Fill in the blank.
(5x)2 = _x2

Answer:

f(x) = 10n

Step-by-step explanation:

If met with questions like these, the term "for each" means to multiply. simply write an equation that multiplies n and 10. Also "f(x)" can be substituted for "y" if that is what your instructor taught you.

Answer:

Simplifying the expression 8z+x−5−9z+2:

8z - 9z + x - 5 + 2

= -z + x - 3

Therefore, 8z+x−5−9z+2 simplified to -z + x - 3.

Answer:

the product of some number (call it x) and 7 is:

7⋅x or just 7x

now take 15 less than that:

7x−15 or y=7x−15

Answer:

I got -1/2

Step-by-step explanation:

The frequency of a horse on a merry-go-round refers to the number of revolutions it completes in a given time period.

The outer ring has the largest radius, followed by the middle ring and then the inner ring. Since the horses move at the same angular speed, the horse in the outer ring will have the largest circumference to cover in each revolution, resulting in the highest frequency.

Therefore, the horse in the outer ring has the largest frequency.

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The answer choice which represents a triangle which is similar to PQR is; Choice D.

As evident in the task content; the answer choice which represents a triangle simar to triangle PQR is to be determined.

On this note, by determining the ratio of the sides given; 21 / 18 = 7 / 6.

On this note, the answer choice which represents a triangle which is similar to triangle PQR is the triangle in which the ratio is sides is same.

Hence, in Choice D; 17.5 / 15 = 7 / 6. Ultimately, the similar triangle is choice D.

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Answer:

(5,2)

Step-by-step explanation:

The x is 5, and y is 2.

Answer:

L: (5,2)

Step-by-step explanation:

Answer:

  188.57 cm³

Step-by-step explanation:

You want the total volume of a cone of height 14 cm topped by a hemisphere of radius 3 cm.

The volume of the hemisphere is ...

  V = 2/3πr³

The volume of the cone is ...

  V = 1/3πr²h

The sum of these volumes is ...

  V = 2/3πr³ +1/3πr²h = (π/3)r²(2r+h)

  V = (22/21)(3 cm)²(2·3 cm +14 cm) = (22/21)(9)(20) cm³

  V ≈ 188.57 cm³

The volume of the figure is about 188.57 cm³.

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Answer:

Scenario 1 represents a greater speed

Step-by-step explanation:

scenario 1 - find equation of line on graph to compare

- use the points given to find the slope

rate = slope = (y2-y1)/(x2-x1) = (240-60)/(4-1) = 60

y intercept = 0

line equation -> y = 60x

for every mile, 60 miles are traveled

scenario 2 - interpret the equation

for every mile, 50 miles are traveled

Scenario 1 represents a greater speed

To find the probability that at least 7 Coffleton residents recognize the brand name, we need to use the binomial distribution formula.

The binomial distribution formula is given by:P(X = k) = nCk * pk * (1 - p)n - kWhere,X = Number of successesk = Number of successes we want to findP(X = k) = Probability of finding k successesn = Total number of trialsp = Probability of successnCk = Combination of n and kThe question does not provide the values of n and p. Hence, let's assume that n = 10 and p = 0.6. Therefore, q = 0.4 (since p + q = 1).We need to find P(X ≥ 7).

This means we need to find the probability of getting 7 or more successes.P(X ≥ 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)Now, let's use the binomial distribution formula to calculate each of these probabilities.P(X = 7) = 10C7 * 0.6^7 * 0.4^3= 0.2668P(X = 8) = 10C8 * 0.6^8 * 0.4^2= 0.1209P(X = 9) = 10C9 * 0.6^9 * 0.4^1= 0.0282P(X = 10) = 10C10 * 0.6^10 * 0.4^0= 0.0060Therefore, P(X ≥ 7) = 0.2668 + 0.1209 + 0.0282 + 0.0060= 0.4220Therefore, the probability that at least 7 Coffleton residents recognize the brand name is 0.4220 (or approximately 42.20%).

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Answer:

8.4 cm^3 to the nearest tenth.

Step-by-step explanation:

The ratio of the volumes of the 2 cones is the ratio of the cubes of their radii.

So:

5^3 / 2^3 = 131 / v

v = 2^3 * 131 / 5^3

= 8 * 131 / 125

= 8.384.

The volume of smaller cone is 8.4 cm³

The volume of a cone formula is given as one-third the product of the area of the circular base and the height of the cone. According to the geometric and mathematical concepts, a cone can be termed as a pyramid with a circular cross-section. By measuring the height and radius of a cone, you can easily find out the volume of a cone. If the radius of the base of the cone is "r" and the height of the cone is "h", the volume of cone is given as V = (1/3)πr²h.

By applying Pythagoras theorem on the cone, we can find the relation between volume and slant height of the cone.

We know, h² + r² = L²

⇒ h = √(L² - r²)

where,

h is the height of the cone,

r is the radius of the base, and,

L is the slant height of the cone.

The volume of the cone in terms of slant height can be given as V = (1/3)πr²h = (1/3)πr²√(L² - r²).

Given:

The ratio of the volumes of the 2 cones is the ratio of the cubes of their radii.

Then,

5³ / 2³ = 131 / v

v = 2³ * 131 / 5³

v = 8 * 131 / 125

v = 8.384 cm³

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Theodore's speed was 4 miles per hour.

What is Distance?

Distance is defined as the space between two points in space.

Theodore biked 1 1/3 miles in 20 minutes.

To find his speed, we can use the formula:

speed = distance / time

where distance is measured in miles and time is measured in hours.

First, we need to convert the time to hours. Since there are 60 minutes in an hour, we can divide 20 minutes by 60 to get:

20 minutes / 60 = 1/3 hours

Therefore, Theodore biked 1 1/3 miles in 1/3 hour.

Now we can plug in the distance and time into the formula:

speed = distance / time

speed = (4/3) miles / (1/3) hours

speed = (4/3) miles * (3/1) hours [multiply numerator and denominator by 3]

speed = 4 miles per hour

Therefore, Theodore's speed was 4 miles per hour.

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Given:

XY = 8n + 4

YZ = 4n + 8

XZ = 15n - 9

Y between X and Z so, XY + YZ = XZ

So,

8n + 4 + 4n + 8 = 15 n - 9

solve to find n

So, combine like terms

12 n + 12 = 15 n - 9

12 n - 15 n = -9 - 12

-3 n = -21

divide both sides by -3

n = -21/-3 = 7

So,

The length of XZ = 15n - 9 = 15 * 7 - 9 = 96

The intrinsic value of the PUT option is $0. It means the option has no inherent value based on the given information.

To determine the intrinsic value of a PUT option, we compare the strike price (X) with the current market price (S) of the underlying asset. If the strike price is higher than the market price, the intrinsic value is the difference between the strike price and the market price. However, if the market price is higher than the strike price, the intrinsic value is $0.

In the given information, we have the following data:

- Strike price (X): $90

- Market price (S): $47.78

Since the market price is lower than the strike price (47.78 < 90), the intrinsic value of the PUT option is $0. This means that exercising the option would not result in any profit because it is currently out of the money.

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Answer:

$605

Step-by-step explanation:

The correct question is

Taho Earns His Regular Pay Of $11 Per Hour For Up To 40 Hours Of Work Per Week. For each hour over 40 hours of work per week. Taho earns 1½ times his regular pay. How much does Taho earn in a week in which he works 50 hours?

a. $550

b. $605

c. $625

d. $750

e. $825

For the first $40 that Taho works, he earns $11 x 40 = $440

For the extra $10 (since he worked 50 hrs that week)

1½ of $11 per hr = 1.5 x $11 = $16.5

for the 10 days extra = $16.5 x 10 = $165

total pay = $440 + $165 = $605

Answer:

Ahmed=2/5×200

=400/5

=80

sister=3/5×200

=600/5

=120

You are 18 years old this year.

Let's call your age this year "x". Next year, your age will be "x + 1".

We know that the sum of the digits of "x" is three times bigger than the sum of the digits of "x + 1". Let's call the sum of the digits of "x" "s1", and the sum of the digits of "x + 1" "s2".

So we have the equation:

s1 = 3 * s2

If we add the digits of "x + 1", we get "s2 = a + b", where "a" and "b" are the digits of "x + 1".

Expanding the equation and substituting "s2":

s1 = 3 * (a + b)

Expanding the left side of the equation:

s1 = 3a + 3b

So the sum of the digits of "x" is three times the sum of the digits of "x + 1".

Now we need to find the values of "x" for which "s1" is three times bigger than "s2".

One possible solution is "x = 18", because:

So the answer is that you are 18 years old this year.

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You are 18 years old this year.

Let's call your age this year "x". Next year, your age will be "x + 1".

We know that the sum of the digits of "x" is three times bigger than the sum of the digits of "x + 1". Let's call the sum of the digits of "x" "s1", and the sum of the digits of "x + 1" "s2".

So we have the equation:

s1 = 3 * s2

If we add the digits of "x + 1", we get "s2 = a + b", where "a" and "b" are the digits of "x + 1".

Expanding the equation and substituting "s2":

s1 = 3 * (a + b)

Expanding the left side of the equation:

s1 = 3a + 3b

So the sum of the digits of "x" is three times the sum of the digits of "x + 1".

Now we need to find the values of "x" for which "s1" is three times bigger than "s2".

One possible solution is "x = 18", because:

"s1" = 1 + 8 = 9

"s2" = 1 + 9 = 10

9 = 3 * 10

So the answer is that you are 18 years old this year.

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Answer:

110

Step-by-step explanation:

Rate or proportion shows the relationship between the variation in the  number of two variables.

Given that the ratio of alternative songs to total songs is 9:14.

Total songs = 308

Since the to every 14 total songs, there is 9 alternative songs.

Thus,

Number of alternative songs = \(\frac{9}{14}\) x 308

                                                = 198

There are 198 alternative songs in the music library.

The number of songs that are NOT alternative songs = 308 - 198

                                                                                         = 110

Thus, there are 110 songs that are NOT alternative songs.

Answer: 13%

Step-by-step explanation:

Step 1:

5000

10% of 5000=500

5% of 5000=250

25%=500+500+250= 1250 rupees

so...

5000-1250= 3750 INR, which is the original price, BEFORE THE 25% WAS ADDED

but..

They only want a 10% discount of the price which is 25% above the cost (5000). So essentially we want to find  15%, because 25%-10%=15%

so if...

10%=500

5%=250

15%=750 INR

this means the price with the 10% discount off 25%= 4250 INR (5000-750)

now we need to find the percentage change. For this we need to subtract the price with the 15% discount with the price BEFORE THE 25% was added

e.g 4250-3750= 500INR

Then.. divide this price with the original price before the 25% was added

e.g 500/3750= 2/15=0.13

So...

Convert 0.13 into a percentage=13%

The PERCENTAGE PROFIT of the owner is 13%

P.S Please could someone double check this answer as I am only 15 years old and may have gotten some working out wrong! Thank you

The correct system of equations can have infinitely many solutions if the equations are dependent or when one or more equations are linearly dependent on the others, leading to redundant information or multiple representations of the same relationship.

To solve a system of equations using Gaussian elimination, we'll need the specific system of equations. If you provide the equations, I can help you apply the Gaussian elimination method to solve the system.

Regarding the explanation for a system having infinitely many solutions, it occurs when the system is dependent or when one or more equations are linearly dependent on the others. In such cases, the equations represent multiple representations of the same relationship or contain redundant information, resulting in an infinite number of solutions.

In Gaussian elimination, when solving a system of equations, we aim to transform the system into row-echelon form or reduced row-echelon form to determine the solutions. If, during the elimination process, we encounter a row of zeros followed by a non-zero entry, it indicates that the system is dependent, and there are infinitely many solutions.

In summary, a system of equations can have infinitely many solutions if the equations are dependent or when one or more equations are linearly dependent on the others, leading to redundant information or multiple representations of the same relationship.

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Answer:

1, 2, 4, 5, 8, 10, 20, 40

Step-by-step explanation:

There are 5 erasers to accompany the 20 pencils based on the given ratio.

If the ratio of pencils to erasers is 4:1, and there are 20 pencils, we can determine the number of erasers by setting up a proportion.

The proportion can be written as:

pencils/erasers = 4/1

Given that there are 20 pencils, we can substitute this value into the proportion:

20/erasers = 4/1

To solve for erasers, we can cross-multiply:

\(20*1=4*erasers\)

\(20 = 4*eraser\)

Since there is only 1 unit assigned to erasers, we multiply the unit value (5) by the number of eraser units (1) to find the total number of erasers, which is 5.

Dividing both sides by 4:

20/4 = erasers

5 = erasers

Therefore, there are 5 erasers.

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Answer:

1

Step-by-step explanation:

Step 1:

2x + 5 = 7

Step 2:

2x = 2

Answer:

x = 1

Hope This Helps :)

Answer:

x = 1

Step-by-step explanation:

Step 1: Write equation

2x + 5 = 7

Step 2: Solve for x

Subtract 5 on both sides: 2x = 2

Divide both sides by 2: x = 1

Step 3: Check

Plug in x to verify if it's a solution.

Substitute: 2(1) + 5 = 7

Multiply: 2 + 5 = 7

Add: 7 = 7

The reference angle that has a sin value of 1/2 is π/6 radians or 30 degrees. Therefore, the value of θ is π/6 radians or 30 degrees.

Given that sin θ = 14/28, we can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 14. This yields sin θ = 1/2.

The value of sin θ equal to 1/2 corresponds to the angle θ being π/6 radians or 30 degrees in the first quadrant.

In general, the trigonometric function sin θ represents the ratio of the length of the side opposite the angle θ to the length of the hypotenuse in a right triangle. For sin θ to be positive, the angle θ must lie in the first or second quadrant. Since we are assuming θ to be an acute angle, it falls within the first quadrant.

In the first quadrant, the reference angle that has a sin value of 1/2 is π/6 radians or 30 degrees. Therefore, the value of θ is π/6 radians or 30 degrees.

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Answer: 1.  x = 2

2. x = -2

Step-by-step explanation:

The horizontal asymptote of f(x) is y = 0.

x = 7 is not a vertical asymptote of f(x).

x = -7 is not a vertical asymptote of f(x).

(a) To find the horizontal asymptote of f(x), we examine the behavior of the function as x approaches positive infinity and negative infinity. Taking the limit of f(x) as x approaches infinity, we get:

lim(x→∞) [(x - 7)/(x^3 - 49x)]

By dividing both the numerator and denominator by x^3, we can simplify the expression:

lim(x→∞) [(1/x^2 - 7/x^3)/(1 - 49/x^2)]

As x approaches infinity, the terms involving 1/x^2 and 7/x^3 become increasingly small, approaching zero. Thus, the limit simplifies to:

lim(x→∞) [0/(1 - 0)]

Which equals 0. Therefore, the horizontal asymptote of f(x) is y = 0.

(b) To determine if x = 7 is a vertical asymptote of f(x), we check the behavior of the function as x approaches 7 from both sides. Taking the limit of f(x) as x approaches 7, we get:

lim(x→7) [(x - 7)/(x^3 - 49x)]

Substituting x = 7 into the expression, we have:

(7 - 7)/(7^3 - 49 * 7) = 0/0

The result is an indeterminate form, indicating that x = 7 is not a vertical asymptote of f(x).

(c) Similarly, to check if x = -7 is a vertical asymptote of f(x), we take the limit of f(x) as x approaches -7:

lim(x→-7) [(x - 7)/(x^3 - 49x)]

Substituting x = -7, we have:

(-7 - 7)/(-7^3 - 49 * -7) = 0/0

Again, the result is an indeterminate form, indicating that x = -7 is not a vertical asymptote of f(x).

In conclusion, the function f(x) has a horizontal asymptote at y = 0, and neither x = 7 nor x = -7 are vertical asymptotes of f(x).

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The length of the actual park for 273 inches drawing is 126 yards. If the answer need is on inches, the actual park will be 4536 inches.

As per given the scale is 13 inches : 6 yards where the left sides describes the drawing length and the right describes the actual park length.  Assume the actual park for 273 as x ,then do the comparison:

13 : 6 = 273 : x

13 x = 6 x 273  

13x = 1638

x = 1638 : 13

x = 126

Hence, the length of the actual park is 126 yards

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Answer:The length of the actual park for 273 inches drawing is 126 yards. If the answer need is on inches, the actual park will be 4536 inches.

Step-by-step explanation:

How to calculate the actual park?

As per given the scale is 13 inches : 6 yards where the left sides describes the drawing length and the right describes the actual park length.  Assume the actual park for 273 as x ,then do the comparison:

13 : 6 = 273 : x

13 x = 6 x 273  

13x = 1638

x = 1638 : 13

x = 126

Hence, the length of the actual park is 126 yards

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Answer:

108$

Step-by-step explanation:

Answer:

Gold square = 4

Blue triangle = 3

Step-by-step explanation:

Red hexagon = 6, and there are 4 red hexagons.  So the total is 24.

Therefore, the total on the other side must also be 24.

That means the 4 blue triangles add up to 12, and the 3 gold squares add up to 12.

So each blue triangle is 3, and each gold square is 4.