There are eight​ groups of students, each working on a science project in the gym. Each group has the same number of students. Mr. Davids asks for 44​ students from each group come with him to get more supplies. Now there are a total of 5656​ students in the gym.

a. Write an equation to represent this situation, where xx​ represents the number of students in each group.

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b. How many students are in each group? Simplify your answer completely.

The proportion EF/DF = BC/AC is true. Hence, option A is the accurate answer to this question.

We are given that the two triangles ΔABC and ΔDEF are similar.

According to the definition of a similar triangle, we know that the ratio of the corresponding sides is proportional and the corresponding angles are always congruent.

Since ΔABC and ΔDEF are similar, this implies that -

∠A corresponds to ∠D,

∠B corresponds to ∠E, and

∠C corresponds to ∠F.

Thus we can say -

EF/DF = BC/AC

AB/DF = DE/AC

AB/EF = DE/BC

Only option A satisfies the condition. Hence, the proportion EF/DF = BC/AC is true.

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The complete question is -

The triangle abc and triangle def are similar. Which proportion must be true?

The total surface area is π[(4/3)x]² + π(4/3)x². The base area is greater than the lateral area.

An equation is an expression that shows how numbers and variables are related using mathematical operations. Equations can be linear, quadratic, cubic and so on.

Given the cone. The surface area (SA) is given by the equation:

SA = πr² + πrs

where r is the radius of the cone and s is the slant height.

Given that the slant height is x and the radius of the cone is 4/3 the slant height = (4/3)x

Hence:

SA = πr² + πrs

substituting:

SA = π[(4/3)x]² + π(4/3)x(x)

SA = π[(4/3)x]² + π(4/3)x²

The base area = π[(4/3)x]², the lateral area =  π(4/3)x²

The base area is greater than the lateral area.

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The cost of a pair of pants is $17.

And the cost of a shirt is $31.

One or many equations having the same number of unknowns that can be solved simultaneously are called simultaneous equations. And the simultaneous equation is the system of equations.

Given:

The total cost of 5 shirts and 3 pairs of pants is $206.

The total cost of a shirt and a pair of pants is $48.

Let y be the cost of a pair of pants and x be the cost of a shirt.

That means,

we have the system of equations,

x + y = 48   {equation 1}

5x + 3y = 206   {equation 2}

Multiply 5 to the equation 1 and then subtract equation 2 to equation 1,

we get,

2y = 34

y = 17

And x = 48 - 17 = 31.

Hence, $17 is the cost of a pair of pants.

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Volume of the composite shape is =  114 ft³

Volume is a measure of three-dimensional space.

A composite shape can be defines as a shape created with two or more basic shapes. We often refer to composite shapes as compound and complex shapes as well.

Now, According to the question:

The shape above shows two cuboid joined together.

Volume of the base cuboid = lbh

= 6×3×1 = 18ft³

Volume of the second cuboid = lbh

= 4×3×8 = 96 ft³

Volume of the composite shape = 18ft³ + 96ft³

= 114 ft³

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The measure of angle ABC from the given circle D is 34°.

The angles at the circumference subtended by the same arc are equal. More simply, angles in the same segment are equal.

Given that, circle with the center D and measure of arc AC is 34°.

The measure of arc = m∠ABC

m∠ABC =34°

Therefore, the measure of m∠ABC is 34°.

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Answer:

First option: 37°, 11°,  132°

Step-by-step explanation:

The sum of the three interior angles of a triangle must add up to 180°

Only the first option 37°, 11° and 132° add up to 180°
37 + 11 + 132 = 48 + 132 = 180°

You don't need to add up all the other sets of angles completely. Just look at the units place

Option 2, units sum = 4 + 6 + 1 =11; does not end in a 0, ends in 1

Option 3: units sum = 1 + 0 + 2; does not end in a 0, ends in 3

Option 4: units sum = 0 + 1 + 5 ends in a 6

The volume of the triangular prism is 433.013cm^3.

Triangular prism formulas

volume = 0.5 * b * h * length , where b is the length of the base of the triangle, h is the height of the triangle, and length is prism length. area = length * (a + b + c) + (2 * base_area) , where a, b, c are sides of the triangle and base_area is the triangular base area.

We are given that;

Base area of prism = 10cm

Breadth of prism= 10cm

Height of prism = 10cm

Now,

To find the volume of triangular prism

Volume = base area × length of the prism

=10x43.3013cm

=433.013

Therefore, the volume of prism will be 433.013cm^3

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The measurement of the angle 1 in the given parallel lines is 35° whereas the value of x is 15.

Parallel lines are those straight lines that are always the same distance apart from each other.

Given that, two lines RS and TU are parallel, and ∠ 7 = 3x-10 and ∠ 3 = 2x+5,

We need to find ∠ 1

Since, ∠ 7 and ∠ 3 are corresponding angles between two parallel lines therefore, both are congruent,

Therefore,

3x-10 = 2x+5

x = 15

Now, ∠ 1 = ∠ 3 as they are vertically opposite angles,

Therefore,

∠ 1 = 2(15)+5

∠ 1 = 35°

Hence, the measurement of the angle 1 in the given parallel lines is 35° whereas the value of x is 15.

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The figure was not given so the figure is attached.

Answer: To find the ordered pair that is a solution of the equation y = 4x - 7, we need to substitute the values of x and y into the equation and see if it is true.

If (x, y) is a solution, then y = 4x - 7 must be true for that particular x and y.

Option A: (2, 1)

Substituting x = 2 and y = 1 into the equation, we get:

1 = 4 * 2 - 7

1 = 8 - 7

1 = 1

Since the equation is true for x = 2 and y = 1, (2, 1) is not a solution of the equation.

Option B: (4, 9)

Substituting x = 4 and y = 9 into the equation, we get:

9 = 4 * 4 - 7

9 = 16 - 7

9 = 9

Since the equation is true for x = 4 and y = 9, (4, 9) is a solution of the equation.

Option C: Both (2, 10) and (4, 9)

Substituting x = 2 and y = 10 into the equation, we get:

10 = 4 * 2 - 7

10 = 8 - 7

10 = 3

Since the equation is not true for x = 2 and y = 10, (2, 10) is not a solution of the equation.

So, the only ordered pair that is a solution of the equation y = 4x - 7 is (4, 9). The answer is B) only (4, 9).

Step-by-step explanation:

Miss Carol's bank account is losing money at a daily rate of $15, After giving money to her friend, Miss Carol's account balance fell by $65 leaving her with $435.

We must calculate Miss Carol's account balance's daily decline in order to ascertain the rate of change in her bank account.

Since Miss Carol lent her friend $65 this month, her account balance is reduced by $65, leaving her with $500 - $65 = $435.

The information that her account is losing $15 every day can then be put to use. We can write this as:

Rate of change = -$15 per day

The negative symbol signifies a declining amount on her account.

Therefore, Miss Carol's bank account is losing money at a daily rate of

$15, After giving money to her friend, Miss Carol's account balance fell by $65 leaving her with $435.

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On solving the provided question we can say that by bodmas ((4 / 3) / (1/4)) + ((2 / 5) / (1/4)) + ((4 / 15) / (1/4)) =8

The acronym BODMAS helps children learn the hierarchy of math operations (the correct order for solving math problems). The acronym BODMAS is made up of the following terms:

B Bracket, O Degrees (Power/Exponent or Square Root), D Division, M Multiplication, A Addition, and S Subtraction. BODMAS is also known as PDMAS in some areas. It symbolizes exponents, division, multiplication, addition and subtraction. It also represents brackets. The BODMAS rule states that parentheses must be handled first, then powers or roots (that is, of), division, multiplication, addition, and finally subtraction. Known as BODMAS in India and the UK, PEMDAS is primarily used in the US. However, they are identical to each other. The parentheses, order, and order of addition, subtraction, multiplication, and division are the same for the two rules.  

by bodmas

((4 / 3) / (1/4)) + ((2 / 5) / (1/4)) + ((4 / 15) / (1/4)) =8

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Answer:ez

Step-by-step explanation: blah blah blah blah

Answer:

This is a math problem. To solve it, you need to use algebra. Let me show you how.

Let x be the number of badges Katya sold. Then we can write an equation using the given information:

46 × 1.40 + 32 × 1.50 + 0.90 × x = 134

Simplifying the equation, we get:

64.4 + 48 + 0.9x = 134

Subtracting 64.4 and 48 from both sides, we get:

0.9x = 21.6

Dividing both sides by 0.9, we get:

x = 24

Therefore, Katya sold 24 badges.

Step-by-step explanation:

Answer:

To solve the problem, Sarah used the equation:

Left-handed people = (11/100) * Total people

Step 1: Plug in the total number of people (30) into the equation.

Left-handed people = (11/100) * 30

Step 2: Simplify the right side of the equation.

Left-handed people = (11/100) * 30

Left-handed people = 3.3

Step 3: Round the answer to the nearest whole number.

Left-handed people = 3

So, Sarah expects 3 people in a class of 30 to be left-handed. Each step of Sarah's work is justified because she used the percentage formula to find the number of left-handed people in a class and rounded the answer to the nearest whole number.

By using Python to calculate the value of sin4 is a simple process that involves understanding the concept of radians and using the sine function available in Python's math module.

A radian is a unit of measurement for angles. It is defined as the angle formed when the arc length of a circle is equal to the radius of that circle. This means that an angle of 1 radian is equal to the angle formed by an arc length of 1 radius on a circle.

The sine function, denoted as sin(x), is a mathematical function that takes an angle x as input and returns the ratio of the opposite side to the hypotenuse in a right-angled triangle with an angle x.

Now, we can proceed to calculate the value of sin4 using Python. In Python, the sine function is available in the math module, so we will need to import this module at the beginning of our code. We will then use the sin() function to calculate the sine of 4 radians as follows:

import math

sin4 = math.sin(4)

Here, we are calling the sin() function and passing it the value of 4 as an argument. Since the sine function in Python accepts radians, we do not need to convert 4 to degrees.

Finally, we store the result of this calculation in a variable called sin4. This variable will now hold the value of the sine of 4 radians, which we can use in our program as needed.

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Answer:

[tex]x = \frac{17}{3} = 5\frac23 = 5.\overline6[/tex].

Step-by-step explanation:

No idea what your question is, but [tex]x = \frac{17}{3} = {5\frac23} = 5.\overline{6}[/tex].

The lower bound for the weight 21.58 g correct to 2 decimal places is 21.57 g. This is because the next smallest value based on the rounding is obtained rounding down the number in second decimal place, which is 5.

To find the lower bound for the weight 21.58 g correct to 2 decimal places, we need to consider the next smallest number that can be represented to 2 decimal places.

Since the second decimal place is 8, the next smallest number is obtained by rounding down the number in the second decimal place, which is 5. Therefore, the lower bound for 21.58 g correct to 2 decimal places is: 21.57g

Note that the weight could be more precise than what we are given, but to represent it to 2 decimal places we have to make an assumption about the last digit.

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The surface area of the given cylinder is 602.88 square centimeters.

The surface area of the cylinder is: A = 2πr(r+h)

where 'r' is the radius of the base (circle) of the cylinder

'h' is the height of the cylinder

The cylinder with a height of 10 cm and a radius of 6 cm.

⇒ A = 2πr(r+h)

Here h = 10 cm and r = 6 cm

Substitute the known values in the above formula,

⇒ A = 2(3.14)(6)(6+10)

⇒ A = (12.56)(6)(16)

Apply the multiplication operation, and we get

⇒ A = 602.88

Therefore, the surface area of the given cylinder is 602.88 cm².

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The total number of cupcakes packed is 846 cupcakes.

percentage, a relative value indicating hundredth parts of any quantity.

Let's first find out the number of boxes of each size:

40% of 60 boxes = 24 boxes are medium

35% of 60 boxes = 21 boxes are small

The remaining 60 - 24 - 21 = 15 boxes are large

Now we can calculate the total number of cupcakes packed:

24 boxes x 15 cupcakes per medium box = 360 cupcakes in medium boxes

21 boxes x 6 cupcakes per small box = 126 cupcakes in small boxes

15 boxes x 24 cupcakes per large box = 360 cupcakes in large boxes

Therefore, the total number of cupcakes packed is 360 + 126 + 360 = 846 cupcakes.

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The system using substitution has its solution to be (-1.8, -1.2)

From the question, we have the following parameters that can be used in our computation:

3x-2y=3

y=6+4x

By susbstitution, we have the following equation

3x - 12 - 8x = 3

Evaluate the like terms

so, we have the following representation

-5x = 9

Divide by 5

x = -1.8

So, we have

y= 6 + 4 * -1.8

Evaluate

y = -1.2

Hence, the value of y is -1.2

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According to the above, we can infer that the value of FE is: 10 cm

To find the value of FE we must analyze the image of this triangle. Additionally, we must take into account the information we know, that is, the length of two sides (5 cm) and the height (4 cm), the area (20cm²).

So we must use the formula for the area of a triangle and isolate the values that we do know to find the value of the base.

According to the above, the value of segment FE is 10 cm.

Note: This question is incomplete. Here is the complete information:

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The measure of BC from the triangle ABC is 40.82 units.

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

Given that, in triangle ABC, AB=21 units and AC=35 units.

By using Pythagoras theorem,

BC²=AB²+AC²

BC²=21²+35²

BC²=441+1225

BC²=1666

BC=√1666

BC=40.82

Therefore, the measure of BC is 40.82 units.

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Answer:R(d)=0.30d+75

Step-by-step explanation:

Note:  This equation, as requested, only shows the cost of

rental on a daily basis.  In order to solve for more than 1

day the equation should be:  Cost = .3r+ 100d or something

similar... with r representing miles driven, d representing

total number of days for the rental.

The two states will never have the same median house value.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The intercepts are given by the values of each home in 1950, thus:

The slopes are given by the average change over the 50 years, hence:

As the number of years must be positive, Delaware starts with the higher income and has a higher yearly increase, the two states will never have the same median house value.

Solving 35500 + 1416x = 55000 + 1508x, we would end up with a negative value of x.

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The IQR of the data is 10 years and option B is the correct answer.

The dispersion of the middle 50% of the sample is measured by the interquartile range, or IQR, which is the difference between the top and lower quartiles.

The given data is:  2, 4, 5, 5, 5, 7, 9, 10, 12, 14, 15, 15, 18, 20, 24.

The median of the data is:

M = 15 + 1 /2 = 16/2 = 8th value.

M = 10

Ignoring the median divide the data into two parts.

The lower quartile median is 4th term:

Q1 = 5

The upper quartile median is 12th term:

Q2 = 15

IQR = Q2 - Q1

IQR = 15 - 5 = 10 years.

Hence, the IQR of the data is 10 years and option B is the correct answer.

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Answer:

hey there here's your answer !!!!

Step-by-step explanation:

For two-digit numbers, there is the TENS place and the ONES place. Let's take a closer look at the place value for the number 12. The 1 is in the TENS place, and the 2 is in the ONES place. That's because the number 12 is made up of 1 ten and 2 ones.

Time for working for history is 50 minutes.

First we need to multiply to make the fractions have equal denominators so we can add/subtract.

Science: 1/3 x 4/4=4/12

Math: 1/4 x 3/3=3/12

Now we can find the time she spent on history (I assume this is what you are looking for)

Total time-math time-science time=history time

12/12-4/12-3/12

=5/12

Macy spent 5/12 of her time working on history.

so totak fo 2 hours she spent 5/12 time to work on history

so 2 hours*5/`12 = 5/6 hours = 50 minutes

Q- Macy spent 2 hours working on homework she spent 1/4 of that time working on math he spent 1/3 of her time working on science find time for working for history.

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Answer:

68

Step-by-step explanation:

-2[-4+ 3(2 - 32 + 4 · 2 -3) - 3]  Start in the center and work your way out.

-2[-4 + 3(2 - 32 + 8 -3) - 3]

-2[-4 + 3(-30 + 8 - 3) -3]

-2[-4 + 3(-22 -3) -3]

-2[-4 + 3(-25)-3]

-2[-4 -27 -3}

-2[-31 - 3]

-2(-34)

68