Subject:Mathematics ​

Answer:

h = \(-\frac{17}{6}\)

Step-by-step explanation:

7 + 2(1 + 6h) = -25

Distribute,

7 + 2 + 12h = -25

Simplify,

7 + 2 + 12h = -25

9 + 12h = -25

-9            -9

12h = -34

/12      /12

h = \(-\frac{17}{6}\)

Answer:

x = 6

y = - 4

Step-by-step explanation:

3x + 4y = 2

2x + 2y = 4

Time the second equation by -2

3x + 4y = 2

-4x - 4y = - 8

-x = -6

x = 6

Now we put 6 in for x and solve for y

3(6) + 4y = 2

18 + 4y = 2

4y = -16

y = - 4

Let's Check

3(6) + 4(-4) = 2

18 - 16 = 2

2 = 2

So, x = 6 and y = -4 is the correct answer.

Answer: four million two hundred fifty thousand.

Step-by-step explanation:

a. the growth of the amount of money in the account over time, with the rate of growth proportional to the current amount of money in the account. b. the continuous growth of the amount of money in the account over time, with the initial amount of $1800 as the starting point.

(a) The differential equation satisfied by M, the amount of money in the account at time t, measured in years since 2010 is:

dM/dt = rM

This is a first-order, linear, homogeneous differential equation with constant coefficients. It describes the growth of the amount of money in the account over time, with the rate of growth proportional to the current amount of money in the account.

(b) To solve the initial value problem if $1800 is put into an account in 2010, we need to find the function M(t) that satisfies the differential equation dM/dt = rM with the initial condition M(0) = 1800.

The solution to this differential equation is M(t) = 1800 * e^(rt), where e is the base of the natural logarithm. This exponential function describes the continuous growth of the amount of money in the account over time, with the initial amount of $1800 as the starting point.

Note that the interest rate r will determine the rate of growth of the account. If r is positive, the account will grow over time, while if r is negative, the account will shrink over time.

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The critical heat flux (CHF) is the maximum heat flux that can be transferred from a surface to a boiling liquid before the boiling process transitions from a stable regime to an unstable regime. The CHF is an important parameter in the design of heat transfer systems, as exceeding the CHF can lead to boiling crisis, which can cause severe damage to the system.

The CHF for a fluid depends on various factors such as fluid properties, surface properties, and flow conditions. One of the commonly used correlations for calculating CHF is the Kutateladze number (Ku) correlation, which is given by:

q_c = C (ρ_L^2 g Δh_f)^0.5 (σ/ρ_L)^0.1

where q_c is the critical heat flux, ρ_L is the liquid density, g is the acceleration due to gravity, Δh_f is the latent heat of vaporization, σ is the surface tension, and C is a constant that depends on the surface properties and flow conditions.

Using this correlation, we can calculate the CHF for the given fluids at 1 atm:

For mercury at 1 atm:

Density of mercury, ρ_L = 13,534 kg/m^3

Latent heat of vaporization of mercury, Δh_f = 2.66 x 10^5 J/kg

Surface tension of mercury, σ = 0.48 N/m

Acceleration due to gravity, g = 9.81 m/s^2

Using the Kutateladze number correlation with a constant value of C = 0.028, we get:

q_c = 0.028 * (13,534^2 * 9.81 * 2.66 x 10^5)^0.5 * (0.48/13,534)^0.1

q_c = 2.44 x 10^6 W/m^2

For ethanol at 1 atm:

Density of ethanol, ρ_L = 789 kg/m^3

Latent heat of vaporization of ethanol, Δh_f = 8.51 x 10^5 J/kg

Surface tension of ethanol, σ = 0.022 N/m

Acceleration due to gravity, g = 9.81 m/s^2

Using the Kutateladze number correlation with a constant value of C = 0.027, we get:

q_c = 0.027 * (789^2 * 9.81 * 8.51 x 10^5)^0.5 * (0.022/789)^0.1

q_c = 1.17 x 10^6 W/m^2

For refrigerant R-134a at 1 atm:

Density of R-134a, ρ_L = 1245 kg/m^3

Latent heat of vaporization of R-134a, Δh_f = 2.03 x 10^5 J/kg

Surface tension of R-134a, σ = 0.011 N/m

Acceleration due to gravity, g = 9.81 m/s^2

Using the Kutateladze number correlation with a constant value of C = 0.026, we get:

q_c = 0.026 * (1245^2 * 9.81 * 2.03 x 10^5)^0.5 * (0.011/1245)^0.1

q_c = 1.35 x 10^6 W/m^2

For water at 1 atm:

Density of water, ρ_L = 1000 kg/m^3

Latent heat of vaporization of water, Δh_f = 2

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Answer:

Step-by-step explanation:

GH bisects ∠FGI.

So,  ∠HGI =∠FGH

6x - 17 = 5x - 8      {Add 17 to both sides}

        6x = 5x - 8 + 17

        6x = 5x + 9     {Subtract 5x form both sides}

  6x - 5x = 9

a) x = 9

b) ∠FGH  = 5* 9 - 8

               = 45 - 8

  ∠FGH  = 37

c) ∠HGI = 6*9 - 17

            = 54 - 17

   ∠HGI = 37

d) ∠FGI = ∠FGH + ∠HGI

            = 37 + 37

  ∠FGI = 74  

We assume that with a linear relationship between two variables, for any fixed value of x, the observed residuals follows a normal distribution.

This assumption is based on the Central Limit Theorem, which states that when the sample size is large enough, the distribution of sample means will be approximately normal, regardless of the shape of the underlying population distribution.

In the case of a linear relationship between two variables, we can assume that the residuals (the difference between the observed y values and the predicted values based on the linear regression model) follow a normal distribution with mean 0 and constant variance. This assumption is important because it allows us to use statistical methods that rely on normality, such as hypothesis testing and confidence intervals.

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Using BODMAS, the solutions of the expressions are: (1) 9, (2)-12, (3) 0.27, and (4) 0.24

We should know that BODMAS is a mathematical approach which means

In each of the expressions, we must follow the approach

1)    \(\frac{(6+3)^{2} }{3*9}\)

Simplifying this we have 9²/9=81/9

=9

2)  \(\frac{3^{2} -6*2}{(12-8)/2^{2} *10}\)

Using BODMAS we have

(9-12)/4/40

-3÷1/9

⇒-3*4

=-12

(3)   \(\frac{4.5+2*2.5^{2}-6 }{8*4+9}\)

Using BODMAS we have

(4.5+2*6.25-6)/32+9

⇒(4.5+12.5-6)/41

=11/41=0.27

4     (\(\frac{3.5+16-2.5^{2} }{10.5-6*11}\))

Using BODMAS we have  

(3.5+16-6.25)/10.5-66

Simplifying

(13.25)/-55.5

=0.24

Therefore, the values when simplified are  (1) 9, (2)-12, (3) 0.27, and (4) 0.24

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The diameter of the ball is approximately 16.67 meters.

To find the diameter of the ball, we can use the relationship between the distance traveled and the number of revolutions.

The circumference of a circle is given by the formula C = πd, where C is the circumference and d is the diameter.

Given that the ball rolls a distance of 3.5 meters and makes 15.0 revolutions, we can calculate the circumference of the path it travels:

C = 3.5 m * 15.0 = 52.5 m

Since each revolution covers the circumference of the ball, we have C = πd. Plugging in the known value for C, we can solve for the diameter (d):

52.5 m = πd

Dividing both sides of the equation by π, we get:

d = 52.5 m / π

Using a calculator, we can evaluate this expression:

d ≈ 16.67 meters

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In statistical hypothesis testing, we compare the p-value of a test to the level of significance (α) to determine whether to reject or fail to reject the null hypothesis.

a) α=0.10, P-value=0.05: Since the p-value is greater than the level of significance, we fail to reject the null hypothesis.

b) α=0.061, P-value=0.027: Similar to situation a), the p-value is greater than the level of significance, so we fail to reject the null hypothesis.

c) α=0.01, P-value=0.034: Here, the p-value is less than the level of significance, so we reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis.

d) α=0.01, P-value=0.023: In this case, the p-value is less than the level of significance, so we reject the null hypothesis and conclude that there is significant evidence to support the alternative hypothesis.

Therefore, we reject the null hypothesis in situations c and d as the p-values are less than the level of significance. While in situations a and b, we fail to reject the null hypothesis as the p-values are greater than the level of significance.

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Answer:

y = 4x + 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the gradient and c the y- intercept )

here m = 4 , then

y = 4x + c ← is the partial equation

to find c substitute (2, 9 ) into the partial equation

9 = 8 + c ⇒ c = 9 - 8 = 1

y = 4x + 1 ← equation of line

Free samples or product trials as a type of sales promotion can be both beneficial and detrimental. They encourage consumers to try a product at reduced risk, but they can also reduce the perception of value for the product or service.

Offering free samples or product trials is a common sales promotion strategy to attract customers and encourage them to try a product or service. This approach has several benefits. Firstly, it lowers the perceived risk for consumers as they can experience the product without making a financial commitment upfront. This can be especially effective for new or unfamiliar products, as it allows potential customers to test the product's quality and functionality.

However, there can be drawbacks to this sales promotion technique. Providing free samples or trials can create the perception that the product or service has less value or is of lower quality. Consumers may develop a mindset of expecting free or discounted offerings, and it can undermine the willingness to pay the full price in the future. Additionally, if the free samples or trials are not managed effectively, it may attract individuals who are not genuinely interested in the product, leading to wastage of resources and potentially diluting the brand image.

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Answer:

The big container holds 60 gallons

The small container holds 40 gallons

Step-by-step explanation:

If the small container held 40 gallons of gasoline then double that would be 80 gallons and 20 gallons less than that would be 60 gallons.

The probability of that an incoming call to the service centre is 0.0219. And the probability that an incoming call is a request for purchasing more products is 0.135.

Probability of an event gives the possibility of an event which is never greater than 1 and the probability of impossible event is 0 and the probability of sure event is 1.

Probability = number of favourable cases/ total number of outcomes

a) The probability that an incoming call to the customer service = Probability of incoming calls to the service centre * probability of remaining number of calls in the centre = 0.73* 0.03 = 0.0219.

b) the probability that an incoming call is a request for purchasing more products = Probability of request of calls  in the service centre * probability of request of purchase. = 0.5 * 0.27 = 0.135.

Hence, the probability that incoming call to the service is 0.0219 and of the request of purchase is 0.135.

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Answer:

D

Step-by-step explanation:

To find the scale factor for a dilation, we find the center point of dilation and measure the distance from this center point to a point on the preimage and also the distance from the center point to a point on the image. The ratio of these distances gives us the scale factor,

J-(2,2)

A-(4,4)

--

G-(-2,-2)

C-(-4,-4)

--

H-(4,4)

B-(8,8)

No, The 3 house do not form of a right triangle because,

⇒ 1.2² + 1.9² < 2.4²

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We know that;

Right triangle is satisfy the Pythagoras theorem.

If the sides of triangle are a, b and c.

Hence, We get;

⇒ a² + b² = c²

Here, The three distance are 1.2, 1.9 and 2.4.

Hence, We get;

⇒ 1.2² + 1.9²

⇒ 5.05

⇒ 2.4²

⇒ 5.76

Thus, We get;

⇒ 1.2² + 1.9² < 2.4²

Hence, The 3 house do not form of a right triangle because,

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Jared bought 7 cans of paint. Let the number of red paint cans that Jared bought be x. The number of black paint cans he bought would be 7 - x. A can of red paint costs $3.75 and a can of black paint costs $2.75.

He spent $22 in all. Therefore we can write:3.75x + 2.75(7 - x) = 22 Multiplying out the second term and collecting like terms gives:0.5x + 19.25 = 22Subtracting 19.25 from both sides:0.5x = 2.75Dividing by 0.5:x = 5.5Since Jared can't buy half a can of paint, we should round the answer to the nearest integer. Hence, he bought 5 cans of red paint and 2 cans of black paint. The total cost of the 5 cans of red paint would be 5 x $3.75 = $18.75.The total cost of the 2 cans of black paint would be 2 x $2.75 = $5.50.The total cost of all 7 cans of paint would be $18.75 + $5.50 = $24.25.We spent more than Jared's budget. The value of $24.25 exceeds Jared's budget of $22. Hence, there is a problem with this problem statement.

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Answer:

if it says greatest change then its 6:30 to 7:00

Step-by-step explanation:

Answer:

6:30-7:00

Step-by-step explanation:

Answer:

Step-by-step explanation:

8)

88x + 8y = 40

8y = -88x +40

y = -11x +5

9)

m= -11

10)

+5

Answer: 18 oatmeal cookies.

Step-by-step explanation:

Simplify divide 24 by 3/4 to find how many oatmeal cookies Lucas made.

24 x 3 = 72/4 = 18

The solution is 6 - 2(10) degrees Celsius was the temperature after 5 hours.

Here, we have,

initially it was 6°,

30 minutes later it went down to 6 - 2,

30 minutes later it went down to 6 - 2 - 2

let's check the change per intervals of 30 minutes

so after 1 interval of 30 minutes, it went down to 6 - 2

after 2 intervals of 30 minutes, it went down to 6 - 2 - 2, or just 6 -2(2)

after 3 interval of 30 minutes, it went down to 6 - 2 - 2 - 2, or just 6 -2(3)

after "x" intervals of 30 minutes, it went down to 6 - 2(x).

now, how many 30 minutes intervals are there in 5hours?  well, 10.

so after 5 hours, x = 10, thus it went down 6 - 2(10) degrees Celsius.

Hence, The solution is 6 - 2(10) degrees Celsius was the temperature after 5 hours.

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Answer:

Step-by-step explanation:

for 3x +y = -5

it's \(x = \frac{-5 -y}{3}\)

and for 2x + 3y = -8 it's

\(x = \frac{-8 - 3y}{2}\)

1 x 20

2 x 10

4 x 5    (these go the other way round as well, like 10 x 2, etc)

all factors of 20 = 1,2,4,5,10,20

hope this helps!

Answer:

5√2 or 7.07 units

Step-by-step explanation:

To find the distance between two points, we want to use the distance formula: d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Plug in the given values of (4​,1) and ​(9​,6​)

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

d = √[(9 - 4)² + (6 - 1)²]

Simplify the parentheses.

d = √[(5)² + (5)²]

Simplify the exponents.

d = √[25 + 25]

Add.

d = √[50]

Evaluate the radical.

5√2 or 7.07

Round the decimal.

5√2 or 7.07 units

Hope this helps!

Answer:

3/8

Step-by-step explanation:

If 1/4 is equaled to 1. This is 1 dived by 4 to get the 1/4.

Then 1.5 would be divided by 4 to get 3/8

The relation that is not a function from B to U is option b.

To determine which relation is not a function from B to U, we need to check if each element in B is associated with exactly one element in U. If there is any element in B that is associated with more than one element in U, then it is not a function.

Let's analyze each of the options:

a. {(b, b), (e, c), (d, b), (c, a)} This relation is a function because each element in B is associated with exactly one element in U.

b. {(d, a), (c, e), (e, e), (c, a)} This relation is not a function because the element 'c' in B is associated with both 'e' and 'a' in U. The element 'c' should be associated with exactly one element in U for it to be a function.

c. {(e, a), (b, a), (d, a), (c, b)} This relation is a function because each element in B is associated with exactly one element in U.

d. {(e, e), (b, c), (d, a), (c, b)} This relation is a function because each element in B is associated with exactly one element in U.

Among the given options, option b is the relation that is not a function from B to U.

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The coordinate of the midpoint of the line segment with endpoints -2 and 12 is 5.

To find the coordinate of the midpoint of a line segment,

we can use the formula:

Midpoint = (Endpoint1 + Endpoint2) / 2

In this case, the endpoints of the line segment are -2 and 12. Let's substitute these values into the formula to find the midpoint:

Midpoint = (-2 + 12) / 2

             = 10 / 2

               = 5

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The coordinate of the midpoint of the line segment p b, with endpoints at -2 and 12 on the number line, is 5.

To find the coordinate of the midpoint, we need to calculate the average of the coordinates of the endpoints. The midpoint is the point that divides the line segment into two equal parts. In this case, the coordinates of the endpoints are -2 and 12. To find the midpoint, we add the coordinates of the endpoints and divide the sum by 2.

Sum of the coordinates: -2 + 12 = 10

Dividing the sum by 2: 10 ÷ 2 = 5

Therefore, the coordinate of the midpoint of the line segment p b is 5.

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