Who invented algebra?

Answer and Step-by-step explanation:

It is in the picture.

Since x is less than -1, everything will be shaded to the left of the line that is made. The line would also be dotted since x is only less than and NOT less than or equal to.

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The probability that the exactly 5 are white and 2 are red is126/1716 and,

the probability that at least 5 of the balls are white is 133/1716

Given that:-

Total number of balls in the urn = 13

Number of white balls = 6

Number of red balls = 7

Number of randomly selected balls = 7

We have to find the probability that the exactly 5 are white and 2 are red and the probability that at least 5 of the balls are white.

Probability that exactly 5 balls are white and  2 are red, P(x = 5) = \(\frac{^6C_5*^7C_2}{^{13}C_7}\) = 126/1716 = 21/286

We know that,

Probability that atleast 5 balls are white = P(x = 5) + P(x = 6)

We know that,

P(x = 6) = \(\frac{^6C_6*^7C_1}{^{13}C_7}\) = 7/1716

Hence,

Probability that atleast 5 balls are white = 126/1716 + 7/1716 = 133/1716.

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Answer:

To find the square root of 0.327 up to 2 decimal places, you can use a calculator or mathematical software. The square root of 0.327 is approximately 0.57.

A. The student is no more than 65 inches tall P(x ≤ 65) = 0.5. B. The student is between 63 and 67 inches tall. P(63 ≤ x ≤ 67) = 34%. C. The student is between 61 and 69 inches tall. P1615 x ≤ 69) = 47.5%. D. The student is between 59 and 71 inches tall. P(59≤ x≤71) = 49.85%

Using the mean and standard deviation provided in Part A, we can standardize each of the given ranges to use the empirical rule, which states that for a normal distribution, approximately:

68% of the data falls within one standard deviation of the mean

95% of the data falls within two standard deviations of the mean

99.7% of the data falls within three standard deviations of the mean

To standardize a value x, we can use the formula: z = (x - μ) / σ, where μ is the mean and σ is the standard deviation.

a) To find P(x ≤ 65), we can standardize 65 using the formula above:

z = (65 - 65) / 2 = 0

Since z = 0, we can look up the corresponding probability in the standard normal distribution table, which is 0.5. Therefore, P(x ≤ 65) = 0.5.

b) To find P(63 ≤ x ≤ 67), we can standardize both values:

z1 = (63 - 65) / 2 = -1

z2 = (67 - 65) / 2 = 1

Using the empirical rule, we know that approximately 68% of the data falls within one standard deviation of the mean. Since our range is within one standard deviation of the mean, we can estimate that P(63 ≤ x ≤ 67) is approximately 68% / 2 = 34%.

c) To find P(61 ≤ x ≤ 69), we can standardize both values:

z1 = (61 - 65) / 2 = -2

z2 = (69 - 65) / 2 = 2

Using the empirical rule, we know that approximately 95% of the data falls within two standard deviations of the mean. Since our range is within two standard deviations of the mean, we can estimate that P(61 ≤ x ≤ 69) is approximately 95% / 2 = 47.5%.

d) To find P(59 ≤ x ≤ 71), we can standardize both values:

z1 = (59 - 65) / 2 = -3

z2 = (71 - 65) / 2 = 3

Using the empirical rule, we know that approximately 99.7% of the data falls within three standard deviations of the mean. Since our range is within three standard deviations of the mean, we can estimate that P(59 ≤ x ≤ 71) is approximately 99.7% / 2 = 49.85%.

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² = QR² - QT²

= 13² - 5²

= 169 - 25

= 144

TR = √144

TR = 12 cm

Menentukan panjang PR

PR = 2 × TR

= 2 × 12 cm

PR = 24 cm

For the function, the x-intercept of g(x) is at (5,0).

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input.

Given f(x) = ln(x)

and g(x) = -f(x - 4)

the function is

g(x) = -ln(x - 4)

when x = 5

g(x) = -ln(5 - 4)

g(x) = -ln1

g(x) = 0

the coordinates are (5, 0)

Hence the x-intercept is (5, 0).

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Answer:

A

Step-by-step explanation:

The ratio of yes votes to no votes is 4 to 7, which can be simplified to 2 to 7/2 or 2:3.5. This means that for every 3.5 no votes, there are 2 yes votes. Since there were 3794 no votes, there were 3794/3.5 = <<3794/3.5=1082>>1082 sets of yes and no votes.

The total number of votes is therefore 21082 + 3794 = <<21082+3794=6858>>6858 votes.

For finding a 95% confidence interval:

a) The sample mean is x = 16.13.

The sample standard deviation is s = 6.948.

The degrees of freedom are df = 10.

The critical value of t for a 95% confidence interval is t = 2.228.

The margin of error is ME = t × s/√n = 2.228(6.948)/√11 = 4.263.

The 95% confidence interval is x ± ME = 16.13 ± 4.263 = (11.867, 20.393).

b) The 95% confidence interval is (11.867, 20.393).

This means that we are 95% confident that the true population mean number of visits per physical therapy patient is between 11.867 and 20.393 visits.

c) This is because the confidence interval is a range of values that is likely to contain the true population mean. If many samples of the same size are taken from the same population, then about 95% of the confidence intervals from these samples will contain the true population mean.

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Step-by-step explanation:

s1 = 5

s2 = s1 × -2 = 5×-2 = -10

s3 = s2 × -2 = -10 × -2 = 20

...

now, we could do all that manually.

but there is also a formula for geometric sequence.

in fact, there are 2 - one for finite and one for infinite sequences.

and I was not completely honest, each of these 2 had some sub-forms depending on the size of the multiplier or ratio.

since we need the sum of the first 5 terms, which of the 2 do you think we need ?

of course, finite, because 5 is a normal number we can "touch". it is not infinity.

so, the formulas for finite sums of geometric sequences are :

if |r| < 1, Sn = a(1 - r^n)/(1 - r)

if |r| > 1, Sn = a(r^n - 1)/(r - 1)

if r = 1, Sn = na

if r = -1, then Sn = a or 0 depending on if n is odd or even.

the sequence is in general

s1 = a

sn = sn-1 × r

in our case a = 5, r = -2.

so, what form of the formula do we need ?

|-2| = 2, and 2 > 1, so ...

S5 = 5(-2^5 ‐ 1)/(-2 - 1) = 5(-32 - 1)/-3 = 5×-33/-3 =

= 5 × 11 = 55

quick check, as the 5 terms are

5

-10

20

-40

80

and their sum is : 55

correct !

Arithmetic operations provide meaningful results for variables that c. are quantitative.

For all real numbers, the four fundamental arithmetic operations in mathematics are: Finding the sum in addition ('+') Subtraction (Difference-finding; "-" Multiplication (Identifying the result; "" Finding the quotient in division (")

The commutative laws of addition and multiplication, such as a + b = b + a and ab = ba, the associative laws of addition and multiplication, such as a + (b + c) = (a + b) + c and a(bc) = (ab)c, as well as the distributive law, which links addition and...

Therefore, option C is correct.

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The measure of three angles of triangular backyard are 28°, 31°  and 121°.

Given that, a home has a triangular backyard.

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

Let the measure of first angle be x.

The second angel of the triangle is 3 more than the first angel = x+3

The third angel is 9 more than four times the first angel = 4x+9

Using angle sum property of a triangle

x+x+3+4x+9 = 180°

⇒ 6x + 12 = 180

⇒ 6x = 168

⇒ x = 28°

So, x+3 = 31° and 4x+9 = 121°

Therefore, the measure of three angles of triangular backyard are 28°, 31°  and 121°.

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The value of length BC is 18.9

Cosine Rule states that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

Therefore,

c² = a² + b² - 2abcosC

To find the length BC we use cosine rule.

c² = 13² + 7² - 2(13)(7)cos140

c² = 218 - 182cos140

c² = 218-(-139.42)

c² = 218+139.2

c² = 357.2

c = √357.2

c = 18.9

Therefore, the length of BC is 18.9

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In the triangle, the value of the side BC is 18.9cm to 1 decimal place

The side BC can be found using the cosine formula, Remember that Cosine Rule states that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

The cosine formula states that

c² = a² + b² - 2abcosC

To find the length BC we use cosine rule.

c² = 13² + 7² - 2(13)(7)cos140

c² = 218 - 182cos140

c² = 218-(-139.42)

c² = 218+139.2

c² = 357.2

c = √357.2

c = 18.9

In conclusion, the value of  the length of BC is 18.9cm

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Question 24 :

P594.65 : 35 days

P594.65/7 : 35/7 days

P84.95 : 5 days

⇒ A. P84.95

Question 25 :

88.75 + 85.5 + 90.5 + 87.25 / 4

352/4

88

⇒ B. 88

Question 26 :

I = P × r × t

I = 580.00 × 0.065 × 1

I = P37.70

⇒ B. P37.70

Answer:

13

Step-by-step explanation:

use distance formula \(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\d= \sqrt{(7-2)^2+(7-(-5))^2} =13\)

Answer:

4 5/8

Step-by-step explanation:

Rewriting our equation with parts separated

=4+12+18

Solving the fraction parts

12+18=?

Find the LCD of 1/2 and 1/8 and rewrite to solve with the equivalent fractions.

LCD = 8

48+18=58

Combining the whole and fraction parts

4+58=458

Answer:

The answer is 32.63

Step-by-step explanation:

Answer:

= −26.97

Step-by-step explanation:

Answer:

B. A one-sample z-interval for a sample proportion

Step-by-step explanation:

In this experiment we are only given the sample. Neither the population nor the two samples nor difference between two samples is given .

So we are left only with the option B which satisfies the required conditions.

We will estimate the sample proportion and then perform, the test.

The test are performed on the basis of the statistics given.

We have the sample and the proportion that it is not longer than 35 centimeters.

Therefore option B is the correct choice.

B. A one-sample z-interval for a sample proportion

The functions for this problem are defined as follows:

The functions for this problem are given as follows:

The addition and subtraction functions for this problem are given as follows:

At x = -2, the numeric value of the subtraction function is given as follows:

(t - s)(-2) = -2³ - 5(-2)²

(t - s)(-2) = -28.

The product function for this problem is given as follows:

(ts)(x) = \(5x^5\)

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On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 4, negative 3), (0, negative 1), and (2, 0). Everything to the left of the line is shaded.

Inequality of a graph is represented with the greater then(<), less then(>) or with the other inequity signs. The inequality line on the graph is represented with the dotted lines.

The given linear inequality is,

\(2y > x - 2\)

Solve it further,

\(2y > x - 2\\2y-x > - 2\)

Change the inequality with changing the sign of it,

\(x-2y < 2\)

The inequality equation is graphed, which can be shown in the image provided below. In this graphed equation,

Thus, on a coordinate plane, a dashed straight line has a positive slope and goes through (negative 4, negative 3), (0, negative 1), and (2, 0). Everything to the left of the line is shaded.

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Answer:

(80)+40=120

Step-by-step explanation:

(50+30)+40

120

The required simplified value is 120.

Given that,
Top simplify the expression following the associative property.
(50 + 30) + 40.

In mathematics, it deals with numbers of operations according to the statements. There are ,four major arithmetic operators, addition, subtraction, multiplication and division,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
= (50 + 30) + 40
Simplification, using associative property, in parenthesis 50 + 30 become 80.

= 80 + 40
Again using associative property, 80 + 40 become 120
= 120

Thus, the reequired simplified value is 120.

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The figure in the question is a kite and the value of the angle 4 is equal to 40°

A kite has 4 interior angles and the sum of these interior angles is 360°. In these angles, it has one pair of opposite angles that are obtuse angles and are equa

Let us represent the angle 3 with x, so that;

angle 1 = 2x,

angle 2 = x + 20

angle 1 + angle 4 = one of the pair of opposite angles

angle 1 + angle 3 + 90° = 180° {sum of interior angles of a triangle}

2x + x + 90°= 180°

3x = 180° - 90° {subtract 90° from both sides}

x = 90°/3 {divide through by 3}

x = 30°

so;

angle 1= 60°

angle 2 = 50°

sum of interior angles of kite (quadrilateral) = 360°

2(angle 3) + 2(angle 2) + 2(angle 1 + angle 4) = 360°

60° + 100° + 2(60° + angle 4) = 360°

60° + 100° + 120° + 2(angle 4) = 360° {open bracket}

280° + 2(angle 4) = 360°

2(angle 4) = 360° - 280° {subtract 280° from both sides}

2(angle 4) = 80°

angle 4 = 80°/2 {divide through by 2}

angle 4 = 40°

Therefore, the angle 4 of the kite is equal to the value of 40°.

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a) On a coordinate plane, points are at (1, 48.1), (2, 50.9), (3, 62.4), (4, 67), (5, 76.5), (6, 83.9), (7, 86.8), (8, 88.1), (9, 79.2), (10, 69.9), (11, 59.5), (12, 49.6)  best represents the data.

This is because the data represents a set of paired values, with the months as the independent variable (x) and the average maximum monthly temperature as the dependent variable (y). A scatter plot is the appropriate graph for displaying this type of data.

Option a shows the correct placement of the data points on a scatter plot, with the x-axis representing the months and the y-axis representing the average maximum monthly temperature. The points are clearly organized in a sequence from January to December, with an upward trend in temperature from the winter months to the summer months, followed by a gradual decrease in temperature in the fall and winter months.

Option b has the correct range of temperatures, but the points are not arranged in a logical sequence and are scattered randomly across the graph. Option c also has a similar issue with random placement of points and does not reflect the actual values in the data set. Option d only has three points and does not represent the complete data set.

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Answer:

I THINK ANSWER IS 12 because DIAGONALS BISECT EACHOTHER

Answer:

x=-5

Step-by-step explanation:

since the y's cancel out, set the first equation equal to the second and solve like you'd normally do.

let's bear in mind that complex roots never come alone, their conjugate sister is always with her, so if we have the complex root of "i" or namely "0 + i", her conjugate is also coming along, or "0 - i", so we really have four roots, so

\(\begin{cases} x = 0+i &\implies x -i=0\\ x = 0-i &\implies x +i=0\\ x = \sqrt{2} &\implies x -\sqrt{2}=0\\ x = 3 &\implies x -3=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x -i )( x +i )( x -\sqrt{2} )( x -3 ) = \stackrel{0}{y}}\hspace{5em}\stackrel{\textit{we are assuming that}}{a=1} \\\\\\ 1( x -i )( x +i )( x -\sqrt{2} )( x -3 ) = y\implies ( x -i )( x +i )( x -\sqrt{2} )( x -3 ) = y \\\\[-0.35em] ~\dotfill\)

\(\stackrel{ \textit{difference of squares} }{( x -i )( x +i )}\implies x^2 - i^2\implies x^2-(-1)\implies x^2+1 \\\\[-0.35em] ~\dotfill\\\\ (x^2+1)( x -\sqrt{2} )( x -3 )\implies (x^2+1)(x^2-3x-x\sqrt{2}+3\sqrt{2}) \\\\\\ (x^2+1)[x^2-x(3+\sqrt{2})+3\sqrt{2}] \\\\\\ x^4-x^3(3+\sqrt{2})+3x^2\sqrt{2}+x^2-x(3+\sqrt{2})+3\sqrt{2} \\\\\\ \boxed{x^4-x^3(3+\sqrt{2})+x^2(3\sqrt{2}+1)-x(3+\sqrt{2})+3\sqrt{2}~~ = ~~y}\)

Answer: it’s A B and E on edge <3 just did it

Step-by-step explanation:

Answer:

A

B

E

Step-by-step explanation:

Answer:

To find the z-score, we use the formula:

z = (x - mu) / (sigma / sqrt(n))

where:

x = sample mean = $5100

mu = population mean = $5000

sigma = population standard deviation = $250

n = sample size = 64

Substituting the values, we get:

z = (5100 - 5000) / (250 / sqrt(64))

z = 2.56

Therefore, the z-score that corresponds to a sample average of $5100 is 2.56 (rounded to four decimals).

Step-by-step explanation:

I clicked on the black picture. thought is was the box to enter the answer.