Simplify (a^2-7a+12)/(a^2-2a-8) if a cannot be 4

Therefore , the solution of the given problem of probability comes out to be a)1/78 ,b)65/624 ,c)1/4 ,d)0 and e)12/13.

The basic goal of any considerations technique is to assess the probability that a statement is accurate or that a specific incident will occur. Chance can be represented by any number range between 0 and 1, where 0 normally indicates a percentage but 1 typically indicates the level of certainty. An illustration of probability displays how probable it is that a specific event will take place.

Here,

a.

P(Bert gets a Jack and Ernie rolls a five) = P(Bert gets a Jack) * P(Ernie rolls a five)

= (4/52) * (1/12)

= 1/78

b.

P(Bert gets a heart and Ernie rolls a number less than six) = P(Bert gets a heart) * P(Ernie rolls a number less than six)

= (13/52) * (5/12)

= 65/624

c.

P(Bert gets a face card and Ernie rolls an even number) = P(Bert gets a face card) * P(Ernie rolls an even number)

= (12/52) * (6/12)

= 1/4

d.

P(Bert gets a red card and Ernie rolls a fifteen) = 0

e.

Ernie rolls a number that is not twelve, and Bert draws a card that is not a Jack:

A regular 52-card deck contains 48 cards that are not Jacks,

so the likelihood that Bert will draw one of those cards is 48/52, or 12/13.

On a 12-sided dice with 11 possible outcomes,

Ernie rolls a non-12th-number (1, 2, 3, etc.).

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The required value of the x in the given expression log₂ (x) = 3 is x = 8.

Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression.

Here,
The logarithmic equation log₂(x) = 3 can be rewritten in exponential form as 2³ = x, since the base 2 raised to the power of 3 is equal to x.

So, the solution to the equation is x = 8.

Therefore, log₂(8) = 3.

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The equation 2 log₅ x = log₅ 4 + log₅ 9 has two solutions: x = 6.

To solve the equation 2 log₅ x = log₅ 4 + log₅ 9, we can use logarithmic properties to simplify and find the value of x.

Using the properties of logarithms, we can rewrite the equation as follows:

2 log₅ x = log₅ (4 * 9)

Next, we simplify the right side:

2 log₅ x = log₅ (36)

Now, we can use the property of logarithms that states logₐ b = c is equivalent to aᶜ = b. Applying this property, we have:

x² = 36

Taking the square root of both sides, we get:

x =  √36

Since the square root of 36 can be either positive or negative, we have two possible solutions:

x = 6

It's important to note that when working with logarithmic equations, we must always check if the obtained solutions satisfy the domain restrictions of the original equation. In this case, since the logarithm has a base of 5, the solution x = 6.

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$54.28 rounded to the nearest 10 dollars is $50.00

The sentence with proper subject-verb agreement is the student as well as the teacher want to go to the museum. In this sentence, the subject is what we call a compound subject, meaning that the verb refers and agrees with more than just one singular word.

The compound subject is "student" and "teacher" and they are connected by "as well as", which functions as a coordinating conjunction would. That's why the verb should conjugate in its plural form.

Option A is incorrect because the structure inside parentheses is not related to the verb and does not influence its conjugation. Options C and D have a verb in the singular form for a compound subject - that would demand a plural conjugation.

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Answer:

x ≈ 30,37

y ≈ 29,00

Step-by-step explanation:

Use trigonometry:

\( \sin(38°) = \frac{9}{x} \)

Now, use the property of the proportion to find x:

\(x = \frac{9}{ \sin(38°) } ≈30.37\)

Do the same thing to find y:

\( \tan(38°) = \frac{9}{y} \)

\(y = \frac{9}{ \tan(38°) } ≈29.00\)

Answer:

648

Step-by-step explanation:

FInd volume of bottom half (9x6x12)

find voume of pyramid 1/3Bh 1/3(11)(54)

Answer:

The answer is 16pi or 50.3cm² to 1 d.p

Step-by-step explanation:

The non shaded=area of shaded

d=8

r=d/2=4

A=pir³

A=p1×4²

A=pi×16

A=16picm² or 50.3cm² to 1d.p

Answer:

3.45 cm (3 s.f.)

Step-by-step explanation:

We have been given a 5-sided regular polygon inside a circumcircle. A circumcircle is a circle that passes through all the vertices of a given polygon. Therefore, the radius of the circumcircle is also the radius of the polygon.

To find the radius of a regular polygon given its side length, we can use this formula:

\(\boxed{\begin{minipage}{6 cm}\underline{Radius of a regular polygon}\\\\$r=\dfrac{s}{2\sin\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

Substitute the given side length, s = 8 cm, and the number of sides of the polygon, n = 5, into the radius formula to find an expression for the radius of the polygon (and circumcircle):

\(\begin{aligned}\implies r&=\dfrac{8}{2\sin\left(\dfrac{180^{\circ}}{5}\right)}\\\\ &=\dfrac{4}{\sin\left(36^{\circ}\right)}\\\\ \end{aligned}\)

The formulas for the area of a regular polygon and the area of a circle given their radii are:

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{nr^2\sin\left(\dfrac{360^{\circ}}{n}\right)}{2}$\\\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a circle}\\\\$A=\pi r^2$\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}\)

Therefore, the area of the regular pentagon is:

\(\begin{aligned}\textsf{Area of polygon}&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(\dfrac{360^{\circ}}{5}\right)}{2}\\\\&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(72^{\circ}\right)}{2}\\\\&=\dfrac{\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}}{2}\\\\&=\dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}\\\\&=110.110553...\; \sf cm^2\end{aligned}\)

The area of the circumcircle is:

\(\begin{aligned}\textsf{Area of circumcircle}&=\pi \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\\\\&=\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\&=145.489779...\; \sf cm^2\end{aligned}\)

The area of the shaded area is the area of the circumcircle less the area of the regular pentagon plus the area of the small central circle.

The area of the unshaded area is the area of the regular pentagon less the area of the small central circle.

Given the shaded area is equal to the unshaded area:

\(\begin{aligned}\textsf{Shaded area}&=\textsf{Unshaded area}\\\\\sf Area_{circumcircle}-Area_{polygon}+Area_{circle}&=\sf Area_{polygon}-Area_{circle}\\\\\sf 2\cdot Area_{circle}&=\sf 2\cdot Area_{polygon}-Area_{circumcircle}\\\\2\pi r^2&=2 \cdot \dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\\end{aligned}\)

                                                 \(\begin{aligned}2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)-16\pi}{\sin^2\left(36^{\circ}\right)}\\\\r^2&=\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}\\\\r&=\sqrt{\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}}\\\\r&=3.44874763...\sf cm\end{aligned}\)

Therefore, the radius of the small circle is 3.45 cm (3 s.f.).

Answer:

120 four digit numbers can be created from the gives.

Step-by-step explanation:

Solution

You are given 5 digits in the givens.

1 3 5 7 9

Therefore

5 * 4 * 3 * 2 is the answer to your question. 4 and 3 and 2 determine that none of the digits can be repeated. That equals 120.

True. Summarizing allows you to focus on the important information by finding the introduction, topic sentence and conclusion.

Summarizing is a technique that helps to distill the main points of a text by identifying the introduction, topic sentence, and conclusion. It involves condensing the information to focus on the most important aspects and omitting unnecessary details.

This process enables the reader to grasp the core message of the text quickly and efficiently.

By summarizing, one can communicate the key ideas in a concise and clear manner, making it easier for others to understand and engage with the information presented.

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Answer: -4t + 1590

Step-by-step explanation:

Given : Josh works as a tutor for $11 an hour and as a waiter for $15 an hour.

This month, he worked a combined total of 106 hours at his two jobs.

Let t be the number of hours Josh worked as a tutor this month.

Then, the number of hours Josh worked as a waiter = 106 -t

Then, the total money earned this month ( in dollars)

= 11 (No. of hours worked as a tutor)+ 15 (No. of hours worked as a waiter)

=11(t) + 15(106-t)

= 11t+1590-15t

= -4t+1590

Hence, the expression for the combined total dollar amount he earned this month =

The algebraic expression to this problem is 11x + 15y = 106

Algebraic expressions have variables, numbers, and operations. A variable is a letter that represents an unknown amount.

Let number of hours Josh worked as a tutor be x hour.

Let number of hours Josh worked as a waiter be y hours.

The equation becomes -

11x + 15y = 106

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In order to have a function we can't repeat any value in the x, therefore in order to have a function represented in the table the question mark must be 2

Answer:

Step-by-step explanation:

FIRST, plug in.

h=12           r=4

V = 3.14 (4)^2 (12)

V = 3.14 (16) (12)

V =  50.24 (12)

V = 602.88 in.^3

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Answer:

(x+4)^2  -25

Step-by-step explanation:

x²+8x-9 in the form  (x+k)² +h.

We need to complete the square.

x^2 +8x   -9

Take the coefficient of x.

8

Divide by 2.

8/2 =4

Square it.

4^2 = 16

Add this then subtract i.

x^2 +8x+16    -16   -9

The x^2 +8x+16 becomes  (x+4) ^2  and we can simplify the remaining terms.

(x+4)^2  -25

Answer:

The equation

c x 2 > k

l x 3 ?> c > k

g = 30 = c + l + k

this equation is the same as...

Cecile read twice as many books as Kami.

Laura read 3 times as many books as Kami, but possibly less than Cecile.

Gigi read 30 books. 30 books is the same as all 3 girls combined.

To find out how many books each girl read, you need to find 3 unequal numbers that add up to 30. These numbers are substituted, only because they can be anything at all, and I want to prevent confusions.

hope this helps!

First, we apply the distributive property of multiplication:

Subtracting 5x from the above equation we get:

Now, subtracting 30 we get:

Finally, dividing by 2 we get:

Answer: x=35.

The percent change in Pilar's shell collection from the beginning of the day to the end is,  22.5%

Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".

Given that,

Pilar has 40 shells in her collection.

She collects 6 more shells in the morning and 3 more shells in the afternoon.

The percent change in Pilar's shell collection from the beginning of the day to the end = ?

At the beginning of the day, Pilar has 40 shells.

In the morning, she collects 6 more shells, bringing her total to

= 40 + 6

= 46 shells.

Then, in the afternoon, she collects 3 more shells, bringing her total to

=46 + 3

= 49 shells.

To find the percent change in Pilar's shell collection from the beginning of the day to the end, we can use the formula:

percent change = (final value - initial value) / initial value * 100%

Plugging in the values we have:

percent change = (49 - 40) / 40 x 100%

percent change = 9 / 40 x 100%

percent change = 22.5%

Therefore, there is a 22.5% increase in Pilar's shell collection from the beginning of the day to the end.

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A.

1. Mode: No mode. Median: 24. Mean: 30.875. Range: 50.

2. Mode: No mode. Median: 33.5. Mean: 43.9. Range: 85.

3. Mode: No mode. Median: 46. Mean: 43.571. Range: 61.

4. Mode: No mode. Median: 17. Mean: 18. Range: 28.

5. Mode: No mode. Median: 10.5. Mean: 13.5. Range: 27.

6. Mode: 15. Median: 22.5. Mean: 25.857. Range: 31.

B.

7. Mode: 4.3. Median: 4.2. Range: 2.1.

8. Mode: 18.6. Median: 18.6. Range: 0.8.

C.

9. Mode: No mode. Median: 4/9.

10. Mode: No mode. Median: 5/24.

The probability that less than 59 customers arrive in an hour during tomorrow's morning rush will be 0.0521.

From the information given, it was stated that coffee shop serves an average of 72 customers per hour during the morning rush and we eat to find the probability that less than 59 customers arrive in an hour during tomorrow's morning rush.

This will be done by using the Poisson distribution:

P(x <= 58) = [e^-72 × (72)^x]/x!

= 0.0521

Therefore, the probability that less than 59 customers arrive in an hour during tomorrow's morning rush will be 0.0521.

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Answer:

-6

Step-by-step explanation:

Answer:

4.6% (nearest tenth)

Step-by-step explanation:

percent error = (|approx - actual| ÷ actual) × 100

percent error = (|16 - 15.3| ÷ 15.3) × 100

                      = 4.6% (nearest tenth)

\( \sf\% \: error = \frac{ |approx - actual| }{actual} \times 100\)

\( \tt\% \: error = \frac{ |16 - 15.3| }{15.3} \times 100\)

\( \tt\% \: error = \frac{ |0.7| }{15.3} \times 100\)

\( \tt\% \: error = \frac{ |0.7| }{ \frac{153}{10} } \times 100\)

\( \tt\% \: error = \frac{0.7}{ \frac{153}{10} } \times 100\)

\( \tt\% \: error = \frac{ \frac{7}{10} }{ \frac{153}{10} } \times 100\)

\( \tt\% \: error = \frac{7 }{ 153 } \times 100\)

\( \tt\% \: error = \frac{7 00}{ 153 } \)

\( \tt\% \: error =4.57\%\)

Answer:

  (e)  b h a k

Step-by-step explanation:

You want the order of operations involved in the transformation ...

  g(x) = a(bx -h) +k

The Order of Operations tells you that multiplication takes precedence over addition, and expressions inside parentheses are evaluated first.

We note there is an expression in parentheses here: (bx -h). In that expression is a multiplication operation (bx) and an addition operation (_-h).

The multiplication is done first, so evaluating this expression in parentheses, we ...

Once the parenthetical expression is evaluated, we proceed to the main event. Again, multiplication and addition are required. That means the next two steps are ...

In summary, the operations we perform during evaluation of the transformation successively apply the parameters ...

  b h a k

Answer:

Blue rectangle, pink rhombus, green parallelogram (bottom left)

Step-by-step explanation:

Blue rectangle has two pairs of parallel side because it makes 90°

Pink rhombus has 2 pairs top and diagonal.

Green parallelogram (bottom left) is same thing.

Step-by-step explanation:

Improper fractions have a numerator that is larger than the denominator

1 = 6/6

 so  1  1/6  = 7/6

The equivalent decimal and mixed number for given letter C is,

⇒ C = 8.2 ; 8 2/10

We have to given that,

A number line is shown in image.

Since,

A number lines are the horizontal straight lines in which the integers are placed in equal intervals.

And, All the numbers in a sequence can be represented in a number line. This line extends indefinitely at both ends.

Now, By given number line,

Point C is two point left from point 8.

Hence, The point C is denoted as,

⇒ C = 8.2

⇒ C = 82/10

⇒ C = 8 2/10

Therefore, the equivalent decimal and mixed number for given letter C is,

⇒ C = 8.2 ; 8 2/10

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In linear equation , 240 liters of 90% solutions will be used.

What are a definition and an example of a linear equation?

Let x be the quantity of 75% antifreeze solution and y be the quantity of 90% antifreeze solution,

Since, the total quantity of the mixture = 360,

⇒ x + y = 360 ----- (1),

Also, the resultant solution is of  85% antifreeze solution,

⇒ 75 % of x + 90% of y = 85% of 360

0.75x + 0.90y = 0.85 × 360

0.75x + 0.90y = 306

75x + 90y = 30600 -----(2),

Equation (2) - 75 × equation (1),

We get,

15y = 3600

⇒ y = 240

Hence, 240 liters of 90% solutions will be used.

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The proportion equivalent with Two-thirds would be 6/9.

Since we know that the proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

We are given that the  proportion with Two-thirds

If you actually divide it’ll make since , so first  we want to divide the 2 , then you want to multiply the third of the two

2/3 x 3/3

6/9

thus, the answer will be 6/9.

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