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Answer:

[tex]\frac{45}{45}=1[/tex]    

[tex]1<\frac{6}{3}[/tex]

[tex]\frac{2}{7}<1[/tex]

[tex]\frac{64}{23}>1[/tex]

Step-by-step explanation:

Given the statements

we have to insert the greater than, less than, or equal sign to make each statement true.

[tex]\text{Statement 1: }\frac{45}{45}?1[/tex]

[tex]\frac{45}{45}...1[/tex]

[tex]1...1[/tex]

which are equal

∴ [tex]1=1[/tex]

[tex]\text{Statement 2: }1?\frac{6}{3}[/tex]

[tex]1...\frac{6}{3}[/tex]

[tex]1...2[/tex]

2 is greater than 1

∴ [tex]1<2[/tex]

[tex]\text{Statement 3: }\frac{2}{7}?1[/tex]

[tex]\frac{2}{7}...1[/tex]

[tex]0.286...1[/tex]

1 is greater than 0.286

∴ [tex]0.286<1[/tex]

[tex]\text{Statement 4: }\frac{64}{23}?1[/tex]

[tex]\frac{64}{23}...1[/tex]

[tex]2.783...1[/tex]

2.783 is greater than 1

∴ [tex]2.783>1[/tex]

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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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 y-intercept of a function is where the graph crosses the y-axis, represented by 'b' in the equation y = mx + b. If a table doesn't show x as zero, one can use the line of best fit by inserting the median x and y values and the slope into the formula b = y - mx to calculate the y-intercept.

The y-intercept of a continuous function can be understood as the point where the function's graph crosses the y-axis. It is typically represented by the variable b in the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept. In the context of the problem provided, if the student is examining a table of values representing a linear relationship, they should look for the value of y when x equals zero to determine the y-intercept directly.

However, if the data does not include an x-value of zero, they could use the line of best fit to calculate the y-intercept by plugging the median x and y values, along with the determined slope, into the formula b = y - mx, where y and x are the medians. For example, if given a slope (m) of 0.09, sum of median x values as 1264, and sum of median y values as 219.5, the y-intercept (b) would be calculated as b = 219.5 - 0.09(1264), which simplifies to approximately 35.25.

This calculation would be necessary if the student is working with data that does not directly provide a scenario where x = 0, such as exam scores or years in a dataset stating from year 1. It's important to note that in some real-world applications, a y-intercept may not be meaningful if the x-value cannot be zero, like in the case of time-based data where the year 0 does not exist.

The y-intercept of the continuous function is (-2). This means that the graph of the function intersects the y-axis at the point (0,-2).

The y-intercept of a continuous function represents the point where the graph of the function intersects the y-axis. In other words, it is the value of y when x is equal to zero.

Looking at the given points:

(0,-6), (-2, 0), (-6, 0), (0,-2), and 0

We can determine the y-intercepts by identifying the points where x is equal to zero.

Let's go through the points one by one:

1. (0,-6): This point does not have a y-intercept because the x-coordinate is not zero.

2. (-2, 0): This point also does not have a y-intercept because the x-coordinate is not zero.

3. (-6, 0): Again, this point does not have a y-intercept because the x-coordinate is not zero.

4. (0,-2): Finally, this point does have a y-intercept because the x-coordinate is zero. Therefore, the y-intercept is -2.

5. 0: This is not a point, but simply the value of zero. It does not have a y-intercept because it does not represent a point on the graph.

To summarize, the y-intercept of the continuous function is (-2). This means that the graph of the function intersects the y-axis at the point (0,-2).

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.

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.

Learn more about the cone here:

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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 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]

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.