Please find the missing side length using trig!

The third side is between 7 and 17 inches long.

This theorem states that for any triangle, the sum of the lengths of the first two sides will always be greater than the length of the third side.

A triangle's two sides have lengths of 5 and 12 inches.

According to the triangle Inequality (theorem), any triangle's two sides must add up to more than its third side.

The length of the third side will be,

5 + 12 = 17 inches

It is to be noted that the difference between the two sides cannot be less on the third side.

The third side must be greater than,

12 – 5 = 7 inches.

As a result, the third side's length ranges from 7 to 17 inches.

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Answer:

Step-by-step explanation:

in: mi

3:2

5:x

3*1.6667=5

2*1.6667=3.3334/

becaus the first answer was rounded up, the last one needs to be rounded down.

so the answer, rounded up to the nearest hundredth is 3.34

(rounded up to the nearest whole number is 3)

The steps to set up the study and the limitations that would be faced are explained below .

The Steps to setup the study are  :

(i) Recruit a large and diverse group of participants who are willing to stick to the prescribed diets for the duration of the study.

(ii) Divide the participants randomly into two or more groups. One group would be given a diet high in trans fats, and the other group(s) would be given a diet low in trans fats.

(iii) Monitor the health status of the participants closely throughout the study .

(iv) At the end of the study, compare the health outcomes of the different groups of participants to determine whether there is a significant difference in health outcomes .

The Limitations of this type of study include :

⇒ the difficulty of controlling all aspects of participants' diets, since participants may consume other foods outside of what is provided to them.

⇒ the study may not be long enough to detect long-term effects of trans fats on health.

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The given question is incomplete , the complete question is

One way that researchers study the effects of trans fats on people's health is by setting up controlled experiments. For example, in an experimental feeding trial, participants agree to stick to specific diets that the researchers prescribe. In this case, the researchers might vary the proportions of saturated, unsaturated, and trans fats in the diet of each participant. Throughout the study, the health status of the participants is monitored closely.

Suppose that you are a researcher designing an experimental feeding trial. How would you set up your study and what limitations would you face ?

Answer:

I think it's

Step-by-step explanation:

usually involves reading the pattern on the table while keeping in mind that x goes on top and y on

Answer:

Step-by-step explanation:

You want to know the slope of the line segment between (-4, -3) and (3, -3), and its relation to the x-axis.

The slope of a line between two points (x1, y1) and (x2, y2) is given by the formula ...

  m = (y2 -y1)/(x2 -x1)

For the given points, the slope is ...

  m = (-3 -(-3))/(3 -(-4)) = 0/7 = 0

The slope of the line segment is zero.

The line segment has the same slope as the x-axis. It is parallel to the x-axis.

__

Additional comment

The equation of the line segment is ...

  y = -3 . . . for -4 ≤ x ≤ 3

The equation of the x-axis is ...

  y = 0

The standard deviation of the number of lemons used is equal to 14.7.

Mathematically, the mean for these set of data would be calculated by using this formula:

Mean = [F(x)]/n

F(x) = 47 + 45 + 61 + 44 + 16

F(x) = 213.

Mean = 213/5

Mean = 42.6

Next, we would calculate the standard deviation of this data set by using this formula:

SD = √(1/n × ∑(xi - u₁)²)

SD = √(1/5 × (47 - 42.6)² + (45 - 42.6)² + (61 - 42.6)² + (44 - 42.6)² + (16 - 42.6)²)

Standard deviation, SD = √(1073.2/5)

Standard deviation, SD = 14.7.

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Answer:

The flagpole is 15 ft tall.

Step-by-step explanation:

In this problem, we are asked to create a proportion of similar triangles to solve for the height of a flagpole.

We are given an equation with the proportion:

[tex]\dfrac{h}{6\text{ft}}=\dfrac{\square}{\square}[/tex]

We can fill in the blanks as follows:

[tex]\dfrac{h}{6\text{ft}}=\dfrac{25 \text{ft}}{10 \text{ft}}[/tex]

Notice that the heights of the triangles compared are both in the numerator, and the lengths of both triangles are in the denominator.

Then, to solve for the height of the flagpole, we can isolate the variable h in the proportion.

[tex]\dfrac{h}{6}=\dfrac{25}{10}[/tex]

↓ multiply both sides by 6

[tex]h = \dfrac{150}{10}[/tex]

↓ simplify the fraction

[tex]h = 15 \text{ ft}[/tex]

So, the flagpole is 15 ft tall.

The frequency of each class interval 103 - 107, 108 - 112 and 113 - 117 are 2, 2 and 4 respectively.

A grouped frequency distribution is the distribution of data into various classes with equal width with the frequency being the number of outcomes in that class.

Given are the hottest recorded temperatures (in °F) for eight cities throughout North America.

113   110   108   104   117   116   113   103

The class intervals are 103 - 107, 108 - 112 and 113 - 117.

In the distribution, the frequency of a class is the number of temperatures that class.

The temperatures in the class 103 - 107 are 103 and 104.

Frequency of 103 - 107 = 2

The temperatures in the class 108 - 112 are 108 and 110.

Frequency of 108 - 112 = 2

The temperatures in the class 113 - 117 are 113, 113, 116 and 117.

Frequency of 113 - 117 = 4

Hence the frequency are 2, 2 and 4 for the intervals 103 - 107, 108 - 112 and 113 - 117 respectively.

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Answer: 54 is 18.24% of 296

Step-by-step explanation:

54:296*100 =

(54*100):296 =

5400:296 = 18.24

Now we have: 54 is what percent of 296 = 18.24

Question: 54 is what percent of 296?

Percentage solution with steps:

Step 1: We make the assumption that 296 is 100% since it is our output value.

Step 2: We next represent the value we seek with x

Step 3: From step 1, it follows that 100% = 296

Step 4: In the same vein, x% = 54

Step 5: This gives us a pair of simple equations:

100% = 296 (1)

x% = 54 (2)

Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS (left-hand side) of both equations have the same unit (%); we have

100% over x% = 296 over 54

Step 7: Taking the inverse (or reciprocal) of both sides yields

x% over 100% = 54 over 196

x=18.54

To convert a percentage to a decimal, divide the percentage by 100, The correct answer is B. 0.609.

When the decimal places in the factors are tallied together, they equal the number of decimal places in the product. A decimal number is one with a whole and a fraction part separated by a decimal point.

A base-10 representation of numeric values is used in the decimal numbering system. The system is widely used in daily life to complete routine tasks like grocery shopping, stock trading, keeping track of football scores, or scrolling through cable channels. Decimal numbers include 7, 28, 199, and 532.11.

To convert a percentage to a decimal, divide the percentage by 100.

So, 60.9% as a decimal would be:

60.9 / 100 = 0.609

Therefore, The correct answer is B. 0.609.

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Answer:

(x + 7)(x - 3) = 75 square feet.

Step-by-step explanation:

Given that x represents the side length of the mural in Ashwin's classroom, the hallway mural's length is x + 7 feet and its width is x - 3 feet. The area of the hallway mural can be found by multiplying these two binomials, (x + 7)(x - 3), to get x^2 + 4x - 21.

If each side of the classroom mural is 8 feet long, the hallway mural would have sides of 15 feet and 5 feet, so its area would be 75 square feet, which is the answer.

Sullivan received half as many candy as Carter did, or half as many candies as Sullivan received.

" Amount is defined as the representation of total quantity of given object."

According to the question,

Number of candies Sullivan got = s

Number of candies Carter got = 2s

Compare the given amount of data we get,

Number of candies Carter got = 2(Number of candies Sullivan got )

This shows Carter got twice number of candies comparison to Sullivan.

or

Number of candies Sullivan got = 1/2 (Number of candies Carter got)

Sullivan got half number of candies compare to Carter.

Hence, we conclude Carter got twice number of candies in comparison to Sullivan or Sullivan got half number of candies compare to Carter.

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The Cupcake Café’s recipe for cheesecake calls for 2/3 cup of cream cheese.42 cups of cream cheese does the café use to make 63 cheesecakes.

What is word problem?

A word problem is a mathematical problem or puzzle that is presented in the form of a written description or narrative, rather than as a simple equation or formula. It typically involves a scenario or situation that requires mathematical calculations or problem-solving skills to arrive at a solution. Word problems can be found in a variety of settings, including in math textbooks, standardized tests, and real-life situations. They often require the reader to identify and interpret relevant information, apply mathematical concepts and formulas, and use critical thinking skills to arrive at a correct answer.

To make 63 cheesecakes, the Cupcake Café would use:

(2/3 cup of cream cheese per cheesecake) x (63 cheesecakes)

= 42 cups of cream cheese.

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a)  The test was designed to have a 5% chance of making a Type I error. b) Reject H0 since p-value < significance level. c) Type I error (false positive) if H0 is true and rejected.

A significance test is used to determine whether there is sufficient evidence to reject a null hypothesis, which is a statement about a population parameter, such as a proportion, mean, or standard deviation. The significance level, often denoted by α, is the probability of making a Type I error, which is rejecting the null hypothesis when it is actually true. The commonly used significance level is 0.05, which means that the test is designed to have a 5% chance of making a Type I error.

In this scenario, the sample proportion is 0.12 and the p-value is 0.03, which is the probability of observing a sample proportion as extreme as 0.12 or more extreme, assuming that the null hypothesis is true. Since the p-value is less than the significance level, we have strong evidence against the null hypothesis, and we reject it. Therefore, we conclude that the proportion is significantly different from the hypothesized value.

If the null hypothesis is actually true, and we reject it based on the sample data, we have made a Type I error. In other words, we have falsely concluded that there is a difference when there is not. False positive is another name for this mistake. Conversely, a Type II error occurs when we fail to reject the null hypothesis when it is actually false, and this error is also known as a false negative.

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The complete question is:

A significance level of 0.05 is used when conducting a proportion-related significance test. 0.12 is the sample statistic. P-value equals 0.03.

a) What chance of a Type I error was the test designed for, if H0 were true?

b) What judgement would you draw on this test (reject or fail to reject)?

c) What kind of error, if any, was there as a result of this test?

Answer: 1 [tex]\frac{4}{5}[/tex]

Step-by-step explanation:

Make it a mixed number then simplify if you can. I hope this helps.

The given sequence appears to be an arithmetic sequence, as the difference between consecutive terms is 9. To find the 43rd term, we can use the formula for the nth term of an arithmetic sequence:

a_n = a_1 + (n - 1)d

where a_n is the nth term, a_1 is the first term (11 in this case), n is the term number (43 in this case), and d is the common difference (9 in this case).

Plugging in the values, we get:

a_43 = 11 + (43 - 1) * 9

a_43 = 11 + 42 * 9

a_43 = 11 + 378

a_43 = 389

So the 43rd term of the sequence is 389.

4.1. The boys' masses range from a minimum of 32 kg to a maximum of 82 kg.

4.2. The girls' masses range from a minimum of 35 kg to a maximum of 67 kg.

5: To create the frequency table, we need to tally the number of male and female learners in each mass interval. Here are the tallies:

Mass interval Tally

40 - 49,9 kg |||| (4 females)

50 - 59,9 kg ||||||| (7 females)

60 - 69,9 kg ||||| (5 females)

70-79,9 kg || (2 males)

80 - 89,9 kg || (2 males)

Note: The vertical lines represent the tallies, with each line representing one learner.

6: By looking at the frequency table, we can compare the number of male and female learners in each mass interval. We can see that there are more female learners in the lower mass intervals (40-49.9 kg, 50-59.9 kg, and 60-69.9 kg) compared to male learners. On the other hand, there are more male learners in the higher mass intervals (70-79.9 kg and 80-89.9 kg) compared to female learners

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Answer: 22k

Step-by-step explanation:

The solution to the equation is k = 2/9

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

3 ( 2k + 3 ) = 6 - ( 3k - 5 )   be equation (1)

On simplifying , we get

3 ( 2k ) + 9 = 6 - 3k + 5

6k + 9 = 11 - 3k

Adding 3k on both sides , we get

9k + 9 = 11

Subtracting 9 on both sides , we get

9k = 2

Divide by 9 on both sides , we get

k = 2/9

Therefore , the value of k is 2/9

Hence , the solution is k = 2/9

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To solve this system of linear equations, we need to find the values of x and y that make both equations true at the same time. One method to solve this is to use elimination or substitution.

First, let's rearrange the first equation:

y = 2x

Next, we can substitute y = 2x into the second equation:

-7x + 3y = 2

-7x + 3(2x) = 2

-7x + 6x = 2

-x = -2

So, x = 2.

Finally, we can use the first equation to find y:

y = 2x

y = 2 * 2

y = 4

So, the solution to the system of equations is (x, y) = (2, 4).

no

4x6=24

24x1=24

hence 24 is the lowest common multiple , i hope this helped xx

Answer:  Choice D

Explanation:

The notation [tex]-\infty < \text{x} < \infty[/tex] says x is anything between negative infinity and positive infinity. Basically x is any real number. This is because the curve stretches forever to the left and right. Any number can be the x input.

Step-by-step explanation:

inscribed angles subtended by the same arc are equal.

the angle FGH is "based" on the same arc (FH) as the angle FJH.

so, FGH = FJH = 56°.

Answer:

D

Step-by-step explanation:

[tex]100(1 + \frac{016}{12}) ^{12(20)}[/tex]

331.02

Answer:

D. $220.00

Explanation :

Pt(1+r/n) n

The points on the graph of the equation represent the solution set to the equation.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Given is the equation as -

- x - y = 4

The given equation is -

- x - y = 4

x + y = 4

The graph of the given equation will represent a straight line. All the points on the line represent the solution set to the equation.

Therefore, the points on the graph of the equation represent the solution set to the equation.

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{Question in english -

How can i solve this?

- x - y = 4}

Answer:

Step-by-step explanation: (a) To expand (1 + e^x) + (e^3x) in ascending powers of x to the term x^2, we can use the Taylor series expansion.

The Taylor series expansion for e^x is given by:

e^x = 1 + x + x^2/2! + x^3/3! + ...

So,

e^x = 1 + x + x^2/2! + x^3/3! + ...

and

e^3x = 1 + 3x + 9x^2/2! + 27x^3/3! + ...

Now, we can substitute these expansions into the original equation to get:

(1 + e^x) + (e^3x) = 1 + (1 + x + x^2/2! + x^3/3! + ...) + (1 + 3x + 9x^2/2! + 27x^3/3! + ...)

Expanding, we get:

(1 + e^x) + (e^3x) = 2 + x + 4x + x^2/2! + 9x^2/2! + ...

So, to the term x^2, the expansion becomes:

(1 + e^x) + (e^3x) = 2 + x + 4x + (x^2/2! + 9x^2/2!) + ...

which simplifies to:

(1 + e^x) + (e^3x) = 2 + x + 4x + 11x^2/2! + ...

(b) The coefficient of x^2 in the expansion is 11/2!. So, n = 11/2! = 11/2.

At least number of students who must have signed up to have all nine clubs is equal to 207.

Number of clubs school going to start after school = 9 clubs

At least number of students need to sign up in each one of the club is equal to 23 students.

At least number of students need to sign up to have all in nine clubs is equal to :

At least number of student in 1 club  > 23

⇒ At least number of student in 9 club  > 23 × 9

At least number of student in 9 club  > 207

Therefore, at least number of students need to signed up to have in all nine given clubs are 207 students.

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The measures of angles of a rhombus are ∠KNL = 90° , ∠KJL = 50° , ∠MLK = 100° and ∠JKM = 40°

A Rhombus has four sides of the same length, its perimeter can be determined using the formula Perimeter = 4a, where "a" stands for the side's length.

When the two diagonals of a rhombus are known,

The perimeter = 2√p² + q²

where 'p' and 'q' are the diagonals.

Given data ,

Let the rhombus be represented as JKLM

where MK and JL are the diagonals and N is the midpoint of intersection

The measure of MK = 24

The measure of JL = 20

The measure of NK = 12

The measure of ∠MJL = 50°

Now , the diagonals of a rhombus bisect each other , so

NK = MK/2 = 12

And , NL = JL / 2 = 10

Now , to calculate the measure of ML ,

In triangle MNL, ∠N = 90°

MN = NK = 12 , NL = 10

Using Pythagorean theorem of triangles , we get

ML² = MN² + NL²

ML² = 12² + 10²

ML² = 244

ML = √244

On simplifying the equation , we get

ML = 2√61 = 15.62

The measure of ML = measure of JM = 15.62 ( all sides are equal )

The measure of ∠KNL = 90° ( diagonals of a rhombus are perpendicular bisectors )

∠KJL = ∠MJL (diagonals bisect angles)

The measure of ∠KJL = 50°

∠MJK = ∠KJL + ∠MJL = 50 + 50 = 100°

∠MJK = ∠MLK (opposite angles are equal)

The measure of ∠MLK = 100°

∠NJK + ∠JNK + ∠JKM = 180° (sum of angles in triangle)

50 + 90 + ∠JKM = 180

The measure of ∠JKM = 40°

∠JKL = 2 x ∠JKM (diagonal bisect angle)

The measure of ∠JKL = 2 x 40

The measure of ∠JKL = 80°

∠JKL = ∠JML (opposite angles are equal)

The measure of ∠JML = 80°

Hence , the measures of rhombus is solved

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