Solve the triangle. Round each angle to the nearest degree and round each Side to the nearest hundredth. Do not use rounded answers in your calculations to find missing measures.

The three quartiles is the value of Q₂ [Median] is 73 (on the 7th value), The value of Q₁ is 70 (the 3.5th value), The value of Q₃ is 77 (is the 10.5th value). and Interquartile range = Q₃ - Q₁ = 77 - 70 = 7

A quartile is a particular kind of quantile that splits the total number of data points into four roughly equal portions, or quarters. Quartiles are a type of order statistic since they require the data to be arranged from smallest to largest in order to be computed.

The median of the data set is the number in the midpoint between the smallest number (minimum) and the first quartile (Q1).

The median of a data set is known as the second quartile (Q2).

The median value and the highest value (maximum) in the data set are the two values that make up the third quartile (Q3).

To find the quartiles, first, we need to put the data in ascending order.

65,  68,  70,  70,  71,  72,  73,  74,  75,  77,  77,  78,  80

The value of Q₂ [Median] is on the 7th value, which is 73

The value of Q₁, the lower quartile, is the 3.5th value [(3rd value+4th value)/2] , which is 70

The value of Q₃, the upper quartile, is the 10.5th[(10th value+11th value)/2]  value, which is 77

and

Interquartile range = Q₃ - Q₁ = 77 - 70 = 7.

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Answer:

The length of the short side was 12 and the length of the long side was 32

Step-by-step explanation:

We will say that the length is the shorter side, and be using l as the variable, and that width is the longer side, and be using w as the variable. The first two equations we have are:

w = l + 20

And

2(2l + 3w) = 240

We will start with the second equation, then substitute in the first equation for w. We have:

4l + 6w = 240

Divide both sides by 2:

2l + 3w = 120

Then, we substitute in l + 20 for w, giving us:

2l + 3l + 60 = 120

Subtract 60 from both sides and combine like terms:

5l = 60

l = 12

So, the original length was 12, now substituting this into our first equation gives us:

w = 12 + 20 = 32

So the original width was 32. So, the length of the short side was 12 and the length of the long side was 32.

Hope this helped!

The type of data that would be used to describe the number of students enrolled at Evergreen Valley College is quantitative - discrete.

What is algebra ?

Algebra is a branch of mathematics in which arithmetic operations and other formal manipulations are applied to abstract symbols rather than specific numbers. Geometry is the branch of mathematics that deals with the shape of objects, their spatial relations, and the properties of the space the objects are in.

It's going to be quantitative because the number of students at a college can only take on certain numerical values, those that are into jurors continuous. All values can be taken by quantitative variables. Maybe 479.4, not just 479 or 480.

The type of data that would be used to describe the number of students enrolled at Evergreen Valley College is quantitative - discrete.

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Answer:

Quantitative discrete due to the fact that’s the current quantity

Answer:

Step-by-step explanation:

1. When multiplying, exponents must be added, not multiplied as shown in the problem.

Error: [tex]3(-2)x^{2*4}[/tex]

Correct: [tex]3(-2)x^{2+4} = -6x^{6}[/tex]

2. The coefficients have been added, not multiplied.

Error: [tex](4+3)a^{2+5}[/tex]

Correct: [tex](4*3)a^{2+5} = 12a^{7}[/tex]

3. The exponent was miscalculated.

Error: [tex]x^{6+3}[/tex]

Correct: [tex]x^{6+3+1} = x^{10}[/tex]

4. The exponent was miscalculated, the two values have different bases, so they cannot be calculated using that method.

Error: [tex]6^{4+3}[/tex]

Correct: [tex]3^4*2^3 = (3*2)^3*3 = 3*6^3[/tex]

Answer:

See below.

Step-by-step explanation:

Given:

[tex]\left(3x^2\right)\left(-2x^4\right)=3\left(-2\right)x^{2 \cdot 4}=-6x^8[/tex]

Error:

The exponent product rule has been used incorrectly.

The exponents should be added not multiplied.

Correction:

[tex]\left(3x^2\right)\left(-2x^4\right)=3\left(-2\right)x^{2 +4}=-6x^6[/tex]

Correct answer:

[tex]-6x^6[/tex]

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

Given:

[tex]4a^2 \cdot 3a^5=(4+3)a^{2+5}=7a^7[/tex]

Error:

The numbers 4 and 3 have been added when they should have been multiplied.

Correction:

[tex]4a^2 \cdot 3a^5=(4 \cdot 3)a^{2+5}=12a^7[/tex]

Correct answer:

[tex]12a^7[/tex]

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

Given:

[tex]x^6 \cdot x \cdot x^3=x^{6+3}=x^9[/tex]

Error:

The exponent of the x-term has been ignored:  x = x¹

Correction:

[tex]x^6 \cdot x \cdot x^3=x^{6+1+3}=x^{10}[/tex]

Correct answer:

[tex]x^{10}[/tex]

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

Given:

[tex]3^4 \cdot 2^3=6^{4+3}[/tex]

Error:

The exponent product rule is only applicable when the bases are the same:  a⁴ · a³ = a⁴⁺³

Correction:

[tex]3^4 \cdot 2^3=81 \cdot 8=648[/tex]

Correct answer:

[tex]648[/tex]

Answer:

Hi!

slope of a line passing through the point (2,1) and (2,-1)

as you can see the abscisas of the point is same which means x-axis

now by formula

m = slope y2-y1/x2-x1

-9-1/2-2

-10/0 when there's zero in denominator this mean answer is infinity ♾️

This mean line is parallel to Y-axis

so when we're hanging out

Answer: the slope is undefined

Step-by-step explanation:

Slope = y2-y1 divided by x2-x1

slope = -9 - 1 divided by 2 - 2

slope = -10 divided by 0

Any slope with 0 as the denominator is always undefined.

Let ww represent the number of hours washing cars, and tt represent the number of hours tutoring.

The inequality representing the total number of hours Arianna must work between both jobs is:

ww + tt ≥ 10

This inequality states that the number of hours spent washing cars plus the number of hours spent tutoring must be greater than or equal to 10 hours. This represents all possible combinations of hours washing cars and hours tutoring that Arianna can work in a given week while meeting the requirement that she must work no less than 10 hours altogether between both jobs.

The algebraic expression that corresponds to the sentence "I think of a number, subtract 4, then divide by three" is given as follows:

(n - 4)/3.

The sentence for this problem is given as follows:

"I think of a number, subtract 4, then divide by three".

The number is unknown, hence the variable used to represent the number is given by n.

Then the subtraction of the number n by 4 is represented by the expression presented as follows:

n - 4.

The division of the entire expression by 3 means that the parenthesis has to be applied to (n - 4), due to the precedence of operators, hence:

(n - 4)/3.

The problem asks for the algebraic expression that represents the sentence.

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The probability that x equals 1 is 0.3151.

What are examples and probability?

The quantity of success-producing options. the total number of outcomes that could occur.

                     For instance, the chance of flipping a coin and obtaining heads is 1 in 2, as there is only one way to acquire a head and there are a total of 2 possible outcomes (a head or tail). We specify P(heads) = 12.

0.05x0.6302 1!(10-1)! =10x0.05x0.6302 = 0.3151 ">

Since the binomial distribution is a discrete distribution, it accepts discrete random variables. This shows that the random variable x can only accept integer values and cannot take the value 0.5000 because it is on an interval scale (continuous). Therefore, the statement that the maximum probability happens when x equals 0.5000 is false.

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Since 4x2+1 cannot equal 0, the solution to the above expressions issue indicates that (4x20+1) has no real factors.

It is necessary to substitute a number for each variable and conduct arithmetic operations in order to verify an algebraic equation. The response variable in the example above is comparable to 6, as 6 plus 6 = 12. Knowing the values of the variables will enable us to replace the original values with those known, allowing us to evaluate the expression.

Here,

It is significant to remember that the current ratio of a term's coefficient

Words 8x3 and 2x have a coefficient ratio of 8:2 (4:1), whereas phrases 12x2 and 3 have a coefficient ratio of 12:3 (4:1) This implies that the original sentence should be divided into the following categories: This indicates that the original phrase, which is written as, should be combined as follows:

=> (8x³+2x)(12x²+3)=2x(4x²+1))3(4x²+1),

before figuring out that (4x2+1)=(2x3)(4x2+1) is the common component.

Since 4x2+1 cannot equal 0 due to the fact that 4x20 for x R, (4x20+1) has no real factors. Since 4x2+1 cannot equal 0, the solution to the above expression issue indicates that (4x20+1) has no real factors.

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One is a unique number as it is only a positive integer that is neither prime nor composite.

If the numeral is a positive integer and there are no duplicate digits, it will be considered unique. The fact that one is the only positive integer that is neither prime nor composite makes it a unique number. It is the only positive integer that can be divided by each other and itself. As a result, only one can be regarded as the lowest common denominator among all other integers.

Given that it is the identity element for multiplication, every integer multiplied by one equals the original number. Additionally, it is the additive identity element, which means that any integer plus one equals itself. Every number may be stated as a power of one, which is the foundation of the number system.

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Answer: The father will be twice as old as the son in 24 years.

Step-by-step explanation:

12+24=36

48+24=72

72/2=36

Hope this helps!!!

The difference between the estimate in part a and the actual value calculated in part b is the equation (Estimate - Actual Value). In this case, the equation is (50 - 41.2) = 8.8.

An equation is a mathematical statement that two expressions are equal. It is usually written using an equal sign (=) and may also include numbers, variables, operators, and other mathematical symbols. Equations are used to describe relationships between different values, such as the area of a circle or the slope of a line. Equations can be used to solve for a single unknown value, or to find the relationship between different values.

Given that the difference between the estimate and actual value is 8.8, I think my estimate was reasonable. This is because the difference between the estimate and actual value is relatively small, which suggests that my estimate was close to the actual value. Therefore, my estimate was reasonable.

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Angles BAD and ADC are both right angles (definition of a rectangle).

Rectangle ABCD is provided in Statement 1.

Because the opposing sides of a rectangle are congruent, claim number two

By the reflexive quality of congruence, according to Statement 3. Statement

Because a rectangle's angles are all right angles, claim 4

Statement 5: Because all right angles are congruent, angles BAD and ADC are congruent.

Statement 6: According to SAS, triangles BAD and CDA are congruent.

7th statement: CPCTC

The statement Statement 4 was omitted:

Angles BAD and ADC are both right angles (definition of a rectangle) is statement below completes Anastasia's proof.

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Answer:

Prime number - 17

Square number - 16

Step-by-step explanation:

Ok, so a prime number is a number with no factors other than 1 and the number itself.

14 = 2 x 7

15 = 3 x 5

16 = 4 x 4

17 = 1 x 17

18 = 3 x 6

So, every number here except 17, has three or more factors,.

So, the prime number here is 17.

If you look at 16, you see that 16 = 4 x 4

A square number means that it has a whole number, which when multiplied to itself, gets you that number.

So, 16 is the required square number

Thanks

Answer:

i think u are in 10th standard srry if i am wrong

B. The third term in the sequence has a value of 1.

The notation f(3) = 1 means that the value of the function f at the input 3 is equal to 1. In other words, when the input of the function is 3, the output is 1.

This notation does not indicate anything about the first term or common difference or common ratio of the sequence.

Since J, P, and L are the midpoints of KH, HM, and MK, respectively, the values of x, y, and z are as follows;

x = 4.75.

y = 6.

z = 1.

In Geometry, the centroid theorem states that the centroid of a triangle is located at two-third (2/3) of the distance from the vertex to the midpoint of the (opposite) sides.

Generally speaking, the centroid of a triangle simply refers to the point where the three (3) medians of the triangle meet or intersect. By applying the centroid theorem to triangle KHM (ΔKHM);

Side HQ = 2/3(LH)

y = 2/3(3 + y)

3y = 2(3 + y)

3y = 6 + 2y

y = 6.

Side KQ = 2/3(KP)

7 = 2/3(7 + 2x - 6)

21 = 2(1 + 2x)

10.5 = 1 + 2x

2x = 9.5.

x = 4.75.

Side QM = 2/3(JM)

4 = 2/3(2z + 4)

12 = 2(2z + 4)

6 = 2z + 4

2z = 2.

z = 1.

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The team plots alternatives on a two by two matrix using the 2x2 Matrix decision support technique. The matrix diagram is a straightforward square divided into four equal quadrants, sometimes known as a four blocker or magic quadrant. A decision criterion, such as cost or effort, is represented by each axis.

A diagonal matrix in linear algebra is a matrix with all zero entries outside of the primary diagonal; the word typically applies to square matrices. The major diagonal's components can either have zero or nonzero elements.

The redundant column vectors are all taken out of the kernel when determining the basis of a matrix, leaving only the linearly independent column vectors. A basis is therefore merely the sum of all the linearly independent vectors.

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Therefore , the solution of the given problem of median comes out to be  R students still present (maximum) =35

The number that precisely falls in the center of a sorted collection is the median value. An average or maximum probability metric is the difference between the initial and final 50% of the data. Different algorithms are employed to compute the average and mode depending on if you do have an unusual or perhaps even number of data points.

Here,

Median is 55

P :Q: R :S :average of 45 :50: 55 :65

The number of pupils within every section needs to be as low as possible 

R is a mean

P differs by 1: 10 from the mean.

Q is 1.5 away from the mean.

Then S will just have three students, or three times five, to keep the population's mean constant.

R students still present (maximum):

=> 40 - 1- 1-3

=> 35

Therefore , the solution of the given problem of average comes out to be  R students still present (maximum) =35

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The ladder will reach 15 feet length up the building.

1. The ladder is 20 feet long

2. The ladder is set up 5 feet from the base of the building

3. Subtract the 5 feet from the length of the ladder (20 feet)

4. The answer is 15 feet

The 20-foot ladder is set up 5 feet from the base of the building. To calculate how far up the building the ladder reaches, we need to subtract the 5 feet from the length of the ladder. The answer is 15 feet. This means the ladder will reach 15 feet up the building (5 feet from the base). This can also be visualized by imagining that the remaining 15 feet of the ladder is being used to reach up the building. The 5 feet of the ladder not used to reach up the building is used to support the ladder on the ground.

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This exponential function represents growth at a rate of 26.2% per unit increase in x.

This represents growth at a rate of 26.2% per unit increase in x.

This is an exponential function, so it will represent either growth or decay. To determine whether it is growth or decay and what rate it is, we need to look at the coefficient of the exponential term, which in this case is 1.262. Since this is larger than 1, the function is growing, and the rate of increase is equal to the coefficient minus 1, which is 26.2%.

This exponential function represents growth at a rate of 26.2% per unit increase in x.

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A bird with a weight greater than 13 ounces lives in the southern region

Z = (x – mean)/standard deviation

Le x be weight for birds

For the northern region  

Z = (13 – 10)/3

Z = 1

For the southern region

Z = (13 – 16)/2.5

Z = -1.2

to find in what region is more likely to find a bird with 13 ounces, we calculate the probability for each z value

For the northern region  

P (x>13) = P(z > 1)

Then we use the z table to find the area under the curve.

P (x>13) = 0.1587

For the southern region

P (x>13) = P(z > 1.2)

Then we use the z table to find the area under the curve.

P (x>13) = 0.8849

Is it more likely that a bird with a weight greater than 13 ounces lives in the southern region

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Answer: 720, 1440, 2160, 2880

Step-by-step:

Create arbitrary variable a, such that 7200 = a + 2a + 3a + 4a.

Reduce to get 720 = a

and plug in a into the set {a, 2a, 3a, 4a} to get the answer

Zeros to the right of a number are significant as long as there is a decimal point present are described the the significance of zeros in a reported number.

Significant Zeros : If a zero is found between significant digits, it is valid. If the number is decimal, zeros can be used as placeholders (meaningless) to the left of significant digits. For example, if the mass is 32 g, there are 2 significant digits. Expressed in kilograms, the mass of 0.032 kg should have two significant digits. The zeros to the right of the decimal point that are not just placeholders are significant. These significant zeros are to the right of any significant non-zero digits. The zeros to the left of the 20.00 cm decimal point are also significant, as they are among the significant digits. If a decimal point is present, all digits from the first non-zero digit (to the right) are significant. If there is no decimal point, trailing zeros are considered insignificant unless scientific notation makes the quantity clear.

Start on the left and move right until you reach the first non-zero number..

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Complete question:

Which option(s) correctly describes the procedure used to determine the number of significant digits in a reported quantity? select all that apply.

a) Trailing zeros in whole number, 600 are asumed significant

b) Zeros to left of first non-zero number is not significant

c) zeros to the right of a number are significant as long as there is a decimal point present.

d)zeros between non-zero numbes are not significant.

With 20 counselors, there should be 250 boys at Laura's summer camp.

To determine how many boys should be at camp with 20 counselors, we can use the proportion of boys to counselors that existed at the camp when there were 200 boys and 16 counselors.

The proportion of boys to counselors when there were 200 boys and 16 counselors is 200/16 = 12.5 boys per counselor.

If we want to know how many boys should be at camp with 20 counselors, we can use this proportion and the number of counselors we have (20) to calculate the number of boys.

To calculate this, we can use the following formula:

Number of boys = (Proportion of boys to counselors) x (Number of counselors)

So for 20 counselors, the number of boys should be:

12.5 x 20 = 250 boys

So with 20 counselors, there should be 250 boys at Laura's summer camp.

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Answer:

200 + 50 + 8 + 0.5 +0.03 = 258.53

Answer: Gill is 16 now

Step-by-step explanation: If the horse was 3 one year ago, and gill is five times as old as it, shed be 15. one year from now, the horse is 5 and Gill is 17, which combined, is 22. If she is 17 in one year, she is 16 now.

The difference between the given values of |-10| and 19 is - 9

What is an algebraic expression ?

Algebraic expression can be defined as the combination of variables , constants and exponents .

Algebraic expressions are the idea of expressing numbers the use of letters or alphabets with out specifying their actual values. The fundamentals of algebra taught us the way to explicit an unknown value the use of letters such as x, y, z, and so on. these letters are called here as variables. An algebraic expression may be a aggregate of both variables and constants. Any cost this is placed before and extended by way of a variable is a coefficient.

Given values ,

|-10| and 19

the difference ,

|-10| - 19 = 10-19

= -9

Hence, The difference between the given values of |-10| and 19 is - 9

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Answer: s=6

Step-by-step explanation: so you have -7=s+(-13)

simplify: -7=s-13

add 13:

By using The Pythagoras theorem, the expression g = f/2 represents the relationship between g and f if j = h and k = m option (A), i.e. g = 1/2  is correct.

Pythagoras theorem:

The Pythagorean Theorem, also known as the Pythagorean Theorem, describes the relationship between the three sides of a right triangle. According to the Pythagorean theorem, the square of the hypotenuse equals the sum of the squares of the other two sides of the triangle. If AB and AC are the sides and BC is the hypotenuse of the triangle then BC2 = AB2 + AC2 .where AB is the base, AC is the height or altitude and BC is the hypotenuse.

The area of ​​the square formed by the longest sides (hypotenuses) of right-angled triangles is equal to the sum of the areas. The number of squares formed by the other two sides of a right triangle. In a right triangle, the formula for the Pythagorean theorem is expressed as:

c² = a² + b²

where

'c' = hypotenuse of a right triangle

'a' and 'b' are the other two legs.

In the question:

It is given that:

If j = h and k = m

From the given question, C is a right-angle triangle as j = h and k = m

From the definition of the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides

         h² +k²= g²

From the triangle ΔABC

(j + h)² +(m + h)² = f²

⇒ (h + h)² +(k+ k)² = f²

⇒ (2h)² +(2k)²= f²

⇒ 4h²+ 4k² = f²

⇒ 4(h²+k²) = f²

⇒ 4×g² = f²

⇒ (2g)² = f²

⇒ 2g = f

⇒ g = f/2

Thus, the expression g = f/2 represents the relationship between g and f if j = h and k = m option (A) is correct.

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