gina wilson quiz 4-3

(25) The equation of volume is x³+5x²+4x-84 = 0.

(26) Rational zeros = ±{1, 2, 3, 4, 6, 7, 14, 21, 42, 84}

(27) The dimension of the box is 3, -4.-3.5i and -4+3.5i.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

Give that,

The equation for the volume of box,

V= x³+5x²+4x.

(24)

The volume of the box is 84,

⇒x³+5x²+4x = 84

⇒x³+5x²+4x-84 = 0

The equation of volume is x³+5x²+4x-84 = 0.

(25)

To find rational zeros,

Coefficient of constant term = -84

Factor of constant term =± {1, 2, 3, 4, 6, 7, 14, 21, 42, 84}

Coefficient of leading term = 1

Factor of leading term =± 1

Rational zeros = ±{1, 2, 3, 4, 6, 7, 14, 21, 42, 84}

(26)

To find the dimension of the box,

Find factor of equation x³+5x²+4x-84 = 0

The factors are 3, -4.-3.5i and -4+3.5i.

The dimension of the box is 3, -4.-3.5i and -4+3.5i.

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The solutions to the quadratic equation are:

x = (2 + √7)/3

x = (2 - √7)/3

To solve the quadratic equation 3x² - 4x = 2 by completing the square, follow these steps:

Step 1: Move the constant term to the right side of the equation:

3x² - 4x - 2 = 0

Step 2: Divide the entire equation by the coefficient of x² to make the coefficient 1:

(3/3)x² - (4/3)x - (2/3) = 0

Simplifying, we get:

x² - (4/3)x - (2/3) = 0

Step 3: Take half of the coefficient of x, square it, and add it to both sides of the equation:

x² - (4/3)x + (-4/6)² - (-4/6)² - (2/3) = 0

Simplifying, we have:

x² - (4/3)x + (4/6)² - 16/36 - 12/36 = 0

x² - (4/3)x + (2/3)² - 28/36 = 0

x² - (4/3)x + (2/3)² - 7/9 = 0

Step 4: Rewrite the left side of the equation as a perfect square trinomial:

(x - 2/3)² - 7/9 = 0

Step 5: Add 7/9 to both sides of the equation:

(x - 2/3)² = 7/9

Step 6: Take the square root of both sides of the equation:

x - 2/3 = ±√(7/9)

Step 7: Solve for x by adding 2/3 to both sides:

x = 2/3 ± √(7/9)

Simplifying the square root:

x = 2/3 ± √7/3

Therefore, the solutions to the quadratic equation are:

x = (2 + √7)/3

x = (2 - √7)/3

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The probability of a type II error is β = P(accept H0 | H1 is true) = P(z > -2.07) = 0.9818. Hence, the correct option is (a) 0.9818.

Given, Current mean time = 88 minutes

Standard deviation = 7.9 minutes

New method mean assembly time for a sample of 24 computers = 72 minutes

Hypotheses: The hypotheses are:H0: µ ≥ 88 (the current method is used)H1: µ < 88 (the new method is used)

Sample size is n = 24

The level of significance α is not given, so we assume it as 0.05, i.e., α = 0.05.

Firstly, we need to calculate the critical values of the test.

To calculate the critical values of the test, we need to calculate the standard error of the sample mean: Standard error of the sample mean= σ/√n = 7.9/√24=1.61Then, the test statistic is given by: z = (x - µ) / (σ / √n) where x is the sample mean.

The sample mean is x = 72.z = (72 - 88) / (7.9 / √24) = -4.56

The critical value of z for a left-tailed test with α = 0.05 is -1.645.

Now, to find the probability of a type II error, we need to find the probability of not rejecting the null hypothesis when it is false.

That is, the probability of accepting the current method when the new method is used.

The probability of a type II error is given by: β = P(accept H0 | H1 is true)

We need to find the probability of accepting H0 when µ < 88. This probability depends on the true value of the mean assembly time under the new method.

Let's consider that the new method has a mean assembly time of 80 minutes, i.e., µ = 80.

Then, the probability of not rejecting H0 is the probability of a z-score less than -1.645 - the critical value of z.z = (72 - 80) / (7.9 / √24) = -2.07P(z > -2.07) = 0.9818

Therefore, the probability of a type II error is β = P(accept H0 | H1 is true) = P(z > -2.07) = 0.9818. Hence, the correct option is (a) 0.9818.

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Answer:

1227 is correct ................................................

Step-by-step explanation:

Answer:

Is 6 part of the equation?

Answer:

A is the answers for the question

Step-by-step explanation:

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To obtain the residuals from the fit in 8.4a and plot them against y and x, as well as prepare a normal plot, we need the specific details of the fit and the data used.

WE know that residuals represent the differences between the observed values and the predicted values from a statistical model or regression analysis.

Since the residuals against y and x can help identify patterns or trends in the data that may indicate issues with the model's fit.

A normal plot, known as a Q-Q plot, compares the distribution of the residuals to a theoretical normal distribution. If the residuals closely follow a straight line in the normal plot, the residuals are normally distributed, which is an assumption of many statistical models.

Interpreting these plots involves examining the patterns and deviations from expected behavior. If the residuals exhibit a consistent pattern, it might indicate that the model does not capture all the relevant information in the data.

Thus if the residuals appear randomly scattered around zero with no discernible pattern, it suggests that the model adequately explains the data. Deviations in the normal plot may indicate departures from the assumption of normality in the residuals, which could impact the reliability of statistical inferences.

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Normal faults assume a more shallow dip angle with depth; when the fault plane becomes nearly horizontal, these faults are termed as thrust fault.

Since,

A reverse fault in which the dip of the fault plane is so small as to be almost  horizontal is called thrust fault. In thrust faults, the hanging wall moves almost horizonatlly over the footwall.

Hence,

Normal faults assume a more shallow dip angle with depth; when the fault plane becomes nearly horizontal, these faults are termed as thrust fault.

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Answer:

1

Step-by-step explanation:

The factors of 5 are: 1, 5

The factors of 11 are: 1, 11

The factors of 13 are: 1, 13

Therefore the greatest/highest common factor is 1.

The critical value for this two-tailed test is 2.6759.

To conduct a two-tailed test at the 0.01 level of significance with a sample of 55 observations, we use the t-distribution because the population standard deviation is unknown. The critical value is determined by dividing the significance level (0.01) by 2 to account for both tails of the distribution. This gives an alpha level of 0.005. Using the degrees of freedom for a sample of size 55 (54 degrees of freedom), we find the corresponding critical value from a t-distribution table or calculator. In this case, the critical value is approximately 2.6759 when rounded to four decimal places.Since the population standard deviation is unknown, we'll use the t-distribution instead of the standard normal distribution. The degrees of freedom for a sample of size 55 is 54. Using a t-distribution table or a statistical calculator, the critical value for an alpha level of 0.005 and 54 degrees of freedom is approximately 2.6759 (rounded to four decimal places).

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The y-intercept represents the initial height when the were planted.

The height of both plants will never be the same.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

The equations y = 13.6x + 21 and y = 9.4x + 21 represent the heights of two flower plants in a garden in millimeters.

We know y-intercept is when x = 0,

Therefore,  y = 21 and y = 21 represent the initial height when they were planted.

The height of the plants will never be the same because the initial height was the same but one plant is growing faster than the other.

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Answer:

The area= 1 in The perimeter= 5 in

Step-by-step explanation:

:)

Answer:

c

Step-by-step explanation:

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Answer:

A

Step-by-step explanation:

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Answer:

Step-by-step explanation:

plato answer

Answer:

The answer is true

Step-by-step explanation:

Answer:

\(I'(-2,-4), J'(-4,4), K'(4,4)\)

Step-by-step explanation:

Assuming the dilation is centered at the origin, it is known that for a dilation of scale factor \(k\) centered at the origin, \((x,y) \to (kx,ky)\).

The angle between the two vectors (4,1) and (-8,3) will be 145.4°.

It is defined as the quantity that has magnitude as well as direction also the vector always follows the sum triangle law.

It is possible to calculate the angle () between two vectors using the formula

\(\rm \theta = cos ^{-1} \frac{ (a.b)}{|a||b|}\)

Calculate dot product:

=a · b

= ax · bx + ay · by

= 4 · (-8) + 1 · 3

= - 32 + 3

= -29

=|a|

= √ax² + ay²

= √4² + 1²

= √16 + 1

= √17

=|b|

=√ bx² + by²

= √(-8)² + 3²

= √64 + 9

= √73

\(\rm \alpha = cos ^{-1} \frac{ (a.b)}{|a||b|}\)

α = 145.40771131249005°

Thus, the angle between the two vectors (4,1) and (-8,3) will be 145.4°.

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The given expression can be solved by using types of the polynomial.

The algebraic expression is a trinomial is \(\rm 2x^3-x^2\).

We have to determine, which algebraic expression is a trinomial?

According to the question,

‘Tri’ stands for three and ‘mial’ stands for terms thus an algebraic expression with three unlike terms are called trinomials.

The definition of polynomial needs integer exponents of variable and integer coefficients of the variable.

To determine the algebraic expression is a trinomial following all the steps given below.

1. The algebraic expression is,

\(\rm x^3+x^2-\sqrt{1}\)

The expression is not trinomial as well as polynomial because it contains a square root function.

2.  The algebraic expression is,

\(\rm 2x^3-x^2\)

The expression is trinomial because it has degree 3 and it's a polynomial.

3. .  The algebraic expression is,

\(\rm 4x^3-x^2-\dfrac{1}{x}\)

The expression is not trinomial degree 4 due to 1/x and thus not a trinomial.

4. . The algebraic expression is,

\(\rm x^6-x-\sqrt{6}\)

The expression is not trinomial as well as polynomial because it contains a square root function.

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Answer:

The company will pay 43 + 24h dollars to hire both Jill and Kyle your welcome

Step-by-step explanation:

Answer:

No photo / not enough info to answer

Step-by-step explanation:

Answer:

4. (d) option is correct because -7-(-5) = -7+5 ( Because - and - makes a plus .

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The rate of change of the area is 3868.48 cm2/min

What in math is a rate?

A rate is a unique ratio where the two words are expressed in several units. For instance, the price is 69 for 12 ounces if a 12-ounce can of maize costs 69. This is not a proportion of two comparable units, like shirts. This ratio compares two dissimilar units: ounces and cents

A = A(r) (r)

r = r(t) (t)

A = A(r(t))

The chain rule can be used to resolve this kind of issue.

Rate of area change:

(dA/dr)(dr/dt) = dA/dt

A=r2 dA/dr = 2r

dr/dt [given] = 7 cm/min

(2r)(7 cm/min) = (dA/dt)

If r = 88 cm,

dA/dt = 2π (88 cm) (7 cm/min) ≅ 3868.48 cm2/min

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Answer:

Bosian used the wrong conversion for converting Gallons to Quarts. The correct conversion is: 1 gallon = 4 Quarts and correct solution is: 5 gallon = 20 quarts

Step-by-step explanation:

Bosian Conversion from Gallons to Quarts

He had 5 gallons

He said that 1 gallon = 5 quarts

So, 5 gallons = 5*5 = 25 quarts

Mistake of Bosian:

He used the wrong conversion: i.e, 1 gallon = 5 quarts

The correct conversion is:

1 gallon = 4 quarts

Correct Solution:

1 gallon = 4 quarts

So, 5 gallons = 5*4 = 20 quarts

Answer:

a= 55.5

b= 45

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Answer:

see explanation

Step-by-step explanation:

Using the rule of exponents

\(\frac{1}{a^{m} }\) ⇔ \(a^{-m}\)

64 = \(2^{6}\) , then

\(2^{p}\) = \(\frac{1}{64}\) = \(\frac{1}{2^{6} }\) = \(2^{-6}\)

Since the bases on both sides are equal, both 2, then equate exponents

p = - 6

The transmitted intensity i1 is approximately 19.32 watts per square meter.

An indicator of a physical phenomenon's strength or power, such as light, sound, or radiation, is its intensity. It is often expressed in terms of the quantity of energy being transmitted or received per unit area or volume. For instance, the intensity of light is expressed in watts per square metre, while the strength of sound is expressed in watts per square metre per hertz. Distance, direction, and the qualities of the medium through which the phenomenon is transmitted can all have an impact on intensity.

To find the transmitted intensity (i1), we need to use the formula:

\(i1 = i0 * cos(θ0 - θta)\)

where i0 is the initial intensity, \(θ0\)is the initial angle, and \(θta\) is the transmitted angle.

Step 1: Calculate the difference between the angles:
\(Δθ = θ0 - θta\) = 25.0 degrees - 40.0 degrees = -15.0 degrees

Step 2: Convert the angle difference to radians:
\(Δθ\)(in radians) = -15.0 degrees *\((\pi /180)\) ≈ -0.2618 radians

Step 3: Calculate the cosine of the angle difference:
\(cos(Δθ) ≈ cos(-0.2618)\)≈ 0.9659

Step 4: Calculate the transmitted intensity (i1):
i1 = i0 * \(cos(Δθ)\) = 20.0\(W/m^2\) * 0.9659 ≈ 19.32 \(W/m^2\)

So, the transmitted intensity i1 is approximately 19.32 watts per square meter.

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The expected winning and the value of that prize, which gives an expected winning is c. $3.13 per ticket.

The expected winnings per ticket in the raffle can be calculated by adding the products of the probability of the expected value of winning each prize. The predicted wins per ticket may be computed as the total of each prize's value multiplied by its probability of winning, i.e.

Expected winnings per ticket

= (1/800) × $400 + (4/800) × $200 + (12/800) × $125 + (30/800) × $60 + (753/800) × $0

If we condense the equation, we obtain:

Calculating the total wins anticipated per ticket

= $0.50 + $1.00 + $1.88 + $0.75 + $0

Expected winnings per ticket = $3.13

Therefore, if you buy a ticket, the expected winnings per ticket are $3.13.

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Complete question:

For a fundraiser, there is a raffle with 800 tickets, each costing $15. 1 ticket will win a $400 prize, 4 tickets will win a $200 prize, 12 tickets will win a $125 prize, 30 tickets will win a $60 prize, and the remaining tickets will win nothing. if you buy a ticket, what are the expected winnings per ticket? question options:

a) $5.36

b) $5.63

c) $5.33

d) $5.66

Step-by-step explanation:

the area of a parallelogram is

baseline × height

to multiply (like the other answer) just length and width, that only works for real rectangles, as then due to the 90° angles the length is also the height to the width and vice versa.

so the area here is

12 × 12 = 144 in²

Answer:

Given,

p (x)=2x-3

g (x)=6x+4

p (x)×g (x)=?

Step-by-step explanation:

p (x)×g (x)=(2x-3)(6x+4)

=2x (6x+4)-3 (6x+4)

=12x^2+8x-18x-12

=12x^2-10x-12