The mean age of a family of seven is 23 years. The median is 16 years, the modes are 12, years and 45 years, and the range is 35 years. Find the ages of the seven family members

Answer:6cm

Step-by-step explanation:You can use the formulas  or  to solve for diameter using volume. I will use the first forumla for this problem.

Substitute 113 for "V"

Multiply in the parenthesis

Divide by pi (3.14)

678 ÷ 3.14 = 215.923567

Apply the exponent

d = 5.99907...

d = 6 cm

Answer: 126 Spelling Words

Answer:

Step-by-step explanation:

On the first day, Ms. Dubacek gave 6 new spelling words.

On each subsequent day, she gave an additional 3 new spelling words.

Therefore, on the second day of school, she gave a total of 6 + 3 = 9 new spelling words.

On the third day of school, she gave a total of 6 + 3 + 3 = 12 new spelling words.

We can see a pattern emerging here: on each day, she gives 6 more words than the previous day.

So on the 21st day of school, she will have given a total of:

6 + (9 + 12 + 15 + ... + 60)

To find the sum of this arithmetic series, we can use the formula:

S = n/2 * (a + l)

where:

S = the sum of the series

n = the number of terms in the series

a = the first term in the series

l = the last term in the series

In this case, we have:

n = 19 (since we're counting from the second day of school to the 21st day)

a = 9 (since that was the total number of spelling words given on the second day)

l = 60 (since that will be the total number of spelling words given on the 21st day)

So, plugging in these values, we get:

S = 19/2 * (9 + 60) = 19/2 * 69 = 655.5

Therefore, by the end of the 21st day of school, Ms. Dubacek will have given her students a total of 6 + 655.5 = 661.5 new spelling words (rounded to the nearest whole number, this is 662).

The number of possible outcomes is 10.

To find the number of possible outcomes find the number of outcomes when the coin is flipped and the number of outcomes when the spinner is spinning.

Multiply the number of outcomes from the coin by the number of outcomes from the spinner.  

Here we have

Enola is designing a new board game,

She flips a coin and spins a spinner with 5 equal-sized sections labeled Monday, Tuesday, Wednesday, Thursday, Friday    

No of possible outcomes when a coin is flipped = 2 [Head and Tail]  

No of possible outcomes when she spins a spinner = 5

[ i.e Monday, Tuesday, Wednesday, Thursday, Friday ]  

Hence, No of out comes = 2 × 5 = 10

Therefore,

The number of possible outcomes is 10.

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The detail that best suppοrts the inference that the autο manufacturing industry suppοrts green sοlutiοns is-

"Pyrοlysis generates lοw-cοst energy that can be used in the autοmοbile manufacturing industry".

The pyrοlysis prοcess is the thermal decοmpοsitiοn οf materials at elevated temperatures, οften in an inert atmοsphere.

Given is that an engineer at an envirοnmentally minded technοlοgy cοmpany has cοme up with a prοcess tο cοnvert tire waste frοm the autοmοbile industry intο clean energy.

The detail that best suppοrts the inference that the autο manufacturing industry suppοrts green sοlutiοns is -

"Pyrοlysis generates lοw-cοst energy that can be used in the autοmοbile manufacturing industry".

Therefοre, the detail that best suppοrts the inference that the autο manufacturing industry suppοrts green sοlutiοns is -

"Pyrοlysis generates lοw-cοst energy that can be used in the autοmοbile manufacturing industry".

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Statements B, C, and D are not true. Diego would travel a greater distance from D to B than from C to D. He would also create different angles at ΔBDA and ΔBDC, and the distance traveled from A to B would not be the same as from B to C.

According to the given figure, Diego attempts to walk in a sequence of lines to create ΔABD and ΔCDB. He can traverse each side only once and cannot jump from point to point. We need to determine which of the following statements are not true:

A) The distance Diego travels from A to B is the same as the distance traveled from C to D. This statement is not true because the distance from A to B is the sum of the lengths of AB and BD, whereas the distance from C to D is the sum of the lengths of CD and BD, and BD is being counted twice.

B) The distance Diego travels from D to B is the same as the distance traveled from C to D. We cannot determine the truth of this statement without more information about the lengths of the sides.

C) The distance Diego travels from A to B is the same as the distance traveled from B to C. This statement is not true because the distance from A to B is the sum of the lengths of AB and BD, whereas the distance from B to C is the sum of the lengths of BC and BD, and BD is being counted twice.

D) The angle Diego creates at ΔBDA has the same measure as the angle he creates at ΔBDC. This statement is not true because the angles at ΔBDA and ΔBDC are vertical angles, which are congruent, but not necessarily equal to each other.

E) The angle Diego creates at ΔDAB has the same measure as the angle he creates at ΔBCD. We cannot determine the truth of this statement without more information about the angles.

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Answer:

-45

Step-by-step explanation:

Answer:

-45, just take off the absolute bars

Step-by-step explanation:

Each input value has exactly one corresponding output value, which satisfies the definition of a function.

A function is a relation between two sets of values where each input value (independent variable) corresponds to exactly one output value (dependent variable). In this case, the input values are the values of "x" column, and the output values are the values of "y" column.

Looking at the given table, for each unique value of "x", there is a unique corresponding value of "y".

For example, when "x" is 25, "y" is 5; when "x" is -25, "y" is -5; when "x" is 36, "y" is 6; and when "x" is -36, "y" is -6.

Therefore, each input value has exactly one corresponding output value, which satisfies the definition of a function.

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Answer:

Rectangle pyramid

What is a rectangle pyramid ?

A rectangular pyramid is a pyramid, which has a rectangular-shaped base. If we look at the bottom view of this pyramid, it looks like a rectangle. Hence, the base has two parallel sides equal.

A pyramid crowns at a point on top of the base, which is known as the apex. A rectangular pyramid can be a right pyramid or oblique pyramid. If it is a right rectangular pyramid, then the apex lies right over the center of the base and if it is an oblique rectangular pyramid, the apex is not directly over the center of the base, but at some angle from the center.

Apart from the rectangular pyramid, there are other types of pyramids based on the shape of their bases, such as:

1) Triangular Pyramid

2) Square Pyramid

3) Pentagonal Pyramid

4) Hexagonal Pyramid

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The trigonometric ratios gives the values required.

The three main trigonometric ratios that we need are the sine the cosine and the tangent.

1) The hypotenuse is;

c^2 = 5^2 + 12^2

c = √5^2 + 12^2

c = 13

Then;

sin x + cos x

= 5/13 + 12/13

= 17/13

2) The adjacent is;

13^2 = x^2 + 5^2

x^2 = 13^2 - 5^2

x = √13^2 - 5^2

x = √ 169 - 25

x = 12

Cos p = 12/13

3) The adjacent is;

13^2 = x^2 + 12^2

x^2 = 169 - 144

x = 5

2sinx + 1/2Cos x

2(12/13) + 1/2 (5/13)

144/13 + 5/26

=293/26

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The area of the triangle LKJ is 150 square meters

From the question, we have the following parameters that can be used in our computation:

The figure

The area of a shape is the measurement of the size of the region enclosed by the shape in a two-dimensional plane.

It is the amount of space inside the shape, usually measured in square units, such as square meters or square feet.

From the figurr, we have

KM^2 = LM * MJ

Substitute the known values in the above equation, so, we have the following representation

12^2 = LM * 16

So, we have

LM = 9

Next, we have

Area = 1/2 * LM * KM

So, we have

Area = 1/2 * 12 * (9 + 16)

Evaluate

Area = 150

Hence, the value of the area is 150

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By answering the above question, we may state that Graphical equation depictions of exponential development in statistical charts, such as bar charts, pie charts, and line graphs. a triangle-shaped logarithmic graph

When two assertions are connected by a mathematical equation, the equals symbol (=) is used to denote equality. In algebra, a mathematical statement that establishes the equivalence of two mathematical expressions is referred to as an equation. In the equation 3x + 5 = 14, for instance, the equal sign places a space between the integers 3x + 5 and 14. To comprehend the connection between the two phrases written on the opposing sides of a letter, utilise a mathematical formula. Frequently, the logo and the specific piece of software are the same. as in, for instance, 2x - 4 = 2.

Mathematicians use graphs to visually express or chart facts or values in a logical way. Usually, a graph point will show the relationship between two or more objects. A graph is a non-linear data structure made up of nodes, also known as vertices, and edges. The nodes, sometimes referred to as vertices, should be joined with glue. Vertices in this graph are 1, 2, 3, and 5, whereas edges are 1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Graphical depictions of exponential development in statistical charts, such as bar charts, pie charts, and line graphs. a triangle-shaped logarithmic graph

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Monica should report the mode, because the mode of a data set is always the value that appears the greatest number of times. Option C is correct.

Therefore, the probability that at least one of the dice shows the number 2, given that the sum of the dice is 4, is 1 - (1/5) = 4/5, or 0.8, which is the probability that at least one of the two dice is a 2.

It is founded on the likelihood that something will occur. The rationale for probability is the central tenet of theoretical probability. For instance, there is a 12% chance that a coin will land on its head when flipped.

There are five possible ways to obtain a sum of 4 with two 6-sided dice: {(1,3),(2,2),(3,1),(2,1),(1,2)}.

Out of these five possible outcomes, there is only one outcome where neither of the dice show a 2, which is {(1,3)}.

Therefore, the probability that at least one of the dice shows the number 2, given that the sum of the dice is 4, is 1 - (1/5) = 4/5, or 0.8, which is the probability that at least one of the two dice is a 2.

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The probability that at least one of a pair of fair 6-sided dice shows the number 2, given that the sum of the dice is 4 is 1/3.

The measure of the likelihood or chance of an event occurring is known as Probability. It is a quantitative measure that ranges from 0 (indicating an impossible event) to 1 (indicating a certain event).

Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes in a given situation or experiment. Probability theory is a branch of mathematics that deals with the study of random events, and it is widely used in many fields such as statistics, physics, economics, finance, and more.

If the sum of the dice is 4, then the possible pairs are (1, 3), (2, 2), and (3, 1). Out of these three pairs, only one has at least one die showing the number 2, which is (2, 2).

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Answer:

the final price of Ray's laptop is 89.1% of the original price.

Step-by-step explanation:

To find the composite function that can be used to calculate the final price of Ray's laptop, we need to find the composition of the two functions given:

f(c) = 1.08c (function for calculating the price of the laptop with tax)

c(p) = 0.75p (function for calculating the sale price of the laptop)

We can find the composite function f(c(p)) by substituting c(p) into the formula for f(c):

f(c(p)) = 1.08c(p)

Substituting c(p) with 0.75p, we get:

f(c(p)) = 1.08(0.75p)

Simplifying, we get:

f(c(p)) = 0.81p

Therefore, the composite function that can be used to calculate the final price of Ray's laptop is f(c(p)) = 0.81p.

This means that to find the final price of the laptop, we need to take the original price, multiply it by 0.75 to get the sale price, and then multiply the sale price by 1.08 to add the sales tax. In other words, the final price is:

final price = f(c(p)) = 0.81p = 1.08(0.75p)

final price = 0.81p + 0.081p

final price = 0.891p

Therefore, the final price of Ray's laptop is 89.1% of the original price.

The height of the pole is 336 feet.

The 24 foot shrub has a 6 foot shadow . The height of the pole that has an 84 foot shadow is as follows:

Hence. let's use proportion to find the height of the pole.

Therefore,

let

h = height of the pole

Hence,

24  /h = 6 / 84

cross multiply

6h = 84 × 24

6h = 2016

divide both sides by 6

h = 2016 / 6

h = 336 ft

Therefore,

height of the pole = 336 ft

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The converse of the [tex]H[/tex]inge theorem indicates that the angle subtended by the segment [tex]\overline{LM}[/tex], (∠K) which is less than the length of the segment [tex]\overline{OP}[/tex], will be less than the measure of the angle subtended by the segment [tex]\overline{OP}[/tex], which is 90°

The h-i-n-g-e theorem, which is also known as the open mouth theorem states that two triangles that have a pair of corresponding congruent sides and which have different measure of the included angle between the sides, then the third side of the triangle with the larger included angle will be longer.

The h-i-n-g-e theorem can be deduced from the triangle inequality theorem.

The corresponding congruent sides in the two triangles are;

[tex]\overline{KL}[/tex] is congruent to [tex]\overline{ON}[/tex], [tex]\overline{KM}[/tex] is congruent to [tex]\overline{NP}[/tex]

[tex]\overline{LM}[/tex] = 7 is less than [tex]\overline{OP}[/tex] = 9

Therefore;

[tex]\overline{LM}[/tex] < [tex]\overline{OP}[/tex]

m∠N = 90°, therefore, the converse of the h-i-n-g-e theorem, indicates that the angle subtended by the segment [tex]\overline{LM}[/tex] is less than the angle subtended by the angle [tex]\overline{OP}[/tex], which is 90°

The angle ∠K is less than the angle ∠N

m∠K < m∠N = 90°

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Answer:

Step-by-step explanation:

To find the hiker's elevation above sea level upon reaching High Point Vista, we need to add up the elevation gain from the start of the trail to High Point Vista. We can use the table to do this:

Elevation gain from start to Old Cabin: -32.78 ft (negative because the hiker loses elevation)

Elevation gain from Old Cabin to Ruby Falls: 8634 ft

Elevation gain from Ruby Falls to Thunder Gorge: -14725 ft (negative because the hiker loses elevation)

Elevation gain from Thunder Gorge to High Point Vista: 346.47 ft

To find the hiker's elevation above sea level at High Point Vista, we add up these elevation gains:

179 ft (start) - 32.78 ft + 8634 ft - 14725 ft + 346.47 ft = -5668.31 ft

The negative value means that the hiker is below sea level at High Point Vista, which is not possible. Therefore, there must be an error in the elevation gain listed for one of the points of interest. It's possible that the elevation gain for Ruby Falls is incorrect, as it seems unlikely that the hiker would gain more than 8000 ft in elevation between Old Cabin and Ruby Falls. Without more information, it's difficult to say for sure where the error lies.

Answer:

20B

Step-by-step explanation:

Answer:

20B

Step-by-step explanation:

Answer:25% of the number is 30

Step-by-step explanation:

Let's call the number we're looking for "x". We can use the information given in the problem to set up two equations:

10% of x is 12:

0.1x = 12

35% of x is 42:

0.35x = 42

Now we can solve for x:

0.1x = 12

x = 120

0.35x = 42

x = 120

We get the same value for x from both equations, which confirms that our solution is correct. Now that we know x = 120, we can find 25% of that number:

25% of 120 = 0.25 x 120 = 30

Therefore, 25% of the number is 30.

Answer:

10 weeks

Step-by-step explanation:

40 books= ? weeks

4 books.  = 1 week

so do 40/4 and get 10

Answer:

10 weeks

Step-by-step explanation:

Answer:

Step-by-step explanation:

FG = FE, ∴ ΔFGE is isosceles.

∴∠G = ∠E (Base angle in isosceles triangle are equal)

So ∠G = 63°

If your parents are buying a house for $187,500. their realized income be before each month is $5250.

Loan amount = $187,500 - (187,500 * 20%)

Loan amount = $ 150,000

Monthly rate = 4.65% / 12 = 0.3875%

Interest rate for the first month is:

Interest rate = $ 150,000 * 0.3875% = $ 581.25.

Loan repayment =$ 1,575 - $ 581.25 = $ 993.75.

Amount  parents owe = $ 150,000 - $ 993.75 = $149,006.25

Second  month Loan = $ 1,575 - ($149,006.25 * 0.3875%) = $ 997.60

Second month ending amount owe = ( $149,006.25 - $997.60)

Second month ending amount owe =  $ 148,008.65

A monthly loan payment that is not more than 30% of monthly income will be used to find the realized income.

Realized income = $ 1,575/30% = $ 5,250

Therefore the realized income is $5250

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In flowchart, If the dice do not show the same number, add 0 points to the player's score.

A flowchart quick answer is what it sounds like.

A flowchart is a diagram that shows a procedure, a system, or a computer algorithm. It is a diagrammatic representation of a particular problem's solution, but more significantly, it breaks out the crucial actions that must be taken in order to solve the problem.

1.Roll three dice

2.Compare numbers on the dice

3.If two dice show the same number, add 10 points to the player's score

4.If three dice show the same number, add 25 points to the player's score

5.If the dice do not show the same number, add 0 points to the player's score.

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Answer: 1.24

Step-by-step explanation:

40% abundance in decimals = 0.4

0.4 multiplied by 3.1 = 1.24

Answer:

EPIC: They Troy Saga Full Speed

Step-by-step explanation:

Six hundred men, six hundred men under my command

With only one goal in mind

Make it back alive to our homeland

Six hundred men, six hundred miles of open sea

But the problem's not the distance

It's what lies in between

And Ithaca's waiting Ithaca's waiting

My kingdom is waiting The kingdom is waiting

Penelope's waiting for me

So full speed ahead, full speed ahead

Answer:

17m−5n)(17n−5m) when u expand it your answer would be −85m 2+314mn−85n 2

Step-by-step explanation:

Answer: From part b, we know that the number of sides in my envelope is t + q = 10 + 6 = 16, and the number of sides in my partner's envelope is 2t - q = 20 - 6 = 14.

To determine the number of sides in both envelopes combined, we add these values: 16 + 14 = 30.

Therefore, the combined number of sides in both envelopes is 30.

Step-by-step explanation:

Answer:

Step-by-step explanation: OK so is A'B'C'D' a translation, rotation, or reflection of ABCD? OK so A'B'C'D' is a rotation i believe because like you i'm on the same thing. Is A"B"C"D" a translation, rotation, or reflection of A'B'C'D'? OK so A"B"C"D" is a reflection i believe i'm not really sure on that one. Suppose the measure of angle B is 89°. Which other angle must be 89°? OK so angle A, angle C, and angle B. But I really don't get what you trying to ask? Hope I kind of helped, like i said im in 8th grade and it is kind of hard for me too.

The number of times both spins will be even numbers is 25.

The probability of an occurrence is a figure that represents how likely it is that the event will take place. It is represented by a number between 0 and 1.

It is given that the spinner is spun twice.

The theoretical probability of both spins being even numbers is = [tex]\frac{9}{36}[/tex]

When the experiment is repeated 100 times, the number of times both spins come out to an even number =  [tex]\frac{9*100}{36}[/tex]

                                                           = [tex]25[/tex]

Therefore, the number of times both spins will be even numbers is 25.

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The quantity of gas that was consumed in the first 3 hours is; 6 gallons.

As evident in the task content;

Speed refers to the magnitude of the velocity or the rate distance is traversed in a given time.

the speed of the vehicle = 60 miles per hour

the quantity of gasoline = 10 gallons.

Since G (t) = 10 - 2t

When t = 3

G (3) = 10 - 2(3)

G(3) = 4 gallons

Ultimately, the quantity of gas consumed in the first 3 hours is;

10 gallons - 4 gallons

= 6 gallons.

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