how many inches is 2 1/6 ft​

Answer:

Step-by-step explanation:

y=-6

y=-10

y=-2

Answer:

y = 5u², u=x-6

Explanation:

Given the function:

We want to express f(x) as a composition of two functions.

Let u = x-6

Therefore, the function y=5(x−6)² as a composition y=f(g(x)) of two simpler functions y=f(u) and u=g(x)

Answer:

Step-by-step explanation:

3⅙ - ⅚ = 19/6 - ⅚ = 14/6 = 7/3 = 2⅓

Given expression \(\frac{2x^3+11x^2-21x}{x^2+3x}\) is equivalent to  \(2x+5 -\frac{36}{x+3}\).

What do you mean by algebraic expression?

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables.

Variables and constants can both be used in an algebraic expression.

There are 3 main types of algebraic expressions which include:

Monomial Expression

Binomial Expression

Polynomial Expression

Given expression:

\(\frac{2x^3+11x^2-21x}{x^2+3x}\)       for \(x\) ≠ -3 or 0.

Using long division method and euclid lemma

On dividing \(2x^3+11x^2-21x\) by \(x^2+3x\) we get, (given in the snip)

As we know division can be written as

dividend = divisor × quotient + remainder

\(2x^3+11x^2-21x = (2x+5)(x^2+3x)-36x\)

⇒ \(2x^3+11x^2-21x = 2x+5 -\frac{36x}{x^2+3x}\)

⇒  \(2x^3+11x^2-21x = 2x+5 -\frac{36}{x+3}\)

Therefore, given expression \(\frac{2x^3+11x^2-21x}{x^2+3x}\) is equivalent  to  \(2x+5 -\frac{36}{x+3}\).

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Answer:

6x + 10

Step-by-step explanation:

Since this doesn't have an equal sign, all you can do is simplify the expression.

Use the distributive property:

\(2(3x + 5)\\2*3x + 2*5\\6x + 10\)

So the answer is 6x + 10

Answer:

Since the part we can see is half of the whole figure, and there are six sides then in total there are 12 sides. A "12-gon" is called a dodecahedron. This is the answer.

Dodecahedron is the name of the platonic solid, option A is correct.

a polygon is a plane figure made up of line segments connected to form a closed polygonal chain

A dodecahedron or duodecahedron is any polyhedron with twelve flat faces.

The most familiar dodecahedron is the regular dodecahedron with regular pentagons as faces, which is a Platonic solid.

A regular dodecahedron has 12 faces and 20 vertices, whereas a regular icosahedron has 20 faces and 12 vertices. Both have 30 edges.

Hence,  dodecahedron is the name of the platonic solid shown.

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Answer:

\(x = 9.4\)

\(y = 17.7\)

Step-by-step explanation:

Given: The figure

Required: Find x and y

The relationship between length x, length 15 and angle 32 is as follows:

\(tan \theta = \frac{opp}{adj}\)

So, we have:

\(tan\ 32= \frac{x}{15}\)

Cross multiply:

\(x =15*tan\ 32\)

\(x = 15 * 0.6248693519\)

\(x = 9.3730402785\)

\(x = 9.4\) --- approximated

Similarly:

The relationship between length y, length 15 and angle 32 is as follows:

\(cos \theta = \frac{adj}{hyp}\)

So, we have:

\(cos\ 32= \frac{15}{y}\)

Cross Multiply:

\(y * cos\ 32= 15\)

Solve for y

\(y = \frac{15}{cos\ 32}\)

\(y = \frac{15}{0.84804809615}\)

\(y = 17.6876760506\)

\(y = 17.7\) --- approximated

Answer:

3240 degrees.

Step-by-step explanation:In geometry, an icosagon or 20-gon is a twenty-sided polygon. The sum of any icosagon's interior angles is 3240 degrees.

The image of the point L(-4,0) after a dilation with a center of (0,0) and a scale factor of 7 is the point L'(-28,0).

A dilation with a center of (0,0) and a scale factor of 7 means that every point in the plane will be multiplied by a factor of 7 from the origin.

To find the image of the point L(-4,0) after a dilation with a center of (0,0) and a scale factor of 7, we can simply multiply the coordinates of L by the scale factor.

The coordinates of the image point L' will be:

L' = (-4 × 7, 0 × 7) = (-28, 0)

Therefore, the image of the point L(-4,0) after a dilation with a center of (0,0) and a scale factor of 7 is the point L'(-28,0).

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Answer: \(\frac{4}{5}\), 3

Step-by-step explanation:

1. Simplify: 5b2−19b+12=0

2. Factor by grouping: (5b−4)(b−3)=0

3. If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0: 5b−4=0, 5b-4=0b−3=0

4. Set 5b−45b-4 equal to 0 and solve for b: b=\(\frac{4}{5}\)

5. Set b−3b-3 equal to 0 and solve for b: b=3
6. The final solution is all the values that make (5b-4)(b-3)=0 true: b =  \(\frac{4}{5}\), 3

Approximately 99.7% of scores lie in the shaded region.

We have,

The empirical rule, also known as the 68-95-99.7 rule, provides an estimate of the percentage of scores that lie within a certain number of standard deviations from the mean in a normal distribution.

According to this rule:

Approximately 68% of scores lie within 1 standard deviation of the mean.

Approximately 95% of scores lie within 2 standard deviations of the mean.

Approximately 99.7% of scores lie within 3 standard deviations of the mean.

Now,

In the given scenario, the shaded region represents the area between -2 and 3 standard deviations from the mean on the x-axis.

This encompasses the area within 3 standard deviations of the mean.

And,

Since 99.7% of scores lie within 3 standard deviations of the mean, we can estimate that approximately 99.7% of scores lie in the shaded region.

Therefore,

Approximately 99.7% of scores lie in the shaded region.

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Answer:

Step-by-step explanation:

This is a test of 2 independent groups. Let μ1 be the mean dissolution time for disk-shaped ibuprofen tablets and μ2 be the mean dissolution time for oval-shaped ibuprofen tablets.

The random variable is μ1 - μ2 = difference in the mean dissolution time for disk-shaped ibuprofen tablets and the mean dissolution time for oval-shaped ibuprofen tablets.

We would set up the hypothesis.

a) The null hypothesis is

H0 : μ1 = μ2 H0 : μ1 - μ2 = 0

The alternative hypothesis is

H1 : μ1 ≠ μ2 H1 : μ1 - μ2 ≠ 0

This is a two tailed test.

For disk shaped,

Mean, x1 = (269.0 + 249.3 + 255.2 + 252.7 + 247.0 + 261.6)/6 = 255.8

Standard deviation = √(summation(x - mean)²/n

n1 = 6

Summation(x - mean)² = (269 - 255.8)^2 + (249.3 - 255.8)^2 + (255.2 - 255.8)^2+ (252.7 - 255.8)^2 + (247 - 255.8)^2 + (261.6 - 255.8)^2 = 337.54

Standard deviation, s1 = √(337.54/6) = 7.5

For oval shaped,

Mean, x2 = (268.8 + 260 + 273.5 + 253.9 + 278.5 + 289.4 + 261.6 + 280.2)/8 = 270.7375

n2 = 8

Summation(x - mean)² = (268.8 - 270.7375)^2 + (260 - 270.7375)^2 + (273.5 - 270.7375)^2+ (253.9 - 270.7375)^2 + (278.5 - 270.7375)^2 + (289.4 - 270.7375)^2 + (261.6 - 270.7375)^2 + (280.2 - 270.7375)^2 = 991.75875

Standard deviation, s2 = √(991.75875/8) = 11.1

b) Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(x1 - x2)/√(s1²/n1 + s2²/n2)

Therefore,

t = (255.8 - 270.7375)/√(7.5²/6 + 11.1²/8)

t = - 3

c) The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [7.5²/6 + 11.1²/8]²/[(1/6 - 1)(7.5²/6)² + (1/8 - 1)(11.1²/8)²] = 613.86/51.46

df = 12

We would determine the probability value from the t test calculator. It becomes

p value = 0.011

d) Since alpha, 0.05 > than the p value, 0.011, then we would reject the null hypothesis. Therefore, we can conclude that at 5% significance level, the mean dissolve times differ between the two shapes

Answer:

25%

Step-by-step explanation:

to find the original cost of a single shirt:

4000 / 500 = $8

how much did they markup:

10 - 8 = 2

percent markup:

2/8 = 0.25 x 100 = 25%

About 16% of the books have fewer than 150 pages

Given data ,

The numbers of pages in the books in a library follow a normal distribution

The mean number of pages is 180 and the standard deviation is 30 pages

Now , about 68% of the books will have a number of pages within one standard deviation of the mean, or between 150 and 210 pages

And , using a standard normal distribution table or a calculator that has a normal distribution function.

Using a standard normal distribution table, we find that the area to the left of -1 (which corresponds to a z-score of -1) is about 0.16

Hence , 16% of the books have fewer than 150 pages

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The function values are f(10) = 198 and g(-6) = 24/7; the range of h(x) is 3/5 < h(x) < 31/25 and the inverse function is p-1(x) = -(1 + 3x)/(5 + x)

Given that

f(x) = 2x^2 - 2

g(x) = 4x/(x - 1)

So, we have

f(10) = 2(10)^2 - 2 = 198

g(-6) = 4(-6)/(-6 - 1) = 24/7

Here, we have

h(x) = (7x - 4)/5x

Where

1 < x < 5

So, we have

h(1) = (7(1) - 4)/5(1) = 3/5

h(5) = (7(5) - 4)/5(5) = 31/25

So the range is 3/5 < h(x) < 31/25

Here, we have

P(x) = (5x - 1)/(3 - x)

So, we have

x = (5y - 1)/(3 - y)

This gives

3x - xy = 5y - 1

So, we have

y(5 + x) = -1 - 3x

This gives

y = -(1 + 3x)/(5 + x)

So, the inverse function is p-1(x) = -(1 + 3x)/(5 + x)

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When Jackson wrote different patterns for the rule "subtract 5", the patterns that he could have written include

A. 27, 22, 17, 12, 7

D. 100, 95, 90, 85, 80

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc. In this case, when Jackson wrote different patterns for the rule "subtract 5", the patterns that he could have written include 27, 22, 17, 12, 7 and 100, 95, 90, 85, 80. In this cases, there are difference of 5.

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Complete question

Jackson wrote different patterns for the rule "subtract 5". Select all of the patterns that he could have written.

27, 22, 17, 12, 7

5, 10, 15, 20, 25

55, 50, 35, 30, 25

100, 95, 90, 85, 80

75, 65, 55, 45, 35

Answer: The machine depreciates during the fifth year by $4000.

Step-by-step explanation:

Given: The resale value of a certain industrial machine decreases over a 8-year period at a rate that changes with time.

When the machine is x years old, the rate at which its value is changing is 200(x - 8) dollars per year.

Then, the machine depreciates A(x) during the fifth year as

\(A(x) =\int^{5}_1200(x - 8)\ dx\\\\=200|\frac{x^2}{2}-8x|^{5}_1\\\\=200[\frac{5^2}{2}-\frac{1^2}{2}-8(5)+8(1)]\\\\=200 [12-32]\\\\=200(-20)=-4000\)

Hence, the machine depreciates during the fifth year by $4000.

According to the Angle Addition Postulate, the measure of m∠ABD = 202°.

According to the Angle Addition Postulate, an angle's measure is equal to the sum of the measures of any two adjacent angles. The Angle Addition Postulate can be used to determine the measurement of a missing angle or to determine the angle produced by two or more other angles.

Given:

The angle measures:

m∠ABC=37°,

and m∠⁡C⁣B⁣D= 165⁢°.

So, according to the angle addition postulate;

m∠ABD = m∠ABC + m∠CBD

Substituting the values,

m∠ABD = 37° + 165⁢°

m∠ABD = 202°

Therefore, the angle measure of m∠ABD = 202°.

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Answer:

Step-by-step explanation:

1)

total area = rectangle area + 2 triangle area

                =  length * width = 2 ( \(\frac{1}{2}\) * base * height )

                =  7.5 * 6 + 2 (  \(\frac{1}{2}\) * 3 * 4 )

                = 57 ft²

2)

separate it into two rectangles:

length * width + length * width

  6  *   2  +  9 * 4

      48 cm²

3)

parallelogram area =  base * height

                                = 20 * 25

                                 = 500 in²

Answer:

the correct answer is 193

Step-by-step explanation:

25×1-0=25

25×2-1=49

49×2-1=97

97×2-1=193

The expected value of x is (m+1)/2, and m must be a positive integer.

The expected value of x is the average value of x that we would expect to get if we selected an integer from the set {1, 2, ..., m} many times. To find the expected value of x, we multiply each possible value of x by its probability of being selected and then sum these products. In this case, each integer in the set {1, 2, ..., m} has an equal probability of being selected, so the expected value is (1 + 2 + ... + m) / m = (m(m+1)) / 2m = (m+1) / 2. So the expected value of x is (m+1)/2, and m must be a positive integer.

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Answer:

3.6

Step-by-step explanation:

hey, how this helps and is right haha

The area of the triangle, when a = 2 and c = 3, is 1512 square centimeters.

We must apply the formula for the area of a triangle, which is provided by: to determine the triangle's area.

(1/2) * Base * Height = Area

We can enter the values of a = 2 and c = 3 into the formula given that the base length is 3ac2 and the height is 2 centimetres greater than the base length.

Base length =\(3ac^2 = 3 * 2 * (3^2) = 3 * 2 * 9 = 54\) centimeters

Height is calculated as Base Length + 2 (54 + 2 = 56 centimetres).

Using these values as a substitute in the formula, we obtain:

Area =\((1/2) * 54 * 56 = 1512\) square centimeters

centimetres square

It's crucial to understand that the calculation assumes the triangle is a right triangle with the specified base and height and that the given values of a and c are accurately used in the formula.

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The equation of the line in slope-intercept form is y = (3/4)x.

To write the equation of a line in slope-intercept form, we need to use the slope-intercept form equation: y = mx + b,

where m is the slope and b is the y-intercept.

Given that the line passes through the point (-8, 5) and has a slope of 3/4, we can substitute the values into the equation to find the y-intercept (b).

First, let's find the value of b using the point-slope form equation: y - y1 = m(x - x1), where (x1, y1) is a point on the line.

Using (-8, 5) as the point and 3/4 as the slope, we have:

5 - 5 = (3/4)(-8 - x)

0 = (3/4)(-8 - x)

0 = (-3/4)(8 + x)

0 = -6 - (3/4)x

Next, we can solve for x:

(3/4)x = -6

x = -6 \(\times\) (4/3)

x = -8

Now that we have the value of x, we can substitute it back into the equation to find the value of b:

0 = -6 - (3/4)(-8)

0 = -6 + 6

0 = 0

So, the value of b is 0.

Finally, we can write the equation of the line in slope-intercept form:

y = (3/4)x + 0

y = (3/4)x.

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In an arithmetic sequence where t1=91 and t25=374, the sum of the first 50 terms is 18,425.

Formula for the sum of an arithmetic sequence is given as

\(Sn = (n/2) x [2a1 + (n-1)d]\)

where

Sn is the sum of the first n terms,

a1 is the first term

d is the common difference and

n is the number of terms.

Given that t1 = 91 and t25 = 374.

To find d, we can use the formula for the nth term of an arithmetic sequence:

\(tn = a1 + (n-1)d\)

Substitute n = 25, t25 = 374, and a1 = 91, we get:

374 = 91 + 24d

d = 11

Substitute d in the Sn formula

S₅₀ = (50/2) x [2(91) + (50-1)(11)]

S₅₀ = 25 x [182 + 49 x 11]

S₅₀= 25 x 737

S₅₀ = 18,425

Therefore, the sum of the first 50 terms is 18,425.

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The shortest distance from A to B in the diagram is 17 m.

The shortest distance from D to B can be found as follows:

using Pythagoras theorem,

c² = a² + b²

where

Therefore,

DB² = 15² + 8²

DB² = 225 + 64

DB² = 289

DB = √289

DB = 17 m

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Answer:

B, 17 m

Step-by-step explanation:

Founders 23

Answer: The number of freshman who chose education as their major is greater than the number of freshman who chose science or other as their major ANSWER- D

Step-by-step explanation:

Answer:

Step-by-step explanation:

There are 105 ways for a visitor to visit six American cities while adhering to the guidelines and without taking the sequence of the stops into account.

i) To find the number of ways to choose 6 cities out of 13 when the order of the visits does not matter, we can use the combination formula:

\(${{13}\choose{6}} = \frac{13!}{6!(13-6)!} = 1,716$\)

Therefore, there are 1,716 ways for the tourist to visit six American cities without considering the order of visits.

ii) To find the number of ways to choose 6 cities out of 13 when the order of the visits does matter, we can use the permutation formula:

\($P_{13,6} = \frac{13!}{(13-6)!} = 1,235,520$\)

Therefore, there are 1,235,520 ways for the tourist to visit six American cities while considering the order of visits.

iii) To find the number of ways to choose 6 cities out of 13 when the order of the visits does not matter and the tourist wants to visit at least three cities on the east coast and at least two on the west coast, we can use the inclusion-exclusion principle.

First, we calculate the total number of ways to choose 6 cities out of 13:

\(${{13}\choose{6}} = 1,716$\)

Then, we calculate the number of ways to choose 6 cities without any restrictions on the coast:

\(${{7}\choose{3}}{{3}\choose{2}}{{3}\choose{1}} = 210$\)

Here, we have used the multiplication principle to find the number of ways to choose 3 cities out of 7 on the east coast, 2 cities out of 3 on the west coast, and 1 city out of 3 in the middle of the country.

However, this count includes the cases where the tourist visits only one or none of the west coast cities, which does not meet the requirement of visiting at least two west coast cities. So we need to subtract these cases from the count.

The number of ways to choose 6 cities while visiting only one or none of the west coast cities is:

\(${{7}\choose{3}}{{3}\choose{1}}{{3}\choose{2}} + {{7}\choose{3}}{{3}\choose{0}}{{3}\choose{3}} = 105$\)

Here, we have used the multiplication principle to find the number of ways to choose 3 cities out of 7 on the east coast, 1 city out of 3 on the west coast, and 2 cities out of 3 in the middle of the country, or to choose 3 cities out of 7 on the east coast and all 3 cities in the middle of the country.

Therefore, the number of ways to choose 6 cities while visiting at least three cities on the east coast and at least two cities on the west coast is:

\($210 - 105 = 105$\)

So, there are 105 ways for the tourist to visit six American cities while meeting the given requirements and without considering the order of visits.

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The number of tickets which should be sold to $24 and $40 are 4500 and 1500 respectively.

Given, A 6000-seat theater has tickets for sale at $24 and $40.

How many tickets should be sold at each price for a sellout performance to generate a total revenue of $168,000 = ?

first, assign variables:

X = # of $24 tickets,  Y = # or $40 tickets

write equations based on the data presented:

"6000 seat theater..."

   X + Y = 6000 ...equation 1

"total revenue of 168,000"

The revenue from each type of ticket is the cost times the number sold, so:

  24X + 40Y = 168,000 .....equation 2

from equation 1:

   X = 6000 - Y

substitute this into equation 2:   (replace X with 6000-Y)

   24 (6000 - Y) + 40Y = 168,000

expand:

144,000 -24Y + 40Y = 168,000

rearrange and simplify:

    16Y = 168,000 - 144,000

    y = 24000/16

     Y = 1500

from equation 1:

     X = 6000 - 1500

     X = 4500

hence the number of tickets for sale at $24 should be 4500.

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