In a class of students, the following data table summarizes how many students passed
a test and complete the homework due the day of the test. What is the probability that
a student completed the homework given that they failed the test?
Completed the homework
Did not complete the homework
Passed the test Failed the test
8
2
3
сл

The composition value of two functions g of f of x, i e., g(f(x)) where f(x) = x² +2x -4 and g(x) = 3x +1, is equals to the 3x² + 6x -11.

The composition of two functions g and f, g(f(x)) is the new function we result by performing f first, and then performing g. It can be written as (g º f)(x). The domain of composed function is same as domain of first function or subset of domain of first function. Similarly, range of composed function is same as range second function or subset that. The g(f(x)) can be solved by first we apply f, then apply g to that result. We have f(x) = x² + 2x -4 and g(x) = 3x + 1 and we have to determine g(f(x)). Now, for determining value of (g∘f)(x)= g(f(x)), first we apply f to x to result f(x) and then to apply g to f(x) to get g(f(x)). That is f to x= f(x) = x² + 2x - 4

and g to f(x), we replace x in g(x) by f(x) for g(f(x)).

=> g(f(x)) = 3 f(x) + 1

=> g(f(x)) = 3 ( x² + 2x -4) + 1

= 3x² + 6x - 12 + 1

= 3x² + 6x -11

Hence, required value is 3x² + 6x -11.

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Groups A, B, and C have means of 4, 6, and 8, respectively. There are 15 cases in total, with equal sample sizes in each group. Within is 120. 16-7. 16-4a, the value of omega-squared is 0.25.

What is omega-squared?

       In statistics, omega-squared is a measure of effect size that can be used for one-way ANOVA to determine how much variance is due to the treatment or independent variable. It is calculated by dividing the between-group variance by the total variance, which includes both the within-group and between-group variance.

       Omega-squared is used to determine the percentage of variance accounted for by a particular factor or treatment. It is represented as ω2 and ranges from 0 to 1, with higher values indicating a stronger relationship between the independent variable and the dependent variable.

       The formula for omega-squared is as follows:

                         ω2=SSBetween / SSTotalSSWithin

                              = SSTotal - SS Between

         Where SSTotal is the sum of squares for the total variance.SSBetween is the sum of squares between the groups, and within is the sum of squares within the groups.

     The given information is:

                       Mean of group A = 4Mean of group

                                                 B = 6Mean of group

                                                 C = 8Total cases

                                                    = 15SSWithin

                                                    = 120

             We can calculate the sum of squares between the groups as follows:

                        SSTotal = SSBetween + SSWithinSSTotal

                                      = (nA + nB + nC - 1) × (σA² + σB² + σC²)SSBetween

                                      = SSTotal - SS Within SS Between

                                      = (3 - 1) × (42 + 62 + 82) - 120SSBetween

                                      = 80 Next,

           we can calculate the total variance as:

                      SSTotal = SSWithin + SSBetweenSSTotal

                                    = 120 + 80SSTotal

                                     = 200

            Now, we can calculate omega-squared as follows:

                     ω2 = SSBetween / SSTotalω2

                           = 80/200ω2

                           =0.4

       Hence, the value of omega-squared is 0.25.

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The value of x -8.

An equation is a mathematical statement containing two algebraic expressions flanked by equal signs (=) on either side.

It shows that the relationship between the left and right printed expressions is equal.

All formulas hav LHS = RHS (left side = right side).

You can solve equations to determine the values ​​of unknown variables that represent unknown quantities.

If a statement does not have an equals sign, it is not an equation. A mathematical statement called an equation contains the symbol "equal to" between two expressions of equal value.

Hence, the value of x -8.

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The volume of lemon juice in the glass is 0.38 cubic inches.

Explanation:

Given,

Let the volume of the lemonade in the glass be V cubic inches

Therefore, the volume of lemon juice in the lemonade is [tex]$\frac{1}{12}$[/tex] V cubic inches

Volume of water in the lemonade is [tex]$\frac{11}{12}$[/tex] V cubic inches

The volume of the cylindrical glass is given by:

[tex]$V_{\text{cylindrical glass}} = \pi r^2h$[/tex]

Here,

Radius r = 1 inch

Height h = 6 inches

[tex]$V_{\text{cylindrical glass}} = \pi r^2h = \pi (1)^2(6) = 6 \pi$[/tex]

Since the glass is half full of lemonade, the volume of lemonade in the glass is:

[tex]$V_{\text{lemonade}} = \frac{1}{2}V_{\text{cylindrical glass}} = \frac{1}{2} 6 \pi = 3\pi$[/tex]

The volume of lemon juice in the lemonade is given by:

[tex]$V_{\text{lemon juice}} = \frac{1}{12}V$[/tex]

Therefore

[tex]$V_{\text{lemon juice}} = \frac{1}{12}3\pi = \frac{1}{4}\pi = 0.7854$[/tex] cubic inches

Hence, the volume of lemon juice in the glass is 0.38 cubic inches (rounded to the nearest hundredth).

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In response to the stated question, we may state that As a result, the area final polynomial in standard form is: -25pi + 50

The size of a surface area can be represented as an area. The surface area is the area of an open surface or the border of a three-dimensional object, whereas the area of a planar region or planar region refers to the area of a shape or flat layer. The area of an item is the entire amount of space occupied by a planar (2-D) surface or form. Make a square with a pencil on a sheet of paper. A two-dimensional character. On paper, the area of a form is the amount of space it takes up. Assume the square is made up of smaller unit squares.

To calculate the area of the darkened areas, subtract the area of the circle from the area of the square.

Then, determine the square's side length. Because the circle's diameter is ten, the radius is five. Because the diagonal of a square equals the diameter of a circle, we can use the Pythagorean theorem to calculate the side length:

[tex]s^2 + s^2 = 10^2\\2s^2 = 100\\s^2 = 50\\s = \sqrt(50) = 5 * \sqrt(2)[/tex]

The square's area is then:

[tex]A_{square} = s^2 = (5 * \sqrt(2))^2 = 50[/tex]

The circle's area is:

[tex]A_{circle} = pi * r^2 = pi * 5^2 = 25 * pi[/tex]

The shaded region's area is:

[tex]A_{shaded} = A_{square} - A_{circle} = 50 - 25 * pi[/tex]

As a result, the final polynomial in standard form is:

-25pi + 50

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Answer:

We can use the Pythagorean theorem to find the length of side R:

R^2 = 15^2 + 14^2

R^2 = 225 + 196

R^2 = 421

R = √421

So, we have:

sin S = S/15

cos R = 14/√421

sin S/cos R = (S/15)/(14/√421) = S/(15*14/√421) = S/(210/√421) = S√421/210

Therefore, the expressions for sin S and cos R in simplest terms are:

sin S = S/15

cos R = 14/√421

sin S/cos R = S√421/210

Runners and sprinters could be on the track team is 25 distance.

Distance:

Distance is a qualitative measurement of the distance between objects or points. In physics or common usage, distance can refer to a physical length or an estimate based on other criteria (such as "more than two counties"). The term Distance is also often used metaphorically to refer to a measure of the amount of difference between two similar objects.

According too the Question:

Based on the based Information:

15× 5÷3

canceling all the common factor, we get:

5 × 5 = 25

Now, the Product or Quotient is 25.

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Answer:

b: 70

Step-by-step explanation:

10 times 5 is 50 and 4 times 5 is 20. 50 plus 20 is 70

The length of the shortest altitude of the triangles is 15 units by using Heron’s formula.

We have, The sides of a triangle have lengths of 15, 20, and 25.

To find, The length of the shortest altitude of the triangle.

Steps to solve the problem:

Area = 1/2 * base * height

Area of the triangle = 1/2 * 20 * h ⇒ 10h

A = √(s(s-a)(s-b)(s-c))

Where a, b, and c are the sides of the triangle, and s is the semi-perimeter of the triangle.

According to the given problem, the sides of the triangle are 15, 20, and 25.

s = (a + b + c)/2

= (15 + 20 + 25)/2

= 30

Therefore, the area of the triangle can be calculated as:

A = √(30(30-15)(30-20)(30-25))

= √(30*15*10*5)

= 150 sq. units

Therefore, we can write the formula for the area of the triangle as:

150 = 10 h

h = 15 units

Therefore, the length of the shortest altitude of the triangle is 15 units.

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To create an indicator variable for student status in a regression model, two binary variables should be created. One should be for Undergraduate and another for Graduate, taking on the value of 1 if the participant is in that category and 0 otherwise.Option A is correct.

For the following, an indicator variable can be created to include in a regression model:

a. Two Variables. One variable has Undergraduate = 1 and 0 otherwise and another variable that has Graduate = 1 and 0 otherwise

b..  A variable named Undergraduate: For this option, we would create an indicator variable named Undergraduate that takes the value of "Yes" if the participant is an undergraduate and "No" otherwise. This variable would be coded as 1 for "Yes" and 0 for "No.

c. A variable named Undergraduate: For this option, we would create an indicator variable named Undergraduate that takes the value of "A" if the participant is an undergraduate and "B" otherwise. This variable would be coded as 1 for "A" and 0 for "B".

d. A variable named Undergraduate: For this option, we would create an indicator variable named Undergraduate that takes the value 1 if the participant is an undergraduate and 0 otherwise. This variable would be coded as 1 for Undergraduate and 0 for Graduate.

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Move all terms that don't contain [tex]y[/tex] to the right side and solve.

Answer: x = 15

Step-by-step explanation:

Expand 1.4(x+5): 1.4x+7+1.6x = 52

Combine like terms: 3x+7 = 52

Subtract 7 from both sides: 3x = 45

Divide both sides by 3: x = 15

Answer:

The answer is x=15

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1. Expand the expression

1.4x+7+1.6x=52

2. Simplify

3x+7=52

3. Separate the constants and variables

3x=52−7

4. Add or subtract numbers

3x=45

5. Divide both sides by 3

6. Simplify

x=15

The following is the correct sequence of steps to prove that if n is a perfect square, then n + 2 is not a perfect square:

Step 1: Assume n = m², for some non-negative integer m.

Step 2: If m = 0, then n + 2 = 2, which is not a perfect square. The smallest perfect square greater than n is (m + 1)².

Step 3: Expand (m + 1)² to obtain (m + 1)² = m² + 2m + 1 = n + 2m + 1 > n + 2 + 1 > n + 2.

Step 4: Let's assume m ≥ 1.

Step 5: Hence, n + 2 is not a perfect square.

The first step in the sequence involves making an assumption to start the proof. The second step entails the derivation of the smallest perfect square greater than n. In the third step, we expand the (m + 1)² expression to get n + 2m + 1. The fourth step is an important one, as it shows that m must be greater than or equal to 1.

In the final step, we conclude that n + 2 is not a perfect square.

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Answer:

10 sides

Step-by-step explanation:

We can use the formula for the sum of the interior angles of a polygon to solve this problem. The formula for the sum of the interior angles of a polygon with n sides, where S is the sum of the interior angles, and n is the number of sides of the polygon is:

S = (n - 2) x 180 degrees

If the sum of the interior angles is 1440 degrees, we can set this equal to the formula and solve for n:

1440 = (n - 2) x 180

Dividing both sides by 180, we get:

8 = n - 2

Adding 2 to both sides, we get:

n = 10

Therefore, a polygon with a sum of interior angles of 1440 degrees has 10 sides.

The supplementary angles of the given angles are 154 degrees, 136 degrees, 135 degrees, 44 degrees, 45 degrees, and 26 degrees, respectively.

Supplementary angles are pairs of angles that add up to 180 degrees. To find the supplementary angle of each given angle, we simply subtract the angle from 180 degrees.

Therefore, the supplementary angles of the given angles are:

Therefore, the supplementary angles of the given angles are 154 degrees, 136 degrees, 135 degrees, 44 degrees, 45 degrees, and 26 degrees, respectively.

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long is 5 ft tall and is standing in the light of a 15 ft lamp post her shadow is 4 ft long

To solve the given problem, let's proceed to the solution-

          We know that the Height of the girl = is 5 ft

          The height of the lamp post = is 15 ft

          The length of the shadow = is 4 ft

          Distance between the girl and the lamp post (initially) = 15 - 5 = 10 feet

  the distance between the girl and the lamp post (after walking) is x.

        So, the length of the shadow after walking x distance from the lamp post is given by√(x² + 5²) We need to find the increase in the length of the shadow.

      So, the increase in the length of the shadow is given by(√(x² + 5²) - 4) ft.

     We need to find this increase for x = 11. As x increases, the value of the above expression will also increase.

     So, if we substitute x = 11, then we will get the minimum increase in the length of the shadow.

     Therefore, the increase in the length of the shadow when the girl walks 1 ft away from the lamppost

            = (√(11² + 5²) - 4) ft

            = (sqrt(146)-4)ft ~ 10.6 ft.

  Hence, if she walks 1 ft farther away from the lamp post her shadow will lengthen by 10.6 ft.

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Answer:

an = a1 + (n-1)d

Untuk barisan ini, kita dapat menentukan a1 = 4 dan d = 3, karena selisih antar suku bertambah 3. Jadi, rumusnya menjadi:

an = 4 + (n-1)3

a5 = 4 + (5-1)3

a5 = 4 + 12

a5 = 16

Jadi, suku ke-5 dari barisan ini adalah 16.

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The domain of a step function is all real numbers. The equation G(x) = -[x] + 3 can be expressed as G(x) = { -x for x < 0; 3 for x ≥ 0}. The domain of G(x) is all real numbers.

To explain further, a step function can be expressed as two separate equations, one for x < 0 and one for x ≥ 0. The equation for x < 0 is G(x) = -x and the equation for x ≥ 0 is G(x) = 3. The domain of G(x) is all real numbers. This means that any x value, whether it is greater than or less than 0, will be included in the domain of G(x).

Let's the width of the given rectangle be x. Then the length will be 5x.

We know that,

[tex] \bf \implies Perimeter_{( Rectangle)} = 2 ( Length + Width) [/tex]

[tex] \sf \implies 2( x+5x) = 72 [/tex]

[tex] \sf \implies 2\times 6x = 72 [/tex]

[tex] \sf \implies 12x =72 [/tex]

[tex] \bf \implies x = 6 [/tex]

Hence, the width of the rectangle is 6 m and the length is 5*6 =30 m

[tex]\bf\implies Area_{( Rectangle) }= Length \times Width [/tex]

[tex] \bf \implies Area _{( Rectangle)} = 30 \times 6 [/tex]

[tex] \bf \implies Area _{( Rectangle) }= 180 m^2 [/tex]

Therefore, the area of the given rectangle is 180 metre square.

Answer:

We can use the formula for the area of a triangle which is given by:

Area = (1/2) x base x height

Where the base and height are the two sides that form the right angle.

Looking at the given triangle, we can see that the sides 3 in. and 5 in. form the right angle, so the base is 3 in. and the height is 5 in.

Therefore, the area of the triangle is:

Area = (1/2) x 3 in. x 5 in.

Area = 7.5 in²

Alternatively, we could also use the sides 2.5 in. and 6 in. to find the area of the triangle. In this case, the base would be 2.5 in. and the height would be 5 in. (since the 6 in. side is not perpendicular to the 2.5 in. side). So the area of the triangle would still be:

Area = (1/2) x 2.5 in. x 5 in.

Area = 6.25 in²

Either way, the area of the triangle is approximately 7.5 in² or 6.25 in², depending on which set of sides we use.

Step-by-step explanation:

The equilibrium concentration of HI(g) is 0.031 mole. It is less than the initial concentration of HI(g) which is 0.75 mole. Thus, the correct answer is less than.

At 1,000 K, the value of Ke for the reaction is 2.6 x 10-2, in an experiment, 0.75 mole of HI(g), 0.10 mole of of H2(g), H2(g), and 0.50 mole of 12(g) are placed in a 1.0 L container and allowed to reach equilibrium at 1,000 K. We need to determine whether the equilibrium concentration of HI(g) will be greater than, equal to, or less than the initial concentration of HIGG).

In this problem, we need to calculate the concentration of HI(g) at equilibrium. The given reaction is as follows:H2(g) + I2(g) ⇌ 2HI(g)We are given the following information:Initial concentration of HI(g) = 0.75 moleInitial concentration of H2(g) = 0.10 moleInitial concentration of I2(g) = 0.50 moleVolume of container = 1.0 LAt equilibrium, let's consider the concentration of HI(g) as x mole. According to the balanced chemical equation, H2 and I2 are the reactants while HI is the product.

Therefore, the concentration of H2 and I2 will decrease by x mole as they react with each other to form HI at equilibrium. Hence, the concentration of HI(g) will increase by 2x mole since 2 moles of HI are produced from the reaction of 1 mole of H2 and 1 mole of I2. Now, we can write the expression for equilibrium constant (Ke) as follows:Ke = [HI]2 / [H2] [I2]2.6 x 10-2 = (2x)2 / [(0.10 - x) (0.50 - x)]2.6 x 10-2 (0.10 - x) (0.50 - x) = 4x2(0.10 - x) (0.50 - x) = 4x2 - 2.6 x 10-2 (0.10 - x) (0.50 - x)8.54 x 10-3 x2 - 0.365 x + 0.02425 = 0x = 0.031 mole

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Answer:30

Step-by-step explanation: the formula is base x height over 2, so (6x10)/2 is 30.

the 7th number is 8. Answer B is correct. The sum of the first 6 numbers can be found by multiplying the average by the number of numbers:

sum of first 6 numbers = 6 x 15 = 90

Let the 7th number be x. Then the sum of all 7 numbers is:

sum of all 7 numbers = sum of first 6 numbers + 7th number = 90 + x

The new average is 1 less than the original average, so:

new average = 15 - 1 = 14

This means that the sum of all 7 numbers divided by 7 is 14:

(sum of all 7 numbers)/7 = 14

Substituting the expression we found for the sum of all 7 numbers, we get:

(90 + x)/7 = 14

Multiplying both sides by 7, we get:

90 + x = 98

Subtracting 90 from both sides, we get:

x = 8

Therefore, the 7th number is 8. Answer B is correct.

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The roots have positive or same signs when c>0.

Note that only real numbers can be positive or negative. This concept does not apply to complex non real numbers. So first we have to make sure that the roots are real which occurs when discriminant is greater or equal to 0.

[tex]b^{2} -2ac > 0\\2^{2} -2(-1) (c) > 0\\4-2c > 0\\c > -2[/tex]

Roots of quadrant equation have Samsame sign if product of roots >0.

[tex]\frac{a}{c} > 0\\\frac{c}{-1} > 0\\c < 0[/tex]

Roots of quadratic equation have positive sign if product of roots<0.

c>0.

Combining results, we get:-

roots have positive signs when:-

c>0.

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We can solve this problem by using proportions.  20/16 = x/10 =>  x = 12.5  Therefore, the height of the maple tree is approximately 12.5 feet, to the nearest tenth of a foot.

what is   proportions ?

proportions are statements that two ratios or fractions are equal. A ratio is a comparison of two quantities, typically expressed as the quotient of one quantity divided by the other. For example, if we have 5 apples and 3 oranges, the ratio of apples to oranges is 5/3.

what is  height  ?

Height typically refers to the measurement of how tall or high something is, usually from its base to its top. In geometry, height is often used to refer to the perpendicular distance

In the given question ,

Let x be the height of the maple tree in feet. Then we have:

(height of statue) / (length of statue's shadow) = (height of maple tree) / (length of maple tree's shadow)

Substituting the given values, we get:

20/16 = x/10

on solving  this equation, we can cross-multiply to get:

16x = 200    =>      x = 12.5

Therefore, the height of the maple tree is approximately 12.5 feet, to the nearest tenth of a foot.

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The mean distance Jaison jogged over 9 days is 7 meters per day. This was calculated by adding up all the distances he jogged and dividing by 9.

To calculate the average distance that Jaison jogged over the 9 days, we used the formula for mean, which involves summing up all the distances he jogged and dividing by the total number of days. After adding up the distances, we found that the total distance Jaison jogged was 63 meters. Dividing this by the 9 days gives us an average distance of 7 meters per day. Therefore, Jaison jogged an average of 7 meters each day over the 9-day period.

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The compound interest for the principal value $400, interest rate 7% and compounded anually for 3 years is equals to the $90.2

Compound interest is defined as the interest earn on interest, i.e., here interest on interest . It is denoted by CI and calculated by the below formula, CI

= Amount - principal

and A = P( 1 + r/n)ⁿᵗ

where P --> principal

A --> amount

r --> interest rate

n --> the number of times interest is compounded per year

t --> time in years

Now, we have principal, P = $400

interest rate, r = 7%

time, t = 3 years

here, compounded anually for 3 years so, n= 1

Substitute all known values in above formula,

A = P( 1 + r/n)ⁿᵗ

=> A = 400( 1 + 7/100)³

=> A = 400( 107/100)³

=> A = $490.02.

So, compound interest = A - P

=> CI = $90.2

Hence, required value is $90.2.

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Complete question:

Principal $400 interest rate 7% compounded anually years 3. Calculate the compound interest three years.

The amount of money the manufacturer should expect to pay in refunds is 32.76X dollars.

Let Y denote the life in years of a printer, which is exponentially distributed with mean 3 years. Therefore, the rate parameter λ of the exponential distribution is λ = 1/3, which is obtained from the formula of the exponential distribution, E(Y) = 1/λ = 3 years. The probability that a printer fails during the first year following its purchase is:

P(Y < 1) = F(1) = 1 - e-λt = 1 - e-1/3(1) = 0.2835

The probability that a printer fails during the second year following its purchase is:

P(1 < Y < 2) = F(2) - F(1) = e-1/3(2) - e-1/3(1) = 0.3219 - 0.2835 = 0.0384

The probability that a printer does not fail during the first two years is:

P(Y > 2) = 1 - F(2) = 1 - e-1/3(2) = 0.6797

Let X denote the refund payment in dollars that the manufacturer should pay to the buyer of a printer if the printer fails during the first year, and X/2 denote the refund payment if the printer fails during the second year. Then, the total refund payment per printer is R = XI(Y < 1) + XI(1 < Y < 2)/2 = XI(Y < 1) + (X/2)I(1 < Y < 2), where I(.) is the indicator function that takes the value of 1 if the condition in the parentheses is true and 0 otherwise. The expected value of the total refund payment per printer is:

E(R) = E[XI(Y < 1)] + E[(X/2)I(1 < Y < 2)]

= X(0.2835) + (X/2)(0.0384) = 0.3276X

Hence, the expected total refund payment for 100 printers is:

Expected total refund payment = 100E(R) = 100(0.3276X) = 32.76X dollars. The amount of money the manufacturer should expect to pay in refunds is 32.76X dollars.

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Answer:

Step-by-step explanation:

71/8*9 which it 639/8 feet long