(50/34.2)^1.5 = 10-t

Answer:

Set the denominator in 4x equal to 0 to find where the expression is undefined. x=0

The domain is all values of x that make the expression defined.

Interval Notation: (−∞,0)∪(0,∞)

Set-Builder Notation: {x|x≠0}

The range is the set of all valid y values. Use the graph to find the range.

Interval Notation: (−∞,4)∪(4,∞)

Set-Builder Notation: {y|y≠4}

Determine the domain and range.

Domain: (−∞,0)∪(0,∞), {x|x≠0}

Range: (−∞,4)∪(4,∞), {y|y≠4}

Step-by-step explanation:

Answer

x = 6°

Explanation

The key to solving this is shown in the attached image below

So, we can see that the relation between all of this is that

5x + 17 = ½ [(37x + 5) - (23x - 5)]

5x + 17 = ½ (37x + 5 - 23x + 5)

5x + 17 = ½ (37x - 23x + 5 + 5)

5x + 17 = ½ (14x + 10)

5x + 17 = 7x + 5

5x - 7x = 5 - 17

-2x = -12

Divide both sides by -2

(-2x/-2) = (-12/-2)

x = 6°

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Answer:

y=(x-5)^2 - 6

Step-by-step explanation:

Subtracting the 5 to the x moves the parabola 5 units to the right. Putting the -6 at the end moves the parabola down 6 units.

Answer:

\(y=\left(x-5\right)^{2}-6\)

Step-by-step explanation:

I graphed the original parabola and the new parabola on the graph below. I moved the original parabola down 6 and right 5.

Answer:

x = 31°

Step-by-step explanation:

the triangle on the right is isosceles because two sides are equal, which means the two base angles are equal

if we subtract 56 from 180, then divide by 2 we have each base angle equal to 62°

the base angle, adjacent to the obtuse angle in the triangle on the right, is supplemental to the obtuse angle, so 180 - 62 = 118

the triangle on the right is isosceles also because two sides are equal, which means the two other angles are equal

if we subtract 118 from 180 we get 62, so each of the other two angles are 32°

The table showing the distance traveled by the boat at various times should be completed as follows;

Time (h)                  0      0.5     1      1.5     2     2.5      3

Distance (mi)          0       1        2      3       4      5        6

In Mathematics, a proportional relationship produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the data points contained in the table as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 3/1.5

Constant of proportionality, k = 2.

When x = 0.5, the distance is given by;

y = 2x

y = 2(0.5) = 1 mile.

When x = 1, the distance is given by;

y = 2x

y = 2(1) = 2 miles.

When x = 2, the distance is given by;

y = 2x

y = 2(2) = 4 miles.

When x = 2.5, the distance is given by;

y = 2x

y = 2(2.5) = 5 miles.

When x = 3, the distance is given by;

y = 2x

y = 2(3) = 6 miles.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The interquartile range is least affected by an outlying value in the data set of the range, interquartile range, and variance is True.

Max to min value is the range. Range can substantially change if there are any outliers.

Since the threshold values for Q3 and Q1 are not outliers, the IQR won't change.

Outliers cause variance to be misinterpreted since they vastly increase variance.

Interquartile range:

You may determine the spread of the midpoint of your distribution using the interquartile range.

The interquartile range contains half of the values for any distribution that is ordered from low to high. The first 25% of values are found in the first quartile (Q1), while the last 25% are found in the fourth quartile (Q4).

The third quartile (Q3) less the first quartile (Q1) is the interquartile range (Q1). This provides us with the data set's middle half's range.

The interquartile range is calculated using only 2 values, much like the range. The IQR, however, is less impacted by outliers because the two values are more likely to be average scores because they are drawn from the middle of the data set.

The IQR provides a reliable indicator of variability for both skewed and normal distributions.

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By using the formulae of VAT Percentage we have required VAT percentage as 10%.

Given is S.P=Rs 450 (Selling Price)

            S.P+VAT =Rs 495 (Selling Price+ Value added Tax)

Now we have to find Amount of VAT that is how much value added tax is imposed in the selling price.

To find out Amount of VAT we have to take Selling Price (S.P) and subtract it from Selling Price with VAT.

Amount of VAT = (S.P + VAT )- S.P

                           = Rs 495 - Rs 450

                           = Rs 45

VAT Percent = Amount of VAT /Selling Price x 100

Percentage of VAT = \(\frac{45}{450} .100\)

                                = 10 %

So VAT percentage is 10%.

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The system of equations [x - 3y = -1 and -6x + 19y = 6] can be solved, resulting in x = -1 and y = 0.

To solve the system of equations [x - 3y = -1 and -6x + 19y = 6], we can use the method of substitution or elimination.

Let's solve it using the method of elimination.

First, we can multiply the first equation by 6 and the second equation by -1 to eliminate the x terms.

This gives us [6x - 18y = -6 and 6x - 19y = -6].

Now, subtracting the first equation from the second eliminates the x terms, leaving us with -y = 0. Solving for y, we find y = 0.

Substituting this value back into the first equation, we get x - 3(0) = -1, which simplifies to x = -1.

Therefore, the solution to the system of equations is x = -1 and y = 0.

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Step-by-step explanation:

They can be found by considering where the second derivative changes signs. In similar to critical points in the first derivative, inflection points will occur when the second derivative is either zero or undefined.

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Answer:

12 units

Step-by-step explanation:

Find the absolute value of the difference , that is

d = | - 7 - 5 | = | - 12 | = 12 or

d = | 5 - (- 7) | = | 5 + 7 | = | 12 | = 12

The distance from -7 to 5 on a number line is 12 units. This distance between two integers is calculated by using a number line and the absolute value of the difference between those two integers.

Calculating the distance from -7 to 5 on the number line:

⇒ | 5 - (-7) |

⇒ | 12 |

= 12 units

Therefore, there are 12 units in between the given two integers -7 and 5 on a number line which is shown below

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Answer:

537/100s.

Step-by-step explanation:

Let us consider the black paint in the mixture = 7x

and white paint in the mixture = 12x

total quantity of mixture = 600ml

according to the question , black : white paint = 7 : 12

quantity of black paint = \(\frac{7}{19}\) × 600= 221.052

quantity of white paint =  \(\frac{12}{19}\) × 600 = 378.94

{ 221.052ml black paint + 378.94 ml white paint = 599.99 ml grey paint }

Ans :- It would be 221.052 ml of black paint

The value of x in the variation is -2/9

y varies inversely as x and the value of y is 18 and x is 1/2

the first step is to calculate the constant k

k= y/x

k= 18 ÷ 1/2

k= 18 × 2/1

k= 36

From the calculation above the value of k which is the constant is 36

The next step is to calculate x. The value of x can be calculated as follows

k = y/x

36= -10/x

cross multiply

36x= -10

x= -10/36

x= -2/9

Hence the value of x in the variation is -2/9

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Answer:

6:50 p.m.

Step-by-step explanation:

150 miles / 60 mph = 2.5 hours

2 hours after 4:20 p.m. is 6:20 p.m.

30 minutes (1/2 hour) after 6:20 p.m. is 6:50 p.m.

The simplified form of the complex fraction (1/2) / (2/y) is y/4.

A complex fraction is a fraction in which either the numerator, the denominator, or both contain fractions. In other words, it is a fraction that has one or more fractions within it.

Complex fractions are written in the form:

(a/b) / (c/d)

where a, b, c, and d are numbers, and b, c, and d are not equal to zero.

To simplify a complex fraction, we can convert it into a simpler form by following a few steps.

1: Invert the denominator of the inner fraction.

(1/2) / (2/y) becomes (1/2) * (y/2).

2: Multiply the numerators and denominators.

(1/2) * (y/2) = (1 * y) / (2 * 2) = y/4.

By multiplying the numerators and denominators, we get the simplified complex fraction y/4.

In this case, the complex fraction (1/2) / (2/y) simplifies to y/4, where y is a non-zero number.

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Answer:

d). 6p²+p-2 f).k²+8k+16

According to the question we have  approximately 99.74 percent of customers are willing to pay between $1.20 and $1.80 for a pint of frozen yogurt.

To answer this question, we will use the normal distribution formula and z-score.

First, we need to find the z-score for the lower limit of $1.20:

z = (1.20 - 1.50) / 0.10 = -3

Next, we need to find the z-score for the upper limit of $1.80:

z = (1.80 - 1.50) / 0.10 = 3

Now, we can use a z-table to find the area under the curve between these two z-scores.

The area to the left of z = -3 is 0.0013, and the area to the left of z = 3 is 0.9987.

To find the area between these two z-scores, we subtract the area to the left of z = -3 from the area to the left of z = 3:

0.9987 - 0.0013 = 0.9974

Therefore, approximately 99.74% of customers are willing to pay between $1.20 and $1.80 for a pint of frozen yogurt.

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Answer:

density

Step-by-step explanation:

the number of population distributed in a certain area, that is generally in km², is the density.

It can be calculated with the following data: Number of population/km²

Extra information: it obviously is an approximated value, because in certain areas it can be much higher (metropolis, for example, generally have a very high population density, meanwhile in the countryside it can be much lower). Generally, it varies from area to area.

The number of individuals in a population divided by the area that the population takes up is known as the density of the population.

Population density refers to the number of individuals in a population per unit of area. It is a measure of how crowded or dispersed a population is within a given area.

Population density is calculated by dividing the total population of an area by the total land area or water area of that region. The resulting number is often expressed in individuals per square kilometer or square mile, depending on the units of measurement used.

Population density is an important ecological concept because it can affect the ability of a population to survive and thrive within a given area. Populations that are too dense may experience competition for resources, disease outbreaks, and other negative effects.

On the other hand, populations that are too dispersed may have trouble finding mates and maintaining genetic diversity. Population density can also be used to track changes in populations over time, and to inform conservation and management efforts.

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The solution to the simultaneous equations is x = 2 and y = 11. First, we can write the equations in matrix form:

[5 1] x + [37] y = [0]

[6 -2] x + [34] y = [0]

Then, we can find the inverse of the coefficient matrix:

A = [5 1; 6 -2]

A^-1 = [-1/16; 1/8; 1/8; -1/16]

Multiplying both sides of the equations by A^-1, we get:

[-1/16] x + [1/8] y = [0]

[1/8] x + [-1/16] y = [0]

Solving for x and y, we get:

x = -37/16

y = 34/16

Simplifying, we get:

x = 2

y = 11

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A scatter plot would be the best choice to indicate whether there was a negative relationship between stock and bond returns.

A scatter plot is a type of graph used to display the relationship between two variables. It is also known as a scatter chart or scattergram. The graph consists of a series of points, each representing a single observation or measurement of two variables. The position of each point is determined by its values on the two variables. In a scatter plot, one variable is plotted on the x-axis and the other variable is plotted on the y-axis.

This type of graph would show the relationship between two variables, in this case stock and bond returns, on a single graph. It would provide a visual representation of any negative or positive correlation between the two variables.

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Answer:

Part 2

A. 10

B. 20

C. 15.4

Part 3

A. 96

B.96

C.24

D. 12

Step-by-step explanation:

I am not sure of the last part but I hope the first to help you

for the area of a triangle it is b*h*1/2 and for a rectangle it is bh

The Borda count method is commonly used in situations where preferences or rankings need to be determined. Among the options provided, the organization that uses the Borda count method is:

d. the Toastmasters International Speech contests, to rank the top three competitors.

The Borda count method is often employed in competitions or contests where participants are ranked based on the preferences or votes of the judges or audience. In the case of Toastmasters International Speech contests, the Borda count method is used to calculate the overall rankings of the competitors by assigning points to each ranking position and summing them up. This allows for a fair and systematic determination of the top three performers based on the aggregated preferences of the judges or audience members.

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Answer:

a is Angle L is 67.5 degrees. Angles F and L are opposite each other, yet the same angle degree.

Step-by-step explanation:

p(1) = 1

Let p(x) = x2 + bx = c

then, p(p(x)) = (x2 + bx + c)² + b(x2 + bx + c) + c

Sum of roots of p(p(x)) is given by = - (coefficient of x3/constant term)

= -2b/c2+bc+c = f(a,b) (say)

For critical points,

∂f/∂c = 0 and ∂f/∂b = 0

= 2b(2c+b+1)/c2+bc+c = 0 and - {( c2+bc+c)²- 2b (c)/ ( c2+bc+c)²}= 0

= b(2c+b+1) =0  

= b= 0 or b= - (1+2c)  = -(2c(c+1))/c2+bc+c = 0

If c=0 , b= -1  => c= 0 or c=-1

If c = -1 ,b = 1

thus we have the following possibility for (b,c)

(0,0) , (0,-1) , (-1,0) ,(1,-1).

At (0,0) f(0,0) = not defined

(0,-1) f(0,-1) = 0

(1,-1) f(1,-1) = 2

(-1,0) is not possible.

p(x) = (x2 +x-1)² + (x2 +x-1) -1

= p(1) = (1+1-1)² + (1+1-1) -1

= 1

Hence, p(1) = 1

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The conclusion about the functions is they have the same y-intercept.

The complete question is added as an attachment

The function is given as:

f(x) = (x + 4)^2

From the attached graph, the graph has a y-intercept at:

y = 16

This can be represented as:

(0, 16)

Next, we set x = 0 in f(x) = (x + 4)^2

f(0) = (0 + 4)^2

Evaluate

f(0) = 16

This means that the y-intercept of f(x) = (x + 4)^2 is (0, 16)

So, the functions have the same y-intercept

Hence, the conclusion about the functions is they have the same y-intercept.

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Answer: They have the same y-intercept

Step-by-step explanation:

Therefore, in about 15 years and 2 months, the senior class will have about 100 students.

An equation is a statement that expresses the equality of two mathematical expressions using mathematical symbols such as variables, numbers, and mathematical operations. The equality is represented by an equal sign "=" between the two expressions. Equations are used to represent mathematical relationships and solve problems in various fields such as physics, chemistry, engineering, and economics.

Given by the question.

Let P be the initial population of the senior class in the high school, and r be the rate of decrease in population per year (in decimal form).

Then, we can write the following equation to represent the situation:

P\((1-r)^{n}\) = 100

We know that the current population of the senior class is 320, so we can substitute these values into the equation:

320\((1-0.07)^{n}\) = 100

Simplifying the equation, we get:

\(0.93^{n}\) = 0.3125

Taking the natural logarithm of both sides, we get:

n ln (0.93) = ln (0.3125)

Dividing both sides by ln (0.93), we get:

n = ln (0.3125) / ln (0.93)

Using a calculator, we find that n is approximately equal to 15.21 years.

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Answer:1

Step-by-step explanation:

Answer:

Step-by-step explanation:

y= 63 degrees

x=54 degrees

Answer:

Y=63

X=54

Step-by-step explanation:

Y is 63 because their adjacent sides are congruent.

X is 54 because 180-63-63 is 54