if 3 -letter words'' are formed using the letters a, b, c, d, e, f, g, how many such words are possible for each of the following conditions:

The rental cost for each movie and each video game is 2.25.

One month Trey rented three movies and five video games for a total of 35.

3 M + 5V = 33

6 M + 2 V = 24

Divides bottom equation by 2:

3 M + 5 V = 35

3 M + V = 20

subtracts:

 4V = 21

 V = 21/4 = $5.25

3 M + 5.25 = 12

3 M = 6.75

M = 2.25

Let x = cost to rent a movie and y = cost to rent a video game

3x + 5y = 33

6x + 2y = 24

Multiply the first equation by -2:

-6x - 10y = -66

6x + 2y = 24

Add the equations to get -8y = -42

So, y = 5.25 and x = 2.25.

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The area of a rectangle is given as:

Area = Length x width

The area of the rectangle is 57 square feet.

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

Length = 19 feet

Width = 3 feet

The area of the rectangle.

= 19 x 3

= 57 square feet.

Thus,

The area of the rectangle is 57 square feet.

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Answer:

0.009

Step-by-step explanation:

0.00892

first significant figure will be

0.00900

or = 0.009

i hope this helps

Answer:

0.009

Step-by-step explanation:

0.00892(a significant figure is a number greater than zero)

so the first number after zero is 8

the next number is 9, so round 9 up and it becomes 1.

Add 1 to 8 to give you 9

=0.00900 or 0.009

Hope it helped you

a) The Test statistic of the hypothesis is; 0.81

b) The p-value from the test statistic is; 0.20897.

c) The final conclusion is that there is not sufficient evidence to reject the null hypothesis that (p1 - p2) = 0

Test statistic is defined as a number, calculated from a statistical test, used to find if your data could have occurred under the null hypothesis. In this case, we are dealing with proportions and as such the test statistic has the formula;

z = (p1 - p2)/standard error

p1 = 53/90 = 0.59; s1 = √(0.59 * 0.41/90) = 0.052

p2 = 48/90 = 0.53; s2 = √(0.53 * 0.47/90) = 0.053

Hence, for the distribution of differences, the mean and the standard error are given as follows:

Mean: p = 0.59 - 0.53 = 0.06

Standard error: s = √(0.052² + 0.053²) = 0.074

a) Test statistic = p/s = 0.06/0.074

Test statistic = 0.81

b) From p-value from z-score calculator, we get that;

p-value = 0.20897.

c) The p-value is greater than the significance value of 0.05, we fail to reject the null hypothesis and conclude that there is not suffucuent evidence to reject the null hypothesis that (p1 - p2) = 0

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Answer:

6x² + 5x + 1

Step-by-step explanation:

(4x² + x − 4) + (2x² + 4x + 5)

1. Expand the brackets to get
4x² + x − 4 + 2x² + 4x + 5

2. Group common terms (terms with same power as well as the constant)
4x² + 2x² + x + 4x - 4 + 5

3. Simplify
4x² + 2x² = 6x²
x + 4x = 5x
-4 + 5 = 1

4. Solution is
6x² + 5x + 1

A student selected at random from the class has a 0.5 is 50% chance of not participating in sports, according to the probability notion.

A probability is calculated by dividing the entire number of possible outcomes by the desired outcomes.

In this issue:

The total number of students is 30 (8 + 7 + 3 + 12).

3 + 12 = 15 of the total don't participate in sports.

Hence:

p =D/T = 15/30 = 0.5

There is a 50% chance that a student who was randomly selected from the class does not participate in sports.

A student selected at random from the class has a 0.5 is 50% chance of not participating in sports, according to the probability notion.

The complete question is :in a class of students, the following data table summarizes how many students playing instrument or a sport. What is the probability that student plays an instrument given that they play a sport?

play an instrument and a sport: 3

play an instrument but does not play a sport: 8

does not play an instrument but plays a sport: 7

does not play an instrument or a sport: 12

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Answer:

To solve this equation, you can use cross multiplication to eliminate the fractional terms. Doing so gives you 11 * 17 = 13 * x. Solving for x gives you x = (11 * 17)/13. Dividing these two numbers gives you approximately x = 8.46. Rounding this number to the nearest tenth gives you x = 8.5. Therefore, the value of x that makes the equation true is approximately 8.5.

According to the question
Let the number be x

[tex]x+\frac{1}{x}=\frac{5}{2} \\\\\ \frac{x^{2}+1}{x} = \frac{5}{2} \\\\\\\ By \\ cross-multiplication \\\\x^{2}+1 = \frac{5}{2} * x\\\\2x^{2}+2 = 5x\\\\2x^{2}-5x+2 = 0\\\2x^2-4x-1x+2 = 0\\2x(x-2)-(x-2)=0\\(2x-1)(x-2)=0\\\\therefore,\\\\x = \frac{1}{2}\\or\\x = 2[/tex]

The p-value of the test is 0, which is less than the standard significance level of 0.05, thus we can conclude that the proportion respondents who rated themselves as above average drivers is greater than 0.7.

We may test the following using the example data:

In reality, 812.35 respondents identified as better drivers than average.

We can infer that the proportion of respondents who rated themselves as above average drivers is greater than 0.7 because the test's p-value is 0, which is less than the standard significance level of 0.05. 77% of the sample of 1055 adults rated themselves as above average drivers, so 0.77(1055) = 812.35.

As a result, 812.35 respondents actually assessed themselves as better drivers than average.

We examine if the proportion is 7/10=0.7 at the null hypothesis.

H0 is that, with p = 0.7.

If the proportion is larger than 70%, we test for the alternative hypothesis, which is H1:p>=0.7.

The test statistic comes from:

The parameters for this issue are p dash = 0.77, p = 0.7, and n = 1055.

As a result, the test statistic's value is:

z = 351.758 root

The likelihood of discovering a sample proportion above 0.77, calculated as 1 minus the p-value of z = root of 351.758, is the test's p-value.

According to the z-table, the p-value for z = root of 351.758 is 1, and 1 - 1 equals 0.

Since the test's p-value is zero and is below the conventional significance level of 0.05, we can infer that a higher proportion of respondents than 0.7 evaluated themselves as above-average drivers.

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The center of the circle lies on the x-axis. The radius of the circle is 3 units. The radius of this circle is the same as the radius of the circle whose equation is x² + y² is 9.

The radius of a circle is the distance between the circle's centre and any point on its circumference. It is usually represented by the letters 'R' or 'r'. This number is significant in almost all circle-related formulas. A circle's area and circumference are also measured in terms of radius.

The standard equation of a circle is expressed as:

x² + y²+2gx+2fy+C=0

Centre is (-g, -f)

radius = √g²+f²-C

Given a circle whose equation is 2+ y²-2x-8=0.

Get the centre of the circle

2gx = -2x

2g=-2

g=-1

Similarly, 2fy = 0

f=0

Centre = (-(-1), 0) = (1, 0)

This shows that the center of the circle lies on the x-axis

r = radius = √g²+f²-C

radius = √1²+02-(-8)

radius =√9 = 3 units

The radius of the circle is 3 units.

For the circle x² + y² = 9, the radius is expressed as:

r² = 9

r = 3 units

Hence the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

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

Explanation:

1/4 = 0.25

1/2 = 0.5

24 & 1/2 = 24.5

The rope is 24.5 ft long and you want sections of length 0.25 ft each.

Let x be the number of sections we can make.

1 section is 0.25 ft long

x of them combine to 0.25x feet long

Set this equal to 24.5 and solve for x

0.25x = 24.5

x = (24.5)/(0.25)

x = 98

There will be 98 sections of equal length (each being 0.25 ft)

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

Another way to look at it:

1 foot of rope gets you four sections of 0.25 ft each

24 feet of rope gets you 24*4 = 96 sections.

Another 0.5 ft adds another 0.5*4 = 2 sections to get to a total of 96+2 = 98

Answer:

425.39 ft

Step-by-step explanation:

[tex]\frac{1}{2}mv^2=mgh\\\frac{1}{2}v^2=gh\\v^2=2gh[/tex]

h = [tex]\frac{v^2}{2g} = \frac{165^2}{2 * 32}=\frac{27225}{64}=425.39ft[/tex]

To find the coordinates of a point on a circle with radius 10 corresponding to an angle of 325 degrees, you can use the following formula:

(x, y) = (r * cos(θ), r * sin(θ))

where (x, y) are the coordinates of the point, r is the radius of the circle, and θ is the angle in radians.

To convert the angle from degrees to radians, you can use the following formula:

θ (radians) = θ (degrees) * (π / 180)

Substituting the values into the formula and converting the angle to radians, you get:

(x, y) = (10 * cos(325 * (π / 180)), 10 * sin(325 * (π / 180)))

= (-5.5, 9.5)

Therefore, the coordinates of the point on the circle with radius 10 corresponding to an angle of 325 degrees are (-5.5, 9.5).

What are the coordinates point?

The coordinates of a point in a coordinate system are a set of numerical values that specify the position of the point in relation to an origin. In a two-dimensional coordinate system, such as the Cartesian coordinate system, a point is represented by an ordered pair (x, y), where x and y are the coordinates of the point. The x-coordinate represents the point's position along the horizontal axis, and the y-coordinate represents the point's position along the vertical axis.

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Answer:

x = 35

Important things to know:

1. A + (x + 110) will equal 180 degrees

2. The interior angles of a triangle will equal 180 degrees.

With these two pieces of knowledge, you can substitute the value of A as "180 - (x+110)" because A = 180-(x+110)

Step-by-step explanation:

Answer:

The answer is 4

Step-by-step explanation:

The group candidate is 8

with a division between the number of candidates and the number of selection will the result.

8 candidates ÷ 2 candidates = 4

The way in which 2 candidates can be selected from the pool of 8 candidates to be a city commissioner is 4.

Based on the given parameters, the value of the money to invest initially is $994.8

The given parameters about the compound interest are

Principal Amount, P = $2130

Interest Rate, R = 6.4%

Time, t = 12

Number of times, n = 12 i.e. monthly

To calculate the amount, we have:

A = P + CI

Where

C = P(1 + R)^t

So, we have

A = P(1 + R)^t

This can be rewritten as

A = P(1 + R/n)^nt

Substitute the known values in the above equation

2130 = A * (1 + 6.4%/12)^(12*12)

So, we have

A = 2130/[(1 + 6.4%/12)^(12*12)]

Evaluate the expression

A = 994.8

Hence, the amount of the investment is $994.8

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After writing y = kx, we'll solve for k putting the given corresponding values of x and y.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Suppose we have two variables x and y and they are directly proportional and some values of x and y are given.

If we see that y has a bigger corresponding value than x, we'll write

y = kx,

In the case of inverse variation, we write y = k/x.

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Answer:

Total interest paid:$112.65

Total payments:$632.65

Step-by-step explanation:

The value of X is 9 units it is solved by using the properties of Similar Triangles

What are Similar Triangles?

Two objects are comparable in Euclidean geometry if they have the same form or one has the same shape as the mirror image of the other. More exactly, one can be created by evenly scaling the other, potentially with extra translation, rotation, and reflection.

Solution:

In the given question

Triangle ABC and Triangle DEC are similar by AAA property

By using the properties of Similar Triangle

We can say that AC/DC = BC/EC

26/8 = (x+4)/4

13 = x + 4

x = 9 units

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cylinder

A cylinder is a three-dimensional solid figure with two identical circular bases connected by a curved surface at a specified distance from the center, which is the height of the cylinder. Toilet paper wicks and cold drink cans are examples of cylinders.

A cone is a three-dimensional shape that smoothly narrows from a flat base (usually a circular base) to a point called the vertex or apex that forms the axis to the center of the base. A cone can also be defined as a pyramid with a circular cross-section instead of a cone with a triangular cross-section. These cones are also known as circular cones.

The cylinder and cone have the same radius because they both have the same base area.

The volumes of the cylinder and the cone are equal,

Cylinder Volume = Cone Volume

; Ûr2h=1/3 Ûr2h

(5×5)= 1/3×5×h

h=12

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Hence, the driving second car cost Romney per year pays is $ [tex]16364[/tex].

What is the selling price?

The selling price of a product or service is the seller’s final price, i.e., how much the customer pays for something. The exchange can be for a product or service in a certain quantity, weight, or measure.

Here given that,

Romney bought a car with $[tex]6000[/tex] down payment, and paid the remaining cost by installments, which totaled $[tex]15000[/tex]. Romney then sold the car after [tex]10[/tex] years for $[tex]5500[/tex].

So, he sold his car in $[tex]15000(6000)=90000000[/tex].

And he is paying installment in every month which is $ [tex]15000[/tex].

So, in case of second car he paied $ [tex]5500[/tex] and his installments of every month would be

[tex]\frac{90000000}{5500}=16364[/tex] $

Hence, the driving second car cost Romney per year pays is $ [tex]16364[/tex].

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In a one-tailed T-test, if the test statistics and the t-value are under the null hypothesis, then p-value = ρ > to alternate hypothesis is true.

Critical zones in hypothesis testing are ranges of distributions where the values correspond to outcomes that are statistically significant. Analysts set the significance level (alpha) and whether the test is one-tailed or two-tailed in order to determine the size and location of the key regions.

The likelihood of rejecting an accurate null hypothesis is the significance level.

A test statistic's sample distribution assumes that the null hypothesis is true.

As a result, you need to shade the necessary fraction of the distribution to depict the crucial areas on the distribution for a test statistic. You shade 5% of the distribution using the typical significance threshold of 0.05.

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A function showing the value of the account after t years, where the annual growth rate can be found from a constant in the function is f(t) = 2900 × (1.0624)^t and APY is 6.24%.

Compound interest in simple words is the interest earning for your savings with the interest which those savings earn.

The formula for calculating the amount in Compound Interest is,

A = P( 1 + [tex]\frac{r}{n}[/tex] )ⁿᵇ

where A is the amount, P is the principal, r is the rate of interest, n is the number of times interest compounded in a year and b is the number of years.

Here, P = $2900, r = 6.1% = 0.061, n = 4 (quarterly) and b = t years

A = 2900 (1 + [tex]\frac{0.061}{4}[/tex])^4t

A = 2900 (1.0153)^4t

A = 2900 × (1.0624)^t

So A can be said as a function of t.

f(t) = 2900 × (1.0624)^t

Percentage of growth per year (APY) = ( 1 + [tex]\frac{r}{n}[/tex] )ⁿ - 1

                                                              = (1 + [tex]\frac{0.061}{4}[/tex])⁴ - 1

                                                              = 1.0624 - 1

                                                              = 0.0624 = 6.24%

Hence the function of the value of the account after t years is f(t) = 2900 × (1.0624)^t, where the value 1.0624 is a constant.

Percentage of growth per year is 6.24%.

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The required value of dosage in mg/min is given as 8 mg/min.

A ratio is the relation between two numbers as a / b. A proportion is the equality of two ratios as a / b = c / d.

Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.

Given that,

The dose administered per hour is 60 mL/hr.

And, the infusion is given as 4g for 500 mL.

In order to calculate the dosage in mg/min, ratio and proportion method can be used as follows,

The 500 mL is for 4g.

Then for 1 mL, there is 4/500 g.

Thus, for 60 mL, there is 4/500 × 60 g.

Since 1 g = 1000 mg.

The above expression can be written as,

4/500 × 60 × 1000 mg = 480 mg

Now, the dosage can be calculated as,

480 mg/hr

= 480/60 mg/min

= 8 mg/min

Hence, the dosage in milligram per minutes is given as 8 mg/min.

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Answer:

2^3 = 8

Step-by-step explanation:

The graph of the given function f(x)=|x−6|−4 is shown where the line is parallel to the x-axis.

A graph is a structure that resembles a set of items in discrete mathematics, more specifically in graph theory, in which some pairs of objects are conceptually "connected."

The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.

Write the equation in the form y = MX + b to determine the slope m and the y-intercept.

This will allow you to graph the equation using the slope and y-intercept (0, b).

So, the given function is: f(x)=|x−6|−4

Take f(x) as 0 which means:

f(x)=|x−6|−4 = 0

Now, graph the function as follows:
(Refer to the graph attached below)

The line is parallel to the x-axis.

Therefore, the graph of the given function f(x)=|x−6|−4 is shown where the line is parallel to the x-axis.

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