Abigail poured 8 x 10 milliliters of water into a beaker to use for an experiment. How is 8 x 10 written as a whole number?
​

Answer:

m = -5

n = -2

Step-by-step explanation:

5m + 6n = -37

10m + 4n = -58 multiply first equation by -2

-2 × 5m + 6n = -37

-10m + (-12n) = 74 now add two equations up

10m - 10m + 4n - 12n = 74 - 58 add/ subtract like terms

-8n = 16 divide both sides by -8

n = -2

to find the value of m, replace n with -2 in the first equation

5m + 6*(-2) = -37

5m - 12 = -37 add 12 to both sides

5m = -25 divide both sides by 5

m = -5

When ΔG° > 0, the response is non-spontaneous. Therefore, an equilibrium mixture contains more reactants than products. Therefore, the value of the equilibrium constant is less than 1.

Reactant Favoured:

A reaction favorable to the product is a reaction that proceeds spontaneously in the forward direction when all concentrations (or partial pressures) have a standard state value of 1 M (or 1 bar). If Kc > 1, the product concentration is greater than the reactant concentration at equilibrium.

Product Favoured:

The equilibrium constant expression is a mathematical relationship that shows how product concentrations vary with reactant concentrations. If the value of K is greater than 1, the reaction product is favored. If the K value is less than 1, it is favorable for the reactants in the reaction.

Now,

When ΔG° > 0, the response is non-spontaneous. Therefore, an equilibrium mixture contains more reactants than products. Therefore, the value of the equilibrium constant is less than 1.

A spontaneous reaction is a reaction in which the conditions under which the reaction occurs favor the formation of the product. A non-spontaneous reaction is a reaction in which the formation of product is not favored under the given conditions. For a reaction to be non-spontaneous, one or both driving forces must favor the reactants over the products.

Learn more about Constant:

https://brainly.com/question/17367653

#SPJ4

1. The number of students that the art academy has per teacher is 16.

2. The number of students that the art academy has per tutor is 9.

3. With 108 students, the art academy requires 12 tutors, given the student-to-tutor ratio of 9:1.

In this situation, we can use the mathematical operation of division to state the ratio of students to either teachers or tutors.

The parts of the division operation include the dividend, the divisor, and the quotient, which is the result of applying the divisor to the dividend.

The number of teachers for 80 students = 5

1. The number of students per teacher = 16 students (80/5)

The number of tutors for 36 students = 4

2. The number of students per tutor = 9 students (36/4)

3. If the students are 108, the number of tutors = 12 tutors (108/9)

Thus, after determining the quotients, we can relate the number of students to teachers and tutors using ratios.

Learn more about mathematical operations at https://brainly.com/question/20628271

#SPJ1

An arts academy requires there to be 5 teachers for every 80 students and 4 tutors for every 36 students.

Answer:

The answer is 0.01201778632

Step-by-step explanation:

To write our number as a fraction, the order of the steps is:

First, we define our number:

x = 0.1717...

So we start with the step 3.

Now notice that there are two repeating decimals, so we need to multiply both sides by 100 (as many zeros as repeating decimals)

100*x = 10*0.1717... = 17.1717...

This is step 5.

Now we can subtract the original number in both sides so we remove the repeating decimals:

100*x - 0.1717... = 17.1717... - 0.1717...

99*x = 17

These are steps 4 and 2.

Finally, we divide both sides by 99 to get:

x = 17/99

Which is step 1.

And that is our number written as a fraction.

Learn more about repeating decimals:

https://brainly.com/question/22063097

#SPJ1

The account balance after 3 years with continuous compounding at an interest rate of 3% will be approximately $5,142.62.

The formula accrued amount compounded continuously is expressed as;

\(A = P\ *\ e^{rt}\)

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given that:

Principal P = $4,700

Compounded contiously

Time t = 3 years

Interest rate r = 3%

Accrued amount A = ?

First, convert rate R as a percent to r as a decimal

r = R/100

r = 3/100

r = 0.03

Plug these values into the above formula and solve for accrued amount.

\(A = P\ *\ e^{rt}\\\\A = 4,700\ *\ e^{(0.03\ *\ 3) }\\\\A = 4,700\ *\ e^{(0.09) }\\\\A = 5,142.62\)

Therefore, the accrued amount is $5,142.62.

Option A) $5,142.62 is the correct answer.

Learn more about compound interest here: brainly.com/question/27128740

#SPJ1

Answer:

Pythagorean Theorem = a^2 + b^2= c^2

Step-by-step explanation:

(3)^2+ (4)^2 = C

3^2= 9

4^2= 16

9+16=25

(2 legs no hypotenuse)

9^2+ b^2=7^2

9^2 = 81

7^2= 49

81-49= 32

(you have to sqaure root it because the oppsite of sqaured is sqaured root)

32 squared = 5.657

and rounded is 5.7

Answer: the common ratio (r) is -2/5, |r| is less than 1, and the sum of the given series Σn=2^n/(-5)^n+1 is -4/175.

Step-by-step explanation:

In the given geometric series Σn=2^n/(-5)^(n+1), we can determine the common ratio (r) and the condition for convergence by analyzing the ratio of consecutive terms.

The general form of a geometric series is Σn=0 to ∞ ar^n, where a is the first term and r is the common ratio.

Comparing the given series to the general form, we have:

a = 2^2/(-5)^3 = 4/(-125) = -4/125

To find the common ratio (r), we divide the (n+1)th term by the nth term:

r = (2^(n+1))/(-5)^(n+2) divided by 2^n/(-5)^(n+1)

= (2^(n+1))*((-5)^(n+1))/((-5)^(n+2))*2^n

= 2/(-5)

= -2/5

To ensure convergence, we need the absolute value of the common ratio (|r|) to be less than 1.

|r| = |-2/5| = 2/5 < 1

Since |r| is less than 1, the given series Σn=2^n/(-5)^n+1 converges.

To determine the sum of the series, we use the formula for the sum of an infinite geometric series:

Sum = a/(1 - r)

Plugging in the values, we have:

Sum = (-4/125)/(1 - (-2/5))

= (-4/125)/(1 + 2/5)

= (-4/125)/(5/5 + 2/5)

= (-4/125)/(7/5)

= (-4/125) * (5/7)

= -20/875

= -4/175

Raja is junk seller. He sells many things. Here is given the list of junk.

Check the Raja's rate list and solve the following questions.

\(\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered} \small\boxed{\begin{array}{c|c} \bf{Kind \: of\:junk} & \bf{Price \: of \: 1 \: kg } \\ \dfrac{\qquad\qquad\qquad}{ \sf News \: Paper} &\dfrac{\qquad \qquad\qquad}{ \sf Rs.5} & \\ \dfrac{\qquad\qquad\qquad}{ \sf Iron} &\dfrac{\qquad\qquad\qquad}{ \sf Rs.10} & \\ \dfrac{\qquad\qquad\qquad}{ \sf Brass} &\dfrac{\qquad\qquad\qquad}{ \sf Rs.50} & \\ \dfrac{\qquad\qquad\qquad}{ \sf Plastic} &\dfrac{\qquad\qquad\qquad}{ \sf Rs.8}&\end{array}} \end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\)

1. How much money will you pay to Raju for 20 kg of newspapers?

\(\quad{\longrightarrow{\sf{Cost \: of \: 1 \: kg \: newspaper = Rs.5}}}\)

\(\quad{\longrightarrow{\sf{Cost \: of \: 20 \: kg \: newspaper = Rs.20 \times 5}}}\)

\(\quad{\longrightarrow{\sf{Cost \: of \: 20 \: kg \: newspaper = Rs.100}}}\)

\(\quad{\longrightarrow{\underline{\boxed{\sf{\purple{Cost \: of \: 20 \: kg \: newspaper = Rs.100}}}}}}\)

∴ We need to pay Rs.100 for buy 20 kg of newspapers.

\(\rule{200}{1.5}\)

2. What is the cost of 5 kg Iron?

\(\quad{\longrightarrow{\sf{Cost\: of \: 1 \: kg \: iron = Rs.10}}}\)

\(\quad{\longrightarrow{\sf{Cost\: of \: 5 \: kg \: iron = Rs.10 \times 5}}}\)

\(\quad{\longrightarrow{\sf{Cost \: of \: 5 \: kg \: iron = Rs.50}}}\)

\(\quad{\longrightarrow\underline{\boxed{\sf{\purple{Cost \: of \: 5 \: kg \: iron = Rs.50}}}}}\)

∴ The cost of 5 kg iron is Rs.50.

\(\rule{200}{1.5}\)

3. What is the cost of 9 kg Plastic?

\(\quad{\longrightarrow{\sf{Cost \: of \: 1 \: kg \: plastic = Rs.8}}}\)

\(\quad{\longrightarrow{\sf{Cost \: of \: 9 \: kg \: plastic = Rs.8 \times 9}}}\)

\(\quad{\longrightarrow{\sf{Cost \: of \: 9 \: kg \: plastic = Rs.72}}}\)

\(\quad{\longrightarrow\underline{\boxed{\sf{\purple{Cost\: of \: 9 \: kg \: plastic = Rs.72}}}}}\)

∴ The cost of 9 kg plastic is Rs.72.

\(\rule{200}{1.5}\)

4. What is the cost of 7 kg Brass?

\(\quad{\longrightarrow{\sf{Cost \: of \: 1 \: kg \: brass = Rs.50}}}\)

\(\quad{\longrightarrow{\sf{Cost\: of \: 7 \: kg \: brass = Rs.50 \times 7}}}\)

\(\quad{\longrightarrow{\sf{Cost \: of \: 7 \: kg \: brass = Rs.350}}}\)

\(\quad{\longrightarrow\underline{\boxed{\sf{\purple{Cost \: of \: 5 \: kg \: brass = Rs.350}}}}}\)

∴ The cost of 7kg brass is Rs.350.

\(\underline{\rule{200pt}{2pt}}\)

The Rosenbrock function has a gradient of (-400(x₂ - x₁²)x₁ - 2(1 – x₁), 200(x₂ - x₁²)) and a Hessian matrix of [[1200, -400], [-400, 200]]. The point (1, 1) is the only local minimizer and the Hessian is positive definite.


To compute the gradient ∇F of the Rosenbrock function F(x) and the Hessian matrix H, let’s start by differentiating F(x) with respect to each component of x.
The Rosenbrock function is defined as:
F(x) = 100(x₂ - x₁²)² + (1 – x₁)²
Where x = (x₁, x₂)ᵀ.
Now, let’s compute the gradient:
∇F = (∂F/∂x₁, ∂F/∂x₂)
To find ∂F/∂x₁, we differentiate each term of F(x) with respect to x₁:
∂F/∂x₁ = ∂/∂x₁ [100(x₂ - x₁²)²] + ∂/∂x₁ [(1 – x₁)²]
Applying the chain rule and simplifying:
∂F/∂x₁ = -400(x₂ - x₁²)x₁ - 2(1 – x₁)
Similarly, to find ∂F/∂x₂, we differentiate each term of F(x) with respect to x₂:
∂F/∂x₂ = ∂/∂x₂ [100(x₂ - x₁²)²]
Applying the chain rule and simplifying:
∂F/∂x₂ = 200(x₂ - x₁²)
Therefore, the gradient ∇F is:
∇F = (-400(x₂ - x₁²)x₁ - 2(1 – x₁), 200(x₂ - x₁²))
Now, let’s compute the Hessian matrix H, which is the matrix of second-order partial derivatives of F:
H = [[∂²F/∂x₁², ∂²F/∂x₁∂x₂],
    [∂²F/∂x₂∂x₁, ∂²F/∂x₂²]]
To find the second-order partial derivatives, we differentiate each component of the gradient ∇F with respect to x₁ and x₂:
∂²F/∂x₁² = -400(x₂ - 3x₁²) + 800x₁² - 2
∂²F/∂x₁∂x₂ = -400x₁
∂²F/∂x₂∂x₁ = -400x₁
∂²F/∂x₂² = 200
Hence, the Hessian matrix H is:
H = [[-400(x₂ - 3x₁²) + 800x₁² - 2, -400x₁],
    [-400x₁, 200]]
To show that x* = (1, 1)ᵀ is the only local minimizer, we need to check the definiteness of the Hessian matrix at this point.
Substituting x₁ = 1 and x₂ = 1 into the Hessian matrix H:
H(1, 1) = [[-400(1 – 3) + 800 – 2, -400],
          [-400, 200]]
Simplifying:
H(1, 1) = [[1200, -400],
          [-400, 200]]
The Hessian matrix at x* = (1, 1)ᵀ is positive definite because all of its eigenvalues are positive.
Therefore, x* = (1, 1)ᵀ is the only local minimizer of the Rosenbrock function, and the Hessian matrix at this point is positive definite.

Learn more about Rosenbrock function here: brainly.com/question/13992332
#SPJ11

To investigate whether there is an association between cell phone brand and age-group, the researcher can conduct a chi-squared test of independence.

This test compares the observed frequencies in the contingency table to the expected frequencies if there were no association between the variables. If the test results in a p-value less than the chosen significance level (usually 0.05), then the researcher can reject the null hypothesis of no association and conclude that there is evidence of an association between cell phone brand and age-group. The degrees of freedom for this test would be (3-1) * (4-1) = 6.

More on chi-squared test: https://brainly.com/question/30696573

#SPJ11

Answer:1000

Step-by-step explanation:what about 1000 people

Answer:

Step-by-step explanation:

Given equation:

Make c the subject:

Divide all terms by 0.9:

Now make r the subject:

Divide all terms by 1.89:

Confirmed that both equations are equivalent with the initial one.

These are helpful when finding one of the variables if the value of another variable is given.

Answer:. r = - 10/21 c + 9

Step-by-step explanation:

Answer:

8X

Step-by-step explanation:

it says the product, which is multiplication

of a number (lets call it X) and 8

so its 8*X

Answer:

8x

Step-by-step explanation:

it says the product, which is basically multiplication  of a number (which lets call X) and 8

so its 8*X

HOPE I HELPED

PLS MARK BRAINLIEST  

DESPERATELY TRYING TO LEVEL UP

✌ -ZYLYNN JADE ARDENNE

JUST A RANDOM GIRL WANTING TO HELP PEOPLE!

                      PEACE!

When the patient recovery time from a specific surgical procedure is normally distributed, with a mean of 5.2 days and a standard deviation of 2.3 days, the probability of spending more than 2 days in recovery will be 0.61.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. Information about the likelihood that something will happen is provided by probability. For instance, meteorologists use weather patterns to forecast the likelihood of rain. Probability theory is used in epidemiology to comprehend the connection between exposures and the risk of health effects.

Here,

z=(X-μ)/σ

X=2

μ=5.2

σ=2.3

Z=(2-5.2)/2.3

Z=-1.39

-1.39+1

=0.39

1-0.39=0.61

The probability of spending more than 2 days in recovery will be 0.61 when the patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.2 days and a standard deviation of 2.3 days.

To know more about probability,

https://brainly.com/question/11234923?referrer=searchResults

#SPJ4

The given equation solved for z is z = s/(r - 6c⁴)

From the questions, we are to solve the given equation for the specified value

The given equation is

s = zr - 6zc⁴

The specified value is z.

Thus, we are to solve for z.

Solving for z

s = zr - 6zc⁴

First, factor out z

s = z(r - 6c⁴)

Now, divide both sides by r - 6c⁴

s/(r - 6c⁴) = z(r - 6c⁴)/r - 6c⁴

s/(r - 6c⁴) = z

∴ z = s/(r - 6c⁴)

Hence, the given equation solved for z is z = s/(r - 6c⁴)

Learns more on Solving equations here: https://brainly.com/question/19041791

#SPJ1

(L2) An inscribed circle is one that encompasses a polygon so that it passes by each of the polygon's vertices.

A circumcircle, not an inscribed circle, is a circle that encircles a polygon at each vertex. A circle that is enclosed within a polygon and intersects each side of the polygon exactly once is said to be inscribed. A circumcircle, on the other hand, is a circle that goes through every vertex of the polygon, with its center located at the point where the perpendicular bisectors of the polygon's sides converge. The greatest circle that can be drawn within a polygon is the circumcircle, while the largest circle that can be drawn inside a triangle is the inscribed circle.

Learn more about polygon

https://brainly.com/question/24464711

#SPJ4

Answer:

yes

Step-by-step explanation:  

25=x he can hear the players voice because if it wasent talking loud it would be impossible to hear it would sound like whispering

Answer:

Step-by-step explanation:

Here it is

Answer:

y = 2w - 1 + aw

Step-by-step explanation:

Given

y - aw = 2w - 1 ( isolate y by adding aw to both sides )

y = aw - 1 + aw

Answer:

Step-by-step explanation:

25, 000 = 5,000 + 600n

Answer:

the thalia age be 19 years

Step-by-step explanation:

Let us assume her brother age be x

Now the thalia age be x - 3

Now the equation would be

x + x - 3 = 41

2x = 41 + 3

2x = 44

x = 22

thalia age be

= 22 - 3

= 19

Hence, the thalia age be 19 years

And, her brother age be 22 years

The same is to be considered

The statement to prove is that PQ is the shortest segment from point P to plane M when PQ is perpendicular to plane M.

To prove that PQ is the shortest segment from point P to plane M, we can use the concept of perpendicularity. When PQ is perpendicular to plane M, it forms a right angle with the plane.

In Euclidean geometry, it is known that the shortest distance between a point and a plane is along the line perpendicular to the plane passing through the point.

Therefore, since PQ is perpendicular to plane M, it follows that PQ is the shortest segment from point P to plane M. This can be mathematically proven using the principles of geometry and the definition of perpendicularity.

Learn more about Euclidean geometry here :

brainly.com/question/31120908

#SPJ11

The correct option a.) 0.70, the z test statistic for the given sample distribution rounded to the hundredths place.

The formula given for z test;

z = p' - p/√(pq/n)

p' = sample proportion

p = Number of infested samples(trees)/ Number of samples

p' = 127/1000 = 0.127

p = 12%

p = 0.12

q = 1 - 0.12

q = 0.88

n is umber of samples = 1000

Then,

z = 0.127 - 0.12/√(0.88 × 0.12/1000)

z = 0.007/√0.0001056

z = 0.007 /0.0102761861

z = 0.6811865737

z = 0.70 (rounded to the hundredths place.)

Thus, the z test statistic for the given sample distribution rounded to the hundredths place  is 0.70.

To know more about the z-test statistic, here

https://brainly.com/question/14453510

#SPJ4

To simplify the difference quotient expression for f(x) = 3x^2 – 7, we first need to plug in f(x+h) and f(x) into the expression and simplify it.

Let's start by finding f(x+h): f(x+h) = 3(x+h)^2 – 7 = 3(x^2 + 2xh + h^2) – 7 = 3x^2 + 6xh + 3h^2 – 7 Now, let's plug in f(x) and f(x+h) into the difference quotient expression and simplify: [f(x+h) - f(x)]/h = [(3x^2 + 6xh + 3h^2 – 7) - (3x^2 - 7)]/h = [3x^2 + 6xh + 3h^2 - 7 - 3x^2 + 7]/h = (6xh + 3h^2)/h = 6x + 3h So the simplified difference quotient expression is 6x + 3h.

Now we can plug this into the difference quotient expression: [(f(x+h) - f(x))/h] = [(3(x^2 + 2xh + h^2) - 7 - (3x^2 - 7))/h] Simplify the expression: = [(3x^2 + 6xh + 3h^2 - 7 - 3x^2 + 7)/h] = [(6xh + 3h^2)/h] Now, divide by h: = 6x + 3h The simplified difference quotient expression is 6x + 3h.

To know more about divide click here

brainly.com/question/29189189

#SPJ11

The mean cooking time for a random sample of 16 orders is less than 7.0 minutes is 0.4356.

The z-score can be calculated as follows:

\(z = (x - μ) / σ\)

Where x is the mean cooking time, μ is the population mean cooking time, and σ is the population standard deviation.

For the given problem, x = 7.0, μ = 7.7, and σ = 2.1. Therefore,

\(z = (7.0 - 7.7) / 2.1 = -0.3 / 2.1 = -0.1428\)

Therefore, the probability that the mean cooking time for a random sample of 16 orders is less than 7.0 minutes is equal to the probability of a z-score less than -0.1428. This probability can be found using the z-table and is equal to 0.4356.

Thus, the probability that the mean cooking time for a random sample of 16 orders is less than 7.0 minutes is 0.4356. This can be interpreted as follows: 43.56% of the time, the mean cooking time of a random sample of 16 orders at the restaurant during the lunch hour will be less than 7.0 minutes.

Learn more about Probability here :

https://brainly.com/question/11092946

#SPJ4

The missing side lengths in the right triangle include the following:

a) c = 2√41 units.

b) a = 2√7 units.

c) b = 4 units.

d) c = 50 units.

In Mathematics and Geometry, Pythagorean's theorem is represented by the following mathematical equation (formula):

c² = a² + b²

Where:

a, b, and c represents the length of sides or side lengths of any right-angled triangle.

Part a.

Based on the information provided about the side lengths of this right-angled triangle, we have the following equation:

c² = a² + b²

c² = 8² + 10²

c² = 64 + 100

c = √164

c = 2√41 units.

Part b.

c² = a² + b²

a² = c² - b²

a² = 8² - 6²

a² = 64 - 36

a = √28

a = 2√7 units.

Part c.

c² = a² + a²

b² = c² - a²

b² = 5² - 3²

b² = 25 - 9

b = √16

b = 4 units.

Part d.

c² = a² + b²

c² = 30² + 40²

c² = 900 + 1600

c = √2500

c = 50 units.

Read more on Pythagorean theorem here: brainly.com/question/15430861

#SPJ1