how many 5 letter words can be made from mathisfun if each word must have 2 consonants and 3 vowels?

Four lines be chosen from four horizontal lines and four vertical lines in a plane such that a rectangular region is enclosed in 36 ways.

The four horizontal lines can be chosen in 4 choose 2 = 6 ways because we have to pick 2 out of 4, and the four vertical lines can be chosen in 4 choose 2 = 6 ways as well as

4C2 = 4!/ (2!×2!)

4C2 = 6

The total number of ways to pick four lines that enclose a rectangular region is 6×6 = 36, where each combination of two horizontal lines and two vertical lines forms a rectangle.

It's important to notice that the order of choosing the lines doesn't matter, so we use the combination formula (nCr) instead of permutation formula (nPr).

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We have,

nth term = 4n+1

Putting n = 3, we have the 3rd term, i.e.,

4(3) + 1 = 12 + 1 = 13

Answer:

13

The length of HE is 4 units.

Given that GH is tangent to both circle A and circle E, we can use the property of tangents that states that a tangent line to a circle is perpendicular to the radius drawn to the point of tangency.

If we let r be the radius of circle A and circle E, and let HE be the length of the line segment from the center of the circles to the point of tangency, we can use the Pythagorean Theorem to determine the length of HE.

The Pythagorean theorem is a fundamental result in mathematics that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Since GH is tangent to both circles, it is perpendicular to the radius of both circles and we can create a right triangle with legs HE and r. We can use the Pythagorean theorem to find the length of HE

HE^2 + r^2 = GH^2

We can use the information given to find the value of GH, then we can solve for HE using the equation above.

We know that GH is tangent to both circles, which means that GH is equal to the diameter of both circles. So GH = 2r

Substituting this value into the equation above:

HE^2 + r^2 = (2r)^2

HE^2 = 2r^2 - r^2 = r^2

HE = √(r^2) = r

Given that HE = r and r = radius of circle A and Circle E, HE = radius of Circle A = radius of Circle E.

Therefore, the length of HE = radius of Circle A or Circle E = 4 units.

So, the length of HE is 4 units.

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Answer:

Step-by-step explanation:

Brad's solution to find the surface area of the composite figure is not correct.

In his solution, Brad adds the surface areas of the triangular prism and the rectangular prism separately,

but it's not taking into account that the two prisms share a face that is 14 by 20.

When finding the surface area of a composite figure, it's important to take into account any shared faces.

Since the two prisms share a face that is 14 by 20, Brad should subtract this area from one of the prisms,

otherwise he will be counting it twice in the final result.

The correct method would be:

Rectangular prism: (2 * 8 * 14) + (2 * 14 * 20) + (2 * 8 * 20) = 1,104 cm^2

Triangular prism: (1/2 * 14 * 12) + (1/2 * 13 * 15) + (3 * 14 * 20) = 1,008 cm^2

Subtracting shared area: 1,104 cm^2 + 1,008 cm^2 - (14 * 20) = 2,096 cm^2.

So Brad's solution is incorrect, the correct surface area of the composite figure is 2,096 cm^2.

Answer:90x567

Step-by-step explanation:

The required number of tiles required is 100

as per detail stated above,

the length of the side of the square tile is (s) = 5m

the length of the side of the square pavement (S) is 50m

the area of square tile whose side length is 5 m is

area = side (s) times side (s)

area = 5 x 5

area = 25

now the second area

the area of the square pavement whose side length is 50m is

area = side (s) times side (s)

area = 50 x 50

area = 2500[tex]m^2[/tex]

now to find

the required number of tiles  = area of the square pavement by the area of the square tile

therefore

the required number of tiles are =

=> 2500/25

=> 100

therefore the required number of tiles are 100.

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Answer:

Step-by-step explanation:

Answer:

D = (2x + 3)² + (x-2)(2x + 3)

Factoring D, we get:

D = (2x + 3)² + (x-2)(2x + 3)

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

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

The total surface area of the prism will be 290.125 Square units.

The surface area of a rectangular prism is the measure of how much-exposed area a prism has. Surface area is expressed in square units.

The surface area of a rectangular prism is given by:

SA = 2 (lh +wh + lw )

where

l = 3

w = 4.25

h = 18.25

SA = 2 (3x18.25 + 4.25x18.25 + 3x4.25)

SA = 2 (54.75 + 77.5625 + 12.75)

SA = 2 (146.0625)

SA = 290.125 square units

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One of the right triangles that are given which can be used to approximate PQ of the given triangle above is triangle labelled 3 and it's value = 9.5.

A right triangle is defined as the triangle that is has one of its angle equal to 90 degrees.

Therefore, the value of the side of the triangle PQ can be obtained using the Pythagorean formula;

c² = a² + b²

c² = PR = 7²

a² = 6.4²

b² = PQ = ?

b² = c² - a²

b² = 49+40.96

b² = 89.96

b= √ 89.96

b = 9.5.

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The double integral for [tex]3xy^2/x^2+1[/tex] is 8㏑(2).

[tex]3\int\limits^1_0 \int\limits^2_2 \frac{xy^2}{x^2 + 1} \, dy dx[/tex]  

3* 1/2 (㏑(2) - ㏑(1) ) * 1/3 (8+8)

8㏑(2)

A multiple integral in mathematics is a definite integral of a function with multiple real variables, such as f(x, y), or f(x, y) (x, y, z). In the real-number plane, integrals of functions of two variables over an area are referred to as double integrals, and integrals of functions of three variables over a region in real-number three-dimensional space are referred to as triple integrals.

The Cauchy formula for repeated integration can be used to calculate multiple integrals of a single-variable function.

The double integral of a positive function of two variables represents the volume of the region between the surface defined by the function (on the three-dimensional Cartesian plane where z = f(x, y)) and the plane that contains its domain, just as the definite integral of a positive function of one variable represents the area of the region between the graph of the function and the x-axis.

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Answer:

[tex]\frac{5x-3}{4}[/tex]

Step-by-step explanation:

[tex]x=\frac{4y+3}{5} \\ 5x=4y+3\\ 5x-3=4y\\ \frac{5x-3}{4} =y[/tex]

The fraction 1/9 is greater than the fraction 1/11.

Comparing fractions involves a set of rules related to the numerator and the denominator. When any two fractions are compared, we get to know the greater and the smaller fraction.

To compare unlike fractions:

Step 1: Observe the denominators of the given fractions: .

Step 2: Now, let us convert them in such a way that the denominators become the same.

Step 3: Compare the fractions:

Step 4: The fraction with the larger numerator is the larger fraction.

The given fractions are 1/9 and 1/11.

Here, LCM of denominator 9 and 11 is 99

Then, fractions becomes 11/99 and 9/99

11/99>9/99

1/9>1/11

Therefore, the fraction 1/9 is greater than the fraction 1/11.

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The equation for situation 1 is y = 3.5x

The equation for situation 2 is y = 3x

The equation for situation 3 is y = (5/2)x

The equation for situation 4 is  (1/2)x = y

The constant of proportionality is the ratio that relates two given values in what is known as a proportional relationship. It is also known as unit rate and it is usually expressed by k. That is k = y/x

Situation1

A dump truck is hauling loads of dirt to a construction site. After 20 loads, there are 70 square feet of dirt.

k = y/x = 70/20 = 3.5

For every 70 square feet of dirt, there are 2 loads.

y = kx

y = 3.5x

Situation 2

I am making a water and salt mixture that has 2 cups of salt for every 6 cups.

k = 6/2 = 3

This means in every 3 cups there is 1 cup of salt

y = 3x

Situation 3

A store has a "4 for $10" sale on hats.

k = 10/4 = 5/2

This means $5 for 2 hats.

y = (5/2)x

Situation 4

For every 48 cookies I bake, my students get 24.

k = 24/48 = 1/2

This means 1 student gets 2 cookies

y = (1/2)x or (1/2)x = y

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A combination chart can be made up of the area, bar, column, dot, and line charts.

Bar charts are one of the most common data visualizations. Each data series can be represented by a different type of chart. They are all then displayed simultaneously on the same chart.

Adding a chart type that displays over another chart type can give you an immediate comparison of two or more data series over a dimension such as time.

Combination charts enable you to compare different series of data through different types of charts on the same axes simultaneously. This is useful for visualizing large quantities of data in varied formats.

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Answer:

To solve this problem, we will use the following steps:

Step 1: Since a pair of dice are tossed, we have 36 possible outcomes (6 outcomes for each die).

Step 2: To find the probability that doubles are rolled, we can find the number of outcomes that result in doubles and divide that by the total number of possible outcomes.

Step 3: To find the probability that the sum on the two dice is less than 7, we can find the number of outcomes that result in a sum of less than 7 and divide that by the total number of possible outcomes.

Step 4: We will use this probability to find the conditional probability of rolling doubles, given that the sum on the two dice is less than 7.

Step 5: To find the number of outcomes that result in doubles, we can consider rolling (1,1), (2,2), (3,3), (4,4), (5,5), (6,6) which are 6 outcomes.

Step 6: To find the number of outcomes that result in a sum of less than 7, we can consider rolling (1,1), (1,2), (1,3), (1,4), (1,5), (2,1), (2,2), (2,3), (2,4), (2,5), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (5,1), (5,2) which are 18 outcomes.

Step 7: To find the conditional probability of rolling doubles, given that the sum on the two dice is less than 7, we can find the number of outcomes that result in doubles and sum less than 7 which are (1,1), (2,2), (3,3), (4,4), (5,5) which are 5 outcomes.

Step 8: We can calculate the probability by dividing the number of outcomes that result in doubles and sum less than 7 by the number of outcomes that result in a sum less than 7.

5/18 = 0.278

Final Answer: The probability of rolling doubles, given that the sum on the two dice is less than 7, is 0.278 or 27.8%.

Answer:

19

Step-by-step explanation:

Substitute x = -4/5 and solve for b.

5x² + bx + 12 = 0

5(-4/5)² + b(-4/5) + 12 = 0

16/5 − 4/5 b + 12 = 0

16 − 4b + 60 = 0

4b = 76

b = 19

Answer:

Step-by-step explanation:

El número A = 52 es una solución del sistema de ecuaciones lineales.

En esta pregunta tenemos un sistema de dos ecuaciones lineales con dos incógnitas, de modo que existe la posibilidad de una solución única. Primero, escriba el sistema de ecuaciones descrito en el enunciado de la pregunta:

A / 4 = B / 9

A + B = 169

Segundo, despeje la variable A de la segunda ecuación del sistema de ecuaciones:

B = 169 - A

Tercero, elimine la variable B en la primera ecuación del sistema de ecuaciones y despeje la variable A:

A / 4 = (169 - A) / 9

9 · A = 4 · (169 - A)

9 · A = 676 - 4 · A

13 · A = 676

A = 52

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Check the picture below.

As per the given divisor and product, the value of e is 5.

The term divisor in math is defined as a number which divides another number and it is a part of the division process.

Here we have given that let us consider that s denote the set of all positive divisors of 60⁵

Here we also know that the product of all the numbers in s equals 60ⁿ for some integer n.

As per the given condition, the terms are written as,

=> s =  60⁵

=> s = 60ⁿ

Here we have to compare the given values then we the expression like the following,

=> 60⁵ = 60ⁿ

As per the rule of exponent, the value of e = 5.

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The area of a rectangle is increasing at a constant rate of 3.5 cm²/s when the length is increasing at a constant rate of 3 cm/s and the width is increasing at a constant rate of 0.5 cm/s.

The area of a rectangle is calculated as length multiplied by width (A = L x W). At the given time, the length is 5 cm and the width is 1.2 cm, so the area is 6 cm². When the length is increasing at a constant rate of 3 cm/s, and the width is increasing at a constant rate of 0.5 cm/s, then the area is increasing at a rate of 3.5 cm²/s. This can be calculated by multiplying the constant rate of increase of the length and width together (3 x 0.5 = 1.5). This is the rate of increase of the area and is expressed as 3.5 cm²/s This can be calculated by multiplying the constant rate of increase of the length and width together (3 x 0.5 = 1.5).

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Answer:

x= -9.17

Step-by-step explanation:

To solve for x, we can use the information provided about the rectangle to set up an equation. Since opposite sides of a rectangle are congruent (have the same length), we know that MO = NP.

Therefore, we can set up the equation:

-6x + 10 = 65

To solve for x, we can subtract 10 from both sides:

-6x = 55

And then divide both sides by -6:

x = -9.17

When plotting points on a quadratic inequality, the "included" points refer to the points that satisfy the inequality, and the "not included" points refer to the points that do not satisfy the inequality.

Generally, A quadratic inequality is an inequality that can be written in the form of

ax^2 + bx + c > 0 or ax^2 + bx + c < 0,

where a, b, and c are constants and x is a variable.

These types of inequalities can be solved using the same methods as solving quadratic equations, with the added step of testing the solutions in the original inequality to determine whether they are valid solutions.

Simply put, an equation of the kind with the greatest degree two and no equal sign is known as a quadratic inequality. There is a technique for resolving quadratic inequalities called the wavy curve approach. It is the same to solve quadratic equations as it is to solve quadratic inequalities.

For example, if the inequality is "y > x^2," the points that are above the parabola y = x^2 would be included, and the points that are below the parabola would be not included.

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Answer:

Sin A / A = Sin B / B         Law of Sines

Sin 73 / X = Sin 59 / 18     Application of Law of Sines

X = Sin 73 / Sin 59 * 18 = .956 / .857 * 18 = 20.1

The ratio in simplest form in the three cases is 5 : 6, 36 : 29 and 1 : 5.

30 treadmills to 36 elliptical machines can be simplified to 5 treadmills to 6 elliptical machines. To simplify, you can divide both numbers by their greatest common factor, which in this case is 6.

30/6 = 5 and 36/6 = 6

So 30 : 36 = 5 : 6

180 red marbles to 145 blue marbles can be simplified to 12 red marbles to 11 blue marbles. To simplify, you can divide both numbers by their greatest common factor, which in this case is 5.

180/5 = 36 and 145/5 = 29

180 : 145 = 36 : 29

In the word "flashlight", the ratio of vowels to total letters is 2:8. The word "flashlight" has 2 vowels (a,i) and 10 total letters. To simplify divide by 2.

2 : 10 = 1 : 5

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The infinite series for the given indefinite integral will be as [tex]\int\ {\frac{cos(x) - 1}{x} } \, dx[/tex] Σ[infinity]n=1  [tex](-1)^n \frac{x^{2n}}{(2n)} . \frac{1}{(2n)!} + C[/tex].

We know that the infinite series also called as Maclaurin series

the Maclaurin series for cos(x)

cos(x) = Σ[infinity]n=0  [tex](-1)^n \frac{x^{2n}}{(2n)!}[/tex]

cos(x) = [tex]1 - \frac{x^2}{2!} + \frac{x^4}{4!} - .. + (-1)^n \frac{x^{2n}}{(2n)!}[/tex]

cos(x) - 1 = Σ[infinity]n=1 [tex](-1)^n \frac{x^{2n}}{(2n)!}[/tex]

Now, divide both sides by x

cos(x) -1/x = Σ[infinity]n=1 [tex](-1)^n \frac{x^{2n-1}}{(2n)!}[/tex]

[tex]\int\ {\frac{cos(x) - 1}{x} } \, dx =[/tex] [tex]\int { } \,[/tex] Σ[infinity]n=1 [tex](-1)^n \frac{x^{2n-1}}{(2n)!} dx[/tex]

or [tex]\int\ {\frac{cos(x) - 1}{x} } \, dx =[/tex] Σ[infinity]n=1 [tex](-1)^n \frac{x^{2n}}{(2n)} . \frac{1}{(2n)!} + C[/tex]

Therefore, [tex]\int\ {\frac{cos(x) - 1}{x} } \, dx =[/tex] Σ[infinity]n=1 [tex](-1)^n \frac{x^{2n}}{(2n)} . \frac{1}{(2n)!} + C[/tex]

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The perimeter of a rectangle is the total distance covered by its boundaries or the sides. Since there are four sides of a rectangle, thus, the perimeter of the rectangle will be the sum of all four sides. Since the perimeter is a linear measure, therefore, the unit of the perimeter of rectangle will be in meters, centimeters, inches, feet, etc.

Perimeter of rectangle = 42 cm.

2 × (l + b) = 42

l + b = 21

So l + b = 2 + 19 ; 3+ 18; 4+17; 5+16; 6+ 15 ; 7+14 ; 8+13 ; 9+12; 10 +11:

Area for l × b =  2× 19= 38 sq.cm

Area for second case = 3* 18=54sq.cm

Area for third case = 4* 17=68sq.cm

Area for fourth case = 5* 16=80sq.cm

Area for fifth case = 6* 15=90sq.cm

Area for sixth case =7* 14=98sq.cm

Area for seventh case =8* 13=104sq.cm

Area for eighth case =9* 12=108sq.cm

Area for ninth case =10* 11=110sq.cm

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The total displacement of the car after 5hrs is 0km.

                s =sf– si

where, s = displacement.

In the given graph, there is the change in distance covered with the time that is:

Thus, the displacement will be 0 km as the final point and initial point are the same.

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Answer:

First and last one

Step-by-step explanation:first and last one

Answers to all the questions form 1 to 10 are illustrated below.

The circumference of a circle is the distance around the circle which is 2πr.

The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.

We know the angle formed at the center of a circle is twice the angle formed at the circumference.

Answering each one in short.

1. x = 136/2 = 68°.

2. x = 146/2 = 73°.

3. x = 2×49 = 98°.

4. x = 2×62° = 124°.

5. As m∠O = 100°, x = 100/2 = 50°.

6. m∠O = 360 - 100 - 150 = 110°, x = 110/2 = 55°.

We know the angle formed by the same chords at the circumference is equal in measure.

7 . x = 18°.

8. x = 27°.

9. x = 180 - 55 - 90 = 35°.

10. x = 180 - 12 - 91 = 77°.

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A type II error in this context would be when the inspector incorrectly fails to reject the null hypothesis (H0), meaning they accept the null hypothesis that the humidity level absorbed is 3% when it is actually more than 3%.

A hypothesis test is a statistical procedure used to evaluate a hypothesis by using sample data. Brainly experts can use hypothesis tests to verify the accuracy of their answers by collecting sample data, analyzing it and making a conclusion. Hypothesis testing involves formulating a null and alternate hypothesis, generating a test statistic, and using the test statistic to make a decision. Brainly experts can use hypothesis testing to check the validity of their answers and to ensure that they are providing accurate information to their users.

This type of error would result in potentially hazardous components being approved for use and could lead to catastrophic accidents. In other words, if the inspector fails to reject H0 when it is false, it could lead to unsafe components being used and put the health and safety of people in danger.

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The third term of the geometric series is 7*(1/2)^2 = 3.5 and the second term is 7*(1/2)^1 = 3.5. When the third term is divided by the second term, the result is 1.

A geometric series is a sequence of numbers where each term is obtained by multiplying the previous term by a constant. In this particular series, the first term is 7 and the sum is 4. This means that the constant is 1/2. To find the third term, we multiply the second term by the constant, which gives us 7*(1/2)^2 = 3.5. To find the result when the third term is divided by the second term, we divide 3.5 by 3.5, which gives us 1. This is true for any infinite geometric series with the same first term and sum, because the ratio between every two consecutive terms is always the same.

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