The width of the river is approximately 9.17 m.
Let us consider the given figure. Using trigonometry ratios, we can find the width of the river. Suppose the width of the river is AC or BC = x meters. We need to find the value of x.
Given: AB = 10 m, ∠A = 45°, and ∠B = 60°Step 1:Find ∠AOC and ∠BOC using ∠A = 45°, and ∠B = 60°.∠AOC = ∠A + ∠C = 45° + ∠C∠BOC = ∠B + ∠C = 60° + ∠CStep 2:Find the value of ∠COC from the sum of the angles of the triangle OAC.
∠COC = 180° − (∠AOC + ∠AOC) =
180° − (45° + 45°) = 90°
Step 3:Now, we can find the length of OC.OC = AC tan ∠COC = x tan 90° = Undefined (As the tan 90° = Undefined)Step 4:Next, we can find the length of OA and OB using the sin function.
OA = AC / sin ∠AOC
= x / sin (45° + ∠C) OB
= BC / sin ∠BOC
= x / sin (60° + ∠C)
Step 5:We know that OA + OB = AB = 10 m.
Substitute the values of OA and OB in the above equation and simplify. OA + OB = x / sin (45° + ∠C) + x / sin (60° + ∠C)
= 10sin (45° + ∠C)sin (60° + ∠C)
= 10 / [2(√2 + √6)] sin (45° + ∠C)sin (60° + ∠C)
= (5 − √3) / 8 cos (30° − ∠C) / cos (30° − ∠C) × sin (45° + ∠C) / sin (60° + ∠C)
= (5 − √3) / 8 × 2 / √3 = (5 − √3) / 4 cos (30° − ∠C) / cos (30° − ∠C) × (1 / sin (45° + ∠C)) = (5 − √3) / 4cos (30° − ∠C) / sin (75° + ∠C)
= (5 − √3) / 4(1 / 2 cos (30° − ∠C)) = (5 − √3) / 4 tan (30° − ∠C)
= (5 − √3) / 3∠C
= 30° − tan −1[(5 − √3) / 3]
Putting the value of ∠C in x tan (90°) = x × Undefined, and the value of x in OA, we get, OA = x / sin (45° + ∠C)OA = 9.17 m (approx)Therefore, the width of the river is approximately 9.17 m.
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Let b cannot equal 1 and consider the integral 1 to b (6x-9) dx a) what value of b will make this integral equal to 0? b) sketch a graph of y=6x-9 on the interval from x=1 to x=b to verify your answer in (a)
a) To find the value of b that makes the integral equal to 0, we need to solve the integral:
∫(1 to b) (6x - 9) dx = 0
Applying the fundamental theorem of calculus, we can find the antiderivative of the integrand and evaluate it at the limits of integration:
[3x² - 9x] (from 1 to b) = 0
Substituting the limits, we have:
(3b² - 9b) - (3(1)² - 9(1)) = 0
Simplifying further:
3b² - 9b - 6 = 0
Now we can solve this quadratic equation for b using the quadratic formula or factoring:
b² - 3b - 2 = 0
Factoring the quadratic equation, we get:
(b - 2)(b + 1) = 0
Setting each factor to zero, we find two possible values for b:
b = 2 or b = -1.
However, since b cannot equal 1 (as stated in the problem), the only valid solution is b = 2.
b) To verify our answer, we can sketch a graph of y = 6x - 9 on the interval from x = 1 to x = b = 2. The graph will be a straight line with a slope of 6 and y-intercept at -9.
On the interval [1, 2], the line starts at the point (1, -3) and ends at the point (2, 3). By calculating the area under this line, we find that the integral from 1 to 2 of (6x - 9) equals 0, confirming our previous result.
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An IV blood administration is in place. A bag of 376 ml is hung at
1100hrs. How long will this bag take to infuse at maximum time?
The time it would take for the bag to infuse at the maximum time would be the value of 1. 5 hours.
How to find the time ?The maximum rate of infusion for an IV bag is 250 ml/hour. This means that the maximum time it would take for the bag to infuse is:
= Quantity in bag / Maximum rate of infusion
Therefore, it will take:
= 376 ml / 250 ml/hour
= 1. 5 hours to infuse the entire bag
In conclusion, the time it would take for the bag to infuse at the maximum time is 1. 5 hours.
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Cinia has made a pyramid model for her history project at school. The pyrarrid model has a square base. Each triangular side of the model has a
base length of 10 centimeess and a slant height of ē. 9 centimeters. Olivia wants to wrap the pyramid in wrapping paper before putting it into her
school bag
How much wrapping paper will Ona need to cover the pyramid?
Olivia will need 280 square centimeters of wrapping paper to cover the pyramid for her history project.
To calculate the amount of wrapping paper Olivia will need to cover the pyramid, we need to find the total surface area of the pyramid, including the base and the triangular sides.
The base of the pyramid is a square, so its area can be found by squaring the length of one side. Given that the base length is 10 centimeters, the area of the base is 10^2 = 100 square centimeters.
The triangular sides of the pyramid are all congruent, so we can calculate the area of one triangular side and multiply it by the number of sides (4 in this case) to get the total area.
To find the area of one triangular side, we can use the formula for the area of a triangle:
Area = (1/2) * base * height
In this case, the base length is 10 centimeters, and the height is the slant height of 9 centimeters.
Area = (1/2) * 10 * 9 = 45 square centimeters
Since there are four triangular sides, the total area of the triangular sides is 4 * 45 = 180 square centimeters.To calculate the total surface area, we need to add the area of the base and the area of the triangular sides:
Total surface area = base area + triangular side area
Total surface area = 100 + 180 = 280 square centimeters
Therefore, Olivia will need 280 square centimeters of wrapping paper to cover the pyramid for her history project.
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A hockey goalie loses 235rating points each time his team loses. If his team loses 8 games in a row, what number represents the change in the goalie's rating points?Negative 20 and StartFraction 4 over 5 EndFractionNegative 4 and StartFraction 4 over 5 EndFraction16 and three-fifths20 and four-fifths
The change in the goalie's rating points after his team loses 8 games in a row is -20 and 4/5.
The goalie loses 235 rating points each time his team loses. If his team loses 8 games in a row, we need to calculate the total change in his rating points.
To find the total change, we multiply the loss per game (235) by the number of games lost (8).
235 * 8 = 1880
Therefore, the goalie's rating points decrease by 1880. However, the answer options provided are in mixed number format, so we need to convert 1880 to a mixed number.
To convert 1880 to a mixed number, we divide 1880 by the denominator (5) and express the remainder as the numerator:
1880 ÷ 5 = 376 with a remainder of 0
Hence, the mixed number representation of 1880 is 376 and 0/5, which simplifies to 376.
Therefore, the change in the goalie's rating points after losing 8 games in a row is -376, or in mixed number form, -376 and 0/5, which further simplifies to -376 and 4/5.
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Eva drove to work in rush hour traffic, going just 30 miles in 1 hour and 18 minutes. Later that day, she left work early to avoid the rush and was able to take the same route home in 31 minutes. What was Eva's average speed overall?
Hence, Eva's average speed overall is 35.29 miles per hour
The given information can be tabulated as follows: Distance, Time, Speed
Eva drove to work30 miles1 hour 18 minutes1.18 hours
Eva drove to work30 miles1.18 hours
Eva left work31 minutes0.52 hours
Eva left work30 miles0.52 hours
It is given that Eva drove to work in rush hour traffic, going just 30 miles in 1 hour and 18 minutes, i.e. 1.18 hours.
Her speed during this time can be calculated as follows:
Speed = Distance / Time
Speed = 30 / 1.18 = 25.42 miles per hour
Similarly, when Eva left work early to avoid the rush and was able to take the same route home in 31 minutes, i.e. 0.52 hours.
Her speed during this time can be calculated as follows:
Speed = Distance / Time
Speed = 30 / 0.52 = 57.69 miles per hour
Therefore, Eva's average speed overall can be calculated as follows:
Average speed = Total distance / Total time
Total distance = 30 + 30 = 60 miles
Total time = 1.18 + 0.52 = 1.7 hours
Average speed = 60 / 1.7 = 35.29 miles per hour
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A vendor has $22.00 and wants to buy bushels of corn. The vendor finds a farmer who sells each bushel of corn for $3.00 and charges a fixed delivery fee of $5.50.
The vendor cannot purchase a fraction of a bushel, the vendor can afford to buy a maximum of 5 bushels of corn with the given amount of money.
To determine how many bushels of corn the vendor can afford to buy, we need to consider the cost of each bushel of corn and the fixed delivery fee. Here's how we can calculate it:
Subtract the fixed delivery fee from the total amount of money the vendor has:
$22.00 - $5.50 = $16.50
Divide the remaining amount of money by the cost per bushel of corn to find the maximum number of bushels the vendor can buy:
$16.50 ÷ $3.00 = 5.5 bushels
Since the vendor cannot purchase a fraction of a bushel, the vendor can afford to buy a maximum of 5 bushels of corn with the given amount of money.
Please note that in this calculation, we assumed that the vendor would spend all of the available money on purchasing corn, without considering any additional expenses or constraints.
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Which estimate at a 95% confidence level most likely comes from a small sample?
A. 93% (±24%)
B. 82% (±8%)
C. 78% (±4%)
D. 87% (±6%)
The estimate at a 95% confidence level that most likely comes from a small sample is 93% (±24%). The correct option is A
What is margin of error ?The range of values that is most likely to include the true population parameter is known as the margin of error. The standard error, a gauge of the sample statistic's variability, is used to determine the margin of error.
Option A in this situation has the most margin of error of the four, at 24%. In comparison to the other options, this indicates that the true population parameter is probably within 24% of the sample statistic. This implies that option A's sample size is smaller than that of the other options.
Therefore, the estimate at a 95% confidence level that most likely comes from a small sample is 93% (±24%).
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When performing a dilation or a composition of a dilation and rigid transformations on a triangle, what properties of the original triangle preserved?
When performing a dilation or a composition of a dilation and rigid transformations on a triangle, several properties of the original triangle are preserved. In both cases, the shape and orientation of the triangle remain the same while the size and location of the triangle change.
During a dilation, the original triangle is extended or shrunk in size uniformly. All sides of the triangle are extended or shrunk by the same factor, which is the scale factor of the dilation. The angle measures of the triangle remain unchanged during dilation, and the corresponding angles of the dilated triangle remain equal.In a composition of a dilation and rigid transformation, the original triangle is first dilated and then subjected to a rigid transformation like rotation, translation, or reflection.
The shape and orientation of the original triangle are preserved, and the size and location of the dilated triangle change. The angle measures of the triangle remain unchanged during dilation, and the corresponding angles of the dilated triangle remain equal. During the subsequent rigid transformation, the corresponding sides and angles of the dilated triangle are also preserved.
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In order for a ladder to reach a height of 10 feet it needs to be placed at a 75⁰ angle to the ground. The ground already has an elevation of 15⁰.what degree does the ladder need to me set at?
To reach a height of 10 feet while accounting for the ground elevation of 15⁰, the ladder needs to be set at an angle of approximately 80.77⁰.
When placing the ladder on the ground, we need to consider both the desired height and the ground elevation. Let's denote the angle at which the ladder needs to be set as x⁰.
To find the value of x⁰, we can use trigonometry. In this case, we'll use the tangent function. The tangent of an angle is equal to the ratio of the length of the opposite side to the length of the adjacent side. In this scenario, the opposite side is the height of the ladder (10 feet), and the adjacent side is the horizontal distance the ladder needs to cover on the ground.
The tangent of an angle is given by the formula: tan(x⁰) = opposite/adjacent.
To calculate the adjacent side, we can use the height of the ladder and the ground elevation angle: adjacent = height / tan(ground elevation).
Plugging in the values, we have: adjacent = 10 / tan(15⁰).
Solving this equation gives us the value of the adjacent side. We can then find x⁰ by taking the arctan of the ratio: x⁰ = arctan(adjacent/height).
Calculating this value, we find x⁰ ≈ 80.77⁰.
Therefore, the ladder needs to be set at an angle of approximately 80.77⁰ to reach a height of 10 feet, accounting for the ground elevation of 15⁰.
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Brenda found a store online where he can buy a package of 8-tshirts .these t-shirts sell at the time rate as the t-shirts jacob bought .how much does brendan pay for the package of 8t-shirts?
The amount that Brenda would pay for the 8 t- shirts at the same rate would be $ 37. 60.
How to find the amount paid ?To determine how much Brenda pays for the package of 8 T-shirts, we need to calculate the price per T-shirt based on Jacob's purchase and then multiply it by 8.
Jacob bought 7 T-shirts for $32.90, so the price per T-shirt can be calculated as:
Price per T-shirt = Total cost / Number of T-shirts
Price per T-shirt = $32.90 / 7
Price per T-shirt = $4.70
The cost of 8 shirts is therefore:
Total cost = Price per T-shirt * Number of T-shirts
Total cost = $4.70 x 8
Total cost = $37.60
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Missing detail is:
Jacob bought 7 T shirts for $32.90 Kyle bought 12 T shirts for $60.00
10 year ago, the ratio o fjeremy's age to ranyd's age to Kaden's age was 4:3:1. the sum of thie r presesnt age is 102. Find randy's age now
To find Randy's age now, we need to use the information provided about the ratio of Jeremy's age, Randy's age, and Kaden's age 10 years ago, as well as the sum of their present ages. By setting up equations based on the given information, we can solve for Randy's age now.
Let's assume that Jeremy's age 10 years ago was 4x, Randy's age was 3x, and Kaden's age was x. This satisfies the given ratio of 4:3:1.
Now, 10 years have passed, so we need to consider their present ages. Jeremy's present age would be 4x + 10, Randy's present age would be 3x + 10, and Kaden's present age would be x + 10.
The sum of their present ages is given as 102, so we can set up the equation:
(4x + 10) + (3x + 10) + (x + 10) = 102
Simplifying the equation, we have:
8x + 30 = 102
Subtracting 30 from both sides, we get:
8x = 72
Dividing both sides by 8, we find:
x = 9
Therefore, Randy's age now is 3x + 10, which is equal to 3(9) + 10 = 37 years.
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Que es la circunferencia
Answer: you can also search what you said in eniglish aand it would give u a calculater _--_- (
Step-by-step explanation:The circumference is the length of any great circle, the intersection of the sphere with any plane passing through its centre. A meridian is any great circle passing through a point designated a pole.
Identify the expression as an equation containing factors, a fractional equation, or a proportion.
2x/x+7 - x/x+3 = 1 + 1/x^2+10+21
A. Proportion
B. Fractional Equation
C. Equation containing fractions
The given expression is an equation containing fractions.
Given expression is:
[tex]$$\frac{2x}{x+7} - \frac{x}{x+3} = 1 + \frac{1}{x^2+10x+21}$$[/tex]
We can rewrite the given expression as follows:
[tex]$$\frac{2x(x+3)-x(x+7)}{(x+7)(x+3)}=\frac{x^2+10x+22}{(x+3)(x+7)}$$[/tex]
Simplifying the numerator and denominator of the above expression,
we get:[tex]$$\frac{x^2-4x-21}{(x+7)(x+3)} = \frac{x^2+10x+22}{(x+7)(x+3)}$$[/tex]
On simplifying, we get the following equation:
[tex]$$x^2-4x-21=x^2+10x+22$$[/tex]
Simplifying the above equation, we get:
$$14x=-43$$
On dividing by 14 on both sides,
we get:[tex]$${x=-\frac{43}{14}}$$[/tex]
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A regulation baseball has a diameter of about 3 in. What is the best approximation for the volume of this baseball? 14. 13 in³ 28. 26 in³ 84. 78 in³ 113. 04 in³ baseball with diameter of 3 inches.
The best approximation for the volume of a regulation baseball with a diameter of about 3 inches is 14 in³.
The volume of a sphere is given by the formula V = (4/3)πr³, where V represents the volume and r represents the radius. In this case, we have the diameter, which is 2 times the radius.
The radius of a baseball with a diameter of about 3 inches is approximately 3/2 = 1.5 inches.
Substituting the radius into the volume formula:
V = (4/3)π(1.5)³ = (4/3)(3.14)(1.5)³ = (4/3)(3.14)(3.375) ≈ 14 in³
Therefore, the best approximation for the volume of the baseball is 14 in³.
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Three minus eleven times a number is more than twenty one minus five times the number (show work)
The solution to the equation is x is less than 1.
Let's assume the number as "x".
The given statement can be translated into an equation as follows:
3 - 11x > 21 - 5x
To solve this equation, we can start by simplifying both sides:
3 - 11x > 21 - 5x
Next, let's gather the terms with x on one side and the constant terms on the other side by adding 11x and subtracting 21 from both sides:
3 - 11x + 11x - 5x > 21 - 5x + 11x - 21
Simplifying further, we get:
-16x > -x
Now, we can divide both sides by -16, but since we are dividing by a negative number, we need to reverse the inequality sign:
-16x / -16 < -x / -16
x < 1
Therefore, the solution to the equation is x is less than 1.
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Write it as a fact family
12. 4-3. 2=9. 2
The fact family 12, 4, 3, 2, and 9 demonstrates the relationship between addition and subtraction. In this fact family, when we subtract 3 from 4, the result is 1. If we then add 2 to 1, we get 3. Furthermore, when we subtract 2 from 9, the result is 7. If we add 7 and 2 together, the sum is 9.
In the given fact family, the numbers 4 and 3 are related through subtraction. When we subtract 3 from 4, we get 1. This is represented by the equation 4 - 3 = 1.
On the other hand, the numbers 2 and 1 are related through addition. If we add 2 to 1, the sum is 3. This is represented by the equation 1 + 2 = 3.
Similarly, the numbers 9 and 2 are related through subtraction and addition. When we subtract 2 from 9, we get 7, represented by the equation 9 - 2 = 7. By adding 7 and 2 together, the sum is 9, represented by the equation 7 + 2 = 9.
Therefore, the fact family 12, 4, 3, 2, and 9 demonstrates the relationship between addition and subtraction within the given numbers.
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Does the table represent a function? Why or why not?
xy
3 1
4 3
5 2
6 5
6 6
A. Yes, because every x-value corresponds to exactly one y-value.
B. No, because one x-value corresponds to two different y-values.
C. Yes, because there are different y-values.
D. No, because the y-values are positive.
Option A, "Yes, because every x-value corresponds to exactly one y-value," accurately describes the situation presented in the table. Option A is the proper response, so.
The table represents a function.
A mathematical relationship known as a function is one in which every input (x-value) has exactly one corresponding output (y-value). In the given table:
xy
3 1
4 3
5 2
6 5
6 6
Every x-value in the table corresponds to exactly one y-value. There are no repeated x-values, and for each x-value, there is only one corresponding y-value. The definition of a function is met by this.
The answer given in Option A, "Yes, because every x-value corresponds to exactly one y-value," appropriately sums up the situation shown in the table. Option A is the proper response, so.
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D. If y/z = 0. 7, what is the measure of α to the nearest degree?
If y/z = 0.7, then α can be determined using the trigonometric ratio "tan".
Since y/z = 0.7, we can let y = 7x and z = 10x. Thus, y + z = 7x + 10x = 17x.Also, we have tan α = y/x = (7/10)x/x = 7/10.So, we have tan α = 7/10.Thus, α = tan⁻¹(7/10).
Now, we can use a calculator to evaluate the angle to the nearest degree.
Using a scientific calculator, we can compute tan⁻¹(7/10) ≈ 35.54°.
Hence, the measure of α to the nearest degree is 36° (since we round up to the nearest degree).
That α measures 36° to the nearest degree.
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The scatter plot below shows data that were collected to compare the amount of television a student watched (hours per week ) and his or her GPA
A reasonable correlation coefficient for these data would be
The scatter plot shows a comparison between the amount of television watched by students (in hours per week) and their GPA. a reasonable correlation coefficient for these data would be close to 0, indicating a weak or negligible correlation.
Based on the scatter plot, we can observe the general trend of the data points. If the points on the plot are more closely clustered around a straight line, it indicates a stronger correlation between the two variables. Conversely, if the points are more spread out and do not follow a clear pattern, it suggests a weaker correlation. To determine the correlation coefficient, we need to assess the direction and strength of the relationship.
If the data points on the scatter plot exhibit a clear upward or downward trend, it indicates a positive or negative correlation, respectively. The correlation coefficient ranges between -1 and 1, with values closer to -1 or 1 indicating a stronger correlation. A correlation coefficient of 0 indicates no linear relationship. Given that the scatter plot does not show a clear pattern or trend, it suggests a weak or no correlation between the amount of television watched and GPA. Therefore, a reasonable correlation coefficient for these data would be close to 0, indicating a weak or negligible correlation.
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Which triangle is a translation of triangle X?
On a coordinate plane, triangle X is shifted 3 units down and 4 units to the left to form triangle B.
Triangle B is a translation of triangle X.
What is translation?
The term "translation" refers to the movement of an object from one position to another. The object being translated is the same size and shape as it was before being moved. It is merely moved to a new location. Each point on the object is moved the same distance and in the same direction, resulting in a new figure that is similar to the original.
Let's find out which triangle is a translation of triangle X.
Given that Triangle X is moved 3 units down and 4 units to the left to create triangle B. We can figure out that triangle B is the translated version of triangle X.
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Which histogram depicts a higher standard deviation.
Histograms visualize the distribution and spread of data. A higher standard deviation implies greater variability in the data points. In a histogram, a wider shape indicates a larger spread of data and thus a higher standard deviation. Therefore, the histogram with a broader shape depicts a higher standard deviation.
To determine which histogram depicts a higher standard deviation, we need to look for the histogram with a greater spread or dispersion of data. In a histogram, a higher standard deviation indicates that the data points are more spread out or have a larger variability. This means that the values are more scattered from the mean. Therefore, the histogram with a wider and more spread-out shape would depict a higher standard deviation, as it indicates a greater variability in the data.
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A subwoofer box for sound costs $260. 40 after a price increase. The cost before the price increase was $240. 0. What was the approximate percent of the price increase
Will be awarded brainliest :) PLS HELPP
The approximate percent of the price increase is approximately 8.5%. To find the approximate percent of the price increase, we can use the following formula: Percent Increase = ((New Value - Old Value) / Old Value) * 100
To calculate the approximate percent of the price increase, we can follow these steps:
Determine the old value: In this case, the old value is the cost before the price increase, which is given as $240.0.
Determine the new value: The new value is the cost after the price increase, which is given as $260.40. Calculate the difference: Subtract the old value from the new value to find the increase in price. In this case, it is $260.40 - $240.0 = $20.40.
Calculate the percent increase: Divide the difference by the old value, then multiply by 100 to express it as a percentage. In this case, it is (20.40 / 240.0) * 100 ≈ 8.5%.
Therefore, the approximate percent of the price increase is approximately 8.5%. This means that the price increased by around 8.5% from its original value of $240.0 to the new value of $260.40.
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Jen is a member of their school’s women soccer club. She noticed that the angle formed at the corner of the soccer field was similar to her lesson in Math that morning. Which type of angle is it?
An angle is a geometric figure formed by two rays or lines that share a common endpoint called the vertex.
If Jen noticed that the angle formed at the corner of the soccer field was similar to her math lesson, we can explore the different types of angles she might be referring to.
Right Angle: A right angle measures exactly 90 degrees and forms a square corner. It is a common angle found in everyday life, such as the corners of buildings or the intersection of two perpendicular lines. Right angles are often studied in geometry due to their properties and applications in various mathematical concepts.
Acute Angle: An acute angle measures less than 90 degrees. It is a smaller angle that appears sharp and pointed. Examples of acute angles can be found in triangles, where all three angles are acute.
Obtuse Angle: An obtuse angle measures more than 90 degrees but less than 180 degrees. It is a wider angle that appears larger and open. Examples of obtuse angles can be found in shapes like rectangles or triangles with one angle greater than 90 degrees.
Straight Angle: A straight angle measures exactly 180 degrees, forming a straight line. It is a flat angle that doesn't bend or deviate. Straight angles are commonly found in line segments or in shapes like straight edges of polygons.
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Mark wants to buy a video game for $39.99, he has a 30% discount and then pays 5% sales tax. What is the final cost of the video game?
Given the cost of the video game is $39.99, Mark gets a discount of 30%.Content loaded means there's enough information available to solve the problem. Here's how to find out the final cost of the video game. First, calculate the discount on the cost of the video game:$39.99 × 30/100 = $11.997
This gives us the discount that Mark gets on the video game. So, the cost of the video game after discount will be: Cost of the video game = $39.99 - $11.997 = $27.993Now, let's add the sales tax. The sales tax is 5%. Thus, the sales tax will be: Sales tax = $27.993 × 5/100 = $1.39965So, the final cost of the video game will be :Final cost = $27.993 + $1.39965 = $29.39265Thus, the final cost of the video game after the discount and the sales tax is $29.39.
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On Monday, you bought 4 cheeseburgers and 6 fries for $62. Tuesday, you bought 7 cheeseburgers and 4 fries for $76. What is the cost of a (cheeseburger, fry)?
The cost of cheeseburgers = $4
And, The cost of fries = $5
We have,
On Monday, you bought 4 cheeseburgers and 6 fries for $62.
And, On Tuesday, you bought 7 cheeseburgers and 4 fries for $76.
Let us assume that,
The cost of cheeseburgers = x
And, The cost of fries = y
Hence, We get;
4x + 6y = 62 .. (i)
7x + 4y = 76 .. (ii)
From (i);
4x + 6y = 62
2x + 3y = 31 .. (iii)
Multiply by 2 in (ii) and multiply 7 in (iii), then subtract,
8y - 21y = 152 - 217
- 13y = - 65
y = 5
From (i);
4x + 3 (5) = 31
4x + 15 = 31
4x = 31 - 15
4x = 16
x = 4
Thus, The cost of cheeseburgers = $4
And, The cost of fries = $5
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Molly has biweekly gross earnings of $839. 52. By claiming 1 more withholding allowance, Molly would have $16 more in her take home pay. How many withholding allowances does Molly currently claim? a. 1 b. 2 c. 3 d. 4 Please select the best answer from the choices provided A B C D.
Molly currently claims 2 withholding allowances which can be determined by using rules of allowance.
Given that,
Molly has biweekly gross earnings of $839. 52.
By claiming 1 more withholding allowance,
Molly would have $16 more in her take-home pay.
We have to determine,
How many withholding allowances does Molly currently claim?
According to the question,
Molly has biweekly gross earnings of $839. 52.
By claiming 1 more withholding allowance,
Molly would have $16 more in her take-home pay.
The withholding allowance is used by a person to pay less amount of tax on his or her income to the government.
Molly has biweekly gross earnings of $839. 52.
By claiming 1 more withholding allowance,
Molly would have $16 more in her take-home pay.
Therefore,
It is given that Molly has taken 1 more withholding allowance to pay tax less by the amount of $16.
So he must have possessed at least 1 allowance previously and added 1 more.
So, the minimum number of allowance possessed by Molly = 2
Hence, Molly currently claims 2 withholding allowances.
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Elizabeth’s credit card computes her finance charges using the previous balance method and a 30-day billing cycle. The table below shows Elizabeth’s credit card transactions in July. Date Amount ($) Transaction 7/1 969. 26 Beginning balance 7/3 45. 00 Payment 7/10 67. 48 Purchase 7/12 20. 00 Payment 7/28 85. 00 Payment If Elizabeth has an APR of 14. 61%, how much will her July finance charge be? a. $9. 97 b. $12. 62 c. $11. 80 d. $10. 80.
To calculate Elizabeth's finance charge using the previous balance method, we need to determine the average daily balance and then apply the APR (Annual Percentage Rate) to calculate the finance charge.
First, let's calculate the average daily balance:
Beginning Balance: $969.26
Days until payment: 2 (from July 1st to July 3rd)
Payment: $45.00
Days until purchase: 7 (from July 3rd to July 10th)
Purchase: $67.48
Days until payment: 2 (from July 10th to July 12th)
Payment: $20.00
Days until payment: 16 (from July 12th to July 28th)
Payment: $85.00
To calculate the average daily balance, we sum up the balances for each day and divide it by the total number of days in the billing cycle (30 days).
Average Daily Balance = (969.26 × 2 + 0 × 7 + 67.48 × 2 + 0 × 16) / 30 = $85.95
Next, we can calculate the finance charge using the APR:
Finance Charge = Average Daily Balance × (APR / 365) × Number of Days in the Billing Cycle
Finance Charge = 85.95 × (0.1461 / 365) × 30 ≈ $9.97
Therefore, Elizabeth's July finance charge will be approximately $9.97. The correct answer is option a.
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The perimeter of a rectangle is 22cm and the length of each side is a natural number. How many different areas in centimeter squared can the rectangle have?
option B is the correct answer.
The perimeter of a rectangle is 22 cmLet the length of the rectangle be 'l' and the breadth be 'b'As per the question, the perimeter of the rectangle is given by;Perimeter = 2(l + b) => 2(l + b) = 22 => l + b = 11.As we know that the area of a rectangle is given by;Area = l × b
Therefore, the different areas of the rectangle are; l × b1 × (11 - 1) = 10 cm²2 × (11 - 2) = 18 cm²3 × (11 - 3) = 24 cm²4 × (11 - 4) = 28 cm²5 × (11 - 5) = 30 cm²6 × (11 - 6) = 30 cm²7 × (11 - 7) = 28 cm²8 × (11 - 8) = 24 cm²9 × (11 - 9) = 18 cm²10 × (11 - 10) = 10 cm²Hence, there are only 8 different areas of the rectangle i.e., 10 cm², 18 cm², 24 cm², 28 cm², 30 cm².
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1. Use each of the Numbers once, In any order. To form at least TWO number sentences that equal the target number
TARGET NUMBER: 2
17, 5, 8, 2, 9
2. Let A=3 B=28 C=50
D=12 E=2 F=18
Write a minimum of 5 different
relationship statements for the
variables.
Ex. DE=B-2E
Using 17 + 5 - 8 + 9 - 2 = 21 and 2 + 9 - 8 + 17 - 5 = 15 as two number sentences, we can form the target number of 2.
1) 2C = BF
2) B - 3E = A
3) C - A = 2D
4) F - A + B = 47
5) 3E - B + 2A = 8
In the first statement, the variable C is multiplied by 2, and the result is equal to the product of variables B and F. In the second statement, the product of variables E and 3 is subtracted from B, and the result is equal to A.
In the third statement, the difference between variables C and A is equal to twice the value of variable D. In the fourth statement, the sum of variables F and B is subtracted from A, and the result is equal to 47.
In the fifth statement, twice the value of variable A is added to 3 times the value of variable E, and this sum is subtracted from the value of variable B, which gives 8.
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What is the explicit formula for the sequence below?4, – 12, 36, – 108,...A.tn=(−3)n−1B.tn=4(−3)n−1C.tn=4(3)n−1D.tn=4(−3)n
The explicit formula for the given sequence 4, -12, 36, -108,... is D. tn = 4(-3)n. Option D
In the given sequence, each term is obtained by multiplying the previous term by -3. This indicates an exponential decay pattern with a common ratio of -3.
To derive the explicit formula, we start with the initial term 4 and observe that each subsequent term can be obtained by multiplying the previous term by -3:
Term 1: 4
Term 2: -3 × 4 = -12
Term 3: -3 ×(-12) = 36
Term 4: -3 × 36 = -108
We can generalize this pattern by using the formula tn = ar^(n-1), where tn represents the nth term, a is the initial term, and r is the common ratio. In this case, a = 4 and r = -3. Thus, the explicit formula for the sequence is tn = 4(-3)n which matches option D.
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