-3*10^2t=-28 Solve the equation for
t
Express the solution as a logarithm in base-
10

It will take the train 53.33 seconds to pass completely through the tunnel.

We have,

First, let's convert the speed from km/h to m/s:

54 km/h = 54000 m/3600 s = 15 m/s

We need to find the total distance the train travels, which is the sum of its length and the tunnel's length:

So,

distance = 180 m + 620 m = 800 m

Now we can use the formula:

time = distance/speed

time = 800 m / 15 m/s

time = 53.33 seconds

Therefore,

It will take the train 53.33 seconds to pass completely through the tunnel.

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The options provided for the domain and range of the given graph are incorrect. The correct descriptions for the domain and range are as follows:

Domain: The domain represents the set of all possible input values, or the x-values, of the graph. Since no specific information is given about the graph or its equation, the domain is not specified. In this case, the correct answer is:

Domain: Not specified

Range: The range represents the set of all possible output values, or the y-values, of the graph. Similarly, without any specific information about the graph or its equation, the range is not specified. Therefore, the correct answer is:

Range: Not specified

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The restricted domain of the function is 0≤s≤25

The equation is a(s) = 37.5s - 1.5s²  models the function represented in the table

a(s) = s(37.5 - 1.5s)

The critical points are s=0 or

37.5 - 1.5s

37.5 = 1.5s

s=25

As area can not be negative, the area should be positive

s< 0 and s>25

Therefore, restricted domain is 0≤s≤25

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The required set of ordered pairs that represent a function is {(−5, −4), (−3, −2), (−1, 0), (0, −1), (0, 3)}. Option A is correct.

Given functions,
A=  {(−5, −4), (−3, −2), (−1, 0), (0, −1), (0, 3)}
B= {(−4, −4), (−4, −3), (−4, −2), (−4, −1), (−4, 0)}
C = {(−3, −4), (−3, 0), (−2, −3), (0, −2), (2, −1)}
D = {(−5, −2), (−3, −2), (−2, −2), (−1, −2), (0, 0)}

The other sets have repeated x-values with different y-values, which violates the definition of a function where each x-value can only have one corresponding y-value.

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Answer: The awnser is D

Step-by-step explanation: Hope this helps

We can see here the proof of complex functions to geometry was contributed by the Norwegian mathematician Caspar Wessel.

A complex function is one that accepts a complex number as input and outputs another complex number. It is a function that, in other words, has the complex numbers as a codomain and a subset of the complex numbers as its domain.

Wessel demonstrated in his article that complex functions and complex numbers may both be used to represent curves and points in the plane. This research was a significant advancement in the field of complex analysis and opened the path for its growth into a potent instrument for addressing geometric problems.

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The solution of the equation [tex]\rm 5^{-x/16} = 5[/tex] will be negative 16.

Given that:

Equation, [tex]\rm 5^{-x/16} = 5[/tex]

In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.

Take log on both sides, then we have

(-x / 16) log 5 = log 5

-x / 16 = 1

x = -16

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The equation of the circle is (x + 6)² + (y - 1)² = 7² and it's center is (-6, 1)

The standard equation of a circle is given by:

(x - h)² + (y - k)² = r²

Where (h,k) is the coordinates of center of the circle and r is the radius.

In the given problem, the equation is;

x² + y² + 12x - 2y - 12 = 0

This can be rewritten as;

(x + 6)² + (y - 1)² = 7²

The center of the circle is (-6, 1)  from the coordinates (h, k) of the equation of the circle.

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The volume of cylinder B include the following: D. 80π cubic units.

In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

Note: Radius of cylinder B = 2r

Height of cylinder B = 2h

By substituting the parameters, we have the following:

Volume of cylinder B = π × (2r)² × 2h

Volume of cylinder B = π × 4r² × 2h

Volume of cylinder B = π × 8r²h

Volume of cylinder B = 8 × πr²h

Volume of cylinder B = 8 × 10π

Volume of cylinder B = 80π cubic units.

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The value of the missing angle x is: 38°

We know that the sum of angles in a triangle is 180 degrees and as such:

∠DAE = 180 - (82 + 68)

∠DAE = 30°

Now, we know that alternate angles are congruent. Thus:

∠DAE ≅ ∠ADC = 30°

Opposite angles of a parallelogram are equal (or congruent) Consecutive angles are supplementary angles to each other (that means they add up to 180 degrees).

Thus:

∠BAE = ∠BDE = 82 + 30

= 112°

Thus:

∠ABC = ∠ACB = 68°

Thus:

∠BAC = 180 - 2(68)

∠BAC = 44°

Thus:

x = 112 - (44 + 30)

x = 112 - 74

x = 38°

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Using the Pythagorean triple formula the numbers 8, 15 and 17 are Pythagorean triple and as such will form a right-angle triangle.

Pythagorean triples are x² = y² + z² where x, y and z are the three positive integers. These triples are represented as (x, y, z). Here, y is the perpendicular, z is the base and x is the hypotenuse of the right-angled triangle.

In this problem, to determine if the given numbers will form a right-angle triangle, we have to check if the numbers are Pythagorean triple.

In doing so, we would use the previous formula given as;

x² = y² + z²

In a Pythagorean triple, the largest side is the hypothenuse.

17² = 8² + 15²

289 = 64 + 225

289 = 289

The numbers are equal and they're Pythagorean triple.

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To determine the interval in which about 95% of the data lies, we can use the concept of standard deviation and the properties of the normal distribution.

Given that the average monthly mileage is 1,100 miles and the standard deviation is 100 miles, we can apply the empirical rule (also known as the 68-95-99.7 rule) for normally distributed data. According to this rule:

- Approximately 68% of the data lies within one standard deviation of the mean.

- Approximately 95% of the data lies within two standard deviations of the mean.

- Approximately 99.7% of the data lies within three standard deviations of the mean.

Since the standard deviation is 100 miles, we can conclude that about 95% of the data lies within two standard deviations of the mean.

Therefore, the interval within which about 95% of the data lies is:

1,100 miles ± (2 * 100 miles) = 1,100 miles ± 200 miles

So, the interval is from 900 miles (1,100 miles - 200 miles) to 1,300 miles (1,100 miles + 200 miles).

d = 5t + 20

your answer is there so i'll be on my way, Have a nice day!!

Answer:

220 in.²

Step-by-step explanation:

top face - rectangle: A = LW = 4 in. × 2 in. = 8 in.²

bottom face - rectangle: A = LW = 9 in. × 2 in. = 18 in.²

left face - rectangle: A = LW = 12 in. × 2 in. = 24 in.²

right upper face - rectangle: A = LW = 8 in. × 2 in. = 16 in.²

right lower face - rectangle: A = LW = 4 in. × 2 in. = 8 in.²

middle horizontal face - rectangle: A = LW = (9 - 4) in. × 2 in. = 10 in.²

front L-shaped face - 2 rectangles: A = (12 × 4 + 5 × 4) in.² = 68 in.²

back L-shaped face - same as front L-shaped face: A = 68 in.²

total surface area = (8 + 18 + 24 + 16 + 8 + 10 + 68 + 68) in.²

total surface area = 220 in.²

The area of the figure is 24.28 cm²

Any figure that we can break and form more than one basic shape from is called a composite figure.

The composite figure can be broken into a right triangle, a rectangle and a semi circle.

area of triangle = 1/2 bh

= 1/2 × 4 × 3

= 2 × 3

= 6 cm²

area of the rectangle = l × w

= 3 × 4

= 12 cm²

area of the semi circle = 1/2 πr²

= 1/2 × 3.14 × 2²

= 3.14 × 2

= 6.28cm²

Therefore the area of the composite figure =

6 + 12 +6.28

= 24.28 cm

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The most specific correct name for this figure is a trapezoid.

A trapezoid is a quadrilateral with only one pair of parallel sides. >>>This figure is a trapezoid.

An isosceles trapezoid is a trapezoid in which the top and bottom sides are parallel, while the remaining two non-parallel sides have the same length. >>> this figure is not an isosceles trapezoid.

A parallelogram has opposite sides parallel. >>>  This figure is not a parallelogram.

A quadrilateral is a four-sided polygon, having four edges and four corners. >>>This figure is a quadrilateral.

The sample mean percentage x is 62.3% and the sample standard deviation S is 8.08%.

To find the percentage of hospitals that provide at least some charity care, we need to use the given sample data.

(a) Using a calculator with mean and sample standard deviation keys, we can find the sample mean percentage x and the sample standard deviation S.

[tex]x = \frac{56.9 + 55.9 + 52.5 + 65.7 + 59.0 + 64.7 + 70.1 + 64.7 + 53.5 + 78.2}{10}\\\\ = 62.3% \\\\\\\\S = \sqrt{\frac{((56.9 - 62.3)^2 + (55.9 - 62.3)^2 + ... + (78.2 - 62.3)^2) }{ 9}}\\\\ = 8.08\%[/tex]

Therefore, the sample mean percentage x is 62.3% and the sample standard deviation S is 8.08%.

(b) To find a 90% confidence interval for the population average u of the percentage of hospitals providing at least some charity care, we can use the formula:

[tex]CI = x \pm z*(S/sqrtn)[/tex]

where CI is the confidence interval, x is the sample mean percentage, z is the z-score for the desired confidence level (90% in this case), S is the sample standard deviation, and n is the sample size (10 in this case).

From the z-table, the z-score for a 90% confidence level is 1.645.

Plugging in the values, we get:

CI = 62.3 ± 1.645*(8.08/sqrt(10)) = (55.5%, 69.1%)

Therefore, we can be 90% confident that the true population average percentage of hospitals providing at least some charity care is between 55.5% and 69.1%.

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Answer:

100

Step-by-step explanation:

square root(L^2 + W^2)

The value of c that makes z = 4 an extraneous solution is c = -1.

We need to find the value of c that makes z = 4 an extraneous solution, which means that 4 is not a valid solution of the original equation but appears to be one when substituted into the equation.

First, we substitute z = 4 into the equation:

√ (3/2 x + 10) = cz + 8

√ (3/2 x + 10) = c(4) + 8

√(16) = 4c + 8

4 = 4c + 8

4c = -4

c = -1

Therefore, the value of c that makes z = 4 an extraneous solution is c = -1.

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∠b and 76° are alternate angles. They are equal.

So, m∠b = 76

That's it :)

The domain and the range of the table of values are Domain = {-15, 0, 9, 33, 44, 45} and Range = {21, 33, 57, 15, 97, 46}

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

The table of values

The above table of values can be represented as a list of ordered pairs

The rule of a table of values is that

using the above as a guide, we have the following:

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Answer:

Marcela used the Associative Property of Addition.

Step-by-step explanation:

The Associative Property of Addition states that when adding three or more numbers, the grouping of the addends does not change the sum. In other words, no matter how the addends are grouped, the sum remains the same. More specifically:

For any three numbers a, b, and c, (a + b) + c = a + (b + c)

For example: (2 + 3) + 4 = 2 + (3 + 4) = 9

So, if Marcela used the Associative Property of Addition to add her grocery bills, she grouped the addends in a different order, but still arrived at the same sum.

The value of the expression 10 ÷ 40 using the long division method will be 0.25.

The expression is given below.

10 ÷ 40

Division means the separation of something into different parts, sharing of something among different people, places, etc.

The division is given below by the long division method. Then

40 ) 100       ( 0.25

      - 80

         200

      - 200

            0

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The value of solution of the expression is,

⇒ - 5 (- 6w + 2u - 5)

Since, Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

Expression is,

⇒ - 5 (- 6w + 2u - 5)

Now, By using distributive property we get;

⇒ - 5 (- 6w + 2u - 5)

⇒ - 5 × - 6w - 5 × 2u - 5 × - 5

⇒ 30w - 10u + 25

Thus, The value of solution of the expression is,

⇒ - 5 (- 6w + 2u - 5)

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The properties of quadratic functions cause this "death ray" effect is discussed below.

The "death ray" effect refers to the phenomenon where a quadratic function appears to have a sharp point or vertex that shoots off to infinity in a graph. This effect is caused by the properties of quadratic functions, specifically:

The degree of the quadratic function: Quadratic functions have a degree of 2, which means they have a leading term that is a squared variable (x²). This leads to a graph that is a parabola.

The coefficient of the squared term: The coefficient of the squared term in the quadratic function determines the shape of the parabola. If the coefficient is positive, the parabola opens upward, and if the coefficient is negative, the parabola opens downward.

However, when the coefficient of the squared term is negative (a < 0), the graph of the quadratic function opens downward, and the vertex represents the maximum point of the parabola.

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The length of the two tied strings on the number line would be between 96 and 97.

We first need to convert both the lengths of the strings to inches, since the knot's length is given in inches.

The first string is 3 3/4 feet long, which is equivalent to 45 inches (since 1 foot = 12 inches, and 3 3/4 feet = 45 inches).

The second string is 1 1/2 yards long, which is equivalent to 54 inches (since 1 yard = 36 inches, and 1 1/2 yards = 54 inches).

The total length of the two strings before the knot is tied is 45 inches + 54 inches = 99 inches.

Subtracting the length of the knot (2 1/2 inches) from the total length of the two strings gives us:

99 inches - 2 1/2 inches = 96 1/2 inches

Therefore, the length of the two tied strings on the number line would be between 96 and 97.

Since we know that the length is closer to 97 inches than 96 inches, we can mark the length at point 97 on the number line

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The equation that can be used to calculate the base areas of the rectangular prisms is B = V/6

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

Volume of rectangular prisms

The volume of rectangular prisms is calculated as

V = Bh

Where

B = Base area

h = height

Given that

h = 6 inches,

We have

V = B * 6

Divide both sides by 6

B = V/6

This means that the the equation to calculate the base areas is B = V/6

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Complete question

Mr. James is teaching his studens about the volume of rectangular prisms.He has various rectangular prisms with a height of 6 inches

Which equation can be used to find B, the area of the base with volume V

The linear function that is modeled by the given table is:

y = -4x + 7

A general linear function is written as:

y = ax + b

Where a is the slope and b is the y-intercept.

If we know two points on the line (x₁, y₁) and (x₂, y₂) then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

Here we can use the first two points on the table:

(-11, 51) and (-5.5, 29)

Then the slope is:

a = (29 - 51)/(-5.5 + 11)

a = -4

Then the linear function is:

y = -4x + b

We know that when x = -5.5, the value of y is 29

29 = -4*-5.5 + b

29 = 22 = b

29 - 22 = b

7 = b

The linear function is:

y = -4x + 7

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Answer:

Step-by-step explanation:

7247.1977343

The square root of (35 x 35 x 35) is approximately 207.57.

The square root of (35 x 35 x 35) can be found by simplifying the expression under the radical sign:

√(35 x 35 x 35) = √(35³)

On simplifying 35³ to get:

√(35³) = √(42,875) ≈ 207.57

Therefore, the square root of (35 x 35 x 35) is approximately 207.57.

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standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-7}-\stackrel{y1}{6}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-4)}}} \implies \cfrac{-7 -6}{0 +4} \implies \cfrac{ -13 }{ 4 } \implies - \cfrac{13}{4}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{- \cfrac{13}{4}}(x-\stackrel{x_1}{(-4)}) \implies y -6 = - \cfrac{13}{4} ( x +4) \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{4}}{4(y-6)=4\left( - \cfrac{13}{4} ( x +4) \right)}\implies 4y-24=-13(x+4) \\\\\\ 4y-24=-13x-52\implies 13x+4y-24=-52\implies \boxed{13x+4y=-28}[/tex]