During one week, a truck driver spent 51 hours driving 3,468 miles. Which rate best represents the relationship between the miles and the hours?

The solution of the equation 3z minus 2 is equal to 46 is 16.

The given equation '3z minus 2 is equal to 46' can be written as

    3z - 2  =   46

Now solving for z because the value of z will give the required solution of the given equation. So now finding the z from the equation:

   3z = 46  + 2

   3z =  48

   z = 48/3

   z = 16

The value of the z is 16 which represents the solution of the given equation i.e 3z minus 2 is equal to 46.

Therefore it is concluded that the solution of the equation 3z minus 2 is equal to 46 is 16.

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The probability that a sequence will contain exactly one 0 as calculated from the data given is found to be 3/8.

Taking into consideration the sequences where the digit 0 occurs , we will get the possibilities of getting 0 and 1 as 2 .

The number of sample points in the  sample space will be ,

2 x 2 x 2 = 8 sample points.

These sample space are, S = {111, 110, 101, 011, 100, 010, 001, 000},

Now , the sequence having all three 0 as seen from the sample space is found to be 3.

So the  probability becomes , P(0) = no of favorable outcomes / total number of outcomes =3/8.

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The differential dy when x = 1 and dx = 0.3 is approximately 8.901.

When evaluating the differential dy of the function y = tan(5x + 3), we can use the formula dy = f'(x) * dx, where f'(x) represents the derivative of the function with respect to x. In this case, the derivative of tan(5x + 3) can be found using the chain rule, resulting in f'(x) = 5sec^2(5x + 3).

Substituting the given values into the formula, we have f'(1) = 5sec^2(5*1 + 3) = 5sec^2(8).

Evaluating sec^2(8) gives us a numerical value of approximately 9.867.

Multiplying f'(1) by the given dx of 0.3, we get dy = 5sec^2(8) * 0.3 ≈ 8.901.

To find the differential dy in this case, we applied the chain rule to differentiate the given function. The chain rule is a fundamental concept in calculus used to find the derivative of composite functions. By applying the chain rule, we were able to find the derivative of the function tan(5x + 3) and subsequently evaluate the differential dy. Understanding the chain rule is essential for solving problems involving derivatives of composite functions.

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From the above-mentioned data, it can be inferred that: When the price of good 1 decreases, the substitution effect causes the individual to change consumption of good 1 by 10 while the income effect causes the individual to change consumption of good 1 by −6.

The total effect can be calculated as the sum of both substitution and income effects. The total effect = substitution effect + income effect= 10 - 6= 4Thus, the total effect is 4.Now, to determine whether good 1 is normal or inferior, we need to consider the sign of the income effect.

If the income effect is negative, the good is inferior, and if it's positive, the good is normal.Since the income effect here is negative (-6), we can conclude that good 1 is inferior.

According to the given data, we can calculate the total effect, which is the sum of the substitution and income effects.  The substitution effect refers to the change in consumption of a good due to the relative price change, while the income effect refers to the change in consumption of a good due to the purchasing power change.  when the price of good 1 decreases, the substitution effect causes the individual to change consumption of good 1 by 10, while the income effect causes the individual to change consumption of good 1 by −6. Therefore, the total effect can be calculated as the sum of both substitution and income effects, which is 10 - 6 = 4.From the data, it can also be determined whether good 1 is normal or inferior. A good is considered normal when its income effect is positive and inferior when its income effect is negative. Since the income effect here is negative (-6), it can be concluded that good 1 is inferior.Thus, the total effect is 4, and good 1 is inferior.

The total effect is 4, and good 1 is inferior.

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The following are the statement justifications and explanatory reasons ;

(a) AD + DB = AB; Is justified by segment addition postulate

Reason

Segment addition postulate states that let A and B represent two points,

Then a third D can be on the line joining A and B, if and only if the

relationship between the points is according to the equation, AD + DB = AB

only

(b) m∠1 + m∠2 = m∠CDB; Is justified by angle addition postulate

Reason

Angle addition postulate states that given that a point B lies between an angle m∠AOC, then we have;

m∠AOC = m∠AOB + m∠BOC

(c) ∠2 ≅ ∠6; Is justified by vertically opposite angles theorem

Reason

Vertical angles formed by the crossing of two lines are always equal

(d) If D is the midpoint of \(\overline{AB}\), then AD = \(\dfrac{1}{2}\)×AB; Definition of midpoint

Reason

The midpoint of a line is the point that is of equal distance from both ends of the of the line. It is the point halfway between the endpoints

(e) If \(\underset{DF}{\rightarrow}\) bisects ∠CDB then ∠1 ≅ ∠2; Definition of angle bisector

Reason

An angle bisector is a ray or line that divides an angle into two angles that are congruent

(f) m∠ADF + m∠FDB = 180°; Linear pair postulate

Reason

The linear pair postulate states that where we have two angles that form a linear pear (their addition forms a straight line), then the two angles are supplementary  (their sum is 180°)

(g) ∠ADF and ∠4 are supplements, then m∠ADF + m∠4 = 180°; Definition of supplementary angle

Reason

Supplementary angle are defined as angles that when added together, have a sum of 180°

(h) If ∠4 is complementary to ∠5, and ∠6 is complementary to ∠5, then ∠4 ≅ ∠6; Transitive property

Reason

Transitive property states that given three real numbers, a, b, and c, if a = b and c = b, then a = c

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The statement that 99% of all confidence intervals with a 99% confidence level should contain the population parameter of interest is false.

A confidence interval (CI) is essentially a range of estimates for an unknown parameter in frequentist statistics. The most frequent confidence level is 95%, but other levels, such 90% or 99%, are infrequently used for generating confidence intervals.

The confidence level is a measurement of the proportion of long-term associated CIs that include the parameter's true value. This is closely related to the moment-based estimate approach.

In a straightforward illustration, when the population mean is the quantity that needs to be estimated, the sample mean is a straightforward estimate. The population variance can also be calculated using the sample variance. Using the sample mean and the true mean's probability.

Hence we can generally infer that the given statement is false.

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The distribution of values taken by a statistic in all possible samples of the same size from the same population is known as the sampling distribution of the statistic.

In other words, it refers to the distribution of a particular statistic, such as the sample mean or sample proportion, if we were to take all possible samples of a given size from a population.

The sampling distribution is an important concept in statistics because it allows us to make inferences about a population based on a sample.

By examining the sampling distribution of a statistic, we can determine the range of values that the statistic is likely to take and calculate the probability of observing a particular value or range of values.

This information can be used to make inferences about the population parameter from which the sample was drawn.

For example, suppose we want to estimate the mean income of all individuals in a particular city. We could take a random sample of individuals from the city and calculate the sample mean.

The sampling distribution of the sample mean would then give us information about the range of values that the true population mean is likely to take, as well as the probability of observing a particular sample mean.

This information could be used to construct confidence intervals or perform hypothesis tests to make inferences about the population mean.

In summary, the sampling distribution is a key concept in statistics that allows us to make inferences about a population based on a sample. It refers to the distribution of values taken by a statistic in all possible samples of the same size from the same population.

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Answer:

$32.89

Step-by-step explanation:

Starting Value: $87.50

After Gas: $87.50 - $36.19 = $51.31

After Chips: $51.31 - $5.87 = $45.44

After Happy Meal: $45.44 - $12.55 = $32.89

Therefore, Dan has $32.89 left

Answer: True

Step-by-step explanation

A-p-e-x

Answer:

No solution.

Step-by-step explanation:

y + 3x - 4y = 0 + 0.75x

- 3y + 3x = 0 + 0.75x

- 3y + 3x - 0.75x = 0 + 0.75x - 0.75x

- 3y + 2.25x = 0

Answer:

6

Step-by-step explanation:

The kinetic energy will the ball acquire from the bat is 2× 10² J

According to the question

Bat stays in contact for 5.0 X 10⁻³ and the ball travels at a speed of 2.0 X 10⁴.

An object's kinetic energy is the power it has as a result of motion. It is explained as the amount of effort required to move a mass-based body from rest to the indicated velocity.

The body keeps its kinetic energy, which it acquired during acceleration, unless its speed changes.

A mass m object moving at a speed v has kinetic energy 1/2 mv² according to classical mechanics.

Favg= -1/2 MV²

K= -1 2 ( 5.0 x 10⁻³)²

K = - 1/2 ×25 × 10⁻⁶

K = 2× 10² J

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Answer:

$69.50 for a full tank;

6.833% of a tank is 3 gallons of fuel.

Step-by-step explanation:

$3.39 * 20.5 = $69.495 -> $69.50

20.50 / 3.0 = 6.833%

Answer:

14/15

Step-by-step explanation:

simple

3/5 + 1/3= 14/15

Answer:

x = -3

Step-by-step explanation:

f(x) = 4x + 11

f(x) = -1

Substitute -1 for f(x)

-1 = 4x + 11

Subtract 11

-12 = 4x

Divide by 4

-3 = x

x = -3

The value of x is -3 when f(x) = -1.

A function is a relation where every input is connected to only one possible output from a set of available inputs.

The given function is f(x) = 4x + 11.

Substitute f(x) =-1 into the given function:

-1 = 4x + 11

4x = -1 -11

4x = -12

x = -3

Hence, the value of x is -3 when f(x) = -1.

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Answer:

\(x^{2}\)-25

Step-by-step explanation:

formula for areas of rectangles= width x height

width=x-5

height=x+5

(x-5)(x+5)= \(x^{2}\)-5x+5x-25

since the 5x's cancel out each other

              =\(x^{2}\)-25 will be the answer

The area of rectangle is \((x^{2} -25)\) unit square.

The area of rectangle is product of length and width.

         \(Area = length*width\)

Given that length is \((x+5)\) and width is \((x-5)\).

    \(Area=(x+5)*(x-5)\\\\Area=x^{2} -5x+5x-25=x^{2} -25\)

Hence, the  area of rectangle is \((x^{2} -25)\) unit square.

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a.  [cov(X,Y)]^2 ≤ var(X) var(Y). b. E(max{X², Y²}) ≤ 1 + √(1 - p²).

(a) To show that [cov(X,Y)]^2 ≤ var(X) var(Y), we'll use the Cauchy-Schwarz inequality and properties of covariance and variance.

The covariance between two random variables X and Y is defined as:

cov(X,Y) = E[(X - μ_X)(Y - μ_Y)]

where μ_X and μ_Y are the means of X and Y, respectively.

The variance of a random variable X is defined as:

var(X) = E[(X - μ_X)^2]

Applying the Cauchy-Schwarz inequality, we have:

[cov(X,Y)]^2 ≤ var(X) var(Y)

Now, let's prove this inequality step by step.

Step 1: Consider the random variable Z = X - αY, where α is a constant.

Step 2: Calculate the variance of Z:

var(Z) = E[(Z - μ_Z)^2]

      = E[(X - αY - μ_X + αμ_Y)^2]

      = E[((X - μ_X) - α(Y - μ_Y))^2]

      = E[(X - μ_X)^2 - 2α(X - μ_X)(Y - μ_Y) + α^2(Y - μ_Y)^2]

      = var(X) - 2α cov(X,Y) + α^2 var(Y)

Step 3: To ensure var(Z) ≥ 0, we have:

var(Z) ≥ 0

var(X) - 2α cov(X,Y) + α^2 var(Y) ≥ 0

Step 4: Consider the quadratic expression in terms of α:

α^2 var(Y) - 2α cov(X,Y) + var(X) ≥ 0

Step 5: Since this quadratic expression is non-negative, its discriminant must be less than or equal to zero:

[2 cov(X,Y)]^2 - 4 var(X) var(Y) ≤ 0

[cov(X,Y)]^2 ≤ var(X) var(Y)

Thus, we have proved that [cov(X,Y)]^2 ≤ var(X) var(Y).

(b) Given that X and Y have mean 0, variance 1, and covariance p, we need to show that E(max{X², Y²}) ≤ 1 + √(1 - p²).

Let's consider the maximum of X² and Y² as Z = max{X², Y²}.

The expectation of Z, denoted by E(Z), can be calculated as follows:

E(Z) = E(max{X², Y²})

    = P(X² ≥ Y²)E(X² | X² ≥ Y²) + P(X² < Y²)E(Y² | X² < Y²)

Since X and Y have mean 0, we can rewrite this as:

E(Z) = P(X² ≥ Y²)E(X²) + P(X² < Y²)E(Y²)

Now, let's calculate the probabilities:

P(X² ≥ Y²) = P(X ≥ Y) + P(X ≤ -Y)

P(X² < Y²) = P(-X < Y) + P(X < -Y)

Using the properties of the standard normal distribution, we can express these probabilities in terms of the correlation coefficient ρ, where p = ρ.

P(X ≥ Y) = P(X + Y ≤ 0)

         = P(X + Y ≤ 0 | ρ)  [Since X and Y are standard normal variables, their joint distribution depends only on ρ]

         = P(Z ≤ -ρ)        [Z = X + Y is a standard normal variable]

Similarly, we

can obtain:

P(X ≤ -Y) = P(Z ≤ -ρ)

P(-X < Y) = P(Z ≤ ρ)

P(X < -Y) = P(Z ≤ ρ)

Substituting these probabilities into the expression for E(Z), we get:

E(Z) = (P(Z ≤ -ρ) + P(Z ≤ ρ))E(X²) + (P(Z ≤ -ρ) + P(Z ≤ ρ))E(Y²)

    = 2P(Z ≤ -ρ) + 2P(Z ≤ ρ)  [Since E(X²) = E(Y²) = 1]

Using the properties of the standard normal distribution, we can express P(Z ≤ -ρ) and P(Z ≤ ρ) as follows:

P(Z ≤ -ρ) = P(Z ≤ -ρ | ρ)  [Since Z depends only on ρ]

         = P(X + Y ≤ -ρ | ρ)

Similarly,

P(Z ≤ ρ) = P(X + Y ≤ ρ | ρ)

Since X and Y have covariance p, we know that X + Y has covariance 2p. Therefore,

P(Z ≤ -ρ) = P(X + Y ≤ -ρ | 2p)

P(Z ≤ ρ) = P(X + Y ≤ ρ | 2p)

By using the symmetry of the standard normal distribution, we can rewrite these probabilities as:

P(Z ≤ -ρ) = P(-Z ≥ ρ | 2p)

P(Z ≤ ρ) = P(Z ≤ ρ | 2p)

Since the standard normal distribution is symmetric, P(-Z ≥ ρ) = P(Z ≥ ρ). Therefore,

P(Z ≤ -ρ) = P(Z ≥ ρ | 2p)

Substituting these probabilities back into the expression for E(Z), we have:

E(Z) = 2P(Z ≤ -ρ) + 2P(Z ≤ ρ)

    = 2(P(Z ≥ ρ | 2p) + P(Z ≤ ρ | 2p))

    = 2P(Z ≥ ρ | 2p) + 2P(Z ≤ ρ | 2p)

    = 2P(|Z| ≥ ρ | 2p)

Now, we use the inequality P(|Z| ≥ ρ) ≤ 1 - ρ², which holds for any random variable Z:

E(Z) = 2P(|Z| ≥ ρ | 2p)

    ≤ 2(1 - ρ² | 2p)

    = 2 - 2ρ²

Finally, since Z = max{X², Y²}, and both X and Y have variance 1, the maximum of their squared values is at most 1. Therefore, we have:

E(max{X², Y²}) ≤ 2 - 2ρ²

              ≤ 1 + √(1 - p²)  [Since ρ = p]

Hence, we have shown that E(max{X², Y²}) ≤ 1 + √(1 - p²).

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the sale price is $18.75

Answer:

80.5

Step-by-step explanation:

The value of "m" represents the length of side G F in the kite F G H K. The value of "m" is 3.5. Given that sides G F and F K are congruent, we can conclude that their lengths are equal.

We are given that the length of side G H is 5 m 1 and the length of side H K is 3 m 7.

To find the value of "m," we need to find the length of side G F.

Since G F and F K are congruent, we can set up an equation:

5 m 1 = 3 m 7

To solve for "m," we need to subtract 3 m from both sides of the equation:

5 m - 3 m = 3 m - 3 m + 7

This simplifies to:

2 m = 7

Now, we can solve for "m" by dividing both sides of the equation by 2:

m = 7 ÷ 2

m = 3.5

Therefore, the value of "m" is 3.5.

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The volume of a cone can be calculated using the formula \(V = (1/3) * * r2 * h\), where V is a constant roughly equal to 3.14159, r is the radius, and h is the height.

When the required values are substituted, the answer is \(V = (1/3) * 3.14159 * (1.75 feet)2 * 2.1\) feet.

The assessment of this expression yields V = 5.6688 cubic feet. The cone has a radius of 1.75 feet, a height of 2.1 feet, and a volume of approximately 5.6688 cubic feet."Pitch" is the technical word for the rotating movement of an airplane's nose. Pitch describes the rotation of the aircraft's nose around its lateral axis, either upward or downward. A plane is said to be in a positive pitch attitude when its nose is pointing up, and a negative pitch attitude when it is pointing down. Pitch control is essential for maintaining the correct flying path and managing the aircraft's height.

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Answer:

Step-by-step explanation:

7m=28

m=4

-30=p-17

p= -13

z= -18

Answer:I

I am not exactly sure which one you're talking about but I am going to assume that you're talking about the 2nd one, but the answer would be p = 15

The opposite of a function is its inverse

The ordered pairs that represent the inverse of function f(x) are (-2,4), (-2,-2), (-2,-1)

From the function, we have the following ordered pairs

(x,y) = (4,-2), (-2,-2), (-1,-2)

The inverse of a function (x,y) is (y,x).

So, we have:

(y,x) = (-2,4), (-2,-2), (-2,-1)

Hence, the ordered pairs that represent the inverse of function f(x) are (-2,4), (-2,-2), (-2,-1)

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Answer:

−4−7

=−4+−7

=−11

Step-by-step explanation:

if its the same sign add, different signs keep the sing of the larger number

Answer:

9.9\(cm^{3}\)

Step-by-step explanation:

Formula:

1/3(area of the base x height)

1/3 [2.175(2.175)(6.3)]

1/3(4.730625)(6.3)

1/3(29.8029375)

9.9343125

Is the perimeter of the base is 8.7, we need to divide that by 4 (2.175) to find out the side length of the square.  The area of the square, we need to multiply 2.175 by 2.175.

9.9343125 rounded to the nearest tenth is 9.9

Helping in the name of Jesus.

Answer:

Step-by-step explanation:

25, i think

Answer:

See below

Step-by-step explanation:

Period = 1 day      

Periodic interest = .045 / 365       (since there are 365 days in a year)

V(t) = 6000 *  ( 1 + .045/365)^t      where t is in days

V(t) = 6000 * (1+.045/365)^(t * 365)       where t is in years

Answer:

A. 1,250 m

Step-by-step explanation:

6,000 m - 4,750 m = 1,250 m