help with these two pages

Answer:

A

Step-by-step explanation:

Answer: C.5

Step-by-step explanation:

Answer:

\(\displaystyle \frac{d}{dx} \Big [ \frac{3}{x^2} \Big ]=-\frac{6}{x^3}\)

Step-by-step explanation:

We can use either the Power Rule or the Quotient Rule to find the derivative of 3/x².

Rewrite \(\displaystyle \frac{3}{x^2}\) as \(\displaystyle 3\cdot \frac{1}{x^2}\) which is equivalent to \(3\cdot x^-^2\).

Now we can apply the power rule to 3x⁻². Subtract 1 from the exponent and multiply the coefficient by -2.

This can be rewritten as \(\displaystyle -\frac{6}{x^3}\).

Substituting 3 for f(x) and x² for g(x), we get:

Simplify.

Using exponent rules, we can rewrite this as:

This can be rewritten as \(\displaystyle -\frac{6}{x^3}\), which is the same as what we got using the product rule.

Answer:

\(\displaystyle \frac{d}{d x}\left[\frac{3}{x^2}\right] = -\frac{6}{x^{3}}\).

Step-by-step explanation:

Let \(f(x)\) and \(g(x)\) denote two functions of \(x\). Assume that \(g(x) \ne 0\). The quotient rule states that:

\(\displaystyle \frac{d}{d x}\left[\frac{f(x)}{g(x)}\right] = \frac{{f}^\prime(x) \cdot g(x) - f(x) \cdot g^{\prime}(x)}{{(g(x))}^2}\).

In this question:

Find \({f}^{\prime}(x)\) and \({g}^{\prime}(x)\).

Notice that the value of \(f(x)\) is constantly \(3\) regardless of the value of \(x\). By the constant rule, \({f}^{\prime}(x) = 0\).

For \({g}^{\prime}(x)\), consider the power rule:

if \(m\) represents a rational number (such as \(2\),) then by the power rule, \(\displaystyle \frac{d}{d x}\left[{x}^{m}\right] = m\, {x}^{m-1}\).

Apply this rule to find \({g}^{\prime}(x)\).

\(\begin{aligned}{g}^{\prime}(x) &= \frac{d}{d x} \left[x^{2}\right] \\ &= 2\, x^{2 - 1} \\ &= 2\, x\end{aligned}\).

Substitute \(f(x) = 3\), \({f}^{\prime}(x) = 0\), \(g(x) = x^{2}\), and \({g}^{\prime}(x) = 2\, x\) into the quotient rule expression to find \(\displaystyle \frac{d}{d x}\left[\frac{3}{{x}^{2}}\right]\):

\(\begin{aligned}&\; \frac{d}{d x}\left[\frac{3}{{x}^{2}}\right] \quad \genfrac{}{}{0em}{}{\leftarrow f(x) = 3}{\leftarrow g(x) = {x}^{2}} \\ =&\; \frac{d}{d x}\left[\frac{f(x)}{g(x)}\right]\\ =&\; \frac{{f}^\prime(x) \cdot g(x) - f(x) \cdot g^{\prime}(x)}{{(g(x))}^2} \\ =& \; \frac{0 \, x^2 - 3\, (2\, x)}{\left({x}^{2}\right)} \\ =&\; -\frac{6}{x^{3}}\end{aligned}\).

Therefore, \(\displaystyle \frac{d}{d x}\left[\frac{3}{{x}^{2}}\right] = -\frac{6}{x^{3}}\).

Answer:

196 miles

Step-by-step explanation:

distance (D) is calculated as

D = S × T ( S is average speed and T is time in hours )

here T = 3 and a half hours = 3.5 hours and S = 56 , then

D = 56 × 3.5 = 196 miles

Answer:

8 degrees

Step-by-step explanation:

Answer:

I'm pretty sure it would be 5x

Step-by-step explanation:

Answer:

97.2

In mixed number form its 97 1/5

Answer:

Below in bold.

Step-by-step explanation:

If one angle is x then the other is x+40 degrees.

These angles sum to 180 as we have a parallelogram, so

x + x + 40 = 180

2x = 140

x = 70.

So the angles are 70 and 110

110 ,70,110,70 are the angles

Let's say that angle 1 is x

This means another angle will be x - 40

The sum of all 4 angles is 360

The sum of two angles 180

x + x - 40 = 180

2x = 220

x = 110

180 - 110 = 70 meaning that each side has an angle measuring 110 degrees and an angle measuring 70. And 110 - 70 = 40 like you mentioned

Alicia read 140 minutes more then Henry in 2 week .

What is arithmetic?

Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, involution, and extraction of roots.

Main body:

Henry read for 20 minute each day.

Alicia rate for 30 minute each day.

as they read 7 day of a week , so

total minutes read by Henry = 2 *7 *20

                                               = 280 minutes

total minutes read by Alicia = 2 *7 *30

                                              =420 minutes

difference between henry , alicia reading = 420 - 280 = 140 minutes.

Hence , Alicia read 140 minutes more then Henry in 2 week .

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The company's claim can be evaluated using a hypothesis test. The null hypothesis, denoted as H0, assumes that the true proportion of chips that do not fail in the first 1000 hours is 55% or lower.

Ha stands for the alternative hypothesis, which assumes that the real proportion is higher than 55%. This test has a significance level of 0.01.

A sample of 800 chips was taken based on the information provided, and it was discovered that 60% of them do not fail in the first 1000 hours. A one-sample percentage test can be used to verify the assertion.  The test statistic for this test is the z-score, which is calculated as:

\(\[ z = \frac{{p - p_0}}{{\sqrt{\frac{{p_0(1-p_0)}}{n}}}} \]\)

If n is the sample size, p0 is the null hypothesis' assumed proportion, and p is the sample proportion.

If we substitute the values, we get:

\(\[ z = \frac{{0.6 - 0.55}}{{\sqrt{\frac{{0.55(1-0.55)}}{800}}}} \]\)

The z-score for this assertion is calculated, and we find that it is approximately 2.86.

In order to determine whether there is sufficient data to support the company's claim, we compare the computed z-score with the essential value. At a significance level of 0.01 the critical value for a one-tailed test is approximately 2.33.

Because the estimated z-score (2.86) is larger than the determining value (2.33), we reject the null hypothesis. Therefore, the company's assertion that more than 55% of the chips do not fail in the first 1000 hours of use is supported by sufficient data at the 0.01 level.

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Answer:get the government ewual

Step-by-step explanation:

You have to get the government equal

(a) P(Ac) = 6/10

(b) P(A∪B) = 7/10

(c) P(A|B) = 2/5

(d) P(B|A) = 2/4

(e) P(B|Ac) = 3/6

(f) A and B are not independent since P(A∩B) ≠ P(A) * P(B).

(g) A and B are not mutually exclusive since P(A∩B) ≠ 0.

(a) To find the complement of event A, we subtract the probability of A from 1: P(Ac) = 1 - P(A) = 1 - 4/10 = 6/10.

(b) To find the union of events A and B, we sum their probabilities and subtract the probability of their intersection: P(A∪B) = P(A) + P(B) - P(AB) = 4/10 + 5/10 - 2/10 = 7/10.

(c) To find the conditional probability of A given B, we use the formula P(A|B) = P(A∩B) / P(B) = (2/10) / (5/10) = 2/5.

(d) To find the conditional probability of B given A, we use the formula P(B|A) = P(A∩B) / P(A) = (2/10) / (4/10) = 2/4 = 1/2.

(e) To find the conditional probability of B given Ac (complement of A), we use the formula P(B|Ac) = P(Ac∩B) / P(Ac). Since A and B are mutually exclusive, P(Ac∩B) = 0. Therefore, P(B|Ac) = 0 / (6/10) = 0.

(f) A and B are not independent because P(A∩B) = 2/10 ≠ (4/10) * (5/10) = 2/25.

(g) A and B are not mutually exclusive because P(A∩B) = 2/10 ≠ 0. Mutually exclusive events cannot occur together, but in this case, there is a non-zero probability of their intersection.

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Answer: Mr. Waddle weighs 328 lbs

Step-by-step explanation:

Mr. Waddle weighs 159 lbs aged 28 yrs old in 1988

He weighed 169 lbs aged 31 yrs old in 1991

Declan's reasoning does make sense. This is because 3/4 and 1/2 have the same denominator, and 3/4 is a larger fraction than 1/2.

Therefore, it is reasonable to assume that 3/4 is greater than 6/12 because 6/12 simplifies to 1/2. Simplifying fractions means dividing the numerator and denominator by the same number, in this case, 6 is divisible by 2, so we can reduce the fraction to 1/2.

So, Declan is correct in his reasoning that 3/4 is greater than 6/12. It is important to understand the relationship between fractions and their denominators to make such comparisons accurately.

3/4 = 9/12

1/2 = 6/12

6/12 = 6/12

Since 9/12 (which is equivalent to 3/4) is greater than 6/12 (which is equivalent to 1/2), we can say that 3/4 is indeed greater than 6/12.

Therefore, Declan's reasoning is correct.

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If quadrilaterals WXYZ and QRST are congruent, the possible pair of measurements is mX = 140° and mY = 94°.

To determine whether two quadrilaterals are congruent, the measures of their corresponding angles must be equal.

Let's analyze the given measurements of angles in quadrilateral WXYZ and determine which pair is possible if they are congruent figures.

Angle measures in quadrilateral WXYZ:

mW = 47°

mX = 94°

mY = ?

mZ = ?

To determine the pair of measurements that is possible if the quadrilaterals are congruent, we need to find a pair of angles in quadrilateral QRST that matches the given angle measures in WXYZ.

Option 1: mX = 94° and mZ = 79°

This option does not match the given angle measures in WXYZ, so it is not possible if the figures are congruent.

Option 2: mW = 47° and mY = 140°

This option also does not match the given angle measures in WXYZ, so it is not possible if the figures are congruent.

Option 3: mW = 47° and mX = 140°

This option does not match the given angle measures in WXYZ, so it is not possible if the figures are congruent.

Option 4: mX = 140° and mY = 94°

This option matches the given angle measures in WXYZ, where mX = 94° and mY = 94°.

Therefore, if quadrilaterals WXYZ and QRST are congruent figures, this pair of measurements is possible.

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Answer:

y = -2000x + 30,000 is the correct answer.

Step-by-step explanation:

For slope intercept equation we first determine the intercept on the axis.

The intercept is a constant value, c, in the slope intercept equation.

In this case, the constant value is 30,000.

Our height, y, is directly proportional to minute,x, taken to descend.

y = mx + c

M is the slope/ gradient which is -2000 since the airplane is descending.

Since the plane descends 2000 feet per minute, its height after 1 minute should be:-

y = -2000(1) + 30,000

y = 28,000

This calculation confirms our above answer.

Answer:

HCF=4

LCM=10080

HCF x LCM = Product of the two given numbers is verified because 403200=40320

Step-by-step explanation:

HCF of 160 and 252

HCF is the product of common prime factors

Prime Factorisation of 160: 2x2x2x2x2x5

Prime Factorisation of 252: 2x23x3x7

HCF= 2x2

HCF=4

40 and 63 doesn't come in any other table together so,

HCF= 2 x 2 = 4

Now, finding LCM of 160 and 252

LCM is the product of all factors of both numbers, while if any factor is common, it is considered once.

Prime Factorisation of 160: 2x2x2x2x2x5

Prime Factorisation of 252: 2x23x3x7

In the given factors 2x2 is common so, it is considered once.

LCM= 2x2x2x2x2x3x5x7

LCM= 10080

Now, checking:

HCF x LCM = Product of the two given numbers.

4x10080=160x252

403200=40320

So, It is verified that HCF x LCM = Product of the two given numbers.

The third component of the vector v is -3.

The third component of the vector \(\(v=a-2b+\frac13c\)\) can be found by using the given vectors a, b, and e.

We know that the vectors a, b, and e are given as:

\($$a=[-1,2,0], b=[-1,1,1], e=[3,0,-3]$$\)

Now we can substitute these values in the expression for v to get:

\($$v=a-2b+\frac13e$$$$= \begin{bmatrix}-1\\2\\0\end{bmatrix} - 2\begin{bmatrix}-1\\1\\1\end{bmatrix}+\frac13 \begin{bmatrix}3\\0\\-3\end{bmatrix}$$$$=\begin{bmatrix}-1\\2\\0\end{bmatrix} - \begin{bmatrix}-2\\2\\2\end{bmatrix} + \begin{bmatrix}1\\0\\-1\end{bmatrix}$$$$=\begin{bmatrix}2\\0\\-3\end{bmatrix}$$\)

Therefore, the third component of the vector v is -3.

An alternative method is to simply calculate the third component of each vector and then substitute those values in the expression for v. Using this method, we get:

\($$v_3=a_3-2b_3+\frac13e_3$$$$=0-2(1)+\frac13(-3)$$$$=-3$$\)

So, the third component of the vector v is -3.

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The equation of the axis of symmetry for the given function is x = 1.

To find the equation of the axis of symmetry for the function f(x) = -4x² + 8x - 28, we can use the formula:

x = -b / (2a)

where "a" and "b" are coefficients in the quadratic equation ax² + bx + c.

In this case, a = -4 and b = 8. Plugging these values into the formula, we get:

x = -8 / (2*(-4))

x = -8 / (-8)

x = 1.

The axis of symmetry for a quadratic function in the form of \(f(x) = ax^2 + bx + c\)  can be found using the formula x = -b / (2a).

In the case of the given quadratic function f(x) = -4x² + 8x - 28, the coefficient of \(x^2\) is a = -4 and the coefficient of x is b = 8.

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Answer:

ravi's is 440 and malcolm's is 520 i think

Step-by-step explanation:

To find the ratio of the area of 11 million km² to the area of the Pacific Ocean (165 million km²), we can express it as a fraction:

Ratio = Area of 11 million km² / Area of the Pacific Ocean

Ratio = 11 million km² / 165 million km²

To simplify the fraction, we can divide both the numerator and the denominator by 11 million:

Ratio = (11 million km² / 11 million km²) / (165 million km² / 11 million km²)

Ratio = 1/15

Therefore, the ratio of the area of 11 million km² to the area of the Pacific Ocean is 1/15.

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Answer:

8. X + Y = an even number

Step-by-step explanation:

if X and Y are a odd number then if you add them you get an even number

Answer:

2m

Step-by-step explanation:

GCF of 8 and 18 is 2 and m is the only variable in both parts of the equation.

Answer:

5/18

Step-by-step explanation:

Here,

total numbering balls n(S) = 18

total number of winning balls n(B) = 5

Therefore,

Probability or winning chances P(B)=

n(B)/n(S)

= 5/18

We can find sample mean by:

Sample Mean = Sum of terms \(\div\) Number of Terms

We can find range by:

Range = Highest Value (H) - Lowest Value (L)

Sample mean:

Sample mean represents the measure of the center of the data. Any population's mean is estimated using the sample mean.

An average value found in a sample is termed the sample mean. the sample mean so calculated is used to find the variance and thereby the standard deviation.

Sample Mean = Sum of terms \(\div\) Number of Terms

\(& =\frac{\sum x i}{n} \\& =\frac{\left(x_1+x_2+x_3+\ldots+x_n\right)}{n}\)

Range:

The range formula determines the difference between the highest and the lowest values in a given set of numbers.

In distribution, the large range means higher variability whereas the small range means low variability.

The range formula includes the other aspects of statistics such as mean, median, and mode. Hence, the formula to calculate the range is:

R = Highest Value (H) - Lowest Value (L)

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How do you find the sample mean and range?

A nurse should empty a Hemovac wound suction device when it is half full to ensure proper functioning and prevent discomfort or injury to the patient due to the device becoming too heavy.

The rationale for a nurse to empty a Hemovac wound suction device when it is half full is to ensure the device is functioning correctly and to prevent it from becoming too heavy and potentially causing discomfort or injury to the patient.

When a Hemovac wound suction device is half full, it may start to lose suction, which can result in less efficient drainage of fluid from the wound site. By emptying the device, the nurse can ensure that the device is functioning correctly and that the suction pressure is maintained.

Additionally, allowing the device to become too full can make it heavy and uncomfortable for the patient, potentially causing discomfort or injury to the wound site. Therefore, emptying the device when it is half full can help prevent these complications and ensure that the patient remains comfortable throughout the healing process.

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To find an equation of a plane containing the three given points (5,0,5), (2,2,6), and (2,3,8) with a coefficient of x equal to 3, we can use the point-normal form of a plane equation. The equation of the plane is 3x + 2y - z = 7.

Let's consider the three given points as (x₁, y₁, z₁), (x₂, y₂, z₂), and (x₃, y₃, z₃). To find the equation of the plane, we need to determine its normal vector, which can be found using the cross product of two vectors in the plane.

We can choose two vectors from the given points, such as (5,0,5) - (2,2,6) = (3, -2, -1) and (5,0,5) - (2,3,8) = (3, -3, -3).

Calculating the cross product of these two vectors, we get (-6, -6, -6), which is the normal vector of the plane. Now, we can write the equation of the plane in point-normal form:

A(x - x₁) + B(y - y₁) + C(z - z₁) = 0,

where A, B, and C are the components of the normal vector and (x₁, y₁, z₁) is one of the given points. Substituting the values, we have

-6(x - 5) - 6(y - 0) - 6(z - 5) = 0.

Simplifying the equation, we get -6x + 30 - 6y - 6z + 30 = 0, which can be rewritten as -6x - 6y - 6z + 60 = 0. Since we want the coefficient of x to be 3, we can multiply the entire equation by -1/2, resulting in 3x + 3y + 3z - 30 = 0. Finally, simplifying further, we obtain the equation of the plane as 3x + 2y - z = 7.

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