Factorise the following x^2+6x+8

The solution to this question is [tex]2x^{2} +5x-18[/tex] which is area of base of rectangular prism.

Synthetic division, which is frequently used to determine a polynomial's zeros, is described as a streamlined method of dividing a polynomial with another polynomial equation of degree 1. Comparatively easier to calculate than the long division method, this division method is carried out manually.

we know that the volume of a rectangular prism as where V is volume ,A is area ,H is height

Now, we are given

V=[tex]2x^{3}+9x^{2} -8x-36[/tex]

h=x+2

now, we can find A

V=A*h

A=V/h

now, we can plug it

[tex]\frac{2x^{3}+9x^{2} -8x-36}{x+2}[/tex]

now, we can use synthetic division method

so, we can write it as

A=[tex]\frac{2x^{3}+9x^{2} -8x-36}{x+2} = 2x^{2} +5x-18[/tex]

So the area of base=[tex]2x^{2} +5x-18[/tex]

Therefore ,the solution to this question is [tex]2x^{2} +5x-18[/tex] which is area of base of rectangular prism.

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The answer to the parts for the given standard deviation are 859, 629 , 308, 477.

What is standard deviation?

Standard Deviation may be a live that shows what quantity variation (such as unfold, dispersion, spread,) from the mean exists

Main body:

1 )

mean=5.6

sd=1.2

total number 1000 find number weight between 4 to 9 pounds

z=x-mue/sd

⇒ 4-5.6/1.2=-1.6/1.2 =-1.33

z value by table = 0.09176

⇒z=7-5.6/1.2=1.4/1.2 = 1.666

z value by table =0.95154

effective value  0.95154 -0.09176 = 0.8598

number of children =1000 x 0.8598=859.8

babies expect to weigh between 4 and 7 pounds are 859.

2)

less than 6 pounds

z=6-5.6/1.2=0.4/1.2=0.333

z value by table = 0.62930

number of children born less than 7 pounds =0.62930 x 1000=629.3

means 629 children less than 6 pounds

3)

more than 5 pounds

z=5-5.6/1.2= -0.6/1.2= -0.5

z value as per table -0.5 = 0.30854

number of children born 1000 x 0.30854=308.5

number of children born more than 5 pounds are 308

4)

weight between 5.6 to 8 pounds

z=5.6-5. 6/1.2=0/1.2 =0

value of z by table 0.5

z=8-5. 6/1.2=2.4/1.2 = 2

value of z by table 0.97725

0 value will be 0.97725-0.5000=0.4772

number of children born between 5.6 to 8 pounds=0.4772 x 1000 = 477.2 means 477.

Hence the value are as follows

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Answer:

The equation is 15x + 2.50y = 800, where x is the number of care packages and y is the number of food satchels. Solving for y, we get y = 32. Therefore, each package contained 32 food satchels.

Step-by-step explanation:

The option that could be the sides of a Right Triangle is 2.5 cm, 6.5 cm, 6 cm   , the correct option is (a) .

In the question ,

it is given that ,

four options are given that have the three sides of the triangle ,

we have to select the sides that forms a right triangle .

If the sides form a right triangle , then

square of the longest side is equal to square of the other two sides .

In option (a) the  sides are given as 2.5 cm, 6.5 cm, 6 cm .

So ,

(6.5)² = 6² + (2.5)²

42.25 = 42.25

Since LHS = RHS ,

So , Yes , the sides given in option (a) forms a right triangle .

Therefore , the correct option is (a) .

The given question is incomplete , the complete question is

Which could be the sides of a right triangle ?

(a) 2.5 cm, 6.5 cm, 6 cm

(b) 2 cm, 2 cm, 5 cm

(c) 1.5 cm, 2.5 cm, 4 cm

(d) 2 cm, 3 cm, 5 cm

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The solutions to the logarithm equations are;

1)  Log₅3 = 0.6826

2)  Log₅(27/50) = -0.383

How to solve logarithm Equations?

There are different rules of logarithm such as;

Product rule which is; Log a + Log b = Log (ab)

Quotient rule which is; Log a - Log b = Log(a/b)

Power rule which is; Log aˣ = x log a

We are given that;

Log₅2 = 0.4308

Log₅27 = 2.0478

We know that 27 = 3³. Thus;

Log₅27 = Log₅3³

Using power rule, we have;

Log₅3³ = 3Log₅3

Thus;

Log₅27 = 3Log₅3 = 2.0478

1) We want to solve Log₅3

We have;

3Log₅3 = 2.0478

Thus;

Log₅3 = 2.0478/3 = 0.6826

2)  Log₅(27/50)

Using quotient rule, we have;

Log₅27 -  Log₅50

This can also be expressed as;

Log₅3³ - Log₅ (25 * 2)

= 3Log₅3 - [2Log₅5 + Log₅2]

= 2.0478 - 2 - 0.4308

= -0.383

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The temperature of the liquid at noon would be of:

-2.25ºC.

The linear function in this problem is defined in the slope-intercept format, as follows

y = mx + b.

In which the coefficients of the function are given as follows:

The values of these coefficients are given as follows:

m = -3/4, b = 0.

Then the function that gives the temperature in x hours after 9 A.M. is of:

y = -3/4x.

Noon is three hours after 9 A.M., hence the estimate is given as follows:

y = -3/4(3) = -9/4 = -2.25ºC.

The problem states that the initial temperature is of 0ºC at 9 A.M.

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Answer:

9/20

Step-by-step explanation:

(9/10)*(1/2)

(9/20) times

Answer: tis answer would be 9 over 20

Step-by-step explanation:

Answer:

760ft

Step-by-step explanation:

Use the formula: πr^2h where r = radius(diameter/2) and h = height

radius: 11/2 = 5.5

pi: 3.14

Height: 8

3.14*5.5^2*8

= 759.88

Rounded: 760 ft

Ordinary points: Point an is a regular point whenever functions p1(x) having p0(x) are logical at x = a.

Singular points: There are two types of singular points: regular and irregular.

Whenever functions p1(x) with p0(x) are analytical at x = a, point an is an ordinary point.

Use the steps below to get a series solution centered on a regular solitary point x0. enter ∞ n=0 cn(x − x0)n+rinto the formula.

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No the results did not deviate significantly from what would be expected due to chance.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a larger range, a low standard deviation suggests that the values tend to be near to the established mean. The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

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The goal is to determine whether or not the following binary operations are closed.

A. Subtraction of positive integers: Under normal substation operation, a set of positive integers is not near. Since 1∈Ζ⁺ and 2∈Ζ⁺ but (2-1) = ₋1∉Z⁺.

B. A division of nonzero integers: Non-zero integer set Z/{0} is not closed under the operation. Since 1∈Z/{0} and 2∈ Z/{0} but 1/2 ∉ Z/{0}.

C.  Function composition of polynomials with real coefficients: The set of polynomials with real coefficients is closed when using the typical binary operator. Use the obvious conclusion that a polynomial is a combination of two polynomials [tex]f(x)[/tex] and [tex]g(x)[/tex]. Since every polynomial coefficient is real, every polynomial's composition will also have real coefficients.

D. The multiplication of 2×2 matrices with integer entries: Under the action of standard matrix multiplication Μ₂ₓ₂ (Z), the collection of matrices with integer elements, is close.

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Answer:

f(3) = 5

f(8) = 3

f(-1) = 0

Step-by-step explanation:

Just plug in the number from the parentheses into the inequalities and whichever makes the inequality true plug into that equation so for example f(3) = ?

first plug 3 into the inequalities: 3 ≤ 0, 0 < 3 ≤ 5, 3 > 5

then find the one that's true which is: 0 < 3 ≤ 5  

then plug into the equation that corresponds to that inequality: 2(3) - 1 → 6 - 1 = 5

The angles are ∠1=42°

∠2=48°

∠3=90°

∠4=42°

∠5=48°

∠6=132°

∠7=90°

∠8=48°

∠9=90°

∠10=132°

∠11=90°

∠12=90°

∠13=48°

∠14=48°

∠15=90°

∠16=90°

∠17=90°

∠18=48°

∠19=48°

∠20=90°

∠21=48°

∠22=42°

In Euclidean geometry, an angle is the figure formed by two rays, known as the sides of the angle, that have a common termination, known as the vertex of the angle. Angles formed by two rays are located in the plane that contains the rays.

An angle in Plane Geometry is a figure formed by two rays or lines that share a common endpoint. "Angle" comes from the Latin word "angulus," which means "corner." The two rays are referred to as the sides of an angle, while the common endpoint is referred to as the vertex.

In Euclidean geometry, an angle is the figure formed by two rays known as the sides.

∠1=42°

∠1+∠2=90°

∠2=48°

In ΔABF,

∠2+∠3+42°=180°

48°+∠3+42°=180°

∠3=90°

∠4=42°

Now, ∠3+∠4+∠5=180°

90°+42°+∠5=180°

∠5=48°

∠5+∠6=180°

∠6=132°

∠7=90°

∠8=48°

∠7+∠9=180°

∠9=90°

∠10=132°

∠11+∠3=180°

∠11=90°

∠11+∠12=180°

∠12=90°

∠16=∠11=90°

∠12=15=∠90°

∠13=48°

∠14=48°

∠17=90°

∠1+∠17+∠18=180°

42°+90°+∠18=180°

∠18=48°

∠19=48°

Now, ∠19+∠20+42°=180°

∠20=90°

∠21=48°

Now, ∠21+∠22=90°

∠22=42°

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The quadratic equation y = x² - x - 2 has a domain with all real numbers and a range with all values equal to or greater than - 9 / 4.

The domain of a function is the set of values of x that belongs to the functions and the range of the function corresponds to its set of values of y. In this case we find the definition of a quadratic equation, of which we must determine its domain and range. A brief manner to determine them is modifying the function by deriving its vertex form:

y - k = C · (x - h)²

Where:

First, write the quadratic equation:

y = x² - x - 2

Second, modify the equation into its vertex form:

y + 1 / 4 = x² - x + 1 / 4 - 2

y + 9 / 4 = x² - x + 1 / 4

y + 9 / 4 = (x - 1 / 2)²

The domain of all quadratic functions is all real numbers and the range of the quadratic function y = x² - x - 2 is y ≥ - 9 / 4 as the vertex constant is greater than zero.

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The two inequalities that models the situation are as follows:

6x + 14y ≤ 65

x + y > 8

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤.

Marta buys x candles and y books at a store.

Therefore,

Hence, the inequalities are as follows:

6x + 14y ≤ 65

x + y > 8

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The total number of oranges present in the bag was 21.

For the stated question.

Let the total number of oranges in the bag be 'x'.

Total stale oranges = 7.

Thus,

Probability (first orange is stale) = Total stale oranges/ Total oranges.

Probability (first orange is stale) = 7/x

Probability (second orange is stale) = 6/(x - 1).

But, probability to pick two stale oranges is 2/21

7/x . 6/(x - 1) = 2/21

On solving,

x ² - x - 441 = 0

x = 21

Thus, the total number of oranges present in the bag was 21.

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Critical value used to test the claim that the mean number of restaurant employees is less than 15 at the 1% significance level is - 2.431

The square root of the variance is used to calculate the standard deviation, a statistic that gauges a dataset's dispersion from its mean. The variation from the mean of each data point is used to determine the standard deviation, which is equal to the square root of variance.

It is basically the average of the given numbers.

The given data is

Sample Size = n = 38

Sample mean = X = 12.6

Sample Standard deviation = S = 2.4

= n - 1 = 38 - 1 = 37

μ₀ = μ ≥ 15

μ₁ = μ < 15 ( left tailed )

d = 0.01

Hence, Critical value = - 2,431

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If she can play, the coach estimates they will score 78 points. If she is not able to play, the coach estimates they will score 62 points. The team doctor estimates there is a 60-40 chance she will play.

Therefore, P(x) Outcome Expected Value: 71.6 %

Given in the question:

If she is playing, estimate score is 78 points.

If she is not playing, estimated score is 62 points.

chances : 60% to 40%

Therefore, the expected outcome value is :

P(X) = 78 × 60% + 62× 40%

       = 71.6%

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Answer:

B

Step-by-step explanation: It is very simple. All you have to do is to do 350 000 divided by 700 which gives you 500. That's your answer!

The system of linear equations which has a solution of (1,-10) is y2 and y4

Dependent: There are countless possible solutions to the system. The same lines are depicted on the equation graphs.

Independent: There is only one solution to the problem. The equations' graphs come together at a single point.

Inconsistent: There is no fix for the system.

There are three ways to solve systems of linear equations in two variables: graphing. substitution method. elimination method

line y2 cross line y4 at (1,-1)

Hence the solution is y2 and y4

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If the slope of a basic regression analysis—in which y is the dependent variable and x is the independent variable—is positive, then there must be a positive correlation between x and y.

Regression analysis is a group of statistical procedures used in statistical modeling to determine the associations between a dependent variable and one or more independent variables. A statistical technique that demonstrates the link between two or more variables is regression analysis. The approach examines the connection between a dependent variable and independent variables, often represented in a graph. A statistical method called regression links a dependent variable to one or more independent (explanatory) variables. A regression model can demonstrate whether changes in one or more of the explanatory variables are related to changes in the dependent variable.

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If x represents the full length of a certain species of newts then, the mean of the sampling distribution and standard deviation are 216, and 0.31 respectively.

Central Limit Theorem for mean: When a random sample of size n is taken from a population with a mean and standard deviation, the sample mean approaches the normal distribution with mean and standard deviation σ/sqrt (n) as the sample size increases.

Sampling distribution of the sample mean:

using, Central Limit Theorem, the mean of the sampling distribution is μ_{x-bar} = 216.

The standard deviation of the population is σ = 3.1 and the sample size is n =103, people

The standard deviation σ/√n= 3.1/√103 =0.31.

As a result, the sample mean for the 103 sample size, following normal distribution has a mean of μ_{x-bar} = 216 and a standard error of μ_{x-bar} = 0.31.

x-bar ≈ N (216, 0.31)

μ_{x-bar}  = 216

σ_{x-bar}  =0.31

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(complete question)

Let X represent the full length of a certain species of newt. Assume that X has a normal probability distribution with a mean of 110.6 inches and a standard deviation of 4.9 inches. You intend to measure a random sample of n = 103. find the mean of the sampling distribution and standard deviation.

In this case, the standard error would be standard error = 2.50 / sqrt(41) = 0.342 and the z-score would be z = (5.61 - 5.00) / 0.342 = 1.71

A z-score value is the numerical measured value of the relationship of a value to the mean of a group of values and it is measured in the terms of standard deviations from mean value.

The z-score is measured by formula z=(x- μ)/ a where x is the raw score, μ is the population mean and a is the population standard deviation. So to calculate z-score, we subtract the population mean from the raw score and divide it by the population standard deviation.

standard error = population standard deviation / sqrt(sample size)

standard error = 2.50 / sqrt(41) = 0.342

Next, you would need to calculate the z-score for the observed mean wait time of 5.61 minutes.

z = (observed mean - population mean) / standard error

z = (5.61 - 5.00) / 0.342

z= 1.71

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The chi-square goodness of fit test assesses whether the observed counts of a categorical variable follow a hypothetical proportion population distribution.

The chi-square fit test of goodness assesses whether the proportions of a category or individual outcome in a sample follow a hypothetical proportion population distribution.

In other words, if you take a random sample, the observed proportions follow the values ​​suggested by theory.

Analysts often use the goodness-of-fit chi-square test to determine whether the proportions of categorical results are equal. Alternatively, the analyst can specify the proportions to include in the test.

Alternatively, this test can assess whether observed results follow a discrete probability distribution, for example, Poisson distribution.

As a hypothesis test, the chi-square test of goodness can be used to infer the entire population based on a sample.

Thus, it is true that the the chi-square goodness of fit test assesses whether the observed counts of a categorical variable follow a hypothetical proportion population distribution.

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There are no solutions to linear equations of the following equation  

5-4x-7-10x=-8x-4-6x-10, because if they have the same variable term but different constant values on opposite sides of the equation.

A linear equation can be generated by equating a linear polynomial over some field with zero coefficients. The values that, when substituted for the unknowns, make the equality true are the solutions of such an equation.

The phrase linear equation is frequently used to refer to this specific scenario, in which the variable is appropriately referred to as the unknown.

Each solution in the case of two variables can be regarded as the Cartesian coordinates of a point on the Euclidean plane. A linear equation's solutions form a line in the Euclidean plane, and every line can be seen as a set.

Given equation is ,

5-4x-7-10x=-8x-4-6x-10

-14x-2=-14x-14

If a linear equation has the same variable term but different constant values on opposite sides of the equation, it has no solutions.

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We insert m and c values inside the slope-intercept form to get a linear equation that expresses the volume of water in the bottle in terms of t:  w = 5t + 5.

Let w be the quantity of water in the bottle after turning on the faucet.

The following points can be drawn from the provided statement:

(t1, w1) = (4, 25)

(t2, w2) = (11, 60)

The equation of a line's slope-intercept form is:

w = mt + c

Put the values to find slope m.

m = (w2 - w1)/(t2 -t1)

m = 60 - 25 / 11 - 4

m = 5

Put m = 5, t = 4 and w = 2 in equation of the line;

w = mt + c

25 = 5(4) + c

c = 5

We insert m and c values inside the slope-intercept form to get a linear equation that expresses the volume of water in the bottle in terms of t:

w = 5t + 5

Thus, the linear equation that models the amount of water in the bottle  is w = 5t + 5.

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P(X = 4, Y = 2) = 0.055131

P(X = Y) = 0.35607

From the information given:

X represent no of Canon SLR

The PMF is given as:

X   :    0         1        2           3        4

p(x) :  0.1       0.2   0.3     0.25   0.15

p = P(customers that purchase the camera & also purchase an extended warranty.

As a result, the conditional distribution Y provided X approaches a Binomial distribution with n = x and p = 0.55 as the parameter.

[tex]\frac{Y}{X}[/tex] ~ Bin ( n= x , p =0.55) y

     = 0.1 ........ x and X = 0,1,2,3,4.

The condition probabilities Y given X is:

[tex]P (\frac{Y = 0}{X = 0} ) =1[/tex]

[tex]P (\frac{Y = 0}{X = 1} ) = 0.45 and P (\frac{Y = 1}{X = 1} ) =0.55[/tex]

[tex]P (\frac{Y = 0}{X = 2} ) = 0.2025 and P (\frac{Y = 1}{X = 2} ) =0.495, P (\frac{Y = 2}{X = 2} ) =0.3025[/tex]

[tex]P (\frac{Y = 0}{X = 3} ) = 0.091125 and P (\frac{Y = 1}{X = 3} ) =0.334125, \\P (\frac{Y = 2}{X = 3} ) =0.408375 and P (\frac{Y = 3}{X = 3} ) = 0.166375[/tex]

[tex]P (\frac{Y = 0}{X = 4} ) = 0.0.041006 and P (\frac{Y = 1}{X = 4} ) =0.0.200475, P (\frac{Y = 2}{X = 3} ) =0.367538[/tex]

[tex]P (\frac{Y = 3}{X = 4} ) = 0.299475 and P (\frac{Y = 4}{X = 4} ) =0.091506[/tex]

Now, the joint P.D (probability Dist.) of X & Y is expressed as:

[tex]P (\frac{Y = y}{X = x} ) = P (\frac{Y = y. X = x}{X = x} )[/tex]

[tex]P( X = x , Y = y) = P(\frac{Y = y}{X =x} ) * P(X =x)[/tex]

The Joint P.D is;

                      Y                                                                      Total

             0              1                    2             3          4

X     0     0.1            0                  0              0         0                  0.1

      1      0.09        0.11              0               0         0                 0.2

  2    0.06075  0.1485      0.09075          0         0                 0.3

  3    0.022781 0.083531 0.102094   0.041594  0                0.25

  4    0.006151  0.030071  0.055131  0.044921  0.013726    0.15

Total  0.279682 0.372103  0.247974  0.086515 0.013726       1

(a)

P(X=4,Y=2)

From the table above:

P(X=4,Y=2)

 = 0.055131

(b)

P(X= Y)

= (P = 0 , Y = 0) + P( X =1, Y =1) + P( X=2, Y=2) + P(X=3,Y=3) + P(X=4,Y=4)

= 0.1 + 0.11 + 0.09075 + 0.041594 + 0.013726

= 0.35607

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We prove that QR≅SR, using SAS to show triangle PRQ is congruent to triangle PRS. So option B is correct.

In the given question;

Given: PR bisects ∠QPS. PQ=12 units, and PS=12 units.

Prove: QR≅SR

We have to find how we prove QR≅SR.

As we can see that;

PQ = PS

Since PR is bisector.

So PR is common in both triangles PRQ and PRS.

PR=PR

Since PR is bisector.

So ∠PRQ=∠PRS

As we know that if two sides and one angle are congruent, then using the Side-Angle-Side (SAS) Theorem, the both triangle is congruent.

So ∠PRQ≅∠PRS

So QR≅SR

Hence, we prove that QR≅SR, using SAS to show triangle PRQ is congruent to triangle PRS. So option B is correct.

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Answer:

x = 0.6 , x = 2

Step-by-step explanation:

the absolute value function always gives a positive value, that is

| - a | = | a | = a

the expression inside the bars, however , can be positive or negative, so

9 - 8x = 2x +3 ( subtract 2x from both sides )

9 - 10x = 3 ( subtract 9 from both sides )

- 10x = - 6 ( divide both sides by - 10 )

x = 0.6

Or

- (9 - 8x) = 2x + 3

- 9 + 8x = 2x + 3 ( subtract 2x from both sides )

- 9 + 6x = 3 (add 9 to both sides )

6x = 12 ( divide both sides by 6 )

x = 2

As a check

substitute these values into the equation and if both sides are equal then they are the solutions.

x = 0.6

left side = | 9 - 8(0.6) | = | 9 - 4.8 | = | 4.2 | = 4.2

right side = 2(0.6) + 3 = 1.2 + 3 = 4.2= left side

-------------------------------------------------------

x = 2

left side = | 9 - 8(2) | = | 9 - 16 | = | - 7 | = 7

right side = 2(2) + 3 = 4 + 3 = 7 = left side

the solutions to the equation are x = 0.6 and x = 2