A tabletop in the shape of a trapezoid has an area of 5,658 square centimeters. Its longer base measures 119 centimeters, and the shorter base is 65 centimeters. What is the height?
The height of the tabletop is
centimeters.

The good estimate of the volume of the cone is 56.70 cubic inches whose radius is 1.9 inches and height of the wooden cone is 15 inches.

It is defined as the three-dimensional shape in which the base is a circular shape and if we go from circular base to top the diameter of the circle reduces and at the vertex, it becomes almost zero.

Yadira made a wooden cone with a radius of 1.9 inches and a height of 15 inches therefore,

The radius of the wooden cone r = 1.9 inches

The height of the wooden cone h = 15 inches

We know the volume of a cone is given by:

[tex]\rm V = \pi r^2 \frac{h}{3}[/tex]

Put the values of the r and h, we get:

   [tex]\rm V = \pi( 1.9^2) \frac{15}{3}[/tex]

V = 3.61×5×π

V = 56.70 cubic inches

Thus, the good estimate of the volume of the cone is 56.70 cubic inches whose radius is 1.9 inches and height of the wooden cone is 15 inches.

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Final answer:

The solution to the system of equations y = -1/5x + 1 and y = x + 4 is found by setting the equations equal to each other, solving for x, and then substituting back to find y. The solution is the ordered pair (-5, -1).

Explanation:

The student is asking to find the ordered pair that represents the best estimate for the solution to a system of linear equations. The given system of equations is: y = −1/5x + 1 and y = x + 4. To find the solution, we need to determine where the two lines intersect, which will give us the coordinates (x, y) of the solution.

To find the intersection, we can set the two equations equal to each other since they both equal y: −1/5x + 1 = x + 4. Then, we would solve for x:

Add 1/5x to both sides to get 1 = 6/5x + 4

Subtract 4 from both sides to get −3 = 6/5x

Multiply both sides by 5/6 to get x = −3 × (5/6)

Which simplifies to x = −5

Now we substitute x back into either of the original equations to find y. For instance, using the second equation y = x + 4, we find that:

y = (−5) + 4 = −1

Therefore, the ordered pair that is the solution to the system of equations is (-5, -1).

Answer:

17 heartbeats in 15 seconds as a unit rate is-

1.13 over 1

hope it is clear to you

When using elimination to solve the system of equations, subtracting the first equation from the second eliminates the y variable, resulting in the equation 3x = 3, which simplifies to x = 1.

When solving the system of equations by elimination, we align the equations vertically and subtract or add them to eliminate one of the variables. Let's consider the given system:

3x - y = 7
6x - y = 10

By subtracting the first equation from the second, we eliminate variable y. The subtraction works as follows:

(6x - y) - (3x - y) = (10) - (7)

Which simplifies to:

3x = 3

From this resulting equation, we can easily solve for x:

x = 3 / 3
x = 1

This is the first part of the solution. After finding the value of x, we substitute back into either of the original equations to solve for y.

The cost of the flour per ounce will be $0.06 per ounce. Then the correct option is A.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

A 5-pound of flour costs $4.80.

We know that in one pound, there are 16 ounces. Then the number of ounces in 5 pounds is calculated as,

⇒ 5 x 16

⇒ 80 ounces

Then the cost of the flour per ounce will be given as,

⇒ $4.80 / 80

⇒ $0.06 per ounce

The cost of the flour per ounce will be $0.06 per ounce. Then the correct option is A.

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The total cost is $2,260.

The question involves calculating the total cost of purchasing dining room furniture with an initial down payment and subsequent monthly payments. First, we account for the down payment: $1,900 (cash price) - $100 (down payment) = $1,800 remaining balance. This balance will be paid over 24 months at $90 per month, thus 24 * $90 = $2,160. The total cost of the furniture, including the down payment, would then be the sum of the down payment and the total of the monthly payments: $100 + $2,160 = $2,260.

The total cost of the dining room furniture with this payment plan is $2,260.00.

The total cost for the dining room furniture with the given payment plan.

1. Down Payment: $100.00

2. Monthly Installments: $90.00 for 24 months

Calculate the total cost of the furniture before any payments are made:

[tex]\[ \text{Cash Price} = \$1,900 \][/tex]

The total amount paid through monthly installments:

[tex]\[ \text{Monthly Installment} = \$90.00 \times 24 \text{ months} = \$2,160.00 \][/tex]

Finally, let's add the down payment to the total amount paid through installments to find the overall cost:

[tex]\[ \text{Total Cost} = \$100.00 + \$2,160.00 = \$2,260.00 \][/tex]

Final answer:

The equivalent expression to 15x+50, by factoring out the greatest common divisor, is 5(3x+10).

Explanation:

The question is asking for an equivalent expression to the linear algebraic expression 15x+50. By examining the coefficient and constant term, we note that both terms are divisible by 5. Therefore, we can factor out 5 to simplify the expression. The steps for simplification are as follows:

Find the greatest common divisor (GCD) of the coefficients, which in this case is 5.

Divide each term by the GCD.

Express the factored form using the distributive property.

By applying these steps:

The GCD of 15 and 50 is 5.

Dividing each term by 5 gives us 3x + 10.

Thus, we can write the expression as 5(3x + 10), which is equivalent to the original expression 15x + 50.

The matching of the given numbers to there standard notation is given as follows:

     232,000,000------ 2.32E8

     0.00000431 ------  4.31E-6

 2,320,000,000 ----- 2.32E9

 0.000000000000431 ----- 4.31E-13

We know that the standard  notation of a number is given by:

There must be only one digit before the decimal and rest after that.

Also, it there is a shift of the decimal to the right then the power goes to negative and positive if shift is to the left.

1)

        232,000,000

Here we have to take the decimal 8 digits from the left and the number in standard notation will be given by:

              [tex]2.32\times 10^8[/tex]

which is written as:  2.32E8

2)

      0.00000431

Here we have to shift the decimal 6 digits to the right.

Hence, the number is expressed as:

           [tex]4.31\times 10^{-6}[/tex]

which is written as: 4.31E-6

3)

       2,320,000,000

Here the decimal is to be put 9 digits from the left and hence the number is represented as:

           [tex]2.32\times 10^9[/tex]

which is given by: 2.32E9

4)

         0.000000000000431

Here we will shift the decimal 13 places to the right and hence the number is given by:

            [tex]4.31\times 10^{-13}[/tex]

which is given by:  4.31E-13

The height of Mel in the air is decreasing at a faster rate than victor's height in the air.

Given information:

Mel slides down water-slide A and Victor slides down water-slide B.

After 1 second, height achieved by [tex]\rm{Mel}= 50\; \text{Ft}[/tex]

After 5 seconds, the height remained is 35 feet.

In another case,

Now, the expression is used for evaluating the slope of the equation are formulated below:

[tex]\bold{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

Where, [tex]m[/tex] is the slope and [tex]x[/tex] and [tex]y[/tex] are respective coordinates.

Hence, for Mel's case, apply the formula of slope and solve it further:

[tex]\begin{aligned}m_1&=\dfrac{35-50}{5-2} \\m_1&=-5 \end{aligned}[/tex]

So, the rate of change of Mel's height is 5 feet per second.

And for victor's case, slope will be:

[tex]m_2=\dfrac{50-60}{4-1} \\\\m_2=-3.33[/tex]

The rate of change of victor's height is 3.33 feet per second.

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The answer is Jasons!

Answer:

Step-by-step explanation:

There are 3 data sets given as

I)   x                         7 8 9 10 11 12 13    Total

   Frequ                  1  2  1   2  2 0     2

Mean dev|x-10|*f    3 4  1   0    3  0   6      17

II)     x                         7 8 9 10 11 12 13    Total

   Frequ                     2  3 0  0  1  1   3

Mean dev|x-10|*f        6  6  0  0 1  2 9     24

III)   x                         7 8 9 10 11 12 13    Total

   Frequ                     0 0 4  4  1  0 1

Mean dev|x-10|*f        0  0 4 0 1  0 3        8

Thus we find the middle one Jason has the highest deviation.