The diameter of a circle is 222 units. What is the radius of the circle?

Answer:

Step-by-step explanation:

x^2 - 17 x + 60

we should find two numbers such that their sum is equal to -17 and product is equal to 60

The two numbers are -12 and -5

now, x^2 - 12 x - 5 x + 60 { splitting the middle term }

x ( x- 12 ) - 5 ( x - 12 )

= ( x - 5 ) ( x - 12 )

hope this helps

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Answer:

Step-by-step explanation:

\(x^2-17x+60\quad \implies\quad a=1\,,\quad b=-17\,,\quad c=60\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\dfrac{-(-17)\pm\sqrt{(-17)^2-4\cdot1\cdot60}}{2\cdot1}=\dfrac{17\pm\sqrt{289-240}}{2}=\dfrac{17\pm\sqrt{49}}{2}\\\\x_1=\dfrac{17-7}{2}=5\quad,\qquad x_2=\dfrac{17+7}{2}=12\\\\\\x^2-17x+60=(x-5)(x-12)\)

or:

    x² - 17x + 60 =

= x² - 12x - 5x +60 =

= x(x - 12) - 5(x - 12) =

= (x - 12)(x - 5)

Answer:

4 is a factor. Also, (3n - 5) is a factor.

The factored form of 12n - 20 is:

4(3n - 5)

Step-by-step explanation:

We're looking for the biggest number (sometimes its a variable with the biggest exponent, but not this time)

that goes into 12n and also goes into 20. 4 is the biggest number that goes into both 12n and 20. So we factor it out...this is like "un-distributive property" (if you have been studying distributive property, this is like reversing it)

12n - 20

= 4(3n - 5)

The value of b in the equation (a+b)m/c - K = p/r can be found by evaluating (p/r * c - am + Kc) divided by m.

Starting with the equation:

(a+b)m/c - K = p/r

First, multiply both sides of the equation by c to eliminate the denominator:

(a+b)m - Kc = p/r * c

Next, distribute the m to the terms inside the parentheses:

am + bm - Kc = p/r * c

Rearrange the equation to isolate the term containing b:

bm = p/r * c - am + Kc

Finally, divide both sides of the equation by m to solve for b:

b = (p/r * c - am + Kc) / m

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Answer:

204

Step-by-step explanation:

3.4[6(4)+6^2]=

3.4[24+36]=

3.4[60]=

204

Hope this helps!

Answer:

D

Step-by-step explanation:

all answers are x = 0. If we put 0 instead of X.

y=0^4+3×0^3-2×0+7

y=0+0+0+7

y=7

Answer:

1. 7

2. 12

3. 31

4. 1

Step-by-step explanation:

The probability that exactly one 6 is rolled is 42.9%

Rolling a six-sided dice and an eight-sided die can yield a variety of results. The probability of rolling exactly one 6 out of the two dice is 6/14, or approximately 42.9%.

This is calculated by taking the total number of ways to roll one 6 (6) and dividing it by the total number of combinations possible (14). This means that there is a 42.9% chance of rolling one 6 when two dice are rolled.

The probability will be calculated by:

6/14

= 0.429

0.42× 100

=42.9

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1. 8/3
2. 16/3
3. 123

*some words for 20 symbols*

Answer:

Step-by-step explanation:

The range is the set of second numbers of the ordered pairs.

  {-5, 1, 4, 5}

__

The domain is the set of first numbers of the ordered pairs.

  {-5, -3, 0, 2}

__

Additional comment

It is generally convenient to write the elements of a set in sorted order.

\( \orange{\underline{\huge{\bold{\textit{\green{\bf{QUESTION}}}}}}} \)

What do these fractions add up to?

\( \huge\mathbb{\red A \pink{N}\purple{S} \blue{W} \orange{ER}}\)

\( \red{\mathbb{EQUATION-->}}\)

\( \frac{9}{16} + \frac{1}{2}\\ \blue{ \mathbb { {LCM}}}\\ \frac{9}{16} + \frac{1 \times 8}{2 \times 8} \\ \frac{9}{16} + \frac{8}{16} \\ \frac{9 + 8}{16} \\ \frac{17}{16} \)

The answer is 17 out of 16

To deduce if two line segments are parallel, we need to examine their corresponding angles. Therefore,  "none." is correct.

According to the information given, we have a missing value represented by m7. To find if any line segments are parallel, we can use the following rules:

1. If two lines are intersected by a transversal, and corresponding angles are congruent, then the lines are parallel.

2. If two lines are intersected by a transversal, and alternate interior angles are congruent, then the lines are parallel.

3. If two lines are intersected by a transversal, and alternate exterior angles are congruent, then the lines are parallel.

Let's consider each statement one by one:

Statement 1: m7 = 90 degrees. This statement represents a right angle. However, knowing that one angle is right does not provide enough information to deduce the lines' parallelism.

Statement 2: m7 = 135 degrees. This statement represents an angle greater than 90 degrees. Similarly, having this information alone is insufficient to deduce the lines' parallelism.

Statement 3: m7 = 45 degrees. This statement represents an angle less than 90 degrees. Again, having this information alone is not enough to deduce the lines' parallelism.

Given the information provided, we cannot deduce the parallelism of any line segments. Therefore,  "none." is correct.

In summary, without additional information about the relationships between angles formed by the line segments, we cannot determine whether the line segments are parallel or not.

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The matrix of the relation r={(1,2),(2,3),(3,4),(4,5)} on the set x={1, 2, 3, 4, 5}; ordering of x:1,2,3,4,5 is as follows.

\($$\begin{pmatrix} 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 \end{pmatrix}$$\)

A relation is a set of ordered pairs.

The matrix of a relation is constructed by using its ordered pairs with their respective values as its entries, and its rows and columns by its domain and range, respectively.

So, the relation r is given as{(1,2),(2,3),(3,4),(4,5)}

The elements in the rows of the matrix correspond to the elements of x, while the elements in the columns of the matrix correspond to the elements of x as well, in that order.

So, the matrix of r on x can be written as:

\($$\begin{pmatrix} 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 \end{pmatrix}$$\)

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Ndidi rides y km at 10 km/hr, then walks 0.5y km at 3 km/hr. She is away from. home less than 4hours.Range of the values of Y is =24/7

Let's call the total time spent riding and walking t hours. We know that t is less than 4 hours, so:

t = time spent riding + time spent walking < 4 hours

The time spent riding is given by y / 10 km/hr and the time spent walking is given by 0.5y / 3 km/hr. So, we can write the inequality as:

t = y / 10 + 0.5y / 3 < 4

Expanding and simplifying the expression on the left side gives:

7/6y < 4 * 6/7

Multiplying both sides by 6/7 gives:

y < 4 * 6/7 * 6/7 = 24/7

So, the range of values of y is 0 < y < 24/7 km. This means that Ndidi rode less than 24/7 km, but more than 0 km.

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The unconditional mean E(Y) of the autoregressive model AR(1) is 10.5.

To compute the unconditional mean E(Y) of the autoregressive model AR(1) given by 1.05 + 0.9Y + ε, we can use the property of linearity in expectation and solve for the mean value.

The model can be rewritten as:

Y = (1.05 + ε) / (1 - 0.9)

Since ε follows a normal distribution with mean 0 and variance 0.01, we know that E(ε) = 0.

Using the linearity of expectation, we can compute the unconditional mean E(Y) as follows:

E(Y) = E((1.05 + ε) / (1 - 0.9))

= (1.05 + E(ε)) / (1 - 0.9)

= 1.05 / (1 - 0.9)

= 1.05 / 0.1

= 10.5

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Step-by-step explanation:

\(ĀB = (12 \times 2) \\ = 24\)

Answer:

noooooooooooooooooooooooooooo

Step-by-step explanation:

yeahhhhhhhhhhhhhhhhhhhhhhhhhhhh

The correct option is A, the lower quartile (Q1) and it is 75.

We must comprehend the quartiles of the box plot in order to calculate the number below which 25% of the data lies.

A box plot's interquartile range (IQR), which contains the middle 50% of the data, is represented by the box.

The median, which splits the data into two equally sized half, is shown by the line inside the box.

Here, the box has a line at 79 and spans from 75 to 82.

Accordingly, the lower quartile (Q1) and the upper quartile (Q3) are both situated near the box's boundary, which is 75 and 82, respectively.

The line inside the box, which is 79, is the median (Q2).

The first quartile (Q1) or the 25th percentile must be identified in order to establish the number below which 25% of the data lies.

The first quartile in a box plot symbolizes the number below which 25% of the data is found.

Since Q1 is located at the lower boundary of the box, which is 75, 25% of the data lies below the score of 75.

Hence the correct option is A.

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Answer:

10 × 2/5 = 20/5 = 4

Step-by-step explanation:

When you are multiplying a whole (big) number times a fraction, you multiply the whole (big) number times the TOP number (numerator) and put that on top. Keep the bottom number (denominator) the same.

10 × (2/5)

= (10×2) / 5

= 20/5

= 4

The standard deviation for a chi square distribution for given degree of freedom is 7.0711.

The chi-square distribution is parameterized by the number of degrees of freedom (df). As the number of degrees of freedom increases, the shape of the distribution becomes more symmetrical and approaches a normal distribution.

The standard deviation (σ) of a chi-square distribution with k degrees of freedom is given by the formula:

σ = sqrt(2k)

Therefore, for a chi-square distribution with 25 degrees of freedom:

σ = sqrt(2(25)) = sqrt(50) ≈ 7.0711

Rounding this to four decimal places gives a standard deviation of approximately 7.0711.

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Given:

Nana has a water purifier that filters \(\dfrac{1}{3}\) of the contaminants each hour.

Water has contaminants = \(\dfrac{1}{2}\)

To find:

The function that gives the remaining amount of contaminants in kilograms, C(t), t hours after Nana started purifying the water.

Solution:

Let C(t) be the remaining amount of contaminants in kilograms after t hours.

Initial amount of contaminants = \(\dfrac{1}{2}\)

Decreasing rate is \(\dfrac{1}{3}\) .

Using the exponential decay model:

\(C(t)=C_0(1-r)^t\)

where, \(C_0\) is initial amount of contaminants, r is the decreasing rate and t is time in hours.

Substituting the values, we get

\(C(t)=\dfrac{1}{2}(1-\dfrac{1}{3})^t\)

\(C(t)=\dfrac{1}{2}(\dfrac{2}{3})^t\)

Therefore, the required function is \(C(t)=\dfrac{1}{2}(\dfrac{2}{3})^t\).

Answer:

\(\frac{1}{2} (\frac{2}{3} )^t\)

Step-by-step explanation:

It's correct on Khan.

Answer:

what

Step-by-step explanation:

theres no answers?

Answer:

(A) A trend line can be used to make predictions in real-world situations.

(B) A scatterplot that shows no correlation between the variables does not have a trend line.

(D) A regression line and trend line are equivalent terms.

Step-by-step explanation:

Answer:

Kelly's mistake is y > 2x-1

She can fix by the inequality: y ≥ 2x-1

Step-by-step explanation:

y ≥ 2x-1

y ≤ -x+5

y > 2x-1 should be greater than less than; y ≥ 2x-1 to point (2,3)

Answer:

J' = -3, -3

K' = -3, 4

Step-by-step explanation:

You can count the vertices to the left by 6 and down by 3

Or you can subtract

J' = 3 - 6  ,  0 - 3

K' = 3 - 6  , 7 - 3

The equation  -x + 3 = y has a slope of 1 and a y-intercept of 3. The equation y = 1 - 3r has a slope of -3 and a y-intercept of 1. The equation  X = y has a slope of 1 and a y-intercept of 0. The equation y = 3x - 1 has a slope of 3 and a y-intercept of -1.

To identify the slope and y-intercept of each linear function's equation, we can rewrite the equations in slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.
Let's go through each equation step by step:
1. -x + 3 = y:
To rewrite this equation in slope-intercept form, we need to isolate y on one side. Adding x to both sides, we get 3 + x = y. Now the equation is in the form y = x + 3. The slope, m, is 1, and the y-intercept, b, is 3.
2. y = 1 - 3r:

This equation is already in slope-intercept form, y = mx + b. The slope, m, is -3, and the y-intercept, b, is 1.
3. X = y:
To rewrite this equation in slope-intercept form, we need to isolate y. Subtracting x from both sides, we get -x + y = 0. Rewriting, we have y = x. The slope, m, is 1, and the y-intercept, b, is 0.
4. y = 3x - 1:
This equation is already in slope-intercept form, y = mx + b. The slope, m, is 3, and the y-intercept, b, is -1.

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Step-by-step explanation:

To solve both questions you will have to use the Pythagoras theorem

\( {c}^{2} = {a}^{2} + {b}^{2} \)

c being the hypotenuse

so to find AB we say

\( {ap}^{2} = {pb}^{2} + {ab}^{2} \)

To make AB the subject of the formula, we take PB over. Therefore:

\( {ab}^{2} = {ap}^{2} - {pb}^{2} \)

now we just substitute

\( {ab}^{2} = {13}^{2} - {5}^{2} \)

\( {ab}^{2} = 169 - 25\)

\( {ab}^{2} = 144\)

square root both sides of the equation

\(ab = 12\)

We then use the same formula to find AQ(which is a hypotenuse)

\( {aq}^{2} = {ab}^{2} + {bq}^{2} \)

\( {aq}^{2} = {12}^{2} + {9}^{2} \)

\( {aq}^{2} = 144 + 81\)

\( {aq}^{2} = 225\)

square root both sides

\(aq = 15\)

Answer:

essentially the answer is 33