Peggy wants to run 5 miles in less than 60 minutes. What inequality shows what her rate should be?
A. 1 mi < 60 min
B. 3 mi < 60 min
C. 1 mi < 12 min
D. 2 mi < 30 min

Answer: 7^3/7^6= 1/343

Step-by-step explanation: We move 7^-6 to a denominator because we cannot have a negative exponent in the numerator.

So it would be 7^3/7^6

Which then would be 7*7*7/7*7*7*7*7*7

Which would equal 343/117649

Simplify and you get 1/343

The exponential model fits the data better than the quadratic model.

Based on the scatter plot, it appears that the exponential model would fit the data better, as the data points follow a clear decreasing exponential trend. A quadratic model would not fit the data as well, as it would predict a U-shaped curve instead of a decreasing trend.

To confirm this, we can fit both models to the data and compare their goodness of fit statistics, such as the R-squared value or the mean squared error (MSE).

Here are the formulas for the quadratic and exponential models:

Quadratic model: y = a + bx + cx^2

Exponential model: y = a * e^(bx)

Using a regression tool, we can find the coefficients for each model that best fit the data:

Quadratic model: y = 72.73 - 36.36x + 4.55x^2

Exponential model: y = 69.47 * e^(-0.078x)

We can then calculate the R-squared value and MSE for each model. The R-squared value measures the proportion of variance in the dependent variable (lead usage) that is explained by the independent variable (year), and the MSE measures the average squared difference between the predicted values and actual values.

Quadratic model:

R-squared = 0.786

MSE = 416.6

Exponential model:

R-squared = 0.971

MSE = 38.2

The R-squared value for the exponential model is much higher than that of the quadratic model, indicating that the exponential model explains more of the variance in the data. Additionally, the MSE for the exponential model is much lower than that of the quadratic model, indicating that the exponential model's predictions are closer to the actual values.

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--The complete question is, Compare the fit of a quadratic model and an exponential model for lead usage. which model fits the data better?

Year    Lead(thousands tons)

1940    70

1950    35

1960    10

1970      5

1980     0.01--

The given equation is

First, we add 4 on each side.

Then, we multiply 10 on each side.

Answer:

see explanation

Step-by-step explanation:

If (x - 1) is a factor then f(1) = 0

Given

f(x) = x³ - 13x² + 32x - 20 , then

f(1) = 1³ - 13(1)² + 32(1) - 20

     = 1 - 13 + 32 - 20

     = 0

Since f(1) = 0 then (x - 1) is a factor

Using Synthetic division

 1  | 1  - 13   32   - 20

      ↓    1   - 12      20    

     -----------------------------

      1    - 12   20     0 ← remainder

quotient = x² - 12x + 20 = (x - 2)(x - 10)

Then

x³ - 13x² + 32x - 20 = (x - 1)(x - 2)(x - 10) ← in factored form

Answer: 2x-y=2= y=−2x+2

4x+y=4= y=-4x+4

Step-by-step explanation:

Answer: if you Solve by Substitution you get (point form: (1, 0)  

(equation form: x = 1, y = 0)

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Solve for x:

y = −4x + 4

y = 2x − 2

Answer:

D) 5

Step-by-step explanation:

we see that every 4 hours 20 miles are traveled.

so, the rate of change of miles travels over hours is

20/4 = 5/1 = 5

in other words, the speed was 5 mph.

Answer:

B

Step-by-step explanation:

Answer: 200 in ^2

Step-by-step explanation:

The probability that the colour changes, while she is watching, is 1/7

Concept: Event probability = number of favorite results /Total number of results

It is given that the traffic light runs repeatedly in the following time cycle: green for 30 seconds, then yellow at 3  seconds, and then red for 30 seconds.

This means that the traffic light passes through 63 seconds to complete one-time cycle.

It is also given that Leah chooses a random 3 second time interval to watch the light.

We should find the probability that the color changes while Leah is looking.

The green light will change after 30 seconds and after three seconds it will change to yellow light, that is at 33 second it is yellow and after another 30 seconds it will change to red light.

Now let time t=0

The light changes at three different times: t=30,t = 33 and t = 63

This means that the light will change if Leah watches at intervals [27,30]

, [30,33] or [60,63]

Since each interval is 3 seconds and there are 3 intervals, Leah will have a chance of 9 seconds.

That makes a total of 9 seconds out of 63

⇒Probability that Leah watches the color change=Number of seconds she watches/Total seconds

=9/63=17

∴ The probability that Leah observes the color change is 1/7

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The identified parameters are:

ta = 6 minutes

tθ = 11 minutes

∂a = 4 minutes

∂θ = 20 minutes

ra = 1/6 minutes^(-1)

rθ = 1/11 minutes^(-1)

ta: Mean time between calls to the center

tθ: Effective response time

∂a: Standard deviation of the time between calls to the center

∂θ: Standard deviation of the effective response time

ra: Rate of calls to the center (inverse of ta, i.e., ra = 1/ta)

rθ: Rate of effective response (inverse of tθ, i.e., rθ = 1/tθ)

Given information:

Mean time between calls to the center (ta) = 6 minutes

Standard deviation of time between calls (∂a) = 4 minutes

Effective response time (tθ) = 11 minutes

Standard deviation of effective response time (∂θ) = 20 minutes

Using this information, we can determine the values of the parameters:

ta = 6 minutes

tθ = 11 minutes

∂a = 4 minutes

∂θ = 20 minutes

ra = 1/ta = 1/6 minutes^(-1)

rθ = 1/tθ = 1/11 minutes^(-1)

So, the identified parameters are:

ta = 6 minutes

tθ = 11 minutes

∂a = 4 minutes

∂θ = 20 minutes

ra = 1/6 minutes^(-1)

rθ = 1/11 minutes^(-1)

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1) Estimate value of the product of 2/3 and 0.55 is, 2/3.

2) The fraction part is, 55 / 100

3) The product of the two numbers is, 11/30

We have to given that,

Estimate the product of 2/3 and 0.55.

And, Convert the decimal 0.55 to a fraction.

And, The product of the two numbers.

Now,

Estimate the product of 2/3 and 0.55,

So, we can round 0.55 to the nearest whole number, which is 1.

Then, multiply 2/3 by 1 to get an estimate of the product.

so, The correct answer is 2/3.

Now, we can convert the decimal 0.55 to a fraction,

= 0.55

= 55/100

= 11/20

Thus,  The correct answer is, 55/100.

And,  the product of 2/3 and 0.55,

= 2/3 x 55/100

= 110/300

= 11/30.

Hence, The correct answer is, 110/300 or 11/30

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Maria's book is 8 days late.

What is linear equation?

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant.

Let, the late fee for library books is $2. 00 plus 15 cents each day for a book that is late.

Maria's fee for a late book was $3. 20.

As late fee consists of  $2.00 fine plus $0.15D fee or each day:

So,

LF = $2.00 + $0.15D

where D is number of days.

Here late fee for book is $3.20

⇒          $3.20 = $2.00 + $0.15D

$3.20 - $2.00 = $0.15D

             $1.20 = $0.15D

                   D = $1.20/$0.15

                   D = 8

Hence, Maria's book is late for 8 days.

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the probability that a randomly selected passenger car gets more than 35 mpg is approximately 0.3665.

the probability that the average mpg of four randomly selected passenger cars is more than 35 mpg is approximately 0.087

the probability that all of the passenger cars get more than 35 mpg is approximately 0.015.

We need to find \(P(X > 35),\) where X is the mpg rating of a randomly selected passenger car.

The standard normal distribution and Table 1, we have:

\(z = (35 - 33.8) / 3.5 = 0.34\)

\(P(X > 35) = P(Z > 0.34) = 0.3665\)

\(P(\bar X > 35)\), were \(\bar X\) is the sample mean mpg rating of four randomly selected passenger cars.

The population standard deviation, we use the t-distribution with \(n-1\) degrees of freedom (were \(n = 4\)) and Table 1. We have:

\(t = (35 - 33.8) / (3.5 / \sqrt(4)) = 1.83\)

Using Table 1 with 3 degrees of freedom (\(n-1 = 4-1\)), we find:

\(P(T > 1.83) = 0.087\)

We need to find \(P(X1 > 35\) and \(X2 > 35\) and \(X3 > 35\) and \(X4 > 35\)), where X1, X2, X3, and X4 are the mpg ratings of four randomly selected passenger cars.

Since the mpg ratings of the four cars are independent and identically distributed, we have:

\(P(X1 > 35\)and\(X2 > 35\) and \(X3 > 35\) and \(X4 > 35\)) =\(P(X > 35)^4\)

From part (a), we know that\(P(X > 35) = 0.3665.\)

\(P(X1 > 35\)and \(X2 > 35\) and\(X3 > 35\) and \(X4 > 35) = 0.3665^4 \approx 0.015\)

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Answer:

Step-by-step explanation:

6 no answer 0,9

7 no answer -3,-10

8 no answer -10,2

9 no answer 2,0

hope this helps u!!

Answer:

the answer is (5g+4h)(5g-7h)

Step-by-step explanation:

25g^2-15gh-28h^2

=(25g^2+20gh)+(-35gh-28h^2)

=5g(5g+4h)-7h(5g+4h)

=(5g+4h)(5g-7h)

Answer: when the value on each side of the equal sign is the same

Step-by-step explanation: for example, 9=9 is a true equation. 5+4 = 9 is a true equation

The budgets of Hong Kong, the United States of America, and Korea differ in contents, formats, advantages, and disadvantages. While each budget has its strengths and weaknesses, they all aim to provide a clear and transparent financial plan for their respective countries.

A budget is a financial plan that estimates expected income and expenditure for a specific period. It may include income, expenses, debts, and savings. Budgets may vary from country to country and can be analyzed by comparing their contents, formats, advantages, and disadvantages. Here are the budgets of Hong Kong, the United States of America, and Korea:

United States Budget:

Korean Budget:

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The  product of prime polynomials which is equivalent to 30x3 – 5x2 – 60x is option C) 5x(2x – 3)(3x + 4).

We have 30x³ - 5x² - 60x

We take common value out so

5x(6x² - x - 12)

By following the factorization method we get,

6x² - x - 12

b²-4ac = -1² - 4x6x(-12)

= 289

x = -b ± √289/2a

= 1 ± 17/-2

x = 3/2 or x = -4/3

So,

6x² - x - 12

6(x-3/2)(x-(-4/3))

(2x-3) (3x+4)

Therefore,

30x³ - 5x² - 60x = 5x(6x² - x - 12)

= 5x (2x-3) (3x+4)

The  product of prime polynomials is equivalent to 30x3 – 5x2 – 60x is 5x(2x – 3)(3x + 4).

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The area of a triangle is computed as follows:

where b is the base, and h is the height

Replacing with A = 54, h = 18, and solving for b, we get:

The base of the triangle is 6 in

The measure of an angle ∠TQU is 26.6° if  PQ=3 and QR=4

In Euclidean geometry, an angle is the figure formed by two rays, known as the sides of the angle, that have a common termination, known as the vertex of the angle. These are referred to as dihedral angles. An angle can also be defined by two intersecting curves, which is the angle of the rays lying tangent to the respective curves at their point of intersection.

Angle can also refer to a rotation or the measurement of an angle. This measurement is the ratio of the length of a circular arc to its radius.

Given,

Rectangle PQRS has PQ=3 and QR=4

The points T and U are on side PS such that PT=US=1

As PQRS is rectangle so opposite sides of rectangle should be equal.

PS=QR and PQ=RS

QR=4, PS=4

But, PS=PT+TU+US

4=1+TU+1

TU=4-2

TU=2

And PU=PT+TU

1+2=3

PU=3

Consider, ΔQPU, Right angled at P.

We know that,

tan Q=PU/PQ

tan Q=3/3

tan Q=1

Q=tan⁻¹

Q=45°

∠PQU=45°

Now, let us consider ΔQPT is right angled at P

tan Q=PT/PQ

tan Q=1/3

Q= tan⁻¹(1/3)

Q=18.43°

∠PQT=18.43°

∠PQU=∠PQT+∠TQU

45°=18.43°+∠TQU

∠TQU=45°-18.43°

∠TQU=26.57°

∠TQU≈26.6°

Therefore, the measure of ∠TQU is 26.6°.

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If x is reduced by 1/3, 3x will be reduced by 1/3 x 3 = 1

Because y = 3x, y will also be reduced by 1.

Answer:

0

Step-by-step explanation:

-4(-3 + 5 + (-2))

-4(-3 + 5 -2)

-4 • 0

0

Answer:

= 0

Step-by-step explanation:

-4(-3 + 5 +(-2 ))

get rid of the "( )"

-4 (- 3 + 5 - 2)

calculate the sum

-4 x 0

anything times 0 = 0 so the answer is;

0

Answer:

0.000065 km

Step-by-step explanation:

To get from cm to km you need to divide 6.5 by 0.000001 which equals 0.000065km

By the limit comparison test, the series ∑(1+9^n)/(4n) from n=1 to infinity diverge

We are asked to determine whether the series ∑(1+9^n)/(4n) from n=1 to infinity is convergent or divergent.

We can use the ratio test to determine the convergence of the series. Let's compute the ratio of the (n+1)th term to the nth term:

[(1+9^(n+1))/(4(n+1))] / [(1+9^n)/(4n)]

= (1+9^(n+1))/(1+9^n) * (n/ (n+1))

As n approaches infinity, the term (n/(n+1)) approaches 1, and the ratio becomes:

(1+9^(n+1))/(1+9^n)

Since the ratio does not approach a finite value as n approaches infinity, the ratio test is inconclusive. Therefore, we cannot determine the convergence of the series using the ratio test.

However, we can use the limit comparison test with the series 1/n^p, where p=1/2. Let's compute the limit of the ratio:

lim n→∞ [(1+9^n)/(4n)] / [1/n^(1/2)]

= lim n→∞ (n^(1/2) * (1+9^n))/(4n)

= lim n→∞ (n^(1/2) + 9^n/ (4n^(1/2)))

Since the first term approaches infinity as n approaches infinity and the second term approaches zero, the limit diverges. Therefore, by the limit comparison test, the series ∑(1+9^n)/(4n) from n=1 to infinity diverges.

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Answer:

To find the acceleration of the object, we need to use the equation:

acceleration = (final velocity - initial velocity) / time

In this case, the initial velocity of the object was 240 m/s, the final velocity was 0 m/s, and the time was 1 minute. Plugging these values into the equation, we get:

acceleration = (0 m/s - 240 m/s) / (1 minute) = -240 m/s / 1 minute = -240 m/s^2 / 60 s = -4 m/s^2

Thus, the acceleration of the object is -4 m/s^2, which corresponds to answer choice A.

Vertices of triangle dilated about the origin by a scale factor of 1/3, and then translated 2 units left and 3 units down

coordinates of A'B'C' are

A' (-1,-1)

B'(0,0)

C' (1,-2)

Given :

The vertices of a triangle are A(3,6), B(6,9), and C(9.3).

When the vertices by dilated by origin by scale factor 'k', then we multiply 'k' with each vertices

It is dilated about the origin by a scale factor of 1/3

So we multiply (x,y) by scale factor

\((x,y) - (\frac{1}{3}x,\frac{1}{3}y)\\A(3,6) - (\frac{1}{3}(3),\frac{1}{3}(6))->(1,2)\\\\B(6,9) - (\frac{1}{3}(6),\frac{1}{3}(9))->(2,3)\\\\C(9,3) - (\frac{1}{3}(9),\frac{1}{3}(3))->(3,1)\\\\\)

Now we translate 2 units left and 3 units down

For 2 units left , we subtract 2 from x

For 3 units down , we subtract 3 from y

So (x,y) becomes (x-2, y-3)

Lets apply this rule to our new vertices

\((1,2) \; becomes \; (-1,-1)\\(2,3) \; becomes \; (0,0)\\(3,1) \; becomes \; (1,-2)\\\)

coordinates are

A' (-1,-1)

B'(0,0)

C' (1,-2)

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Answer:

A 5kW solar system is made up of 20 solar panels, assuming that the panels have 250-watt capacity. The size of each panel will be approximately 1.6 m x 1 m, so at least 32 m² of roof space is needed to suit the space needs of this system.25 Oct 2021

Answer:

Part A: by finding equation and x value is size.

Take two coordinates: (20, 1/5), (40,2/5)

slope:

\(\frac{y2-y1}{x2-x1}\)

\(\frac{\frac{2}{5} -\frac{1}{5} }{40-20}\)

\(\frac{0.2}{20}\)

\(0.01\) ......this is slope, unit rate.

Equation:

y - y1 = m( x - x1 )

y - 1/5 = 0.01(x - 20)

y = 0.01x ........this is the equation

The y determines the size of kilowatts of energy

So y = 5

5 = 0.01x

x = 500 square feet

500 square feet is required to produce 5 kilowatts of energy.

Answer:

DONT ASK ME

Step-by-step explanation: