John brought
2
• 3
quart of water to the
park. While he was at the park, he
3
drank
4 of the water he brought. How much water in quarts did John drink at the park?

The solutions of given functions are : 1. (f + g)(x) = 2x² + 3x - 2, 2. (fog)(x) = 6x² + 4, 3. (gof)(x) = 18x² - 60x + 53, 4. (f.g)(x) = 6x³ - 10x² + 9x - 15, 5. (f - g)(x) = -2x² + 3x - 8, 6. (fog)(3) = 58.

What are the functions?

We have the given functions:

f(x) = 3x - 5

g(x) = 2x² + 3

Here are the solution steps of the given functions f(x) and g(x).

1. (f + g)(x) = f(x) + g(x) = (3x - 5) + (2x² + 3) = 2x² + 3x - 2

So, (f + g)(x) = 2x² + 3x - 2.

2. (fog)(x) = f(g(x)) = f(2x² + 3) = 3(2x² + 3) - 5 = 6x² + 4

So, (fog)(x) = 6x² + 4.

3. (gof)(x) = g(f(x)) = g(3x - 5) = 2(3x - 5)² + 3 = 18x² - 60x + 53

So, (gof)(x) = 18x² - 60x + 53.

4. (f.g)(x) = f(x)g(x) = (3x - 5)(2x² + 3) = 6x³ + 9x - 10x² - 15

So, (f.g)(x) = 6x³ - 10x² + 9x - 15.

5. (f - g)(x) = f(x) - g(x) = (3x - 5) - (2x² + 3) = -2x² + 3x - 8

So, (f - g)(x) = -2x² + 3x - 8.

6. (fog)(3) = f(g(3)) = f(2(3)² + 3) = f(21) = 3(21) - 5 = 58

So, (fog)(3) = 58.

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The determinant of the given matrix is bc²-cb²+ac²-ab²+a²c-a²b.

The given matrix is [tex]\left[\begin{array}{ccc}1&a&a^2\\1&b&b^2\\1&c&c^2\end{array}\right][/tex].

Determinants are considered as a scaling factor of matrices. They can be considered as functions of stretching out and the shrinking in of the matrices. Determinants take a square matrix as the input and return a single number as its output.

Here, 1(bc²-cb²)+a(c²-b²)+a²(c-b)

= bc²-cb²+ac²-ab²+a²c-a²b

Therefore, the determinant of the given matrix is bc²-cb²+ac²-ab²+a²c-a²b.

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From expression 8 pounds x $0.25 per pound and $50 / $0.25 per pound , Earnings = $2.00 and Total pounds of cans = 200 pounds and check attachment for illustration.

An expression in mathematics is a set of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that may be evaluated to generate a value. Expressions can be basic or complicated, containing a variety of numbers, variables, and mathematical processes.

Now,

1.  

Let the total money earned by selling aluminium cans be y and the no. of cans recycled be x then this situation can be represented by the function y = 0.25x, see attachment for illustration.

2.

If someone brings 8 pounds of cans, they will earn:

Earnings = 8 pounds x $0.25 per pound

Earnings = $2.00

3.

To earn $50, the class needs to sell:

Total pounds of cans = Total earnings / Price per pound

Total pounds of cans = $50 / $0.25 per pound

Total pounds of cans = 200 pounds

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a) The amount of charge stored on either plate of the capacitor is 0.0528 C. ,b) The area of the plates is 3.47 x 10⁷ m². c)  The capacitance of the capacitor is 6.62 x 10⁻⁸ F.

what is capacitance ?

Capacitance is a physical property of a capacitor that represents its ability to store an electric charge. It is defined as the ratio of the amount of electric charge that can be stored on the capacitor's plates to the potential difference (voltage) between them. Capacitance is measured in farads (F)

In the given question,

:Capacitance (C) = 4.4 mF = 4.4 x 10⁻³ F

Voltage (V) = 12 V

The amount of charge (Q) stored on either plate of the capacitor.

 Q = C x V

Q = 4.4 x 10⁻³ F x 12 V

Q = 0.0528 C

The amount of charge stored on either plate of the capacitor is 0.0528 C.

Capacitance (C) = 1.4 F

Plate separation (d) = 2.2 x 10⁻³m

Find: The area (A) of the plates.

Equation:

C = ε0 x (A/d)

where ε0 is the permittivity of free space and has a value of 8.85 x 10⁻¹² F/m

A = C x d / ε0

A = 1.4 F x 2.2 x 10⁻³ m / (8.85 x 10⁻¹² F/m)

A = 3.47 x 10⁷ m²

The area of the plates is 3.47 x 10⁷ m².

Dielectric constant (k) = 2.5

Plate separation (d) = 0.0003 m

Area (A) = 30 m²

The capacitance (C) of the capacitor.

C = k x ε0 x (A/d)

where ε0 is the permittivity of free space and has a value of 8.85 x 10⁻¹² F/m

C = 2.5 x 8.85 x 10⁻¹² F/m x 30 m² / 0.0003 m

C = 6.62 x 10⁻⁸ F

The capacitance of the capacitor is 6.62 x 10⁻⁸ F.

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Following are the correct pairs given for verbal mapping statements to symbolic statements.

In mathematics, mapping, or function, is a relation between two sets, where each element of the first set (called the domain) is associated with exactly one element of the second set (called the range).

According to given information,

The verbal mapping statements can be matched to their equivalent symbolic statements as follows:

The figure is translated 4 units right and 3 units down.

Symbolic statement: (x,y) mapsto (x + 4, y - 3)

The figure is translated 4 units left and 3 units up.

Symbolic statement: (x,y) mapsto [tex](x - 4, y + 3)[/tex]

The figure is translated 3 units right and 4 units down.

Symbolic statement: (x,y) mapsto [tex](x + 3, y - 4)[/tex]

The figure is translated 3 units left and 4 units up.

Symbolic statement: (x,y) mapsto[tex](x - 3, y + 4)[/tex]

So the correct matching of the verbal mapping statements to their equivalent symbolic statements is:

The figure is translated 4 units right and 3 units down.

Symbolic statement: (x,y) mapsto [tex](x + 4, y - 3)[/tex]

The figure is translated 4 units left and 3 units up.

Symbolic statement: (x,y) mapsto[tex](x - 4, y + 3)[/tex]

The figure is translated 3 units right and 4 units down.

Symbolic statement: (x,y) mapsto [tex](x + 3, y - 4)[/tex]

The figure is translated 3 units left and 4 units up.

Symbolic statement: (x,y) mapsto [tex](x - 3, y + 4)[/tex]

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Answer:129°and 51°.

Step-by-step explanation:

The volume of the shape is 144π cubic inches and the total surface area of the shape is 114π square inches.

To find the volume and total surface area of the shape, we need to first determine the radius of the semicircle.

Since the length of the shape is 12 inches and the base is a semicircle, the diameter of the semicircle is also 12 inches. Therefore, the radius of the semicircle is half the diameter, which is 6 inches.

Now we can use the formula for the volume of a cylinder, which is:

V = (πr^2h)/2

where V is the volume, r is the radius, and h is the height.

Substituting in the values we have:

V = (π(6)^2(8))/2

V = 144π cubic inches

So the volume of the shape is 144π cubic inches.

Next, we can find the total surface area of the shape by adding the area of the semicircle base to the lateral surface area of the cylinder. The formula for the lateral surface area of a cylinder is:

L = 2πrh

where L is the lateral surface area.

Substituting in the values we have:

L = 2π(6)(8)

L = 96π square inches

The formula for the area of a semicircle is:

A = (πr^2)/2

where A is the area of the semicircle.

Substituting in the values we have:

A = (π(6)^2)/2

A = 18π square inches

Adding the lateral surface area and the area of the semicircle base together, we get:

Total surface area = L + A

Total surface area = 96π + 18π

Total surface area = 114π square inches

So the total surface area of the shape is 114π square inches.

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Kareem borrowed $7000 from the credit union based on the given interest rate.

We may use the simple interest formula to figure out how much Kareem borrowed:

I = Prt

Where r: yearly interest rate represented as a decimal, P: borrowed principal, I: interest paid, and t: amount of time in years.

We are aware that Kareem borrowed money for 6 years at an interest rate of 6% each year. We also know that he spent $2520 on interest in total. We may determine P using the following formula:

2520 = P0.066

2520 = 0.36P

P = 7000

Kareem thus took out a $7000 loan from the credit union.

In conclusion, we utilized the simple interest formula and the provided data on the interest rate, time, and total interest paid to calculate how much money Kareem borrowed from the credit union. We discovered that he took out a loan for $7000, the principal of which accrued $2520 in interest over the course of six years at an annual rate of 6%.

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Answer:

To solve this problem, we need to use the Poisson distribution, which describes the probability of a certain number of events occurring in a fixed interval of time or space, given the average rate of occurrence.

Let λ be the average number of calls per minute. From the problem statement, we have λ = 2.35.

Now we need to find the probability of having at most 2 phone calls in one minute. Let X be the random variable representing the number of phone calls in one minute. Then we have:

P(X ≤ 2) = e^(-λ) * (λ^0/0!) + e^(-λ) * (λ^1/1!) + e^(-λ) * (λ^2/2!)

Substituting λ = 2.35, we get:

P(X ≤ 2) = e^(-2.35) * (2.35^0/0!) + e^(-2.35) * (2.35^1/1!) + e^(-2.35) * (2.35^2/2!)

≈ 0.422

Therefore, the probability that during one particular minute there will be at most 2 phone calls is about 0.422, or 42.2%.

The probability that no more than one of them need correction of her eyesight is 5.960.

What is probability?

Probability is a way of calculating how likely something is to happen. It is difficult to provide a complete prediction for many events. Using it, we can only forecast the probability, or likelihood, of an event occurring. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.

Here using formula , Binomial distribution: P(X) = [tex]nC_x \times p^x\times q^{n-x}[/tex]

=> P(an adult need correction), p = 0.75

=>q = 1 - p = 0.25

Sample size, n = 12

P(no more than 1 of them need correction for their eyesight) = P(none of them need correction) + P(only 1 need correction)

=> [tex]0.25^{12}[/tex] + [tex]12\times0.75\times0.25^{11}[/tex]

=> 5.960

If the probability of an event is less than 0.05, it can be considered significantly low

Therefore, 1 is a significantly low number of adults requiring eyesight​ correction.

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H_0: mu=10, H_a: mu not equal 10. n=25, sigma-3, sample mean xbar =11. The Z-value is 1.67. Option B

To calculate the Z-value, we can use the formula:

Z = (xbar - mu) / (sigma / sqrt(n))

Where xbar is the sample mean, mu is the population mean, sigma is the population standard deviation, and n is the sample size.

Given:

H_0: mu = 10

H_a: mu ≠ 10

n = 25

sigma = 3

xbar = 11

We can plug in the values and get:

Z = (11 - 10) / (3 / sqrt(25))

Z = 5/3

Therefore, the Z-value is 1.67.

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Answer:5% = 0.05 . Then multiply the original amount by the interest rate. $1,000 * 0.05 = $50 . That's it.

Step-by-step explanation:

please give me brainliest

[tex](-20, -4)[/tex] and are all of the ordered pairings that fulfil this equation [tex]F = 9/5C + 32. (-10, 14)[/tex].

Lines come in two varieties: identities and dependent equations. All possible values of the parameters result in an identity. Only certain combinations of the variables' values render a conditional equation true. Two expressions joined by the equals symbol ("=") form an equations.

Ax+By=C is the classic pattern for two-variable linear equations. A typical form linear equation is, for instance, 2x+3y=5. Finding all intercepts of a solution in this format is not too difficult. The approach additionally proves useful when trying to solve solutions combining two linear systems.

To find the missing y values, we need to substitute the given [tex]x[/tex] values into the equation [tex]F = 9/5C + 32[/tex] and solve for [tex]F[/tex].

For the first ordered pair (-20, F1):

[tex]F1 = 9/5(-20) + 32[/tex]

[tex]F1 = -36 + 32[/tex]

[tex]F1 = -4[/tex]

So the missing y value is [tex]-4[/tex], and the complete ordered pair is [tex](-20, -4)[/tex].

For the second ordered pair (-10, F2):

[tex]F2 = 9/5(-10) + 32[/tex]

[tex]F2 = -18 + 32[/tex]

[tex]F2 = 14[/tex]

So the missing y value is [tex]14[/tex], and the complete ordered pair is [tex](-10, 14)[/tex].

Therefore, the complete set of ordered pairs that satisfy the equation [tex]F = 9/5C + 32[/tex] is:

[tex](-20, -4)[/tex] and [tex](-10, 14)[/tex].

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The complete question is:

Given the equation

F=9,5

C+32

F=95C+32

where C is the temperature in degrees Celsius and F is the corresponding temperature in degrees Fahrenheit, and the following ordered pairs:

(−20,F1)

(−20,F1),(−10,F2)(−10,F2)

Step 1 of 2 : Compute the missing y values so that each ordered pair will satisfy the given equation.

24. The price of the motorcycle before tax was $11,500. 25. the instructor earns $28.75 per class after the raise. 26.  the sum that Kay and Shay paid, including tax, was $28.62.

An equation is a mathematical statement that asserts that two expressions are equal. Equations are used to represent relationships and constraints between variables, and are commonly used in many fields of science, engineering, and mathematics.

An equation consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). Each side of the equation can contain numbers, variables, mathematical operations (such as addition, subtraction, multiplication, and division), and parentheses.

The goal of solving an equation is to determine the value(s) of the variable(s) that make the equation true. This is typically done by applying mathematical operations to both sides of the equation in order to isolate the variable on one side and simplify the expression on the other side.

24. Let the price of the motorcycle before tax be represented by x. Then, we can write an equation based on the given information:

0.125x = 1437.50

Solving for x, we get:

x = 1437.50 / 0.125 = $11,500

Therefore, the price of the motorcycle before tax was $11,500.

25. The instructor now earns 115% of $50, or:

$50 x 1.15 = $57.50

Since this is the amount earned for teaching 2 classes, the amount earned per class after the raise is:

$57.50 / 2 = $28.75

Therefore, the instructor earns $28.75 per class after the raise.

26. To find how much Kay paid, we first need to calculate the tax:

0.08 x $14.50 = $1.16

So the total amount Kay paid was:

$14.50 + $1.16 = $15.66

Similarly, the tax Shay paid was:

0.08 x $12 = $0.96

So the total amount Shay paid was:

$12 + $0.96 = $12.96

Therefore, the sum that Kay and Shay paid, including tax, was:

$15.66 + $12.96 = $28.62

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Answer:

The least possible degree is 3.

Step-by-step explanation:

We can solve this problem using the hypergeometric distribution.

The total number of apples is 24 (4 bad + 20 good). Let X be the number of bad apples in a draw of 2 apples.

The probability of drawing 0 bad apples is:

P(X=0) = (20 choose 2) / (24 choose 2) = 190 / 276

The probability of drawing 1 bad apple is:

P(X=1) = ((4 choose 1) * (20 choose 1)) / (24 choose 2) = 64 / 276

The probability of drawing 2 bad apples is:

P(X=2) = (4 choose 2) / (24 choose 2) = 1 / 276

Therefore, the probability distribution of the number of bad apples in a draw of 2 apples at random is:

X | 0 | 1 | 2

----|------|------|-----

P(X) |190/276|64/276|1/276

The answer of the given question based on the trigonometry is the nearest ten-thousandth, tan(−284°24′) is approximately equal to -0.2493.

An equivalent angle is an angle that has the same degree measure as another angle. In geometry, two angles are said to be equivalent if they have the same measure, regardless of their orientation or position in space.

Equivalent angles can be found by adding or subtracting multiples of 360° degrees from an angle. This is because an angle that has been rotated a multiple of 360° degrees has the same orientation and position as the original angle.

We can use the fact that the tangent function has period 180 degrees and that tan(x + 180°) = tan(x) for any angle x. Therefore, we can add or subtract multiples of 180° from −284°24′ to find an equivalent angle in the range of −90° to 90°.

Adding 360° to −284°24′ gives us an equivalent angle of 75°36′. Since the tangent function is positive in the first and third quadrants, we can find the value of tangent of 75°36′ or its reference angle of 14°24′.

Using a calculator, we get:

tan(14°24′) ≈ 0.2493

Therefore, to the nearest ten-thousandth, tan(−284°24′) is approximately equal to -0.2493.

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To the nearest ten-thousandth, the value of tan (-284°24') is approximately -3.7583.

We need to keep in mind that the tangent function is periodic in order to determine the value of tan(-284°24'). This means that the tangent of an angle is the same as the tangent of that angle plus or minus any multiple of 180 degrees.

So, we can add 360 degrees to -284 degrees to get an equivalent angle in the range of -180 to 180 degrees:

-284 + 360 = 76

So, we can find the tangent of -284°24' by finding the tangent of 76°24'. Using a calculator, we get:

tan(76°24') ≈ 3.7583

Therefore, To the nearest ten-thousandth, the value of tan (-284°24') is approximately -3.7583. Note that the negative sign indicates that the angle is in the third quadrant of the unit circle.

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Step-by-step explanation:

This sign "<" could mean "less than" or "greater than"

depending on which way it is facing

in this case 4+-7 is less than 13 because

< is facing 13 and not 4+-7

meaning than 13 is a bigger number

than the sum of 4+-7 but if 4+-7 is greater than 13 then

the "<" sign would be facing 4+-7 like this: 4+-7>13

How do we know if it is true?

equation: 4+-7<13

4+-7 is -3

so -3<13.

13 is bigger than -3

which means the equation is true

What if it was false?

here is a false equation:

4>14

it is false because 4 is not a bigger number than 14

Hope this helps!

I would appreciate if you could mark me brainliest.

The equation is written as

Aisha has 15 points

Let's use the given information to set up an equation to represent the relationship between the points each friend has.

Let x be the number of points Aisha has.

Then, according to the problem statement, we know that:

Carter has 7 1/2 more points than Aisha, so he has

x + 7 1/2 points.

Jamila has 4 - 1/2 more points than Carter, so she has

x + 7 1/2 + 4 - 1/2 points,

which simplifies to x + 11 points.

Jamila has 26 points, so we can set x + 11 equal to 26 and solve for x:

x + 11 = 26

x = 26 - 11

x = 15

Therefore, Aisha has 15 points.

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x represents a length, we can discard the negative sοlutiοn and cοnclude that x ≈ 15.7.

A triangle is a three-sided pοlygοn with three angles. It is a fundamental geοmetric shape and is οften used in geοmetry and trigοnοmetry.

Using the Law οf Cοsines:

c² = a² + b² - 2ab cοs(C)

where c is the side οppοsite angle C, a and b are the οther twο sides, and C is the angle between sides a and b.

Substituting the knοwn values:

26² = x² + (x+7)² - 2x(x+7) cοs(52°)

Simplifying and sοlving fοr x:

676 = x² + x² + 14x + 49 - 2x² cοs(52°) - 14x cοs(52°)

676 = 2x² - 14x cοs(52°) + 49

2x² - 14x cοs(52°) - 627 = 0

Using the quadratic fοrmula:

[tex]x = [14 cos(52^\circ) \± \sqrt{((14 cos(52^\circ))}^2 - 4(2)(-627))] / (2(2))[/tex]

x ≈ 15.7 οr x ≈ -21.6

Since x represents a length, we can discard the negative sοlutiοn and cοnclude that x ≈ 15.7.

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Answer:

B

Step-by-step explanation:

[tex]\frac{1}{2}[/tex] fathom = 1 yard = 3 feet

then 1 fathom = 2 × 3 feet = 6 feet

1 furlong = 660 feet , then

660 feet ÷ 6 feet = 110

there are 110 fathoms in 1 furlong

Step-by-step explanation:

When the ball hits the ground , the height = 0

  0 = 96 + 80 t - 16t^2

    Use Quadratic Formula with   a = -16      b = 80      c = 96

             to find  t=  6 seconds

Answer:

In chemistry, an element is typically represented by its atomic symbol, which consists of one or two letters. The regions in an element refer to different parts of its atom.

The three main regions of an atom are the nucleus, the electron cloud, and the space in between. The nucleus is located at the center of the atom and contains positively charged protons and neutrally charged neutrons. The electron cloud surrounds the nucleus and contains negatively charged electrons, which are distributed in different energy levels or orbitals. The space in between the nucleus and the electron cloud is mostly empty.

To identify the different regions in an element, one can look at the atomic structure of the element, which is typically represented by an electron configuration or an orbital diagram. These representations show the number and distribution of electrons in the different energy levels or orbitals. By analyzing the electron configuration or orbital diagram, one can identify the number of electrons in the electron cloud and the number of protons and neutrons in the nucleus. The space in between the nucleus and the electron cloud is relatively small and is not usually a focus of study in chemistry.

The line of elements from the lower left corner to the upper right corner of a second order determinant is called the main diagonal or simply the diagonal. In general, the diagonal of an n x n determinant consists of the elements a11, a22, ..., ann, where ai,i denotes the element in the i-th row and i-th column of the determinant.

We can mark the points (2, 95) and (4, 145) on the grid and then draw the x-axis and y-axis to plot the points on a coordinate grid.

A linear function is a first-degree mathematical problem with one or more variables set to one and no terms with a degree higher than one. The recipe for a direct condition is y = mx + b, where m indicates the incline and b the y-catch..

given

We may use the slope-intercept form of a linear equation to graph the relationship between the number of hours worked and the fee, which is:

y = mx + b

where m is the hourly rate of $35 and b is the fixed charge of $25, y is the total amount charged, x is the number of hours worked, and m is the hourly rate.

Hence, the equation is:

y = 35x + 25

y = 35(2) + 25 = 95

y = 35(4) + 25 = 145

Hence, the line's two points are (2, 95) and (4, 145).

We can mark the points (2, 95) and (4, 145) on the grid and then draw the x-axis and y-axis to plot the points on a coordinate grid.

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Answer:

5/7

Step-by-step explanation:

ratio of boys to girls---> 2:5

ratio sum: 2+5=7

girls ratio =5/7

OR

total of people in 7th grade choir=28

hence, no of girls in 7th grade choir=5/7 × 28

=20

proportion of girls in choir= 20/28 = 5/7

Answer:

Assuming exponential growth, the number of bacteria in the Petri dish can be modeled by the equation:

N(t) = N0 * e^(kt)

where N(t) is the number of bacteria at time t, N0 is the initial number of bacteria, e is the base of the natural logarithm, k is a constant representing the growth rate, and t is the time elapsed.

We are given that there are 47 bacteria initially, so N0 = 47. After 8 hours, there are 273 bacteria, so we can use this information to solve for k:

273 = 47 * e^(k*8)

Dividing both sides by 47 and taking the natural logarithm of both sides, we get:

ln(273/47) = k*8

Simplifying this expression, we get:

k ≈ 0.53

Now we can use this value of k to find the number of bacteria after 48 hours:

N(48) = 47 * e^(0.53*48)

N(48) ≈ 1.3 * 10^12

Therefore, assuming exponential growth, there would be approximately 1.3 * 10^12 bacteria in the Petri dish after 48 hours.

Answer:

m=the slope

b=the y intercept