In a geometric sequence, the first term, a_1, is equal to 3, and the third term, a_{3}, is equal to 192 Which number represents the common ratio of the geometric sequence?

The inequality that represents the more minutes needed to reach 80% of the battery is 3x + 40 ≤ 80. And the number of minutes will be 13.33 minutes.

Inequality is defined as an equation that does not contain an equal sign.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Let 'x' be the number of minutes and 'y' be the total battery percentage. Then the equation is given as,

y = 3x + 40

The inequality that represents the more minutes are needed to reach 80 of battery is given as,

3x + 40 ≤ 80

Simplify the inequality, then we have

3x + 40 ≤ 80

3x ≤ 40

x ≤ 13.33 minutes

The inequality that represents the more minutes needed to reach 80% of the battery is 3x + 40 ≤ 80. And the number of minutes will be 13.33 minutes.

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1. It should be noted that HD = EM and HE = OM. In this case, the opposite sides are equal in the rectangle.

2. It should be noted that EHO = HOM = OME = MEH = 90°. In this case, all angles are equal to 90°.

Postulates are assertions that, in the absence of evidence, are taken to be true. Postulates have two functions: they define undefined terms and act as a foundation for the proof of subsequent propositions.

A line segment is determined by two points. A line segment may be extended along a line indefinitely. The other information is attached.

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Answer:

c

Step-by-step explanation:

The proof for the congruence of triangles GHI and GFJ are given below.

Two or more triangles are said to be congruent if and only if sides and angles of one triangle is equal to the corresponding sides and angles of another triangle.

From the figure,

1) Line segment FJ ⊥ line segment FH (given)

2) ∠HGI = ∠FGJ (It is also given)

3) HI = FJ (Given). So HI ≅ FJ

4) HI ⊥ FH (given)

5) Since both the angles F and H are right angles,

∠F ≅ ∠H (since all right angles are congruent)

6) So we get that two angles and a non included side of ΔGHI are equal to the corresponding two angles and a non included side of ΔGFJ.

So by AAS congruence theorem, ΔGHI ≅ ΔGFJ.

Hence the given two triangles are congruent.

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Answer: B. 0.058 hectometers

Step-by-step explanation: To convert millimeters to hectometers, you need to divide the number of millimeters by 10,000.

Given that there are 580 millimeters, the conversion to hectometers can be calculated as follows:

580 millimeters ÷ 10,000 = 0.058 hectometers

The correct equations are:8x^3 * (3x^2) = 24x^5, 6b^3 * (-2b^3) = -12b^6, 3a^3 * (-3a^4) = -9a^7. The equations are correct because they follow the rules of algebra. The equation 4x^3 * (6x^2) = 24x^5 is not correct.

The distributive property of multiplication over addition allows us to multiply a factor by each term inside a set of parentheses. In the equation 8x^3 * (3x^2), we can use the distributive property to multiply 8x^3 by each term inside the parentheses, giving us 24x^5.

Similarly, the product of two negative numbers is positive, which explains why the equation 6b^3 * (-2b^3) equals -12b^6.

Finally, multiplying two terms with the same base means we add the exponents, so in the equation 3a^3 * (-3a^4), we get -9a^7.

Therefore, these equations are correct and follow the rules of algebra.

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Answer:

The minimum value is 2.5.

Step-by-step explanation:

This is a sine wave that is parallel to the x axis.  It will never go below 2.5, as shown on the graph.

Option D. The faculty should use the median to make their argument. The median will be lower than the mean since the mean is influenced by the few extremely high salaries.

Mean is the average of any data set whereas the median is the middle value we get after arranging the data in ascending order.

So for example, if the salaries of any 5 faculty members are as follows:

$10,000 , $50,000 , $80,000 , $150,000 , $160,000

Mean= (10,000+50,000+80,000+150,000+160,000) / 5

Mean= $90,000

Median= (5+1) / 2

Median= 6/2

Median= 3rd value

As the data is already arranged in ascending order, Median is $80,000

Hence, if the faculty want to give the community the impression that they deserve higher salaries, they should advertise the median of their current salaries.

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Answer:

x + y = -9

Step-by-step explanation:

let x = -8, y = -1

the equation that passes through the point (-8,-1) is x + y = -9

The estimated probability  that Roger runs less than 5 km in his next tennis match is  33%.

The dot plot summarizes the distance Roger ran in his recent tennis matches. To estimate the probability that he will run less than 5 km in the next match, we can use the data from the dot plot.

So according to question, there are kilometres as :

3 km, 4 km, 5 km, 6 km, and 7 km.

Total matches he played

for 3 km- 1 match , for 4 km- 2 matches , for 5 km- 4 matches, for 6 km- 0 matches, and for 7 km- 2 matches.

Out of 9 matches, he ran less than 5 km in 3 matches.

So the probability that Roger runs less than 5 km in his next tennis match is: 3/9  = 1/3

So the percentage will be : 33.33%   ≈ 33%

Therefore, the estimated probabilityrobability that Roger runs less than 5 km in his next tennis match is 1/3 or about 33%.

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Answer: 33%

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

Answer:

the number of shirts sold

Step-by-step explanation:

that's what the question is asking

Step-by-step explanation:

an inscribed angle has its vertex on the circle, and the sides of the angle are two chords of the circle.

the inscribed angle is half the size of the arc angle (the angle at the center of the circle) of the arc that the two sides cut out of the circle.

110° is the arc angle (at the center of the circle) of the arc GJ.

for the inscribed angle GFJ the vertex is F, and the angle there is half of the arc angle :

angle GFJ = 110/2 = 55°

the second problem is the opposite "direction".

we have the inscribed angle FJH = 36°.

and we want the arc angle FH.

now, since the inscribed angle is half of the arc angle, the arc angle is twice the inscribed angle :

arc angle FH = 36×2 = 72°

Answer:

2. $9.99

3. 45 tickets for $27

4. 20 cents

Step-by-step explanation:

2. 79.92/8 = 9.99

3. 27/45 0.6 and 15/20 = 0.75 and 60 cents is less than 75 cents

4. 6/30 = 20

Answer:

Step-by-step explanation:

79.92/8= 9.12 per cd

15/20= .75

27/45=.6 better deal because it is .60 cents per ticket

6/30= .20 per can

Answer:

29/5

Step-by-step explanation:

hope this helps

Answer:

hope this helps

Step-by-step explanation:

The number of children and adults that swam at the public pool are 247 and 208 respectively

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 4x − 4y = 4.

Represent the number of children by x and the number of adult by y

this means;

x+y = 455 equation 1

1.75x + 2.5y = 952.25 equation 2

using substitution method,

x = 455-y

substitute 455-y for x in equation 2

1.75(455-y) + 2.5y = 952.25

796.25-1.75y+2.5y = 952.25

0.75y = 952.25-796.25

0.75y = 156

divide both sides by 0.75

y = 156/0.75

y = 208

substitute 208 for y in equation 1

x = 455-208

x = 247

therefore the number of children and adults in the pool are 247 and 208 respectively.

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Answer:

So the simplified expression is:

2x - 4 / (x^2 + 9x + 20)

Step-by-step explanation:

To simplify the expression, we need to simplify the numerator and denominator separately, and then simplify the entire expression.

Starting with the numerator:

4x^2 + 12x - 16

For the denominator:

The first fraction: 2x + 10 can be simplified as follows: 2x + 10 = (2)(x) + (2)(5) = 2x + 10

The second fraction: 6x + 24 over x^2 + 9x + 20

We can simplify the denominator by using partial fraction decomposition. To do that, we need to write the denominator as a sum of simpler fractions, each with a numerator that is a constant. In other words, we write:

6x + 24 / (x^2 + 9x + 20) = (A x + B) / (x^2 + 9x + 20) + (C x + D) / (x^2 + 9x + 20)

Multiplying both sides by the denominator, we get:

6x + 24 = (A x + B)(x^2 + 9x + 20) + (C x + D)(x^2 + 9x + 20)

Expanding the right-hand side, we obtain:

6x + 24 = Ax^3 + (A 9 + B) x^2 + (A 20 + B 9 + C) x + (B 20 + D)

Comparing the coefficients of the polynomials on both sides, we get the following system of linear equations:

A = 0

B = 6

C = 0

D = -24

Therefore, the partial fraction decomposition of the denominator is:

6x + 24 / (x^2 + 9x + 20) = (6x + 24) / (x^2 + 9x + 20)

Putting it all together, we have:

4x^2 + 12x - 16 / (2x + 10) / (6x + 24) / (x^2 + 9x + 20) = (4x^2 + 12x - 16) / (2x)(6x + 24) / (x^2 + 9x + 20) = 2x - 4 / (x^2 + 9x + 20)

So the simplified expression is:

2x - 4 / (x^2 + 9x + 20)

The probability of the sample mean annual insurance cost being greater than $620 is very low, that is 0.00317% which indicating that it is unlikely to happen by chance.

Probability is a branch of mathematics that deals with the likelihood of an event happening. It is used in various fields, such as insurance, finance, and science.

To calculate the probability, we need to use the central limit theorem, which states that the distribution of sample means of a population approaches a normal distribution as the sample size increases. We also need to know the mean and standard deviation of the population.

Assuming that the population is normally distributed, we can use the following formula to calculate the probability:

z = (x - μ) / (σ / √(n))

where z is the z-score, x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case, we don't know the population mean and standard deviation, but we can use the sample mean and standard deviation as estimates. Let's say we have a sample of 100 insurance costs with a mean of $600 and a standard deviation of $50.

Now, we can calculate the z-score:

z = (620 - 600) / (50 / √(100)) = 4

The z-score of 4 indicates that the sample mean of $620 is 4 standard deviations away from the mean of $600. We can use a standard normal distribution table or a calculator to find the probability of getting a z-score of 4 or higher. The probability is very small, approximately 0.0000317 or 0.00317%.

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The probability that a student choosen at random likes english but not maths is 299/676.

Let A be the event that a student likes math, and B be the event that a student likes English.

From the given information, we know that:

P(A) = 15/26

P(B) = 13/26

P(neither A nor B) = 9/26

To find the probability that a student chosen at random likes English but not math, we can use the formula:

P(B and not A) = P(B) - P(A and B)

The probability of A and B can be found by multiplying the probabilities of A and B together, since they are not independent:

P(A and B) = P(A) × P(B) = (15/26) × (13/26) = 195/676

Substituting the given probabilities into the formula, we get:

P(B and not A) = (13/26) - (195/676)

Simplifying, we get:

P(B and not A) = 299/676

Therefore, the probability that a student chosen at random likes English but not math is 299/676.

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The whole number whose sum is 72 cannot be in the ratio C. 3/4.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them

The whole number must   be divided by sum of two ratio particularly

A.5 + 7=12

72 can be divided by 12

B.3+5=8

72 can be divided by 8

C.4+3=7

72 can not be divided by 7

D.4+5=9

72 can be divided by 9

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The whole number whose sum is 72 cannot be in the ratio

A. 5/7

B. 3/5

C. 3/4

D. 4/5

The perimeter of the updated blueprint would be = 62units.

The percentage that she can use to multiply the dimensions of the stage so that the dimensions of the image is half the size of the original blueprint would be = 50%.

To calculate the perimeter of the blueprint is to add the sides of the whole blue print that was given. That is;

= 10+4+2+4+2+4+10+2+2+8+2+2

= 62 units.

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Anwer: EG=EF+EG => 6x+12+48=144

6x=144-12-48

6x=84

x=14

d)x=14

The equation that represent the graph is C = 1.5m + 200.

A moving company charges a one time fee and cost per miles of it service. Therefore, the relationship is between the total cost and the number of miles.

Therefore, let's use equation to represent the relationship between the total cost C and number of miles travelled, m.

Hence, using slope intercept form

y = mx + b

where

Hence,

using (0, 200) (200, 500)

m = 500 - 200 / 200 - 0

m = 300 / 200

m = 1.5

Hence,

y-intercept = 200

Therefore, the equation is C = 1.5m + 200

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The Equivalent Fraction of -117 / 63 is -13/7.

The fractions with distinct numerators and denominators but the same value are said to be equivalent fractions.

For example, 2/4 and 3/6 are equivalent fractions, because they both are equal to the ½.

A rule that says the outcome of multiplying the numerator and denominator of a fraction by the same nonzero number is a fraction equal to the original fraction.

Given:

We have the Fraction -117 / 63

As, Equivalent fraction can have different numerators but the denominators should be necessarily same.

Now, simplifying the fraction

= -117/ 63

= - (13 x 9) / (7 x 9)

= -13 / 7

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Answer:

60 degrees

Step-by-step explanation:

The probability that the next component brought in for repair is a compact disc player given that it is already known to be an audio component is 0.83 or 83%.

Probability is a fundamental concept in mathematics, statistics, and various fields of science. It is used to measure the likelihood of an event occurring

In the given scenario, we are told that a certain shop repairs both audio and video components. Let A denote the event that the next component brought in for repair is an audio component, and let B be the event that the next component is a compact disc player. We are also given that P(A) = 0.6 and P(B) = 0.5.

The probability of B given A, denoted by P(B|A), represents the probability that event B will occur given that event A has already occurred. In other words, it tells us how likely it is that the next component brought in for repair is a compact disc player given that it is already known to be an audio component.

To calculate P(B|A), we use the formula for conditional probability:

P(B|A) = P(A and B) / P(A)

Here, P(A and B) denotes the probability that both events A and B occur. We know that event B is contained in event A, so it follows that P(A and B) = P(B). Therefore:

P(B|A) = P(B) / P(A)

Substituting the given values, we have:

P(B|A) = 0.5 / 0.6

P(B|A) = 5/6 or 0.83 (rounded to two decimal places)

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Complete Question:

A certain shop repairs both audio and video components. Let A denote the event that the next component brought in for repair is an audio component, and let B be the event that the next component is a compact disc player (so the event B is contained in A).  Suppose that P(A) = .6and P(B) = .5. What is P(B|A) ?

The maximum and minimum values are 34.5 and 2

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

P = 2x + 7y

Subject to:

4x - 2y <= 5

x >= 1

0 <= y <= 4

Next, we plot the constraints on a graph

From the graph, we have the following vertices

(1, 0), (4, 0) and (3.25, 4)

This gives

P = 2(1) + 7(0) = 2

P = 2(4) + 7(0) = 8

P = 2(3.25) + 7(4) = 34.5

Hence, the minimum is 2 and the maximum is 34.5

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