Scott has a rectangular garage that has a length of 234 inches. The width is 1. 5 times shorter than the length. What is the area of his garage? ​

Answer:

A

Step-by-step explanation:

reminder that 1 hour = 60 minutes , then

1 hour 50 minutes = 60 + 50 = 110 minutes

Brooke finished in 110 minutes, so was faster by 10 minutes

Answer:

6

Step-by-step explanation:

Add 6+3 and then divide 2 and then you get 6

Answer:

Resultant speed = 12 km/h.

Bearing is 107.14 degrees.

Step-by-step explanation:

This can be represented by a triangle of velocities with lengths 15 and 5 with the included angle = 45 degrees.

To find the velocity of the resultant  we use cosine rule:

v^2 = 15^2 + 5^2 - 2*5*15cos 45

v^2 = 143.934

v = 12.0 km/h to the nearest tenth.

To find the bearing we use the sine rule to find the angle down from due east>

12 / sin 45 = 5/ sin x

sin x =  5 sin 45 / 12 = 0.2946278

x = 17.14 degrees.

Bearing is therefore 90 + 17.14 = 107.14 degrees.

The recurrent input of the given sequence an = (12^n − n^2), where n is a positive integer, cannot be determined.

To determine the recurrent input of a sequence, we look for a pattern or formula that generates the terms of the sequence based on previous terms. However, in this case, the given sequence is defined directly by the formula an = (12^n − n^2).

There is no recurrence relation or dependency on previous terms in the sequence. Each term is solely determined by the value of n. Therefore, there is no underlying recurrent input or relationship between the terms that can be expressed through a recurrence relation. The sequence is entirely defined by the given formula without any recursive pattern, making it impossible to determine a recurrent input.

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The trigonometric ratio sine compares the lengths of the right triangle's two sides. Sin, though commonly abbreviated to sin, is actually pronounced sine.

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Answer:

10 miles

Step-by-step explanation:

Find how much she runs during one track practice by dividing 8 by 4. This gives you the equation 2x, with x being the number of track practices.

Answer: 10 miles after 5 track practices.

Step-by-step explanation: Lets find the unit rate of this problem. Remember that unit rate means the denominator will always have a 1.

8/4 converted to a unit rate is 2/1

The unit rate is 2 miles per every 1 track practice.

We can use the unit rate to solve how many miles Leslie would have ran after 5 track practices.

2/1 x 5 = 10/5

So, Leslie would have ran 10 miles after 5 track practices.

The given expression in postfix notation is: x = a b * c * d * e f g * - * h i * j * k * l - /

To convert the given expression into postfix (reverse Polish) notation, we follow the rules of postfix notation where the operators are placed after their operands. The expression is:

x = (a * b * c * d * (e - f * g)) / (h * i * j * k - l)

To convert this expression into postfix notation, we can use the following steps:

Step 1: Initialize an empty stack and an empty postfix string.

Step 2: Read the expression from left to right.

Step 3: If an operand is encountered, append it to the postfix string.

Step 4: If an operator is encountered, perform the following steps:

a) If the stack is empty or contains an opening parenthesis, push the operator onto the stack.

b) If the operator has higher precedence than the top of the stack, push it onto the stack.

c) If the operator has lower precedence than or equal precedence to the top of the stack, pop operators from the stack and append them to the postfix string until an operator with lower precedence is encountered. Then push the current operator onto the stack.

d) If the operator is an opening parenthesis, push it onto the stack.

e) If the operator is a closing parenthesis, pop operators from the stack and append them to the postfix string until an opening parenthesis is encountered. Discard the opening and closing parentheses.

Step 5: After reading the entire expression, pop any remaining operators from the stack and append them to the postfix string.

In postfix notation, the operands are listed first, followed by the operators. The expression is evaluated from left to right using a stack-based algorithm. This notation eliminates the need for parentheses and clarifies the order of operations.

By converting the original expression to postfix notation, it becomes easier to evaluate the expression using a stack-based algorithm or calculator.

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The Factored form of 3x^2 - 11x + 6 is (x - 3)(3x - 2).

The quadratic expression 3x^2 - 11x + 6, we can use the method of factoring by grouping. Here's the step-by-step process:

Step 1: Multiply the coefficient of x^2 (3) by the constant term (6) in the expression.

  3 * 6 = 18.

Step 2: Find two numbers that multiply to give 18 and add up to the coefficient of x (-11).

  The numbers -2 and -9 fit this criteria because -2 * -9 = 18 and -2 + (-9) = -11.

Step 3: Split the middle term (-11x) into two terms using the numbers found in step 2.

  3x^2 - 2x - 9x + 6.

Step 4: Group the terms and factor out the greatest common factor (GCF) from each group.

  (3x^2 - 2x) - (9x - 6).

  x(3x - 2) - 3(3x - 2).

Step 5: Notice that the terms (3x - 2) are common in both groups. Factor it out.

  (x - 3)(3x - 2).

So, the factored form of 3x^2 - 11x + 6 is (x - 3)(3x - 2).

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The speed of the water drop when it strikes the hood is approximately 14.0 m/s downward, and the speed of the car at that moment is approximately 29.3 m/s to the east.

The drop appears to have a velocity of approximately 29.3 m/s to the west and 14.0 m/s downward with respect to the passenger in the car.

The drop appears to have an acceleration of approximately 3 m/s² to the west and 9.8 m/s² downward with respect to the passenger in the car.

(To determine the speed of the water drop and the speed of the car when the drop strikes the hood,

use the kinematic equations of motion.

First, we can find the time it takes for the drop to fall 10m using the kinematic equation:

distance h = 10m,

\(h = 1/2 at^2\)

where

h is the vertical distance,

a is the acceleration due to gravity (9.8m/s²), and t is the time.

Substituting the values, we have;

\(10 = 1/2 (9.8) t^2 \\

t^2 = 20/9.8 \\

t ≈ 1.43 seconds\)

Next, find the final velocity of the drop using the kinematic equation:

\(v = vo + at\)

where v is the final velocity,

vo is the initial velocity (which is 0m/s for the drop),

a is the acceleration due to gravity, and

t is the time we just calculated.

Substituting the values, we have

v = 0 + (9.8)(1.43)

v ≈ 14.0 m/s downward

Finally, find the speed of the car when the drop strikes the hood using the kinematic equation:

\(v = vo + at\)

v = 25 + (3)(1.43)

v ≈ 29.3 m/s to the east

Therefore, the speed of the water drop when it strikes the hood is approximately 14.0 m/s downward, and the speed of the car at that moment is approximately 29.3 m/s to the east.

To determine the velocity and acceleration

The velocity of the water drop with respect to the passenger in the car is simply the vector difference between the velocity of the water drop and the velocity of the car:

v_drop,p = v_drop - v_car

where v_drop is the velocity of the water drop (14.0 m/s downward) and

v_car is the velocity of the car (29.3 m/s to the east).

Substituting the values, we get:

v_drop,p = (0, -14.0, 0) - (29.3, 0, 0)

v_drop,p = (-29.3, -14.0, 0) m/s

Thus, the drop appears to have a velocity of approximately 29.3 m/s to the west and 14.0 m/s downward with respect to the passenger in the car.

The acceleration of the water drop with respect to the passenger in the car is simply the vector difference between the acceleration of the water drop and the acceleration of the car:

a_drop,p = a_drop - a_car

where a_drop is the acceleration due to gravity (9.8 m/s² downward) and

a_car is the acceleration of the car (3 m/s² to the east).

Substituting the values, we have,

a_drop,p = (0, -9.8, 0) - (3, 0, 0)

a_drop,p = (-3, -9.8, 0) m/s²

Therefore, the drop appears to have an acceleration of approximately 3 m/s² to the west and 9.8 m/s² downward with respect to the passenger in the car.

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The equation y = -7 defines a function.

In this equation, the value of y is fixed and constant for any given x. Regardless of the value of x, the equation y = -7 will always give the same output as y = -7. Thus, each input value of x corresponds to a unique output value of y, satisfying the definition of a function.

The equation y = -7 defines a function. In a function, each input value must correspond to a unique output value. In the given equation, regardless of the value of x, the equation y = -7 will always yield the same output value of y = -7. This means that for any given x, there is only one corresponding value of y, satisfying the requirement of a function. The equation represents a horizontal line on a graph, where all points on the line have the same y-coordinate of -7. This indicates that there is a unique output value for every possible input value of x. Therefore, the equation y = -7 defines a function.

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The sample is a systematic sample.

What is sample?

In statistics, a sample is a subset of individuals or objects selected from a larger population. Samples are used in statistical analyses to draw conclusions or make inferences about the entire population.

A sample is typically less time-consuming and less expensive to collect and analyze than the entire population, making it a practical and efficient way to conduct research.

A systematic sample is a type of probability sampling method in which every nth member of a population is selected to be included in the sample.

In this case, the network administrator is analyzing the company's network logs every third day, which means they are selecting every third day's data for analysis.

This is a systematic approach to selecting the data for analysis, making it a systematic sample.

Therefore, the sample is a systematic sample.

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Based on the given information, it is not possible to determine the p-value, decision to reject (rh0) or failure to reject (frh0) without additional data or context.

To assess whether the relaxation exercise slowed brain waves, a statistical analysis should be conducted on a sample from the population.

The analysis would involve measuring brain waves before and after the exercise and comparing the results using appropriate statistical tests such as a t-test or ANOVA. The p-value would indicate the probability of observing the data if there was no effect, and the decision to reject or fail to reject the null hypothesis would depend on the predetermined significance level.

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Answer:

-26

Step-by-step explanation:

sub in the x value

-4+3-(2(-5)+5)^2

-4+3-(-10+5)^2

-4+3-(5)^2

-1-25

-26

Marcus is 59.5 inches tall.(?)

Step-by-step explanation:

it's because Zoey is 63.75 inches tall and Zoey is just 4.25 inches taller than Marcus so 63.75 minus 4.25 is equal to 59.5.(not sure)

Density of liquid b = 0.4 g/cm³.

Let the volume of liquid B added be V cm³.

The total volume of the mixture = Volume of A + Volume of B = 150 + V cm³

Using the formula:

Density = Mass/Volume

Density of C = (Mass of C) / (Volume of C)

1.1 = 220 / (150 + V)

Solving for V, we get:

V = 100 cm³

Therefore, the volume of liquid B added is 100 cm³.

The total mass of the mixture = Mass of A + Mass of B = (Density of A x Volume of A) + (Density of B x Volume of B)

220 = (1.2 x 150) + (Density of B x 100)

Solving for Density of B, we get:

Density of B = (220 - 180) / 100 = 0.4 g/cm³

Therefore, the density of liquid B is 0.4 g/cm³.

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ANSWER:

To calculate the money spend on a membership,Assuming a 2% increase each year, the cost of the zoo membership for the second year would be $81.60 (which is $80 + 2% of $80). For the third year, it would be $83.23 (which is $81.60 + 2% of $81.60). This pattern would continue for each subsequent year.

To calculate the total cost of the membership over 20 years, you can use the formula for the sum of a geometric series:

Total cost = a(1 - r^n) / (1 - r)

where:
a = initial cost = $80
r = common ratio = 1.02 (since the cost is increasing by 2% each year)
n = number of years = 20

Plugging in the values, we get:

Total cost = 80(1 - 1.02^20) / (1 - 1.02)
Total cost = $1,978.16

Therefore, you would spend a total of $1,978.16 on a zoo membership over 20 years if the cost increases by 2% each year starting from an initial cost of $80.

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You would spend $1943.79 on a membership over 20 years.

To calculate the total cost of a zoo membership over 20 years, considering a 2% annual increase, we can use the formula for the sum of a geometric series:

Sum = \(a * (1 - r^n) / (1 - r),\)

where:

a is the initial cost of the membership,

r is the common ratio (1 + annual increase rate),

n is the number of years.

In this case, the initial cost of the membership (a) is $80, the annual increase rate is 2% (or 0.02), and we want to calculate the total cost over 20 years (n = 20).

Let's substitute these values into the formula:

Sum = \(80 * (1 - (1 + 0.02)^2^0) / (1 - (1 + 0.02)).\)

Calculating this expression:

Sum = \(80 * (1 - 1.02^2^0) / (1 - 1.02)\)

≈ 80 * (1 - 1.485947) / (-0.02)

≈ 80 * (-0.485947) / (-0.02)

≈ 80 * 24.29735

≈ 1943.788

Therefore, you would spend approximately $1943.79 on a zoo membership over 20 years.

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Answer:

Step-by-step explanation:

A(triangle) = 6 x 6 : 2 = 18

A(rectangle) = 6 x 9 = 54

Radius of circle = 6 : 2 = 3

A(semi-circle) = 3 x 3 x pi : 2 = 14.13

A(figure) = 18 + 54 + 14.13 = 86.13

The total area of the geometry will be 86.13 square units.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

The geometry is the sum of a triangle, a rectangle, and a semicircle.

Then the area of the geometry is the sum of the area of the triangle, the area of the rectangle, and the area of the semicircle.

A = Area of triangle + Area of rectangle + Area of a semicircle

A = (1/2) × 6 × 6 + 6 × 9 + π × 6² / 8

A = 18 + 54 + 14.13

A = 86.13

The total area of the geometry will be 86.13 square units.

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Answer:

lol every teacher is crazy

Step-by-step explanation:

Using the 14c calibration on the x-axis, the approximate age of the neanderthal fossils is (C) 40,110 years old.

So, using calibration on the x-axis, the approximate age of the neanderthal fossils came out to be 40,110 years old.

Therefore, using the 14c calibration on the x-axis, the approximate age of the neanderthal fossils is (C) 40,110 years old.

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The correct question is given below:
Using the 14c calibration on the x-axis, what is the approximate age of the neanderthal fossil?

a. 5,730 years old

b. 34,380 years old

c. 40,110 years old

d. 45,840 years old

There are 30 adults in the swimming pool.

The ratio is a quantitative approach that shows the relation between two proportions.

From the given relation, the ratio of of the children to adults = 8 : 3

The total number of the ratio = 8 + 3 = 11

Given that there are 110 people in the population.

The number of adults that are there will be:

\(\mathbf{=\dfrac{3}{11}\times 110}\)

= 30 adults

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The measure of angle D in the convex pentagon ABCDE is 132°

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the measure of angle D, hence:

angle A = x - 40.

∠A + ∠B + ∠C + ∠D + ∠E = 540° (sum of angle in a pentagon)

3(x - 40) + 2x = 540

x = 132°

The measure of angle D in the convex pentagon ABCDE is 132°

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Answer/Step-by-step explanation:

Given :  

The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x):

To Find: two types of transformations that can be used to transform f(x) to g(x).

=================================================================

Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 points)

Solution Part A:

f(x) = x/5  + y/(-10) = 1  

=> 2x  - y  =  10

=================================================================

Part B: Solve for k in each type of transformation. (4 points)

Solution Part B:

g(x) = x/(-3) + y/6  = 1

=> 2x  -  y  = - 6  

=================================================================

an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points)

Solution Part C:  

Transformations :

g(x)  = f(x)  +  16

g(x) = f(x + 8)

The probability of a type I error in the case of the new blood test is 0.022.

Given;

It is not always possible to identify rare diseases by screening. A blood test that has been created by researchers is thought to be reasonably dependable. In 97% of those who suffer from a sickness, it produces a favorable response. However, 5% of those tested who do not have the condition received an incorrectly positive response. Take into account the null hypothesis that "the person does not have the disease."

A: The individual does not have the disease

B: The individual does have the disease

We know that,

Type I Error is rejecting the true null hypothesis

P (Type I Error) = P(Positive reaction to an individual who does not have the disease)

                         =0.022

Hence, the probability of a type I error is 0.022.

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First we find the value of \(x\). This is quite simple as it's a right angled triangle with one of the angles already given. The main concept is vertically opposite angles meaning if 2 lines intersect, the opposite 2 angles are equal.

So the angle \(55x - 1\) is for the interior of the triangle too. Now due to angle sum postulate, \(36x + 55x -1 + 90 = 180\)

Simplify this and you get: \(91x = 91\)

Hence, \(x = 1\)

Now, we need to find the value of angle \(A\) which is \(36x\) which is basically \(36 * 1\) when we replace \(x\) with \(1\).

Henceforth, angle \(A\) is equal to \(36\) so option \(C\) is correct. :D

===================================================

Explanation:

Place point B at the intersection of the lines where the 90 degree angle is located.

Place point C at the other intersection point.

So we have triangle ABC.

Since we have a right angle, this means angle B is 90 degrees.

Angle C is 55x-1 degrees because it's vertical to the angle shown. Vertical angles are congruent.

See the diagram below.

-------------

From here we use the idea that all three angles of any triangle always add to 180

A+B+C = 180

(36x) + (90) + (55x-1) = 180

91x+89 = 180

91x = 180-89

91x = 91

x = 91/91

x = 1

Use this x value to find angle A and C

A = 36x = 36*1 = 36

C = 55x-1 = 55*1-1 = 54

Finding angle C is optional since your teacher just wants angle A, but it's useful to help check our answer

A+B+C = 36+90+54 = 180

So this confirms we have the right x value.

To solve the given system, we have to graph each equation.

Let's find the points when x = 1, x = 2.

The points for the first line are (1, -2) and (2, -4). Now, let's plot these points and draw the line

Now, let's repeat the process for the second equation.

For x = 0, and x = 1, we have

The points are (0, 5) and (1, 8). Let's graph the second line

As you can observe in the image above, the lines intersect at (-1, 2).

The probability that a student's score is less than 81 points on the reading ability test is 0.9772. We would expect approximately 489 students to earn a score less than 81 points if 500 students took the reading ability test. The probability of randomly selecting 35 students (all from the same class) that have a sample mean reading ability test score between 66 and 68 is approximately 0.2190.

To find the probability that a student's score is less than 81 points, we need to standardize the score using the z-score formula:

z = (x - μ) / σ

where x is the student's score, μ is the mean score, and σ is the standard deviation. Plugging in the values, we get:

z = (81 - 65) / 8 = 2.00

Using a standard normal distribution table or calculator, we can find the probability of a z-score less than 2.00 to be approximately 0.9772. Therefore, the probability that a student's score is less than 81 points is 0.9772.

Since the distribution is normal, we can use the normal distribution to estimate the number of students who would earn a score less than 81. We can standardize the score of 81 using the z-score formula as above and use the standardized score to find the area under the normal distribution curve. Specifically, the area under the curve to the left of the standardized score represents the proportion of students who scored less than 81. We can then multiply this proportion by the total number of students (500) to estimate the number of students who would score less than 81.

z = (81 - 65) / 8 = 2.00

P(z < 2.00) = 0.9772

Number of students with score < 81 = 0.9772 x 500 = 489

Therefore, we would expect approximately 489 students to earn a score less than 81 points.

The distribution of the sample mean reading ability test scores is also normal with mean μ = 65 and standard deviation σ / sqrt(n) = 8 / sqrt(35) ≈ 1.35, where n is the sample size (number of students in the sample). To find the probability that the sample mean score is between 66 and 68, we can standardize using the z-score formula:

z1 = (66 - 65) / (8 / sqrt(35)) ≈ 0.70

z2 = (68 - 65) / (8 / sqrt(35)) ≈ 2.08

Using a standard normal distribution table or calculator, we can find the probability that a z-score is between 0.70 and 2.08 to be approximately 0.2190. Therefore, the probability of randomly selecting 35 students (all from the same class) that have a sample mean reading ability test score between 66 and 68 is approximately 0.2190.

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The equation of the sphere in standard form 16x2 + 162 + 1622 = 96x - 24 - 128 is \((x - 3)^2 + y^2 + z^2 = (81sqrt(17) / 2)^2\)

To write the equation of the sphere in standard form, we need to rearrange the terms so that the variables are on one side and the constant is on the other side.

The standard form of the equation of a sphere is:

\((x - h)^2 + (y - k)^2 + (z - l)^2 = r^2\)

where (h, k, l) is the center of the sphere and r is the radius.

So, let's start by rearranging the terms in the given equation:

\(16x^2 + 162 + 162^2 - 96x + 24 + 128 = 0\)

We can simplify the constants on the left side:

\(16x^2 - 96x + 162^2 + 24 + 128 = 0\)

Now we can complete the square for the x terms:

\(16(x^2 - 6x + 9) + 162^2 + 24 + 128 - 16(9) = 0\)

\(16(x - 3)^2 + 162^2 + 24 + 128 - 144 = 0\)

\(16(x - 3)^2 + 162^2 + 8 = 0\)

Finally, we can divide both sides by 16 to get the equation in standard form:

\((x - 3)^2 + (y - 0)^2 + (z - 0)^2 = (-1/2)162^2 - 1/2(8)\)

The center of the sphere is (3, 0, 0), and the radius is the square root of the constant term on the right side:

\(r = sqrt[(-1/2)162^2 - 1/2(8)] = 81sqrt(17) / 2\)

Therefore, the equation of the sphere in standard form is:

\((x - 3)^2 + y^2 + z^2 = (81sqrt(17) / 2)^2\)

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