A trucking firm wants to purchase 10 trucks that will provide exactly 28 tons of additional shipping capacity. A model A truck holds 2 tons, a model B truck holds 3 tons, and a model C truck holds 5 tons. How many trucks of each model should the company purchase to provide the additional shipping capacity?

The logarithmic function can be written exponentially as follows.\(t = 8^y.\)

Exponents and logarithms are inverse operations of one another. We can rewrite an equation in logarithmic form as log_a(b) = x if it has the form axe = b. A number's logarithm is the exponent that must be raised in order to obtain that number. For instance, since 102 = 100, log_10(100) = 2. Similar to this, we can express an equation in exponential form, such as axe = b, if it is in logarithmic form, such as log_a(b) = x. The inverse function of the logarithmic function is the exponential function. As a result, when we apply a logarithm to an exponential expression, the original exponent is returned, and the opposite is true.

The given logarithmic expression is \(log_{8}(t) = y.\)

We know that if we have an equation in the form \(a^x = b\), we can rewrite it in logarithmic form as \(log_a(b) = x\) and vice versa.

Thus, \(log_{8}(t) = y\)

\(t = 8^y\)

Hence, the logarithmic function can be written exponentially as follows.\(t = 8^y.\)

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Answer:

? = 92°

Step-by-step explanation:

the chord- chord angle ? is half the sum of the measures of the arcs intercepted by the angle and its vertical angle, that is

? = \(\frac{1}{2}\) (LM + AK) = \(\frac{1}{2}\) (120 + 64)° = \(\frac{1}{2}\) × 184° = 92°

Answer:

the answer is 66.67%

Step-by-step explanation:

54.90-18.30=36.60

36.60÷54.90×100=66.666666666... or 66.67%

The sequence is decreasing as n increases and sequence converges to the value 0.

The given sequence is defined as aₙ = 1 / (7n + 3).

To determine if the sequence converges or diverges, we need to analyze its behavior as n approaches infinity.

As n increases, the denominator 7n + 3 also increases which means that the values of aₙ will get smaller and smaller, approaching zero as n becomes larger.

The sequence converges to the value 0.

The sequence is decreasing as n increases.

The sequence converges to the value 0.

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Answer:

A,D and E

Step-by-step explanation:

Step-by-step explanation:

x = number of cards

the production costs (PC) per day are

PC(x) = 264 + 1.1x

the sales (S) are

S(x) = 5.1x

the profit (P) per day is sales minus costs

P(x) = S(x) - PC(x) = 5.1x - (264 + 1.1x) =

= 5.1x - 264 - 1.1x = 4x - 264

we need to find the value of x, so that P(x) = 52.

52 = 4x - 264

316 = 4x

x = 316/4 = 79

79 cards must be delivered daily to make a profit of $52.

Originality is the quality of being unique, new, and innovative. It requires creativity, imagination, inspiration, and nonobviousness. Special or interesting aspects may be present, but they are not sufficient to define originality.

Originality refers to the quality of being unique, new, and innovative. It involves creating something that has not been seen or experienced before. The best description of originality is that it is having a low probability and being unique.

An original idea, product, or work of art is something that has not been copied or imitated from others. It represents a new perspective or approach that can offer a fresh insight into a problem or challenge. Originality requires a high level of creativity, imagination, and inspiration, as well as a willingness to take risks and explore new possibilities.

Nonobviousness is also an important factor in originality. It means that the idea or invention is not something that would be obvious to someone skilled in the same field or industry. In other words, an original idea should not be something that could be easily predicted or anticipated.

Special or interesting are also characteristics of originality, but they are not sufficient to define it. An idea or product can be special or interesting without being truly original. For example, a new flavor of ice cream may be interesting, but it may not be original if it has already been created by someone else.

Convergent thinking, on the other hand, involves finding a single solution to a problem. It is the opposite of divergent thinking, which involves generating multiple ideas and possibilities. Convergent thinking is important for finding effective solutions to problems, but it is not the same as originality.

In conclusion, originality is the quality of being unique, new, and innovative. It requires creativity, imagination, inspiration, and nonobviousness. Special or interesting aspects may be present, but they are not sufficient to define originality.

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Answer:

The first type of solid shapes to be discovered are known as Platonic solids, which include the cube, the tetrahedron, the octahedron, the dodecahedron, and the icosahedron

Answer:

The minimum exam score to be awarded an A is about 8.52.

Step-by-step explanation:

Let X represent the scores on a common final exam.

It is provided that X follows a normal distribution with mean, μ = 71 and standard deviation, σ = 9.

It is provided that according to the department policy is that the top 10% of students receive an A.

That is, P (X > x) = 0.10.

⇒ P (X < x) = 0.90

⇒ P (Z < z) = 0.90

The corresponding z-score is:

z = 1.28

Compute the value of x as follows:

\(z=\frac{x-\mu}{\sigma}\\\\1.28=\frac{x-71}{9}\\\\x=71+(1.28\times 9)\\\\x=82.52\)

Thus, the minimum exam score to be awarded an A is about 8.52.

Answer:

the segment bisector should be the line n

the length of XY= 6

Step-by-step explanation:

since segment, XY is bisected, we know that each side is equal to the other

so in order to find the length of the segment, you need to set each side equal to the other

5x+8=9x+12

8=4x+12

-4=4x

x=-1

then, you plug -1 into both functions

5(-1)+8=3

9(-1)+12=3

then simply add these two numbers together to get 3+3=6

Ordered pair for the equation 4x-y=5 which is a solution of a given equation is (0,-5).

An ordered pair refers to a pair of two numbers or variables written inside the bracket and separated by comma.

To find an ordered pair of a equation we just need to find the values of x and y which will satisfy the given equation.

Here given equation is 4x-y=5

So we will put x=0 and y=-5

⇒ 4(0)-(-5)=5

Therefore (0.-5) satisfy given equation.

Hence (0.-5) is an ordered pair of 4x-y=5.

Note:- There are many ordered pairs that satisfy the given equation.

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Answer:

23.2, exact is 22.9333334

Step-by-step explanation:

28 2/3 is around 28.5 ,4/5 is .75

28.5 * .75 = 21.375

Answer:

Below

Step-by-step explanation:

c x = r/ d    divide both sides by 'c'

x = r / (dc)     done.

The solutions to the equations using function machine are x = 7, x = 5, b = 10, b = 5, n = 7, w = -4, k = 8 and h = 3

From the question, we have the following equations that can be used in our computation:

Using a function machine, we have:

Equation (a)

3x + 4=25

This becomes

x  ⇒ [  ] ⇒ [  ]  = [  ]

So, we have

x  ⇒ [ 21 ] ⇒ [ +4 ]  = [ 25 ]

This means that

x = 21/3

x = 7

Equation (b)

3x - 4 = 11

This becomes

x  ⇒ [  ] ⇒ [  ]  = [  ]

So, we have

x  ⇒ [ 15 ] ⇒ [ -4 ]  = [ 11 ]

This means that

x = 15/3

x = 5

Equation (c)

4b - 10 = 30

This becomes

b  ⇒ [  ] ⇒ [  ]  = [  ]

So, we have

b  ⇒ [ 40 ] ⇒ [ -10 ]  = [30]

This means that

b = 40/4

b = 10

Equation (d)

4b + 10 = 30

This becomes

b  ⇒ [  ] ⇒ [  ]  = [  ]

So, we have

b  ⇒ [ 20 ] ⇒ [ +10 ]  = [30]

This means that

b = 20/4

b = 5

Equation (e)

5n + 2 = 37

This becomes

n  ⇒ [  ] ⇒ [  ]  = [  ]

So, we have

n  ⇒ [ 35 ] ⇒ [ +2 ]  = [37]

This means that

n = 35/5

n = 7

Equation (f)

2w + 10 = 2

This becomes

w  ⇒ [  ] ⇒ [  ]  = [  ]

So, we have

w  ⇒ [ -8 ] ⇒ [ +10 ]  = [2]

This means that

w = -8/2

w = -4

Equation (g)

3k + 4 = 28

This becomes

k  ⇒ [  ] ⇒ [  ]  = [  ]

So, we have

k  ⇒ [ 24 ] ⇒ [ +4 ]  = [28]

This means that

k = 24/3

k = 8

Equation (h)

6h - 7 = 11

This becomes

h  ⇒ [  ] ⇒ [  ]  = [  ]

So, we have

h  ⇒ [ 18 ] ⇒ [ -7 ]  = [11]

This means that

h = 18/6

h = 3

Hence, the value of h is 3

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If the two angles are complementary, then their sum is 90 degrees.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees.

If the two angles are complementary, then their sum is 90 degrees.

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The length of the zip wire is approximately 25.42 meters.

To calculate the length of the zip wire, we can use trigonometry and the given information about the angle and the distance between the two posts.

Given:

Distance between the two posts: 25m

Angle of the zip wire to the horizontal: 10°

We can use the trigonometric function cosine (cos) to find the length of the zip wire. Cosine relates the adjacent side to the hypotenuse of a right triangle.

In this case, the adjacent side is the distance between the two posts (25m) and the hypotenuse is the length of the zip wire that we want to calculate.

Using the cosine function:

cos(angle) = adjacent/hypotenuse

cos(10°) = 25m/hypotenuse

To find the hypotenuse (length of the zip wire), we can rearrange the equation:

hypotenuse = 25m / cos(10°)

Using a calculator or trigonometric tables, we can find the value of cos(10°) to be approximately 0.9848.

Therefore, the length of the zip wire is:

hypotenuse = 25m / 0.9848 ≈ 25.42m

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Answer:

I believe that the correct answer is letter A

Answer:

The next two numbers following:

431

141311

1114111321

311431131211

are:

132114132113111221

AND

11131221141113122113312211

Step-by-step explanation:

I shall explain the pattern below:

431 (just the digits 4, 3, and 1)

141311 (one 4 becomes 14, one 3 becomes 13, one 1 becomes 11 -> looking at each digit of the previous number, 431)

1114111321 (one 1 becomes 11, one 4 becomes 14, one 1 becomes 11, one three becomes 13, two consecutive 1s becomes 21 -> looking at each digit of the previous number, 141311)

311431131211 (three consecutive 1s becomes 31, one 4 becomes 14, 3 more consecutive 1s becomes 31, one 3 becomes 13, one 2 becomes 12, and one 1 becomes 11 -> looking at each digit of the previous number, 1114111321)

NEXT TWO NUMBERS:

one 3 (13), two consecutive 1s (21), one 4 (14), one 3 (13), two consecutive 1s (21), one 3 (13), one 1 (11), one 2 (12), two consecutive 1s (21)

that makes: 132114132113111221

one 1 (11), one 3 (13), one 2 (12), two consecutive 1s (21), one 4 (14), one 1 (11), one 3 (13), one 2 (12), two consecutive 1s (21), one 3 (13), three consecutive 1s (31), two consecutive 2s (22), one 1 (11)

that makes: 11131221141113122113312211

The rule is that the next number is essentially the previous number with the number of times each digit appears consecutively before each digit of the previous number. I know that sounds convoluted. Hopefully it makes enough sense. Let me know if I should explain more fully.

Answer:

-24

Step-by-step explanation:

8(-3) is 8 multiplied by (-3) and thus the answer is -24

Answer:

the answer is -24 hope I helped

Answer:

Step-by-step explanation:

6cm

Answer:

he needs to collect at least 56 more

Step-by-step explanation:

c+64\(\geq\)120

c\(\geq\)120-64

c\(\geq\)56

Answer:56 more

Step-by-step explanation:

The Probability that the randomly chosen coin is gold, given that it is small, is 4/5 or 0.8 when expressed as a decimal.

To find the probability that the randomly chosen coin is gold, given that it is small, we need to determine the number of small gold coins and the total number of small coins.

From the given information, Marco has 12 small gold coins and 3 small silver coins, making a total of 12 + 3 = 15 small coins.

The probability that the coin is gold, given that it is small, can be calculated as the ratio of the number of small gold coins to the total number of small coins:

P(Gold|Small) = Number of Small Gold Coins / Total Number of Small Coins

P(Gold|Small) = 12 / 15

Simplifying the fraction, we have:

P(Gold|Small) = 4 / 5

Therefore, the probability that the randomly chosen coin is gold, given that it is small, is 4/5 or 0.8 when expressed as a decimal.

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Answer:

The decision rule is

Fail to reject the null hypothesis

The conclusion is  

There is no sufficient evidence to conclude that the mean CPA of all students who vote is lower than the CPA of students who do not vote

Step-by-step explanation:

From the question we are told that

       The first sample size  is  \(n_1 =  114\)

       The sample mean is  \(\= x_1 =  2.71\)

       The standard deviation is  \(s_1 =  0.64\)

      The second sample size is   \(n_2 =  123 \)

      The sample mean is   \(\= x_2 =  2.79\)

      The level of significance is  \(\alpha  =  0.05\)

      The standard deviation is   \(s_2 =  0.56 \)

The null hypothesis is  \(H_o  :  \mu_1 = \mu _2\)

The alternative hypothesis is  \(H_a :  \mu_1 <  \mu_2\)

Generally the test hypothesis is mathematically represented as

      \(t =  \frac{\= x_1 - \= x_2}{ \sqrt{ \frac{s_1^2 }{n_1} + \frac{s_2^2}{n_2}  } }\)

=> \(t =  \frac{2.71 - 2.79}{ \sqrt{ \frac{0.64^2 }{ 114} + \frac{0.56^2}{123}  } }\)

=> \(t =  -1.01 \)

Generally given that variance are not equal (the standard deviation  squared of both population are not equal ) the degree of freedom  is mathematically represented as

\(df  =  \frac{[\frac{s_1^2}{n_1 } + \frac{s_2^2}{n_2}  ]}{\frac{[\frac{s_1^2}{n_1}]^2 }{n_1 - 1} + \frac{[\frac{s_2^2}{n_2}]^2 }{n_2 - 1}}\)

=>  \(df  =  \frac{[\frac{0.64^2}{114} + \frac{0.56^2}{123}  ]}{\frac{[\frac{0.64^2}{114}]^2 }{114 - 1} + \frac{[\frac{0.56^2}{123}]^2 }{123 - 1}}\)

=>  \(df  =  225\)

Generally from the t distribution table the the probability of  (t < -1.01) at a degree of freedom of \(df  =  225\)is  

      \( p-value  = P(t <  -1.01 ) =  0.15679\)

Generally the value obtained we see that  \(p-value  > \alpha\) so

The decision rule is

Fail to reject the null hypothesis

The conclusion is  

There is no sufficient evidence to conclude that the mean CPA of all students who vote is lower than the CPA of students who do not vote

Answer:

w(25) = 96

There are 96 wolves in the year 2020

Step-by-step explanation:

Given:

\(w(x)=14\cdot 1.08^{x}\)

w(25) =

\(w(25)=14\cdot 1.08^{25}\\\\= 14 * (6.848)\\\\=95.872\\\\\approx 96\)

Number of years : 1995 + 25 = 2020

In 2020, there are 96 wolves

Answer:

Over the last 7 years, a corporation's debt grew by $1,630, 300. Calculate the average rate at which the company's debt was growing in dollars per minute.

Round your answer to the nearest hundredth if necessary. (For the purposes of this calculation, use 365 days/year.)

The debt was growing at an average rate of ___ dollars per minute.

Using the z-distribution, as we are working with a proportion, considering that the estimate is of 90%, the 95% lower​ limit is of 0.8785.

A confidence interval of proportions is given by:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which:

In this problem, we have that:

Hence, the lower bound of the interval will be given by:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.9 - 1.96\sqrt{\frac{0.9(0.1)}{750}} = 0.8785\)

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The asterisk (*) represents the vertex of the angle, the initial side is the positive x-axis, and the terminal side is the red line segment that forms an angle of 8/3 π with the positive x-axis.

What is the standard position of angles?

Standard position simply means that the vertex of the angle is at the origin of the circle and that one ray of the angle is on the positive x-axis. The other ray of the angle is placed at the angle measure formed by traveling counter-clockwise along the circle.

To draw an angle in standard position with measure 8/3 π, follow these steps:

Start with the positive x-axis.

Counterclockwise, rotate the initial side of the angle until it coincides with the positive x-axis.

Starting from the initial side on the positive x-axis, rotate the terminal side of the angle in a counterclockwise direction until the angle measures 8/3 π.

The resulting angle will have a measure of 8/3 π and will look like the following:

       |

       |

--------*-----------

       |

       |

Here, the asterisk (*) represents the vertex of the angle, the initial side is the positive x-axis, and the terminal side is the red line segment that forms an angle of 8/3 π with the positive x-axis.

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Answer:

16 cm shorter, 149 cm

Step-by-step explanation: