Determine the value of k a) So that x+2 is a factor of x3 - 2kx² + 6x-4 b) So that 3x-2 is a factor of 3x3 - 5x² + kx + 2

Answer:

0.630

Step-by-step explanation:

Simply evaluating, we get v (0) = 1, v (0.31831) = 0.630, v (2) = 1.566. Thus, the minimum velocity over the interval [ 0, 2] is 0.630.

To find the daily mileage for which the Ultimo charge is twice the Primo charge, we can set up an equation and solve for the unknown value.

Let's start by defining some variables:
- Let x be the daily mileage.
- The Primo car rental agency charges $45 per day plus $0.40 per mile, so the Primo charge can be expressed as 45 + 0.40x.
- The Ultimo car rental agency charges $26 per day plus $0.85 per mile, so the Ultimo charge can be expressed as 26 + 0.85x.
According to the question, we need to find the value of x for which the Ultimo charge is twice the Primo charge. Mathematically, we can write this as:
26 + 0.85x = 2(45 + 0.40x)
Now, let's solve this equation step-by-step:
1. Distribute the 2 to the terms inside the parentheses on the right side of the equation:
26 + 0.85x = 90 + 0.80x
2. Move all the x terms to one side of the equation and all the constant terms to the other side:
0.85x - 0.80x = 90 - 26
3. Simplify and solve for x:
0.05x = 64
x = 64 / 0.05
x = 1280
Therefore, the daily mileage for which the Ultimo charge is twice the Primo charge is 1280 miles.

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The minimum surface area of the container is approximately 275.52 cm².

Let's suppose that the length, width, and height of the rectangular container are l, w, and h, respectively. We know that the container has a square base, so l = w. Also, we know that the volume of the container is 864 cm³, so we have:

l × w × h = 864

Since l = w, we can write this as:

l² × h = 864

We want to minimize the surface area of the container, which consists of the area of the base (l²) and the area of the four sides (2lh + 2wh). We can express the surface area in terms of l and h:

Surface Area = l² + 2lh + 2wh

Using the equation l² × h = 864, we can solve for h in terms of l:

h = 864 / (l²)

Substituting this into the equation for the surface area, we get:

Surface Area = l² + 2l(864 / l²) + 2w(864 / (lw))

Simplifying and using l = w, we get:

Surface Area = 2l² + 1728/l

To find the minimum surface area, we can take the derivative of this expression with respect to l, set it equal to zero, and solve for l:

d/dl (2l² + 1728/l) = 4l - 1728/l² = 0

4l = 1728/l²

l³ = 432

l = ∛432 ≈ 8.77 cm

Since the container has a square base, the length and width are both 8.77 cm. Using the equation l² × h = 864, we can solve for h:

h = 864 / (8.77)² ≈ 10.85 cm

Therefore, the minimum surface area of the container is:

Surface Area = 2(8.77)² + 2(8.77)(10.85) ≈ 275.52 cm²

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Answer:

The secant function is undefined for angles where the cosine function equals zero, because dividing by zero is undefined. Therefore, we need to find the values of Θ where cos Θ = 0.

The cosine function equals zero at 90° and 270° (or π/2 and 3π/2 in radians), so we have:

cos 90° = 0, cos 270° = 0

Therefore, the angles that satisfy sec Θ = undefined are:

Θ = 90° + 360°k, Θ = 270° + 360°k

where k is an integer (positive, negative, or zero) that allows us to generate all possible angles in the range 0° ≤ Θ ≤ 360°.

So, the solutions for Θ are:

Θ = 90° + 360°k, Θ = 270° + 360°k

where k is an integer.

Step-by-step explanation:

The probability that the mean years of education of this sample is at most 7.6 years is 0.841.

Let X be the mean years of education of this sample. Then X follows a Normal Distribution, N(7.4, 3.4).

We want to find P(X <= 7.6).

Using the Z-Score Table, we find that P(X <= 7.6) = 0.8413.

So, the probability that the mean years of education of this sample is at most 7.6 years is 0.841.

To calculate this, we first find the Z-Score of 7.6

Z = (x - mean) / sd

Z = (7.6 - 7.4) / 3.4

Z = 0.5882

Then, we look up the Z-Score of 0.5882 in the Z-Score Table and find the probability associated with it.

P(X <= 7.6) = 0.8413

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The volume of the solid that is formed when the area bounded by x y=1, y=0, x=1, and x=2 is rotated about the line x=-1 is (14π/3) cubic units.

The solid that is formed when the area bounded by

xy=1, y=0, x=1, and

x=2 is rotated about the line

x=-1 is given by the disk method.

To find the volume of the solid, we integrate the area of each disk slice taken perpendicular to the axis of revolution,

which in this case is the line x=-1.

The area of each disk slice is given by the formula π(r^2)δx

where r is the radius of the disk and δx is its thickness.

To find the radius r of each disk slice, we consider that the distance between the line

x=-1 and the line

x=1 is 2 units.

Hence,

the radius of the disk is r=2-x.

Hence, the volume of the solid is given by:

V= ∫1^2 π(2-x)^2 dx

= π ∫1^2 (x^2-4x+4) dx

= π[(x^3/3)-(2x^2)+4x]

evaluated between

x=1 and

x=2= π [8/3-8+4-1/3+2-4]

= (14π/3) cubic units

Therefore, the volume of the solid that is formed when the area bounded by x y=1,

y=0,

x=1, and

x=2 is rotated about the line

x=-1 is (14π/3) cubic units.

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We can conclude that we are 96% confident that the true population mean falls within the calculated confidence interval.

To find the 96% confidence interval for the true population mean of 4-day-old infants, we can follow these steps:

Step a: State the Critical Values:

Since the sample size is large and the population standard deviation is known, we can use the Z-distribution. For a 96% confidence level, we need to find the critical Z-values. The critical Z-value for a two-tailed test with a 96% confidence level is found by subtracting (1 - 0.96)/2 from 1 and looking up the corresponding value in the standard normal distribution table. The critical Z-value for a 96% confidence level is approximately 1.96.

Step b: State the Margin of Error:

The margin of error is calculated by multiplying the critical Z-value by the standard deviation divided by the square root of the sample size.

Margin of Error = Z * (Standard Deviation / √(Sample Size))

Step c: Confidence Interval:

The confidence interval is calculated by subtracting and adding the margin of error to the sample mean.

Confidence Interval = (Sample Mean - Margin of Error, Sample Mean + Margin of Error)

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Answer:

\(-\frac{2}{5}\)

Step-by-step explanation:

Given expression:

           2x + 5y = -10

The equation of a straight line is;

            y = mx + c

y and x are the coordinates

m is the slope

c is the intercept

 Now;

          let us write the given expression in slope intercept format;

            2x + 5y  = -10

                    5y = -2x - 10

                     y = \(-\frac{2x}{5}\)  - 2

So, the slope of the line is \(-\frac{2}{5}\)

Answer:

AB = 21

Step-by-step explanation:

Tales' theorem

\(\frac{12}{14} =\frac{18}{AB}\)

\(AB=\frac{(14)(18)}{12}\)

\(AB=21\)

Hope this helps

(i)Given that:

AE || BD

AB = ? [Let AB be x]

BC = 3

ED = 12

DC = 4

We know that

By Basic Proportionality Theorem,

AB/BC = ED/DC

On substituting these values in the above formula

⇛ AB / 3 = 12 / 4

On applying cross multiplication then

⇛ x(4) = (12)3

⇛ 4x = 36

Shift the number 4 from LHS to RHS.

⇛ x = 36÷4

⇛ x = 36/4

Therefore, AB = 9

Answer: The value of AB for the given problem is 9.

Similarly,

(ii) Given that:

EB || DC

AE = 14

ED = 12

AB = ? [Let AB be X]

BC = 18

We know that

By Basic Proportionality Theorem,

AE / ED = AB / BC

On substituting these values in the above formula

⇛ 14 / 12 = x / 18

On applying cross multiplication then

⇛ 14(18) = (12)x

⇛ 252 = 12x

Shift the number 252 from LHS to RHS.

⇛ X = 256÷12

⇛ X = 21

Therefore, AB = 21

Answer: The value of AB for the given problem is 21

Additional comment:

Basic Proportionality Theorem

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Answer:

79%

Step-by-step explanation:

The expression is 6 times 1 equals 6/6 + 2 = 8

Expression:

An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Let's say P is worth 1

9 times 1 equals 9

3 times 1 equals 3

9 - 3 = 6

6 + 2 = 8

So the expression equivalent to 9p minus 3p 2 is 8.

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When using a one-way within-groups ANOVA, the variability due to individual differences is reduced, resulting in a more accurate assessment of the effect of the independent variable on the dependent variable.

To minimize the variation between individuals, their scores are evaluated within the same group rather than comparing them across different groups.

The within-groups ANOVA method utilizes identical individuals in different conditions or treatments to counteract personal variances, thereby enabling a more accurate measurement of the independent variable's impact.

By adopting this method, the analysis gains greater statistical strength, resulting in a more heightened aptitude to identify genuine effects of the independent factor on the dependent element.

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The volume of water in the fish tank for the given time value is 0, 5, 7, 9, 11, and 13 liters.

The equation V = 3 + 2t expresses a time function, which represents the volume of fish tank as a function of time. It means that after t time, volume V is given by the equation. In the given table. t = 0,1,2,3,4,5. Hence, the volume can be determined by substituting the value of t in the equation.

When t = 0

V = 3 + 2(0) = 3 liter

When t = 1

V = 3 + 2(1) = 5 liter

When t = 2

V = 3 + 2(2) = 7 liter

When t = 3

V = 3 + 2(3) = 9 liter

When t = 4

V = 3 + 2(4) = 11 liter

When t = 5

V = 3 + 2(5) = 13 liter

Note: The question is incomplete. The complete question probably is: A 40-liter fish tank is being filled with a faucet at a constant rate of 2 liters per minute. Before the faucet is turned on, the fish tank has a volume of 3 liters. The volume of water V in the fish tank is a function of time t. Time is measured in minutes and volume of water is measured in liters. Use the equation V = 3 + 2t to complete the function table.

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The theorem that shows that TUV ≅ WVU is law of congruent triangles

If two triangles have the same size and shape they are called congruent triangles. If we flip, turn or rotate one of two congruent triangles they are still congruent. If the sides of two triangles are the same then the triangles must have the same angles and therefore must be congruent.

Therefore two triangles are said to be congruent if the three sides and the three angles of both the angles are equal in any orientation.

from the shape,

Since line UW = VT and Line UV is common to both ∆TUV and ∆WUV, then TU = VW

Therefore ∆TUV and ∆WUV are congruent.

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Therefore, the degrees of freedom for the treatment source of variation is 3.

In ANOVA (Analysis of Variance), the total variability of a dataset is divided into different sources of variation, such as treatment, error, and total. The treatment source of variation represents the differences between the means of the groups being compared. The degrees of freedom for the treatment source of variation refer to the number of independent pieces of information used to estimate the variability due to treatment. It is calculated as the number of groups minus one. In this case, with four groups, the degrees of freedom for the treatment source of variation is 3. This value is used in calculating the F-statistic and determining if there are significant differences between the group means.

The degrees of freedom for the treatment source of variation can be calculated using the formula:

Degrees of freedom (treatment) = number of groups - 1

In this case, there are 4 groups, so the degrees of freedom for the treatment source of variation would be:

Degrees of freedom (treatment) = 4 - 1 = 3

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For a sample of 72 batteries, the probability that the average battery life of the sample exceeds 1173.8 minutes is 0.9918.

It states a battery life variance of 8100 minutes and a median battery life of 1192 minutes.

In a sample of 72 batteries, find the probability that the average battery life (x) of the sample exceeds 1173.8 minutes.

Due to the large sample size (n = 72), we can use the central limit theorem to assume that the sample mean follows a normal distribution with mean μ = 1192 and standard deviation σ = sqrt(8100/72) = 30.

So the z-score for x= 1173.8 is

z = (x - μ) / (σ / sqrt(n))

= (1173.8 - 1192) / (30 / square(72))

= -2.4

You can use a standard normal distribution table or calculator to find the probability that a  standard normal random variable is greater than -2.4. This is 0.9918 (rounded to four decimal places).

Therefore, for a sample of 72 batteries, the probability that the average battery life of the sample exceeds 1173.8 minutes is 0.9918 (rounded to four decimal places) if the claim is correct. 

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Step-by-step explanation:

P = IV

2000 W = I (120 V)

I = 16.7 A

P = E/t

P = (2000 W × 8 hr) / (1 day)

P = 16,000 W·hr/day

P = 16000 W·hr/day × (365 day / yr)

P = 5,840,000 W·hr/yr

P = 5,840,000 W·hr/yr × (1 kW / 1000 W)

P = 5840 kW·hr/yr

C = 5840 kW·hr/yr × (0.25 $/kW/hr)

C = $1460/yr

Answer:

£2120

Step-by-step explanation:

First, you need to find 3% of £2000

£2000 ÷ 100 = 20

20 x 3 = £60

Since you gain £60 per year, you gain £120 for two years

£2000 + £120 =

£2120

Step-by-step explanation:

Expanded 300+60+.1+.02+.004

exponential you can't have on if you don't have an exponent

\(\huge\text{Hey there!}\)

\(\mathsf{x^3 + 2x = 40}\)

\(\large\text{Subtract 40 to both sides:}\)

\(\mathsf{x^3 + 2x - 40 = 40 - 40}\)

\(\large\text{Simplify it:}\)

\(\mathsf{x^3 + 2x - 40 = 40 - 40}\)

\(\mathsf{x^3 + 2x - 40= 0}\)

\(\large\text{If you're familiar with the cubic formula use that to solve this portion:}\)

\(\large\textsf{If you're unfamiliar with the cubic formula we will study that another}\\\large\textsf{time whenever you're ready to understand it }\heartsuit\)

\(\mathsf{x = 3.22524}\)

\(\mathsf{x \approx 3}\)

\(\huge\text{Therefore, your answer should be: \boxed{\mathsf{3.22524}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

The shape is an irregular pentagon

Answer:

140

Step-by-step explanation:

arc AB = 140 because is inscribed by a central angle so the arc and the angle are equal

Answer: ab=14.7

Step-by-step explanation:

  The ant's entire distance travelled along its semicircular journey is its total distance travelled overall. The ant is travelling around a circle with radius R, thus the distance it has travelled is equal to half of the circle's circumference, πR.

The change in the ant's position is represented by a vector quantity called the displacement of the ant. The ant in this scenario begins at one end of the semi-circular path and moves 2R away from the beginning point to reach the other end. The direction of the displacement vector is from the starting point to the ending point, and the displacement's magnitude is equal to the 2R distance between the two points.

    So, the option c is most suitable option.

Therefore, πR and 2R are the ant's displacement and the distance travelled, respectively.

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The value of k maintains maintain the length of each segment of the dilated figure, to choose k = 1.

A process of changing the size of an object or a shape without changing its shape. The shape can be a point, a line segment, a polygon, etc. It should be noted that the shape can be enlarged or  but the proportion of each dimension of the shape and the angles remain the same.

ΔPQR is dilated (enlarged) to ΔP'Q'R' and the angles are the same. The coordinates of the vertices of ΔPQR have been changed after dilation.

P(1,3)  → P' (3,9)

Q(3,1)  → Q' (9,3)

R(1,1)  → R' (3,3)

How to Calculate the Scale Factor in Dilation?

The scale factor can be calculated when the original dimension and the changed dimension is given. Let us find the scale factor of a triangle with the original dimensions and scaled up dimensions. As seen above, after dilation, the coordinates of ΔPQR changed as follows:

P(1,3)  → P' (3,9)

Q(3,1)  → Q' (9,3)

R(1,1)  → R' (3,3)

Let us consider each vertex one by one:

Vertex P:

The x-coordinate 1 changed to 3 and the y-coordinate 3 changed to 9. This shows that both the coordinates of P' became thrice the coordinates of P.

Vertex Q:

The x-coordinate 3 changed to 9 and the y-coordinate 1 changed to 3. This again shows that both the coordinates of Q' became thrice the coordinates of Q.

Vertex R:

The x-coordinate 1 changed to 3 and the y-coordinate 1 changed to 3. As we can see, both the coordinates of R' became thrice the coordinates of R

Therefore, the scale factor in this dilation is 3. Every coordinate of ΔPQR is multiplied by the scale factor of 3 to obtain the enlarged Δ P'Q'R'. In other words, if the scale factor is k, the coordinates (x,y) are transformed to (k x, k y).

(x,y)  → (k x, k y).

The scale factor can also be calculated directly by using the formula: Scale factor = Dimension of the new shape ÷ Dimension of the original shape

The coordinates of the new vertices by the coordinates of the original vertices, we can get the scale factor. For example, let us take the dimensions of vertex P (1, 3) and  P' (3, 9).

Take the x-coordinate of P' = 3 and the x-coordinate of P = 1.

Substitute the values in the formula: 3 ÷ 1 = 3.

Now, take the y-coordinate of P' = 9  and the y-coordinate of P = 3.

the same formula: 9 ÷ 3 = 3. Thus, the scale factor of 3 from both the coordinates.

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difference in order   percents in order

30                              33%

120                             100%

25                               50%

9                                  8%

Answer:

D. 9

Step-by-step explanation:

9 is the degree of polynomial

Answer:

You will earn $15.75, $13.50, or $18 depending on how you are getting paid

Step-by-step explanation:

If you are getting paid a flat rate not by the hour, then simply multiply $3.50 by 3.5 to get $15.75

If you are getting paid by the hour, and only by full hours, the you get $3.50 for the first, second, and third hour, but not for the fourth hour because it has only been a half hour, so only $13.50.

If you are getting paid for each hour that you start, then you get $3.50 for four hours, or $18.00 total

The probability that exactly 2 employees were over 50 if the dismissed employees were selected at random is 0.2048.

We have to determine the probability that exactly 2 employees were over 50 if the dismissed employees were selected at random. It is given that the town recently dismissed 6 employees to meet their new budget reductions. It is also given that the town had 4 employees over 50 years of age and 17 under 50 years of age. Therefore, total employees in the town = 4 + 17 = 21.

If we assume that all the employees have an equal probability of being selected, then the total number of ways of selecting 6 employees from 21 employees can be given by:21C6 = (21*20*19*18*17*16)/(6*5*4*3*2*1) = 54264Now, the number of ways of selecting exactly 2 employees over 50 from 4 employees over 50 can be given by:4C2 = (4*3)/(2*1) = 6Also, the number of ways of selecting exactly 4 employees under 50 from 17 employees under 50 can be given by:17C4 = (17*16*15*14)/(4*3*2*1) = 2380.

Therefore, the number of ways of selecting 2 employees over 50 and 4 employees under 50 from the total 6 employees can be given by:6C2 * 17C4 = (6*5/2*1) * (17*16*15*14/4*3*2*1) = 3246320.

Hence, the probability that exactly 2 employees were over 50 if the dismissed employees were selected at random is given by:3246320/54264 = 0.2048 (rounded to four decimal places).

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The area covered by the pool and the cement walkway is 304  square feet. The width of the walkway would be 5 feet

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

Let x be represent the width of the walkway.

The pool measures 25 ft by 10ft . If the walkway must have a uniform width around the entire pool, then the total length of the pool and the walkway =  25+ x + x = 25 + 2x

The total width of the pool and the walkway = 10 + x + x = 10 + 2x

The area covered by the pool and the cement walkway is 304  square feet. This means that;

(25 + 2x)(10 + 2x) = 304

250 + 50x + 20x + 4x^2 = 304

4x^2 + 70x + 250 - 304 = 0

4x^2 + 70x - 54 = 0

x(x + 20) - 5(x + 20) = 0

(x - 5)(x + 20) = 0

x = 5 or x = - 20

Thus The width cannot be negative.

Therefore, the width of the walkway is 5 feet.

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