3. Shown is a rectangular based pyramid. The apex E is directly over the centre E of the base. B 8cm 10cm с 5cm D AD = 8cm CD = 5cm CE = 10cm a. Calculate the height of the pyramid b. Calculate the angle EBD​

We have 72-tenths left.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. When used in conversational English, a fraction indicates the number of components of a particular size, as in one-half, eight-fifths, and three-quarters.

To divide 80 tenths by 9 ones, we first convert the 9 ones to tenths. 9 ones is equivalent to 90 tenths.

Next, we divide 80 by 90:

80 / 90 = 0.8888... (rounded to four decimal places)

To multiply, we multiply 0.8888... by 9:

0.8888... * 9 = 8

Finally, to subtract, we subtract 8 from 80:

80 - 8 = 72

So, we have 72-tenths left.

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It should be noted that the amount based on the information will be $1600.00.

From the information, the state government gives property owners a tax rebate with the anticipation that each property owner will spend approximately p% of the rebate, and in turn each recipient of this amount will spend p% of what he or she receives, and so on.

We've been given the rebate as well.

Sum of an infinite Geometric Series = A/(1-r)  

Rebate A $400.00

Rate 75.00%

Sum of an infinite Geometric Series = $400/(1-75%)

= $1600.00

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Answer:

[tex]4g^5[/tex]

Step-by-step explanation:

[tex]\sqrt{16g^{10}}=\sqrt{16}*\sqrt{g^{10}}=4g^5[/tex]

The unit rate for 2/3 pound for every 1/4 table spoon will be 2.667 pounds per table spoon.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

In 1/4 table spoon, there is 2/3 pound. Then the units rate is given by the division of the numbers 2/3 and 1/4. Then the rate is given as,

Rate = (2/3) ÷ (1/4)

Rate = (2/3) x (4/1)

Rate = 8 / 3

Rate = 2.667 pounds per table spoon

The unit rate for 2/3 pound for every 1/4 table spoon will be 2.667 pounds per table spoon.

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The correct expansion of the given expression would be = 2x 2x²+2x (-5)+3.2x²+3• (-5). That is option C.

The given expression of equations;

(2x + 3)(2x² - 5). That is the product of 2x+3 and 2x²-5

= 2x *2x² + 2x*(-5) + 3*2x²+3×(-5)

= 4x³ - 10x+ 6x²-15

= 10x⁵ -10x-15.

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Answer:c

Step-by-step explanation:

did it

Answer:

see below

Step-by-step explanation:

perimeter = 2*(6.25x - 3.5 + 3.5 x +6) =2(9.75x+2.5) = 19.5x+5

Answer:

a) See attached image

b) AA (or AAA) similarity; either one is correct

c) The statue is 22 meters tall

Step-by-step explanation:

Let's assume the height of the statue is h (to be determined)

a) First let's create a diagram to model this scenario. See attached image
 One of the properties of a mirror reflection is that the angle of incidence i.e. the angle at which light strikes the mirror = angle of reflection i.e. the angle at which the light reflects off the mirror

These angles are shown as α and β in the diagram

The two triangles we choose to solve this problem are
ΔABC and ΔCED

Given that ∠BCA is a complementary angle to angle of reflection and ∠ECD is complementary to the angle of incidence, it follows that

m∠BCA = m∠CED

m∠BAC of ΔABC = m∠ECD of ΔECD = 90°

Therefore the third angles of both triangles are also equal

b) By the AA (or AAA) or Angle-Angle Similarity theorem, the two triangles are similar

Therefore the ratio of the sides must be the same for corresponding sides

Therefore
[tex]\dfrac{AB}{DE} = \dfrac{AC}{CD} \\\\Given AD = 12, CD = 3\\\\\dfrac{AD}{CD} = \dfrac{12}{3}= 4\\\\\therefore \\\\\dfrac{AB}{ED} = 4\\\\[/tex]

Since ED is the height of the girl = 5.5 meters and AB = height of the statue = h

we get
[tex]\dfrac{h}{5.5} = 4\\\\h = 4 \times 5.5\\\\h = 22\\\\[/tex]

Answer (c) height of statue = 22 meters

So the total cost of tying the lace around the tablecloth is $18.36.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10.

Here,

The length of the boundary of the square table cloth is 4 times its side length, so the length of the boundary is 4 * 54 cm = 216 cm.

To convert the length from centimeters to meters, we divide by 100:

216 cm / 100 = 2.16 meters

Finally, to find the cost of sticking the lace around the table cloth, we multiply the length of the lace by the cost per meter:

2.16 meters * ₹8.5 per meter = ₹18.36

So the cost of sticking the lace around the table cloth is ₹18.36.

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a) Sample mean is arithmetic average of data values. The sample mean of provide data values is 10.

b) The five-number summary of the sample is minimum = 4, Q1 = 4.5, median = 9 , Q3 = 15.5 and maximum= 16.

The population mean is denoted by greek letter, μ and sample mean is a random variable; which is written as x-bar and x-bar stands for individual values it takes. The sample mean is a statistic measure obtained by calculating the arithmetic mean of sample values ( values of variable in sample). The sample mean formula is: x-bar = ( Σxᵢ) / n

Now, we have to calculate sample mean of following data values, 12,8,15,16,5,4.

Sum of values, Σ xi = 12 + 8 + 15 + 5 + 4 + 16 = 60

Number of values = 6

So, Sample mean, = ( Σ xi ) / n = 60/6 = 10

The five-number summary includes following :

So, Steps to determine the five-number summary:

Now, the sample set is 12,8,15,16,5,4. Arrange the data values in ascending order, 4,5,6,12,15,16. So, Minimum value

= 4 , Maximum value = 16 ,Median = mean of 6 and 12 = (6 + 12)/2 = 9. The vales written as(4, 5, ) 6, 12, (15, 16 ). The value of first quartile, Q₁ = median of lower ( 4,5) = (4+5)/2

= 9/2 = 4.5. Similarly, Third quartile, Q₃

= (15+16)/2= 31/2 = 15.5. Thus, the five-numer summary is minimum = 4, Q₁

= 4.5, median = 9 , Q₃ = 15.5 and

maximum = 16.

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Complete question:

Consider the sample set 12,8,15,16,5,4 and answer the below questions:

(a)[2 pts] what is the notation of the sample mean? find the sample mean.

(b)[3 pts] find the five-number summary of the sample.

Answer:

141

Step-by-step explanation:

First, you need to identify the pattern. As we have 3 terms, the pattern is +18 then +30. So, we can determine the next term is +18. 75 + 18 = 93. 93 is the 4th term. We can also determine the next term is +30. 93 + 30 = 123. 123 is our 5th term. Based off of what we know, we can determine the next term will be +18. 123 + 18 = 141. This proves our 6th term is 141.

I hope this helped. If this isn't correct, I apologize. This is based off of the 3 terms shown. If this helped, leave a heart and leave stars.

The required 2 properties to describe the relationship between DE and AC are  1. DE || AC and 2. DC = AC / 2.

Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.

Here,
From the figure,
AD = BD and BE = EC

It implies that D and E are the midpoints of the side AB and BC,
So, 1. for the given triangle line joining the midpoints of the triangle always parallel to the third side of the triangle.
DE || AC

And when DE || AC then the measure of DE is equal to half of the measure of AC.
DC = AC / 2

Thus, the required 2 properties are 1. DE || AC and 2. DC = AC / 2.

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Answer:

Step-by-step explanation:

Sandra, Deacon, and Breanna read a total of 5 + 6 + 7 = 18 books. Since one book was read by all three children, we need to subtract it once from the total. Therefore, they read 18 - 1 = 17 different books.

Sara needed 8 test tubes for 3 different experiments. The first experiment required 2 test tubes, leaving 8 - 2 = 6 test tubes for the other two experiments. Since the two experiments required the same number of test tubes, each one required 6/2 = 3 test tubes.

It is unclear what the question is asking. Please provide more information or a specific question.

Branson and his sister Beatrice combined their allowance of $7 each to buy a movie for $12. They spent a total of 7 x 2 = $14 on the movie. Therefore, they had 14 - 12 = $2 left to buy fruit salad. They bought 2 containers of fruit salad for $1 each, leaving them with $0. They split the containers evenly between them, so each of them got 2/2 = 1 container of fruit salad.

Before Cam broke his right arm, he could type 9 words per minute on his phone. After he broke his arm, he could only type 6 words per minute. The difference between the number of words he could type in 5 minutes before and after he broke his arm is 5 x (9 - 6) = 5 x 3 = 15 words.

Gisselle saved $6 every week for 8 weeks, so she saved a total of 6 x 8 = $48. She found a used bicycle for $50, so she did not have exactly enough for the bicycle. She was $50 - $48 = $2 short.

Metric System is a decimal system of measurement that is based on the meter, kilogram, and second and is used in most countries around the world. It is also known as the International System of Units (SI).

The Metric System is the most common measuring system used in the world today. It is a decimal system based on the meter, kilogram, and second and is officially known as the International System of Units (SI). This system was initially developed in France in the late 18th century and is now used in most countries around the world. The Metric System is based on powers of 10 and each unit is related to the next unit by a factor of 10. For example, a kilometer is equal to 1000 meters, a milliliter is equal to 0.001 liters, and a centimeter is equal to 0.01 meters. The Metric System is used to measure length, area, mass, weight, temperature, and volume. It is used in many different industries and applications including science, engineering, medicine, and agriculture. The Metric System has become the international standard for scientific measurements and is accepted by most countries as the preferred system of measurement. The Metric System is also easier for students to learn and use than other systems of measurement.

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The probability that the student is female and studying abroad is equal to 0.057. It means 5.7% of student is female studying abroad.

Given,

Undergraduate students who study abroad = 9.5% = 0.095 undergraduate

female students who travel for study. = 0.60

male undergraduates who travel for study. = 0.40

undergraduate female students who do not study abroad. = 0.49

Those male undergraduates who do not study abroad. = 0.51

Probability refers to potential. It is a field of mathematics that generally examines how the random events happen. The value is expressed as a number between 0 and 1. To determine how likely an event is to occur, probability has been introduced in mathematics.

We know that ,

the probability that the student is female and studying abroad =

0.60 * 0.095 = 0.057

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To subtract two fractions, we must find a common denominator and subtract the numerators.

The entire circle represents one whole.

To find the fraction for the shaded region, we must subtract [tex]\dfrac{1}{2}[/tex] and [tex]\dfrac{3}{7}[/tex] from one whole:

[tex]1-\dfrac{1}{2}-\dfrac{3}{7}[/tex]

One whole minus half the whole would leave us with just half:

[tex]\dfrac{1}{2}-\dfrac{3}{7}[/tex]

Now, to find a common denominator, multiply the numerator and denominator of each fraction by the denominator of the other fraction:

[tex]\dfrac{1*7}{2*7}-\dfrac{3*2}{7*2}\\\\= \dfrac{7}{14}-\dfrac{6}{14}[/tex]

Now, subtract normally:

[tex]\dfrac{7}{14}-\dfrac{6}{14}\\\\= \dfrac{1}{14}[/tex]

[tex]\dfrac{1}{14}[/tex]

The value of the expression for the given condition is 4.2.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's bis as follows:

Expression: (Math Operator, Number/Variable, Math Operator)

Given expression,

0.7d - 2.1f

and d = 15, f = 3

substitute the values,

0.7d - 2.1f

=> 0.7(15) - 2.1(3)

=> 10.5 - 6.3 = 4.2

Hence the value of the expression is 4.2.

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Answer:

(x + 11)² + (y - 15)² = 81

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (- 11, 15 ) and r = 9 , then

(x - (- 11) )² + (y - 15)² = 9² , that is

(x + 11)² + (y - 15)² = 81

It is not possible to determine the probability of survival on the second try if the cylinder is not spun, as the outcome of the first try has no bearing on the outcome of the second try if the cylinder is not spun.

The cylinder serves to randomly distribute the bullet among the chambers, so if the cylinder is not spun, the bullet will remain in the same chamber, and the outcome of the second try will be determined by the initial placement of the bullet in the cylinder.

In a typical scenario where a revolver with a single bullet is used, the probability of survival on the first try is 1/6, and the probability of survival on the second try (assuming the cylinder is spun) is also 1/6. However, without spinning the cylinder, the outcome of the second try is fixed and cannot be determined probabilistically.

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The answer is 38.7% which is option b., is Jordan's DTI (debt-to-income) ratio to the nearest tenth.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

To calculate Jim's DTI (debt-to-income) ratio, we need to divide his total monthly debt payments by his gross monthly income.

His total monthly debt payments are:

$2,600 (mortgage payment)

$250 (lease payment)

$500 (credit card payments)

$400 (speed boat payment)

then,

Total Monthly Debt Payments =  $3750

now,

His gross monthly income is his annual salary of $102,000 divided by 12 months which is $8,500

we get,

DTI = Total Monthly Debt Payments / Gross Monthly Income

= $3,750 / $8,500 + 1200

=0.387

=38.7%

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The minimum number of rotations required for a 3500 km race is 52,800 rotations.

This is calculated by dividing the total distance of the race, 3500 km, by the circumference of the wheel, which is 2πr, where r is the radius of the wheel. The radius of the wheel must be between 27.5 cm (half of 55 cm) and 37.5 cm (half of 75 cm). So, the minimum number of rotations is given by 3500/(23.14r), where r is the minimum radius of the wheel. Substituting in r = 27.5 cm, we get the minimum number of rotations required for a 3500 km race as 52,800.

To arrive at this result, we must first calculate the circumference of the wheel, which is given by 2πr, where r is the radius of the wheel. Since the diameter of the wheel must be between 55 cm and 75 cm, the radius of the wheel must be between 27.5 cm (half of 55 cm) and 37.5 cm (half of 75 cm).

We then divide the total distance of the race, 3500 km, by the circumference of the wheel, which is given by 2πr. Substituting in the minimum radius of the wheel, 27.5 cm, we get the minimum number of rotations required for a 3500 km race as 52,800.

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For quadrilateral ABCD,

m∠AED = 145°

m∠DAE = 145°

m∠BCE = 145°

Consider the following diagram.

ABCD is a rhombus.

Here, the measure of angle EDA=35º

From the figure we can observe that,

∠AED + ∠EDA =180° ................(Linear pair of angles)

⇒ ∠AED = 180° - 35°

⇒ ∠AED = 145°

Also,

∠DAE + ∠EDA = 180° (Linear pair)

⇒ ∠DAE = 180° - 35°

⇒ ∠DAE = 145°

Now we find m∠BCE

We can observe that ∠BCE and ∠DAE are opposite angles .

So, ∠BCE = ∠DAE

⇒ m∠BCE = 145°

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The complete question is:

Quadrilateral ABCD is a rhombus. Given that m∠EDA=35º, what are the measures of m∠AED, m∠DAE, and m∠BCE

To correct the error, Lonnie should write 3 3/4 instead of three and three over four.

A fraction is a mathematical concept that can be used to express a portion of a whole or a number that can be written as the ratio of two integers. In a fraction, the top number is referred to as the numerator, while the bottom number is referred to as the denominator.

Here,

Lonnie has made a mistake in writing the number of packages of pasta. The correct way to write the amount of pasta is 3 3/4 packages. The fraction 1/3 of a fourth package of pasta means that Lonnie has 1/3 of the fourth package and the three whole packages, making it a mixed number, which is a whole number and a fraction combined. To correct the error, Lonnie should write 3 3/4 instead of three and three over four.

Thus, to correct the error, Lonnie should write 3 3/4 instead of three and three over four.

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Answer:

Step-by-step explanation:

a. Each marble has a volume of 0.013 liters.

b. 23.4 liters of water would be necessary if William uses 200 marbles.

a. To determine the volume of each marble, we can use the information that 85 marbles fill a tank with a volume of 20.9 liters of water:

Volume of each marble = (26 liters - 20.9 liters) / 85 marbles = 0.26 liters - 0.247 liters/marble = 0.013 liters/marble

So, each marble has a volume of 0.013 liters.

b. To determine the amount of water necessary if William uses 200 marbles, we can use the formula:

Volume of water = Total volume of tank - Volume of marbles

Volume of water = 26 liters - (200 marbles * 0.013 liters/marble) = 26 liters - 2.6 liters = 23.4 liters

So, 23.4 liters of water would be necessary if William uses 200 marbles.

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Complete question:

William has a 26-liter glass tank. First, he wants to put some marbles in it, all of the same volume. Then, he wants to fill the tank with water until it is completely full. If he uses 85 marbles, he will have to add 20.9 liters of water.

a. What is the volume of each marble?

b. How much water is necessary if William uses 200 marbles?

Based on the Tuesday rate, $100 United States dollars is equal to 843.64 French francs.

1. From the tables, the Tuesday rate is 0.119 US dollars to 1 French franc.

2. To find the exchange rate, multiply the number of US dollars by the exchange rate: 100 x 0.119 = 11.90.

3. To find the amount in French francs, divide the US dollars by the exchange rate: 11.90 / 0.119 = 843.64 French francs.

Therefore, $100 United States dollars is equal to 843.64 French francs based on the Tuesday rate.

At the Tuesday exchange rate, one hundred United States dollars is equal to eight hundred and forty-three point sixty-four French francs. This means that for every one hundred US dollars, you can get eight hundred and forty-three point sixty-four French francs in exchange.

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Option A is the correct answer. The expression is (x+3)(x+7).

The given equation is x²+10x+21

we have to find the roots of the equation

x²+10x+21 =0

x²+3x+7x+21

x(x+3)+7(x+3)

(x+3),(x+7)

Now, we need to remember to factorize the given expression, x²+10x+21, and have to choose two numbers when you add them you get "10" and when you multiply them you get "21".

These numbers are:

7 and 3

Because:

7+3=10

7*3=21

Therefore, you get that the factorization of the expression  is the following:

(x+3)(x+7)

We can conclude that this factorization matches the first option.

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Answer:

18.7 units

Step-by-step explanation:

In this right-angled triangle, you are provided with:

Two angles (i.e. 36° and 90°)

One side (i.e. Line AC, which is 11 units)

Line AB is known as the 'hypotenuse' of the right-angled triangle, which is what needs to be determined.

On the basis of 36° angle:

The side opposite (i.e. Line AC)  is known as the 'opposite' or 'perpendicular side'

The side adjacent (i.e. Line BC) is known as the 'adjacent' or 'base'

Trigonometric function:

The trigonometric function, which connects an angle, it's opposite side and the hypotenuse is the 'sine function':

sinФ = [tex]\frac{opposite}{hypotenuse}[/tex]

sin36° = [tex]\frac{11}{x}[/tex]

Cross-multiplication is applied:

x needs to be isolated and made the subject of the equation:

xsin36° = 11

≡ x = [tex]\frac{11}{sin36^{o}}[/tex]

∴ x = 18.7 units (Rounded off to 3 significant figures)

Expanding the expression a(b + c) = ab + ac, the value of ac is positive if both a and c are positive or if both a and c are negative.

By Multiplying the term outside the brackets by each term inside the brackets

Using this method you can distribute the outer terms into the inner terms. You can multiply the term outside the brackets by the first term inside the brackets. Then multiply the outside term by the second term. If there are more than two tribes, then continue to distribute the tribes until the tribe has no remainder. Keep the signs (positive or negative) in parentheses.

For example:

2(x-3) = 10

2(x) – (2)(3) = 10

2x – 6 = 10

We also know that the distribution characteristic state is a(b + c) = ab + ac.

Because plus times plus is plus and minus times minus is plus. When expanding the phrase a(b + c) = ab + ac, the value of ac is positive if both a and c are positive, and the value of ac is negative if both a and c are negative.

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Liters of water (w) it would take to water 40 flower pots, if it took 9 liters of water to water 24 flower pots when assuming same amount of water is used on each pot is 15.

Therefore the answer is 15.

To find the amount of water Vito would need to water 40 flower pots, we can use the following formula:

w = (9 liters) * (40 pots) / (24 pots)

Simplifying:

w = 15 liters

So, Vito would need 15 liters of water to water 40 flower pots, assuming he uses the same amount of water on each pot.

--The question has some errors, answering to the question below--

"Vito uses 9 liters of water to water 24 flower pots. He is wondering how many liters of water (w) it would take to water 40 flower pots. He assumes he'll use the same amount of water on each pot."

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The letter on the number line that stands in for the numerals after it On the number line, B stands for -38.

The number line that displays negative numbers is presented to us. On the number line, we are aware that the number rises as we travel to the right.

As per the data given in the above question are as bellow,

The details provided are as bellow,

We can observe that the number line has a grading scale of 1, meaning that each subsequent mark is separated by one unit.

B is four points away from a 42.

This suggests that to get B, we just need to add 4 to -42.

So:

B = -42 + 4

B = -38

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Note : The complete question would be as bellow,

What integer does the letter B represent on the number line above?

What integer does the letter B represent on the number - 1