answer in simplest radical form

The simplified exponential function is determined as x⁴.

An exponential function is a mathematical function used to calculate the exponential growth or decay of a given set of data.

To simplify an exponential function, we will apply the rules of exponent as shown below;

The given exponential function;

= (∛ x² )⁶

The given expression is simplified as follows;

= [tex](x^2) ^{\frac{1}{3} \times 6}[/tex]

= ( x² )²

= x⁴

Thus, the simplified exponential function is determined by applying the rules of multiplication of powers.

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The closure property does not hold for division of polynomials because the result may not be a polynomial itself.

The closure property states that if you perform an operation on two elements within a certain set, the result of that operation will also be within the same set.

In the case of addition, subtraction, and multiplication, this property holds true, but it does not apply to the division of polynomials.

When dividing polynomials, the result may not always be a polynomial. Division involves dividing the coefficients of the terms and subtracting exponents, which can result in fractional or negative exponents.

These fractional or negative exponents indicate that the result is not a polynomial, but rather a rational function or a polynomial with non-integer exponents.

For example, consider dividing the polynomial x^2 by the polynomial x. The result is x, which is a polynomial. However, if you divide x^2 by x^2 + 1, the result is 1 / (1 + 1/x^2), which is a rational function, not a polynomial.

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Answer:478.85 in2

Step-by-step explanation:

Just divide LOL

3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

To express 3 1/2 cups as a multiplication expression using the unit "1 cup" as a factor, you can write it as:

3 1/2 cups = (3 + 1/2) cups = 3 cups + 1/2 cup

Since there are 1 cup in each term, we can rewrite it as:

3 cups + (1/2) cup

Now, we can express each term as a multiplication expression:

3 cups = 3 * 1 cup = 3

(1/2) cup = (1/2) * 1 cup = 1/2

Putting it all together, the multiplication expression is:

3 * 1 cup + (1/2) * 1 cup = 3 + 1/2

Therefore, 3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

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Answer:

42°

Step-by-step explanation:

According to Exterior Angle Theorem,

an exterior angle of a ∆ is equal to the sum of the opposite interior angles.

So,

h+96°=138°

h=138°-96°

h=42°

Answer:

x = 4

Step-by-step explanation:

since the triangle is equilateral then the vertex angles are congruent, each 60°

using the sine ratio in the right triangle with x as its hypotenuse and the exact value

sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , then

sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{\sqrt{12} }{x}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

x × [tex]\sqrt{3}[/tex] = 2[tex]\sqrt{12}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )

x = [tex]\frac{2\sqrt{12} }{\sqrt{3} }[/tex] = 2 × [tex]\sqrt{\frac{12}{3} }[/tex] = 2 × [tex]\sqrt{4}[/tex] = 2 × 2 = 4

Answer:

The answer is 11

Step-by-step explanation:

brother only=12-8=4

sister only=13-8=5

brother and sister =8

neither of them=x

28=4+8+5+x

28=17+x

x=28-17

x=11

Answer:

  11

Step-by-step explanation:

You want to know the number of students with no brother or sister, given that 12 of 28 have at least one brother, 13 have at least one sister, and 8 have both.

The attachment shows the two-way table that can be formed from the given information. The four given numbers are shown in green at lower right. The other numbers in the table are filled in to make the totals accurate.

The number of students not having either a brother or sister is 11.

__

Additional comment

In terms of probability, which is the fraction that each event is of the total, you have ...

  P(B∪S) = P(B) +P(S) -P(B∩S) . . . . . . . useful relation to memorize

  P(B'∩S') = 1 -P(B∪S) = 1 -(12/28 +13/28 -8/28) = 11/28

This tells you 11 of the 28 students do not have a brother or sister.

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Using the context surrounding the word trough in line 9 of "Concrete Mixers," explain what a trough looks like and what it does on a concrete mixer. .

sorry I can't delete it this not answer your question

Answer:

Option B

Step-by-step explanation:

704 cubic centimeters

The missing part indicated in the figures are ? = 12, TX = 9 and x = 20

Figure a

The missing part can be calculated using the following equation

?/(11 - 5) = 22/11

Evaluate the difference

?/6 = 22/11

So, we have

? = 6 * 22/11

Evaluate the expression

? = 12

Figure b

The missing part can be calculated using the following equation

TX/3 = 6/2

So, we have

TX = 3 * 6/2

Evaluate

TX = 9

Figure c

The value of x can be calculated using the following equation

1/4x + 6 = 2x - 29

So, we have

x + 24 = 8x - 116

Evaluate

-7x = -140

Divide

x = 20

Hence, the value of x is 20

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134 degrees is equivalent to the measure of arc RS

In order to determine the measure of the arc RS, we will use the theorem below:

The measure of the angle at the vertex is half that of its intercepted arc. Based on the theorem, we can set up the equation:

arcRS = 2m<Q
arcRS = 2(67)
arcRS = 134 degrees

Hence the measure of the arc RS from the given circle is equivalent to 134 degrees

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The slant height of the cone is approximately 29.29 cm to the nearest tenth of a centimeter.

To solve the problem, we must first understand what the lateral area of a cone is. The lateral area of a cone is the curved surface area of the cone, which does not include the area of the base. It can be calculated by multiplying the slant height of the cone by the circumference of the base.

Using the formula for the lateral area of a cone, we can write:

Lateral area = πrℓ

where r is the radius of the base, and ℓ is the slant height.

Substituting the given values of lateral area and radius, we get:

574π = π(19.6)ℓ

Simplifying the equation, we get:

574 = 19.6ℓ

ℓ = 574/19.6

ℓ ≈ 29.29 cm

In conclusion, we can find the slant height of a cone with a given lateral area and radius by using the formula for lateral area and solving for the slant height. In this case, the slant height was found to be approximately 29.29 cm.

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Answer:

548 > 373

Step-by-step explanation:

548 is greater than 373 because when we compare the digits from left to right, we find that the first digit of 548 (5) is greater than the first digit of 373 (3). Therefore, we can conclude that 548 is greater than 373.

The ">" symbol is used to represent "greater than" in mathematical comparisons.

Hope this helps!

Answer:

Both students scored in the top 10% of their classes.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

In this question:

Top 10% = Above the 100 - 10 = 90th percentile.

The 90th percentile of scores is X when Z has a pvalue of 0.9, that is, Z = 1.28.

So, the student who had a z-score above 1.28 scored in the 90th percentile of their class.

In student A's class the mean was 78 and the standard deviation of 5. He scored 87.

We have that [tex]\mu = 78, \sigma = 5, X = 87[/tex]

Then

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{87 - 78}{5}[/tex]

[tex]Z = 1.8[/tex]

1.8 > 1.28, so student A scored in the top 10% of his/her class.

Student B's class the mean was 76 with a standard deviation of 4. Scored 87.

We have that [tex]\mu = 76, \sigma = 4, X = 87[/tex]

Then

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{87 - 76}{4}[/tex]

[tex]Z = 2.75[/tex]

2.75 > 1.28, so student B also scored in the top 10% of his/her class.

Both students scored in the top 10% of their classes.

The dependent and independent variables are distance from destination and time respectively.

Rate of change = change in y/Change in x

Rate of change= (244-285)/(20-0)

Rate = -2.05

When the helicopter reaches its destination , y = 0

We can write the traveling equation in the form y = mx + c

Where :

c= intercept ; m = slope

y = -2.05x + 285

At y = 0

0 = -2.05x + 285

-2.05x = - 285

x = 285/2.05

x = 139.02

Hence, the helicopter will reach its destination after 139 minutes .

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Substituting the given variable cost per book for Method 1 (which is not specified), we can calculate the value of 'x' that makes the costs equal for the two methods.

Let's assume the number of books produced is denoted by 'x'. We need to find the value of 'x' for which the costs from the two methods are the same.

For the first method, the total cost is the sum of the one-time fixed cost and the variable cost per book:

Total cost for Method 1 = 44,907 + (variable cost per book) * x

For the second method, the total cost is the sum of the one-time fixed cost and the variable cost per book:

Total cost for Method 2 = 22,907 + (23.25 * x)

To find the number of books produced when the costs from the two methods are equal, we set the total costs equal to each other and solve for 'x':

44,907 + (variable cost per book) * x = 22,907 + (23.25 * x)

Subtracting (23.25 * x) from both sides and rearranging the equation:

21,000 = 23.25 * x - (variable cost per book) * x

21,000 = x * (23.25 - (variable cost per book))

Dividing both sides by (23.25 - (variable cost per book)):

x = 21,000 / (23.25 - (variable cost per book))

Substituting the given variable cost per book for Method 1 (which is not specified), we can calculate the value of 'x' that makes the costs equal for the two methods.

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The cost of the molding is given as follows:

$119.30.

The circumference of a circle of radius r is given by the equation presented as follows:

C = 2πr.

The parameters for this problem are given as follows:

d = 9 -> r = 4.5.

(as the radius is half the diameter)

Hence the circumference is given as follows:

C = 2 x π x 4.5

C = 28.27 ft.

The cost is of $4.22 per ft, hence the total cost is given as follows:

4.22 x 28.27 = $119.30.

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The function represented by the graph with the given transformations is |–x| + 2.

The function represented by the given transformations is |–x| + 2.

Let's analyze the transformations step by step:

Reflection across the x-axis:

Reflecting the parent absolute value function across the x-axis changes the sign of the function. The positive slopes become negative, and the negative slopes become positive. This transformation is denoted by a negative sign in front of the function.

Translation right 2 units:

Translating the function right 2 units shifts the entire graph horizontally to the right. This transformation is denoted by subtracting the value being translated from the input of the function.

Combining these transformations, the function |–x| + 2 results. The negative sign reflects the function across the x-axis, and the subtraction of 2 units translates it right. The absolute value is applied to the negated x, ensuring that the function always returns a positive value.

Thus, the function represented by the graph with the given transformations is |–x| + 2.

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Answer: -lx-2l

Step-by-step explanation:

Answer:

28. 0.2461 or 24.61%.

29. 0.00058275 or 0.058275%.

Step-by-step explanation:

Question 28:

we can use the binomial probability formula to calculate the probability:

[tex]\boxed{\bold{P(X = k) = (nCk) * p^k * (1 - p)^(n - k)}}[/tex]

Where:

In this case, we have n = 9 babies, and each baby has a 50% chance of being a girl (p = 0.5). We want to find the probability that exactly 4 of them are girls (k = 4).

Using the formula, we can calculate the probability as follows:

[tex]\bold{P(X = 4) = (9C4) * (0.5)^4 * (1 - 0.5)^(9 - 4)}[/tex]

Calculating the values:

Now, we can substitute these values into the formula:

P(X = 4) = 126 * 0.0625 * 0.03125 = 0.2461 or 24.61%

Therefore, the probability that exactly 4 out of 9 babies are girls is approximately 0.2461 or 24.61%.

Question 29:

We need to calculate the number of possible outcomes to calculate this probability, where the gambler correctly predicts the top 3 finishers in order and divides it by the total number of possible outcomes.

The total number of possible outcomes is the number of permutations of 13 horses taken 3 at a time.

This can be calculated as:

[tex]13P3 = \frac{13! }{(13 - 3)! }= \frac{13! }{ 10! }=\frac{13*12*11*10! }{ 10! }= 13 * 12 * 11 = 1,716[/tex]

Now,

To calculate the number of favorable outcomes where the gambler predicts the top 3 finishers correctly, we need to consider that there is only one correct order for the horses to finish.

Therefore, there is only one favorable outcome.

The probability of the gambler winning his bet is given by:

[tex]\boxed{\bold{P\:(winning) = \frac{Number\: of \:favorable\: outcomes }{ Total \:number \:of \:outcomes}}}[/tex]

[tex]P(winning) = \frac{1 }{1,716}=0,00058275 \: or\:0.058275%[/tex]

Therefore, the probability that the gambler will win his bet is approximately 0.00058275 or 0.058275%.

Answer:

28)  0.246 = 24.6%

29)  1/286 = 0.350%

Step-by-step explanation:

We can model the given scenario as a binomial distribution.

[tex]X \sim \text{B}(n,p)[/tex]

where:

Given the probability that a baby is born a girl is 0.5, and the number of babies is 9:

[tex]\boxed{X \sim \text{B}(9,0.5)}[/tex]

where the random variable X represents the number of babies who are girls.

To find the probability that at exactly 4 babies are girls, we need to find P(X = 4).

To do this, we can use the binomial distribution formula:

[tex]\boxed{\displaystyle \text{P}(X=x)=\binom{n}{x} \cdot p^x \cdot (1-p)^{n-x}}[/tex]

Substitute the values of n = 9, p = 0.5 and x = 4 into the formula:

[tex]\begin{aligned}\displaystyle \text{P}(X=4)&=\binom{9}{4} \cdot 0.5^4 \cdot (1-0.5)^{9-4}\\\\&=\dfrac{9!}{4!\:(9-4)!} \cdot 0.5^4 \cdot 0.5^{5}\\\\&=126 \cdot 0.0625 \cdot 0.03125\\\\& = 0.24609375\end{aligned}[/tex]

Therefore, the probability that 4 babies from a sample of 9 babies are girls is 0.246 (3 s.f.) or 24.6%.

We can also use the binomial probability density function of a calculator to calculate P(X = 4).

Inputting the values of n = 9, p = 0.5 and x = 4 into the binomial pdf:

[tex]\text{P}(X=4)=0.24609375[/tex]

Therefore, this confirms that the probability that 4 babies from a sample of 9 babies are girls is 0.246 (3 s.f.) or 24.6%.

[tex]\hrulefill[/tex]

To calculate the probability that the gambler will win his bet, we need to determine the number of favorable outcomes (winning combinations) and the total number of possible outcomes.

The gambler wins if he picks the top three horses in any order. There are 6 ways for the three winners to be arranged in the top three.

There are a total of 13 horses in the race.

Therefore, the total number of possible outcomes is:

[tex]13 \times 12 \times 11 = 1716[/tex]

Therefore, the probability that the gambler will win his bet is:

[tex]\begin{aligned} \sf Probability &=\sf \dfrac{Favorable \;outcomes}{Total\;outcomes}\\\\&=\dfrac{6}{1716}\\\\&=\dfrac{1}{286}\\\\ & \approx0.350\%\; \sf (3\;d.p.)\end{aligned}[/tex]

The value of angle k is determined as  60⁰.

The value of angle m is determined as 120⁰.

The measure of angle m and k is calculated by applying the following theorem as follows;

The value of angle k is calculated as;

60 + 2k = 180 (opposite angles of a cyclic quadrilateral are supplementary)

60 + 2k = 180

2k = 180 - 60

2k = 120

k = 120/2

k = 60⁰

The value of angle m is calculated as;

m + 60 = 180  (opposite angles of a cyclic quadrilateral are supplementary)

m = 180 - 60

m = 120⁰

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The percentage of debit shoppers has increased.

21% (2006) < 40% (2009)

In 2006, the percentage of debit shoppers is 21%.

In 2009, the percentage of debit shoppers is 40%.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

We have,

In 2006:

A sample of 200 in-store shoppers showed that 42 paid by debit card.

The percentage of debit shoppers in 2006.

= 42/200 x 100

= 42/2

= 21%

In 2009:

A sample of the same size showed that 80 were paid by debit card.

The percentage of debit shoppers in 2009.

= 80/200 x 100

= 40%

Thus,

The percentage of debit shoppers has increased.

21% (2006) < 40% (2009)

In 2006, the percentage of debit shoppers is 21%.

In 2009, the percentage of debit shoppers is 40%.

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The quadratic equation from the given root is 4x² - 41x + 45 = 0

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

Roots = 5/x and 4

The equation of the function can be calculated as

(x - root) * (x - root) = 0

using the above as a guide, we have the following:

(x - 5/4) * (x - 9) = 0

When expanded, we have

(4x - 5)(x - 9)/4 = 0

This gives

4x² - 5x - 36x + 45 = 4 * 0

So, we have

4x² - 41x + 45 = 0

Hence, the quadratic equation from the given root is 4x² - 41x + 45 = 0

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Answer:

a. How would you categorize this situation as a function? Circle one:

Linear function

Quadratic function

Exponential function

None of the above

The given situation can be categorized as a linear function.

Step-by-step explanation:

ham

Answer: 14.4 ft^2

Step-by-step explanation: The formula for the area of a triangle is A=1/2(b)(h). B is the base of the triangle and h is the height. First solve for the top part of the triangle. A=1/2(2)(3.2). A=3.2 ft^2. The 2 triangles on top are congruent, so you can multiply the area for the 1st triangle by 2 to get the combined area of the 2 top triangles. 3.2*2=6.4 ft^2.

Now we will solve for the 2 bottom triangles. A=1/2(2)(4). A=4 ft^2. The 2 triangles on the bottom are also congruent, so multiply the area that we got by 2 to get the combined area of both bottom triangles. 4*2=8 ft^2.

Finally, add both values to get the total area. 6.4+8=14.4 ft^2.

(a) √2 · √8. The simplified surd expression is 4.

(b) √80. The simplified surd expression is  4√5.

(c) √5/√20. The simplified surd expression is  1/2.

(d) √20. The simplified surd expression is  2√5.

The given surd expression is simplified as follows;

(a) √2 · √8

we can simplify it as;

√2 · √8 = √(2 x 8) = √16 = 4

(b) √80

we can simplify it as;

√80 = √ (16 x 5) = √16  x √5 = 4√5

(c) √5/√20

we can simplify it as;

√5/√20  x  √20 / √20

= (√5  x √20 ) /(20)

= √100 / 20

= 10/20

= 1/2

(d) √20

we can simplify it as;

√20 = √4  x √5 = 2√5

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Answer:

0.79

Step-by-step explanation:

Printer A has the better rate of cost per page because the approximate rate of Printer A, $0.24 per page, is greater than the approximate rate of Printer B, $0.23 per page.

Rate demonstrates how many times one number can fit into another number. It contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

In this case, Printer A prints 100 pages for $23.99. The rate is:

[tex]\sf = \dfrac{\$23.99}{100}[/tex]

[tex]\sf = 0.2399\thickapprox\$0.24 \ per \ page[/tex]

Printer B prints 275 sheets for $63.99. The rate is:

[tex]\sf = \dfrac{\$63.99}{275}[/tex]

[tex]\sf = 0.2327\thickapprox\$0.23 \ per \ page[/tex]

Therefore, based on the above calculations, we can see that Printer A has the better rate of cost per page because the approximate rate of Printer A, $0.24 per page, is greater than the approximate rate of Printer B, $0.23 per page.

So option (A) is correct.

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[tex]-2x+6=12\\2x=-6\\x=-3[/tex]

Answer:

139284 238

Step-by-step explanation:

Answer:

15, 14, 13, 12, 11 and so on

Step-by-step explanation: