I need help with my homework please. Part B only

Answer:

(-5, 5)

Step-by-step explanation:

The function increases from x = -11 to x = -5.

The function decreases from x = -5 to x = 5.

the function increases from x = 5 to x = 11.

Answer: (-5, 5)

Answer:

12 girls =)

Step-by-step explanation:

Make a table labeled girls and boys like this

2|3

4|6

6|9

8|12

Multiply until you get to 8 boys

The inverse of f(x) = x^(7/9) using exponential notation is f(x) = x^(9/7)

An inverse function in mathematics is a function that "undoes" another function.

In other words, if f(x) yields y, then y entered into the inverse of f yields the output x.

An invertible function is one that has an inverse, and the inverse is represented by the symbol f⁻¹.

The given function is of the form

f(x) = x^(7/9), this is equivalent to ⁹√x⁷

say f(x) = y, then

f(x) = y = x^(7/9)

y = x^(7/9)

solving for the inverse, of y = x^(7/9)

y = x^(7/9)

y^(9/7) = x

interchanging the letters

y = x^(9/7)

hence the inverse function is solved to be f⁻¹(x) = x^(9/7)

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Answers:

Domain as an inequality:  \(\boldsymbol{-\infty < \text{x} < \infty}\)

Domain in interval notation:  \(\boldsymbol{(-\infty , \infty)}\)

Range as an inequality:  \(\boldsymbol{-3 \le \text{y} \le 3}\)

Range in interval notation:  [-3, 3]

=================================================

Explanation:

The domain is the set of allowed x inputs. This graph goes on forever in both directions, so we can plug in any real number for x. There are no restrictions to worry about.

As an inequality, we write \(-\infty < \text{x} < \infty\) to basically say "x is between negative infinity and infinity". In other words, x is anything on the real number line.

That inequality condenses into the interval notation of \((-\infty , \infty)\)

Always use curved parenthesis for either infinity, because we can't ever reach infinity. It's not a number on the number line but rather a concept.

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

Now onto the range.

Recall the range is the set of possible y outputs. We look at the lowest and highest points (aka min and max) to determine the boundaries for the range.

In this case, the smallest y can get is y = -3

The largest it can get is y = 3

The range is any value of y such that \(-3 \le \text{y} \le 3\) which in word form is "any value between -3 and 3, inclusive of both endpoints".

That inequality condenses to the interval notation [-3, 3]

We use square brackets to include the endpoints as part of the range.

Answer:

\(\textsf{Domain}: \quad (-\infty, \infty) \quad -\infty < x < \infty\)

\(\textsf{Range}: \quad [-3,3] \quad -3\leq y\leq 3\)

Step-by-step explanation:

The domain of a function is the set of all possible input values (x-values).

The range of a function is the set of all possible output values (y-values).

Interval notation

Inequality notation

From inspection of the given graph, the function is continuous and so the domain is not restricted.

Therefore, the domain of the function is:

From inspection of the given graph, the minimum value of y is -3 and the maximum value of y is 3.  Both values are included in the range.

Therefore, the range of the function is:

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:

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

\( \LARGE{ \underline{\underline{ \tt{Required \: answer:}}}}\)

The above quadrilateral is a square because of the marking shown for the equilaterality of sides.

We have,

We need to find:

Solution:

x is the side of the square and y is the diagonal. Hence,

\( \large{ \boxed{ \sf{x = 13}}}\)

And for finding the diagonal which can use the Pythagoras theoram where the leg sides (p and b) are the sides of the triangle. Hence,

➝ y = √13² + 13²

➝ y = √338.

\( \large{ \boxed{ \sf{y = 13 \sqrt{2} }}}\)

The correct option is Option (D)

☃️\( \large{ \purple{ \bf{FadedElla}}}\)

In this case, the complement would be selecting a number less than or equal to 7; the probability of this occurring is \(\boxed{\frac{7}{10}}.\)

Answer:

it is 3/10

Step-by-step explanation:

Answer:

2\( {}^{5} \)

Step-by-step explanation:

2×2×2×2×2 = 2\( {}^{5} \)

The given set is (3, 4, 5, ...} is infinite set.

A set with an infinite number of elements is one that cannot be numbered. A set that has no last element is said to be endless. A set that can be put into a one-to-one correspondence with a suitable subset of itself is said to be infinite. No issue with the in-class assignment.

The stars in the clear night sky, water droplets, and the billions of cells in the human body are just a few examples of endless sets of objects that surround us. A set of natural numbers, however, serves as the best illustration of an infinite set in mathematics. There is no limit to the amount of natural numbers.

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Answer:

Proper and Improper Fractions. Mathematicians use three categories to describe fractions: proper, improper, and mixed. Fractions that are greater than 0 but less than 1 are called proper fractions. In proper fractions, the numerator is less than the denominator.

Step-by-step explanation:

Answer: r= 5/2 or r= 2 1/2

Step-by-step explanation:

9514 1404 393

Answer:

  x = 12

Step-by-step explanation:

The rule here is that the product of the lengths from the external point of intersection (angle vertex) to the intersections with the circle is the same for both secants. The tangent counts as intersecting the circle twice. So, we have ...

  (6)(6) = (3)(x)

  x = 36/3 = 12 . . . . . divide by the coefficient of x

To find out how many of the 39 practice trials would be faster than 62 seconds, we need to calculate the proportion of trials that fall within the range of more than 62 seconds.

We can use the z-score formula to standardize the values and then use the standard normal distribution table (also known as the z-table) to find the proportion.

The z-score formula is:

z = (x - μ) / σ

Where:

x = value (62 seconds)

μ = mean (61 seconds)

σ = standard deviation (1.5 seconds)

Calculating the z-score:

z = (62 - 61) / 1.5

z ≈ 0.6667

Now, we need to find the proportion of values greater than 0.6667 in the standard normal distribution table.

Looking up the z-score of 0.6667 in the table, we find the corresponding proportion is approximately 0.7461.

To find the number of trials faster than 62 seconds, we multiply the proportion by the total number of trials:

Number of trials = Proportion * Total number of trials

Number of trials = 0.7461 * 39

Number of trials ≈ 29.08

Rounding to the nearest whole number, approximately 29 of the 39 practice trials would be faster than 62 seconds.

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The probability of those that favors building the health center is 0.196

The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event. The formula for probability is given by; P(E) = Number of Favorable Outcomes/Number of total outcomes.

In a recent survey, 70% of the community favored building a health center in their neighborhood. If 14 citizens are chosen, find the probability that exactly 8 of them favor the building of the health center.

According to the scenario, 70% of the community favoured in building a health centre.

Hence , p=0.7.

In order to find the probability, binomial theorem will be used as follows :

= 0.196

Hence, The probability is 0.196

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Answer:

4

Step-by-step explanation:

The number in the ten thousands place of 542,970 is the 4.

Hope this helps.

Answer:

You just find the volume of the cup and subtract the volume of the froth (whatever that is).

V(cup) = pi * r^2 * h

...........= pi * 4.3^2 * 11.2

...........= 650.586cm^3

V(froth) = pi*r^2*h

............= pi*4.3^2*0.4

.............=23.232cm^3

V(hot chocolate) = V(cup) - V(froth)

.........................= 650.586 - 23.232

.........................= 627cm^3

Answer:

10 is your r

Step-by-step explanation:

Note: ^ is for Start of the line, $ is for end of the line ,* means 0 or more, + means 1 or more, [ab] means either a or b and {} is for specific number of times, () is for grouping.

A task in which it is necessary to create regular expressions to define five different languages. The alphabet used is A = {a, b}. The languages ​​are:

L1, which has exactly one "a" but any number of "bs".

L2, which has an odd number of "as" and an even number of "bs".

L3, which contains exactly two "as" or exactly two "bs", although not necessarily adjacent.

L4, which has all "bs" appearing before any "a" or all "as" appearing before any "b".

L5, where there can be any number of "as", but the number of "bs" must be even, although the "bs" need not be adjacent.

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Answer:

The 90%  confidence level is  \(19.15< L < 20.85\)

Step-by-step explanation:

From the question we are told that

     The sample size is  \(n = 64\)

     The mean age is  \(\= x = 20 \ years\)

      The standard deviation  is   \(\sigma = 4 \ years\)

Generally  the degree of freedom for this data set is mathematically represented as

        \(df = n - 1\)

substituting values

        \(df = 64 - 1\)

        \(df = 63\)

Given that the level of confidence is  90%  the significance level is mathematically evaluated as

          \(\alpha = 100 - 90\)

         \(\alpha =\)10 %  

         \(\alpha = 0.10\)

Now   \(\frac{\alpha }{2} = \frac{0.10}{2} = 0.05\)

Since we are considering a on tail experiment

The  critical value for half of  this significance level at the calculated  degree of freedom is obtained from the critical value table as

           \(t_{df, \frac{ \alpha}{2} } = t_{63, 0.05 } = 1.669\)

   The margin for error is mathematically represented as

          \(MOE = t_{df , \frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }\)

substituting values  

          \(MOE = 1.699 * \frac{4 }{\sqrt{64} }\)

         \(MOE = 0.85\)

he 90% confidence interval for the true average age of all students in the university is evaluated as follows

           \(\= x - MOE < L < \= x + E\)

substituting values  

         \(20 - 0. 85 < L < 20 + 0.85\)

         \(19.15< L < 20.85\)

Answer:

.05x+.04(x-1,900)=185

.05x+.04x-76=185

.09x=185+76

.09x=261

x=261/.09

Step-by-step explanation:

Answer:

4 7/8, 4 2/3, 4 1/6, 3 11/12

Step-by-step explanation:

To make it easier, convert it into decimals

4 2/3=4.666...

3 11/12=3.9166...

4 1/6=4.166...

4 7/8=4.875

Answer:100,000

Step-by-step explanation:

Answer:

a. 95%

Step-by-step explanation:

We solve this question, using z score formula.

Z score formula = (x - μ)/σ/√n

where x is the raw score

μ is the population mean

σ is the population standard deviation.

n is number of samples

For z1, where x1 = 460, μ = 500, σ = 20, n = 140

z score formula = (460 - 500)/ 20

= -40/20

= -2

We find the probability of the z score using the z score table.

P(x = 460) = P(z = -2)

= 0.02275

For z2, where x2 = 540, μ = 500, σ = 20

z score formula = (540 - 500)/20

= 40/20

= 2

We find the probability of the z score using the z score table.

P(x = 540) = P(z = 2)

= 0.97725

The probability that the cargo containers will weigh between 460 pounds and 540 pounds is calculated as:

= 460 < x < 540

= P(z = 2) - P(z = -2)

= 0.97725 - 0.02275

= 0.9545

Converting to percentage

0.9545 × 100

= 95.45%

Therefore,the percentage of the cargo containers will weigh between 460 pounds and 540 pounds is 95%

Answer: x^2 -x-6

Step-by-step explanation:

Mat

The product of  (x + 2)(x - 3) is x² - x - 6

"It is a mathematical statement which consists of constants, variables and mathematical operations."

For given question,

We have been given an algebraic expression (x + 2)(x - 3)

We need to find the product of (x + 2)(x - 3).

(x + 2)(x - 3)

= x (x - 3) + 2(x - 3)

= x² - 3x + 2x - 6

= x² - x - 6

Therefore, the product of  (x + 2)(x - 3) is x² - x - 6

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Answer:

17\(\sqrt{5}\)

Step-by-step explanation:

using the rule of radicals

\(\sqrt{ab}\) ⇔ \(\sqrt{a}\) × \(\sqrt{b}\)

simplifying the given radicals

\(\sqrt{45}\)

= \(\sqrt{9(5)}\)

= \(\sqrt{9}\) × \(\sqrt{5}\)

= 3\(\sqrt{5}\)

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

\(\sqrt{20}\)

= \(\sqrt{4(5)}\)

= \(\sqrt{4}\) × \(\sqrt{5}\)

= 2\(\sqrt{5}\)

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

Then

5\(\sqrt{45}\) + 3\(\sqrt{20}\) - 4\(\sqrt{5}\)

= 5(3\(\sqrt{5}\)) + 3(2\(\sqrt{5}\)) - 4\(\sqrt{5}\)

= 15\(\sqrt{5}\) + 6\(\sqrt{5}\) - 4\(\sqrt{5}\) ← collect like radicals

= 21\(\sqrt{5}\) - 4\(\sqrt{5}\)

= 17\(\sqrt{5}\)

Answer:

answers below :)

Step-by-step explanation:

Hi there!

with a ratio of 1:1.6, we can find these answers.

1. 19.2 km, multiply 12 by 1.6

2. 96. km, multiply 12 by 6 to find the total amount of miles traveled, then

multiply 60 by 1.6 to get 96.

I hope this helps!

The graph of the function y = 5|x - 4| is added as an attachment

From the question, we have the following parameters that can be used in our computation:

y = 5|x - 4|

The above function is an absolute value function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

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The side length of the cube is 5.6 feet (rounded to the nearest tenth).

We can calculate the side length of a cube with a volume of 141 cubic feet using the formula for cube volume , which is \(V = s^3\), where V is the volume and s is the side length.

We can calculate s by taking the cube root of both sides of the equation:

\(s = (V)^{(1/3)\)

Substituting V = 141, we get:

\(s = (141)^{(1/3)\)

By using a calculator to evaluate this expression, we may determine:

s ≈ 5.6

As a result, the cube's side length is roughly 5.6 feet (rounded to the closest tenth). This indicates that if we increase the side length by three, it will become longer. (\(s^3\)), we will get the volume of the cube, which is 141 cubic feet.

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The number of watts will be 4700 watts to the nearest 100 watt.

It should be noted that 1 watt equals to 3.41 Btu per hour.

In this case, the air conditioner is rated at 16000 BTU per hour.

Therefore, the number of watt will be:

= 16000/3.41.

= 4692

= 4700 watts to the nearest 100 watt.

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