Witch expression is equivalent to 3(4x + 2)?

A. 7x + 5
B. 7x + 21
C. 12x +2
D. 12x+ 21

A linear regression equation that represents the data set is y = 39.7x + 1127.8. Also, the number of new cases for 2011 is equal to 1525 cases.

In this scenario, the Year since 2002 (x) would be plotted on the x-axis of the scatter plot while the New cases (y) would be plotted on the x-axis of the scatter plot.

From the Excel sheet, you should right click on a data point on the graph (scatter plot), select format trend line and then tick the box to display an equation for the linear regression (line of best fit) on the graph.

By critically observing the scatter plot (see attachment) which models and shows the relationship given in the table, an equation for the linear regression is given by:

y = 39.7x + 1127.8

For 2011, the value of x is given by:

x = 2011 - 2002 = 9 + 1 = 10 years.

Now, we can determine the new cases for 2011:

y = 39.7(10) + 1127.8

y = 397 + 1127.8

y = 1524.8 ≈ 1525 cases.

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This set {σ ∈ S4 : σ(1) = 3} contains the following elements of S4: (13), (23), (34), (24), (14), (12)(34), (13)(24), (14)(23) and  {σ ∈ S4 : σ(2) = 2} this set contains the following elements of S4: (12), (21), (13)(24), (24)(13).

The group S4 is the symmetric group on 4 elements and has 24 elements. We can list all of its subgroups as follows:

Now, let's consider the sets (a) and (b) and see if they are subgroups of S4:

(a) {σ ∈ S4 : σ(1) = 3}

This set contains the following elements of S4: (13), (23), (34), (24), (14), (12)(34), (13)(24), (14)(23). We can check that this set is not a subgroup of S4 because it is not closed under composition. For example, (13)(14) = (134) is not in the set.

(b) {σ ∈ S4 : σ(2) = 2}

This set contains the following elements of S4: (12), (21), (13)(24), (24)(13). We can check that this set is a subgroup of S4. It is closed under composition, inverses, and contains the identity element e. Therefore, it is a subgroup of S4 and is isomorphic to the cyclic group of order 2.

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Step-by-step explanation:

this pentagon has 5 and clearly equally sized sides.

that means that the perimeter is simply 5 times one side length.

and one side length is therefore :

105 / 5 = 21 m

and that means

3 + 2w = 21 m

2w = 18

w = 9

Answer:

700

Step-by-step explanation:

175 divided by 3 is 58.3 and then you multiply 58.3 by 12 and get 700

Answer:

-10

Step-by-step explanation:

Answer:

 309

Step-by-step explanation:

-42 x -7 = 294 + 15 = 309

The axis of symmetry of the function f(x) = x² - 6x-1 is equal to 3.

In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical equation:

Axis of symmetry, Xmin = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

By substituting the parameters, we have the following:

Axis of symmetry, Xmin = -b/2a

Axis of symmetry, Xmin = -(-6)/2(1)

Axis of symmetry, Xmin = 6/2

Axis of symmetry, Xmin = 3.

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The Least common multiple (LCM)  The time at which both bells will ring together is 10:45 am, and the Subsequent times will be 11:30 am, 12:15 pm, 1:00 pm, and so on, with an interval of 45 minutes between each occurrence.

The time at which both bells will ring together, we need to find the least common multiple (LCM) of the intervals at which each bell rings.

The first bell rings every 45 minutes, and the second bell rings every minute. We want to find the point at which both intervals align, meaning they both divide evenly into the same amount of time.

To find the LCM, we can list the multiples of each interval until we find a common multiple.

Multiples of 45 minutes: 45, 90, 135, 180, 225, 270, 315, 360, 405, ...

Multiples of 1 minute: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...

From the lists above, we can observe that the least common multiple occurs when both intervals coincide at the same time, which is 45 minutes.

Thus, the two bells will ring together every 45 minutes.

If we consider the initial adjustment time of 10:00 am, the first time both bells will ring together is at 10:45 am. After that, they will continue to ring together every 45 minutes throughout the day.

Therefore, the time at which both bells will ring together is 10:45 am, and the subsequent times will be 11:30 am, 12:15 pm, 1:00 pm, and so on, with an interval of 45 minutes between each occurrence.

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Answer:

x = 159; y = 140

Step-by-step explanation:

a = 40

a + y = 180

y = 180 - 40

y = 140

b = 61

b = (180 - x) + a

61 = 180 - x + 40

x = 159

Answer:

m∠x = 159°

m∠y = 140°

Step-by-step explanation:

Given information

∠a = 40°

Given formula

∠a + ∠y = 180° (Supplementary angles)

Substitute values into the formula

40 + ∠y = 180

∠y = 180 - 40

\(\Large\boxed{\angle y=140^\circ}\)

Given information

∠b = 61°

∠c = Supplementary angle of ∠b

Given formula

∠b + ∠c = 180°

Substitute values into the formula

61 + ∠c = 180

∠c = 180 - 61

∠c = 119°

Determine the value of ∠x

∠x = ∠a + ∠c (Exterior angle theorem)

∠x = (40) + (119)

\(\Large\boxed{\angle x=159^\circ}\)

Hope this helps!! :)

Please let me know if you have any questions

Answer:  The measures of angles P and S cannot be determined without the value of x.

Step-by-step explanation:  

Since a parallelogram has opposite angles that are congruent, we can determine the measures of angles P and S based on the given angles Q and R.

Angle P is opposite angle Q, so ∠P = ∠Q = (x + 15) degrees.

Angle S is opposite angle R, so ∠S = ∠R = (6x - 10) degrees.

Answer:

C)  ∠P = 140°;  ∠S = 40°

Step-by-step explanation:

If PQRS is a parallelogram, angle Q is adjacent to angle R.

As adjacent angles of a parallelogram sum to 180°, set the sum of angle Q and angle R to 180°, and solve for x:

⇒ ∠Q + ∠R = 180°

⇒ (x + 15)° + (6x - 10)° = 180°

⇒ x + 15 + 6x - 10 = 180

⇒ 7x + 5 = 180

⇒ 7x = 175

⇒ x = 25

Substitute the found value of x into the expressions for angle Q and angle R:

⇒ ∠Q = (x + 15)°

⇒ ∠Q = (25 + 15)°

⇒ ∠Q = 40°

⇒ ∠R = (6x - 10)°

⇒ ∠R = (6(25) - 10)°

⇒ ∠R = (150 - 10)°

⇒ ∠R = 140°

The opposite angles of a parallelogram are equal.

Angle P is opposite angle R, so ∠P = 140°.

Angle Q is opposite angle S, so ∠S = 40°.                  

The inequalities that define the unshaded region for this problem is given as follows:

For the solid line, we have that it has a slope of 4 with an intercept of 0, and the values that are above the line are shaded, hence the inequality is given as follows:

y ≥ 4x.

For the dashed line, we have a line with a slope of 1 and an intercept of -4, and the values that are below the line are shaded, hence the inequality is given as follows:

y < x - 4.

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Answer:

"I can find the maximum or minimum by looking at the factored expression of a quadratic function by reading off its roots and taking the arithmetic average of them to obtain the \(x\)-coordinate of the quadratic function, and then substituting that value into the function."

Step-by-step explanation:

Because of the symmetry of quadratics (which is the case here because we have two factors of degree 1, so we are dealing with a polynomial of degree 2, which is a fancy way of saying that something is a quadratic), the \(x\)-coordinate of the extremum (a fancy way of saying maximum or minimum) is the (arithmetic) average of the two roots.

In the factored form of a quadratic function, we can immediately read the roots: 3 and 7. Another way to see that is to solve \((x-3)(x-7)=0\), which gives \(x-3=0 \vee x-7=0\) (the 'V' stands for 'or'). We can take the average of the two roots to get the \(x\)-coordinate of the minimum point of the graph (which, in this case, is \(x=\frac{3+7}{2} = \frac{10}{2} = 5\)).

Having the \(x\)-coordinate of the extremum, we can substitute this value into the function to obtain the maximum or minimum point of the graph, because that will give the \(y\)-coordinate of the extremum.

Answer: 86 memory sticks should be purchased

Step-by-step explanation: If he needs to be a stick for each teacher, and there are 86 teachers, then he needs to be 86 sticks.

Answer:

C. 6

Step-by-step explanation:

to divide by a fraction multiply by the recirpocal of that fraction.

8/3 ÷ 9/4

reduce the numbers with GCF 4 which equals 2/3 x 9

reduce the numbers with GCF 3 which equals 2x3= 6

Answer:

x+x+10=90 being Right angle triangle.

2x=90-10

2x=80

x =40

then x+10= 40 + 10

= 50

\(\large\bold{{Question :}}\)

From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm find the radius of the circle.

\(\large\bold\red{\underline{Solution :-}}\)

Here, O is the center of the circle.

⟼ Given :

⟼ To Find : We have to find the radius OP.

Since QP is tangent, OP perpendicular to QP.

(Since, Tangent is Perpendicular to Radius ⠀⠀⠀⠀⠀⠀⠀at the point of contact)

So, ∠OPQ=90°

⟼ By Applying Pythagoras Theorem :

OP² + RQ² = OQ²

OP² + (24)² = (25)²

OP² = 625 - 576

OP² = 49

OP = √49

OP = 7 cm

Hence, The Radius is 7 cm

⠀⠀

⠀

Here after drawing the diagram for the question we came to knew that the length of line OQ is 25 cm and length of line PQ is 24 cm.

So line OQ is hypotenuse , line OP is perpendicular , line PQ is base.

Let us simply apply the concept of Pythagoras theorem to find out the length of line OP.

\(: \: \implies \: \sf{(Hypotenuse) {}^{2} \: = \: (Base) {}^{2} \: + \: (Perpendicular) {}^{2} } \\ \\ : \: \implies \: \sf{(OQ) {}^{2} \: = \: (OP) {}^{2} \: + \: (PQ) {}^{2} } \\ \\ : \: \implies \: \sf{(25) {}^{2} \: = \: (OP) {}^{2} \: + \: (24) {}^{2} } \\ \\ : \: \implies \: \sf{(OP) {}^{2} \: = \: (25) {}^{2} - \: (24) {}^{2}} \\ \\ : \: \implies \: \sf{(OP) {}^{2} \: = \: (25 \times 25) - \: (24 \times 24)} \\ \\ : \: \implies \: \sf{(OP) {}^{2} \: = \: (625) - \: (576)} \\ \\ : \: \implies \: \sf{(OP) {}^{2} \: = \: 625 - \: 576} \\ \\ : \: \implies \: \sf{(OP) {}^{2} \: = \: 49} \\ \\ : \: \implies \: \sf{OP \: = \: \sqrt{49} } \\ \\ : \: \implies \: \red{\bf{OP \: = \: 7}}\)

★ Therefore,

The answer to the expression is  (x+3)/(x-1)

You should recall that a quadratic expression is an algebraic expression of the form ax2 + bx + c = 0, where a ≠ 0

The given expressions are

(x² - 3x - 18) / (x²- 7x +6

(x²-6x +3x +19) / (x²-x -6x +6)

This implies that {(x²-6x)+(3x-18)} / {(x²-x) -(6x+6)}

⇒[x(x-6)+3(x-6)] / [x(x-1) - 6(x-1)]

This means that [(x+3)(x-6)] / [(x-6)(x-1)]

Dividing by (x-6) to have

Therefore the value of the expression is (x+3)/(x-1)

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9514 1404 393

Answer:

  x = 1/6

Step-by-step explanation:

The relevant rules of exponents are ...

  (a^b)/(a^c) = a^(b-c)

  (a^b)^c = a^(bc)

__

The fraction inside parentheses evaluates to ...

  3^(3/4 -3/8) = 3^(3/8)

Then the whole expression evaluates to ...

  (3^(3/8))^(4/9) = 3^((3/8)(4/9)) = 3^(12/72) = 3^(1/6)

The value of x is 1/6.

Answer:

The answer is 28.8, When finding the Volume of a shape, you multiply all numbers.

Answer:

Step-by-step explanation:

1)

Congruency shortcuts:  

HL, SSS, SAS, ASA, and AAS

where S=side

A=angle

H=hypotenule

L=leg

HL is only for a right triangle

If you can prove sides and angles are congruent according to those 5 rules, you have proven the triangles are congruent

Similarity shortcuts:

AA, SAS, SSS

We have triangle similarity if (1) two pairs of angles are congruent (AA) (2) two pairs of sides are proportional and the included angles are congruent (SAS), or (3) if three pairs of sides are proportional (SSS)

2)

BG ≅ GD              >Given from image

IG ≅ GO               >Given from image

<BGI ≅ <DGO        >Vertical Angles

ΔBGI  ≅ ΔDGO        >SAS            

You have proven that the triangles are congruent because you used the shortcut by proving a side and angle and a side are congruent so SAS makes them congruent

Answer:

1/2 feet per second.

Step-by-step explanation:

PA BRAINLIEST

HOPE ITS HELP

GOD BLESS

Let n be an odd integer. By definition, n must be an integer not divisible by 2. Hence, when n2 is divided by 8, the remainder must be 1.

Let n be an odd integer. First, we can express n as 2k+1, where k is an integer. Next, when we square n, we get (2k+1)2. Expanding this gives 4k2+4k+1. Dividing this by 8 gives 4k2+k as the quotient and 1 as the remainder. This proves that the square of an odd integer always have a remainder of 1 when divided by 8.

To summarize, when an odd integer n is squared, the remainder when the result is divided by 8 is always 1. This is because an odd integer is not divisible by 2, and so the quotient will not be a whole number when divided by 8.

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Answer:

(-1/12)(x-3)(x-8)

or

\(-\frac{x^2-11x+24}{12}\)

Step-by-step explanation:

If something has x intercepts of (3,0) and (8,0) we can write the following

y=(x-3)(x-8)

To make the y intercept (0,-2) we will mulitply this by some constant, a

y=a(x-3)(x-8)

to solve for a set y= -2 and x=0

a(0-3)(0-8)= -2

a(-3)(-8)= -2

24a= -2

a= -1/12

Which means our final equation is

(-1/12)(x-3)(x-8)

which in standard form is equal to

\(-\frac{x^2-11x+24}{12}\)

Answer:

Yes, since the total pay of $120 is more than the $100 cost of the MP3 player.

Step-by-step explanation:

hourly pay: $5/hour

number of hours: 24 hours

total pay = hourly pay × number of hours

total pay = $5/hour × 24 hours

total pay = $120

MP3 player costs $100.

Total pay is $120.

Answer: Yes, since the total pay of $120 is more than the $100 cost of the MP3 player.

The mean, median, range, and standard deviation  for the new data set must all be 7 greater than for the original data set.

The mean is the sum of all the values divided by the number of values. Adding the number 6 to the original data set of 30 positive integers increases the sum of all the values by 6, which means the mean for the new data set must be 7 greater than the mean for the original data set.

The formula for the mean is: Mean = (Sum of Values)/(Number of Values)

For the original data set: Mean = (Sum of Values)/30

For the new data set: Mean = (Sum of Values + 6)/31

Therefore, the mean for the new data set must be 7 greater than the mean for the original data set.

The median is the middle value in a set of data. Adding the number 6 to the original data set of 30 positive integers increases the total number of values to 31, which means the median is calculated differently for the new data set than the original data set. The median for the new data set must be 7 greater than the median for the original data set.

The formula for the median is: Median = (n+1)/2

For the original data set: Median = (30+1)/2 = 15.5

For the new data set: Median = (31+1)/2 = 16.5

Therefore, the median for the new data set must be 7 greater than the median for the original data set.

The range is calculated by subtracting the smallest value from the largest value in a data set. Adding the number 6 to the original data set of 30 positive integers increases the largest value by 6, which means the range for the new data set must be 7 greater than the range for the original data set.

The formula for the range is: Range = (Largest Value) - (Smallest Value)

For the original data set: Range = (Largest Value) - 13

For the new data set: Range = (Largest Value + 6) - 13

Therefore, the range for the new data set must be 7 greater than the range for the original data set.

The standard deviation is a measure of how spread out the values in a data set are. Adding the number 6 to the original data set of 30 positive integers increases the total number of values by 1, which means the standard deviation for the new data set must be 7 greater than the standard deviation for the original data set.

The formula for the standard deviation is: Standard Deviation = √ (Sum of (Values - Mean)2 / Number of Values)

For the original data set: Standard Deviation = √ (Sum of (Values - Mean)2 / 30)

For the new data set: Standard Deviation = √ (Sum of (Values - Mean)2 / 31)

Therefore, the standard deviation for the new data set must be 7 greater than the standard deviation for the original data set.

The mean, median, range, and standard deviation for the new data set must all be 7 greater than for the original data set

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Answer:

My answer: B

Step-by-step explanation:

The probability mass function of random variable X which represents the number of blue marbles drawn in 2 draws with replacement.

X | P(X)

0 | 0.390625

1 | 0.46875

2 | 0.140625

The probability of drawing exactly one blue marble = 0.46875

Complete Question

A bag contains red and blue marbles, such that the probability of drawing a blue marble is 3/8. an experiment consists of drawing a marble, replacing it, and drawing another marble. The two draws are independent. A random variable assigns the number of blue marbles to each outcome.

To write the Probabilty mass function, we have to establish that in two draws with replacement, the possible number of blue marbles that can be drawn is 0, 1 and 2.

Probability of drawing a blue marble = P(B) = (3/8)

Probability of not drawing a blue marble = P(B') = 1 - (3/8) = (5/8)

- Probability of drawing 0 blue marbles in 2 draws with replacement = P(B') × P(B') = (5/8) × (5/8) = (25/64) = 0.390625

- Probability of drawing one blue marble in 2 draws with replacement

= [P(B) × P(B')] + [P(B') × P(B)]

= (2) × (3/8) × (5/8) = (30/64) = (15/32) = 0.46875

- Probability of drawing two blue marble in 2 draws with replacement = P(B) × P(B)

= (3/8) × (3/8) = (9/64) = 0.140625

The probability mass function of random variable X which represents the number of blue marbles draan in 2 draws with replacement.

X | P(X)

0 | 0.390625

1 | 0.46875

2 | 0.140625

b) Probability of drawing one blue marble in 2 draws with replacement

= [P(B) × P(B')] + [P(B') × P(B)]

= (2) × (3/8) × (5/8) = (30/64) = (15/32) = 0.46875

So, B is the answer.

Answer: a.)Within your skills and abilities

Step-by-step explanation: i hope this helps :)

Knowing your personal strengths and weaknesses will help to keep your goal a. Within your skills and abilities.

Understanding what makes you tick is part of knowing yourself. It entails figuring out your priorities, talents, and limitations, as well as your habits, inclinations, and ways of thinking. The following is a list of the advantages and significance of understanding oneself

Knowing your personal strengths and weaknesses will help you

can change your personality flaws and improve on your weaknesses.

You’ll have more emotional intelligence, which is key to knowing others.

So, Knowing your personal strengths and weaknesses will help to keep your goal  Within your skills and abilities.

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Answer:

To solve the equation sin 2x = 4cos 2x, we can use the trigonometric identity:

sin 2x = 2sin x cos x

cos 2x = cos^2 x - sin^2 x = 1 - 2sin^2 x

Substituting these identities into the equation, we get:

2sin x cos x = 4(1 - 2sin^2 x)

Expanding and simplifying, we get:

2sin x cos x = 4 - 8sin^2 x

Rearranging, we get:

8sin^2 x + 2sin x cos x - 4 = 0

We can factor the left-hand side of this equation:

(2sin x - 1)(4sin x + 4) = 0

Setting each factor equal to 0 and solving for sin x, we get:

2sin x - 1 = 0 or 4sin x + 4 = 0

sin x = 1/2 or sin x = -1

If sin x = 1/2, then x is a multiple of π/6, so the general solution in this case is:

x = π/6 + 2πn or x = 5π/6 + 2πn

Where n is an integer.

If sin x = -1, then x is a multiple of π plus an odd multiple of π/2, so the general solution in this case is:

x = π/2 + πn

Where n is an integer.

Therefore, the general solution for sin 2x = 4cos 2x is:

x = π/6 + 2πn or x = 5π/6 + 2πn or x = π/2 + πn

Where n is an integer.

Answer:

12 < x < 13

Step-by-step explanation:

Pythagorean Theorem: a^2 + b^2 = c^2

a is 6, b is 11, c is x.

We have to first replace the items in the Theorem, do the exponents, then add.

1) 6^2 + 11^2 = x^2

2) 36 + 121 = x^2

3) 157 = x^2

To finally solve it we must square root everything

4) sqrt(157) = sqrt(x^2)

5) x = 12.52

So x has to be between 12 and 13

The total volume is the one in option C, 708 cubic centimeters.

We know that this prism can be divided into two prisms, and remember that the volume of a prism is equal to the product between its dimensions.

Then the volume of the first prism is:

V = 8cm*6cm*13cm = 624 cm³

And the volume of the second prism is:

v' = 3cm*4cm*7cm = 84 cm³

Adding that we will get:

total volume =  624 cm³+  84 cm³ = 708 cm³

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