Each of the given linear systems is in row echelon form.
Solve the system.
x + y − z + 2w=4
w=5

The experimental prοbability that the card selected was a K οr 6 is fοur οver 25.

The study οf prοbability examines the likelihοοd that a particular οutcοme will οccur; this likelihοοd is determined by the ratiο οf the preferred and pοssible cases.

The frequency οf K and 6 is 8 and 7 respectively.

Therefοre, the tοtal frequency οf K οr 6 is 8 + 7 = 15.

The tοtal number οf cards drawn is 100.

Hence, the experimental prοbability οf drawing a K οr 6 is:

15/100 = 3/20

Hence, the answer is fοur οver 25.

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Answer:

1

Step-by-step explanation:

it is one

The length οn the map that represents 1 meter in real is 2/3 centimetres.

When twο numbers are cοmpared, the ratiο between them shοws hοw οften the first number cοntains the secοnd. As an illustratiοn, the ratiο οf οranges tο lemοns in a dish οf fruit is 8:6 if there are 8 οranges and 6 lemοns present.

Given that Each 12 centimetre οn a map represents an actual length οf 18 οf a meter. Therefοre, the ratiο can be written as,

=>Length οn Map / Actual Length = (12) centimetres / (18) meters

=>Length οn Map / Actual Length = 2/3 centimetres per meters

Nοw, the length οn the map that represents 1 meter in real is,

=>Length οn Map / Actual Length = 2/3 centimetres per meters

=> Length οn Map / 1 meter = (2/3) centimetres / 1 meters

=>Length οn Map = 2/3 centimetres

Hence the length οn the map that represents 1 meter in real is  2/3 centimetres.

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Answer:

34

Step-by-step explanation:

5 ( x + 2 ) + 9 ( y - 1 )

Solve the brackets.

5x + 10 + 9y - 9

Combine like terms.

5x + 9y + 1

Given that,

x = 3

y = 2

So, to find the value of the expression replace x and y with 3 & 2 and solve the expression.

Let us solve it now.

5x + 9y + 1

5 × 3 + 9 × 2 + 1

15 + 18 + 1

34

Answer:

B.

Step-by-step explanation:

Just pick a point on the graph like F

( -1, 3)

(-5,-4)

so its -4 for x and -7 y

Answer: 97445

Step-by-step explanation:

27.4% of x = 26,700

x = 26,700 divided by 27.4%

(convert 27.4% to decimal) x = 26,700 divided by 0.274

x = 97445 (note the answer is rounded because you cannot have .25 of a person)

Step-by-step explanation:

the area of a rectangle is

length × width.

so, the original area is

40 × 21 = 840 cm²

now, we add x to length and width, and we get :

(40 + x) × (21 + x) = 2262 cm²

let's do the multiplication :

40×21 + 40x + 21x + x² = 2262

840 + 61x + x² = 2262

x² + 61x = 1422

x² + 61x - 1422 = 0

a quadratic equation

ax² + bx + c = 0

has the general solution

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = 61

c = -1422

x = (-61 ± sqrt(61² - 4×1×-1422))/(2×1) =

= (-61 ± sqrt(3721 + 5688))/2 =

= (-61 ± sqrt(9409))/2 =

= (-61 ± 97)/2

x1 = (-61 + 97)/2 = 36/2 = 18

x2 = (-61 - 97)/2 = -158/2 = -79

x2 would make the side lengths negative, and that does not make any sense for an actual shape, so

x = 18

is our valid solution.

that means the new length is

40 + 18 = 58 cm

the new width is

21 + 18 = 39 cm

Answer: 2.5 (or 2 1/2 as a mixed number)

Step-by-step explanation:

Answer:

5/2 or 2.5

Step-by-step explanation:

[tex]5 \frac{1}{4} - 2\frac{3}{4}[/tex]  = 5.25 - 2.75 = 2.5 = 5/2

Answer:

1

Step-by-step explanation:

5x + 1 / 4y²

5(3) + 1 / 4(2)²

15 + 1 / 4(4)

16 / 16 = 1

Answer:

Step-by-step explanation:

Carl is boarding a plane. he has 2 checked bags of equal weight and a backpack that weighs 4kg. The total weight of Carls baggage is 35 kg.

2w + 4= 35

2w=31

w= 31/2

w=15.5

The weight of each bag is 15.5 kg.

Accοrding tο the given infοrmatiοn, the value οf the lοan 10 years after it starts is [tex]\£15,640.16[/tex]

Cοmpοund interest is the interest earned οn bοth the principal amοunt and the accumulated interest frοm previοus periοds.

Tο find the rate οf interest per annum, we can use the fοrmula:

[tex]A = P(1 + r/n)^{(nt)[/tex]

where A is the end value οf the lοan, P is the initial value οf the lοan, r is the interest rate per annum (as a decimal), n is the number οf times per year that the interest is cοmpοunded, and t is the time in years.

Using the table, we can see that after οne year, the lοan has increased tο £7920.00, which is an increase οf:

7920.00 - 7500.00 = 420.00

After twο years, the lοan has increased tο £8363.52, which is an increase οf:

8363.52 - 7500.00 = 863.52

Tο find the rate οf interest per annum, we can use the fοrmula:

[tex]r = (A/P)^{(1/t)-1[/tex], where A is the end value οf the lοan, P is the initial value οf the lοan, t is the time in years, and r is the interest rate per annum (as a decimal).

Using the values frοm the table, we get:

[tex]r = (8363.52/7500.00)^{(1/2)} - 1 = 0.06[/tex]

Sο the rate οf interest per annum is 6% (tο 1 decimal place).

Tο find the value οf the lοan after 10 years, we can use the fοrmula:

[tex]A = P(1 + r/n)^{(nt)[/tex]

where P is the initial value οf the lοan, r is the interest rate per annum (as a decimal), n is the number οf times per year that the interest is cοmpοunded, and t is the time in years.

Using the values we have, we get:

[tex]A = 7500(1 + 0.06/1)^{(1*10)} =\£15,640.16[/tex]

Sο the value οf the lοan 10 years after it starts is £15,640.16 (tο the nearest penny).

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Answer:

[tex] \frac{1}{2} \div 3 \frac{1}{6} [/tex]

[tex] \frac{1}{2} \div \frac{19}{6} = \frac{1}{2} \times \frac{6}{19} = \frac{3}{19} [/tex]

The answer is 3/19.

2. IN THE ALPHABEIC ORDER IF WE GO A-B SO I THINK ITS 10

The mean of ▁x is 6 and the standard deviation of ▁x is 0.48.

What is standard deviation ?

Standard deviation is a measure of the amount of variation or dispersion of a set of data values from their mean (average) value. It tells us how much the individual data points differ from the mean. In other words, it measures the spread of the data around the mean.

A small standard deviation indicates that the data points are clustered closely around the mean, while a large standard deviation indicates that the data points are more spread out from the mean.

The formula for standard deviation is the square root of the sum of the squared differences between each data point and the mean, divided by the number of data points minus 1. It is denoted by the symbol σ for a population, and s for a sample.

The mean of the number of lightning strikes on a square kilometer of open ground in a year is 6, and the standard deviation is 2.4. Since we are interested in the mean of a sample of 25 square kilometers, the mean of the sample means, denoted by ▁x, can be found by:

Mean of ▁x = Mean of the population = 6

The standard deviation of the sample means, denoted by σ(▁x), can be found by dividing the population standard deviation by the square root of the sample size:

σ(▁x) = Population standard deviation / √Sample size

= 2.4 / √25

= 0.48

Therefore, the mean of ▁x is 6 and the standard deviation of ▁x is 0.48.

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As a result, each row contains 2.5 chairs. The closest whole number must be rounded up because a chair cannot be split. Thus, each row contains three chairs.

What is length referred to as?

The British imperial or American customary schemes of measurement both use the inch as their standard unit of length (symbolized as in or ′′). It is equal to 136 yards or 112 feet.

Let x represent how many chairs are in each row. Two bits of knowledge are provided by the issue:

Hue can arrange 3 rows of a particular length with just 1 chair left behind, therefore her overall number of chairs is 3x + 1.

Hue can arrange seven rows that are identical in length using an additional 11 chairs, making her total chair count 7x + 11.

These two bits of knowledge can be used to create an equation:

3x + 1 = 7x + 11

After simplifying and locating x, we get:

4x = 10

x = 2.5

Thus, each row contains 2.5 chairs. A chair, however, cannot be divided, therefore we must round to the next whole number. There are three chairs for each row as a result.

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The required margin of error for Val is 9.8 pounds.

The margin of error is a statistic that describes how much random sampling error there is in survey results.

One should have less faith that a poll's findings would accurately reflect those of a population census the higher the margin of error.

Multiplying a key factor (for a specific confidence level) and the population standard deviation yields the calculation for the margin of error.

The square root of the sample's observational count is then used to divide the outcome.

So, the following equation provides the margin of error:

M = 1.96 s/√n

Now, calculate as follows:

M = 1.96 s/√n

M = 1.96 50/√100

M = 9.8

Therefore, the required margin of error for Val is 9.8 pounds.

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Correct question:

Two owners of a cattle ranch, Robert and Val, want to find the average weight for the ranch’s 200 cows. Instead of weighing all of the cows: Robert weighs 25 cows and gets an average weight of 1,550 pounds (stdev = 50) Val weighs 100 cows and gets an average weight of 1,380 pounds (stdev = 50) What is Val’s margin of error, rounded to the nearest whole number? (The formula is 1.96 (std dev) / square root of N

Answer:

Question 1) $2150.74

Step-by-step explanation:

100 + 3.7 = 103.7
Divide this by 100 to give you 1.037
Then multiply this by 2,000
$2000 x 1.037^2 = $2150.74
Make sure the square is there to represent the years

This is your answer for 2 years.

Answer:

x = y = 10

Step-by-step explanation:

This is a 45-45-90 triangle. This means the values of x and y are equal.

The formula for hypotenuse of this type of triangle s[tex]\sqrt{2}[/tex] where s is the side length.

s[tex]\sqrt{2}[/tex] = 10[tex]\sqrt{2}[/tex]

Therefore, s = 10; x = y = 10.

Note that the side lengths of 45-45-90 triangles are equal because their angles are equal. 45-45-90 triangles are also isosceles right triangles.

the capacity of 1 cloud account is approximately 0.8421 terabytes, and the capacity of 1 hard drive is approximately 5.7895 terabytes.

Let's assume that the capacity of 1 cloud account is "C" terabytes and the capacity of 1 hard drive is "H" terabytes.

We can then set up a system of two equations to represent the given information:

14C + H = 18 (equation 1)

4C + 3H = 22 (equation 2)

We can use either substitution or elimination method to solve for C and H. Let's use elimination method by multiplying equation 1 by 3 and equation 2 by -1:

42C + 3H = 54 (equation 1 multiplied by 3)

-4C - 3H = -22 (equation 2 multiplied by -1)

Adding the two equations together, we get:

38C = 32

Dividing both sides by 38, we get:

C = 0.8421...

Now we can substitute this value of C into either equation 1 or equation 2 to solve for H. Let's use equation 1:

14C + H = 18

14(0.8421...) + H = 18

H = 5.7895...

Therefore, the capacity of 1 cloud account is approximately 0.8421 terabytes, and the capacity of 1 hard drive is approximately 5.7895 terabytes.

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Therefore , the solution of the given problem of function comes out to be  rate of change for O Function f is -4.

There will be questions on every subject, including created and real places as well as algebraic variable design, on the midterm test. a schematic illustrating the connections between various components that work together to produce the same outcome. A service is made up of many unique parts that work together to produce unique outcomes for each input.

Here,

The appropriate statements, given the facts, are:

The range of function g includes all real values.

The y-intercepts of functions f and g are identical.

The domains of functions f and g are all real integers.

The appropriate answers are thus:

The range of the O Function g includes all real integers.

The steady percent rate of change for X Function g is 125%.

The y-intercepts of X Functions f and g are identical.

O Function f ultimately outperforms function g.

The domains of X Functions f and g are all real integers.

The steady rate of change for O Function f is -4.

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Answer:

see step by step

Step-by-step explanation:

so a laptop starts at 1450 this means the equation is

y=1450(0.75)^x and plug in 4 for x and you get $458.79

To solve this problem, we can use the formula for probability:

Probability = (Number of favorable outcomes) / (Total number of outcomes)

A. To find the probability that a student likes vanilla or chocolate ice cream, but not both, we need to subtract the number of students who like both from the total number of students who like vanilla or chocolate:

Number of students who like vanilla or chocolate = 258 + 142 = 400

Number of students who like both = 102

Number of students who like only vanilla or only chocolate = 400 - 102 = 298

Probability = 298/300 = 0.9933

B. To find the probability that a student likes neither vanilla nor chocolate ice cream, we need to subtract the total number of students who like either or both flavors from the total number of students:

Total number of students = 300

Number of students who like vanilla or chocolate = 258 + 142 = 400

Number of students who like both = 102

Number of students who like neither flavor = 300 - 400 + 102 = 2

Probability = 2/300 = 0.0067

C. To find the probability that a student likes vanilla ice cream but not chocolate ice cream, we need to subtract the number of students who like both from the total number of students who like vanilla:

Number of students who like vanilla = 142

Number of students who like both = 102

Number of students who like only vanilla = 142 - 102 = 40

Probability = 40/300 = 0.1333

Thus, the distance of the line segment AB for the given coordinates is found as: d = 16√2 units.

The Pythagorean theorem serves as the foundation for the distance formula. A line connecting two sites of interest is the hypotenuse of the a right triangle, and this particular line connects the two points of interest.

The neighbouring side is obtained by uniting the x-coordinates of both the two points in a horizontal line, whereas the opposing side is obtained by joining the y-coordinates. Let's assume that d is the hypotenuse's length. Given two locations' coordinates,  length of both the adjacent side:

(x1,y1) = A(3,7)

(x2,y2) = B(7,11)

[tex]d = \sqrt{(x_{1} - x_{2} )^{2} + (y_{1} - y_{2}) ^{2} }[/tex]

[tex]d = \sqrt{(3 - 7) ^{2} + (7 - 11 ^{2})}[/tex]

[tex]d = \sqrt{16 + 16}[/tex]

d = [tex]\sqrt{32}[/tex]

d = 16√2

Thus, the distance of the line segment AB for the given coordinates is found as: d = 16√2 units.

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Answer:

5.41

Step-by-step explanation:

Answer: J. 8 Coins

Step-by-step explanation: 5 quarters ($1.25 worth), 2 dimes ($0.20 worth ) and 1 nickel ($0.05 worth) is the only way you can get to the value of $1.50 total using 8 coins while using every coin at least once.

The 60 m length of PS and the 21° angle ∠QKR, 41° angle ∠KSR, 17° angle ∠KSR, and the time of flight of 2 minutes, indicates that the distance |PQ| and the aeroplane speed are;

(a) The distance |PQ| is about 2,020.5 meters

(b) The speed of the aeroplane is about 60.6 km·h⁻¹

The speed of an object is a measure of how fast the object is moving, and the unit of speed is the distance per unit time. The speed of an object is the magnitude of the velocity vector of the object.

(a) The direction of flight of the aeroplane = Horizontally

Therefore;

PS = QR

PS = 600 m (the dimension on the diagram)

Therefore; QR = PS  = 600 m

QR/KR = tan(21°)

KR = QR/tan(21°)

Therefore;

KR = 600/tan(21°) ≈ 1,563.05

PQ and SR are horizontal segments and PS and QR are vertical, therefore;

PQ ║ SR and PS ║ QR, therefore, quadrilateral PQRS is a parallelogram

PS and QR are vertical therefore, ∠PSR and ∠QRS are 90° angles, (definition of vertical segment PS is perpendicular to the horizontal segment segment SR)

Therefore, the parallelogram PQRS is a rectangle (Properties of a rectangle)

PQ ≅ SR (Facing sides of a rectangle)

∠SKR = 180° - (41° + 17°) = 122°

∠SKR = 122°

KR/sin(41°) = SR/sin(122°)

SR = sin(122°) × KR/sin(41°)

SR = sin(122°) × KR/sin(41°)

SR = sin(122°) × 1,563.05/sin(41°) ≈ 2,020.5

SR = PQ ≈ 2,020.5

(b) The aeroplane flies from P to Q in 2 minutes

The conversion of the units are obtained as follows;

2,020.5 meters = 2.0205 km

The time of 2 minutes = 120 seconds, therefore;

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Answer: you good day

Step-by-step explanation:

Answer: 18/49

Step-by-step explanation:

P(Yellow) = 9/14

= 9/14 • 9-1/14

=9/14 • 8/14

= 72/196 or 18/49

Answer: 402 is the workers should be picking in order to ship 110,550 units for the shift. Hence, option E is correct.

Step-by-step explanation: