A rectangle has a length of 9 cm and width of (3x-y)cm the area of the rectangle is 72cm^2

PQRS is a kite where PQ = 4xcm and QR = ycm

The perimeter of the kite PQRS IS 33cm

Calculate the values of x and y
You must show your working
Do not use a trial and improvement method.

The lengths of the base and height are, 13 miles and 52 miles respectively.

Given that;

The area of a parallelogram is, 676 square miles

And, the height is four times the length of the base,

Hence, We get;

Length of base = x

Height = 4x

Since, Area of the parallelogram = Base × Height

Hence, We get;

676 = x × 4x

x² = 676 / 4

x² = 169

x = √169

x = 13 miles

Thus, Length of base = x = 13 miles

Height = 4x = 4 x 13

                  = 52 miles

Thus,, The lengths of the base and height are, 13 miles and 52 miles respectively.

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Selina will get £153.78 of interest by the end of 3 years.

To calculate the total amount of interest Selina will get by the end of 3 years, we need to use the compound interest formula:

A = P[tex](1 + r/n)^{(nt)}[/tex]

where:

A = the amount of money at the end of the time period

P = the principal amount (the amount initially invested)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time period (in years)

In this case, we have:

P = £2000 (the amount initially invested)

r = 2.5% per annum = 0.025 (as a decimal)

n = 1 (the interest is compounded annually)

t = 3 (the time period is 3 years)

So, plugging in the values into the formula, we get:

A = 2000[tex](1 + 0.025/1)^{(1×3)}[/tex]

= 2000[tex](1.025)^{3}[/tex]

= 2000(1.07689)

= £2,153.78 (rounded to the nearest penny)

To find the total amount of interest Selina will get, we need to subtract the principal amount from the final amount:

Total interest = £2,153.78 - £2,000

= £153.78

Therefore, Selina will get £153.78 of interest by the end of 3 years.

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The area of the plot of land that has a top view as shown on a map above is calculated as: C. 112 square meters

The shape of the plot of land can be decomposed into two different triangles and 1 rectangle.

Area of triangle 1 = 1/2 * base * height

base = 8 m

height = 5 m

Area of triangle 1 = 1/2 * 8 * 5 = 20 square meters

Area of triangle 2 = 1/2 * base * height

base = 8 m

height = 7 m

Area of triangle 2 = 1/2 * 8 * 7 = 28 square meters

Area of the rectangle = length * width = 8 * 8

= 64 square meters.

Therefore, we have:

Area of the plot of land = 64 + 28 + 20

= 112 square meters.

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Answer- 24 spins

The probability of getting an E on a single spin is 1/4. The probability of not getting an E on a single spin is 3/4.

To find the expected number of spins before getting 6 E's, we can use the negative binomial distribution.

The formula for the expected value of a negative binomial distribution is:

E(X) = r * (1/p)

where:

- X is the random variable representing the number of spins until the 6th E appears

- r is the number of successes we want (in this case, 6)

- p is the probability of success (in this case, 1/4)

E(X) = 6 * (1/(1/4)) = 24

Therefore, Marcus's prediction for the number of total spins before the letter E appears 6 times is 24.

So the answer is 24 spins.

The rectangular prism with the specified length, width, and height has a surface area of 164 in².

A prism is a polyhedron in geometry that has n parallelogram faces that connect the n-sided polygon basis, the second base, which is a translated duplicate of the first base, and the n faces.

The bases are translated into all cross-sections that are parallel to them.

According to their intended use, prisms can be divided into four primary categories: dispersion prisms, deflection or reflection prisms, rotating prisms, and offset prisms.

So, simply said, a rectangular prism is a solid three-dimensional object having six rectangular faces.

The expression for a rectangular prism's surface area is:

S.A = 2( wl + hl + hw )

We enter the values provided into the expression above:

S.A = 2( wl + hl + hw )

S.A = 2( (3in × 10in) + (4in × 10in) + (4in × 3in) )

S.A = 2( 30in² + 40in² + 12in² )

S.A = 2( 82in² )

S.A = 164in²

Therefore, the rectangular prism with the specified length, width, and height has a surface area of 164 in².

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Correct question:

What is the surface area of the prism?

BMED is a trapezoid and OD is equals to BD/2. Proof of these is given below.

It should be noted that to prove that BMED is a trapezoid, we need to show that either BM || ED or BM || DE. We will show that BM || DE.

Since O is the midpoint of AM, we have OA = OM, and thus triangle ODM is isosceles. Therefore, OD = DM.

Also, since E is the midpoint of DC, we have DE || AB (because AB is also a mid-segment of triangle ADC). Therefore, angle ADE = angle ABC.

Using the fact that angles in a triangle add up to 180 degrees, we have:

angle EDC + angle ADE + angle CED = 180 degrees

Substituting angle ADE = angle ABC, we get:

angle EDC + angle ABC + angle CED = 180 degrees

But angle CED = angle BCD (because they are alternate interior angles formed by transversal BD cutting parallel lines DC and AB). Therefore:

angle EDC + angle ABC + angle BCD = 180 degrees

This means that angles BCD, ABC, and EDC are all on the same line, and thus angle BCD + angle ABC = 180 degrees.

Now, using the fact that angles in a triangle add up to 180 degrees, we have:

angle BAC + angle ABC + angle ACB = 180 degrees

Substituting angle BCD + angle ABC = 180 degrees, we get:

angle BAC + angle BCD + angle ACB = 180 degrees

Since triangle BCD is isosceles (because BD is an angle bisector), we have angle BCD = angle CBD. Therefore:

angle BAC + angle CBD + angle ACB = 180 degrees

But angle ACD = angle ACB + angle CBD, so:

angle BAC + angle ACD = 180 degrees

This means that triangle ABC is similar to triangle ACD.

Now, since BM is a median of triangle ABC, we have:

BM = 1/2 AC

But triangle ADC is similar to triangle ABC, so:

AC = 2 AD

Therefore:

BM = AC/2 = AD

So we have BM || DE, and BM = DE, which means that BMED is a trapezoid.

2. To prove that D is the midpoint of AE, we will use the fact that BMED is a trapezoid. Since BM || DE, we have:

BD/DM = BE/EM

But DM = OD (since triangle ODM is isosceles) and EM = DC/2 = AC/4 (since E is the midpoint of DC and AC is a mid-segment of triangle ADC).

Therefore:

BD/OD = BE/(AC/4)

But we also have:

BE = BD + DE = BD + BM = 2BD

Substituting this into the previous equation, we get:

BD/OD = 2BD/(AC/4)

Simplifying:

BD/OD = 8BD/AC

This means that:

OD = AC/8

But we also know that AC = 2AD, so:

OD = AD/4

Since O is the midpoint of AM, we also have:

OD = OM = AM/2

Therefore:

AD/4 = AM/2

This means that:

AD = 2AM/4 = AM/2 = OD

So D is the midpoint of AE, and CD = 2AD.

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In a triangle ABC. [AM] is the median relative to [BC] and O is the midpoint of [AM]. (BO) cuts [AC] at D. Let E be the midpoint of [DC]. 1) Prove that BMED is a trapezoid. 2) Prove that D is the midpoint of [AE); deduce that CD = 2AD. 3) Prove that OD == BD.

Answer:$8.99

Step-by-step explanation:

Answer:

---------------------

Perimeter is the sum of side lengths.

Given sides:

Find the perimeter by adding up side lengths:

Answer:

Step-by-step explanation:

a coordinate plane has given a coordinate to each an every point we draw on that. So when we have to find the radius of this circle , we have to find a pair of coordinates.

So I am taking these coordinates; (0,3) and (0,7)

So the radius = 7-3= 4 units

Answer:

If a person weighs 150 pounds and their shoes weigh 10 pounds, then the person's weight in pounds is 150 x .10 = 15 pounds.

The surface area of the cylinder to the nearest tenth is 82.2 in²

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface.

The surface area of cylinder is expressed as;

A = 2πr(r+h) . Where r is the radius and h is the height of the cylinder.

A = 2 × 3.14 × 1.7( 1.7+6)

= 10.68× 7.7

= 82.2 in²( nearest tenth)

Therefore the surface area of the cylinder is 82.2

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Answer: the slope of line = y2-y1÷x2-x1

Step-by-step explanation:x1=1 x2=-1 y1=9 y2=6

                                              slope=(6-9)÷(-1-1)

                                               slope= (-3)÷(-2)

                                                answer= 3

                                                               2

2 ¼ hours + 1 ½ hours = 3 ¾ hours

Jordan studied for his science test for 3 ¾ hours this weekend.

Science is a systematic process that produces knowledge in the form of testable predictions and universe-related explanations that can be organized and placed into order.

In general, science entails an effort to learn about universal truths or how fundamental laws work. Learning about the components of the universe and how they operate right now, in the past, and perhaps in the future is done through science.

Although science is intricate and multifaceted, its most significant traits are simple: Learning understanding what is in the natural world, how it functions, and how it came to be the way it is through science.

2 ¼ hours + 1 ½ hours = 3 ¾ hours

Jordan studied for his science exam for 3 ¾ hours this weekend.

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Jordan spent a total of 3 hours and 45 minutes studying for his science test this weekend.

what is arithmetic sequence.

An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.

Jordan studied for 2 ¼ hours on Saturday and 1 ½ hours on Sunday for his science test. To find the total number of hours he studied, we can add these two amounts.

2 ¼ hours is the same as 2 + ¼ hours, or 2 hours and 15 minutes.

So, we have:

2 hours and 15 minutes (Saturday) + 1 hour and 30 minutes (Sunday)

To add these two amounts, we can first add the hours and then add the minutes separately.

2 hours + 1 hour = 3 hours

15 minutes + 30 minutes = 45 minutes

Therefore, Jordan spent a total of 3 hours and 45 minutes studying for his science test this weekend.

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The solution to the given problem of the triangle comes out to be AC are 20 units long.

If a polygon contains at least one more segment, it is a hexagon. It is a simple rectangle in shape. Anything identical to a standard triangle form can only be distinguished from it by edges across A and B. Euclidean geometry does not completely describe the cube, despite the fact that its edges are all collinear. A triangle is formed by a circle with five sides and three angles.

Here,

If DE is the midpoint of triangle ABC, DE is parallel to AC and has a length of 50% of AC.

Let's use "x" units to represent the length of AC.

Given the information, DE equals 10 units, or 50 percent of AC's length. So that we may create the equation:

=>  DE = AC/2

When we enter DE's value as 10 units, we get:

=> 10 = x/2

To separate x, we multiply both sides of the equation by 2 and obtain:

=> 2 * 10 = x

=> x = 20

Therefore, AC is 20 units long.

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Answer:

Step-by-step explanation:

To find x and the degree measure of each angle, we can use the fact that the sum of the angles in a triangle is always 180 degrees.

(a) Writing an equation to find x, we have:

mZH + m<1 + m<J = 180

(2x - 3) + (5x + 7) + x = 180 (substituting given angle measures)

8x + 4 = 180 (combining like terms)

8x = 176

x = 22

Therefore, x = 22 is the solution to the equation.

(b) To find the degree measure of each angle, we can substitute x = 22 into the given expressions:

mZH = 2x - 3 = 2(22) - 3 = 41 degrees

m<1 = 5x + 7 = 5(22) + 7 = 117 degrees

m<J = x = 22 degrees

Therefore, the degree measures of the angles are mZH = 41 degrees, m<1 = 117 degrees, and m<J = 22 degrees.

The area of the parallelogram is 30 square inch.

A parallelogram is simply a quadrilateral with two pairs of parallel sides.

The area of parallelogram is expressed as:

A = base × height

From the diagram:

Plug the given values into the above equation and solve for area.

Area = base × height

Area = 10 in × 3 in

Area = 30 in²

Therefore, the area is 30 in².

Option D) 30 in² is the correct answer.

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An equation in slope-intercept form for the line shown in the given graph is equal to y = -5x + 5.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (5 - 20)/(0 + 3)

Slope (m) = -15/3

Slope (m) = -5.

At data point (0, 5) and a slope of -5, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = -5(x - 0)

y - 5 = -5x

y = -5x + 5

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Answer: a) x=23. b) x=12

Step-by-step explanation:

a) Alternate angles are equal
b) corresponding angles add to 180 degrees

Answer:

Prove the following identitics: tan 0 + cot 0 = I/(sin 0 cos 0) 0 + tan 0 sec 0 = cosec 0 'sec? 0. 18 cosec = cosec? 0 = tan? 0 cot2 19 sec? 0 sin ' 0 =cos? 0 'sin? 20 cos4 (sec 0 + tan 0) (sec 0 _ tan 0) = 1 2 sin? 0 = cOs? 0 _ 'sin? 0. 22 2 cos? 0_I=1 23 sec? 0 + cosec 0 = sec? 0 cosec? sin? , COs? 24 sec" 0 cosec" 0 = cos 0 sin" 0 25 =I tan 0 + 1 cot? 0 +4 26 (sec? 0 1) (cosec? 0 1) = [ 27 ((sec? 0 _0)+ V(cosec" 0 _ !) = sec € cosec 0 28 (sec? tan? 0) + V(cosec? 0 ~ cot? 0) = 2 cos? 0 29 =1 sin sec? 0 _ 1 sec 0 cosec 0 tan 0 + cot 0 30 tan 0 cot 0 sec 0 + cosec 0 cos 0 sin 0 31 =l V( + tan? 0) V( + cot? 0) Eliminate 0 from the following equations: 32 x = 4 cos 0, y = b sin 0. 33 x = 4 cot 0,y = b cosec 0. 34 x=a tan 0,y =b cos 0. 35 x = ] sin 0, y = [ + cos 0, 36 x =a sec 0,y = b +c cos 0. 37 x=a cosec 0, y = b sec 0. 38 X=l+ tan 0,y = cos 0. 39 x=sin 0 + cos 0,y = sin 0 40 cos X = sCc 0 + tan 0, y = sCc 0 ~ tan 0.

5/3 is greater than 1 (it's 1.67), and the product will be located on a number line to the right of 2/3. As a result, "The product will be located to the right because is greater than 1." is correct.

The area model, linear model, and set model are the three major types of fraction models. Evidence demonstrates that allowing pupils to deal with all three models is critical for establishing a conceptual knowledge of fractions.

The student is utilizing the model to calculate the product of 5/2 and 2/3, or (5/2) x (2/3).

To multiply fractions, simply multiply their numerators and then their denominators. So:

(5/2) x (2/3) = (5 x 2) / (2 x 3) = 10/6 = 5/3

Because 5/3 is greater than 1 (it's 1.67), the product will be located on a number line to the right of 2/3. As a result, "The product will be located to the right because is greater than 1." is correct.

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Complete question:

Answer:

127. my answer needs to be 20+ character sooooooooooooo

The water property that explains why the air temperature significantly changed but the water temperature stayed relatively the same is the property of specific heat.

Water's high specific heat capacity allows it to absorb and retain heat energy without much change in temperature, explaining why its temperature did not shift despite significant changes in the air temperature. Air has low specific heat capacity, while water has high.

Therefore, This caused the stream water temperature to remain stable despite environmental changes. Air temps change quickly due to its lower heat capacity.

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The mass of water vapor (g) / mass of dry air (kg) is the humidity measure of  the mixing ratio

The mixing ratio is defined as the mass of water vapor in grams divided by the mass of dry air in kilograms in a mixture of air and water vapor. It is a useful parameter for meteorologists and atmospheric scientists to describe the amount of water vapor in the atmosphere, particularly in the upper atmosphere where the relative humidity may be very low.

Relative humidity is the ratio of the partial pressure of water vapor in the air to the equilibrium vapor pressure at a given temperature and pressure, expressed as a percentage. Vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases at a given temperature in a closed system. Absolute humidity is the mass of water vapor per unit volume of moist air.

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Answer: no 3 is grade then -6 as 3 is positive number and 6 is negative number so positive is greater then negative number.

Step-by-step explanation:

In order to indicate if a number is greater than or less than another, we use the symbols > and <. For example, 10 is greater than 3, so we write it 10 > 3.

Answer:

  see attached

Step-by-step explanation:

You want a clock face with an angle of 240° between the hour and minute hands.

There are 22 possible locations for the minute hand such that the long arc between the hour and minute hands is 240°. The two of these that do not involve fractions of a second are 4:00 and 8:00.

The next occurrence will be 21 minutes 49 1/11 seconds later. And the one after that will be 43 minutes 38 2/11 seconds later, or 1 hour 5 minutes and 27 3/11 seconds after the first occurrence of the pair.

A clock face illustrating 8:00 is attached. You may need to scale it to your desired radius.

You can set your compass to 2" and draw the clock face circle. The points for 12 and 8 can be located by using the 10:00 position as the center of arcs with the same radius. Where those arcs intersect the original circle are the locations of 12 and 8.

2.29 is less than the MAD of 2.53, it would not be unlikely to get a box with 31 red pencils based on the MAD for the given data set.

To determine whether it would be unlikely to get a box with 31 red pencils based on the Mean Absolute Deviation (MAD) for the given data set, we first need to calculate the MAD.

Step 1: Calculate the mean of the data set

The given data set is: 22, 28, 30, 28, 35, 30, 28

The mean is calculated by adding up all the numbers and dividing by the total number of values:

Mean = (22 + 28 + 30 + 28 + 35 + 30 + 28) / 7 = 201 / 7 = 28.71 (rounded to two decimal places)

Step 2: Calculate the absolute deviations

The absolute deviation for each data point is calculated by finding the absolute difference between the data point and the mean:

|22 - 28.71| = 6.71

|28 - 28.71| = 0.71

|30 - 28.71| = 1.29

|28 - 28.71| = 0.71

|35 - 28.71| = 6.29

|30 - 28.71| = 1.29

|28 - 28.71| = 0.71

Step 3: Calculate the MAD

The MAD is the mean of the absolute deviations:

MAD = (6.71 + 0.71 + 1.29 + 0.71 + 6.29 + 1.29 + 0.71) / 7 = 17.71 / 7 = 2.53 (rounded to two decimal places)

Now, to determine whether it would be unlikely to get a box with 31 red pencils, we can compare 31 with the MAD. If the difference between 31 and the mean (28.71) is greater than the MAD (2.53), then it would be unlikely.

Difference = 31 - 28.71 = 2.29

Since 2.29 is less than the MAD of 2.53, it would not be unlikely to get a box with 31 red pencils based on the MAD for the given data set.

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The yearly average inflation rate during that time is 3.75% (option d).

First, we need to adjust the value of $1 in 1860 to its equivalent value in 2018 using the given purchasing power ratio of 1:28.95. This means that $1 in 1860 is equivalent to $28.95 in 2018.

Next, we need to find the CPI for 1860 and 2018. According to the Bureau of Labor Statistics, the CPI for 1860 is not available. However, we can use the CPI for 1913 as a proxy, as it was the year when the CPI was first introduced. The CPI for 1913 was 9.9.

Using the CPI for 1913 as the beginning CPI and the CPI for 2018 as the ending CPI, we can calculate the inflation rate as follows:

Inflation rate = (252.146 - 9.9) / 9.9 x 100% = 3.72%

Hence the correct option D (3.75%).

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The area under the X2 curve with 5 degrees of freedom to the right of 1.61, 9.24 and 15.09 is 0.078, 0.0001 and 0 respectively.

Area is a two-dimensional measure of a surface, such as a length multiplied by a width. It is used to measure the size of a space, such as a room, or a piece of land. Area can also be used to measure the size of a shape, such as a circle or a square. Area is usually measured in units such as square meters (m2) or square feet (ft2).

(a)1.61

The area under the X2 curve with 5 degrees of freedom to the right of 1.61 can be calculated using the following formula:

Area = 1 - Φ(x; df)

Where Φ(x; df) is the cumulative distribution function of the chi-square distribution, and df stands for the degrees of freedom.

For df = 5, Φ(1.61; 5) = 0.922.

Therefore, the area under the X2 curve with 5 degrees of freedom to the right of 1.61 is equal to 1 - 0.922 = 0.078.

(b) 9.24

For df = 5, Φ(9.24; 5) = 0.9999.

Therefore, the area under the X2 curve with 5 degrees of freedom to the right of 9.24 is equal to 1 - 0.9999 = 0.0001.

(c) 15.09

For df = 5, Φ(15.09; 5) = 1.

Therefore, the area under the X2 curve with 5 degrees of freedom to the right of 15.09 is equal to 1 - 1 = 0.

In conclusion, the area under the X2 curve with 5 degrees of freedom to the right of 1.61, 9.24 and 15.09 is 0.078, 0.0001 and 0 respectively.

Complete questions as follows-

find the area under the x2 -curve with 5 degrees of freedom to the right of (a) 1.61 (b) 9.24 (c) 15.09.

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The Central Limit Theorem describes the relationship between the distribution of sample means and the population distribution that the samples are taken from.

The Central Limit Theorem (CLT) states that if you take random samples of a population and calculate the mean of each sample, the distribution of those sample means will be approximately normally distributed, regardless of the underlying population distribution.

This means that as the sample size increases, the distribution of sample means becomes more and more normal. The CLT is a fundamental concept in statistics because it allows us to make inferences about population parameters based on sample statistics. It is widely used in hypothesis testing, confidence intervals, and other statistical applications.

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