Susan will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $53 and costs an additional $0.13 per mile driven. The second plan has an initial fee of 40 and costs an additional $0.18 per mile driven.

Answer:

wage

Step-by-step explanation:

wage describes that type of hourly income

Answer:

wage

Step-by-step explanation:

its her being paid.

The velocity of a car relative to the train can be found by subtracting the velocity of the train from the velocity of the car relative to the ground. This can be represented mathematically as: VCT = VCG - VTG, where VCT is the velocity of the car relative to the train, VCG is the velocity of the car relative to the ground, and VTG is the velocity of the train relative to the ground.

To understand this formula, we need to know the concept of relative velocity. Relative velocity refers to the velocity of an object with respect to another object. In this case, the car and the train are moving with respect to the ground, but we want to find the velocity of the car with respect to the train.

Let's assume that the car is moving at 60 km/h relative to the ground and the train is moving at 80 km/h relative to the ground in the same direction. Then, the velocity of the car relative to the train can be found as:

VCT = VCG - VTG
VCT = 60 - 80
VCT = -20 km/h

The negative sign indicates that the car is moving in the opposite direction of the train. Therefore, the velocity of the car relative to the train is 20 km/h in the direction opposite to the train.

In conclusion, to find the velocity of the car relative to the train, we need to subtract the velocity of the train from the velocity of the car relative to the ground. This is an important concept in physics and is used in many real-life situations.

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Answer:

21 hours

Step-by-step explanation:

If he worked 2/3 at home you need to divide 31.5 by 3 = 10.5

Then multiply by 2 = 21

Hope this helps! Have a great day :)

Answer:

OK

Step-by-step explanation:

Answer:

-30=-30

Step-by-step explanation:

Always true.

Answer:

m=4

Step-by-step explanation:

Answer:

The answer would be 4. It may seem like a lot of steps but its a lot easier then you think haha

Step-by-step explanation:

13-5 = 2m + 5 - 5  (Subtract 5 from both sides of the equation)  

8 = 2m (Simplify)

8/2  = 2m/2 ( Divide both sides of the equation by the same term)

m= 4  (Solution)

Answer: Use a variable

w

to represent the width of the room.

From the given information find that

10

w

=

80

, hence

w

=

8

.

So the room is

8

meters by

32

meters.

Explanation:

Let

w

represent the width of the room in meters.

Then the length of the room is

4

w

.

So the perimeter of the room is

w

+

4

w

+

w

+

4

w

=

10

w

.

Given that the perimeter is

80

meters, that translates as:

10

w

=

80

Divide both sides by

10

to get

w

=

8

.

Hence the width of the room is

8

meters and the length is

4

w

=

32

meters.

Step-by-step explanation:

The dimensions of the room are 5 meters long and 5 meters wide.

The perimeter of a rectangular room is equal to twice the sum of its length and width. In this case, the perimeter of the rectangular room is equal to 2 x (length + width) =  10 meters.

Therefore, we can write:
2 x (L + W) = 10

To find the dimensions of the room, we need to solve the equation for L and W.
L + W = 5
L = 5 - W

Substitute this equation for L in the original equation:
2 x (5 - W + W) = 10
2 x (5) = 10
10 = 10

Therefore, L = 5 and W = 5, so the dimensions of the room are 5 meters long and 5 meters wide.

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The equation for temperature change is T = -1.5t + 29 and the number line is plotted.

What is a number line?

A picture of numbers on a straight line is called a number line. It serves as a guide for contrasting and arranging numbers. Any real number, including all whole numbers and natural numbers, can be represented by it.

Let T represent the temperature in degrees Celsius, and let t represent the time in hours after lunchtime.

Then write an expression for the situation as follows:

T = -1.5t + 29

Here, -1.5t represents the decrease in temperature per hour, since the temperature is dropping at a rate of 1.5 degrees Celsius per hour.

Adding 29 to -1.5t gives the initial temperature of 29 degrees Celsius at lunchtime.

To illustrate this situation on a number line diagram, we can plot the temperature T as a function of time t.

The diagram would have time t on the horizontal axis and temperature T on the vertical axis.

Label the point (0, 29) on the diagram to represent the temperature at lunchtime, and the point (x, 16) to represent the temperature at sunset, where x is the number of hours after lunchtime.

Then draw a straight line connecting these two points to represent the linear relationship between temperature and time.

The line slopes downward from left to right, indicating that the temperature is decreasing over time.

Therefore, the number line diagram is plotted.

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On Tuesday at lunchtime, it was 29 degrees Celsius. By sunset, the temperature had dropped to 16 degrees Celsius. Please write an expression for the situation, and draw a number line diagram.

The trigonometric identity that is true is:

sin G = cos I. Option D

First, we need to know that;

One acute angle in a right triangle has a sine value equal to the cosine value of the other acute angle.

From the information given, we have;

In a right scalene triangle GHI, where both angle G and angle I are acute, the value of sin G is equivalent to cos I.

Several alternatives, including sin G = sin I, cos G = cos I, tan G = tan I, sin G = tan I, sin G being the inverse of cos I, and cos G being the inverse of cos I, are invalid for a right scalene triangle with a known right angle.

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Answer:

ADB=50°

Step-by-step explanation:

Angles subtended by the same segment are equal

Therefore,the angle ∠\(ADB=40\) degree.

What are the angles?

An angle is a form of geometrical shape, that is constructed by joining two rays to each other at their end-points.

Here given that ∠\(ACB=50\) degree and we know alternates angles are equal so ∠\(CAD=50\) degree.

And \(AD\) is parallel to \(BC\).

Therefore, the diagonals of a rhombus are at right angled.

So, ∠\(AOD=90\) degree

Now, In Δ\(AOD\),

∠\(ADO+\)∠\(DAO+\)∠\(AOD=180\) degree

∠\(ADO+50+90=180\)

∠\(ADO=+140=180\)

∠\(ADO=180-140\)

∠\(ADO=40\) degree

or

∠\(ADB=40\) degree.

Hence, the angle ∠\(ADB=40\) degree.

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Answer:

z=15

Step-by-step explanation:

The fraction can also be written as:

So multiply 3 on each side to isolate z

The correct answer is (d) The price must be replaced with a relative price, and the marginal values must be replaced with the corresponding Marginal Rates of Substitution.

When the value of a public good cannot be expressed in monetary terms, the Samuelson condition still holds, but some modifications are required. In this case, the per-unit price (p) used in the Samuelson condition needs to be replaced with a relative price, which represents the trade-off between the public good and other goods or services. Additionally, the marginal values (MV) of the public good need to be replaced with the Marginal Rates of Substitution (MRS), which measure the rate at which one person is willing to substitute the public good for another good.

Therefore, to determine the efficient level of the public good, the modified Samuelson condition uses a relative price and the corresponding Marginal Rates of Substitution.

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Answer: (y^{2}x^{3}⋅5)/4

Step-by-step explanation:

Convert to Radical Form

    \((5x^3y^2)\frac{2}{8}\)

Reduce the expression \(\frac{2}{8}\) by cancelling the common factors.

Factor 2 out of 2.

    \(5x^3y^2\frac{2(1)}{8}\)

Factor 2 out of 8.

     \(5x^3y^2 \frac{2(1)}{2(4)}\)

Cancel the common factor.

     \(5x^3y^2 \frac{1}{4}\)

Combine 5 and \(\frac{1}{4}\).

     \(x^3y^2\frac{5}{4}\)

Combine \(x^{3}\) and \(\frac{5}{4}\) .

     \(y^2\frac{x^3(5)}{4}\)

Combine \(y^{2}\) and \(\frac{x^3*5}{4}\)

     \(\frac{y^2x^3*5}{4}\)

The factor that does NOT control the stability of a slope is the angle of repose for intact bedrock. The angle of repose refers to the steepest angle at which a pile of loose material remains stable without sliding. It is mainly applicable to loose materials like soil and granular substances, not intact bedrock.

Bedrock stability depends on factors such as its strength, fracturing, and geological properties, rather than the angle of repose. Factors that control the stability of a slope include whether the slope is rock or soil. Rock slopes tend to be more stable than soil slopes due to the cohesive nature of intact rock.

The amount of water in the soil also affects slope stability, as excessive water can increase pore pressure and reduce the shear strength of the soil, leading to slope failure. Additionally, the orientation of fractures, cleavage, and bedding in the rock can influence slope stability by creating planes of weakness or strength.

To summarize, while the angle of repose is a significant factor in slope stability, it is not applicable to intact bedrock. The stability of a slope is influenced by the type of material (rock or soil), the presence of water, and the orientation of fractures and bedding.

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Answer:

When we say that an allele is "fixed," it means that a particular allele has reached a frequency of 100% in a population.

Step-by-step explanation:

Alleles are different forms of a gene that occupy the same position on homologous chromosomes. In a population, different alleles can exist for a specific gene. However, through various evolutionary processes such as natural selection, genetic drift, or gene flow, one allele may become predominant and eventually fixate within the population.

The fixation of an allele can occur through different mechanisms. For example, if a beneficial allele provides a selective advantage to individuals carrying it, it is more likely to increase in frequency and eventually become fixed in the population. On the other hand, genetic drift, which is the random change in allele frequencies due to chance events, can also lead to the fixation of an allele, especially in small populations.

Once an allele is fixed in a population, it means that all future generations will inherit that allele, and no alternative alleles will be present at that particular gene locus.

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Step-by-step explanation:

You can put the value of x into the equation to solve for y. Hopes this works.

The Area Of The Circle Is 452.16

The Circumference Of The Circle Is 75.36

Answer:

$113.94

18.99 multiplied by 6 is 113.94

The planes that contain point W from the given image are;

Plane V

Plane VWY

Plane RYV

A coordinate plane is a graphing and description system for points and lines. A vertical y-axis and a horizontal x-axis make up the coordinate plane.

From the attached image, we see that the planes whose name contains V also contains W.

The plane B contains the line XR and the Line YV as well as the W at the line YV.

Finally, the plane m also contains line YV and obviously the same as plane RYU.

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The above question is a mathematical proof of the relationship between Lines and angles related to a Rhombus. See the proof below.

We know,

A Rhombus is a parallelogram with four sides (that is a quadrilateral). It's sides however are all of equal length.

we have,

∠DEC ≅ ∠BFC  Reason = All Right Angles with Equal dimensions are congruent.

∠C ≅ ∠C  Reason = It is the same angle for the two Right angles above which are congruent, hence Reflexive Property.

Δ DEC ≅ Δ BFC  Reason = Angle Angle Side. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.

 ≅   Reason = The corresponding parts of congruent triangles are congruent. Also, it is a parallelogram with all congruent sides.

ABCD is a Rhombus Reason = Its sides are all congruent.

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complete question:

Given: ABCD is a parallelogram, FC is congruent to EC, DE bisects BC and BF bisects DC Prove: ABCD is a rhombus

Answer:

35.60

Step-by-step explanation:

Multiply the original price $89 times the mark down percentage 60%

You get 53.40, then subtract it from 89.

Answer:

She paid $35.60 for the jacket.

Step-by-step explanation:

Answer:

A unit rate is a rate with 1 in the denominator

Step-by-step explanation:

Answer:

y = 1/5x + 32/5

Step-by-step explanation:

Answer: Answer on the bottom below

Step-by-step explanation: And p.s this is worth 18 points because it needed to divide the points in two.- Have a brilliant day mate ^_^

The largest angle in the pentagon with consecutive even interior angle sizes is 112 degrees.

Let's assume the smallest interior angle of the pentagon is x degrees. Since the angles are consecutive even numbers, the other four angles can be expressed as x + 2, x + 4, x + 6, and x + 8 degrees.

The sum of the interior angles of a pentagon can be calculated using the formula: (n - 2) * 180 degrees, where n is the number of sides of the polygon. For a pentagon, the sum of the interior angles is (5 - 2) * 180 = 3 * 180 = 540 degrees.

Now, let's add up the five angles of the pentagon:

x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 540

Simplifying the equation:

5x + 20 = 540

5x = 540 - 20

5x = 520

x = 520 / 5

x = 104

So, the smallest interior angle, x, is 104 degrees. The largest interior angle is x + 8 = 104 + 8 = 112 degrees.

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The length of the rectangle is \(8x^2y^3\) inches when  the area of the rectangle is \(48x^3y^5\) square inches.

To find the length of the rectangle, we can use the formula for the area of a rectangle, which is:

Area = length x width

We are given that the area of the rectangle is \(48x^3y^5\) square inches, and its width is \(6xy^2\) inches. Therefore, we can substitute these values into the formula to get:

\(48x^3y^5 = length * 6xy^2\)

Simplifying this equation, we can cancel out the common factors of 6x and \(y^2\) on both sides to get:

\(8x^2y^3 = length\)

Therefore, the length of the rectangle is \(8x^2y^3\) inches.

To verify our answer, we can substitute the length and width back into the formula for the area of a rectangle and check if it matches the given area:

Area = length x width = \((8x^2y^3) * (6xy^2) = 48x^3y^5\)

Since this matches the given area, we can be confident that our answer is correct. Therefore, the length of the rectangle is \(8x^2y^3\) inches.

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Interpreting a correlation requires careful consideration of factors such as causation, confounding variables, nonlinearity, outliers, and sample characteristics.

Interpreting a correlation between two variables can be difficult for several reasons:

Causation vs. correlation: Correlation measures the strength and direction of the relationship between two variables but does not imply causation. Just because two variables are correlated does not mean that one variable causes the other. It is essential to avoid making causal claims based solely on correlation.

Confounding variables: Correlations can be influenced by the presence of confounding variables that affect both variables being studied. Without accounting for these confounding factors, it can be challenging to determine the true nature of the relationship between the variables of interest.

Nonlinear relationships: Correlation coefficients, such as Pearson's correlation coefficient, measure linear relationships between variables. If the relationship is nonlinear, the correlation may not accurately capture the association. It is crucial to consider other types of analysis or transformations to capture more complex relationships.

Outliers and influential observations: Extreme values or outliers in the data can have a significant impact on correlation coefficients. These outliers may distort the correlation and lead to incorrect interpretations. It is important to examine the data for influential observations that may unduly influence the correlation results.

Sample size and representativeness: The size and representativeness of the sample can affect the reliability and generalizability of correlation results. Small or biased samples may not provide a representative picture of the population, leading to misleading interpretations.

Overall, it is important to use correlations as part of a broader analysis and consider additional evidence before drawing definitive conclusions about the relationship between variables.

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Answer:

y=-3x+4

Step-by-step explanation:

I just use desmos to graph it and find the line of fit.