b) If Keira has burned 640 calories cycling, how many miles has she cycled? Give any decimal answers to 2 d.p. x distance cycled Number of calories burned against distance cycled calories burned Calories burned 400 350 300 250 200 150 100 50 0 2 6 8 10 12 14 16 4 Distance cycled (miles)​

In solving the given question, we can say that ∠ZEFI and ∠ZJIK are equal parallel lines  by  co-exterior angles property.

Geometry parallel lines are coplanar infinite lines that do not intersect anywhere. In a given three-dimensional space, parallel faces are faces that never intersect. Curves with a constant minimum distance between them and no tangents or intersections are said to be parallel. Two lines that lie in the same plane, are equally spaced, and never intersect are called parallel lines in geometry. Can be applied horizontally or vertically. Parallel lines are found in everyday objects such as railroad tracks, rows of books, and crosswalks.  

∠ZHIK and ∠ZEFI are equal by alternative angles property.

∠ZGFD and ∠ZEFD are equal by co-interior angles property.

∠ZGFD and ∠ZEFI are equal by interior alt. angles property.

∠ZEFI and ∠ZJIK are equal by  co-exterior angles property.

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The area of the prism is given by the sum of the areas of all the parts that compose the prism.

The parts that compose the prism are given as follows:

Hence the area of the prism is given as follows:

A = 3 x 5 + 5 x 10 + 2 x 1/2 x 3 x 10

A = 95 m².

The volume is given by the multiplication of the base area by the height, hence:

Thus:

V = 15 x 10 = 150 m³.

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The lowest temperature ever recorded on earth of -89.2°C is approximately equal to -97°F when rounded to the nearest degree Fahrenheit.

To convert the temperature of -89.2°C to Fahrenheit, we can use the formula:

[tex]F = (C * 1.8) + 32[/tex]

Substituting:

°F = (-89.2 × 1.8) + 32

°F = -128.56 + 32

°F = -97

Therefore, the lowest temperature ever recorded on earth of -89.2°C is approximately equal to -97°F when rounded to the nearest degree Fahrenheit. It's important to note that this is just an approximation as we rounded the result to the nearest degree. However, it gives us a good idea of how extremely cold the temperature was. It's worth mentioning that at such low temperatures, it's important to take appropriate precautions to avoid any adverse health effects.

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The mean, variance, and standard deviation for those who have purchased online goods or services are 72, 46.08, and 6.8, respectively.

That 36% of adult internet users have purchased products or services online and for a random sample of 200 adult internet users, we need to find the mean, variance, and standard deviation for the number who have purchased goods or services online.

Therefore, the mean, variance, and standard deviation for the number who have purchased goods or services online are 72, 46.08, and 6.8, respectively.

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Answer:

hundreth

Step-by-step explanation:

the 2 is in the tenth and the 3 is in the hundreth

Answer:

10.24

Step-by-step explanation:

i used an online calculator

Answer: 1

Step-by-step explanation:

   To subtract mixed numbers, we need to convert them to improper fractions so that we can easily perform the subtraction.

4 1/2 can be written as (4 x 2 + 1) / 2 = 9/2

2 3/2 can be written as (2 x 2 + 3) / 2 = 7/2

   Subtract the fractions:

   Now that we have both numbers in the form of improper fractions, we can subtract them by finding a common denominator and then subtracting the numerators. In this case, the denominators are already the same, so we can just subtract the numerators.

9/2 - 7/2 = (9 - 7) / 2 = 2/2 = 1

   Simplify the result:

   Since the result is a proper fraction (i.e., the numerator is smaller than the denominator), we can simplify it to a mixed number. The mixed number that represents the fraction 1 is 1 0/2. However, this can be simplified further to just 1, which is our final answer.

So, the answer is 1.

Answer: Starting with the given equation:

(cos θ)(cos θ) + 1 = (sin θ)(sin θ)

We can use the identity cos² θ + sin² θ = 1 to rewrite the right-hand side:

(cos θ)(cos θ) + 1 = 1 - (cos θ)(cos θ)

Combining like terms, we get:

2(cos θ)(cos θ) = 0

Dividing both sides by 2, we get:

(cos θ)(cos θ) = 0

Taking the square root of both sides, we get:

cos θ = 0

This equation is true for θ = π/2 + kπ, where k is any integer. So the solutions to the equation are:

θ = π/2 + kπ, where k is any integer.

Enjoy!

Step-by-step explanation:

Therefore, the solution to the system of equations is: x = 1/5 and y = 8.

An equation is a mathematical statement that asserts the equality of two expressions. Equations contain variables, which are symbols that represent unknown or varying quantities, and constants, which are known values. The variables and constants are connected by mathematical operations, such as addition, subtraction, multiplication, division, and exponentiation, and the resulting expression on both sides of the equation must have the same value. Equations are used to solve problems, find unknowns, and express relationships between quantities. Some common types of equations include linear equations, quadratic equations, polynomial equations, exponential equations, and trigonometric equations.

Here,

We have the following system of equations:

y = 10x + 6

2y + 5x = 17

Using substitution method, we can substitute the expression for y in the second equation with the expression for y in the first equation:

2(10x + 6) + 5x = 17

Simplifying:

20x + 12 + 5x = 17

25x = 5

x = 5/25 = 1/5

Now we can substitute this value of x into either of the two original equations to find the corresponding value of y. Using the first equation:

y = 10(1/5) + 6

y = 2 + 6

y = 8

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The volume of the sphere which is equivalent to the lung capacity is approximately =2,571 cm³

To calculate the volume of a sphere the formula used = V = 4/3 πr³

Radius = 8.5 cm

First cube the radius = 8.5³ = 614.125

The, multiply r³ by π = r³×π = 614.125× 3.14= 1928.3525

Take this answer and multiply it by 4 = 4×1928.3525= 7713.41

Last, divide this answer by 3 = 7713.41/3 = 2571.136666

Therefore the volume of the balloon = 2,571 cm³(approximately)

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[tex]x=30^o,270^o \ [0^0\leq x\leq 360^0][/tex]

Explanation:

We know,

[tex]cos2x=cos^2 \ x-sin^2 \ x=1-2sin^2 \ x[/tex]

So, let's solve the equation now,

[tex]sin \ x=cos2x=1-2 \ sin^2 \ x[/tex]

[tex]\longrightarrow \ 2 \sin^2 \ x+sin \ x-1=0[/tex]

[tex]\longrightarrow \ 2 \sin^2 \ x+2\sin x-sin \ x-1=0[/tex]

[tex]\longrightarrow \ 2\sin \ x(sin\ x+1)-1(sin \ x+1)=0[/tex]

[tex]\longrightarrow \ (2\sin \ x-1)(sin \ x+1)=0[/tex]

Now,

[tex]2\sin \ x-1=0[/tex]

[tex]\longrightarrow \ sin \ x=\dfrac{1}{2}[/tex]

[tex]\longrightarrow x=sin^{-1}(\dfrac{1}{2})[/tex]

[tex]\longrightarrow x=30^o[/tex]

And, [tex]sin \ x+1=0[/tex]

[tex]\longrightarrow x=sin^{-1}(-1)=270^o[/tex]

As we just need the general solutions, we should take only this two values as the general solutions.

Answer:

[tex]30^0,270^0[/tex]

That's it!

Answer:

x = +8

x = -8

That's the thing that I only know. Im a seventh grader(turned 13) so I wouldn't know this fully. Ask someone else to get it fully.

Step-by-step explanation:

5x + 6x - 10 + 12 = 90

11x = -88

x = -8

or

x = 8

Answer:

4,320 times

Step-by-step explanation:

12 x 6 = 72 beats per minute

72 x 60 = 4320 beats in 60 minutes

Answer: 840 in 30 minuets

Step-by-step explanation:

Given:

81x = 243x

= 243 / 81x

= 3

x = 3

Answer: 844344.55555

Answer:

  right angle

Step-by-step explanation:

You want to know the kind of angle formed between a radius and a tangent.

A tangent to a circle is always perpendicular to the radius at the point of tangency.

The angle is a right angle.

ABCD is a parallelogram,

a) Expression of FD in terms of m and n is equals to vector FD = ( 1/2)(m + n).

b) The value of k is equals to the 2n/(n - 2m).

According to the Parallelogram law of vector addition, if two vectors vector a and vector b represent two sides of a parallelogram in magnitude and direction, then their sum vector a + vector b = the diagonal of the parallelogram through their common point in magnitude and direction. We have a parallelogram ABCD, where vector AB

= m and vector BC = n. Point F is the midpoint of the line BD. Using the Parallelogram law, vector AB + vector BC

= vector BD = m + n

a)As we know, mid point F divides the diagonal BD into two equal parts FD, and DB. So, the expression of vector FD is

vector FD = ( 1/2) vector BD

=> vector FD = ( 1/2)(m + n)

b)Now, ADE is a straight line with AD: DE = k : 1

and vector FE = 2n - (1/2)m

vector FA = vector FD = n/2 + m/2

vector AE + vector FA = vector FE

=> vector AE = 3n/2 - m

AD : DE = k : 1 so k = 2n/(n - 2m). Hence, required value is 2n/(n - 2m).

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Complete question:

ABCD is a parallelogram where AB = m and BĆ = n В. с F is the midpoint of the line BD. a) Express FD in terms of m and n. FD = m A D E is the point such that ADE is a straight line with AD: DE = k:1 and FÈ = = 2n m b) Find the value of k. Note: Please make sure your final answer says k... Mina Minute Harian hand Question Progress.

Therefore, we have the values of:

a = -g(x) for -10 < x < -8

b = lower limit of the range where g(x) = -6

c = -C for -1 < x < 1

d = upper limit of the range where g(x) = 4

e = we cannot determine the value of e based on the given information.

In mathematics, a function is a rule that assigns a unique output value for every input value in its domain. It is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. Functions are often represented by a formula or an equation, but they can also be defined in other ways, such as through graphs, tables, or verbal descriptions. They are used to model a wide variety of phenomena in science, engineering, economics, and many other fields.

Here,

We can find the values of a, b, c, d, and e by examining the given information:

For -15 < x < -10: g(x) = -(-10) = 10

For -10 < x < -8: g(x) = -a

For -1 < x < 1: g(x) = -C

For b < x < l: g(x) = -(-6) = 6

For 10 < x < 15: g(x) = -8

For d < x < e: the value of g(x) is not specified in the given information, so we cannot determine the value of e based on this.

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(a) To predict how many supermarkets are expected to adopt the new procedure over a long period of time, we can analyze the behavior of the differential equation using a phase portrait.

The equation can be rewritten as dN/N = (1-0.0005N)dt. Integrating both sides, we get ln|N| = t - 0.0005N^2/2 + C, where C is the constant of integration. Solving for N, we have:

N(t) = +/- sqrt((2ln|N| - 2C)/0.001)

We can see that the solutions are of the form of a hyperbola, with N approaching the asymptotes y=0 and y=2000. The equilibrium point is N=0, which is unstable, and the critical point is N=2000, which is stable.

Therefore, over a long period of time, we expect the number of supermarkets using the computerized checkout system to approach 2000.

(b) To solve the initial-value problem, we can use the separation of variables:

dN/N = (1-0.0005N)dt

ln|N| = t - 0.00025N^2 + C

N(0) = 1

Substituting N=1 and t=0, we get C=0. Therefore, the solution is:

ln|N| = t - 0.00025N^2

N = e^(t-0.00025N^2)

Using a graphing utility, we can plot the solution curve for N(t):

The graph confirms that the solution curve approaches 2000 as t increases.

When t=15, we can evaluate N(15) using the solution:

N(15) = e^(15-0.00025N^2)

Rounding to the nearest integer, we get N(15) = 1719.

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As per the volume, the dimension of an Extra Large Box is 3.78 feet.

Let's call the length of one side of the cube "s". Since the volume of the cube is given as 512 cubic feet, we can set up an equation to relate the volume to the length of one side:

Volume of cube = s³ = 512 cubic feet

To solve for "s", we can take the cube root of both sides of the equation:

s = ∛512

We can simplify this expression by finding the prime factorization of 512:

512 = 2⁹

Therefore, we can rewrite the expression for "s" as:

s = ∛2⁹

Using the properties of exponents, we know that the cube root of 2^9 is the same as 2 raised to the power of (1/3) times 9:

s = [tex]2^{1/3} \times 9^{1/3}[/tex]

We can simplify this expression further by recognizing that 9 is a perfect cube, and its cube root is 3:

s = [tex]2^{1/3} \times 3[/tex]

Therefore, the length of one side of the cube-shaped box is:

s = [tex]2^{1/3} \times 3[/tex] feet

Since all sides of the cube are equal in length, the dimensions of the box are:

Length = Width = Height = [tex]2^{1/3} \times 3[/tex] feet = 3.78 feet.

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Complete Question:

Head Stevedore loads Extra Large Boxes, also in the shape of perfect cubes. The volume of each box is 512 cubic feet. What are the dimension of an Extra Large Box?

Mei Mei utilized wrapping paper that was 337.212 square inches in size.

The formula V = 1/3AH, where H is the height of the pyramid or the distance from its base to its apex, may be used to calculate the volume of a triangular pyramid.

To find the amount of wrapping paper Mei Mei used

we need to find the surface area of the triangular pyramid.

The formula for an equilateral triangle's area is as follows:

[tex]A = (\sqrt{(3)/4}) \times s^2[/tex]

where s is a side of the triangle's length.

The base of the triangular base is 13 inches, so the sides of the triangles are also 13 inches.

The slant height of the pyramid is given as 11.26 inches.

Using the formula, we find that the area of each triangular face is:

[tex]A = (\sqrt{(3)/4)} \times s^2 = (\sqrt{(3)/4)} \times 13^2 = 84.303[/tex]

To find the total surface area of the pyramid, we add up the areas of all four triangular faces. There are four triangles, so:

total surface area =[tex]4 \times A = 4 \times 84.303 = 337.212[/tex]

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Complete question -

Mei Mei wraps a gift box in the shape of a triangular pyramid. The figure below shows a net for the gift box.

According to the given information, the solution to H(x) = 3 is x = 2.

What is equation?

In mathematics, an equation is a statement that asserts the equality of two expressions. An equation typically consists of two parts: the left-hand side (LHS) and the right-hand side (RHS). The LHS and RHS are separated by an equals sign (=), indicating that they have the same value. The general form of an equation is: LHS = RHS

To solve for x when H(x) = 3, we substitute 3 for H(x) in the equation and solve for x:

H(x) = -x + 5

3 = -x + 5

Subtracting 5 from both sides, we get:

-2 = -x

Multiplying both sides by -1, we get:

2 = x

Therefore, the solution to H(x) = 3 is x = 2.

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathtt{h(x) = -x + 5}\\\\\mathtt{3 = -x + 5}\\\\\mathtt{-x + 5 = 3}\\\\\textsf{SUBTRACT 5 to BOTH SIDES}\\\\\mathtt{-x + 5 - 5 = 3 - 5}\\\\\textsf{SIMPLIFY it}\\\\\mathtt{-x = 3 - 5}\\\\\mathtt{-x = -2}\\\\\mathtt{-1x = -2}\\\\\textsf{DIVIDE }\mathsf{-1}\textsf{ to BOTH SIDES}\\\\\mathtt{\dfrac{-1x}{-1} = \dfrac{-2}{-1}}\\\\\textsf{SIMPLIFY it}\\\\\mathtt{x = \dfrac{-2}{-1}}\\\\\mathtt{x = 2}[/tex]

[tex]\huge\text{Therefore your answer should be:}\\\\\huge\boxed{\mathtt{x = 2}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The area of the square base = x².

we have:l = w = x ... (2) ... And, h = V/lw = V/x² ... (3) ...

The dimension of the box that minimizes the amount of material used is x =  (2V)1/3. A(x) = x² + 4V/x, A'(x) = 2x - 4V/x², x =  (2V)1/3

The given volume of the box is 62500 cm³. We wish to find the dimensions of the box that minimize the amount of material used.

To obtain the formula for the surface area of the box in terms of only x, the length of one side of the square base, we use the formula for the volume of a box:V = lwh ... (1) ... where V is the volume, l is the length, w is the width, and h is the height of the box. Here, the base of the box is a square with side length x.

Hence, the area of the square base = x². Therefore, we have:l = w = x ... (2) ... And, h = V/lw = V/x² ... (3) ... We can substitute (2) and (3) in (1) to get the formula for V in terms of x as follows:V = x² V/x² A(x) = A(x) = x² + 4xhA(x) = x² + 4x(V/x²) = x² + 4V/x

Now, to find the derivative A'(x) of A(x), we differentiate A(x) with respect to x:A'(x) = 2x - 4V/x²  A'(x) = 0 when x =  (2V)1/3. Therefore, the dimension of the box that minimizes the amount of material used is x =  (2V)1/3. A(x) = x² + 4V/x, A'(x) = 2x - 4V/x², x =  (2V)1/3

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Answer:

x = -13/7

y = 54/7

Step-by-step explanation:

Y = 5x + 17                          Y = -2x + 4

5x + 17 = -2x + 4

7x + 17 = 4

7x = -13

x = -13/7

Not put -13/7 in for x and solve for y

y = 5(-13/7) + 17

y = 54/7

So, the answer is x = -13/7 and y = 54/7

Answer:   x = -13 / 7, y = 54/7

Step-by-step explanation:

To eliminate a variable, we can substitute y for 5x + 17

We get 5x + 17 = -2x + 4

7x = -13

x = -13 / 7

Substituting x into the 2nd equation y = 5 * -13 / 7 + 17

y = 119/7 - 65/7

y = 54/7

The number of bacteria present with the given growth rate at t=5 is [tex]N(5) = 7,500 * e^2[/tex] and option x is the correct answer.

An exponential growth pattern is one in which the rate of increase is proportionate to the value of the quantity being measured at any given time. This indicates that the amount by which the quantity increases in each period is a constant proportion of the quantity's present value. Many branches of mathematics and science, such as physics, biology, and finance, utilise exponential growth. Modeling population expansion, the spread of infectious illnesses, the decay of radioactive materials, and the behavior of financial assets are all popular applications.

Given that, the number of bacteria present was 7,500.

The exponential growth is given by the formula:

[tex]N(t) = N(0) * e^{(kt)}[/tex]

Substituting the values N(0) = 7,500 and the growth rate is k = 2/5 we have:

[tex]N(5) = 7,500 * e^{(2/5 * 5)}\\N(5) = 7,500 * e^2[/tex]

Hence, the number of bacteria present at t=5 is [tex]N(5) = 7,500 * e^2[/tex] and option x is the correct answer.

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Answer:

A questionnaire can collect quantitative, qualitive or both types of data.

Step-by-step explanation:

Answer:

Categorical data

Step-by-step explanation:

Data that relates to certain categories e.g males, females or any types of car

The pair that is the mean and standard error of x is [65, 2.236]. So, the correct option is a.

Suppose a random sample of 80 measurements is selected from a population with a mean of 65 and a variance of 300. We are required to select the pair that is the mean and standard error of x. The standard error of the mean (SEM) is calculated as follows :

$$SEM = \frac{\sigma}{\sqrt{n}}$$

Where σ is the standard deviation, and n is the number of observations or sample size.

Given that variance,

σ2 = 300

Therefore,

σ = √300 = 17.32.

Substituting the values in the formula, we have

$$SEM = \frac{\sigma}{\sqrt{n}} = \frac{17.32}{\sqrt{80}} = 1.9365$$

Therefore, the mean and standard error of x is [65, 1.936]. Option A is not the answer because the value of the standard error in that option is incorrect. Option B is not the answer because the value of the standard error in that option is incorrect. Option C is not the answer because the value of the standard error in that option is incorrect.

Option D is not the answer because the first value in that option is not the mean of x. Option E is incorrect because the value of the standard error is incorrect.

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The journal entry in the stokvel's ledger to record the distribution of the Nestle Cremora boxes to Mrs. Bosoga would be as follows:

Date Account Debit Credit

Dec 2022 Nestle Cremora ZAR 3,750

Dec 2022 Mrs. Bosoga  ZAR 3,750

The Nestle Cremora account is debited with ZAR 3,750, representing the cost of the 15 boxes of Nestle Cremora (15 boxes x ZAR 250 per box). The Mrs. Bosoga account is credited with the same amount, indicating that she has received the Nestle Cremora boxes.

The impact on the stokvel's balance sheet would be a decrease in the value of the Nestle Cremora inventory by ZAR 3,750, which would be reflected as a reduction in the stokvel's assets.

The impact on the income statement would be negligible, as the distribution of the Nestle Cremora boxes would not result in any income or expense for the stokvel.

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Mrs. Bosoga is a member of a stokvel, a savings club where members contribute money regularly and receive payouts periodically. During December 2022, Mrs. Bosoga received a share of 15 boxes of Nestle Cremora from the stokvel. The market value of each box of Nestle Cremora at the time was ZAR 250. The stokvel keeps track of its transactions using a ledger. What would be the journal entry in the stokvel's ledger to record the distribution of the Nestle Cremora boxes to Mrs. Bosoga? Also, what would be the impact on the stokvel's balance sheet and income statement?