what is the area, in square inches, of a right triangle with a 24-inch leg and a 25-inch hypotenuse?

Number of seats allocated to state A = 12

Number of seats allocated to state B = 18

Number of seats allocated to state C =22

Number of seats allocated to state D = 38

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

Percentage of Population of state A = 258/1858 x 100 = 13.88%

Now, Number of seats allocated to state A = 13.88% of 45

                                                                       = 12.492 = 12 (whole number)

Percentage of Population of state B = 377/1858 x 100 = 20.29%

Now, Number of seats allocated to state A = 20.29% of 90

                                                                       = 18.261 = 18 (whole number)

Percentage of Population of state C = 456/1858 x 100 = 24.54%

Now, Number of seats allocated to state A = 13.88% of 90

                                                                       = 22

Number of seats allocated to state D = 90-(12+18+22) = 38

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The polyhedron with 10 vertices and 7 faces has 15 edges.

What is polyhedron?

A polyhedron is a three-dimensional object or solid that has flat faces, straight edges, and sharp corners or vertices. It is a geometric shape that is bounded by a finite number of polygons, which are shapes with straight sides.

Based on the Euler's formula for polyhedra, which states that the number of vertices plus the number of faces minus the number of edges is always equal to 2, we can solve for the number of edges:

10 (vertices) + 7 (faces) - E (edges) = 2

Simplifying the equation:

10 + 7 - E = 2

17 - E = 2

E = 17 - 2

E = 15

Therefore, the polyhedron with 10 vertices and 7 faces has 13 edges.

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I'm Saying 30C + 100

Step-by-step explanation:

Answer:

y = [tex]\frac{1}{5}[/tex] x + 7

Step-by-step explanation:

y = mx + b  

You need to find m (the slope) and b (y-intercept)

If you start a the far left point and go to the next point that is graphed on the line, you will see that you moved up 1 space and right 5 to land back on the line.  This is your rise / run.  The slope is 1/5.

The y -intercept is where the line crosses the y axis.  It crosses at 7

There are only 2 possible solutions for B, 1 and 3, so that the number forms the two-digit numbers 16 and 36, which are the positive squares of the positive integers 4 and 6.

Now, we have been given a two-digit number, B6.

The numbers whose squares are 2 digit numbers are:

1, 4, 9, 16, 25, 36, 49, 64, 81

From this list, it is evident that there are 2 numbers that end with 6 and are perfect positive squares of a number, in this case, 4 and 6.

4x4 = 16, 6x6 = 36.

Therefore, B can take 2 values, 1 and 3. These are the only distinct possible values of positive integers for B to take.

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The three consecutive integers are 137 , 138 and 139

Given that

Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers.

Consecutive Even Numbers:

Even numbers are numbers that end with 0, 2, 4, 6 or 8. The examples of consecutive even numbers are:0, 2, 4, 6, 8, 10, 12, …

Consecutive Odd Numbers:

Odd numbers are numbers that end with 1, 3, 5, 7 or 9. The examples of consecutive odd numbers are:1, 3, 5, 7, 9, 11, 13, 15, ….

there are three consecutive integers

let's assume that consecutive integers are x, x+1 and x+ 2

given that  the sum of the first and the third number is two hundred and seventy-six

x + (x+2) = 276

2x + 2 = 276

2x = 276 - 2

2x = 274

x = 137

The three consecutive integers are 137 , 138 and 139

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The proof of the vertical angle theorem as required is explained in the answer below:

What are vertical angles?

Vertical angles are two angles that have the same properties and measure of their angles. Majorly these angles are opposite to each other and formed by the same extended lines.

So that, the required proof of the vertical angle theorem is;

             STATEMENT                                            REASON

1. AC intersect BD at E                                       Given

2. m<AEB m<DEA = 180^o                                 Linear pair theorem

3. m<DEC + m<DEA = m<AEB + m<DEA           Substitution property

4. m<DEC = 180^o - m<BEC                                Subtraction property

5. m<DEC = m<AEB                                             Vertical angle theorem

Therefore it can be deduced in the diagram that;

m<DEC = m<AEB           (vertical angle theorem)

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The two step equation for the scenario that your cousin is in where they pay for their textbooks is:

7x + 20 = 230

x = (230 - 20) / 7

The cost of the textbooks would be $30.

The total amount paid by your cousin in order to be able to cover a book for their 7 classes and the fee for art class is $ 230.

Assuming that the cost of each book from his 7 classes is denoted as x, then the expression would be:

= 7 x number of classes

= 7x

This amount is then added to the cost of the art class which is $ 20 so it becomes:

= 7x + 20

The two step equation is therefore:

7x + 20 = 230

x = (230 - 20) / 7

The cost of the textbooks is:

x = (230 - 20) / 7

x = $ 30

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Answer:

4) is the least with 14.111°

1) is next with 17.9°

2) is next with 30.22°

5) is next with 65.84°

3) is the greatest with 86.82°

Step-by-step explanation:

1) csc θ = 3.2547

1/sinθ = 3.2547

sinθ = 1/3.2547

θ = [tex]sin^{-1}[/tex] 1/3.2547 or 17.9 ° ( I checked using a calculator here)

[tex]sin^{-1}[/tex]x is also known as arcsin.

Now, i will do the rest the same way.

2) θ = arccos(0.8641) = 30.22°

3) θ = arctan(17.9926) = 86.82°

4) θ = arcsin(0.2438) = 14.111°

5) θ = arctan(1/0.4485) = 65.844°

So, now u can tell the orders.

Pls mark as brainliest. This took a while. Cheers.

Answer: 3.65, 3.7, 323

Step-by-step explanation:

The numbers from least to greatest are as follows:

3.65, 3.7, 323

Hope this helps

For the given perimeter and side length of the triangle , the equation and the measure of the longest side length of the triangle is given by :

Equation : x + 278 = 450 and side length = 172cm.

As given in the question,

The given measurements of the triangle are :

Perimeter of the triangle = 450cm

Measure of the two side length are :

Side length 1 = 128 cm

Side length 2 = 150 cm

let 'x' be the measure of the longest side length of the triangle we have,

Perimeter of the triangle = Side length 1 + Side length 2 + side length 3

⇒ 450 cm = 128 + 150 + x

⇒ 450 = 278 + x

Equation to represent the relation :

x + 278 = 450

Measure of the longest side of the triangle is :

⇒ x = 450 - 278

⇒ x = 172 cm

Therefore, the equation and the measure of the longest side length of the triangle with given perimeter and other side length is equal to

Equation : x + 278 = 450 and side length = 172cm.

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Answer: z=23

Step-by-step explanation:

Since the sum of all interior angles of a triangle is 180, let's use that to solve this problem.

First, let's set up an equation.

z+62+95=180

Next step is to simplify the left side of the equation, which leaves us with:

z+157=180

Lastly, subtract 157 from both sides of the equation and we get the final answer:

z = 23

The required Confidence interval for the given data is CI = 0.6 - 0.7 ± 1.96[tex]\sqrt{\frac{0.6(1-0.6)}{50}+\frac{0.7((1-0.7)}{50} }[/tex].

Hypothesis testing is a methodical process for determining whether research study findings are consistent with a specific idea that pertains to a population. To evaluate a hypothesis about a population, hypothesis testing uses sample data.

We have,

x1 = 30,  x2 = 35

n1 = 50, n2 = 50

p1 = x1/n1 = 30/50 = 0.6

p2 = x2/n2 = 35/50 = 0.7

Then,

at α= 0.05, the critical value taken by table of z

Zc = 1.96

CI =[tex]P_{1}-P_{2}[/tex] ±[tex]\sqrt{\frac{P_{1}(1-P_{1})}{n_{1}}+\frac{P_{2}((1-P_{2})}{n_{2}} }[/tex]

CI = 0.6 - 0.7 ± 1.96 [tex]\sqrt{\frac{0.6(1-0.6)}{50}+\frac{0.7((1-0.7)}{50} }[/tex]

This is our needed answer,So option (D) is correct.

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Assuming that the y-axis tick marks will be separated by 50 (50, 100, 150, and so on). The largest value that should appear on the y-axis is 400.

Largest value:

The maximum value of a dataset is often called the maximum value (max for short), and the minimum value is often called the minimum value (or min). The difference between the maximum and minimum values, sometimes called the range, is calculated by subtracting the minimum value from the maximum value.

Researchers varied the time of the experiment to measure the activity of the enzyme on glucose-6-phosphate (substrate). This happened because the enzyme acted on glucose-6-phosphate to produce glucose and a phosphate ion (Pi).

The concentration of phosphate ions was measured in the experiment. Therefore, time is the independent variable plotted on the x-axis and phosphate ion concentration is the dependent variable plotted on the y-axis.

The measured phosphate ion concentration ranges from 0 to 355. The maximum possible value is 355, so the y-axis range must be between 0 and 400. So the maximum value on the y-axis is 400.

50 units should separate the y-axis ticks. All tick marks are evenly spaced.

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In mathematics, having an infinitely large amount or cardinality is referred to as having an infinity many.

Endless sets actually have an infinite number of components. If a set has continuity on both sides or is unbounded from start to finish, we can refer to it as infinite. For instance, the set of whole numbers W = 0, 1, 2, 3, etc. is an infinite set since it has an unlimited number of items. The set of real numbers is one of the uncountably infinite sets. Dots are used to symbolize the elements of an infinite set to denote the set's infinity.

There are some properties of infinite many solutions.

The superset of an infinite set is also infinite.

The subset of an infinite set may or may not be infinite.

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Answer:

L = -7

Step-by-step explanation:

5L - 6 - 7L = 8

combine like terms

5L - 7L - 6 = 8

-2L - 6 = 8

add 6 to both sides

-2L = 14

divide by -2

L = -7

Angle C is the biggest.

The longest side in a triangle is opposite the largest angle, and the shortest side is opposite the smallest angle.

Answer:

56.5 cm

Step-by-step explanation:

Circumfrence= pi× diameter

= 3.14×18 = 56.52 cm

3SF: 56.5 cm

if you used the same experimental design, but instead used an endotherm, you would expect to see a difference in the organism's ability to regulate its body temperature

If the same experimental design was used but with an endotherm (an organism that generates heat internally) instead of an ectotherm (an organism that relies on external sources of heat), I would expect to see a difference in the organism's ability to regulate its body temperature. Endotherms have a higher metabolic rate and are able to generate heat internally, whereas ectotherms rely on external sources of heat to regulate their body temperature. This means that endotherms would be less affected by changes in external temperature and would be able to maintain a more stable body temperature. Additionally, endotherms would likely have a higher tolerance for cold temperatures. I came to this conclusion because endotherms have internal heat regulation mechanisms that allow them to maintain a stable body temperature, whereas ectotherms do not.

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the ratio 1 is to 2 is equivalent to 3: 6

What is an equivalent ratios?

A ratio compares two quantities named as antecedent and consequent, by the means of division. For example, when we cook food, then each ingredient has to be added in a ratio. Thus, we can say, a ratio is used to express one quantity as a fraction of another quantity.

Two ratios are equivalent to each other if one of them can be expressed as the multiple of the other. Hence, to get the equivalent ratio of another ratio, we have to multiply the two quantities (antecedent and consequent) by the same number.

Given ratios are 2:1 and 3:1

we can write it as 2/1 and 3/1.

The lcm of 2 and 3 is 6.

Multiply denominator of both ratio with 6, we get

2/6 and 3/6 And we can see both the ratios are not equal.

Hence, there are not equivalent ratios.

4:1 and 8:3 are equivalent ratios -----> is false, because 4:1 is equivalent to 8:2

11:2 and 2:11 are equivalent ratios------> is false (because, are reciprocal ratios, not equivalent ratios)

3:1 and 9:3 are equivalent ratios ------> is true

because 3:1 multiply both sides by 3 -----> 3*3:1*3=9:3

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The dimensions size on the scale drawing is 6.5 inches by 3.5 inches.

Dimensions in mathematics are the measure of the size or distance of an object or region or space in one direction. In simpler terms, it is the measurement of the length, width, and height of anything.

In Geometry we can have different dimensions, The number of dimensions is how many values are needed to locate points on a shape.

Multiplying the actual dimensions by the scale gives the scale dimensions:

 (0.5 in)/(6 ft) × {78 ft, 42 ft}

 = {39/6 in, 21/6 in}

 = {6.5 in, 3.5 in}

Therefore, the dimensions size on the scale drawing is 6.5 inches by 3.5 inches.

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For given circle value of arc KT will be 147m.

What is a circle?

A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident. A circle is also termed as the locus of the points drawn at an equidistant from the center. The distance from the center of the circle to the outer line is its radius. Diameter is the line which divides the circle into two equal parts and is also equal to twice of the radius.

The equation of circle in the plane is given as:

(x-h)^2 + (y-k)^2 = r^2

where (x, y) are the coordinate points

(h, k) is the coordinate of the center of a circle

and r is the radius of a circle.

and Area of circle = πr²

Circumference of circle=2πr

Now,

as for a given circle when the vertex of angle falls outside of circle

then (larger arc-smaller arc/2)=angle

Therefore,  55=(KT-37)/2

KT=110+37

KT=147m

Hence,

              Value of arc KT will be 147m.

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Answer:

  251.5 square units

Step-by-step explanation:

You want to know the area of the given pentagonal figure.

The figure can be decomposed into a (top) triangle that is 21 units wide and (19-8) = 11 units high, along with a (bottom) trapezoid that is 8 units high and has bases of 21 units and 13 units. The area of the figure is the sum of the areas of these parts.

The area of the triangle is ...

  A = 1/2bh

  A = 1/2(21)(11) = 115.5 . . . . square units

The area of the trapezoid is ...

  A = 1/2(b1 +b2)h

  A = 1/2(21 +13)(8) = 136 . . . . square units

The area of the pentagon shown is the sum of these areas:

  115.5 +136 = 251.5 . . . . square units

The perimeter of the shaded region is 18 units.

The circumference of a circle is defined as the linear distance around it. In other words, if a circle is opened to form a straight line, then the length of that line will be the circle's circumference.

The result of the lengths of the sides is the perimeter of any polygon. In the case of a triangle: Perimeter = Sum of the three sides.

If we connect the centers of the circles, this will form an equilateral triangle.

The two sides of this triangle meeting at any vertex will pass through the points of tangency where one circle meets the other two, these two tangent points form the endpoints of one side of the shaded region.

Since the vertex angle of the triangle = 60°, then the arc formed by one side of the shaded region

= 1/6 the circumference of the circle

= 1/6 × 36

= 6 units

So, the perimeter of the shaded region is 3 times this

= 3 × 6

= 18  units

Therefore, the perimeter of the shaded region is 18 units.

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System components in mathematics involves the study of equations and their solutions, shapes and their properties, rate of change and area under a curve, angles and their relationships, and the properties of numbers.

1. Algebra: This is the study of equations and their solutions, as well as the manipulation of symbols and operations.

2. geometry: This involves the study of shapes and the properties of space, such as angles and distances.

3. Calculus: This involves understanding the rate of change of a function and the area under a curve.

4. Trigonometry: This involves the study of angles and their relationships to one another and to other types of measurements.

5. Number Theory: This involves the study of the properties of numbers, such as divisibility, primes, and multiplicative functions.

System components in mathematics involves the study of equations and their solutions, shapes and their properties, rate of change and area under a curve, angles and their relationships, and the properties of numbers.

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Answer:

16

Step-by-step explanation:

The side lengths of the original square was 2.  2 x 2 = 4

.25 x 2 = .5

The squares are now 1/2 x 1/2.  One of the 4 original squares will now need 4 new smaller size squares to cover the one square.

4 x 4 = 16

On Earth, the golf ball would travel much farther and higher than on the moon due to the difference in gravity. On the moon, the gravity is only 1/6th the strength of Earth's, making it much easier for the golf ball to travel farther and higher. On Earth, the golf ball would travel farther and higher due to the stronger gravitational pull.

Sale price of the mattress is $700.

What is a sales price in math?

The price after the original price has been reduced by a discount.

The discount equals the difference between the price paid for and it's par value. Discount is a kind of reduction or deduction in the cost price of a product.

Mattress that is of $1000 is sold at  discount 30%.

Original price of mattress = $1000

Percentage of discount on mattresses = 30%

So,

Amount of discount on mattresses

= [ 30 / 100 ] × 1000

= $300                        

sale price of the mattresses = $1000 - $300 = $700

Therefore, the sale price of the mattresses is $700.

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