinite), As x approaches -(infinite) y approaches -(infinite), & As x approaches -(infinite) y approaches a constant.

Step-by-step explanation:

u/4 - 4 = -20

Add 4 to both sides:

u/4 = -16

Multiply both sides by 4:

u = -64

Answer:

u=-64

Step-by-step explanation:

u/4 -4 = -20

First add 4 to both sides.

u/4=-16

Now multiply both sides by 4

u=-64

Answer:

The answer is "Option C"

Step-by-step explanation:

Answer:

2317.44

Step-by-step explanation:

Solution for What is 408 percent of 568:

408 percent *568 =

(408:100)*568 =

(408*568):100 =

231744:100 = 2317.44

Answer:

2317.44

Step-by-step explanation:

Your answer is the second option, she should choose the rectangular tiles because the total cost will be $8 less.

To find this answer we need to first find the total cost for using square tiles, and the cost for using rectangular tiles, and compare them. We can do this by finding the area of each tile individually, calculating how many tiles we would need, and multiplying this by the cost for one tile:

Square tiles:

The area of one square tile is 1/2 × 1/2 = 1/4 ft. Therefore we need 40 ÷ 1/4 = 160 tiles. If each tile costs $0.45, this means the total cost will be $0.45 × 160 = $72

Rectangular tiles:

The area of one rectangular tile is 2 × 1/4 = 2/4 = 1/2 ft. Thus we need 40 ÷ 1/2 = 80 tiles. Each tile costs $0.80, so the total cost will be 80 × $0.80 = $64.

This shows us that the rectangular tiles will be cheaper by $8.

I hope this helps! Let me know if you have any questions :)

Answer:

B

Step-by-step explanation:

E2020 : )

For the ODE

[tex]ty'+2y=\sin t[/tex]

multiply both sides by t so that the left side can be condensed into the derivative of a product:

[tex]t^2y'+2ty=t\sin t[/tex]

[tex]\implies(t^2y)'=t\sin t[/tex]

Integrate both sides with respect to t :

[tex]t^2y=\displaystyle\int t\sin t\,\mathrm dt=\sin t-t\cos t+C[/tex]

Divide both sides by [tex]t^2[/tex] to solve for y :

[tex]y(t)=\dfrac{\sin t}{t^2}-\dfrac{\cos t}t+\dfrac C{t^2}[/tex]

Now use the initial condition to solve for C :

[tex]y\left(\dfrac\pi2\right)=9\implies9=\dfrac{\sin\frac\pi2}{\frac{\pi^2}4}-\dfrac{\cos\frac\pi2}{\frac\pi2}+\dfrac C{\frac{\pi^2}4}[/tex]

[tex]\implies9=\dfrac4{\pi^2}(1+C)[/tex]

[tex]\implies C=\dfrac{9\pi^2}4-1[/tex]

So the particular solution to the IVP is

[tex]y(t)=\dfrac{\sin t}{t^2}-\dfrac{\cos t}t+\dfrac{\frac{9\pi^2}4-1}{t^2}[/tex]

or

[tex]y(t)=\dfrac{4\sin t-4t\cos t+9\pi^2-4}{4t^2}[/tex]

Answer:

3ab

Step-by-step explanation:

area = length * width

width = area/length

width = (12ab^2)/(4b)

width = 3ab

Answer:

a) [tex]f^{-1} (x) = \frac{1}{2} Cos^{-1} (\frac{x-1}{3} ) +\frac{3}{2}[/tex]

The inverse of given function

[tex]f^{-1} (x) = \frac{1}{2} Cos^{-1} (\frac{x-1}{3} ) +\frac{3}{2}[/tex]

Step-by-step explanation:

Step(i):-

Given function f(x) = 3 cos (2 x -3) + 1

Let y = f(x) = 3 cos (2 x -3) + 1

     y = 3 cos (2 x -3) + 1

   ⇒ y - 1 =  3 cos (2 x -3)

   ⇒   [tex]cos ( 2 x - 3 ) =\frac{y -1}{3}[/tex]

  ⇒[tex]cos ^{-1} ( cos (2 x - 3)) = Cos^{-1} (\frac{y-1}{3} )[/tex]

We know that inverse trigonometric equations

cos⁻¹(cosθ) = θ

[tex]2 x - 3 = Cos^{-1} (\frac{y-1}{3} )[/tex]

[tex]2 x = Cos^{-1} (\frac{y-1}{3} ) +3[/tex]

[tex]x = \frac{1}{2} Cos^{-1} (\frac{y-1}{3} ) +\frac{3}{2}[/tex]

Step(ii):-

we know that   y= f(x)

The inverse of the given function

                         [tex]x = f^{-1} (y)[/tex]

                    [tex]f^{-1} (y) = \frac{1}{2} Cos^{-1} (\frac{y-1}{3} ) +\frac{3}{2}[/tex]

The inverse of given function in terms of 'x'

                     [tex]f^{-1} (x) = \frac{1}{2} Cos^{-1} (\frac{x-1}{3} ) +\frac{3}{2}[/tex]

conclusion:-

 The inverse of given function

[tex]f^{-1} (x) = \frac{1}{2} Cos^{-1} (\frac{x-1}{3} ) +\frac{3}{2}[/tex]

Answer:

The relationship between the areas of the three squares is that square A plus square B equals the area of square C.

The sum of the square of a and b is equal to the area of square of c

Data;

This theorem is used to calculated a missing side from a right angle triangle when we have the value of at least two sides.

Given that

[tex]c^2 = a^2 + b^2[/tex]

This indicates a relationship such that the sum of square of two sides is equal to the area of the square of one side. I.e the area of the square of c is equal to the sum of the square of both a and b.

Learn more on Pythagoras Theorem here;

https://brainly.com/question/231802

━━━━━━━☆☆━━━━━━━

▹ Answer

(3x + 4) * (4x - 5)

▹ Step-by-Step Explanation

12x² + x - 20

Rewrite

12x² + 16x - 15x - 20

Factor out

4x(3x + 4) - 15x - 20

4x(3x + 4) - 5(3x + 4)

Factor

(3x + 4) * (4x - 5)

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

2m + 1

Step-by-step explanation:

Simply combine like terms. m terms go with m terms and constants go with constants.

Answer:

2m + 1

Step-by-step explanation:

3m + 1 - m =

= 3m - m + 1

= 2m + 1

Answer:  x = -10

Step-by-step explanation:

see image

A) congruent sides implies congruent angles A = 64°

B) Use the Triangle Sum Theorem: 64° + 64° + B = 180° --> B = 52°

C) B and C are complimentary angles: 52° + C = 90°  --> C = 38°

D) Use the Triangle Sum Theorem knowing that congruent sides implies congruent angles: 38° + 2D = 180°  --> D = 71°

∠2) D and ∠2 are supplementary angles: 71° + ∠2 = 180°  --> ∠2 = 109°

Solve for x:

109° = x + 119

 -10  = x

Answer:

x = -10

Step-by-step explanation:

Find the measure of angle m∠2

The triangles are isosceles triangles, the base angles are equal.

The other base angle is also 64°.

Using Triangle Sum Theorem.

64 + 64 + y = 180

y = 52

The top angle is 52°.

The whole angle is 90°.

90 - 52 = 38

The second triangle has base angles equal.

Using Triangle Sum Theorem.

38 + z + z = 180

z = 71

The two base angles are 71°.

Angles on a straight line add up to 180°.

71 + m∠2 = 180

m∠2 = 109

The measure of m∠2 is 109°

Find the value of x

m∠2 = x + 119

109 = x + 119

x = 109 - 119

x = -10

Answer:

The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is (-11.937, -6.863).

Step-by-step explanation:

We have to calculate a 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams.

The sample 1 (Fiberglass), of size n1=26 has a mean of 33.4 and a standard deviation of 2.2.

The sample 2 (Carbon), of size n2=26 has a mean of 42.8 and a standard deviation of 4.3.

The difference between sample means is Md=-9.4.

[tex]M_d=M_1-M_2=33.4-42.8=-9.4[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{2.2^2}{26}+\dfrac{4.3^2}{26}}\\\\\\s_{M_d}=\sqrt{0.186+0.711}=\sqrt{0.897}=0.9473[/tex]

The critical t-value for a 99% confidence interval is t=2.678.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_{M_d}=2.678 \cdot 0.9473=2.537[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M_d-t \cdot s_{M_d} = -9.4-2.537=-11.937\\\\UL=M_d+t \cdot s_{M_d} = -9.4+2.537=-6.863[/tex]

The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is (-11.937, -6.863).

In this way, we can calculate the individual duration of each one and the duration time, knowing that the sample means:

The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is -11.937 and -6.863.

We have to calculate a 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams. The sample 1 (Fiberglass), of size n1=26 has a mean of 33.4 and a standard deviation of 2.2. The sample 2 (Carbon), of size n2=26 has a mean of 42.8 and a standard deviation of 4.3. The difference between sample means is Md=-9.4.

[tex]Sm_d= \sqrt{\frac{\sigma^2_1}{n_1} +\frac{\sigma^2_2}{n_2}} = \sqrt{(0.186)+(0.711) }= 0.9473[/tex]

The critical t-value for a 99% confidednce interval is t=2.678. The margin of error (MOE) can be calculated as:

[tex]MOE=t*8M_d = (2.678)(0.9473)= 2.537[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL= M_d-t*SM_d = -9.4-2.537= -11.937\\UL= M_d+t*SM_d= -9.4+2.537= -6.863[/tex]

The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is (-11.937, -6.863).

See more about statistics at brainly.com/question/2289255