mince pies and 2 jars of cranberry sauce costs £4.80 10 mince pies and 3 jars of cranberry sauce costs £7.60 How much does a mince pie and a jar of cranberry sauce cost each?

The correct statement that establishes the identity is the third one: "The reciprocal of the cosine of an angle is equal to the secant of the angle."

Here's how you can prove this using the other three statements:

"The tangent of an angle is equal to the sine of the angle divided by the cosine of the angle."

"The reciprocal of the sine of an angle is equal to the cosecant of the angle."

"The reciprocal of the cosine of an angle is equal to the secant of the angle."

"The reciprocal of the tangent of an angle is equal to the cotangent of the angle."

To prove the identity, we can start by substituting the first statement into the equation on the left side of the identity:

$1 + \tan^2 (-0) = 1 + \left( \frac{\sin (-0)}{\cos (-0)} \right)^2 = 1 + \frac{\sin^2 (-0)}{\cos^2 (-0)}$

Next, we can use the fourth statement to write the right side of the identity in terms of the cotangent:

$1 + \frac{\sin^2 (-0)}{\cos^2 (-0)} = 1 + \frac{1}{\cot^2 (-0)} = \frac{1}{\cot^2 (-0)}$

Now we can use the second statement to write the right side of the identity in terms of the cosecant:

$\frac{1}{\cot^2 (-0)} = \frac{1}{\frac{1}{\sin^2 (-0)}} = \csc^2 (-0)$

Finally, we can use the third statement to write the right side of the identity in terms of the secant:

$\csc^2 (-0) = \frac{1}{\sec^2 (-0)} = \sec^2 (-0)$

Therefore, the third statement establishes the identity.

The requried, "a" and "b" are positive numbers, the minimum sum (a + b) is 13.711.

To find the minimum sum of two positive numbers whose product is 47, we can use the concept of the arithmetic mean-geometric mean inequality (AM-GM inequality).

The AM-GM inequality states that for any two positive numbers, the arithmetic mean (average) is always greater than or equal to the geometric mean. Mathematically, it can be expressed as:

AM ≥ GM

For two positive numbers "a" and "b," the arithmetic mean is (a + b) / 2, and the geometric mean is √(ab).

Given that the product of the two numbers is 47 (ab = 47), we want to find the minimum value of their sum (a + b).

Using the AM-GM inequality:

(a + b) / 2 ≥ √(ab)

Substitute ab = 47:

(a + b) / 2 ≥ √47

Now, let's solve for the minimum sum (a + b):

a + b ≥ 2(√47)

a + b ≥ 2 * √(47)
a + b ≥  13.711.        

Since "a" and "b" are positive numbers, the minimum sum (a + b) is 13.711.

Learn more about the minimum sum of numbers here:

https://brainly.com/question/33367738

#SPJ12

answer : y = 4/5x - 22/5

y = mx + b

get m or slope (aka "rate" or "speed")

(fun fact : see how the graph is a straight line? a lot of calculus is trying to get the rate or speed or slope of a curved graph)

(-3,-6) (2,-2)

(y2 - y1)/(x2-x1)

-2 + 6/2 + 3

m = 4/5

(if you make the 2 points a triangle bottom is 5 and the right side is 4)

line formula

y - y1 = m (x - x1)

y + 6 = 4/5 ( x + 2 )

y = 4/5x + 8/5 - 6

y = 4/5x + 8/5 - 30/5

y = 4/5x - 22/5

side note : since the graph doesnt go thru (0,0) the graph is NOT PROPORTIONAL

The line 't' is y = -0.75x + 2 which has a slope of negative 0.75 and the y-intercept is 2.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The line t that passes through the points (0, 2) and (8, -4) is given as,

(y - 2) = [(- 6 - 2) / (8 - 0)](x - 0)

y - 2 = - 0.75x + 0

y = -0.75x + 2

The line 't' is y = -0.75x + 2 which has a slope of negative 0.75 and the y-intercept is 2.

More about the linear equation link is given below.

https://brainly.com/question/11897796

#SPJ1

Answer:

1

Step-by-step explanation:

For function f(x), the average rate of change from x = a to x = b is:

average rate of change = (f(b) - f(a))/(b - a)

Here we have:

f(a) = f(-3) = -2.88

f(b) = f(2.5) = 2.62

average rate of change = (2.62 - (-2.88))/(2.5 - (-3)) = 1

Answer:

  34. x = 3 1/3

  35. x = 5.2

Step-by-step explanation:

Given figures involving triangles with angle bisectors and parallel segments, you want to solve for x.

In each case, you need to make use of two proportional relationships. An angle bisector divides the triangle proportionally. An segment parallel to one side of the triangle divides it proportionally.

Using the angle bisector relation, you have ...

  QP/PT = QS/ST

  x/3 = 5/ST   ⇒   x = 15/ST

Using the parallel segment relation, you have ...

  PT/QR = ST/SR

  3/2 = ST/3   ⇒   ST = 9/2

Using the value of ST in the equation for x gives ...

  x = 15/(9/2) = 30/9 = 10/3

  x = 3 1/3

Using the angle bisector relation, you have ...

  EF/ED = CF/CD

  7.2/9 = CF/6   ⇒   CF = 6(7.2/9) = 4.8

Using the parallel segment relation, you have ...

  CB/BA = CF/FE

  x/7.8 = 4.8/7.2

  x = 7.8(4.8/7.2)

  x = 5.2

__

Additional comment

In each case, we assigned a numerical value to the intermediate variable (ST, CF). We didn't actually need to do that.

The function which can be used to find the relation between distance and time is f(t) = 130t.

As we know the train travels 260 kilometers in 2 hours,

then the distance traveled in one hour will be 130 kilometers.

distance = 130

when time = 0 ,

distance also = 0 , as the train has not started moving yet.

Then , the function which can tell bout the  relation will be ,

f(t) = 130t

where d = f(t)

Distance is a scalar quantity which tells us about how far an object is from its starting position. Distance don't have a direction.

The distance unit of measurement in the SI

SI unit of distance is meter  in the International System of Units.

Using this as the fundamental unit and a few formulae, a large number of different derived units or quantities are produced, including volume, area, acceleration, and speed.

Distance is measured also  using the C.G.S. and M.K.S in metric unit system.

To learn more about distance

brainly.com/question/15172156

#SPJ4

Answer:

To calculate how long it will take for the plane to reach 18,000 ft, first find the difference between the plane's current altitude and its target altitude:

35,600 ft - 18,000 ft = 17,600 ft

Then, divide this difference by the rate of descent to find the time it will take for the plane to reach its target altitude:

17,600 ft / 3,200 ft/mile = 5.5 miles

Since the rate of descent is given in feet per mile, this result is equivalent to the time it will take for the plane to reach its target altitude. Therefore, it will take the plane 5.5 miles (or a similar amount of time) to reach 18,000 ft.

In the given cylinder we know that it takes the water around 3.14 minutes to rise 1 ft.

One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid.

It is regarded as a prism with a circle as its base in basic geometry.

In several contemporary fields of geometry and topology, a cylinder can alternatively be characterized as an infinitely curved surface.

So, we know that:

The rate at which water is being filled is 4 ft³.

The radius of the cylinder is 2 ft.

Now, the time in which the level of water in the tank rises when the tank is half full:

Area of cylinder: πr²

πr² =  12.566 ft³

Next, multiply 4 by 12.566 to get how quickly the water is rising:

12.566 ft³/4 ft³/min = 3.14 m

According to this, a foot of water rises every roughly 3.14 minutes, or 1/3.14 - 0.318 ft/min, or 3.82 in/min.

Therefore, in the given cylinder we know that it takes the water around 3.14 minutes to rise 1 ft.

Know more about a cylinder here:

https://brainly.com/question/29953553

#SPJ4

To compare the two quantities, divide the number of giraffes by the number of penguins There are 5 times as many giraffes as penguins at the zoo.

To compare the two quantities, you need to divide the number of giraffes by the number of penguins.

30 giraffes / 6 penguins = 5

This means that there are 5 times as many giraffes as penguins at the zoo.

There are 5 times as many giraffes as penguins at the zoo. To compare the two quantities, divide the number of giraffes by the number of penguins (30/6 = 5). This means that there are 5 times more giraffes than penguins at the zoo.

Learn more about number here

https://brainly.com/question/10547079

#SPJ4

Answer:

1. m<AOB = 50 degree

2. m<COD = 90 degree

3. m<BOD = 130 degree

4. m<AOD = 180 degree

Step-by-step explanation:

1. We see that <AOB has one leg at 0 and the other leg at 50 degrees, so the <AOB is 50 degrees.

2. We see that <COD has one leg at 0 and the other leg at 90 degrees, so the <COD is 90 degrees

3. We see that <BOD has one leg at 50 and the other leg at 180 leg, so the <BOD is 180 - 50 = 130 degree

4/ We see that <AOD has one leg at 0 and the other leg at 180 degrees, so the <AOD is 180 - 0 = 180 degrees

The value of θ will -45° or 26.56°

Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation.

Given that, cosec²θ = cotθ + 3

Solving for θ,

∵ cosec²θ = cot²θ+1

∴ cot²θ+1 = cotθ + 3

cot²θ-cotθ-2 = 0

Factorizing and solving, we get

(cotθ+1)(cotθ-2) = 0

cotθ+1 = 0

cotθ = -1

θ = -45°

or, cotθ-2 = 0

cotθ = 2

θ = 26.56°

Hence, The value of θ will -45° or 26.56°

For more references on Trigonometric Identities, click;

https://brainly.com/question/24377281

#SPJ1

Answer:

d = 0

Step-by-step explanation:

7.5d = 2.5d

Divided both sides by factors and we get

d = 0

Answer:

64 divided by 2= 32 80 divided by 32= 2.5

The rate of change of function A is greater than the rate of change of function B.

The y-intercept of function A is less than the y-intercept of function B.

The rate of change is also called the slope of a linear equation and is defined as the rate of change of y-values divided by the corresponding change in x-values.

For function A, we are told that the line passes through the points (2, 3) and (-1, -3). The rate of change is gotten from the formula;

Rate of change = (y₂ - y₁)/(x₂ - x₁)

Rate of change = (-3 - 3)/(-1 - 2)

Rate of change = -6/-3

Rate of change = 2

For function B, we are given that the equation of the line is;

y = ¹/₂x + 2

Now, formula for equation of a line in slope intercept form is;

y = mx + c

where ;

m is slope and c is y-intercept

Thus, slope is 1/2 and y-intercept is 2

For function A, we can find the y-intercept as;

3 = 2(2) + c

c = 3 - 4

c = -1

Read more about Rate of change at; https://brainly.com/question/8728504

#SPJ1

Answer:

no

Step-by-step explanation:

we can test it

10=7(1)+5

10=7+5

10=12

not a solution

hopes this helps

the correct answer from each drop-down menu. which formulas return true,.if the value in cell b4 is 12 and the value in c4 is 29.: A. =B4=12 AND C4=29

The correct answer is A. =B4=12 AND C4=29, as this is the only formula that returns true if the value in cell b4 is 12 and the value in c4 is 29.

Both B. =(B4=12) AND (C4=29) and D. =(B4+C4)=41 are correct, but they do not fit the given criteria.

C. =B4+C4=41 does not return true for the given values, as 12 + 29 does not equal 41.

Learn more about formula here

https://brainly.com/question/1293486

#SPJ4

Answer:

1/2 a cup of flour

Step-by-step explanation:

Sugar to flour ratio:
2 to 1
That means for every 2 sugar Harris needs 1 cup flour
There are twice as many cups of sugar of cups of flour
Since 1/2 times 2 is 1 that means the ratio is ture

2 to 1 = 0.5 to 1

Hope this helps :) im kinda bad at explaining

The probability that Jeff has to play the game exactly 5 times i.e he keeps playing until he wins prize is (0.25)⁵.

We have, a fast-food restaurant runs a promotion which consists some food items with games pieces. 1 in 4 game pieces is a winner. This means, probability of winning game or sucess (p) = 1/4 . Since number of trials is fixed, trials are independent and probability of success is constant in each trial, we can use Binomial distribution. The Binomial distribution probability formula is

P(X= x) = ⁿCₓ(p)ˣ(1-p)⁽ⁿ⁻ˣ⁾

where,n --> number of trials

p --> probability of success

x --> number of times for a specific outcome within n trials

ⁿCₓ --> number of combinations

we have calculate the probability that he has to play the game exactly 5 times, i.e

x = 5 . Jeff keeps playing until he wins and he wins when he play exactly 5 times so,n= 5

Now, plugging all known values in above formula we get,

P(X= 5) = ⁵C₅(0.25)⁵(1-0.25)⁰

=> P(X= 5) = ⁵C₅(0.25)⁵(0.75)⁰

=> P(X= 5) = 1× (0.25)⁵× 1 = (0.25)⁵

Hence, required probability is (0.25)⁵

To learn more about binomial Probability distribution, refer:

https://brainly.com/question/9325204

#SPJ4

Answer:

only A ans bellow

Step-by-step explanation:

let k= -4

A. k * (k - 1) * ( k - 2)

= -4 * (-4 -1) * ( -4 -2)

= -4* (-5) * (-6)

= 20*-6

= -120

B. k * ( k+1)

= -4 * ( -4+1)

= -4 * (-3)

= + 12

C. k * (-50)

= -4 * (-50)

= + 200

D . (50 - k)

= 50 - (-4)

= 50 + 4

= + 54

Mark me the brainliest

if k is negative then k(k-1)(k - 2) will be definitely negative.

A number system is defined as a system of writing to express numbers.

Given that k is a  negative integer.

We need to find which of the given options are defnitely negative.

Let us consider k as -3.

k(k-1)(k - 2)

-3(-3-1)(-3-2)

-3(-4)(-5)=-60

Which is negative.

k(k+1)=-3(-3+1)=6 +ve

k (-50)=-3(-50)=150 +ve

(50-k)​=50-(-3)=53 +ve.

Hence, if k is negative then k(k-1)(k - 2) will be definitely negative.

To learn more on Number system click:

https://brainly.com/question/22046046

#SPJ2

Answer: 11

Step-by-step explanation: To raise the winning percentage to 75%, the team needs to win 3 more games out of 4, for a total of 3/4=75% of the games. Since the team has already won 8 games, they need to win 8+3=11 games in a row to raise the winning percentage to 75%

Answer:

w = 9

Step-by-step explanation:

Use a slope formula to solve. Subtract the y's put that on top and subtract x's and put that on the bottom. This calc should equal 2 that was given.

(8-6)/(10-w) = 2

2/(10-w) = 2

Cross-multiply.

2 = 2(10-w)

Distributive property

2 = 20 - 2w

Add 2w

2 + 2w = 20

Subtract 2

2w = 18

divide by 2

w = 18/2 = 9

Or you can logic it out...8-6 is 2 on top. Need a 1 on the bottom (bc 2/1 is 2) 10-9 is 1 for on the bottom. w = 1

Answer:

x⁵ - 1/3x² -1

Step-by-step explanation:

In order to write polynomials in standard form:

1) Find the degree (power) of each term

2) Arrange them in descending order (largest to smallest)

We have : -1 + x⁵ - 1/3x²

The degree of -1 is 0 since there is no power.

The degree of x⁵ is 5.

The degree of - 1/3x² is 2.

Now arranging them in descending order:

x⁵ has the largest degree, followed by - 1/3x² and then -1, so the polynomial in standard form is:

x⁵ - 1/3x² -1

Answer: a)

Step-by-step explanation:

To find [tex]\frac{dy}{dx}[/tex], we will have to use implicit differentiation, and because the base is [tex]dx[/tex], we will take the deriviative of both sides with respect to [tex]x[/tex].

To derive [tex]y[/tex] with respect to [tex]x[/tex], just derive the term with respect to y then multiply the term with [tex]\frac{dy}{dx}[/tex].

So [tex]\frac{d}{dx} x^{2}[/tex] is just [tex]2x[/tex], [tex]\frac{d}{dx} y^{2}[/tex] is [tex]2y \frac{dy}{dx}[/tex], and  [tex]\frac{d}{dx} 289[/tex] is 0. Now substitue each term with it's deriviative.

[tex]2x + 2y \frac{dy}{dx} = 0[/tex]

Now, just solve for  [tex]\frac{dy}{dx}[/tex] when [tex]x[/tex] is 8 and [tex]y[/tex] is 15

[tex]2(8) + 2(15)\frac{dy}{dx} = 0[/tex]

[tex]16 + 30\frac{dy}{dx} = 0[/tex]

[tex]\frac{dy}{dx} = \frac{-16}{30} = \frac{-8}{15}[/tex]

So the answer is choice a)

The value of the fifth term in the given sequence as represented in the task content is; -35.

It follows from the task content that the value of the fifth term in the given sequence is to be determined.

On this note, it follows from the observation that the given sequence is arithmetic and the nth term, T (n) = a + ( n - 1 ) d.

where, a = first term = 1

and d = common difference = -8 - 1 = -17 - (-8) = -9.

Therefore, the fifth term is given as;

T (5) = 1 + ( 5 - 1 ) -9

= 1 + (4 × -9)

= 1 - 36

= -35.

On this note, the fifth term of the sequence as required is; -35.

Read more on arithmetic sequence;

https://brainly.com/question/6561461

#SPJ1

Answer:

x = -3

Step-by-step explanation:

See the picture below

Answer: If the prices paid for a model of a new car are approximately normally distributed with a mean of $17,000 and a standard deviation of $500, it means that the majority of the prices paid for the car will fall within a certain range around the mean. Specifically, approximately 68% of the prices paid will be within one standard deviation of the mean, which in this case would be between $16,500 and $17,500. Approximately 95% of the prices paid will be within two standard deviations of the mean, which would be between $16,000 and $18,000. And approximately 99.7% of the prices paid will be within three standard deviations of the mean, which would be between $15,500 and $18,500. This shows that the prices paid for the car are relatively consistent, with only a small percentage falling outside of the range determined by the mean and standard deviation.

Step-by-step explanation:

Answer:

The answer is C, 3/4 of a box

The linear function is  f(x) = 3x -5.

A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

Given linear function expression,

f(x) = mx + b

From the table,

x = -2

then, 1 = -2m +b       ......equation 1

Put x = 0

then, b = -5

Substitute the value of b to the equation 1, we get

m = 3

Finally, the function is f(x) = 3x -5

Therefore, the linear function is  f(x) = 3x -5

To learn more about the function;

brainly.com/question/28303908

#SPJ1

Answer: x

≥

3

−

3

y

Step-by-step explanation: