Olga wrote all the natural numbers from 1 to k. Including 1 and k. How many numbers did she write?

"The value of [tex]\angle1 +\angle3[/tex] lies between [tex]90^{\circ} < \angle1+\angle3< 180^{\circ}[/tex].

[tex]\angle 1,\angle2, \angle3[/tex] have the following relationships.

We have to find the sum of measure of [tex]\angle1[/tex] and the measure of [tex]\angle3[/tex].

We know that the angle sum property of triangle states that the sum of all angles of a triangle is equal to [tex]180 ^{\circ}[/tex].

[tex]\angle 1+\angle 2+\angle3= 180^ {\circ}[/tex]

[tex]\angle1+\angle3= 180-\angle2[/tex]

So, the value [tex]\angle1 and \angle3[/tex] is always greater than [tex]90{^\circ}[/tex] because [tex]\angle 3[/tex] is the obtuse angle and it is being added to [tex]\angle1[/tex],

so it is always greater than right angle and less than [tex]180^{\circ}[/tex].

Hence the value of [tex]\angle1 +\angle3[/tex] lies between [tex]90^{\circ} < \angle1+\angle3< 180^{\circ}[/tex].

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Answer:

1/2

50%

Step-by-step explanation:

Answer:

Step-by-step explanation:

Volume = πr2h/3

radius of the cone is 11 inches

height of the cone is 4.5 inches

V= (3.14 *(121)*4.5)/3= 569.91 inches3

The correct answer is 2000 mm.

To convert the length of the gold wire from meters to millimeters, one must know the conversion factor between these two units. There are 1000 millimeters in 1 meter. Therefore, to convert 2 meters to millimeters, one multiplies the length in meters by 1000.

Calculation:

2 meters * 1000 millimeters/meter = 2000 millimeters

Thus, the length of the gold wire in millimeters is 2000 mm.

To find the rate of change of the interval (3,10) for the given function, you need to calculate the difference in the function values at those two time points and divide it by the difference in time. The rate of change of the interval (3,10) is: ((900(1 + 0.4^10)) - (900(1 + 0.4^3))) / (10 - 3)

The given function f(t) = 900(1 + 0.4^t) models an investment of $900 at a rate of 4% over time, where t represents time in years. To find the rate of change of the interval (3,10), you need to find the difference in the function values at those two time points and divide it by the difference in time.

So, the rate of change of the interval (3,10) is:

((900(1 + 0.4^10)) - (900(1 + 0.4^3))) / (10 - 3)

Answer:

k = +- 2sqrt(J)

Step-by-step explanation:

This is the correct answer, I just took the test and this is right!

Answer:

7(8x+5) ≠48x+35 when x = 2.

That is; the two expressions are not equivalent when x = 2

Step-by-step explanation:

To solve this, we need to follow the steps below

We will substitute x = 2 in the first  expression and simplify, then we will now substitute x =2 in the other expression and simplify, at the end of the simplification, we will compare the two expression to see if they are equal.

First lets open up the bracket, that is; 7(8x + 5)=56x + 35

Now substitute x = 2 in 56x + 35

56 x + 35 = 56(2) + 35 = 112 + 35 = 147

56 x + 35 = 147   when x = 2

Next is to substitute x = 2 in 48x + 35

48(2) + 35 =96 + 35 =131

The value of 48x + 35 = 131   when x =2

147 ≠ 131

Therefore the two expressions are not equivalent when x = 2

The number 16 is 4/5 fractional part of 20.

What is mean by Fraction?

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

Let the fraction part of 16 = x

So, We can formulate;

⇒ 16 = x × 20

⇒ x = 16 / 20

⇒ x = 4/5

Thus, The number 16 is 4/5 fractional part of 20.

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General Idea:

We need to apply the below formula to find the trend line from the given x and y values.

[tex] (1)\; mean:\; \bar{x}\;=\;\frac{\sum x_i}{n}, \; \;\bar{y}\;=\;\frac{\sum y_i}{n}\\ \\ (2) \;trend\; line: \; y=A+Bx, \;B=\frac{S_{xy}}{S_{xx}}, \;\;A=\bar{y}-B\bar{x}\\ \\ Where:\\ \\ S_{xx}=\frac{\sum x_i^2}{n}-\bar{x}^2\\ \\S_{xy}=\frac{\sum x_iy_i}{n}-\bar{x} \cdot \bar{y} [/tex]

Applying the concept:

In the graph given the trend line passes through two points (1, 8) and (7, 1).

We need to make use of the two point formula to find the equation of trend line

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

Substituting the points (1, 8) and (7, 1) in the above formula to find slope we get...

[tex] m = \frac{1-8}{7-1}=\frac{-7}{6} [/tex]

The point slope form of an equation which is used to write the equation of line when we know a point and slope is given below:

[tex] y-y_1=m(x-x_1) [/tex]

Substituting the values in the above formula we get ...

[tex] y-8=\frac{-7}{6}(x-1)\\Distributing \; -7/6\; in\; the\; right\; side\; of\; the\; equation \\ \\ y-8=\frac{-7}{6}x+\frac{7}{6}\\ Adding\; 8\; on\; both\; sides\\ \\ y-8+8=\frac{-7}{6} x+\frac{7}{6} +8\\ Combining \; like \; terms\\ \\ y=\frac{-7}{6}x+\frac{7}{6}+\frac{8 \cdot 6}{1 \cdot 6}\\ \\ y=\frac{-7}{6}x+\frac{7}{6}+\frac{48}{6}\\ \\ y=\frac{-7}{6} x+\frac{55}{6} [/tex]

Conclusion:

The equation best represents a trend line for the scatter plot is Option B.

B. y=−7/6x+55/6

Dividing 98.52 by 10 involves moving the decimal one place to the left, resulting in 9.852. This process is the same for all decimals when dividing by powers of 10, such as 10, 100, or 1000.

When we divide a number by powers of 10, we're effectively moving the decimal point to the left by as many places as there are zeros in the power of ten. For instance, dividing 1.9436 by 10 moves the decimal one place to the left, becoming 0.19436. Similarly, dividing 98.52 by 10 moves the decimal one place to the left as well, giving us the simplified answer of 9.852.

If we were to multiply a number by powers of 10, we would do the opposite, moving the decimal to the right. For example, to multiply 45.86 by 100, you would move the decimal two places to the right to get 4586.

In conclusion, 98.52 divided by 10 is 9.852. Even if the answer is rounded, the process remains the same; you simply adjust the decimal point accordingly based on the power of 10 you are dividing by.

Answer:A and D

Step-by-step explanation: