Last year at a certain high school, there were 50 boys on the honor roll and 120 girls on the honor roll. This year, the number of boys on the honor roll increased by 22% and the number of girls on the honor roll increased by 15%. By what percentage did the total number of students on the honor roll increase? Round your answer to the nearest tenth (if necessary).

Answer:

Domain=[67,78]

Step-by-step explanation:

To find domain:

  ⇒ must define what is a domain

       ⇒ Domain is the set of input values or the values of the x-axis of

           graph that is covered by the function

Based on the definition:

    ⇒ 67 ≤ x ≤ 78 is the domain of the function

Answer: 67 ≤ x ≤ 78 where x is a whole number

Hope that helps!

By using the facts given, 60.5 cm is 0.605 m or 0.605 meters.

Given: Convert 60.5 cm to meters

And the facts are as follows:

1000 milli-meters (mm) - 1 meter (m)

100 centimeters (cm) - 1 meter (m)

10 decimeters (dm) - 1 meter (m)

1 deka-meter (dam) -10 meters (m)

1 hectometer (hm) - 100 meters (m)

1 kilometer (km) - 1000 meters (m)

What is the length?

Length is the measurement of something from one point to another point.

Length can also be the distance between two points.

The shortest length between two times is known as displacement.

There are different ways to measure the length between two points or objects.

The SI unit of length is metered (m)

Also, kilometers or miles are used to measure large distances.

How to convert from centimeters (cm) to meters (m)?

1 meter or 1 m is equivalent to 100 centimeters or 100 cm. So let us apply the unitary method.

100 cm = 1 m

So 1 cm = 1 / 100 m

Therefore, x cm will be x / 100 m

Let’s solve the problem.

Given 60.5 cm to show in meters

So 100 cm = 1 m

1 cm = 1 / 100 m

60.5 cm = 60.5 / 100 m

60.5 cm = 0.605 m

Hence by using the facts given 60.5 cm is 0.605 m or 0.605 meters.

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For figure {0}, the number of tiles will be equal to 2.

Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function

Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Equation : A mathematical equation is used to equate two expressions.

Given is a graph as shown in the image.

The line passes through point -

(3, 8) and (4, 10)

So, the slope of the line will be -

m = (10 - 8)/(4 - 3)

m = 2

y = 2x + c

For the point (3, 8), we can write -

8 = 6 + c

c = 2

For figure {0}, the number of tiles will be equal to 2.

Therefore, for figure {0}, the number of tiles will be equal to 2.

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Percent to the nearest whole number = 7%

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

Probability = (Number of possible outcomes)/(Total number of outcomes)

Total number of outcomes = 2 + 15 + 2 + 11 = 30

Number of possible outcomes = 2

Probability = 2/30 = 1/15 = 0.0666

Percent to the nearest whole number =  0.0666 *100 = 7%

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Answer:7

Step-by-step explanation:

The change in wavelength of the radio signal is 100m

The change in wavelength of the radio can be calculated using the velocity of the given radio signal.

\(c = v \lambda\\\)

Let's substitute the values and solve.

But then, we have to convert the velocity from km to m

\(1km = 1000m\\3000km = x\\x = 3000000m\)

Let's proceed to solve this.

\(c = \lambda v\\3.0*10^8 = \lambda * 3.0^6\\\lambda = \frac{3.0*10^8}{3.0*10^6} \\\lambda = 1.0*10^2m\\\lambda = 100m\)

The wavelength of the radio signal is 100m.

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The values of (2/3 + 6/3), ( 4/6 + 9/6 ) and ( 6/6 + 6/6 ) are 8/3, 13/6 and 2 respectively.

Given that;

1) 2/3 + 6/3

We combine the numerators over the common denominators

= ( 2 + 6 ) / 3

= 8/3

2) 4/6 + 9/6

We combine the numerators over the common denominators

= ( 4 + 9 ) / 6

= 13/6

3) 6/6 + 6/6

We combine the numerators over the common denominators

= ( 6 + 6 ) / 6
= 12/6

= 2

The values of (2/3 + 6/3), ( 4/6 + 9/6 ) and ( 6/6 + 6/6 ) are 8/3, 13/6 and 2 respectively.

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Answer:

0.84

Step-by-step explanation:

21/25 is equal to 0.84.

Hopefully this helps!

Brainliest please?

if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).

Calculating the loan amount for each brand by subtracting the down payment from the cash price:

Loan amount for Daewoo = RM1,899 - RM300 = RM1,599

Loan amount for Daikin = RM1,699 - RM300 = RM1,399

Loan amount for Mitsubishi = RM1,999 - RM300 = RM1,699

Calculating the interest charge for each brand:

Interest charge for Daewoo = Loan amount for Daewoo * Interest rate = RM1,599 * 0.04 = RM63.96

Interest charge for Daikin = Loan amount for Daikin * Interest rate = RM1,399 * 0.04 = RM55.96

Interest charge for Mitsubishi = Loan amount for Mitsubishi * Interest rate = RM1,699 * 0.04 = RM67.96

To find the monthly installment price, divide the total amount (cash price + interest charge) by the number of monthly installments:

Monthly installment price for Daewoo = (Cash price of Daewoo + Interest charge for Daewoo) / Number of monthly installments = (RM1,899 + RM63.96) / 18 ≈ RM107.22

Monthly installment price for Daikin = (Cash price of Daikin + Interest charge for Daikin) / Number of monthly installments = (RM1,699 + RM55.96) / 18 ≈ RM98.89

Monthly installment price for Mitsubishi = (Cash price of Mitsubishi + Interest charge for Mitsubishi) / Number of monthly installments = (RM1,999 + RM67.96) / 18 ≈ RM116.72

Therefore, if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).

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Probabilities are used to determine the chances of an event

The probability is given as:

\(P(Black\ n\ Black)=0.36\)

Apply probability formula

\(P(Black) \times P(Black)=0.36\)

Express as squares

\(P(Black)^2=0.36\)

Take the square root of both sides

\(P(Black)=0.6\)

Hence, the probability of choosing a black counter is 0.6

In (a), we have:

\(P(Black)=0.6\)

Using the complement rule, we have:

\(P(White) = 1 - P(Black)\)

So, we have:

\(P(White) = 1 -0.6\)

Evaluate

\(P(White) = 0.4\)

The probability that both counters are white is then calculated as:

\(P(White\ and\ White) = P(White) \times P(White)\)

So, we have:

\(P(White\ and\ White) =0.4 \times 0.4\)

\(P(White\ and\ White) =0.16\)

Hence, the probability that both counters are white is 0.16

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After the double rotation, the vertices of the quadrilateral MNPQ are transformed to M'', N'', P'', and Q''. The shape of the quadrilateral may have changed, but the order of the vertices remains the same.

When a quadrilateral MNPQ is rotated counterclockwise at 90 degrees about the origin, each vertex undergoes a transformation.

The new positions of the vertices after this rotation can be denoted as M', N', P', and Q'. The order of the vertices remains the same.

Next, when the rotated quadrilateral M'N'P'Q' is further rotated counterclockwise at 270 degrees about the origin, each vertex undergoes another transformation.

The new positions of the vertices after this rotation can be denoted as M'', N'', P'', and Q''. Again, the order of the vertices remains the same.

It's important to note that a 270-degree counterclockwise rotation is equivalent to a 90-degree clockwise rotation.

The result of the double rotation is equivalent to a single clockwise rotation of 90 degrees.

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Answer: the first thing is your answer :)

thx for the points

Step-by-step explanation:

g

(

x

)

=

x

2

−

3

The parent function is the simplest form of the type of function given.

f

(

x

)

=

x

2

The transformation being described is from

f

(

x

)

=

x

2

to

g

(

x

)

=

x

2

−

3

.

f

(

x

)

=

x

2

→

g

(

x

)

=

x

2

−

3

The horizontal shift depends on the value of

h

. The horizontal shift is described as:

g

(

x

)

=

f

(

x

+

h

)

- The graph is shifted to the left

h

units.

g

(

x

)

=

f

(

x

−

h

)

- The graph is shifted to the right

h

units.

In this case,

h

=

0

which means that the graph is not shifted to the left or right.

Horizontal Shift: None

The vertical shift depends on the value of

k

. The vertical shift is described as:

g

(

x

)

=

f

(

x

)

+

k

- The graph is shifted up

k

units.

g

(

x

)

=

f

(

x

)

−

k

- The graph is shifted down

k

units.

Vertical Shift: Down

3

Units

The graph is reflected about the x-axis when

g

(

x

)

=

−

f

(

x

)

.

Reflection about the x-axis: None

The graph is reflected about the y-axis when

g

(

x

)

=

f

(

−

x

)

.

Reflection about the y-axis: None

Compressing and stretching depends on the value of

a

.

When

a

is greater than

1

: Vertically stretched

When

a

is between

0

and

1

: Vertically compressed

Vertical Compression or Stretch: None

Compare and list the transformations.

Parent Function:

f

(

x

)

=

x

2

Horizontal Shift: None

Vertical Shift: Down

3

Units

Reflection about the x-axis: None

Reflection about the y-axis: None

Vertical Compression or Stretch: None

image of graph

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

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Answer: A

Step-by-step explanation:

The three angles in a triangle add to \(180^{\circ}\). Therefore, each angle measures \(\frac{180^{\circ}}{3}=60^{\circ}\).

The period of the frequency factor b that is given in the diagram above would be = 0.2 sec.

The frequency of a water wave is defined as the number of times the wave completes a cycle within a given period of time. While the period is the time it takes for the completion of a cycle.

The dot the represents the frequency factor b is the green dot on the wave table. Therefore the period as traced from the graph= 0.2 sec.

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Hey there mate :)

The answer is :-

\( - \frac{2 \sqrt{3} }{2} \)

Click on attached image.

Explanation is attached as image. Please check.

Answer:

The answer is B

Step-by-step explanation:

2

Answer:

The answer is (B) 2

Step-by-step explanation:

I took the test on edge and also the person above me is correct hope that you have a wonderful day. (✿◠‿◠)

The sum of two opposite interior angles of a triangle is equal to the opposite exterior angle of a triangle

Therefore,

( 5x - 101 )° + ( x + 36 )° = ( 9x - 164 )°

5x + x - 106 + 36 = 9x - 164

6x - 65 = 9x - 164

6x - 9x = - 164 + 65

- 3x / - 3 = - 99 / - 3

x = 33

The first interior angle

= ( 5x - 101 )°

= ( 5 ( 33 ) - 101 ) °

= ( 165 - 101 )°

= 64°

The second interior angle

= ( x + 36 )°

= ( 33 + 36 )°

= 69°

The exterior angle

= ( 9x - 164 )°

= ( 9 ( 33 ) - 164 )°

= ( 297 - 164 )°

= 133°

The parameters of the exponential function in this problem are given as follows:

The standard format of an exponential function is given as follows:

y = c(1 - a)^t.

This is the case for a decaying exponential function, and the meaning of each parameter is given as follows:

In this problem, the function is given as follows:

f(x) = 1.1(0.44)^x.

Hence the values for the parameters are given as follows:

Then the percent of change is of -56%, as it is a decaying exponential function with a = 0.56.

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Answer:

111

Step-by-step explanation:

2^3[2^(x+1) + 2^(x+4) - 2^(x+2) - 2^(x-3)] =

2^(x+4) + 2^(x+7) - 2^(x+5) - 2^x =

2^x (2^4 + 2^7 - 2^5 -1) =

2^x (16+128-32-1) =

2^x (111) =

111 × 2^x = a × 2^x

so, the value of a = 111

Answer:

a = 111

Step-by-step explanation:

Given expression:

\(2^3(2^{x+1}+2^{x+4}-2^{x+2}-2^{x-3})\)

\(\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c\)

\(\implies 2^3(2^x \cdot 2^1+2^x \cdot 2^4-2^x \cdot 2^2-2^{x-3})\)

\(\textsf{Apply exponent rule} \quad a^{b-c}=\dfrac{a^b}{a^c}\)

\(\implies 2^3\left(2^x \cdot 2^1+2^x \cdot 2^4-2^x \cdot 2^2-\dfrac{2^x}{2^3}\right)\)

Simplify:

\(\implies 8\left(2^x \cdot 2+2^x \cdot 16-2^x \cdot 4-2^x \cdot \dfrac{1}{8}\right)\)

Factor out \(2^x\) :

\(\implies 8\left(2^x \left[2+16-4- \dfrac{1}{8}\right]\right)\)

Simplify:

\(\implies 8\left(2^x \left[\dfrac{111}{8}\right]\right)\)

\(\implies 111 \cdot 2^x\)

Therefore, a = 111

Answer:

yessir best anime character in existence

Answer: yes

Step-by-step explanation:

yes thats sick

Using DeMoivre’s theorem, the answer in regular form would be (5 + 5√3i)⁷ = -5000000 + 8660254.03i

The De Moivre's Theorem is used to simplify the computation of powers and roots of complex numbers and is used in together with polar form.

Convert the complex number to polar form. The polar form of a complex number is z = r(cos θ + isin θ),

r = |z|  magnitude of z

it becomes

r = √((5)² + (5√3)²) = 10

θ = arg(z) is the argument of z.

θ = atan2(b, a) = atan2(5√3, 5) = π/3

(5 + 5√3i) = 10 × (cos π/3 + i sin π/3)

De Moivre's theorem to raise the complex number to the 7th power

(5 + 5√3i)⁷

= 10⁷× (cos 7π/3 + i sin 7π/3)

= 10⁷ × (cos 2π/3 + i sin 2π/3)

Convert this back to rectangular form:

Real part = r cos θ = 10⁷× cos (2π/3) = -5000000

Imaginary part = r sin θ = 10⁷ × sin (2π/3) = 5000000√3 = 8660254.03i

∴  (5 + 5√3i)⁷ = -5000000 + 8660254.03i

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Answer:10^7 (1/2 - √3/2 i)

Step-by-step explanation:

To use DeMoivre's theorem, we first need to write the number in polar form. Let's find the magnitude and argument of the number:

Magnitude:

|5 + 5√(3i)| = √(5^2 + (5√3)^2) = √(25 + 75) = √100 = 10

Argument:

arg(5 + 5√(3i)) = tan^(-1)(√3) = π/3

So the number can be written in polar form as:

5 + 5√(3i) = 10(cos(π/3) + i sin(π/3))

Now we can use DeMoivre's theorem:

(5 + 5√(3i))^7 = 10^7 (cos(7π/3) + i sin(7π/3))

To simplify, we need to find the cosine and sine of 7π/3:

cos(7π/3) = cos(π/3) = 1/2

sin(7π/3) = -sin(π/3) = -√3/2

Explanation:

So the final answer in rectangular form is:

10^7 (1/2 - √3/2 i)

Answer:

-2

Step-by-step explanation:

Point A = 1

Point B = - 5

Midpoint :

Check the picture below.

\(\tan(26^o )=\cfrac{\stackrel{opposite}{x}}{\underset{adjacent}{5.7}}\implies 5.7\tan(26^o)=x\implies 2.78\approx x\)

Make sure your calculator is in Degree mode.

Answer: 840,960,000

Step-by-step explanation:

20 blinks*60 mins= 1,200/hr

1,200*24 hrs in a day= 28,800 blinks/day

28,800*365 days in a year= 10,512,00 blinks/ year

10,512,000*80 years= 840,960,00

840,960,000= 8.4096* 10^8

The problem can be translated into an equation as follows: 8x = (1/3)(x+2)

the answer that represents this situation is: 8x = (1/3)(x+2)

Simplifying the right side of the equation:

8x = (1/3)x + (2/3)

Multiplying both sides of the equation by 3 to eliminate the fraction:

24x = x + 2

Subtracting x from both sides of the equation:

23x = 2

Dividing both sides of the equation by 23:

x = 2/23

Therefore, the answer that represents this situation is:

8x = (1/3)(x+2)

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Answer: 80 ft squared

Step-by-step explanation:

For the square, the formula is base times height which, in this case, are both 8. 8 x 8 = 64. Next, the triangle below is (8 x 4)/2 because the formula for a triangle is base x height divided by 2. 8  x 4 = 32 divided by 2 is 16.

64 + 16 = 80

So, your answer will be 80ft squared

Hope this helped!

The two tanks differ in terms of Filling rates and initial volumes.

We can work with the equation for tank A, which represents a linear relationship between the volume of liquid in the tank (y) and the time it has been filling (x).

The equation y = 75x + 110 tells us that the tank A is filling at a constant rate of 75 units per minute, starting with an initial volume of 110 units.

To analyze the data for tank B, we would need to know the volumes of the tank at different times as it is being filled.

If the relationship for tank B is also linear, we could find the equation that represents it by using two points from the table and the slope-intercept form of a linear equation (y = mx + b). Once we have both equations, we can compare them to see how the two tanks differ in terms of filling rates and initial volumes.

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Answer:

Amount of sales

Step-by-step explanation:

The dependent variable also called the measured or predicted variable is simply the variable obtained due to inputs in of the independent variable. It is the variable which is being measured in an experiment. Here, the test is that the number of sales depends on the number of contact. Here, the number of contacts will has an influence or determines the amount of sales, hence, the number of contacts is the independent variable while the amount of sales is the dependent variable.

The area of the rectangle will be 150 square meters.

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.

Given that:-

The area will be calculated as follows:-

From the given condition in the question, we can form two linear equations they are:-

The length of a rectangle is 5 m longer than its width.

L = w + 5

L - w = 5

The perimeter of the rectangle is 50 m.

P = 2 (L + w )

2 ( L+ w ) = 50

L + w = 25

by solving the two equations we will get the values of L and w.

L - w = 5  or w = L - 5

L + w = 25

L + L - 5 = 25

2L = 30

L = 30 / 2

L = 15

Put the value of L in any equation to get w.

L - w = 5

15 - w = 5

w = 10

Now the area of the rectangle will be:-

A = L x w

A = 15 x 5

A = 150 square meters.

Therefore the area of the rectangle will be 150 square meters.

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