use your graphing calculator to solve the equation graphically in the interval [4,7]
x^3 -4.6x^2 -7.03x = -20.332
make sure your answer is accurate to atleast three decimals

the pooled sample variance  р = 6 n = 16 n2 = 2 ,  The correct answer is option A. s = 5.23

To calculate s, the pooled sample variance that should be used in the pooled-variance t test, using the given information, we can use the formula for pooled variance: Pooled variance = [(n1 - 1)s1² + (n2 - 1)s2²] / (n1 + n2 - 2) Where s1² and s2² are the sample variances, n1 and n2 are the sample sizes, and n1 + n2 - 2 is the degrees of freedom. The given information is: p = 6n = 16n2 = 2n1 = n - n2 = 16 - 2 = 14 Substituting these values into the formula: Pooled variance = [(14-1)×6² + (2-1)×0²] / (14 + 2 - 2)= (78 + 0) / 14= 5.57 Using the formula for sample variance: Sample variance, s² = (Σ(x - μ)²) / (n - 1) We need to calculate the variance of the second sample with n2 = 2, so we'll use the formula on this sample only. x = (7 + 5) / 2 = 6μ = 6 (since the population mean is not given, we assume it to be equal to the sample mean) x1 = 7, x2 = 5 Sample variance = [(7 - 6)² + (5 - 6)²] / (2 - 1)= 2/1= 2 Using the formula for sample standard deviation: s = √(s²)= √(2)≈ 1.41 Rounding s to two decimal places, we get s ≈ 5.23. Therefore, option A is the correct answer.

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In the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units.

In the best-case scenario analysis for Automatic Transmissions, Inc.'s new gear assembly project, the company assumes the upper limit of the ±15 percent range for its estimates. For the price per unit, they take a 15 percent increase, resulting in a value of $1081. Similarly, the variable cost per unit is increased by 15 percent to $391. The fixed costs are also adjusted upwards by 15 percent, reaching $3.91 million. Finally, the quantity is decreased by 15 percent, leading to a value of 45,050 units.

On the other hand, in the worst-case scenario analysis, the company assumes the lower limit of the ±15 percent range for its estimates. The price per unit is decreased by 15 percent, resulting in $799. The variable cost per unit is decreased to $289. The fixed costs are adjusted downwards to $2.89 million. Lastly, the quantity is increased by 15 percent to 60,950 units.

Therefore, in the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units

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Applying the definition of congruent triangles:

1. QS = 57 units; TV = 57 units

2. m∠B = 3°; m∠Q = 3°

The triangles that are congruent to each other have corresponding parts that are congruent, that is their corresponding sides and angles are equal to each other.

1. Given that triangles QRS and TUV are congruent triangles, therefore:

QS = TV [corresponding congruent sides]

QS = 4v + 5

TV = 5v - 8

Therefore:

4v + 5 = 5v - 8

4v - 5v = -5 - 8

-v = -13

v = 13

QS = 4v + 5 = 4(13) + 5 = 57 units

TV = 5v - 8 = 5(13) - 8 = 57 units

2. Given that triangles ABC and PQR are congruent, therefore:

m∠B = m∠Q

m∠B = 2v + 1

m∠Q = 8v - 5

Therefore:

2v + 1 = 8v - 5

2v - 8v = -1 - 5

-6v = -6

v = -6/-6

v = 1

m∠B = 2v + 1 = 2(1) + 1 = 3°

m∠Q = 8v - 5 = 8(1) - 5 = 3°

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If a machine that works at a constant rate can fill 40 bottles of milk in 3 minutes, Then the machine will take approximately 18 minutes to fill 240 bottles.

Constant rate is a rate of change is constant when the ratio of the output to the input stays the same at any given point on the function.

Given that machine take 3 minutes to fill 40 bottles

So for 1 minute the machine fill \(\frac{40}{3}\) = 13.3333 bottles.

That is in 1 minute the machine fill approximately 14 bottles.

So the machine take a time to fill 240 bottles is \(\frac{240}{14} = 18.461\).

Thus the machine take approximately 18 minutes to fill 240 bottles.

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Answer:

the vertex is 89

Step-by-step explanation:

Using the formula for volume of cube and with the provided volume and side, the answer is 6cm.

A cube is a three-dimensional solid object in geometry that is surrounded by six square faces, facets, or sides, three of which meet at each vertex.

We get the volume of a cube by thrice multiplying the side length.

Suppose we have a side length of cube = l cm

The required formula is for volume is:

\(V = l ^ {3}\)

As per question, the side length of cube = z

l=z

V = z³

V=216 ³

\(l=\sqrt[3]{216}\)

\(l=6cm\)

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The likelihood that understanding testing positive for HIV with this test is tainted with HIV is almost 0.104 or 10.4%

To illuminate this issue, we will utilize Bayes' hypothesis. Let's characterize the taking after occasions:

A: the persistent is contaminated with HIV

B: the persistent tests positive for HIV

We need to calculate P(A|B), the likelihood that an understanding is contaminated with HIV given that they tried positive for HIV.

By Bayes' hypothesis:

P(A|B) = P(B|A) * P(A) / P(B)

where

1. P(B|A) is the likelihood of testing positive for HIV given that the persistent is tainted with HIV (97%)

2. P(A) is the predominance of HIV within the clinic (8%)

3. P(B) is the likelihood of testing positive for HIV, which can be calculated utilizing the law of adding up to likelihood:

P(B) = P(B|A) * P(A) + P(B|A') * P(A')

where

1. P(B|A') is the likelihood of testing positive for HIV given that the persistent isn't tainted with HIV (4%)

2. P(A') is the complement of A, i.e., the likelihood of a quiet not being tainted with HIV (1 - 8% = 92%)

Substituting the values we have:

P(B) = 0.97 * 0.08 + 0.04 * 0.92 = 0.0736

P(B) =  0.0736

Hence,

P(A|B) = 0.97 * 0.08 / 0.0736 ≈ 0.104

P(A|B) = 0.104

So the likelihood that understanding testing positive for HIV with this test is tainted with HIV is almost 0.104 or 10.4% (adjusted to three decimal places). 

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Step-by-step explanation:

=> 2r + 7 = 16

=> 2r = 16 - 7

=> r = 9/2

=> r = 4.5

Answer:

r= 1/2

Step-by-step explanation:

Subtract  7   from both sides of the equation

2 + 7 = 1 6

2 + 7 − 7 = 1 6 − 7

Simplify

2 = 1 6 − 7

Subtract  16r  from both sides of the equation

2 = 1 6 − 7

2 − 1 6 = 1 6 − 7 − 1 6

Simplify

-14r= -7

Divide both sides of the equation by the same term

− 1 4 = − 7

-14r=-7

− 1 4 − 1 4

Simplify

r= 1/2

The required ratios: a. Purchasers to non purchasers is 37:13 b. Non Purchasers to purchasers is 13:37 c. Purchasers to total customers is 37:50 d. Non Purchasers to total customers is 13:50

So, based on the information-

Non purchasers = 13

Purchasers = 37

Total customers = 50

Finding ratio by keeping the values as per the requirement -

a. Purchasers to non purchasers = 37:13

b. Non Purchasers to purchasers = 13:37

c. Purchasers to total customers = 37:50

d. Non Purchasers to total customers = 13:50

Hence, the ratios are a. 37:13, b. 13:37, c. 37:50 and d. 13:50.

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Answer:yes

Step-by-step explanation:

but if the y intercept is 0 then it’ll show like: y= 3x which is equal to y=3x plus or minus 0

No, a piecewise function does not always have an x and y intercept.

A piecewise function is a function that is defined by multiple sub-functions, each of which applies to a certain interval of the main function's domain.

An x-intercept is the point where the function crosses the x-axis, and a y-intercept is the point where the function crosses the y-axis.

It is possible for a piecewise function to not have an x or y intercept if none of the sub-functions cross the x or y axis. For example, the piecewise function f(x) = {2x + 1 for x < 0, -2x + 1 for x > 0} does not have an x or y intercept because neither of the sub-functions cross the x or y axis.

In conclusion, a piecewise function does not always have an x and y intercept. It depends on the sub-functions that make up the piecewise function.

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Answer:

k = - 1

Step-by-step explanation:

calculate the gradient (slope) m of AB using the slope formula and equate to 4

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 3, 4 ) and (x₂, y₂ ) = (k, 12 )

m = \(\frac{12-4}{k-(-3)}\) = \(\frac{8}{k+3}\) , then

\(\frac{8}{k+3}\) = 4 ( multiply both sides by (k + 3 ) )

4(k + 3) = 8 ( divide both sides by 4 )

k + 3 = 2 ( subtract 3 from both sides )

k = - 1

Answer:

-5 X x > 2(-5 X x) +3

-5x >2(-5x + 3)

-5x > -10x + 6

-5x + 10x > 6

5x > 6

x > 6/5

Answer:

The slope of the linear equation is 0.1998, and it means that the calories in a beef hot dog is increasing with the rate of 0.1998 calories per milligram of sodium.

Step-by-step explanation:

Answer:

m=7

Step-by-step explanation:

subract 35 from both sides to isolate the variable. Then you should be left with 5m=35. From there, divide both sides to isolate the variable even more, and you should be left with m=35/5 which is 7.

Answer: m=7

Step-by-step explanation:

\(5m+35=70\)

subtract 35 on both sides

\(5m+35-35=70-35\)

\(5m=35\)

divide 5 on both sides

\(35/5=7\)

\(m=7\)

Answer:

find the width and length

Step-by-step explanation:

Ansta c

es decir la pendiente es -1/3 y la intersección con el eje y es -2/5 segun mis calculoslanation:

Answer:not sure

Step-by-step explanation:

This was my bad place in mathe

Answer:

The Distance between the points is B. 48

Answer:

  x = -8/7

Step-by-step explanation:

You want the zero(s) of the rational expression (7x²+29x+24) /(5x²+ 19x+12).

The zeros will be the values of x that make the numerator of the simplified form of the expression be zero.

  \(\dfrac{7x^2+29x+24}{5x^2+19x+12}=\dfrac{(x+3)(7x+8)}{(x+3)(5x+4)}=\dfrac{7x+8}{5x+4}\)

This is zero when ...

  7x +8 = 0

  x = -8/7 . . . . . . . subtract 8, divide by 7

The zero of the rational expression is x = -8/7.

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The time taken by the planes when they are 2000 miles apart is 2 hours.

We all know that formula of distance, speed and time is given by  distance = speed*time or time = distance/speed

Let x be the number of hours that the two planes will be 2000 miles apart.

Let 430x be the distance traveled by the first plane at 430 miles per hour

and 570x be the distance traveled by the second plane at 570 miles per hour.

here, 430x +570x =2000 is the total distance travelled by the first plane and the second plane

Solving yields the following steps:

1000x = 2000

Dividing 1000 to both sides of the above equation, we get

1000x/1000=2000/1000

So the value of x will be equivalent to 2

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The only relative extremum of the function f(x) = x^4 - 4x^3 is a relative minimum at x = 3.

To find the relative extrema of the function f(x) = x^4 - 4x^3, we need to find the critical points and then determine whether they correspond to relative maxima, relative minima, or neither.

First, we find the first derivative of f(x) by using the power rule:

f'(x) = 4x^3 - 12x^2

Next, we find the critical points by setting the derivative equal to zero and solving for x:

4x^3 - 12x^2 = 0

4x^2(x - 3) = 0

So the critical points are x = 0 and x = 3.

To determine whether these critical points correspond to relative maxima, relative minima, or neither, we use the second derivative test. We find the second derivative of f(x) by using the power rule:

f''(x) = 12x^2 - 24x

Then we evaluate the second derivative at each critical point:

f''(0) = 0 - 0 = 0

f''(3) = 12(3)^2 - 24(3) = 36 > 0

Since f''(0) = 0 and f''(3) > 0, we can conclude that: x = 0 is not a relative extremum because the second derivative test is inconclusive.

x = 3 is a relative minimum because the second derivative test shows that f''(3) is positive, which means that the graph of the function is concave up at x = 3, and therefore x = 3 corresponds to a relative minimum.

Therefore, the only relative extremum of the function f(x) = x^4 - 4x^3 is a relative minimum at x = 3.

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Answer:

Step-by-step explanation:

To convert square meters to square centimeters, we need to multiply by the conversion factor (100 cm / 1 m)^2.

So,

3.9 m² = 3.9 × (100 cm / 1 m)²

3.9 m² = 3.9 × 10,000 cm²

3.9 m² = 39,000 cm²

Therefore, 3.9 square meters is equal to 39,000 square centimeters.

Answer:

see explanation

Step-by-step explanation:

basically Gauss' method simplifies to

Sum = (number of terms) ÷ 2 × (1st term + last term)

43

S₂₀₀ = 200 ÷ 2 × (1 + 200) = 100 × 201 = 20,100

44

S₄₀₀ = 400 ÷ 2 × (1 + 400) = 200 × 401 = 80,200

45

S₈₀₀ = 800 ÷ 2 × (1 + 800 ) = 400 × 801 = 320,400

46

S₂₀₀₀ = 2000 ÷ 2 × (1 + 2000) = 1000 × 2001 = 2,001,000

Answer:

Sum = (number of terms) = 2 x (1st term + last term) 43

43. S200 = 200 = 2 × (1+200) = 100 201 = X 20,100

44 400 400 = 2 × (1+400) = 200 × 401 = 80,200

45 S800 = 800 = 2 × (1+800) = 400 × 801 = 320,400

46 S2000 = 2000 2 × (1+ 2000) = 1000 × 2001 = 2,001,000

Based on the provided information, the number of subjects examined is not explicitly mentioned. However, the given t-value (t(29) = 2.001) suggests that the study involved a sample size of 30 participants, as denoted by the degrees of freedom (df) in parentheses.

The notation t(29) = 2.001 represents a t-test, a statistical test used to determine if there is a significant difference between the means of two groups. In this case, the subscript "29" in t(29) denotes the degrees of freedom (df), which is calculated by subtracting 1 from the sample size. Therefore, df = 30 - 1 = 29.

Since the degrees of freedom are 29, it indicates that the sample size used in the study was 30 participants. The t-value of 2.001 represents the magnitude of the t-statistic, which measures the difference between the means of the two groups being compared.

The critical value for significance is not provided, but the statement "p < 0.05" suggests that the obtained p-value is less than 0.05, indicating statistical significance. However, the exact p-value is not given, so the level of significance cannot be precisely determined.

Overall, the information provided implies that the study involved a sample of 30 subjects, and the t-value and p-value suggest a significant result.

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The standard form equation for the ellipse is (x - 1)^2/3 + (y - 1)^2/1/3 = 1 after completing the square.

To convert the given equation, 2x^2 + 6y^2 - 12y - 4x + 2 = 0, to standard form for an ellipse, we need to complete the square for both the x and y terms.

Starting with the x-terms:

Group the x-terms together: 2x^2 - 4x

Factor out the coefficient of x^2/2: 2(x^2 - 2x)

To complete the square, we need to add and subtract the square of half the coefficient of x (-2/2)^2 = 1:

2(x^2 - 2x + 1 - 1)

Next, we simplify the y-terms:

Group the y-terms together: 6y^2 - 12y

Factor out the coefficient of y^2/6: 6(y^2 - 2y)

Similarly, we add and subtract the square of half the coefficient of y (-2/2)^2 = 1:

6(y^2 - 2y + 1 - 1)

Now we can rewrite the equation:

2(x^2 - 2x + 1) + 6(y^2 - 2y + 1) - 2 - 6 = 0

Simplifying further:

2(x - 1)^2 + 6(y - 1)^2 - 8 = 0

Finally, to put it in standard form, divide the entire equation by -8 to get:

(x - 1)^2/4 + (y - 1)^2/8/3 = 1

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The cylinder with maximum volume has a radius of 6.5 feet and a height of 2.5 feet.

Let the radius and height of the cylinder be r and h, respectively. Since the cylinder is inscribed in the cone, its height and radius must satisfy the following conditions:

The height of the cylinder must be equal to the height of the cone, i.e. h = 2.5 feet.

The radius of the cylinder must be less than or equal to the radius of the base of the cone, i.e. r ≤ 6.5 feet.

To maximize the volume of the cylinder, we can use the formula for the volume of a cylinder:

V = πr^2h

Substituting h = 2.5, we get:

V = 2.5πr^2

Now, we can express the volume of the cylinder in terms of a single variable, r. To do this, we use the fact that the cylinder is inscribed in the cone, so the cross-sectional area of the cylinder is a fraction of the cross-sectional area of the cone. Specifically, the ratio of the areas is equal to the square of the ratio of the radii:

r/6.5 = h/2.5

Solving for h, we get:

h = 2.5r/6.5

Substituting into the formula for the volume of the cylinder, we get:

V = 2.5πr^2 = 2.5πr^2(h/2.5) = πr^2(2r/6.5)

Simplifying, we get:

V = (4π/13)r^3

To find the value of r that maximizes V, we can take the derivative of V with respect to r and set it equal to zero:

dV/dr = (4π/13)3r^2 = 0

Solving for r, we get:

r = 0

This is not a valid solution since r must be greater than zero. Therefore, we must look for a maximum value of V on the interval 0 < r ≤ 6.5.

To do this, we can evaluate V at the endpoints of the interval and at any critical points in the interior. Since we already know that there are no critical points, we just need to evaluate V at the endpoints:

V(0) = 0

V(6.5) = (4π/13)(6.5)^3 ≈ 724.06

Therefore, the cylinder with maximum volume has a radius of 6.5 feet and a height of 2.5(6.5/6.5) = 2.5 feet.

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Answer:

4(6+7)

Explanation:

24+28

(4×6)+(4×7)

4(6+7)