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Answer:

2.9

Step-by-step explanation:

11.02÷3.8= 2.9

Answer:

2.9

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Computing the total number of counters in the class as 1,108, the mean number of counters that the 46 children have is 24.

The mean refers to the average value.

The average is the quotient of the total value divided by the number of items in the data set.

The number of boys in the class = 26

The number of girls in the class = 20

The total number of boys and girls in the class = 46

The mean number of counters that the boys have = 28

The total number of counters that the boys have = 728 (28 x 26)

The mean number of counters that the girls have =19

The total number of counters that the girls have = 380 (19 x 20)

The total number of counters that the class has = 1,108 (728 + 380)

The average or mean number of counters in the class = 24 (1,108 ÷ 46)

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Answer:

a. 1.25 laps per min

b. .8 min per lap

c. 17.6 minutes

Step-by-step explanation:

The laps per minute are 5 / 4, The time per lap is 4 / 5 minutes per lap, and   The time taken to swim 22 laps is 17.6 minutes.

One of the fundamental mathematical operations is division, which involves breaking a bigger number into smaller groups with the same number of components.

Given:

It takes Andre 4 minutes to swim 5 laps,

(a)  Calculate the number of laps per minute as shown below,

The number of laps per minute = Total number of laps / total time

The number of laps per minute = 5 / 4 laps per minute

(b)  Calculate the time per lap as shown below,

The time per lap = total time / total lap

The time per lap = 4 / 5 minutes per lap

(c)  Calculate the time taken to swim 22 laps as shown below,

The time taken to swim 22 laps =  time taken per lap × 22

The time taken to swim 22 laps =  4 / 5 × 22

The time taken to swim 22 laps =  88 / 5

The time taken to swim 22 laps = 17.6 minutes

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Answer:

Step-by-step explanation:

To find the unit price for each brand, we will divide the price of the box by the number of spoons in the box.

Unit price for the Brand A spoons:

$1.99 ÷ 25 = $0.0796 ≈ $0.08

Unit price for the Brand B spoons:

$3.89 ÷ 42 = $0.0926 ≈ $0.09

The better buy:

Brand A is the better buy, as its unit price is lower at $0.08 per spoon compared to Brand B's unit price of $0.09 per spoon.

Answer:

okay i'll keep this in mind

Step-by-step explanation:

SOLUTION:

Step 1:

In this question, we are given the following:

Determine the slope of the line represented by the equation

16x + 4y = 8.



Step 2:

In determining the slope of the equation:

CONCLUSION:

Hence , the slope of the line, m = - 4

Answer:

The answer to your question is 17.65

Answer: 17.65%

Step-by-step explanation:

X/100 = 15/85 (cross multiplication)

(100*15)/85 = 17.65%

(This helps: %/100 = is/of (cross multiplication)

Answer:

4

Step-by-step explanation:

So we know that RT is 36.

Note that RT is the combined length of RS and ST. Therefore:

\(RT=RS+ST\)

Substitute. RT is 36, RS is 6x+1 and ST is x+7:

\(36=(6x+1)+(x+7)\)

Combine like terms and add:

\(36=7x+8\)

Subtract 8 from both sides:

\(28=7x\)

Divide by 7:

\(x=4\)

So, our answer is 4 :)

The Trapezoid EFGH's GH length is 5 units.

The shape of a trapezoid is used to describe a lobster trap with a void (trapezoid). The bottom (5m) and top (5m) sides of this trapezium are parallel (8m). Although it is upside down, this trapezium also features parallel top and bottom sides. Nonetheless, it is a trapezium.

Trapezoid EFGH and Trapezoid ABCD are comparable to one another based on the image, indicating that their respective sides are proportional.

Let's establish a ratio for the lengths of the parallel sides of the two trapezoids using the dimensions provided:

BC/FG = AB/EF

We can change the values provided by:

12/6 = 10/GH

The left side of can be made simpler by:

2 = 10/GH

Now we can solve for GH by multiplying both sides by GH:

2GH = 10

Finally, we can solve for GH by dividing both sides by 2:

GH = 5

Therefore, the length of GH in units is 5.

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A simple path which visits all vertices can be found using a linear-time algorithm.

How to handle visited vertex is the issue.

The time complexity isn't really linear as you follow because of the many visits.

If not, the following straightforward example will show that your algorithm is flawed:

1 --> 2 -----------> 3 --> 4

       \         /

        --> 5 -->

After finding 1-2-3-4 in the initial search, the search returns to 2 and finds 1-2-5-3. Now that number 3 has been visited, the search halts and ultimately fails.

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Answer: 120,000

Step-by-step explanation:  

10,000 x 12 = 120,000

Answer: (6,-6)

Step-by-step explanation:

To find the coordinates of point B, we can use the midpoint formula:

Midpoint formula: The midpoint M of a line segment with endpoints (x1, y1) and (x2, y2) is given by:

M = ((x1+x2)/2, (y1+y2)/2)

Here, we know that the midpoint M is (4, -2), and one endpoint A is (2, 2). Let B be the other endpoint, so we can use the midpoint formula to find B:

4 = (2+x2)/2 --> 8 = 2+x2 --> x2 = 6

-2 = (2+y2)/2 --> -4 = 2+y2 --> y2 = -6

Therefore, point B has coordinates (6, -6).

As for the second question, without a graph or information about the equation of line t and point P, it is not possible to determine which points lie on the line passing through P and perpendicular to t.

Answer:

50 : 60

10 : 12

Step-by-step explanation:

5 : 6

= 5 / 6

= ( 5 / 6 ) x ( 10 / 10 )

= ( 5 x 10 ) / ( 6 x 10 )

= 50 / 60

= 50 : 60

5 / 6

= ( 5 / 6 ) x ( 2 / 2 )

= ( 5 x 2 ) / ( 6 x 2 )

= 10 / 12

= 10 : 12

Answer:

A. Using the lens equation, 1/p + 1/q = 1/f, and substituting f = 5 cm and q = 7 cm, we can solve for p:

1/p + 1/7 = 1/5

Multiplying both sides by 35p, we get:

35 + 5p = 7p

Simplifying and rearranging, we get:

2p = 35

Therefore, the distance from the lens to the object, p, is:

p = 35/2 cm

B. Solving the lens equation, 1/p + 1/q = 1/f, for q, we get:

1/q = 1/f - 1/p

Substituting f = 5 cm, we get:

1/q = 1/5 - 1/p

Multiplying both sides by 5qp, we get:

5p = qp - 5q

Simplifying and rearranging, we get:

q = 5p / (p - 5)

Therefore, the expression that gives q as a function of p is:

q = 5p / (p - 5)

C. Here is a sketch of the graph of q(p):

The graph is a hyperbola with vertical asymptote at p = 5 and horizontal asymptote at q = 5. The image distance q is positive for object distances p greater than 5, which corresponds to a real image. The image distance q is negative for object distances p less than 5, which corresponds to a virtual image.

D. Taking the limit of q as p approaches infinity, we get:

lim q(p) = 5

This represents the horizontal asymptote of the graph. As the object distance becomes very large, the image distance approaches the focal length of the lens, which is 5 cm.

Taking the limit of q as p approaches 5 from the positive side, we get:

lim q(p) = -infinity

This represents the vertical asymptote of the graph. As the object distance approaches the focal length of the lens, the image distance becomes infinitely large, indicating that the lens is no longer able to form a real image.

In order for the lens to form a real image, the object distance p must be greater than the focal length f. When the object distance is less than the focal length, the lens forms a virtual image.

Answer:

4

Step-by-step explanation:

The x-intercept occurs when y=0, if you think about it graphically.  Plug y=o into your equation:

10x - 5(0) = 40

10x = 40 (divide each side by 10)

x=4

Given statement solution is :- It takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

To determine the number of months it takes to pay off the credit card and the total amount paid, including interest, we can follow these steps:

Step 1: Calculate the monthly interest rate.

The APR (Annual Percentage Rate) is given as 9.5%. To find the monthly interest rate, we divide this by 12 (the number of months in a year):

Monthly interest rate = 9.5% / 12 = 0.0079167

Step 2: Determine the monthly payment.

The monthly payment is given as $400.

Step 3: Calculate the interest and principal paid each month.

The interest paid each month can be calculated by multiplying the monthly interest rate by the current balance.

Principal paid = Monthly payment - Interest paid

Step 4: Track the remaining balance each month.

Starting with the initial balance of $1,367.90, subtract the principal paid each month to determine the new balance.

Step 5: Repeat Steps 3 and 4 until the balance reaches zero.

Continue calculating the interest and principal paid each month, updating the balance, until the remaining balance becomes zero.

Step 6: Determine the total number of months and the total amount paid.

Count the number of months it takes to reach a balance of zero. Multiply the number of months by the monthly payment ($400) to find the total amount paid.

Let's calculate the number of months and the total amount paid, including interest:

Month 1:

Interest paid = 0.0079167 * $1,367.90 = $10.84

Principal paid = $400 - $10.84 = $389.16

New balance = $1,367.90 - $389.16 = $978.74

Month 2:

Interest paid = 0.0079167 * $978.74 = $7.75

Principal paid = $400 - $7.75 = $392.25

New balance = $978.74 - $392.25 = $586.49

Month 3:

Interest paid = 0.0079167 * $586.49 = $4.64

Principal paid = $400 - $4.64 = $395.36

New balance = $586.49 - $395.36 = $191.13

Month 4:

Interest paid = 0.0079167 * $191.13 = $1.51

Principal paid = $400 - $1.51 = $398.49

New balance = $191.13 - $398.49 = -$207.36 (Paid off)

It takes 4 months to pay off the credit card. Now, let's calculate the total amount paid, including interest:

Total amount paid = 4 * $400 = $1600

Therefore, it takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

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Here according to angle sum property all angles sum u up 180°

So,

\(8x + 2 + 60 + 70 = 180 \\ 8x + 132 = 180 \\ 8x = 180 - 132 \\ 8x = 48 \\ x = \frac{48}{8} \\ x = 6\)

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Answer:

1)Solving the expression \(1-2(2x+1)=1-(x-1)\) we get \(\mathbf{x=-\frac{1}{3}}\)

2) solving the equation \(3.6x-6.1=5.9-2.4x\) we get \(\mathbf{x=2}\)

Step-by-step explanation:

We need to solve the expressions:

1) \(1-2(2x+1)=1-(x-1)\\\)

Solving

\(1-2(2x+1)=1-(x-1)\)

First solving the brackets

\(1-4x-2=1-x+1\)

Simplifying

\(-1-4x=-x\)

Adding 4x on both sides

\(-1-4x+4x=-x+4x\\-1=3x\)

Switching the sides

\(3x=-1\)

Divide both sides by 3

\(\frac{3x}{3}=-\frac{1}{3}\\x= -\frac{1}{3}\)

So, Solving the expression \(1-2(2x+1)=1-(x-1)\) we get \(\mathbf{x=-\frac{1}{3}}\)

2) \(3.6x-6.1=5.9-2.4x\)

Solving:

\(3.6x-6.1=5.9-2.4x\)

Adding 6.1 on both sides

\(3.6x-6.1+6.1=5.9-2.4x+6.1\\3.6x=12-2.4x\)

Adding 2.4x on both sides

\(3.6x+2.4x=12-2.4x+2.4x\\6x=12\\\)

Divide both sides by 6

\(\frac{6x}{6}=\frac{12}{6}\\x=2\)

So, solving the equation \(3.6x-6.1=5.9-2.4x\) we get \(\mathbf{x=2}\)

The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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Answer:(3t)^2

Step-by-step explanation:

Steps below

Answer:

this is obtuse

Step-by-step explanation:

ONE OF THEM IS GREATER THAN 90 DEGREES :)

Answer:

v=2144.66

Step-by-step explanation:

V=4/3πr^3
sub in r which is 8

V=4/3 * π * 8^3
V=4/3 * π * 512

From the resulting solution, the correct linear inequality graph is Graph C.

Given the inequality equation below:

2(2x-1)+7< 13 or -2x+5 ≤ -10.​

Simplify the expression

2(2x-1)+7< 13

Expand

4x - 2 + 7 < 13

4x + 5 < 13

4x < 13 - 5

4x < 8

x < 2

For the inequality -2x+5 ≤ -10.

-2x+5 ≤ -10

-2x  ≤ -15

x  ≥ 7.5

Hence the solution to the given system of inequalities are x < 2 and x  ≥ 7.5

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1. Relation 1 is a function

2. Relation 2 is a function

3. Relation 3 is not a function

4. Relation 4 is a function

From the question, we have the following parameters that can be used in our computation:

The relations (1) to (4)

Relation (1)

This relation is a function

This is because each range value point to unique domain values

Relation (2)

This relation is a function

This is because each range value point to unique domain values

Relation (3)

This relation is not a function

This is because domain values w have different range values.

Relation (4)

This relation is a function

This is because each range value point to unique domain values

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Answer:

Step-by-step explanation:

(5x - 1) (5x - 1)

= \((5x - 1)^{2}\)

Using laws of exponents,

\((a - b)^{2} = a^{2} - 2ab + b^{2}\)

here, a = 5x, b = 1

so it becomes,

\(5x^{2}\) - 2 × 5x × 1 + \(1^{2}\)

\(25x^{2}\) - 10x + 1

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