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3 years ago

What is the circumference of the circle if r = 3,5 feet?

Mathematics

1 answer:

Nady [450]3 years ago

8 0

Answer:

21.98

Step-by-step explanation:

C=2πr C=2d are the formulas of circumference so that would mean the diameter of the circle is 7 since 2 times the radius is the diameter. We then multiply the diameter 7 by PI to get 21.98

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Everett is rolling a block with the numbers 1, 2, 3, 4, 5, and 6 on it. Finley is drawing one disk from a basket of three disks:

ioda

Option A:

The probability that Everett and Finley end up with an even number and a blue disk is $\frac{1}{6}$ .

Solution:

Given data:

Everett is rolling a block with numbers = {1, 2, 3, 4, 5, 6}

Finley is drawing one disk from basket with colors = {blue, red, yellow}

Total number of numbers = 6

Total number of colors = 3

$$\text { Probability }=\frac{\text {Number of possible outcomes}}{\text {Total number of outcomes}}$

$P\text{(Even number)} =\frac{3}{6}$

$P\text{(Blue disk)} =\frac{1}{3}$

$P\text{(Even number and Blue disk)} =\frac{3}{6}\times\frac{1}{3}$

$$=\frac{3}{18}$

Divide numerator and denominator by the common factor 3.

$$=\frac{3\div3}{18\div3}$

$$=\frac{1}{6}$

Option A is the correct answer.

Hence the probability that Everett and Finley end up with an even number and a blue disk is $\frac{1}{6}$ .

3 0

3 years ago

Which of the following graphs shows the solution set for the inequality below? 3|x + 1| < 9

Bas_tet [7]

Step-by-step explanation:

The absolute value function is a well known piecewise function (a function defined by multiple subfunctions) that is described mathematically as

$f(x) \ = \ |x| \ = \ \left\{\left\begin{array}{ccc}x, \ \text{if} \ x \ \geq \ 0 \\ \\ -x, \ \text{if} \ x \ < \ 0\end{array}\right\}$ .

This definition of the absolute function can be explained geometrically to be similar to the straight line $\textbf{\textit{y}} \ = \ \textbf{\textit{x}}$ , however, when the value of x is negative, the range of the function remains positive. In other words, the segment of the line $\textbf{\textit{y}} \ = \ \textbf{\textit{x}}$ where $\textbf{\textit{x}} \ < \ 0$ (shown as the orange dotted line), the segment of the line is reflected across the x-axis.

First, we simplify the expression.

$3\left|x \ + \ 1 \right| \ < \ 9 \\ \\ \\\-\hspace{0.2cm} \left|x \ + \ 1 \right| \ < \ 3$ .

We, now, can simply visualise the straight line, $y \ = \ x \ + \ 1$ , as a line having its y-intercept at the point $(0, \ 1)$ and its x-intercept at the point $(-1, \ 0)$ . Then, imagine that the segment of the line where $x \ < \ 0$ to be reflected along the x-axis, and you get the graph of the absolute function $y \ = \ \left|x \ + \ 1 \right|$ .

Consider the inequality

$\left|x \ + \ 1 \right| \ < \ 3$ ,

this statement can actually be conceptualise as the question

$``\text{For what \textbf{values of \textit{x}} will the absolute function \textbf{be less than 3}}"$ .

Algebraically, we can solve this inequality by breaking the function into two different subfunctions (according to the definition above).

Case 1 (when $x \ \geq \ 0$ )

$x \ + \ 1 \ < \ 3 \\ \\ \\ \-\hspace{0.9cm} x \ < \ 3 \ - \ 1 \\ \\ \\ \-\hspace{0.9cm} x \ < \ 2$

Case 2 (when $x \ < \ 0$ )

$-(x \ + \ 1) \ < \ 3 \\ \\ \\ \-\hspace{0.15cm} -x \ - \ 1 \ < \ 3 \\ \\ \\ \-\hspace{1cm} -x \ < \ 3 \ + \ 1 \\ \\ \\ \-\hspace{1cm} -x \ < \ 4 \\ \\ \\ \-\hspace{1.5cm} x \ > \ -4$

*remember to flip the inequality sign when multiplying or dividing by

negative numbers on both sides of the statement.

Therefore, the values of x that satisfy this inequality lie within the interval

$-4 \ < \ x \ < \ 2$ .

Similarly, on the real number line, the interval is shown below.

The use of open circles (as in the graph) indicates that the interval highlighted on the number line does not include its boundary value (-4 and 2) since the inequality is expressed as "less than", but not "less than or equal to". Contrastingly, close circles (circles that are coloured) show the inclusivity of the boundary values of the inequality.

3 0

3 years ago

Amy has a piece of wood that measures 42 inches. The model shows the length remaining after she cut a piece from the 42-inch pie

Hitman42 [59]

Answer:

She has 42 pieces of wood each of 1 inch of length.

Step-by-step explanation:

Amy has 42 inches piece of wood.

She has to cut an inch.

After cutting pieces of inch each she counts the pieces to be 42.

Mathematically

Total length / unit lenght = Number of pieces

42 inches/ 1 inch= 42 pieces.

She has 42 pieces of wood each of 1 inch of length.

6 0

3 years ago

What color is a carrot

777dan777 [17]

Answer:

uh i think its a carrot uh

Step-by-step explanation:

uhh

5 0

3 years ago

Read 2 more answers

BRAINLIEST + 20 POINTS!!!!!!!!!!!! THANKS AND 5 STAR RATING!!!!!!!!!!!

vesna_86 [32]

Answer:

3 and 5/16

Step-by-step explanation:

3+(2+8)2-:4*((1)/(2))^(4)=53/16

3 0

3 years ago