v2 – v – 20 = 0 solve the equation by factoring

Answer:

16 servings and 1920 calories in  1 snack bag

Step-by-step explanation:

12 ounces divided by 3/4 = 16 servings

120 calories/servings x 16 servings = 1920 calories in 1 snack bag

Answer:

Step-by-step explanation:

The formula for the area of a circle is:

A = πr^2

where A is the area, π (pi) is approximately 3.14, and r is the radius.

Substituting the given radius of 17 inches into the formula, we get:

A = 3.14 × 17^2

A = 3.14 × 289

A = 907.06

Therefore, the area of the circle is approximately 907.06 square inches.

Answer:

907.46

Step-by-step explanation:

Area of a circle formula is πr^2

It says the radius is 17

**Simplify**

(3.14)(17)^2=907.46

Answer:

5

Step-by-step explanation:

Answer:

The first option

Step-by-step explanation:

Got it right :)

Answer:no but maybe

Step-by-step explanation:if you distribute the 3 and multiply the 3 with box the 2 and 1 you would get 6x+3 which is not equal to 5x+4 but if you take one from the 6 and add it to the 3 it would be even so i dont know but maybe

The meters of separation between the hunter and the deer in a straight line is 138.9m

In order to calculate the required distance, we will be using the distance formula expressed as:

\(D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Given the coordinate of the distance C(-5, 8) and V(7, 1), substitute the coordinates into the formula as shown:

\(D=\sqrt{(7-(-5))^2+(1-8)^2}\\D=\sqrt{(12)^2+(-7)^2}\\\\D=\sqrt{144+49}\\D = \sqrt{193}\\D = 13.89units\)

Convert the distance to meters

Since 1unit = 10m

13.89units = 138.9m

Hence the meters of separation between the hunter and the deer in a straight line is 138.9m

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In conclusion, the calculations below proves that since points B, C, H, I lie on a single circle, then O lies on this circle too.

The inscribed angle theorem states that the measure of an inscribed angle whose vertex lies on a circle is half of the intercepted arc subtended at a point on the circle.

Note: The point of concurrency of three altitudes in a triangle is referred to as orthocenter.

In triangle ABC, O is orthocenter. Thus, by applying the inscribed angle theorem to the circle, we have:

∠BOA = 2∠BAC.                ......equation 1.

Assuming H is orthocenter; Thus, the angle formed by angles BAC and BC at H are supplementary angles:

∠BAC + BHC = 180°.

BHC = 180° - ∠BAC.     ......equation 2.

Assuming I is incenter; Thus, the angle formed by BIC is given by:

∠BIC = 90° + ∠A/2.          ......equation 3.

Since points B, C, H, I lie on a single circle and the angles formed in the same side of an arc of a circle are equal, we have:

BIC = BHC                      ......equation 4.

Substituting the parameters into eqn. 4, we have;

180° - ∠BAC = 90° + ∠A/2.

∠BAC + ∠BAC/2 - 3∠BAC/2 = 180° - 90°

∠BAC = 90° × 2/3

∠BAC = 60°.

From eqn. 1, we have:

∠BOA = 2∠BAC.

∠BOA = 2 × 60

∠BOA = 120°.

In conclusion, this proves that since points B, C, H, I lie on a single circle, then O lies on this circle too.

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The minimum distance between the origin and the plane 3x + y + 2z = 28, using the Lagrange Multipliers is 8.73 units.

In the question, we are asked to use Lagrange multipliers to find the minimum distance between the origin and the plans 3x + y + 2z = 28.

Lagrange multipliers state that if we want to minimize a function, f(x, y, z), subject to a constraint g(x, y, z) = constant, then ∇f = λ∇g.

We want to minimize the distance, and the distance formula says that the distance from the origin to a point (x, y, z), is given as:

D = √(x² + y² + z²), which can also be shown as:

D² = x² + y² + z².

The gradient of this function is: (2x + 2y + 2z), which needs to be equal to the gradient of the constraint equation multiplied by the constant, λ, that is, λ(3, 1, 2), which gives:

2x = 3λ, or, x = (3/2)λ,

2y = λ, or, y = λ/2, and,

2z = 2λ, or, z = λ.

Substituting these in the equation of the plane, 3x + y + 2z = 28, we get:

3(3/2)λ + λ/2 + λ = 28,

or, 6λ = 28,

or, λ = 28/6 = 14/3.

Thus, we get:

x = (3/2)λ = 7,

y = λ/2 = 7/3, and,

z = λ = 14/3.

Substituting these in the distance formula, we get:

D = √(7² + (7/3)² + (14/3)²) = √(49 + 49/9 + 196/9) = √(686/9) = 8.73.

Thus, the minimum distance between the origin and the plane 3x + y + 2z = 28, using the Lagrange Multipliers is 8.73 units.

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The implied population in the information provided is (e) the nitrogen concentration (mg nitrogen/1 liter of water) in the entire lake.

The information states that government agencies are monitoring water quality and its effect on wetlands, specifically focusing on the concentration of nitrogen in water draining from fertilized lands. To study this, twenty-eight samples of water were taken at random from a lake, and the nitrogen concentration was determined for each sample.

The purpose of taking these samples and analyzing the nitrogen concentration is to make inferences about the overall nitrogen concentration in the entire lake. The goal is to assess the impact of nitrogen on fish and wildlife in the lake. Therefore, the implied population in this case is the nitrogen concentration in the entire lake, which is the target of the monitoring efforts.

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Answer:

Step-by-step explanation:

4

The length of side a is determined as 13.92 by applying sine rule of triangle.

The length of side a is calculated by applying the following formulas shown below;

Apply sine rule as follows;

a / sin (83) = 13 / sin (68)

Simplify the expression as follows;

multiply both sides of the equation by " sin (83)".

a = ( sin (83) / sin (68) ) x 13

a = 13.92

Thus, the value of side length a is determined as 13.92 by applying sine rule as shown above.

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Answer:

Flour need for 1 cup of water = \(1\frac{7}{8}\) cups

Step-by-step explanation:

Given:

Cups of water = \(1\frac{1}{3}\) = 4/3

Cups of flour = \(2\frac{1}{2}\) = 5/2

Find:

Flour need for 1 cup of water

Computation:

Flour need for 1 cup of water = Cups of flour / Cups of water

Flour need for 1 cup of water = (5/2) / (4/3)

Flour need for 1 cup of water = 15/8

Flour need for 1 cup of water = \(1\frac{7}{8}\)

Answer:

2 lawns : $50

Step-by-step explanation:

The minimum height of the cone is 17.87 in (approx)

In geometry, the cylinder is a fundamental 3 dimension shape that has two parallel circular bases at a distance. The two circular bases are joined by a curved surface, at a fixed distance from the center.  

Total surface area, A = 2πr²+ 2πrh square units

The volume of the Cylinder, V = πr²h cubic units

Here we have

A cylindrical can with an open top is to be constructed so that

The volume of the cone is 167 in³  

As we know volume of cone = (1/3) πr²h

=> (1/3) πr²h = 167

=> h = 501/πr²  

As we know Surface Area of the cone = 2πrh + 2πr²  

Substitute h = 501/πr² in Surface Area of cone  

=> SA = 2πr(501)/πr² + 2πr²  

=> SA = 1002r⁻¹+ 2πr²        

Differentiate SA with respect to r

=> SA' = (-1) 1002r⁻²+ 4πr  

=> SA' = - 1002r⁻² + 4πr  

Here  - 1002r⁻² + 4πr = 0

=>  - 501r⁻² + 2πr = 0  

=>  - 501/r² + 2πr = 0  

=>  [-501 + 2πr³ ]/r² = 0

=>  [-501 + 2πr³ ] = 0  

=>  2πr³ = 501

=>  πr³ = 250.5

=>  r³ = 79.70

=>  r = 8.92  (approx)

Hence the height of the cone, h = 501/πr²    

= 501/π(8.92)

= 17.87 (approx)

Therefore,

The minimum height of the cone is 17.87 in (approx)  

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To estimate the regression in the given model Yi = B0 + B1Xi + B2Ziui, where the variance of Ui is Σi^2 = Σ(zi^2), you can use the method of weighted least squares (WLS). The weights for each observation can be determined by the inverse of the variance of Ui, that is, wi = 1/zi^2.

In the given model, Yi = B0 + B1Xi + B2Ziui, the error term Ui is assumed to have a constant variance, given by Σi^2 = Σ(zi^2), where zi represents the individual values of Z.

To estimate the regression coefficients B0, B1, and B2, you can use the weighted least squares (WLS) method. WLS is an extension of the ordinary least squares (OLS) method that accounts for heteroscedasticity in the error term.

In WLS, you assign weights to each observation based on the inverse of its variance. In this case, the weight for each observation i would be wi = 1/zi^2, where zi^2 represents the variance of Ui for that particular observation.

By assigning higher weights to observations with smaller variance, WLS gives more importance to those observations that are more precise and have smaller errors. This weighting scheme helps in obtaining more efficient and unbiased estimates of the regression coefficients.

Once you have calculated the weights for each observation, you can use the WLS method to estimate the regression coefficients B0, B1, and B2 by minimizing the weighted sum of squared residuals. This involves finding the values of B0, B1, and B2 that minimize the expression Σ[wi * (Yi - B0 - B1Xi - B2Ziui)^2].

By using the weights derived from the inverse of the variance of Ui, WLS allows you to estimate the regression in the presence of heteroscedasticity, leading to more accurate and robust results.

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Answer:

(0, -4)

Step-by-step explanation:

Given the inequality expression

y>−2x+y≤4

This can be splitted into

y>−2x+y .... 1

and -2x+y≤4 .... 2

From1;

y>−2x+y

y - y >−2x

0 >−2x

-2x < 0

x > 0/-2

x>0

Substitute x = 0 into 2

-2(0)+ y ≤4

y≤4

Hence the solution is (0, -4)

Answer:

The answer would be (1,3)

Step-by-step explanation:

Answer:

-22, -28

\(\displaystyle \large{a_n=-6n+2}\)

Step-by-step explanation:

Given:

Since the sequence doesn’t have common ratio, find common difference by subtracting the next term with previous term:

-10-(-4) = -10+4 = -6

-16-(-10):= -16+10 = -6

Therefore, there is a common difference which is -6. Hence, this sequence is arithmetic sequence.

To find next term, add the term with common difference:

-16-6 = -22

-22-6 = -28

Therefore, the finished sequence is -4, -10, -16, -22, -28

Next, find the rule which is the general term (nth term) for this sequence. The formula/rule is:

\(\displaystyle \large{a_n=a_1+(n-1)d}\)

Where \(\displaystyle \large{a_n}\) is nth term, \(\displaystyle \large{a_1}\) is first term and \(\displaystyle \large{d}\) is common difference. We know that first term is -4 and common difference is -6. Hence:

\(\displaystyle \large{a_n=-4+(n-1)(-6)}\\\\\displaystyle \large{a_n=-4-6n+6}\\\\\displaystyle \large{a_n=-6n+2}\)

Thus, the rule is \(\displaystyle \large{a_n=-6n+2}\)

Answer:

This is an experiment because a treatment was applied to a group.

Step-by-step explanation:

There are two groups, The first group used the computer program while the second group did not therefore this is an experiment. An experiment involves changing an independent variable to see how it affects a dependent variable. The dependent variable in this case  determining the effect of a new computer program on learning while the independent variables was testing with the computer program and not testing with the program.

(a) The z-score corresponding to x = 25 is -1. (b)The z-score corresponding to x = 42 is 2.4.(c) The raw score corresponding to z = -3 is 15. (d)  The raw score corresponding to z = 1.5 is 37.5.

For a normal distribution with mean μ = 30 and standard deviation σ = 5:

(a) To find the z-score corresponding to x = 25, we use the formula:

z = (x - μ) / σ

Substituting the values, we get:

z = (25 - 30) / 5 = -1

Therefore, the z-score corresponding to x = 25 is -1.

(b) To find the z-score corresponding to x = 42, we again use the formula:

z = (x - μ) / σ

Substituting the values, we get:

z = (42 - 30) / 5 = 2.4

Therefore, the z-score corresponding to x = 42 is 2.4.

(c) To find the raw score (x) corresponding to z = -3, we use the formula:

z = (x - μ) / σ

Rearranging the formula, we get:

x = μ + zσ

Substituting the values, we get:

x = 30 + (-3) x 5 = 15

Therefore, the raw score corresponding to z = -3 is 15.

(d) To find the raw score (x) corresponding to z = 1.5, we use the same formula:

x = μ + zσ

Substituting the values, we get:

x = 30 + 1.5 x 5 = 37.5

Therefore, the raw score corresponding to z = 1.5 is 37.5.

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Answer:

18.27

Step-by-step explanation:

0 . 8 7

×     2 1

0 . 8 7

1 1    

1 7 . 4 0

1    

1 8 . 2 7

Answer:

18.27

Step-by-step explanation:

0.87 × 21

Multiply 0.87 and 21 to get 18.27.

= 18.27

Answer:

0,1

2,2

4,3

6,4

Step-by-step explanation:

Some Examples

4 = 1/2 (6) + 1

4 = 3 + 1

4=4

----------

2 = 1/2 (2) + 1

2 = 1 + 1

2 = 2

h

0

2

4

6

...................

Answer:

Ratio Needed

Step-by-step explanation:

In order to solve this problem, we need the ratio. Please give me the ratio, so that I can help you ASAP. Thanks!

Answer:

d=5

Step-by-step explanation:

distance between two points d=√[(x2-x1)²+(y2-y1)²]

d=√[(0-4)²+(6-3)²]

d=√[16+3²]

=√(16+9)

=√25

=5

Answer:

5

Step-by-step explanation:

use the distance formula for points (x1, y1) and (x2, y2)

d² = (x2 -x1)² +(y2-y1)²

for the points (4, 3) and (0, 6) we have

d² = (4-0)² +(3-6)² ; solve what is in parentheses

d² = 4² + (-3)²; square the numbers

d² = 16+9 ; add

d² = 25 ; square root both sides

d= √25

d= 5

To answer the question, no, the n-tuple (x,x,x,....x) does not necessarily have to consist of non-negative values.

An n-tuple is a sequence of n elements, and in mathematics, it can refer to a sequence of real numbers, complex numbers, or other types of mathematical objects. In the case of the given set of n-tuples, it specifies that the n-tuple consists of real numbers and that all the elements in the tuple have the same value, which is denoted by x.

The definition of the set only specifies that the elements are real numbers and that they are all equal to each other. Therefore, the elements in the tuple can be positive, negative, or zero.

However, if the context of the problem or application requires the elements to be non-negative, then this restriction should be explicitly stated.

For example, if the n-tuple represents a set of quantities that cannot be negative, such as lengths, areas, or volumes, then it is appropriate to specify that the elements are non-negative real numbers.

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2a , 1st exp= a2 + ab

= a(a+b)

2nd exp = a2-b2

= (a+b) (a-b)

HCF = (a+b)

b, 1 st exp= (a+b)2

= (a+b)(a+)

2 nd exp = a2-b2

= (a+b) ( a-b)

HCF = (a+b)

c, 1 st exp= (a-1)2

= (a+1) (a-1)

2nd exp= a2-1

= (a+1)(a-1)

HCF = (a-1)

d, 1st exp= (x-2)(x-3)

= x(x-3)-2(x-3)

= x2 - 3x - 2x + 6

= x2- 5x+ 6

= x2 - (3+2)x + 6

=x2 -3x-2x+ 6

= x(x-3) -2(x-3)

=(x-3)(x-2)

2 nd exp = (x+2) (x-3)

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

= x2 - 3 x+ 2x -6

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

=(x-3) ( x+ 2)

HCF = (x-3)

The 10th percentile of pit depths is 780μm. A certain pit with 780 μm deep is at the 10th percentile. The proportion of pits have depths between 800 and 830 μm is 7.33%.

A)

To find the 10th percentile of pit depths, we need to use the z-score table. Where x = μ + zσ, here we are looking for the z-score, for the given 10th percentile.

Using the standard normal distribution table, we get the value of -1.28 which corresponds to the 10th percentile.

Therefore,

x = 818 - 1.28 * 29x = 779.88 = 780μm.

So, 780μm is the 10th percentile of pit depths.

B)

We are given that the mean is 818 μm and standard deviation is 29 μm. A certain pit is 780 μm deep. To find the percentile for this, we need to find the z-score for this given pit.

x = 780 μm, μ = 818 μm, σ = 29 μm

Now, z-score can be found as,

z = (x - μ) / σ = (780 - 818) / 29 = -1.31

We can find the percentile using the standard normal distribution table.

Therefore, the given pit is at the 10th percentile.

C)

We are given that the mean is 818 μm and standard deviation is 29 μm. The proportion of pits with depths between 800 and 830 μm can be calculated as follows:

P(z < (X- x) / σ) - P(z < (830 - 818) / 29) - P(z < (800 - 818) / 29)

P(z < -0.41) - P(z < -0.62) = 0.3409 - 0.2676 = 0.0733

(rounded off to four decimal places)

Therefore, approximately 7.33% of pits have depths between 800 and 830 μm.

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Answer:

(-22, 10)

Step-by-step explanation:

So the midpoint equation is defined as: \(m=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})\). The order of the pairs don't matter since addition is associative, as long as you put the values where they are supposed to be (x in x spot, and y in the spot)

So, let's say the unknown end point is \((x_2, y_2)\)

We know what the midpoint is so we can solve for these values. Let's start with the x-value

\(-14=\frac{-6+x_2}{2}\)

Multiply both values by 2

\(-28=-6+x_2\)

Now add 6 to both sides

\(-22=x_2\)

Now let's do the same thing with the y-value

\(9=\frac{8+y_2}{2}\)

Multiply both sides by 2

\(18=8+y_2\)

Subtract 8 from both sides

\(10=y_2\)

So the other end point is \((-22, 10)\)

13.) -3/4

14.) takes a lot of work

15.)5

16.) corresponding

14.) d=24

15.)25x+5=26x

Answer:

13.) -3/4

14.) takes a lot of work

15.)5

16.) corresponding

14.) d=24

15.)25x+5=26xStep-by-step explanation: