Structure of an unknown atom 2. 5. What is the symbol of this atom and the charge of the nucleus?

The expression – 0. 75p can be simplified to -0.75p.

This means Harriet can find the new price of an item by finding 25% of the original price.What is the meaning of the terms mentioned in the question?Clearance rack has items for 75% off

This implies that if an item is marked for $1, it can be bought for $0.25.

Thus, the amount reduced is $0.75.

So, Harriet uses the expression -0.75 to find the new price of an item that originally costs dollars.-0.75p means that the amount is reduced by 75% of the original price p.

When we subtract 75% from 100%, we get 25%.

Hence, Harriet can find the new price of an item by finding 25% of the original price which is 0.25p or 25% of p. Answer: The expression – 0. 75p can be simplified to -0.75p. This means Harriet can find the new price of an item by finding 25% of the original price.

To know more about simplified, visit:

https://brainly.com/question/17579585

#SPJ11

S is transitive. Since S is reflexive, symmetric, and transitive, it is an equivalence relation.

To prove that S is an equivalence relation, we need to show that it satisfies three conditions: reflexivity, symmetry, and transitivity.

Reflexivity: For any ordered pair (a, b), we have a + b = b + a. So, (a, b) S (a, b), and S is reflexive.

Symmetry: If (a, b) S (c, d), then a + d = b + c. Rearranging this equation gives us d + a = c + b, which implies that (c, d) S (a, b). Therefore, S is symmetric.

Transitivity: If (a, b) S (c, d) and (c, d) S (e, f), then we have a + d = b + c and c + f = d + e. Adding these two equations gives us a + 2d + f = b + 2c + e. Rearranging this equation, we get (a, b) S (e, f). Hence, S is transitive.

Since S is reflexive, symmetric, and transitive, it is an equivalence relation.

Learn more about transitive here

https://brainly.com/question/24606230

#SPJ11

[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{"y" varies inversely with "x"}}{y = \cfrac{k}{x}}\hspace{5em}\textit{we also know that} \begin{cases} x=3\\ y=3 \end{cases} \\\\\\ 3=\cfrac{k}{3}\implies 9 = k\hspace{9em}\boxed{y=\cfrac{9}{x}} \\\\\\ \textit{when x = 4, what's "y"?}\qquad y=\cfrac{9}{4}\implies y=2\frac{1}{4}[/tex]

When x = 4, y = 9/4. y will be equal to 9/4 or 2.25.

When a variable y varies inversely as x, it means that their product remains constant. We can represent this relationship mathematically as y = k/x, where k is the constant of variation.

To find the value of k, we can substitute the given values into the equation. Given that

y = 3 when x = 3,

we can write the equation as follows:

3 = k/3

To solve for k, we can multiply both sides of the equation by 3:

9 = k

Now that we have determined the value of k, we can use it to find y when x = 4. Substituting the values into the equation:

y = 9/4

Therefore, when x = 4, y = 9/4. Thus, y is equal to 9/4 or 2.25.

For more such answers on the Constant of variations

https://brainly.com/question/25215474

#SPJ8

Rounding to the nearest integer, the predicted calorie count for a cereal with 14 grams of sugar per serving is approximately 163 calories.

An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers. In the language of mathematics,

To calculate the predicted calorie count for a cereal with 14 grams of sugar per serving using the predictive regression equation y^ = 94.639 + 4.918x, we substitute x = 14 into the equation.

y^ = 94.639 + 4.918(14)

y^ = 94.639 + 68.852

y^ ≈ 163.491

Know more about integer here:

https://brainly.com/question/15276410

#SPJ11

The given information is :In ΔPQR, the measure of ∠R=90°, the measure of ∠Q=7°, and PQ = 9.4 feet.

We need to Find the length of QR to the nearest tenth of a foot.To solve the given problem, we will use trigonometric ratios as we have one angle and one side. From the diagram, we can write trigonometric ratio as: [tex]tan 7 = QR / PQTan 7 can be written as follows :tan 7 = (QR / PQ)tan 7 = (QR / 9.4)[/tex]Now, let's multiply both sides by 9.4,tan 7 × 9.4 = QRSolving the above equation for QRQR = 1.28 ft.Hence, the length of QR to the nearest tenth of a foot is 1.3 feet.

To know more about the word measure visits :

https://brainly.com/question/28913275

#SPJ11

Answer:

total number of votes = 6,492

Step-by-step explanation:

We are given that the ratio of yes to no votes is 7 to 5

This means
[tex]\dfrac{\text{ number of yes votes}}{\text{ number of no votes}}} = \dfrac{7}{5}[/tex]

Number of no votes = 2705

Therefore
[tex]\dfrac{\text{ number of yes votes}}{2705}} = \dfrac{7}{5}[/tex]

[tex]\text{number of yes votes = } 2705 \times \dfrac{7}{5}\\= 3787[/tex]

Total number of votes = 3787 + 2705 = 6,492

Answer:

Step-by-step explanation:

Here is a "tree diagram" for this problem. The fractions in parentheses give the probabilities a bead of the indicated color being drawn at each stage. For example, the figure (2/5) after "Red" in the "First Draw" column comes from the fact that at this stage there are 2 red beads out of 5 beads all together in the jar. The figure (1/4) in the top box in the "Second Draw" column comes from the fact that now, after one red has been removed, there is only 1 red of 4 beads.

We have:

y(4) + y''' + y'' = 0

First, let's rewrite the equation using the common notation for derivatives:

y'''' + y''' + y'' = 0

Now, we need to find the characteristic equation, which is obtained by replacing each derivative with a power of r:

r^4 + r^3 + r^2 = 0

Factor out the common term, r^2:

r^2 (r^2 + r + 1) = 0

Now, we have two factors to solve separately:

1) r^2 = 0, which gives r = 0 as a double root.

2) r^2 + r + 1 = 0, which is a quadratic equation that doesn't have real roots. To find the complex roots, we can use the quadratic formula:

r = (-b ± √(b^2 - 4ac)) / 2a

Plugging in the values a = 1, b = 1, and c = 1, we get:

r = (-1 ± √(-3)) / 2

So the two complex roots are:

r1 = (-1 + √(-3)) / 2
r2 = (-1 - √(-3)) / 2

Now we can write the general solution of the differential equation using the roots found:

y(x) = C1 + C2*x + C3*e^(r1*x) + C4*e^(r2*x)

Where C1, C2, C3, and C4 are constants that can be determined using initial conditions or boundary conditions if provided.

To know more about constants, visit:

https://brainly.com/question/31730278

#SPJ11

At the end of the year, the amount in the account had decreased by 21%. The amount of money Martina has in her account after the 21% decrease is $6794.

Last year, Martina opened an investment account with $8600. At the end of the year, the amount in the account had decreased by 21%.

Let us calculate how much money she has in the account after a year.Solution:

Amount of money Martina had in her account when she opened = $8600

Amount of money Martina has in her account after the 21% decrease

Let us calculate the decrease in money. We will find 21% of $8600.21% of $8600

= 21/100 × $8600

= $1806.

Subtracting $1806 from $8600, we get;

Money in Martina's account after 21% decrease = $8600 - $1806

= $6794

Therefore, the money in the account after the 21% decrease is $6794. Therefore, last year, Martina opened an investment account with $8600.

At the end of the year, the amount in the account had decreased by 21%. The amount of money Martina has in her account after the 21% decrease is $6794.

To know more about investment, visit:

https://brainly.com/question/15105766

#SPJ11

The given indefinite integrals can be evaluated as

a) ∫6etdt = 6et + c

b) ∫2rdr = r^2 + c

c) ∫10x^2 0dx = (10/3)x^3 + c

In calculus, an indefinite integral represents a family of functions that differ from each other only by a constant. It is also known as an antiderivative because it is the opposite operation of differentiation.

The indefinite integral of a function f(x) is denoted as ∫f(x)dx, where dx represents the variable of integration. The result of integrating a function is called an antiderivative or a primitive of the function.

For part a), the indefinite integral of 6e^t is simply 6e^t + C, where C is the constant of integration.

For part b), the indefinite integral of 2r is r^2 + C, where C is the constant of integration.

For part c), the indefinite integral of 10x^2 is (10/3)x^3 + C, where C is the constant of integration.

For more such questions on indefinite integrals.

brainly.com/question/29133144

#SPJ11

The eigenvector corresponding to the eigenvalue λ = 4 is: v = [-3, -1, 1]

To determine if λ = 4 is an eigenvalue of the matrix

2 2 -4

3 -1 4

0 1 5

we need to check if there exists a non-zero vector v such that Av = λv, where A is the given matrix.

We have the equation:

A - λI = 0

where I is the identity matrix and 0 is the zero matrix. Let's substitute the values:

A - 4I =

2 2 -4

3 -1 4

0 1 5

4 0 0

0 4 0

0 0 4

Performing the subtraction, we get:

-2 2 -4

3 -5 4

0 1 1

Now, we set this resulting matrix equal to the zero matrix:

-2v₁ + 2v₂ - 4v₃ = 0

3v₁ - 5v₂ + 4v₃ = 0

v₂ + v₃ = 0

Simplifying the system of equations, we have:

-2v₁ + 2v₂ - 4v₃ = 0

3v₁ - 5v₂ + 4v₃ = 0

v₂ = -v₃

We can choose v₃ as a free variable and set v₃ = 1, which gives us v₂ = -1. Then, substituting these values back into the equations, we find:

-2v₁ + 2(-1) - 4(1) = 0

3v₁ - 5(-1) + 4(1) = 0

Simplifying these equations, we get:

-2v₁ - 6 = 0

3v₁ + 9 = 0

Solving these equations, we find v₁ = -3 and v₂ = -1.

Therefore, the eigenvector corresponding to the eigenvalue λ = 4 is:

v = [-3, -1, 1]

To know more about eigenvector refer to-

https://brainly.com/question/31013028

#SPJ11

the correct answer is B. ŷ = -157 + 40.2x; yes, because the r-value is high. The regression line would be a good predictor of other data points because of the strong linear relationship between x and y, as indicated by the high r-value.

To determine the line of regression, we can use linear regression analysis. The regression line is a straight line that best represents the relationship between the two variables. It is determined by minimizing the sum of squared deviations between the observed values and the predicted values of the response variable.

Using a calculator or statistical software, we can find that the regression line for this data set is:

ŷ = -22.2933 + 32.0472x

The r-value (correlation coefficient) for this data set is 0.969, which is relatively high. This indicates a strong positive linear relationship between x and y.

To learn more about variable visit:

brainly.com/question/17344045

#SPJ11

The conditional statement "T → (8<5)" is true because the antecedent "T" is false, and by the truth table of a conditional statement, a conditional with a false antecedent is always true, regardless of the truth value of the consequent.

what is antecedent?

In logic, an antecedent is the first part of a conditional statement (if-then statement) that precedes the word "if." It is the statement that implies or asserts the truth of the consequent. For example, in the conditional statement "If it is raining, then I will stay inside," the antecedent is "it is raining."

To learn more about antecedent visit:

brainly.com/question/24734058

#SPJ11

The composite function f(g(x)) consists of an inner function g and an outer function f. When doing a change of variables, the likely choice for a new variable u is: b) u = g(x)

The composite function f(g(x)) consists of an inner function g and an outer function f. When doing a change of variables, the likely choice for a new variable u is: b) u = g(x).
This is because when you choose u = g(x), you can substitute u into the outer function f, making it easier to work with and solve the problem.

A composite function, also known as a function composition, is a mathematical operation that involves combining two or more functions to create a new function.

Given two functions, f and g, the composite function f(g(x)) is formed by first evaluating the function g at x, and then using the result as the input to the function f.

In other words, the output of g becomes the input of f. This can be written as follows:

f(g(x)) = f( g( x ) )

The composite function can be thought of as a chaining of functions, where the output of one function becomes the input of the next function.

It is important to note that the order in which the functions are composed matters, and not all functions can be composed. The domain and range of the functions must also be compatible in order to form a composite function.

Read more about composite function.

https://brainly.com/question/5614233

#SPJ11

The decomposition of wood alcohol (CH3OH) to produce methane (CH4) and oxygen (O2) at 25°C and 1 atm is not thermodynamically feasible.

To explain further, we can consider the enthalpy change (∆H) associated with the reaction. The decomposition of wood alcohol can be represented by the equation:

CH3OH → CH4 + 1/2O2

By comparing the standard enthalpies of formation (∆Hf) for each compound involved, we can determine the overall enthalpy change of the reaction. The standard enthalpy of formation for wood alcohol (∆Hf(CH3OH)) is known to be negative, indicating its formation is exothermic. However, the standard enthalpy of formation for methane (∆Hf(CH4)) is more negative than the sum of ∆Hf(CH3OH) and 1/2∆Hf(O2).

This means that the formation of methane and oxygen from wood alcohol would require an input of energy, making it thermodynamically unfavorable at 25°C and 1 atm. Therefore, under these conditions, the decomposition of wood alcohol to methane and oxygen would not occur spontaneously.

Learn more about sum here:

https://brainly.com/question/17208326

#SPJ11

lim n → [infinity] (n^2+2n+1)/n^4 * 3^n = 0 (by the ratio test), we can conclude that the limit lim n → [infinity] (a_n+1 / a_n)^3/2 = 1. Therefore, the series converges by the Ratio Test.

To determine whether the series [infinity] n = 1 (−1)n − 1 3n 2nn3 converges or diverges, we can use the Ratio Test.

Using the Ratio Test, we calculate:

lim n → [infinity] |a_n+1 / a_n|

= lim n → [infinity] |(-1)^(n+1) * 3^(n+1) * 2n * (n+1)^3 / (n^3 * (-1)^n * 3^n * 2n)|

= lim n → [infinity] |(3/2) * (n+1)^3 / n^3|

= lim n → [infinity] (3/2) * [(n+1)/n]^3

= (3/2) * lim n → [infinity] (1 + 1/n)^3

= (3/2) * 1

= 3/2

Since the limit of |a_n+1 / a_n| is less than 1, by the Ratio Test, the series converges absolutely.

To identify a_n, we can rewrite the given series as:

∑ (-1)^n-1 * (2n/n^3) * (1/3)^n

Therefore, a_n = (-1)^n-1 * (2n/n^3) * (1/3)^n.

To evaluate the limit lim n → [infinity] (a_n+1 / a_n)^3/2, we can simplify the expression as follows:

lim n → [infinity] (a_n+1 / a_n)^3/2

= lim n → [infinity] |-1 * (2(n+1)/(n+1)^3) * (n^3/(2n)) * (3/1)^n|^3/2

= lim n → [infinity] |-2/3 * (n^2+2n+1)/n^4 * 3^n|^3/2

= |-2/3 * lim n → [infinity] (n^2+2n+1)/n^4 * 3^n|^3/2

Since lim n → [infinity] (n^2+2n+1)/n^4 * 3^n = 0 (by the ratio test), we can conclude that the limit lim n → [infinity] (a_n+1 / a_n)^3/2 = 1. Therefore, the series converges by the Ratio Test.

To know more about Ratio Test refer to

https://brainly.com/question/15586862

#SPJ11

To find the radius of the circle with the polar equation r^2 - 8r(3cosθ + sinθ) + 15 = 0, we can use the following steps:

Complete the square for the terms involving r(3cosθ + sinθ).

We can do this by adding and subtracting the square of half the coefficient of r(3cosθ + sinθ) to the equation:

r^2 - 8r(3cosθ + sinθ) + 15 = 0

r^2 - 8r(3cosθ + sinθ) + 9(3^2 + 1^2) - 9(3^2 + 1^2) + 15 = 0

(r - 3cosθ - sinθ)^2 - 9(3^2 + 1^2) + 15 = 0

(r - 3cosθ - sinθ)^2 = 9(3^2 + 1^2) - 15

(r - 3cosθ - sinθ)^2 = 63

Take the square root of both sides to solve for r:

r - 3cosθ - sinθ = ±√63

r = 3cosθ + sinθ ±√63

Since the radius of a circle is always positive, we can discard the negative square root and obtain:

r = 3cosθ + sinθ + √63

Now we need to find the value of r when θ = π/4, since this will give us the radius of the circle at that point. Substituting θ = π/4 into the equation for r, we get:

r = 3cos(π/4) + sin(π/4) + √63

r = 3(√2/2) + (√2/2) + √63

r = (√2 + 1) + √63

r ≈ 8.765

Therefore, the radius of the circle with the given polar equation is approximately 8.765, which rounded to the nearest whole number is 9.

To Know more about   radius of the circle refer here

https://brainly.com/question/31291491#

#SPJ11

The slant height of the cone is approximately 6.37 inches.

To find the slant height of the cone, we can use the formula for the surface area of a cone, which is given by A = πr(r + l), where A is the surface area, r is the radius, and l is the slant height. We are given that the surface area is 16.8π square inches and the radius is 3 inches. Substituting these values into the formula, we get 16.8π = π(3)(3 + l).

To solve for l, we can simplify the equation: 16.8π = 9π + πl. By subtracting 9π from both sides, we get 7.8π = πl. Dividing both sides by π, we find that the slant height, l, is approximately 7.8 inches.

Therefore, the slant height of the cone is approximately 6.37 inches.

Learn more about height here:

https://brainly.com/question/32560368

#SPJ11

the approximate diameter of the basketball is 9.0 inches.

To find the diameter of the basketball, we can use the formula for the volume of a sphere:

V = (4/3)πr^3

Given that the volume of the basketball is approximately 381.7 in^3, we can set up the equation:

381.7 = (4/3)(3.14)(r^3)

Simplifying the equation:

381.7 = 4.1867r^3

Dividing both sides by 4.1867:

r^3 = 91.288

Taking the cube root of both sides to solve for r:

r ≈ 4.5

The radius of the basketball is approximately 4.5 inches. To find the diameter, we double the radius:

d ≈ 2r ≈ 2(4.5) ≈ 9.0

To know more about equation visit:

brainly.com/question/29538993

#SPJ11

The correct answer is D. No, because the vertical scale exaggerates the differences between brands.

Step 1: Examine the information presented in the graph. The graph shows the strength of three paper towel brands: Brand X, Brand Y, and Brand Z. The strength values are represented on the y-axis, ranging from 90 to 100 with increments of 5.

Step 2: Compare the strength values of the brands. According to the graph, Brand X has a strength of 100, Brand Y has a strength of 105, and Brand Z has a strength of 110.

Step 3: Evaluate the claim made by the makers of Brand Z. They claim that Brand Z is twice as strong as Brand X.

Step 4: Assess the accuracy of the claim. Based on the actual strength values provided in the graph, Brand Z is not exactly twice as strong as Brand X. The difference in strength between the two brands is only 10 units.

Therefore, the claim made by the makers of Brand Z is not supported by the graph. The graph does not show a clear indication that Brand Z is twice as strong as Brand X. The vertical scale of the graph exaggerates the differences between the brands, leading to a potential misinterpretation of the data. Therefore, it is not valid to agree with the claim based solely on the information provided in the graph.

To know more about graph , visit:

https://brainly.com/question/15685482

#SPJ11

Therefore, we have successfully completed the proof that △QRS ≅ △QTS.

To complete the proof that △QRS ≅ △QTS, we need to show that they are congruent triangles based on the given information.

Given: QS bisects ∠RQT and ∠RST

Proof:

QS bisects ∠RQT and ∠RST (Given)

∠RQS ≅ ∠SQS (Angle bisector definition)

∠SQR ≅ ∠SQT (Angle bisector definition)

QR ≅ ST (Given)

∠QSR ≅ ∠QTS (Vertical angles are congruent)

△QRS ≅ △QTS (By angle-angle-side congruence)

By showing that ∠RQS ≅ ∠SQS and ∠SQR ≅ ∠SQT (angles are bisected), QR ≅ ST (given), and ∠QSR ≅ ∠QTS (vertical angles), we can conclude that △QRS ≅ △QTS based on the angle-angle-side (AAS) congruence criteria.

To know more about proof,

https://brainly.com/question/30405113

#SPJ11

To find the volume of a cylinder, we use the formula:

Volume = πr^2h

where r is the radius of the cylinder and h is the height of the cylinder.

In this case, the radius (r) is given as 2/22 units and the height (h) is given as 9/99 units.

Plugging these values into the formula, we get:

Volume = π(2/22)^2(9/99)

Volume = π(1/11)^2(1/11)

Volume = π(1/121)(9/1)

Volume = 9π/121

So the volume of the cylinder is 9π/121 cubic units. Since the question asks for an approximate decimal answer, we can use the value of π as 3.14 and get:

Volume ≈ 9(3.14)/121

Volume ≈ 0.232 cubic units

Therefore, the volume of the cylinder is approximately 0.232 cubic units.

To learn more about volume of a cylinder click here : brainly.com/question/15891031

#SPJ11

the general solution of the differential equation is given by cos y = C√(x^2 + 1) The correct option is (d) None of these.

We are given the differential equation:

(x^2 + 1) tan y dy/dx = x

We can solve this equation by separation of variables. We begin by multiplying both sides by dx/tan y:

(x^2 + 1) dy/tan y = x dx

Next, we can use the substitution u = x^2 + 1, which implies du/dx = 2x:

dy/tan y = (x du)/(2u - 2)

We can separate the variables as follows:

(tan y) dy = (x du)/(2u - 2)

We can integrate both sides:

∫(tan y) dy = (1/2)∫(x du)/(u - 1)

Using the substitution v = u - 1, which implies du = dv, we get:

∫(tan y) dy = (1/2)∫x dv/v

Integrating the right-hand side using ln |v| as the antiderivative, we get:

∫(tan y) dy = (1/2) ln |v| + C

Substituting back for v, we get:

∫(tan y) dy = (1/2) ln |u - 1| + C

Substituting back for u and simplifying, we get:

∫(tan y) dy = (1/2) ln |x^2 + 1| + C

Integrating the left-hand side using ln |cos y| as the antiderivative, we get:

ln |cos y| = (1/2) ln |x^2 + 1| + C

Simplifying and exponentiating both sides, we get:

cos y = ±C√(x^2 + 1)

Therefore, the general solution of the differential equation is given by:

cos y = C√(x^2 + 1)

where C is an arbitrary constant. Hence, the correct option is (d) None of these.

Learn more about differential equation here

https://brainly.com/question/1164377

#SPJ11

The equation of the plane tangent to the following surface 4xy+yz+5xz−40=0; at the given point (2,2,2) is  18x + 10y + 12z = 80. Gradient vector of the surface at that point is used to find the equation of plane.

To find an equation of the plane tangent to the surface at the given point, we need to find the gradient vector of the surface at that point. The gradient vector is perpendicular to the tangent plane, so we can use it to write the equation of the plane.

First, we need to find the partial derivatives of the surface with respect to x, y, and z:

∂/∂x (4xy + yz + 5xz - 40) = 4y + 5z

∂/∂y (4xy + yz + 5xz - 40) = 4x + z

∂/∂z (4xy + yz + 5xz - 40) = y + 5x

At the point (2,2,2), these partial derivatives evaluate to:

∂/∂x (4xy + yz + 5xz - 40) = 4(2) + 5(2) = 18

∂/∂y (4xy + yz + 5xz - 40) = 4(2) + 2 = 10

∂/∂z (4xy + yz + 5xz - 40) = 2 + 5(2) = 12

So the gradient vector is:

∇f = <18, 10, 12>

At the point (2,2,2), the equation of the tangent plane is:

18(x - 2) + 10(y - 2) + 12(z - 2) = 0

18x - 36 + 10y - 20 + 12z - 24 = 0

18x + 10y + 12z - 80 = 0

18x + 10y + 12z = 80

So the equation of the tangent plane at (2,2,2) is 18x + 10y + 12z = 80.

To learn more plane  : https://brainly.com/question/1655368

#SPJ11

The rectangular tank initially filled with water measures 28 cm by 18 cm by 12 cm. After draining 0.78 liters of water from the tank, there is 5,268 milliliters (or 5.268 liters) of water left in the tank.

To determine the amount of water left in the tank, we need to calculate the initial volume of water in the tank and subtract the volume of water drained. The volume of a rectangular tank is given by the formula: length × width × height.

The initial volume of water in the tank is calculated as follows:

Volume = 28 cm × 18 cm × 12 cm = 6,048 cm³.Since 1 liter is equal to 1,000 cm³, the initial volume can be converted to liters:

Initial volume = 6,048 cm³ ÷ 1,000 = 6.048 liters.

Next, we subtract the drained volume of 0.78 liters from the initial volume to find the remaining amount:

Remaining volume = Initial volume - Drained volume = 6.048 liters - 0.78 liters = 5.268 liters.

To convert the remaining volume to milliliters, we multiply it by 1,000:

Remaining volume in milliliters = 5.268 liters × 1,000 = 5,268 milliliters.

Therefore, after draining 0.78 liters of water from the tank, there is 5,268 milliliters (or 5.268 liters) of water left in the tank.

Learn more about volume here:

https://brainly.com/question/13338592

#SPJ11

There will be about an 18% chance that a student participates in student council, that the student participates in after-school sports.

A = Student participates in student council

B = Student participates in after-school sports

To P(A | B) = P(A ∩ B)/P(B). P(A | B) literally means "probability of event A, given that event B has occurred."

P(A ∩ B) is the probability of events A and B happening, and P(B) is the probability of event B happening.

so:

P(A | B) = P(A ∩ B)/P(B)

P(A | B) = 11% / 62%

P(A | B) = 0.11 / 0.62

P(A | B) = 0.18

There will be about an 18% chance, that the student participates in after-school sports.

Learn more about probability here;

https://brainly.com/question/9326835

#SPJ1

If the slope of "fitted-line" is given to be 8.42, then the correct interpretation is Option(c), which states that "On average, every $1 million increase in salary is linked with 8.42 point increase in "winning-percentage".

The "Slope" of the "fitted-line" denotes the change in response variable (which is winning percentage in this case) for "every-unit" increase in the predictor variable (which is salary of head coach, in millions of dollars).

In this case, the slope is 8.42, which means that on average, for every $1 million increase in salary of "head-coach", there is an increase of 8.42 points in "winning-percentage".

Therefore, Option (c) denotes the correct interpretation of slope.

Learn more about Slope here

brainly.com/question/29075872

#SPJ1

The given question is incomplete, the complete question is

Abigail gathered data on different schools' winning percentages and the average yearly salary of their head coaches (in millions of dollars) in the years 2000-2011. She then created the following scatterplot and regression line.

The fitted line has a slope of 8.42.

What is the best interpretation of this slope?

(a) A school whose head coach has a salary of $0, would have a winning percentage of 8.42%,

(b) A school whose head coach has a salary of $0, would have a winning percentage of 40%,

(c) On average, each 1 million dollar increase in salary was associated with an 8.42 point increase in winning percentage,

(d) On average, each 1 point increase in winning percentage was associated with an 8.42 million dollar increase in salary.

The answer is as follows.List 1: 2, 2, 2, 12, 17List 2: 0, 1, 5, 10, 19List 3: 3, 4, 5, 6, 7

To list 5 numbers which have a mean of 7 is an easy task. We will get 5 numbers whose average is 7. Each of the three lists will have different 5 numbers that will make up the mean as 7. We can take any values for this, and the sum of the values should be 35. So, let's choose 5 random numbers for this task such that their sum is 35: List 1: 2, 2, 2, 12, 17List 2: 0, 1, 5, 10, 19List 3: 3, 4, 5, 6, 7We have listed three different sets of five numbers such that the mean of each set is 7. These values will be different for each list. Hence, the answer is as follows.List 1: 2, 2, 2, 12, 17List 2: 0, 1, 5, 10, 19List 3: 3, 4, 5, 6, 7

Learn more about Value here,How do you calculate present value?

https://brainly.com/question/30390056

#SPJ11

For any integer input x in the domain of relation a, if x is related to 2, then the output will be u2.

Based on the given information, we know that the domain of the relation a is the set of integers. Additionally, we know that 2 is related to y under relation a, with the output being u2.

Therefore, we can conclude that for any integer input x in the domain of relation a, if x is related to 2, then the output will be u2. However, we do not have enough information to determine the outputs for other inputs in the domain.

In other words, we know that the relation a contains at least one ordered pair (2, u2), but we do not know if there are any other ordered pairs in the relation.

The correct question should be :

In the given relation a, if an integer input x is related to 2, what is the corresponding output?

To learn more about relations visit : https://brainly.com/question/26098895

#SPJ11

The two numbers whose sum is 100 and whose product is a minimum are: x= 50 and y= 50.

To find two numbers whose sum is 100 and whose product is a minimum, we can use the Second Derivative Test. Let's start by defining the two numbers as x and y. We know that:

x + y = 100

We want to find the minimum value of xy. So, let's define a function f(x) = xy. We can rewrite this function in terms of one variable:

f(x) = x(100 - x) = 100x - x^2

Now, let's find the critical point of this function by taking the derivative:

f'(x) = 100 - 2x

Setting f'(x) = 0 to find the critical point:

100 - 2x = 0
x = 50

So, the critical point is x = 50. To determine whether this is a minimum or maximum, we need to find the second derivative:

f''(x) = -2

Since f''(50) < 0, we know that the critical point x = 50 is a maximum. Therefore, to find the minimum value of f(x), we need to evaluate f at the endpoints of the interval [0, 100]:

f(0) = 0
f(100) = 0

Since f(x) is decreasing from x = 0 to x = 50, and increasing from x = 50 to x = 100, the minimum value of f(x) occurs at x = 50. Therefore, the two numbers whose sum is 100 and whose product is a minimum are:

x = 50
y = 100 - x = 50

So, the two numbers are 50 and 50.

To know more about Second Derivative Test, refer to the link below:

https://brainly.com/question/30404403#

#SPJ11