Help
the high school concert choir has 7 boys and 15 girls. the teacher needs to pick three soloists for the next concert but all of the members are so good she decides to randomly select the three students for the solos.
a) in how many ways can the teacher select the 3 students?
b) what is the probability that all three students selected are girls
c) what is the probability that at least one boy is selected?

Answer:

Please check the explanation.

Step-by-step explanation:

Given the equation

\(-x + 2y = 4\)

a) writing the equation in the slope-intercept form

We know that the slope-intercept form of the equation of the line is

\(y=mx+b\)

where m is the slope of the line

so writing the equation in the slope-intercept form

\(-x + 2y = 4\)

\(2y=4+x\)

\(y=\frac{1}{2}x+2\)

b) Identify the slope of the line represented in part a

As the equation in slope-intercept form is

\(y=\frac{1}{2}x+2\)

Here,

m = slope = 1/2     ∵ \(y=mx+b\)

c) What is the slope of the line perpendicular to the line in steps a and b

As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line, so

As the slope = 1/2

So the slope of the perpendicular line will be: -2

d. Write the equation of the perpendicular line in slope-intercept form.

Therefore, the point-slope form of the equation of the perpendicular line that goes through (-2,1) is:

\(y-y_1=m\left(x-x_1\right)\)

substituting the values m = -2 and the point (-2,1)

\(\:y-1=-2\left(x-\left(-2\right)\right)\)

\(y-1=-2\left(x+2\right)\)

Add 1 to both sides

\(y-1+1=-2\left(x+2\right)+1\)

\(y=-2x-3\)

The slope for the situation is $2.96

Since the food delivery service charges $5.92 for every 2 meals delivered, plus a $2.50 service fee.

We need to find the slope for the food delivery service charge.

Since we have $5.92 for every 2 meals delivered, the slope is

$5.92/2 meals = $2.96

So, the slope for the situation is $2.96

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Answer:

The slope for the situation is $2.96

Step-by-step explanation:

Answer:

CP = Rs 500

Step-by-step explanation:

Given that,

Selling price of a book, SP = Rs 550

Profit percent = 10%

We need to find the cost price of the book. The formula for profit percent is given by :

Answer:

\(\frac{3^{n} }{3^{2(n-1)} }\)

Step-by-step explanation:

3²⁻ⁿ is the simplification of  3ⁿ/9ⁿ⁻¹ in powers of 3.

An expression is combination of variables, numbers and operators.

The given expression is  3ⁿ/9ⁿ⁻¹

three power n divided by nine power n minus one.

To express to the power of 2, we have few properties of exponentials.

aˣ/aⁿ=aˣ⁻ⁿ

aˣ.aⁿ=aˣ⁺ⁿ

The given expression is

3ⁿ/9ⁿ⁻¹

3ⁿ/(3²)ⁿ⁻¹

3ⁿ/3²ⁿ⁻²

3ⁿ.3⁻²ⁿ⁺²

When bases are same then we will add the powers

3ⁿ⁻²ⁿ⁺²

3²⁻ⁿ

Hence 3²⁻ⁿ is the simplification of  3ⁿ/9ⁿ⁻¹ in powers of 3.

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Answer:

commutative property

Step-by-step explanation:

it is

Option- 3 is correct that is both a and b are true.

a. The statement is true that is cosx = \(1 - \frac{sinx}{cscx+cotx}\)

b. The statement is true that is sinx = \(1 - \frac{cosx}{secx+tanx}\)

Given that,

a. We have to prove the statement is true or false.

Statement: cosx = \(1 - \frac{sinx}{cscx+cotx}\)

Now, Take the right hand side

= \(1 - \frac{sinx}{cscx+cotx}\)

= \(1 - \frac{sinx}{\frac{1}{sinx} +\frac{cosx}{sinx} }\)

By using LCM

= \(1 - \frac{sinx}{\frac{1+cosx}{sinx} }\)

= \(1 - \frac{sinx\times sinx}{1+cosx} }\)

= \(1 - \frac{sin^2x}{1+cosx} }\)

= \(\frac{1+cosx - sin^2x}{1+cosx} }\)

We know from trigonometric identities 1 - sin²x = cos²x

= \(\frac{cos^2x+cosx }{1+cosx} }\)

= \(\frac{cosx(1+cosx )}{1+cosx} }\)

= cosx

LHS = RHS

Therefore, The statement is true

b. We have to prove the statement is true or false.

Statement: sinx = \(1 - \frac{cosx}{secx+tanx}\)

Now, Take the right hand side

= \(1 - \frac{cosx}{secx+tanx}\)

= \(1 - \frac{cosx}{\frac{1}{cosx} +\frac{sinx}{cosx} }\)

By using LCM

= \(1 - \frac{cosx}{\frac{1+sinx}{cosx} }\)

= \(1 - \frac{cosx\times cosx}{1+sinx} }\)

= \(1 - \frac{cos^2x}{1+sinx} }\)

= \(\frac{1+sinx - cos^2x}{1+sinx} }\)

We know from trigonometric identities 1 - cos²x = sin²x

= \(\frac{sin^2x+sinx }{1+sinx} }\)

= \(\frac{cosx(1+sinx )}{1+sinx} }\)

= sinx

LHS = RHS

Therefore, The statement is true

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Answer:

A (equals -320.0064 just like in the question)

The estimated current total cost for the installed and insulated tank is $12,065.73.

The first step is to calculate the surface area of the tank. The surface area of a cylinder is calculated as follows:

surface_area = 2 * pi * r * h + 2 * pi * r^2

where:

r is the radius of the cylinder

h is the height of the cylinder

In this case, the radius of the cylinder is 1 meter (half of the diameter) and the height of the cylinder is 1 meter. So the surface area of the tank is:

surface_area = 2 * pi * 1 * 1 + 2 * pi * 1^2 = 6.283185307179586

The insulation will add a thickness of 0.05 meters to the surface area of the tank, so the total surface area of the insulated tank is:

surface_area = 6.283185307179586 + 2 * pi * 1 * 0.05 = 6.806032934459293

The cost of the insulation is $40 per square meter and the cost of labor is $95 per square meter, so the total cost of the insulation and labor is:

cost = 6.806032934459293 * (40 + 95) = $1,165.73

The original cost of the tank was $10,900, so the total cost of the insulated tank is:

cost = 10900 + 1165.73 = $12,065.73

Therefore, the estimated current total cost for the installed and insulated tank is $12,065.73.

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Amount of iced-tea consumed during party was 92 cups, which is equivalent to 23 quarts. It's important to note difference between volume units such as cups and quarts, and the conversion factor between them.

To determine the number of cups of iced-tea that were consumed during the party, we need to subtract the amount that remained from the total amount that was in the drink dispenser at the start of the party.

One cup of iced tea is equal to 1/16 of a quart, so 7 cups is equal to

7 * (1/16) = 7/16 quarts.

Thus, the total amount of iced tea that was consumed during the party is 912 quarts -

7/16 quarts = 912 - 7/16

= 912 - 7 * (1/16)

= (912 * 16 - 7 * 1) / 16

= 1476 / 16

= 92.25 cups, rounded down to the nearest whole number, which is 92 cups.

It is important to note that the answer is given in cups and not quarts. Quarts is a unit of volume and cups is a unit of volume as well, but they are not equivalent. 1 quart is equal to 4 cups. If we wanted to express the amount of iced tea consumed in quarts, we would multiply the answer by 1/4.

In conclusion, the number of cups of iced tea consumed during the party is 92 cups, and if we express this in quarts it is equivalent to

92 * (1/4) = 23 quarts.

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The assumption that is NOT true about the error term E in regression analysis is (a) the expected value of the error term is one. The correct statement is that the expected value of the error term is zero.

The assumption that is NOT true about the error term E in regression analysis is (a) the expected value of the error term is one.

In regression analysis, the error term E, also known as the residual or the disturbance term, represents the unexplained variation in the dependent variable. The assumptions about the error term in regression analysis are as follows:

a) The expected value of the error term is zero, not one. This assumption is known as the zero conditional mean assumption or the assumption of no systematic bias. It states that, on average, the error term does not have a systematic relationship with the independent variables.

b) The variance of the error term is the same for all values of x. This assumption is called homoscedasticity. It means that the spread or dispersion of the error term is constant across different levels of the independent variables.

c) The values of the error term are independent. This assumption implies that the errors for different observations in the dataset are not correlated or dependent on each other. Each observation's error term is assumed to be unrelated to the errors of other observations.

d) The error term is normally distributed. This assumption, known as normality, states that the errors follow a normal distribution. It is important for various statistical tests and estimation methods used in regression analysis.

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The expression for the area of the flower garden is (45+2x)(20+2x) - 900.

Area of vegetable garden:

\(A_v = 45 ft * 20 ft\) = 900 sq ft

Dimensions of entire garden:

Length = 45 ft + 2x

Width = 20 ft + 2x

Area of entire garden:

\(A_e = (45+2x)(20+2x)\)

Area of flower garden:

\(A_f = A_e - A_v = (45+2x)(20+2x) - 900 sq ft\)

So, the expression for the area of the flower garden is (45+2x)(20+2x) - 900.

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Answer:

a) 1.07, b) 0.1423

Step-by-step explanation:

Answer:

\(P=24\: m\)

\(A=41.52 \m^{2}\)

Step-by-step explanation:

El perímetro de un hexágono se calcula de la siguiente manera:

\(P=6*l\)

l es el lado del hexágono l = 4 m

Entonces P es:

\(P=6*4=24\: m\)

El área del hexágono puede calcularse de la siguiente manera:

\(A=\frac{P*Ap}{2}\)

P es el perímetro = 24 m

Ap es la apotema = 3.46 m

El Area sera:

\(A=\frac{24*3.46}{2}\)

\(A=41.52 \m^{2}\)

Espero te haya sido de ayuda!

Answer:

length=70cm

width=7cm

Step-by-step explanation:

total ratio=10 + 1

=11

length(2)=10/11 x 154 cm

=10 x 14cm

=140cm

one length is 140 cm/2=70cm

width(2)=1/11 x 154cm

=14cm

one width is 14cm/2=7cm

The length and the width should be considered as the 70 cm and 7 cm.

Since

The perimeter of a rectangle is 154 cm.

The ratio of the length to the width is 10: 1.

So here total ratio=10 + 1

=11

Now length 2 should be

=10/11 x 154 cm

=10 x 14cm

=140cm

So,

one length is 140 cm/2=70cm

Now

width(2)=1/11 x 154cm

=14cm

And,

one width is 14cm/2=7cm

hence, The length and the width should be considered as the 70 cm and 7 cm.

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The following functions are analytic:

1. f(z) = iz

2. f(z) = \(e^(^-^2^x^)(cos^2^y - isin^2^y^)\)

4. f(z) = \(e^x(cosy - isiny)\)

5. f(z) = \(Re(z^2) - iIm(z^2)\)

8. f(z) = \(i/z^8\)

11. f(z) = cos(x)cos(hy) - isin(x)sin(hy)

Analytic functions are those that can be expressed as power series expansions, meaning they have derivatives of all orders in their domain. In the given list of functions, we need to determine if each function satisfies this criterion.

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The possible number of minutes he has used his phone for a month is 1205.

Phone Service refers to the routing of calls and telephone services across an IP-based telecommunications network that you access using permitted electronic equipment and/or device(s).

Shen pays a monthly cost of $20 for his phone service.

He also has to pay $0.09 each minute of use.

The smallest amount he has been charged in a month is $128.45.

In this case,

128.45 = ( 20 + 0.09m )

We must find a solution for m.

128.45 = ( 20 + 0.09m )

Take 20 off both sides.

128.45 -20 = 0.09 m

108.45 = 0.09 m

Dividing both the sides of the equation by 0.09,

m = 108.45/0.09= 1205 minutes

The possible number of minutes he has used his phone for a month is 1205.

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The values of the given logarithmic functions are as follows:loga (256) ≈ 3.44loga (48) ≈ 2.4loga (0.75) ≈ -0.18loga (12) ≈ 1.54loga (3) ≈ 0.68loga (2.25) ≈ 0.5Total words used = 116

To find the values of the given logarithmic functions, we need to use the properties of logarithms and rewrite each of the logarithmic functions in terms of the logarithms of 4 and 3.Logarithmic properties used:

\(Property 1:  loga b^c = c loga b\)

Property 2: loga b + loga c = loga (b*c)

Property 3: loga b - loga c = loga (b/c)

Let's now evaluate each of the given logarithmic functions using these properties.

a) loga (256)

We know that 256 is a power of 4, so let's write 256 as 4^4.

Therefore, loga (256) = loga (4^4) = 4 loga 4.

Using the hint given, loga​(4)

≈0.86,

we can write loga 4 = 0.86

Therefore, loga (256) ≈ 4 x 0.86 = 3.44Answer: loga (256) ≈ 3.44b) loga (48)We can write 48 as 3 * 16.

Therefore, loga (48) = loga (3*16) = loga 3 + loga 16.

Using the hint given, loga​(3)

≈0.68 and loga 16

= loga (4^2) = 2 loga 4,

we can write loga 16 = 2 x 0.86

= 1.72

Therefore, loga (48) = 0.68 + 1.72 = 2.4

Answer: loga (48) ≈ 2.4c) loga (0.75)We can write 0.75 as 3/4.

Therefore, loga (0.75)

= loga (3/4)

= loga 3 - loga 4

Using the hint given, loga​(4)≈0.86 and loga​(3)≈0.68,

we can write loga 3 = 0.68 and loga 4 = 0.86

Therefore, loga (0.75) = 0.68 - 0.86 = -0.18

Answer: loga (0.75) ≈ -0.18d) loga (12)

We can write 12 as 3*4.

Therefore, loga (12)

= loga (3*4)

= loga 3 + loga 4

Using the hint given, loga​(4)

≈0.86 and loga​(3)

≈0.68, we can write loga 3

= 0.68 and loga 4

= 0.86

Therefore, loga (12)

= 0.68 + 0.86 = 1.54

Answer: loga (12)

≈ 1.54e) loga (3)

Given that loga​(3)

≈0.68, loga (3)

≈ 0.68Answer: loga (3)

≈ 0.68f) loga (2.25)

We can write 2.25 as 9/4.

Therefore, loga (2.25)

= loga (9/4) = loga 9 - loga 4

Using the hint given, loga​(4)

≈0.86 and loga​(3)

≈0.68, we can write loga 9

= 2 loga 3

= 2 x 0.68

= 1.36 and loga 4

= 0.86

Therefore, loga (2.25)

= 1.36 - 0.86

= 0.5Answer: loga (2.25)

≈ 0.5

Therefore, the values of the given logarithmic functions are as follows: loga (256) ≈ 3.44loga (48) ≈ 2.4loga (0.75) ≈ -0.18loga (12) ≈ 1.54loga (3) ≈ 0.68loga (2.25) ≈ 0.5

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Answer:

Step-by-step explanation:

First, change the fractions into decimals, then use the knowledge of the number line system to know which is greater or smaller than who.

-7/5  -1.4

3/4   0.75

so the numbers are -1.4, 16, -1, 3.2, -6.5, 0, 0.75

from greatest to least:

= 16, 3.2, 0.75, 0, -1, -1.4, -6.5

The simplified form of the given expression is 8.5.

In arithmetic, the operation and interpretation of a function to make it simpler or easier to grasp is known as simplifying, and the process itself is known as simplification.

The expression is given in the question, as follows:

11 1/2 - (3 1/3 + 2 2/5)(1 - 28/43)

Convert the mixed numbers into fractions:

23/2 - (10/3 + 12/5)(1 - 28/43)

Taking LCM and solving the expression to get:

23/2 - (86/15)(15/43)

23/2 - 2

19/2

8.5

Thus, the solution to the given expression is 8.5.

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Answer: 10

Step-by-step explanation:

√( 7^2 + 7^2 ) = 10

Answer:

-7x²-13x+2

Step-by-step explanation:

-7x²-14x+1x+2

Answer:

y = -2, -9

Step-by-step explanation:

Hope this helps!

The value of x shown in the right angled triangle is 15.9 units

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

Pythagoras theorem shows the relationship for the sides of a right angled triangle. It is given by:

Hypotenuse² = Adjacent² + Opposite²

From the diagram, substituting:

17² = x² + 6²

x² = 17² - 6²

x² = 253

x = 15.9 units

The value of x is 15.9 units

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a) The infinite series in sigma notation is described by this expression:

\(y = \sum \limits_{i=1}^{\infty} \frac{1}{i\cdot (i+2)}\)     (1)

b) The explicit formula for the n-th partial sum is represented by the following expression:

\(y = \frac{1}{i\cdot (i+2)}\), i ∈ \(\mathbb{N}\)     (2)

An infinite series is monotonous when it is bounded, that is, when the limit of the infinite series exists. In this case, we have an evidence of monotony in the denominators of the terms of the given series. In two consecutive terms, the latter always have a denominator greater than the former.

a) The series in sigma notation is now described below:

\(y = \sum \limits_{i=1}^{\infty} \frac{1}{i\cdot (i+2)}\)

b) The explicit formula for the n-th partial sum is defined by the expression within the sum, which is now presented below:

\(y = \frac{1}{i\cdot (i+2)}\), i ∈ \(\mathbb{N}\)  

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Answer:

7-B (congruent)

8-D (supplement)

9-B (congruent)

10-B (congruent)

11-D (supplement)

Step-by-step explanation:

7- 1 and 3 are congruent using the corresponding angles theorem

8- they are supplements using the same side interior angle theorem

9- they are congruent using alternate interior angle theorem

10- they are congruent using the alternate exterior angle theorem

11- they are supplements using the same side exterior angle theorem

ur wlcm :)

brainliest?

Answer:

anything thats not in the range of 2.645 and 2.824 next time please include options or a picture

Step-by-step explanation:

The two column proof to justify the complementary angles are;

Statement 1. ∠1 and ∠2 are complementary

∠2 and ∠3 are complementary

Reason 1: Given

Statement 2: m∠1 + m∠2 = 90°

Reason 2: Definition of Complementary Angles

Statement 3. m∠2 + m∠3 = 90°

Reason 3: Definition of Complementary Angles

Statement 4: m∠1 + m∠2 = m∠2 + m∠3

Reason 4: Transitive property of equality

Statement 5: m∠1 = m∠3

Reason 5: Substitution Property of Equality

Complementary angles are defined as angles that sum up to 90 degrees.

Now, from the question, we are given that;

∠1 and ∠2 are complementary, and ∠2 and ∠3 are complementary.

From the image attached, we can get a two column proof based on the given questions as;

Statement 1. ∠1 and ∠2 are complementary

∠2 and ∠3 are complementary

Reason 1: Given

Statement 2: m∠1 + m∠2 = 90°

Reason 2: Definition of Complementary Angles

Statement 3. m∠2 + m∠3 = 90°

Reason 3: Definition of Complementary Angles

Statement 4: m∠1 + m∠2 = m∠2 + m∠3

Reason 4: Transitive property of equality

Statement 5: m∠1 = m∠3

Reason 5: Substitution Property of Equality

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Complete Question is;

Identify the correct justification for each step, given that ∠1 and ∠2 are complementary, and ∠2 and ∠3 are complementary.

1. ∠1 and ∠2 are complementary

∠2 and ∠3 are complementary

2. m∠1 + m∠2 = 90°

3. m∠2 + m∠3 = 90°

4. m∠1 + m∠2 = m∠2 + m∠3

5. m∠1 = m∠3

The geometric sequences in the options are:

1, 5, 25, 125, 625...

2, 4, 8, 16, 32...

1, -1, 1, -1, 1...

Geometric sequence is a type of sequence in which the ratio of every two successive terms is a constant.

This ratio is  also called the common ratio of the geometric sequence. In other words, in a geometric sequence, every term is multiplied by a constant which results in its next term.

Let's check if the common ratios are constant (the same):

Sequence 1:

Common ratio; 65/64  ≠ 66/65   [No]

Sequence 2:

Common ratio: 5/1 = 25/5 (i.e. 5)  [Yes]​

Sequence 3:

Common ratio: 4/2 = 8/4 (i.e. 2)  [Yes]

Sequence 4:

Common ratio: 3/2  ≠ 5/3  [No]​ ​

Sequence 5:

Common ratio: -1/1 = 1/(-1) (i.e. -1)  [Yes]

Sequence 6:

Common ratio: 8/14 ≠  2/8  [No]

Sequence 7:

Common ratio: 1/1 ≠ 2/1  [No]

Sequence 8:

Common ratio: 8/5 ≠  11/8  [No]

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Answer:

Step-by-step explanation:

x + 2y = 7   ⇒  x = 7 - 2y

- 2x + 3y = 14

- 2(7 - 2y) + 3y = 14

-14 + 4y + 3y = 14

-14 +7y +14 = 14 +14

   7y = 28

     y = 4

x = 7 - 2y = 7-2(4) = 7 - 8 = -1