3x *5 ≤23 give the value of x

(4, -2) is the solution of the given system of equations

The given system of linear equations are

2x-12y=16

4x-19y=22

The missing number in 1st step is 1/2

The missing number in 2nd step is -4

The missing number in 3rd step is 1/5

The missing number in 4th  step is 6

The solution of the equation is 4 and -2

Hence, (4, -2) is the solution of the given system of equations

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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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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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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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Answer:

1 / 12

Step-by-step explanation:

" of " here means multiply

1 / 12  x  1

= 1 / 12

The correct option is D, There was 1.5 inches in the rain gauge before the rain began, and the rain fell at a rate of 0.75 inch per hour.

A general linear equation is written as:

y = ax + b

Where a is the slope and b is the y-intercept.

If a line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

We can use the first two points:

a = (4.5 - 3.75)/(4 - 3)

a = 0.75

Then we can write:

y = 0.75x + b

replacing the values of the first point we will get:

3.75 = 0.75*3 + b

3.75 - 0.75*3 = b = 1.5

Then the rate is 0.75 and the initial amount is 1.5

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The step with the proof that has a flaw is Step 2, AB ≅ BC, Symmetric Property.

Step 2 is the flaw in the proof. The symmetric property states that if AB = BC, then BC = AB. It does not justify that AB = BC in the first place.

Therefore, the proof needs additional steps to justify that AB and BC are congruent. One possible way to do this is to use the definition of a midpoint and the segment addition postulate as follows:

Step 1 | B is the midpoint of AC | Given

Step 2 | AB + BC = AC | Segment Addition Postulate

Step 3 | AB + AB = AC | Definition of midpoint (since B is the midpoint of AC)

Step 4 | 2AB = AC | Simplification

Step 5 | AB = AC/2 | Division Property of Equality

Step 6 | AB = BC | Substitution Property of Equality

Step 7 | _____ | Q.E.D.

Step 6 follows from the fact that B is the midpoint of AC, so AC = 2AB. Substituting AC/2 for AB in Step 2 gives AB + BC = AC/2 + BC, which simplifies to AB = BC. Therefore, Step 6 uses the transitive property of equality, which is a valid property of equality.

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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:

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:

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:

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]

[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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Step-by-step explanation: Well to begin, you take 15$ and multiply it by 4, since he wants to buy 4 of those tickets, which is 60$. Then, take the 10$ and multiply it by 2 since he wants 2 of those tickets, which is 20$, you then apply 10% to 60 and 20 by taking 10 percent of 60, then adding  it to 60 once have that, which is 66, you take the 3% and find 3% of 66, then add the answer of that to 66, which is 67.98$, you then do the same thing to the 20$.

Sorry if this didnt help, im sure it didnt because im a very bad explainer, but i tried..

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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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 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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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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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:

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.

The notation P(The lights go out|There is a thunderstorm outside) reads the probability of "The lights go out" given "There is a thunderstorm outside."If two events are independent, then the probability of one doesn't affect the other.

The two events are independent if the probability P(The lights go out) is equal to the probability that the lights go out and the probability P(There is a thunderstorm outside) is equal to the probability that there is a thunderstorm outside.

Conditional probability and independent events are related in the sense that if two events are independent, then the conditional probability of one event occurring given the other event is simply the probability of the first event happening. In other words, if events A and B are independent, then P(A|B) = P(A).

On the other hand, if two events are dependent, then the conditional probability of one event occurring given the other event is different from the probability of the first event happening. The conditional probability takes into account the additional information provided by the occurrence of the second event.

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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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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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The decimal number that corresponds with the number  [ 2001 ] 11 would be A. 2663

To convert the number [2001]11 to a decimal number, we can use the formula:

Decimal number = a0 + a1 x b¹  + a2 x b ² + ... + an x b ⁿ

Given the number, [ 2001 ] 11, we would have :

a0 = 1

a1 = 0

a2 = 0

a3 = 2

b = 11

With the formula, the decimal number corresponding to the number would be:

Decimal number = 1 + 0 x 11 ¹  + 0 x 11 ² + 2 x 11 ³

Decimal number = 2663

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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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Answer: 11100 m

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

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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