The ratio of the interior angles of a triangle is 1 : 1 : 4. What are the angle measures? Write the angle measures from least to greatest.

Answer: The sequence has a common difference of 3, since each term is 3 more than the previous one. To find the 22nd term, we can use the formula for the nth term of an arithmetic sequence:

a_n = a_1 + (n-1)d

where a_1 is the first term, d is the common difference, and n is the term number we want to find.

In this case, we have:

a_1 = 1 (the first term)

d = 3 (the common difference)

n = 22 (the term number we want to find)

Substituting these values into the formula, we get:

a_22 = 1 + (22-1)3

= 1 + 21*3

= 64

Therefore, the 22nd term is 64.

Using the formula for the nth term, we can also check that the sequence up to the 22nd term is:

1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64.

Step-by-step explanation:

The regression line equation is given as y = -0.95X + 8.99

The chill factor when  the wind is 27 miles per hour is -16.66

Using a regression calculator, the regression line calculation is given as

Calculation Summary

Sum of X = 45

Sum of Y = 20

Mean X = 6.4286

Mean Y = 2.8571

Sum of squares (SSX) = 113.7143

Sum of products (SP) = -108.5714

Regression Equation = ŷ = bX + a

b = SP/SSX = -108.57/113.71 = -0.95477

a = MY - bMX = 2.86 - (-0.95*6.43) = 8.99497

y = -0.95477X + 8.99497

y = -0.95X + 8.99

b. The chill factor when the wind is 27 miles per hour

We would solve for this using the regression line output above

y = -0.95X + 8.99

here x = 27

y =  -0.95 * 27 + 8.99

y = -25.65 + 8.99

= -16.66

Final answer y =  -16.66

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Answer:

77in^2

Step-by-step explanation:

L=15

W=5

The total is 75 but nearest is 77

The logarithm base 7 of 49 i.e. [tex]log_749[/tex] is 2.

What is the natural logarithm?

The natural logarithm, denoted by ln(x), is a mathematical function that gives the logarithm of a number x with respect to the base e, where e is the mathematical constant approximately equal to 2.71828.

The logarithm base 7 of 49 can be evaluated by asking the question: "To what power must 7 be raised to obtain 49?"

We can see that 7 raised to the power of 2 equals 49, so:

[tex]log_749 = 2[/tex]

Therefore, the logarithm base 7 of 49 is 2.

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Answer: 8a+2b-4 + 3b-5 Determine the sign:8 a + 2 b - 4 + 3 b - 5R.

Step-by-step explanation: 8 a + 5 b - 9. Based on the given conditions, formulate: 8a+2b-4 + 3b-5 Determine the sign:8 a + 2 b - 4 + 3 b - 5R.

Answer:

Step-by-step explanation:

what number is 8% less than 200?

how do you solve this step by step?

200 : 100 x 8 =

16

200 - 16 =

184

When gathering data, using two or more methods to confirm results is called option (c) triangulation

Triangulation involves using multiple methods or sources to collect data in order to validate or confirm results. By using different methods, researchers can obtain a more complete and accurate understanding of the phenomenon being studied, reducing the risk of bias or error. For example, a researcher might use both surveys and interviews to gather information about a particular group of people.

This approach can help to ensure that the data collected is reliable and can be used with confidence to draw conclusions. Triangulation is widely used in social science research, but can also be applied in other fields where multiple sources of information are available.

Therefore, the correct option is (c) triangulation

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Answer:

£90

Step-by-step explanation:

1/5 =3

5/5=15

1/6=15

6/6=90

The exact value of the volume of the sphere is V = 1.333π cm³ and the exact value is V = 3.14 cm³

A sphere is defined as symmetrical and round in shape. It is also referred to as a three dimensional solid, that has all its surface points at equal distances from the center.

The formula for the volume of a sphere is:

V = ⁴/₃πr³

where:

V = volume

r = radius

The radius of a sphere is half its diameter.

We are given diameter = 2 cm

Thus: r = 2/2 = 1 cm

V = ⁴/₃π * 1³

V = 1.333π cm³

V = 3.14 cm³

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Answer:

1.) 18

2.) 162.5

3.) 4 hours

Step-by-step explanation:

Rule: speed= distance/time

Rule: distance= time x speed

Rule: time= distance/speed

1). 90/5= 18

2). 2.5 x 65= 162.5

3). 320/80= 4

Answer: 804.25 yards3

Step-by-step explanation: : Explanation We have height (H) = 4 yards Diameter = 4x4 = 16, Radius (r) = 16/2 = 8, volume and cylinder V = nr2h. V= 3.14 x 8x8x4, V= 804.25 yards 3

The monthly Net income paycheck is $1125

Gross income is the sum of all wages, salaries, profits, interest payments, rents, and other forms of earnings, before any deductions or taxes. The gross income is the addition of the taxes and the net income.

The gross income = net income + tax

The tax is 25% of the gross income

= 25/100 × 1500

= $375

The net income = 1500-375

= $1125

Therefore the monthly net income paycheck is $1125

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The surface area and volume of the two cuboids are 124 sq.ft, 72 cubic f

Surface area refers to the total area that the surface of a three-dimensional object covers. It is the sum of the areas of all the faces or surfaces of the object. The surface area is measured in square units, such as square centimeters (cm²) or square feet (ft²), depending on the system of measurement used.

It seems like you have provided two sets of dimensions. Let's calculate the surface area and volume for both the cuboids:

Given that,

Dimensions: 9 ft x 4 ft x 2 ft

Surface area of cuboid 1 = 2(lw + lh + wh)

= 2(94 + 92 + 4*2) sq.ft

= 2(36 + 18 + 8) sq.ft

= 2(62) sq.ft

= 124 sq.ft

Volume of cuboid 1 = l * w * h

= 9 * 4 * 2 cubic ft

= 72 cubic ft

Cuboid 2:

Dimensions: 3 ft x 1 ft x 2 ft

Surface area of cuboid 2 = 2(lw + lh + wh)

= 2(31 + 32 + 1*2) sq.ft

= 2(3 + 6 + 2) sq.ft

= 2(11) sq.ft

= 22 sq.ft

Volume of cuboid 2 = l * w * h

= 3 * 1 * 2 cubic ft

= 6 cubic ft

Therefore, the surface area and volume of the two cuboids are as follows: Surface area = 124 sq.ft, Volume = 72 cubic ft

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Answer: There would 20-gon

The given figure appears to be a parallelogram.

A parallelogram is a quadrilateral with two pairs of parallel sides. In the given figure, we can see that opposite sides are parallel, so it is a parallelogram.

We can also find that the measure of angle A is 120 degrees because the adjacent angles to angle A are 30 and 30 degrees, and the sum of adjacent angles in a parallelogram is 180 degrees. Similarly, the measure of angle C is 60 degrees.

The formula to find the area of a parallelogram is:

Area = base x height

We can choose any base and its corresponding height to find the area of the parallelogram. In the given figure, we can choose AB as the base and the perpendicular distance from AB to line DC as the height. Let's call this distance h.

From the figure, we can see that triangle ADE is a 30-60-90 triangle. The ratio of the sides in a 30-60-90 triangle is 1:sqrt(3):2. So, if AD is x, then DE is x*sqrt(3) and AE is 2x.

Since AE is parallel to DC, we can say that the height h is the same for triangles ADE and CFB. So, we can use triangle CFB to find the value of h.

Triangle CFB is a right triangle with angles 30, 60, and 90 degrees. The length of CB is 4 units and the length of CF is 2 units. So, the length of FB is 2*sqrt(3) units (using the ratio 1:sqrt(3):2). Therefore, the area of triangle CFB is:

Area = (1/2) x base x height

Area = (1/2) x 4 x 2

Area = 4

Since the area of triangle CFB is equal to the area of triangle ADE, we can say that:

Area of parallelogram ABCD = 2 x area of triangle CFB

Area of parallelogram ABCD = 2 x 4

Area of parallelogram ABCD = 8 square units

So, the area of the parallelogram is 8 square units.

Answer:

To find the height of the water tank, we need to know the length of one side of the cube-shaped tank.

Let's assume that the length of one side of the tank is 'x' meters.

The volume of the cube-shaped tank is given as 512 cubic meters, so we have:

The volume of the tank = (length of one side)^3

512 = x^3

Taking the cube root on both sides, we get:

x = 8

Therefore, the length of one side of the tank is 8 meters.

Since the tank is a cube, the height of the tank is also 8 meters.

Step-by-step explanation:

Answer:

8 meter

Step-by-step explanation:

Volume of cubical tank = Area of base * height

Volume of cubical tank = a * a * a

[ all 3 sides of a cube are equal, assume the side as 'a' ]

Volume = a³

a³ = 512

a = ∛512

a = 8 meter

As all dimensions of a cubical tank are equal, height of this tank = 8 meter.

An exponential function showing the relationship between y and t is y = [tex]1.024^t[/tex] x 380,000

Now let's consider the population after t years. We can use the formula we just derived to write:

y = [tex]1.024^t[/tex] x 380,000

This equation represents an exponential function where the initial population is 380,000 and the growth rate is 2.4%. The base of the exponential function is 1.024, which represents the factor by which the population grows each year.

This function relates the city's population to the number of years since the start of the study and can be written as:

y = [tex]1.024^t[/tex] x 380,000

This function can be used to make predictions about the city's population at any point in the future, given the number of years since the start of the study.

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The total number of students in the college is expressed as: 5x

The parameters given are:

1/2 of the students who learn the flute also learn the violin.

3 times as many students learn the violin as learn the flute.

x students learn both the flute and the violin

Thus, the total who learn the flute = 2x

Number who learn only flute = x

Since 3 times as many students learn the violin as learn the flute. Then, 3x students only learn the violin.

Thus, total number of students at the college is:

x + x + 3x = 5x

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Complete question is:

Every student at a music college learns the flute, the violin, or both the flute and the violin. 1/2 of the students who learn the flute also learn the violin. 3 times as many students learn the violin as learn the flute. x students learn both the flute and the violin. Find an expression, in terms of x, for the total number of students at the college. Flute X Violin​

The most appropriate graphical representation for the grams of fiber from 1,000 different breakfast cereals sold in the United States is given as follows:

Histogram, because there is a large set of data.

A histogram is a graphical representation of the distribution of numerical data. It consists of a series of adjacent rectangles, or bins, that are used to represent the frequency distribution of the data. The height of each bin corresponds to the number of data points that fall within a particular range or interval.

For this problem, we have that each bin will represent the number of observations in an interval of grams of fiber.

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The irregular pοlygοn has 6 sides.

When the sides οf a pοlygοn are nοt equal tο οne anοther and the angles may alsο nοt be equal in size, the pοlygοn is said tο be irregular. Fοr instance, a rectangle is a fοur-sided pοlygοn that οnly has equal οppοsed sides but equal-sized angles. It is therefοre an irregular pοlygοn.

Here the formula for n-sided polygon is

=> (n-2) *180

In the given irregular polygon on interior angle is 105 and  rest is 125. Then,

=> (n-2)*180 = 105 + 125(n-1)

=> 180n- 360 = 105+ 125n -125

=> 180n -125n = 360-20

=> 55n  = 340

=> n = 340/55

=> n = 6

Hence the irregular polygon has 6 sides.

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Answer: 90ft

Step-by-step explanation:

To solve, you have to use similar triangles. the ratios of the lengths of the sides of the triangles are the same (because the sun makes the same angle with the objects.

[tex]\frac{6.2ft}{2.5ft}[/tex] = [tex]\frac{height of tree}{36.2ft}[/tex]

(2.48)(36.2ft) = 89.776ft

=90ft

Answer:

B

Step-by-step explanation:

A negative exponent in the numerator is a positive exponent in the denominator.

(4/3)^-3 in the numerator is (4/3)^3 in the denominator.

A zero exponent makes the expression equal 1.

((3/4)^5)^0 = (3/4)^0 = 1

A power raised to a power is the product of the powers.

((3/4)^3)^4 = (3/4)^12

Put everything together, and you get B.

The equation to represent the number of cookies sold and profit earned is p=0.25c

In mathematics, a straight line is a geometric object that extends infinitely in both directions and has a constant slope. It is also known as a line or a linear function.

From the given graph;

The graph represents the straight line passing through origin.

Let Number of cookies sold=c

and profit earned be p.

The linear equation is p=mc+b

Taking the value;

c=2

p=0.5

0.5=2m+b....... Equation1

Taking another value,

c=4

p=1

1=4m+b....... Equation2

Subtracting Equation 1 from 2, we get

0.5=2m

m=.25

Putting the value of m=0.25 in the equation1, we get

.5=.25×2+b

b=0

Hence, the equation to represent the number of cookies sold and profit earned is p=0.25c.

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The area of the triangle is 62.35 square units. Option D

First, using the cosine identity, we have;

cos θ = adjacent/hypotenuse

cos 60 = x/12

find the value

x = 6

Using the sine identity,

sin 60 = x/12

x = 10. 49

Sum of the base = Line AD + Line DB = 6 + 6 = 12

Using the formula for area of a triangle;

Area = 1/2 base × height

Area = 1/2 × 12 × 10. 39

Multiply the values, we get;

Area = 62. 35 square units

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The measure of the angles and arc length for the circle are:

a: m∠BAD = 40°; b. arc CE = 48°; c. m∠BCD = 40°; d. m∠ADC = 42°; e.  m∠ABE = 66°.

Hence, the distinction between chord length versus arc length is that the former provides the distance between two places, whilst the latter provides the entire area covered across two points.

The chord's length is equal to twice the angle's radius multiplied by its sine.

The arrow theorem and central angle theorem are other names for the inscribed angle arc  theorem. The measuring of the central angle equals equal to twice the value of the inscribed angle occupied by the same arc, according to this theorem.

arc BD = 80°

arc AC = 84°

∠CBE = 24°

Thus,

a: m∠BAD

m∠BAD = 1/2(arc BD)

m∠BAD = 1/2(80°)

m∠BAD = 40°

b: arc CE

m∠CBE = 1/2(arc CE)

24° = 1/2(arc CE)

24°*2 = arc CE

arc CE = 48°

c: m∠BCD

m∠BCD = 1/2(arc BD)

m∠BCD = 1/2(80°)

m∠BCD = 40°

d: m∠ADC

m∠ADC = 1/2(arc AC)

m∠ADC = 1/2*84°

m∠ADC = 42°

e: m∠ABE

m∠ABE = 1/2(arc AC + arc CE)

m∠ABE = 1/2(84° + 48°)

m∠ABE = 1/2(132°)

m∠ABE = 66°

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From 1940 to 1970 the price of bread increased by 250%.

From 1970 to 1990 the price of bread increased by 300%.

From 1940 to 1990 the price of bread increased by 750%.

The variable x, which represents the number of students who receive an offer, is a discrete variable.

The variable can take on one or more exact values, a countable number of values, or values that are finite, such as the number of students in a class, the number of cars in a parking lot, the number of seeds in a bag, and so on, if the variable is a discrete variable. A variable is referred to as continuous if it can take on an infinite number of values (although the values may be restricted to a certain range), and those values are not limited to specific points on a continuum.

For three students who are undergoing interviews at Brookwood Institute, the experimental results are defined in terms of the outcomes of the three interviews. Each interview would yield one of two possible results: either an offer for a job or no offer.

As a result, for each of the three interviews, there are two possible outcomes. If we multiply the possibilities for each of the three interviews, we get a total of eight possible outcomes, which can be listed as follows:

NNN, NNO, NON, NOO, ONN, ONO, OON, and OOO.

Let's assume that an 'O' represents an offer, while an 'N' represents no offer. The variable x represents the number of students who receive an offer. Since the variable can only take on one of four discrete values (0, 1, 2, or 3), it is a discrete variable.

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The probability of completion is the same for Drug A and Drug B, The test statistic is 3.1234, with 1 degree of freedom, and the p-value is 0.0762. The 90% confidence interval for the estimated odds ratio is 2.4444, and the interval is (0.5957, 14.1111). Based on the study design, the most appropriate sampling model for describing the data in this problem is the multiple hypergeometric model,

To test the hypothesis that the probability of completion is the same for Drug A and Drug B, we can use a two-sample test of proportions. We can use a normal approximation to the binomial distribution to calculate the test statistic and p-value. Specifically, we can use the following R code:

# Set up the data

n1 <- 20

n2 <- 19

x1 <- 19

x2 <- 12

# Calculate the test statistic and p-value

p1 <- x1/n1

p2 <- x2/n2

pooled_p <- (x1 + x2) / (n1 + n2)

se <- sqrt(pooled_p * (1 - pooled_p) * (1/n1 + 1/n2))

z <- (p1 - p2) / se

p_value <- 2 * pnorm(abs(z), lower.tail = FALSE)

# Print the results

cat("Test statistic:", round(z, 2), "\n")

cat("p-value:", p_value, "\n")

# Draw a conclusion

if (p_value < 0.05) {

 cat("There is significant evidence to suggest that the completion rates differ between Drug A and Drug B.")

} else {

 cat("There is not enough evidence to suggest that the completion rates differ between Drug A and Drug B.")

}

The sampling model appropriate for this test is the multinomial model.

To compute a 90% confidence interval for the odds ratio comparing the odds of not completing the study between groups A and B, we can use the following R code:

# Calculate the odds ratio and its standard error

odds1 <- (n1 - x1) / x1

odds2 <- (n2 - x2) / x2

odds_ratio <- odds1 / odds2

log_odds_ratio <- log(odds_ratio)

se_log_odds_ratio <- sqrt(1/x1 + 1/(n1 - x1) + 1/x2 + 1/(n2 - x2))

# Calculate the confidence interval

alpha <- 0.1

z_alpha <- qnorm(1 - alpha/2)

lower <- exp(log_odds_ratio - z_alpha * se_log_odds_ratio)

upper <- exp(log_odds_ratio + z_alpha * se_log_odds_ratio)

# Print the results

cat("Odds ratio:", round(odds_ratio, 2), "\n")

cat("90% confidence interval:", round(lower, 2), "-", round(upper, 2), "\n")

# Interpret the results

cat("We are 90% confident that the true odds ratio of not completing the study for Drug A versus Drug B lies between", round(lower, 2), "and", round(upper, 2), ".\n")

In this case, we can use an asymptotic interval since both sample sizes are greater than 10 and the sample proportions are not too close to 0 or 1.

The sampling model appropriate for this analysis is the multiple hypergeometric model.

Based on the study design, the appropriate sampling model for describing the data in this problem is the repeated measures model. Inferences in parts (I) and (II) are based on the multinomial model and the multiple hypergeometric model, respectively, since they are appropriate for comparing proportions and odds ratios between two groups with binary outcomes.

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--The given question is incomplete, the complete question is given

"A clinical trial to compare the effectiveness of two treatments for schizophrenia was conducted involving 39 patients, twenty of whom were randomly assigned to receive Drug A, with the other 19 receiving Drug B. The design of the study called for each patient’s severity of symptoms to be assessed at baseline (before randomization and the onset of treatment) and at 4 follow-up occasions. Although all 39 patients were assessed at baseline, some patients did not return for one or more of the scheduled follow-up measurements, and investigators were concerned that attrition rates (the proportion of subjects dropping out of the study) may not be the same in each treatment and that failure to account for such differences in the analysis could bias the results of such an analysis. Among the 20 patients assigned to Drug A, complete data (observations at all follow-up occasions) were obtained on 19 subjects. Among the 19 subjects assigned to Drug B, complete data were obtained on 12 subjects. Use R coding to help answer the questions.

I. Test the hypothesis that the probability of completion is the same for Drug A and Drug B using the most appropriate method for this task. Be sure to identify clearly what method you use and draw an appropriate conclusion in the context of the problem.

II. Compute a 90% confidence interval for the odds ratio comparing the odds of not completing the study between groups A and B. Use an exact p-value based interval, an exact mid-p-value based interval, or an asymptotic interval, whichever you think is most appropriate, and justify your choice. Be sure to interpret the estimated odds ratio and the interval you obtain for it in the context of the problem.

III. Based on the study design, what sampling model is most appropriate for describing the data in this problem: the Poisson, multinomial, product multinomial, or multiple hypergeometric model? What sampling model are your inferences in parts (I) and (II) based on?"--

Answer:

When a point is reflected over the x-axis, its y-coordinate is multiplied by -1, while its x-coordinate remains the same.

So, if point J has coordinates (-8, -12), its reflection over the x-axis, J', will have coordinates (-8, 12).

Therefore, J' is located at the point (-8, 12).