Translate from algebra to English: 14 < 21.

Answer:

Work done = 3750 Joules

Step-by-step explanation:

The force acting in the body should be resolved to it's horizontal component before we can use ut to solve for the problem

Horizontal component= 150 * cos 60

Horizontal component= 150*0.5

Horizontal component= 75N

Work done= Force * distance

Work done= 75*50

Work done= 3750 Nm

Work done = 3750 Joules

Answer:

alpha = 2

beta = -6

Step-by-step explanation:

let everything inside the ln be 'a'

use the chain rule to to differentiate ln a with respect to a

since the differentiation of lnx is 1/x , the differentiation of lna will be 1/a

after the differentiation, you will get: [tex]\frac{1}{a}[/tex] X [tex]\frac{d[(x+1)^{2}X (2x-1)^{2} ] }{dx}[/tex]

you need to use the product rule to differentiate the second part, then multiply 1/a by both the equations being added

replace a with its actual value

you will get [tex]\frac{2}{x + 1}[/tex] and [tex]\frac{-6}{2x -1}[/tex]

by comparing it to the given equation, we get α = 2  and  β = -6

Answer:

  5 pounds

Step-by-step explanation:

The only thing added or removed from the container was heat, which has no weight. The water has the same weight regardless of its chemical phase (solid, liquid, gas, plasma).

  5 pounds

Answer:

Subtraction Property of Equality

Step-by-step explanation:

When solving an equation for a variable (in this case n), we want to move all of the n-terms to 1 side and the non-n terms to the other side. To do this, we can subtract 5.2 from both sides to leave 2.5n by itself. The property we used to do this is the Subtraction Property of Equality which states that if you subtract a quantity from one side of an equation, you must also subtract that same quantity from the other side of the equation.

Answer: A is the right one

Step-by-step explanation:

Consider the linear equation, 2.5n + 5.2 = 35.2.

What property will be used to complete the first step in solving for n?

subtraction property of equality

multiplication property of equality

division property of equality

distributive property

Answer:

nxjhbfhbfwihsfnjkfdbjbshcxbdbjibebfhdhwhhdhdhffvnfnjehrhffbfgnfjrjhhfrj

Step-by-step explanation:

Answer:

Hey there!

We have cosine 61=y/500

cosine 61(500)=242.4 ft.

Let me know if this helps :)

Answer:

a. The probability of a value between 75.0 and 90.0 is 0.40173

b. The probability of a value of 75.0 or less is 0.35942

c. The probability of a value between 55.0 and 70.0 is 0.19712

Step-by-step explanation:

To solve for this we make use of the z score formula.

z = (x-μ)/σ,

where

x = raw score

μ = the population mean

σ = the population standard deviation.

a. Compute the probability of a value between 75.0 and 90.0.

When x = 75

μ =80.0 and σ = 14.0.

z = (x - μ)/σ

z = 75 - 80/ 14

z = -0.35714

z = -0.36 to 2 decimal places

Using the z score table to find the probability

P(x = 75) = P(z = -0.36)

= 0.35942

For x = 90

z = 90 - 80/14

z = 0.71429

z = 0.71 to 2 decimal place

Using the z score table to find the probability

P(x = 90) = P(z = 0.71)

= 0.76115

The probability of a value between 75.0 and 90.0 is:

75 < x < 90

= P( x = 90) - P(x = 75)

= 0.76115 - 0.35942

= 0.40173

Therefore, probability of a value between 75.0 and 90.0 is 0.40173

b. Compute the probability of a value of 75.0 or less.

For x = 75

From the question, we know that

mean of 80.0 and a standard deviation of 14.0.

z = (x - μ)/σ

z = 75 - 80/ 14

z = -0.35714

z = -0.36 approximately to 2 decimal places.

P-value from Z-Table:

P(x ≤ 75) = 0.35942

c. Compute the probability of a value between 55.0 and 70.0.

For x = 55

From the question, we know that

mean of 80.0 and a standard deviation of 14.0.

z = (x - μ)/σ

z = 55 - 80/ 14

z = -1.78571

z = -1.79 approximately to 2 decimal places

Using the z score table to find the probability

P(x = 55) = P(z = -1.79)

= 0.036727

For x = 70

z = 70 - 80/14

z = -0.71429

z = - 0.71 approximately to 2 decimal place.

Using the z score table to find the probability

P(x = 70) = P(z = -0.71)

= 0.23885

The probability of a value between 55.0 and 70.0 is:

55 < x < 70

= P( x = 70) - P(x = 55)

= P( z = -0.71) - P(z = -1.79)

= 0.23885 - 0.03673

= 0.19712

Answer:

According to the picture you have AD AND BC

Step-by-step explanation:

Answer:

[tex]\sqrt{11.5} =w[/tex] (Width)

[tex]4\sqrt{11.5}= Length[/tex]

Step-by-step explanation:

Area of a rectangle: 46 = w(L)

L = 4w

Substitute

46 = 4[tex]w^{2}[/tex]

Divide both by 4

[tex]11.5=w^{2}[/tex]

[tex]\sqrt{11.5} =w[/tex] (Width)

[tex]4\sqrt{11.5}= Length[/tex]

Answer:

The equations needed to solve this problem are:

y = 12 + 6x

y = 12x

The number of posters completed by each Avenger will be 24.

Step-by-step explanation:

The information provided are:

Ms. Ironperson has completed 12 posters and will complete 6 more per day.

Mr. Thoro has not started yet but can make 12 per day.

The variable x denotes the number of days and y denotes the number of posters.

So, after x day the number of poster completed by Ms. Ironperson will be:

y = 12 + 6x

And after x day the number of poster completed by Mr. Thoro will be:

y = 12x

Thus, the equations needed to solve this problem are:

y = 12 + 6x

y = 12x

Compute the value of x as follows:

12x = 12 + 6x

6x = 12

x = 2

The number of posters completed by each Avenger is:

y = 12x = 12 × 2 = 24

Thus, the number of posters completed by each Avenger will be 24.

Answer:

The answer is 6

Step-by-step explanation:

2 x 5 = 10

10 - 4 = 6

Hope this helps!

Answer:

6

Step-by-step explanation:

2 x 5 = 10

10 - 4 = 6

I hope this helps!

Answer:

Slope= 2

Step-by-step explanation:

Rate of change can simply be called slope

So the rate of change or slope of the linear function that passes through the points (2, 9) and (-1, 3) is

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

Where y2= 3

Y1= 9

X2= -1

X1= 2

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

Slope= (3-9)/(-1-2)

Slope= -6/-3

Slope= 2

Answer:

-5

Step-by-step explanation:

Answer:

y = -4/3x +8

Step-by-step explanation:

Slope intercept form is

y = mx+b where m is the slope and b is the y intercept

4x+3y = 24

Subtract 4x from each side

3y = -4x+24

Divide each side by 3

y = -4/3x +24/3

y = -4/3x +8

Answer: y = -4/3x +8

Answer:

[tex]|-8|<|-10| \Longleftrightarrow 8 < 10[/tex]

[tex]\text{Which property is shown by } 4+(5+6)=(4+5)+6?[/tex]

[tex]\text{It is the associative property of addition}[/tex]

You can group the addends in any combination and it won't change the result.

Answer:

$9261

$1261

Step-by-step explanation:

Principal: $8000

Interest rate: 5% PA compounded annually

Time: 3 years

Answer:

R = { ( 3 , 1 ) , (4 , 1) , (4 , 2) }

Step-by-step explanation:

Which ordered pairs are in the relation {(x, y) | x > y + 1} on the set {1, 2, 3, 4}

Assuming that:

R should be the set of real numbers such that:

R = { (x,y) | x > y + 1}  on the set {1, 2, 3, 4}

Then:

The ordered pairs for the relation can be computed as:

R = { ( 3 , 1 ) , (4 , 1) , (4 , 2) }

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

Explanation:

The equation should be h(t) = -16t^2 + (initial height). If you subtract off the initial height, then you'll have a negative starting height, which is not correct. Try plugging t = 0 into h(t) = -16t^2 - (initial height) and you'll see what I mean.

The initial height is 5184. We want to find the t value when h(t) = 0. So we want to find the time value when the height is 0.

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

h(t) = -16t^2 + (initial height)

h(t) = -16t^2 + 5184

0 = -16t^2 + 5184

16t^2 = 5184

t^2 = 5184/16

t^2 = 324

t = sqrt(324)

t = 18

It takes 18 seconds for the rope to hit the ground.

Answer:

Step-by-step explanation:

[tex] \sf{3 - x = 5x + 21}[/tex]

Move 5x to left hand side and change it's sign

⇒[tex] \sf{ - x - 5x + 3 = 21}[/tex]

Move 3 to right hand side and change it's sign

⇒[tex] \sf{ - x - 5x = 21 - 3}[/tex]

Collect like terms

⇒[tex] \sf{ - 6x = 21 - 3}[/tex]

Subtract 3 from 21

⇒[tex] \sf{ - 6x = 18}[/tex]

Divide both sides of the equation by -6

⇒[tex] \sf{ \frac{ - 6x}{ - 6} = \frac{18}{-6}} [/tex]

Calculate

⇒[tex] \sf{x = -3}[/tex]

Hope I helped!

Best regards!!

Answer:

x = - 3

Step-by-step explanation:

3 - x = 5x + 21

- x + 3 = 5x + 21

(- x + 3) + (- 3 - 5x) = (5x + 21) + (- 3 - 5x)

(- x + 3) + (- 5x - 3) = (5x + 21) + (- 5x - 3)

- x + 3 - 5x - 3 = 5x + 21 - 5x - 3

- x - 5x + 3 - 3 = 5x - 5x + 21 - 3

- 6x = 18

x = - 18/6

x = - 3

Answer:

8.9375

Step-by-step explanation:

2.75×3.25=8.9375

According to the question it said increase to and that is why I only multiplied but if the question said increase by then I would have to add my product (8.9375) to the original height of the photo.

Answer:

8x−14

Step-by-step explanation:

3x - 4 + 5x - 10

=3x+−4+5x+−10

Combine Like Terms:

=3x+−4+5x+−10

=(3x+5x)+(−4+−10)

Answer:

[tex] x = \sqrt{30} [/tex]

Step-by-step explanation:

BD is the altitude of the right ∆ which divides the hypotenuse to create two line segments, CD, and AD.

According to the right triangle altitude theorem,

[tex] BD = \sqrt{CD*AD} [/tex]

CD = 3, AD = 7, therefore,

[tex] BD = \sqrt{3*7} [/tex]

[tex] BD = \sqrt{21} [/tex]

Find x using Pythagorean theorem

[tex] x^2 = BD^2 + CD^2 [/tex]

[tex] x^2 = (\sqrt{21})^2 + 3^2 [/tex]

[tex] x^2 = 21 + 9 [/tex]

[tex] x^2 = 30 [/tex]

[tex] x = \sqrt{30} [/tex]

Answer:

Step-by-step explanation:

First of all we need to convert 14.0 acres to m²

1.00 acre = 4046.86 m²

14.0 acres = 14 × 4046.86 = 56656.04 m²

Area of a circle = πr²

where

r is the radius

To find the radius substitute the value for the area into the above formula and solve for the radius

That's

[tex]56656.04 = \pi {r}^{2} [/tex]

Divide both sides by π

We have

[tex] {r}^{2} = \frac{56656.04}{\pi} [/tex]

Find the square root of both sides

[tex]r = \sqrt{ \frac{56656.04}{\pi} } [/tex]

r = 134.29139

r = 134.29 m to 2 decimal places

Hope this helps you

Answer:

we have no way of knowing

Step-by-step explanation:

it could be a jedi mind trick.

Answer:

Step-by-step explanation:

To solve this question we use ratio and proportion

If in 20 days they ride 3,653.6 km , then

in 1 day they will ride [tex] \frac{3653.6 \times 1}{20} [/tex]

We have the final answer as

Hope this helps you

Answer:

4 sq. units

Step-by-step explanation:

Because the vertices of S₂ are the midpoints of S₁, the area of S₂ will be half of that of S₁ which is 16 / 2 = 8. Similarly, because the same process is carried out on S₂ to make S₃, the area of S₃ is 8 / 2 = 4 sq. units.

Answer:

hope this helps friend

Step-by-step explanation:

A = a^2

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Answer:

[tex][P(X_{1})\times P (X_{2})]>[\frac{9}{4}\times P (H_{1})][/tex]

Step-by-step explanation:

Let the candy "Honey Bunny" be labelled as H and the other candies as X.

It is provided that the machine is running out of "Honey Bunny".

So, Lisa wants to program it so that the probability of getting a candy other than "Honey Bunny" twice in a row is greater than 9/4 times the probability of getting "Honey Bunny" in one try.

        P (X₁) × P (X₂)

        P (H₁)

The inequality is as follows:

[tex][P(X_{1})\times P (X_{2})]>[\frac{9}{4}\times P (H_{1})][/tex]

Answer:

(1-p)^2>9/4p

Step-by-step explanation:

Answer:

Decision rule : The  p-value  <  [tex]\alpha[/tex] so  the  null hypothesis is rejected

The test statistics is  [tex]t = -2.8[/tex]

The  manger will not be manager be satisfied that the company is not under-filling since the company is under-filling its cups

Step-by-step explanation:

From the question we are told that

    The  sample size is  n  =  16

     The  sample  mean is  [tex]\= x = 5.85[/tex]

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

      The  null hypothesis is  [tex]H_o : \mu \ge 6[/tex]

       The alternative  hypothesis is  [tex]H_a : \mu < 6[/tex]

       The  level of significance is  [tex]\alpha = 0.05[/tex]

Generally the test statistics is mathematically represented as

        [tex]t = \frac{ \= x - \mu }{ \frac{\sigma }{ \sqrt{n} } }[/tex]

=>    [tex]t = \frac{ 5.86 - 6 }{ \frac{ 0.2}{ \sqrt{ 16} } }[/tex]

=>   [tex]t = -2.8[/tex]

The  p-value is obtained from the z-table  the value is  

       [tex]p-value = P(Z < -2.8 ) = 0.0025551[/tex]

     [tex]p-value = 0.0025551[/tex]

 Given that the [tex]p-value < \alpha[/tex] we reject the null hypothesis

Hence there is sufficient evidence to support the concern of the quality control manager. and the manger will not be satisfied that since the test proof that the company is under-filling its cups

Answer:

[tex]\Huge \boxed{-2-m}[/tex]

Step-by-step explanation:

2 + m

Rewrite with variable first.

m + 2

m + 2

Can’t be simplified further.

m - (-2)

Distribute negative sign.

m + 2

-2-m

Rewrite with variable first.

-m - 2

The last expression is not equivalent to m+2.

Standard polynomial form means that the terms are arranged from highest to lowest degree.

The leading coefficient is the number before the highest degree.

The degree of the polynomial is the power of the variable attached to the leading coefficient.

1) This is not in standard polynomial form.

The leading coefficient is -1.

This is a second-degree polynomial.

2) This is in standard polynomial form.

The leading coefficient is 3.

This is a fourth-degree polynomial.

3) This is not in standard polynomial form.

The leading coefficient is 3.

This is a fifth-degree polynomial.

4) This is in standard polynomial form.

The leading coefficient is -4.

This is a fifth-degree polynomial.

5) This is not in standard polynomial form.

The leading coefficient is -5.

This is a third-degree polynomial.

6) This is not in standard polynomial form.

The leading coefficient is -1.

This is a sixth-degree polynomial.

7) This is in standard polynomial form.

The leading coefficient is 2.

This is a second-degree polynomial.

8) This is in standard polynomial form.

The leading coefficient is 1.

This is a second-degree polynomial.

9) This is in standard polynomial form.

The leading coefficient is 1.

This is a third-degree polynomial.

10) This is not in standard polynomial form.

The leading coefficient is 6.

This is a fourth-degree polynomial.

Answer: 49+64i

Step-by-step explanation:

Concept to know:

i=√-1

i²=-1

i³=-i

[tex]i^{4}[/tex]=1

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

 (-5+8i)(3-8i)

=-15+40i+24i-64i²

=-15+64i-64i²

=-15+64i+64  (remember, i²=-1)

=49+64i

Hope this helps!! :)

Please let me know if you have any question or need further explanation