12 boys of the 60 students attended band camp. What
percentage of students were girls?
Go​

Answer:

34

Step-by-step explanation:

Angle A and B are complementary which means they both add up to 90 degrees. Angle A is x+22 while angle B is only x. If we add both together, we can call angle A+B to be 2x+22. We can rewrite this as 2x+22=90. Take the 22 over to the other side and its sign changes so it is now 2x=90-22. 90-22=68 so now we have 2x=68. To isolate the x divide both sides by 2 which gives us x=34.

Answer:

To find the total distance, we need to add up the distance the student ran in the first 5 days and the distance the student ran in the next 5 days.

Distance for the first 5 days = 3 1/2 miles/day × 5 days = 17.5 miles

Distance for the next 5 days = 4 1/4 miles/day × 5 days = 21.25 miles

Total distance = Distance for the first 5 days + Distance for the next 5 days

Total distance = 17.5 miles + 21.25 miles

Total distance = 38.75 miles

Therefore, the student ran a total of 38.75 miles during these 10 days.

Answer:

  25 yards long, 5 yards wide

Step-by-step explanation:

The given parameters can be used with the area and perimeter formulas for a rectangle to form an equation that can be solved for the dimensions.

The length and width can be represented by x and y. The formulas for area and perimeter give two equations relating these two variables:

  A = LW   ⇒   125 = xy

  P = 2(L+W)   ⇒ 60 = 2(x +y)

Using the second equation to write an expression for y, we have ...

  y = 30 -x

Substituting into the first equation gives ...

  125 = x(30 -x)

This suggests we can find x by looking for factors of 125 that total 30.

  125 = 1(125) = 5(25)

Factor totals are 126 and 30. This means we have ...

  x = 5, y = 30-5 = 25

or

  x = 25, y = 30 -25 = 5

The rectangle dimensions are 5 yards by 25 yards.

__

Additional comment

The two equations can also be solved graphically, as in the attachment.

The rectangle will be 25 yards long, and 5 yards wide.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.

The given parameters can be used with the area and perimeter formulas for a rectangle to form an equation that can be solved for the dimensions.

The length and width can be represented by x and y. The formulas for area and perimeter give two equations relating to these two variables:

 A = LW   ⇒   125 = xy

 P = 2(L+W)   ⇒ 60 = 2(x +y)

Using the second equation to write an expression for y, we have ...

y = 30 -x

Substituting into the first equation gives ...

125 = x(30 -x)

This suggests we can find x by looking for factors of 125 that total 30.

125 = 1(125) = 5(25)

Factor totals are 126 and 30. This means we have.

x = 5, y = 30-5 = 25

x = 25, y = 30 -25 = 5

Therefore, the rectangle will be 25 yards long, and 5 yards wide.

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Answer:

A

Step-by-step explanation:

To find the transformation, we need to take a point and the point to which it has been translated.

Let's take A and A'.

⇒ A = (2, -2)

⇒ A' = (-2, 1)

Change in x : -4 (shifted 4 units left)

Change in y : 3 (shifted 3 units up)

This means to obtain A'B'C'D' from ABCD, the graph has to be :

shifted 4 units left and 3 units up

When it comes to arrays in mathematics, it usually involves objects or numbers that are arranged in rows and columns.In order for a set of squares to be considered an array, it must meet certain requirements. These requirements are:All rows must have the same number of squares. All columns must have the same number of squares. Squares must be organized in an orderly manner. A set of squares that does not meet these requirements is not an array.

An array is a set of objects or values that are organized in a specific order. It is used in programming, mathematics, and other fields to make data manipulation and analysis easier.

When it comes to arrays in mathematics, it usually involves objects or numbers that are arranged in rows and columns.In order for a set of squares to be considered an array, it must meet certain requirements. These requirements are:All rows must have the same number of squares. All columns must have the same number of squares. Squares must be organized in an orderly manner. A set of squares that does not meet these requirements is not an array.

For example, if a set of squares is arranged in a random or disorganized manner, it cannot be considered an array because it does not meet the orderly requirement. Additionally, if the number of squares in each row or column is different, it cannot be considered an array because it does not meet the uniformity requirement.

Overall, it is important to remember that an array is a specific type of organization and cannot be applied to any random set of objects or values.

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The DJ will charge them $575.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given that,

Booking fee for DJ = $350

Rate for an hour = $45

Let x be the number of hours DJ is lasting.

Expression to find the total charge for x hours is 350 + 45x.

The Martins want to book the DJ for a party that will last 5 hours.

Cost for the DJ party for Martins = 350 + (45 × 5) = $575

Hence the cost for the DJ party booked by Martins is $575.

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Using a geometric sequence, it is found that the rule for the number of matches played in the nth round is given by:

\(a_n = 64\left(\frac{1}{2}\right)^n\)

The rule makes sense for values of n of at most 6, as in the last round, which is the 6th and final round, 1 game is played.

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

\(a_n = a_1q^{n-1}\)

In which \(a_1\) is the first term.

In this problem, we have that:

Thus, the rule is:

\(a_n = 64\left(\frac{1}{2}\right)^n\)

The last round is the final, in which 1 game is played, hence:

\(1 = 64\left(\frac{1}{2}\right)^n\)

\(\left(\frac{1}{2}\right)^n = \frac{1}{64}\)

\(\left(\frac{1}{2}\right)^n = \left(\frac{1}{2}\right)^6\)

\(n = 6\)

Hence, the rule makes sense for values of n of at most 6, as in the last round, which is the 6th and final round, 1 game is played.

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Answer:

Instructions are below.

Step-by-step explanation:

Giving the following information:

Monthly fixed cost= $6,000

Variable cost per occupied room per night= $20

Revenue per occupied room per night= $75

First, we need to structure the total cost formula:

Total cost= 6,000 + 20*x

x= occupied room

Now, we can find the expression for total revenue:

Revenue= selling price per unit*units - fixed cost - unitary variable cost*units

Revenue= 75*x - 6,000 - 20*x

I assume that the 12 rooms will be occupied for the 30 days:

Revenue= 75*(12*30) - 6,000 - 20*(12*30)

Revenue= $13,800

Finally, we need to determine the break-even point in units:

Break-even point in units= fixed costs/ contribution margin per unit

Break-even point in units= 6,000 / (75 - 20)

Break-even point in units= 109 rooms

On percentage= (109/360)*100= 30.28%

After considering the given data we come to the conclusion that the length of AB is 12.124 units, under the condition that A (-3, 5) and B (4, -2) are the given coordinates.

The distance between two points in a plane can be found using the distance formula which is an application of the Pythagorean theorem. The formula is given by d=√ ( ((x₂ – x₁ )² + (y₂ – y₁ )²)

Here (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

Applying the given coordinates of A (-3, 5) and B (4, -2), we can evaluate the distance between them as follows:

d = √( (4 - (-3))² + (-2 - 5)² )

 = √(7² + (-7)²)

 = √(98 + 49)

 = √147

 = 12.124

Therefore, the length of AB is approximately 12.124 units.

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Answer:

1). A. Add/subtract a quantity to/from only one side  

2) B. No

Step-by-step explanation:

Given equation A

5x-2+x = x-4

Given equation B

5x+x = x-4

We can see that the difference between equation A and B is the 2 that subtracted from the left hand sides of the equation A. All other functions and constants remains the same.

For us to be able to get equation B from A, we need to simply add 2 to the left hand side of equation A to cancel out the -2 that is there as shown:

From equation A:

\(5x-2+x = x-4\)

Add 2 to the left hand side of the equation

\(5x-2+x+2 = x-4\)

Simplify

\(5x-2+2+x = x-4\\5x+0+x = x-4\\5x+x = x-4\)

We can see that the resulting function gives the equation B

Hence the option B is correct i.e Add/subtract a quantity to/from only one side  

Let us find the solution to equation A and B

For equation A:

\(5x-2+x = x-4\\5x+x-2 = x-4\\6x-2 = x-4\\6x-x = -4+2\\5x = -2\\x = -2/5\)

For equation B:

\(5x+x = x-4\\5x+x-x = 4\\6x-x = 4\\5x = 4\\x= 4/5\)

Since we got different solution for x in both equation, hence both equation are not equivalent.

Answer:

Add/subtract the same quantity to/from both sides .... and yes

Step-by-step explanation:

got the answer from khan.

Answer:

53\(x_{123}\) == 134 cf

Step-by-step explanation:

A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a​

The height of the building is approximately 78.63 meters.

The following is a step-by-step explanation of how to solve the problem. We'll need to use some trigonometric concepts and formulas to find the solution.

Therefore, the height of the building is approximately 78.63 meters.

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Answer:

Step-by-step explanation:

\(\sqrt{2} cos x-1=0\\cos x=\frac{1}{\sqrt{2} } =cos (\frac{\pi }{4} ),cos (2\pi -\frac{\pi }{4} )\\cos x=cos(2n\pi +\frac{\pi }{4} ),cos(2n\pi +\frac{7\pi }{4} )\\x=2n\pi +\frac{\pi }{4} ,2n\pi +\frac{7\pi }{4} \\n=0\\x=\frac{\pi }{4} ,\frac{7\pi }{4}\)

The simplified expression involving complex numbers is given as follows:

5 + 5i.

Complex numbers are number that have a real and an imaginary part, and are defined as follows:

z = a + bi.

In which:

The basic relation of complex numbers is given as follows:

i² = -1.

The fraction for this problem is given as follows:

(2 + i)(4 - 2i)/(1 + i).

The numerator is simplified as follows:

(2 + i)(4 - 2i) = 8 - 4i + 4i - 2i² = 8 + 2 = 10.

Hence the fraction is of:

10/(1 + i).

To remove the complex number from the denominator, the entire fraction is multiplied by the conjugate of the denominator, hence:

10/(1 + i) x (1 - i)/(1 - i) = 10(1 + i)/(1 - i²) = 10(i + 1)/2 = 5 + 5i.

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Answer:

Since the computed value of t= -4.654 does not fall in the critical region we therefore accept the null hypothesis . We conclude that there is sufficient evidence to indicate a difference in the means time served for fraud is less than that for firearms offenses.

Step-by-step explanation:

Fraud                                        Firearm

15.2      9.2                              20.1          15.7

11.2       15.8                             20.4          9.8

7.2         5.2                             13.1           13.5

7.7         4.9                            20.7           23.1

7.4        9.8                            10.4            22.2            

∑ 93.6                                             169                    

Fraud  (X1i)²                                      Firearm(X2j)²

231.04      84.64                           404.01          246.49

125.44      249.64                          416.16          96.04

51.84        27.04                            171.61           182.25

59.29       24.01                            428.49           533.61

54.76        96.04                            108.16           492.84

∑1003.79                                                  3079.66          

We formulate the null and alternative hypothesis as

H0: μ1 - μ2 ≤ 0 i.e. the fraud meantime is less than that for firearms offenses.

Ha: μ1-  μ2  > 0  i.e. the fraud meantime is greater than that for firearms offenses.

We set the significance level at ∝= 0.01

The test statistic, if  H0 is true , is

t=  x1`1- x`2/ Sp√1/n1+ 1/n2

which has a student t- distribution with ν= n1+ n2 -2 = 18 degrees of freedom

The critical region consists of all t- values which are greater than or equal to  t> t(0.01)(18)= 2.522

Computations :

X1`= ∑X1i/n1 = 93.6/10= 9.36

X2`=∑X2j/n2=169/10 = 16.9

∑( X1i- x`1)² = ∑X1i²- (∑X1i)²/n1

= 1003.79 - 876.096/10

= 100.379- 87.6096

=12.7694

∑( X2j- x`2)² = ∑X2j²- (∑X2j)²/n2

= 3079.66 - 28561/10

= 3079.66- 2856.1

=223.56

Sp²= 12.7694+223.56/18= 13.129

Sp = √13.129 =3.623

t= 9.36-16.9/ 3.623√0.1+0.1

t= -7.54/ 1.62

t= -4.654

Conclusion: Since the computed value of t= -4.654 does not fall in the critical region we therefore accept the null hypothesis . We conclude that there is sufficient evidence to indicate a difference in the means time served for fraud is less than that for firearms offenses.

The meantime served for fraud is less than that for firearms offenses.

The expression P(A + B) = P(A) + P(B) - P(AB) is proved.

Proved is shown below.

A set is a collection of items where there are operations such as:

Union of sets, the intersection of sets, complements of sets.

We have,

Consider A = {1, 2, 3, 4, 5}

B = {2, 3, 4, 6, 7}

P (A + B) = P (A U B)

P (AB) = P (A ∩ B) (Common values}

P (AB) = {2, 3, 4}

P (A + B ) = {1, 2, 3, 4, 5, 6, 7}

Now,

P(A + B) = P(A) + P(B) - P(AB)

{1, 2, 3, 4, 5, 6, 7} = {1, 2, 3, 4, 5} + {2, 3, 4, 6, 7} - {2, 3, 4}

{1, 2, 3, 4, 5, 6, 7} = {1, 2, 2, 3, 3, 4, 4,5, 6, 7} - {2, 3, 4}

{1, 2, 3, 4, 5, 6, 7} = {1, 2, 3, 4, 5, 6, 7}

Thus,

P{A + B) = P(A) + P(B) - P(AB) proved.

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Answer:

Just use a calculator.

8.66666666667

8.45833333333

8.08333333333

8.29166666667

Step-by-step explanation:

The value of x= 4.

This is the boundary or contour length of a 2D geometric shape.

Depending on their size, multiple shapes may have the same circumference. For example, imagine a triangle made up of wires of length L.

The same wire can be used to create a square if all sides are the same length.

The length covered by the perimeter of the shape is called the perimeter. Therefore, the units of circumference are the same as the units of length.

As we can say, the surroundings are one-dimensional. As a result, you can measure in meters, kilometers, millimeters, etc.

Inches, feet, yards, and miles are other globally recognized units of circumference measurement.

According to our question-

cos(60)= x/8

x=1/2*8

x=4

Hence, The value of x= 4.

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The domain value that corresponds to a range value of 4 is,

⇒ x = 1/2

Given that;

Function is,

y = 4x + 2

Since, the equation equal to the range value:

4 = 4x + 2

Then, we can solve for "x":

4 - 2 = 4x

2 = 4x

x = 1/2

Now that we have the value of "x", we can find the corresponding value of "y" by substituting it into the given equation:

y = 4x + 2

y = 4(1/2) + 2

y = 4 + 2

y = 6

Therefore, the domain value that corresponds to a range value of 4 is,

⇒  x = 1/2

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Answer:

22.5%

Step-by-step explanation:

Find new values:

124(1−0.25)=93

125(1−0.2)=100

Last Year: Boys 124 & Girls 125

This Year: Boys 93 & Girls 100

Total: Last Year 249 & This Year 193

249(1−r)=193

249(1−r)/249=193/249

1−r=0.7751

−r=−0.2249(Subtracted 1)

r=0.2249(Divided by -1)

Final Answer: 22.5%(Multiply by 100 and round to nearest 10th)

The thermometer reading would be 73.48°C.

The boiling point of water is generally considered to be 100°C. According to the given information, the temperature of the liquid in the thermometer is 26.52°C lower than the boiling point of water. Therefore, to find the thermometer reading, we subtract 26.52 from 100.

100 - 26.52 = 73.48

Hence, the thermometer reading would be 73.48°C.

In this scenario, we are assuming that the thermometer is calibrated to measure temperature in Celsius. The boiling point of water at standard atmospheric pressure is 100°C, and the given information states that the liquid in the thermometer is 26.52°C lower than the boiling point.

By subtracting 26.52 from 100, we obtain a reading of 73.48°C.

Thermometers work by utilizing the principle that certain substances, such as mercury or alcohol, expand or contract with changes in temperature. The expansion or contraction is measured using a scale, which is marked with various temperature values.

In this case, the thermometer is calibrated in Celsius, so we refer to the Celsius scale. By subtracting 26.52 from 100, we find the temperature at which the liquid in the thermometer is settled, which is 73.48°C.

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Answer:

the savings is 6000

Step-by-step explanation:

We are told that the ratio of savings to expenditure is 2: 8, that is, that person saves 2 when he spends 8.

They tell us to find the savings when the cost is 24,000, so we are left with:

24000 * 2/8 = 6000

which means that when 24000 are spent the savings is 6000

Answer:

B. 37 units

Step-by-step explanation:

DE = 4x + 1

AB = 11x - 25

DE is a midsegment of the ∆ABC

Therefore:

DE = ½(AB) => Triangle Midsegment Theorem

4x + 1 = ½(11x - 25)

2(4x + 1) = 11x - 25

8x + 2 = 11x - 25

Collect like terms

8x - 11x = -2 - 25

-3x = -27

-3x/-3 = -27/-3

x = 9

✔️DE = 4x + 1

Plug in the value of x

DE = 4(9) + 1 = 36 + 1

DE = 37

Answer:

40.375

Step-by-step explanation:

I hope this helps

Answer:

I think soup B if i get it wrong sry

Step-by-step explanation:

Answer:

Soup A

Step-by-step explanation:

154 = 11x14

so 7x14 = 98 (answer for soup a ratio table)

154=14x11

for soup b: 6x11 = 66 (answer for soup b ratio table)

soup A has more sodium per cups because it has 98 grams for 154 cups while B only has 66 gram for 154 cups

Answer:

31.42 m

Step-by-step explanation:

circumference = (pi)d

circumference = 3.14159 * 10 m

circumference = 31.4159 m

Answer: 31.42 m

Answer: circumference =31.42m

Step-by-step explanation:

Answer:

1a8?

Step-by-step explanation:

thi is how

The incorrect statement for the given condition is;

⇒ |a| > b

What is Number line?

Number line is a horizontal line where numbers are marked at equal intervals one after another form smaller to greater.

Given that;

A number line shows 'a' to the left of 0 and 'b' to the right of 0. Point a is closer to 0 than point b.

Now,

Since, Point a is closer to 0 than point b.

And,  Number 'a' to the left of 0 and 'b' to the right of 0.

Hence,

Let the number 'a' = - 1

Then, The number 'b' = 2

So, We get;

|a| = |-1| = 1

And, |b| = 2

Clearly, |a| < b

Thus, The incorrect statement for the given condition is;

⇒ |a| > b

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Answer:

(C) Multiply first equation by -2 and second equation by 3, solution (1, 1)

Step-by-step explanation:

Simultaneous equations are set of equations which possess a common solution. The equations can be solved by eliminating one of the unknowns by multiplying each of the equations in a way that a common coefficient is obtained in the unknown to be eliminated.

Given the simultaneous equations:

3x - 5y = -2

2x + y = 3

First step:

Multiply first equation by -2 and multiply second equation by 3,

-6x + 10y = 4

6x + 3y = 9

Second step:

Add the two equations together,

13y = 13

Divide both sides by 13

y = 1

Third step:

Put y = 1 in the first equation

3x - 5(1) = -2

3x - 5 = -2

3x = 5 - 2

3x = 3

Divide both sides by 3:

x = 1

solution (x,y) = (1,1)

Option C

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Answer:

<

Step-by-step explanation:

1) Substitute 5 into the question

2) Work out the sides

3) Put it into an inequality

5 < 7

Hope this helps, have a great day!

The entropy of the outcome of this experiment = 9

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

Given that,

A coin having probability p=2/3

Heads is flipped 6 times

If the coin is flipped 6 times

The Total Number of Trial in the Experiment =2/3

It comes up heads 6 times

This Means: Number of Successful Outcome of HEADS =6

In an experimental probability,

Experimental probability of the coin’s coming up heads

=Number of Successful Outcome of HEADS/Total Number of Trials in the Experiment

= 6/(2/3)

= 6*3/2

= 18/2

= 9

Therefore,

The entropy of the outcome of this experiment = 9

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