y = ax² + bx, where a and b are numbers. When x = 3, dy/dx = 18. When x = 5,dy/ dx = y. Work out the values of a and b. Give any decimal answers to 1 d.p.​

The simplified form of the expression given is 17/11.

What is simplifying an expression?

To simplify an expression, create a similar expression devoid of any similar terms. Therefore, we will rewrite the expression using the fewest number of terms possible.

To represent a mathematical expression in the simplest form possible is to simplify it. The expression is reduced to its most basic form when any redundant or redundant parts have been eliminated using the fundamental properties of numbers, exponents, algebraic rules, etc.

Consider, the given expression.

2/2 x 85/55

⇒  170 / 110

⇒ 17 / 11

Hence, the simplified form of the expression given is 17/11.

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Here that everything is divided equally, we can say that the percentage of the diagram that is shaded equals the number of shaded parts divided by the total number of parts in the diagram.

How many of these portions to darken is determined by the fraction's numerator:

By being able to see how these charts interfere with one another, you may better comprehend the solar access at that location. This graph depicts the surrounding skyline as seen from a certain place and the course of the sun.

P= [tex]r^{2}[/tex]

P = 6*6 =36 cm

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Answer:

Step-by-step explanation:

Look at the input and apply the rule. For example, if the rule is "Subtract 5" and the input is 9 then you subtract 5 from 9 to get 4, and 4 is the output. Let's take a look at some examples:

Explanation:

The two interior angles 55 and 6x+8 add to the exterior angle 14x-1; this exterior angle is not adjacent to the interior angles mentioned.

Refer to the Remote Interior Angle Theorem for more information.

So,

55+(6x+8) = 14x-1

6x+63 = 14x-1

6x-14x = -1-63

-8x = -64

x = -64/(-8)

x = 8

Then we can determine angle T

angle T = 6x+8 = 6*8+8 = 56 degrees

Probability is the branch of mathematics dealing with numerical descriptions of how likely a situation is to occur, or how likely it is that a proposition is true.

An expression for the probability of an event.

Probability of an event = Required number of event / Total number of possible events

Required number of events = 84

Total number of events = 320

Find the probability that both customers selected without replacement say service is poor.

customers say service is poor = 84 / 320

customer selected without saying service is poor= 83 / 319.

The final probability is: 84 ÷ 320 ×83 ÷ 319.

      = 6972 ÷ 201080

     = 1743 ÷ 25520

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Answer:

x=2.5 and y=-1

Step-by-step explanation:

Firstly we have to state the formula to avoid making mistakes when calculating the points.

So we use the midpoint formula to be able to calculate; midpoint=(x1+x2 , y1+y2)

2 2

So when calculating x we are goin to take the coordinates A(-4,5) and C(9,y)

then we substitute into the formula accordingly so since x will be the midpoint calculation we will say, (-4+9) =2.5 meaning x = 2.5

2

Next, inorder to find y we will ...

5+y=2 and then we will have to get rid of the

2

denominator by multiplying the denominator to both sides of the equals sign. The 2 will cancel each other out then 2×2 =4 an equation will be formed ; 5+y=4 work it out then it will bring you to y= -1 as the answer

Rotation, dilation, reflection and translation are all a type of transformation.

The transformation, i.e., f: X X, is a function, f, that maps to itself. Following the transformation, the pre-image X changes into the image X. Any operation, including translation, rotation, reflection, and dilation, may be used to create this transformation.

A rectangular array of numbers is called a matrix, and different operations are provided for it. The components are arranged in vertical columns and horizontal rows.

Rotation, dilation, reflection and translation are all a type of transformation.

A rectangular array of numbers or other objects arranged in a grid position system is called a matrix.

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The correct null hypothesis in the given situation is:

(A) H0: p = 0.27; Ha: p > 0.27

Any variation between the selected attributes that you observe in a collection of data is thought to be the result of chance, according to the null hypothesis.

For instance, any discrepancy between the average profits in the data and zero is caused by chance if the expected earnings for the gambling game are actually equal to zero.

So, the population proportion serves as the parameter.

The American Academy of Periodontology found that 27% of US individuals admit to lying to their dentist about how frequently they floss their teeth.

So, the following is the null hypothesis:

H0: p = 0.27

Dr. Garcia, a periodontist, thinks that the percentage should be higher than 27% since he feels it is too low.

Consequently, the competing theory is:

H0: p > 0.27

Therefore, the correct null hypothesis in the given situation is:

(A) H0: p = 0.27; Ha: p > 0.27

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Complete question:

The American Academy of Periodontology released a survey, revealing that 27% of US adults admit they lie to their dentist about how often they floss their teeth. Periodontist Dr. Garcia believes that the percentage seems low, so he decides to conduct his own hypothesis test to determine the true proportion. What should he write as the null and alternative hypotheses for this situation?

Answer Options:

A: H0: p = 0.27; Ha: p > 0.27

B: H0: p = 0.27; Ha: p < 0.27

C: H0: p = 0.27; Ha: p ≠ 0.27

D: H0: μ = 0.27; Ha: μ > 0.27

E: H0: μ = 0.27; Ha: μ < 0.27

The dimensions that will minimize the cost of 5920

Here is the process. Volume is the volume of a cylinder plus the volume of a sphere.

The surface area of a cylinder without the top and bottom plus twice the surface area of a spherical constitutes the cost of the material.

C = 2πrh + 2(4πr2)

Put what you discovered for h in this formula.

Consider Cost's derivative with regard to r. After that, zero out the derivative and find r.

Utilize the radius, r, value once you have it to solve for the height, h.

now,

V = πr2h + (4/3)πr3 = 5920

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Answer:

Gordon

Step-by-step explanation:

The domain is the x values and the range is the y values.  The y values are the not the same.  The y values for function A are all positive and the y values for function B are all negative.

The x values are the same for both functions, so the domain is the same for both functions.

Therefore ,a result, the answer to the variable problem (B) is incorrect because, even though the adjusted R-square has a lower value .

A variable is a quality that may be measured and take on several values. A few examples of variables are height, age, salary, province of birth, school grades, and kind of dwelling.

Here,

Given : The adjusted r-squared number is always lower than the s n value The added variable always causes the modified r-squared value to fall.

If a new variable is included to the regression, the r-squared result cannot drop.

. When comparing several regression models, the adjusted r-squared is more helpful than the r-squared.

Therefore ,a result, the answer to the variable problem (B) is incorrect because, even though the adjusted R-square has a lower value than the R-square, it might not drop as you add more variables.

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On solving the provided question, we can say that 0.003 X 100 when we multiply with decimal it gets shifted to right side

Integer and non-integer numbers are often expressed using the decimal numeral system. The Hindu-Arabic numeral system has been expanded to include non-integer values. Decimal notation is the name for the method used to represent numbers in the decimal system. A decimal is a number with a whole and a fractional component. Decimal numbers, which are in between integers, are used to express the numerical value of full and partially whole amounts. A decimal point separates the complete number and the fractional portion of a decimal number. The dot between the whole number and the fractions is known as the decimal point. A decimal number is, for instance, 25.5. In this instance, 25 is the entire number, while 5 is the

here,

for example

0.003 X 100

when we multiply with decimal it gets shifted to right side

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Answer: 2

Step-by-step explanation:

Answer:

y = 6x

Step-by-step explanation:

In the table, for every x value, the y value is that number multiplied by 6.

For example:

x = 1

y = 6

And:

x = 8

y = 48

By using a trigonometric relation, we will see that the hypotenuse of the right triangle is:

x = 22

We want to find the value of x on the right triangle.

Notice, it is the hypotenuse of the right triangle.

We know one angle on the triangle, and also the adjacent cathetus, then we can use the trigonometric relation:

cos(a) = (adjacent cathetus)/hypotenuse

We can replace the known values to get:

cos(30°) = 11*√3/x

(√3)/2 = 11*√3/x

Now we can solve this for x.

Dividing both sides by √3 we get:

1/2 = 11/x

x/2 = 11

x = 2*11

x = 22

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A circle passes through the three vertices of an isosceles triangle that has two sides of length 3 and a base of length 2. So the area of this circle is 81π/32.

These are the specified parameters:

Sides of an isosceles triangle

a = 3

b = 3

c = 2

Find the height of an isosceles triangle

h² = a² - (c/2)²

    = 3² - 1²

    = 9 - 1

    = 8

h = √8

h = 2√2

Find the area of the triangle

A = 1/2 × c × h

  = 1/2 × 2 × 2√2

  = 2√2

Find the length of the radius of the circle

r = abc / (4 A)

 = (3 × 3 × 2) / (4 × 2√2)

 = 9/4√2

 = 9√2/8

Fnd the area of the circle

A = π × r²

  = π × (9√2/8)²

  = 81π/32

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The radius of the cone is , r = √(154 cm²/π) cm and the slant height is

L = √( 154 /π+ h²) cm.

To find the radius and slant height of the cone, we can use the formula for the total surface area of a cone, which is πr² + πrL, where r is the radius, L is the slant height, and π is pi.

Given that the curved surface area of the cone is 2/3 of its total surface area, we know that the total surface area of the cone is 462 cm², and the curved surface area is (2/3) * 462 cm² = 308 cm².

The formula for the curved surface area of a cone is πrL, where r is the radius, and L is the slant height.

So we know that:

πrL = 308 cm²

We also know that:

πr² + πrL = 462 cm²

Now we can solve for the radius and slant height of the cone by substituting the first equation into the second equation and solving the system of equations.

πrL = 308 cm²

πr² + πrL = 462 cm²

πr² = 462 cm² - 308 cm²

πr² = 154 cm²

r² = 154 cm²/π

Solving for r

r = √(154 cm²/π) cm

Now we can use the radius to find the slant height, by using the formula of slant height L = √(r² + h²) where h is the height of the cone.

Given that we do not have the height of the cone provided, we can't solve for the slant height.

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Step-by-step explanation:

the curved surface area is 2/3 of 462 cm².

462 × 2/3 = 308 cm²

that leaves 1/3 of 462 cm² for the base area, a circle.

462 × 1/3 = 154 cm²

the area of a circle is pi×r²

so, in our case

pi×r² = 154

r² = 154/pi

radius = r = sqrt(154/pi) = 7.001408606... cm

the slant height l

l = sqrt(r² + h²)

with h being the internal height.

to get l we have the total surface area A

A = pi×r(r + sqrt(h² + r²)) = pi×r(r + l)

A/(pi×r) = r + l

l = A/(pi×r) - r = 462/(pi×7.001408606...) - 7.001408606... =

= 14.00281721... cm

Answer:

Step-by-step explanation:

2 7/9 divided by 2

First, convert the mixed number into a improper fraction:

25/9

Then multiply by the reciprocal of 2, by multiplying it by 1/2,

which turns into 25/8

Turn it into a mixed number: 1 7/18 OR 25/8

There are 5 integer values of M that satisfy the given inequality.

An integer is a whole number, which means it is a number that can be written without a fractional or decimal component. Integers include positive numbers (e.g. 1, 2, 3), negative numbers (e.g. -1, -2, -3), and zero.

They are also often represented using the symbol "Z". Integers are a subset of the set of real numbers.

If M/20 is strictly between 1/3 and 3/5, then we have the following inequalities:

1/3 < M/20 < 3/5

To solve this, we can multiply both sides of the inequality by 20 to get rid of the denominator on the left side:

6 < M < 12

This tells us that M is an integer that lies strictly between 6 and 12 (i.e., 6 < M < 12), and the integers between 6 and 12 are 7, 8, 9, 10, and 11. Therefore there are 5 integer values of M that satisfy the inequality.

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Answer in standard form:  2x+y = 3

Answer in slope intercept form:   y = -2x+3

Both equations describe the same line. Select one of those formats to write to your teacher.

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

Reason:

The equation 2x+y = 9 solves to y = -2x+9; it is of the form y = mx+b

The parallel line will also have a slope of -2. Parallel lines have equal slopes, but different y intercepts.

The slope-intercept answer is of the form y = -2x+b

Plug in (x,y) = (-1,5) and solve for b.

y = -2x+b

5 = -2*(-1)+b

5 = 2+b

3 = b

b = 3

We go from y = -2x+b to y = -2x+3 which is in slope intercept form.

Adding 2x to both sides gets us 2x+y = 3 which is in standard form.

Answer:

108 degrees

Step-by-step explanation:

The sum of the measures of the interior angles of a polygon is given by the formula:

(n-2) x 180 degrees

Where n is the number of sides of the polygon. In the case of a pentagon, the number of sides is 5, so we can use the formula to find the sum of the measures of the interior angles of a pentagon:

(5-2) x 180 = 3 x 180 = 540

If we know that the pentagon is regular, meaning that all its angles have the same measure, we can use this information and the formula above to find the measure of each interior angle.

If we divide the sum of the measures of the interior angles by the number of sides, we get the measure of each interior angle of the regular pentagon.

540/5 = 108 degrees

So, the measure of each interior angle of a regular pentagon is 108 degrees

The coefficient of determination (R^2) tells you the proportion of the variance in the dependent variable that is predictable from the independent variable(s).

It tells you how well the independent variable(s) are able to predict the dependent variable. An R^2 of 1 indicates a perfect fit, and an R^2 of 0 indicates that the model does not explain any of the variance in the dependent variable.

The residual plot is a graph that shows the residuals (the difference between the observed value of the dependent variable and the predicted value) on the vertical axis and the predicted value of the dependent variable on the horizontal axis.

The residual plot is used to check for patterns in the residuals, which can indicate a problem with the model. For example, if the residuals are not randomly dispersed around zero, it may indicate that the model is not a good fit for the data. The standard error of the estimate (s) is a measure of the average distance that the data points fall from the fitted line. It represents the average distance that the observed values deviate from the true values. Lower values of s indicate a better fit of the model to the data.

Overall, the R^2, residual plot and s are used to evaluate the goodness of fit of the model.

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1. To get Equation B from Equation A, we add/subtract the same quantity to/from both sides.

2. Equation A is equivalent to Equation B

What is an equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign.

Here, we have

1.  We are given the equation :

2x - 1 = 5x .............(A)

To get Equation B from A, we would subtract 2x from both sides of the equation.

2x - 2x - 1 = 5x - 2x

- 1 = 3x...... (B)

Hence, to get Equation B from Equation A, we add/subtract the same quantity to/from both sides.

2. Based on the previous answer,

2x - 1 = 5x  is equal to  -1 = 3x.

Hence, both Equation A and Equation B are equivalent expressions.

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1000 is the amount of garbage that was initially dumped in the landfill before any additional garbage was added. i.e: It is the quantity of garbage on Day 0.

The initial function given in the problem is n = 2000x + 1000.

The definition of a function's initial value is its starting value, which is unaffected by any variables used in the function.

The given function is:

n = 2000x + 1000

where the amount of trash is n, and the number of days is x. We'll set the variable (x) equal to zero to obtain the starting value.

Therefore, initially:

n = 2000(0) + 1000 = 1000

This indicates that the trash had a value of 1000 at day zero.

Therefore 1000 represents the amount of trash that was originally present in the landfill before dumping any extra trash.

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The equations can be framed as:

For Novelists

3 x 5 = 15

and, For Artists:

3 x 3 = 9 artists

A key part to understanding ratios is that it isn't part over whole. Ratios say that there are 5 novelists Per 3 poets.

This can be rephrased to say that there are 5 novelists per 8 TOTAL people.

From here, we can use fractions:

5/8 = x/24

where x is the number of novelists

Now,

Multiplying the left side by 3/3 yields 15/24

Therefore,

there are 15 novelists at the workshop.

We can use the same method for the poets :

3/8 = y/24

= 9/24

Complete Question:

A writing workshop enrolls novelists and poets in a ratio of 5:3.  There are 24 people at the workshop.  How many novelists are there?  How many poets are there?  Write a system of equations to model each situation.  Solve by any method.

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A function is a relation between sets where for each input, there is exactly one output.

A mathematical phrase, rule, or law establishes the link between an independent variable and a dependent variable (the dependent variable). Functions can be found everywhere in mathematics, and they are essential for building physical connections in the sciences.

The German mathematician Peter Dirichlet initially offered the contemporary definition of function in 1837: A variable y is said to be a function of the independent variable x if there is a relationship between them such that whenever a numerical value is assigned to x, there is a rule that determines a specific value of y.

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By square root, power and sign properties, the expression - 16 · y is the square root of 16 · y² for y < 0.

Let be n a real number, x is the square root of n if and only if n = x², that is:

x = √n

In addition, we find by sign properties the following two cases according to sign of variable y:

Now we proceed to find the square root of 16 · y² for y < 0. First, write the square root described in statement:

√(16 · y²)

Second, use square root and power properties:

√16 · √y², where y < 0.

- 16 · y

In conformity with square root, power and sign properties, the square root 16 · y² for y < 0 is the expression - 16 · y.

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The size of the largest angle of the given triangle can be calculated using cosine rule : c² = b² + a² - 2abcosC , where 'C' represents the largest angle of the triangle.

As given in the question,

Let the given triangle be ABC,

Side opposite to ∠A, ∠B, and ∠C is BC, AC, and AB respectively.

BC = a

AC =b

AB = c

let us consider ∠C be the largest angle of the given triangle.

Value of ∠C can be calculated by substituting other values in the cosine rule given by :

cosine rule : c² = b² + a² - 2abcosC

If Pythagoras theorem satisfied then largest angle is right angle.

Therefore, the size of the largest angle of the given triangle can be calculated using cosine rule : c² = b² + a² - 2abcosC

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Answer: [tex]4y=-3x+16[/tex]

Step-by-step explanation:

For there to be infinitely many solutions, the equations must represent the same graph.

The points [tex](0,4)[/tex] and [tex](4,1)[/tex] lie on the line. So, the slope is [tex]\frac{4-1}{0-4}=-\frac{3}{4}[/tex]. As the [tex]y[/tex]-intercept is [tex](0,4)[/tex], the equation is [tex]y=-\frac{3}{4}x+4[/tex].

Multiplying both sides by [tex]4[/tex] yields [tex]4y=-3x+16[/tex].