Simplify the fraction (4t^2-16/8) / (t-2/6)

Answer:

  There are none.

Step-by-step explanation:

3 is a divisor of the modulus, so the product mod 6 will be either 3 or 0.

In the modular arithmetic problem 3 x ? = 1 (mod 6), the correct positive number replacement for the question mark is 3.

The problem given is a modular arithmetic equation: 3 x ? = 1 (mod 6). To solve for the question mark (?), we need to find a number that when multiplied by 3 and divided by 6, leaves a remainder of 1. Since we are working with mod 6, the potential replacements for the question mark can only be positive numbers less than 6.

The steps to find the solution are as follows:

Try each positive number less than 6 to see which, when multiplied by 3, yields a remainder of 1 when divided by 6.

By testing, we find that 3 x 5 = 15, and 15 mod 6 = 3 x 6 + 1 (15 = 2*6 + 3).

Since we need a remainder of 1, and not 3, we should keep looking.

Next, 3 x 3 = 9, and 9 mod 6 = 1 since 9 = 1*6 + 3 = 3 x 3.

Thus, the number that satisfies the equation is 3 since it makes the modular equation true: 3 x 3 = 9, and 9 mod 6 = 3 x 6 + 3, which gives us a remainder of 1.

The correct positive number replacement for the question mark making the statement true is 3.

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\[/tex]

[tex]\bf \left( \cfrac{20x^5y^2}{5x^{-3}y^7} \right)^{-3}\implies \left( \cfrac{5x^{-3}y^7}{20x^5y^2} \right)^3\implies \left( \cfrac{5^3x^{-3\cdot 3}y^{7\cdot 3}}{20^3x^{5\cdot 3}y^{2\cdot 3}} \right)\implies \cfrac{5^3}{20^3}\cdot \cfrac{x^{-9}y^{21}}{x^{15}y^6} \\\\\\ \cfrac{1}{64}\cdot \cfrac{y^{21}\cdot y^{-6}}{x^{15}\cdot x^9}\implies \cfrac{1}{64}\cdot \cfrac{y^{21-6}}{x^{15+9}}\implies \cfrac{y^{15}}{64x^{24}}[/tex]

Answer:

Simplify inside the parentheses by dividing coefficients, subtracting the exponents on like bases, and raising the resulting expression to the –3 power. Then, write bases with positive exponents.

Raise the numerator and denominator to the –3 power. Then, using the power of a power property, multiply the exponents. Divide the coefficients and subtract the exponents on like bases, then write with positive exponents.

Step-by-step explanation:

Answer:

Answer:

24.32%

2610 is 24.32% of 10730

Step-by-step explanation:

Solution:

2610 is what percent of 10730?

2610 is P% of 10730

Equation: Y = P% * X

Solving our equation for P

P% = Y/X

P% = 2610/10730

p = 0.2432

Convert decimal to percent:

P% = 0.2432 * 100 = 24.32%

Answer:

The probability of the randomly selected student being a graduate is 24%.

Step-by-step explanation:

From the charts we can see that there 8120 students that are Undergraduates and 2610 students that are Graduates. We add this up to get the total number of students in the University 10730. This Gives us the following fraction of Graduates in the University.

[tex]\frac{2610}{10730} =  0.243[/tex]

[tex]0.243*100  = 24.3[/tex]  ...we multiply by 100 to turn the decimal into a percent

We can then round to the nearest percentage which is 24%.

So the probability of the randomly selected student being a graduate is 24%.

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

Subtract the average from the sales to get the deviation.

Aug. 1700 - 1412.50 = 287.50

Sept. 1125 - 1412.50 = -287.50

Oct. 1850 - 1412.50 = 437.50

Nov. 1500 - 1412.50 = 87.50

Dec. 1050 - 1412.50 = -362.50

The monthly deviation from the average exists at 287.50, -287.50, 437.50, 87.50, and -362.50.

Estimating the mean average enables you to specify the deviation from the mean by computing the difference between the mean and each value.

Subtract the average from the sales to acquire the deviation.

Aug. 1700 - 1412.50 = 287.50

Sept. 1125 - 1412.50 = -287.50

Oct. 1850 - 1412.50 = 437.50

Nov. 1500 - 1412.50 = 87.50

Dec. 1050 - 1412.50 = -362.50

The monthly deviation from the average exists at 287.50, -287.50, 437.50, 87.50, and -362.50.

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Answer:

34

Step-by-step explanation:

Patrick play 6 minutes on the second quarter and 10 on the last two quarters

Answer: Patrick played 6 minutes during the second quarter.

Step-by-step explanation:

Since we have given that

Length of each quarter = 10 minutes

Ralph played the whole first quarter, the first 4 minutes of the second quarter, and the whole fourth quarter.

whereas, Patrick played the rest of the second quarter, third quarter.

Length of second quarter Patrick played is given by

[tex]10-4\\\\=6\ minutes[/tex]

Hence, Patrick played 6 minutes during the second quarter.

The measure of angle MNP also means the measure of angle N.

N = (1/2)(arc MP)

N = (1/2)(180°)

N = 90°

The measure of angle MNP is 90°.

The measure of ∠MNP is 90.

An arc of a circle is any part of the circumference. The angle subtended by an arc at any point is the angle formed between the two line segments joining that point to the end-points of the arc.

As, the degree of the arc of a circle is usually 2 times the measure of the corresponding angle.

The measure of angle MNP

MNP = (1/2)(arc MP)

MNP = (1/2)(180°)

MNP = 90°

Hence, the measure of angle MNP is 90°.

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Answer:

a(n) = -3 - 2(n-1)

Step-by-step explanation:

The most general formula for the nth term of an arithmetic sequence (such as this sequence is) is

a(n) = a(1) + c(n-1), where c is the common difference.

Here a(1) = -3 and c = -2.

Thus,

a(n) = -3 - 2(n-1).

Answer:

The answer is A.  Check the picture attached.

Step-by-step explanation:

Answer: sinA = a/c

Explanation: Since A is the angle, b is the adjacent side and c is the hypotenuse since it is across the 90 degree point. Side a is the opposite side, sine is opposite/hypotenuse.

Answer:

The confidence interval is between 52.2% and 55.8%

Step-by-step explanation:

Since the study showed that 54% of the people involved in the study had experienced flu-like symptoms, and the margin of error is 1.8%, which is relatively small margin of error, we can easily come to the confidence interval. Since the margin of error goes both ways, above and below the official percentage, in order to get to the confidence interval we need to deduct the margin of error from the percentage, and also, separately, to add the margin of error to the percentage.

54 - 1.8 = 52.2

So the low border of the confidence level is 52.2%.

54 + 1.8 = 55.8

So the high border of the confidence level is 55.8%.

Answer:

the interval  is between 52.8% and 55.8%

Step-by-step explanation:

Answer:

(b + 2)^2

Step-by-step explanation:

b^2 + 4b + 4

It's perfect square: a^2 + 2ab + b^2 = (a + b)^2

So

b^2 + 4b + 4 = (b + 2)^2

Answer:

(b + 2)(b + 2)

Step-by-step explanation:

Factor the polynomial.  

b^2 + 4b + 4

Sum of 4 which product is 4

Sum: 1 + 3 = 4

      2 + 2 = 4

Product: 1 × 4 = 4

             2 × 2 = 4

We use 2 × 2 because it sum is the same as the product of 4. Because 2 and 4 are perfect square so we have:

b² + 4b + 4  splitted  as

(b + 2)(b + 2) or (b + 2)²

Answer:

no photo???

Step-by-step explanation:

Grant made an error in simplifying the expression.

The error in Grant's work is that he simplified the expression incorrectly. Let's go through the correct steps to simplify the expression:

So, the correct simplified expression is -1.05.

Answer:  14

Step-by-step explanation:

f(x) = 3x + 2

To find f⁻¹, swap the x's and y's and solve for y --> Note: f(x) is y

x = 3y + 2

x - 2 = 3y

[tex]\dfrac{x-2}{3}=y[/tex]

[tex]\implies f^{-1}(x)=\dfrac{x-2}{3}[/tex]

[tex]\implies f^{-1}(14)=\dfrac{14-2}{3}[/tex]

[tex]\implies f^{-1}(14)=\dfrac{12}{3}[/tex]

[tex]\implies f^{-1}(14)=4[/tex]

f(f⁻¹(14)) = f(4)

              f(4) = 3(4) + 2

                     = 12 + 2

                     = 14

NOTE: the simplified version is .... f and f⁻¹ cancel out, leaving you with 14

Answer:

$148.50.

Step-by-step explanation:

Hourly wage for time and a half = 11 * 1.5

=$16.50

For 9 hours she earns 16.50 * 9

= $148.50.

Answer:

Step-by-step explanation:

Answer:

The correct answer is option B.  44°

Step-by-step explanation:

From the figure we can see a circle, and an angle subtended.

The angle from an arc subtended n the other arc of a circle is half the angle made by the arc in center.

To find the measure of m<ABC

Here the central angle of arc AC is 88°,

<ABC is half the central angle made by arc AC

Therefore m<ABC = 88/2 = 44°

The correct answer is option B.  44°

Answer:

sin θ/2=5√26/26=0.196

Step-by-step explanation:

θ ∈(π,3π/2)

such that

θ/2 ∈(π/2,3π/4)

As a result,

0<sin θ/2<1, and

-1<cos θ/2<0

tan θ/2=sin  θ/2/cos θ/2

such that

tan θ/2<0

Let

t=tan θ/2

t<0

By the double angle identity for tangents

2 tan θ/2/1-(tanθ /2)^2  = tanθ

2t/1-t^2=5/12

24t=5 - 5t^2

Solve this quadratic equation for t :

t1=1/5 and

t2= -5

Discard t1 because t is not smaller than 0

Let s= sin θ/2

0<s<1.

By the definition of tangents.

tan θ/2= sin θ/2/ cos θ/2

Apply the Pythagorean Algorithm to express the cosine of θ/2 in terms of s. Note the cos θ/2 is expected to be smaller than zero.

cos θ/2 = -√1-(sin θ/2)^2 = - √1-s^2

Solve for s.

s/-√1-s^2 = -5

s^2=25(1-s^2)

s=√25/26 = 5√26/26

Therefore

sin θ/2=5√26/26=0.196....

Answer:

  Subtract 14 from both sides of the equation.

Step-by-step explanation:

The subtraction property of equality tells you the equal sign only remains valid if you subtract the same value from both sides of the equation.

Here, we want the 14 on the left side to be replaced by 0. Thus we must add its opposite. Since we must do the same thing to both sides of the equation, we must subtract 14 from both sides of the equation.

Answer:

Last option:  Subtract 14 from both sides of the equation.

Step-by-step explanation:

To solve the equation [tex]x+14=21[/tex] you must solve for the variable "x".

To calculate the value of the variable "x" it is important to remember the Subtraction property of equality. This states that:

[tex]If\ a=b\ then\ a-c=b-c[/tex]

Therefore, applying this property, you should subtract 14 from both sides of the equation to find the value of the variable "x". Then:

[tex]x+14-(14)=21-(14)\\\\x=7[/tex]

Answer:

  A.  8

Step-by-step explanation:

The sale price is 40% off the regular price, so is 60% of the regular price. The number of CDs Jenny can buy is ...

  $80/(0.60×$15.99) = 8.33 ≈ 8

Jenny can buy 8 CDs with her gift card.

Answer:

D, 4.62

Step-by-step explanation:

e = √(1 - b²/a²)

To solve for a, first square both sides:

e² = 1 - b²/a²

Then subtract 1 from both sides:

e² - 1 = -b²/a²

Multiply both sides by -1:

1 - e² = b²/a²

Multiply by a²:

(1 - e²) a² = b²

Divide by 1 - e²:

a² = b² / (1 - e²)

Take the square root:

a = b / √(1 - e²)

So the answer is D.

When b = 4 and e = ½:

a = 4 / √(1 - (½)²)

a = 4 / √(1 - ¼)

a = 4 / √¾

a = 8 / √3

a ≈ 4.62

Answer: D and 4.62

Step-by-step explanation:

Answer:

Hi,

The answer is (-0.383,1) and (2,∞).

Step-by-step explanation:

See the attachment.

g(x) is a parabolic function, and the Image is always ≥ 0.

f(x) is a exponential function, and the Image is always ≥ 0.

At x = -0.383 , g(x) = 0.588 and f(x) = 0.588.

For x=(-0.383, 1), g(x) is greater than f(x).

At x = 1, g(x) = 1 and f(x) = 1.

For x=(1, 2), f(x) is greater than g(x).

At x= 2, g(x) = 16 and f(x) = 16

For x=(2,∞), g(x) is greater than f(x)

Answer:

graph of h(x)= a slope of 2, and the y-intercept is 0.

graph of g(x)= a slope of 1, and a y-intercept of 6.

graph of f(x)= a slope of 1, and a y-intercept of -6.

Step-by-step explanation:

The equation would be h(x)=(x-6)+(x+6) which is also equal to h(x)= 2x if you combine like terms. f(x) and g(x) equations are pretty straight forward.

Answer:

[tex]h(x)=2x[/tex]

Step-by-step explanation:

The given functions are

[tex]f(x)=x-6\\g(x)=x+6[/tex]

To answer the question, we need to sum both functions each other, as follows

[tex]h(x)=f(x)+g(x)[/tex]

Replacing each function, we have

[tex]h(x)=x-6+x+6\\h(x)=2x[/tex]

The image attached shows each function.

Therefore, the combined function is

[tex]h(x)=2x[/tex]

Answer:

he function is negative for all real values of x where –6 < x < –2 (True)

Step-by-step explanation:

(x+2) can be written as

x + 2 = 0

x = -2

(x+6) can be written as

x + 6 = 0

x = -6

Both of these can be written as -6 < x < -2

1) he function is positive for all real values of x where x > –4.

(All values are between -2 and -6 and they are negative therefore this statement is false.)

2) True (explained above)

3) The function is positive for all real values of x where x < –6 or x > –3.

(x>-2 includes -3 but x>-3 does not include -3 therefore, this is false.)

4) The function is negative for all real values of x where x < –2. (It is not negative for all values as there is a limit between -2 and -6.)

!!

Answer:

D.  ∛4a^2 / a

Step-by-step explanation:

∛4a / ∛a^2

= ∛(4a)* ∛a / ∛a^2 * ∛a

= ∛4a^2 / ∛a^3

= ∛4a^2 / a

Answer is D.  ∛4a^2 / a

Answer:

d     4 ^1/3 a^2/3

    ------------

    a

Step-by-step explanation:

(4a) ^ 1/3

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

( a^2) ^ 1/3

We know  that (bc)^d = b^d * c^d   and m^n^p = m^(n+p)

(4) ^ 1/3 * (a) ^ 1/3

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

( a) ^(2* 1/3)

(4) ^ 1/3 * (a) ^ 1/3

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

( a) ^(2/3)

We know that when we divide powers with the same base, we subtract the exponents

(4) ^ 1/3 * (a) ^ (1/3 - 2/3)

4 ^ (1/3) * a ^ -1/3

4 ^1/3

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

a^ 1/3

We can multiply the top and bottom by a^2/3

4 ^1/3 a^2/3

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

a^ 1/3 * a^2/3

4 ^1/3 a^2/3

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

a

Answer:

c

Step-by-step explanation:

c

The question related to a mathematical model is not completely clear. It seems to reference an algebraic variable 'c' with a value of 16, but without more context, a more specific answer cannot be provided.

Unfortunately, the question you asked is not fully clear. It seems like there is a part missing from the formula you're asking about. However, if you've mentioned that the answer is c 16, it suggests you are referring to a Model which is not clearly described in the question.

If you're referring to an algebraic problem or a model related to algebra, then c could be a variable and 16 its corresponding value. Without more information, I'm afraid I can't provide a more precise answer. Please provide additional details for better understanding of your question.

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Answer:

A. 10mn3

Step-by-step explanation:

To do such division, you need to divide each term (-50, m3 and n5) by its counterpart below.

So, to divide –50m3n5 by –5m2n2, we must do

–50 / -5 = 10

m3 / m2 = m

n5 / n2 = n3

So, overall we have 10mn3

That's easy like that.

Answer:

The correct answer option is B. Construct a line perpendicular to XP through point A.

Step-by-step explanation:

We are given an incomplete figure of construction of a perpendicular line and we are to determine whether which of the given answer options is the next step in the construction.

From the given marks, we can deduce that a perpendicular line to XY is being constructed, passing through P.

So the next step must be to construct a line perpendicular to XP through point A to complete the construction.

The next step in the construction is:

From the given construction we may observe that the construction is of a line segment perpendicular to line segment XY.

The steps of construction are as follows:

1) Take a line segment XY.

2) Take a compass and open the  compass more than half the length of XY and then make the arc by keeping the compass one's at X and then at Y.

3) The point where the arc meet draw a straight line such that it pass through the point P.

4) AP will be the perpendicular line to XY and point P is the mid-point of XY.

Answer:

0.1 cm

Step-by-step explanation:

given : volume = 24 cm³, length = 20 cm, width = 12 cm

Use formula :

Volume = Length x width x height

height = Volume / (length x width) = 24 / (20 x 12) = 0.1 cm

Answer: Second option is correct.

Step-by-step explanation:

Let the original price of chair be 'p'.

Number of chairs = 4

Discount rate = 25%

So, Amount of discount would be

[tex]\dfrac{25}{100}p\\\\=0.25p[/tex]

So, Cost of each chair after discount would be

[tex]p-0.25p[/tex]

So, Cost of all 4 chairs would be

[tex]4(p-0.25p)[/tex]

Hence, Second option is correct.

Answer:

25% is being taken off the original price, p, of each patio chairs.

That means the price of each patio chair is the full price, p, minus 25% of the original price.

1) To find 25% of the original price, multiply p (original price) by the decimal form of 25%, or 0.25. That means 25% off original price = 0.25p.

2) Now subtract 0.25p from the original price of the chairs to find the price of each (1) chair. p - 0.25p

Shylah is buying 4 chairs at that discounted price. That means you need to multiply the discounted price,  p - 0.25p, by 4. Shylah is paying 4(p-0.25p) total for the 4 chairs, which is answer choice B.

Since you can choose more than one choice, you can simplify 4(p-0.25p) by subtracting what is in the parathesis, then multiplying, following the order of operations:

4(p-0.25p)

= 4(0.75p)  

= 3p

That is answer choice A.

--------

Answer: Choices A and B, 3p and 4(p−0.25p).

Step-by-step explanation:

Choices A and B, 3p and 4(p−0.25p).

Answer:

  2-fold

Step-by-step explanation:

The symbol has reflectional symmetry about the line containing the slash, and about the perpendicular bisector of the slash. There are two (2) axes of reflectional symmetry.

Answer:

2 fold because you would fold it in half like paper.

Step-by-step explanation:

Answer:

[tex]\large\boxed{a.\ -30}[/tex]

Step-by-step explanation:

[tex]\dfrac{y}{3}+8=-2\qquad\text{subtract 8 from both sides}\\\\\dfrac{y}{3}+8-8=-2-8\\\\\dfrac{y}{3}=-10\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup^1\cdot\dfrac{y}{3\!\!\!\!\diagup_1}=(3)(-10)\\\\y=-30[/tex]