A math test took 50 minutes to complete. The test ended at 3:55. What time did the test begin?

Answer:

The answer would be A. He determined pounds per dollar by dividing 10 by 25 but wrote the unit rate as a dollar value.

QUESTION 1

The area of a triangle is given by

[tex]Area=\frac{1}{2}\times base\times heigth[/tex]

The length of the base of the triangle is [tex]6\:in.[/tex] and the vertical height is [tex]8\:in.[/tex].

We substitute these values into the formula to obtain,

[tex]Area=\frac{1}{2}\times 6\times 8[/tex]

[tex]Area=3\times 8[/tex]

[tex]Area=24\:in^2[/tex]

The area of the triangle is 24 square inches.

The correct answer is A

QUESTION 2

The company logo is made up of three triangles and a square.

The length of the square is [tex]7\:cm[/tex]

The area of a square is given by

[tex]Area=l^2[/tex]

[tex]\Rightarrow Area=7^2[/tex]

[tex]\Rightarrow Area=49cm^2[/tex].

The area of one of the triangles is

[tex]Area=\frac{1}{2}\times base \times height[/tex]

The height of the triangle is [tex]4cm[/tex].

The base of the triangle is on one side of the square, so it is [tex]7cm[/tex].

The area now becomes

[tex]Area=\frac{1}{2}\times 7 \times 4[/tex]

[tex]\Rightarrow Area=7 \times 2[/tex]

[tex]\Rightarrow Area=14cm^2[/tex].

Since there are three identical triangles, we multiply the area of one triangle by 3 to get area of the three triangles.

[tex]Area\:of\:the\:three\:triangles=3\times14=42cm^2[/tex]

The area of the logo is equal to the area of the square plus the area of the three identical triangles.

[tex]Area\:of\:logo=49+42=91cm^2[/tex]

Hence the area of the logo is [tex]91cm^2[/tex]

QUESTION 3

Since the figure is made up of two rectangles and two right triangles, we find their areas and sum them to get the area of the figure.

The area of a rectangle is given by

[tex]Area=l\times w[/tex]

The width of the bigger rectangle is [tex]5[/tex] and the length is [tex]25[/tex].

[tex]Area\:of\:bigger\: rectangle=25\times 5[/tex]

[tex]Area\:of\:bigger\: rectangle=125\:square\:units[/tex]

The width of the smaller rectangle is [tex]8[/tex].

The length of the smaller rectangle is [tex]25-(6+6)=25-12=13[/tex].

[tex]Area\:of\:smaller\: rectangle=13\times 8[/tex]

[tex]Area\:of\:smaller\: rectangle=104\:square\:units[/tex].

The two triangles are identical, so we find the area of one and multiply by 2

[tex]Area\:of\:triangle=\frac{1}{2}\times base \times heigth[/tex]

[tex]Area\:of\:triangle=\frac{1}{2}\times 6 \times 8[/tex]

[tex]Area\:of\:triangle=3 \times 8[/tex]

[tex]Area\:of\:triangle=24\:square\:units[/tex]

[tex]\Rightarrow Area\:of\:the\:two\:triangles=2\times24=48\:square\:units[/tex]

The area of the figure is

[tex]=125+104+48=277\:sqaure\:units[/tex]

The correct answer is C

Answer:

r(p(x))=73

Step-by-step explanation:

To find the value of r(p(x)), the equation for p(x) which is 2x + 1, is substituted into every place that there is a x in the equation of r(x).

[tex]r(x)=4x-3\\r(p(x))=4(2x+1)-3\\r(p(x))=8x+4-3\\r(p(9))=8(9)+4-3\\r(p(9))=73[/tex]

Answer:

d

Step-by-step explanation:

Answer:

A. Barry spends $9 on lunch daily.

Step-by-step explanation:

We are required,

To find the situation in which one constant is changing at a constant rate in relation to the other quantity.

So, according to the options, we have,

A. Barry spends $9 on lunch daily.

Let x= number of days and as the cost of lunch each day is $9

Then, the total cost of the lunch y, is [tex]y=9x[/tex]

Thus, this situation changes the variable with constant rate.

B. The market value of a new computer decreases by 6% every year.

Let, a= fixed initial value of the computer and x= number of years.

Since, the rate of decrease in value = 6% = 0.06

Then, the market value of the computer per year, y, is given by,

[tex]y=a(1-0.06)^x\\\\y=a(0.94)^x[/tex]

Thus, this situation changes the variable exponentially.

C. Nathan's investments increase in value by 13.5% each month.  

Let, a= fixed initial investment and x= number of months.

Since, the rate of increase = 13.5% = 0.135

Then, the investment per month, y, is given by,

[tex]y=a(1+0.135)^x\\\\y=a(1.135)^x[/tex]

Thus, this situation changes the variable exponentially.

D. The number of ants in a colony doubles every 8 weeks.

Let, x= number of weeks where 'x' belongs to the se {1,8,16,24,...}.

Since, the number of ants is doubling every 8 weeks.

So, the number of ants in the colony, y, is [tex]y=2^x[/tex]

Thus, this situation changes the variable exponentially.

The equation of the plane containing the two given lines is found by calculating the normal vector through the cross product of direction vectors and then using the normal vector with a point from the lines to form the plane's equation, which is 26x + y - 7z = 53.

To find the equation of a plane that contains two given lines, we must first find two direction vectors that represent the lines. In this case, we are given the lines r1(t) = (2, 1, 0) + t(1, 2, 4) and r2(t) = (2, 1, 0) + t(4, 1, 15). The direction vectors for these lines are (1, 2, 4) and (4, 1, 15), respectively. To find the normal vector to the plane, we take the cross product of these two direction vectors.

Let's calculate the cross product:
(1, 2, 4) * (4, 1, 15) = (2*15 - 4*1, 4*4 - 15*1, 1*1 - 2*4) = (26, 1, -7).

The normal vector to the plane is (26, 1, -7), which also represents the coefficients of the variables in the plane's equation. Since both lines pass through the point (2, 1, 0), we can use this point and the normal vector to find the plane's equation.

The general form of the plane's equation is 'Ax + By + Cz + D = 0', where (A, B, C) is the normal vector to the plane. Plugging in the point (2, 1, 0) and the normal vector (26, 1, -7), we get:

26*(x - 2) + 1*(y - 1) - 7*(z - 0) = 0
26x - 52 + y - 1 - 7z = 0
26x + y - 7z = 53

And this is the Equation to the required plane containing the two given lines.

Answer:

1 over 14

Step-by-step explanation:

The sectors labeled are B, Y, G, C, P, F, O, V, M, A, D, E, H, and R.

Total number of sectors = 14.

When Victoria spins the spinner 18 times, and it stops at the letter B 10 times.

When Victoria spins the spinner  the theoretical probability that this time it will stop at the letter B = Favourable  outcomes ÷total numner of outcomes.

Favourable outcomes =1 and Total number of outcomes = 14.

Hence Theoritical Probability = 1 over 14.

The linearization L(x) of the function y=e8xln(x) at a=1, is given by L(x) = f(a) + f'(a)(x - a). Following the steps of calculating the function at a=1, determining its derivative and evaluating this at a=1, then substituting these into the linearization formula, this comes out to be L(x) = 1 + 8(x - 1).

The linearization of a function at a point is approximately equivalent to the function's tangent line at that point. The formula for linearization, L(x), can be given as L(x) = f(a) + f'(a)(x - a). In this case, find the linearization L(x) of y=e8xln(x) at a=1. To do this, we'll follow a step-by-step process:

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To solve the expression 1/7 - 3(3/7n - 2/7), distribute the 3 to the terms inside the parentheses, simplify the expression inside the parentheses, and combine like terms to get the simplified form of 7n - 1/7.

To solve the expression 1/7 - 3(3/7n - 2/7), we need to follow the order of operations which is Parentheses, Exponents, Multiplication and Division (from left to right), and finally Addition and Subtraction (from left to right).

First, distribute the 3 to the terms inside the parentheses: 1/7 - (9/7n - 6/7).

Next, simplify the expression inside the parentheses: 1/7 - 9/7n + 6/7.

Finally, combine like terms by subtracting and adding the fractions: 7n - 1/7.

So, the simplified form of the expression 1/7 - 3(3/7n - 2/7) is 7n - 1/7.

Final answer:

The algebraic expression 1/7 - 3(3/7n - 2/7) can be simplified by distributing the -3 and combining like terms to yield a final expression of 1 - 9/7n.

Explanation:

The student is asking for help in solving an algebraic expression. The problem given is 1/7 - 3(3/7n - 2/7). To solve this, we need to apply the distributive property and then simplify the expression. Here's how we can solve it step by step:

Distribute the -3 to the terms inside the parenthesis: -3 * (3/7)n = -9/7n and -3 * (-2/7) = 6/7.

The expression now becomes 1/7 - 9/7n + 6/7.

Combine like terms, which are the constant fractions: 1/7 + 6/7 = 7/7 = 1.

The final simplified expression is 1 - 9/7n.

The equivalent factored form of 12x4 - 42x3 - 90x2 is 6x(x - 5)(2x + 3).

The equivalent factored form of 12x4 - 42x3 - 90x2 is 6x(x - 5)(2x + 3).

We can factor out the greatest common factor, which is 6x. That leaves us with 2x3 - 7x2 - 15x.

Then we can factor by grouping, which involves grouping terms that have a common factor. By factoring out an x from the first two terms, we get x(2x2 - 7x - 15). By factoring out a -5 from the last two terms, we get -5(2x2 - 7x - 15). This gives us the final factored form of 6x(x - 5)(2x + 3).

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To find the number of nickels for the tenth frame, we calculate 5  imes 5^9, which equals 9,765,625 nickels. This is a geometric sequence where the common ratio is 5, and the first term for the first frame is 5 nickels.

The question asks about the payment received for making picture frames where the payment is multiplied by 5 for each subsequent frame. To find out the number of nickels for the tenth frame, we can use the concept of geometric sequences, where each term is found by multiplying the previous term by a common ratio. The common ratio in this case is 5.

For the first frame, you get 5 nickels. For the second frame, 5 multiplied by 5 is 25 nickels. To find the payment for the tenth frame, we multiply the payment of the first frame by the common ratio to the power of the frame number minus one: 5  imes 5^(10-1) = 5  imes 5^9.

Calculating 5 to the power of 9 gives us 1,953,125. Multiplying this by 5 gives us 9,765,625 nickels for the tenth frame.

I'm guessing its A:

If tomorrow is not my birthday, tomorrow is not Monday                        

Answer:

1 and 3/2 or 1 and 1 1/2

Step-by-step explanation:

3➗3=1 and 11➗11= 1 so a. is 1/1 or 1.

9/10➗3/5 or 9➗3=3 and 10➗5=2 so it is 3/2 or 1 1/2 so the answers are 1 and 1 1/2! Hope this helps.

Final answer:

The area of a circle with a radius of 2m is 12.56 m² and the circumference is 12.56 m when using 3.14 for π, with both answers having two significant figures due to the radius given with two significant figures.

Explanation:

The area (A) and the circumference of a circle with radius 2m can be found using the formulas A = πr² and C = 2πr. Using 3.14 as the value for π, the calculations would be A = (3.14)(2m)² = 12.56 m² for the area, and C = 2(3.14)(2m) = 12.56 m for the circumference. It is important to note that when performing calculations, the result should have the same number of significant figures as the quantity with the fewest significant figures used in the calculation.