(i) Are there values of k such that the curve y = (k + 3)x² - 3x lies completely above the line y = x + k? Justify your answer. (ii) Explain the relationship between the curve and the line in part (i).​

Answer:280 is the greatest value for this situation.

It cost 35 dollars per half hour to rent the JetSki. This means to rent the ski for one full hour, you would pay 70 dollars.

If you can rent the Jetski at a max of 4 hours this would be 70 x 4 which is 280. Lastly we must add in an insurance fee, which is a one time cost. 280 +15 is 195. This means our greatest value is 280, while the cheapest would be 50. (35+15)

I hope this helps & Good Luck <3 !!!

Answer: (i) To find the total weight of compost required:

First, find the volume of one bowl: We can use the formula for the volume of a sphere to find the volume of one hemispherical bowl. The radius of the sphere is equal to half the diameter of the bowl, which is 21 cm / 2 = 10.5 cm. The volume of one hemispherical bowl is given by the formula (4/3)πr^3/2, where r is the radius. Plugging in the values, we get:

(4/3)π(10.5)^3/2 = (4/3) * (22/7) * (10.5)^3/2 = 532.8 cm³

Multiply by the number of bowls: To find the total volume of compost required, multiply the volume of one bowl by the number of bowls: 532.8 cm³ * 16 bowls = 8544.8 cm³

Multiply by the weight of compost per cm³: To find the total weight of compost, multiply the total volume by the weight of compost per cm³: 8544.8 cm³ * 2.31 gm/cm³ = 19824.9 gm = 19.82 kg

So, the total weight of compost required is 19.82 kg.

(ii) To find the amount of polythene required:

First, find the circumference of one bowl: The circumference of the circle is equal to 2π times the radius. So, the circumference of one bowl is 2π * 10.5 cm = 21π cm.

Find the length of the polythene: To find the length of the polythene, we need to find the length of the curved surface of the bowl. We can use the formula for the circumference of a circle, which is 2πr, where r is the radius. The curved surface of the bowl is half the circumference of the circle, so the length of the polythene is 21π cm / 2 = 10.5π cm.

Multiply by the number of bowls: To find the total length of the polythene, multiply the length of one bowl by the number of bowls: 10.5π cm * 16 bowls = 168π cm = 528 cm (rounded to the nearest cm)

So, the total amount of polythene required is 528 cm.

Step-by-step explanation:

Bold = reason (in reasons 3 and 4 the formatting is odd and goes into the next line)

Statement                                                                     Reason

1. line segment ʜᴏ is parallel to line segment EL,             1. Given

line segment HN intersects line segment OE at W,

the measure of HW is equal to the measure of NW*

2. angle HWO is congruent to angle NWE             2. Vertical angle theorem

3. angle OHW is congruent to angle WNE         3. alternate interior angles theorem

*4. line segment HW is congruent to line segment NW  4. definition of congruent

5. triangle HOW is congruent to triangle NEW    5. ASA postulate

*step 4 might not be needed; I don't know whether the "given" is saying that the measure of line segment HW is equal to the measure of line segment NW, or if it's saying that the two line segments are congruent

You might have to change the reasons for the statements, but this is the gist of how to prove it.

The final value of the investment is £2517.04.

Calculate the total amount earned over 6 months at 0.5% per month

At 0.5% per month, the investment of £2500 will earn £12.50 per month for six months.

Therefore, the total amount earned over 6 months is £12.50 x 6 = £75.

Determine the value of the investment after 6 months

The value of the investment after 6 months will be the initial investment plus the total amount earned over 6 months.

Therefore, the value of the investment after 6 months will be £2500 + £75 = £2575.

Determine the total amount lost over 9 months at 0.25% per month

At 0.25% per month, the investment of £2575 will lose £6.44 per month for nine months.

Therefore, the total amount lost over 9 months is £6.44 x 9 = £57.96.

Calculate the final value of the investment

The final value of the investment will be the value of the investment after 6 months minus the total amount lost over 9 months.

Therefore, the final value of the investment is £2575 - £57.96 = £2517.04.

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The final value of the investment would be £2491.97. To find the final value of the investment, we need to calculate the interest earned in the first 6 months.

When the rate was 0.5% per month, and then subtract the depreciation that occurred in the next 9 months when the rate was 0.25% per month.

First, calculate the interest earned in the first 6 months:

Next, add this interest to the initial investment to get the value after 6 months:

Finally, calculate the depreciation in the next 9 months:

Subtract the depreciation from the value after 6 months to get the final value:

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55 balls can be stacked in a pile with a triangular base having 10 balls on each edge. So, the answer is B. 55.

To determine the number of balls that can be stacked in a pile having a triangular base with 10 balls on each edge, we can use the formula for the triangular number sequence:

n(n+1) ÷ 2

where n is the number of balls on each edge of the triangular base. In this case, n = 10, so we have:

10(10+1) ÷ 2 = 55

So the answer is B. 55 balls can be stacked in a pile with a triangular base having 10 balls on each edge.

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Answer:

Step-by-step explanation:

To find the sine of angle M, we can use the sin function, which relates the sides of a right triangle to the sine of one of its angles. In this case, we have a right triangle with sides MO, NM, and ON, so we can use the following formula:

sin(M) = MO / ON

We know that MO = 8 and ON = 15, so we can calculate the sine of angle M as follows:

sin(M) = 8 / 15

So, the ratio that represents the sine of angle M is 8/15.

Jenna will have total money, y= 166 + 23x.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

Jenna had saved $166.

She will earn $23 per day of work

If x represents the number of days she works the she will earn

= 23x

So, She will have total

= 166+ 23x

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The minimum frequency of radiation is 0.603 × 10¹⁵ and the longest wavelength is 4.97 × 10⁻⁷.

Planck's equation is an equation which describes about the amount of spectral radiance radiated by a black body at a certain wavelength in thermal equilibrium.

We have the Planck's Equation,

E = hv,

where E is the energy, h is the Planck's constant = 6.63 x 10⁻³⁴ J and v is the frequency of radiation.

We have in the question E = 4.0×10⁻¹⁹ J

Substituting,

4.0×10⁻¹⁹ = (6.63 x 10⁻³⁴) v

v = (4.0×10⁻¹⁹) / (6.63 x 10⁻³⁴)

  = 0.603 × 10¹⁵

Also we have the equation to find the wavelength,

v = c / λ, where c is the speed of the light = 3 × 10⁸ and λ is the wavelength.

λ = c / v = (3 × 10⁸) / (0.603 × 10¹⁵)

             = 4.97 × 10⁻⁷

Hence the minimum frequency and the longest wavelength of radiation for which the detector registers a response are 0.603 × 10¹⁵ and 4.97 × 10⁻⁷ respectively.

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Using the method of least squares, the faculty group obtained,  the estimated y-intercept of the line is For a 1-point increase in an administrator's rating, we estimate the administrator's raise to increase $14,000.

The relationship between the variables is calculated and represented as an equation in regression analysis. The dependent variable, independent variables, and line equation constants are all included in this equation. Variables may be related in ways that are linear, quadratic, polynomial, etc.

In this instance, the performance is the independent variable and the increase is the dependent variable. Simple linear regression is the name of the equation, which is shown as a straight-line equation.

Regression analysis makes use of the relationship between independent and dependent variables' relationship equation to forecast the values of the dependent variable y given the values of the independent variable x.

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Answer: 60

A triangle can only be 180 degrees so if one side is 60 so is the other two sides

On solving the provided question, we can say that the equation are cost of producing t units is C = 3t2 + 8t, revenue generated from sales is R = 4t2 + t if t>0 then C = 43t and is t>7 then C =D = 32t

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

the equation are

cost of producing t units is C = 3t2 + 8t,

revenue generated from sales is R = 4t2 + t

if t>0

then C = 43t

and is t>7

then C =D = 32t

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Answer:

The equation for babysitting can be written as y = 20x + 5, where y is the total cost and x is the number of hours.

The slope of the equation is 20, which represents the rate of change in the total cost (y) with respect to the number of hours (x).

The slope represents the rate at which the total cost changes for each unit change in the number of hours. In this case, for each hour of babysitting, the total cost increases by $20.

The y-intercept of the equation is 5, which represents the cost when x = 0, i.e. when there is no babysitting time.

The y-intercept represents the starting value of the total cost, in this case, the amount charged for babysitting even when there is no babysitting time.

Step-by-step explanation:

The bearing of the flight from Elgin to Canton is 231.23°. The solution has been obtained by using law of sines.

What is law of sines?

The ratio of the side length to the sine of the opposing angle is how the law of sines is typically defined. That is true for all three triangle sides, regardless of their sides and angles.

Let the angle formed at Canton be C.

The angle formed at Naples =  90 - 44 = 46°

Using law of sines,

⇒sin (46 ) / 720  =  sin C / 500

⇒500 * sin ( 46 ) / 720  =  sin C

⇒arcsin ( 500 * sin (46) / 720 )  = C  

⇒C ≈ 38.77°

The bearing angle (clockwise from north) of the flight from Elgin to Canton is calculated as follows:

⇒270° - 38.77°

⇒231.23°

Hence, the bearing of the flight from Elgin to Canton is 231.23°.

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The figure of the question has been attached below.

The simplest form of the polynomial is (x²)-3x+1.

A polynomial is a mathematical expression consisting of constants, variables, and exponents. It can be written in the form of a polynomial equation, which is a mathematical equation with one or more variables.

In this example, we have two functions, f(x) and g(x). The polynomial of these two functions can be written in simplest form by combining the functions together.

The polynomial of f(x) and g(x) is written in simplest form as (x²)-3x+1.

This means that for any value of x, the polynomial will evaluate to the value given by the equation.

If x=2, then the polynomial will evaluate to (2(2)²)-3(2)+1=3.

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If a ranger in a 120 m high tower on a plain first noted that the angle of depression to a fire was 4°. The fire travelled 31,968 meters.

Distance = d = v * t

Let v represent speed of the fire .

Where :

t = time elapsed in seconds = 20 * 60 = 1200 seconds

Using the tangent function:

d / v = tan(6°) - tan(4°)

Simplify this expression using the identity:

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))

Applying this to the above equation, we get:

d / v = (tan(6°) - tan(4°)) / (1 + tan(6°)tan(4°))

Using a calculator to evaluate the tangent values

d / v = 26.64 / v

d = 26.64 * v

Substituting the value of t, we get:

d = 26.64 * v

= 26.64 * 1200

= 31,968 meters (rounded to the nearest meter)

Therefore the fire travelled 31,968 meters.

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The complete question is:

A ranger in a 120 m high tower on a plain first noted that the angle of depression to a fire was 4°. Twenty minutes later the angle of depression was 6°. The fire travelled                         m (to nearest metre)

During the party, 6 3/4 pizzas were consumed.

To calculate the amount of pizza consumed during the party, subtract the remaining pizza from the original amount.

The original quantity of pizza was 9 3/8 pizzas, and the remaining quantity was 2 5/8 pizzas, resulting in:

6 3/4 pizzas = 9 3/8 - 2 5/8 pizzas

During the party, 6 3/4 pizzas were consumed.

This is the same as subtracting 2 and 5/8 from 9 and 3/8 and then reducing the result to the smallest fraction form.

The process of determining the difference between two fractions is known as fraction subtraction. To subtract two fractions, do the following:

Check that the fractions have a common denominator: If the denominators are not the same, you must find one. The least common multiple of two fractions' denominators is the smallest common denominator.

Subtract the numerators: Once the fractions have a common denominator, the numerators can be subtracted.

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The diagram that represent the distance and the journeys is added as an attachment

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

Using the above as a guide, we have the following:

Next, we create the diagram (see attachment)

The attached figure represents the required diagram

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The probability that a patient who has been diagnosed with cancer truly has the illness 0.406

It is known from prior experience that there is a 0.05 chance of choosing a cancer-positive adult over 40 in a certain area of the nation. What is the likelihood that an adult over the age of 40 will be given a cancer diagnosis if the probability of a doctor correctly diagnosing a person with cancer as having the disease is 0.78 and the probability of a doctor incorrectly diagnosing a person without cancer as having the disease is 0.06.

We wish to compute P(C | D) this time. Bayes rule is used in this process.

[tex]& P(C \mid D)=\frac{P(C n D)}{P(D)} \\\\& =\frac{P(C) P(D \mid C)}{P(C) P(D \mid C)+P\left(C^{\circ}\right) P\left(D \mid C^*\right)} \\\\& =\frac{0.05 * 0.78}{(0.05 * 0.78)+(0.95 * 0.06)} \\\\& =\frac{0.039}{0.039+0.057} \\\\& =\frac{0.039}{0.096} \\\\& =0.406[/tex]

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The perimeter and area of the figure is  [tex]6y^{2} + 10x^{2} y[/tex] and [tex]15x^{2} y^{3}[/tex] respectively.

What are the perimeter and area?

The complete length of a shape's boundary is referred to as the perimeter in geometry. The measurements of all the sides of a figure are added to find its perimeter. The area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. The area of a plane figure is the area that its perimeter encloses.

Given shape is a rectangle,

So, the perimeter of the figure = [tex]2(3y^{2} + 5x^{2} y)[/tex] = [tex]6y^{2} + 10x^{2} y[/tex]

And,

Area of the figure [tex]= 3y^{2} *5x^{2} y = 15x^{2} y^{3}[/tex]

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Check the picture below.

[tex]\cfrac{24+x}{24}~~ = ~~\cfrac{36+12}{36}\implies \cfrac{24+x}{24}=\cfrac{48}{36}\implies \cfrac{24+x}{24}=\cfrac{4}{3} \\\\\\ 72+3x=96\implies 3x=24\implies x=\cfrac{24}{3}\implies x=8[/tex]

A graph which represents this situation include the following: B. graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 30 through the point 1 comma 40.

In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:

y = mx + c

Where:

In Mathematics, the y-intercept is also referred to as an initial value and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

In this scenario, the y-intercept of this equation can be calculated as follows;

y = 30 + 10x

y = 30 + 10(0)

y = 30

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The function that represents the balance after t years is ,

FV = $470( 1.011)^4t

The formula for calculating future value:

FV = P (1 + r)^nm

Where:

FV = Future value

P = Present value

R = interest rate

m = number of compounding

N = number of years

here, we have,

given that,

P = Present value= $470.

R = interest rate = 4.4%/4 =

m = number of compounding =4

N = number of years = t

FV = $470( 1.011)^4t

Hence,  The solution is, a function to represent the balance A in the account after t years is, FV = $470( 1.011)^4t

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Answer:

Ten thousands

Step-by-step explanation:

20 x 1000 = 20,000 therefore, ten thousands

From the given figure, conclude that ∠VWZ = 27°. This can be solved by using SAS theorem.

The triangles are congruent if two sides and the included angle of one triangle are equivalent to two sides and the included angle of another triangle. Congruent refers to figures that are similar in all respects, primarily in terms of size and shape. Congruence describes how two congruent figures relate to one another.

From the given picture, it is clear that WXYV is a rectangle.

∠VYX = 90°

As we know, ∠YVX + ∠VYX + ∠VXY = 180°

or, 5x - 12° + 90° + 2x - 3° = 180°

or, 7x = 180° - 90° + 15°

or, 7x = 105°

or, x = 15°

thus, ∠VXY = 2x - 3° = 27°

next comparing ΔVYX and ΔYVW we get:

VY = VY

WV = XY

So, ∠VYX = ∠XVW = 90°

From SAS theorem,

ΔVYX ≅ ΔYVW

∠VWX = ∠VXY = 27°

Thus, ∠VWX = 27°

and ∠VWX and ∠VWZ is same.

Therefore, ∠VWZ = 27°

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Answer: 11 (Or I'm wrong)

Step-by-step explanation: -2 -1 0 1 2 3 4 5 6 7 8 9 10 11

Answer:

1.6

Step-by-step explanation:

[tex]\displaystyle \frac{f(b)-f(a)}{b-a}\\\\=\frac{f(9)-f(1)}{9-1}\\ \\=\frac{15.8-3}{8}\\ \\=\frac{12.8}{8}\\ \\=1.6[/tex]

Factorized form of polynomial is 3(−b²c+bc²−c²a+ca²−a²b+ab²).

This process of finding two or more expressions whose product is the given expression is known as the factorization of algebraic expressions.

Given polynomial

(b - c)³ + (c - a)³ + (a - b)³

Factoring the polynomial

Calculation is attached below.

we get,

3(−b²c+bc²−c²a+ca²−a²b+ab²)

Hence,

3 and (−b²c+bc²−c²a+ca²−a²b+ab²) are factors of given polynomial.

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The exact binomial probability that the total number rolled will add up to 3 or less is 1/12.

The exact binomial probability that the total number rolled will add up to 3 or less is calculated as follows;

The total number that can be rolled with 2 dice is 2 to 12, with 7 being the most likely outcome (the sum of two dice has a maximum of 7).

The probability that the total number is 3 or less is the sum of the probabilities of rolling a 2 and a 1;

The probability P = (1/36) + (2/36)

P = 3/36

P = 1/12

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