Solve for X, Leave in simplest radical form.

23/20 students in barbara's class have both a cat and a dog.

In mathematics, a fraction is used to denote a portion or component of the total. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction.

Given that,

The number of students in barbara's class having a pet cat = 2/5

The number of students in barbara's class having a pet dog = 3/4

Thus, the fraction of the students in barbara's class have both a cat and a dog = 2/5+3/4 = 8+15/20= 23/20

Hence, 23/20 students in barbara's class have both a cat and a dog.

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Answer:

I think the answer is A. I hope this is helpful

Answer:

3 green apples and 7 red apples.

Step-by-step explanation:

1. Start with the ratio of green apples to red apples, which is 3 to 7.

2. Multiply 3 (the number of green apples) by any number to get a number that is divisible by 7 (the number of red apples).

3. In this case, multiplying 3 by 2 gives 6, which is divisible by 7.

4. Since 6 is divisible by 7, that means that the solution is 3 green apples and 7 red apples.

The value of x using trigonometry is √6.

The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.

The area of mathematics known as trigonometry examines the link between the ratios of a right-angled triangle's sides to its angles. Trigonometric ratios, such as sine, cosine, tangent, cotangent, secant, and cosecant, are employed to analyze this connection.

The measurement of angles and issues relating to angles are covered in the fundamentals of trigonometry. Trigonometry has three fundamental operations: sine, cosine, and tangent. The cotangent, secant, and cosecant are three crucial trigonometric functions that may be derived from these three fundamental ratios or functions. These functions serve as the foundation for all the key ideas in trigonometry.

In the triangle base = [tex]\sqrt{2}[/tex] and height as x

The value of the angle is [tex]60\x^{o}[/tex]

so tanθ = tan[tex]60\x^{o}[/tex]

[tex]\frac{height }{base} = tan60\x^{o} \\[/tex]

⇒ x = √3 * √2

⇒ x = √6

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The data from the 9 students represents the number of hours that they spend on the computer on a typical day. It forms a distribution known as a frequency distribution.

A frequency distribution is a tabular representation of data that shows how often each value or set of values of a variable occurs in a data set. The data set is typically divided into a number of classes or bins, and the frequency of each class is recorded.

In this case, the data represents the number of hours that 9 students spend on the computer on a typical day. Each student is represented by one data point, and the frequency of each value (the number of hours) is recorded.

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A number multiplied by 1 is the number itself. So,1 is a factor of every number.

1 is the factor of every number as one divides every number exactly, without leaving any remainder behind, and gives the quotient as the number itself.

1 is the greatest factor of itself and the smallest factor of any other number.

There are some properties of factors one:

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Answer: 174

Step-by-step explanation: In the first year, the population of 32 goats increases by 71/10032 = 22.72 goats

So the population after 1 year would be 32+22.72 = 54.72 goats

In the second year, the population of 54.72 goats increases by 71/10054.72 = 38.9792 goats

So the population after 2 years would be 54.72+38.9792 = 93.69 goats

It's important to note that the answer provided (93) is the population after one year, not two years. The population after two years would be 174 goats.

Step-by-Step Explanation:

[tex]x + \frac{2}{5} = \frac{1}{3} \\ = > x = \frac{1}{3} - \frac{2}{5} \\ = > x = \frac{5 - 6}{15} \\ = > x = \frac{ - 1}{15} [/tex]

Answer:

A) x = -1/15

Answer:

Step-by-step explanation:

Divide 138 by 12.

The answer would be 11.5.

Lets leave the 0.5 right now.

So, there would be 11 teams left and the other people left will be in the small group.

Now, multiply 12 by 11. You get 132. Subtract that from 138 and you get the remainder which is 6.

Hence, the number of people in the small group would be 6.

Thanks

Answer:

11 teams & 6 people in the small group

Step-by-step explanation:

138 = 11.5

12

So we can take it as 11 teams

12 × 11 = 132

138 -132 = 6

Therefore remaining people are added to small group

A value of about 32.9 years. The remaining balance will not reach $3,317 for 33 years, rounded up to the closest year.

Interest is often expressed as an annual percentage of the borrowed amount. This percentage represents the loan's interest rate. For instance, a bank will pay interest if you deposit money in an account savings account.

The initial deposit into the personal savings account is denoted by P, and the yearly interest rate is denoted by r. The following formula determines the account balance after t years:

A = Pe^(rt)

P = $1,000, r equals 5.8%, as Well as a is $3,317 in this scenario. To determine how many years it will be for such balance to reach $3,317, apply the following formula:

3,317 = 1,000e^(5.8% * t)

You must isolate t over one portion of the equation to find the solution:

t = ln(3,317 / 1,000) / (5.8% / 100)

That amounts to:

t = ln(3.317) / 0.058

Calculating this yields a result of around 32.9 years. The remaining balance will not reach $3,317 for 33 years, rounded up to the closest year.

Therefore, 33 years are needed to complete the process.

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The surface area of the ice is 16π square inches. At a rate of 10 cubic inches per min, the outer surface area of the ice is changing at  10/16π square inches per min.

To calculate this we have given:

The diameter of the spherical ball is 8 inches, so the radius of the ball is 8/2 = 4 inches.

The volume of a sphere is given by the formula (4/3)πr³, where r is the radius of the sphere.

The volume of the spherical ball with 2 inches of ice is (4/3)π(4³) = (4/3)π64 cubic inches.

The volume of the ice is the volume of the spherical ball with 2 inches of ice minus the volume of the spherical ball without the ice, which is (4/3)π(4³) - (4/3)π(4³ - (2³)) = (4/3)π64 - (4/3)π32 = 32π cubic inches

At a rate of 10 cubic inches per min, the thickness of the ice is decreasing at:

10 cubic inches / 32π cubic inches = 10/32π inches per min

To find the rate at which the outer surface area of the ice is changing, we can use the formula for the surface area of a sphere which is 4πr².

The surface area of the ice is 4π(4-2)³ = 4π4 = 16π square inches.

At a rate of 10 cubic inches per min, the outer surface area of the ice is changing at:

10 cubic inches / 16π square inches = 10/16π square inches per min

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The solution to the linear system is [tex]|A_x|=\left[\begin{array}{cc}17&3\\9&-3\end{array}\right]{,|A|=\left[\begin{array}{cc}5&3\\-8&-3\end{array}\right]} ,|A_y|=\left[\begin{array}{cc}5&17\\-8&9\end{array}\right]\\[/tex]

An equation is a expression that shows the relationship between numbers and variables.

A linear system of equation:

Ax + By = C

Dx + Ey = F

Can be solved using:

[tex]|A_x|=\left[\begin{array}{cc}C&B\\F&E\end{array}\right]{,|A|=\left[\begin{array}{cc}A&B\\D&E\end{array}\right]} ,|A_y|=\left[\begin{array}{cc}A&C\\D&F\end{array}\right]\\\\Hence:\\\\x=\frac{|A_x|}{|A|} ,y=\frac{|A_y|}{|A|}[/tex]

Hence, for:

5x + 3y = 17

-8x - 3y = 9

[tex]|A_x|=\left[\begin{array}{cc}17&3\\9&-3\end{array}\right]{,|A|=\left[\begin{array}{cc}5&3\\-8&-3\end{array}\right]} ,|A_y|=\left[\begin{array}{cc}5&17\\-8&9\end{array}\right]\\[/tex]

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If he left home 50 minutes before the class started he was 53.7 minutes late for his class.

Given that,

Speed of the bike = 16 feet per second = 10.9091 miles/hour

Distance from home to bus stop = 5 miles

Total time taken to reach bus stop = distance/ speed = 5 miles/10.9091 miles/hour= 0.458 hours = 27.5 minutes

Then, speed of the bus = 25 miles per hour

Distance from bus stop to campus = 25 miles

Total time taken to reach campus = distance/ speed = 25 miles/25 miles/hour= 1 hour= 60 minutes

Then, speed of the bike = 16 feet per second = 10.9091 miles/hour

Distance from campus to bike rack = 480 yards =  0.2727 miles

Total time taken to reach bike rack = distance/ speed = 0.2727 miles/ 10.9091 miles/hour= 0.249 hour= 15 minutes (approximately)

Then, the Speed of walking = 2.5 miles per hour

Distance from bike rack to class = 250 feet =  0.047 miles

Total time taken to reach class = distance/ speed = 0.047 miles/ 2.5 miles/hour= 0.0188 hour= 1.2 minutes (approximately)

Thus, total time taken to reach class = 27.5 minutes+60 minutes+15 minutes+1.2 minutes = 103.7 minutes
Therefore, If he left home 50 minutes before the class started he was 53.7 minutes late for his class.

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If Researcher like to know if data provide convincing evidence that the true proportion of American adults who work more than one job differs from 12% , then we can say that , (a) Yes, the conditions of inference are met .

The size of the random sample (n) = 100 ;

the number of persons that work on more than one job is (x) = 18 ;

the difference is 12% that means (p) = 0.12 ,

So , [tex]q=1-p = 1-0.12 = 0.88[/tex] ;

To check for the inference ,

we calculate , [tex]n\times p = 100\times 0.12 = 12 > 5[/tex] and

[tex]n\times q = 100\times 0.88 = 88 > 5[/tex] ,

Both the conditions are true .

Therefore , we can say that the Conditions for the inference are met .

The given question is incomplete , the complete question is

According to historical data, it is believed that 12% of American adults work more than one job. To investigate if this claim is still accurate, a random sample of 100 American adults is selected. It is discovered that 18 of them work more than one job. A researcher would like to know if the data provide convincing evidence that the true proportion of American adults who work more than one job differs from 12%. Are the conditions for inference met ?

(a) Yes, the conditions for inference are met.

(b) No, the 10% condition is not met.

(c) No, the Large Counts Condition is not met.

(d) No, the randomness condition is not met.

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According to the Pythagorean theorem length of the third side is  [tex]\sqrt{5}[/tex].

What is Pythagorean theorem?

The hypotenuse square in a right-angled triangle is equal to the sum of the squares of the other two sides, according to the Pythagoras theorem. A and B are the triangle's two legs, and C is the hypotenuse, hence this theorem can be written as c2 = a2 + b2. These triangles are also referred to as Pythagorean triangles.

Here in given right triangle side = 2 and hypotenuse = 3.

Now using Pythagorean theorem then,

=> [tex]side^2+side^2=hypotenuse^2[/tex]

=> [tex]side^2+2^2=3^2[/tex]

=> [tex]side^2[/tex]+4=9

=>  [tex]side^2[/tex] = 9-4 = 5

=> side = [tex]\sqrt{5}[/tex]

Hence third side length of the right triangle is [tex]\sqrt{5}[/tex].

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Answer:

B

Step-by-step explanation:

There are a total of 16 fingerboards. 4 of these are white. The probability that he will select a white fingerboard is 1/4. B represent 1/4.

The the probability of finding a white finger board is 0.25.

Probability is the measure of how likely are the chance for any event to happen.

Given is that David has a Collection of nine gray fingerboards 4 white fingerboards and 3 yellow fingerboards.

We can write the probability of finding a white finger board as -

P{white} = 4/16

P{white} = 1/4

P{white} = 0.25

Therefore, the the probability of finding a white finger board is 0.25.

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The measure of angle ∠CXA is 134°

What is the Isosceles triangle?

In geometry, an isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case.

Triangle ABC is an isosceles triangle where AB = BC

∵ AB = BC

- The base angles in the isosceles triangle are congruent

∴ m∠BAC = m∠BCA

∵ m∠ BCA = 46° ⇒ given

∴ m∠ BAC = 46°

- The sum of the measures of the interior angles in any triangle is 180°

∵ m∠BAC + m∠BCA + m∠ABC = 180°

- Substitute the values of angle BAC and BCA in the equation above

∴ 46 + 46 + m∠ABC = 180

∴ 92 + m∠ABC = 180

- Subtract 92 from both sides

∴ m∠ABC = 88°

- BF, AD, and CE are bisectors segments of angles B, A, and C and they are intersected at point X

∵ CE bisects ∠BCA

∵ X ∈ CE

∴ m∠XCA = 1/2 m∠BCA

∴ m∠XCA = 1/2 (46) = 23°

∵ AD bisects ∠BAC

∵ X ∈ AD

∴ m∠XAC = 1/2 m∠BAC

∴ m∠XAC = 1/2 (46) = 23°

- In Δ AXC

∵ m∠XAC = 23° ⇒ proved

∵ m∠XCA = 23° ⇒ proved

∵ m∠CXA + m∠XAC + m∠XCA = 180° ⇒ interior angles of Δ

Substitute the values of angles XAC and XCA

∴ m∠AXC + 23 + 23 = 180

∴ m∠CXA + 46 = 180

- Subtract 46 from both sides

∴ m∠CXA = 134°

Hence, The measure of angle ∠CXA is 134°.

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The complete question is:

Isosceles triangle ABC contains angle bisectors segment BF, segment AD, and segment CE that intersect at X. triangle ABC with diagonals BF, AD, and EC that intersect at point X If segment BA is congruent to segment BC and m∠BCA = 46°, what is m∠CXA?

Answer:

Step-by-step explanation:

a) The probability of obtaining 2 heads when a coin is thrown twice is (2/5) * (2/5) = 4/25.

b) To find the probability of obtaining at least one head, we can find the probability of obtaining no heads (0 heads) and subtract that from 1. The probability of obtaining 0 heads is (3/5) * (3/5) = 9/25. The probability of obtaining at least one head is 1 - (9/25) = 16/25.

Answer:

It is 1/2

Probability is (No of favourable outcomes/ No. of possible outcomes )

or 4/8 = 1/2

Answer:

1/2

Step-by-step explanation:

hope this helps.

The area covered by the roller in one full revelation is 1674 square inches.

Step-by-step explanation:

Given that You are using a 9 inch paint roller to paint a wall of your bedroom. The roller has a dimension of 158 inches as diameter and a nap thickness of 14 inch, as shown,

The nap is the fuzzy materials on the surface roller. How much area does the roller cover in one full revelation

The parameters to be considered are:

Diameter = 158 inches

Thickness = 14 inches

After one revolution rolling, the dimensions of the length will be:

L = 14 + 158 + 14

L = 186 inches.

Let the width be equal to 9 inches

The area covered = L × W

Substitute L and W into the formula

Area = 186 × 9

Area = 1674 square inches.

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Answer:

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

Given:

Solve it in below steps:

Answer:

[tex] \sf \: v \geqslant 13.2[/tex]

Step-by-step explanation:

Now we have to,

→ find the required value of v.

The equation is,

→ 5 + 12.5v ≥ 170

Then the value of v will be,

→ 5 + 12.5v ≥ 170

→ 12.5v ≥ 170 - 5

→ 12.5v ≥ 165

→ v ≥ 165 ÷ 12.5

→ [ v ≥ 13.2 ]

Hence, the value of v is 13.2.

Answer:

  43.5 square units

Step-by-step explanation:

You want to know the area of shading in a 12 by 7 rectangle with a white right triangle of side length 9 removed.

The area of the white triangle is ...

  A = 1/2bh

  A = 1/2(9)(9) = 40.5 . . . . square units

The area of the rectangle is ...

  A = LW

  A = (12)(7) = 84 . . . . square units

The shaded area is the area of the rectangle that is not included in the triangle.

  Shaded area = 84 -40.5 = 43.5 . . . . square units

__

Additional comment

The given figure cannot actually be constructed. The triangle is too large to be inscribed in the rectangle. An inscribed right triangle can have a side length between 7 and √74 ≈ 8.6.

method of least squares is  not a measure of central tendency which is not involved in the typical measures.

The central tendency of the dataset are defined as  three important measures namely mean, median and mode. The mean shows the average value of the dataset. which can be calculated as the sum of all the values in the dataset which are  divided by the number of values. and  it is considered as the arithmetic mean. Some  of the other measures of mean which is  used to find the central tendency are as mentioned as:

Geometric Mean , Harmonic Mean ,Weighted Mean.

Median is the middle value of the dataset in which the it  is arranged in the ascending order or in descending order. When the dataset  which contains an even number of values, then the median value of the dataset can be calculated by taking the mean of the middle two values.

The mode shows  the frequently occurring value in the dataset. Sometimes the dataset are arranged and which contain multiple modes and in some situations , it does not contain any mode at all.

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Answer to Problem 13 is  34.5  

Answer to Problem 15 is  22.9  

==================================================

Work Shown for Problem 13

sin(x)/17 = sin(91)/30

sin(x) = 17*sin(91)/30

sin(x) = 0.56658036

x = arcsin(0.56658036) or x = 180-arcsin(0.56658036)

x = 34.51210645 or x = 180-34.51210645

x = 34.51210645 or x = 145.48789355

x = 34.5 or x = 145.5

If x = 34.5, then the missing unmarked angle is 180-x-91 = 180-34.5-91 = 54.5 which is a valid angle (since it's between 0 and 180).

If x = 145.5, then the missing unmarked angle is 180-x-91 = 180-145.5-91 = -56.5; but this is NOT valid because the angle needs to be between 0 and 180 (i.e. negative angles aren't allowed)

In short, x = 34.5 is valid while x = 145.5 is not valid.

Therefore, the only possible answer is   34.5  

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

Work Shown for Problem 15

sin(x)/20 = sin(119)/45

sin(x) = 20*sin(119)/45

sin(x) = 0.38871987

x = arcsin(0.38871987) or x = 180-arcsin(0.38871987)

x = 22.87486940 or x = 180-22.87486940

x = 22.87486940 or x = 157.1251306

x = 22.9 or x = 157.1

If x = 22.9, then the missing unmarked angle is 180-x-119=180-22.9-119 = 38.1 which is valid since it's between 0 and 180.

If x = 157.1, then 180-x-119=180-157.1-119 = -96.1 which is NOT a valid angle since it's not between 0 and 180. This allows us to rule out the case that x = 157.1

The only possible answer is therefore   22.9  

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

Side notes:

234 is the sum of the rotcaf of all the even numbers between 1 and 25.To solve this question use the concept of series.

A rotcaf is the sum of the largest factors of the number that is smaller than the number and the number that is obtained by adding two numbers, the rotcaf of 9, for instance, is 9, 3, or 12.

Here given that,

even numbers between 1 and 25 which is: 2,4,6,8,10,12,14,16,18,20,22,24

for finding rotcaf:

(2 + 1) , (4 + 2), (6 + 3), (8 + 4),.....(24 + 12)

Here two series are present:

(1, 3, 5, 7,......23) and (2,4,6,8,......24)

Now, sum of the series is:

= [12 /2 {2+24}] + [12/2 {1 + 12}

= 156 + 78

= 234

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jj is a transformation of f and the significance of those places in your neighbourhood which are named after famous personalities and prepare a

Question 10

[tex]\frac{\sin x}{7}=\frac{\sin 85^{\circ}}{8}\\\\\sin x=\frac{7\sin 85^{\circ}}{8}\\\\x \approx 60.7^{\circ}, 119.3^{\circ}[/tex]

However, the second case does not satisfy the angle sum of a triangle, so [tex]x \approx 60.7^{\circ}[/tex].

Question 12

[tex]\frac{\sin x}{19}=\frac{\sin 34^{\circ}}{12}\\\\\sin x=\frac{19\sin 34^{\circ}}{12}\\ \\ x \approx 62.3^{\circ}, 117.7^{\circ}[/tex]

Both of these cases satisfy the angle sum of a triangle.

Answer:

a^n(a+1)

This is just to reach the minimum character limit.

Answer:

Step-by-step explanation:

The expression in terms of m is 12m + 2.75.

To find the total cost of ordering 5 movie tickets, we plug in 5 for m: 12(5) + 2.75 = 62.75.

The volume of the largest right circular cylinder (in cubic units) that fits in a sphere of radius 4 units is 154.7 cubic units.

First, draw a diagram. The diagram shows the cylinder inscribed in the sphere. Given that in the diagram the height, h, we can find the radius of the cylinder in terms of r using the Pythagorean Theorem.

h represents half of the total height of the cylinder. choose h instead of h² to simplify things better.

To find the volume of the cylinder, we need to multiply the area of the top by the total height of the cylinder. In other words;

V = π(radius of cylinder)²(height of cylinder)

V = π(√r²−h²)²(2h)

V = 2πh(r²−h²)

V = 2π(r²h−h³)

d/dxV(h) = 2π(r²−3h²) = 0

The 2π divides out and we are left with;

r²−3h² = 0

After some rearranging;

h² = r²/3

Take the square root of both sides.

h = r/√3

To find the volume, we need to put this into the volume equation.

V = 2πh(r²−h²) = 2π(r/√3){r²−(r/√3)²}

V = (2πr/√3)(r²−r²/3)

V = (2πr/√3){(3r²−r²)/3}

V = (2πr/√3)(2r²/3)

V = 4πr³/3√3

V = 4√3πr³/9

Now, put the value of r in the above equation, and we get

V = 4√3π(4)³/9

V = 256√3π/9

V = 154.7 cubic units

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