Question 14 (5 points)
Solvex² - 2x=15 by applying the quadratic formula.
Ox= 1 + √14i, x = 1 - √√14i
Ox = -5, x = 3
Ox = 5, x = -3
Ox= -1 + √14i, x = -1 - √√14i

The value of k should be less than 6.

Equation is defined as a relation that equates two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. A quadratic equation is of the form -

ax² + bx + c = 0.

Given is the quadratic equation as -

kx² - 2kx + 6 = 0

For no real roots, We can write -

b² - 4ac < 0

(-2k)² - 24k < 0

4k² - 24k < 0

k(4k - 24) < 0

k < 0 and 4k - 24 < 0

k < 0 and k < 6

k < 6

Therefore, the value of k should be less than 6.

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Answer:The lateral surface area of the triangular prism will be 84 square feet.correct option is D.

What is the surface area of the triangular prism?Let the sides of the triangle be a, b, c, and a height of H. Then the surface area of the prism is given as SA = H(a + b + c)A triangular prism has bases with three congruent sides, each measuring 4 feet. The height of each triangle is approximately 3.5 feet.The distance between the triangular bases is 7 feet.Then the lateral surface area will beSA = 7 (4 + 4 + 4)SA = 7 x 12SA = 84 square feet. the correct option is D

Step-by-step explanation:

The amount of zinc oxide need to be added to 450 g of 1.5% ointment to make a 11% zinc oxide ointment is 48 gram.

A fraction represent the number of parts in total or whole. Fraction is sometimes denoted in percentage, e.g. 20% means a fraction of 20/100.

In the given problem, let w is the amount of zinc oxide need to be added.

Original weight of Zinc oxide = 1.5% x 450 g

After adding w gram of zinc oxide, weight of zinc oxide = 1.5% x 450 + w

Original weight of ointment = 450 g

After adding w gram of zinc oxide, weight of ointment = 450 + w

Hence, the new fraction of zinc oxide:

(1.5% x 450 + w) / (450 + w) = 11%

1.5% x 450 + w = 11% x 450 + 11% w

9.5% x 450 = 89% w

w = 48

Hence, the amount of zinc oxide need to be added is 48 gram.

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The inverse function of f(x) is [tex]\frac{x + 2}{3}[/tex] and [tex]f^{-1}(13)[/tex] = 5

What is an inverse function?

An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by [tex]f^{-1}[/tex] One should not confuse (-1) with exponent or reciprocal here.

if f(x) = 3x - 2

setting y = 3x - 2 and making x the subject of the formulae,

we have

3x - 2 = y

3x = y + 2

x = [tex]\frac{y + 2}{3}[/tex]

replacing y with x and x with  [tex]f^{-1}[/tex](x)

[tex]f^{-1}[/tex](x) =   [tex]\frac{x + 2}{3}[/tex]

the value of  [tex]f^{-1}[/tex](13) , we substitute x = 13,

[tex]f^{-1}[/tex](13) = 13 + 2 / 3

[tex]f^{-1}[/tex](13) = 15/3

[tex]f^{-1}[/tex](13) = 5

In conclusion, the inverse function is  [tex]f^{-1}[/tex](x) = [tex]\frac{x + 2}{3}[/tex] and  [tex]f^{-1}[/tex](13) = 5

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The points of the vertices of the triangle after reflection on the line y = -x is given by A'(3,-3) , B'(-3,-6) and B'(-3,-6)  .

We know that when a point is reflected around a line on the coordinate axes then the coordinates reflect following some rules.

Now when the point (a,b) is reflected around the line y = -x then ,the coordinates of the image becomes (-b,-a)

Therefore :

A(3,-3)→A'(3,-3 , does not change as the point lies on the line y=-x)

B(6,3)→B'(-3,-6)

C(3,3)→B'(-3,-6)

In a transition known as reflection over a line k, each point of the original figure (pre-image) must have an image that is the same distance from the line of reflection as the first comment but is on the other side of the line. Remember that a flip is a reflection. The size of the figure does not alter when it is reflected.

A figure created by a line reflection that is consistent with the original figure is called an isometry (a transformation that preserves length). Because naming the figure in a reflection implies changing the order of the letters, a reflection is more accurately referred to as a non-direct or opposing isometry .

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Answer: 3 -3 -3

-3 -6 -3

Step-by-step explanation:

A 36-month-old boy has the expected height, as an adult is 66 inches.

What is a linear equation?

A linear equation is an algebraic equation with only a constant and a first-order (linear) term of the form y=mx+b, where m is the slope and b is the y-intercept. The above is sometimes referred to as a "linear equation of two variables," where y and x are the variables.

We have,

The equation: y = 3.5x - 60,

The height of the 36-month-old boy is 36 inches,

we just need to use the value of x = 36 in the equation, and then we get the value of y:

y = 3.5x - 60

y = 3.5 * (36) - 60

y = 66 inches

Hence, his expected height, as an adult is 66 inches.

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The total number of pieces that Preston's brother has left is 24.

What is the subtraction operation?

In mathematics, the operation of eliminating items from a collection is represented by the subtraction operation. The negative symbol (-) is used to denote subtraction.

Given, Preston and his brother collected 53 pieces of candy.

Each of them ate 5 pieces of candy.

And, Preston had 19 pieces left.

The number of candies Preston's brother have left = 53 - (5*2 + 19) = 24

Hence, the total number of pieces that Preston's brother has left is 24.

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Answer:

-5

Step-by-step explanation:

its because each term is being mutliplied by -5

hopes this helps please mark brainliest

Answer:

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

The mean is 65.0646 and standard deviation is 39.082 when we can see the complete form of the table in the picture.

Given that,

As seen in the spreadsheet file P05 63.xlsx, two gamblers engage in a game of wheel-based roulette. Each gambler lays four bets, but each uses a different strategy, as will be seen later. Use the probabilities to determine the distribution of each gambler's net earnings after four bets. Then calculate their net wins' mean and standard deviation. You can get going with the file.

We have to find the mean and standard deviation.

We know that,

In the picture we can see the complete table.

Here, we calculated probability as,

For example take a first row

P(red=4, black=0, green=0) = (18/37)⁴ + 0 + 0 = 0.056

So the mean is 65.0646 and standard deviation is 39.082.

Therefore, The mean is 65.0646 and standard deviation is 39.082 when we can see the complete form of the table in the picture.

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If an environmentalist group wishes to measure the amount of dissolved oxygen per liter of water in a local stream, then the detailed solution is down below.

A dataset's variability is quantified by its standard deviation. It is determined by taking the square root of the variance, which is the sum of the squared deviations between each value in the dataset and its mean. How far a dataset's individual values deviate from its mean is determined by its standard deviation. A low standard deviation suggests that the dataset's values are close to the mean, whereas a large standard deviation suggests that the dataset's values are widely dispersed. When comparing the spread of two or more datasets, standard deviation is frequently utilised. It is a widely used statistical measure of dispersion.

How to solve?

a. The point estimate for the average amount of dissolved oxygen is 4.62 mg.

b. The distribution to use to construct the confidence interval is student-t.

c. Provide the values A - E for this problem on the following graph.

A. The sample mean is 4.62 mg.

B. The sample standard deviation is 0.92 mg.

C. The degrees of freedom for the student-t distribution is 45 - 1 = 44.

D. The t-value for a 90% confidence interval with 44 degrees of freedom is 1.699.

E. The error bound or margin of error is 0.92 mg * 1.699 = 1.57 mg.

d. The Confidence Interval is (4.62 - 1.57, 4.62 + 1.57) = (3.05, 6.19) mg, which means the error bound (or margin of error) is 1.57 mg.

e. The interpretation of this interval is that the environmentalists are confident that the true amount of dissolved oxygen in the stream is between 3.05 mg and 6.19 mg.

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The two numbers among them are such that one divides the other.

The Collection of well-defined objects or elements is known as a set. The objects in a set are called elements. The Set contains a finite number of elements. The Set is denoted by any capital letter like A, B etc. Elements of the set can be numbers, alphabets etc.

The elements of the set are listed inside the curly brackets { ..... }. There are various types of sets. Cardinal number or cardinality denotes the number of elements in the set. Cardinality is denoted by n( X ) where X is a set. The number of subsets of the set is given by 2^n.

As per the question,

Let us divide the set into two sets,

                A   =   { 1, 3 . . . . . n }    and   B   =   { 2, 4 . . . . . . 2n }

A and B contain the same number of elements i.e. two sets have equal sizes. Element of B is one of the elements of A multiplied by 2 or elements of B multiplied by 2. So, if we remove the powers of 2 i.e we divide each element by [tex]2^{k}[/tex]. Then there exist another 2 sets [tex]A ^{'}[/tex] and [tex]B^{'}[/tex] such that [tex]A ^{'}[/tex] U [tex]B^{'}[/tex] = [tex]A ^{'}[/tex] .

By using the pigeonhole principle, [tex]A ^{'}[/tex] consists of n elements and we add +1 to it additionally.

Therefore, When we are given n + 1 numbers from set { 1, 2 . . . .  2n }, there are two numbers among them such that one divides the other.

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Answer:

”fih” weighs 56 ounces

Step-by-step explanation:

8p=f

f+p=63

f- fih

p- parakeet

p+8p=63

9p=63

/9.  /9

p=7

Parakeet weighs 7 ounces now to find the weight of the fih

8(7)=f

56=f

Fih weighs 56 ounces

Hopes this helps please mark brainliest

Yes, there is a relationship exists between blood pressure and all of the factors recorded.

Blood pressure is the force of blood acting against the artery walls. The proper circulation of blood from the heart to the body's organs and tissues depends on normal pressure. Blood is pushed into the remainder of the body with each heartbeat. Pressure is higher close to the heart and lower farther away.

The amount of blood the heart pumps and the size of the arteries through which it travels are two factors that affect blood pressure. The pressure is typically higher the more blood being pumped and the narrower the artery. Systole, when the heart contracts, and diastole, when the heart relaxes, are both used to assess blood pressure.

Start by entering the data into the data table in Minitab. Select Multiple Regression, and then click OK in the Regression Analysis window. Choose Weight and Age as the Dependent and Pulse and Stress as the Independent variables in the Multiple Regression box. Next, select the OK button located in the Output box. The multiple regression fit is represented by the three values: umbcr: The weight and age regression coefficient has an umbcr value of 85.4. This indicates that the blood pressure rises by 0.84 mm Hg for every unit increase in weight and by 1.14 mm Hg for every unit increase in age.

Agc: The regression coefficient for age and weight has an agc value of 1.75. Accordingly, the heart rate rises by 0.075 beats per minute for every unit increase in weight and by 0.135 beats per minute for every unit increase in age. Weight BSA: The weight and body surface area's regression coefficient, or weight BSA, is 2.10. In other words, the body surface area grows by 0.21 square metres for every unit increase in weight and by 0.41 square metres for every unit increase in age.

Hypertension persistence: The regression coefficient for hypertension persistence is 87.01 years, and this number represents the persistence of hypertension. This means that the blood pressure rises by 3.06 mm Hg for every additional year of hypertension. Pulse: The pulse value, or the regression coefficient for pulse, is 905 beats per minute. This indicates that the blood pressure rises by 2.49 mm Hg for every additional beat per minute in the heartbeat. Stress index: The regression coefficient for the stress index is 943, and this is the stress index value. This means that the blood pressure rises by 2.35 mm Hg for every 1 unit increase in the stress index.

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The population proportion's 90% confidence interval is 0.824 < p < 0.876 when 85% of California people (428 out of 506 polled) believe that education is one of the state's most problems.

Given that,

85% of California people (428 out of 506 polled) believe that education is one of the state's most problems. For the true percentage of California adults who believe that education is one of the state's top problems, we want to build a 90% confidence interval.

We have to find the population proportion's 90% confidence interval.

We know that,

Let

n = 506, p = 0.85

90% Confidence interval :

At α = 0.1, two critical value, z base c = normal variable(0.1/2) = 1.645

Lower Bound = p - z base c×√(p ×(1- p)/n) = 0.85 - 1.645×√(0.85×0.15/506) = 0.824

Upper Bound = p + z base c×√(p ×(1- p)/n) = 0.85 + 1.645×√(0.85×0.15/506) = 0.876

0.824 < p < 0.876

Therefore, The population proportion's 90% confidence interval is 0.824 < p < 0.876 when 85% of California people (428 out of 506 polled) believe that education is one of the state's most problems.

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Answer:

6

Step-by-step explanation:

8 cube root is 2

there are 3 different lengths

3x2=6

There are 8 zeroes at the end of [tex]20!^{2}[/tex]

Here, we are given an expression- [tex]20!^{2}[/tex]

To find the number of zeroes in any expression, we need to find the number of multiples of 10 in the expression.

10 is made up of 2 prime numbers, that are- 2 and 5

Thus, the number of multiples of 5 and 2 will give us the number of zeroes.

In 20!, the multiples of 5 will be- 5, 10, 15 and 20

⇒ there are total 4 multiples of 5 in 20!

Now, looking at the multiples of 2, we can see that there will definitely be more than 4 multiples, some of them are- 2, 4, 6, 8, 10 and so on

But since there are only 4 multiples of 5, there will be only 4 multiples of 10 and hence only 4 zeroes in the expansion of 20!

If we square 20!, the number of zeroes will also double and become 8

Thus, there are 8 zeroes at the end of [tex]20!^{2}[/tex]

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The margin error is the amount that is added to and subtracted from a point estimate in order to create a confidence range for the population parameter.

The margin error, or error rate, in statistics refers to how inaccurate survey results utilizing random samples are. A larger statistical margin of error indicates a decreased likelihood of relying on a survey's or poll's results, indicating a decreased level of trust in the results' capacity to fairly represent a community. It is an essential tool for market research since it demonstrates the level of trust that should be placed by the researchers in survey results.

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The commission which real estate agency gets is $16885.

The commission which the agent get is $76750

The selling price for a house = $ 307,000

The commission rate for real estate agency = 5.5 %

The commission rate for the agent = 25 %

So, the commission which real estate agency gets:

= 5.5 % of $307,000

= 0.055 × $ 307,000

= $16885

The commission which agent get:

= 25% of $ 382,000

= 0.25 × $ 307,000

= $76750

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The average of a sum and the sum of the averages are not same.

The average of a sum is mean of sum of data. Total sum divided by total number of sum.

Whereas , The sum of the average is sum of mean of data. Total sum of averages of data.

These two terms are not same.

For example : Assume x₁ , x₂ , x₃ , . . . , xₙ be a data

S₁ , S₂ , . . . , Sₙ be sum of data

A₁ , A₂ , . . . , Aₙ be average of data

where n is total number of sum of data

The Average of sum will be = S₁ + S₂ + . . . + Sₙ / n

The sum of average will be = A₁ + A₂ + . . . + Aₙ

Hence, The average of sum and Sum of average are different.

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Answer:

A triangle where the angles in the inside are 100 degrees, 40 degrees, and 40 degrees.

Step-by-step explanation:

The angles inside a triangle always add up to 180 degrees

And an obtuse triangle is a triangle whose biggest angle is bigger than 90 degrees

100 is biggest angle out of the three angles we're using to make the triangle and 100 is bigger than 90.

Adding the three angles we're using also makes 180 (100 + 40 + 40)

The type of graph for a rational function is hyperbola

The parent function of a rational function is f(x)=1x and the graph is a hyperbola . The domain and range is the set of all real numbers except 0 . An excluded value in a rational function, is any x -value that makes the function value y undefined.

A hyperbola is an open curve with two branches, the intersection of a plane with both the halves of a double cone. The plane need not be parallel to the axis of the cone; the hyperbola will be symmetrical in any case.

Therefore, Hyperbola is the type of graph for a rational function.

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In Asian nations, augmentation rhinoplasty is one of the most often performed cosmetic operations, with silicone implants being the most frequently utilized component.

Despite potential benefits, the use of alloplastic materials in rhinoplasty is frequently avoided in Western nations due to worries about the possibility of infection and implant extrusion. The silicone augmentation rhinoplasty has become a widespread operation in Asia due to the region's cumulative experience with long-term positive results.

Surgical technique, implant design, and surgeon expertise all have a substantial impact on the likelihood of complications with silicone implants. If precautions are taken, silicone implants can be used safely for nasal dorsal augmentation.

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The rate constant of the scenario is 4 minutes

From the question, we have the following parameters that can be used in our computation:

Half completed in 2 minutes

This means that the full completion is 4 minutes

These parameters can be represented as

(x, y) = (1, 4)

The rate constant of the statement can then be represented as the slope and the slope is then calculated as

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (0, 0) and (1, 4)

Substitute the known values in the above equation

So, we have the following equation

rate constant = (4 - 0)/(1 - 0)

Evaluate the quotient

rate constant = 4

Hence, the rate constant is 4 minutes

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Every linear equation represents a relationship between the x and y values, a table of values represents just a few of the line's points.

In the given question we have to explain about a linear equation in a table.

We can generate a table of values for any line since every linear equation represents a relationship between the x and y values. These are the only x and y values for the specified line that are accurate. In other words, a table of values represents just a few of the line's points.

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Using the angle of elevation we calculate the height of the smaller building to be approximately 8.99 meters.

Let the height of the smaller building be x.

Distance between the two buildings = 18.5 meters.

Angle of elevation = 18°

From the properties of trigonometric ratios we know that:

tan 18° = (15 - x) / 18.5 as tan is the ratio of perpendicular and base of a triangle.

solving we get :

15 - x = 6.011 m

or, x = 8.99 m

The shorter building is approximately 8.99 meters tall.

The angle of elevation is described as "the angle formed between the horizontal line and the line of sight when an observer looks upwards" in mathematics. It is always higher and at a greater angle than the observer.

An angle of depression is produced when someone looks down, which is the opposite of an angle of elevation.

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The slope of that line is 1.031.

Given data,

There is a line through the origin that divides the region bounded by the parabola y = 5x - 3x² and the x-axis into two regions with equal area,

y = 5x - 3x²

5x - 3x² = 0

x(5 - 3x) = 0

x = 0 , x = 5/3

→ Area under y = 5x - 3x² is A = [0 to 5/3] 5x - 3x² dx

A = [0 to 5/3] 5x²/2 - 3x³/3

A = [0 to 5/3] 5x²/2 - x³

A = 5(5/3)2/2 - (5/3)3 = 125/54

∴ The lines passing through the origin are in the form of y = mx,

mx = 5x - 3x²

3x² + mx - 5x = 0

3x² + x(m -5) = 0

x(3x + (m -5)) = 0

x = 0 , x = (5 -m)/3

→ Area under y = 5x - 3x² and y = mx is (125/54)/2 = 125/108

∴ (5 -m)3/18 - (5 -m)3/27 = 125/108

(5 -m)3/54 = 125/108

(5 -m)3 = 125/2

(5 -m) = 3.9685

m = 5 - 3.9685

m = 1.0315

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In a case wherby Becky has a paper route and It takes her 50 minutes to deliver newspapers to her 40 customers  the unit rate in newspapers per minute is 4/5 customers per minutes.

The concept of raqte will be used, Rate can be described as the degree of something measured per unit of something else.

From the question,

50 minutes  will be used to deliver newspapers to her 40 customers, then thye rate can be written as 40 customers/ 50 minutes

This can be simplified as :

4 customers/5 minutes

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Step-by-step explanation:

Sin, Cos, and Tangent are the three common trig functions.

Sine, when given an angle, is a right triangle ratio between the opp side of the angle /hypotenuse(the side opposite of the right triangle),

SOH

Cosine, when given an angle, is a right triangle ratio between the adj side of the angle/hypotenus(the side opposite of the right triangle)

CAH

Tangent, when given an angle, is a right triangle ratio between the opp side of the angle/ adj side of the angle

TOA.

So

given an angle, alpha,

[tex] \sin( \alpha ) = \frac{o}{h} [/tex]

[tex] \cos( \alpha ) = \frac{a}{h} [/tex]

[tex] \tan( \alpha ) = \frac{o}{a} [/tex]

Problem 1, we know that the angle of reference is 53.1, the side adjacent to that angle is 30 cm, and we are trying to find x. and y.

Solving for x, the side length x is opposite of the angle 53.1

We have an angle, the adjacent side of the angle and the opposite side is what we are trying to find.

We use TAN

[tex] \tan(53.1) = \frac{x}{30} [/tex]

We know

[tex] \tan(53.1) = 1.33[/tex]

so

[tex]1.33 = \frac{x}{30} [/tex]

[tex]40 = x[/tex]

Now, since we know the side length of x, we have two ways to solve for y, which is the hypotenuse.

Remember the hypotenuse is the angle opposite of the 90° angle(right angle)

We could use Sine or Cosine

[tex] \sin( 53.1) = \frac{40}{y} [/tex]

[tex]0.8 = \frac{40}{y} [/tex]

[tex]y = \frac{40}{0.8} [/tex]

[tex]y= 50[/tex]

or

[tex] \cos(53.1) = \frac{30}{y} [/tex]

[tex]0.6 = \frac{30}{y} [/tex]

[tex]y = 50[/tex]

So x=40, y=50

2. Do the same steps above

Solving for x,

[tex] \sin(30) = \frac{x}{90} [/tex]

[tex]45 = x[/tex]

Solving for y,

[tex] \cos(30) = \frac{y}{90} [/tex]

cos(30)

[tex] \cos(30) = \frac{ \sqrt{3} }{2} [/tex]

so

[tex] \frac{ \sqrt{3} }{2} = \frac{y}{90} [/tex]

[tex]y = 45 \sqrt{3} = 77.942[/tex]

The graph of function f(x) is the one in option D.

To graph the function f(x), we just need to graph all the points on the table on a coordinate axis and then connect the points with a line.

Here we have the points:

(-2, 16/9)

(-1, 4/3)

(0, 1)

(1, 3/4)

(2, 9/16)

The graph of the five points can be seen in the image below.

Comparing it with the given options, we can see that the correct option is D.

(you can see that is not A because the first point is incorrect).

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