3х + 2y = 5
4х + 5y = 16

Answer:

10 < x

Step-by-step explanation:

ten (10) less than (<) a number (x)

Answer:

This is a often mistake when being asked to write an expression. The words "is less than" and "less than" have different meaning. The phrase, "is less than" means 6 < k. The phrase "less than" means 6 - k.

I'll make a example with your problem. (I am adding a "x" on it cause it's easier for me to interrupt. But means the same as yours.)

"10 less than a number x"

10 - x

"10 is less than a number x"

10 < x

Answer:

2:4, 4:8, 32:64, 8/16, 14/28

Answer: 158.26cm³

Step-by-step explanation:

First, we.need to calculate the volume of the cylinder and this will be:

Volume = πr²h

Volume = 3.14 × 3² × 8

Volume = 3.14 × 9 × 8

Volume = 226.08cm³

Since the jar is 70% full, the volume will be:

= 70% × 226.08cm³

= 0.7 × 226.08cm³

= 158.26cm³

Note:

Radius = Diameter/2 = 6cm/2 = 3cm

Answer:

12

Step-by-step explanation:

If you add the ratio you will get 8 and 1 in the ratio number represents

6 people so 5-3=2

Therefore, the no. of girls minus boys= 6×2=12

so you need 12 more boys to make it to be a ratio of 1:1

This shows that Harry is 2 times older than Larry

Given the following parameters

Let the number of times harry is older than Larry be x such that;

14 = x * 7

7x = 14

Divide both sides by 7

7x/7 = 14/7

x = 2

This shows that Harry is 2 times older than Larry

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Answer:

the answer might be 125,000 yards maybe

Answer:

Step-by-step explanation:

\(0.09* \frac{1.21}{3.3}*0.00024= 0.09 * \frac{1.21*10}{3.3*10}*0.00024\\\\=0.09*\frac{12.1}{33}*0.00024\\\\= 0.09 * \frac{1.1}{3}*0.00024\\\\= 0.09 * 1.1 * 0.00008\)

= 0.00000792

= 7.92 * \(10^{-6}\)

x = 0 and Reduced cost = -4: This combination is not possible for decision variable x and its corresponding reduced cost.

Based on the complementary slackness condition in linear programming, the values of the decision variable x and its corresponding reduced cost can provide insights into the feasibility and optimality of the solution.

In the given scenarios:

x = 20 and Reduced cost = -4:

This combination is possible as a non-zero value of x with a negative reduced cost indicates that x is a non-basic variable and has a potential to increase in order to improve the objective function value.

x = 0 and Reduced cost = -4:

This combination is not possible because if x is a non-basic variable with a reduced cost of -4,

it implies that increasing x from zero would improve the objective function value, violating the complementary slackness condition.

x = 0 and Reduced cost = 0:

This combination is possible as x can be a basic variable with a reduced cost of zero,

indicating that it is at its lower bound and does not need to change.

x = 20 and Reduced cost = 0:

This combination is possible as a non-zero value of x with a reduced cost of zero implies that x is a non-basic variable and has already reached its upper bound,

so it does not need to change to improve

the objective function value.

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Answer:

A.

\(C= 28.3 \ \ feet\)

Step-by-step explanation:

Formula for Circumference is

\(C=2\pi r\)

We know radius is half of diameter

\(r=\frac{d}{2} \\r=\frac{9}{2}\)

\(C=2(3.14)\frac{9}{2}\)

\(C=(3.14)9\\C=28.3 feet\)

Based on the information, we can determine convergence or divergence of series.The given options do not provide a clear representation of potential outcomes.It is not possible to select correct option.

The given series is "nvž enn |||-) En=12 100 1-) Σπίο 3* 2"-1 ||-) En=2 n". In the series, we have the characters "nvž enn |||-)" which indicate the series notation. The characters "En=12 100 1-" suggest that there is a summation of terms starting from n = 12, with 100 as the first term and a common difference of 1. The characters "Σπίο 3* 2"-1 ||-) En=2 n" indicate another summation, starting from n = 2, with a pattern involving the operation of multiplying the previous term by 3 and subtracting 1.

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Statistical power is a measure of the ability to reject the null hypothesis when it is false. It represents the probability of correctly identifying a true effect or relationship in a statistical hypothesis test.

A high statistical power indicates a greater likelihood of detecting a significant result if the null hypothesis is indeed incorrect. The power of a statistical test depends on several factors, including the sample size, the effect size (the magnitude of the true effect or difference), the chosen significance level (often denoted as α), and the variability or noise in the data. Increasing the sample size or effect size generally increases the statistical power, while a lower significance level or higher variability decreases it.

Power analysis is commonly used to determine an appropriate sample size for a study, ensuring that it is adequately powered to detect the desired effect. A higher power is desirable as it reduces the chances of a Type II error (failing to reject the null hypothesis when it is false) and increases the chances of correctly detecting real effects or relationships.

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The value of the expression \(4\frac{1}{10}\times-4\times\frac{5}{12}\) is \(-6\frac{5}{6}\).

A mathematical statement expressed as a string of numbers and unknowable variables is known as a numerical expression. Statements can be used to create numerical expressions.

The given, expression is \(4\frac{1}{10}\times-4\times\frac{5}{12}\).

= (41/10) × (- 4) × (5/12).

= (41×-4×5)/(10×12).

= (-820/120).

= - 82/12.

= - 41/6.

= \(-6\frac{5}{6}\).

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Answer:

final answer = 8.74 And the explanation due to the subtraction process

A 10 cm deep beaker mercury will have the same hydrostatic pressure as 133.5 cm deep water.

The hydrostatic pressure exerted by a fluid is given by:

P = ρ.g.h

Where:

ρ = fluid density

g = gravitational acceleration

h = fluid depth

We want to compare 2 types of fluid, water and mercury.

Divide both sides of the equation by h

P/h = ρ.g

Since pressure is held constant, then the fluid density is inversely proportional to the fluid depth.

Therefore,

h_water : h_mercury = ρ_mercury : ρ_water

Given that:

ρ_mercury = 13.55 ρ_water and h_mercury = 10 cm

Then,

h_water : 10 = 13.55 ρ_water : ρ_water

h_water : 10 = 13.55 : 1

h_water = 13.55 × 10 = 135.5 cm

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The distance traveled is -102/3 units, which represents the total displacement of the object during that time interval.

The area of the wound after 4 days is -96 square centimeters.

To find the distance traveled by the object,

Integrate the velocity function over the desired time interval.

The distance function, S(t), is obtained by integrating the absolute value of the velocity function,

S(t) = ∫|v(t)| dt

Given that v(t) = 3t² - 5t + 7,

Compute the distance traveled from time t = 0 to t = 2,

S(t) = ∫|3t² - 5t + 7| dt

To find the definite integral, split the interval [0, 2] into two regions

[0, 2] and [2, 2].

This is because the absolute value of the velocity function changes sign at t = 2.

For the interval [0, 2], the absolute value of the velocity function simplifies to v(t) = 3t² - 5t + 7,

S1(t) = ∫(3t² - 5t + 7) dt

= t³/3 - (5t²)/2 + 7t | [0, 2]

= (2³/3 - (52²)/2 + 72) - (0³/3 - (50²)/2 + 70)

= 8/3 - 20/2 + 14 - 0

= 8/3 - 10 + 14

= 8/3 + 4

= 20/3

For the interval [2, 2], the absolute value of the velocity function becomes v(t) = -(3t² - 5t + 7),

S2(t) = ∫(-(3t² - 5t + 7)) dt

= -t³/3 + (5t²)/2 - 7t | [2, 2]

= -(2³/3) + (52²)/2 - 72 - (2³/3) + (52²)/2 - 72

= -8/3 + 20/2 - 14 - 8/3 + 20/2 - 14

= -8/3 + 10 - 14 - 8/3 + 10 - 14

= -8/3 + 6 - 14

= -8/3 - 8 - 14

= -8/3 - 24 - 14

= -8/3 - 38

= -8/3 - 114/3

= -122/3

Therefore, the total distance traveled by the object from time t = 0 to t = 2 is,

S(t) = S1(t) + S2(t)

= 20/3 - 122/3

= -102/3

For the second question,

The area of a healing skin wound changes at a rate given by dA/dt = -5t² + 1, and A(1) = 5 square centimeters.

To find the area of the wound in 4 days,

Integrate the rate of change of area with respect to time over the interval [1, 4],

A(4) = A(1) + ∫[1, 4] (-5t² + 1) dt

Integrating the expression,

A(4) = 5 + [-5(t³/3) + t] | [1, 4]

= 5 + [-5(4³/3) + 4 - (-5(1³/3) + 1)]

= 5 + [-320/3 + 4 - (-5/3 + 1)]

= 5 + [-320/3 + 12/3 + 5/3]

= 5 + [-320/3 + 17/3]

= 5 + [-320 + 17]/3

= 5 + [-303]/3

= 5 - 101

= -96

Therefore, the distance travelled and area of the wound is  equal to -102/3 units and -96 square centimeters respectively.

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The value of tensions are:

T₁ = 231/74

T₂ = -329/66

T₃ = 8/33

We can use Gaussian elimination to solve the system of equations:

5T₁ + 3T₂ + 5T₃ = 70

T₁ + 2T₂ + 4T₃ = 24

4T₁ + 2T₂ = 40

First, we'll use the third equation to eliminate T₂ from the first two equations:

4T₁ + 2T₂ = 40   (equation 3)

T₁ + 2T₂ + 4T₃ = 24   (equation 2)

Multiplying the third equation by 2 and subtracting it from the second equation:

T₁ + 2T₂ + 4T₃ = 24   (equation 2)

- 8T₁ - 4T₂ = -80   (2 × equation 3)

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

-7T₁ + 4T₃ = -56

Now we have two equations:

5T₁ + 3T₂ + 5T₃ = 70   (equation 1)

-7T₁ + 4T₃ = -56   (from previous step)

Multiplying the first equation by 7/5 and adding it to the second equation:

5T₁ + 3T₂ + 5T₃ = 70   (equation 1)

-7T₁ + 4T₃ = -56   (from previous step)

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

T₁ + 7T₃ = 14

Now we can use the third equation to eliminate T₂ from the first equation:

4T₁ + 2T₂ = 40   (equation 3)

5T₁ + 3T₂ + 5T₃ = 70   (equation 1)

Multiplying the third equation by 3/2 and subtracting it from the first equation:

4T₁ + 2T₂ = 40   (equation 3)

-11T₁ - T₃ = -35   (3 × equation 3 - 5 × equation 1)

Now we have two equations:

T₁ + 7T₃ = 14   (from previous step)

-11T₁ - T₃ = -35   (from this step)

Multiplying the second equation by -7 and adding it to the first equation:

T₁ + 7T₃ = 14   (from previous step)

74T₁ = 231

Therefore, T₁ = 231/74.

Substituting this value back into the equation T₁ + 7T₃ = 14, we get:

(231/74) + 7T₃ = 14

7T₃ = (74/231) × 20

T₃ = 8/33

Finally, substituting T₁ = 231/74 and T₃ = 8/33 into the equation -11T₁ - T₃ = -35, we get:

-11(231/74) - (8/33) = -329/66

Therefore, T₂ = -329/66.

So, the tensions are: T₁ = 231/74 T₂ = -329/66 T₃ = 8/33

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The probability that he'll use both the bus and the train is 0.2222

What is probability and example?

Probability = the number of ways of achieving success. the total number of possible outcomes. For example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½ .

There are just two ways in which Justin use both the bus and the train on the same day:

1. He used bus in the morning and train in the evening

2. He used train in the morning and bus in the evening

Additionally, every day he has 9 possible ways to used the transportation, 3 in the morning multiply by 3 in the evening. This is:

       3         *         3           =  9

p= 0.222

So, the probability is calculate as a division between the possible ways in which he use both transportations and the total possible ways. This is:

p=0.222

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The number of additional gifts Jeff can buy with the remaining cost is 1.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

As per the given,

Total cost = $15 + $20 = $35

Total spent = $50

Remaining = $50 - $35 = $15

Since one gift cost $10

Thus, 15/10 = 1.5 since the number of gifts will be the whole number so it will be round to bottom 1 gift.

Hence "With the money still available, Jeff can purchase 1 more present".

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The rate of change of the circle diameter with respect to the radius is a constant value of 2.

The diameter of a circle is twice the radius, so we can write:

Diameter = 2 * Radius

To find the rate of change of the diameter with respect to the radius, we can take the derivative of both sides of this equation with respect to the radius:

diameter/d(radius) = d(2 * radius)/d(radius)

The derivative of 2*radius with respect to radius is simply 2, so we can simplify the equation:

diameter/d(radius) = 2

Therefore, the rate of change of the circle diameter with respect to the radius is a constant value of 2. This means that if we increase the radius by a small amount, the diameter will increase by twice that amount. Conversely, if we decrease the radius by a small amount, the diameter will decrease by twice that amount.

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Answer:

1:18

Step-by-step explanation

18*2=36

18*3=54

so the propotion is 1 to 18, for every 1 hour 18 dollars are added

Answer:

3/4

Step-by-step explanation:

to add fractions you have to let them have the same denominator or bottom number

so to make 3 and 12 the same number you would multiply 3 by 4

when multiplying the bottom number of a fraction by 4 you multiply the top too

so 2/3 becomes 8/12

then you can add

1/12 + 8/12 is 9/12

at the end you can simplify 9/12 into 3/4 by dividing the equation by 3/3 or both the top and bottom by 3

Answer:

3/4 meters

Step-by-step explanation:

We can use ratios to solve

8m         2 m

------- = -----------

3m         x m

Using cross products

8*x = 3*2

Divide each side by 8

8x/8 = 6/8

3/4 meters

Answer:

x = 3/4 m

Step-by-step explanation:

Construct two similar right triangles that share an angle of elevation.  The two vertical sides represent the heights of the person and the tree and are 2 m ad 8 m respectively.  The two horizontal sides represent the shadow cast by the person and that cast by the tree, respectively.  Because the triangles are similar, we can write the following equation of ratios:

 8 m       3 m

--------- = --------

 2 m         x

... where x is the length of the shadow cast by the person.

Cross multiplying, we get:

8x = 6m, or x = 6/8 m, or x = 3/4 m

Answer:

y = 4x + 15

Step-by-step explanation:

Using 'y=mx+c' form,

Since m = 4,

y = 4x + c

Substituting (-5, -5) into the above equation:

-5 = -20 + c

c = 15

Hence,

y = 4x + 15

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When we divide the polynomial x³ - 3x² - 10x + 24 by x - 2, we get x² - x - 12.

Given,

The polynomial;

x cubed minus 3 x squared minus 10 x + 24  = x³ - 3x² - 10x + 24

We have to divide the given polynomial by x - 2.

Polynomial Division;-

Divide the first term of the dividend by the first term of the divisor to divide polynomials using long division. The quotient's initial term is this. Dividend is calculated by multiplying the new term by the divisor. The new dividend is this variation.

Here,

x³ - 3x² - 10x + 24 ÷ x - 2

           x² - x - 12

x - 2)  x³ - 3x² - 10x + 24

      -(x³ - 2x²)

             - x² - 10x

            - x² - 2x

                   - 12x + 24

                  - 12x + 24

                                 0

Therefore,

We get x² - x - 12 when we divide the polynomial x³ - 3x² - 10x + 24 by x - 2

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Answer:

406

Step-by-step explanation:

6+(4x100)

Answer:

24 centimeter square

Step-by-step explanation:

Volume = L x W x H

= 4 x 2 x 3

= 24 centimeter square

Answer: 8.21, 8.7, 8.84, 9.1

Step-by-step explanation:

The predicted weight of a lizardfish that is 12 cm long, based on the given model, is approximately 13.80 grams.

The predicted weight of a lizardfish that is 12 cm long, based on the given regression model lnW = -5.36 + 3.216lnL, is approximately 13.80 grams.

To calculate the predicted weight, we substitute the value of L = 12 cm into the regression equation. Taking the natural logarithm of both sides, we get:

lnW = -5.36 + 3.216ln(12)

Evaluating the right-hand side of the equation, we have:

lnW ≈ -5.36 + 3.216ln(12)

≈ -5.36 + 3.216(2.48491) [ln(12) ≈ 2.48491]

≈ -5.36 + 7.99604

≈ 2.63604

Taking the inverse of the natural logarithm (exponential function), we find:

W ≈ e^(2.63604)

≈ 13.80 grams

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