Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.
y =
630(0.94)

Answer:

\(Total\ Rent = 49 + 5m\)

Step-by-step explanation:

Given

Rent per day = $49

Addition = 5 cents per mile

Required

Determine the rent for a day and m miles

First, we need to generate a formula from the given parameters;

Let d represent number of days and m represent additional miles;

\(Total\ Rent = 49 * d + 5 * m\)

\(Total\ Rent = 49 d + 5 m\)

Solving for the rent for a day and m miles

We have that: d = 1 and m = m

Substitute these in the formula above

\(Total\ Rent = 49 * 1 + 5 * m\)

\(Total\ Rent = 49 + 5m\)

Hence, the total rent is

\(Total\ Rent = 49 + 5m\)

take x as the side of the cube.

surface area = 6a^2

= 6x^2

take 2x as the next cube

surface area = 6(2x)^2

= 6 x 4 x x^2

= 24x^2

cube two is 4 times more than cube 1 in surface area wise.

HOPW THIS HELPS AND PLEASE MARK ME AS BRAINLIEST.

Answer:

y = 245/2

Step-by-step explanation:

y = k x^2

Where k is the constant of variation

Let y= 40 and x=4

40 = k *(4)^2

40 = k*16

40/16 = k

5/2 = k

y =5/2 x^2

Let x=7

y = 5/2 (7)^2

y = 5/2(49)

y = 245/2

Answer:

7

Step-by-step explanation:

derivate of 7x = 1(7)x⁰, or 7

derivate of 4 is 0

derivative of 7x + 4 = 7

Answer:

The last one 8512

Step-by-step explanation:

5×10÷5+2168

Answer:

  JL = 78

Step-by-step explanation:

The shorter segment is a midline, so is half the length of the longer one.

  2(5x-16) = 4x +34

  5x -16 = 2x +17 . . . . . divide by 2

  3x = 33 . . . . . . . . . . add 16-2x

  x = 11 . . . . . . . . . . divide by 3

Then segment JL is ...

  JL = 4x +34 = 4(11) +34 = 44+34

  JL = 78

If this experiment was performed many times you would expect that the average number of heads is 5.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

From the graph,

The theoretical probability of getting 5 heads in ten flips of a fair coin.

= 0.25

= 25%

And,

The theoretical probability of getting 0 and 10, 1 and 9, 2 and 8, 3 and 7, and 4 and 6 heads is equal.

The average number of heads.

= (0 + 10)/2 = 5

Similarly,

(1 + 9)/2 = 10/2 = 5

(2 + 8)/2 = 10/2 = 5

(3 + 7)/2 = 10/2 = 5

(4 + 6)/2 = 10/2 = 5

So,

If this experiment was performed many times you would expect that the average of heads is 5.

Thus,

The expected average number of heads is 5.

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Answer:

5

Step-by-step explanation:

The answer above is correct.

Answer:

$3.50

Step-by-step explanation:

Answer:

Step-by-step explanation:

We can find the distance between line l and point P by finding the distance between point P and the closest point on line l.The slope of line l is 0, since both points have the same y-coordinate. Therefore, line l is a horizontal line. The y-coordinate of any point on line l is 1.To find the closest point on line l to point P, we need to find the point on line l that has a y-coordinate of 7. Since line l is horizontal, any point on line l with a y-coordinate of 7 will work. Let's choose the point (5, 7), which is on the same horizontal line as line l.Now we can find the distance between point P and the point (5, 7):sqrt((5-(-2))^2 + (7-1)^2) = sqrt(49 + 36) = sqrt(85)Therefore, the distance between line l and point P is sqrt(85).

The Taylor polynomial 2()t2(x) centered at x=a for ()=4sin(), =2 is given by:

2()t2(x) = 4sin(a) + 8cos(a)(x-a) - 8sin(a)(x-a)^2

The Taylor polynomial 3()t3(x) centered at x=a for ()=4sin(), =2 is given by:

3()t3(x) = 4sin(a) + 8cos(a)(x-a) - 8sin(a)(x-a)^2 - 32/3cos(a)(x-a)^3

in these equations, sin(a) and cos(a) are the values of sine and cosine at the point a=2.

The Taylor polynomials are approximations of the function ()=4sin() near the point a=2. The polynomial 2()t2(x) is a second-degree polynomial that approximates the function to within an error of O((x-a)^3), while 3()t3(x) is a third-degree polynomial that approximates the function to within an error of O((x-a)^4).

The coefficients of these polynomials are derived from the derivatives of the function at the point a, evaluated using the formula for Taylor coefficients. These polynomials can be used to estimate the value of the function at points near a=2.

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The probability that the number of correct answers is fewer than 4 on the medical admissions test, with random guessing, is approximately 0.916 (rounded to three decimal places).


To find the probability that the number of correct answers is fewer than 4, we need to calculate the cumulative probability for x = 0, 1, 2, and 3.
The probability mass function (PMF) for a binomial distribution is given by the formula:
P(x) = C(n, x) * p^x * (1 – p)^(n – x)
Where:
P(x) is the probability of getting x successes
C(n, x) is the number of combinations of n items taken x at a time (n choose x)
P is the probability of success (correct answer)
N is the number of trials (questions)
We can calculate the probability for each value of x and then sum them up to get the cumulative probability.
P(x < 4) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3)
Let’s calculate this step by step:
P(x = 0) = C(8, 0) * (0.25)^0 * (1 – 0.25)^(8 – 0) = 1 * 1 * 0.75^8 = 0.1001
P(x = 1) = C(8, 1) * (0.25)^1 * (1 – 0.25)^(8 – 1) = 8 * 0.25 * 0.75^7 = 0.2670
P(x = 2) = C(8, 2) * (0.25)^2 * (1 – 0.25)^(8 – 2) = 28 * 0.25^2 * 0.75^6 = 0.3116
P(x = 3) = C(8, 3) * (0.25)^3 * (1 – 0.25)^(8 – 3) = 56 * 0.25^3 * 0.75^5 = 0.2370
Now, we can sum these probabilities:
P(x < 4) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3)
= 0.1001 + 0.2670 + 0.3116 + 0.2370
= 0.9157
Therefore, the probability that the number of correct answers is fewer than 4 is approximately 0.916 (rounded to three decimal places).

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In this problem, we are given a variable resistor R and an 8-Ω resistor in parallel. We are asked to find the rate at which the resistance R is changing when it is equal to 6.0 Ω.

Given that RT = 8R / (8 + R), we can differentiate this equation with respect to time t using the quotient rule. Let's denote dR/dt as the rate of change of R with respect to time. Applying the quotient rule, we have:

dRT/dt = \([ (8)(dR/dt)(8 + R) - (8R)(dR/dt) ] / (8 + R)^2\)

To find the rate at which R is changing when R = 6.0 Ω, we substitute R = 6.0 into the above equation:

dRT/dt = \([ (8)(dR/dt)(8 + 6.0) - (8)(6.0)(dR/dt) ] / (8 + 6.0)^2\)

Simplifying further, we have:

dRT/dt = \([ (8)(dR/dt)(14) - (48)(dR/dt) ] / (14)^2\)

dRT/dt = (112(dR/dt) - 48(dR/dt)) / 196

dRT/dt = 64(dR/dt) / 196

dRT/dt = 16(dR/dt) / 49

Therefore, the rate at which R is changing when R = 6.0 Ω is equal to 16/49 times the rate of change of RT.

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The probability that fewer than 3 out of 12 randomly selected adult smartphone users use their smartphones in meetings or classes is approximately 0.0539.

To find the probability that fewer than 3 out of 12 randomly selected adult smartphone users use their smartphones in meetings or classes, we can use the binomial probability formula.

The binomial probability formula is given by:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

where:

- P(X = k) is the probability of exactly k successes,

- n is the number of trials,

- k is the number of successes,

- p is the probability of success in a single trial, and

- C(n, k) is the combination of n choose k.

In this case, n = 12, k can be 0, 1, or 2, and p = 0.59 (the probability of using smartphones in meetings or classes).

Now we can calculate the probabilities for each value of k and sum them up:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

P(X = 0) = C(12, 0) * 0.59^0 * (1 - 0.59)^(12 - 0)

P(X = 1) = C(12, 1) * 0.59^1 * (1 - 0.59)^(12 - 1)

P(X = 2) = C(12, 2) * 0.59^2 * (1 - 0.59)^(12 - 2)

Calculating these probabilities and summing them up will give us the desired probability that fewer than 3 out of 12 users use their smartphones in meetings or classes.

Let's calculate the probabilities.

P(X = 0) = C(12, 0) * 0.59^0 * (1 - 0.59)^(12 - 0)

Using the combination formula, C(12, 0) = 1, and simplifying the equation:

P(X = 0) = 1 * 1 * (1 - 0.59)^12 = 0.0003159

P(X = 1) = C(12, 1) * 0.59^1 * (1 - 0.59)^(12 - 1)

Using the combination formula, C(12, 1) = 12, and simplifying the equation:

P(X = 1) = 12 * 0.59^1 * (1 - 0.59)^11 = 0.0065294

P(X = 2) = C(12, 2) * 0.59^2 * (1 - 0.59)^(12 - 2)

Using the combination formula, C(12, 2) = 66, and simplifying the equation:

P(X = 2) = 66 * 0.59^2 * (1 - 0.59)^10 = 0.0470972

Now, let's sum up these probabilities to find P(X < 3):

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

P(X < 3) = 0.0003159 + 0.0065294 + 0.0470972 = 0.0539425

Therefore, the probability that fewer than 3 out of 12 randomly selected adult smartphone users use their smartphones in meetings or classes is approximately 0.0539.

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To evaluate the left and right Riemann sums for n=10 over the interval [0,5], we will use tabulated values of f. The Riemann sum is a method used to approximate the area under a curve by dividing the interval into subintervals and evaluating the function at specific points within each subinterval.

The left Riemann sum uses the left endpoints of the subintervals, while the right Riemann sum uses the right endpoints. In this case, we are given tabulated values of f, which means we have specific function values at certain points. To evaluate the left and right Riemann sums, we will use these tabulated values.

First, we divide the interval [0,5] into 10 equal subintervals since n=10. Each subinterval will have a width of (5-0)/10 = 0.5. For the left Riemann sum, we evaluate the function at the left endpoints of each subinterval. Starting from the left endpoint of the interval, we use the tabulated values of f to find the corresponding function values for each subinterval and sum them up.

For the right Riemann sum, we evaluate the function at the right endpoints of each subinterval. Starting from the right endpoint of the interval, we use the tabulated values of f to find the corresponding function values for each subinterval and sum them up.

By evaluating the left and right Riemann sums, we can approximate the area under the curve represented by the function f over the interval [0,5]. The Riemann sum provides an estimation of the integral of the function and is a fundamental concept in calculus for understanding and approximating areas and other quantities.

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the price per pack of cards that will produce the maximum income is $200. To find the maximum possible income per day, substitute this price back into the equation for I(p):

I(200) = (1000 + 10((5 - 200)/0.02)) * 200.

Calculate the value of I(200) to find

To find the points on the curve where the slope of the tangent is 2, we need to find the coordinates (x, y) that satisfy both the equation of the curve and the condition for the slope.

The slope of the tangent to the curve can be found by taking the derivative of the function f(x).

we differentiate f(x) with respect to x:

f'(x) = 3x² - 8x + 5.

We set f'(x) equal to 2 and solve for x:

3x² - 8x + 5 = 2.

Rearranging the equation:

3x² - 8x + 3 = 0.

Now we can solve this quadratic equation either by factoring or using the quadratic formula. Let's use the quadratic formula:

x = (-b ± √(b² - 4ac))/(2a),

where a = 3, b = -8, and c = 3.

Plugging in the values:

x = (-(-8) ± √((-8)² - 4*3*3))/(2*3)  = (8 ± √(64 - 36))/6

 = (8 ± √28)/6  = (4 ± √7)/3.

So, we have two possible x-values: x1 = (4 + √7)/3 and x2 = (4 - √7)/3.

To find the corresponding y-values, we substitute these x-values into the equation of the curve:

For x = (4 + √7)/3:

y1 = (4 + √7)³ - 4(4 + √7)² + 5(4 + √7) + 5.

For x = (4 - √7)/3:y2 = (4 - √7)³ - 4(4 - √7)² + 5(4 - √7) + 5.

These are the exact coordinates of the points on the curve where the slope of the tangent is 2.

For the card game Cardle, let's denote the price per pack of cards as p. The number of packs sold per day is given by the equation:

N(p) = 1000 + 10((5 - p)/0.02).

The income per day is given by the product of the number of packs sold and the price per pack:

I(p) = N(p) * p.

Substituting N(p) into the equation for I(p):

I(p) = (1000 + 10((5 - p)/0.02)) * p.

To find the maximum possible income, we can take the derivative of I(p) with respect to p, set it equal to zero, and solve for p:

I'(p) = 0.

Differentiating I(p) with respect to p and setting it equal to zero:

1000 - 10/0.02(5 - p) - 10(5 - p)/0.02 = 0.

Simplifying the equation:

1000 - 500 + 5p - 10p + 500 = 0,

-5p + 1000 = 0,5p = 1000,

p = 200.

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By using first principle, the value of Dy/Dx is,

⇒ Dy/Dx = - 7 / x²

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ y = 7 / x

Now, Differentiate the function with respect to x, we get;

⇒ y = 7 / x

⇒ Dy/ Dx = D / Dx (7 / x)

                = 7 D/Dx (1/x)

                = 7 (- 1 × x⁻¹⁻¹ )

                = 7 (- x⁻²)

                = - 7 / x²

⇒ Dy/Dx = - 7 / x²

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Answer:

25

Step-by-step explanation:

4 times 3 is 12

5 times 3 is 15

15 plus 12 is 25

Hello!

(4*3) + (3*5)

= 12+15

= 27

The store should price its broilers at $22.25 to maximize profit.

In this problem, we are given a profit function of a store that sells chickens and toasters.

The profit function is defined as P(p1, p2) = -3960 + 178p1, where p1 is the retail price of a broiler and p2 is the retail price of a toaster.

To maximize profit, we need to find the values of p1 and p2 that will give us the highest possible value for P.

To do this, we can use the concept of partial derivatives. We take the partial derivative of P with respect to p1, which gives us 178. T

his tells us that for every $1 increase in the price of a broiler, the store's profit will increase by $178.

We then take the partial derivative of P with respect to p2, which gives us 0. This means that the store's profit is not affected by the price of a toaster.

To find the optimal values of p1 and p2, we set the partial derivative of P with respect to p1 equal to zero and solve for p1.

This gives us p1 = 22.25. We then substitute this value of p1 back into the profit function to find the value of P at this point. This gives us P(22.25, 0) = 1083.5.

Therefore, the store should price its broilers at $22.25 to maximize profit. The price of the toaster does not affect the store's profit, so it can be set at any value.

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The slope is down 1 right 5 which can be written as -1/5.

Since we are going to go left 4, we are going to times -4 and 1/5 in order to know how much we have to go up. -4 * -1/5 = 4/5 + 6 = 6 4/5

Equation: f(x) or y = -1/5x + 34/5

Answer:

The answer is 1168

Step-by-step explanation:

(4^5)+(12^2)=1168

Answer:

1168

Step-by-step explanation:

4^5 is 1024

12^2 is 144.

1024+144=1168

The corresponding degree measure for a rotation of 6π/5 radians is 216 degrees.

This means that the locksmith needs to adjust the tumbler by rotating it 216 degrees in order to open the bank vault.

To convert the given rotation of 6π/5 radians into degrees, we can use the conversion factor that 180 degrees is equal to π radians.

Let's perform the conversion:

Degree measure = (Radian measure \(\times\) 180 degrees) / π

Degree measure = (6π/5 \(\times\) 180 degrees) / π

Simplifying the expression:

Degree measure = (6 \(\times\) 180 degrees) / 5

Degree measure = 1080 degrees / 5

Degree measure = 216 degrees.

Note: The conversion factor between degrees and radians is based on the relationship between the circumference of a circle and the angle subtended by that circle.

A circle has a total angle of 360 degrees, which corresponds to 2π radians.

Therefore, the conversion factor between degrees and radians is:

1 radian = (180/π) degrees

1 degree = (π/180) radians

This means that to convert from degrees to radians, you can multiply the degree measure by (π/180).

And to convert from radians to degrees, you can multiply the radian measure by (180/π).

For example:

To convert 45 degrees to radians: 45 \(\times\) (π/180) = π/4 radians.

To convert 3π/2 radians to degrees: (3π/2) \(\times\)(180/π) = 270 degrees.

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Answer:

81 degrees

Step-by-step explanation:

Step-by-step explanation:

Here,

X+128+100+51=360

X+279=360

X=360-279

:.x=81

Answer:

I'm glad you asked!

Step-by-step explanation:

5/18 pounds per person.

he problem already says what to do, we need to divide because that's what Karen is doing, she is spliting or dividing the pounds of candy for 3 people. So, we just need to divide 5/6 by 3,

\(\frac{5}{6} \div 3 = \frac{5}{6} \times \frac{1}{3} =\frac{5}{18}\)

The probability of selecting blue marble and green marble is 1/13.

A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event is 1 which is equivalent to 100%.

Probability = sample space/total outcome

total outcome = 13

The probability of picking blue in the first pick = 6/13

since there is no replacement, the total outcome for the second pick = 12

The probability of picking green in the second pick = 2/12 = 1/6

Therefore the probability of selecting blue and green marble = 6/13 × 1/6

= 1/13

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Answer:

the values 9 and 10 satisfy the given inequality.

Step-by-step explanation:

Given inequality is:

\(5<b-3\)

In order to find, which value of b satisfies the given inequality, we have to put the given values one by one in the inequality

Putting b = 8

\(5<8-3\\5 <5\)

The inequality is not true for b=8.

Putting b=9

\(5<9-3\\5<6\)

As the inequality is true for b=9, it satisfies the inequality.

Putting b=10

\(5<10-3\\5<7\)

As the inequality is true for b=10, it satisfies the inequality.

Hence,

the values 9 and 10 satisfy the given inequality.

Answer:

The answer is b=9 and b=10

Step-by-step explanation:

The main answer is √1280x10y7 = 8√10xy³.

The expression √1280x10y7 can be simplified as 8√10xy³. To understand this, let's break it down:

Within the radical, we have √1280. To simplify this, we can factor out perfect squares. The prime factorization of 1280 is 2^7 * 5. Taking out the largest perfect square, which is 2^6, we are left with 2√10.

Next, we have x and y terms outside the radical. These terms can be simplified separately. In this case, we have x^1 and y^7, so we can rewrite them as x and y^6 * y.

Combining these factors, we get the simplified expression 8√10xy³. This means we have 8 times the square root of 10, multiplied by x, and multiplied by y cubed.

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