An equilateral triangle with side length 3 cm is shown in the diagram, work out the height of the triangle.
Give your answer rounded to 1 DP.

Step-by-step explanation:

let's write this properly that we are not confusing ourselves :

s = ½×a×t²

a = 30 ft/sec²

t = 6 sec

so,

s = ½ × 30 ft/sec² × (6 sec)² = ½ × 30 ft/sec² × 36 sec² =

= ½ × 30 ft × 36 = 15 ft × 36 = 540 ft

s = 540 ft

In 1798, the first vaccination (for small pox) was discovered. The most notable achievement of these efforts has been the elimination of smallpox sickness from the world.

Hence, option (c) is correct choice.

In 1721, Lady Mary Wortley Montagu introduced smallpox vaccination to Europe by requesting that her two children be immunised against the disease, as she had seen done in Turkey. Dr. Edward Jenner developed the world's first effective vaccination. He discovered that those who had cowpox were resistant to smallpox.

Edward Jenner, a rural doctor from Berkeley (Gloucestershire), England, conducted the world's first vaccine in 1796. Jenner injected an eight-year-old kid, James Phipps, with pus from a cowpox lesion on a milkmaid's hand.

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The coordinates of point H are (-1,-3). This is obtained by using the midpoint formula and solving for the coordinates of point H, given the midpoint of GH and the coordinates of point G.

To find the coordinates of point H, we can use the midpoint formula, which states that the midpoint of a line segment is the average of the coordinates of its endpoints.

If the midpoint of GH is (1,-4) and the coordinates of point G are (3,-5), we can write: (1,-4) = [(3 + x)/2, (-5 + y)/2]

where x and y are the coordinates of point H. We can solve for x and y as follows:

2(1,-4) = (3 + x, -5 + y)

(2, -8) = (3 + x, -5 + y)

2 = 3 + x --> x = -1

-8 = -5 + y --> y = -3

Therefore, the coordinates of point H are (-1, -3).

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The dilated figure coordinates will be A(-6,6); B(3,3); C(3,-3); D(-3,0) E.g. If a figure is drawn by the help of lines and the length of all the four lines are equal, then the resultant figure is known as Square Shape.

Figures are nothing but a kind of drawing which we make using lines and arcs. Figures can be 2-D or 3-D. In mathematics these figures are studied by calculating their's area, perimeter, surface area, volume, etc.

In mathematics when we draw a figure using line and arcs and the resultant figure has some specific pre-defined properties then such figures are called shapes.

The coordinates of the given figure ABCD are

A=(-2,2); B=(1,1); C=(1,-1) and D=(-1,0)

As we have to dilate the figure by the factor of 3 from the origin which means we have to enlarge the figure 3 times with same origin, then we simply multiply the coordinates of the given figure by 3.

Dilated coordinates will be

A=(-2×3,2×3)=(-6,6)

B=(1×3,1×3)=(3,3)

C=(1×3,-1×3)=(3,-3)

D=(-1×3,0×3)=(-3,0)

Therefore, New dilated coordinates of the figure are A(-6,6); B(3,3); C(3,-3) and D(-3,0).

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nah I don't think I want to.

Based on the information and the dimensions of the scaled figure, we can infer that the dimensions of the actual figure are 2.1 meters by 3.9 meters.

To calculate the measures of the original figure we must apply a rule of three. In this case, the logic that we must use is: if 2 centimeters are equivalent to 1 meter, how much is 4.2 cm and 7.8 cm respectively.

According to the above, the measurements of the original figure are: 2.1 meters by 3.9 meters.

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The probability that randomly selected mechanical component weighs: more than 11.5 lbf is 0.0099, less than 8.7 lbf is 0.3208,  less than 5.0 lbf is 0.0228, between 6.2 lbf and 7.0 lbf is 0.1314, between 10.3 lbf and 14.0 lbf is 0.0436, between 6.8 lbf and 8.9 lbf is 0.3464.

We can use the standard normal distribution and z-scores to answer these questions:

P(X > 11.5) = P(Z > (11.5 - 8) / 1.5) = P(Z > 2.33) = 0.0099

Therefore, the probability that a randomly selected mechanical component weighs more than 11.5 lbf is 0.0099, or about 1%.

P(X < 8.7) = P(Z < (8.7 - 8) / 1.5) = P(Z < 0.47) = 0.3208

Therefore, the probability that a randomly selected mechanical component weighs less than 8.7 lbf is 0.3208, or about 32%.

P(X < 5.0) = P(Z < (5 - 8) / 1.5) = P(Z < -2) = 0.0228

Therefore, the probability that a randomly selected mechanical component weighs less than 5.0 lbf is 0.0228, or about 2%.

P(6.2 < X < 7.0) = P((6.2 - 8) / 1.5 < Z < (7 - 8) / 1.5) = P(-1.2 < Z < -0.67) = 0.1314

Therefore, the probability that a randomly selected mechanical component weighs between 6.2 lbf and 7.0 lbf is 0.1314, or about 13%.

P(10.3 < X < 14.0) = P((10.3 - 8) / 1.5 < Z < (14 - 8) / 1.5) = P(1.53 < Z < 2.67) = 0.0436

Therefore, the probability that a randomly selected mechanical component weighs between 10.3 lbf and 14.0 lbf is 0.0436, or about 4%.

P(6.8 < X < 8.9) = P((6.8 - 8) / 1.5 < Z < (8.9 - 8) / 1.5) = P(-0.47 < Z < 0.60) = 0.3464

Therefore, the probability that a randomly selected mechanical component weighs between 6.8 lbf and 8.9 lbf is 0.3464, or about 35%.

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____The given question is incomplete, the complete question is given below:

Suppose that the weight of a mechanical component is normally distributed with mean p = 8.0 Ibf and standard deviation = 1.5 lbf. Answer the following questions: 1. If you randomly select a mechanical component, what is the probability that it weighs more than 11.5 lbf? 2. If you randomly select a mechanical component, what is the probability that it weighs less than 8.7 lbf? 3. If you randomly select a mechanical component, what is the probability that it weighs less than 5.0 lbf? 5. If you randomly select a mechanical component, what is the probability that it weighs between 6.2 lbf and 7.0 lbf? 6. If you randomly select a mechanical component, what is the probability that it weighs between 10.3 lbf and 14.0 lbf? 7. If you randomly select a mechanical component, what is the probability that it weighs between 6.8 lbf and 8.9 lbf?

All the angles of the given parallelogram found using the properties of the parallelogram are 38°,38°, 142° and 142°.

What is meant by a parallelogram?

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size. On the same side of the transversal, the interior angles are supplementary. 360 degrees is the sum of all interior angles. The qualities of a parallelogram are shared by the shapes of a square and a rectangle.

Given the two opposite angles of parallelogram as (4x-50)° and

(60 - x)°.

We are asked to find all the angles of the parallelogram.

As said earlier, opposite angles of parallelogram are equal.

So,

4x-50 =  60 - x

5x = 110

x = 22

So the opposite angles are:

4x-50 = 4*22- 50 = 38°

Adjacent angles are supplementary. So,

38 + y = 180

y = 142°

Sum of all angles of parallelogram should be 360°.

38+38+142+142 = 360°.

Therefore all the angles of the parallelogram are 38°,38°, 142° and 142°.

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Answer:

hope this helps

Step-by-step explanation:

This means car traveled 18 miles on ONE gallon of gas.

You should get 20 to 30 miles per gallon of petrol on average when driving your car. Some automobiles, nevertheless, can go up to 60 miles per gallon. Your car's efficiency varies depending on a number of factors, including miles. Car weight, unsafe driving practices, the environment, and shoddy maintenance are a few of the contributing causes.

Vehicle mileage was x miles.

x miles of gasoline equals x gallons of fuel.

Gasoline consumption is inversely proportional with the distance driven by an automobile.

distance traveled by car  = K× Gasoline used  

Using unitary method,

Distance traveled by car in 1 gallon of gas  = 18 × 1 miles.

Distance traveled by car in 1 gallon of gas  = 18 miles

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The perimeter of a rectangle with given length and width is 28 feet.

The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).

Given that, length of a rectangle = 8 feet and the width of a rectangle = 6 feet.

Here, perimeter= 2(8+6)

= 2×14

= 28 feet

Therefore, the perimeter of a rectangle is 28 feet.

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The function f(x) = x⁵ - x³ + x is odd. It satisfies the condition f(-x) = -f(x), making it an odd function.

To determine whether the function f(x) = x⁵ - x³ + x is even, odd, or neither, we need to test if the function satisfies the following conditions for all x:

f(-x) = f(x) for even functions

f(-x) = -f(x) for odd functions

If the function satisfies neither of these conditions, then it is neither even nor odd.

Testing f(-x) = f(x):

f(-x) = (-x)⁵ - (-x)³ + (-x) = -x⁵ + x³ - x

f(x) = x⁵ - x³ + x

Since f(-x) is not equal to f(x), the function is not even.

Testing f(-x) = -f(x):

f(-x) = (-x)⁵ - (-x)³ + (-x) = -x⁵ + x³ - x

-f(x) = -(x⁵ - x³ + x) = -x⁵ + x³ - x

Since f(-x) = -f(x), the function is odd.

Therefore, the given function f(x) = x⁵ - x³ + x is odd.

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There are 180 different starting lineups that can be created for the college team.To find the number of different starting lineups that can be created for the college team, we need to use the combination formula.

The number of ways to choose k items from a set of n distinct items is given by the formula:

nCk = n! / (k! * (n-k)!)

where "!" denotes the factorial function, which means the product of all positive integers up to that number.

In this case, we want to choose 2 guards out of 5, 2 forwards out of 4, and 1 center out of 3. So the total number of different starting lineups that can be created is:

(5C2) * (4C2) * (3C1)

= (5! / (2! * 3!)) * (4! / (2! * 2!)) * (3! / (1! * 2!))

= (10) * (6) * (3)

= 180

Therefore, there are 180 different starting lineups that can be created for the college team.

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There are 20 different combinations of committees that can be formed since no person can serve on more than one committee.

In order to form committees of 4, 3, and 2 people, we must first determine how many combinations are possible. There are 9 people in total, so the first committee must consist of 4 people. That leaves 5 people. The second committee must consist of 3 people, leaving 2 people for the final committee. To calculate the total number of combinations, we must multiply the number of choices for each committee. For the first committee, there are 9C4 combinations, for the second committee there are 5C3 combinations, and for the third committee there are 2C2 combinations. Multiplying these together, we obtain 9C4 x 5C3 x 2C2 = 20 combinations. Therefore, there are 20 different combinations of committees that can be formed since no person can serve on more than one committee.

The complete question: A group of 9 people is going to be formed into committees of 4, 3, and 2 people. How many can be formed if no person can serve on more than one committee?

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By empirical rule, 99.7% of the students have a grade point average which is between 1.38 and 3.84.

Suppose that the grade point average of undergraduate students at one university has a bell-shaped distribution with a mean of 2.61 and a standard deviation of 0.41.

Here, μ = 2.61 , σ = 0.41

Using the empirical rule :

The first part of the empirical rule states that 68% of the data values will fall within 1 standard deviation of the mean. To calculate "within 1 standard deviation," you need to subtract 1 standard deviation from the mean, then add 1 standard deviation to the mean. That will give you the range for 68% of the data values.

2.61 − 0.41 = 2.2

2.61 + 0.41 = 3.02

The range of numbers is 2.2 to 3.02

The second part of the empirical rule states that 95% of the data values will fall within 2 standard deviations of the mean. To calculate "within 2 standard deviations," you need to subtract 2 standard deviations from the mean, then add 2 standard deviations to the mean. That will give you the range for 95% of the data values.

2.61 − 2(0.41) = 1.79

2.61 + 2(0.41) = 3.43

The range of numbers is 1.79 to 3.43

Finally, the last part of the empirical rule states that 99.7% of the data values will fall within 3 standard deviations of the mean. To calculate "within 3 standard deviations," you need to subtract 3 standard deviations from the mean, then add 3 standard deviations to the mean. That will give you the range for 99.7% of the data values.

2.61 − 3(0.41) = 1.38

2.61+3(0.41) = 3.84

The range of numbers is 1.38 to 3.84.

Hence, 99.7% of the students have a grade point average which is between 1.38 and 3.84.  

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The information from the given set have the following solutions for:

a) X ∪ Y = {1, 3, 5, 6, 7, 9}

b) X ∩ Z = {1, 9}

c) X' = {2, 4, 6, 8}

In mathematics, a set is a collection of distinct objects, called elements or members, that share a common property or are grouped together for some reason. A set can be finite or infinite.

For the universal set S = {1, 2, 3, 4, 5, 6, 7, 8, 9}

Z = {1, 2, 4, 6, 8, 9}

X = {1, 3, 5, 7, 9}

Y = {1, 5, 6, 7}

we shall evaluate for the following:

X ∪ Y = {1, 3, 5, 6, 7, 9} {all the elements in X and Y}

X ∩ Z = {1, 9} {the elements common to X and Z}

X' = {2, 4, 6, 8} {all the elements in the universal set not in X}

Therefore, the information from the given set have the following solutions for:

a) X ∪ Y = {1, 3, 5, 6, 7, 9}

b) X ∩ Z = {1, 9}

c) X' = {2, 4, 6, 8}

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Answer:

8

Step-by-step explanation:

Let's call the number of 27c stamps in the book "x". The number of 32c stamps in the book would then be $6.00 / $0.32 = 18.75 stamps, but since stamps come in whole numbers, we'll round down to 18 stamps. So the total number of stamps in the book is x + 18.

The total value of the 27c stamps is $0.27 * x. The total value of the 32c stamps is $0.32 * 18 = $5.76. The total value of both stamp types is $6.00, so we have the following equation:

$0.27x + $5.76 = $6.00

Solving for x:

$0.27x = $0.24

x = $0.24 / $0.27 = 8.89 stamps, rounded down to the nearest whole number, which is 8 stamps.

So the answer is B) 8.

Zachariah has a higher ratio of American stamps than Khai because 7 over 12 is less than 15 over 24.

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a) The connection of the literacy principle to assessments created and used by preceptors and others directly involved in classrooms is fairly straightforward. Less egregious is the connection of the principle to assessments created and assessed by parties outside the classroom. Tradition has allowed and indeed encouraged some assessments to serve responsibility or monitoring purposes without sufficient regard for their impact on pupil literacy.

b) To satisfy the literacy principle, assessment must change in ways consonant with the current changes in tutoring, literacy, and class. In the history, pupil literacy was frequently viewed as a unresistant process whereby scholars flashed back what preceptors told them to flash back . harmonious with this view, assessment was frequently allowed of as the end of literacy. The pupil was assessed on commodity tutored preliminarily to see if he or she flashed back it. also, the mathematics class was seen as a fractured collection of information given meaning by the schoolteacher.

c) The alternate chance gave scholars the occasion not simply to redo the questions on which they were unprofitable in the first stage but, more importantly, to give lesser attention to the essay questions they had little time to address. similar two- stage testing basically formalizes what numerous preceptors of writing do in their courses, giving scholars an occasion to revise their work after the schoolteacher or other scholars have read it and offered suggestions.

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The percentage for the markup for the wheelbarrow is 40%.

It is important to note that the percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100

In this case, the retailer sells wheelbarrows for $21 that were acquired at a cost of $15. The markup will be:

= Selling price - Cost price

= $21 - $15

= $6

Markup percentage will be:

= Markup / Cost price × 100

= [tex]\frac{6}{15}[/tex]× 100%

=0.4*100%

= 40%

Therefore, the percentage for the markup is 40%.

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The equation 7(2W + 3) = 14W + 20 has no solution because it produces a false statement when you distribute 

       14 W + 21 = 14 W + 20

because 21 ≠ 20.

To make it have infinitely many solutions, you need to make that statement always true.  You can do this by changing the "20" on the right side to be "21":

    7(2W + 3) = 14W + 21

This equation is always true, no matter what value of W you pick.

The power of the snow machine is 10,000 Joules per second.

power is simply the amount of energy transferred or converted per unit time.

It is expressed as;

P =  work-done / time

P = ( force × displacement ) / time.

Given the data in the question;

Plug the given values into the above formula and solve for P.

P = ( 1000N × 1000m ) / 100s

P = ( 1000000Nm / 100s

P = 10,000 Nm/s

P = 10,000 J/s

Therefore, the power of the machine is  10,000 J/s.

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Answer:

Step-by-step explanation:30 x 2 = 60 because 8:9 get simplify by 2 and you just times the 30 with 2

Answer:

Let the common multiple be x

John's score is 8x Peter's is 9x

8x/9x-30=4/3

24x=36x-120

12x=120

x=10

John's score is 8 x 10=80

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The measurements required to provide a 95% confidence interval in the true mean to within plus minus 0.28v  are 2 measurements and they are 1.24v and 1.8v .

Given that, based on 51 measurements of time-dependent electrical signal, the standard deviation is 1.52 v

The 95 confidence interval in its true mean value is 0.28 and the measurements required to provide a 95% confidence interval in the true mean to within plus minus 0.28v  are 2 measurements and they are 1.24v and 1.8v

A Standard Deviation of the R.V.(random variable), a sample, and a statistical population, the data set, or the probability distribution is the square root of the its variance

A True Mean refers to a population mean. It actually would not have a population mean, because since it is the either impossible to get and probably the time consuming and too much expensive to get it.

Therefore, the 95 confidence interval in its true mean value is 0.28 and the measurements required to provide a 95% confidence interval in the true mean to within plus minus 0.28v  are 2 measurements and they are 1.24v and 1.8v

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Answer:

Let's call the total area of the common space "A". Since the quiet area takes up one-third of the space, its area is A/3.

The scale of the plan is 1 ft.: 4 cm, which means that one foot on the plan represents 4 cm in real life. So, the area of the social area on the plan is 4 times smaller than the actual area of the social space.

Therefore, the actual area of the social space is (A - A/3) = 2A/3. And the area of the social area on the plan is (2A/3) / 4.

Area of the social area on the plan is (2A/3) / 4.

Here,

Let the total area of the common space "A".

Since the quiet area takes up one-third of the space, its area is A/3.

The scale of the plan is 1 ft.: 4 cm

So,

One foot on the plan represents 4 cm in real life.

So, the area of the social area on the plan is 4 times smaller than the actual area of the social space.

Therefore, the actual area of the social space is (A - A/3) = 2A/3.

Thus the area of the social area on the plan is (2A/3) / 4.

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The Translation to  algebraic expression is shown below.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

To create a variable expression for a circumstance in the actual world:

For example, the sum of a and b can be written as

= a+ b

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Answer:

10/x is a nonlinear equation. Linear equations represent a straight line in a graph, whereas nonlinear equations are used to represent curves. In this case, the degree of variable y is 1 and the degrees of the variables in the equation violate the linear equation definition, which means that the equation is not a linear equation.

The diameter of the circle with a circumference of 20 ft is 6.37 ft.

The circumference of a circle is the distance around the circle which is 2πr.

The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.

The diameter of the circle can be obtained by the equation of the circumference formula with the given circumference of 20 ft.

Therefore, 2πr = 20.

2r = 20/π.

2r = 6.37 ft.

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