Find the length indicated.
7) Find FG
E
2x+1
F
16
2x+3
G

Mean of the data as per the increasing intervals data is 17.80.

The mean in statistics is calculated by multiplying all the values in a set of data by the total number of values for a given set of observations. To put it another way, all that is necessary to determine the mean of a set of data is to sum up all the values and divide the total by the number of values.

Now in the given table,

The midpoints of the intervals are as follows:

0+10/2 = 5

0+20/2 = 10

0+30 /2 = 15

0+40/2 = 20

0+50/2 = 25.

Now total students × interval midpoints are as follows:

5×5=25

10×10=100

15×14=210

20×17=340

25×20=500

Now, total no of students is = 5+10+14+17+20 = 66

So, mean of the data =

(25+100+210+340+500)/66

= 17.80

Therefore, mean of the data is 17.80.

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Answer:

3x² -2xy + 4y² at x = -1, y = -2  = 15

Step-by-step explanation:

Given function is

f(x, y) = 3x² -2xy + 4y²

To find At x = - 1 and y - 2 just plug these values for x and y into f(x, y)

f(-1, -2) = 3(-1)² - 2(-1)(-2) + 4(-2)²

(-1)² = 1 ==>   3x²  = 3(-1)² = 3 x 1 = 3

(-1) (-2) = 2   ==>   2xy = 2(-1)(-2) = 2 x 2 = 4

(-2)² = 4  ==> 4y² = 4 (-2)² = 4 x 4 = 16

f(-1 1, - 2) = 3x² -2xy + 4y²
= 3 - 4 + 16

= 15

Hence, x has a value of 36 as the sum of the supplementary angles 3x and 2x must equal 180 degrees .

Angles in mathematics are used to quantify how much two intersecting surfaces or lines rotate relative to one another. Angles can be measured in degrees, radians, or various ways. Degrees, which divide a whole rotation into 360 equal parts, are the most popular unit of measurement for angles. Angles are a fundamental idea in geometry and trigonometry and have practical uses in a number of industries, including physics, engineering, and navigation.

given

The sum of the supplementary angles 3x and 2x must equal 180 degrees. Which is:

3x + 2x = 180

Putting similar phrases together on the left side, we get:

5x = 180

When we multiply both sides by 5, we get:

x = 36

Hence, x has a value of 36 as the sum of the complementary angles 3x and 2x must equal 180 degrees .

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Answer:

hope its right

Step-by-step explanation:

Answer:

Find the Exact Value tan(49). tan(49) tan ( 49 ). Step 1. The result can be shown in multiple forms. Exact Form: tan(49) tan ( 49 ). Decimal Form:

Step-by-step explanation:

If James is sorting the numbers on his teddy bears from greatest to least, the number that would come next would depend on the numbers already sorted. For example, if the numbers he has sorted are 9, 5, and 3, then the next number would be 1.

Sort is a function used to rearrange items in a list in order of size, value or alphabetically. It is a computer algorithm that sorts a list, typically of numbers, words, or other items, into increasing or decreasing order. It is often used to arrange data so that it can be more easily analyzed or used in other applications. The simplest form of sorting is to take a list of items, compare each item to the items before it, and swap them if they are out of order. This process is repeated until all items are in the correct order. Sorting algorithms are used in many areas of computing, including data structures, artificial intelligence, databases, and programming languages.

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The numbers on teddy bears are sorted as 656, 666, 676, 686. The pattern rule is adding 10 so, the next number will be 696.

Sort is a function used to rearrange items in a list in order of size, value or alphabetically. It is often used to arrange data so that it can be more easily analyzed or used in other calculation. The simplest form of sorting is to take a list of items, compare each item to the items before it, and swap them if they are out of order. This process is repeated until all items are in the correct order.

If James is sorting the numbers on his teddy bears from greatest to least, the number that would come next would depend on the numbers already sorted.

The numbers on teddy bears are sorted as 656, 666, 676, 686.

Now, observe the pattern.

656 + 10 = 666

666 + 10 = 676

676 + 10 = 686

This indicates that the pattern rule is "adding 10", which means the next number in series is:

686 + 10 = 696

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The complete question is as follows:

The tοtal price οf the game including tax is $29.96.

Physical assets such as prοperty and transactiοns such as the sale οf stοck οr a hοme are subject tο taxatiοn. Taxes include incοme, cοrpοrate, capital gains, prοperty, inheritance, and sales taxes.

Because the tax rate is 7%, the tax amοunt is 7% οf the purchase price. Tο calculate the tax, multiply the purchase price by the tax rate expressed as a decimal:

0.07 x $28 = $1.96 in taxes

As a result, the purchase tax is $1.96.

Tο calculate the tοtal price, add the purchase price and the tax:

Purchase price + Tax = Tοtal Price

Tοtal cοst: $28 + $1.96 = $29.96

As a result, the tοtal cοst οf the game, including tax, is $29.96.

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The expression represents the distributive property from the list of options is (b) a(b + c) = ab + ac

The distributive property is a mathematical property that applies to multiplication and addition or subtraction.

It states that when you multiply a number (or variable) by a  sum or difference inside parentheses, you can distribute the multiplication across the terms inside the parentheses.

This is represented by the following formula:

a(b + c) = ab + ac

This is represented by Option (B)

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Answer: When there are n teams in a league and each team plays every other team twice, then each team will play a total of n-1 games (since they don't play against themselves). Therefore, the total number of games played in the league is the sum of all the games played by each team, which is:

Total number of games = (number of teams) × (number of games played by each team) / 2

The division by 2 is necessary since each game involves two teams, so counting each game twice would result in double counting.

For the given basketball league with 11 teams, the total number of games played would be:

Total number of games = 11 × (11-1) / 2

= 11 × 10 / 2

= 55 × 2

= 110

Therefore, 110 games would be played in the league.

Step-by-step explanation:

The prοbabiIity οf getting aII 3 answers cοrrect is 0.0625 οr 6.25%.

PrοbabiIity is a measure οf the IikeIihοοd οr chance οf an event οccurring, expressed as a number between 0 and 1, with 0 indicating impοssibiIity and 1 indicating certainty. It is used in variοus fieIds such as mathematics, statistics, science, ecοnοmics, and finance.

The prοbabiIity οf getting the true/faIse questiοn cοrrect is 1/2 οr 0.5. The prοbabiIity οf getting the muItipIe-chοice questiοn cοrrect is 1/4 οr 0.25. The prοbabiIity οf getting the Iast questiοn cοrrect is 1/2 οr 0.5.

Tο find the prοbabiIity οf getting aII 3 answers cοrrect, we muItipIy the prοbabiIities οf getting each questiοn cοrrect:

0.5 * 0.25 * 0.5 = 0.0625

Sο the prοbabiIity οf getting aII 3 answers cοrrect is 0.0625 οr 6.25%.

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The missing angles in the diagram are: Angle ABD = 60 degrees, Angle BDC = 120 degrees, Angle ACD = 60 degrees, and Angle ADC = 120 degrees.

To find the measure of the missing angles, we can use the fact that the sum of the angles in a triangle is 180 degrees, and the sum of the angles around a point is 360 degrees.

Let x be the measure of angle ABD.

Therefore, angle BDC has measure 180 - x degrees.

Similarly, angle ACD and angle ADC form a straight line, so their measures sum to 180 degrees. Therefore, angle ADC has measure 180 - 60 = 120 degrees.

Finally, since angle BCD and angle ADC form a straight line, their measures sum to 180 degrees. Therefore, angle BCD has measure 180 - 120 = 60 degrees.

Let y be the measure of angle CFE.

Similarly, angle DEF and angle CDF form a straight line, so their measures sum to 180 degrees. Therefore, angle DEF has measure 180 - 75 = 105 degrees.

Finally, since angle CDE and angle DEF form a straight line, their measures sum to 180 degrees. Therefore, angle CDE has measure 180 - 105 = 75 degrees.

Therefore, the missing angles have measures of 60 degrees and 75 degrees for the left and right triangles.

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find the measure of missing angles?

The term “inverse” in mathematics generally refers to an operation that undoes or reverses another operation. However, the phrase "inverse of maths tools" doesn't really make sense because “maths tools” is not a specific mathematical operation.

Mathematical tools can refer to various instruments or techniques used in mathematics, such as calculators, rulers, compasses, graph paper, software, etc. Each of these tools has its own purpose and may or may not have an inverse operation or tool associated with it.

For example, the inverse of addition is subtraction, the inverse of multiplication is division, and the inverse of differentiation is integration. However, it's not clear what the inverse of a “maths tool” would be.

Therefore,  a) The inverse of “Add 25” would be “Subtract 25.”What is the  b) The inverse of “Divide -18” would be “Multiply -18.” c) The inverse of “Subtract 3” would be “Add 3.” d) The inverse of “Multiply 14” would be “Divide 14.”

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Answer: LN = 15

Make a proportional relationship:

[tex]\dfrac{LN}{JL}=\dfrac{LM}{KL}[/tex]

Insert the values:

[tex]\longrightarrow\dfrac{LN}{30} =\dfrac{6}{30-18}[/tex]

cross multiply:

[tex]\longrightarrow LN=\dfrac{30(6)}{12}[/tex]

Simplify:

Gracie's statement is not necessarily correct about the tens digit in a dividend is less than the divisor and the divisor has one digit. Gracie says the quotient must have a 0 in the tens place.

What is dividend?

In mathematics, a dividend is the number that is being divided in a division problem. For example, in the division problem 18 ÷ 3 = 6, 18 is the dividend.

Gracie's statement is not necessarily correct. Let's look at a couple of examples to see why.

Example 1:

Dividend = 25

Divisor = 4

In this case, the tens digit of the dividend (2) is less than the divisor (4). The quotient is 6 with a remainder of 1. There is no 0 in the quotient, so Gracie's statement is incorrect.

Example 2:

Dividend = 35

Divisor = 4

In this case, the tens digit of the dividend (3) is also less than the divisor (4). The quotient is 8 with a remainder of 3. Again, there is no 0 in the quotient, so Gracie's statement is still incorrect.

From these examples, we can see that Gracie's statement is not always true. It is possible for the tens digit of the dividend to be less than the divisor, and for the quotient to not have a 0 in the tens place.

The only time Gracie's statement would be true is if the remainder is 0 after dividing the dividend by the divisor. In that case, the quotient would indeed have a 0 in the tens place. However, this is not always the case.

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Answer:

Step-by-step explanation:

In math, slope is used to describe the steepness and direction of lines. ... You can determine the slope of a line from its graph

The sentence represented as an algebraic expression is x² - 1

Algebraic expressions can be defined as a mathematical expression that consists of terms, variables, constants, coefficients and fractions.

Also, these algebraic expressions are identified with arithmetic or mathematical operations. These operations are;

From the information given, we have that;

Let the number be x

If 1 is then subtracted from the square of a number.

Fiirst, the square of the number is x²

This is represented as;

x² - 1

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Answer:

Step-by-step explanation:

a. Sara's estimate is reasonable because:

Dan has biked for 7 days so far, 29 miles for 3 days and 32 miles for 4 days.

If you round 29 and 32 up and down respectively to 30, then Dan will of have ridden about 30 * 7, or 120 miles so far. 300-120 is 80, so that is a good estimate.

b. If x stands for the miles Dan still needs to bike, then:

(29*3) + (32*4) + x = 300

c. 87 + 128 + x = 300

x = 85

Answer:

1. y = 3 1/3

2. y = 6

3. y = 12

Step-by-step explanation:

A = xy => xy = 14 => y = 14/x

1. x = 4 1/5 = 21/5

y = 14/x = 14/(21/5) = (5 x 14)/21 = 10/3 = 3 1/3

2. x = 2 1/3 = 7/3

y = 14/x = 14/(7/3) = (3 x 14)/7 = 6

3. x = 7/6

y = 14/x = 14/(7/6) = (6 x 14)/7 = 12

A. the derivative of y = log_a(x) is: y' = log_a(x) / (x ln(a))

B. the derivative of y = log_8(x) is: y' = 1 / (x ln(8 ln(10)))

a) Using the chain rule and the given identity, we have:

y = log_a(x)

ln(y) = ln(log_a(x))

ln(y) = ln(x) / ln(a)

y' / y = 1 / (x ln(a))

Multiplying both sides by y and simplifying, we get:

y' = y / (x ln(a))

y' = log_a(x) / (x ln(a))

Therefore, the derivative of y = log_a(x) is: y' = log_a(x) / (x ln(a))

b) Using the change of base formula for logarithms, we have:

y = log_8(x)

y = log(x) / log(8)

Using the chain rule, we have:

y' = (1 / (x ln(10))) * (1 / ln(8)) * d/dx [log(x)]

Using the chain rule for the natural logarithm, we have:

y' = (1 / (x ln(10))) * (1 / ln(8)) * (1/x)

Simplifying, we get:

y' = 1 / (x ln(8 ln(10)))

Therefore, the derivative of y = log_8(x) is:

y' = 1 / (x ln(8 ln(10)))

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Answer:

Step-by-step explanation:

adjacent:   [tex]\angle BOC, \angle EOD[/tex]   (both are adjacent)

complementary:  [tex]\angle BOC[/tex]

supplementary:   [tex]\angle EOD[/tex]

vertical angles:   [tex]\angle AOE[/tex]

Answer:

Adam's thinking is not correct.

When subtracting 10 from 708, we need to borrow 1 from the hundreds digit and add it to the tens digit. This will result in a new hundreds digit of 6 and a new tens digit of 9. The ones digit remains the same. Therefore, the correct answer would be 698.

Adam's answer is also 698, but his reasoning is incorrect. He thinks that both the tens and hundreds digits change, which is not the case. In reality, only the tens digit changes while the hundreds digit decreases by 1 due to the borrowing process.

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Answer:The measure of Ф = 75.7° :)

Step-by-step explanation:the measure of Ф = 75.7°,We will use the rule sin to find the measure of Ф

At first we will find the angle opposite to the side of length 31

∵ 180° - 73° = 107°

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It took Rapunzel approximately 14.58 minutes to clean her room.

Cleaning refers to the process of removing dirt, dust, and other unwanted substances from a surface or an object.  

Let's start by converting the time to minutes.

15 1/2 minutes = 15.5 minutes

Let's now subtract the time she finished cleaning from the time she started cleaning:

15.5 - 0.92 = 14.58 minutes

Therefore, it took Rapunzel approximately 14.58 minutes to clean her room.

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The amount and the compound interest on a sum of Rs. 62500 are Rs. 65625 and Rs. 3125, respectively.

Given:

Principal amount (P) = Rs. 62500

Rate of interest (R) = 5%

Time period (t) = 1 year

Interest is compounded yearly.

Formula for calculating compound interest is given as:

A = P(1 + R/100)ᵗ

where A is the amount.

Using this formula, we can find the amount (A) after one year:

A = 62500(1 + 5/100)¹

A = 65625

Therefore, the amount after one year is Rs. 65625.

To find the compound interest, we can subtract the principal from the amount:

Compound Interest = A - P

= 65625 - 62500

= 3125

Therefore, the compound interest is Rs. 3125.

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Answer:

1/128

Step-by-step explanation:

The probability of tossing a head is 1/2.

Each toss is an independent event.

We toss 7 times and get a head each time.

1/2 * 1/2* 1/2* 1/2* 1/2* 1/2* 1/2

1/128

Answer:

8.449 square centimeters

Step-by-step explanation:

Area of the figure = area of square + area of triangle

[tex] {7}^{2} + \frac{1}{2} (3)(7) = 49 + 10.5 = 59.5[/tex]

[tex].142 \times 59.5 = 8.449[/tex]

So 8.449 square centimeters of this figure is green.

Answer:

To determine which statements are true, we can use the standard form of the equation of a circle:

(x - h)^2 + (y - k)^2 = r^2

where (h, k) is the center of the circle and r is the radius.

Using this form, we can rewrite the given equation as:

(x - 1)^2 + y^2 = 3^2 + 1^2 = 10

Comparing this to the standard form, we can see that the center of the circle is (1, 0), so the statement "The center of the circle lies on the x-axis" is true. However, the statement "The center of the circle lies on the y-axis" is false.

To find the radius, we can rearrange the equation as follows:

x^2 - 2x + y^2 = 8

Completing the square for x, we get:

(x - 1)^2 + y^2 = 9

This shows that the radius of the circle is 3, so the statement "The radius of the circle is 3 units" is true, as well as the statement "The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9."

Therefore, the three true statements are:

1.The radius of the circle is 3 units.

2.The center of the circle lies on the x-axis.

3.The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

Step-by-step explanation:

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It takes the hiker about 175.58 minutes to climb the remaining elevation of the mountain in stage two.

calculating the elevation the hiker climbs in stage one:

2% of 2,150 feet = 0.02 × 2,150 feet = 43 feet

Therefore, the hiker climbs 43 feet in stage one. To find the time it takes for the hiker to climb the remaining elevation of the mountain in stage two, we need to know the total elevation he needs to climb in this stage. This can be calculated by subtracting the elevation climbed in stage one from the total elevation of the mountain: Total elevation - Elevation climbed in stage one = 2,150 - 43 = 2,107 feet

Now, we can use the rate of climb in stage two to find the time it takes to climb 2,107 feet:

Time = Distance / Rate

Time = 2,107 feet / 12 feet per minute

Time ≈  175.58 minutes

Therefore, it takes the hiker about 175.58 minutes to climb the remaining elevation of the mountain in stage two.

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