What is the approximate value of x.

Answer:

translated up 4 units and s(t)= 22.5t + 775

Step-by-step explanation:

first one count spaces between lines. second one add the t's together and the numbers to get final answers

Answer:

remainder = 6

Step-by-step explanation:

by the Remainder theorem

A polynomial divided by (x - a) then the remainder is equal to f(a), so

f(x) = 3x² + 2x - 10 divided by (x - 2) , then remainder is f(2)

f(2) = 3(2)² + 2(2) - 10 = 3(4) + 4 - 10 = 12 + 4 - 10 = 6

Answer: remainder = 6

Step-by-step explanation:

Answer:

The closest I can get is 8b

Step-by-step explanation:

Since we don't know what b is, you have to have 8b

Solve for x values that satisfy a quadratic inequality to write interval notation. This usually involves factoring the quadratic and putting it equal to zero, then utilizing the inequality sign to select viable solutions. After finding the answers, write (a,b) to indicate the interval of x-values that make the inequality true. The interval notation for -3 and 5 is (-3,5).

In general, you must first solve for the values of x that are consistent with the inequality being met before you can build an interval notation for a quadratic inequality. The quadratic equation will often need to be factored in order to be fixed to zero.

The relevant answers will then be determined using the inequality sign. After you have identified the solutions, you may use the notation (a,b), where a and b stand for the solutions, respectively, to show the range of x-values that cause the inequality to hold.

The interval notation, for instance, might appear as follows if the responses were -3 and 5. (-3,5).

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The maximum possible number of handshakes at the party can be calculated using the formula n(n-1)/2, where n is the number of people attending. This formula is derived from the fact that each person can shake hands with every other person except themselves.

Let's assume that there are n people attending the party. In order to maximize the number of handshakes, we want each person to shake hands with every other person except themselves.

Now, let's consider the first person. They can shake hands with (n-1) other people, as they cannot shake hands with themselves. Similarly, the second person can shake hands with (n-1) other people, but they have already shaken hands with the first person, so they can only shake hands with (n-1)-1 = (n-2) remaining people.

Following this pattern, the third person can shake hands with (n-1)-2 = (n-3) people, the fourth person can shake hands with (n-1)-3 = (n-4) people, and so on. The last person, the nth person, can shake hands with (n-1)-(n-2) = 1 person.

By summing up the number of handshakes for each person, we get (n-1) + (n-2) + (n-3) + ... + 1, which is the sum of the first (n-1) natural numbers. This sum can be calculated using the formula n(n-1)/2.

Therefore, the maximum possible number of handshakes at the party is n(n-1)/2.

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Answer:

Step-by-step explanation:

You want to compare the average rates of change on the interval [-6, -3] of the functions f(x) = 4x² and g(x) = 8x².

The average rate of change of p(x) on the interval [a, b] is given by ...

  ARC = (p(b) -p(a))/(b -a)

The average rate of change is ...

  ARC = (f(-3) -f(-6))/(-3 -(-6))

  ARC = (36 -144)/3 = -108/3 = -36

The average rate of change of f(x) on [-6, -3] is -36.

The average rate of change is ...

  ARC = (72 -288)/3 = -216/3 = -72

The average rate of change of g(x) on [-6, -3] is -72.

The ratio of the rates of change is ...

  ARC(g(x))/ARC(f(x)) = -72/-36 = 2

The average rate of change of g(x) is 2 times that of f(x).

__

Additional comment

We hope you noticed that g(x) is f(x) scaled vertically by a factor of 2. That scale factor is the ratio of the rates of change of the two functions.

Answer:

Mala had 14 sweets at the start.

Step-by-step explanation:

7 x 2 = 14

To check, 14/2 = 7. (Dividing by 2 is the same as multiplying by 1/2)

Answer:

The image was dilated by a scale factor of 2. (x,y) -> (2x,2y)

Step-by-step explanation:

Answer:

19/3 (6 1/3)

Step-by-step explanation:

Answer:

11 unit

Step-by-step explanation:

Applying,

s = √[(y₂-y₁)²+(x₂-x₁)²]...................... Equation 1

Where s = length of the side formed.

From the question,

Given: x₁ = -2, x₂ = 9, y₁ = 5, y₂ = 5

Substitute these values into equation 1

s = √[(9+2)²+(5-5)²]

s = √(11²)

s = 11 unit.

Hence the length of the side formed by the vertices is 11 unit

The answer is (C) 126.

The sum of a geometric series can be found using the formula: S = a * (1 - r^n) / (1 - r), where a is the first term, r is the common ratio, and n is the number of terms.

In this case, the first term (a) is 2, the common ratio (r) is 2 (since each term is double the previous term), and the number of terms (n) can be found by noticing that 64 is equal to 2^6.

Substituting these values into the formula, we get: S = 2 * (1 - 2^6) / (1 - 2)

Simplifying further, we have: S = 2 * (1 - 64) / (-1)

S = 2 * (-63) / (-1)

S = 126

Therefore, the sum of the geometric series 2+4+8+...+64 is 126.

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The sum of the geometric series 2 + 4 + 8 + ... + 64 is 126. Hence, the answer is (C) 126.

The provided series is a geometric series with a common ratio of 2.

To determine the sum of the series, we can use the formula for the sum of a geometric series:

\(\[S = \frac{a \cdot (1 - r^n)}{1 - r}\]\)

where:

S is the sum of the series,

a is the first term of the series,

r is the common ratio,

and n is the number of terms.

In this case, the first term (a) is 2, the common ratio (r) is 2, and the number of terms (n) can be determined by finding the exponent that makes 64 the last term. Since 2 raised to the power of 6 (2⁶) equals 64, there are 6 terms in the series.

Using the formula, we can calculate the sum of the series:

\(\[S = \frac{{2 \cdot (1 - 2^6)}}{{1 - 2}}\)

\(= \frac{{2 \cdot (1 - 64)}}{{1 - 2}}\)

\(= \frac{{2 \cdot (-63)}}{{-1}}\)

= 2 * 63

= 126

Therefore, the correct answer is (C) 126.

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Answer:

9.5 feet

Step-by-step explanation:

To calculate volume, the formula is V = l*w*h.

We have the volume, length, and height, so we just need to plug it in to find the width. 256.5 = 4.5*w*6. Calculate this, and it'll become 256.5 = 27w. Then we divide both sides by 27 to find w. 256.5/27 = 27w/27. 9.5 = w. Width is 9.5 feet.

The type of distribution which is utilized for the nominal data is option  b. Binomial distribution.

The appropriate distribution for nominal data is a binomial distribution.

The binomial distribution is used when the data consists of two possible outcomes.

The two outcomes such as success or failure, heads or tails, or pass or fail.

In nominal data, the categories do not have any inherent order.

And there is no numerical value associated with each category.

The binomial distribution gives the probability of obtaining a certain number of successes in a fixed number of independent trials.

The required probability of success is the same for each trial.

Therefore, option b.  binomial distribution is considered as more appropriate distribution for the nominal data.

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Answer:

the trapezoid

Step-by-step explanation:

area of trapezoid = 672

area of kite = 648

the formula for the kite area is 1/2×diagonal 1×diagonal 2

the formula for the trapezoid area is 1/2×(base 1 +base 2)× height

The sum of the given series corresponds to value -5.5.

Given series is \(\[11+14+17+20+23+26+29+32+35+38+ \cdots \]\)

The first term of this series is a=11 and the common difference is d=3.

Since we know the formula for finding the sum of an arithmetic sequence is:

S = (n/2)(2a + (n - 1)d), where n is the number of terms, a is the first term, and d is the common difference.

Substituting n=10, a=11, d=3, we have:

S = (10/2)(2(11)+(10-1)3) = 5(2*11+9*3) = 305.

Now, we need to find the sum of the series s using the formula,

s = a/(1-r)

Where r=common ratio

Substituting a=11 and r=3 in the formula, we get:

s = 11/(1-3) = 11/(-2) = -5.5.

Therefore, sum of the series s is -5.5.

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then for 5 tablespoons you use 12.5 ounces of milk

Answer:

Step-by-step explanation:

√2, √3 are irrational numbers.

√4  = 2 is not irrational.

The correct option regarding the number of kettles that can be filled with the potion is given as follows:

C. Between 2 and 3.

The number of kettles is obtained applying the proportions in this problem, dividing the total number of litters by the number of liters of each kettle.

The parameters for this problem are given as follows:

Hence the number of kettles is obtained as follows:

11/4 = 2.75.

Meaning that the correct option is given by option C.

A kettle holds 4 liters of magic potion. There are 11 liters of potion.

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Answer:

$8.90

Step-by-step explanation:

((2)(2.90))+(3.10)= $8.90

'""""""""""""""""""""""""""""""""""8.9$""""""""""""""""""""

In both the Vendor Compliance at Geoffrey Ryans (A) and Operational Execution at Arrows Electronics cases, there are common problems and challenges. These include issues related to vendor management.

One of the key problems faced by both companies is vendor compliance. This refers to the ability of vendors to meet the requirements and standards set by the company. Both cases highlight instances where vendors fail to meet compliance standards, leading to disruptions in the supply chain and operational inefficiencies. This problem affects the overall performance and profitability of the companies.

Another challenge faced by both companies is operational execution. This encompasses various aspects of operations, including inventory management, order fulfillment, and delivery. In both cases, there are instances where operational execution falls short, leading to delays, errors, and customer dissatisfaction. This challenge requires the companies to streamline their processes, improve communication and coordination, and enhance overall operational efficiency.

Overall, the problems and challenges in both cases revolve around effective vendor management, supply chain optimization, and operational excellence. Addressing these issues is crucial for both companies to improve their performance, meet customer demands, and maintain a competitive edge in the market.

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Step-by-step explanation:

\(\large\underline{\sf{Solution-}}\)

Given expression is

\(\rm :\longmapsto\:tan75\degree + cot75\degree \)

Consider

\(\rm :\longmapsto\:tan75\degree \)

\(\rm \:  =  \: tan(45\degree + 30\degree )\)

\(\rm \:  =  \: \dfrac{tan45\degree + tan30\degree }{1 - tan45\degree \times tan30\degree } \)

\(\rm \:  =  \: \dfrac{1 + \dfrac{1}{ \sqrt{3} } }{1 - 1 \times \dfrac{1}{ \sqrt{3} } } \)

\(\rm \:  =  \: \dfrac{1 + \dfrac{1}{ \sqrt{3} } }{1 - \dfrac{1}{ \sqrt{3} } } \)

\(\rm \:  =  \: \dfrac{ \sqrt{3} + 1 }{ \sqrt{3} - 1} \)

On rationalizing the denominator, we get

\(\rm \:  =  \: \dfrac{ \sqrt{3} + 1 }{ \sqrt{3} - 1} \times \dfrac{ \sqrt{3} + 1 }{ \sqrt{3} + 1 } \)

\(\rm \:  =  \: \dfrac{ {( \sqrt{3} + 1)}^{2} }{ {( \sqrt{3}) }^{2} - {(1)}^{2} } \)

\(\rm \:  =  \: \dfrac{3 + 1 + 2 \sqrt{3} }{3 - 1} \)

\(\rm \:  =  \: \dfrac{4+ 2 \sqrt{3} }{2} \)

\(\rm \:  =  \: \dfrac{2(2+ \sqrt{3} )}{2} \)

\(\rm \:  =  \: 2 + \sqrt{3} \)

\(\rm\implies \:\boxed{\tt{ tan75\degree = 2 + \sqrt{3} \: }}\)

Now,

\(\rm :\longmapsto\:cot75\degree \)

\(\rm \:  =  \: \dfrac{1}{tan75\degree } \)

\(\rm \:  =  \: \dfrac{1}{2 + \sqrt{3} } \)

On rationalizing the denominator, we get

\(\rm \:  =  \: \dfrac{1}{2 + \sqrt{3} } \times \dfrac{2 - \sqrt{3} }{2 - \sqrt{3} } \)

\(\rm \:  =  \: \dfrac{2 - \sqrt{3} }{ {(2)}^{2} - {( \sqrt{3}) }^{2} } \)

\(\rm \:  =  \: \dfrac{2 - \sqrt{3} }{4 - 3} \)

\(\rm \:  =  \: 2 - \sqrt{3} \)

\(\bf\implies \:\boxed{\tt{ cot75\degree = 2 - \sqrt{3} \: }}\)

Now, Consider

\(\rm :\longmapsto\:tan75\degree + cot75\degree \)

\(\rm \:  =  \: 2 + \sqrt{3} + 2 - \sqrt{3} \)

\(\rm \:  =  \: 4\)

Hence,

\(\rm\implies \:\boxed{\tt{ tan75\degree + cot75\degree = 4 \: }}\)

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

\(\rm :\longmapsto\:tan75\degree + cot75\degree \)

\(\rm \:  =  \: tan75\degree + \dfrac{1}{tan75\degree } \)

\(\rm \:  =  \: \dfrac{ {tan}^{2}75\degree + 1}{tan75\degree } \)

\(\rm \:  =  \: \dfrac{1}{\dfrac{tan75\degree }{1 + {tan}^{2} 75\degree } } \)

\(\rm \:  =  \: \dfrac{2}{\dfrac{2tan75\degree }{1 + {tan}^{2} 75\degree } } \)

We know,

\(\rm :\longmapsto\:\boxed{\tt{ \frac{2tanx}{1 + {tan}^{2} x} = sin2x}}\)

\(\rm \:  =  \: \dfrac{2}{sin150\degree } \)

\(\rm \:  =  \: \dfrac{2}{sin(180\degree - 30\degree )} \)

\(\rm \:  =  \: \dfrac{2}{sin30\degree } \)

\(\rm \:  =  \: 2 \times 2\)

\(\rm \:  =  \: 4\)

Hence,

\(\rm\implies \:\boxed{\tt{ tan75\degree + cot75\degree = 4 \: }}\)

Answer:

B

Step-by-step explanation:

The \(x\) intercepts are where \(f(x)=0\).

\(2x^2+7x-9=0 \\ \\ (2x+9)(x-1)=0 \\ \\ x=-\frac{9}{2}, 1\)

The \(y\) intercept is where \(x=0\).

\(f(0)=2(0)^2+7(0)-9=-9\)

Answer: 3 bags

Step-by-step explanation:

Since a bag has 8 buns, 3 bags would total 24 buns. 2 bags would be 16 buns which is not up to 20 buns. 3 bags is what she'll need as its the best option.

Tabetha's monthly installment for the patio set is approximately $121.46.

To calculate the different components involved in Tabetha's patio set purchase:

(1) Calculate the tax amount:

Tax rate = 6%

Tax amount = Tax rate * Purchase price = 0.06 * $2500 = $150.

(2) Compute the total loan amount:

Loan amount = Purchase price + Delivery fee + Tax amount = $2500 + $100 + $150 = $2750.

(3) Identify the remaining letters in the formula I=Prt:

I = Interest amount

P = Loan amount

r = Interest rate

t = Time period (in years)

(4) Find the interest amount:

I = Prt = $2750 * 0.03 * 2 = $165.

(5) Find the total amount to be paid in 2 years:

Total amount = Loan amount + Interest amount = $2750 + $165 = $2915.

(6) Find the monthly installment:

The loan term is 2 years, which means there are 24 months.

Monthly installment = Total amount / Loan term = $2915 / 24 = $121.46 (rounded to two decimal places).

This represents the amount she needs to pay each month over the course of 2 years to fully repay the loan, including the principal, interest, taxes, and delivery fee.

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The function rule g(x) after the given transformations of the graph of f(x)= 3x is g(x) = 1/9x

Transformation techniques -

The act of shifting an object's location on the xy plane is referred to as transformation.

Given the parent function

f(x) = -3x

If the function is not reflected over x-axis, the resulting function will be f(x) =  3x

If the resulting function is compressed by a factors of 1/8, hence the final function rule will be;

g(x) = 1/9( 3x)

g(x) = 1/9x

Hence the function rule g(x) after the given transformations of the graph of f(x)=3x is g(x) = 1/9x.

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Given the following sentence:

" In a recent poll, 3% of the people surveyed were in favor of the new law "

We will write the given percentage as a decimal

So, 3% = 3/100 = 0.03

so, the answer will be 0.03

The correct option is D. 48.

The value of the composite function g(f(-1)) is 48.

The process of integrating two or so more functions to create a single function is known as function composition. A function represents a piece of labor.

Now, according to the question, the given functions are-

f(x) = 5x² + 2 and g(x) = x² – 1

First, we must determine f(-1). Consider the f(x) expression and substitute -1 for x.

f(x) = 5x² + 2

f(-1) = 5(-1)² + 2

f(-1) = 5(1) + 2

f(-1) = 5 + 2

f(-1) = 7

We now know that f(-1) equals 7, hence g(f(-1)) is like g. (7). We'll use the g(x) equation now, substituting 7 for x.

g(x) = x² - 1

g(7) = 7² - 1

g(7) = 49 - 1

g(7) = 48

Therefore, the result for the composite function g(f(-1)) is 48.

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The correct question is-

Consider these functions: f(x) = 5x² + 2 g(x) = x² – 1 What is the value of g(f(-1))? A. 2 B. 8 C. 22 D. 48