the possible answers are
- GPS
- PSG
- GSP
- SGP​

The probability of a student taking a math class and a physics class is [tex]\frac{7}{15}[/tex].

What is probability?

To determine the possibility of an event, one might utilise probability as a technique. Only the probability of an event occurring can be determined using it. A scale where 1 denotes a specific occurrence and 0 signifies impossibility.

We are given that the probability of the student taking a physics class is [tex]\frac{2}{3}[/tex].

Also, it is given that the probability of a student taking a math class given that the student takes a physics class is [tex]\frac{7}{10}[/tex].

So, probability of a student taking a math class and a physics class is:

⇒ Probability =  [tex]\frac{2}{3}[/tex] *  [tex]\frac{7}{10}[/tex]

⇒ Probability = [tex]\frac{14}{30}[/tex]

⇒ Probability = [tex]\frac{7}{15}[/tex]

Hence, the probability of a student taking a math class and a physics class is  [tex]\frac{7}{15}[/tex].

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Answer:

378

Step-by-step explanation:

[tex]\frac{14}{x}[/tex] = [tex]\frac{1}{27}[/tex]  Cross multiply and solve for x

x = (14)(27)

x = 378

Helping in the name of Jesus.

Answer:

7x = 126 is the equation

She sold 18 t-shirts.

Step-by-step explanation:

Since she sold t-shirts for 7 each, we need to find how many T-shirts she sold. 126 dollars is how much she made, so we need to divide.

126/7 = 18.

The equation would be:

7x = 126.

Answer:

slope = 15

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (1, 6) and (x₂, y₂ ) = (2, 21) ← 2 ordered pairs from the table

m = [tex]\frac{21-6}{2-1}[/tex] = [tex]\frac{15}{1}[/tex] = 15

the linear relationship is then of the form

y = mx + c ( m is the slope and c the y- intercept )

from the table the point (0, - 9 ) crosses the y- axis at - 9 ⇒ c = - 9

y = 15x - 9 ← linear relationship

The union of J and K is: J ∪ K = {7, 14, 21, 28, 35, 42, 56, 70} . Note that 14, 28, and 42 are included in both sets, but we only include them once in the union.

What is a set ?

In mathematics, a set is a collection of distinct objects, called elements or members of the set. Sets are often denoted by curly braces {} enclosing the list of elements, separated by commas. For example, the set of natural numbers less than 5 can be written as {0, 1, 2, 3,

The union of two sets J and K, denoted by J ∪ K, is the set that contains all the elements that are in J or K, or in both.

In this case, J = {7, 14, 21, 28, 35, 42} and K = {14, 28, 42, 56, 70}. To find the union of J and K, we simply combine all the elements in both sets, removing any duplicates.

Therefore, the union of J and K is: J ∪ K = {7, 14, 21, 28, 35, 42, 56, 70}

Note that 14, 28, and 42 are included in both sets, but we only include them once in the union.

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The number of books that each kid in Mr. Johnson's sixth-grade class read during the summer was recorded. 5 books have been read on average by Mr. Johnson's students.

There are six students in Mr. Johnson's sixth-grade class, and their number of books read is 0, 2, 4, 6, 8, and 10.

To find the median, we need to find the middle value in the list of numbers. If there is an odd number of values, then the median is the middle number. If there is an even number of values, then the median is the average of the two middle numbers.

In this case, there are six numbers, which is an even number, so we need to find the average of the two middle numbers, which are 4 and 6.

The average of 4 and 6 is (4 + 6)/2 = 5.

Therefore, the median number of books read by Mr. Johnson's students is 5.

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The prοfit exceeds the cοst as y > 1000 + 15x. Sο, οptiοn 4 is cοrrect.

Gaining anything is knοwn as prοfit. When the Selling price ( SP ) οf the prοduct is mοre than the cοst price ( CP ) οf the prοduct, we gain prοfit. Oppοsite tο the prοfit is lοss i.e. lοsing anything is called lοss. When the Selling price ( SP ) οf the prοduct is less than the cοst price ( CP ) οf the prοduct, we get a lοss.

Prοfit can be calculated by the fοrmula,

Prοfit   =   Selling Price - Cοst price

     P   =   SP - CP

Lοss can be calculated by the fοrmula,

Lοss   =   Cοst price - Selling price

   L    =   CP - SP

As per the questiοn,

x  =    number οf units prοduced

expressiοn   =   1000 + 15x

⇒  When y > 1000 + 15x, then prοfit exceeds cοst:

x   =   50  & y   =   1750

x   =   100  & y   =   2500

x   =   150  & y   =   3250

x   =   200  & y   =   4000

x   =   0  & y   =   1000

Therefοre, the graph in the 1st οptiοn is cοrrect as the prοfit exceeds the cοst.

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Complete question:

The cost of a small business is given by the expression 1000 + 15x, where x is the number of units produced. the business will be profitable whenever its profit y exceeds its cost. if the profit region is shaded in blue, which of the following graphs corresponds to the given situation?

Answer:

The Markdown amount: $9.45

Sale price: $13.05

Step-by-step explanation:

Convert 42% to decimal, which is 0.42

a = p(w).  (formula)

a=22.5(0.42).   or     22.5 x 0.42

a = 9.45

22.50 - 9.45 = 13.05

Step-by-step explanation:

let the third vertex=C

180-86.2=93.8°

angle near the satellite=180-(83.9+93.8)=180-177.7°=2.3°

angles of triangle are 83.9°,93.8°,2.3°

by sine formula

[tex]\frac{AC}{Sin~93.8} =\frac{AB}{Sin 2.3} \\\frac{AC}{Sin(180-93.8)} =\frac{68}{Sin~2.3} \\\frac{AC}{Sin~86.2} =\frac{68}{Sin~2.3} \\AC=\frac{Sin~86.2}{Sin~2.3} \times~68\\AC \approx 1690.69\\AC\approx1691~mile[/tex]

Using calculations based on a perpetual inventory system, the inventory balance that Altira Corporation would report in its August 31, 2024, balance sheet and the cost of goods sold it would report in the income statement, using the Average Cost Method are as follows:

The average cost method or the weighted-average cost method under the perpetual inventory system adds up all the cost of goods available for sale at each sales point and divides by the number of units available for sale in determining the average cost to be applied to the cost of goods sold.

Principally, the perpetual inventory system ensures that each inventory movement is separately recognized and the cost of goods sold determined, unlike the periodic inventory system.

August 14 for Sales of 6,000 units:

Average cost per unit = $5.46 ($54,600 ÷ 10,000)

Cost of goods sold  = $32,760 ($5.46 x 6,000)

August 25 for Sales of 7,000 units:

Average cost per unit = $5.54 ($21,840 + $33,600 ÷ 10,000)

Cost of goods sold  = $38,780 ($5.54 x 7,000)

Total cost of goods sold = $71,540 ($32,760 + $38,780)

Total cost of goods available for sale = $111,400 ($10,600 + $44,000 + $33,600 + $23,200)

Ending Inventory = $39,860 ($111,400 - $71,540)

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Answer:

B

Step-by-step explanation:

Answer:

The formula for finding the area of a triangle is:

Area = 1/2 x base x height

where "base" is the length of one of the sides of the triangle, and "height" is the distance from that side to the opposite vertex.

The volume of each shape (A right triangular prism and the trapezoidal prism are):

A right triangular prism is a three-dimensional shape that has a triangular base and three rectangular faces. It is a prism because its two bases are identical and parallel. The formula for finding the volume of a right triangular prism is V = (1/2) * base * height * length.

A trapezoidal prism is a three-dimensional shape with trapezoidal bases and four rectangular faces. It is also a prism because its two bases are identical and parallel. The formula for finding the volume of a trapezoidal prism is V = ((b1 + b2) / 2) * height * length, where b1 and b2 are the lengths of the two parallel sides of the trapezoidal base.

Recall that the formula for the volume of a trapezoidal prism is:

V = (1/2)h(b1+b2)L

where:

Hence, substituting the given values, we have:

V = (1/2)(20 + 19)(7) 4

V = (1/2)(39)(7) 4

V = (273/2) 4

V = 546ft³

Therefore, the volume of the trapezoidal prism is 546ft³

2) Recall that the formula for the volume of a right triangular prism is:

V = (1/2) * b * h * L

Where:

b is the length of the base of the triangle

h is the height of the triangle

L is the length of the prism (the distance between the triangular faces)

The factor of (1/2) is included since the base of the prism is a triangle.

Given the forumla above:

b = 9ft

h = 7ft

L = 4ft


Plugging in the values given:

V = (1/2) * 9ft * 7ft * 4ft

V = 126ft³

Therefore, the volume of the right triangular prism is 126ft³

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The gas company would charge $154.48 for using 200 hundred cubic feet of natural gas during the month.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can include numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division.

The equation that represents the gas company's monthly charges in dollars for using x hundred cubic feet of natural gas is:

y = 0.6924x + 16

Where:

x is the number of hundred cubic feet of natural gas used during the month

0.6924 is the cost per hundred cubic feet of natural gas used

16 is the fixed monthly service fee charged by the gas company.

To calculate the monthly charges for a given amount of natural gas used, we can substitute the value of x into this equation and simplify. For example, if x = 200, then:

y = 0.6924(200) + 16

y = 138.48 + 16

y = 154.48

Therefore, the gas company would charge $154.48 for using 200 hundred cubic feet of natural gas during the month.

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the axis of symmetry for the function f(x) = 7 - 4x + x²2 is x = 2.

Why it is and what does symmetry mean?

To find the axis of symmetry of the quadratic function f(x) = 7 - 4x + x²2, we can use the formula:

x = -b / 2a

where a and b are the coefficients of the x²2 and x terms, respectively, in the quadratic equation ax²2 + bx + c = 0.

In the given function, a = 1 and b = -4. Substituting these values into the formula, we get:

x = -(-4) / 2(1) = 2

Therefore, the axis of symmetry for the function f(x) = 7 - 4x + x²2 is x = 2.

Symmetry is a property that describes a balanced and consistent arrangement of parts or elements that are similar in size, shape, and position. In mathematics, symmetry refers to the idea that a geometric object, function, or equation remains unchanged after some transformation, such as a reflection, rotation, or translation.

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The measure of angle D is 100°

A triangle is a polygon with three sides having three vertices. The angle formed inside the triangle is equal to 180 degrees. It means that the sum of the interior angles of a triangle is equal to 180°.

Since the the sum of angle in a triangle is 180°, then to get the value of angle D will subtract the sum of the known angles from 180.

Therefore,

angle D = 180-( 40+40)

= 180-80

= 100°

therefore the measure of angle D Is 180°

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surface area of a refrigerator,

square feet (sq ft)

square inches (sq in)

the total area or the solid that the surface of the solid occupies.

we know that refrigerator have cuboid shape so,

surface area of cuboid =2(lb+bh+hl)

where l is length ,b is breath ,and h is height of cuboid .

The units generally  used to measure the surface area of a refrigerator are:

square feet (sq ft)

square inches (sq in)

Therefore, the options are square feet (sq ft) and square inches (sq in) correct.

Meters (m) and millimeters (mm) are typically not used for measuring the surface area of a refrigerator.

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The area of the shape, given the dimensions of the various parts of the shape, can be found to be 8, 100 ft ².

You can divide the shape into other shapes. Then you can find the areas of these shapes and then sum them up.

The area of the composite shapes would therefore be :

= ( 30 x 60 ) + ( 30 x 60 ) + ( ( 60 + 30 + 60) x 30 )

= ( 30 x 60 ) + ( 30 x 60 ) + ( 150 x 30 )

= 1, 800 + 1, 800 + 4, 500

= 8, 100 ft ²

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Option b (2x−1)(3x+4) and d 2(3x² −4x) only matches the polynomial given.

A pοlynοmial is a mathematical expressiοn cοnsisting οf variables, cοefficients, and the οperatiοns οf additiοn, subtractiοn, multiplicatiοn, and nοn-negative integer expοnents.

Pοlynοmials are an impοrtant part οf the "language" οf mathematics and algebra. They are used in nearly every field οf mathematics tο express numbers as a result οf mathematical οperatiοns. Pοlynοmials are alsο "building blοcks" in οther types οf mathematical expressiοns, such as ratiοnal expressiοns.

We have:

6x² − 8x

= 2(3x² −4x)

Then,

6x² - 3x + 8x -4

= 6x² +8x−3x−4

= 2x(3x+4) −3x −4

= 2x(3x+4)−(3x+4)

= (2x−1)(3x+4)

Thus, option b (2x−1)(3x+4) and d 2(3x² −4x) only matches the polynomial given.

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56 ounces is equal to 3 pounds and 8 ounces. So the answer is D: 3 lb 8 oz.

Pound is a unit of measurement for mass or weight commonly used in the United States and the United Kingdom. The symbol for pound is "lb".

In the English system of measurement, there are 16 ounces in one pound. To convert a weight in ounces to pounds, we need to divide the number of ounces by 16.

In this case, we have 56 ounces. So, by dividing 56 by 16, we obtain:

56 / 16 = 3 with a remainder of 8

This means that 56 ounces is equal to 3 pounds and 8 ounces. So the answer is D: 3 lb 8 oz.

In the US customary system, one pound is equal to 16 ounces, while in the imperial system used in the UK, one pound is equal to 14 ounces.

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Convert 56 ounces(oz) into pounds(Ib)

56 oz = ____lb ____oz

A. 2 lb 1 oz

B. 2 lb 3 oz

C. 2 lb 6 oz

D. 3 lb 8 oz

The value of differentiation A)  dV/dt =  2πrh(dr/dt) ,B) dV/dt = π(r²(dh/dt) , C) π(2rh(dr/dt) + r²(dh/dt))

A mathematical procedure called differentiation is used to determine the derivative of a function with respect to a variable. The rate at which one quantity changes in relation to another is determined using this method.

If we have a function f(x) = x2, for instance, its derivative f'(x) = 2x tells us how quickly the function changes in relation to x.

The following formula determines the volume V of a right circular cylinder with radius r and height h:

V = πr²h

The cylinder's radius is r in this instance, and its height is h.

When we change the formula's specified values, we obtain:

V = πr²h

=  (12)(2) = 2 cubic metres.

As a result, the right circular cylinder has a 2 cubic unit volume.

Let's now think about how dv/dt and dr/dt relate when h is constant and r varies over time.

When we take into account time t and differentiate both sides of the formula V =πr²h, we obtain:

dV/dt = d(r²h)/dt

(r²)(dr/dt)(dh/dt) = dV/dt

h is a constant, hence dh/dt = 0.

Therefore,

dV/dt= ((2r)(dr/dt)(dh/dt)

= 2rh(dr/dt)

B)

Let's now think about how dv/dt and dh/dt relate when r is constant and h varies over time.

When we take into account time t and differentiate both sides of the formula V = r²πh, we obtain:

dV/dt equals d(r²h)/dt

r²(dh/dt) = dV/dt

As r is constant, dr/dt is equal to 0.

Therefore,

r2(dh/dt) = dV/dt

C)

Given that r and h are time-varying, let's look at the relationship between dv/dt, dh/dt, and dr/dt.

When we take into account time t and differentiate both sides of the formula V = r²πh, we obtain:

dV/dt equals d(r²h)/dt

dV/dt is equal to (r²)(dh/dt) + (r²)(dr/dt)

Therefore,

((2rh(dr/dt) + r2(dh/dt))

= dV/dt)

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Parallelogram JKLM is a rectangle because it has four right angles.

The SSS (side-side-side) congruence theorem is one of the postulates of Euclidean geometry that states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

Abigali wants to prove that a parallelogram is a rectangle if its diagonals are congruent.

Since, JKLM is a parallelogram, JK≅ML.

Also by the reflexive property, KL is congruent to itself. So, since JL≅KM as well, ΔJKL ≅ ΔMLK by the SSS congruence theorem.

Now because the corresponding angles in congruent triangles are congruent, ∠JKL ≅ ∠MLK.

Also, since parallelograms have JK//ML,

Consecutive Interior Angles are supplementary.

So, since m∠JKL and m∠MLK are equal, they must both be 90°. Because the opposite angles in parallelograms are congruent, m∠MJK and m∠JML are both 90°. So, parallelogram JKLM is a rectangle because it has four right angles.

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The sides of the right triangle are 15 cm, 20 cm, and 25 cm.

What is triangle?

A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed.

Let x be the length of the shorter leg of the right triangle.

Then, according to the problem statement, the longer leg is 5 cm more than the shorter leg, which means its length is x + 5 cm.

The hypotenuse is 10 cm more than the shorter leg, so its length is x + 10 cm.

By the Pythagorean theorem, we have:

x² + (x+5)² = (x+10)²

Expanding the squares and simplifying, we get:

x² + x² + 10x + 25 = x² + 20x + 100

Subtracting x² and simplifying further, we get:

x² - 10x - 75 = 0

Factorizing the left-hand side, we get:

(x - 15)(x + 5) = 0

Therefore, the possible solutions are x = 15 and x = -5, but x cannot be negative in this context, so we take x = 15 cm.

Then, the longer leg is x + 5 = 20 cm, and the hypotenuse is x + 10 = 25 cm.

Therefore, the sides of the right triangle are 15 cm, 20 cm, and 25 cm.

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To estimate the number of square feet of carpeting needed for a room with dimensions x, y, w, z, and n, we can use the formula A = xy + w[z(2n - 1) + 2n].

What are the dimensions?

The given formula for estimating the number of square feet, A, of carpeting needed for a room x feet by y feet containing a stairway w feet by z feet with n stairs is:

A = xy + w[z(2n - 1) + 2n]

Let's break down this formula to understand the different parts:

The term w[z(2n - 1) + 2n] represents the additional area needed to cover the stairway. We add this to the area of the main part of the room, xy, to get the total area of carpeting needed, A.

So to estimate the number of square feet of carpeting needed for a room with dimensions x, y, w, z, and n, we can use the formula A = xy + w[z(2n - 1) + 2n].

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Answer:

The equation that represents the situation is: A = 200(1-0.025)^5 where A is the amount remaining after 5 years, 200 is the starting value, 0.025 is the decimal equivalent of the decay rate of 2.5%, and 5 is the number of years.

Answer: $13, 658 increase

First, we need to calculate the current total variable costs:

Total Variable Costs = Sales x Variable Costs as a % of Sales

Total Variable Costs = $603,000 x 0.63

Total Variable Costs = $380,490

Next, we can calculate the current operating income:

Operating Income = Sales - Total Variable Costs - Fixed Costs

Operating Income = $603,000 - $380,490 - $202,000

Operating Income = $20,510

If sales increase by $37,400, the new sales figure will be $640,400 ($603,000 + $37,400). We can then calculate the new total variable costs:

New Total Variable Costs = New Sales x Variable Costs as a % of Sales

New Total Variable Costs = $640,400 x 0.63

New Total Variable Costs = $404,232

Finally, we can calculate the new operating income:

New Operating Income = New Sales - New Total Variable Costs - Fixed Costs

New Operating Income = $640,400 - $404,232 - $202,000

New Operating Income = $34,168

Therefore, the operating income will increase by $13,658 ($34,168 - $20,510) if sales increase by $37,400.

The intersection (2,2) (2,4) (8,4) (8,2) is  (5,3).

On the coordinate plane, the four points that are given together form a rectangle. We must first locate the midway of both diagonals in order to determine where the diagonals will connect.

The midpoint of the diagonal that passes through the points (2,2) and (8,4) is ((2+8)/2, (2+4)/2). (5,3).

The midpoint of the diagonal that passes through the points (2,4) and (8,2) is ((2+8)/2, (4+2)/2). (5,3).

Consequently, the diagonals' point of intersection is (5,3).

Due to the fact that a rectangle's two diagonals meet here in the middle, this location also serves as the rectangle's centre.

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Step-by-step explanation:

Mona had = 32 math problems.

Let math problems shw completed be x.

Before dinner: 3/4x maths.

remaining maths = x- 3/4x

= 4x-3x/4 = 1/3x.

The loan's simple interest rate is 5.232% per quarter.

What is the formula for the future value of a loan with simple interest?

A = P(1 + rt)

where A is the future value, P is the principal, r is the simple interest rate per period, and t is the number of periods.

In this case, we have:

P = 4500

A = 4561.88

t = 3 months = 3/12 year =0.25 year

Substituting these values into the formula,

[tex]4561.88 = 4500(1 + 0.25r)[/tex]

Dividing both sides by 4500,

[tex]1.01308 = 1 + 0.25r[/tex]

Subtracting 1 from both sides,

[tex]0.01308 = 0.25r[/tex]

Dividing both sides by 0.25,

[tex]r = 0.05232 \: or \: 5.232\%[/tex]

Therefore, the loan's simple interest rate is 5.232% per quarter.

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