Paul woke up for school at 7:30 AM. He took 14 minutes to get ready, 9 minutes to
finish his breakfast and 39 minutes to commute to school. At what time did he
reach the school?

By the use of factor decomposition and algebra properties, we conclude that the rational number 48/192 is equal to the rational number 1/4.

In this question we should simplify a rational number into its simplest form based on two facts. First, that all natural numbers except 1 and the prime numbers are products of prime numbers and, second, the simplification of the fraction can be done by using the following algebra property:

(a · c)/(b · c) = a/b, where a, b, c are natural numbers.     (1)

Along with power properties.

Now we proceed to simplify the rational number:

48/192 = (2⁴ × 3) / (2⁶ × 3)

48/192 = 1 / 2²

48/192 = 1 / 4

By the use of factor decomposition and algebra properties, we conclude that the rational number 48/192 is equal to the rational number 1/4.

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Answer:

4

Step-by-step explanation:

Answer: [tex]\frac{-7+\sqrt{49-4(15)(-12)} }{30}[/tex]

Step-by-step explanation:

Use the quadratic formula:

[tex]\frac{-b+-\sqrt{b^{2}-4(ac) } }{2a}[/tex]

Substitute the values, A = 15, b = 7, c = -12

[tex]\frac{-7+-\sqrt{7^{2}-4*(15*-12) } }{2*15}[/tex]

Simplify to answer:

[tex]\frac{-7+49-4(15)(-12)}{30}[/tex]

I hope this helps!

Answer:

In math, calculus deals with the finding and properties of derivatives and integrals of functions, by methods originally based on the summation of infinitesimal differences. The two basic types of calculus are differential calculus and integral calculus.

Step-by-step explanation:

hope it helps

sorry if I'm wrong

The complete table is shown below.

Complete the table as follows:

[tex]2^{2} = 2*2 = 4\\3^{2} = 3*3 = 9\\4^{2} = 4*4 = 16\\5^{2} = 5*5=25\\6^{2} =6*6=36\\7^{2} =7*7=49\\8^{2} =8*8=64\\9^{2} =9*9=81\\10^{2} =10*10=100\\11^{2} =11*11=121[/tex]

Therefore, the complete table has been shown.

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The question you are looking for is here:

Complete the table by squaring each positive x-value listed 2, 3,4,5,6,7,8,9,10,11.

Answer:

104 miles.

Step-by-step explanation:

5 inches is 2 * 2.5 inches so the distance required is 2*52 = 104 miles.

If the factors of the polynomial were (x-5) and (x-6), the values of x that would make the polynomial equal to zero would be 5 and 6.

5 - 5 = 0

6 - 6 = 0

Assuming the polynomial is (x-5)(x-6), if one factor is 0 then anything multiplied by 0 is still 0.

Hope this helps!

Answer:

[tex]x=-\frac{1}{2},\frac{5}{2}[/tex]

Step-by-step explanation:

1) Split the second term in [tex]4{x}^{2}-8x-5[/tex]  into two terms.

1- Multiply the coefficient of the first term by the constant term.

[tex]4\times -5=-20[/tex] to -8 and multiply to -−20?

2 and −10

3 - Split -8x as the sum of 2x and -10x.

[tex]4x^2+2x-10x-5[/tex]

2)  Factor out common terms in the first two terms, then in the last two terms.

[tex]2x(2x+1)-5(2x+1)=0[/tex]

3) Factor out the common term [tex]2x+1[/tex].

[tex](2x+1)(2x-5)=0[/tex]

4) Solve for [tex]x[/tex].

1 - Ask: When will (2x+1)(2x-5) equal zero?

When 2x + 1 = 0 or 2x - 5 = 0

2 - Solve each of the 2 equations above.

[tex]x=-\frac{1}{2},\frac{5}{2}[/tex]

Answer:

the side length of hypotenuse is 16.28

Step-by-step explanation:

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

= [tex]11^{2}+12^{2}= C^{2}[/tex]

= [tex]121+144=c^{2}[/tex]

= [tex]265= c^{2}[/tex]

= [tex]\sqrt{265} = c[/tex]

= [tex]c = 16.28\\[/tex]

Answer:

A = 42.5° (nearest tenth)

B = 47.5° (nearest tenth)

C = 90°

a = 11

b = 12

c = √(265) = 16.3 (nearest tenth)

Step-by-step explanation:

Information:

Side a is opposite angle A.

Side b is opposite angle B.

Side c is opposite angle C.

From inspection of the triangle:

To find the missing side length, use Pythagoras Theorem:

Pythagoras Theorem

a² + b² = c²

(where a and b are the legs and c is the hypotenuse of a right triangle).

Substitute the given values of a and b into the formula and solve for c:

⇒ 11² + 12² = c²

⇒ 121 + 144 = c²

⇒ c² = 265

⇒ c = √(265)

To find one of the missing angles, use the Sine Rule.

Sine Rule

[tex]\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]

(where A, B and C are the angles and a, b and c are the sides opposite the angles)

Substitute the given values into the formula:

[tex]\implies \sf \dfrac{\sin A}{11}=\dfrac{\sin B}{12}=\dfrac{\sin 90^{\circ}}{\sqrt{265}}[/tex]

Solve for angle A:

[tex]\implies \sf \dfrac{\sin A}{11}=\dfrac{\sin 90^{\circ}}{\sqrt{265}}[/tex]

[tex]\implies \sf \dfrac{\sin A}{11}=\dfrac{1}{\sqrt{265}}[/tex]

[tex]\implies \sf \sin A=\dfrac{11}{\sqrt{265}}[/tex]

[tex]\implies \sf A=\sin^{-1} \left(\dfrac{11}{\sqrt{265}}\right)[/tex]

[tex]\implies \sf A=42.51044708...^{\circ}[/tex]

Therefore, A = 42.5° (nearest tenth)

Interior angles of a triangle sum to 180°:

⇒ A + B + C = 180°

⇒ 42.5° + B + 90° = 180°

⇒ B + 132.5° = 180°

⇒ B = 47.5°

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The dividend is [tex]2x^2+9x+7[/tex] while the divisor is x + 1

Option A is correct

The coefficient outside the division block is -1.

This means that the divisor = x + 1

Also, the coefficients of the dividend are:

2, 9, 7

The highest exponent is 2 since there are three terms in the polynomial. Three terms show that the expression is a quadratic expression

Therefore, the dividend is [tex]2x^2+9x+7[/tex]

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An analyst obtains the salaries of all 200 federal appeals court judges in 2017 and computes the mean salary to be $215,000. the $215,000 is a parameter.

Therefore, an analyst obtains the salaries of all 200 federal appeals court judges in 2017 and computes the mean salary to be $215,000. the $215,000 is a parameter.

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The product of the given fractions, -2/9(-5/3), is: 10/27.

Given the fractions, -2/9(-5/3), recall that minus multiplied by minus equals plus.

So therefore, the product of the two fractions would be a positive number. Thus:

-2/9(-5/3) = (-2 × -5)/(9 × 3)

-2/9(-5/3) = 10/27

Therefore, the product is: 10/27.

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The graphed inequality is:

[tex]y \geq \frac{1}{3}*x - 1[/tex]

We know that the line is solid, and the region above and to the left is shaded, then the inequality is of the form:

y  ≥ line.

Now we need to get the linear equation.

It is of the form;

y = a*x + b

Where a is the slope and b is the y-intercept. Because it passes through (0, -1), we know that the y-intercept is -1.

And knowing that the line passes through (0, -1) and (3, 0), the slope is:

[tex]a = \frac{- 1 - 0}{0 - 3} = \frac{1}{3}[/tex]

Then the inequality is:

[tex]y \geq \frac{1}{3}*x - 1[/tex]

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The ratio of the radius of the smaller circle to the radius of the larger circle as required in the task is; 3:8.

It follows from the task content that the circumference of the smaller circle is; 12cm while that of the bigger circle is; 32cm.

Since, the circumference of a circle is directly proportional to the radius of the circle from the formula; C = 2πr.

The ratio is therefore; 12:32, in which case, when expressed in its simplest form is; 3:8.

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The quadrants in which all the coordinates given are located is; As explained below.

1) (2, 4) is located in Quadrant I where both x and y-values are positive.

2) (0, -3) is located in Quadrant II where x - values are positive but y-values are negative.

3) (-1, 1/2) is located in Quadrant IV.

4) (-2 1/2, -7) is located in Quadrant III where x and y values are both negative.

5) (0, 6) is located in Quadrant I where both x and y-values are positive.

6) (-5, 0) is located in Quadrant IV where x is negative but y is positive.

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The reasonable value for the range of the given function is: A. 75.

The range of a function is the output that a corresponding input value would give as a relation.

In this scenario, the grade you get is a function of number of hours you study. Range is the grade (output), while the domain is hours of study (input).

The given possible range values in the options are, 75, 1.25, -30, 1/2.

A reasonable value of a a grade cannot be a negative number, neither can it be 1.25, nor 1/2.

Therefore, the reasonable value of the range is: A. 75.

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The null hypothesis be is =15 and the alternative hypothesis be  is ≠15

According to the statement

Mean length of time on death row is 17.4 years

Standard deviation of 6.3 years.

Now we determine the hypothesis with mean time 15 years then

P value outcome is 0.00015

So, The null hypothesis be  is =15 and the alternative hypothesis be is ≠15

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Answer:

-1728:512

Step-by-step explanation:

(-12)³ = -1728

8³ = 512

ratio is -1728:512

Answer:

1

Step-by-step explanation:

Points on a coordinate plane are written as (x,y) coordinates. The vertical axis is the y axis. If your point is "one unit up" its y-value is 1. (The horizontal axis is the x-axis. The x-value is 6.)

N-acetyltyrosine ethyl ester may likely have a higher Vmax.

Km is inversely proportional enzyme affinity for substrate. The lower the Km, the higher the enzyme affinity for substrate and vice versa.

Vmax is the maximum velocity of the reaction when the enzyme is fully saturated with substrate.

Based on the Km values, chymotrypsin has higher affinity for N-acetyltyrosine ethyl ester, thus, N-acetyltyrosine ethyl ester may likely have a higher Vmax.

In conclusion, the Vmax is the maximum velocity of an enzyme-catalyzed reaction.

Note that the complete question is given below:

The Km for the reaction of chymotrypsin with N-acetylvaline ethyl ester is 8.8 x 10-2 M, and the Km for the reaction of chymotrypsin with N-acetyltyrosine ethyl ester is 6.6 x 10-4 M.

Which of the following substrates is likely to give a higher value for Vmax?

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14) theorem

15) sides

16) separately

17) equilateral

18) supplementary

Answer:

1)3×-8

-24

Step-by-step explanation:

2)bshejejnenenejejkejehrh

The are of the triangle is mathematically given as

a=62.4in^2. This is further explained below.

Generally, the equation for the area is  mathematically given as

a= 0.5(base X height)

Therefore

a= 0.5 (10.4 x 12)

a=62.4in^2

In conclusion, The area of the triangle is

a=62.4in^2

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Answer:

6 hours.

Step-by-step explanation:

Speed = distance / time.

Carla travels  3 * 12 = 36 miles before Zari leaves the shop.

So Zari travels x miles in the same time as Carla travels x- 36 miles.

So 18 = x/t and 12 = (x - 36)/t

From first equation x = 18t so we have the equation

12 = (18t - 36/t

18t - 36 = 12t

6t = 36

t = 6 hours.

Answer:

1. (x + 8)(x + 3)

2. (x - 9)²

Step-by-step explanation:

Given trinomials:

1. [tex]x^2+11x+24[/tex]

2. [tex]x^2-18x+81[/tex]

..................................................................................................................................................

When factoring trinomials of the form ax² + bx + c:

..................................................................................................................................................

1) x² + 11x + 24

Step 1: Multiply the leading coefficient (1) and the last term (24).

[tex]\implies 1 \times 24 = \boxed{24}[/tex]

Step 2: Find the product factors that sum up to the middle term's coefficient (11).

[tex]\begin{array}{| c | c |}\cline{1-2} \sf Factors\:of\:24 & \sf Sum\:of\:factors\\\cline{1-2} 1, 24\ \| -1, -24 & 25\ \| -25 \\\cline{1-2} 2, 12\ \| -2, -12 & 14\ \| -14 \\ \cline{1-2} 3, 8\ \| -3, -8 & 11\ \| -11 \\\cline{1-2} 4, 6 \ \| -4, -6 & 10\ \| -10 \\\cline{1-2}\end{array}[/tex]

[tex]\implies 3x+8x=11x[/tex]

Step 3: Rewrite the polynomial with those factors, replacing the middle term.

[tex]\implies x^2+3x+8x+24[/tex]

Step 4: Factor by grouping.

[tex]\implies \overbrace{(x^2+3x)}^x+\overbrace{(8x+24)}^8\ \ \textsf{[ Factor out $x$ and $8$. ]}[/tex]

[tex]\implies x\overbrace{(x+3)}^{\textsf {Factor out}}+8(x+3)[/tex]

[tex]\implies \boxed{(x+8)(x+3)}[/tex]

The factored form of the given trinomial is [tex](x+8)(x+3)[/tex].

..................................................................................................................................................

2) x² - 18x + 81

Step 1: Multiply the leading coefficient (1) and the last term (81).

[tex]\implies 1 \times 81 = \boxed{81}[/tex]

Step 2: Find the product factors that sum up to the middle term's coefficient (-18).

[tex]\begin{array}{| c | c |}\cline{1-2} \sf Factors\:of\:81 & \sf Sum\:of\:factors\\\cline{1-2} 1, 81\ \| -1, -81 & 81\ \| -81 \\\cline{1-2} 3, 27\ \| -3, -27 & 30\ \| -30 \\ \cline{1-2} 9, 9\ \| -9, -9 & 18\ \| -18 \\\cline{1-2}\end{array}[/tex]

[tex]\implies (-9x)+(-9x)=-18x[/tex]

Step 3: Rewrite the polynomial with those factors, replacing the middle term.

[tex]\implies x^2-9x-9x+81[/tex]

Step 4: Factor by grouping.

[tex]\implies \overbrace{(x^2-9x)}^x+\overbrace{(-9x+81)}^{-9}\ \ \textsf{[ Factor out $x$ and $-9$. ]}[/tex]

[tex]\implies x\overbrace{(x-9)}^{\textsf {Factor out}}-9(x-9)[/tex]

[tex]\implies (x-9)(x-9)[/tex]

[tex]\implies \boxed{(x-9)^2}[/tex]

The factored form of the given trinomial is [tex](x-9)(x-9)\ \textsf{or}\ (x-9)^2[/tex].

The lateral area of the given pyramid is 108 cm².

Any three-dimensional figure's lateral surface area is its side surface area.

In the question, we are asked to find the lateral area of the given pyramid, whose base is a regular hexagon, with a side length of 3 cm, and the slant height of the pyramid is 12 cm.

To determine the lateral area, we determine the area of one lateral face, and then multiply it by the number of lateral faces in the pyramid.

The number of lateral faces = sides of the base = 6 {Since the base is a regular hexagon}.

Area of a lateral face = (1/2)*base*height {Since its a triangle},

or, area of a lateral face = (1/2)*3*12 {Since the base is the side length of the base, and the height is the slant height},

or, area of a lateral face = 18 cm².

Thus, the lateral area of the pyramid = 6 * 18 cm² = 108 cm².

Thus, the lateral area of the given pyramid is 108 cm².

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The equation which can be used to determine x, the number of players the team can bring to the

tournament is 1353 = 943.50 + 31.50x and x = 13 players

1353 = 943.50 + 31.50x

1353 - 943.50 = 31.50x

409.50 = 31.50x

x = 409.50 / 31.50

x = 13 players

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Answer:

B

Step-by-step explanation:

Drop an altitude. Either of the two resulting right triangles with legs of length 5 and x and a hypotenuse of 10.

By the Pythagorean theorem, it follows that the answer is B.