Find the solution for the equation. 3 (n - 4) = -12​

Answer:

-8z +724 + 5y +2c

Step-by-step explanation:

Combine like terms

Answer:

[tex]95 \frac{3}{4} \: inch \leqslant x \leqslant 96 \frac{1}{4} \: inch[/tex]

Step-by-step explanation:

Given that a lumber supplier sells 96 inch Pieces of oak which must be within 1/4 of an inch.

This situation can be represented by the following absolute value inequality:

[tex]|x \: - 96| \: \leqslant \: \frac{1}{4} [/tex].

The absolute value can be thought of as the size of something because length cannot be negative. The length must be no more than 1/4 away from 96.

To simplify this, pretend this is a standard equality, |x-96| = 1/4. 1/4 is the range of acceptable length, 96 is the median of the range, and x is the size of the wood.

First apply the rule |x| = y → x = [tex]\pm[/tex]y

|x-96| = 1/4

x - 96 = [tex]\pm[/tex]1/4

x = [tex]96 \pm 1/4[/tex]

(These are just the minimum, and maximum sizes)

Now with a less than or equal to, the solutions are now everything included between these two values.

Therefore:

[tex]96 - 1/4 \: \leqslant x [/tex] [tex]\leqslant \: 96 + 1/4 [/tex]

With less than inequalities, you must have the lower value on the left, and the higher value on the right.

If x represents the size of the pieces, then the acceptable lengths are represented by this following inequality:

[tex]95 \frac{3}{4} \: inch \leqslant x \leqslant 96 \frac{1}{4} \: inch[/tex]

This is interpreted as x (being the size of the oak) is greater than or equal to 95 3/4, and less than or equal to 96 1/4 in inches.

Answer:

A) The height of the trapezoid is 6.5 centimeters.

B) We used an algebraic approach to to solve the formula for [tex]b_{1}[/tex].  [tex]b_{1} = \frac{2\cdot A}{h}-b_{2}[/tex]

C) The length of the other base of the trapezoid is 20 centimeters.

D) We can find their lengths as both have the same length and number of variable is reduced to one, from [tex]b_{1}[/tex] and [tex]b_{2}[/tex] to [tex]b[/tex]. [tex]b = \frac{A}{h}[/tex]

Step-by-step explanation:

A) The formula for the area of a trapezoid is:

[tex]A = \frac{1}{2}\cdot h \cdot (b_{1}+b_{2})[/tex] (Eq. 1)

Where:

[tex]h[/tex] - Height of the trapezoid, measured in centimeters.

[tex]b_{1}[/tex], [tex]b_{2}[/tex] - Lengths fo the bases, measured in centimeters.

[tex]A[/tex] - Area of the trapezoid, measured in square centimeters.

We proceed to clear the height of the trapezoid:

1) [tex]A = \frac{1}{2} \cdot h \cdot (b_{1}+b_{2})[/tex] Given.

2) [tex]A = 2^{-1}\cdot h \cdot (b_{1}+b_{2})[/tex] Definition of division.

3) [tex]2\cdot A\cdot (b_{1}+b_{2})^{-1} = (2\cdot 2^{-1})\cdot h\cdot [(b_{1}+b_{2})\cdot (b_{1}+b_{2})^{-1}][/tex] Compatibility with multiplication/Commutative and associative properties.

4) [tex]h = \frac{2\cdot A}{b_{1}+b_{2}}[/tex] Existence of multiplicative inverse/Modulative property/Definition of division/Result

If we know that [tex]A = 91\,cm^{2}[/tex], [tex]b_{1} = 16\,cm[/tex] and [tex]b_{2} = 12\,cm[/tex], then height of the trapezoid is:

[tex]h = \frac{2\cdot (91\,cm^{2})}{16\,cm+12\,cm}[/tex]

[tex]h = 6.5\,cm[/tex]

The height of the trapezoid is 6.5 centimeters.

B) We should follow this procedure to solve the formula for [tex]b_{1}[/tex]:

1) [tex]A = \frac{1}{2} \cdot h \cdot (b_{1}+b_{2})[/tex] Given.

2) [tex]A = 2^{-1}\cdot h \cdot (b_{1}+b_{2})[/tex] Definition of division.

3) [tex]2\cdot A \cdot h^{-1} = (2\cdot 2^{-1})\cdot (h\cdot h^{-1})\cdot (b_{1}+b_{2})[/tex] Compatibility with multiplication/Commutative and associative properties.

4) [tex]2\cdot A \cdot h^{-1} = b_{1}+b_{2}[/tex] Existence of multiplicative inverse/Modulative property

5) [tex]\frac{2\cdot A}{h} +(-b_{2}) = [b_{2}+(-b_{2})] +b_{1}[/tex] Definition of division/Compatibility with addition/Commutative and associative properties

6) [tex]b_{1} = \frac{2\cdot A}{h}-b_{2}[/tex] Existence of additive inverse/Definition of subtraction/Modulative property/Result.

We used an algebraic approach to to solve the formula for [tex]b_{1}[/tex].

C) We can use the result found in B) to determine the length of the remaining base of the trapezoid: ([tex]A= 215\,cm^{2}[/tex], [tex]h = 8.6\,cm[/tex] and [tex]b_{2} = 30\,cm[/tex])

[tex]b_{1} = \frac{2\cdot (215\,cm^{2})}{8.6\,cm} - 30\,cm[/tex]

[tex]b_{1} = 20\,cm[/tex]

The length of the other base of the trapezoid is 20 centimeters.

D) Yes, we can find their lengths as both have the same length and number of variable is reduced to one, from [tex]b_{1}[/tex] and [tex]b_{2}[/tex] to [tex]b[/tex]. Now we present the procedure to clear [tex]b[/tex] below:

1) [tex]A = \frac{1}{2} \cdot h \cdot (b_{1}+b_{2})[/tex] Given.

2) [tex]b_{1} = b_{2}[/tex] Given.

3) [tex]A = \frac{1}{2}\cdot h \cdot (2\cdot b)[/tex] 2) in 1)

4) [tex]A = 2^{-1}\cdot h\cdot (2\cdot b)[/tex] Definition of division.

5) [tex]A\cdot h^{-1} = (2\cdot 2^{-1})\cdot (h\cdot h^{-1})\cdot b[/tex] Commutative and associative properties/Compatibility with multiplication.

6) [tex]b = A \cdot h^{-1}[/tex] Existence of multiplicative inverse/Modulative property.

7) [tex]b = \frac{A}{h}[/tex] Definition of division/Result.

Answer:

Step-by-step explanation:

Given the profit made by a company modeled by the function

p = -n² + 300n + 100,000

The company breaks even when p = 0

To get the number of boxes sold when the company breaks even, we will substitute p = 0 into the equation.

0 = -n² + 300n + 100,000

multiply through by -1

0 = n² - 300n - 100,000

n² - 300n - 100,000 = 0

(n² - 500n) + (200n - 100,000) = 0

n(n-500)+200(n-500) = 0

(n+200)(n-500) = 0

n+200 = 0 and n-500 = 0

n = -200 and n = 500

Since n cannot be negative

Hence n = 500

This means that the company breaks even when it sells 500 boxes

Answer:

99.7%

Step-by-step explanation:

Empirical rule formula states that:

• 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ.

• 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ.

• 99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.

From the question, we have mean of 98.18 F and a standard deviation of 0.65 F

The approximate percentage of healthy adults with body temperatures between 96.23 F and100.13 ​F is

μ - 3σ

= 98.18 - 3(0.65)

= 98.18 - 1.95

= 96.23 F

μ + 3σ.

98.18 + 3(0.65)

= 98.18 + 1.95

= 100.13 F

Therefore, the approximate percentage of healthy adults with body temperatures between 96.23 F and 100.13 ​F which is within 3 standard deviations of the mean is 99.7%

Answer:

No -60 is not a solution

Step-by-step explanation:

x = 5/12 = 2.400

-60 is not a solution of 5/12, or 1/12*=5.

Hope I helped.

Answer:

Symbols= P(A^1)

Value: 2/5 , 4/25 , 3/5 , 16/25

Step-by-step explanation:

Slope: 1/2

y-intercept(s): (0, 7/3)

x: 0, 7

y: 7/3, 0

Step-by-step explanation:

y=-3 -1/3(1+2)=2/3.3=1.3=3

y=3

Answer:

The slope is 0

Step-by-step explanation:

Answer:

172.72 centimeters

Step-by-step explanation:

1. 5 ft. = 60 in.

2. 60 in. + 8 in. = 68 in.

3. 68 x 2.54 = 172.72

4. add unit of measurement to your answer

Henry's height in centimeters is 172.72 cm

"A process of finding the value of a single unit, and based on this value we can find the required value. "

For given question,

Henry measured 5 feet 8 inches tall.

There are 2.54 centimeters in 1 inch.

that is, 1 inch = 2.54 cm

First we convert Henry's height in inches.

We know that 1 feet =  12 inches

⇒ 5 feet = 60 inches

so, Henry's height in inches would be,

5 feet 8 inches

= (60 + 8) inches

= 68 inches

From given, 1 inch = 2.54 cm

⇒ 68 inches = 172.72 cm

Therefore, Henry's height in centimeters is 172.72 cm

Learn more about the unitary method here:

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Let

F--------> represent the force

m--------> represent the mass

a-------> represent the acceleration

we know that

The formula that relates three quantities: Force (F), mass (m), and acceleration (a) is equal to

Part a) Solve this equation for a

Divide both sides by the mass

therefore

the answer part a) is equal to

Part b) Let the force be 25 units and the mass be m = 10 units. What is the acceleration, a?

we know that

the formula of acceleration is equal to

in this problem

we have

Substitute the values n the formula

therefore

the answer part b( is equal to

Part c) Let the force be F = 25 units and the acceleration be a = 5 units. What is the mass, m?

we know that

Solve for m

Divide both sides by the acceleration

in this problem

we have

Substitute the values n the formula

therefore

the answer Part c) is

Answer:

[tex]2 \frac{2}{3} [/tex]

Answer:

A-true

Step-by-step explanation:

Answer:

The answer is c. 5 5/8.

Step-by-step explanation:

Its c because your supposed to multiply them. When you multiply them you get 5 5/8. Hope this helped,have a great day!

Answer:

1/4 - 1/3i

Step-by-step explanation:

(4+3i)(-i) / 12i(-i)

= 3 - 4i / 12

Answer:

4/5

Step-by-step explanation:

Answer: The answer will be that x=1

Step-by-step explanation:Isolate the variable by dividing each side by factors that don't contain the variable. Hope this helps!

Answer:

[tex]-8,+735[/tex]

Step-by-step explanation:

The lowest point in New Orleans is 8 feet below sea  level.

This can be represented numerically using [tex]-8[/tex]

(negative sign denotes below sea level)

The highest point in Chicago is 735 feet above sea  level.

This can be represented numerically using [tex]+735[/tex]

(positive sign denotes above sea level)

Answer:

This is correct but if some people are confused it’s a negative integer and a positive integer

Step-by-step explanation:

The answer is ±3[tex]\sqrt{3\\}[/tex]

First, you should make one side of the quadratic 0. You can do this by subtracting 17 from both sides, making the equation

2/3x^2 - 18 = 0

To make everything an integer, you can multiply both sides by 3/2, making the equation

x^2 - 27 = 0

By adding 27 to both sides, you get

x^2 = 27

Now you are practically done! By taking the square root of both sides, you get

x = ±3[tex]\sqrt{3\\}[/tex]

Answer:

Step-by-step explanation:

The maximum profit will be found in the vertex of the parabola, which is what your equation is. You could do this by completing the square, but it is way easier to just solve for h and k using the following formulas:

[tex]h=\frac{-b}{2a}[/tex] for the x coordinate of the vertex, and

[tex]k=c-\frac{b^2}{4a}[/tex] for the y coordinate of the vertex.

x will be the selling price of each widget and y will be the profit. Usually, x is the number of the items sold, but I'm going off your info here for what the vertex means in the context of this problem.

Our variables for the quadratic are as follows:

a = -10

b = 600

c = -3588. Therefore,

[tex]h=\frac{-600}{2(-10)}=30[/tex] so the cost of each widget is $30. Now for the profit:

[tex]k=-3588-(\frac{(600)^2}{4(-10)})[/tex] This one is worth the simplification step by step:

[tex]k=-3588-(\frac{360000}{-40})[/tex] and

k = -3588 - (-9000) and

k = -3588 + 9000 so

k = 5412

That means that the profit made by selling the widgets at $30 apiece is $5412.

Hence,the profit made by selling the widgets at $[tex]30[/tex] apiece is $[tex]5412[/tex].

What is the maximum profit?

Maximum profit, or profit maximisation, is the process of finding the right price for your products or services to produce the best profit.

Here given that,

A company sells widgets. The amount of profit, [tex]y[/tex], made by the company, is related to the selling price of each widget, [tex]x[/tex], by the given equation.

As the maximum profit found in the vertex of the parabola,

Here, [tex]x[/tex] will be the selling price of each widget and [tex]y[/tex] will be the profit.

The number of items sold is [tex]x[/tex].

So, the quadratic equation is:-

[tex]a = -10b = 600c = -3588.[/tex]

Therefore, so the cost of each widget is $[tex]30[/tex].

For the profit:-

[tex]k = -3588 - (-9000) andk = -3588 + 9000 sok = 5412[/tex]

Hence,the profit made by selling the widgets at $[tex]30[/tex] apiece is $[tex]5412[/tex].

To know more about the maximum profit

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Answer:

(a)0.625s (b)1.569s

Step-by-step explanation:

it's Physics, not Math.

Details of the answer:

https://brainly.com/question/13741614

Answer:

With this algebraic representation of physics, we can also apply the mathmatical concept of quadratics to derive the components from this function. You can use the line of symmetry: x = -b/2a. To find the minimum or maximum height because of its association with the vertex. This function is in the standard quadratic form: ax^2 + bx + c where x is t. According to this instance, a being -16, b being 24, and c being 8. t = -b/2a → -24/-32 = 3/4 which also represents the maximum value because a is negative so it is opening downward.

To find the max height, substitute the value of x back into the equation f(3/4) = -16(3/4)^2 + 24(3/4) + 8 →

-9 + 18 + 8 = 17ft [maximum height]

We already solved for the time (x) in terms of t which is 3/4 sec [time of maximum height].

Answer:

no solution

Step-by-step explanation:

the x's cancel out, and if you plug in 0 for x, you get -8=6 (which isn't true)

Given:

A basketball player made 55 baskets in a season.

20% of these baskets were three-point shots.

To find:

The number of three-point shots.

Solution:

We have,

Total number of baskets = 55

Number of three-point shots = 20% of total baskets

Now,

[tex]\text{Number of three-point shots}=\dfrac{20}{100}\times 55[/tex]

[tex]\text{Number of three-point shots}=\dfrac{1}{5}\times 55[/tex]

[tex]\text{Number of three-point shots}=11[/tex]

Therefore, the number of three-point shots did made by the player is 11.

Answer:

? What is the question?

Step-by-step explanation:

Answer:

where is the rest of the question,,?

Step-by-step explanation:

Answer:

3 : 1

Step-by-step explanation:

The biggest circle has a radius of 20 cm

So that means, its area will be,

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

Area = [tex]\pi * 20^{2}[/tex]

A = [tex]\pi * 400[/tex]

=> A = 400[tex]\pi[/tex]

We do not need to solve this because it is nit required

Then, one small circle has an area of,

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

Area = [tex]\pi *5^{2}[/tex]

Area = [tex]\pi *25[/tex]

=> Area = 25[tex]\pi[/tex]

As there are 4 circles in, we get that the area covered by the small squares,

=> [tex]25\pi * 4[/tex]

=> [tex]100\pi[/tex]

So, the amount shaded = 100/400 (We can omit the [tex]\pi[/tex] at this stage because we are finding out a ratio)

=> 1/4

So, there is 1 cut region and the remaining is the uncut region,

As we need to find uncut to cut, the ratio will be,

=> remaining : 1

=> 3 : 1

If my answer helped, kindly mark me as the brainliest!!

Thanks!!

Answer:

D.) 14.2*0.784

Step-by-step explanation:when you calculate it, there is 4 numbers behind the decimal point.

Complete question:

A coin is biased such that a head is three times as likely to occur as a tail. Find the expected number of tails when this coin is tossed twice.

Answer:

1/2

Step-by-step explanation:

Head is 3 times as likely to occur as tail;

Hence,

Sample space for 2 tosses :

{HH, HH, HH, HH, HH, HH, HH, HH, HH, HT, HT, HT, HT, HT, HT, TT}

Expected probability (E(x)) = Σx*p(x)

P(x) = required outcome / Total possible outcomes

x : __________ 0 ______ 1 _______ 2

p(x) : ________9/16_____6/16_____1/16

Σx*p(x) : 0(9/16) + 1(6/16) + 2(1/16)

= 0 + 6/16 + 2/16

= 0 + 3/8 + 1/8

= 4/8

= 1/2

Answer:

The number of tickets sold at the gate is [tex] G = 211.25[/tex]

The number of tickets sold in advance is  [tex]  A = 311.25 [/tex]

Step-by-step explanation:

From the question we are told that

 The cost of a tickets at the gate is [tex]a =  \$ 5[/tex]  

  The cost of a ticket in advance is  [tex]b =  \$ 3[/tex]

Let the number of ticket sold in the gate be G

Let the number of ticket sold in advance  be   A

From the question we are told that

  One hundred more tickets were sold in advance than at the gate and this can be mathematically represented as

       [tex]G  +  100 =  A[/tex]

From the question we are told that

  The total revenue from ticket sales was $1990  and this can be mathematically represented as

    [tex]5 G  +  3A  =  1990[/tex]

substituting for  A in the equation above

    [tex]5 G  +  3[G  +  100]=  1990[/tex]    

    [tex]5 G  +  3G  +  300=  1990[/tex]    

    [tex] 8G  +  300=  1990[/tex]  

    [tex] 8G  =  1690[/tex]

=>  [tex] G = 211.25[/tex]

Substituting this for G in the above equation

     [tex]5 [211.25]  +  3A  =  1990[/tex]

=>    [tex]  3A  =  1990 - 1056.25[/tex]

=>    [tex]  A = 311.25 [/tex]