what’s the coefficients of the polynomials?

a.  The ratio of Es to Ns in percentage is 64%

b. Probability that it will take at least five patients to find one patient on whom the medicine would not be effective is impossible to estimate this probability from the table.

c. The probability that the medicine will be effective on exactly three out of four randomly selected patients is  12.9%

a. The total number of patients in the table is 50.

To calculate the ratio of Es to Ns in percentage, we count the number of Es and Ns and divide the number of Es by the number of Ns and Es combined, and then multiply by 100. Counting the table, we find that there are 32 Es and 18 Ns. So, the ratio of Es to Ns in percentage is:

32 / (32 + 18) * 100 = 64%

b. To estimate the probability that it will take at least five patients to find one patient on whom the medicine would not be effective, we need to look at the runs of Ns in the table. We can see that there are no runs of five or more Ns, so it is impossible to estimate this probability from the table.

c. To estimate the probability that the medicine will be effective on exactly three out of four randomly selected patients, we need to count the number of ways we can choose three Es and one N, and divide by the total number of possible outcomes of selecting four patients from the table. The total number of possible outcomes is:

50 choose 4 = 50! / (4! * (50-4)!) = 230300

The number of ways we can choose three Es and one N is:

32 choose 3 * 18 choose 1 = (32! / (3! * (32-3)!)) * (18! / (1! * (18-1)!)) = 32 * 31 * 30 / (3 * 2) * 18 = 32 * 31 * 30 * 18 / 6 = 297120

So, the estimated probability that the medicine will be effective on exactly three out of four randomly selected patients is:

297120 / 230300 ≈ 0.129 or about 12.9% (rounded to the nearest tenth of a percent).

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John would have the option of taking 10 different cones

The questions says that there is the option of having the flavors that are available ice cream flavors are: chocolate (C), mint chocolate chip (M), strawberry (S), rainbow sherbet (R), and vanilla (V).

The available flavors are then 5 in number

Then the number of scoops that he can have from each of the cone is said to be 2

Hence we would have 5 x 2

= 10

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The distance the boat travels to get to the beach is approximately 5.0 miles.

To see why, we can draw a right triangle on the coordinate plane, with one leg along the x-axis (going 3.5 miles east) and the other leg along the y-axis (going 4 miles south). The hypotenuse of this triangle is the straight distance from the marina to the beach, which is the distance the boat travels.

Using the Pythagorean theorem, we can find the length of the hypotenuse:

c^2 = a^2 + b^2

c^2 = (3.5)^2 + (4)^2

c^2 = 12.25 + 16

c^2 = 28.25

c ≈ 5.0

Therefore, the distance the boat travels to get to the beach is approximately 5.0 miles.

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The function for Drake's monthly phone bill, C(t), is C(t) = 35 + 0.05t, where t represents the number of texts sent.

Drake has two components to his monthly phone bill: the base cost of $35 and the additional cost for texts sent. The base cost is fixed, meaning it does not change, so we can represent it as a constant value in the function (35).

The cost per text is $0.05, which means it varies depending on the number of texts sent (t). To find the total cost (C(t)), we need to add the fixed cost ($35) and the variable cost ($0.05 times the number of texts). Therefore, the function representing Drake's monthly phone bill cost is C(t) = 35 + 0.05t.

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Each serving of cider contains 0.08 tablespoons of cinnamon.

Eric uses 2 tablespoons of cinnamon for a batch of cider that makes 25 servings. To find out how much cinnamon is in each serving, we need to divide the total amount of cinnamon used by the number of servings.

tablespoons/tablespoons= tablespoons per serving

2 tablespoons / 25 tablespoons = 0.08 tablespoons per serving

Therefore, there is 0.08 tablespoons of cinnamon in each serving of cider.

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The model approximates the volume, V, in liters, of air in the lungs during a five-second respiratory cycle using the equation V = -0.0374t + 3 + 0.1525t^2 + 0.1729t.

The given equation represents a mathematical model for estimating the volume of air in the lungs during a respiratory cycle. It is a quadratic equation with three terms: -0.0374t, 0.1525t^2, and 0.1729t.

The term -0.0374t represents the linear decrease in volume over time, indicating that the volume decreases by 0.0374 liters for every second of the respiratory cycle.

The term 0.1525t^2 represents the quadratic relationship between volume and time squared, indicating that the rate of change of volume with respect to time is influenced by the square of time.

The term 0.1729t represents the linear increase in volume over time, indicating that the volume increases by 0.1729 liters for every second of the respiratory cycle.

Overall, this model provides an approximation of the volume of air in the lungs during a five-second respiratory cycle, taking into account both linear and quadratic relationships with time.

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The number of nickels and pennies in the pocket is 5 and 16 respectively.

To find the number of coins, Let's assume the number of nickels is x and the number of pennies is y.

According to the problem, we have two equations:

The total value of the coins is $0.41:

0.05x + 0.01y = 0.41

The total number of coins is 21:

x + y = 21

Now we can solve this system of equations to find x and y. One way to do this is to use substitution.

Solving the second equation for y, we get:

y = 21 - x

Substituting this into the first equation, we get:

0.05x + 0.01(21 - x) = 0.41

Simplifying:

0.05x + 0.21 - 0.01x = 0.41

0.04x = 0.2

x = 5

So we have 5 nickels.

Substituting this into the equation y = 21 - x, we get:

y = 21 - 5 = 16

So we have 16 pennies.

Therefore, the number of nickels and pennies in the pocket is 5 and 16 respectively.

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The value of the variables are a = 1 and b = -1

Given that the equations are;

a - 3 = 2b

4a + 5b- 8 = 0

Using the substitution method, we have;

Make 'a' the subject of formula from equation (1)

a = 2b + 3

Now, substitute the value of the variable in the second equation

4(2b + 3) + 5b - 8 = 0

expand the bracket, we have;

8b + 12 + 5b - 8 = 0

collect the like terms, we get;

8b + 5b = 0 - 5

add or subtract the values

5b = -5

b = -1

Substitute the value of b as =-1

a = 2(-1) +3

expand the bracket

a = -2 + 3

a = 1

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Where the above graph and conditions are given,  the value of k that satisfies g(x) = f(x+k) is k = -2.

We can determine the value of k by using the given relationship between g(x) and f(x+k).

If g(x) = f(x + k), then we can substitute the given values of x in g(x) to get:

g(-1) = f(-1 + k) --> 5 = f(-1 + k)

g(0) = f(0 + k) --> 4 = f(k)

g(1) = f(1 + k) --> 3 = f(1 + k)

g(2) = f(2 + k) --> 2 = f(2 + k)

g(3) = f(3 + k) --> 3 = f(3 + k)

We know that f(x) is a v-shaped graph with a vertex at (0,2) and points at (-1,3) and (1,3). Therefore, we can conclude that f(k) = 4, which means that k is the x-coordinate of the vertex of f(x) shifted to the left or right.

Since the vertex of f(x) is at (0,2), and the x-coordinate of the vertex of f(x+k) is at k, we have:

k = 0 --> vertex of f(x+k) is at (0,2)

k = -1 --> vertex of f(x+k) is at (-1,2)

k = 1 --> vertex of f(x+k) is at (1,2)

k = 2 --> vertex of f(x+k) is at (2,2)

Therefore, the value of k that satisfies g(x) = f(x+k) is k = -2.

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Based on the trend line and slope, Tony's expected salary of $70,000 after 15 years of employment at Company Z is reasonable, as it falls within the range of salaries predicted by the line of best fit.

First, we need to find the equation of the trend line. To do this, we use the least squares regression method to find the line that best fits the data. Let x be the years of employment and y be the annual salary. We can calculate the slope and y-intercept of the trend line using the following formulas

slope = (nΣ(xy) - ΣxΣy) / (nΣ(x²) - (Σx)²)

y-intercept = (Σy - slopeΣx) / n

where n is the number of data points, Σ represents the sum of, and ( )² denotes squared.

We can use the given data to calculate the values needed for the formulas. Let's denote the years of employment as x and the annual salary as y.

x: 1 2 3 4 5 6

y: 45 50 55 60 65 70

n = 6

Σx = 1 + 2 + 3 + 4 + 5 + 6 = 21

Σy = 45 + 50 + 55 + 60 + 65 + 70 = 345

Σxy = (145) + (250) + (355) + (460) + (565) + (670) = 1305

Σ(x²) = 1² + 2² + 3² + 4² + 5² + 6² = 91

Now we can plug these values into the formulas to find the slope and y-intercept

slope = (61305 - 21345) / (691 - 21²) = 5

y-intercept = (345 - 521) / 6 = 20

We can write the equation of the trend line in the form y = mx + b, where m is the slope and b is the y-intercept

y = 5x + 20

Finally, we can use this equation to estimate Tony's salary after 15 years of employment

y = 5(15) + 20 = 95

Based on the trend line and slope, we would expect Tony's salary to be about $95,000 after 15 years of employment.

This is higher than his expected salary of $70,000, so it may not be a reasonable expectation. However, it's important to note that the trend line is just an approximation and there may be other factors that could affect Tony's salary.

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The surface area of the first triangular prism is 174.58 square feet and second triangular prism is 1721.6 square feet.

To calculate the surface area of a triangular prism, we need the measurements of the base and the height of the triangular bases, as well as the length of the prism.

For the first triangular prism with measurements:

Base: 5 ft

Height: 8 ft

Length: 6 ft

To calculate the surface area, we need to find the areas of the two triangular bases and the three rectangular faces. The formula for the surface area of a triangular prism is:

Surface Area = 2 * (Area of triangular base) + (Perimeter of triangular base * Length)

The area of a triangle can be calculated using the formula: Area = 1/2 * Base * Height.

Area of triangular base = 1/2 * 5 ft * 8 ft = 20 ft²

The perimeter of a triangle is the sum of its three sides.

Perimeter of triangular base = 5 ft + 8 ft + √(5 ft² + 8 ft²) = 5 ft + 8 ft + √89 ft ≈ 5 ft + 8 ft + 9.43 ft ≈ 22.43 ft

Surface Area = 2 * 20 ft² + (22.43 ft * 6 ft) = 40 ft² + 134.58 ft² = 174.58 ft²

Therefore, the surface area of the first triangular prism is approximately 174.58 square feet.

For the second triangular prism with measurements:

Base: 6 ft

Height: 2.5 ft

Length: 115 ft

Area of triangular base = 1/2 * 6 ft * 2.5 ft = 7.5 ft²

Perimeter of triangular base = 6 ft + 2.5 ft + √(6 ft² + 2.5 ft²) = 6 ft + 2.5 ft + √40.25 ft ≈ 8.5 ft + 6.34 ft ≈ 14.84 ft

Surface Area = 2 * 7.5 ft² + (14.84 ft * 115 ft) = 15 ft² + 1706.6 ft² = 1721.6 ft²

Therefore, the surface area of the second triangular prism is approximately 1721.6 square feet.

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The surface area of the triangular prism is x - 0 = -3

If the solution to an absolute value equation is x = -3, then we know that the distance between x and 0 is 3 units. Since the absolute value of a number is the distance between the number and 0 on the number line, we can write the absolute value equation that corresponds to x = -3 as:

| x - 0 | = 3

To write this equation in the form x - b = c, we can simplify the absolute value expression by removing the absolute value bars. This gives us two possible equations:

x - 0 = 3 or x - 0 = -3

Simplifying further, we get:

x = 3 or x = -3

Therefore, the absolute value equation in the form x - b = c that has the solution set {x = -3} is:x - 0 = -3

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The mean of a single roll is given as μ = 3.5, and the variance is given as [tex]σ^2[/tex] = 2.92.

The sample size for the first five rolls is n1 = 5, and the sample size for the remaining ten rolls is n2 = 10.

The mean of the sampling distribution of the difference in sample means x¯1−x¯2 is given as:

μ(x¯1−x¯2) = μ(x¯1) - μ(x¯2) = μ - μ = 0

The variance of the sampling distribution of the difference in sample means x¯1−x¯2 is given as:

σ^2(x¯1−x¯2) = (σ^2(x¯1)/n1) + (σ^2(x¯2)/n2)

where σ^2(x¯1) is the variance of the sample mean for the first five rolls and σ^2(x¯2) is the variance of the sample mean for the remaining ten rolls.

Since each roll of the die is independent, the variance of the sample mean for each sample is given as:

σ^2(x¯1) = σ^2/ n1 = 2.92/5 = 0.584

σ^2(x¯2) = σ^2/ n2 = 2.92/10 = 0.292

Substituting these values in the above equation, we get:

σ^2(x¯1−x¯2) = (0.584/5) + (0.292/10) = 0.1468

Therefore, the standard deviation of the sampling distribution of the difference in sample means x¯1−x¯2 is:

σ(x¯1−x¯2) = sqrt(σ^2(x¯1−x¯2)) = sqrt(0.1468) = 0.3835 (rounded to four decimal places)

Hence, the standard deviation of the sampling distribution of the difference in sample means x¯1−x¯2 is 0.3835.

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About 125 students play a sport and about 65 students are in the play.

To find the number of students who play a sport and those who are in the play, we need to use the given percentages and round the answers to the nearest whole.
Find the number of students who play a sport:
Multiply the total number of students (145) by the percentage of students who play a sport (86%).
145 × 0.86 = 124.7
Round the answer to the nearest whole number:
Approximately 125 students play a sport.
Find the number of students who are in the play:
Multiply the total number of students (145) by the percentage of students who are in the play (45%).
145 × 0.45 = 65.25
Round the answer to the nearest whole number:
Approximately 65 students are in the play.

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Answer:

Step-by-step explanation:

(2-5)3=-9. (-9)5 =-45

The form in which is easier to identify the x-intercepts is the one in option B. Intercept form.

If a quadratic equation has a leading coefficient a and x-intercepts x₁ and x₂, then the quadratic equation can be written as:

y = a*(x - x₁)*(x - x₂)

That is called the factored form or the intercept form.

Notice that if the quadratic equation is written in that form, is really easy to identify the x-intercepts of the equation, then that would be the most beneficial form in order for Kristen to quickly identify the coordinates, the correct option is B.

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Vertices faces and edges are only a few of the many attributes of three-dimensional shapes. The 3D shapes' faces are their flat exteriors. An edge is the section of a line where two faces converge.

1) cube

A vertex is the intersection of three edges. A solid or three-dimensional form with six square faces is called a cube. These are the characteristics of the cube.

Every edge is equal.

8 vertex

6 faces  

12 edges

2) Cuboid

When the faces of a cuboid are rectangular, it is often referred to as a rectangular prism. The angles are all 90 degrees each. It has a cuboid.

8 vertex

6 faces

12 edges

3) Prism

A prism is a three-dimensional form with two equal ends, flat faces, and identical sides.l cross-section down the length of it. The prism is typically referred to as a triangular prism since its cross-section resembles a triangle. There is no bend to the prism. A prism has also

6 vertex

9 edges

2 triangles and 3 rectangles

5 faces.

4) Pyramid

A pyramid is a solid object with triangle exterior faces that converge at a single point at its summit. The base of the pyramid may be triangular, square, quadrilateral, or any other polygonal shape. The square pyramid, which has a square base and four triangular faces, is the type of pyramid that is most frequently employed. Take a look at a square pyramid.

5 vertices

5 faces

8 edges

5) Cylinder

The term "cylinder" refers to a three-dimensional geometrical shape.two circular bases joined by a curving surface make up this figure. In a cylinder,

no vertex

2 edges

2 circles on flat faces

one curving face

6) Cone

A cone is a three-dimensional thing or solid with a single vertex and a circular base. A geometric shape known as a cone has a smooth downward slope from its flat, circular base to its top point or apex. In a cone

one vertex

1 edge

1 circle with a flat face.

one curving face

7) Sphere

A sphere is a perfectly round, three-dimensional solid figure, and every point on its surface is equally spaced from the point, which is known as the center. The radius of the sphere is the predetermined distance from the sphere's center.

a sphere is

zero vertex

zero edges

one curving face

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The length of side a is 50 if the angle ∠bac is 50° and the length of side b is 20 and side c is 35 using cosine law.

Length of side b = 20

Length of side c = 35

Angle ∠bac =  50°

To calculate the length of the side a, we need to use the cosine law. The formula is:

[tex]a^2 = b^2 + c^2 - 2bc cos(A)[/tex]

Substituting the given values in the formula, we get:

[tex]a^2 = 20^2 + 35^2 - 2(20)(35)cos(50°)[/tex]

[tex]a^{2}[/tex] = 400 + 1225 + (1400)*(0.642)

[tex]a^{2}[/tex] = 1625 + 898.8

a = [tex]\sqrt{2523.8}[/tex]

a = 50

Therefore we can conclude that the length of side a is 50 using cosine law.

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Answer:

40.7, my answer needs to be 20+ characters sooo....

5.13 U. S. Dollars will it cost to buy a gallon of gas in Canada. The correct answer to the question is A

Given in the question,

Cost of 1 liter gasoline = 1.50 Canadian dollars

1 gallon = 3.8 liters

Thus, to calculate the price of 1 gallon we multiply the cost of 1 liter by 3.8

Cost of 3.8 liters of gasoline = 1.5 * 3.8

= 5.70 Canadian dollars

1 Canadian dollar = 0.9 U. S. dollars

5.70 Canadian dollars = 5.70 * 0.9

= 5.13 U. S. dollars

That is the cost of 1 gallon of gas in Canada is 5 U S dollars and 13 cents.

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Answer:

0.8660

Step-by-step explanation:

sin24=opposite ÷hypotenus

sin24=opposite ÷5

cross multiply

sin24x5=opposite

sin24=0.4067x5

opposite =0.8660

This prompt is about probability. The answers are given as follows;

Identifying the   probability of an event is crucial to making predictions based on its likelihood. T his involves calculating the probability either through historical data or experimentation.

Once determined, utilizing this value enables one to make future predictions regarding the occurrence of such events; for instance, 80% probability of precipitation tomorrow implies an 80% chance of rain.

Calculating probabilities has proven essential to sports betting because it helps bookmakers given some degree of foresight on which teams are going to win specific games or tournaments. Operating under the premise that there will always be two probable outcomes (either one side wins while another loses), these bookmakers could assign numerical values on what percentage they deem worthy enough for each team's chances.

Subsequently, using precise mathematical formulas and equations, bettors assess wagering-related uncertainties based on these predetermined likelihoods before deciding whether or not they should place money bets.

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The height of the outside is given as 17.44 meters

The equation of hyperbola is :

[tex]y^2 - x^2 = 38[/tex]

=>[tex]y^2/38 - x^2/38 = 1[/tex]

(of the form [tex]y^2/a^2 - x^2/b^2 = 1[/tex] and transverse axis is y-axis.)

Here, [tex]a^2 = b^2 = 38[/tex]

[tex]c^2 = a^2 + b^2 = 38+38 = 76[/tex]

( a is the distance of vertices from the center and c is the distance of foci from the center.)

Distance between walls = 2 a = [tex]2*\sqrt(38) = 12.33[/tex] meters at the center

and = [tex]2c = 2*\sqrt(76) = 17.44[/tex] meters at the end when the line joining

end points of the wall on one side is through the foci point.

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the measurement of the couch in the scale drawing would be 15 inches.

We can precisely portray locations, areas, structures, and details in scale drawings at a scale that is either smaller or more feasible than the original.

When a drawing is said to be "to scale," it signifies that each piece is proportionate to the real or hypothetical entity; it may be smaller or larger by a specific amount.

When something is described as being "drawn to scale," we assume that it has been printed or drawn to a conventional scale that is accepted as the norm in the construction sector.

When our awareness of scale improves, we are better able to quickly recognize the spaces, zones, and proposed or existent spatial relationships when looking at a drawing at a given scale.

One metre is equivalent to one metre in the actual world. When an object is depicted at a 1:10 scale, it is 10 times smaller than it would be in real life.

You might also remark that 10 units in real life are equivalent to 1 unit in the illustration.

To determine the measurement of the couch in the scale drawing, we can use the scale factor provided:

1/4 inch = 2 feet

This means that every 1/4 inch in the drawing represents 2 feet in real life.

To find the measurement of the couch in the drawing, we need to convert its actual size to the corresponding size in the drawing using the scale factor.

First, we can convert the actual size of the couch to feet:

10 ft = 10 ft x 12 inches/ft = 120 inches

Next, we can use the scale factor to convert the actual size to the corresponding size in the drawing:

1/4 inch = 2 feet

1 inch = 8 feet (multiplying both sides by 4)

So, 120 inches in real life is equal to:

120 inches / 8 feet per inch = 15 inches in the drawing

Therefore, the measurement of the couch in the scale drawing would be 15 inches.

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The surface area of the pyramid is 390.8 cm².

The surface area of the triangular pyramid is calculated as follows;

S.A = base area   +  ¹/₂ (perimeter + slant height)

The height of the pyramid is calculated by applying Pythagoras theorem;

h = √ (28²  -  14²)

h = 24.2 cm

Area of the base = ¹/₂ x 28 cm x 24.2 cm = 338.8 cm²

The surface area of the pyramid is calculated as follows;

S.A = 338.8 cm²  + ¹/₂ (76 cm + 28 cm)

S.A = 390.8 cm²

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Answer:

1,425

Step-by-step explanation:

I got this one correct

Answer:

252 mi

Step-by-step explanation:

volume= L x W x H

9x 7 x 4 = 252 mi

The inequality to solve is 56 - x > 0. The solution is x < 56. Therefore, the domain of the function g(x) is x < 56. So, the answer is option B.

The function is defined as g(x) = log(56 - x).

The domain of a logarithmic function is all the values that make the argument of the logarithm positive. In other words, the argument of the logarithm (56 - x) must be greater than 0.

So, we solve the inequality 56 - x > 0 for x

56 - x > 0

Subtract 56 from both sides

-x > -56

Divide both sides by -1, and remember to reverse the inequality

x < 56

Therefore, the domain of the function g(x) is all real numbers x such that x < 56. So, the correct answer is B).

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--The given question is incomplete, the complete question is given

" The domain of g(x) = log 56 - x) can be found by solving the inequality

A. 56-x<0 ,B. 56-x>0,C. 56-x>=0, D. 56-x<=0 "--

Answer:

  g(x) = h(x -7) +5

Step-by-step explanation:

Given h(x) defines a parabola that opens upward with a vertex at (-2, -7) and g(x) defines the same parabola with its vertex at (5, -2), you want to express g(x) in terms of h(x).

The graph of f(x) is translated right h units and up k units by ...

  f(x -h) +k

We see that g(x) is a translation of h(x) right by 7 units and up by 5 units. This means (h, k) is (7, 5), and the translated function is ...

  g(x) = h(x -7) +5

__

Additional comment

This is confirmed by the plots in the second attachment.

Answer:  g(x)=h(x-7) +5

Step-by-step explanation:

The graph g(x) has been shifted up 5   (+5)   and right 7

When shift a function, the y change, up/down, goes at end of function

When shift in x direction happens, you take opposite sign so we will do -7

g(x)=h(x-7) +5

The score that marks the 11% of all scores is approximately 56.875 .

To find the score that marks the 11% of all scores, we need to use the standard normal distribution table, also known as the Z-table, since the given distribution is a normal distribution.

The first step is to find the Z-score that corresponds to the 11th percentile, which is given by: Z = invNorm(0.11) ≈ -1.225

Here, "invNorm" represents the inverse of the standard normal cumulative distribution function, which can be computed using statistical software or a calculator.

The second step is to use the Z-score formula to find the raw score that corresponds to this Z-score:Z = (X - μ) / σ

where X is the raw score we want to find, μ is the mean of the distribution, and σ is the standard deviation. Plugging in the values we have:

-1.225 = (X - 63) / 5

Solving for X, we get:

X = -1.225 * 5 + 63 = 56.875

Therefore, the score that marks the 11% of all scores is approximately 56.875

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Therefore, the polynomial p(x) that satisfies the given conditions is:

p(x) = ax^3 + bx^2 + cx + d
p(x) = x^3 - 2x^2 + 3x + 23

So, p(2) = 1(2)^3 - 2(2)^2 + 3(2) + 23 = 9.

To find a polynomial p(2) of degree three, we need four pieces of information. We can use the given values to set up a system of linear equations:

-7a + 2b - 4c + d = 3
-a - b + c - d = 3
7a + b + c + d = -9
8a + 4b + 2c + d = -33

We can solve this system using any method of linear algebra. One way is to use row reduction:

[ -7  2 -4  1 |  3 ]
[ -1 -1  1 -1 |  3 ]
[  7  1  1  1 | -9 ]
[  8  4  2  1 | -33 ]

R2 + R1 -> R1:
[ -8  1 -3  0 |  6 ]
[ -1 -1  1 -1 |  3 ]
[  7  1  1  1 | -9 ]
[  8  4  2  1 | -33 ]

R3 - 7R1 -> R1, R4 - 8R1 -> R1:
[ -8  1 -3  0 |  6 ]
[  0 -7  8 -1 | 51 ]
[  0 -4  4  1 |-51 ]
[  0  4 26  1 |-81 ]

R4 + R2 -> R2:
[ -8  1 -3  0 |  6 ]
[  0 -3 34  0 | 30 ]
[  0 -4  4  1 |-51 ]
[  0  4 26  1 |-81 ]

R3 + (4/3)R2 -> R2:
[ -8  1 -3  0 |  6 ]
[  0 -3 34  0 | 30 ]
[  0  0 50  4 |-11 ]
[  0  4 26  1 |-81 ]

R4 - (4/3)R2 -> R2, R3 - (5/6)R2 -> R2:
[ -8  1 -3  0 |  6 ]
[  0 -3 34  0 | 30 ]
[  0  0  8  4 |-34 ]
[  0  0  8  1 |-103 ]

R4 - R3 -> R3:
[ -8  1 -3  0 |  6 ]
[  0 -3 34  0 | 30 ]
[  0  0  8  4 |-34 ]
[  0  0  0 -3 |-69 ]

Now we can back-substitute to find the coefficients of the polynomial:

d = -69/(-3) = 23
c = (-34 - 4d)/8 = 3
b = (30 - 34c + 3d)/(-3) = -2
a = (6 + 3b - 3c + d)/(-8) = 1

Learn more about polynomial here:

https://brainly.com/question/11536910

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