Why is the sine of an acute angle less than one?

The slope of the graph is equivalent to 6 units.

The general equation of a straight line is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given is the graph showing the amount of water in the tank after the several minutes of it being turned off.

We can write the slope of the graph as -

m = (16 - 10)/(2 - 1)

m = 6

Therefore, the slope of the graph is equivalent to 6 units.

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To simplify the expression 5c−3d−12c+d−6, we can combine like terms:

5c − 12c + d − d − 6 = (-12c + d) + (-6)

Therefore, the expression 5c−3d−12c+d−6 can be simplified to -12c + d - 6.

the probability that the card is either a queen or a diamond is: 4/13

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

the proportion between the total number of conceivable outcomes and the number of outcomes in a comprehensive collection of equally probable alternatives that result in a particular occurrence.

Example: When flipping a coin, there are only two possible outcomes: either it will land on its head or on its tail.

Number of cards, n(S) = 52

Let E = Event of getting a diamond

F = Event of getting a queen

(E ∩ F) = Event of getting a diamond of queen.

Then, n(E) = 13

n(F) = 4 ,

n (E ∩ F)=1

P(E) = 13/52 = 1/4

P (F) = 4/52 = 1/13

P (E ∩ F) = 1/52

(E or F) = P(E ∪ F) = P(E) + P(F) × P(E ∩ F)

P (E or F) = 1/4 + 1/13 - 1/52

P (E or F) = (13 + 4 - 1)/52

P (E or F) = 16/52

P (E or F) = 4/13

The required probability of getting either diamond or a queen is 4/13

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Answer:

Mark the sides BC and DF as congruent---------------------------------------------------We are given a side and an adjacent angle and need to identify the missing side or angle for proof by SAS .SAS is side-angle-side and requires two sides and the included angle to be congruent on both triangles.The missing bit is the other side of the marked angle B and D:sides BC or DF.

Step-by-step explanation:

(0.818  , 1.546)  is the point that is part of solution.

point (0,2) and (2,0) are not the part of solutions.

3y - 2x ≤ 3

y + 3x  ≤ 4

these are the system of inequalities.

What are Inequalities?

Inequality is a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance.

Given in this question,

There are two lines L1 and L2.

From the graph we can find the two points that lies on the line L1 be

(0,1) and (3,3).

similarly From the graph we can find the two points that lies on the line L2 be

(0,4) and (2,-2).

From the two points (x1 , y1) and (x2,y2) we can write the equation of the Line from the following formula :

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex].   This is the equation of line for given two points.

Equation of line L1 :

[tex]y-1=\frac{3-1}{3-0} (x-0)[/tex]

3y - 3 = 2x ----------(ii)

Equation of line L1 : 3y - 2x = 3.

Equation of line L2 :

[tex]y-4=\frac{-2-4}{2-0} (x-0)[/tex]

y   = -3x + 4 ----------(ii)

Equation of line L2 : y + 3x = 4.

The point that is the part of the solution :

putting the value of y from equation (ii) in equation (i).

3(-3x+4) -3 = 2x

-9x-2x = -12+3

-11x = -9

  x = 0.818

y = -3(0.818) +4 = +1.546

so Point of intersection is (0.818  , 1.546)

This is the point that is part of solution.

The point that is not below both the lines are not part of solution.

the point that are not part of solution are:

3y - 2x ≥ 3  ->  (0,2)

y + 3x  ≥ 4   ->  (2,0)

point (0,2) and (2,0) are not the part of solutions.

Inequalities are for shaded portion :

3y - 2x ≤ 3

y + 3x  ≤ 4

these are the system of inequalities.

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Answer: x = 10

Step-by-step explanation:

1. To find x, you need x to be by itself and the only way for it be like that in this situation is by dividing both sides by 7.

2.  7 divided by 7 cancels out and 70 divided by 7 = 10. This means x = 10.

Answer:

10

Step-by-step explanation:

since we have 7x=70

the multiply goes and becomes divide we get 70/7

and by dividing it we get the ans 10

Answer: 294 feet^2

Step-by-step explanation:

Find the volume of the cube.

Find the cube root of the volume.

Plug this answer into the formula for finding the surface area of a cube.

(area = 6 · s2)

Answer:

294cm[tex]^{2}[/tex]

Step-by-step explanation:

A cube has 6 faces

To find out the area of one face, you'd have to do 7x7 (7[tex]^{2}[/tex]).

To find out the total surface area of the cube, use this equation to help you:

AREA= 6(the amount of faces of the cube) × 7[tex]^{2}[/tex](the area of ONE face)

so in other words...

AREA=6×7[tex]^{2}[/tex]

AREA= 294cm[tex]^{2}[/tex]

hope this helped:)

If g varies inversely as the square root of h, this means that the product of g and the square root of h is constant. We can represent this relationship using the equation g*sqrt(h) = k, where k is the constant value.

We are given that g = 9 when h = 121, so we can substitute these values into the equation to find the constant:

9sqrt(121) = k

Simplifying this expression gives us:

k = 911 = 99

Now that we know the value of the constant, we can use the equation to find g when h = 81:

g*sqrt(81) = 99

Solving for g gives us:

g = 99/sqrt(81) = 99/9 = 11

Therefore, when h = 81, g = 11.

The percentage increase in the population from 1965 to 2015 is 35 %.

To calculate the population growth rate (PG), take the difference (subtraction) between the original population and the population at time point 1, divide by the original population, and multiply by 100. The population growth rate (PGR) for that period (10 years) was 12%.

Given:

In the year 1965, the population of country A was 2714000.

In the year 2015, the population of country A was 3663900.

Percentage increase in population 50 years

                         = [tex]\frac{(3663900-2714000)}{2714000}[/tex] × 100

                         = 35 %

Thus, the percentage increase in the population from 1965 to 2015 , i.e, 50 years is 35%.

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Four hemispheres are present in the shaded area. One large hemisphere and three smaller hemispheres each have a radius of 18 cm.

Consequently, the hemisphere's total surface area is 3(pi)R2. A semicircle has a curved line and a straight line that are both equal to the circle's diameter. The curving line is 2R in length while the straight line is (pi)R in length. So, 2R + (pi)R is the semicircle's total perimeter.

The shaded regions' area is calculated as follows:

initially, area of a hemisphere = 2r2 square units

the area of three small hemispheres

(2*3.14*6 r).3 = 226.08 cm2

Area of the larger hemisphere

2*3.14*18^2 = 2034.72cm^2

Total area of the shaded regions = 226.08 + 2034.72 = 2260.8cm^2

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Answer:

2x + 1 = 29

Step-by-step explanation:

There are a lot of answers.

2x + 1 = 29

2x + 1 = 29  Subtract 1 from both sides

2x = 28  Divide both sides by s

x = 14

Start off knowing that x will be 14, then multiply 14 by some number and then add or subtract some number from that and put that on the other side of the equal sign.

x = 14

14 x 2 = 28 and then add 1 to that to get 29

2x + 1 = 29

Answer: Do you want x=14 or for it to equal 14, because I have it both ways. For x=14, an acceptable two step equation would be 2x-5=23. If you want it to equal 14, then you can write 5x-1=14

Step-by-step explanation:

For x=14:

2x-5=23

Add 5 on both sides

2x=28

x=14

For the equation to equal 14:

5x-1=14

Add one on both sides

5x=15

x=3

Using the normal distribution, we have that diameters at the 0.34th percentile are 0.2 standard deviations, that is, 0.127 inches above the mean.

Probability is the likelihood that a particular experiment result will appear a certain number of times. It cannot be less than zero or greater than one. A 100% chance of an outcome occurring exists if the outcome is 1, for example. If the result is greater than 1, there is a greater chance that it will occur.

In a normal distribution with mean  and standard deviation , the z-score of a measure X is given by:

It measures how many standard deviations the measure X is from the mean.

After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

In this problem:

34th percentile is X when Z has a p-value of 0.34, so X when Z = 0.6331.

It means that the diameter is 0.44 standard deviations = 0.6331x0.2 = 0.127 inches above the mean.

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D. A state is Alaska if and only if it is the biggest state in the United States of America is the correct biconditional statement.

This is the correct biconditional statement because it accurately reflects the information given. The statement states that a state is Alaska if and only if it is the biggest state in the United States of America. This is true, as the given information states that Alaska is the biggest state in the United States of America.

Therefore, statement D is the correct biconditional statement that reflects the given information that Alaska is the biggest state in the United States of America.

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With standard deviation of 2 pounds, the range of weight 99.7% of dogs have will be approximately 24–36 pounds.

The term "standard deviation" (or "σ") refers to a measurement of the data's dispersion from the mean. A low standard deviation indicates that the data are grouped around the mean, whereas a high standard deviation shows that the data are more dispersed.

We have given,

Mean weight of Eskimo dogs is μ = 30 pound

Standard deviation of Eskimo dogs is σ = 2 pound

The range of weights would 99.7% of the dogs have,

R =  μ ± 3σ

R = 30 ± 3*2

R = 30 ± 6

R = (30 - 6) , (30 + 6 )

R = 24, 36

With standard deviation of 2 pounds, the range of weight 99.7% of dogs have will be approximately 24–36 pounds.

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The required solution are as follows,
(A) Kyra's equation of line, passes through 15 pts.
(B) Liam's equation of line, passes through 20 pts.
(C) the equation of line passes through 30 pts is y = 4/3x + 5.

A line is a straight curve connecting two points or more showing the shortest distance between the initial and final points.

here,
Drawing the graph on the graph and evaluating which line pass through which points,

(A)

Kyra's equation of a line is y = 1/2 x
And from the graph, it is seen that the line passes through 15pts

Similarly,
(B) passes through 20 pts

(C)

from the graph, it is seen that equation y = 4/3x + 5 passes through 30 points.

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Triangle ABC is translated to triangle EFG because a vertical translation of 10 units and a horizontal translation of 5 units maps triangle ABC onto triangle EFG.

It is the movement of the shape in the left, right, up, and down directions.

The translated shape will have the same shape and shape.

There is a positive value when translated to the right and up.

There is a negative value when translated to the left and down.

We have,

Triangle ABC.

A = (-9, -2)

B = (-9, -7)

C = (-7, -7)

Triangle EFG.

E = (-4, 8)

F = (-4, 3)

G = (-2, 3)

Now,

With a vertical translation of 10 units up on triangle ABC and 5 units right of the horizontal translation will give us triangle EFG.

i.e,

(-9, -2) = (-9 + 5, - 2 + 10) = (-4, 8)

(-9, -7) = (-9 + 5, -7 + 10) = (-4, 3)

(-7, -7) = (-7 + 5, -7 + 10) = (-2, 3)

Thus,

Vertical translation of 10 units up and horizontal translation of 5 units right.

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Answer:

1: Congruent

2: 10

3: 5

Step-by-step explanation:

a. The exponential function that is good model for the country population is:

Pₙ = 8100000(1.02)ⁿ ,

b. It will take 5.27 years to reach 9 million.

An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.

Exponential Function Formula

An exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent.

a. Given,  initial population P₀ = 8100000, Rate of increase R = 2%.

If a constant rate of growth be R% per annum,

then function for population after n years

Pₙ = P₀ x (1+R/100)ⁿ

Population Pₙ = 8100000 × (1+2/100)ⁿ

Pₙ = 8100000(1.02)ⁿ

b. Let after x years population will be 9 million.

then,

9000000 = 8100000 (1 + 2/100)ˣ

(1 + 2/100)ˣ = 9000000/8100000

(1.02)ˣ = 90/81

(1.02)ˣ = 1.11

Taking log on both sides

ln (1.02)ˣ = ln (1.11)

ln(a)ⁿ = n ln(a)

x ln(1.02) = ln (1.11)

x = ln(1.11)/ln(1.02)

x = 5.27 years

Hence, the population will reach 9 million in 5.27 years.

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It will take approximately 4687.9 years for an investment principal of $1500 to reach $1000000 at an interest rate of 14.2% per year

Simple interest is a type of interest calculated only on the principal amount of a loan or deposit, without taking into account the compound interest earned on that principal. It is calculated by multiplying the principal amount, the interest rate and the time period.

The formula of simple interest is given as;

A = P(1 + rt)

where;

In this problem, we have to find the rate first.

The investment doubles after 7 years.

A = p(1 + rt)

2 = 1(1 + r * 7)

2 = (1 + 7r)

2 = 1 + 7r

7r = 2 - 1

7r = 1

r = 1 / 7

r = 0.142

r = 14.2%

The rate is 14.2 %

Now, we can proceed to determine how many years it will take to reach a value of 1000000

Using simple interest formula again;

A = P(1 + rt)

100000 = 1500(1 + 0.142 * t)

1000000 = 1500(1 + 0.142t)

t = 4687.8 years

It will take approximately 4687.8 years

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Answer:

[tex]d=11.3125[/tex]

Step-by-step explanation:

Given

[tex]\frac{-4(-8.625+2d)}{-8} +3=10[/tex]

Lets solve for [tex]d.[/tex]

Start on the left side with the fraction.

Factor -4 out of -8.

[tex]\frac{-4(-8.625+2d)}{-4(2)} +3=10[/tex]

Cancel the common factor of -4.

[tex]\frac{-8.625+2d}{2} +3=10[/tex]

Subtract 3 from both sides.

[tex]\frac{-8.625+2d}{2} =7[/tex]

Multiply both sides by 2.

[tex]\frac{-8.625+2d}{2} *2=14[/tex]

Cancel the common factor of 2.

[tex]-8.625+2d=14[/tex]

[tex]2d-8.625=14[/tex]

Add 8.625 to both sides.

[tex]2d=22.625[/tex]

Divide both sides by 2.

[tex]d=11.3125[/tex]

exponential function in the form y=ab^x by identifying the common ratio (b) and y-intercept (a) in the graph and if the log term involved in the given function then it is a logarithmic

How do you identify an exponential function from a graph?

Given a graph of a line, we can write a linear function in the form y=mx+b by identifying the slope (m) and y-intercept (b) in the graph. GIven a graph of an exponential curve, we can write an exponential function in the form y=ab^x by identifying the common ratio (b) and y-intercept (a) in the graph

and if the log term involved in the given function then it is a logarithmic

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Answer:

-----------------------------------

According the the table the slope is:

Use slope-intercept form:

And substitute one of the ordered pairs, to find the value of b:

The y-intercept is (0, 8).

Observational data collection might be best to study how voters might decide an upcoming ballot issue.

The majority of big data is observational data, such as bank transaction records, user viewing patterns on video streaming services, or social media posts. Observational data, however, can also be sparse data (based on just a few people).

In observational research, participants and phenomena are observed in their most natural environments. Instead of using structured environments like research labs or focus groups, this allows researchers to observe how their subjects make decisions and respond to situations in their everyday lives.

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On solving the provided question, we can say that - the each angle of pentagon is x = 108

A pentagon is a polygon with five sides that is used in geometry. The inner angles of a straightforward pentagon add up to 540°. Simple or self-intersecting pentagons are both possible. A pentagram is a self-intersecting regular pentagon. Five angles and all sides of a regular pentagon are equal. It is referred to as an irregular pentagon if the side lengths and angle measurements do not match. All outside angles, as far as we are aware, balance out inside angles. The polygon's exterior angle total is therefore equal to n(360°/n). There are five sides to a pentagon, therefore n must equal five. Consequently, 5(360°/5) = 360° is the sum of the pentagon's outer angles.

since all sum of pentagon is 540

so, 5x = 540

x = 108

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To determine whether the point [tex](1,2)[/tex] is a solution of inequality  [tex]3x - 2y - 6 > 0[/tex],  we substitute the point in the inequality and if the result is True, then it will be the solution .

What is an Inequality ?

The Inequality is defined as a relationship between two expressions or values that are not equal to each other .

The inequality in the question is given as : [tex]3x - 2y - 6 > 0[/tex] ;

the point is ⇒ [tex](1,2)[/tex] ,

to check the solution , we substitute the values in the inequality as [tex]x=1[/tex]and [tex]y=2[/tex] ;

we get , [tex]3(1) -2(2) - 6 > 0[/tex]

= [tex]3-4-6 > 0[/tex]

= [tex]3-10 > 0[/tex]

= [tex]-7 > 0[/tex],

But we know that , [tex]-7 < 0[/tex] , So , the given point is not the solution of the given inequality .

The given question is incomplete , the complete question is

How do you determine if the given point (1,2)  is a solution of each linear inequality 3x - 2y - 6 > 0  ?

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Surface Area : Volume = 6 : s

A cube is a 3-D solid shape, which has 6 faces. A cube is one of the simplest shapes in three-dimensional space. All the six faces of a cube are squares, a two-dimensional shape.

Surface Area of a Cube = 6a² in a square units

Volume of cube = a³ cubic units

where a is the side length of the cube.

Given length of the cube = s

Surface Area of cube A = 6s²

Volume of cube V = s³

Ratio between Surface Area and volume:

Surface Area / Volume = 6s² / s³

Surface Area / Volume = 6 / s

Surface Area : Volume = 6 : s

Hence the ratio between Surface area and volume of cube is 6 : s.

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Amount of pineapple juice is more in Jo's drink and amount of Orange juice is less in Jo's drink as compare than the tropical punch recipe because these are not in that ratio as in the tropical punch recipe.

Ratio, in math, is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another. In a ratio, two quantities are compared using division. Here the dividend is called the 'antecedent' and the divisor is called the 'consequent'.

The Number of cups of pineapple juice = 222 liters

The Number of cups of orange juice = 333 liters

Thus ,

Total number of cub of juice = 222+333

                                               = 555 cups

In Jo's drink

The Number of cups of pineapple juice = 333 liters

The Number of cups of orange juice = 444 liters

Thus Total number of cub of juice = 333+444

                                                        = 777 cups.

The ratio of amount of pineapple juice and amount of Orange juice is 2:3 in the tropical punch recipe

Whereas the ratio of amount of pineapple juice and amount of Orange juice is 3:4 in Jo's drink

Thus we can see that Amount of pineapple juice is more in Jo's drink And Amount of Orange juice is less in Jo's drink.

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If you know two angles and one side of a triangle, you can use the Law of Cosines to find the length of the other two sides.

The Law of Cosines states that for a triangle with sides a, b, and c, and angles A, B, and C opposite to those sides, the following formula holds:

c² = a² + b² - 2ab cos(C)

Where C is the angle opposite to side c.

So, if you know the measures of two angles (A and B) and the length of one side (c), you can use the Law of Cosines to find the lengths of the other two sides (a and b) by using the following formulas:

a = √(c² + b² - 2bc cos(A))

b = √(c² + a² - 2ac cos(B))

You can use the above equations to find the sides of the triangle, if you have the measures of two angles and one side.

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The domain and range of the logarithmic function is given by:

Domain= [ 0 , ∞ ) and Range = { y ∈ R }.

As given in the question,

Let y = logₐ x be the given logarithmic function.

Logarithmic function is defined for all the positive values.

Domain of the logarithmic function is given by x∈ R , x > 0.

Range of the logarithmic function is inverse of the domain of the exponential function.

x = e^y

Here y is set of all the real numbers.

Range of logarithmic function is set of all the real numbers.

Therefore, domain of the logarithmic function is set of all real number greater than zero and range of the logarithmic function is the set of all the real numbers.

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Answer: In the expression (3)(0.2)³(0.8)5, the value that represents the number of successes is 0.8.

This value is associated with the probability of success in the given expression, usually represented as "p" in a binomial distribution.

0.8 is probability of success

(0.8)5 represents number of successes.

It is important to note that 0.8 is a probability of success which means the probability of getting a success outcome in a single trial, and (0.8)5 is the probability of getting five successful outcomes in five trials.

Step-by-step explanation: