a punch recipe calls for 3 parts orange juice to 2 parts pineapple juice. complete the table to show the relationship between the amounts of orange juice and pineapple juice in the punch recipe.

Answer:y – 9. 4 less than a number. y - 4

Step-by-step explanation:

If the sum of a number and 9, divided by 4, is greater than or equal to -2, the number is -17.

A collection of two or more inequalities in one or more variables is known as a system of inequalities. When there are multiple constraints on a problem's potential solutions and a range of potential solutions are needed, systems of inequalities are used. The maximum or minimum values of a situation with multiple constraints are frequently determined using a system of linear inequalities.

It is given that,the sum of a number and 9, divided by 4, is greater than or equal to -2

Suppose the number is n,

(n+9)/4≥-2

n+9≥-8

n≥-8-9

n≥-17

Thus, if the sum of a number and 9, divided by 4, is greater than or equal to -2, the number is -17.

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Answer:  x=12.8

Step-by-step explanation:

Solution by Cross Multiplication

The equation:

5

8  =  

8

x

The cross product is:

5 * x  =  8 * 8

Solving for x:

x =

8 * 8

5

x = 12.8

Answer:

To solve the proportion 5/8 = 8/x, we can use cross-multiplication, which involves multiplying the numerator of one fraction by the denominator of the other fraction, and vice versa.

So, we have:

5/8 = 8/x

Cross-multiplying, we get:

5x = 8 * 8

Simplifying the right-hand side, we get:

5x = 64

Dividing both sides by 5, we get:

x = 64/5

So the solution to the proportion is:

x = 12.8

Therefore, 8 is proportional to 12.8 in the same way that 5 is proportional to 8.

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Answer:

-11 1/4

Step-by-step explanation:

It is observed that the equation satisfies, therefore, \(X(t) = e^{At} Ce^{Bt}\) is the solution to \(\frac{dX(t)}{dt} = AX(t) + X(t)B\).

Given:

A differential equation is given as:

\(\frac{dX(t)}{dt} = AX(t) + X(t)B\)

where \(X(t) = e^{At} Ce^{Bt}\).

Finding the derivative of \(X(t)\):

\(\frac{dX(t)}{dt} = \frac{d}{dt}(e^{At} Ce^{Bt})\)

\(\frac{dX(t)}{dt} = Ce^{Bt} \frac{d}{dt}(e^{At}) + e^{At} \frac{d}{dt}(Ce^{Bt})\)

\(\frac{dX(t)}{dt} = Ce^{Bt} A e^{At} + e^{At} B e^{Bt} C\)

\(\frac{dX(t)}{dt} = e^{At}(CA + B) e^{Bt} C\)

Substituting the value of \(\frac{dX(t)}{dt}\) in the given differential equation, we get:

\(e^{At}(CA + B) e^{Bt} C = Ae^{At} Ce^{Bt} + e^{At} Ce^{Bt} B\)

This can be simplified as:

\(Ae^{At} Ce^{Bt} + e^{At} Ce^{Bt} B = e^{At}(CA + B) e^{Bt} C\)

Therefore, \(X(t) = e^{At} Ce^{Bt}\)

The given differential equation has been verified with the solution.

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The conclusion that is correct in a two-tailed test at α = .05 is There appears to be no difference in the mean occupancy rates.

From the given values:

Thus, the P-value = 0.1791

Interpret results. Since the P-value (0.1791) is greater than the significance level (0.05), we failed to reject the null hypothesis.

From the above test, we do not have sufficient evidence in favor of the claim that there is a difference in the mean occupancy rates.

Thus, option A is correct.

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Complete Question

The model that describes the number of bacteria in a culture after t days has just been updated from \(P(t) = 7(2)^t\) to \(P(t) = 7(3)^t\) What implications can you draw from this information?

A The growth rate of the bacteria in the culture is 30% per day instead of

    20% per day.

B The final number of bacteria is 3 times as much of the initial value instead

   of 2 times as much.

C The initial number of bacteria is 3 instead of 2

D The number of bacteria triples every day instead of doubling every day

E   None of the above.

Answer:

The correct option is D

Step-by-step explanation:

From the question we are told that

    The first model is  \(P(t) = 7(2)^t\)

    The updated model is \(P(t) = 7(3)^t\)

Generally looking the two models that define the number of bacteria we see that  at the for the first model that the number is being doubled everyday for example if the time is  equal to 1 day  we have that  

     \(P(1) = 7(2)^1\)

      \(P(1) = 2 *  7\)  

Here we see that the constant 7  is being double but in the new model we can see that the number is being triple everyday , taking the same example with t =  1

     \(P(1) = 7(3)^1\)

=>    \(P(1) = 3 *  7 \)

Here we see that the constant 7  is being triple for each day

Hence the implication of the model change is that the number of bacteria will be tripled everyday instead of being doubled everyday

Answer:

x = 6

y = 13

Step-by-step explanation:

since DE and JK are congruent, they are both 18

to find 'y':

3y - 21 = 18

3y = 39

y = 13

DF and JL are diagonals that are congruent so:

9x - 23 = 7x - 11

2x = 12

x = 6

Answer:

5190

Step-by-step explanation:

2.7% of 6000 is 162.

There is a 5 year span between 2009 and 2014.

So just subtract 162 from 6000 5 times, or multiply 162 by 5, then subtract that from 6000.

Hope It Helps!

Answer:

15

Step-by-step explanation:

Rate of change or slope or gradient of a line passes two points (x1, y1) and (x2, y2) could be calculated by:

(y2 - y1)/(x2 - x1)

=> Rate of change of the line passing (1,15) and (3,45):

(45 - 15)/(3 - 1) = 30/2 = 15

Answer:

That's cool.

Step-by-step explanation:

The depreciation equation is given by

where x represents the number of years. Here, the initial value of the car corresponds to x=0, then we have

After one year, the car value corresponds to x=1, that is,

Now, let's find the depreciation percentage by means of a rule of three:

so we have

So the difference between 100% and 86% is 14% This means Nichole's car depreciate 14% each year

Answer:

8

Step-by-step explanation:

8x - 4 = 60

8x = 60 + 4

x = 64/8

x = 8

The statement that shows a discrepancy between the check register and bank statement is: C. Gavin: The balance in his check register is $500 and the balance in his bank statement is $510.

The check register shows a balance of $500, while the bank statement shows a balance of $510.

In the case of Gavin, where the balance in his check register is $500 and the balance in his bank statement is $510, there is a $10 discrepancy between the two.

A possible explanation for this discrepancy could be outstanding checks or deposits that have not yet cleared or been recorded in either the check register or the bank statement.

For example, Gavin might have written a check for $20 that has not been cashed or processed by the bank yet. Therefore, the check register still reflects the $20 in his balance, while the bank statement does not show the deduction. Similarly, Gavin may have made a deposit of $10 that has not yet been credited to his account in the bank statement.

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(a). The values of x for which f(x) = 8, are x = (-1 + √17) / 2 and x = (-1 - √17) / 2.

(b). The equation has no real roots, and f(x) never equals 5.

(c). The equation has no real roots, and f(x) never equals -5.

(d). The graph will confirm that there are two x-intercepts corresponding to the two solutions found.

What is algebraic value?

A general rule is that the algebraic expression should take any of the following forms: addition, subtraction, multiplication, and division. Bring the variable to the left side and the other values to the right side in order to find the value of x.

a.

To find the values of x for which f(x) = 8,

we need to solve the equation x² +10x +32 / x+5 = 8.

We can start by multiplying both sides of the equation by (x+5) to get rid of the fraction:

x² + 10x + 32 = 8(x + 5)

Expanding the right side:

x²  + 10x + 32 = 8x + 40

Subtracting 8x from both sides:

x²  + 2x + 32 = 40

Subtracting 32 from both sides:

x² + 2x = 8

Dividing both sides by 2:

x² + x = 4

Subtracting 4 from both sides:

x² + x - 4 = 0

We can use the quadratic formula to solve this equation:

x = (-b ± √(b² - 4ac)) / 2a

where a = 1, b = 1, and c = -4.

So,

x = (-1 ± √(1² - 4 * 1 * -4)) / 2 * 1

x = (-1 ± √(1 + 16)) / 2

x = (-1 ± √17) / 2

Thus, the two solutions are x = (-1 + √17) / 2 and x = (-1 - √17) / 2. These are the values of x for which f(x) = 8.

b. To show that f(x) never equals 5, we need to show that there is no solution to the equation (x² + 10x + 32)/(x + 5) = 5.

Suppose there is such a solution, say x = a.

Then,

5(x + 5) = x² + 10x + 32

5x + 25 = x² + 10x + 32

-x² + 5x - 7 = 0

This is a quadratic equation and can be solved using the quadratic formula. However, we can see that the equation has no real solutions because the discriminant, b² - 4ac, is negative. Therefore, the equation has no real roots, and f(x) never equals 5.

c. To determine whether f(x) ever equals -5, we can follow a similar approach as in part b.

Suppose there is a solution to the equation (x² + 10x + 32)/(x + 5) = -5. Then,

-5(x + 5) = x² + 10x + 32

-5x - 25 = x² + 10x + 32

x² - 15x + -57 = 0

This is a quadratic equation and can be solved using the quadratic formula. However, we can see that the equation has no real solutions because the discriminant, b² - 4ac, is negative. Therefore, the equation has no real roots, and f(x) never equals -5.

d. To confirm the results of parts a, b, and c, we can plot the graph of the function f(x) = (x² + 10x + 32)/(x + 5) and sketch the result.

The graph of the function will show the x-intercepts and the y-intercepts and will also show any asymptotes.

The graph will confirm that there are two x-intercepts corresponding to the two solutions found.

Hence, (a). The values of x for which f(x) = 8, are x = (-1 + √17) / 2 and x = (-1 - √17) / 2.

(b). The equation has no real roots, and f(x) never equals 5.

(c). The equation has no real roots, and f(x) never equals -5.

(d). The graph will confirm that there are two x-intercepts corresponding to the two solutions found.

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Answer:

The actual speed = 27.12 mi/h

Direction = 36.5° in NE(north of east)

Step-by-step explanation:

As given , A hot air balloon is flying at a constant speed of 20 mi/h at a bearing of N 36° E.

⇒θ = 36°

Let v₀ be the constant speed, then v₀ = 20

Let vₓ be the speed in East direction

     \(v_{y}\) be the speed in North direction

So,

vₓ  = v₀ sin(θ) = 20 sin(36°) + 10 ( As given, There is a 10mi/h cross wind blowing due east.)

⇒vₓ  = 20(0.588) + 10 = 11.76 + 10 = 21.76 mi/h

and   \(v_{y}\)  = v₀ cos(θ) = 20 cos(36°) = 20(0.809) = 16.18 mi/h

Now,

the actual speed = √(vₓ)² + (\(v_{y}\))²

                            = √(21.76)² + (16.18)²

                            = √473.498 + 261.792

                            = √735.29 =  27.12

⇒The actual speed = 27.12 mi/h

Now,

Direction = θ = \(tan^{-1}(\frac{v_{y} }{v_{x} } ) = tan^{-1}(\frac{16.18 }{21.76 } ) = tan^{-1}(0.74) = 36.5\)

⇒ Direction = 36.5° in NE(north of east)

Answer:

27.1 mi / h; N 53° E

Step-by-step explanation

We have a polynomial m(x). We do not know by now its equation, but we can look for that information asked in the graph.

a) End behaviour:

This is referring to the values of the function when x tends to minus infinity and also infinity.

When x becomes really small, the graph indicates that m(x) increases infinitely.

The same happens when x becomes really big.

Both conditions are indicated with arrows at the end of the line.

So the end behaviour is:

- m(x) increases when x tends to minus infinity.

- m(x) increases when x tends to infinity.

b) y-intercept:

Is the value of the function where the function intersects the y-axis. It can also be expressed as m(0), as this is the value of x where the y-axis is located.

This happens at (0,0), so the the y-intercept is y=m(0)=0.

c) x-intercepts:

When m(x) intersects the x-axis, we have the zeros or roots, also called x-intercepts.

In this function we have 4 x-intercepts at points (-4,0), (-3,0), (0,0) and (2,0).

The x-intercepts then are located at x=-4, x=-3, x=0 and x=2.

d) Domain:

This is the set of values of x for which the function m(x) is defined.

There is no discontinuity present in the graph, so we can assume that the domain of m(x) is all the real numbers.

Domain = (-∞, ∞).

e) Range:

This is the set of values that m(x) can take for the values of x for which it is defined. In this case, we are sure we have a minimum value of m(x) at x=1, where m(1) = -21.

There is no defined maximum and the arrows indicate that the function continously increases for both ends, so the maximum limit for the range is written as infinity.

Then, we can define the range as [-21,∞).

Answer:

it is number 4 why because

Answer:

Step-by-step explanation:

√169 = 13

square root and two digits after dot means the result need to has one digit after dot (number of digits after dot divided by 2 because of square root)

so √1.69 = 1.3

Answer:

The graph increases.

Step-by-step explanation:

hope this helps!!

Answer: the graph increases

Step-by-step explanation: did test

Answer:

11

Step-by-step explanation:

all you gotta do is subtract q3 from q1, in this case it's 15-4=11

Answer:

e. linear pair postulate

Step-by-step explanation:

Answer:

Question 1

Given

Use formula and solve for x:

Cost price is N 120

Question 2

Given

Use formula and solve for x:

Cost is N 12500

Therefore , Angela needs to fill this cup 6/7 times.

A fraction represents a component of a whole or, more generally, any number of equal parts. As in one-half, eight-fifths, and three-quarters, a fraction in conversational English denotes the number of components of a specific size.

Here,

To her dough, Angela needs to add 12 cups of milk. She only has a measuring cup that holds 14 cups.

Thus, the number of times angela needs to fill  cup are = 12/14 times

thus ,

=> 12/14 =6/7

Therefore , Angela needs to fill this cup 6/7 times.

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Let f(x) = (ln(x))^se^x. We have to use the chain rule to find the derivative of the given function, f(x).

Chain rule states that, if f(x) = g(h(x)), then f'(x) = g'(h(x)).h'(x).

Given f(x) = (ln(x))^se^x...[1]

Now differentiate, se^x*ln(x)^(s-1) / x + e^x*ln(x)^s...[2]

Therefore, f'(x) = se^x*ln(x)^(s-1) / x + e^x*ln(x)^s...[3]

Hence, the answer is f'(x) = se^x*ln(x)^(s-1) / x + e^x*ln(x)^s.2.

Let f(x) = x^5x. Use logarithmic differentiation to determine the derivative.

Given function, f(x) = x^5xTaking logarithm on both sides,

we get log(f(x)) = 5x*log(x)

Differentiating both sides with respect to x using chain rule, we get

f'(x)/f(x) = 5log(x) + 5x*(1/x)Thus, f'(x) = f(x)[5log(x) + 5] = x^5x[5log(x) + 5]

Let f(x) = 7x tar(x).

We have to use the product rule to find the derivative of the given function, f(x).

Product rule states that, if f(x) = u(x)v(x), then f'(x) = u'(x)v(x) + u(x)v'(x).Given, f(x) = 7x tar(x)...[1]

Now, u(x) = 7x and v(x) = tar(x)

Differentiating both u(x) and v(x), we get u'(x) = 7 and v'(x) = sec^2(x)

Therefore, f'(x) = 7(tar(x)) + 7x sec^2(x)...[2]

Hence, the conclusion is f'(x) = 7(tar(x)) + 7x sec^2(x).

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Step-by-step explanation:

=10+10÷2(40)

=10+5(40)

=10+200

=210

Answer:

Hope the picture will help you.......

Answer:

Step-by-step explanation:

Given

Total no. of observation = 50

Given, No. of observations that told yes = 42

Therefore,

Probability of getting response as yes

\( = \frac{42}{50} \)

\( = \frac{21}{25} \)

In decimal form ,

= 0.84 (Ans)

Answer:

hi ! here is the answer!

Step-by-step explanation:

o get the slope of that line, easy, pick two points IN the line and get their slope let's say hmmm 10 popsicles when the temperature is 40F, so 40,10 and say 20 popsicles when it's 90F, thus 90,20  then x1(40,y110)x2(90,y220)slope=m=riserun⟹y2−y1x2−x1

4 years ago

Answer:

the y-intercept is (0,13)

Step-by-step explanation:

The y intercept is (0,b) in the slope-intercept form of y=mx+b

The y-intercept of the line represented by the equation y = 6x + 13 is the point where the line crosses the y-axis. This happens when x=0, so substituting in this value gives us y=13. Therefore, the coordinates of the y-intercept are (0, 13).

In this case, the equation of the line is given as y = 6x + 13. A y-intercept is the point where the line crosses the y-axis. This takes place when x is equal to 0 because at that point, we are solely on the y-axis. Therefore, if we substitute x = 0 into the equation, we obtain y = 6*(0) + 13, which simplifies to y = 0 + 13, so y = 13. Therefore, the coordinates of the y-intercept are (0, 13).

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