Aliyah rode her bike at a speed of 10 miles per hour for 1.5 hours and then traveled at a speed of 7.5 miles per hour for 2 hours. What is the total distance that Alyah rode her bike during this time?

Answer:

choice 1) 312 cm²

Step-by-step explanation:

area = (16 x 12) + (10 x 12) = 312 cm²

Answer:

312

Step-by-step explanation:

triangle：

10x12/2=60

two triangle：

60x2=120

rectangle：

16x12=192

add up：

120+192=312

Answer:

5+5=55

Step-by-step explanation:

It just is

Answer:

5+5=10

Step-by-step explanation:

Answer:

B. Since \(\triangle ABC \cong \triangle DEF\) by SSS and \(\triangle DEF \cong \triangle GHJ\) by SAS, \(\triangle ABC \cong \triangle GHJ\) by the Transitive Property of Congruence.

The congruent statement and the reason why the triangles are congruent is (b) Since AC ≅ GJ and CB ≅ JH, AB must be congruent to GH. So, ABC ≅ GHJ by SSS

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

Triangles = ABC, DEF and GHJ

There are several theorems that make any two triangles to be congruent

One of these theorems is the SSS congruent theorem

The SSS congruent theorem implies that the corresponding sides of the triangles in question are congruent

From the question, we can see that the following corresponding sides on the triangles ABC and GHJ have the same mark

AC and GJ

CB and JH

This implies that these sides are congruent sides

For the triangle to be congruent by SSS, the following angles must also be congruent

AB must be congruent to GH

Hence, the congruent statement on the congruency of the triangles is (d)

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Answer:

(7, -2)

Step-by-step explanation:

The trapezoid A B C D has points (2, 2), (7, 2), (5, 1), (3, 1).

Transformation of a point is the change in location from an original position to a new position. If a shape is transformed, all its points are also transformed. A transformation can either be a rotation, translation, reflection or dilation.

If a point O(x,y) is reflected across the y axis, the new coordinate of the point is at O'(x, -y), i.e. the x coordinate does not change, but the y coordinate is negated.

Since in trapezoid ABCD, the coordinate of point B is (7, 2). The trapezoid is  reflected across the x-axis, therefore the new coordinate of B' is at (7, -2)

Answer:c

Step-by-step explanation:

I took the test

Answer:

Step-by-step explanation:

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Answer:

Point (5, -1) is located in Quadrant IV of a coordinate plane.

Explanation:

Point (-2,-7) is located in Quadrant III of a coordinate plane, not Quadrant I.

Point (3,-9) is located in Quadrant IV of a coordinate plane, not Quadrant II.

Point (-4, 8) is located in Quadrant Il of a coordinate plane, not Quadrant III.

Answer:

Step-by-step explanation:

Answer:

Slope = -1

Step-by-step explanation:

Since, slope of a line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by,

Slope = \(\frac{y_2-y_1}{x_2-x_1}\)

Therefore, slope of a line passing through two points A(1, 4) and B(3, 2) will be,

Slope = \(\frac{4-2}{1-3}\)

          = (-1)

Therefore, slope of the line is (-1).

Answer:

The volume of the triangular prism is 677.6 cubic meters.

Step-by-step explanation:

The formula for the volume of a triangular prism is:

\(\sf\qquad\dashrightarrow Volume \: (V) = \dfrac{1}{2} \times b\times h \times l \)

where:

Substituting the given values, we have:

\(\sf:\implies Volume \: (V) = \dfrac{1}{2} \times 11 \times 11 \times 11.2\)

\(\sf:\implies \boxed{\bold{\:\:Volume \: (V) = 677.6\: meters^3\:\:}}\:\:\:\green{\checkmark}\)

Therefore, the volume of the triangular prism is 677.6 cubic meters.

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The given statement "if the total change of a function f along a curve c is zero, then c must be a contour of f" is true because a contour of a function f is a curve along which the function has a constant value.

When the total change of a function f along a curve c is zero, it means that the function's value has not changed throughout the curve.

This indicates that the curve c must be a contour of the function f, as the function has a constant value along the curve.

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Answer:

x=9   output 1=20.25

Output 2 equals 27

Step-by-step explanation:

This function is constant, so you do input times 2.25 for each.

The box below 6 is 9 because we are counting by 3

9 x 2.25=20.25

12 x 2.25=27

Hope this helped :)

Answer:

Step-by-step explanation:

muffin times 2.25=output

so 12x2.25=27

and also x=9

so 9x2.25=20.25

(i) The given differential equation is a linear homogeneous equation with constant coefficients. To find the general solution, we first solve the associated auxiliary equation:

\(r^2 - 8r + 17 = 0\).

Factoring the quadratic equation, we get:

\((r - 1)(r - 17) = 0\).

Thus, the roots of the auxiliary equation are \(r = 1\) and \(r = 17\). Since the roots are distinct, the general solution of the homogeneous equation is:

\(y_h(x) = C_1 e^{x} + C_2 e^{17x}\),

where \(C_1\) and \(C_2\) are constants.

To find a particular solution of the non-homogeneous equation, we assume \(y_p(x) = ax + b\) and substitute it into the equation. Solving for \(a\) and \(b\), we find \(a = 5/2\) and \(b = -3/34\).

Therefore, the general solution of the given differential equation is:

\(y(x) = y_h(x) + y_p(x) = C_1 e^{x} + C_2 e^{17x} + \frac{5}{2}x - \frac{3}{34}\).

(ii) The given differential equation is a first-order exact equation. To solve it, we check if it satisfies the exactness condition:

\(\frac{\partial M}{\partial y} = \frac{\partial N}{\partial x}\).

Taking the partial derivatives, we have:

\(\frac{\partial M}{\partial y} = \frac{2x^2}{y^2} + \frac{6}{x}\)

\(\frac{\partial N}{\partial x} = 3 + \frac{6}{y^2}\).

Since \(\frac{\partial M}{\partial y} = \frac{\partial N}{\partial x}\), the equation is exact. To find the solution, we integrate \(M\) with respect to \(y\) while treating \(x\) as a constant:

\(f(x, y) = \int \left(\frac{x^2}{y} + \frac{3y}{x}\right) dy = x^2\ln|y| + \frac{3y^2}{2x} + g(x)\),

where \(g(x)\) is an arbitrary function of \(x\).

Next, we take the partial derivative of \(f(x, y)\) with respect to \(x\) and set it equal to \(N(x, y)\):

\(\frac{\partial f}{\partial x} = 2x\ln|y| - \frac{3y^2}{2x^2} + g'(x) = 3x + \frac{6}{y^2}\).

Comparing the terms, we find that \(g'(x) = 0\) and \(g(x)\) is a constant \(C\).

Therefore, the general solution of the given differential equation is:

\(x^2\ln|y| + \frac{3y^2}{2x} + C = 0\).

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The correct answer is: a) Modify the planned assessed level of control risk because the sample exception rate plus the allowance for sampling risk exceeds the tolerable rate.

In attribute sampling, the auditor evaluates a sample to assess the control risk associated with a particular attribute or characteristic. In this case, the attribute being tested is the exception rate among the documents.

Given the information provided:

Sample size (n) = 50 documents

Number of exceptions found in the sample = 1

Tolerable rate = 6%

Expected population exception rate = 1%

Allowance for sampling risk = 3%

To evaluate the sample results, we need to consider the sample exception rate plus the allowance for sampling risk and compare it with the tolerable rate.

Sample exception rate = (Number of exceptions found / Sample size) * 100

= (1 / 50) * 100

= 2%

Sample exception rate + Allowance for sampling risk = 2% + 3% = 5%

Since the sample exception rate plus the allowance for sampling risk (5%) exceeds the tolerable rate (6%), the auditor needs to modify the planned assessed level of control risk. This means that the auditor should conclude that the control is not operating effectively at the desired level and may need to adjust their assessment of control risk accordingly.

Therefore, the correct answer is a) Modify the planned assessed level of control risk because the sample exception rate plus the allowance for sampling risk exceeds the tolerable rate.

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The proportion of scores below 12.5 in a normally distributed population with a mean of 10 and a standard deviation of 2 can be calculated using the Z-score and the standard normal distribution table. In this case, we need to find the area under the curve to the left of the value 12.5.

The Z-score is calculated as (X - μ) / σ, where X is the value we want to find the proportion for, μ is the mean, and σ is the standard deviation. Substituting the given values, we have (12.5 - 10) / 2 = 1.25.

Using the standard normal distribution table or a statistical calculator, we can find that the area to the left of a Z-score of 1.25 is approximately 0.8944. Therefore, the proportion of scores below 12.5 is approximately 89.44%.

In a normal distribution, the Z-score measures the number of standard deviations a value is from the mean. By calculating the Z-score for the value 12.5, we can use the standard normal distribution table to find the proportion of scores below that value.

The table provides the cumulative probability up to a certain Z-score. In this case, the Z-score of 1.25 corresponds to a cumulative probability of approximately 0.8944.

Since the normal distribution is symmetric, the proportion of scores above 12.5 is equal to the proportion below the mean minus the proportion below 12.5.

Hence, subtracting 0.8944 from 1 (or 100%) gives us approximately 0.1056 or 10.56%. Therefore, the proportion of scores below 12.5 is approximately 89.44%.

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95% confident that the true population mean μ lies between 83.04 and 86.96

Confidence Interval

A confidence interval in statistics refers to the probability that a population parameter will fall between a set of values for a certain proportion of times. Analysts often use confidence intervals than contain either 95% or 99% of expected observations.

First need to determine whether dealing with means or proportions in this problem. The sample and population mean, that  are dealing with means.

One sample mean, this mean creating a confidence interval for one sample (1 Sample  t Interval)

Normally we would check for conditions, but since this is not formulated as a real-world scenario type problem, it is hard to check for randomness and independence. Therefore excluding conditions from this answer.

The formula for constructing a confidence interval for means is as follows:

x ± t ( σ / \(\sqrt{n}\) )

The variables are:

x = 85

σ = 8

n = 64

Plug these values into the formula for the confidence interval

85 ± t ( 8 / \(\sqrt{64}\))

Finding the Critical Value (t)

In order to find t, use this formula:

\(\frac{1 - C}{2} = A\)

The z-score associated with A will give us t

So plug in the confidence interval 95% (.95) into the formula

\(\frac{1 - 0.95}{2} = 0.25\)

Use the calculator or a t-table to find the z-score associated with this area under the curve

t = 1.96

Constructing Confidence Interval

Finish the confidence interval created

= 85 ± 1.96 ( 8 / \(\sqrt{64}\) )

The confidence interval using this formula, to be

(83.04, 86.96)

Interpreting the Confidence Interval

95% confident that the true population mean μ lies between 83.04 and 86.96

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Answer:

A)

Step-by-step explanation:

A systems of equations that are 2 completely separate lines will have 1 solution.

A systems of equations that are the same line will have infinite amount of solutions.

A systems of equation that have parallel lines will have no solution.

We see that B, C, and D are all 2 completely separate lines with their own slope and y-intercept. Therefore, they will have 1 solution.

A is our answer because we see that they have the same slope but different y-intercepts. This means that they are parallel lines and will never intersect each other, thus providing us with no solution.

The solutions of the equation  x² + 2x + 10 = - 3x + 4 are  x=-2 and x=-3

The given equation is x² + 2x + 10 = - 3x + 4.

Take all the terms to the left side

x² + 2x + 10+3x-4=0

Combine the like terms

x²+5x+6=0

x²+2x+3x+6=0

Take out the factors

x(x+2)+3(x+2)=0

(x+3)(x+2)=0

x=-2 and x=-3

Hence, x=-2 and x=-3 are the solutions of the equation  x² + 2x + 10 = - 3x + 4.

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Answer:

Y= -2x+7

Step-by-step explanation:

Answer:

1.5m

Step-by-step explanation:

A hexagon has 6 sides,

so divide 6 by 9.0m

you get 1.5m

Answer:

Step-by-step explanation:

Step 1:

Make a proportion:

10/5 = 22/x

Step 2:

Cross multiply:

10x=22*5

10x=110

Step 3:

Divide by 10 to isolate x:

x=11

In the 1984 domestic violence study conducted by Sherman and Berk, the ethical concern was that they potentially withheld a beneficial treatment.

The domestic violence study conducted by Sherman and Berk in 1984 raised an ethical concern in that they financially profited from the research. This raises the question of whether their motives were purely altruistic or whether they were driven by financial gain. Additionally, the study did not adhere to special protections for vulnerable populations such as women and children who may have been victims of domestic violence. This raises concerns about the validity and generalizability of the study's findings. Furthermore, the study potentially withheld a beneficial treatment, which raises questions about the ethical responsibility of researchers to ensure that their subjects receive the best possible care. Finally, there are also concerns that the researchers may have deceived their subjects, which raises questions about the integrity and transparency of the research process. In conclusion, the ethical concerns raised by this study highlight the need for researchers to carefully consider the impact of their research on vulnerable populations and to ensure that they adhere to the highest ethical standards.
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Knowing how to find the exact value of a radical and being able to approximate its value are both valuable skills in different contexts.

The choice between using the exact value or an approximation depends on the specific context, requirements.

And level of precision needed for the calculations or applications at hand.

Finding the exact value of a radical is valuable when precision and accuracy are required.

In some mathematical or scientific calculations, having the precise value of a radical is necessary for obtaining accurate results.

For example, in engineering, physics, or finance,

where measurements or calculations need to be extremely precise, knowing the exact value of a radical is crucial.

It allows for precise calculations and ensures that the results are as accurate as possible.

On the other hand, approximating the value of a radical is valuable when a rough estimate or an approximation is sufficient.

In many real-life scenarios, such as daily life, quick estimations, or practical applications,

It may not be necessary to know the exact value of a radical.

Approximations provide a close enough value that is easier to work with and can give a quick sense of the magnitude or scale of a quantity.

Approximating the value of a radical can save time and effort, especially when dealing with large or complex numbers.

Determining when to use an approximation versus the exact value depends on the specific requirements of the situation.

If high precision is essential, such as in scientific research or complex calculations, the exact value of a radical must be used.

However, in many practical situations or quick estimations, an approximation is sufficient and can provide a good enough answer.

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Answer:

$3850

Step-by-step explanation:

It is given that,

A girl scout troop makes $1100 in two weekends of selling cookies.

2 weekend = $1100

1 weekend = $550

For 7 weekend, we will multiply $550 by 7 as follows :

7 weekend = $550 × 7

= $3850

So, for 7 weekend she will need $3850.

Answer:

Step-by-step explanation:

just plug the numbers in to get your answer. c=90

a=55, b=50. so basically

(90)^2=(55)^2+(50)^2-2(55)(50)*cos90

Answer:

32.7°

Step-by-step explanation:

Cosine rule

\(c^2=a^2+b^2-2ab \cos C\)

Where:

From inspection of the given triangle:

Substitute the given values into the formula and solve for Y:

\(\begin{aligned}c^2 & =a^2+b^2-2ab \cos C\\\implies 55^2 & = 50^2+90^2-2(50)(90) \cos Y\\3025 & = 2500+8100-9000 \cos Y\\9000 \cos Y & = 2500+8100-3025\\9000 \cos Y & =7575\\\cos Y & =\dfrac{7575}{9000}\\\cos Y & =\dfrac{101}{120}\\Y & =\cos^{-1} \left(\dfrac{101}{120}\right)\\Y & = 32.68346376^{\circ}\\Y & = 32.7^{\circ} \; \sf (nearest \: tenth)\end{aligned}\)

If  your hotel is stories tall and the average story is feet high, the distance is  69 feet.

We can solve this problem using similar triangles. Let's call the distance between you and your hotel "x".

First, we need to determine the height of the building in front of you. Since we know it is five stories tall, and the average story is 10 feet high, its total height is 5 * 10 = 50 feet.

Now, we can use the similar triangles formed by the buildings and your line of sight to set up a proportion:

x / (h + 50) = 60 / h

where "h" is the height of the five-story building, and "h + 50" is the total height of the building and its billboard.

We can cross-multiply to get:

x * h = 60 * (h + 50)

Expanding the right side, we get:

x * h = 60h + 3000

Subtracting 60h from both sides, we get:

x * h - 60h = 3000

Factoring out the h, we get:

h * (x - 60) = 3000

Dividing both sides by h, we get:

x - 60 = 3000 / h

Substituting in the known values, we get:

x - 60 = 3000 / (10 * 32)

Simplifying, we get:

x - 60 = 9.375

Adding 60 to both sides, we get:

x = 69.375

x = 69 feet

Therefore, you are approximately 69 feet away from your hotel.

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The complete question is:

you are standing 60 feet away from a five-story building in los angeles, looking up at its rooftop. your eyes are approximately five feet above the ground. in the distance you can see the billboard on top of your hotel, but the hotel building is completely obscured by the building in front of you. if your hotel is 32 stories tall and the average story is 10 feet high, how far away from your hotel are you?

The best number to simplify a fraction is C Greatest common factor.

The greatest common factor is the highest number that can divide both the numerator and the denominator of the fraction without leaving a remainder.

To find the greatest common factor, list the prime factors of each number, take the common factors, and then multiply them.

For instance, the greatest common factor of 24 and 36 is 12, produced from the common factors of 3 and 4 (2 x 2) multiplied to get 12 (3 x 4).

Thus, it is easier to simplify a fraction using Option C than the other options.

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