The equation and the table show two linear functions.
Function A:
x
-6
0
12
y
3
4
6
Function B: y = x +9
What is the rate of change of the function that has the greater rate of change?
h

The coordinates for the point J are (-5, 6).

The radius 12 represents the center of the circle from each band member to the edge of the circle.

The domain of the circle is -17 ≤ x ≤ 7.

The range of the circle is -6 ≤ y ≤ 18.

In Mathematics and Geometry, the standard form of the equation of a circle is modeled by this mathematical equation;

(x - h)² + (y - k)² = r²

Where:

From the information provided above, we have the following equation of a circle:

x² + y² + 10x - 12y - 83 = 0

x² + 10x + y² - 12y = 83

x² + 10x + (10/2)² + y² - 12y + (-12/2)² = 83 + (10/2)² + (-12/2)²

x² + 10x + 25 + y² - 12y + 36 = 83 + 25 + 36

(x + 5)² + (y - 6)² = 144

(x + 5)² + (y - 6)² = 12²

Therefore, the center (h, k) is (-5, 6) and the radius is equal to 12 units.

By critically observing the graph shown in the image attached below, we can reasonably and logically deduce the following domain and range:

Domain = [-17, 7] or -17 ≤ x ≤ 7.

Range = [-6, 18] or -6 ≤ y ≤ 18.

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After considering the given set of options we conclude that a large sample was used in the evaluation, which means the correct option is Option A.

1/2 is the evaluated expected probability for the given case under the condition that when the die was rolled an even number came out with face number 1 out of 6.

In the event that the cube was rolled 20 times, an even number came up 15 times, or 3/4 of the time. Now the same cube was again rolled 100 times, an even number came up on the recent throw which showed 51 times even, or almost 1/2 the time.

Therefore we can say that the actual results are closer to the expected probability of 1/2 when rolling the cube 100 times because a larger sample size was used.
Hence we are dealing with  larger  sample size, this means that the actual results will be much closer to the expected probability.
This is due to the law of large numbers which states that as the sample size increases, the average of the results will get closer and closer to the expected value .
Therefore, option (a) is correct.
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Option B, three 2-liter tins, is the most cost-effective choice.

1.7.1: To convert 5 litres to cm³, multiply by 1000 cm³ per litre:

5 litres * 1000 cm³/litre = 5000 cm³.

1.7.2: If 1 litre covers 8m², and you need to paint 14.4m² with three coats: 14.4m² * 3 coats = 43.2m².

Divide by 8m²/litre to find litres needed: 43.2m² / 8m²/litre = 5.4 litres.

To find the most cost-effective combination, consider the options:

A: One 5-liter tin and one 2-litre tin.

B: Three 2-liter tins.

Calculate costs including VAT: A: (1 * 439.99 + 1 * 189) * 1.15 = 723.63, B: (3 * 189) * 1.15 = 651.45.

Option B, three 2-liter tins, is the most cost-effective choice.

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The Complete Question

Paint is sold in different sizes as shown below A B 2 litre tin R189 5 litre tin at 439.99 Prices excludes VAT of 15% 1.7.1 Convert the capacity of a 5-litre tin to its volume in cm³ NOTE: 1 litre 1 000 cm³ 1.7.2

According to a paint specialist one needs at least two coats of pain therefore decided that she will paint three coats just to be sure that covered. Remember that the area that needs to be covered is 14.4 How many litres of paint will be needed if 1 litre of paint covers 8m- Looking at the paint quantity diagram and using your answer in QUI 1.7.2 A make use of different combinations of the tins of paint, ther Prudence of which combination will be the most cost effective. Inclu your calculations. 8,84 cm

6.928 units is the apothem of a hexagon with a radius of 8.

The apothem of a regular hexagon is the distance from the center to the midpoint of a side. For a regular hexagon with a radius of 8, the apothem can be found using the formula:

apothem = radius x √3/2

Substituting the given value of the radius, we get:

apothem = 8 x √3/2

apothem = 8 x 1.732/2

apothem = 6.928

Therefore, the apothem of the hexagon is 6.928 units.

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Answer:

Step-by-step explanation:

start by listing the prime numbers which are {2,3,5,7,11,13...}

now we need to find the divisibility test of 819 it can't be divisible by 2 so we shall go for 3 let check

divisible by 3

a number is divisible by 3 if when the digits are added it gives a number which is a multiple of 3

check divisible by 3

819=8+1+9=18

18÷3=6

18 is divisible by 3

now divide 819 by 3 getting 273

273=2+7+3=12

12 is divisible by 3

273÷3=91

91 is not divisible by 3 so we try the other numbers 5

a number is divisible by 5 if only the last digit is a 0 or 5

and 91 doesn't end with 0 or 5 so it is not divisible by 5

divisible by 7

a number is divisible by seven only when u remove the last digit, double it then subtract it from the remaining number and get a multiple of 7

the best way of finding the divisibility of seven is by long division

91÷7=13

we have 13 and 13 is a prime number

13÷13=1

now let's multiply the factors

3×3×7×13=819

therefore the factors are {3²,7,13}

To find the prime factorization of 819, we divide by prime numbers until we can no longer divide. The prime factorization of 819 is 3 x 3 x 7 x 13.

To find the prime factorization of 819, we need to determine the prime numbers that multiply together to give 819. We start by dividing 819 by the smallest prime number, which is 2. Since 819 is an odd number, it is not divisible by 2. So, we move on to the next prime number, which is 3. 819 divided by 3 gives us 273.

Next, we continue dividing 273 by prime numbers until we can no longer divide. Dividing 273 by 3 again gives us 91. Continuing this process, we divide 91 by 7 to get 13. Since 13 is a prime number, we cannot further divide it.

Therefore, the prime factorization of 819 is 3 x 3 x 7 x 13.

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Answer:

  1. diameter

  2. semi-circle

  3. point of tangency

  4. common internal tangent

  5. major arc

  6. radius

  7. center

  8. common external tangent

  9. secant

  10. chord

  11. minor arc

Step-by-step explanation:

You want to identify the elements of the diagram by name.

Common internal tangent — HJ, the line through the point of tangency where two circles touch each other, where neither center is in the other circle.

point of tangency — G (or K or F), a single point where an external geometry touches a circle.

Center — A (or B), the point equidistant from all those on a circle.

chord — GK, a line segment whose endpoints lie on the same circle.

secant — CD, a line that has two points of intersection with a circle.

diameter — EF, a chord that passes through the center of the circle.

common external tangent — KF, a line that is tangent to two circles that are external to each other. It does not cross the line segment between the circle centers.

radius — BF (or BE), a line segment from the circle center to a point on the circle.

semi-circle — arc EGF, an arc whose measure is 180°.

Major arc — arc CDK (or CKD, or GCK, or DCG), an arc whose measure is more than 180°.

Minor arc — CK (or CD, or GD, or GK, or GE, or GF), an arc whose measure is less than 180°.

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The order of the steps which can be used to determine an unknown value using proportion method is as follows:

Option B ---> D---> E---> A----> C.

A ratio can be defined as the expression that compares the quantity of a value that can be found in another value.

The correct step that can be used to find the a missing value when proportion method is used is as follows;

Step 1: Identify the two quantities being compared

Step 2: Write the ratio for the two known quantities

Step 3: Write a ratio that has the unknown and the know quantity.

Step 4: Equate the two ratios

Step 5: Cross multiply and solve for the unknown quantity. Describe the solution.

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[tex]\left[\begin{array}{cccc}-6&-5&-2&-3\\6&5&-1&-3\\4&10&-12&-8\end{array}\right][/tex] is matrix obtained by multiplying row 3 by 2

[tex]\left[\begin{array}{cccc}2&5&-6&-4\\6&5&-1&-3\\6&-5&-2&-3\end{array}\right][/tex] is obtained by interchanging  row 3 and row 1

The given augmented matrix is [tex]\left[\begin{array}{cccc}-6&-5&-2&-3\\6&5&-1&-3\\2&5&-6&-4\end{array}\right][/tex]

The first row operation is given that multiply row 3 by 2

[tex]\left[\begin{array}{cccc}-6&-5&-2&-3\\6&5&-1&-3\\2(2)&5(2)&-6(2)&-4(2)\end{array}\right][/tex]

[tex]\left[\begin{array}{cccc}-6&-5&-2&-3\\6&5&-1&-3\\4&10&-12&-8\end{array}\right][/tex]

Now let us find the matrix by interchanging row 3 and row 1

[tex]\left[\begin{array}{cccc}2&5&-6&-4\\6&5&-1&-3\\6&-5&-2&-3\end{array}\right][/tex]

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Answer: Mandy sold 14,000$ in total sales

Step-by-step explanation: Divide the 5% and the 700, to get a total of 140, then multiply by 100. Hope this helps!

Answer:

plus (+)

Step-by-step explanation:

Assume there is a number such as 1 after the minus:

[tex] - 1 + ( - 1) = - 2[/tex]

Thus - (+) - = +, since they add the minuses.

By using the property of incenter, measures of the sides and the angles will be,

JK = 21.2 units

KL = 26.63 units

JL = 28.33 units

m ∠K = 36°

Since, By the property of incenter,

PM = PN = PO = 7 units

∠MJP = ∠OJP = 32°

∠NLP = ∠OLP = 22°

By the triangle sum theorem,

m∠JKL + m∠KLJ + m∠LJK = 180°

2(m∠NKP) + 2(m∠NLP) + 2(m∠MJP) = 180°

2(m∠NKP) + 2(22°) + 2(32°) = 180°

2(m∠NKP) = 180° - 108°

m∠NKP = 36°

From ΔJMP,

tan(32°) = MP / MJ

tan(32°) = 7/MJ

MJ = 11.20

From ΔPOL,

tan(22°) = OP / OL

tan(22°) = 7/OL

OL = 17.33

From ΔKNP,

tan(36°) = NP / KN

tan(36°) = 7 / KN

KN = 9.63

Therefore, We get;

JK = JM + MK = 21.2 units

KL = LN + KN = 26.63 units

JL = JO + OL = 28.33 units

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The greatest common factor of the polynomial 2x³ - 10 is 2.

By extracting the greatest common factor, we obtain:

= 2(x³/2 - 5)

Therefore, the factored form of the polynomial is 2(x³/2 - 5).

Thus, the greatest common factor of the polynomial 2x³ - 10 is 2.

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The computation of the interest and the maturity value of the loan, using ordinary interest, is as follows:

Interest = $54.30

Maturity value = $1,404.30.

The ordinary interest method is based on the use of 360 days as the ordinary days in a calendar year.

The ordinary interest contrasts with the exact interest, which uses 365 days or the normal calendar days.

Principal = $1,350

Interest rate = 8%

Date borrowed = July 21

Date repaid = January 18

The number of days between July 21 and January 18 = 181 days

Total Interest = Principal x Rate x Time

= $54.30 ($1,350 x 8% x 181/360)

Maturity value = Principal + Total Interest

= $1,404.30 [$1,350 + ($1,350 x 8% x 181/360)]

Thus, based on the ordinary interest method, the maturity value of the loan is $1,404.30.

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The probability that a randomly selected token is red and green is 27/200.

The total token = 9 red + 6 green + 5 blue

The total token = 9 + 6 + 5

The total token = 20

There are 9 red and 6 green.

So, 9 out of 20 is red and 6 out of 20 is green

Let set up an equation:

9/20 × 6/20

= 54/400

= 27/200.

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The down payment would be 20% of the total cost of the dining room set, which is $6,815. So, the down payment would be $1,363.

To calculate the down payment, we'll use the following steps:
1. Determine the total cost of the dining room set, which is $6,815.
2. Find the percentage of the down payment, which is 20%.
3. Multiply the total cost by the percentage to find the down payment amount.
Using these steps, we can calculate the down payment:
Down payment = Total cost × Down payment percentage
Down payment = $6,815 × 0.20
Down payment = $1,363
So, Jess's down payment for the dining room set is $1,363.

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Answer:

1 / 12

Step-by-step explanation:

" of " here means multiply

1 / 12  x  1

= 1 / 12

In agreement, there is no correlation between the values of the graph because there is no constant that determines the relationship between the average of points and the percentage of failures of three points.

Based on the information in the graph, we can infer that there is no correlation between the values in the graph, since neither influences the other (does not modify it). Due to the above, we can establish that the values have no correlation because they are independent and do not depend on each other.

In this case, we can see that the percentage of 35% is in two values: one below 19 and one above 19. This means that there is no correlation because if there were, the values would have an obvious trend.

To conclude we can say that there is no correlation between these values because there is no a constant relationship that determines the location of the points in the graph.

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Answer:

The answer is 2000

Step-by-step explanation:

The 2 means hundred and the two zeroes mean tens and ones if he added a zero at the end it would be 2000 making the 2 to be a thousand which is the correct answer.

Hello;

4 x 500 = 500 + 500 + 500 + 500 = 1000 + 1000 = 2000

you want 1000 => 2000/2 = 1000

(4 x 500)/2 = 2 x 500 = 500 + 500 = 1000

not 4 x 500 but 2 x 500

Answer:

Step-by-step explanation:

The equivalent expression to 2/3 - 1/4x + 1/2x - 1/6 is given as follows:

1/2 + 1/4x.

Like terms are terms that share these two features:

If two terms are like terms, then they can be either added or subtracted, that is, we can use them to simplify an expression.

The expression for this problem is defined as follows:

2/3 - 1/4x + 1/2x - 1/6.

The like terms are simplified as follows:

Hence the simplified expression is given as follows:

1/2 + 1/4x.

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Answer:

h (-2) = -2.6 (repeating)

h(2) =2

h(5) = 4.3 (repeating)

Step-by-step explanation:

for h(-2)

= [tex]\frac{1}{3} (-2^{2} )-4\\\\\frac{1}{3} *4-4\\\\\frac{4}{3} -4=-2.6[/tex]

for h(2)

x = 2, so h(2) = 2

for h(5)

[tex]\frac{1}{3} (5^{2} )-4\\\\\frac{1}{3} *25-4\\\\\frac{25}{3} -4\\\\=4.3[/tex]

It is likely that the contractor's true, on-time completion rate is still around 90%.

Based on the provided dot plot and the sample of last month's on-time completions, the conclusion that can be drawn is:

The dot plot does not provide convincing evidence that the contractor's true, on-time completion rate is less than 90% because 7 or fewer on-time completions happened 19% of the time in the simulation.

This means that the observed 7 out of 10 jobs completed on time in the last month is not significantly different from what would be expected based on the assumption of a 90% completion rate.

Therefore, it is likely that the contractor's true, on-time completion rate is still around 90%.

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The SUV is the more cost-effective choice for the trip than Sedan

To determine which vehicle is the more cost-effective choice for the trip, Belle needs to consider both the rental cost and the fuel cost for each option.

Let's assume the trip is a round-trip of 500 miles.

For the sedan:

Rental cost: $180

Fuel cost: 500 miles x $0.11/mile = $55

Total cost: $180 + $55 = $235

For the SUV:

Rental cost: $200

Fuel cost: 500 miles x $0.06/mile = $30

Total cost: $200 + $30 = $230

Based on these calculations, the SUV is the more cost-effective choice for the trip.

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Answer:

400

Step-by-step explanation:

The value of the first and second integers are 54 and 55 respectively.

Let

First integer = x

Second integer = x + 1

Sum of the integers = 109

So,

First integer + Second integer = Sum of the integers

x + (x + 1) = 109

x + x + 1 = 109

2x + 1 = 109

Subtract 1 from both sides

2x = 109 - 1

2x = 108

divide both sides by 2

x = 108/2

x = 54

Ultimately,

First integer = x

= 54

Second integer = x + 1

= 54 + 1

= 55

Therefore, the solution in 4 steps are;

Step 1: x + (x + 1) = 109

Step 2: 2x + 1 = 109

Step 3: 2x = 108

Step 4: x = 54

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Answer: 11100 m

Step-by-step explanation: I'm Walter H. White

This means that, based on the National Coffee Association's data, we would expect approximately 168 out of the 275 U.S. adults in the sample to drink coffee daily.

To analyze the random sample of 275 U.S. adults, we can use the information provided by the National Coffee Association, which states that 61% of U.S. adults drink coffee daily.

To find the expected number of U.S. adults in the sample who drink coffee daily, we multiply the sample size (275) by the percentage of U.S. adults who drink coffee daily:

Expected number = 275 * 0.61 = 167.75

The expected number of U.S. adults in the sample who drink coffee daily is 167.75. However, since the number of individuals cannot be a fraction, we round the result to the nearest whole number:

Expected number ≈ 168

This means that, based on the National Coffee Association's data, we would expect approximately 168 out of the 275 U.S. adults in the sample to drink coffee daily.

Please note that the rounding process is necessary because the number of individuals in the sample should be a whole number.

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Answer:

Mean and Median 30 and 31 respectively.

Step-by-step explanation:

Mean refers to average of all the observations.

Mean = Sum of all the observations/ Total no. of observations

Mean = 37 + 27 + 1 + 31 + 27 + 40 + 47/ 7

= 210 / 7

= 30

Median refers to middle most value of the series.

In order to find median we need to arrange the given data in ascending order i.e. smallest to largest.

We get,

1, 27, 27, 31, 37, 40, 47

When the no. of observations is odd: (n + 1/ 2)th term

= 7 + 1/ 2

= 4th term

Therefore, Median is 31.

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The graph of the function f(x) =[x+3] is a linear graph and it is represented on the last graph of the attached image.

A linear equation can be written in the form:

y = mx + c

where:

y = dependent variable (usually on the vertical axis).

x = independent variable (usually on the horizontal axis).

m = slope of the line, which determines its steepness.

c = y-intercept, which is the point where the line crosses the y-axis.

From our question,

f(x) =[x+3]

y = f(x)

m = 1

c = 3

To plot our graph, we use the range of values of x which are:

x = 0, -1, -2, -3

By substituting the value of x into the equation we have the equivalent y values;

f(0) = [0 + 3] = 3

f(-1) = [-1 + 3] = 2

f(-2) = [-2 + 3] = 1

f(-3) = [-3 + 3] = 0

Plotting x against y will give us the graph attached.

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