A right triangle has a hypotenuse of 10 cm and one leg that measures 5 square 3 what is the length of the other leg

F'(2) = 3

[tex]\int\limits^x_0 {\sqrt{t^3+1}} \, dt[/tex]

Using Fundamental Theorem of Calculus:

Since x = 2, you now have:

[tex]\int\limits^2_0 {\sqrt{t^3+1} } \, dt[/tex]

so F'(x) = [tex]\sqrt{t^3+1}[/tex]

--> F'(2) = [tex]\sqrt{2^3+1}[/tex] = [tex]\sqrt{9}[/tex] = 3

so F'(2) = 3

F'(2) is the square root of [tex](2^3+1)[/tex], which simplifies to 3.

If F(x) is defined as the integral of [tex]\sqrt(t^3+1)[/tex] dt from 0 to x, then F'(x) represents the derivative of F with respect to x. According to the Fundamental Theorem of Calculus, the derivative of an integral function of this form is simply the value of the function inside the integral evaluated at x. Therefore, F'(2) is the square root of (2^3+1), which simplifies to sqrt(9), or 3.

Answer:

The answer is the option B

[tex]a=24.2\ in[/tex]

Step-by-step explanation:

we know that

In the right triangle of the figure

[tex]sin(27\°)=\frac{11}{a}[/tex]

Solve for a

[tex]a=\frac{11}{sin(27\°)}[/tex]

[tex]a=24.2\ in[/tex]

The probability a two-digit number to be divisible by 5 from 10 to 99 inclusive and chosen at random is 1/5 or 0.2.

Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.

As the probability of an event can not be more than the number 1. Thus he probability of failure of a event is equal to the difference of the 1 to the success of the event.

A two-digit number from 10 to 99, inclusive, is chosen at random. The probability that this number is divisible by 5 has to be find out.

The number of two-digit numbers which is divisible b 5 from 10 to 99 are 18.

[tex](10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95)[/tex]

There are total number from 10 to 99 are 90. Thus, the probability that the chosen number is divisible by 5

[tex]P=\dfrac{18}{90}\\P=\dfrac{1}{5}\\P=0.2[/tex]

Hence, the probability a two-digit number to be divisible by 5 from 10 to 99 inclusive and chosen at random is 1/5 or 0.2.

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Final answer:

The probability that a randomly chosen two-digit number from 10 to 99 is divisible by 5 is 1/5 or 20%.

Explanation:

To find the probability that a randomly chosen two-digit number from 10 to 99 is divisible by 5, we first establish the total number of two-digit numbers, which is 99 - 10 + 1 = 90. Numbers divisible by 5 end in either 0 or 5, so we can count how many of these there are within our range. Starting from 10, the first such number, we have 10, 15, 20, ..., 95. We clearly have two of such numbers per every 10 numbers, resulting in a total of 90/10 * 2 = 18 numbers divisible by 5 between 10 and 99. Hence, the probability is the number of favorable outcomes (numbers divisible by 5), divided by the total number of possible outcomes (two-digit numbers), which gives us a probability of 18/90 = 1/5 or 20%.

The equation will be if x = 3g + 2 after transformation g as subject g = x / 3 - 2 / 3.

An assertion that two mathematical expressions have equal values is known as an equation. An equation simply states that two things are equal. The equal to sign, or "=," is used to indicate it.

Given:

x = 3g + 2

Rearrange the terms as shown below

x - 2 = 3g (Here the constant term is brought to the left)

x - 2 / 3  = g  (Take the term 3 to the left side as shown)

x / 3 - 2 / 3 = g

g = x / 3 - 2 / 3

Thus, the equation will be g = x / 3 - 2 / 3.

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The g subject of the equation x = 3g + 2 is g = (x - 2) / 3.

To make g the subject of the equation x = 3g + 2, you need to isolate g on one side of the equation. Here is a step-by-step guide:

Subtract 2 from both sides of the equation to get x - 2 = 3g.

Divide both sides of the equation by 3 to isolate g, resulting in g = (x - 2) / 3.

Now, g is the subject of the equation, and it can be expressed as g = (x - 2) / 3.

an=2⋅3n−1 would be the answer

To solve 'Evaluate cos((Sin^-1)0)', the arcsin of 0 is determined first, which equals 0 in degrees. Then, find the cosine of this resulting value, which equals 1.

The student's question relates to an evaluation of trigonometric functions: 'Evaluate cos((Sin^-1)0)'. To solve this problem, it's important to recognize the meaning of inverse sine or arcsine. We can denote Sin^-1(0) as an angle, let's call it θ, whose sine value is 0. The sine of an angle will be 0 at 0 degrees. Therefore, Sin^-1(0) = 0 in degrees. Now we need to find out the cosine of this angle. Cosine of 0 degrees is 1, so cos(Sin^-1(0)) = cos(0) = 1. So, the answer is 1.

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Applying the rule of exponents, 2m² × 2m³ will be simplified as:  [tex]4m^5[/tex].

When multiplying exponents with the same base, add the exponents.

The rule is: [tex]a^m \times a^n = a^{(m+n)}[/tex].

Given:

2m² × 2m³

Apply the product rule of exponents for multiplication

(2 × 2)(m²+³)

2m² × 2m³ = [tex]4m^5[/tex]

Therefore , applying the product rule of exponents, 2m² × 2m³ will be simplified as:  [tex]4m^5[/tex].

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Answer:

13

Step-by-step explanation:

x=0.295 this is the correct answer

Answer:

The Probability of drawing shirt is blue is [tex]\frac{2}{7}[/tex]

Step-by-step explanation:

Given : A drawer contains 8 red shirts, 6 blue shirts, and 7 white shirts.

We have to find the probability if a shirt is drawn at random, then the shirt will be blue.

Total number of shirt in drawer = 8 + 6 + 7 = 21

Number of blue shirts = 6

Probability of an event = [tex]\dfrac{\text{number of possible outcomes}}{\text{number of total outcomes}}[/tex]

Event (E) : shirt drawn is blue.

number of possible outcomes = 6

number of total outcomes = 21

Thus, the Probability of drawing shirt is blue is [tex]\frac{6}{21}[/tex]

Simplifying , we get,

The Probability of drawing shirt is blue is [tex]\frac{2}{7}[/tex]

Answer: -1/24(x+5)^2+1

12.56 rounded to the nearest tenth becomes 12.6.

Rounding some number to a specific value is making its value simpler for better readability or accessibility.

The digit in the hundredth place is 6. The next smaller place value is the tenth place.

If the digit in the next smaller place value is 5 or greater, round up:

Since the digit in the tenth place is 5, we round up.

Change the digit in the hundredth place to 0 and increase the digit in the tenth place by 1:

12.56 rounded to the nearest tenth becomes 12.6.

Therefore, 12.56 rounded to the nearest tenth is 12.6.

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The maximum error in calculating the surface area of the box is approximately 176 square centimeters.

The surface area of the rectangular box is given by:

S = 2(wh + lh + lw)

where w, h, and l are the width, height, and length of the box, respectively. The differential of S with respect to each dimension can be expressed as:

dS = 2((h+dh)(w+dw) + (l+dl)(h+dh) + (l+dl)(w+dw)) + 2(wh + lh + lw) - 2S

where dw, dh, and dl represent the maximum error in each measurement, which is given as 0.2 cm. We have to find the maximum error in calculating the surface area, so we need to find the maximum value of dS.

Substituting the given values into the differential expression, we get:

dS = [2*(0.2)*80+2*90*(0.2)]+[2*(0.2)*50+2*80*(0.2)]+[2*(0.2)*50+2*90*(0.2)]

≈ 176

Therefore, the maximum error in calculating the surface area of the box is approximately 176 square centimeters.

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we know that

m∠C=m∠B ----------> by vertical angles

m∠F=m∠B ----------> by corresponding angles

m∠G=m∠B --------> by alternate exterior angles

therefore

the answer is

Angles C, F and G

Answer:

Option A) 20 ... ... ... ✔

Step-by-step explanation:

[tex] \underline{\tt{❖ \: Given \: \: ❖}}[/tex]

[tex] \underline{\tt{❖ \: Solution \: ❖}}[/tex]

We know that interior sum of all angle is 180°

[tex]\; \;\dashrightarrow \;\pmb {2x+3x+4x=180°}[/tex]

[tex]\; \;\dashrightarrow \;\pmb {9x=180°}[/tex]

[tex]\; \;\dashrightarrow \;\pmb {x = \dfrac{180}{9} }[/tex]

[tex] \; \;\dashrightarrow\; \; {\pmb{\underline{\boxed{\red{\frak { x = 20 }}}}}} \; \green\bigstar[/tex]

Answer:

The protection against self-incrimination; it informs them that speaking to law enforcement could incriminate them.

Step-by-step explanation:

In the Supreme Court case Miranda v. Arizona, the court examined the rights protected in the

Fifth and Sixth Amendments to the U.S. Constitution. Ernesto Miranda was arrested after a

crime victim identified him in a police lineup. The police officers questioning him did not inform

him of his Fifth Amendment right that prevents government from forcing citizens to give

evidence against themselves. He also was not informed of his Sixth Amendment right to the

assistance of an attorney. In 1966, the Supreme Court agreed to hear the case and ruled in favor

of Miranda. As a result, police officers now read the Miranda warning to suspects before they are

arrested. This helps ensure suspects understand they have the right to not answer questions, or

say anything at all, if they choose. However, if a suspect chooses to speak despite the Miranda

warning, what they say could be used in court. The Miranda warning also explains that suspects

have the right speak to an attorney.

False, because the IQR of 9 observations is 17 and the IQR of 10 observations is 13.

The given observations are 145, 139, 126, 122, 125, 113, 96, 110, 118, 118.

The Interquartile Range (IQR) formula is a measure of the middle 50% of a data set. The smallest of all the measures of dispersion in statistics is called the Interquartile Range. The difference between the upper and lower quartile is known as the interquartile range.

Interquartile range = Upper Quartile - Lower Quartile

Q2=Q3 - Q1

Ascending order of the given observation is

96, 110, 113, 118, 118, 122, 125, 126, 139, 145

Here, Q1 (median of lower quartile) =113 and

Q3 (median of upper quartile) =126

Q2= 126-113

= 13

The value 96 were removed from the data set, so

110, 113, 118, 118, 122, 125, 126, 139, 145

Q1 =(113+118)/2 =115.5

Q3 =(126+139)/2

= 132.5

Q2 =132.5-115.5

= 17

False, because the IQR of 9 observations is 17 and the IQR of 10 observations is 13.

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Final answer:

The best step to eliminate the x variable from the given system of equations is to multiply the first equation by –2 and the second by 3, facilitating the cancellation of the x terms and allowing for straightforward calculation of y.

Explanation:

To select the best possible first step to solving the system by first eliminating the x variable from the given equations 3x – 9y = 6 and 2x – 11y = 6, we need to make the coefficients of x in both equations equal in magnitude but opposite in sign. This way, when we add the equations together, the x terms will cancel out, leaving us with an equation in terms of y only. Here are the options analyzed:

Multiply the first equation by –2 and multiply the second equation by 3, resulting in –6x + 18y = –12 and 6x - 33y = 18. Adding these together will eliminate the x variable, which is the desired outcome.

Multiplying the first equation by –2 and the second equation by –3 does not effectively eliminate x because it gives us –6x + 18y = –12 and –6x + 33y = –18, which does not help in eliminating x when added or subtracted.

Multiplying the first equation by 2 and the second equation by 3 does not suit our needs for elimination as it results in 6x – 18y = 12 and 6x – 33y = 18, where adding or subtracting does not eliminate x.

Therefore, the correct first step is to multiply the first equation by –2 and multiply the second equation by 3. This approach aligns with standard algebraic methods for solving systems of equations by elimination, providing a clear and effective strategy to simplify the problem by removing one variable, allowing for the straightforward solution of the other.