The distributive property to express 48+72

The  amount of interest earned is $990 when we deposit of $5,500 at 6% for 3 years

percentage, a relative value indicating hundredth parts of any quantity.

We have to find the  amount of interest earned

The deposited amount or principal amount us 5500

Rate of interest is 6% and time is 3 years

The formula for simple interest is I=PRT

I = interest, P = principal, R = rate, T = time in years.

Let us convert 6% to decimal form

Divide 6 by 100

6%=0.06

I = 5500(0.06)(3)

I = $990

Hence, the  amount of interest earned is $990 when we deposit of $5,500 at 6% for 3 years

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~~~~~~~~~~The answer is 366 m/min~~~~~~~~~~~~~~~~~~ First, convert the turtles speed to meters per minute. 27 km/h * 1000 m/km = 27000 m/h / 60 min/h = 450 m/min Now convert the girls speed to meters per minute. 14 dm/s / 10 dm/m * 60 s/min = 84 m/min Now subtract the girl's speed from the turtle's speed. 450 m/min = 84 m/min = 366 m/min

Answer: C. 17

Step-by-step explanation:

Given : An investment is currently worth [tex]2.125\times10^4[/tex] dollars . Ten years ago, the investment was worth [tex]1.25\times10^3[/tex] dollars.

Then, the number of times the value of the investment today is greater than the value of the investment ten years ago is given by :-

[tex]\dfrac{\text{Current investment}}{\text{\text{Yen years ago investment}}}\\\\=\dfrac{2.125\times10^4}{1.25\times10^3}\\\\=\dfrac{2.125}{1.25}\times10^{4-3}\ \ [\because a^m\times a^n=a^{m+n}]\\\\=1.7\times10=17[/tex]

Hence, the value of the investment today is 17 times greater than the value of the investment ten years ago .

1st question - answer is #2

line P & Q = x=3, Y=5

 triangle question, x = 17

Answer:  The required solution is (x, y) = (4, 6).

Step-by-step explanation:  We are given to solve the following system of equations :

[tex]x+3y=22~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\2x-y=2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

From equation (ii), we have

[tex]2x-y=2\\\\\Rightarrow y=2x-2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]

Substituting the value of y from equation (iii) in equation (i), we get

[tex]x+3(2x-2)=22\\\\\Rightarrow x+6x-6=22\\\\\Rightarrow 7x=22+6\\\\\Rightarrow 7x=28\\\\\Rightarrow x=\dfrac{28}{7}\\\\\Rightarrow x=4.[/tex]

From equation (i), we get

[tex]4+3y=22\\\\\Rightarrow 3y=22-4\\\\\Rightarrow 3y=18\\\\\Rightarrowy=\dfrac{18}{3}\\\\\Rightarrow y=6.[/tex]

Thus, the required solution is (x, y) = (4, 6).

Area of the given Circle as the function of its diameter πd²/4

A Circle is the 2D shape which is measured in the terms of its radius.

Given that Area, radius and diameter of the given Circle is a , r and d respectively.

Area of Circle (A) = π X radius²

radius = diameter/2

Therefore replacing radius by diameter we get,

A = π(d/2)²

A = πd²/4

Hence, Area as a function of d is given by A = πd²/4

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Answer:

Option B. 14.8 units³ is the answer.

Step-by-step explanation:

It is given in the question A solid right pyramid which has a regular hexagonal base with area = 7.4 unit²

Height of the pyramid = 6 units.

We have to calculate the volume of the pyramid.

Since volume of the pyramid = (1/3)×Area of the base × height

Volume = (1/3)×7.4×6 = 7.4 × 2 = 14.8 units³

Therefore option B. 14.8 units³ is the answer.

It should be noted that the volume of the pyramid will be 14.8 unit³.

From the information given, the solid right pyramid has a regular hexagonal base with an area of 7.4 units².

The height of the pyramid is also 6 units. Therefore, the volume of the pyramid will be:

= 1/3 × Area of the base × height

= 1/3 × 7.4 × 6

= 14.8 units³

In conclusion, the volume of the pyramid is 14.8 unit³.

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The cosine function is used to find the length of the hypotenuse of a triangle by utilizing the Pythagorean theorem.

The trigonometric function used to find the length of the hypotenuse of a triangle is the cosine function. In a right triangle, the cosine function is defined as the ratio between the length of the adjacent side to the length of the hypotenuse.

To find the length of the hypotenuse, you can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the hypotenuse.

For example, if the lengths of the shorter sides are 9 blocks and 5 blocks, then the length of the hypotenuse would be √(9² + 5²) = √(81 + 25) = √106 = 10.3 blocks.

The solution to the equation is v = 0.

We have,

To solve the equation 7(2 + 5v) = 3v + 14, we can simplify and isolate the variable v.

Expanding the left side of the equation:

7(2 + 5v) = 14 + 35v

Now we have:

14 + 35v = 3v + 14

Next, we can combine like terms:

35v - 3v = 14 - 14

32v = 0

To solve for v, we divide both sides of the equation by 32:

v = 0/32

v = 0

Therefore,

The solution to the equation is v = 0.

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The student's calculations for mean and standard deviation are correct, although the standard deviation was slightly misunderstood. The calculation for the z-score was correct, but the student failed to convert this z-score into a probability.

The question discusses certain calculations about the distribution of gypsy moths in traps placed by a state agriculture department. Your calculation for (a), the

mean

number of moths in 30 traps, is correct. We multiply the mean number of moths in one trap (0.6) by the number of traps (30) to obtain 18. However, for (b), the

standard deviation

of the distribution is incorrectly calculated. In fact, as we apply the formula for standard deviation of sample means σ/√n, where σ is the population standard deviation (0.4) and n is the sample size (30), it comes out to be 0.073 (rounded to ±0.001). Lastly, for (c), using the given values in the

central limit theorem

, the z-score calculator gives us a value of 1.37, but remember, this is a z-score, not a probability. To convert the z-score to a probability, you need to consult a standard normal distribution table or use a calculator with a built-in z-score to probability converter.

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Answer:

|v| = 10.06 units

Step-by-step explanation:

It is given that,

The x component of the vector is, [tex]v_x=7.6\ units[/tex]

The y component of the vector is, [tex]v_y=-6.6\ units[/tex]

We need to find the magnitude of vector v. The magnitude of any vector is calculated as :

[tex]|v|=\sqrt{v_x^2+v_y^2}[/tex]

[tex]|v|=\sqrt{(7.6)^2+(-6.6)^2}[/tex]

|v| = 10.06 units

So, the magnitude of vector v is 10.06 units. Hence, this is the required solution.

Answer:

C.Yes, because every x-value corresponds to exactly one y-value.

Step-by-step explanation:

A function is a relation in which each element of the domain (x) is mapped to one element of the range (y).  This means that no x can be mapped to more than one y; basically it means that no x can repeat.

In this table, no x repeats; each x is mapped to only 1 y.  This means that it is a function.

Answer:

The correct option is C) Yes, because every x-value corresponds to exactly one y-value.

Step-by-step explanation:

Consider the provided table:

x     y

2    1

4    3

6    3

8    4

10   6

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Or we can say that, a function is a set of ordered pairs in which x element has only one y-element associated with it.

Now observe the table for each x element we have only one y element.

Therefore, the table represent a function.

The correct option is C) Yes, because every x-value corresponds to exactly one y-value.

Answer:

#4) 1/2(ab); #5) 3a, 4a, 4ab, 2a

Step-by-step explanation:

#4) Take the top triangle.  The height will be the difference in the y-coordinates of J and M:

b-0 = b

The base of the triangle would be the difference in the x-coordinates of J and K:

a-0 = a

The area is given by the formula A=1/2bh, where b is the base and h is the height; substituting our height and base, we have

A=1/2(b)(a) = 1/2(ab)

#5) To find the midpoint of a section, we add together the x-coordinates and divide by to, and add together the y-coordinates and divide by 2.

The endpoints of FE are (4a, 0) and (2a, 2b).  This makes R:

[tex](\frac{2a+4a}{2},\frac{2b+0}{2})\\\\=(\frac{6a}{2},\frac{2b}{2})\\\\=(3a, b)[/tex]

The length of DF can be found by subtracting the x-coordinates:

4a-0 = 4a

The area is then found by multiplying 1/2 by the base and the height:

A=1/2(4a)(2b) = 1/2(8ab) = 4ab

The length of QR can be found by subtracting the x-coordinates:

3a-a = 2a

Final answer:

The equation representing a direct variation where y varies directly as x with a constant of variation of -3 is y = -3x. It is a linear equation without a y-intercept.

Explanation:

If y varies directly as x, and the constant of variation is -3, the equation that represents this relationship can be written as y = kx, where k is the constant of variation. Since the constant of variation is given as -3, the equation becomes y = -3x. This is a linear equation similar to the form y = mx + b, where m is the slope of the line and b is the y-intercept. In this case, since the constant of variation is -3, the slope of the line is -3 and the y-intercept is 0 because there is no addition or subtraction of a constant in the equation.

To meet their goal of saving $8,000 for their wedding, Mike and Kate need to adjust their plan. Increasing the amount they save each month by $80 (Option B) will allow them to reach their goal.

To determine which option will allow Mike and Kate to meet their goal of saving $8,000 for their wedding, we need to analyze the information given. They saved $4,000 in the first year, which means they saved $4,000 in 12 months. To reach their goal, they need to save an additional $4,000 in 8 months.

Option A: If they stay with saving the same amount they've been saving each month, they will save the same amount each month for the remaining 8 months. Therefore, they will not reach their goal of $8,000.

Option B: If they increase the amount they save each month by $80, they will be saving $80 more each month for the remaining 8 months. This will result in them saving an additional $640 ($80 x 8 months) and reaching their goal of $8,000.

Therefore, the correct answer is Option B - Only option B will allow them to meet their goal.

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The artist has cut off a total of 4 and 3/8 inches of ribbon for his project by multiplying the length of one piece (7/8 inch) by the total number of pieces cut (5).

The question involves a straightforward arithmetic operation of multiplication. Each piece of ribbon the artist cuts measures 7/8 inch, and he cuts off 5 pieces in total. To find the total length of ribbon cut off, we multiply the length of one piece (7/8 inch) by the number of pieces cut (5).

Calculation: \(\frac{7}{8} \text{ inch} \times 5 = \frac{35}{8} \text{ inches} = 4 \frac{3}{8} \text{ inches}\)

Therefore, the artist has cut off a total of 4 and 3/8 inches of ribbon for his project. This example demonstrates a practical application of multiplication in a real-world context, specifically within arts and crafts projects.

Rick, Maya, and Tom worked a total of 1086 minutes.

To calculate this:

1. Convert Rick's hours to minutes: 5 hours and ½ hour = [tex]\( 5 \times 60 + 30 = 330 \) minutes.[/tex]

2. Convert Maya's hours to minutes: 6 hours and 1/10 hour = [tex]c\( 6 \times 60 + 6 = 366 \) minutes.[/tex]

3. Convert Tom's hours to minutes: 6 hours and 30 minutes = [tex]\( 6 \times 60 + 30 = 390 \) minutes.[/tex]

Now, add up all the minutes worked:

[tex]\[ 330 + 366 + 390 = 1086 \] minutes.[/tex]

Therefore, Rick, Maya, and Tom worked a total of 1086 minutes.

- Rick worked for 5 hours and ½ hour, which is 330 minutes.

- Maya worked for 6 hours and 1/10 hour, which is 366 minutes.

- Tom worked for 6 hours and 30 minutes, which is 390 minutes.

Adding these minutes together gives a total of 1086 minutes.

complete question

Rick, Maya, and Tom work in a call center. On a particular day, Rick worked 5 and ½ hours, Maya worked 6.1 hours, and Tom worked 6 hours and 30 minutes. What is the total number of minutes that they worked?