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Answer:

12!

Step-by-step explanation:

А=12*11*10*9*8*7*6*5*4*3*2*1=12!=479001600

The value of CE is 14.7 units.

The diameter of a given circle is a straight line which passes through the center of the circle and divides it into two equal semi-circles.

So that in the given circle with center A, we have;

CE = BD  (diameter of a given circle)

BA = EA = CA = DA    (radius of a given circle)

CE is the diameter of the circle, and BA is the radius, so that;

CE = 2*BA

     = 2*7.35

     = 14.7

CE = 14.7

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Answer:

Starting with the equation:

(x + 1)^2 = 13/4

We can use the square root property, which states that if a^2 = b, then a is equal to the positive or negative square root of b.

Taking the square root of both sides, we get:

x + 1 = ±√(13/4)

Simplifying under the radical:

x + 1 = ±(√13)/2

Now we can solve for x by subtracting 1 from both sides:

x = -1 ± (√13)/2

Therefore, the solutions to the equation are:

x = -1 + (√13)/2 or x = -1 - (√13)/2

Step-by-step explanation:

Step 1: Write the dividend and divisor:

\(\sf\:\frac{{x^3 - 8x^2 + 6x + 41}}{{x - 4}} \\ \)

Step 2: Divide the first term of the dividend by the first term of the divisor:

\(\sf\:\frac{{x^3}}{{x}} = x^2 \\ \)

Step 3: Multiply the divisor (x - 4) by the result (x^2):

\(\sf\:(x - 4) \cdot (x^2) = x^3 - 4x^2 \\ \)

Step 4: Subtract the result from the original dividend:

\(\sf\:(x^3 - 8x^2 + 6x + 41) - (x^3 - 4x^2) = -4x^2 + 6x + 41 \\ \)

Step 5: Bring down the next term from the dividend:

\(\sf\:\frac{{-4x^2 + 6x + 41}}{{x - 4}} \\ \)

Step 6: Repeat steps 2-5 with the new dividend:

\(\sf\:\frac{{-4x^2}}{{x}} = -4x \\ \)

\(\sf\:(x - 4) \cdot (-4x) = -4x^2 + 16x \\ \)

\(\sf\:(-4x^2 + 6x + 41) - (-4x^2 + 16x) = -10x + 41 \\ \)

Step 7: Bring down the next term from the dividend:

\(\sf\:\frac{{-10x + 41}}{{x - 4}} \\ \)

Step 8: Repeat steps 2-5 with the new dividend:

\(\sf\:\frac{{-10x}}{{x}} = -10 \\ \)

\(\sf\:(x - 4) \cdot (-10) = -10x + 40 \\ \)

\(\sf\:(-10x + 41) - (-10x + 40) = 1 \\ \)

Step 9: There are no more terms to bring down, so the division is complete.

Step 10: Write the final result:

The quotient is \(\sf\:x^2 - 4x - 10\\\) and the remainder is 1.

Therefore, the division of \(\sf\:(x^3 - 8x^2 + 6x + 41) by (x - 4) \\\) is:

\(\sf\:(x^3 - 8x^2 + 6x + 41) ÷ (x - 4) \\ \) \(\sf\:= x^2 - 4x - 10 + \frac{{1}}{{x - 4}} \\ \)

Answer:

The number of possible dinner specials are 4368.

Step-by-step explanation:

The number of dinner specials = 5

They include appetizer, a salad, an entree, a side dish, and a dessert.

Possible items to choose from = 16.

They are 1. Appetizer Chicken strips, 2. Shrimp cocktail, 3. Buffalo wings, 4. Potato skins, 5. Salad Garden, 6. Caesar Entree T-bone steak, 7. Pot roast, 8. Lamb Side dish Corn, 9. Rice, 10. French fries, 11. Baked potato, 12. Pinto beans, 13. Dessert Chocolate cake, 14. Brownies, 15. Ice cream, 16. Apple pie

This is a combination problem requiring a combination solution with the following formula and steps:

C (n, r) =? C (n, r) = ?

n choose r

n (objects) =  16

r (sample) =  5

C (n, r) =? C (n, r) = ?

C (n, r) =C (14,5) C (n, r) =C (16,5)

=16! (5! (16−5)!) =16! (5! (16−5)!)

= 4368

The portfolio depicted as a box-and-whisker plot has a random selection of one stock, with probabilities of 0.51, 0.50, and 0.50.

The probability is frequently described as the ratio of favourable results to all favourable results in the sample. The likelihood of an occurrence P(E) = (The number of favorable events) is how it is stated (Sample space).

Probability is just the possibility that something will happen. When we don't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes. Biostatistics seems to be the analysis of occurrences with a probability distribution.

Given the box plot,

(a)

\(P(X < 51) = 0.51\)

(b)

\(P(22 < X < 51) = 0.50\)

(c)

\(P(X \geq 30) = 0.50\)

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Answer:

3/10

Step-by-step explanation:

4+6+10

=20

6/20

=3/10

Answer:

c

Step-by-step explanation:

assume base 10

-logy = x

\( \frac{1}{ log(y) } = x\)

log base x y = 5 turns into the format x^ 5 = y

implement that to get c

Answer:

424.8571428571429

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

360 - 98 = 262

Step-by-step explanation:

Answer:

15.5

Step-by-step explanation:

5+2x5-1+6/4=15.5

using a calculator this answer is correct.

Answer:

£460

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 5%/100 = 0.05 per year,

then, solving our equation

I = 2300 × 0.05 × 4 = 460

I = £ 460.00

The simple interest accumulated

on a principal of £ 2,300.00

at a rate of 5% per year

for 4 years is £ 460.00.

the correct option is D:

" The inverse relation must pass the vertical line test."

Remember that a relation is only a function if each value in the domain is only mapped into a single value in the range.

All functions need to pass what is called the "vertical line test" this means that if you draw a vertical line on the graph of the function, the vertical line can intersect the graph at most one time. If the vertical line intercepts the graph two or more times, then it is not a function.

From this we conclude that the correct option is D:

" The inverse relation must pass the vertical line test."

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Answer:

-17&14/16

-17

17&4/32

17.225

17&17/40

Answer:

1 to 3

Step-by-step explanation:

With ratios, if you can simplify them while still being proportional, they are still the same ratio, just represented differently and 2 and 6 can both be divided by 2, and when you do you get 1 and 3

In order to achieve the desired 3% boric acid solution, the 5% and 2% boric acid solutions must be combined.

To do this, we will use the following equation:

Volume of 5% solution (x) + Volume of 2% solution (y) = 60 mL

To solve for x and y, we will use the substitution method. We will start by solving for y first.

Now that we have y, we can substitute it into the original equation.

Finally, we can substitute x back into the equation for y to find our final answer.

Therefore, you will need 20 mL of 5% boric acid solution and 0 mL of 2% boric.

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Answer: -7

Step-by-step explanation:

First, lets use the functions to find the answer to f(-8) and g(4)

f(-8) is the same as asking for the value of y when x is -8

Therefore, f(-8) = -5 (according to the graph)

Using the same rule, g(4) would be the value of y when x = 4 which,

according to the graph, g(4) = 3

Plug these values back into the original equation to get:

\(-1*f(-8)-4*g(4)=?\\=-1*-5-4*3\\\)

using the order of operations, we will multiply the values first

\((-1*-5)+(-4*3)\\=5+(-12)\\=5-12\\=-7\)

Answer:

-7

Step-by-step explanation:

Answer:

1920 is 40 thousand  and 1950 is 45 thousand

Step-by-step explanation:

Not all intersecting lines are perpendicular.

Perpendicular lines require a 90-degree angle of intersection, creating the formation of right angles.

Nonetheless, unlike perpendicular lines that necessitate exactly 90 degrees of intersections, other types of driven lines can be at varying angles beside these.

As such, it is critical to highlight that in general intersecting lines come with different angles of intersection, and only those featuring exact 90-degree angle of intersection become normal cases of intersecting lines, becoming one among many subtypes existing today.

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Therefore, it would take approximately 19.02 years for an investment to at least double its original amount at a semi-annual compound interest rate of 3.62%.

When an investment is made with a certain amount, the compound interest rate is used to calculate the return on investment. In addition, the number of times interest is compounded each year can have an impact on the investment's outcome.

This question asks about how long it would take for an investment to double at a semi-annual compound interest rate of 3.62%.

To solve for how long it would take for an investment to double at a semi-annual compound interest rate of 3.62%, we need to use the formula for the future value of an annuity:

Future value of an annuity = Payment (1 + r/n)^(nt)where:r is the annual interest raten is the number of times interest is compounded per year Payment is the original amount is the number of years

To solve for t, we can rearrange the formula as follows:t = log(Payment/Future value of an annuity) / log(1 + r/n)where log is the natural logarithm.

The future value of the investment is double the original amount, so we can plug in 2 for Future value of an annuity and simplify the formula to get:t = log(2) / log(1 + 0.0362/2)t = 19.02 years

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The correct option regarding the number of bags filled by Nina, using proportions, is given as follows:

Between 20 and 30 bags.

A proportion is a fraction of an amount, and this fraction is combined with the unit rates of the problem and basic arithmetic operations, especially multiplication and division, to find the desired amounts in the context of the problem.

In this problem, a proportion is applied to find the number of bags filled by Nina, which is given by the division presented as follows:

Number of bags = Number of treats / Treats per bag.

The values of these parameters are given as follows:

Hence the numeric value of the expression is:

Number of bags = 78/3 = 26.

Which is a number between 20 and 30.

The problem states that Nina had 78 treats, and each bag has 3 treats, then it asks the correct option regarding the number of bags.

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Answer:

The appropriate solution is "570". The further explanation is given below

Step-by-step explanation:

(1)

Choosing the right 1 member out of 5 seniors throughout the state.  

The remaining 2 candidates would be chosen from some of the other 13 committee members within a week of choosing 1 member from either the 5 in-state representatives.

So, throughout this case, the number among approaches p is supplied by:

⇒  \(p=5C_1\times 13C_2\)

       \(=5\times 78\)

       \(=390\)

(2)

Choosing the right one person of the legislature out of three non-senior members of the state  

In this scenario, as already mentioned, the second participant needs to be chosen from the 5 qualified out-of-state citizens. Currently that we would have chosen 2 members out of 14 members in all, the 3rd member should be chosen out of another leftover 12 people.  

Therefore, the amount of forms, throughout this case q, seems to be:

⇒  \(q=3C_1\times 5C_1\times 12C_1\)

       \(=3\times 5\times 12\)

       \(=180\)    

So that the total no. of ways will be:

⇒  \(p+q\)

⇒  \(390+180\)

⇒  \(570\)

Answer:

\(\displaystyle{f(x)=3^x-5}\)

Step-by-step explanation:

Being translated up-down means that the value exists outside of x. Therefore, we can cancel B and C choice since those are horizontal (left-right) translation.

Our only choice is A and D. However, D is being translated up since it's +5. Thus, the only correct answer that a function is being translated down is:

\(\displaystyle{f(x)=3^x-5}\)

or A choice.

I think you were asking how many roots does the polynomial 7+5r⁴-32² have in all

For no. of total roots of a polynomial, we notice the highest power of the variable. Here, the variable is 4, whose highest power (degree) is 4. So, the polynomial above will have 4 roots in all.

And if you're asked to calculate no. of real roots or no. of complex roots, then Rather than using The concept of derivates, you can use Descarte's Sign Rule

Let, we call the polynomial, f(r) = 7+5r⁴ - 32²

We need to write the polynomial in simplest form, if we do, we will be having;

→ f(r) = 5r⁴ - 1017

Note the sign change of each term, how many times the sign changed , like from +ve to +ve doesn't counts, +ve to -ve counts 1 and then -ve to +ve again counts 1, so no. of sign change of f(r) will give the total no. of +ve real roots

Now, replace r by -r, and do the same, notice no. of sign changes, so no. of sign change of f(-r) will give the total no. of -ve real roots

So, we will be having total no. of real roots, as the sum of those obtained in above two cases.

And, no. of complex roots will be given by Degree (highest power) - no. of real roots,as the root can only be of two natures either real or complex. If you apply Descarte's Rule in the above polynomial, you will obtain two complex and two real roots (Refer for attachment for better understanding)

Answer:

1. A

2. Simplification: (not sure)

\( \frac{ - 3x {}^{5} + 6x { }^{2} - 4x - 15 }{9x {}^{2} - 12x + 4 } \)

The length of Marisa's garden is 10

The given parameters are:

Perimeter = 32 feet

Width = 6 feet

The perimeter is calculated as:'

Perimeter = 2 * (Length + width)

So, we have

2 * (Length + 6) = 32

Divide by 2

Length + 6 = 16

Subtract

Length = 10

Hence, the length of Marisa's garden is 10

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5x + 4 - 12 + 4x - 9 + 2y=360

The average rate of change of the school's enrollment during this time period is -49 students per year. This means that on average, the enrollment at the college has been decreasing by 49 students per year.

To determine the average rate of change of the school's enrollment during the given time period, we can use the formula:

Average rate of change = (Change in enrollment) / (Change in time)

The change in enrollment is calculated by subtracting the initial enrollment from the final enrollment, while the change in time is calculated by subtracting the initial year from the final year.

Given that in 2004 there were 975 students enrolled and in 2009 there were 730 students enrolled, we can calculate the change in enrollment:

Change in enrollment = 730 - 975 = -245 students

The change in time can be calculated as:

Change in time = 2009 - 2004 = 5 years

Now we can calculate the average rate of change:

Average rate of change = (-245 students) / (5 years) = -49 students per year

Therefore, the average rate of change of the school's enrollment during this time period is -49 students per year. This means that on average, the enrollment at the college has been decreasing by 49 students per year.

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The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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