An arch of a bridge is made up by bending a steel beam into the shape of a semi circle 20m

the sine and cosine of the two non-right angles in a right triangle are related to each other by their complementary nature.

How to find middle angle?

In a right triangle, the middle angle is the angle opposite the hypotenuse. To find this angle using trigonometry, you can use either the sine, cosine, or tangent ratio. Let's say that the two legs of the right triangle are a and b, and the hypotenuse is c. Then, you can use the following trig ratios to find the middle angle:

Sine ratio: sin(theta) = a/c

Cosine ratio: cos(theta) = b/c

Tangent ratio: tan(theta) = a/b

To find the middle angle, you would use the inverse sine, cosine, or tangent function, depending on which ratio you used. For example, if you used the sine ratio, you would take the inverse sine of a/c to find the angle: theta = sin²-1(a/c).

What is the relationship between the sine and cosine of the two non-right angles in a right triangle, and how do they define the ratios sine, cosine, and tangent?

In a right triangle, the two non-right angles are complementary, which means that their sum is 90 degrees. Let's call these angles alpha and beta. The sine and cosine of these angles are defined as follows:

Sine of alpha: sin(alpha) = opposite leg / hypotenuse

Cosine of alpha: cos(alpha) = adjacent leg / hypotenuse

Sine of beta: sin(beta) = adjacent leg / hypotenuse

Cosine of beta: cos(beta) = opposite leg / hypotenuse

Note that the opposite and adjacent legs are relative to the angle being considered. The ratios sine, cosine, and tangent are defined in terms of these ratios:

Sine ratio: sin(theta) = opposite leg / hypotenuse

Cosine ratio: cos(theta) = adjacent leg / hypotenuse

Tangent ratio: tan(theta) = opposite leg / adjacent leg

Therefore, the sine and cosine of the two non-right angles in a right triangle are related to each other by their complementary nature. If you know the value of one of these ratios, you can use it to find the value of the other using the fact that sin(alpha) = cos(beta) and cos(alpha) = sin(beta). This relationship is known as the complementary angle identities.

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The number of positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, are not divisible by either 5 or 7 is 4680.

Step by step explanation:
The number of positive integers with exactly four decimal digits between 1000 and 9999 inclusive can be obtained as follows:

Total number of four decimal digits = 9999 − 1000 + 1 = 9000
Numbers that are multiples of 5 are obtained by starting with 1000 and adding 5, 10, 15, 20, ..., 1995, that is, 5k, where k = 1, 2, 3, ..., 399.

Therefore, the number of positive integers with exactly four decimal digits that are multiples of 5 is 399.

Numbers that are multiples of 7 are obtained by starting with 1001 and adding 7, 14, 21, 28, ..., 1428, that is, 7m, where m = 1, 2, 3, ..., 204.

Therefore, the number of positive integers with exactly four decimal digits that are multiples of 7 is 204.

Note that some numbers in the interval [1000, 9999] are divisible by both 5 and 7. Since 5 and 7 are relatively prime, the product of any number of the form 5k by a number of the form 7m is a multiple of 5 × 7 = 35.

The numbers of the form 35n in the interval [1000, 9999] are

1035, 1070, 1105, 1140, ..., 9945, 9980.
We can check that there are 285 numbers of this form.

To find the number of positive integers with exactly four decimal digits that are not divisible by either 5 or 7, we will subtract the number of multiples of 5 and 7 and add the number of multiples of 35.

Therefore, the number of positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, are not divisible by either 5 or 7 is

9000 - 399 - 204 + 285 = 4680.

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Equation A is converted to equation B by multiplying or dividing both parts by a non-zero constant. Thus, option C is correct.  

If a function accepts more than one value, it is said to be nonconstant (if there is more than one element in its range).

As an illustration, a polynomial with real numbers as its domain and codomain becomes nonconstant. Just observing that and means the function accepts at least two distinct values allows us to demonstrate this.

Starting with the variable solely on a single side of the equation, we can start resolving equation A for x:

[tex]x/4 + 1 = -3\sx/4 = -3 - 1\sx/4 = -4[/tex]

We obtain x = -16 by multiplying both of the equation's sides by 4.

Starting with the variable with one of the equation's equations, we can solve equation B for x:

[tex]x + 4 = -12[/tex]

Therefore, We obtain [tex]x = -16[/tex] by deducting  [tex]4[/tex] from both of the equation's components.

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Answer: Incorrect

Step-by-step explanation:

Your friend Frans' claim is incorrect. A row of zeros in the reduced matrix means that the corresponding equation in the system is redundant and does not provide any additional information. This does not necessarily mean that the system does not have a unique solution. In fact, a row of zeros in the reduced matrix is common when solving systems of linear equations using Gaussian elimination, and it can still lead to a unique solution or even an infinite number of solutions. Therefore, Frans' claim is wrong.

The rate of change of the area of a square with respect to the length z, the diagonal of the square is  dA/dz = 2z; rate = 6. The correct answer is C.

We know that the area A of a square is given by A = s², where s is the length of the sides of the square. Also, we know that the diagonal of the square (z) is related to the sides by the Pythagorean theorem: s² + s² = z² or 2s² = z² or s² = z²/2.

Taking the derivative of both sides of the equation s² = z²/2 with respect to z, we get:

2s ds/dz = 2z/2

s ds/dz = z

Now, since the area A is given by A = s², we can take the derivative of both sides of this equation with respect to z:

dA/dz = d/dz (s²) = 2s ds/dz

Substituting the value of s ds/dz obtained earlier, we get:

dA/dz = 2s (z/s) = 2z

Therefore, the correct option is (c) dA/dz = 2z, and the rate of change of the area of the square with respect to the length z is 2z. When z = 3, the rate of change is 2(3) = 6. So, the answer is (c) dA/dz = 2z; rate = 6.

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The expressions that have values less than 0 are a) and b)

According to the question

Here's how you can use a number line to solve this problem:

For example in expression a) -5 + 3, start at zero and move 5 units to the left (because of the negative sign on 5), and then move 3 units to the right. The final position is at -2, which is to the left of zero. Therefore, expression a) has a value that is less than zero.

Similarly expression b) has a value that is less than zero.

Also expressions c) and d) can be solved in the same way. If the final position is to the right of zero, the expression does not have a value that is less than zero.

In conclusion, expressions a) and b) have a value that is less than zero, while expressions c) and d) do not.

What is a number line?

A number line is a visual representation of real numbers arranged in a straight line used to compare, add, and subtract numbers.

What is meant by expressions?

An expression is a combination of numbers, variables, and mathematical operations used to represent a quantity or a mathematical statement.

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The value of x -8.

An equation is a mathematical statement containing two algebraic expressions flanked by equal signs (=) on either side.

It shows that the relationship between the left and right printed expressions is equal.

All formulas hav LHS = RHS (left side = right side).

You can solve equations to determine the values ​​of unknown variables that represent unknown quantities.

If a statement does not have an equals sign, it is not an equation. A mathematical statement called an equation contains the symbol "equal to" between two expressions of equal value.

Hence, the value of x -8.

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Answer:

n > 10

Step-by-step explanation:

2n > 20

2n/2 > 20/2

n > 10

a) Option A, A x2 statistic provides strong evidence in favor alternative hypothesis if its value is a large positive number.

b) Option B, The null hypothesis that sex and personal goals are not related vs. the alternative hypothesis that sex and personal goals are related.

c) Option B, The variables considered in a chi-squared test used to evaluate a contingency table B. are categorical.

(a) A x2 statistic provides strong evidence in favor of the alternative hypothesis if its value is a large positive number. The x2 statistic is used in hypothesis testing to determine whether there is a significant difference between observed and expected frequencies. A large positive value indicates that the observed frequencies are significantly different from the expected frequencies, which supports the alternative hypothesis.

(b) The hypotheses being tested in a chi-squared test on a contingency table are the null hypothesis that sex and personal goals are not related vs. the alternative hypothesis that sex and personal goals are related. This test determines whether there is a significant association between two categorical variables.

(c) The variables considered in a chi-squared test used to evaluate a contingency table are categorical. These variables cannot be averaged or assumed to be normally distributed. The chi-squared test is used to analyze the relationship between two or more categorical variables, where each variable has a discrete set of categories.

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The measures of central tendency include mean and mode, which include a third measure called median.

The three measures for determining central tendency are mean, median, and mode. The mean, also known as average, is the result of dividing the total number of observations by the number of observations. The mode is the value that occurs the most frequently, whereas the median is the midpoint value in the ordered set of observations.

The average or middle of a dataset can be discovered with the aid of central tendency measures. The most frequent value is the mode. The median is the midpoint of an ordered dataset. Mean: the product of the total number of values and their sum.

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Correct question is:

The measures of _________ include mean and mode. The third of those measures is ________.

Dividing the sum of all data values by the total frequency will give us the_____.

Answer:

16/(8×2)=

16/8×2=

16-8/2=

8/2=

4

Step-by-step explanation:

first we subtract 8 from 16 and divide the result by 2.

The time becomes infinity, i(t) will become constant, i.e., lim t→[infinity] i(t) = 0.

The current of the given LR-series circuit can be determined using the formula I = (E/R) * (1 - e^-Rt/L).The current i(t) if i(0) = 0 in the LR-series circuit is given by i(t) = 0.125A. The current as t → [infinity] is given by lim t→[infinity] i(t) = 0.How to solve this?The formula for the current in the LR-series circuit is given by:Where E is the electromotive force, R is the resistance, L is the inductance, t is time and I is the current.I = (E/R) * (1 - e^-Rt/L)Given E = 20V, R = 40Ω, L = 0.1H, and i(0) = 0Substitute these values in the above formula.I = (20/40) * (1 - e^-40t/0.1)I = 0.5(1 - e^-400t)I = 0.5 - 0.5e^-400tSo the current is i(t) = 0.5 - 0.5e^-400t.Limit of t as t → [infinity] means that when the time is allowed to run infinitely, then the current will become constant. Hence, when the time becomes infinity, i(t) will become constant, i.e., lim t→[infinity] i(t) = 0. Answer: The current is i(t) = 0.5 - 0.5e^-400t. Limit of t as t → [infinity] means that when the time is allowed to run infinitely, then the current will become constant. Hence, when the time becomes infinity, i(t) will become constant, i.e., lim t→[infinity] i(t) = 0.

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(a) Starting with the 75% estimate for Italians, the sample you must collect in order to estimate the proportion of PTC tasters within ± 0.1 with 90 % confidence is n = 51.

(b) The sample size required if you made no assumptions about the value of the proportion who could taste PTC is n = 68.

(a) To estimate the sample size needed to find the proportion of PTC tasters within ± 0.1 with 90% confidence, we will use the formula for sample size estimation in proportion problems:
n = (Z² * p * (1-p)) / E²

Where n is the sample size, Z is the Z-score corresponding to the desired confidence level (1.645 for 90% confidence), p is the proportion of PTC tasters (0.75), and E is the margin of error (0.1).

n = (1.645² * 0.75 * (1-0.75)) / 0.1²
n = (2.706 * 0.75 * 0.25) / 0.01
n ≈ 50.74

Since we need a whole number, we round up to the nearest whole number:
n = 51

(b) If no assumptions were made about the proportion of PTC tasters, we would use the worst-case scenario, which is p = 0.5 (maximum variance):

n = (1.645² * 0.5 * (1-0.5)) / 0.1²
n = (2.706 * 0.5 * 0.5) / 0.01
n ≈ 67.65

Again, rounding up to the nearest whole number:
n = 68

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The probability that the second dice lands on an even number given that the first one landed on an odd number is 1/2 or 0.5.

Step-by-Step Explanation:Let A be the event that the first dice rolls an odd number, and let B be the event that the second dice rolls an even number. We want to find P(B|A), which is the probability of B given A. This can be found using the formula:P(B|A) = P(A and B) / P(A) We know that P(A) = 1/2, as half the numbers on a six-sided dice are odd.

To find P(A and B), we need to find the probability that both dice roll the desired numbers simultaneously. Since we know that the first dice rolled an odd number, only half of the numbers are possible for the second dice to be even. Therefore, P(A and B) = 1/2 x 1/2 = 1/4. So:P(B|A) = P(A and B) / P(A) = (1/4) / (1/2) = 1/2 or 0.5. Therefore, the probability that the second dice lands on an even number given that the first one landed on an odd number is 1/2 or 0.5.

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The conclusion we can draw from the circle graph is (2) Jazz is the preferred music for 56 students.

From the circle graph, we can draw the following conclusions:

Pop is the preferred music for 35% of the sample, which is equivalent to 0.35 x 400 = 140 students.

Therefore, conclusion (1) is incorrect.

Jazz is the preferred music for 14% of the sample, which is equivalent to 0.14 x 400 = 56 students.

Therefore, conclusion (2) is correct.

The combined percentage of Hip Hop, Rock, and Jazz is 13% + 25% + 14% = 52%, which is more than half of the sample.

Therefore, conclusion (3) is incorrect.

Hip Hop and Pop are the preferred music for 25% + 35% = 60% of the sample, which is equivalent to 0.6 x 400 = 240 students.

Therefore, conclusion (4) is incorrect.

Therefore, the only correct conclusion that can be drawn from the circle graph is that Jazz is the preferred music for 56 students.

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Based on the randomization distribution, a difference in means of -7, -4, and 6 are very unlikely to ever occur just by random chance. A difference in means of 1 and -0.5 are relatively unlikely to occur but might occur occasionally.

The difference in means refers to the numerical difference between the average values of two groups or samples. It is a measure of the distance between the means of two datasets, and is often used to compare the central tendencies of the groups or samples.

To create a randomization distribution for the test for a difference in means using StatKey, we can follow these steps:

"Randomization Tests" from the list of options select.

Select "Test for a Difference in Means" from the list of randomization tests.

"Two Independent Groups"as we are comparing two groups is to be delected.

Click on the "Upload" button and select the "arrival_time.csv" file provided in the dataset.

choose"Test Hypothesis" button to run the test.

Under the "Randomization Distribution" section, select "Create a Randomization Distribution" and choose a large number of samples, such as 5,000.

Select the "Create Distribution" button to generate the randomization distribution.

To determine the likelihood of each possible difference in means occurring just by random chance, we can compare the observed difference in means with the randomization distribution.

The table below summarizes the results possible difference in means:

Difference in Means Likelihood

          -7                             Very unlikely to ever occur just by random                        

                                                chance

           1                      Relatively unlikely to occur but might occur    

                                     occasionally

          -4                       Very unlikely to ever occur just by random chance

         -0.5               Relatively unlikely to occur but might occur                          

                                       occasionally

            6                      Very unlikely to ever occur just by random chance

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The approximate circumference of spaceship Earth is 160m

The formula for calculating the volume of a sphere is given as;

V = 4/3 πr³

Given that;

Now, substitute the values

65417 = 1. 3 ×3.14r³

Multiply the values

65417 = 4. 082r³

Make r the subject

r³ = 16025. 722

Find the cube root

r = 25. 2m

The circumference is expressed as;

Circumference = 2πr

Substitute the values, we have;

Circumference = 2× 3.14 × 25.2

Circumference = 160 m

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The solutions of the system of equations are option (A) (3, 7) and (-3, -5)

To solve the system of equations, use the concept of substitution, which involves solving one equation for one variable and then substituting that expression into the other equation to eliminate one variable and solve for the other variable.

In this case, solve equation (1) for y in terms of x and substitute that expression into equation (2), which allowed us to solve for x. Then we used the values of x to find the corresponding values of y.

Here we have

y = 2x + 1 --- (1)

y = x²+ 2x -8 --- (2)

From (1) and (2)

=>  x²+ 2x - 8 = 2x + 1

Subtract 2x + 1 from both sides

=>  x²+ 2x - 8 - 2x - 1 =  2x + 1 - 2x - 1  

=> x² - 9 = 0

Now add 9 on both sides

=> x² - 9 = 0 + 9

=> x² = 9

=> x = √9  

=> x = ± 3

From (1)

At x = 3

=> y = 2(3) + 1 = 7

At x = - 3

=> y = 2(-3) + 1 = - 5

Therefore,

The solutions of the system of equations are option (A) (3, 7) and (-3, -5)

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Answer:

C. (0, –5) and (2, –1)

Answer:

an = a1 + (n-1)d

Untuk barisan ini, kita dapat menentukan a1 = 4 dan d = 3, karena selisih antar suku bertambah 3. Jadi, rumusnya menjadi:

an = 4 + (n-1)3

a5 = 4 + (5-1)3

a5 = 4 + 12

a5 = 16

Jadi, suku ke-5 dari barisan ini adalah 16.

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Answer: (5a + 3)(b + 1)

Step-by-step explanation:

We can factor out the common factor of (b + 1) from both terms:

5a(b + 1) + 3(b + 1) = (5a + 3)(b + 1)

Therefore, the expression in complete factored form is (5a + 3)(b + 1).

Answer: Mike is ( 3x + 4 ) years old

Step-by-step explanation:

K -> x y/o

L -> 3x y/o

M -> (3x + 4) y/o

Hi. The terms of the standard charge and insurance charge equations are a little garbled, but it is possible to think that these are the right equations:

Standard charge, S = 18.95 + 0.60M, where 18.95 is the initial fee and 0.60 is the charge for each mile driven.

Insurance charge, I = 4.90 + 0.25M, where 4.90 also represents an initial fee and 0.25 a charge for each mile driven.

Then, the total cos, C = S + I =>

C = (18.95 + 0.60M) + (4.90 + 0.25M) which you can rearrange to show the like terms one next to each other =>

C = (18.95 + 4.90) + (0.60M + 0.25M), now add up the like terms=>

C = 23.85 + 0.85M which is the equation is the most simplified form

Answer: C = 23.85 + 0.85M

Step-by-step explanation:

since we can officially use only one point (the given point), we need to start with the point-slope form :

y - y1 = m(x - x1)

with m being the slope, (x1, y1) being the point.

sadly, to get the slope, we need a second point anyway, because the slope is the ratio

y coordinate difference / x coordinate difference

when going from one point on the line to another.

I recommend to use (0, 50) for the "other" point, as there seems to be the smallest error in the coordinates.

so, when going from (0, 50) to the given point (6, -40) :

x changes by +6 (from 0 to 6).

y changes by -90 (from 50 to -40).

the slope m = -90/+6 = -15/1 = -15

y - -40 = -15(x - 6) = -15x + 90

y + 40 = -15x + 90

y = -15x + 50

that is the slope-intercept form.

m = -15

b = 50

y = -242

-242 = -15x + 50

-292 = -15x

x = -292/-15 = 292/15 = 19.46666666... ≈ 19

The area of the given shape is 109.25 ft² .

What is Area?

Area is a measurement of the amount of space inside a two-dimensional figure or shape. It is the size of the surface of the shape, and it is measured in square units, such as square meters, square centimeters, or square inches.The area of a shape can be found by multiplying the length and width of a rectangle or the base and height of a triangle, or by using specific formulas for other shapes such as circles, trapezoids, or parallelograms

Given : height of triangle = diameter of semicircle = 10 ft

            radius of semicircle = 5 ft

           base of triangle = 14 ft

we know that, The area of given shape :

= area of given triangle + area of semi circle

=  1/2 × base × height  +   πr²/2

= 1/2 × 14 × 10 + (3.14 × 5²)/2

= 70 + 39.25

= 109.25 ft²                                  

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The probability of rolling one of these five numbers is 5/37.

Suppose you roll a special 37-sided die. The probability that one of the following numbers is rolled is as follows:

35 | 25 | 33 | 9 | 19.

The total number of sides of a die is 37. As a result, there are 37 numbers in the die.

Rolling one of the 5 given numbers implies that you can select either 35 or 25 or 33 or 9 or 19.

Therefore, the probability of rolling any of these numbers is:

1 / 37 + 1 / 37 + 1 / 37 + 1 / 37 + 1 / 37 = 5 / 37

So, the probability of rolling one of these five numbers is 5/37.

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The claim of the production manager is not true because more than 4000 insulating washers are defective per day.

The total amount of insulating washer for the electrical devices produced per day = 225,000.

The amount chosen at random for sampling = 200 washers.

The amount shown to be defective in the chosen sample = 4

If every 200 = 4 defective

225,000 = X

Make c the subject of formula;

X = 225000×4/200

X = 900000/200

X = 4,500.

This shows that the claim is wrong because more than 4000 insulating washers are defective per day.

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Answer: 24

Step-by-step explanation: