Point A has coordinates (-4,-2). Point B has coordinates (6,3). Find the coordinates of point P that partition AB in the ratio 3:2

The solution of the system of linear equations, is (1.167, 3.667).

Given that the system of linear equations, y = -2x+6 and y = 4x - 1, we need to find the solution for the same,

y = -2x+6............(i)

y = 4x - 1.......(ii)

Equating the equations since the LHS is same,

-2x+6 = 4x-1

6x = 7

x = 1.167

Put x = 1.16 to find the value of y,

y = 4(1.16)-1

y = 4.66-1

y = 3.667

Therefore, the solution of the system of linear equations, is (1.167, 3.667).

You can also find the solution using the graphical method,

Plot the equations in the graph, the point of the intersection of both the lines will be the solution of the system of linear equations, [attached]

Hence, the solution of the system of linear equations, is (1.167, 3.667).

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Answer:

21.98

Step-by-step explanation:

Answer:

y=1.2x-3

Step-by-step explanation:

I had this as an rsm problem a few weeks ago and forgot how to solve it lol hope this helps

Answer:

i'm too lazy 2 do this rn, but just divide each price by the amount of water per pack. which ever one is the least is ur answer :p

Step-by-step explanation:

Answer:

Store 3

Step-by-step explanation:

May i have brainiest

Answer: 5/2

Step-by-step explanation:

slope equation: (y2-y1)/(x2-x1)

13-3/5-1 = 10/4 or 5/2

Answer:

2.5

Step-by-step explanation:

Gradient (slope) =

\(m = \frac{y2 - y1}{x2 - x1} = \frac{13 - 3}{5 - 1} = \frac{10}{4} = 2 \frac{1}{2} \)

Answer:

C)  1/2  and 8

Step-by-step explanation:

-2x + y = 7              Eq. 1

6x + y = 11               Eq. 2

From Eq. 1:

y = 7 + 2x               Eq. 3

From Eq. 2:

y = 11 - 6x              Eq. 4

Equalyzing Eq. 3 and Eq. 4:

7 + 2x = 11 - 6x

2x + 6x = 11 - 7

8x = 4

x = 4/8

x = 1/2

From Eq. 3:

y = 7 +2* 1/2

y = 7 + 1

y = 8

Check:

From Eq. 2

6x + y = 11

6*1/2 + 8 = 11

3 + 8 = 11

Answer:

-0.24 ; 0.71

Step-by-step explanation:

Given that :

Mean number of siblings (m) = 3.76

Standard deviation (s) = 3.18

Z score associated with 3 siblings

x = 3

Using the relation :

Zscore = (x - m) / s

Zscore = (3 - 3.76) / 3.18

Zscore = - 0.76 / 3.18

Zscore = −0.238993

Zscore = - 0.24

2.) proportion of respondents with more than 2 siblings

Using the z probability calculator :

X > 2

Obtain the standardized score :

Zscore = (x - m) / s

Zscore = (2 - 3.76) / 3.18

Zscore = - 1.76 / 3.18

Zscore = −0.5534591

Zscore = - 0.55

Using the z table :

P(Z ≥ - 0.55) = 1 - p(Z ≤ - 0.55) ; p(Z ≤ - 0.55) = 0.2912

1 - p(Z ≤ - 0.55) = 1 - 0.2912 = 0.7088 = 0.71

The set of ordered pairs above: is a function.

The mapping diagram above: is a function.

y = x²: is a function.

The table above: is not a function.

In Mathematics and Geometry, a function is a mathematical equation which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.

Based on the set of ordered pairs, mapping diagram, and the equation above, we can reasonably infer and logically deduce that it represent a function because the input values (domain, x-value, or independent values) are uniquely mapped to the output values (range, y-value or dependent values).

In this context, we can reasonably infer and logically deduce that the table does not represent a function because the input value (-1) has more than output values (2 and 4 respectively).

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Answer:

430 and 1/2 cubic inches

Step-by-step explanation:

20.5 x 9 x 2.33 equals 429.885, which rounds up to 430 and 1/2 cubic inches

Answer: point b

Step-by-step explanation: took the quiz

Array to represent 5 chairs in rectangle has, 5 rows and 1 column or 1 row and 5 columns.

An array is a way to represent multiplication and division using rows and columns. Rows represent the number of groups. Columns represent the number in each group or the size of each group.

Given,

5 chairs to be arranged in a rectangle.

then,

5 = 5×1

or 5 = 1 × 5

Length of one side of array, rows = 5 or 1
Length of other side of array, columns = 1 or 5

Hence, array will have 5 rows and 1 column or 1 row and 5 columns.

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Answer:

y = 2x + 3

Step-by-step explanation:

You can find the slope on the graph by looking at the points. From one point to the next you go Up2Over1.

Up2Over1 is the slope and in actual algebra it is 2/1, which is just 2.



The slope is 2. Fill in 2 in place of m in

y = mx + b

y = 2x + b

Next the y-intercept which is the b, can also be seen on the graph. The y-intercept is where the graph crosses the y-axis. The line crosses the y-axis at 3. Fill in 3 in place of the b.

y = 2x + 3

Answer:

weight=660 pounds

volume=75 cubic feet

Step-by-step explanation:

44 × 15 = 660

5 × 15 = 75

The weight of 15 bags of garden soil is approximately 297.9 kilograms.The volume of 15 bags of garden soil is approximately 2.78 cubic yards.

To find the weight of 15 bags of garden soil in kilograms, we can use the conversion factor that 1 pound is equal to 0.45359237 kilograms.

Weight of 15 bags in kilograms = 44 pounds/bag * 15 bags * 0.45359237 kg/pound

Weight of 15 bags in kilograms ≈ 297.9 kilograms

Therefore, the weight of 15 bags of garden soil is approximately 297.9 kilograms.

To find the volume of 15 bags of garden soil in cubic yards, we need to first convert the volume of each bag from cubic feet to cubic yards. There are 3 feet in a yard, so 1 cubic yard is equal to 3 feet by 3 feet by 3 feet, which is 27 cubic feet.

Volume of 15 bags in cubic yards = (5 cubic feet/bag * 15 bags) / 27 cubic feet/yard

Volume of 15 bags in cubic yards ≈ 2.78 cubic yards

Therefore, the volume of 15 bags of garden soil is approximately 2.78 cubic yards.

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Answer: 7/5

Step-by-step explanation:

\(12x-15=6-3x\\\\15x-15=6\\\\15x=21\\\\\boxed{x=21/15 \ or\ 7/5}\)

Answer:

1, -1

Step-by-step explanation:

[character limit thing]

You would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample between approximately 264.0 days and 274.1 days.

To find the range in which you would expect to find the middle 98% of most pregnancies, you can use the concept of z-scores and the standard normal distribution.

For the given data:

Mean (μ) = 269 days

Standard deviation (σ) = 17 days

To find the range, we need to find the z-scores corresponding to the 1% and 99% percentiles. Since the normal distribution is symmetric, we can find the z-scores by subtracting and adding the respective values from the mean.

To find the z-score for the 1% percentile (lower bound):

z1 = Φ^(-1)(0.01)

Similarly, to find the z-score for the 99% percentile (upper bound):

z2 = Φ^(-1)(0.99)

Now, we can calculate the z-scores:

z1 = Φ^(-1)(0.01) ≈ -2.33

z2 = Φ^(-1)(0.99) ≈ 2.33

To find the corresponding values in terms of days, we multiply the z-scores by the standard deviation and add/subtract them from the mean:

lower bound = μ + (z1 * σ) = 269 + (-2.33 * 17) ≈ 229.4 days

upper bound = μ + (z2 * σ) = 269 + (2.33 * 17) ≈ 308.6 days

Therefore, you would expect to find the middle 98% of most pregnancies between approximately 229.4 days and 308.6 days.

Now, let's consider drawing samples of size 58 from this population. The mean and standard deviation of the sample means can be calculated as follows:

Mean of sample means (μ') = μ = 269 days

Standard deviation of sample means (σ') = σ / sqrt(n) = 17 / sqrt(58) ≈ 2.229

To find the range in which you would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample, we repeat the previous steps using the mean of the sample means (μ') and the standard deviation of the sample means (σ').

Now, calculate the z-scores:

z1 = Φ^(-1)(0.01) ≈ -2.33

z2 = Φ^(-1)(0.99) ≈ 2.33

Multiply the z-scores by the standard deviation of the sample means and add/subtract them from the mean of the sample means:

lower bound = μ' + (z1 * σ') = 269 + (-2.33 * 2.229) ≈ 264.0 days

upper bound = μ' + (z2 * σ') = 269 + (2.33 * 2.229) ≈ 274.1 days

Therefore, you would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample between approximately 264.0 days and 274.1 days.

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Answer:

A=13×13

=169sqr.units

Answer: bro just take a screen shot of it and then post it.

Step-by-step explanation:

The vector whose magnitude is 3 and whose components I. the I and j direction are equal is; <3√2/2i, 3√2/2j>.

It follows that the magnitude of a vector in terms of its components in the i and j direction is;

M = √(x² + y²).

On this note, since the i and j components are equal; x = y and hence, we have;

3 = √(x² + x²).

3² = 2x²

x² = 9/2

x = 3/√2

x = 3√2/2

On this note, the required vector which is as described is; <3√2/2i, 3√2/2j>.

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Answer:

Answered is x= 55x

Step-by-step explanation:

13x+10 * 12x+20

soln:

or, 13x+12x+10+20

or, 25x+30

:., therefore, x=55x

Answer:

Three different ways (to : / )

Step-by-step explanation:

Examples:

3 to 5

3:5

3/5

Answer:

New price is $12.75

New attendance is 57500

Step-by-step explanation:

For starters, we use the relation.

18 - 3x

Since we don't know the number of times we're expected to deduct $3 from the price.

Again, we have 40000 + 10000x on another hand. Question says to add 10000 people everytime $3 is deducted.

Since (40000 + 10000x) is the number of people, we multiply it by $4.50, the average amount each person spends is then gotten to be

(18 - 3x) (40000 + 10000x) + (40000 + 10000x) (4.5) = 0

Expanding the bracket, we have

[720000 + 60000x - 30000x²] + [180000 + 45000x] = 0, solving further, we have

900000 + 105000x - 30000x² = 0 or

-30000x² + 105000x + 900000 = 0

Then, we find the maximum of a quadratic, by finding the axis of symmetry. Use x = -b/2a

x = -105000 / 2 * -30000

x = -105000 / -60000

x = 1.75

From our earlier equations, the new price then is

18 - 3(1.75) = 18 - 5.25 = $12.75

The new attendance also is

40000 + 10000(1.75) =

40000 + 17500 = 57500

Answer:

TRUE

Step-by-step explanation:

If two angles of a triangle are congruent then the sides opposite those angles are congruent by the converse to the isosceles triangle theorem

CAN YOU DROP A FOLLOW? :)

♥️

Answer:

True

Step-by-step explanation:

This is Converse Isosceles property theorem.

It states that if two angles of a a triangle are congruent, then the sides opposite to those angles are congruent

The maximum and minimum x-coordinates at the point of inflection are, respectively,\($\left(\frac{\pi}{4}+2 \pi n, \sqrt{2}\right)$\) and \($\left(\frac{5 \pi}{4}+2 \pi n,-\sqrt{2}\right)$\), and the function f is defined as f(x)=cos x+sin x for 0≤x≤ 2.

\($\frac{d}{d x}(\cos (x)+\sin (x))$\)

Continuity of \($\cos (x)+\sin (x): \quad 2 \pi$\)

Domain of \($\cos (x)+\sin (x):\left[\begin{array}{cc}\text { Solution: } & -\infty < x < \infty \\ \text { Interval Notation: } & (-\infty, \infty)\end{array}\right]$\)

Range of \($\cos (x)+\sin (x):\left[\begin{array}{cc}\text { Solution: } & -\sqrt{2} \leq f(x) \leq \sqrt{2} \\ \text { Interval Notation: } & {[-\sqrt{2}, \sqrt{2}]}\end{array}\right]$\)

Axis points of interception \($\cos (x)+\sin (x)$\) \(: X Intercepts: $\left(\frac{3 \pi}{4}+2 \pi n, 0\right),\left(\frac{7 \pi}{4}+2 \pi n, 0\right)$,\)

The Y intercept: (0,1)

the asymmetrical \($\cos (x)+\sin (x)$\) : None

Excessive Points of \($\cos (x)+\sin (x): \quad$\) Maximum \($\left(\frac{\pi}{4}+2 \pi n, \sqrt{2}\right)$\) ,  Minimum \($\left(\frac{5 \pi}{4}+2 \pi n,-\sqrt{2}\right)$\)

We put the second derivative of the function equal to zero to get the x-coordinate of the point of inflection. Re-inserting the x-coordinate into the initial function yields the point's y-coordinate.

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Answer:

come india

Step-by-step explanation:

ok

Answer:

a. 1. Two measurements​ (A and​ B) are taken on the same round.

b. No, there is not enough evidence to support the claim that the difference d is significantly different from 0.

c. The 99% confidence interval for the mean difference is (-8.76, 2.26).

This means that we have 99% confidence that the true mean difference of measurements between device A minus device B is within -8.76 and 2.26. As the value 0 is within the interval, we can not claim that there is a significant difference between the population difference between the measurements of both devices: they could be calibrated (mean difference equal to 0) or not.

Step-by-step explanation:

a) This is a matched-pairs because the samples are related: the n-th round is measured with each device, and one measurement is in the sample A and the other is in sample B.

b) For matched pairs data, a new variable "d" is calculated as the difference between each pair, and tested if d is significantly different from 0.

The sample data for d is [9.9, 9.9, -1.6, -1.6, 8.4, 8.4, -1.1, -1.1, 8.7, 8.7, -4.8, -4.8 ].

The mean and standard deviation for d are:

\(M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{12}((-9.9)+(-9.9)+1.6+. . .+4.8)\\\\\\M=\dfrac{-39}{12}\\\\\\M=-3.25\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{11}((-9.9-(-3.25))^2+(-9.9-(-3.25))^2+(1.6-(-3.25))^2+. . . +(4.8-(-3.25))^2)}\\\\\\s=\sqrt{\dfrac{415.39}{11}}\\\\\\s=\sqrt{37.76}=6.15\\\\\\\)

Then, we perform an hypothesis matched pair t-test.

This is a hypothesis test for the population mean.

The claim is that the difference d is significantly different from 0.

Then, the null and alternative hypothesis are:

\(H_0: \mu_d=0\\\\H_a:\mu_d\neq 0\)

The significance level is 0.01.

The sample has a size n=12.

The sample mean is M=-3.25.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=6.15.

The estimated standard error of the mean is computed using the formula:

\(s_M=\dfrac{s}{\sqrt{n}}=\dfrac{6.15}{\sqrt{12}}=1.775\)

Then, we can calculate the t-statistic as:

\(t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{-3.25-0}{1.775}=\dfrac{-3.25}{1.775}=-1.831\)

The degrees of freedom for this sample size are:

\(df=n-1=12-1=11\)

This test is a two-tailed test, with 11 degrees of freedom and t=1.831, so the P-value for this test is calculated as (using a t-table):

\(\text{P-value}=2\cdot P(t<-1.831)=0.094\)

As the P-value (0.094) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the difference d is significantly different from 0.

c. We have to calculate a 99% confidence interval for the mean.

The t-value for a 99% confidence interval and 11 degrees of freedom is t=3.106.

The margin of error (MOE) can be calculated as:

\(MOE=t\cdot s_M=3.106 \cdot 1.775=5.51\)

Then, the lower and upper bounds of the confidence interval are:

\(LL=M-t \cdot s_M = -3.25-5.51=-8.76\\\\UL=M+t \cdot s_M = -3.25+5.51=2.26\)

The 99% confidence interval for the mean difference is (-8.76, 2.26).

This means that we have 99% confidence that the true mean difference of measurements between device A minus device B is within -8.76 and 2.26. As the value 0 is within the interval, we can not claim that there is a significant difference between the population difference between the measurements of both devices: they could be calibrated (mean difference equal to 0) or not.

Answer:

|x+1| = x - 1   has no solution.

Step-by-step explanation:

One interpretation of |x - a| is “the distance between the numbers x and a. So |x - b| = c means that the distance between x and b is equal to c . For this to have any solutions, we need c >= 0. When c >0 there will be exactly two solutions, one to the left of b and one to the right of b. When c = 0, the solution is unique: x = b. So, now you should be able to select the only values for b and c that produce the desired set of solutions.