Find the function rule for g(x).
9. The function f(x)=-6x. The graph of g(x) is f(x) vertically stretched by a factor of 7 and reflected in the x-axis. What is the function rule for g(x)?​

If the original pendulum completed one swing every 1.5 seconds. How long should the new pendulum be is: C. 55.9 centimeters.

Using this formula

T=2π√I/g

Where:

T=1.5 seconds

l =length of pendulum

g= acceleration of gravity=9.8m/s²

Let plug in the formula

1.5 seconds=2π√I/9.8

l/9.8=0.05699

l=0.05699×9.8

l=0.5585

l=55.9 centimeters (Approximately)

Therefore How long should the new pendulum be is: C. 55.9 centimeters.

Learn more about How long should the new pendulum be here:https://brainly.com/question/11616656

#SPJ1

Answer:

\(3(2+7a)=6+\)

\(6 + 21a = 6\)

\(21a + 6 = 6 + 21a\)

answer is 21a

The slope of the line represents the rate of change between the independent variable (number of available staff) and the dependent variable (number of available staff) (wait time).

The slope of the line in this case is -1.62, which means that for every one unit increase in the number of staff available, the wait time decreases by 1.62 units.

In this case, a negative slope indicates that as the number of staff available increases, so does the wait time, indicating a positive relationship between the two variables. In other words, as the number of employees available increases, the wait time decreases.

It is important to remember that the equation models this relationship, and that actual wait times in the real world may not always follow this exact relationship due to other factors that influence wait times.

To learn more about variable.

https://brainly.com/question/17344045

#SPJ4

The correct answer is option c) infinitely many solutions..

To solve the system of equations using the substitution method, we'll substitute the value of y from the second equation into the first equation and solve for x.

Given:

-6x + 2y = 8 ---(1)

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

Substitute equation (2) into equation (1):

-6x + 2(3x + 4) = 8

Simplify:

-6x + 6x + 8 = 8

8 = 8

We obtained a true statement (8 = 8), which means the two equations are equivalent. This solution shows that the system has infinitely many solutions.

Therefore, the correct answer is option c) infinitely many solutions..

know more about substitution method

https://brainly.com/question/22340165

#SPJ11

Answer

D

Step-by-step explanation:

The integral of (x^2 + y) dA over the region A enclosed by a simple closed curve C in R^2 is equal to the integral ∮C (zy dx - zx dy + 3x dy), where z = 0.

To calculate this, we can use Green's theorem, which states that the line integral of a vector field around a simple closed curve is equal to the double integral of the curl of the vector field over the region enclosed by the curve.

In this case, the vector field F = (0, zy, -zx + 3x) and its curl is given by:

curl(F) = (∂(−zx + 3x)/∂y - ∂(zy)/∂z, ∂(0)/∂z - ∂(−zx + 3x)/∂x, ∂(zy)/∂x - ∂(0)/∂y)

       = (-z, 3, y)

Applying Green's theorem, the line integral over C is equivalent to the double integral of the curl of F over the region A:

∮C (zy dx - zx dy + 3x dy) = ∬A (-z dA) = -∬A z dA

Therefore, the integral of (\(x^2\) + y) dA is equal to the integral ∮C (zy dx - zx dy + 3x dy), where z = 0.

Learn more about integral here:

https://brainly.com/question/31433890

#SPJ11

Answer:

We conclude that option A is true as x = 1 is the root of the polynomial.

Step-by-step explanation:

Given the polynomial

\(f\left(x\right)\:=\:x^2\:+\:2x^2\:-\:x-2\)

Let us determine the root of the polynomial shown below.

\(\:0=\:x^2\:+\:2x^2\:-\:x-2\)

\(0=3x^2-x-2\)

switch sides

\(3x^2-x-2=0\)

as

\(3x^2-x-2=\left(3x+2\right)\left(x-1\right)\)

so the equation becomes

\(\left(3x+2\right)\left(x-1\right)=0\)

Using the zero factor principle

\(3x+2=0\quad \mathrm{or}\quad \:x-1=0\)

solving

\(3x+2=0\)

\(3x=-2\)

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

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

and

\(x-1=0\)

\(x=1\)

The possible roots of the polynomial will be:

\(x=-\frac{2}{3},\:x=1\)

Therefore, from the mentioned options, we conclude that option A is true as x = 1 is the root of the polynomial.

Answer:

2

Step-by-step explanation:

You have 7, and you take away five, which leaves you with 2

here is a drawing:

l  l  l  l  l  l  l

x x x x x l  l

Answer:

Do more rolls of the number cube.

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

116-28

88/4

Answer:

4ab² + 20b - 3a

Step-by-step explanation:

This question most likely asks us to simplify the expression, as factoring is not possible...

(ab² + 13b - 4a) + (3ab² + a + 7b),

ab² + 13b - 4a + 3ab² + a + 7b,

ab² + 3ab² + 13b + 7b - 4a + a,

Solution : 4ab² + 20b - 3a

a) The least square estimator is 2.785221.  b) The coefficient of determination is 0.9960514.  c) We would reject the null hypothesis at the 5% significance level.

To calculate the least squares estimators of the slope, the y-intercept, and the variance, we can use the method of simple linear regression.

(a) First, let's calculate the least squares estimators:

Step 1: Calculate the mean of the temperature (x) and maltose sugar content (y):

X = (155 + 160 + 165 + 170 + 175 + 180 + 185 + 190 + 195 + 200 + 205 + 210) / 12 = 185

Y = (25 + 28 + 30 + 31 + 31 + 35 + 33 + 38 + 40 + 42 + 43 + 45) / 12 = 35.333

Step 2: Calculate the deviations from the means:

xi - X and yi - Y for each data point.

Deviation for each temperature (x):

155 - 185 = -30

160 - 185 = -25

165 - 185 = -20

170 - 185 = -15

175 - 185 = -10

180 - 185 = -5

185 - 185 = 0

190 - 185 = 5

195 - 185 = 10

200 - 185 = 15

205 - 185 = 20

210 - 185 = 25

Deviation for each maltose sugar content (y):

25 - 35.333 = -10.333

28 - 35.333 = -7.333

30 - 35.333 = -5.333

31 - 35.333 = -4.333

31 - 35.333 = -4.333

35 - 35.333 = -0.333

33 - 35.333 = -2.333

38 - 35.333 = 2.667

40 - 35.333 = 4.667

42 - 35.333 = 6.667

43 - 35.333 = 7.667

45 - 35.333 = 9.667

Step 3: Calculate the sum of the products of the deviations:

Σ(xi - X)(yi - Y)

(-30)(-10.333) + (-25)(-7.333) + (-20)(-5.333) + (-15)(-4.333) + (-10)(-4.333) + (-5)(-0.333) + (0)(-2.333) + (5)(2.667) + (10)(4.667) + (15)(6.667) + (20)(7.667) + (25)(9.667) = 1433

Step 4: Calculate the sum of the squared deviations:

Σ(xi - X)² and Σ(yi - Y)² for each data point.

Sum of squared deviations for temperature (x):

(-30)² + (-25)² + (-20)² + (-15)² + (-10)² + (-5)² + (0)² + (5)² + (10)² + (15)² + (20)² + (25)² = 15500

Sum of squared deviations for maltose sugar content (y):

(-10.333)² + (-7.333)² + (-5.333)² + (-4.333)² + (-4.333)² + (-0.333)² + (-2.333)² + (2.667)² + (4.667)² + (6.667)² + (7.667)² + (9.667)² = 704.667

Step 5: Calculate the least squares estimators:

Slope (b) = Σ(xi - X)(yi - Y) / Σ(xi - X)² = 1433 / 15500 ≈ 0.0923871

Y-intercept (a) = Y - b * X = 35.333 - 0.0923871 * 185 ≈ 26.282419

Variance (s²) = Σ(yi - y)² / (n - 2) = Σ(yi - a - b * xi)² / (n - 2)

Using the given data, we calculate the predicted maltose sugar content (ŷ) for each data point using the equation y = a + b * xi.

y₁ = 26.282419 + 0.0923871 * 155 ≈ 39.558387

y₂ = 26.282419 + 0.0923871 * 160 ≈ 40.491114

y₃ = 26.282419 + 0.0923871 * 165 ≈ 41.423841

y₄ = 26.282419 + 0.0923871 * 170 ≈ 42.356568

y₅ = 26.282419 + 0.0923871 * 175 ≈ 43.289295

y₆ = 26.282419 + 0.0923871 * 180 ≈ 44.222022

y₇ = 26.282419 + 0.0923871 * 185 ≈ 45.154749

y₈ = 26.282419 + 0.0923871 * 190 ≈ 46.087476

y₉ = 26.282419 + 0.0923871 * 195 ≈ 47.020203

y₁₀ = 26.282419 + 0.0923871 * 200 ≈ 47.95293

y₁₁ = 26.282419 + 0.0923871 * 205 ≈ 48.885657

y₁₂ = 26.282419 + 0.0923871 * 210 ≈ 49.818384

Now we can calculate the variance:

s² = [(-10.333 - 39.558387)² + (-7.333 - 40.491114)² + (-5.333 - 41.423841)² + (-4.333 - 42.356568)² + (-4.333 - 43.289295)² + (-0.333 - 44.222022)² + (-2.333 - 45.154749)² + (2.667 - 46.087476)² + (4.667 - 47.020203)² + (6.667 - 47.95293)² + (7.667 - 48.885657)² + (9.667 - 49.818384)²] / (12 - 2)

s² ≈ 2.785221

(b) The coefficient of determination (R²) is the proportion of the variance in the dependent variable (maltose sugar content) that can be explained by the independent variable (temperature). It is calculated as:

R² = 1 - (Σ(yi - y)² / Σ(yi - Y)²)

Using the calculated values, we can calculate R²:

R² = 1 - (2.785221 / 704.667) ≈ 0.9960514

(c) To conduct an upper-sided model utility test for the slope parameter at the 5% significance level, we need to test the null hypothesis that the slope (b) is equal to zero. The alternative hypothesis is that the slope is greater than zero.

The test statistic follows a t-distribution with n - 2 degrees of freedom. Since we have 12 data points, the degrees of freedom for this test are 12 - 2 = 10.

The upper-sided critical value for a t-distribution with 10 degrees of freedom at the 5% significance level is approximately 1.812.

To calculate the test statistic, we need the standard error of the slope (SEb):

SEb = sqrt(s² / Σ(xi - X)²) = sqrt(2.785221 / 15500) ≈ 0.013621

The test statistic (t) is given by:

t = (b - 0) / SEb = (0.0923871 - 0) / 0.013621 ≈ 6.778

Since the calculated test statistic (t = 6.778) is greater than the upper-sided critical value (1.812), we would reject the null hypothesis at the 5% significance level. This suggests that there is evidence to support a positive linear relationship between mashing temperature and maltose sugar content in this data set.

To learn more about least square estimator here:

https://brainly.com/question/31481254

#SPJ4

The value of the arcsin of 3 is 90 - 100.998i

From the question, we are to determine the inverse sine or arcsine of the given number

The given number is 3

All the values for the sine of angles are less than or equal to 1

That is,

Given an angle θ,

sinθ ≤ 1

From this, we can infer that the arcsine of 3 will be an imaginary number.

The arcsine of 3 is

sin⁻¹(3) = 90 - 100.998i

Hence, the value of the arcsin of 3 is 90 - 100.998i

Learn more on Inverse of Trigonometric functions here: https://brainly.com/question/8120556

#SPJ1

The equivalent system of first-order differential equations for the given problem is: 1. dv1/dt = v2 2. dv2/dt = v3 3. dv3/dt = 2v2 - v1 + 1 + t*e ^t

Given differential equation: x''' - 2x'' + x' = 1 + t*e ^t

Step 1: Define new variables.
Let's introduce new variables:
v1 = x'
v2 = v1'
v3 = v2'

Now we have:
v1 = x'
v2 = v1'
v3 = v2'

Step 2: Rewrite the given equation using new variables.
Substitute the new variables into the given differential equation:
v3 - 2v2 + v1 = 1 + t*e ^t

Step 3: Write the equivalent system of first-order differential equations.
Now we have the following equivalent system of first-order differential equations:
dv1/dt = v2
dv2/dt = v3
dv3/dt = 2v2 - v1 + 1 + t*e ^t

So, the equivalent system of first-order differential equations for the given problem is:

1. dv1/dt = v2
2. dv2/dt = v3
3. dv3/dt = 2v2 - v1 + 1 + t*e ^t

Learn more about differential equations here:

brainly.com/question/25731911

#SPJ11

Answer: 27.27 seconds?

Step-by-step explanation:

25 - 16.26 = 8.74

19/8.74 = 2.2 (Rounded up)

60/2.2 = 27.27

Based on the information the amount that Agnes paid as state income tax is $2,040.

Federal Income Tax is the tax system in the United States, levied and governed by Internal Revenue Services (IRS) which helps determine the tax that is charged on the income earned by individuals, corporates, and various other legal entities.

The first step is to calculate Agnes' federal taxable income.

Federal taxable income=$15449.60/0.284

Federal taxable income= $54,400

The second step is to calculate Agnes' state income tax.

State income tax=0.0375 ×$54,400

State income tax=$2,040

Hence, the amount that Agnes paid as state income tax is $2,040.

Learn more here federal income:

brainly.com/question/12600097

Answer:

its d

Step-by-step explanation:

The Z-value is Z=-2.121 < Zcritical and the p-value will be equal to 0.0169 when the percentage of at least 0.8 of the packages should include 3 ounces.

Given that percentage of at least 0.8 of the packages must include 3 ounces or more of chocolate stars for a candy producer to assert that a bridge mix is predominantly chocolate stars.

Since a random sample of 50 packages are tested by quality control to see if the proportion is less than 0.8 at a significance level of 0.05.

We have to calculate p, the z-score, and the p-value, using Sheet 6 of the Excel document.

We know that,

N=50

n=34

Proportion pbar = n/N=34/50=0.68

H₀: p≥0.8

H₁: p<0.8

Z=pbar-p/√(p(1-p)/N

Z=0.68-0.8/√0.8(1-0.8)/50

Z=-2.121

α=0.05

Reject H₀ if Z<-Zcritical

Z critical for one -tailed (Left) = -1.6449

Z=-2.121<Zcritical

Reject H₀

P(Z < -2.121) = 0.0169

p-value = 0.0169

Since the p-value is less than the significance level of 0.05 the null hypothesis is rejected.

To learn more about value visit:

brainly.com/question/13686040

#SPJ4

The variance of a distribution of means of samples of more than one is A) smaller than the original population variance.

When considering the distribution of means of samples, the central limit theorem states that as the sample size increases, the sampling distribution approaches a normal distribution regardless of the shape of the population distribution. Additionally, the standard error of the mean decreases as the sample size increases.

The variance of a population is denoted by σ^2.

The variance of the distribution of sample means, also known as the sampling distribution, is denoted by σ^2/N, where N is the sample size.

As the sample size (N) increases, the denominator increases, leading to a smaller value for the variance of the distribution of sample means (σ^2/N). Thus, the variance of the distribution of means of samples is smaller than the original population variance.

The variance of a distribution of means of samples of more than one is smaller than the original population variance. This is due to the central limit theorem and the decrease in standard error as the sample size increases.

To know more about central limit theorem , visit

https://brainly.com/question/898534

#SPJ11

The ordered pair (-2, 2) satisfies both inequalities y < -x + 1 and y > x.

The correct option is A: (-2, 2).

To determine which ordered pairs satisfy both inequalities y < -x + 1 and y > x, we need to check each pair's coordinates in both inequalities.

Let's test each ordered pair:

A: (-2, 2)

For y < -x + 1: 2 < -(-2) + 1 → 2 < 3 (True)

For y > x: 2 > -2 → 2 > -2 (True)

B: (1, 1)

For y < -x + 1: 1 < -(1) + 1 → 1 < 0 (False)

For y > x: 1 > 1 → 1 > 1 (False)

C: (0, 0)

For y < -x + 1: 0 < -(0) + 1 → 0 < 1 (True)

For y > x: 0 > 0 → 0 > 0 (False)

D: (-1, -1)

For y < -x + 1: -1 < -(-1) + 1 → -1 < 2 (True)

For y > x: -1 > -1 → -1 > -1 (False)

From the above calculations, we can see that only the ordered pair (-2, 2) satisfies both inequalities y < -x + 1 and y > x. Therefore, the correct answer is option A: (-2, 2).

To learn more about inequality;

brainly.com/question/28823603

#SPJ12

The complete question:

Which ordered pairs make both inequalities y < -x + 1 and y > x true?

A: (2, 2)

B: (1, 1)

C: (0,0)

D: (-1, -1)

Answer:

Step-by-step explanation:

To calculate the gas mass produced, we can use Darcy's Law, which relates the flow of gas through a porous medium to the pressure gradient. The formula for Darcy's Law is:

Q = -k * A * (dP/dx)

Where:

Q is the flow rate (m^3/s)

k is the permeability of the medium (m^2)

A is the cross-sectional area (m^2)

dP/dx is the pressure gradient (Pa/m)

Given:

φ = 0.3

b = 100 m

αp​ = 4 × 10^(-9) Pa^(-1)

ρ = 0.1 hp​ (gas density)

Pressure head (initial) = 100 m

Pressure head (final) = 30 m

Area (A) = 10,000 m^2

First, we need to calculate the permeability (k) using the porosity (φ) and the compressibility (αp​) as follows:

k = φ² * αp​

k = 0.3² * (4 × 10^(-9) Pa^(-1))

k = 9 × 10^(-11) m^2

Next, we can calculate the pressure gradient (dP/dx) by subtracting the final pressure head from the initial pressure head and dividing it by the distance (b):

dP/dx = (Pressure head (final) - Pressure head (initial)) / b

dP/dx = (30 m - 100 m) / 100 m

dP/dx = -0.7 Pa/m

Now, we can calculate the flow rate (Q) using Darcy's Law:

Q = -k * A * (dP/dx)

Q = -9 × 10^(-11) m^2 * 10,000 m^2 * (-0.7 Pa/m)

Q = 6.3 × 10^(-4) m^3/s

Finally, we can calculate the gas mass (m) using the flow rate (Q) and the gas density (ρ):

m = Q * ρ

m = 6.3 × 10^(-4) m^3/s * 0.1 kg/m^3

m = 6.3 × 10^(-5) kg/s

Therefore, the gas mass produced when the pressure head is reduced from 100 m to 30 m over an area of 10,000 m^2 is approximately 6.3 × 10^(-5) kg/s.

To calculate the gas mass produced, Using Darcy's Law and the given values, we can determine the gas mass produced when the pressure head is reduced from 100 m to 30 m over an area of 10,000 m2.

The gas mass produced can be calculated by first determining the permeability (k) using the given values of porosity (φ), compressibility (αp), gas density (ρ), and thickness (b). With the obtained value of k, we can then use Darcy's Law to calculate the gas flow rate. However, since the time period is not specified, we cannot directly calculate the gas mass produced. The gas flow rate obtained from Darcy's Law represents the volume of gas flowing per unit time. To calculate the gas mass produced, we need to integrate the flow rate over time. Without the time component, we cannot determine the exact gas mass produced. Therefore, the calculation of the gas mass produced requires information about the time period or additional data.

Learn more about mass here:

https://brainly.com/question/11954533

#SPJ11

Answer:

Hope this helps

Step-by-step explanation:

-16 - (-16) cab also be written as -16 + 16 which is 0. Iris was not correct because she didn't realize that the first 16 was negative.

Answer:

\((4a)^{-3}*^{-4}\)

\(x^m*x^n=x^{m+n}\)

\((4a)^{-3}*a^{-4}\)

\((-4)^{-3}\: a^{-3}*a^{-4}\)

\(4^{-3}\:a^{-3-4}\)

\(\cfrac{1}{4^3} \:a^{-7}\)

\(\boxed{\frac{1}{64a^{7}} }\)

~

\((3xy)^2*(-4x^3y^2)^3\)

\(9x^2y^2*(64x^9y^6)\)

\(\boxed{-576x^{11}y^8}\)

~

\((4a^{-1}b^5c^{-3})^3\)

\((4)^3(a^{-1})^3(b^5)^3(c^{-3})^3\)

\((4*4*4)\:a^{-1*3}\:b^{5*3}\:c^{-3*3}\)

\(64\:a^{-3}b^{15}c^{-9}\)

\(\boxed{\frac{64b^{15}}{a^3c^9}}\)

Answer: B

Step-by-step explanation:

The slope is the rate of change of the y-value, which is the coefficient of

x when the coefficient of y is 1.

Response:

The slopes are;

1. The common difference between the y-values is constant, therefore,

the points are points on a straight line, which gives;

\(Slope, \ m = \dfrac{-8 - (-12)}{-8 - (-10)} = \dfrac{4}{2} = \underline{2}\)

2. The slope of the line is found as follows;

\(Slope, \ m = \dfrac{1 - 2}{0 - (-4)} = \underline{-\dfrac{1}{4}}\)

\(3. \hspace{0.15 cm} Slope, \ m = \dfrac{-8 - (-7)}{0 - (-7)} = \underline{-\dfrac{1}{7}}\)

\(4. \hspace{0.15 cm} Slope, \ m = \dfrac{3 - 2}{0 - (-2)} = \underline{ \dfrac{1}{2}}\)

\(5. \hspace{0.15 cm} Slope, \ m = \dfrac{-25 - (-11)}{4 - 2} = -\dfrac{14}{2} = \underline{-7}\)

\(6. \hspace{0.15 cm} Slope, \ m = \dfrac{-14 - (-38)}{-5 - (-11)} = \dfrac{24}{6} = \underline{4}\)

The value of the slope, m, and the y-intercept, b, are the coefficient of x and

the constant when the coefficient of y is 1.

Which gives;

7. The slope, m = -4, the y-intercept, b = 6

8. The slope, m = 0, the y-intercept, b = \(\underline{-\frac{1}{4}}\)

9. The slope, m = -4, the y-intercept, b = -1

10. The slope, m = 6, the y-intercept b = -4

11. The slope, m = \(\underline{-\frac{1}{4}}\), the y-intercept is b = 2

12. The slope, m =  \(\underline{\frac{1}{6}}\), the y-intercept b =  \(\underline{\frac{5}{6}}\)

13.  The slope, m = 8, the y-intercept, b = 50

In the possible letter code from a similar question, we have;

\(\begin{array}{ccccccccccccccccc}7&2&12&&5&8&&1&9&&10&3&&13&4&11&6\\P&U&T&&I&T&&O&N&&M&Y&&B&I&L&L\end{array}\right]\)

Learn more about the slope and intercept of a line here:

https://brainly.com/question/10661585

The given parametric equations define a relationship between the variable t and the coordinates (x, y) in a two-dimensional plane. The equation x = sin(t) represents the x-coordinate of a point on the graph, while y = csc(t) represents the y-coordinate. The restriction 0 < t < pi ensures that the values of t lie within a specific range.

In more detail, the equation x = sin(t) indicates that the x-coordinate of a point is determined by the sine function of the corresponding value of t. The sine function oscillates between -1 and 1 as t varies, resulting in a periodic pattern for the x-values.

On the other hand, the equation y = csc(t) represents the reciprocal of the sine function, known as the cosecant function. The cosecant function is defined as the inverse of the sine function, so the y-coordinate is the reciprocal of the corresponding sine value. Since the sine function has vertical asymptotes at t = 0 and t = pi, the cosecant function has vertical asymptotes at those same points, restricting the range of y.

Together, these parametric equations describe a curve in the xy-plane that is determined by the values of t. The specific shape of the curve depends on the range of t and the behavior of the sine and cosecant functions.

To learn more about vertical asymptotes, click here:

brainly.com/question/32526892

#SPJ11

Answer:

$26,000

Step-by-step explanation:

5.6% of $25,000

=$1400

$1400+$25,000= $26,000

Time taken by Miguel car to drive is, 1.6 hour.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

Miguel went for a drive in his new car. He drove at a speed of 53 miles per hour for 84.8 miles.

We know that;

⇒ Speed = Distance / Time

⇒ Time = Distance / Speed

Here, Speed = 53 miles per hour

Distance = 84.8 miles

Hence, We get;

⇒ Time = 84.8 / 53

⇒ Time = 1.6 hour

Thus, Time taken by Miguel car to drive is, 1.6 hour.

Learn more about the divide visit:

https://brainly.com/question/28119824

#SPJ1