Frank joined a fitness club. He paid a $50 registration fee, and dues are $12 per month. Which expression can be used to find the average monthly cost of an x-month membership at the club? y=50+12/xy=50+12x/x y= 50x+12/x y= (50+12)x/x

Answer:

There are many varying characteristics and exceptions to each type of protist.

They have been previously categorized based on what they are not.

Recent studies show that protists have not descended from one common ancestor.

Step-by-step explanation:

Answer:

Step-by-step explanation:

We can find height of triangle by using pythagoras theorem

By theorem  (hypotenuse)^2 = (perpendicular or height)^2 + (base)^2

            =>    Height of triangle = sqrt{(hypotenuse)^{2} - (base)^{2}

Using probability the value of p + q = -0.4

Probability is the likelihood of an event.

Given the Venn diagram and that the probabilities are independent events.

The probability of A or B is given by

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Also, the probability of A and B is given by P(A ∩ B) = P(A)P(B)

So, we have that

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

P(A ∪ B) = P(A) + P(B) - P(A)P(B)

From the Venn diagram, we have that

P(A) = p + q

P(B) = q + 0.6

P(A ∩ B) = q

P(A ∪ B) = 0.2

So, substituting these into the equation, we have that

P(A ∪ B) = P(A) + P(B) - P(A)P(B)

0.2 = p + q + q + 0.6 -  q

0.2 = p + 2q - q + 0.6

0.2 - 0.6 = p + q

-0.4 = p + q

So, the value of p + q = -0.4

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Answer: 1200 mm/s

Step-by-step explanation:

Step 1: As for point B, each small case represent 2mm/s. So, when A is 3 mm/s, B is 12 mm/s

Step 2: Assuming point A: x, Point B: y and y= k, x through (0,0) and (3,12)

So, 12=3k=k=4

so, y=4x

then, x=300 and y = 4×300

which is 1200 mm/s

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Answer:

0=3x-y=-13

Step-by-step explanation:

Answer:

In the equation y+4=3(x-3), we can see that x and y are the variables and 4 and -3 are the constants.

To convert the equation to the form Ax + By = C, we'll first distribute the 3 on the right side:

y + 4 = 3x - 9

Next, we'll move all the terms with x to one side of the equation and all the terms with y to the other side:

-3x + y =  - 13

Now we have the equation in the form Ax + By = C, where A = -3, B = 1, and C = -13.

To determine the value in a ratio when the difference between two amounts is given, divide the difference by the ratio. For example, if the ratio is 3:2 and the difference between the two amounts is 12, then the value of the first amount is 18 (12/3 = 4 x 3 = 18). The value of the second amount is 12 (18 - 12 = 6 x 2 = 12).

1. Identify the ratio given in the problem.

2. Identify the difference between the two amounts.

3. Divide the difference by the ratio to determine the value of the first amount.

4. Subtract the difference from the first amount to determine the value of the second amount.

To determine the value in a ratio when the difference between two amounts is given, divide the difference by the ratio. For example, if the ratio is 3:2 and the difference between the two amounts is 12, then the value of the first amount is 18 (12/3 = 4 x 3 = 18). The value of the second amount is 12 (18 - 12 = 6 x 2 = 12).

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The probability of Amar drawing a spade in the first five attempts is approximately 24.5%, as there are 13 spades in a deck of 52 cards.

The probability of drawing a spade in the first attempt is 13/52 or 25%.

The probability of drawing a spade in the second attempt is 12/51 or 23.5%.

The probability of drawing a spade in the third attempt is 11/50 or 22%.

The probability of drawing a spade in the fourth attempt is 10/49 or 20.4%.

The probability of drawing a spade in the fifth attempt is 9/48 or 18.8%.

The total probability of drawing a spade in the first five attempts is the sum of the above probabilities, which is 24.5%.

The probability of drawing a spade in the first five attempts is 24.5%, calculated by summing the separate probabilities.

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A triangle with the given side lengths 6cm , 8cm , and 10cm represents a scalene right angled triangle.

As given in the question,

For the given triangle,

Side lengths of the given triangle is equal to :

6cm , 8cm , and 10cm

Longest side length of the given triangle is equal to 10cm.

Apply Pythagoras theorem to check whether the given triangle is right angled triangle or not.

( longest side ) ² = ( side 1)² + ( Side 2)²

Hypotenuse = longest side

Side 1 = base

Side 2 = Altitude

In the given triangle,

10²

= 100

= 36 + 64

= 6² + 8²

which satisfies the condition of Pythagoras triplets.

All the sides are of different measure so it is a scalene triangle.

Therefore, a triangle with given side lengths is a scalene right angles triangle.

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The standard error of the mean 0.79

The margin of error  1.55

The standard error of the mean is one of the components of the margin of error.

The margin of error is the multiplication of standard error of the mean and critical value. Margin of error is denoted by E

sample size, n= 40,

Sample mean,   = 25 and

population standard deviation, [tex]\alpha[/tex]= 5

[tex]SE_{x}[/tex]

The standard error of the mean, [tex]SE_{x}[/tex]

[tex]SE_{x}[/tex] = [tex]\alpha[/tex]/√n

[tex]SE_{x}[/tex] = 5/√40

[tex]SE_{x}[/tex] = 5/6.3246

[tex]SE_{x}[/tex] = 0.79

We have to find the critical value  

[tex]\alpha[/tex]/2 = 0.05/2 = 0.025 is ± 1.96

The margin of error, E

E =  [tex]Z_{\alpha /2 }[/tex] * [tex]SE_{x}[/tex]

E= 1.96×0.79

E= 1.55

The standard error of the mean 0.79

The margin of error  1.55

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The requried value of 'a' in the given expression is a = -12.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
8⁻⁵⁵ / 8ᵃ = 8⁻⁴³
8ᵃ = 8⁻⁵⁵ / 8⁻⁴³
8ᵃ = 8 ⁻⁵⁵ ⁺ ⁴³
8ᵃ = 8⁻¹²

Taking logs on both sides
a ln 8 = -12 ln 8   [lnbˣ = x lnb]
a = -12

Thus, the requried value of 'a' in the given expression is a = -12.

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The maximum number of pens he can buy now is 71.

We are given that;

A regular octagon has equal sides = 9 feet and an apothem of 10.9 feet

The cost of the railing if it sells = $7.90 per foot

Now,

Let’s assume that the person has bought x pens.

The total cost of the pens would be 9x dollars.

The shopkeeper has given a discount of 70 dollars. So the total cost of the pens after discount would be 9x - 70 dollars.

We need to find the maximum number of pens he can buy now.

we need to find the maximum value of x such that 9x - 70 ≤ 0.

Solving this inequality gives us x ≤ 70/9 ≈ 7.78.

Therefore, by algebra the answer will be 71.

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Answer: 33 - g = 56

less than means -

is means =

Answer:

y = -0.5x + 5.5

Step-by-step explanation:

A linear function can be represented in the form of y = mx + b, where m is the slope and b is the y-intercept. The slope of a line is the ratio of the change in y to the change in x (rise over run) and the y-intercept is the point where the line crosses the y-axis.

To find the rule for this linear function, we can use the two points (x1, y1) and (x2, y2) to find the slope m:

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

If we use the points (7, 2) and (5, 3) to find the slope, we have:

m = (3 - 2) / (5 - 7) = 1 / (-2) = -0.5

We can also use the point (x1, y1) to find the y-intercept b:

b = y1 - m * x1

If we use the point (7, 2) to find the y-intercept, we have:

b = 2 - (-0.5) * 7 = 2 + 3.5 = 5.5

So the rule for the linear function is:

y = -0.5x + 5.5

We can confirm this rule by checking the point (x=-1,y=6)

y = -0.5(-1) + 5.5 = 6

Answer:

58.27 mm (2 d.p.)

Step-by-step explanation:

Assuming the given prism is a rectangular prism, triangles ADC and ACG are right triangles.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Cos trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

AC is the hypotenuse of right triangle ADC.  

Therefore, we can use the cos trigonometric ratio to create an expression for the length of AC:

[tex]\implies \cos\left(36^{\circ}\right)=\dfrac{AD}{AC}[/tex]

[tex]\implies \cos\left(36^{\circ}\right)=\dfrac{42}{AC}[/tex]

[tex]\implies AC=\dfrac{42}{\cos\left(36^{\circ}\right)}[/tex]

AC is the hypotenuse of right triangle ACG.  

Therefore, we can use the cos trigonometric ratio to create an expression for the length of AG:

[tex]\implies \cos\left(27^{\circ}\right)=\dfrac{AC}{AG}[/tex]

[tex]\implies AG=\dfrac{AC}{\cos\left(27^{\circ}\right)}[/tex]

To find the length of AG, substitute the found expression for AC into the expression for AG:

[tex]\implies AG=\dfrac{\frac{42}{\cos\left(36^{\circ}\right)}}{\cos\left(27^{\circ}\right)}[/tex]

[tex]\implies AG=\dfrac{42}{\cos\left(36^{\circ}\right)} \times \dfrac{1}{\cos\left(27^{\circ}\right)}[/tex]

[tex]\implies AG=\dfrac{42}{\cos\left(36^{\circ}\right)\cos\left(27^{\circ}\right)}[/tex]

[tex]\implies AG=58.2654039...[/tex]

[tex]\implies AG=58.27\;\sf mm \;(2\;d.p.)[/tex]

Answer:

5 cm per hour

if this helps

Step-by-step explanation:

Answer:

6a-2b-3c+4d

Step-by-step explanation:

2a+4a = 6a

b-3b = -2b

-c-2c = -3c

-d+5d = 4d

Answer:

6a - b - 3c + 4d

Step-by-step explanation:

⭐What is a polynomial?

Whenever you add polynomials, the only terms you can perform addition or subtraction on are like terms.

⭐What are like terms?

We are asked to add the two given polynomials. Therefore, we have to add the like terms.

[tex]2a + b - c - d + (4a - 3b - 2c + 5d)[/tex]

a and a, b and b, c and c, and d and d all have the same variable with an exponent of 1.

When adding, make sure to utilize the correct addition rules.

⭐What are the rules for adding real numbers?

2a and 4a are positive. Therefore, 2a + 4a = 6a.

-3b is negative, but b is positive. -3b > b. Therefore, -3b + b = -2b.

-c and -2c are both negative. Therefore, -2c - c = -3c.

-d is negative, but 5d is positive. 5d > -d. Therefore, -d + 5d = 4d.

∴ [tex]2a + b - c - d + (4a - 3b - 2c + 5d) = 6a -b -3c + 4d[/tex]

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The minimum amount of time (in seconds) it takes for a vehicle to pass through the zone without exceeding the posted speed limit of miles per hour is 4.8708 seconds.

We can solve this problem easily by using the Pythagorean Theorem. This is because the distances from the cop car to the road form two legs of a right triangle. This makes the total length of this zone the hypotenuse of this triangle and thus, this problem can be solved using the Pythagoras theorem.

= (150)^2 + (200)^2 = h^2

= 62500 = h^2

= h = 250

Our distance is in feet, but our speed is in miles per hour. Let's convert this distance into miles as well.

= 250 feet × 1 mile/5280 feet = 0.04735 miles

Then, when we use the formula  d = rt

= 0.04735 = 35t

= 0.04735/ 35 ≈ 0.001353

Since our speed was in miles per hour, this time is also in hours. We need to convert this to seconds before we can state our final answer.

= 0.001353 hours × 60 minutes/1 hour × 60 seconds/1 minute = 4.8708 sec

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This simplifies to x<3/2. So the graph of f(x) = –x^2 + 3x + 8 is increasing over the interval (-infinity,3/2)

Generally, The vertex form of a parabola that opens downward is

f(x) = a(x-h)^2 + k,

where (h,k) is the vertex of the parabola.

We know that the vertex of the parabola is at (1.5, 10) so we can use that to find the value of a and h. So,

f(x) = a(x-1.5)^2 + 10

Given that the parabola goes through (- 2, - 2) and (5, - 2), we can substitute these points into the equation to find a and k.

Substituting (-2, -2) into the equation:

-2 = a((-2) - 1.5)^2 + 10

Substituting (5, - 2) into the equation:

-2 = a(5 - 1.5)^2 + 10

Solving these two equations will give you a = -1/2 and k = -8

So the equation is f(x) = -1/2(x-1.5)^2 - 8

The graph of a parabola is increasing on the interval where the derivative is greater than 0.

To find the derivative, we use the power rule and the chain rule:

f'(x) = -1/2(2x-3)

= -x+3/2

So, the graph of f(x) is increasing when -x+3/2 > 0

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Answer:

Step-by-step explanation:

-10.9p + 3.9

-10.9p turns positive.

The (p) is isolated.

10.9 - 3.9= 9.18 = -9.18

Answer

-9.18

Answer:

A = -5

B = -2

C = 3

The mileage of Alyssa's car is a measure of how far the car has traveled per unit fuel.The best method and reasoning to calculate the gas mileage is: D. 243.8 miles ÷ 7.71 gallon s

​The mileage of Alyssa's car is a measure of how far the car has traveled per unit fuel.

The best method and reasoning to calculate the gas mileage is:

D. 243.8 miles ÷ 7.71 gallon s

because dividing a quantity with units of miles by a quantity with units of gallons gives a quantity with units of miles per gallon.

The mileage of the car is calculated by dividing the number of miles traveled by the amount of gas used.

mileage

= 243.8 /7.71

From the given parameters;

The unit of miles traveled is miles

The unit of gallons used is gallons

Because the miles traveled is divided by the gallons used, then the unit of the mileage would be miles per gallon

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A day is a unit of time and cannot be divided into a fraction,  Therefore Wesley would need to run for at least 5 days to meet his goal of 19 miles.

To find out how many days Wesley needs to run to meet his goal, we need to divide the total distance he wants to run (19 miles) by the distance he runs each day (4.2 miles):

19 miles ÷ 4.2 miles/day = 4.52 days

Since a day is a unit of time and cannot be divided into a fraction, Wesley would need to run for at least 5 days to meet his goal of 19 miles.

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The required number of ways to choose a pair of socks, provided that i get two socks of the same color are 50.

Combinations are ways to choose elements from a collection in mathematics where the order of the selection is irrelevant. Let's say we have a trio of numbers: P, Q, and R. Then, combination determines how many ways we can choose two numbers from each group.

We have,

8 white, 6 brown, and 4 blue

So, We need to choose a pair of socks, provided that i get two socks of the same color.

The number of ways are;

Ways to choose 2 white =  C(8,2)  = 28

Ways to choose 2 brown = C(6,2)  = 16

Ways to choose 2 blue  = C(4,2)  = 6

So

28 + 16 +  6  =

50 ways

Thus, required total number of ways are 50.

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You can order 6 different one-topping pizzas. You can order 15 different one-topping pizzas.

What is the combination?

A combination is a method of selecting items from a collection where the order of selection is irrelevant.

The combination is defined as "an arrangement of objects in which the order in which the objects are chosen is unimportant." The combination means "selection of things," where the order is irrelevant.

The formula of combination is nCr = n!/[r!(n-r)!]

Where n is the total number of objects and r is the number of objects those are selected.

Case 1: one-topping pizzas

The number of different toppings is 6.

Selecting one topping is ₆C₁  = 6!/[1!5!] = 6

Case 2: two-topping pizzas

The number of different toppings is 6.

Selecting two topping is ₆C₂  = 6!/[2!4!] = 15

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Answer:

19

Step-by-step explanation:

If g(x) = [tex]x^{2} + 3[/tex], then we will substitute 4 in for x, giving us:

[tex]4^{2} + 3[/tex]

Simplifying:

[tex]16 + 3 = 19[/tex]

So g(4) = 19.

Hope this helped!

If Annual Salary: $24,872; personal exemptions: $1,500.  the income tax withheld per pay is: $29.57 per pay period.

Total taxable income = $24,872 - $1,500

Total taxable income = $23,372

The first $10,000 is taxed at a rate of 2.75%.  The tax owed on the first $10,000 is:

$10,000 * 0.0275

= $275.

The remaining $13,372 ($23,372 - $10,000) is taxed at a rate of 3.25%, so the tax owed on this amount is:

$13,372 * 0.0325

= $434.57

The total tax owed is:

$275 + $434.57

= $709.57

Since the person is paid semimonthly, we divide the annual tax owed by 24 to find the tax withheld per pay period:

$709.57 / 24

= $29.57 per pay period

Therefore the income tax withheld per pay is: $29.57 per pay period.

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Answer:

(a) 8800000

(b) Barcelona had the least population in 2018

(c) The difference in population is 2.9 x [tex]10^{7}[/tex]

Step-by-step explanation:

(a) Since '10' is raised to a positive power, the decimal will be moving in the forward direction, In other words, it will move towards the right. Therefore, the decimal will be moving 6 places forward. After which, the empty slot(s) will be occupied by zeros

8.8 x [tex]10^{6}[/tex] = 8800000

(b) First notice that three out of the five cities have population expressed in [tex]10^{6}[/tex] (where 6 is the least power). Then notice that out of those three cities, the smallest number corresponds to Barcelona (i.e. 5.5).

Therefore, Barcelona had the least population in 2018

(c) Population of:

Tokyo: 3.7 x [tex]10^{7}[/tex]

Ahmedabad: 7.7 x [tex]10^{6}[/tex]

First, make sure the two numbers are expressed in the same standard form (meaning 10 is raised to the same power in both cases):

Tokyo: 3.7 x [tex]10^{7}[/tex] = 3.7 x 10 x [tex]10^{6}[/tex]  =37 x [tex]10^{6}[/tex]

Ahmedabad: 7.7 x [tex]10^{6}[/tex]

Next step:

37 x [tex]10^{6}[/tex] - 7.7 x [tex]10^{6}[/tex]

= (37 - 7.7) x [tex]10^{6}[/tex]

= 29.3 x [tex]10^{6}[/tex]  

= 29 x [tex]10^{6}[/tex] (Corrected to 3 significant figures)

= 2.9 x 10 x [tex]10^{6}[/tex]

= 2.9 x [tex]10^{7}[/tex]