Question 3(Multiple Choice Worth 2 points)
(Laws of Exponents with Integer Exponents LC)

Which is an equivalent expression for five sevenths squared times one third raised to the power of negative three all raised to the power of negative one?

five sevenths squared times one third raised to the power of negative three
five sevenths times one third raised to the power of negative four
seven fifths to the power of negative two times one third to the power of negative three
seven fifths squared times one third cubed

The store can choose to stock up on 60 different types of sweaters for the upcoming fall season.

To determine the number of different types of sweaters the store can choose to stock up on, we need to calculate the total number of possible combinations of colors and textures

The store has 5 different colors and 3 different textures to choose from. Since they will stock the sweater in 3 different colors and 2 different textures, we can use the concept of combinations.

The number of combinations can be calculated using the formula:

C(n, r) = n! / (r!(n - r)!)

Where n represents the total number of options (colors or textures), and r represents the number of choices (colors or textures) the store will stock.

For colors:

n = 5 (total number of colors)

r = 3 (number of colors the store will stock).

C(5, 3) = 5! / (3!(5 - 3)!)

= 5! / (3!2!)

\(= (5 \times 4 \times 3!) / (3! \times 2 \times 1)\)

\(= (5 \times 4) / (2 \times 1)\)

= 10.

For textures:

n = 3 (total number of textures)

r = 2 (number of textures the store will stock)

C(3, 2) = 3! / (2!(3 - 2)!)

= 3! / (2!1!)

\(= (3 \times 2!) / (2! \times 1)\)

\(= (3 \times 2) / (1)\)

= 6

To calculate the total number of different types of sweaters, we multiply the number of color combinations by the number of texture combinations:

Total combinations\(= C(5, 3) \times C(3, 2)\)

\(= 10 \times 6\)

= 60

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Answer:

A

Step-by-step explanation:

A reflection in the line y = -2 and then translation of 2 units right will create the same area so option (C) will be correct.

A graph is a diagram that shows the fluctuation of one variable in relation to one or more other variables.

In order to plot the graph, we need to find out y's values corresponding to x's value

After that, we need to substitute the values of x's and y's into the coordinate geometry.

If we shift the triangle anywhere then there will be no change in the area but if we apply the scale factor then since the dimension changes so its area will also change.

In all options, there is a scale factor so it will change area but in option C

A reflection in the line y = -2 reflection gives a mirror image about y = -2 but no changes in area then translation of 2 units right will shift triangle 2 units right but no effect in the area.

Hence "A reflection in the line y = -2 and then translation of 2 units right will create the same area".

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Answer: The answer is B) y < 0

Answer: B

Step-by-step explanation:

Given:

Total number of spots =1327

1) There are 162 on the first level

2)

3)

Probability of an event is the measure of its chance of occurrence. The correct probabilities are:

Suppose that the sample space is S. Out of which there are two events, A and B, subsets of S.

Then, we can interpret P(A|B) as the probability of that part of A which is in B, with the new sample space as B. (assuming probabililty of B isn't 0).

Symbolically, we write it as:

\(P(A|B) = \dfrac{P(A \cap B)}{P(B)}\)

For three sets, A, B and C:

\(n(A \cup B \cup C) = n(A) + P(B) + P(C) - n(A\cap B) - n(A \cap C) - n(B \cap C) + n(A \cap B \cap C)\)

The problem is incomplete. The corresponding venn diagram is attached below.

We can symbolize the venn diagram as:

\(n(A) = 12+8+6+5 =31\\n(B) = 11+8+5+3 = 27\\n(C) = 4+8+6+3 = 21\\n(A \cap B) = 5+8=13\\n(B\cap C) = 3+8=11\\n(A \cap C) = 6+8=14\\n(A \cap B \cap C) = 8\)

S = sample space = collection of all unique elements.

S is union of A, B and C.

\(n(S) = n(A \cup B\cup C) = 31 + 27 + 21 -13-11-14+8 = 49\)

Checking all the options for their correctness:

We have:

\(P(A|C) = P(A\cap C)/P(C) = \dfrac{n(A\cap C)/n(S)}{n(C)/n(S)} = \dfrac{n(A \cap C)}{n(C)} = \dfrac{14}{21} =\dfrac{2}{3}\)

Thus, its correct.

\(P(C|B) = P(C\cap B)/P(B) = \dfrac{n(C\cap B)/n(S)}{n(B)/n(S)} = \dfrac{n(C \cap B)}{n(B)} = \dfrac{11}{27} \neq \dfrac{8}{27}\)

Thus, this option is incorrect.

Thus, this option is incorrect.

\(P(C) = \dfrac{n(C)}{n(S)}= \dfrac{21}{49} =\dfrac{3}{7}\)

Thus, its correct.

\(P(B|A) = P(B\cap A)/P(A) = \dfrac{n(B\cap A)/n(S)}{n(A)/n(S)} = \dfrac{n(B\cap A)}{n(A)} = \dfrac{13}{31} \neq \dfrac{13}{27}\)

Thus, this option is incorrect.

Thus, the correct probabilities are:

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Answer:

V = 4.22ft^3

Step-by-step explanation:

Length: 2.25ft

Width: 1.5ft

Height: 1.25ft

Length x Width x Height = V

2.25 x 1.5 x 1.25 = 4.22ft, since we're dealing with volume of a 3D space, the answer is 4.22ft^3!

Integral value is finite since the given integral converges when the function is \(\int\limits^\infty_\infty {3xe^{-x^{2} } } \, dx\).

Given that,

Analyze the integral to see if it is convergent or divergent. convergent integrals should be evaluated.

\(\int\limits^\infty_\infty {3xe^{-x^{2} } } \, dx\)

We have to simplify the equation.

Finding the area of the curve's undersurface is the process of integration. To do this, draw as many little rectangles as necessary, then add up their areas.

We know that,

I= \(\int\limits^\infty_\infty {3xe^{-x^{2} } } \, dx\)

Let p = x²then xdx= dp/2

Then

I= \(\int\limits^\infty_\infty {3/2e^{-p} } \, dp\)

I= 3/2(\(e^{-p}\))infinity to minus infinity

I= 3/2 (\(e^{-x^{2} }\))infinity to minus infinity

I=0

Therefore, integral value is finite since the given integral converges when the function is \(\int\limits^\infty_\infty {3xe^{-x^{2} } } \, dx\).

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False. if you are given a graph with two shif table lines, the correct answer will always require you to move both lines.

In a graph with two shiftable lines, the correct answer may or may not require moving both lines. It depends on the specific scenario and the desired outcome or conditions that need to be met.

When working with shiftable lines, shifting refers to changing the position of the lines on the graph by adjusting their slope or intercept. The purpose of shifting the lines is often to satisfy certain criteria or align them with specific points or patterns on the graph.

In some cases, achieving the desired outcome may only require shifting one of the lines. This can happen when one line already aligns with the desired points or pattern, and the other line can remain fixed. Moving both lines may not be necessary or could result in an undesired configuration.

However, there are also situations where both lines need to be shifted to achieve the desired result. This can occur when the relationship between the lines or the positioning of the lines relative to the graph requires adjustments to both lines.

Ultimately, the key is to carefully analyze the graph, understand the relationship between the lines, and identify the specific criteria or conditions that need to be met. This analysis will guide the decision of whether one or both lines should be shifted to obtain the correct answer.

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Answer:bhbehrf

Step-by-step explanation:

Answer:

204 is the answer

Step-by-step explanation:

204 is the answer

Paki heart nalang po kung nakatulong

Answer:

its the 3rd

Step-by-step explanation:

Answer:

$389.73 in change

Step-by-step explanation

500-( (18.95 x 3)+(26.71 x 2) )=

500-(56.85+53.42)=

500-110.27=

389.73

The condition should be satisfied are as np>=5 and n(1-p)>=5.

When both requirements are satisfied, we can utilise the normal distribution to provide probabilistic responses to binomial distribution-related problems.

For instance, let's say we want to know the likelihood that during 100 flips, a coin will land on heads less than or equal to 45 times. In other words, we seek P (X <= 45). Instead, we would discover P (X <= 45.5) in order to approximate the binomial distribution using the normal distribution.

So, the main condition is np>=5 and n(1-p)>=5.

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Answer:

13

Step-by-step explanation:

The common difference is 13 I

12 + 13 = 25

25 + 13 = 38

And so on.....

The number of prime factors of 3×5×7+7 is 3.

To find the number of prime factors, we need to calculate the given expression:

3×5×7+7 = 105+7 = 112.

The number 112 can be factored as 2^4 × 7.

In the first step, we factor out the common prime factor of 7 from both terms in the expression. This gives us 7(3×5+1). Next, we simplify the expression within the parentheses to get 7(15+1). This further simplifies to 7×16 = 112.

So, the prime factorization of 112 is 2^4 × 7. The prime factors are 2 and 7. Therefore, the number of prime factors of 3×5×7+7 is 3.

In summary, the expression 3×5×7+7 simplifies to 112, which has three prime factors: 2, 2, and 7. The factor of 2 appears four times in the prime factorization, but we count each unique prime factor only once. Thus, the number of prime factors is 3.

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Answer:

1.15x - 0.7x

Step-by-step explanation:

You take the manufacturer’s price and add 15 percent, then subtract 70 percent of the used price from the retail price to get the answer.

f(x) = ax² + bx + c

f(1) = 6

f(2) = 11

f(3) = 18

value of a,b,c​

Substitute x = 1 , 2 , 3 in the given polynomial.

★ f(1) = a(1)² + b(1) + c

⟹ 6 = a + b + c -- equation (1)

Similarly,

★ f(2) = a(2)² + b(2) + c

⟹ 11 = 4a + 2b + c -- equation (2)

★ f(3) = a(3)² + b(3) + c

⟹ 18 = 9a + 3b + c -- equation (3)

Subtract equation (1) from (2).

⟹ 4a + 2b + c - (a + b + c) = 11 - 6

⟹ 4a + 2b + c - a - b - c = 5

⟹ 3a + b = 5 -- equation (4).

From equation (3) ,

⟹ 18 - c = 9a + 3b

⟹ 18 - c = 3(3a + b)

Substitute the value of 3a + b from equation (4).

⟹ 18 - c = 3 * 5

⟹ 18 - 15 = c

⟹ 3 = c

substitute the value of c in equation (1).

⟹  6 = a + b + 3

⟹ 6 - 3 = a + b

⟹ 3 = a + b -- equation (5)

Subtract equation (5) from equation (4).

⟹ 3a + b - (a + b) = 5 - 3

⟹ 3a + b - a - b = 2

⟹ 2a = 2

⟹ a = 1

Substitute a value in equation (5).

⟹ 1 + b = 3

⟹ b = 3 - 1

⟹ b = 2

Therefore,

a = 1

b = 2

c = 3.

I hope it will help you.

Regards.

The chances that the coin is unbiased are 0.08 or 8%.

Probability is the measure of the likelihood of an event occurring.

Probability is calculated by dividing the number of successful events by the total number of possible events.

The probability of an event ranges between 0 and 1.

An event with a probability of 0 has no chance of occurring, whereas an event with a probability of 1 is certain to occur.

In the given question, a coin was tossed 500 times.

The result was heads 230 times and tails 270 times.

Let us calculate the probability of getting heads when the coin is tossed.

P(h) = Probability of getting heads = Number of heads/Total number of tosses = 230/500 = 0.46

Similarly, let us calculate the probability of getting tails when the coin is tossed.

P(t) = Probability of getting tails = Number of tails/Total number of tosses = 270/500 = 0.54

The coin is unbiased if the probability of getting heads is equal to the probability of getting tails when the coin is tossed.

P(h) = P(t)0.46

= 0.54 0.54 - 0.46

= 0.08

Thus, the chances that the coin is unbiased are 0.08 or 8%.

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Answer:

30

Step-by-step explanation:

(12 X 2=24)( 24 - 54 = -30) + 60 = 30

Answer:

Step-by-step explanation:

\(12x^2-54x+60\\ \\ 6(2x^2-9x+10)\\ \\ 6(2x^2-4x-5x+10)\\ \\ 6(2x(x-2)-5(x-2))\\ \\ 6(2x-5)(x-2)\)

About 17% of the students who tried out for volleyball did not make the team.

If 83% of the volleyball tryout candidates made the squad, then 83% of the candidates were successful and made the team. The proportion of students that did not make the squad is represented by the remaining percentage, which is 100% minus 83%.

To find this fraction, we can subtract 83% from 100%:

100% - 83% = 17%

Therefore, about 17% of the students who tried out for volleyball did not make the team. The fraction 17/100 or the abbreviation 17/100 can be used to signify this.

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The equation x² + 81 = (x + 10)² is equivalent to \(\sqrt{x^2 + 81} = x + 10\)

The equation is given as:

\(\sqrt{x^2 + 81} = x + 10\)

Square both sides

x² + 81 = (x + 10)²

Although it can be further simplified, the above equation is equivalent to \(\sqrt{x^2 + 81} = x + 10\)

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Answer:

x = 105

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 7, thus

sum = 180° × 5 = 900°

Sum the interior angles and equate to 900

x + 102 + 165 + 123 + x + 11 + 128 + 161 = 900, that is

2x + 690 = 900  ( subtract 690 from both sides )

2x = 210 ( divide both sides by 2 )

x = 105

Answer:

$190

Step-by-step explanation:

Let's call the original price of the jacket "x".

If the new cost of the jacket is $87, we can represent this as x/2-8=87. By solving for x, we see that the original price of the jacket is $190

Answer:

I think the answer would be 182

Step-by-step explanation:

87x2= 174

174+8= 182

The probability that there will be no mutual best friendships is\([(n-1)/n]^{(2n)}\).

Given that there are n users in each group, A and B;

For a user in group A, the probability that this user selects someone who is not their mutual best friend is (n-1)/n

The probability that all users in group A choose someone who is not their mutual best friend is

For each user in group B;

the probability of not choosing their mutual best friend is (n-1)/n,

The probability that all users in group B choose someone who is not their mutual best friend is \([(n-1)/n]^{n}\)

The events of users in group A and users in group B choosing their mutual best friends are independent, therefore;

P(no mutual best friendships) = \([(n-1)/n]^n * [(n-1)/n]^n\)

P(no mutual best friendships) =\([(n-1)/n]^{(2n)}\)

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The vector <-32, 44, 22> is parallel to the line of intersection of the two planes given by the equations 2x - 3y + 5z = 2 and 4x + y - 3z = 7.

To find a vector parallel to the line of intersection of the planes given by the equations 2x - 3y + 5z = 2 and 4x + y - 3z = 7, we first need to find the direction vector of the line of intersection.

We can find the direction vector by taking the cross product of the normal vectors of the two planes. The normal vector of the plane 2x - 3y + 5z = 2 is <2, -3, 5>, and the normal vector of the plane 4x + y - 3z = 7 is <4, 1, -3>. Taking the cross product of these two vectors, we get:

<2, -3, 5> × <4, 1, -3> = <-16, 22, 11>

This vector <-16, 22, 11> is the direction vector of the line of intersection of the two planes.

To find a vector parallel to this line, we can simply multiply the direction vector by a scalar. For example, we can choose a scalar of 2 to get:

2<-16, 22, 11> = <-32, 44, 22>

Therefore, the vector <-32, 44, 22> is parallel to the line of intersection of the two planes given by the equations 2x - 3y + 5z = 2 and 4x + y - 3z = 7.

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Answer:

y+1=4(x-1)

Step-by-step explanation:

Point slope form is:  y-y₁=m(x-x₁)

Answer: -8

Step-by-step explanation:

We see on the graph that there are two points located y=4. They are (7,4) ( -8,4).

So the other value other than 7 is -8!

Answer:

f(1) = 6

Step-by-step explanation:

You just substitute 1 for x, 3+3 = 6

Answer:

f(1)=3(1)+3 = 6

answer is 6

Step-by-step explanation:

In the image line segment SE is the tangent. The secant line making an angle with tangent line SE is NS. So the angle is ∠GSE. So option B is the correct answer.

Tangent is a line which intersect with only a single point on the curve. The point where the line meets is the point of tangency. Tangent line is always perpendicular to the radius drawn to the point of tangency. Here the tangent line is SE, point of tangency is S.

Secant lines are the lines which passes through two points of a curve. A chord drawn to the circle is a secant line. Here there are two secant lines NS and NA. Here only NS makes an angle with the tangent line.

So the angle made by a tangent and secant line is ∠GSE.

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The image for the question is attached below.