What is the common difference of 80,60,45,33.75

Step-by-step explanation:

We have,

[tex]4\dfrac{6}{7}+7\dfrac{3}{14}[/tex]

To find, the common denominator of [tex]4\dfrac{6}{7}+7\dfrac{3}{14}[/tex] = ?

∴ [tex]4\dfrac{6}{7}+7\dfrac{3}{14}[/tex]

= [tex]\dfrac{4\times 7 +6}{7} +\dfrac{7\times 14 +3}{7}[/tex]

[tex]=\dfrac{34}{7} +\dfrac{101}{7}[/tex]

Taking the common as [tex]\dfrac{1}{7}[/tex], we get

=[tex]\dfrac{1}{7}[/tex][tex](34+101)[/tex]

The denominator = 7

∴  The common denominator of [tex]4\dfrac{6}{7}+7\dfrac{3}{14}[/tex] = 7

Hence, the common denominator of [tex]4\dfrac{6}{7}+7\dfrac{3}{14}[/tex] = 7

Answer:

30240

Step-by-step explanation:

There are two primary ways to approach this problem - the logical and the mathematical.

The logical way is very simple:

Since you know that there are 5 digits and each must be different, start with the first digit and work your way up.

The first digit can be any of 10 digits (0–9).

However, the second digit can be any of only 9 digits as 1 digit has already been used and cannot be repeated.

Similarly, applying the same logic, there are only 8 options for the third digit, 7 for the fourth digit, and 6 for the fifth and final digit.

Now, multiply all these numbers together to get the total number of configurations like so:

10⋅9⋅8⋅7⋅6=30240

The more mathematically inclined way requires the use of a special formula. Since in this particular scenario, the order of the numbers matter, we can use the Permutation Formula:

P(n,r)=n!(n−r)!

where n is the number of numbers in the set and r

is the subset.

Since there are 10 digits to choose from, we can assume that n=10

.

Similarly, since there are 5 numbers that need to be chosen out of the ten, we can assume that r=5

.

Now, plug these values into the formula and solve:

=10!(10−5)!

=10!5!

=10⋅9⋅8⋅7⋅6

=30240

The correct equation of the new line parallel to y = 3x + 2 and passing through (1, 6) is y = 3x + 3.

To find the equation of the line that is parallel to the given line y = 3x + 2 and passes through the point (1, 6), we first need to acknowledge that parallel lines have the same slope.

Therefore, the slope of the new line will also be 3. We can use the point-slope form of the equation y - y1 = m(x - x1) to find the equation. Substituting the given point into the equation, we get y - 6 = 3(x - 1).

Simplifying the equation, we find y = 3x + 3. So, the equation of the line that is parallel to the original line and passes through the given point is y = 3x + 3.

24p² + pq - 23q² =

= 24p² + 24pq - 23pq - 23q²

= 24p(p + q) - 23q(p + q)

= (p + q)(24p - 23q)

The required factorization of the given expression is given as  (24p - 23q)(p + q).

A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.

Given expression in the quesiton is 24p2 + pq - 23q²​, we have to factorize the given expression,
So,
24p² + pq - 23q²​,

Substituting pq = 24 pq - 23pq

= 24p² + 24pq - 23pq - 23q²
= 24p(p + q)-23q(p + q)
= (24p - 23q)(p + q)

Thus, the required factorization of the given expression is given as  (24p - 23q)(p + q).

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Solving e²ˣ + 3eˣ- 18 = 0 involves substituting y = ex to transform it into a quadratic equation. Solving this quadratic equation yields a valid solution, y = 3, leading to x = ln(3). Therefore, the solution is x = ln(3).

To solve the equation e²ˣ + 3eˣ- 18, we perform a substitution to convert it into a quadratic form.

Let y =eˣ. Then the equation becomes:

This gives us two solutions for y:

Since y = eˣ, and eˣ must be positive:

Finally, solve for x:

Therefore, the solution to the equation e²ˣ + 3eˣ- 18 = 0  is x = ln(3).

Answer:

Step-by-step explanation:

y = mx + b

slope(m) = 1/9

y int (b) = 8.....or (0,8)

y = 1/9x + 8.....this is ur equation

ur x intercept is : (can be found by subbing in 0 for y

0 = 1/9x + 8

-1/9x = 8

x = 8 * -9

x = - 72....or (-72,0)

The equation of line is y = ( 1/9 )x + 8

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is given by

The slope of the line m = 1/9

So , Slope m = 1/9

The point on the line is given by P = P ( 0 , 8 )

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 8 = ( 1/9 ) ( x - 0 )

y - 8 = ( 1/9 ) x

On simplifying the equation , we get

Adding 8 on both sides of the equation , we get

y = ( 1/9 )x + 8

Therefore , the value of A is y = ( 1/9 )x + 8

Hence , The equation of line is y = ( 1/9 )x + 8

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Answer:

d

Step-by-step explanation:

since since the scale factor is 3 angle ab abyou multiply 6 * 3 to get 18

The length of the Side EF is 18.

A scale factor is defined as the ratio between the scale of a given original object and a new object.

Given that  corresponding sides are AB and EF, and EF is a side of the larger (second) triangle.

scale factor 3 means each length of the second is 3 times as long as the first.

Therefore, the length of the side EF when the length of side AB is 6 units is,

EF = 3 x AB

     = 3 x 6 units

     = 18 units.

Therefore, Side EF is 18.

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Your score in the game is 305 points.

Step-by-step explanation:

Given,

Expression used for score = p + 3b

p = game points

b = triple bonus points

Game points earned by you = p = 245 games point

Triple bonus points = b = 20

Putting these values in given expression

Total points = [tex]245+3*20[/tex]

Total points = [tex]245+60[/tex]

Total points = 305 points

Your score in the game is 305 points.

Keywords: addition, expression

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Answer:

yes

Step-by-step explanation

because it is an algebraic expression. 3a + a are called like terms because they both contain the same letter. To simplify an expression we collect together like terms. You can only add or subtract when the letters are the same.

Answer:

  [tex]y=\sqrt[3]{x+3}+3[/tex]

Step-by-step explanation:

The S-shaped curve is that of the cube root function (choices C or D). The parent function has its critical point at the origin. Here, that has been moved 3 units left and 3 units up.

Replacing x with x-a will move a function's graph to the right by "a" units. Here, we have a=-3, so we expect to see ∛(x-(-3)) = ∛(x+3). The graph of that is moved up 3 units by adding 3 to the function value. This gives ...

  y = ∛(x+3) +3 . . . . . matches choice D

Answer:

Answer:

The True statements are:

The sphere has a diameter of 32 in.

The radius’s length is one-half the length of the diameter.

The volume of the sphere is StartFraction 16,384 Over 3 EndFraction pi inches cubed.

Step-by-step explanation:

      This is false because a radius is half of a diameter. Half of      the given diameter of 8 in is 4 in whereas the radius in the question is 16 in.

        This is false because the volume of the sphere is 4πr³/3 = (16,384/3) π cubic inches.

This is True because a radius is half of a diameter. Half of the given diameter of 32 in is 16 in and  the radius in the question is also 16 in.

This is True because a radius is half of a diameter

This is True because the volume of the sphere is 4πr³/3 = (16,384/3) π cubic inches.

It is the radius’s length that is one-half the length of the diameter

Answer:

Step-by-step explanation:

expenses :

flat fee of 264 + 15 for every attendee (a)

264 + 15a

revenue :

16 per attendee

16a

break even point is when expenses = revenue

264 + 15a = 16a

264 = 16a - 15a

264 = a

total expenses: 264 + 15a......264 + 15(264) = $ 4224

total revenue : 16a......16(264) = $ 4224

attendees taken : 264

Answer:

Step-by-step explanation:

[tex]\frac{h*(a+b)}{2}=\frac{6.7*(7+10.4)}{2}\\\\=\frac{6.7*17.4}{2}=\frac{116.58}{2}=58.29[/tex] cm²

1 foot would be four 1/4 foot pieces.

Multiply total feet by 4:

12 ft x 4 = 48 total pieces.

Answer:

57.97 cm²

Step-by-step explanation:

The area (A) of a trapezium is calculated as

A = [tex]\frac{1}{2}[/tex] h( a + b)

where h is the perpendicular height between the parallel bases and a, b are the bases.

Here h = 6.2, a = 7.9 and b = 10.8, thus

A = 0.5 × 6.2 (7.9 + 10.8)

   = 3.1 × 18.7 = 57.97 cm²

Answer:

Step-by-step explanation:

Area of trapezium = 1/2(a + b)h

a = 7.9cm, b = 10.8cm and h = 6.2cm

Area = 1/2(7.9 + 10.8)×6.2

Area = 1/2 × 18.7 × 6.2

Area = 57.97cm²

Answer: 0.3125

Step-by-step explanation:

Convert the fraction to a decimal by dividing the numerator by the denominator.

For 12 number of aerobics classes, cost for members and nonmembers is same

Solution:

Let "x" be the number of aerobic classes

At a local fitness​ center, members pay a $12 membership fee and ​$3 for each aerobics class

Therefore,

Members pay = 12 + 3(number of classes)

Members pay = 12 + 3x ------- eqn 1

Nonmembers pay ​$4 for each aerobics class

Nonmembers pay = 4x ------- eqn 2

For cost for members and nonmembers be the​ same, eqn 1 must be equal to eqn 2,

12 + 3x = 4x

4x - 3x = 12

x = 12

Thus for 12 number of aerobics classes, the cost for members and nonmembers will be same

Answer:B(0.75+0.25)x

Step-by-step explanation:

Is a discount of 0.75 was given the d real value of the sweatshirt would be a whole number

Which is 1-0.75=0.25

For this case we propose a rule of three:

$ 951 -------------> 100%

x -------------------> 35%

Where "x" is the variable that determines the amount of the discount equivalent to 35%.

[tex]x = \frac {35 * 951} {100}\\x = \frac {33285} {100}\\x = 332.85[/tex]

Thus, the discount is $332.85.

The new price of the computer system is:

$951- $332.85 = $617.5

Answer:

The new price of the computer system is: $617.5

$ 2772 is paid in state income tax

Solution:

Given that, Tina lives in a state that charges her 4.5% state income tax on her federal taxable income

Federal taxable income = $61,600

To find: Amount paid by Tina in state income tax

Tax rate = 4.5 %

Which means, 4.5 % of $61,600 is paid as tax

[tex]Tax\ Rate = 4.5 \% \text{ of } 61600[/tex]

Here, "of" means multiplication or product

[tex]Tax\ Rate = 4.5 \% \times 61600\\\\Tax\ Rate = \frac{4.5}{100} \times 61600\\\\Tax\ Rate = 0.045 \times 61600\\\\Tax\ Rate = 2772[/tex]

Thus $ 2772 is paid in state income tax

4.5% of 61,600

0.045(61,600) = 2772

Answer:

A

Step-by-step explanation:

Consider triangle OAM and OBM. In these triangles,

Thus, triangles OAM and OBM are congruent by SSS postulate.

Congruent triangles have congruent corresponding parts, so

[tex]\angle AOM\cong \angle BOM[/tex]

Hence, OM is angle AOB bisector.

Answer:

a

Step-by-step explanation:

usatestprep

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}x>2\\y\leq4\end{array}\right[/tex]

x = 2

This is a vertical line passing through (2, 0) .

y = 4

This is a horizontal line passing through (0, 4).

<, > - dashed line

≤, ≥ - solid line

<,  ≤ - shaded to the left (down) from the line

>, ≥ - shaded to the right (up) from the line

Answer:

Below.

Step-by-step explanation:

The shaded area will be to the right of the vertical dotted line x = 2, and below the horizontal continuous line y = 4.

Answer:

Step-by-step explanation:30x-18

Elmer's bank contained coins totaling $1.37, calculated by summing the value of each type of coin separately.

To find the total value of the coins in Elmer's bank, we need to calculate the value of each type of coin separately and then sum them up. The value of coins is counted based on their denomination, with pennies being worth 1 cent, nickels 5 cents, dimes 10 cents, and quarters 25 cents.

Adding these amounts gives us a total value of 17 + 20 + 50 + 50 = 137 cents. Therefore, the value of the coins in Elmer's bank is $1.37.

The value of the coins in Elmer's bank is $2.17.

17 pennies = $0.17

4 nickels = $0.20

5 dimes = $0.50

2 quarters = $0.50

Adding these amounts together: $0.17 + $0.20 + $0.50 + $0.50 = $2.17.

Answer:

5

Step-by-step explanation:

Samuel can expect to draw a red card approximately 50 times.

To find out how many times Samuel can expect to draw a red card, we need to calculate the probability of drawing a red card and then multiply it by the number of times he selects a card.

Given:

- Number of red cards = 5

- Number of blue cards = 20

- Number of green cards = 25

- Total number of cards = 5 (red) + 20 (blue) + 25 (green) = 50

The probability of drawing a red card is the ratio of the number of red cards to the total number of cards:

[tex]\[ P(\text{Red}) = \frac{\text{Number of red cards}}{\text{Total number of cards}} = \frac{5}{50} = \frac{1}{10} \][/tex]

Now, to find the expected number of times Samuel will draw a red card, we multiply the probability of drawing a red card by the total number of times he selects a card:

[tex]\[ \text{Expected number of red cards} = P(\text{Red}) \times \text{Total number of selections} \][/tex]

Substituting the values:

[tex]\[ \text{Expected number of red cards} = \frac{1}{10} \times 500 = 50 \][/tex]

So, Samuel can expect to draw a red card approximately 50 times.

Answer:

7.50*35=262.50

Step-by-step explanation:

Answer:

Therefore the correct option is sin(5x).

Step-by-step explanation:

i) The hammer thrower rotates exactly 5 times in 2[tex]\pi[/tex] seconds.

  Therefore one rotation is completed in [tex]\frac{2\pi }{5}[/tex] seconds.

ii) Since the motion of the hammer is represented by a sine function therefore

  one rotation is considered to be one full cycle and the time period of that cycle

  is given in equation i) and it is T = [tex]\frac{2\pi }{5}[/tex]  seconds.

iii) the equation of a sine function is given by sin(2[tex]\pi[/tex][tex]\frac{1}{T}[/tex]) which in this case would

   be sin(2[tex]\pi[/tex] × [tex]\frac{1}{\frac{2\pi }{5}}[/tex] × x) = sin(5x)

iv) Therefore the answer is sin(5x)