April borrows $21000 at an interest rate of 3% to purchase a new automobile. At what rate (in dollars per year) must she pay back the loan, if the loan must be paid off in 5 years?

The length of side b of the given right angle triangle using law of sines is; b = 12.044 m

The law of sines states that when we divide side "a" by the sine of angle A, it is equal to side "b" divided by the sine of angle B, and also equal to side "c" divided by the sine of angle C

Thus;

a/sin A = b/sin B = c/sinC

The parameters are;

B = 42°

c = 18m

Since c is the hypotenuse, it is the side that will be opposite the right angle and so;

C = 90°

Thus, using sine rule;

c/sinC = b/sin B

18/sin 90 = b/sin 42

b = (18 * sin 42)/1

b = 12.044 m

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The required value of exponential function for the given values of x are 1.43, 1 , 0.7.

Calculating the exponential growth or decay of a given collection of data is done using an exponential function, which is a mathematical function. Exponential functions, for instance, can be used to estimate population changes, loan interest rates, bacterial growth, radioactive decay, and disease spread. ​

We have,

f(x) = [tex](0.7)^{x}[/tex]

So, at x = -1

f(x) = (0.7)^-1

f(x) = 1.43

At x = 0

f(x) = (0.7)^0

f(x) = 1

At x = 1

f(x) = (0.7)^1

f(x) = (0.7)

Thus, required value of function are 1.43, 1, 0.7

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The required  initial and final amounts of water contained in the pool are 46 ans 26 gallons of water.

A graph is made up of vertices, or points, and edges, or lines connecting those vertices. In addition to linked and disconnected graphs, weighted graphs, bipartite graphs, directed and uncorrected graphs, and simple graphs, there are many other forms of graphs.

As graph says

The initial amount of water contained in the pool is

at t = 0

= 46 gallons of water

And at t = 5, is final amount of water in pool

= 26 gallon of water

Thus, there are 46 ans 26 gallons of water.

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Answer:

206

Step-by-step explanation:

cube volume = 5*5*5 +3*3*3 = 125+81 = 206

Answer:

1.478 x 10^2 AU

Step-by-step explanation:

To convert this distance to astronomical units (AU), we can use the fact that 1 AU is approximately equal to 93 million miles.

So, 13.8 billion miles is approximately:

13.8 billion miles / 93 million miles/AU = 147.8 AU

In scientific notation, this distance would be written as: 1.478 x 10^2 AU

By performing a change of units, we will see that the caterer should purchase 107.8 lb

First, let's find how many kilograms are needed. We know that the recipe recomends using 0.7kg per person, and there are 70 guests, so an estimate of the mass needed is:

M = 70*0.7kg = 49 kg

Now weneedto do a change of units, we know that:

1 kg =  2.2 lb

Then we can rewrite:

49 kg = 49*(2.2 lb) = 107.8 lb

The caterer should purchase 107.8 pounds

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a. To find the average rate of growth between each pair of years, we can use the formula: (end value - start value) / (end year - start year).

2004 to 2006: (12,440 - 8,574) / (2006 - 2004) = 3,866 / 2 = 1,933 locations/year

2006 to 2007: (15,006 - 12,440) / (2007 - 2006) = 2,566 / 1 = 2,566 locations/year

2005 to 2006: (12,440 - 10,238) / (2006 - 2005) = 2,202 / 1 = 2,202 locations/year

b. To estimate the instantaneous rate of growth in 2006, we can take the average of the last two rates of change from part (a).

(2,566 + 2,202) / 2 = 2,384 locations/year

c. To estimate the instantaneous rate of growth in 2006 by measuring the slope of the tangent line through (2005, 10,238) and (2007, 15,006), we can use the formula:

(15,006 - 10,238) / (2007 - 2005) = 4,768 / 2 = 2,384 locations/year

d. To estimate the instantaneous rate of growth in 2007 by measuring the slope of the tangent line through (2006, 12,440) and (2008, 16,676), we can use the formula:

(16,676 - 12,440) / (2008 - 2006) = 4,236 / 2 = 2,118 locations/year

e. Comparing the growth rates from part (c) and (d), we can see that the growth rate in 2007 is less than the growth rate in 2006. So we can conclude that 2. The rate of growth is decreasing.

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Answer:

Step-by-step explanation:

[tex]-63y^2+27y[/tex]

[tex]-63yy+27y[/tex]

[tex]-9\cdot \:7yy+9\cdot \:3y[/tex]

[tex]9y\left(-7y+3\right)[/tex]

The original cylinder has a radius of 2 units and a height of 13 units, and its volume is given by the formula: V = πr²h = π * 2² * 13 = 104π cubic units.

Original cylinder: The original cylinder has a radius of 2 units and a height of 13 units, and its volume is given by the formula: V = πr²h = π * 2² * 13 = 104π cubic units.

Scaled cylinder 1: The first scaled cylinder has a scale factor of 2, so its radius is 2 * 2 = 4 units and its height is 13 * 2 = 26 units. Its volume is given by: V = πr²h = π * 4² * 26 = 672π cubic units.

Scaled cylinder 2: The second scaled cylinder has a scale factor of 3, so its radius is 2 * 3 = 6 units and its height is 13 * 3 = 39 units. Its volume is given by: V = πr²h = π * 6² * 39 = 1764π cubic units.

Scaled cylinder 3: The third scaled cylinder has a scale factor of 4, so its radius is 2 * 4 = 8 units and its height is 13 * 4 = 52 units. Its volume is given by: V = πr²h = π * 8² * 52 = 3072π cubic units.

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Differentiating the expression [tex]\frac{d}{dx} [(4x-7)^4(7x+8)^5 ][/tex] with respect to x will be [tex]16(4x-7)^3(7x+8)^5 + 35(4x-7)^4(7x+8)^4[/tex]

We are given with

[tex]\frac{d}{dx} [(4x-7)^4(7x+8)^5 ][/tex]

Here we will be using the chain rule. According to the chain rule, we will first have to solve the parentheses as a variable. Then we will have to solve the expression within the parenthesis

First, we will differentiate [tex](4x-7)^4[/tex] keeping [tex](7x+8)^5[/tex] constant. Here we will first assume [tex](4x-7)[/tex] as one variable and differentiate using the formula d/dx[x^n] then we will differentiate 4x - 7 to get just 4. They would be multiplied by one another

Hence we get

[tex]4 X4(4x-7)^3(7x+8)^5[/tex]

[tex]16(4x-7)^3(7x+8)^5[/tex]

Now, we will keep [tex](4x-7)^4[/tex] constant and differentiate [tex](7x+8)^5[/tex] and adding it up we get

[tex]16(4x-7)^3(7x+8)^5 + 5X7(4x-7)^4(7x+8)^4[/tex]

[tex]= 16(4x-7)^3(7x+8)^5 + 35(4x-7)^4(7x+8)^4[/tex]

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Complete Question

[tex]\frac{d}{dx} [(4x-7)^4(7x+8)^5 ][/tex]

There is a difference in average systolic blood pressure between smokers and non-smokers.

To evaluate if average systolic blood pressure differs by smoking status, we need to calculate the mean systolic blood pressure for both smokers and non-smokers. We can calculate the mean systolic blood pressure for smokers by taking the sum of systolic blood pressure values for all smokers in the sample, divided by the number of smokers in the sample. This formula can be written as:

Mean Systolic Blood Pressure for Smokers = (Sum of Systolic Blood Pressure Values for all Smokers) / (Number of Smokers)

Similarly, we can calculate the mean systolic blood pressure for non-smokers by taking the sum of systolic blood pressure values for all non-smokers in the sample, divided by the number of non-smokers in the sample. This formula can be written as:

Mean Systolic Blood Pressure for Non-Smokers = (Sum of Systolic Blood Pressure Values for all Non-Smokers) / (Number of Non-Smokers)

Once we have calculated the mean systolic blood pressure for both smokers and non-smokers, we can compare the two means to evaluate if there is a difference in average systolic blood pressure between smokers and non-smokers.

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Answer: Anything that has the same two numbers

Step-by-step explanation:

You don't have a picture, so I'm basing this off of what I know. A number over another number that is the same is equivalent to one.

The type of sampling used in this example is Convenience sampling.

Convenience sampling is a type of non-probability sampling in which the sample is selected based on the ease of access or availability of the subjects. The sample is selected based on the researcher's convenience, and it does not use a random selection process.

In this case, the reporter chose to interview people in his own apartment building because it was convenient for him and he had easy access to them.

The other options you listed are:

a) Cluster sampling, which is a form of probability sampling in which the sample is selected by first dividing the population into smaller groups or clusters, and then selecting a random sample of those clusters.

b) Voluntary response sampling, which is a type of non-probability sampling where individuals choose to participate in the study.

c) Systematic sampling, which is a form of probability sampling in which the sample is selected by choosing a random starting point and then selecting every nth subject from the population.

d) Attempted census, which is when the researcher tries to include all members of a population in the sample.

Therefore, The type of sampling used in this example is Convenience sampling.

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The amount Jacob has to pay in a month where he used x GB over the limit is  y=25+20x.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Jacob has a smart phone data plan that costs $25 per month that includes 5 GB of data, but will charge an extra $20 per GB over the included amount.

Amount Jacob has to pay in a month where he used 4 GB over the limit is

25+4×20

= $105

Amount Jacob has to pay in a month where he used x GB over the limit is

y=25+20x

Where, y is total amount of money

Hence, the amount Jacob has to pay in a month where he used x GB over the limit is  y=25+20x.

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Answer:

Step-by-step explanation:

I don’t know just 5 point

Answer:

42

Step-by-step explanation:

determinant of matrix

= 5(2) - 8(-4)

= 10 - (-32)

= 10 + 32

= 42

Answer:

32

Step-by-step explanation:

the determinant of matrix

[tex]\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right][/tex] = ad - bc

then

[tex]\left[\begin{array}{ccc}5&-4\\8&2\\\end{array}\right][/tex]

= (5 × 2) - (- 4 × 8) = 10 - (- 32) = 10 + 32 = 42

the fourth one. I know it is correct, you may look it up on the desmos graphing calculator if you have suspicion it is not.

The chance of exactly one of population members A, B, and C being in a sample of 100, drawn randomly from a population of 100,000 is 0.0003%.

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Answer:

20,45 kg,

Step-by-step explanation:

45  Lb * (1 kg / 2,2 Lb) + (12 Austrália * (1 kg / 35 ,2 Austrália)) = 20,45 kg

Um resposta é 20,45 kg.

The equation which represents the graph function is g ( x ) = f ( x - 3 ) + 3

Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.

Identify the even and odd multiplicities of the polynomial functions' zeros.

Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.

The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities

Given data ,

Let the function be represented as A

Now , the value of A is

f ( x ) = x³   be equation (1)

Now , the graph of the function f ( x ) is plotted with the exponent value meeting closely at ( 0 , 0 )

And , the function which describes the function g ( x ) is given by

g ( x ) = f ( x - 3 ) + 3

Hence , the function is g ( x ) = f ( x - 3 ) + 3

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A truth table deconstructs a logic function by outlining all possible outcomes the function might achieve.

A truth table offers a way to map out the potential truth values in an expression and predict their results. The table has a row for each conceivable combination of truth values and a column for each variable in the expression. There is also a column that displays the results of each set of values.

For propositional logic formulations, this tool builds truth tables. There are numerous formats available for entering logical operators. As an illustration, the propositional formula p q r could be represented as p / q -> r, p and q => not r, or p && q ->!r. You can enter the connectives and as T and F.

P Q (Q ∧ P)

F F F

F T F

T F F

T T T

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Answer:

2/n+2

Step-by-step explanation:

The number of​ 18-inch wreaths is 7, and

the number of 22-inch wreaths is 18.

When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."

There are both one-variable and two-variable linear equations.

Given the cost of an 18-inch wreath = $15

cost of a 22-inch wreath = $30

let the number of 18-inch wreaths be x and the number of  22-inch wreaths is y,

the total cost of both wreaths = $645

cost of x 18-inch wreaths = $15x

cost of y  22-inch wreaths = $30y

equation is,

$15x + $30y = $654

and the number of​ 22-inch wreaths sold was four more than twice the number of​ 18-inch wreaths,

y = 4 + 2x

substitute the value of y in the equation

15x + 30y = 645

15x + 30(4 + 2x) = 645

15x + 60x = 645 - 120

75x = 525

x = 525/75

x = 7

and y = 4 + 2x

y = 4 + 2*7

y = 18

Hence store sells 18  22-inch wreaths and 7  18-inch wreaths.

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Probability of less than 50 % democrats for the example based on sample proportion is equal to 0.1562.

Sample size 'n' = 100

Registered voters  'p' = 55%

                                    = 0.55

σ = √ p( 1- p )/ n

  = √0.55( 0.45)/ 100

  = 0.04975

Mean 'μ' = 55%

               = 0.55

Probability of getting less than 50% democrats in a sample size of 100 voters

X = 0.5

Z = ( X - μ ) / σ

  = ( 0.5 - 0.55) / 0.4975

 = -1. 005

 = -1.01

p-value pf -1.01 is equal to 0.156248

Therefore, the probability of getting 50% democrats for the given sample size id equal to 0.1562. The given example represents sample proportion.

The above question is incomplete , the complete question is :

In a congressional district, 55% of the registered voters are Democrats. Which of the following is closest to the probability of getting less than 50% Democrats in a random sample of size 100?

Is this an example of a sample proportion OR a sample mean?

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Reducing the completion average  time for Jobs J and K by one day will shorten the overall project completion time by one day, allowing the project to finish one day early.

In order to finish the project one day early, the completion time for Jobs J and K should be reduced by one day. This is because these two jobs are part of the three critical paths of the project. By reducing the completion time for these two jobs by one day, the entire project will be completed one day early. This is because the critical paths are the paths that will determine the overall project completion time. By reducing the completion time for these two jobs, the overall project completion time will be shortened. This will allow the project to be finished one day earlier than expected.

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Answer:

(x^2 - 7)(4x - 3)

Step-by-step explanation:

first, we split the expression by grouping the first two terms in parentheses and the last two terms in parentheses. this gives us:

[tex](4x^{3}-3x^{2})(-28x+21)[/tex]

next, we factor out the GCF of each group. this gives us:

[tex]x^{2}(4x-3)-7(4x-3)[/tex]

finally, all you have to do is take each factored-out term and put them together into a group/expression. the leftover expression from both groups is the same value, so you get:

[tex](x^{2}-7)(4x-3)[/tex]

hope this helped, good luck!

Answer: In the figure above, clearly the line L is perpendicular to x-axis and passing through the value 'c' on x- axis. So, the equation of a line perpendicular to x axis is x = c

Using properties of triangles, Correct options are A,B and D. AE = EB, EG || AC and AC = 2 EG.

A triangle has three sides, three angles, and three vertices, which are its characteristics.

A triangle's total internal angles are always equal to 180 degrees. This is referred to as the triangle's angle sum property.

Any two triangle sides can add up to a length that is longer than the third side.

A triangle's total angles are always 180 degrees.

A triangle's outside angles are always a sum of 360 degrees.

The total of the parallel interior and exterior angles is additional.

From the given figure,

As E is the mid point of BA,

So, BE = EA

As it is clearly seen that EG is parallel to AC = EG||AC

Further,

As, EG is intersecting AB and BC at mid points,

⇒ AC = 2EG

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