Evaluate the left hand side to find the value of a in the equation in simplest form.

9514 1404 393

Answer:

  3/5

Step-by-step explanation:

Let a, b, c represent the probability of a win by Kaden, Keith, and Kipp, respectively.

  P(bc' | a') = P(a'bc')/P(a')

  P(bc' | a') = (1/2)/(1 -1/6) = (3/6)/(5/6) = 3/5

The probability is 3/5 that Keith beats Kipp when Kaden doesn't win.

Answer:

Step-by-step explanation:

If the diameter is 4 meters, then the radius has to be 2 because the radius is half of the diameter.

Answer:

11 buses

Step-by-step explanation:

Answer:

  b.  40

Step-by-step explanation:

You want the missing leg length in a right triangle with one side of length 9 and the hypotenuse of length 41.

The missing side of any triangle will be between the sum and difference of the other two side lengths.

  c-a < b < c+a

  32 < b < 50

In a right triangle, every side length is less than the length of the hypotenuse:

  b < c

  32 < b < 41

There is only one answer choice in this range: b = 40.

__

Additional comment

You can make use of your knowledge of Pythagorean triples. One of them is {9, 40, 41}, which tells you that b=40.

Or, you can use the Pythagorean theorem to compute b:

  a² +b² = c²

  9² +b² = 41²

  b² = 1681 -81 = 1600

  b = √1600 = 40

For any odd integer, there is a Pythagorean triple with sides 1 unit apart such that those longer side lengths are about half of the square of that odd integer:

  9² = 81 = 40+41

so {9, 40, 41} is a Pythagorean triple.

The simplest of these is ...

  3² = 9 = 4+5   ⇒   {3, 4, 5} is a Pythagorean triple.

\(y \leqslant 2\)

The vertical component is 442.314.

The horizontal component is 309.731.

A vector is a quantity or phenomenon that has two independent properties: magnitude and direction.

Given:

A gun can fire a bullet at 540 m/s.

angle = 55 degrees

Horizontal component

=540 cos 55

=540 * 0.5735

=309.731

Vertical Component

=540 sin 55

=540* 0.8191

=442.314

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Answer:

It's C

Step-by-step explanation:

Answer:

C The third image

Step-by-step explanation:

edge

The sample mean of 4.21 cm is significantly different from the specified target mean of 4.00 cm.

Step 1: State the hypotheses.

- Null Hypothesis (H₀): The mean length of the bolts is 4.00 cm (μ = 4.00).

- Alternative Hypothesis (H₁): The mean length of the bolts is not equal to 4.00 cm (μ ≠ 4.00).

Step 2: Compute the value of the test statistic.

To compute the test statistic, we will use the z-test since the population standard deviation (σ) is known, and the sample size (n) is large (n = 121).

The formula for the z-test statistic is:

z = (X- μ) / (σ / √n)

Where:

X is the sample mean (4.21 cm),

μ is the population mean (4.00 cm),

σ is the population standard deviation (0.83 cm), and

n is the sample size (121).

Plugging in the values, we get:

z = (4.21 - 4.00) / (0.83 / √121)

z = 0.21 / (0.83 / 11)

z = 0.21 / 0.0753

z ≈ 2.79 (rounded to two decimal places)

Step 3: Determine the critical value and make a decision.

With a level of significance of 0.02, we perform a two-tailed test. Since we want to determine if the mean length of the bolts is different from 4.00 cm, we will reject the null hypothesis if the test statistic falls in either tail beyond the critical values.

For a significance level of 0.02, the critical value is approximately ±2.58 (obtained from the z-table).

Since the calculated test statistic (2.79) is greater than the critical value (2.58), we reject the null hypothesis.

Conclusion:

Based on the computed test statistic, there is sufficient evidence to show that the manufacturer needs to recalibrate the machines. The sample mean of 4.21 cm is significantly different from the specified target mean of 4.00 cm, indicating that the machine's output is not meeting the desired length. The manufacturer should take action to recalibrate the machines to ensure the bolts meet the required length of 4.00 cm.

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When a shape is reflected, it must be reflected over a line

The reflection rule is: \(R_{x = 2}(\triangle D EF) = \triangle D'E'F\)

The coordinates of the preimage are:

D(3,6), E(-4,-3), F(6,1)

The coordinates of the image are:

D'(1,6), E'(8,-3), F'(-2,1)

From the given coordinates, we have the following observations

This is shown as follows:

D(3,6) and D'(1,6)

The y-coordinate is:

\(y = 6\)

The average of the x-coordinates

\(x = \frac{3 + 1}{2}\)

\(x = 2\)

E(-4,-3) and E'(8,-3)

The y-coordinate is:

\(y = -3\)

The average of the x-coordinates

\(x = \frac{-4 + 8}{2}\)

\(x = 2\)

F(6,1) and F'(-2,1)

The y-coordinate is:

\(y =1\)

The average of the x-coordinates

\(x = \frac{6 -2}{2}\)

\(x = 2\)

Since the y-coordinates remains unchanged and the average of the x-coordinates is 2.

Then, we can conclude that the triangle was reflected over line \(x = 2\)

Hence, the reflection rule is:

\(R_{x = 2}(\triangle D EF) = \triangle D'E'F\)

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Four triangles can create a set of pattern blocks that includes a total of four rhombuses.

To understand why, it's essential first to understand what pattern blocks are. Pattern blocks are shapes that are commonly used in early childhood education to teach math concepts like geometry, spatial reasoning, and fractions. They come in different shapes, including triangles, squares, hexagons, trapezoids, and rhombuses.

To create a set of pattern blocks using triangles, one can use four equilateral triangles with the same side length. When these triangles are arranged together, they form a larger equilateral triangle, as each external side of each small triangle connects to a side of another triangle. This larger equilateral triangle can then be divided into four smaller rhombuses by using two diagonals (lines connecting opposite corners) to form a "X" shape. Each of these four smaller rhombuses is made up of two adjacent triangles and forms a diamond shape. Therefore, it can be said that four equilateral triangles can form a set of four rhombuses within an equilateral triangle pattern block set.

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Answer:

63°

Step-by-step explanation:

༻﹡﹡﹡﹡﹡﹡﹡༺

hope it helps...

have a great day!!

Step-by-step explanation:

5x - 5° = 40° ( being vertically opposite angles)

5x = 40° + 5°

5x = 45°

x = 45°/ 5

x = 9°

Now

< 1 = 5 * 9° - 5 = 45° - 5° = 40°

Hope it will help :)

Let's assume that the corresponding side of the second triangle is \(\displaystyle\sf x\).

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Therefore, we can set up the following proportion:

\(\displaystyle\sf \left( \dfrac{x}{6.3} \right)^{2} =\dfrac{49}{81}\)

To find \(\displaystyle\sf x\), we can solve the proportion above:

\(\displaystyle\sf \left( \dfrac{x}{6.3} \right)^{2} =\dfrac{49}{81}\)

Taking the square root of both sides:

\(\displaystyle\sf \dfrac{x}{6.3} =\sqrt{\dfrac{49}{81}}\)

Simplifying the square root:

\(\displaystyle\sf \dfrac{x}{6.3} =\dfrac{7}{9}\)

Cross-multiplying:

\(\displaystyle\sf 9x = 6.3 \times 7\)

Dividing both sides by 9:

\(\displaystyle\sf x = \dfrac{6.3 \times 7}{9}\)

Calculating the value:

\(\displaystyle\sf x = 4.9\)

Therefore, the corresponding side of the second triangle is \(\displaystyle\sf 4.9 \, cm\).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

Step-by-step explanation:

let's assume that the corresponding side of the second triangle is .

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Therefore, we can set up the following proportion:

To find , we can solve the proportion above:

Taking the square root of both sides:

Simplifying the square root:

Cross-multiplying:

Dividing both sides by 9:

Calculating the value:

Therefore, the corresponding side of the second triangle is 4.9cm


hope it helped u dear...........

Answer:

Step-byHow do I calculate the mean?

The mean can be calculated only for numeric variables, no matter if they are discrete or continuous. It's obtained by simply dividing the sum of all values in a data set by the number of value

-step explanation:

46+57+66+63+49+52+61+68= 462/8 the total number of observation

the answer 57

Step-by-step explanation:

the distance between 3D points is basically following the same principle as in 2D.

we sum the squares of the x-, y- and z- coordinates and pull the square root of that sum.

distance² = (4 - -3)² + (7 - 5)² + (10 - -1)² = 49 + 4 + 121 =

= 174

distance = sqrt(174) = 13.19090596... ≈ 13.19

Answer:

1 / 5

Step-by-step explanation:

Given that:

Number of white marbles = 5

Number of blue marbles = 3

Number of green marbles = 7

Required is the approximate probability of drawing 2 green marbles, Note that drawing is done without replacement :

Probability = required outcome / Total possible outcomes

Total possible outcomes = sum of all marbles = (5 + 3 + 7) = 15 marbles

First draw:

P(Green) = 7 / 15

Second draw:

Required outcome = 7 - 1 = 6

Possible outcomes = 15 - 1 = 14

P(green) = 6 / 14

Probability of drawing out two green marbles :

(7/15 * 6/14) = 42 / 210 = 1 / 5

Answer: g(x) = 6*x^2 + 15

Step-by-step explanation:

Suppose that we have a function y = f(x)

A vertical stretch by a factor of K is written as:

g(x) = K*f(x).

In this case, we have f(x) = 2*x^2 + 5.

And we know that g(x) is a f(x) after a stretch by a factor of 3.

Then we get:

g(x) = 3*f(x) = 3*(2*x^2 + 5) =  3*2*x^2 + 3*5 = 6*x^2 + 15

g(x) = 6*x^2 + 15

If g(t) is cut in half, then t is doubled. Halving the growth factor halves the rate of growth, reducing the time required for a generation to develop to full size.

Growth factor refers to a mathematical expression or a metric that measures the rate of increase or growth of a quantity over time. It is used in many fields such as biology, economics, finance, and others to quantify the increase in size, population, revenue, or any other variable of interest. The growth factor can be represented as a ratio, percentage, or an exponential function and is used to predict future growth based on past trends.

3 potential points

Three tries are permitted.

If g(t) is divided in half, t is also divided in half. This is because the growth factor is a measure of the rate of growth, and halving it equals halves the rate of growth. As a result, the time required for a generation to develop to full size is cut in half.

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For figure {0}, the number of tiles will be equal to 2.

Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function

Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Equation : A mathematical equation is used to equate two expressions.

Given is a graph as shown in the image.

The line passes through point -

(3, 8) and (4, 10)

So, the slope of the line will be -

m = (10 - 8)/(4 - 3)

m = 2

y = 2x + c

For the point (3, 8), we can write -

8 = 6 + c

c = 2

For figure {0}, the number of tiles will be equal to 2.

Therefore, for figure {0}, the number of tiles will be equal to 2.

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The next three numbers of sequence is,

⇒ 2.8, 8.4, 8.2

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The sequence is,

⇒ 0.4, 0.2, 0.6, 0.4, 1.2, 1.0, 3.0, .., .., ...,

Now,

Since, The sequence is,

⇒ 0.4, 0.2, 0.6, 0.4, 1.2, 1.0, 3.0, .., .., ...,

Clearly, The pattern of the sequence is,

⇒ 0.4 - 0.2 = 0.2

⇒ 0.2 × 3 = 0.6

⇒ 0.6 - 0.2 - 0.4

⇒ 0.4 × 3 = 1.2

⇒ 1.2 - 0.2 = 1.0

⇒ 1.0 × 3 = 3.0

⇒ 3.0 - 0.2 = 2.8

⇒ 2.8 × 3 = 8.4

⇒ 8.4 - 0.2 = 8.2

Thus, Next three terms of the sequence is,

⇒ 2.8, 8.4, 8.2

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Answer:

increases by 30

Step-by-step explanation: its right

1. The probability of selecting a 3 of Diamonds is 1/52.

2. The probability of selecting a Club or Diamond is 1/2.

3. The probability of selecting a number smaller than 9 is 9/13.

1. The probability of selecting a 3 of Diamonds:

There is only one 3 of Diamonds in the deck, and the total number of cards in the deck is 52. Therefore, the probability of selecting a 3 of Diamonds is 1/52.

2. The probability of selecting a Club or Diamond:

There are 13 Clubs and 13 Diamonds in the deck, making a total of 26 cards. The probability of selecting a Club or Diamond is the ratio of the number of favorable outcomes (Club or Diamond) to the total number of possible outcomes (52 cards). Therefore, the probability is 26/52, which simplifies to 1/2.

3. The probability of selecting a number smaller than 9:

There are four suits in the deck (Clubs, Diamonds, Hearts, and Spades), and each suit has cards numbered 2 to 10. So, there are 4 suits * 9 cards per suit = 36 cards that are numbered smaller than 9.

The probability of selecting a number smaller than 9 is the ratio of the number of favorable outcomes (36 cards) to the total number of possible outcomes (52 cards). Therefore, the probability is 36/52, which simplifies to 9/13.

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Using the normal approximation to the binomial, it is found that the probabilities are given as follows:

a) 0.0055 = 0.55%.

b) 0.2296 = 22.96%.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The parameters of the binomial distribution are given as follows:

n = 150, p = 0.889.

Hence the mean and the standard deviation of the approximation are:

Item a:

Using continuity correction, the probability is P(123.5 < X < 124.5), which is the p-value of Z when X = 124.5 subtracted by the p-value of Z when X = 123.5, hence:

X = 124.5:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{124.5 - 133.35}{3.8473}\)

Z = -2.3

Z = -2.3 has a p-value of 0.0107.

X = 123.5:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{123.5 - 133.35}{3.8473}\)

Z = -2.56

Z = -2.56 has a p-value of 0.0052.

Hence the probability is 0.0107 - 0.0052 = 0.0055 = 0.55%.

Item b:

The probability is P(112.5 < X < 130.5), which is the p-value of Z when X = 130.5 subtracted by the p-value of Z when X = 112.5, hence:

X = 130.5:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{130.5 - 133.35}{3.8473}\)

Z = -0.74

Z = -0.74 has a p-value of 0.2296.

X = 112.5:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{112.5 - 133.35}{3.8473}\)

Z = -5.42

Z = -5.42 has a p-value of 0.

Hence the probability is 0.2296 - 0 = 0.2296 = 22.96%.

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Sides:

5n

12n

13n

If n is 1 the triangle have sides: 5, 12, 13

The converse of the pythagorean theorem is: If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle:

Then, a triangle with sides 5, 12, 13 is a right triangle.

If n is 2 the triangle have sides: 10,24, 26

converse of the pythagorean theorem:

Triangle with n=1 and n=2 are similars as the ratio between corresponding side is equal:

Then, with any value of n the triangles are similar triangles.

Similar triangles have different sizes but the correpondign angles are the same (are congruent).

As triangles with sides 5n, 12n, 13n are similar triangles (All of then have the same measure on his correspondig angles) and makes true the Pythagorean theorem, they are right triangles.

Explanation:

5x - 4y + 2z = 21 ...equation 1

-x - 5y + 6z = -24 ....equation 2

-x - 4y + 5z = -21 ...equation 3

Using elimination method:

multiply equation 2 by 5:

-5x - 25y + 30z = -120 ....equation 2a

add equation 2a from 1:

5x - 5x -4y -25y + 2z + 30z = 21 - 120

0 - 29y + 32z = -99

-29y + 32z = - 99 ....equation 4

multiply equation 3 by 5:

-5x - 20y + 25z = -105 ...equation 3a

add equation 1 and 3a

5x - 5x - 4y - 20y + 2z +25z = 21 - 105

0 - 24y + 27z = -84

-24y + 27z = -84 ...equation 5

-29y + 32z = - 99 ....equation 4 (×-24)

-24y + 27z = -84 ...equation 5 (×-29)

696y - 768x = 2376 ...(4a)

696y -783x = 2436 ...(5a)

subtract 5a from 4a

696y - 696y -768x -(-783x) = 2376 - 2436

0 - 768x + 783x = -60

15x = -60

x = -60/15

x = -4

substitute for x in equation 4a:

696y - 768(-4) = 2376

696y + 3072 = 2376

696y = 2376 -3072

696y = -696

y = -696/696

y = -1

substitute for y in equation 4:

-29(-1) + 32z = -99

29 + 32z = -99

32z = -99 - 29

32z = -128

z = -128/32

z = -4

The values of the angles given are: 0,90,180,240,270,360,420,480,540,600,630,660,720 and

he sine of an angle is the trigonometric ratio of the opposite side to the hypotenuse of a right triangle containing that angle.  It is defined as the length of the opposite side divided by the length of the hypotenuse

The given angles are: 0,30,45,90,120,135,180,210,225,240,270,300,315,330,360

2∅  2*∅ = 0, 90,180,240,270,360,420,480,540,600,630,660,720

sin 2∅ = sin0 = 0; Sin90=1;  sin180=0; sin240= -0.8660; sin270 = -1;

Each angle is multiplied by sine sine360 =1; sin420 = 0.8660; sin480= 0.9848; sin540=1; sin600=-0.8660; sin630=-1; sin660=0.8660; sin720= 0.9397

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Answer:

A

Step-by-step explanation:

edge

\(Z_{1} +Z_{2}\) represents Point A i.e., 3i.

Complex numbers are the numbers that are expressed in the form of

a + ib where, a, b are real numbers and  ‘i’ is an imaginary number called “iota”. The value of i = (√-1). For example, 2+3i is a complex number, where 2 is a real number (Re) and 3i is an imaginary number (Im).

Given

The complex numbers z1 and z2 are graphed.

From the graph,

\(Z_{1} =3+i\)

\(Z_{2} =-3+2i\)

\(Z_{1} +Z_{2}= 3+i+(-3+2i)\)

\(Z_{1} +Z_{2}= 3-3+i+2i\)

\(Z_{1} +Z_{2}= 3i\)

Option A is correct.

\(Z_{1} +Z_{2}\) represent Point A i.e., 3i.

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