Here is a map of an island
with cities A, B and C.
Jeremy drives from A to B on
the route shown.
Kia drives from B to C on
the route shown.
C
B
Work out how much further Jeremy drives than Kia.
You must show your working.
Show your working
+
Answer:
km
A
Scale: 1 cm represents 200 km

Area = 18 cm^2

Main steps:

Step 1: Identify the shape

Step 2: Use the correct formula for Area

Step 1: Identify the shape

First, we must identify that the shape is a trapezoid.  A trapezoid is a 4-sided shape that has one pair of parallel sides.  The two sides that are parallel to each other are called the "bases".

Observe that the top line and the bottom line have an arrow on each of them which denotes that those two sides are parallel.

Therefore, the shape is a trapezoid.

Step 2: Use the correct formula for Area

The area of a trapezoid is given by the following formula:

[tex]A_{Trapezoid} = \frac{1}{2}(b_1+b_2)h[/tex], where b1 and b2 are the two "bases", and h is the height (the perpendicular distance between the two parallel sides).  This amounts to finding the average of the two bases, and multiplying by the height.

[tex]A_{Trapezoid} = \frac{1}{2}(b_1+b_2)h[/tex]

[tex]A_{Trapezoid} = \frac{1}{2}((2 cm)+(4 cm))(6 cm)[/tex]

[tex]A_{Trapezoid} = \frac{1}{2}(6 cm)(6 cm)[/tex]

[tex]A_{Trapezoid} = 18 cm^2[/tex]

Step-by-step explanation:

The formula to find the arc length of a circle is:

arc length = (central angle / 360 degrees) x 2πr

where r is the radius of the circle.

In this case, we are given the central angle of the arc, which is 36 degrees, and the length of the chord AB, which is 3 units. To find the radius of the circle, we need to use some trigonometry.

Since angle ABC is an inscribed angle that intercepts arc AC, it is half the measure of arc AC. So, we can find the measure of arc AC as 2 times the measure of angle ABC, which is:

m(arc AC) = 2 x m∠ABC

m(arc AC) = 2 x 36

m(arc AC) = 72 degrees

Now, let's use the law of cosines to find the radius of the circle:

c^2 = a^2 + b^2 - 2ab cos(C)

where a and b are the sides of the triangle and c is the side opposite the angle C.

In triangle ABC, we know that side AB has length 3 units and angle ABC has measure 36 degrees. We also know that angle BAC is a right angle, since it is formed by a chord and a radius of a circle. So, we can use trigonometry to find the length of side AC:

sin(36) = AC / 2r

2r = AC / sin(36)

r = AC / (2 sin(36))

Using the law of cosines, we can find AC:

c^2 = a^2 + b^2 - 2ab cos(C)

AC^2 = 3^2 + (2r)^2 - 2(3)(2r) cos(36)

AC^2 = 9 + 4r^2 - 12r cos(36)

Substituting the expression for r from above, we get:

AC^2 = 9 + 4/((2 sin(36))^2) - 12/((2 sin(36))) cos(36)

AC^2 = 9.259

Taking the square root of both sides, we get:

AC ≈ 3.04 units

Now that we know the radius of the circle and the central angle of the arc, we can use the formula for arc length to find the length of arc AC:

arc length = (central angle / 360 degrees) x 2πr

arc length = (72 / 360) x 2π(3.04)

arc length ≈ 3.03 units

Therefore, the length of arc AC is approximately 3.03 units, rounded to the nearest hundredth.

If Mario asked "5-friends" about the amount they spent on boxes of cards last year, then only 3 friends spent less than $32.

We need to analyze the data given in the table and determine how many friends spent less than $32.00 on boxes of cards last year.

We are given the following data:

⇒ Friend 1 = $36,

⇒ Friend 2 = $32,

⇒ Friend 3 = $31,

⇒ Friend 4 = $12,

⇒ Friend 5 = $30.

We need to determine how many friends spent less than $32.00.

From the data given, we see that Friend 2 spent exactly $32.00, which is not less than $32.00.

So, we need to look at the remaining four friends to determine how many of them spent less than $32.00.

We can see that Friend 3 spent $31.00, which is less than $32.00.

So, at least one friend spent less-than $32.00.

Friend 4 spent only $12.00, which is much less than $32.00.

So, at least two friends spent less than $32.00.

Friend 5 spent $30.00, which is also less than $32.00.

So, at least three friends spent less than $32.00 on boxes of cards last year.

Therefore, three friends spent less than $32.00.

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The given question is incomplete, the complete question is

Mario asked 5 friends how much they spent on boxes of cards last year.

He organized the data in a table.

Friend 1  = $36,

Friend 2 = $32,

Friend 3 = $31,

Friend 4 = $12,

Friend 5 = $30.

How many friends spent less than $32.00?

Answer:

x = 4, -1

Step-by-step explanation:

Move all terms to the left side and set equal to zero. Then set each factor equal to zero.

have a good day :)

The correct formula to calculate the surface area of the cylinder is:

[tex]SA = 2\pi(1.2)^2 + 1.2\pi(3.8)[/tex]

What is cylinder?

A cylinder is a three-dimensional geometric shape that consists of a circular base and a curved surface that is formed by a set of parallel lines that are equidistant from the base. The base can be a circle, and the cylinder can have different heights.

To find the surface area of a cylinder, we use the formula:

[tex]SA = 2\pi r^2 + 2\pi rh[/tex]

where r is the radius of the base of the cylinder, h is the height of the cylinder, and π is pi (approximately 3.14).

The diameter of the cylinder is given as 2.4 centimeters, so the radius (r) is half of that, which is 1.2 centimeters. The height of the cylinder is given as 3.8 centimeters.

Therefore, the correct formula to calculate the surface area of the cylinder is:

[tex]SA = 2\pi(1.2)^2 + 1.2\pi(3.8)[/tex]

This simplifies to:

SA = 2π(1.44) + 4.56π

SA = 2.88π + 4.56π

SA = 7.44π

Finally, to find the amount of wrapping paper needed, we multiply the surface area by the number of cylinders we need to cover.

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The correct statement regarding the meaning of the conditional probability P(B|A) is given as follows:

C. The probability that the sum is 11, given that the first number cube shows a 6.

Conditional probability is the probability of one event happening, considering the result of a previous event.

The notation is P(B|A), which is read as the probability of B happening, considering that A has happened.

The events in this problem are given as follows:

Hence the correct statement regarding the meaning, that is, B given A = sum of 11 given that a six was rolled first, is given by option C.

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Step-by-step explanation:

A: 3x-4y=-2

3x=-2+4y

x =(-2+4y)/3

B: x-y⁴=0

x=y⁴

C: x²-3y=0

x²=3y

x=±√3y

D: |x| + |y| =2

x + y= 2

x =2-y

The surface area of the given shape above would be = 47.2

To determine the surface area of the solid shape above,the surface area of a cone and a cylinder is first determined and then added together.

The formula for the surface area (SA) of cone = πrs + πr²

where;

r = 1

s = 6

S.A = 3.14×1×6 + 3.14×1×1²

= 18.84+3.14

= 21.98

Formula for Surface area of cylinder = 2πr(r+h)

where;

r = 1

h = 3

SA = 2×3.14×1 (1+3)

= 25.12

Therefore, the surface area of the solid shape = 21.98+25.22 = 47.2

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The number of dummy variables to be entered into a regression model is always equal to the number of groups (k) minus 1 because of a statistical concept known as "dummy variable trap" or "multicollinearity".

In the regression analysis we use the variable of dummy to represent a whole group and sort them into group that could be used further in the analyses. A dummy variable takes the value of 0 or 1, depending on whether the observation, belongs to a particular group or not in a data.

Let us assume that we have k groups, so we will need k-1 dummy variable to present the entire group where we create a situation when the sum of all the dummy variable is equal to 1. This creates a perfect multicollinearity, which makes the regression model impossible to estimate.

So, to avoid this problem, we eliminate one group from the model and use k-1 dummy variables to represent the remaining groups for the purpose of easiness in the analysis of the data that we are using for research.

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The value of x as given in the above triangle is x = 12

A hypotenuse is the longest side of a right-angled triangle, the side opposite the right angle, in geometry.

The Pythagorean theorem, states that the square of the length of the hypotenuse is the same as the sum of the squares of the lengths of the other two sides, may be utilized in the calculation the length of the hypotenuse.

Since we have a 45-45-90 triangle, so the sides opposite of the 45-degree angle are the same, while the hypotenuse is √2

6√2(√2) = 6(2) = 12

x = 12

Recall that two of the same roots will become one whole number, for example

√2(√2) = 2

√3(√3) = 3

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The volume of the hemisphere whose radius is 6.8 ft. is 658.2 ft³ rounded to the nearest tenth

The radius of each hemisphere = 6.8 ft.

Volume of sphere = 4/3 πr³

A hemisphere is a 3D geometric object that is made up of half of a sphere, with one side being flat and the other being a bowl-like shape

So by dividing the equation in half we get

Volume of hemisphere = (4/3 πr³ )/2

Volume of hemisphere = 2/3 πr³

Putting the value of r in the equation

Volume of hemisphere = 2/3 × 3.14 × (6.8)³

Volume of hemisphere = 658.2 ft³

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Answer:

# > 1

Step-by-step explanation:

12x? > 12

/ 12.     /12.

? > 1

Any number larger than 1 makes this true.

Required value of f(g(x)), g(f(x)), f(f(x)) are 2x²- 4x + 2 , 2x² -1 and 8x⁴ respectively.

the range of f(g(x)) is [0, ∞), the range of g(f(x)) = = 2x²-1 is [-1,∞) and the range of f(f(x)) is [0, ∞).

What is composition of functions?

Suppose we are given two functions f(x), g(x). We construct a new function h(x) as follows. plug 'x' into g(x) and find its value. then plugin this value into f(x), that is find f(g(x)). Now set h(x) = f(g(x)). This new function h(x) is called the composition of functions f(x) and g(x).

a. f(g(x)) = 2 * (x - 1)² = 2(x² - 2x + 1) = 2x²- 4x + 2 Since fg(x)) is a polynomial its domain is all real numbers. to find the range note that f(g(x)) = 2 * (x - 1) ² . and the range of the square is all non-negative real numbers. So the range of f(g(x)) is [0, ∞).

b. g(f(x)) = (2x²) - 1 =2x² -1.g(f(x)) is a polynomial function, so the domain of g(f(x)) is (-∞, ∞). Note that the range of 2x² is [0, ∞). So the range of g(f(x)) = 2x²-1 is [-1,∞)

c. f(f(x)) = 2 * (2x²)² = 2(4x⁴) = 8x⁴ . Since this is a polynomial function, the domain is (-∞, ∞), and clearly the range is [0, ∞).

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The percentage of students that type less than 30 words per minute are given as follows:

30.61%.

An histogram is a graph that shows the number of times each element of x was observed, or the number of observations in each range of a data-set.

For the histogram in this problem, we have that:

The total number of students is given as follows:

5 + 10 + 14 + 20 = 49.

15 students type less than 30 words per minute, hence the percentage is given as follows:

P = 15/49 x 100%

P = 30.61%.

The histogram is given by the image presented at the end of the answer.

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Answer: y = |x - 1| - 1

Step-by-step explanation:

We will use this form of absolute value equations. a is the slope, which is 1. h is the horizontal shift and k is the vertical shift.

     y = a|x - h| + k

First, we see this graph is shifted one unit down from the parent function (absolute value). We will subtract 1 from the parent function.

     y = |x| - 1

Next, we see it is shifted one unit right from the parent function. We will add this to the equation above. Since we are adding one unit, we will subtract one unit as it's reversed (" -h" in the equation above).

     y = |x - 1| - 1

The domain of f^(-1)(x) is [1, infinity), and the range of f^(-1)(x) is all real numbers.

We are given that;

Function f(z) = Y² + 1.

Now,

Step 1: Replace f(z) with y

y = z^2 + 1

Step 2: Swap x and y

z = y^2 + 1

Step 3: Solve for y

y^2 = z - 1

y = sqrt(z - 1)

Step 4: Replace y with f^(-1)(x)

f^(-1)(x) = sqrt(x - 1)

This is the inverse function of f(z).

Therefore, by domain and range answer will be all real numbers, and the range of f(z) is [1, infinity).

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The volume, in cubic feet, of the sandbox is 12 cubic feet.

The volume V of a rectangular prism is given by the formula:

V = lwh

Where:

l is the representation of length, w is the representation of width, and h is the representation of height.

As per the given information, the length l = 4 1/2 feet, the width w = 5 1/3 feet, and the height h = 1/2 foot.

We need to convert the mixed numbers to improper fractions:

l = 4 1/2 = 9/2

w = 5 1/3 = 16/3

h = 1/2

Substitute the values to the given  formula,

V = (9/2) x (16/3) x (1/2)

V = 48/4

V = 12 cubic feet.

Therefore, the volume of the sandbox is 12 cubic feet.

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Step-by-step explanation:

yes, the inequality is almost correct.

this is the fully correct one :

27 <= 12 + 6x

we want to get at least 27 gallons in the pool.

that means, if we hit exactly 27 gallons, it is a valid solution. therefore we need the "<=".

we want to get at least 27 gallons by starting with already existing 12 gallons and then adding 6 gallons for every minute (e.g. 5 minutes give us 5×6 = 30 gallons additional water).

so, now, let's solve :

27 <= 12 + 6x

15 <= 6x

15/6 <= x

2.5 <= x

therefore, it will take at least 2.5 minutes to fill the pool with at least 27 gallons.

The equation that represents the average sales each day for the real estate company is s = 1/(2h)

To find the equation for f, we need to use the information given in the question. The company hopes to sell houses every other day of the month, which means they sell houses on days 1, 3, 5, 7, and so on. We can write this as:

t = 2n - 1

where n is an integer that represents the number of days since the first of the month.

Now, we need to express the average sales each day, f(t), in terms of n. We can assume that the company sells the same number of houses on each of the days they sell (i.e., on days 1, 3, 5, 7, and so on). Let's call this number of houses "h". Then, the total number of houses sold on the days they sell is:

h + h + h + ... (n times) = hn

The total number of days they sell houses in the month is:

n/2 (since they sell houses every other day)

Therefore, the average number of houses sold each day, f(t), is:

f(t) = hn / (n/2) = 2h

Substituting t = 2n - 1, we get:

f(t) = 2h

So, the equation that represents the average sales each day for the real estate company is:

s = 1/f(t) = 1/(2h)

where h is the average number of houses sold on each of the days they sell (i.e., on days 1, 3, 5, 7, and so on).

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The number of miles she will run each day to meet her daily goal of 42-1/2 miles dor work is 5.5 miles per day, under the given condition that She runs 9-1/2 miles on Sunday furthermore she runs the same distance on each of the 6 remaining day.

In order to find out how many miles she needs to run each day, we have to perform  division of  the total number of miles she needs to run by the number of days she has left

33 miles ÷ 6 days = 5.5 miles per day

Hence, Sam needs to run 5.5 miles per day for the remaining six days in order to meet her goal of running 42-1/2 miles for the week.

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Answer:

Rise/run = - 4/3

The rise is vertical, run is from left to right.  I counted 4 units down from (-3, 2) to (-3, -2) and since it is down, it's negative.  Then, I counted 3 units to the right from (-3, -2) to (0, -2) and the run will always be positive.  Because there is a negative in one of the numbers, the slope will be negative: - 4/3

The probability that the archer gets exactly 4 bull's-eyes out of 8 shots is approximately 0.191

This is an example of a binomial distribution problem, where the archer has a probability of hitting the bull's-eye of 0.49 for each arrow and we want to know the probability of getting exactly 4 bull's-eyes out of 8 shots.

The probability of getting exactly 4 bull's-eyes out of 8 shots can be calculated using the binomial probability formula

P(X = k) = (n choose k) × p^k × (1-p)^(n-k)

where

X is the number of successes (bull's-eyes)

k is the specific number of successes we want (4 in this case)

n is the total number of trials (8 in this case)

p is the probability of success on a single trial (0.49 in this case)

(n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items (also written as "nCk")

Plugging in the numbers, we get

P(X = 4) = (8 choose 4) × 0.49⁴ × (1-0.49)⁴

= (8! / (4! × 4!)) × 0.49⁴ × 0.51⁴

≈ 0.191

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The measure of the secant line VZ is 36.

From the diagram:

Using the Intersecting Secants Theorem:

VY × VZ = VW × VX

Plug in the values and solve for x.

( x + 2 ) × ( x + 2 + 29 ) = ( x + 4 ) × (  x + 4 + 19 )

( x + 2 ) × ( x + 31 ) = ( x + 4 ) × (  x + 23 )

Aplly distrubutive property

x( x + 31 ) + 2( x + 31 ) = x(  x + 23 ) + 4(  x + 23 )

x² + 31x + 2x + 62 = x² + 23x + 4x + 92

Collect and add like terms

x² -  x² + 31x + 2x - 23x - 4x = 92 - 62

31x + 2x - 23x - 4x = 92 - 62

6x = 92 - 62

6x = 30

x = 30/6

x = 5

Now, the value of line VZ will be:

VZ = x + 2 + 29

Plug in x = 5

VZ = 5 + 2 + 29

VZ = 5 + 2 + 29

VZ = 36

Therefore, line VZ is 36.

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Answer:

28 inches.

Step-by-step explanation:

The side length of the square can be found by taking the square root of the area, which is 7 inches.

The perimeter of a square is simply 4 times the length of one of its sides, so the perimeter of this square paper is:

4 x 7 inches = 28 inches

Answer: Cant really show you but use the picture below

Step-by-step explanation:

The slope is 2/5 or basically use the rise over run method. I would start with using x as 0. If so the y would be 3 as seen. So one point is (0,3). From there you can use another number and input it.

The graph that best represents this situation is a line graph. A line graph is a type of chart that uses lines to show the relationship between two variables. In this case, the two variables are the number of stuffed animals Nicole has left and the number of months that have passed. The line graph will start at 60 stuffed animals and decrease by 5 stuffed animals each month until it reaches 0 stuffed animals.

Here is an example of a line graph that represents this situation:

[Image of a line graph with the number of stuffed animals on the y-axis and the number of months on the x-axis. The line starts at 60 and decreases by 5 each month until it reaches 0.]

I hope this helps! Let me know if you have any other questions.

The Z-Score value for a particular sample with mean 70.07 and the standard deviation is 10.27 is equals to 0.97.

In statistics, the z-score is the numeric number of standard deviations by which t a raw score lies above or below the mean value. Positive z score represents value above the mean. We have a sample with sample mean, μ = 70.07

Standard deviations, σ = 10.27

We have to determine z score that corresponds to a raw score of 80. That is value of X = 80. Using the Z-Score formula, [tex]z = \frac{ X - \mu }{\sigma} [/tex]

where X --> raw value

μ --> mean

σ--> standard deviations

Substituents all known values in above formula, [tex]z =\frac{ 80 - 70.07}{10.27} [/tex]

[tex]z= \frac{ 9.93 }{10.27} [/tex]

= 0.97

Hence, required value is 0.97.

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About 1144π cubic inches (or approximately, 3591 cubic inches) of additional air is needed to fully fill the sphere-shaped balloon.

The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius.

In this case, the radius is 8 inches, so the volume of the balloon is:

V = (4/3)π(8^3)

V = 2144π cubic inches

The balloon already has 1000 cubic inches of air, so the amount of air still needed to fill the balloon is:

2144π - 1000 = 1144π cubic inches (rounded to the nearest whole number, this is approximately 3591 cubic inches).

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Step-by-step explanation:

A  true   opposite side are congruent and parallel

B   false   opposite sides are not perpindicular

C  true opposite sides are equal and parallel

D  false   not perpindicular

E false    not necessarily 90 degrees