Which expression is equivalent to √17?

Step-by-step explanation:

Given

6 people = 180g flour

1 person = 180/6 = 30g flour

3 people = 3 x 30 = 90g flour

Answer:

x=5

Step-by-step explanation:

-5(-x - 1) + 4x – 1= 49

Distribute

5x +5 +4x -1 = 49

Combine like terms

9x +4 = 49

Subtract 4 from each side

9x+4-4 = 49-4

9x = 45

Divide by 9

9x/9 =45/9

x = 5

Answer:

\(\huge \boxed{x=5}\)

Step-by-step explanation:

\({\Large -5(-x - 1) + 4x -1= 49}\)

Expand brackets.

\(5x+5+ 4x -1= 49\)

Combine like terms.

\(9x+4=49\)

Subtract 4 from both sides.

\(9x+4-4=49-4\)

\(9x=45\)

Divide both sides by 9.

\(\displaystyle \frac{9x}{9} =\frac{45}{9}\)

\(x=5\)

Answer:

option 1

Answer:

\( \bf \: y = 2 {x}^{2} - 6x - 8\)

It is equation of a parabolla.

It is to be noted that the graph of y = 2x * 2-6x-8 which when simplified is  y = -12x² - 12x. is attached accordingly.

The graph of y = -12x² - 12x is a downward-opening parabola.

It has a concave shape and its vertex is the highest point on the graph. The axis of symmetry is a vertical line passing through the vertex.

The graph may intersect or be tangent to the x-axis at two points, one point, or no points, depending on the discriminant.

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Answer:

18.43 units

Step-by-step explanation:

132/360 cause 360 degrees in circle

π4^r=area of totoal

16π= area

16π*132/360=18.4306769011

Answer:

1.1???????

Step-by-step explanation:

Answer:Its most likely to be D

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

Ileana  have to invest for 8 years :

Simple interest is a simple and straightforward formula for figuring out how much interest will be charged on a loan. Simple interest is calculated by dividing the daily interest rate by the principle and the number of days between payments.

The principal amount must be multiplied by the time, interest rate, and time period in order to calculate simple interest. Simple Interest = Principal x Interest Rate x Time is the written formula.

Principal amount = $15,500

interest = $5,084

Time = ?

Rate = 4.1% simple interest

to find the simple interest :

                                         I = \(\frac{(p*t*r)}{100}\)

       Then:

         Time = \(\frac{I*100}{P*R}\)

                  = \(\frac{(5084*100)}{(15500*4.1)}\)

                  = \(\frac{508400}{63,550}\)

                  = 8 years

Ileana  have to invest for 8 years

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1. The test statistic falls outside the critical t-values therefore we reject the null hypothesis

2. The confidence interval is constructed as CI = x ± (t_(α/2, df) * (σ / √n))

3. The conclusion is there is sufficient evidence to suggest that the mean inside bearing diameter is different from 8.25 cm

1. Hypothesis Testing:

Null hypothesis (H₀): The mean inside bearing diameter is 8.25 cm.

Alternative hypothesis (H₁): The mean inside bearing diameter is not equal to 8.25 cm.

We will conduct a two-sided hypothesis test using a significance level (alpha) of 0.05.

Given:

Sample size (n) = 15

Sample mean (x) = 8.2535 cm

Standard deviation (σ) = 0.002 cm

To test the hypothesis, we will use a t-test since the population standard deviation is unknown and the sample size is small.

Calculate the test statistic (t-value):

t = (x - μ) / (σ / √n)

where μ is the hypothesized mean under the null hypothesis.

t = (8.2535 - 8.25) / (0.002 / √15)

t = 6.77

Calculate the critical t-values for a two-sided test at a 95% confidence level (alpha = 0.05):

Since the sample size is small (n = 15), we will use the t-distribution and degrees of freedom (df = n - 1 = 14) to find the critical t-values.

t_critical = ± t_(α/2, df)

If you look up the critical t-value for alpha/2 = 0.025 and df = 14 in the t-table or use a statistical calculator, we have 2.51

t_critical = 2.51

Compare the test statistic to the critical t-values:

Since the test statistic falls outside the critical t-values, we reject the null hypothesis.

2. Confidence Interval:

To construct a 95% confidence interval, we will use the formula:

CI = x ± (t_(α/2, df) * (σ / √n))

3. Conclusion:

Since the test statistic falls outside the critical t-values, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the mean inside bearing diameter is different from 8.25 cm.

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Answer:

r = -1

Step-by-step explanation:

-3(1+6r)=14-r

Distribute the -3

-3*1 -3*6r = 14-r

-3 -18r = 14 -r

Add 18r to each side

-3-18r+18r = 14-r+18r

-3 = 14+17r

Subtract 14 from each side

-3-14 = 14+17t-14

-17 = 17r

Divide by 17

-17/17 = -17r/-17

-1 =r

Answer:

3 : 2

Step-by-step explanation:

the ratio of jeans : skirts is

9 : 6 ( divide both parts by 3 )

= 3 : 2 ← in simplest form

The ratio of jeans to skirts is 3:2

This can be found by dividing the number of jeans by the number of skirts

The line's image in an equation form is y = 3x - 1.

In Mathematics and Geometry, a dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.

Next, we would write the coordinate rule that represent the dilation by using a scale factor of 2 centered at the point P (3, 8) by using this mathematical equation:

(x, y)  →  (k(x - a) + a, k(y - b) + b)

(x, y)  →  (2(x - 3) + 3, 2(y - 8) + 8)

Since the pre-image y = 3x - 1 is centered at the point P (3, 8), the equivalent y-coordinate can be calculated as follows;

y = 3(3) - 1

y = 9 - 1

y = 8 (True).

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Answer:

2*(4y² + 9)

Step-by-step explanation:

    8y² = 2 * 2 * 2 * y²

    18   = 2 * 3 * 3

GCF = 2

8y² + 18 = 2* 4y² + 2*9

             = 2*(4y² + 9)

Answer:

x = 3; y = 2

Step-by-step explanation:

You would just set each side equal to its opposite so for x, it'll be like:

4x+6=7x-3

and for y:

4y-3=3y+1

I attached my work below as well to help you.

The general solution of the differential equation is:

y = Ax^-5 + Bx^-5ln(x)

where A and B are constants determined by the initial or boundary conditions.

To solve the differential equation x^2y'' + 11xy' + 25y = 0, we can assume the solution to be of the form y = x^r, where r is a constant.

Then, we have:

y' = rx^(r-1)

y'' = r(r-1)x^(r-2)

Substituting these into the differential equation, we get:

x^2y'' + 11xy' + 25y = x^2r(r-1)x^(r-2) + 11xrx^(r-1) + 25x^r = 0

Dividing both sides by x^2, we have:

r(r-1) + 11r + 25 = 0

Simplifying, we get:

r^2 + 10r + 25 = (r+5)^2 = 0

Therefore, r = -5.

Thus, the general solution of the differential equation is:

y = Ax^-5 + Bx^-5ln(x)

where A and B are constants determined by the initial or boundary conditions.

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The quarter mile grounding rule for rural electric utilities for direct-buried jacketed distribution cables says that they must have at least 4 grounds per mile.

A utility cooperative is a specific kind of cooperative that is responsible for providing its members with a public utility, such as power, water, or telecommunications. Profits are either distributed to members as "patronage" or "capital credits," which are dividends paid on a member's investment in the cooperative, or they are reinvested for infrastructure. 

Every consumer is a shareholder and a member of the company. This means that, in contrast to investor-owned utilities where the amount of individual authority is determined by the number of shares held, all members have the same level of personal authority. Many utility cooperatives operate their business in accordance with a set of ideals based on the Rochdale Principles, just like cooperatives active in other industries.

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Answer:

I'm pretty sure it's c like 80% sure not certain though, the x value should shift left 7 so more then likely C

The total cost function considers the costs of labor and capital, the supply function determines the quantity supplied based on the production function, the profit function calculates the difference between revenue and cost, and the demand function for capital reflects the equilibrium between the marginal product of capital and the rental rate.

a. The total cost function (C) for this firm can be calculated by multiplying the cost of labor (w) with the number of hours of labor (L) and adding it to the cost of capital (r) multiplied by the quantity of capital (K).

So, C = wL + rK.

b. The supply function (MC) for assembled calculators [q(P,v)] can be found by taking the derivative of the production function with respect to q. In this case, MC = ∂q/∂k * ∂k/∂P.

To find q, you will need to substitute the given value of P and v into the production function.

c. The profit function (π) for this firm, stated as a function of the parameters "P" and "v", can be calculated by subtracting the total cost (C) from the revenue (P*q).

So, π = P*q - C.

d. The demand function for capital (k) can be obtained by equating the marginal product of capital (∂q/∂k) to the rental rate (v).

Solve for k to find the demand function for k.

e. The above functions (C, MC, π, k) have the form they do because they are derived from economic principles such as cost minimization, profit maximization, and the marginal productivity of inputs.

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The simplified expression is 2(x-2)(x-1) / (x+1).

To simplify the expression (2x-4)(x-1)/(x-3)(x+1)(x-3), we can cancel out common factors and simplify further.

First, let's cancel out common factors between the numerator and the denominator:

(2x-4)(x-1) / (x-3)(x+1)(x-3)

The numerator (2x-4) can be factored out to 2(x-2), and the denominator (x-3)(x-3) can be written as (x-3)^2:

2(x-2)(x-1) / (x-3)^2(x+1)

Now, we can check for any additional common factors that can be canceled out. The (x-3) term appears in both the numerator and the denominator, so we can cancel it out:

2(x-2)(x-1) / (x-3)(x+1)

After canceling out the common factor (x-3), we are left with:

2(x-2)(x-1) / (x+1)

Therefore, the simplified expression is 2(x-2)(x-1) / (x+1).

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Answer:

Shown below.

Step-by-step explanation:

Test Marks          Tally          Frequency          Percentage

1                                                    8                   8/60 = 0.133

2                                                   6                   6/60 = 0.100

3                                                   5                   5/60 = 0.083

4                                                   5                   5/60 = 0.083

5                                                   5                   5/60 = 0.083

6                                                   8                   8/60 = 0.133

7                                                   6                   6/60 = 0.100

8                                                   7                   7/60 = 0.116

9                                                   4                   4/60 = 0.066

10                                                 5                   5/60 = 0.083

Total                                            59                 59/60 = 0.983

For the Tally section, I believe you just fill in tally marks corresponding to the frequency. One of the observations in the table is 0, which is not a column in the frequency table.

Data on graduation rates among athletes at Division I universities indicates that there are varying rates of graduation among student-athletes.

Graduation rates among athletes at Division I universities can depend on various factors such as the sport, academic support programs, and individual commitment to academic success. It is important to note that not all student-athletes may graduate within the traditional four-year timeframe due to athletic commitments and other factors. Some athletes may choose to leave early to pursue professional sports careers or transfer to different universities.

However, universities generally prioritize the academic success of their athletes and provide resources such as tutoring, study halls, and academic advisors to support them. Additionally, the National Collegiate Athletic Association (NCAA) sets academic eligibility standards for student-athletes to ensure they make progress toward graduation. Overall, while there may be variation, Division I universities typically strive to support and promote the graduation of their student-athletes.

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a. The formula that expresses Jacob's horizontal distance to the right of the center of the track in meters, h, in terms of θ is h = r * cos(θ), where r is the radius of the track.

b. The formula that expresses Jacob's vertical distance above the center of the track in meters, v, in terms of θ is v = r * sin(θ), where r is the radius of the track.

In circular motion, we can use trigonometric functions to determine the horizontal and vertical distances traveled by an object at a specific angle θ.

a. The horizontal distance, h, can be calculated using the cosine function. The horizontal component of Jacob's position is given by h = r * cos(θ), where r is the radius of the circular track. Since Jacob starts at the 3-o'clock position, which is to the right of the center, the cosine function is used to determine the horizontal displacement to the right.

b. The vertical distance, v, can be calculated using the sine function. The vertical component of Jacob's position is given by v = r * sin(θ), where r is the radius of the circular track. The sine function is used because we want to measure the vertical displacement above the center of the track.

The formulas for Jacob's horizontal and vertical distances in terms of θ are h = r * cos(θ) and v = r * sin(θ), respectively. These formulas allow us to calculate the specific coordinates of Jacob's position at any angle θ as he runs along the circular track with a radius of 51 meters.

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Answer:

z = 4.1

Step-by-step explanation:

(4.1 + 1.1)

(5.2)

4(5.2) = 20.8

The provided information appears to be a citation for a research paper titled "Annotation Artifacts in Natural Language Inference Data" by Suchin Gururangan, Swabha Swayamdipta, Omer Levy, Roy Schwartz, Samuel R. Bowman, and Noah A. Smith. The paper was published as an arXiv preprint with the identifier arXiv:1803.02324.

The given citation refers to a research paper titled "Annotation Artifacts in Natural Language Inference Data" published in 2018.

The research paper, authored by Suchin Gururangan, Swabha Swayamdipta, Omer Levy, Roy Schwartz, Samuel R. Bowman, and Noah A. Smith, addresses the issue of annotation artifacts in natural language inference data. Natural language inference (NLI) is a task in natural language processing that involves determining the logical relationship between pairs of sentences, such as whether one sentence contradicts or entails the other.

Annotation artifacts refer to systematic biases or inconsistencies in the process of annotating NLI data, which can impact the performance of NLI models. The authors of the paper investigate and analyze these artifacts, aiming to understand their prevalence and impact on NLI performance.

In the paper, the authors propose a new methodology called "stress test evaluation" to identify and quantify annotation artifacts. They conduct experiments on large-scale NLI datasets and observe that the presence of these artifacts significantly affects the behavior of state-of-the-art NLI models.

The research paper contributes to the field of natural language processing by shedding light on the challenges posed by annotation artifacts in NLI data and providing insights for improving NLI models and datasets. The citation provided allows others to access and refer to this research paper for further study and exploration of the topic.

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Answer:

To draw a right triangle with a tangent ratio of 3/2 for one of the acute angles, we can choose any angle whose tangent is 3/2. Let's choose the angle θ.

We know that:

tangent ratio = opposite side / adjacent side

So, we can assign any value we want to the adjacent side, and then calculate the opposite side. Let's say the adjacent side is 2 units. Then, the opposite side would be:

opposite side = tangent ratio * adjacent side = (3/2) * 2 = 3

So, the sides of the triangle are:

adjacent side = 2

opposite side = 3

hypotenuse = √(2^2 + 3^2) = √13

We can now use trigonometry to find the measure of the other acute angle. The tangent of an angle is equal to the opposite side over the adjacent side, so we have:

tan(θ) = opposite side / adjacent side

tan(θ) = 3/2

Taking the inverse tangent of both sides, we get:

θ = tan^(-1)(3/2)

θ ≈ 56.3°

So, the other acute angle of the right triangle is approximately 56.3 degrees.

A plasmid used in both yeast and bacteria requires two different selection markers because the same selection may not work for both hosts and bacteria and yeast recognize different promoters.

When using a plasmid in both yeast and bacteria, it is important to have two different selection markers for several reasons. First, the same selection, such as the presence of an antibiotic, may not be effective in both hosts. Different organisms have varying sensitivities to antibiotics, so a marker that works in bacteria may not work in yeast or vice versa. Therefore, two different selection markers are needed to ensure successful selection in both hosts.

Additionally, bacteria and yeast recognize different promoters, which are DNA sequences that control the initiation of gene expression. Promoters are specific to each organism and play a crucial role in regulating gene expression. By incorporating two different selection markers into the plasmid, each marker can be driven by a promoter recognized specifically by the corresponding host. This ensures that the selection marker is effectively expressed in the appropriate host organism, enabling accurate selection and maintenance of the plasmid.

In summary, using two different selection markers in a plasmid intended for both yeast and bacteria is necessary because the same selection may not be effective in both hosts, and different promoters are recognized by bacteria and yeast. This approach allows for successful selection and maintenance of the plasmid in both organisms.

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At r = 10 cm and h = 20 cm, the cone's volume is growing at a rate of 1047 cm³/s.

The following formula determines the cone's volume:

V = 1/ 3 πr²h

In which r and h are specified in cm, whereas V is given in cm³.

Assume that a circular cone's height h and radius r are both rising at a speed of 2 cm/s.

This indicates that; the rate of change of volume

dh/dt = dr/dt = 2 cm/s.

Increasing the cone's volume at r = 10 cm and h = 20 cm.

dV/dt for r = 10 cm and h = 20 cm.

V = 1/ 3 πr²h

Implicit distinction in use:

V, r, and h are the three variables we have. So

dV/dt = (1/3) [2r.(dr/dt).hπ + r²π(dh/dt)]

dV/dt = (1/3) [2(10).(2).(20)π + (10)²π(2)]

dV/dt = 1047 cm³/s

At r = 10 cm and h = 20 cm, the cone's volume is growing at a rate of 1047 cm³/s.

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Answer:

f(x) = x^2 + 3x + 2.

Step-by-step explanation:

The zeroes of the quadratic function are -1 and -2 so we can write it as:

f(x) = a(x + 1)(x + 2)    where  a is some constant.

Now, when x = 1,  f(x) = 6 so

6 = a(1+1)(1+2)

6 = a*2*3 = 6a

a = 1.

So the function is f(x) = (x + 1)(x + 2) = x^2 + 3x + 2.