Given: m POR = 147° ​

Answer:

24.59 m/s

Step-by-step explanation:

Average speed(m/s) = distance travelled(m) / time taken(s)

Distance = 220 miles

220 miles = 354,056 meters

Time taken = 4 hours

4 hours = 14,400 seconds

Average speed = distance travelled / time taken

= 354,056 / 14,400

= 24.59 meter/seconds

= 24.59 m/s

Expression: 5z² - 2z + 1 = 0

Discriminant formula: b²- 4ac

Identify: a = 5, b = -2, c = 1

Solve for discriminant: (-2)²- 4(5)(1) = 4 - 20 = -16

p = 1 also can be rewritten as 2nd equation: 0m + 1p = 1

Build Augment Matrices by taking coefficient's:

\(\left[\begin{array}{ccc}1&-1&|| \ \ 2\\0&1&|| \ \ 1\end{array}\right]\)

Solve:

Add row 2 to row 1 : R₁ = R₁ + R₂ and restore it back

\(\rightarrow \ \left[\begin{array}{ccc}1+0&-1+1& \ \ \ \ || \ 2+1\\0&1&|| \ \ 1\end{array}\right]\)

\(\rightarrow \ \left[\begin{array}{ccc}1&0& || \ \ 3\\0&1&|| \ \ 1\end{array}\right] \ \ \ = The \quad reduced \quad matrix\)

Solution = (m, p) = (3, 1)

Answer:

14.  -16

15.  m = 3  and  p = 1

Step-by-step explanation:

Discriminant

\(b^2-4ac\quad\textsf{when}\quad ax^2+bx+c=0\)

Given equation:   \(5z^2-2z+1=0\)

Therefore:

Substituting the values into the discriminant:

\(\begin{aligned}\implies b^2-4ac & = (-2)^2-4(5)(1)\\& = 4-20\\& = -16\end{aligned}\)

As the discriminant is negative, this implies there are no real roots.

Augmented Matrices

\(\begin{array}{c}ax+by=p \\cx+dy=q\end{array} \implies \left[\begin{array}{r r | r}a & b & p \\ c & d & q\end{array}\right]\)    

Use elementary row operations to convert into:

\(\left[\begin{array}{r r | r}1 & 0 & h \\ 0 & 1 & k\end{array}\right] \implies \begin{array}{r}x=h\\y=k\end{array}\)

Given:

\(\begin{aligned}m-p & =2\\ p & = 1\end{aligned} \implies \left[\begin{array}{r r | r}1 & -1 & 2 \\ 0 & 1 & 1\end{array}\right]\)

\(\left[\begin{array}{r r | r}1 & -1 & 2 \\ 0 & 1 & 1\end{array}\right] \begin{array}{c}R_1 + R_2 \rightarrow R_1 \\\rightarrow\end{array} \left[\begin{array}{r r | r}1 & 0 & 3 \\ 0 & 1 & 1\end{array}\right]\)

Therefore:  

\(m=3\)

\(p=1\)

The probability of randomly selecting a number that is less than 12 is 11/100 option third tartFraction 11 over 100 EndFraction is correct.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

A box contains cards that are numbered from 1 to 100.

Total number of outcomes = 100

The number less than 12: = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}

Total number of favorable outcomes = 11

The probability = 11/100

Thus, the probability of randomly selecting a number that is less than 12 is 11/100 option third tartFraction 11 over 100 EndFraction is correct.

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Rounded to four decimal places, the p-value is 0.0844.

To determine the p-value for this hypothesis test, we need to follow these steps:

Step 1: State the null and alternative hypotheses.

Null hypothesis: The percentage of readers who own a laptop is 26%.

Alternative hypothesis: The percentage of readers who own a laptop is different from 26%.

Step 2: Determine the test statistic.

We can use a z-test for proportions since we have a large enough sample size and we know the population proportion. The formula for the test statistic is:

z = (p - p) / √(p(1-p) / n)

where p is the sample proportion, p is the hypothesized population proportion, and n is the sample size.

Using the given values, we have:

z = (0.17 - 0.26) / √(0.26(1-0.26) / 100)

z = -1.72

Step 3: Determine the p-value.

Since this is a two-tailed test, we need to find the area in both tails of the standard normal distribution that corresponds to a z-score of -1.72. Using a table or a calculator, we find that the area in the left tail is 0.0422 and the area in the right tail is also 0.0422.

Therefore, the p-value is the sum of the areas in both tails:

p-value = 0.0422 + 0.0422

p-value = 0.0844

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Answer:

b = \(\frac{2}{9}\)

c = \(\frac{4}{9}\)

Step-by-step explanation:

There are two 6 on the board out of 9 numbers

There are four numbers greater than 10 out of the nine possiblilites

Answer:

x=20-21

x= -1

hope helps... :)

Answer:

y = - 3x + 11

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope ( gradient ) and c the y- intercept )

here m = - 3 , then

y = - 3x + c ← is the partial equation

to find c substitute (2, 5 ) into the partial equation

5 = - 3(2) + c = - 6 + c ( add 6 to both sides )

11 = c

y = - 3x + 11 ← equation of line

Answer:

Can I Know Which Language Is This??

Answer:

(0, 1)

Step-by-step explanation:

y > 3x - 1

When x = 0:   y > (3 x 0) - 1  ⇒  y > -1

When x = 1:    y > (3 x 1) - 1  ⇒   y > 2

When x = 2:   y > (3 x 2) - 1  ⇒  y > 5

Therefore the only point that satisfies this is (0, 1)

Answer:

Step-by-step explanation:

Attached is the graphical solution.

We can see one point is within the shaded area -  (0, 1), all the others are outside.

For the given scenario: the Probability of making both shots are A. 0.64 and B. 0.72

a) If a player makes 80% of his foul shots, the probability of making a single foul shot is 0.8. Since the two shots are considered independent events, the probability of making both shots is the product of the individual probabilities.

Therefore, the probability of making both shots is 0.8 * 0.8 = 0.64.

To calculate the probability of making exactly one shot, we need to consider two scenarios: making the first shot and missing the second, or missing the first shot and making the second. Each scenario has a probability of 0.8 * 0.2 = 0.16.

Therefore, the probability of making exactly one shot is 0.16 + 0.16 = 0.32.

Similarly, the probability of missing both shots is 0.2 * 0.2 = 0.04.

b) In this case, the outcome of the second shot depends on the outcome of the first shot. If the player makes the first shot (with a probability of 0.8), the probability of making the second shot is 0.9.

Therefore, the probability of making both shots is 0.8 * 0.9 = 0.72.

If the player misses the first shot (with a probability of 0.2), the probability of making the second shot is 0.7.

Therefore, the probability of making exactly one shot is 0.2 * 0.7 = 0.14.

Since there are only two possible outcomes (making both shots or making exactly one shot), the probability of neither shot being made is 1 - (0.72 + 0.14) = 0.14.

Therefore, for the given scenario:

a) Probability of making both shots: 0.64

  Probability of making exactly one shot: 0.32

  Probability of missing both shots: 0.04

b) Probability of making both shots: 0.72

  Probability of making exactly one shot: 0.14

  Probability of missing both shots: 0.14

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Answer:

Yes OFC

Step-by-step explanation:

As you can see at the 12-second mark the graph shows 1466 wave length for air so the density of the mass will be subtracted from the height

Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

Answer:

b and c

Step-by-step explanation:

since the slope of the graph is pages edited/time, we know that the slope (or rate) of pages edited will be 3 pages every 5 minutes since the slope is constant. is the slope is 3/5 we can determine that it will be

0.6pages edited/1min

Answer:

10403.

Step-by-step explanation:

To find the smallest number that isn't prime and doesn't any factors smaller than 100, we need to multiply the 2 smallest prime numbers greater than 100. The smallest prime number greater than 100 is 101, but we cannot multiply 101 by itself, as the number would become a square. Because of this, we need to multiply 101 by the next smallest prime number, which is 103.

After multiplying 101 by 103, we get 10403.

To check our answer, we can verify each point.

10403 is not prime, as it has 2 factors, 101 and 103.

10403 is not square, as the square root of 10403 is 101.9951.

10403 has 2 factors 101 and 103, both of which are greater than 100.

The prime factorisation of √25 = 5

The prime factorisation of √441 = 21

The simplest form of √25 / 441 is 5 / 21

simplify √25 / 441

Using indices method,

\(\sqrt[n]{ab} = \sqrt[n]{a} .\sqrt[n]{b}\)

Therefore,

The prime factorisation of √25 = 5

The prime factorisation of √441 = 21

The expression √25 / 441 in the simplest form is as follows:

√25 / 441 = 5 / 21

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Answer:

Here are your answers .......

The prime factorisation of √25 = 5

The prime factorisation of √441 = 21

The simplest form of √25 / 441 = 5 / 21

Step-by-step explanation:

Answer:

The 63rd Term Is 309

Step-by-step explanation:

Answer:

1) A and B

2) B only

Step-by-step explanation:

1) In mathematics, a linear equation is an equation that may be put in the form \( {\displaystyle a_{1}x_{1}+\ldots +a_{n}x_{n}+b=0, } \) where \(x_{1}\), \(\ldots, x_{n}\) are the variables, and\( {\displaystyle b, a_{1}, \ldots, a_{n}} \)are the coefficients, which are often real numbers.

Therefore, in the first question only A and B are the answers

The equation of the line that passes through (3, 19) and (9, 25) will be y = x + 16.

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).

Then the equation of the line is given as,

\(\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)\)

The points are given below.

(3, 19) and (9, 25)

The equation of the line that passes through (3, 19) and (9, 25) will be given as,

(y - 25) = [(25 - 19) / (9 - 3)](x - 9)

y - 25 = (6/6)(x - 9)

y - 25 = x - 9

y = x - 9 + 25

y = x + 16

The equation of the line that passes through (3, 19) and (9, 25) will be y = x + 16.

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Answer:

23.3

Step-by-step explanation:

The equation y = -3x - 19 (slope-intercept form) in Ax + By = C form is 3x + y = 19.

The slope-intercept form of a linear equation is a way to express a linear equation in the form y = mx + b, where y represents the dependent variable, x represents the independent variable, m represents the slope of the line, and b represents the y-intercept.

According to the given information:

The given equation, y = -3x - 19, is already in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. However, to write it in the Ax + By = C form, also known as the standard form of a linear equation, we need to rearrange it.

The standard form of a linear equation is Ax + By = C, where A, B, and C are constants, and A is usually required to be a positive integer or zero.

To convert y = -3x - 19 into standard form, we can follow these steps:

Step 1: Move all the terms to one side of the equation.

y + 3x = -19

Step 2: Multiply all the terms by -1 to make the coefficient of x positive.

-1(y + 3x) = -1(-19)

-y - 3x = 19

Step 3: Rewrite the equation with positive coefficients for x and y.

3x + y = 19

So, the equation y = -3x - 19 in Ax + By = C form is 3x + y = 19.

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Answer:

13.5 inches.

Step-by-step explanation:

Hope this helps! :)

A person who studies or involves in stduy and writes word, logic, or mathematical puzzles is known as an Enigmatologist.

In short form, the use of the term Enigmatologist is a general term for anyone who deals with any puzzle science, such as mathematics. However, the word occultism is a new coin coined nearly 30 years ago by the American Will Shortz, the only trained occultist in the world. Shortz graduated from Indiana University with a degree in riddles in 1974 and is now a columnist for the New York Times after many years as editor of the American magazine Games. Hence, someone who studies and writes mathematical, word or logic puzzles.

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Answer:

The decimal is 17.74

Step-by-step explanation:

Answer:

11. 24+25pi

12. 28

Step-by-step explanation:

Triangle area: 8 x 6 x 1/2=24 ft^2

Semi circle area: 5^2pi

Figure area: 24+25pi

12. Count outer squares:  28

In order to simplify and verify trig identities, one needs to use the rules of trigonometry and algebra to manipulate the equation until it is in a simplified form.

The most common trig identities to remember include the Pythagorean identity, reciprocal identities, quotient identities, and sum and difference identities. When simplifying an equation, it is important to remember to include the negative sign when necessary and to factor out any common factors.

After simplifying, it is important to verify the equation. This can be done by plugging in known values for the variables and verifying that the equation is true. By utilizing the rules of trigonometry and algebra, one can simplify and verify trig identities. This process is essential for working with trigonometric functions.

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Answer:

55 MPH

Step-by-step explanation:

55 x 2.4 = 132

33 x 4 = 132

The dissociation curve is a graphical representation of the relationship between the fractional saturation of hemoglobin (Y-axis) and the partial pressure of oxygen (X-axis) under specific conditions. It provides important information about the binding and release of oxygen by hemoglobin.

The dissociation curve for hemoglobin exhibits a sigmoidal (S-shaped) shape. At low partial pressures of oxygen, such as in tissues, hemoglobin has a low affinity for oxygen and only binds a small amount. As the partial pressure of oxygen increases, hemoglobin's affinity for oxygen increases, resulting in a rapid increase in the binding of oxygen molecules. However, once the hemoglobin becomes nearly saturated with oxygen, the curve levels off, indicating that further increases in partial pressure have minimal effects on oxygen binding.

To calculate the fractional saturation of hemoglobin at a given partial pressure of oxygen, you can use the Hill equation:

Y = [O2]^n / ([O2]^n + P50^n)

Where:

Y is the fractional saturation of hemoglobin,

[O2] is the partial pressure of oxygen,

P50 is the partial pressure of oxygen at which hemoglobin is 50% saturated,

n is the Hill coefficient, which represents the cooperativity of oxygen binding.

To determine the P50 value experimentally, the partial pressure of oxygen at which hemoglobin is 50% saturated, you can plot the dissociation curve and identify the point where the curve reaches 50% saturation.

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To calculate the probability that at least two people in a class of 30 share the same birthday, we can use the complement rule, which states that the probability of an event happening is equal to one minus the probability of the event not happening.

If we assume that birthdays are uniformly distributed throughout the year (i.e., each day is equally likely to be someone's birthday), then the probability that no two people in the class share the same birthday is:

365/365 * 364/365 * 363/365 * ... * 336/365

This is because the first person can have any birthday (probability of 365/365), the second person must have a different birthday (probability of 364/365), the third person must have a different birthday than the first two (probability of 363/365), and so on, up to the 30th person, who must have a different birthday than the first 29 (probability of 336/365).

Calculating this probability gives us:

(365/365) * (364/365) * (363/365) * ... * (336/365) ≈ 0.2937

So the probability that no two people in the class share the same birthday is approximately 0.2937.

Using the complement rule, the probability that at least two people in the class share the same birthday is:

1 - 0.2937 = 0.7063

Therefore, the probability that at least two people in a class of 30 share the same birthday is approximately 0.7063, or 70.63%.

To express (3x)2 in radical form, we start by understanding that raising a number to the power of 2 means multiplying the number by itself. In this case, we have (3x)2, which means we need to multiply 3x by itself.

Step 1: Multiply 3x by itself: (3x) * (3x) = 9x²

So, (3x)2 can be expressed in radical form as √(9x²).

The expression 29x10 cannot be expressed in radical form because there is no power or exponent involved. Radical form is used to represent expressions with roots or exponents.

To express W13 in radical form, we need to understand that the expression 7^(1/9) represents the ninth root of 7.

Step 1: Take the ninth root of 7: ∛7

So, W13 can be expressed in radical form as ∛7.

(3x)2 can be expressed in radical form as √(9x²).
29x10 cannot be expressed in radical form because there is no power or exponent involved.
W13 can be expressed in radical form as ∛7.
To express an expression in radical form, we need to understand the power or exponent involved and apply the appropriate radical operation.

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Answer:

equal to x

Step-by-step explanation: