Graph the image of square EFGH after a rotation 90° counterclockwise around the origin.

The probability that student chosen at random is 16 years is 0.28.

The table shows the distribution of student by age in a high school with 1500 students. Therefore, the probability that randomly chosen student is  16 years can be found as follows:

Therefore,

probability = number of favourable outcome to age / total number of possible outcome

Hence,

probability that student chosen at random is 16 years =  420 / 150

probability that student chosen at random is 16 years = 0.28

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The Principle of Constant Proportions states that the relative concentration of seawater ions does not change. This means that regardless of the total amount of dissolved salts in seawater, the proportion of different ions remains relatively constant.

Seawater is composed of various dissolved salts, including sodium, chloride, magnesium, calcium, and others. The Principle of Constant Proportions asserts that while the absolute concentration of these ions may vary, their ratios to one another remain consistent. In other words, if we were to analyze seawater samples from different locations or depths, we would find that the relative percentages of sodium, chloride, and other ions remain constant.

This principle is significant in understanding the composition and behavior of seawater, as it allows scientists to make accurate predictions and interpretations based on the consistent ratios of ions present. It also helps in studying processes like evaporation and precipitation, as the relative proportions of ions remain unchanged even when the total salinity may vary.

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Answer:

The semi-circles form an entire circle with a diameter of 74.

The radius is 37

The area of the rectangle is 95 x 74 = 7030

The area of the circle is 3.142 x 37*37 = 4298.66

The total area is 11328.66

There are 39 elements in the intersection of the two sets.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

Union: -

If set A and set B are two sets, then A union B is the set that contains all the elements of set A and set B. It is denoted as A ∪ B.

Example: Set A = {1,2,3} and B = {4,5,6}, then A union B is:

A ∪ B = {1,2,3,4,5,6}

Intersection:-

If set A and set B are two sets, then A intersection B is the set that contains only the common elements between set A and set B. It is denoted as A ∩ B.

Example: Set A = {1,2,3} and B = {4,5,6}, then A intersection B is:

A ∩ B = { } or Ø

Since A and B do not have any elements in common, so their intersection will give null set.

P(AUB) = P(A) + P(B) - P(A∩B)

Here, P (A) = the number of elements in the set A and so on.

We know that:

                     P (A)= 67

                     P (B)= 72

and                P (AUB) = 100

So, we can solve for the number in the intersection i.e.                     P(A∩B) = P(A) + P(B) - P(AUB)

P(A∩B) = 67 + 72 - 100

P(A∩B) = 139 - 100

P(A∩B) = 39.

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Answer:

y= 30 x=15

set up your proportions for example 9/6 to y/20 and 9/6 to x/10 and then cross multiply

Answer:

The value of x is 7.

Step-by-step explanation:

First, you have to make the left side into 1 fraction by making the denormintor the same and make it into simplest form :

\( \frac{x}{3} + \frac{x}{6} \)

\( = \frac{x \times 2}{3 \times 2} + \frac{x}{6} \)

\( = \frac{2x}{6} + \frac{x}{6} \)

\( = \frac{2x + x}{6} \)

\( = \frac{3x}{6} \)

\( = \frac{x}{2} \)

Next you have to multiply both sides by 2 in order to make x the subject :

\( \frac{x}{2} = \frac{7}{2} \)

\( \frac{x}{2} \times 2 = \frac{7}{2} \times 2\)

\(x = 7\)

Answer:

Step-by-step explanation:Before her deposit on Monday, she had $538 now she has, 538 - 218 + 49 = $369 in her bank account after her withdraw on Friday. Hope this helps, best of luck!

The value of the given integral  ∫2^x/2^x +6. dx would be -3 log |1 + 6/2^x| + C.

Given the integral is ∫2^x/2^x +6. dx

We are supposed to evaluate this integral. In order to evaluate the given integral, let's follow the steps given below.

Step 1: Divide the numerator and the denominator by 2^x to get 1/(1+6/2^x)

So, ∫2^x/2^x +6. dx = ∫1/(1+6/2^x) dx

Step 2: Now, substitute u = 1 + 6/2^x

Step 3: Differentiate both sides with respect to x, we getdu/dx = -3(2^-x)Step 4: dx = -(2^x/3) du

Now the integral is ∫du/u

Integrating both the sides of the equation gives us ∫1/(1+6/2^x) dx = -3 log |1 + 6/2^x| + C

Therefore, the value of the given integral is -3 log |1 + 6/2^x| + C.

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Answer:

7.5

Step-by-step explanation:

Since we are given the price for 5 bags of dog food, we have to find the unit rate. Now to do that we divide the price by the amount.

12.50/5= 2.50

now since we have the unit rate, we take that and multiply the price of one by 3 to find the price of 3

2.50x3=7.50

Hope this helps!

Answer: 7.5 bags

Step-by-step explanation:

$12.50 divided by 5 bags= $2.5 per bag

$2.5*3 bags= $7.5

The radius of the spherical part is 3 inches and the length of the tube is 21 cm.

The capacity of a cylinder, which determines how much material it can hold, is determined by the cylinder's volume. There is a formula for the volume of a cylinder that is used in geometry to determine how much of any quantity, whether liquid or solid, can be immersed in it uniformly.

Given that the volume when the water is fully dipped is 4554 / 7 cm³. The volume when the length is 9 cm empty is 396 cm³.

The two equations can be formed as below:-

4554 / 7 = πr²l + (2/3)πr³

396 = πr²( l - 9 ) + (2/3)πr³

Subtract the second equation from the first,

( 4554 / 7 ) - 396 = 9πr²

9πr² = 254.5

r² = 9

r = 3 cm

The length will be calculated as:-

4554 / 7 = πr²l + (2/3)πr³

4554 / 7 = π( 3 )²l + (2/3)π(3)³

l = 21 cm

Therefore, the tube's length is 21 cm, and the spherical part's radius is 3 inches.

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Answer: E

Step-by-step explanation:

The solution means the intersection point, so in this case, it's (3, 2). The intersection point represents a value that is true for both equations, which is why it's considered the solution.

The below would be most important Algebra 1 Formulas for CST.

Linear Equation:

\(Ax + By + C = 0\)

Equation of Straight Line or Slope:

\(y = mx+b\)

Point-slope form:

\(y-y_{1} = m(x-x_1)\)

Slope when 2 points are given:

\(m = \frac{(y_2 - y_1)}{(x_2-x_1)}\)

Quadratic Equation:

\(Ax^2 + Bx +C = 0\)

When lines are parallel:

Slope of both lines are equal. \(m_1 = m_2\)

When lines are perpendicular:

Slope of perpendicular lines are opposite reciprocals, meaning if the slope of a line \(l_1\) is \(\frac{1}{2}\). The line \(l_2\) perpendicular to \(l_1\) is \(-\frac{2}{1}\).

Work Formula:

Total Work Done = Number of Days \(\times\) Efficiency

where Efficiency is inversely proportional to Time Taken.

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The probability that a random nonnegative Integer less than 100 is 21/100. The correct answer is C.

To find the probability that a random non-negative integer less than 100 is divisible by 9 or by 11, we need to count the number of integers less than 100 that are divisible by 9 or 11 or both.

There are 11 integers less than 100 that are divisible by 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, and 99.

There are 9 integers less than 100 that are divisible by 11: 11, 22, 33, 44, 55, 66, 77, 88, and 99.

However, the number 99 is counted twice in the above list since it is divisible by both 9 and 11.

Therefore, the total number of integers less than 100 that are divisible by 9 or by 11 is 11 + 9 - 1 = 19.

Since there are 100 non-negative integers less than 100, the probability that a random non-negative integer less than 100 is divisible by 9 or by 11 is 19/100.

Therefore, the answer is (C) 21/100.

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Answer:

The volume of the cone is;

Explanation:

Given the cone with diameter 8 feet and height 5 feet;

The volume of cone can be calculated using the formula;

Substituting the given values;

Therefore, the volume of the cone is;

Answer:

C

Step-by-step explanation:

3/4+(-1/8) which is 3/4-1/8. 6/8-1/8 which is 5/8 or option C.

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Answer:

Hello! answer: 1/6

Step-by-step explanation:

The probability of landing on D is 1/6 because there are 6 spots on the spinner you can land on A, B, C, D, E, and F and there is only 1 section labelled "D" therefore the probability of landing on D is 1/6 hope that helps!

Answer:

a

Step-by-step explanation:

Answer:

\(y = - \frac{ {x}^{2} }{16} \)

Step-by-step explanation:

First, notice the diretcrtirx is a negative horinzontal lie so this means we have a parabola facing downwards

Equation of a Parabola with center (h,k) >

\((x - h) {}^{2} = - 4p(y - k)\)

Where p is the distance of the vertex to focus/ or distance to vertex to directrix

This emans that the vertex is halfway of (-4,0) and x=4.

Since this is a upwards parabola, the y value that lies on focal axis doesn't change so know this means that

The vertex is halfway between (-4,0) and (4,0).

So the vertex is (0,0).

Plugging that in we get,

\( {x}^{2} = - 4py\)

The distance to the vertex or either the focus or directrix is 4 so p=4

\( {x}^{2} = - 4(4)y\)

\( {x}^{2} = - 16y\)

\(y = - \frac{ {x}^{2} }{16} \)

The values of b and a for the logarithmic function in this problem are given as follows:

The logarithmic function in the context of this problem has the format given as follows:

\(y = b\log_3{x + a}\)

The vertical asymptote is at x = -4, hence:

\(y = b\log_3{x - 4}\)

When x = 5, y = -1, hence the parameter b is obtained as follows:

\(-1 = b\log_3{5 - 4}\)

0.477b = -1

b = -1/0.477

b = -2.1.

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Answer:

polygon do all the number times each outher divided in half then times 6 for the hight and langht

Step-by-step explanation:

Answer:

a. The greatest possible length is 12 inches as it is the greatest common factor of the three given lengths.

b. There will  be 5 pcs of blue cloth, 4 pcs of gold cloth, and 6 pieces of white cloth.

Step-by-step explanation:

a. What is the greatest possible length of the pieces without having any cloth left over?

Find the greatest common factor for the 3 lengths

60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

The greatest common factor amongst the three given lengths is 12 therefore it is also the greatest possible length.

b. Divide each length by 12.

60/12 = 5pcs   ---blue cloth

48/12 = 4pcs   ---gold cloth

72/12 = 6 pcs  ---white cloth

By considering the given quadratic function the function in vertex form is:
Y = 3(x - (-5))² - 10
Y = 3(x + 5)² - 10

Follow these steps:

Step 1: Identify the coefficients in the given function
The quadratic function is given as Y = ax² + bx + c. In this case, a = 3, b = 30, and c = 65.

Step 2: Calculate the x-coordinate of the vertex
Use the formula x = -b/(2a) to find the x-coordinate of the vertex.
x = -30/(2 * 3) = -30/6 = -5

Step 3: Calculate the y-coordinate of the vertex
Substitute the x-coordinate found in Step 2 into the given function to find the y-coordinate of the vertex.
Y = 3(-5)² + 30(-5) + 65
Y = 3(25) - 150 + 65
Y = 75 - 150 + 65
Y = -10

Step 4: Write the function in vertex form
The vertex form of a quadratic function is Y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. In this case, h = -5 and k = -10. Therefore, the function in vertex form is:
Y = 3(x - (-5))² - 10
Y = 3(x + 5)² - 10

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Answer:

B

Step-by-step explanation:

Columbia was at 16 million with an increase of 530 thousand which is 0.53 of a million so population or P = 16 + 0.53t when t = years

Argentina about the same thing but with different numbers

The system of the equations will be P = 0.53t + 16 and P = 0.34t + 20.6. Then the correct option is B.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

In 1960, the population of Colombia was about 16 million and the population of Argentina was about 20.6 million.

Between 1960 and 2010, the population of Colombia increased by about 530,000 people per year, and the population of Argentina increased by about 340,000 people per year.

530,000 people per year = 0.53 millions per year

340,000 people per year = 0.34 millions per year

Let P represent the population, in millions, and t represent the number of years since 1960.

Then the system of the equations will be

P = 0.53t + 16

P = 0.34t + 20.6

Then the correct option is B.

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In order to solve this quadratic equation by completing the square, let's analyse the coefficient b by comparing the equation with the standard form:

We have b = -12. In order to be a perfect square, the coefficient c needs to be (-12/2)^2 = (-6)^2 = 36

We already have 30, so we just need to add 6:

Answer:

a. 44 cm b. 126 cm

Step-by-step explanation:

a. it is semi circle

perimeter is πd

22/7*14

44 cm

b. it is equilateral triangle

so perimeter is side* 3

42 *3 = 126cm

Answer:

Step-by-step explanation:

(a)

The figure perimeter it is half of a circle with a diameter d₁=14 cm and two halfs of circle with a diameter d₂=14 cm÷2=7 cm.

The length of a circle is  L₀ = πd, where d is the diameter.

Therefore:

\(\bold{L=\frac12d_1+2\cdot\frac12d_2 = \frac12\cdot14\pi+\frac12\cdot2\cdot7\pi=14\pi\,cm\approx44\,cm}\)

(b)

A full circle it is 360°, so the circle sector of 60° is  \(\frac{60^o}{360^o}=\frac16\)  of the circle. So the arc of 60° is ¹/₆ of the full circle length.

The figure is an equilateral triangle and two 60°-sectors of circles with radiuses of length of the triangle's side (r=42 cm).

Its perimetr it's two radiuses, two arcs of 60° and one side of the triangle.

The length of a circle is  L₀ = 2πr, where r is a radius.

Therefore:

\(\bold{L=2r+2\cdot\frac16\cdot 2\pi r+r=3r+\frac23\pi r}\\\\\bold{L=3\cdot42+\frac23\pi\cdot42=(126+28\pi)\,cm\approx214\,cm}\)

The extra amount (difference) that Sara will pay if she picks Option 2 for the purchase of the car is £445.20.

The extra amount that Sara incurs for choosing Option 2 can be described as the finance charge.

The finance charge covers interest and other fees on credit facilities.

The cost of the car Sara is buying = £15,000

Under Option 1, Sara pays £15,000 straight away

Under Option 2, Sarah:

Deposit (down payment) = 20% = £3,000 (£15,000 x 20%)

Mortgage loan = £12,000 (£15,000 - £3,000)

Monthly payments = £345.70

Period of payments = 36 months (3 years x 12)

Total payments = £12,445.20 (£345.70 x 36)

Total payments under Option 2 = £15,445.20 (£3,000 + £12,445.20)

Difference between (extra amount) Option 2 and Option 1 = £445.20 (£15,445.20 - £15,000)

Thus, we can can conclude that Sara incurs a relative finance cost of £445.20 for choosing Option 2 instead of Option 1.

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Answer:

In order

Step-by-step explanation:

x=7/3 or 2.33333

x= 7/2 or 3.5

x= 3/5 or 0.6

x= 2/3 or 0.6666

Answer:

4

Step-by-step explanation:

First, list up all factors of 20, 36, and 76. Then find the greatest factor that is common in the three lists.

20: 1, 2, 4, 5, 10, 20

36: 1, 2, 3, 4, 6, 9, 12, 18, 36

76: 1, 2, 4, 19, 38, 76

Answer:

m

=

0.8

¯

3

Step-by-step explanation: