Erin buys 3 packs of potatoes costing £2 each, 4 packs of carrots for £2 per pack, and 4 turnips costing 90p each. If she pays with a £20 note, how much change would she get in pounds, £?

The answer for 2 + 2 in the addition is determined as 4.

Addition is a mathematical operation that involves combining two or more quantities or values to find their total or sum.

Addition is one of the four basic arithmetic operations, along with subtraction, multiplication, and division.

In addition operation, the two or more numbers are often added to produce result called the sum.

For example, in the equation; 2 + 2 = 4.

2 and 2 are the addends, and 4 is the sum.

We can also preform addition on fractions. decimas, percentages, etc.

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We must conclude that there are infinitely many primes of the form 3k + 2, where k is a non-negative integer.

To adapt the proof:

We can use a similar contradiction argument.

Suppose that there are only finitely many primes of the form 3k + 2, say p1, p2, ..., pn.

Let N = 3p1p2...pn + 2. Note that N is of the form 3k + 2 for some non-negative integer k.

Now, let's consider the prime factorization of N. Either N is prime and of the form 3k + 2, in which case we have found a new prime of the desired form, contradicting our assumption that there are only finitely many such primes. Or, N is composite and has a prime factorization consisting only of primes of the form 3k + 1 (since any prime of the form 3k + 2 would divide N). But this implies that N itself is of the form 3k + 1.

Now, let's consider the number M = 3N + 2. M is also of the form 3k + 2, and so must have a prime factorization consisting only of primes of the form 3k + 1. But since N is of the form 3k + 1, we have

M = 3(3p1p2...pn + 1) + 2 = 9p1p2...pn + 5. This means that M has a prime factorization consisting of primes of the form 3k + 2, which contradicts our assumption that there are only finitely many such primes.

Therefore, we must conclude that there are infinitely many primes of the form 3k + 2, where k is a non-negative integer.

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Answer:

y = -7/2x - 1

Step-by-step explanation:

Using coordinates (-2,6) and (0,-1)

then slope m = (y2-y1)/(x2-x1)

m = (-1 - 6)/(0 - -2) = -7/2

so y = mx+ b

y = -7/2x + b

Using (0,-1)

y = -7/2x + b

-1 = -7/2(0) + b

b = -1

so y = -7/2x - 1

The way Lucy used the statistics from her survey is not valid as the sample size she used (three of her classes at GTCC) is too small to accurately represent the entire population of college students nationwide.

In order to draw valid conclusions about the entire population, the sample size should be representative and large enough to minimize sampling errors. Lucy's sample size is too small and limited to her own classes, which may not be representative of the entire college student population. Therefore, her conclusion that nearly a third of college students plan to continue their education further is not necessarily accurate or reliable. A larger and more representative sample size would be required to obtain more accurate and reliable results.

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Answer:

a. the enclosing boundary of a curved geometric figure, especially a circle.

b. The diameter is the length of the line through the center that touches two points on the edge of the circle.

c. a straight line from the center to the circumference of a circle or sphere

2. a.w b.z c.t d.x

Step-by-step explanation:

that's all i could do pls give brainliest

For a square pyramid, its height, slant height, and base form a right triangle:

Where

a is the length of one side of the base

r is the inner radius of the base (and is equal to half the length of a side of the base)

h is the height

s is the slant height

To determine the height (h) you can apply the Pythagorean theorem that states that the square of the hypothenuse is equal to the sum of the squares of the sides of the right triangle:

Write the expression for the height:

For

s= 91.8inch

r=a/2=24.6/2=12.3in

Replace these values in the expression obtained for h

The height of the pyramid is 90.97inches.

The trigonometric formula sin 2u is an example of a double angle formula. Double angle formulas are useful for simplifying expressions that contain multiples of the same angles.

For example, the double angle formula for sine can be used to transform a product of two sine functions, such as sin2u, into a single sine function. When applied to this formula, the double angle formula for sine simplifies the expression sin2u to 2(sin u)(cos u).

This allows us to more easily evaluate the expression as it is now composed of one single sine function instead of two multiples of the same angle. Double angle formulas can be used for other trigonometric functions as well, such as cos and tan. In fact, there are several double angle formulas for each of these functions.

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Complete question is :

fill in the blank to complete the trigonometric formula. sin 2u is an example of ______.

the surface area of the regular pyramid is approximately  \(40sqrt(14) + 43.3 mm^2.\)To find the surface area of a regular pyramid, we need to find the area of each triangular face and add them together, then add the area of the base.

Let's start with finding the area of each triangular face. Since the pyramid is regular, all the triangular faces will be congruent, so we just need to find the area of one.

We know that the base of the triangle is 10 mm, and the height of the triangle is half the distance between the apex (the point at the top of the pyramid) and the base. Since the pyramid is regular, the apex is directly above the center of the base.

The height of the pyramid can be found using the Pythagorean theorem, where the height of the pyramid (h) is the hypotenuse of a right triangle with the base (b) and half the slant height (s) as the legs.

\(s^2 = hr^2 - (b/2)^2\)

We know the base is 10 mm and the height of the big triangle is 9 mm, so the half slant height is:

\(s = sqrt(h^2 - (b/2)^2) = sqrt(9^2 - (10/2)^2) = sqrt(81 - 25) = sqrt(56) = 2sqrt(14)\)

Now we can find the area of one triangular face using the formula:

Area = 1/2 x base x height

Area = 1/2 x 10 mm x 2sqrt(14) mm = \(10sqrt(14) mm^2\)

Since there are four triangular faces, the total area of the triangular faces is:

4 x 10sqrt(14) mm{power}2 = \(40sqrt(14) mm^2\)

Finally, we need to add the area of the base, which we know is 43.3 \(mm^2.\)

So the total surface area of the pyramid is:

\(Surface Area = 40sqrt(14) mm^2 + 43.3 mm^2 = 40sqrt(14) mm^2 + 43.3 mm^2 = 40sqrt(14) + 43.3 mm^2\)

Therefore, the surface area of the regular pyramid is approximately \(40sqrt(14) + 43.3 mm^2.\)

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Answer:

B) 63°

Step-by-step explanation:

got it right on edge :)

Answer:

B. 63%

Step-by-step explanation:

edg 2023

The duration of this bond is 6.5 years.

Duration is a measure of a bond's sensitivity to changes in interest rates. To calculate the duration of this bond, we need to consider the present value of the bond's cash flows and the timing of those cash flows. In this case, the bond has a face value of $1,000, a coupon rate of 10 percent, and annual coupon payments.

First, we calculate the present value of the bond's cash flows. Since the bond has a coupon rate of 10 percent, the annual coupon payment is $100 ($1,000 x 10%). The bond has a remaining maturity of seven years, so there will be seven coupon payments in total. We can calculate the present value of these cash flows using the formula for the present value of an ordinary annuity:

Present Value = Coupon Payment x [1 - (1 + interest rate)^(-number of periods)] / interest rate

Assuming an interest rate of r, we have:

Present Value = $100 x [1 - (1 + r)^(-7)] / r

Next, we need to find the yield to maturity (YTM) of the bond. YTM is the rate of return an investor would earn by holding the bond until maturity. Since the bond is currently selling for $1,104 in the market, we can set up the following equation:

$1,104 = Present Value + (Coupon Payment / (1 + r)^7)

By solving this equation for r, we can find the yield to maturity. Using a financial calculator or spreadsheet software, we can determine that the yield to maturity is approximately 7 percent.

Now, we can calculate the duration of the bond. The duration formula is the weighted average time until the bond's cash flows are received, where the weights are the present values of the cash flows. In this case, we have seven annual cash flows, so the duration can be calculated as follows:

Duration = [(1 x Present Value of Year 1) + (2 x Present Value of Year 2) + ... + (n x Present Value of Year n)] / Present Value of the Bond

Plugging in the values, we get:

Duration = [(1 x Present Value of Year 1) + (2 x Present Value of Year 2) + ... + (7 x Present Value of Year 7)] / Present Value of the Bond

Calculating the present values for each year using an interest rate of 7 percent, we find:

Present Value of Year 1 = $100 / (1 + 0.07)^1

Present Value of Year 2 = $100 / (1 + 0.07)^2

...

Present Value of Year 7 = $100 / (1 + 0.07)^7

After calculating the present values for each year and plugging them into the formula, we find that the duration of the bond is approximately 6.5 years.

Therefore, the correct answer is 6.5 years.

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Answer:

6 people can go

Step-by-step explanation:

341-30=311

311-45.2x=0

45.2x=311

x=6.88

6.88 people can go but .88 of a person doesnt exist

Step-by-step explanation:

No. 1

sin33° = x / 14

No. 2

Sin Z = 36.87°

No. 3

A = 62

No. 4

C = 36.87°

Hope this helps :)

Answer:

36.87

Step-by-step explanation:

Answer:

angle 3 = 44 degrees

angle 2 = 136 degrees

angle 4 = 136 degrees

Step-by-step explanation:

angle 2 = angle 4

angle 1 = angle 3

angle 1 + angle 2 = 180 degrees

angle 3 +  angle 4 = 180 degrees

Answer:

225%

Step-by-step explanation:

250*.1 = 25

250-25=225$

Answer:

2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

Mars is 6.79 X 10^6 m

Step-by-step explanation:

Mars is at a distance of 206,600,000 km from the Sun at perihelion At aphelion, Earth is at a distance of 152,100,000 km from the Sun. This is a difference of 54,500,000 km, or 34,000,000 miles.  

Answer:

Mars is 6.79 X 10^6 m

Step-by-step explanation:

Make him brainliest!

Answer:

Separating the 3x and -5 apart from the (x+1)

Step-by-step explanation:

It would turn out to be (3x-5)(x+1) !

Factor out x+1 from the expression

(x+1) x (3x-5)

The normalization of a vector of u and v are (15/17)i+(-6/17)j+(8/17)k and (pi/sqrt(pi^2+50))i+(7/sqrt(pi^2+50))j-(1/sqrt(pi^2+50))k, (5/sqrt(26))j-(1/sqrt(26))i and (-1/sqrt(2))j+(1/sqrt(2))i, (7/sqrt(66))i-(1/sqrt(66))j+(4/sqrt(66))k and (1/sqrt(3))i+(1/sqrt(3))j-(1/sqrt(3))k respectively.

To normalize a vector, first find its magnitude, which is the square root of the sum of the squares of its components. Then, divide each component by the magnitude. After normalization, the vector will have a magnitude of 1 and can be used in various calculations such as dot product and cross product.

For vector u,

||u||=sqrt(15^2+(-6)^2+8^2)=17

u_normalized=u/||u||=(15/17)i+(-6/17)j+(8/17)k

For vector v,

||v||=sqrt(pi^2+7^2+(-1)^2)=sqrt(pi^2+50)

v_normalized=v/||v||=(pi/sqrt(pi^2+50))i+(7/sqrt(pi^2+50))j-(1/sqrt(pi^2+50))k

For vector u,

||u||=sqrt(5^2+(-1)^2)=sqrt(26)

u_normalized=u/||u||=(5/sqrt(26))j-(1/sqrt(26))i

For vector v,

||v||=sqrt((-1)^2+1^2)=sqrt(2)

v_normalized=v/||v||=(-1/sqrt(2))j+(1/sqrt(2))i

For vector u,

||u||=sqrt(7^2+(-1)^2+4^2)=sqrt(66)

u_normalized=u/||u||=(7/sqrt(66))i-(1/sqrt(66))j+(4/sqrt(66))k

For vector v,

||v||=sqrt(1^2+1^2+(-1)^2)=sqrt(3)

v_normalized=v/||v||=(1/sqrt(3))i+(1/sqrt(3))j-(1/sqrt(3))k

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The required length of the other leg is \($\sqrt{5}$\) cm. If we need to round to the nearest tenth, we get: \($b \approx 2.2$\) cm

Let's use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. So we have:

\($c^2 = a^2 + b^2$\)

where c is the length of the hypotenuse, a and b are the lengths of the legs.

We are given that the length of the hypotenuse is 3 cm and the length of one leg is 2 cm. Let's substitute these values into the equation above:

\($3^2 = 2^2 + b^2$\)

\($9 = 4 + b^2$\)

\($b^2 = 5$\)

\($b = \sqrt{5}$\)

So the length of the other leg is \($\sqrt{5}$\) cm. If we need to round to the nearest tenth, we get: \($b \approx 2.2$\) cm (rounded to one decimal place).

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The equation of g(x) after the translation up is g(x) = 4x² - 10

The given parameter represents the function f(x) in the question.

This function is given as

f(x) = 4x² - 13

The translation is given as

3 units up.

i.e. a translation up by 3 units

Mathematically, this can be represented as

(x, y) = (x, y + 3)

So, we have

g(x) = f(x) + 3

Substitute the known values in the above equation, so, we have the following representation

g(x) = 4x² - 13 + 3

Evaluate the like terms

g(x) = 4x² - 10

Hence, the equation of g(x) is g(x) = 4x² - 10

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Answer:

42: 1, 2, 3, 6, 7, 14, 21, 42

43: 1, 43

Step-by-step explanation:

As per the side splitter theorem, the segment length would complete the proportion is GJ

In math, the side splitter theorem states that "if a line is parallel to a side of a triangle and the line intersects the other two sides, then this line divides those two sides proportionally".

Here we have to find the segment length that would complete the proportion by using the side splitter theorem.

According to this theorem and by using the following diagram, we can elaborate the following proportion

=> GH/HE = GJ/JF

Here we have identifies that the segment that completes the proportion is GJ, because it must be used according to the theorem.

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Answer:

-2x

Step-by-step explanation:

Answer:

$2.60

Step-by-step explanation:

Simply divide the amount of money paid for the gas by the number of gallons of gas in the tank. So 38.48 \(\div\) 14.8, which equals $2.60.

$2.60 the gas cost per gallon

One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.

Given

Simply divide the amount of money paid for the gas by the number of gallons of gas in the tank. So 38.48 /14.8, which equals $2.60.

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Answer:

$4.70

Step-by-step explanation:

3*5.10= 15.30

20-15.30= 4.7

Answer:

she should get $4.70

Step-by-step explanation:

you need to take 5.10 and multiply by 3 to get $15.3 then do 20 minus 15.30

Answer:

Jun 25, 2018 — Reflection over the y -axis. Vertical stretch by a factor of two. Horizontal translation right two units. Vertical translation up two units. I hope this helps you .. ;]

Step-by-step explanation:

Answer:

the trapezoid

Step-by-step explanation:

area of trapezoid = 672

area of kite = 648

the formula for the kite area is 1/2×diagonal 1×diagonal 2

the formula for the trapezoid area is 1/2×(base 1 +base 2)× height

The equation that can be used to model the total cost is y = 18x

The given parameters are:

Cost = $72

Time = 4 hours

The hourly rate is calculated as:

k = Cost/Time

So, we have

k = 72/4

Evaluate

k = 18

The form of the equation is given as
y = kx

Substitute k = 18 in y = kx

y = 18x

Hence, the equation that can be used to model the total cost is y = 18x

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