brahmagupta’s mathematical discoveries and work came about while studying a branch of science. what was he studying? psychology economics astronomy geology

Answer:

Range: (-∞, 0]

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

When we graph the equation, we should see that our y-values span from -∞ to 0. Since 0 is a closed dot, it is inclusive in the range:

(-∞, 0] or y ≤ 0

The likelihood that a correlation exists in a population, based on knowledge of the actual value of r in a sample from that population is the statistical significance

The matrix must have pivot columns. Otherwise, the equation Ax = 0 would have a free variable, in which case the columns of A would not span R5. Therefore, the correct answer is C.

A pivot column is a column of the matrix that has a non-zero entry in the pivot position and all entries below the pivot are zero. In row echelon form, every row below a pivot column has a zero in the corresponding position. The pivot columns correspond to the linearly independent columns of the original matrix and the number of pivot columns determines the rank of the matrix.

The rank of a matrix is defined as the number of linearly independent columns or rows in the matrix. If the columns of a matrix span Rn, then the rank of the matrix must be equal to n. This means that the matrix must have n linearly independent columns. To ensure that the columns of A span R5, A must have at least 5 pivot columns. If A had fewer pivot columns, then the equation Ax = 0 would have a non-trivial solution, meaning that the columns of A would not be linearly independent and would not span R5.

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18.84 rounded to the nearest tenth is 18.8.

Rounding to place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.

We can see that round a number to the nearest tenth, we need to look at the digit in the hundredth place. In this case, the number is 18.84.

Therefore, digit in the hundredth place is 4.

If the digit in the hundredth place is less than 5, we round down to the previous tenth. If it is 5 or greater, we round up to the next tenth.

Since 4 is less than 5, we round down. Therefore, 18.84 rounded to the nearest tenth is 18.8.

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The statement describes the incidence measure of occurrence, which refers to the number of new cases of a disease or condition that occur in a defined population over a specific period of time.

This statement describes the incidence rate of flu among students living in Dunedin hostels.
The incidence rate is a measure of occurrence that calculates the number of new cases (in this case, students getting sick with the flu) in a specific population (150 students in Dunedin hostels) over a specific time period (3 months). This rate helps us understand the frequency at which the flu is affecting this particular group of students

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Given

One of the zeros of 14² − 42² − 9 is the negative of the other.

To find the value of k.

Explanation:

It is given that,

One of the zeros of 14² − 42² − 9 is the negative of the other.

That implies,

Let α, -α be the zeros of the polynomial f(x) = 14² − 42² − 9.

Then,

Also,

Subtracting (1) and (2) implies,

Hence, the value of k is 0.

The proper way to construct a stem-and-leaf plot to display the data set {62,67,68,73, 73, 79,91,94,95,97} is to include a stem labeled ‘8’ and enter no leaf on the stem. So, the correct choice is option (b).

A stem and leaf graph is like a special table where each data value is separated into a "stem" (the first number) and a "leaf" (usually the last number). Leaves are sorted in ascending order from left to right. We have a data set with values {62,67,68,73, 73, 79,91,94,95,97}. Now, to construct the stem- leaf plot for our data.

Stem | Leaf

6 | 2 7

7 | 3 3 9

9 | 1 4 5 7

For stem and leaf diagram if some values are not present for some stem, then no leaf should be added to that stem. If we skip that stem than it would distort the shape of distribution of the data.

stem | leaf

6 | 2 7

7 | 3 3 9

8 |

9 | 1 4 5 7

Hence, include a stem labeled 8 and enter no leaves on the stem.

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Complete question:

The proper way to construct a stem-and-leaf display for the data set {62, 67, 68, 73, 73, 79, 91, 94, 95, 97} is to

a)exclude a stem labeled ‘8

b)include a stem labeled ‘8’ and enter no leaves on the stem.

c) include a stem labeled ‘(8)’ and enter no leaves on the stem.

d) include a stem labeled ‘8’ and enter one leaf value of ‘0’ on the stem.

The roots of the auxiliary equation for the Cauchy-Euler equation x^3y′′′ − 6y = 0 are: r = 0 (multiplicity 1), r ≈ 2.56208 (multiplicity 1) ,r ≈ -0.78104 ± 1.79303i (multiplicity 2)

To find the roots of the auxiliary equation for the Cauchy-Euler equation x³y′′′ − 6y = 0, we assume a solution of the form y(x) = x^r, where r is a constant.

Substituting this into the Cauchy-Euler equation, we have:

\(x^3(r(r - 1)(r - 2)x^{(r - 3)}) - 6x^r = 0\)

Simplifying this equation, we get:

\(r(r - 1)(r - 2)x^r - 6x^r = 0\)

Factorizing out \(x^r\), we have:

\(x^r(r^3 - 3r^2 + 2r - 6) = 0\)

For the equation to hold, either \(x^r = 0\) or \((r^3 - 3r^2 + 2r - 6) = 0\).

Setting \(x^r = 0\), we find the trivial solution r = 0.

To find the non-trivial solutions, we solve the cubic equation \((r^3 - 3r^2 + 2r - 6) = 0\). Unfortunately, the roots of this cubic equation cannot be expressed in simple, closed form.

Using numerical methods, we can approximate the roots of the cubic equation:

r ≈ 2.56208

r ≈ -0.78104 ± 1.79303i

Therefore, the roots of the auxiliary equation are r = 0, r ≈ 2.56208, r ≈ -0.78104 ± 1.79303i.

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The correlation coefficient may assume any value between -1 and 1. Correct answer option A.

This means that the coefficient might be negative, zero, or positive, with -1 being a perfect negative correlation, 0 representing no connection, and 1 representing a perfect positive correlation.

The correlation coefficient is a numerical measure of two variables' linear connection. It is a measure of the strength of the link between two variables. A correlation coefficient of 1 indicates that there is a perfect positive connection, a coefficient of -1 indicates that there is a perfect negative correlation, and a coefficient of 0 shows that there is no correlation between the two variables.

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Answer:

There is literally no solution!

Step-by-step explanation:

The number of ways to choose 5 people from a total of 15 people is given by 15C5. This can be calculated as follows:15C5 = (15!)/((15-5)! * 5!) = (15 * 14 * 13 * 12 * 11)/(5 * 4 * 3 * 2 * 1) = 3003Therefore, there are 3003 ways to select a committee of 5 people from the group of 15 people. The probability of selecting any given committee is 1/3003.

There are a total of 15 people in the group. A committee of size 5 is to be chosen from a group of 7 men and 8 women randomly. Therefore, the sample space for this situation is 15C5 ways to choose 5 people from a total of 15 people. 15C5 = 3003 ways. That means there are 3003 ways to select 5 people from the group of 15 people. The probability of selecting any given committee is 1/3003. That means the probability of selecting any one committee out of 3003 committees is 1/3003.To compute the probability of selecting any given committee, we first need to determine how many possible committees can be formed from the group of 15 people. The number of ways to choose 5 people from a total of 15 people is given by 15C5. This can be calculated as follows:15C5 = (15!)/((15-5)! * 5!) = (15 * 14 * 13 * 12 * 11)/(5 * 4 * 3 * 2 * 1) = 3003Therefore, there are 3003 ways to select a committee of 5 people from the group of 15 people. The probability of selecting any given committee is 1/3003.

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For a standard normal distribution, a negative value of z indicates that the observed value is below the mean of the distribution.

In a standard normal distribution, which has a mean of 0 and a standard deviation of 1, a negative value of z indicates that the observed value is located below the mean. The z-score represents the number of standard deviations a data point is away from the mean.

A negative z-score means that the observed value is lower than the mean, indicating that it falls to the left of the center of the distribution. This means that the data point is relatively lower compared to the average and can provide information about its position within the distribution and its deviation from the mean.

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Using property of independent events, there should be 12 sophomore girls present in the class.

If the occurrence of one event has no bearing on the likelihood that the other will also occur, then the two events are independent. The likelihood that both occurrences A and B will occur is defined mathematically as being equal to the product of the probabilities of A and B (i.e., P) (A and B)

Given,

There are twelve freshmen boys, sixteen freshmen girls, and nine sophomore boys

and two events are independent if,

p(A ∩ B) = P(A). P(B)

Let sophomore girls present = x

               Freshmen       sophomore        Total

Boys              12                     9                    21

Girls               16                     x                    16 + x

Total              28                 9 + x                37 + x

P(Boys) = \(\frac{21}{37 + x}\)

P(Freshmen) = \(\frac{28}{37 + x}\)

P(Boys ∩ Freshmen) = \(\frac{12}{37 + x}\)

Using p(A ∩ B) = P(A). P(B),

\(\frac{12}{37 + x} = \frac{21}{37 + x} \times \frac{28}{37 + x}\)

\(12(37 + x) = 21 \times 28\\x = 12\)

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Answer:

1:6 or 1/6

Step-by-step explanation:

Because the question asks for the goats to the total number of animals, you have to write the ratio in the same order. So, there are 4 goats, and to find the total number of animals, you just add every number.

5+11+4+4=24

The result would be 4:24, and because you need the ratio in the simplest form, you just divide both sides by the same greatest number. Both 4 and 24 can be divided evenly by 4. So, when you simplify, the answer comes out as 1:6. (Ratios can also be written as fractions, just so you know!! For example, the ratio 1:6 can be written as 1/6; both answers would be correct.)

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Answer:

mZRST = 155°, mZRSU  = 102°

Step-by-step explanation:

Given that mZRST = (12x - 1)º, mZRSU = (9x - 15),  and mZUST = 53°.

We know that mZRSU + mZUST = mZRST (since S is a common point)

So, (9x - 15)º + 53° = (12x - 1)º

Expanding the brackets we have

9x - 15 + 53 = 12x - 1

collecting like terms, we have

53 - 15 + 1 = 12x - 9x

54 - 15 = 3x

39 = 3x

Dividing through by 3, we have

x = 39/3

x = 13°

So, mZRST = (12x - 1)º

= 12(13) - 1

= 156 - 1

= 155°

So, mZRST = 155°

mZRSU = (9x - 15),  

= 9(13) - 15

= 117 - 15

= 102°

So, mZRSU = 102°

Answer:

C

Step-by-step explanation:

Givens

You are given 2 tangent lines.

You are also given a 4 sided figure.

All 4 sided figures have 360 degrees

A radius meets a tangent at 90 degrees

Formula

<BDA + <DCA + <BCA + <BDC = 360

Solution

90 + 90 +40 + <BDC = 360               Combine

220 + <BDC = 360                             Subtract 220 from both sides

220- 220 +BDC =360 - 220

<BDC = 140

Answer: C

Answer:

Step-by-step explanation:

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

1. 9x² + 3x - 4 = 0

Step 02:

Discriminant:

D = b² - 4ac

9x² + 3x - 4 = 0

a = 9

b = 3

c = - 4

D = (3)² - 4(9)(-4) = 9 + 144 = 153

The answer is:

D = 153

for this we locate the point where y = 4, and find its ordered pair on the x-axis, and from the graph, x = - 3

answer: x = - 3

Answer:

2²×3³×7², 42

Step-by-step explanation:

The solution of this question is attached above. Hope this helps and please give brainlist!

Answer:

(2x+5)(x+4)

Step-by-step explanation:

After factoring we can find that it equals

(2x+5)(x+4)

Answer:

(2x +5) (x+4)

Step-by-step explanation:

2x*2+13x+20

(2x +   )(x+  )

Factoring 20 into 4 and 5  so we can get 13 in the middle

(2x +5) (x+4)

2*4 +5 = 13 for the middle term

All three reasons (1, 2, and 3) can be valid for using a normal probability model to represent the distribution of sample means.

1, 2, and 3 are correct.We can use a normal probability model to represent the distribution of sample means for the following reasons:

1. The sample is randomly selected. This ensures that each member of the population has an equal chance of being selected, reducing potential biases and allowing the use of a normal probability model.

2. The distribution of the variable in the population is normally distributed. When the population distribution is normal, the distribution of sample means will also be normally distributed, as stated by the Central Limit Theorem.

3. The sample size is large enough to ensure that sample means will be normally distributed. As the sample size increases, the distribution of sample means approaches a normal distribution, even if the original population distribution is not normal. This is also part of the Central Limit Theorem, which typically suggests a sample size of 30 or more.

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The slant height of a cone that has a lateral area of 320π cm² and diameter of 20 cm is 32 cm.

The lateral area of a cone can be described as follows:

where

r = radius

l = slant height

Therefore,

r = 20 / 2 = 10 cm

l = ?

lateral area = 320π cm²

320π = π × 10 × l

320π = 10πl

divide both sides by 10π

l = 320π / 10π

l = 32 cm

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The equivalent ratio of a/8 in the proportion a/b = 8/15 is a/15. 

The given proportion is: a/b = 8/15.

To find out the ratio that completes the equivalent proportion a/8 = ?Let's begin with the cross product property: In a proportion, the product of the means (the middle terms, b and c) equals the product of the extremes (the first and last terms, a and d).

That is, a/b = c/d, then a x d = b x c.Using this property: a/b = 8/15, now let's plug in the values given to find out the value of ratio for a/8,8a = 15 x a8 = 15Now, a/8 = (8a)/(8 x 15)= a/15

The equivalent ratio of a/8 in the proportion a/b = 8/15 is a/15. 

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Answer:

Let the required% = x

A.T.Q.

x% of 100 = 14

x/100 × 100 = 14

x/100 = 14/100

x =14/100 × 100

x = 14%

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Answer:

14/100 × 100

Step-by-step explanation:

Answer:

x = 5

Step-by-step explanation:

8x + 50 = 90

or, 8x = 90-50

or, 8x = 40

so, x = 5