-
Express x^2 – 5x + 8 in the form (x – a)^2 + b
where a and b are top-heavy fractions.



i got (x-5/2)^2- 7/4
can someone tell me where i’m going wrong please :/

Answer:10 7/24

Step-by-step explanation:

i had the same qustion

Answer:

x = 1.04, w = 2

Step-by-step explanation:

104 = 1.04 × 10²

Answer:

1.04 x \(10^{2}\), so your answer is x = 1.04, w=2

Jaime's total fortune was 4. Rosa received 28% of the fortune which is 4 x 28% = 1.12, Maria received 32% of the fortune which is 4 x 32% = 1.28 and Fidel received the remaining 160 soles.

The fortune of Jaime can be calculated with the following formula:

F = 28% x F + 32% x F + 160

Where F is the total fortune.

Therefore, to find the total fortune we need to solve the equation and we do this by multiplying both sides of the equation by F:

F = 28% x F + 32% x F + 160

F x 100% = 28% x F x 100% + 32% x F x 100% + 160

F x 100% = 28F + 32F + 160

100F = 28F + 32F + 160

100F - 60F = 160

40F = 160

F = 160 ÷ 40

F = 4

Therefore, Jaime's total fortune was 4. Rosa received 28% of the fortune which is 4 x 28% = 1.12, Maria received 32% of the fortune which is 4 x 32% = 1.28 and Fidel received the remaining 160 soles.

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Answer:

Step-by-step explanation:

84%,79%,94%,89% and 100%

18 ( 1 + X )

sorry if my answer wrong

1. Average of the entire data set: 15.47 ounces

  Standard deviation of the entire data set: 1.51 ounces

2. American League:

  Average of drink sizes: 16.8 ounces

  Standard deviation of drink sizes: 2.26 ounces

1. Computing the average and standard deviation of the entire data set:

  Average = (14 + 18 + 20 + 16 + 16 + 12 + 14 + 16 + 14 + 16 + 16 + 16 + 14 + 32 + 16 + 20 + 12 + 16 + 20 + 12 + 16 + 16 + 24 + 16 + 16 + 14 + 14 + 12 + 14 + 20) / 30

          = 464 / 30

          ≈ 15.47 ounces

  Standard deviation = √[((14 - 15.47)² + (18 - 15.47)² + (20 - 15.47)² + ... + (14 - 15.47)²) / 30]

                    ≈ √(68.71 / 30)

                    ≈ √2.29

                    ≈ 1.51 ounces

2. Computing the average and standard deviation for the American League and the National League:

  American League:

  Average (AL) = (14 + 18 + 20 + 16 + 16 + 12 + 14 + 16 + 14 + 16 + 16 + 16 + 14 + 32 + 16) / 15

               = 252 / 15

               ≈ 16.8 ounces

  Standard deviation (AL) = √[((14 - 16.8)² + (18 - 16.8)² + (20 - 16.8)² + ... + (32 - 16.8)²) / 15]

                         ≈ √(76.8 / 15)

                         ≈ √5.12

                         ≈ 2.26 ounces

  National League:

  Average (NL) = (20 + 12 + 16 + 20 + 12 + 16 + 16 + 14 + 14 + 12 + 14 + 20) / 15

               = 200 / 15

               ≈ 13.33 ounces

  Standard deviation (NL) = √[((20 - 13.33)² + (12 - 13.33)² + (16 - 13.33)² + ... + (20 - 13.33)²) / 15]

                         ≈ √(40 / 15)

                         ≈ √2.67

                         ≈ 1.63 ounces

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Answer:

1/2x+1=4

1/2x=3

x=6

Step-by-step explanation:

please pass this on... ( #helpsavelives )

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Answer:

3.14     (or pi )  feet  

Step-by-step explanation:

Entire circle circumference  = pi *d  = 8 pi    feet

45 degrees is a fraction of the entire 360 degrees of the circle

   45 / 360  *  8 pi = pi =  3.14 ft

A. The next four terms in the sequence are 17, 20, 23, and 26.

B. f(n) = 2 + (n - 1) * 3

C.  The sign of f(59) is positive.

Part A:

To determine the next four terms in the sequence, we need to identify the pattern. Let's denote the terms in the sequence as f(n), where n represents the position of the term.

Given that we have not been provided with the sequence explicitly, I will assume that you have a given sequence and will use it to illustrate the process.

Let's say the sequence is: 2, 5, 8, 11, 14, ...

To find the pattern, we observe that each term is obtained by adding 3 to the previous term. So, the common difference between consecutive terms is 3.

Next four terms:

f(5) = f(4) + 3 = 14 + 3 = 17

f(6) = f(5) + 3 = 17 + 3 = 20

f(7) = f(6) + 3 = 20 + 3 = 23

f(8) = f(7) + 3 = 23 + 3 = 26

Therefore, the next four terms in the sequence are 17, 20, 23, and 26.

Part B:

To write the explicit equation for f(n) to represent the sequence, we need to determine the initial term or f(1) and the common difference.

In the given sequence, the initial term is 2, and the common difference is 3. Therefore, we can express the explicit equation for the sequence as:

f(n) = 2 + (n - 1) * 3

Part C:

To determine the sign of f(59), we substitute n = 59 into the explicit equation we derived in Part B:

f(59) = 2 + (59 - 1) * 3

= 2 + 58 * 3

= 2 + 174

= 176

Since f(59) = 176, which is a positive value, the sign of f(59) is positive.

Assuming the pattern continues, the next four terms in the sequence are 17, 20, 23, and 26. The explicit equation for f(n) representing the sequence is f(n) = 2 + (n - 1) * 3. Lastly, the sign of f(59) is positive.

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Answer:

35 dogs

Step-by-step explanation:

DOG:CAT = DOG:CAT

49:28 = x:20

7:4 = x:20

x = 35

To find the minimum sum-of-products (SOP) form of the function F = xy + z, we can simplify the expression using Boolean algebra rules.

Starting with the given expression:

F = xy + z

We can apply the distributive law to factor out z:

F = z + xy

Now, we can write the truth table for F and determine the minterms where F is equal to 1:

x y z F

0 0 0 0

0 0 1 1

0 1 0 0

0 1 1 1

1 0 0 0

1 0 1 1

1 1 0 1

1 1 1 1

From the truth table, we can see that the minterms where F is equal to 1 are:

m(1, 3, 4, 5, 6, 7)

The minimum SOP form is obtained by taking the logical OR of the minterms:

F = m1 + m3 + m4 + m5 + m6 + m7

Converting the minterms to Boolean expressions, we have:

F = xy'z' + xyz' + xy'z + xyz + xy'z' + xyz

Simplifying the expression by removing duplicates and combining terms, we get:

F = xyz' + xy'z + xyz

Therefore, the minimum SOP form of the function F = xy + z is xyz' + xy'z + xyz.

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This is a translation of 2 units to the left and 5 units up, so the correct option is the first one.,

Remember that a vertical translation of N units is:

g(x) = f(x) + N

if N < 0 the translation is down.

if N > 0 the translation is up.

And a horizontal translation of N units is:

g(x) = f(x + N)

If N > 0 the translation is to the right.

if N < 0 the translation is to the left.

Here we have the transformation:

f(x) = x²

g(x) = (x + 2)² + 5

So this is a translation of 2 units to the left and 5 units up.

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9514 1404 393

Answer:

  D B C A

Step-by-step explanation:

The decimal equivalents are ...

  A 0.15 = 0.15

  B 1/10 = 0.10

  C 12% = 0.12

  D 1/20 = 0.05

Least-to-greatest, the order is D B C A.

The probability that the mean number of moths in a sample of size 50 is greater than or equal to 0.6 is 8.08%

The CLT states that the distribution of the sample means of a random variable with a finite mean and standard deviation approaches a normal distribution as the sample size increases.

In this case, the population mean is 0.5, and the population standard deviation is 0.7. Since we have a sample size of 50, the standard deviation of the sample means would be

=> 0.7 / √(50) = 0.099.

Next, we need to calculate the z-score, which measures the number of standard deviations from the mean.

In this scenario, we want to find the probability that the mean number of moths in a sample of size 50 is greater than or equal to 0.6. So, we would plug in x = 0.6, μ = 0.5, σ = 0.7, and n = 50 into the z-score formula. This gives us

=> (0.6 - 0.5) / (0.7 / √(50)) = 1.41.

Using a standard normal distribution table or calculator, we can find that the probability of a z-score of 1.41 or higher is approximately 0.0808. Therefore, the estimated probability that the mean number of moths in a sample of size 50 is greater than or equal to 0.6 is 0.0808 or about 8.08%.

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Complete Question:

The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to detect the moths. Each month, an SRS of 50 traps is inspected, the number of moths in each trap is recorded, and the mean number of moths is calculated. Based on years of data, the distribution of moth counts is discrete and strongly skewed, with a mean of 0.5 and a standard deviation of 0.7. Estimate the probability that the mean number of moths in a sample of size 50 is greater than or equal to 0.6.

Net present value is a measure of profitability. The NPV of an investment is the net cash inflow received over the project's life, less the initial cash outflow, adjusted for the time value of money.

A higher NPV means the project is more lucrative. The profitability index measures the benefit-cost ratio of a project and is calculated by dividing the present value of future cash flows by the initial cash outflow. A profitability index greater than one indicates that the project will be profitable, whereas a profitability index less than one indicates that the project will not be profitable.

Calculation of Net Present Value (NPV) of Project AInitial Outlay = $454,000Net annual cash flows = $68,000Discount Rate = 9%Use the PV of an annuity of $1 table to determine the PV of net cash flows.Using the formula for NPV,NPV of Project A = PV of net cash flows – Initial OutlayNPV of Project A = 68,000 × 7.63930 – 454,000NPV of Project A = $56,201.85Calculation of Profitability Index of Project AProfitability Index of Project A = Present value of future cash flows / Initial OutlayProfitability Index of Project A = 68,000 × 7.63930 / 454,000Profitability Index of Project A = 1.14

Calculation of Net Present Value (NPV) of Project BInitial Outlay = $300,000Net annual cash flows = $47,000Discount Rate = 9%Use the PV of an annuity of $1 table to determine the PV of net cash flows.Using the formula for NPV,NPV of Project B = PV of net cash flows – Initial OutlayNPV of Project B = 47,000 × 6.10338 – 300,000NPV of Project B = $37,100.86Calculation of Profitability Index of Project BProfitability Index of Project B = Present value of future cash flows / Initial OutlayProfitability Index of Project B = 47,000 × 6.10338 / 300,000Profitability Index of Project B = 0.96

The NPV and profitability index calculations show that project A is the better investment since it has a higher NPV and profitability index than project B.

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Answer:

$2.25 is the discounted price for each gallon.

Step-by-step explanation:

So you take 40% and convert it into decimal form, which is 0.4. Then you take $3.75 x 0.4 = 1.5. Then subtract $1.50 from $3.75, and that equals $2.25 each gallon.

Have a nice day!

Answer:

B

Step-by-step explanation:

It has two or more terms.

Answer:

C

Step-by-step explanation:

the correct answer is C

Answer:

25 km

Step-by-step explanation:

Distance covered in 20 min = 5 km

Distance covered in 1 min = 5/20 km or 1/4 km.

Distance covered in 100 min =

1/4 km x 100 = 25 km

The IS relation is given by: Y = (intercept value rounded to two decimal places) + (slope value rounded to two decimal places) in the numerical example of the IS-LM model.

To derive the IS relation, we need to equate aggregate demand (AD) to aggregate supply (AS). Aggregate demand consists of consumption (C), investment (I), government spending (G), and net exports (NX). In this case, we assume net exports to be zero.

Given:

C = 233 + 0.47YD

I = 143 + 0.22Y - 1,094i

G = 299

T = 239

Aggregate demand (AD) = C + I + G

Substituting the given equations into AD:

AD = (233 + 0.47YD) + (143 + 0.22Y - 1,094i) + 299

Simplifying:

AD = 233 + 143 + 299 + 0.47YD + 0.22Y - 1,094i

Combining like terms:

AD = 675 + 0.47YD + 0.22Y - 1,094i

Since we want an equation with Y on the left side, we need to express YD in terms of Y by substituting YD = Y - T.

AD = 675 + 0.47(Y - T) + 0.22Y - 1,094i

AD = 675 + 0.47Y - 0.47T + 0.22Y - 1,094i

Combining like terms again:

AD = (0.47Y + 0.22Y) + (675 - 0.47T - 1,094i)

AD = 0.69Y - 0.47T - 1,094i + 675

Comparing with the IS relation Y = a + bAD, we have:

Y = 0.69Y - 0.47T - 1,094i + 675

Rearranging terms to have Y on the left side:

Y - 0.69Y = -0.47T - 1,094i + 675

0.31Y = -0.47T - 1,094i + 675

Dividing both sides by 0.31:

Y = (-0.47T - 1,094i + 675) / 0.31

Now, we can calculate the intercept and slope terms:

Intercept term = (-0.47T - 1,094i + 675) / 0.31

Slope term = 1 / 0.31

Rounding these values to two decimal places, the IS relation is:

Y = Intercept term + Slope term = (intercept value rounded to two decimal places) + (slope value rounded to two decimal places).

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The expression for the diagonal of the rectangle is √(169x² + 192x + (4x³) + (2304 / x²2) + (192 / x) + 672).

In a rectangle, the length (L) and width (W) are two sides, and the diagonal (D) is the hypotenuse. So, we can use the Pythagorean theorem to find an expression for the diagonal.

Using the formula: D²= L² + W²

Let's find the expression for D in terms of x (since the area function is given in terms of x).

The area of the rectangle is given as A = 12x² + 48x + 48 cm².

We know that the area of a rectangle is given by A = L × W.

Since the length of the rectangle (L) is represented by x in the given area function, we can express the width (W) in terms of x:

W = A / L

= (12x² + 48x + 48) / x

= 12x + 48 + (48 / x)

Now, substituting the expressions for L and W into the Pythagorean theorem:

D² = (L²) + (W²)

= (x²) + [(12x + 48 + (48 / x))²]

Expanding the equation:

D² = x² + (12x + 48)² + (48 / x)² + 2(x²)(12x + 48 + (48 / x))

D = √(169x² + 192x + (4x³) + (2304 / x²2) + (192 / x) + 672)

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The standard deviation of the sampling distribution of X is approximately 0.0704.

The standard deviation of the sampling distribution of X can be calculated using the formula:

\(\sigma = \sqrt{((p * (1 - p)) / n)}\)

Where:

σ is the standard deviation of the sampling distribution of X

p is the proportion of voters that would vote for the incumbent (46% or 0.46)

n is the sample size (50)

Plugging in the values:

\(\sigma = \sqrt{((0.46 * (1 - 0.46)) / 50)} \\\sigma = \sqrt{(0.2484 / 50)} \\\sigma = \sqrt{(0.004968)} \\\sigma = 0.0704\)

The standard deviation of the sampling distribution of X is approximately 0.0704.

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The main answer for the first argument is that we cannot prove that the band could play rock music based on the given premises and rules of inference.

1. Let's assign the following propositions:

  - P: The band could play rock music.

  - Q: The refreshments were delivered on time.

  - R: The New Year's party was canceled.

  - S: Alicia was angry.

  - T: Refunds were made.

2. The given premises can be expressed as:

  (¬P ∨ ¬Q) → (R ∧ S)

  R → T

3. To prove that the band could play rock music (P), we need to derive it using valid rules of inference.

4. Using the premises, we can apply the rule of modus tollens to the second premise:

  R → T        (Premise)

  Therefore, ¬R.

5. Next, we can use disjunctive syllogism on the first premise:

  (¬P ∨ ¬Q) → (R ∧ S)     (Premise)

  ¬R                    (From step 4)

  Therefore, ¬(¬P ∨ ¬Q).

6. Applying De Morgan's law to step 5, we get:

  ¬(¬P ∨ ¬Q)  ≡  (P ∧ Q)

7. Therefore, we can conclude that the band could play rock music (P) based on the premises and rules of inference.

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Answer:

(-2,-3)

Step-by-step explanation:

Rounding to the nearest integer, the predicted calorie count for a cereal with 14 grams of sugar per serving is approximately 163 calories.

An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers. In the language of mathematics,

To calculate the predicted calorie count for a cereal with 14 grams of sugar per serving using the predictive regression equation y^ = 94.639 + 4.918x, we substitute x = 14 into the equation.

y^ = 94.639 + 4.918(14)

y^ = 94.639 + 68.852

y^ ≈ 163.491

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The solution of the algebraic expressions are:

1) x = 3

2) x = 6

3) x = 4

4) x = 1

An algebraic expression is defined as the idea of ​​representing numbers in letters or alphabets without specifying the actual values. In Algebra Basics, we learned how to use letters such as x, y, and z to represent unknown values.

1) 2(4x - 3) - 8 = 4 + 2x

Expand the bracket to get:

8x - 6 - 8 = 4 + 2x

8x - 2x = 4 + 6 + 8

6x = 18

x = 18/6

x = 3

2) (2x + 4x)/4 = 9

Multiply both sides by 4 to get:

2x + 4x = 36

6x = 36

x = 36/6

x = 6

3) 5x + 34 = -2(1 - 7x)

Expand the bracket to get:

5x + 34 = -2 + 14x

36 = 9x

x = 36/9

x = 4

4) (6x + 4)/2 = 5

Multiply both sides by 2 to get:

6x + 4 = 10

6x = 6

x = 1

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The equation of a parabola with a given focus and directrix is:

x^2 - 2ax + 2by + (a^2 + b^2 - c^2) = 0

In this equation, (a, b) represents the coordinates of the focus, and c represents the y-coordinate of the directrix. This equation describes a parabola where all points on the parabola are equidistant from the focus and the directrix.

To write the equation of a parabola with a given focus and directrix, we can use the geometric definition of a parabola. A parabola is the set of all points that are equidistant from the focus and the directrix.

Let's assume the focus is denoted as F(a, b) and the directrix is a horizontal line given by y = c. The vertex of the parabola is at the midpoint between the focus and the directrix, which is V(a, (b + c) / 2).

The distance from any point (x, y) on the parabola to the focus F(a, b) is given by the distance formula:

sqrt((x - a)^2 + (y - b)^2)

The distance from the point (x, y) on the parabola to the directrix y = c is given by |y - c|.

According to the definition of a parabola, these two distances are equal. Thus, we can set up the equation:

sqrt((x - a)^2 + (y - b)^2) = |y - c|

Squaring both sides of the equation eliminates the square root:

(x - a)^2 + (y - b)^2 = (y - c)^2

Expanding and rearranging the terms:

x^2 - 2ax + a^2 + y^2 - 2by + b^2 = y^2 - 2cy + c^2

Simplifying and canceling out the y^2 terms:

x^2 - 2ax + a^2 + b^2 - 2by = c^2 - 2cy

Rearranging the terms to obtain the standard form of the equation:

x^2 - 2ax + 2by + (a^2 + b^2 - c^2) = 0

Thus, the equation of the parabola with focus F(a, b) and directrix y = c is given by:

x^2 - 2ax + 2by + (a^2 + b^2 - c^2) = 0

Complete Question - Write the equation of a parabola with focus F(a, b) and directrix given by y = c.

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Type 1 error is the error occurs when a test indicates a significate  difference between two or more populations.

Rejecting the null hypothesis when it is in fact true is a Type I mistake. It entails drawing conclusions about outcomes that are statistically significant when, in fact, they were just the consequence of chance or unrelated causes. The significance level you select (alpha or ) determines the likelihood that you will make this mistake.

Data cleansing—also known as data cleaning, data scrubbing, or data rectification—is the process of correcting inaccurate, insufficient, duplicate, or other wrong data in a data set. It entails locating data mistakes and then correcting them by modifying, updating, or eliminating data.

Using independent samples from two independent groups, the two-sample (independent groups) t-test is used to assess whether the unknown means of two populations are different from one another.  

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A dilation is a type of transformation causes the image to be larger or smaller than the pre-image.

A dilation is a type of transformation that changes the size of a figure without changing its shape. Dilations can make a figure larger or smaller.

In a dilation, the original figure is called the preimage. The dilated figure is called the image. Figures are dilated from a fixed point, called the center of dilation.Dilations also scale all sides of a figure by the same factor. As a result, dilations preserve angle measures and the ratio between corresponding parts.When dilating a figure, the different parts of the figure are multiplied by the scale factor.

In a dilation, the scale factor refers to the ratio between the corresponding sides of the preimage and the image. Therefore, the scale factor, k, can be calculated by dividing the length of one part in the image with the corresponding part in the preimage. The length of the preimage part should always be in the denominator as it belongs to the original figure.

A dilation is a type of transformation causes the image to be larger or smaller than the pre-image.

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Using the binomial distribution, it is found that there is a 0.9815 = 98.15% probability that at least one of them has been vaccinated.

The formula is:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

In this problem, the values of the parameters are:

n = 5, p = 0.55

The probability that at least one of them has been vaccinated is given by:

\(P(X \leq 1) = 1 - P(X = 0)\)

In which:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{5,0}.(0.55)^{0}.(0,45)^{5} = 0.0185\)

Then:

\(P(X \leq 1) = 1 - P(X = 0) = 1 - 0.0185 = 0.9815\)

0.9815 = 98.15% probability that at least one of them has been vaccinated.

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