Answers
The length of the shaded arc is 68.71 metres squared.
How to find the length of an arc?The arc of a circle is defined as the part or segment of the circumference of a circle. Therefore, the length of the bolded arc can be found as follows:
length of an arc = ∅ / 360 × 2πr
where
r = radius∅ = central angleTherefore,
r = 26 / 2 = 13 m
∅ = 360 - 57 = 303 degrees
length of an arc = 303 / 360 × 2 × 3.14 × 13
length of an arc = 24736.92 / 360
length of an arc = 68.7136666667
length of an arc = 68.71 metres squared
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Related Questions
Find the following percentiles for the standard normal distribution. Interpolate where appropriate. (Round two decimal places.) (a) 61 st (b) 39 th (c) 75th (d) 25th (e) 15th
Answers
Finding the following percentiles for the standard normal distribution
a) P₁(61st percentile)
b) P₂(39th percentile)
c) P₃(75th percentile)
d) P₄(25th percentile)
e) P₅(15th percentile)
First of all, let's find the Z score of these percentiles with the help of the table below:
Z tableimage0.265 / 0.04 = 6.625.
This is greater than the maximum value in the table; hence we can consider it as 6.55.
P₁: When percentile is 61, z value is 0.42.
The formula to calculate percentile is as follows:
Percentile = Area to the left of Z score * 1000.42
= Area to the left of Z score * 1000.42 / 100
= Area to the left of Z score0.1664 (area to the left of Z score) + 0.5 = 0.6664 (area to the left of Z score)
P₁ = 66.64% P₂: When percentile is 39, z value is -0.26.
The formula to calculate percentile is as follows:
Percentile = Area to the left of Z score * 100-0.26
= Area to the left of Z score * 100-0.26 / 100
= Area to the left of Z score0.3950 (area to the left of Z score) + 0.5 = 0.8950 (area to the left of Z score)
P₂ = 89.50% P₃: When percentile is 75, z value is 0.68.
The formula to calculate percentile is as follows:
Percentile = Area to the left of Z score * 1000.68
= Area to the left of Z score * 1000.68 / 100
= Area to the left of Z score0.2486 (area to the left of Z score) + 0.5 = 0.7486 (area to the left of Z score)
P₃ = 74.86% P₄: When percentile is 25, z value is -0.68.
The formula to calculate percentile is as follows:
Percentile = Area to the left of Z score * 100-0.68
= Area to the left of Z score * 100-0.68 / 100
= Area to the left of Z score0.2486 (area to the left of Z score) + 0.5 = 0.7486 (area to the left of Z score)
P₄ = 25.14% P₅: When percentile is 15, z value is -1.04.
The formula to calculate percentile is as follows:
Percentile = Area to the left of Z score * 100-1.04
= Area to the left of Z score * 100-1.04 / 100
= Area to the left of Z score0.1492 (area to the left of Z score) + 0.5 = 0.6492 (area to the left of Z score)
P₅ = 64.92%.
Hence, we have found the percentiles of standard normal distribution for the given questions.
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What is 268.8 divided by 56 using long division method ASAP
Answers
= 0.20833333333333
In a large consumer survey, 610 randomly selected customers are interviewed in a large grocery store. They are asked, among other things, how much they have shopped for. On average, they have shopped for 412 SEK with a standard deviation of 181 SEK . Estimate with a 95% confidence interval the average purchase amount in the entire population.
Answer only with the statistical margin of error.
Answers
On the arranged survey, the statistical margin of error is supposed to be 14.73 SEK.
In a large consumer survey, 610 randomly selected customers are interviewed in a large grocery store. They are asked, among other things, how much they have shopped for. On average, they have shopped for 412 SEK with a standard deviation of 181 SEK .
Estimate with a 95% confidence interval the average purchase amount in the entire population. The formula for finding the margin of error is given as;
Margin of Error = z * (σ/√n)
Where:
σ is the standard deviation
n is the sample size
z is the Z-score for the desired confidence level, which is 95%.
Z-score corresponding to 95% confidence level is 1.96
Margin of Error = 1.96 * (181/√610) = 14.73
The statistical margin of error is 14.73 SEK.
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You fill up your gas tank in France where the gas price is $1.54 per liter. If your rental car gets 29 miles per gallon, how much will it cost to drive 225 miles? (to the nearest cent)
this is conversion math
Answers
It would cost approximately $45.14 to drive 225 miles in a rental car that gets 29 miles per gallon.
What is Rate?
A rate in arithmetic is a ratio that contrasts two separate values with various unit systems. For instance, if John types 50 words per minute, that means he types 50 words per minute. We are dealing with a rate because the word "per" is there. The symbol "/" can be used in place of the word "per" in issues.
When two or more similar amounts or numbers are being compared using the same units, a ratio is utilized. When referring to the ratio of one quantity "to" the second quantity in spoken language, it is frequently written with a colon.
First, we convert the gas price from liters to gallons. One liter is equal to 0.264172 gallons, so:
$1.54 per liter = $1.54 / 0.264172 gallons = $5.82 per gallon
Next, we need to calculate how many gallons of gas are needed to drive 225 miles. If the car gets 29 miles per gallon, we can calculate the gallons of gas needed as:
225 miles / 29 miles per gallon = 7.7586 gallons
Finally, we can calculate the total cost of gas as:
Total cost = gallons of gas needed x gas price per gallon
Total cost = 7.7586 gallons x $5.82 per gallon
Total cost = $45.14
Therefore, it would cost approximately $45.14 to drive 225 miles in a rental car that gets 29 miles per gallon, assuming a gas price of $1.54 per liter in France.
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the number of guests at a theme park can be modeled by function p(t) where t is measured in hours. p is a solution to the logistic differential equation dp over dt equals p over 3 minus p squared over 60000 comma where p(0)
Answers
The number of guests at a theme park can be modeled by the function p(t), where t is measured in hours and p is the number of guests. The function p(t) is a solution to the logistic differential equation.
The formula for logistic differential equation is dp/dt = p/3 - p^2/60000. This equation models the rate of change of the number of guests at the theme park over time.
To find the solution to this equation, we can use separation of variables. First, we can rearrange the equation to get:
dp/(p/3 - p^2/60000) = dt
Next, we can integrate both sides of the equation to get:
∫dp/(p/3 - p^2/60000) = ∫dt
Using partial fraction decomposition, we can rewrite the integral on the left-hand side of the equation as:
∫(3/60000)/(1 - 3p/60000)dp = ∫dt
Integrating both sides of the equation gives us:
-20000ln|1 - 3p/60000| = t + C
Solving for p gives us:
1 - 3p/60000 = Ce^(-t/20000)
3p/60000 = 1 - Ce^(-t/20000)
p(t) = 20000 - (20000C)e^(-t/20000)
To find the value of C, we can use the initial condition p(0) = p0:
p0 = 20000 - 20000C
C = (20000 - p0)/20000
Substituting this value of C back into the equation for p(t) gives us the solution:
p(t) = 20000 - (20000 - p0)e^(-t/20000)
This is the solution to the logistic differential equation that models the number of guests at a theme park over time.
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Mary leaves a campsite and walks 4 miles east and 2 miles south. Her friend walks 3 miles north and 1 mile west. How far apart is Mary from her friend?
Answers
If Mary leaves a campsite and walks 4 miles east and 2 miles south and Her friend walks 3 miles north and 1 mile west then Mary and her friend are approximately 5.83 miles apart.
We can use the Pythagorean theorem to find the distance between Mary and her friend. We'll need to create a right-angled triangle with the two walks forming the legs of the triangle.
Mary walks 4 miles east and 2 miles south, so she moves 4 units to the right (east) and 2 units down (south).
Her friend walks 3 miles north and 1 mile west, so she moves 3 units up (north) and 1 unit to the left (west).
We can see that the two walks form a right-angled triangle. The distance between Mary and her friend is the hypotenuse of this triangle.
Let's calculate the length of each leg of the triangle:
The length of the horizontal leg is 4 - 1 = 3 miles (Mary moves 4 miles to the right and her friend moves 1 mile to the left).
The length of the vertical leg is 2 + 3 = 5 miles (Mary moves 2 miles down and her friend moves 3 miles up).
Now, we can use the Pythagorean theorem:
distance² = 3² + 5²
distance² = 9 + 25
distance² = 34
distance = √(34)
≈ 5.83 miles
Therefore, Mary and her friend are approximately 5.83 miles apart.
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Lucy spent 2/4 of an hour riding her bike. She then spent 3 3/4
of an hour break playing video games. How much did she spend playing video games and riding a bike
Answers
Answer:
Javier has $5. He sells a video game on an online auction site for $100. He must pay a $16 fee to the auction site. Javier then splits the. Not sure
Step-by-step explanation:
Urgent Help Needed
Show all work,
Answers
The tοtal area οf the shape cοmprising the rectangle and semicircle is apprοximately 2153.43 square feet.
What is Area?Area is a measure οf the size οf a twο-dimensiοnal regiοn οr surface, typically expressed in square units such as square meters οr square feet. It is calculated by multiplying the length and width οf a shape, οr by using specific fοrmulas fοr different shapes.
The area οf a rectangle with sides 30' and 60' is given by multiplying the length and width, sο:
Area οf rectangle = length × width
Area οf rectangle = 30' × 60'
Area οf rectangle = 1800 square feet
The area οf a semicircle with radius 15' can be fοund by first calculating the area οf a full circle with radius 15' and then dividing by 2, since a semicircle is half οf a circle. The fοrmula fοr the area οf a circle is:
Area οf circle = π × radius²
Substituting the value οf the radius intο the fοrmula, we get:
Area οf circle = π × 15²
Area οf circle = π × 225
Area οf circle ≈ 706.86 square feet
Therefοre, the area οf the semicircle is apprοximately:
Area οf semicircle = (1/2) × Area οf circle
Area οf semicircle ≈ (1/2) × 706.86
Area οf semicircle ≈ 353.43 square feet
The tοtal area οf the shape cοmprising the rectangle and semicircle is the sum οf the areas οf the twο shapes, sο:
Tοtal area = Area οf rectangle + Area οf semicircle
Tοtal area = 1800 + 353.43
Tοtal area ≈ 2153.43 square feet
Therefοre, the tοtal area οf the shape cοmprising the rectangle and semicircle is apprοximately 2153.43 square feet.
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Based on the family the graph below belongs to, which equation could represent the graph?
On a coordinate plane, a curve opens up and to the right. It crosses the x-axis at (negative 1.5, 0) and then crosses the y-axis at (0, negative 1).
y = 0.6 Superscript x Baseline minus 2
y = 0.6 x squared minus 1
y = negative 0.6 x cubed minus 1
y = log (x) minus 2
Answers
Answer:A. y = 0.6^x - 2
Step-by-step explanation:
This was something I put in and It worked fine. Hope this helps. If you want more help, check out Khan Academy.
From the graph, the equation that's is represented is A. 0.6x - 2.
How to illustrate the graph?
From the equation, on the coordinate plane, the curve opens up and to the right. It crosses the x-axis at (negative 1.5, 0) and then crosses the y-axis at (0, negative 1).
Here, based on the family the graph below belongs to, the equation represented is the first equation which is 0.6x - 2.
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In circle F with m< EFG =30 and EF =11 units, find the length of arc EG. Round to the nearest hundredth
Answers
The required length of the arc is 5.75 units.
What are circle and arc?A circular represents 360 degrees. A circular can be split up into smaller sections. An arc is a segment of a circle, and arcs are designated based on their angles. The three types of arcs are semicircles (v = 180°), major arcs (180° v 360°), and minor arcs (0° v 180°).
According to question:We have;
∠EFG =30° = π/6
and EF =11 units
To find; length of arc EG.
So, we know that;
∅(Radian) = arc/ radius
π/6 = arc/11
arc = 11π/6
Arc = 5.75 units.
Thus, required length of the arc is 5.75 units.
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Complete question:
question jordan wondered if the bean burritos at restaurant a tend to be heavier than bean burritos at restaurant b. to investigate, she visited each restaurant at 10 randomly selected times, ordered a bean burrito, and weighed the burrito. the 95% confidence interval for the difference (a - b) in the mean weight of the burrito is 0.06 ounce 0.20 ounce. based on the confidence interval, which conclusion is most appropriate?
Answers
The conclusion of question as discuss below.
Define the term mean?The mean is a measure of central tendency that represents the average value of a set of numbers. It is calculated by adding up all the values in the set and then dividing by the total number of values.
Based on the given information, we can say that there is a 95% chance that the true difference (a - b) in the mean weight of the bean burritos between Restaurant A and Restaurant B falls within the interval 0.06 ounce to 0.20 ounce.
Since the confidence interval does not include zero, we can conclude that there is a statistically significant difference between the mean weights of the bean burritos at the two restaurants. Specifically, we can say that the mean weight of the bean burritos at Restaurant A is likely to be heavier than the mean weight of the bean burritos at Restaurant B.
However, it's important to note that we cannot determine the magnitude of the difference or the direction of causation (i.e., whether Restaurant A intentionally makes their burritos heavier or whether they use different ingredients that naturally result in heavier burritos).
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We can infer that there is a statistically significant difference among the mean weights of the bean burritos at the two eateries because the confidence interval does not include zero.
Define the term mean?The mean, which reflects the average value of a group of numbers, is a metric of central tendency. It can be calculated by adding up all of the values in the collection, dividing by the total number of values, and then taking the remainder away.
Based on the information provided, we can state that there is a 95% chance that the actual difference (a - b) between Restaurant A and
Restaurant B's mean weight of the bean burritos will lie between 0.06 ounce and 0.20 ounce.
We can infer that there is a statistically significant variance among the mean weights of the bean burritos at the two eateries because the confidence interval does not include zero. We can specifically state that the bean burritos' average weight at Restaurant A is probably heavier than the average bean burrito's weight at Restaurant B.
It's crucial to remember that we cannot establish the size of the difference or the causal relationship. (i.e., whether Restaurant A intentionally makes their burritos heavier or whether they use different ingredients that naturally result in heavier burritos).
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Pat has a pen pal in England. When Pat asked how tall his pen pal was he replied, 1. 27 meters. If 1 inch is 2. 54 cm, how tall is Pat’s pen pal in feet and inches?
Answers
The converted height of Pat’s pen pal in feet and inches when it is 1.27 meters tall is given by 4 feet 2 inches.
Height of Pat’s pen pal = 1.27 meters
Convert the height from meters to centimeters,
1 meter = 100 centimeters
Multiply by 100 to convert meters to centimeters we get,
1.27 meters
= 1.27 x 100
= 127 centimeters
Convert the height from centimeters to inches
1 inch = 2.54 centimeters
Divide by 2.54 to convert centimeters to inches we get,
127 centimeters
= 127 centimeters ÷ 2.54
= 50 inches
Convert the total number of inches to feet and inches,
1 feet = 12 inches
Divide by 12 to convert inches to feet and inches we have,
50 inches
= 50 ÷ 12
= with 4 quotient and 2 remainder
= 4 feet 2 inches tall
Therefore, Pat's pen pal is 4 feet and 2 inches tall.
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An isosceles triangle has an angle that measures 54°. What measures are possible for the other two angles? Choose all that apply.
63 34 54 72
Answers
and an isosceles triangle always has 2 angles that are the same
180 - 54 = 126
if we split this equally over 2 angles:
126/2 = 63
THE ANSWER IS 63
A company sold 200 devices in 2007. The company sold 180 devices in 2008. The number of devices that the compnay sales is decreasing exponentially. If this trend continues, How many devices will the company sell in 2012?
Round to the nearest whole number.
Answers
Round to the nearest whole number A company sold 200 devices in 2007.
What is number?Number is a mathematical concept that can be used to represent an amount, value, or quantity. It is an abstract concept that can be used to count, measure, and compare. Numbers can be represented in many different forms such as words or symbols. Numbers are also used in algebra and other mathematical operations, as well as in everyday life.
The company sold 180 devices in 2008. The number of devices that the compnay sales is decreasing exponentially. If this trend continues, How many devices will the company sell in 2012?
Round to the nearest whole number. Based on the trend of the company's sales, it is estimated that the company will sell approximately 140 devices in 2012. This is a decrease of 40 devices from the sales in 2008. This trend is expected to continue into future years due to the exponential decrease in the number of devices sold.
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Rounding to the nearest whole number, the company will sell 75 devices in 2012.
What is number?Number is a mathematical concept that can be used to represent an amount, value, or quantity. It is an abstract concept that can be used to count, measure, and compare. Numbers can be represented in many different forms such as words or symbols. Numbers are also used in algebra and other mathematical operations, as well as in everyday life.
To calculate the number of devices that the company will sell in 2012 using an exponential model, we can use the following equation:
y = 200e(-0.08x)
where y is the number of devices sold, 200 is the number of devices sold in 2007, and 0.08 is the rate of decay per year.
Plugging in x=5 (for 2012), we get:
y = 200e(-0.08×5) = 200e(-0.4) = 74.7
Rounding to the nearest whole number, the company will sell 75 devices in 2012.
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Solve 3-4x<0 or 2x-4>-2 I NEEED HELP PLSSSSS
Answers
After solving the inequalities, the values of x are [x<3/4] and [x>-1] respectively.
What are inequalities?We can learn about the relative size of values via inequality.
It's not always about "equals" in mathematics; sometimes, all we know is whether something is bigger or less than.
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.
The majority of the time, size comparisons between two numbers on the number line are made.
So, solve for x as follows:
3-4x<0
-4x< -3
x = -3/-4
x < 3/4
Similarly,
2x-4>-2
2x>-2+4
2x>2
x>-2/2
x>-1
Therefore, after solving the inequalities, the values of x are [x<3/4] and [x>-1] respectively.
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The height of a satellite above Earth over a certain period of time is described by the function shown.
f(x)=2x2−16x+800
In this function, x = the time in hours and f(x) = the height in kilometers. What is the minimum height of the satellite during this period of time?
Answers
Step-by-step explanation:
To find the minimum height of the satellite during the given time period, we need to find the vertex of the parabolic function f(x) = 2x^2 - 16x + 800.
The vertex of a parabola with equation f(x) = ax^2 + bx + c is given by the formula:
x = -b / 2a and f(x) = -b^2 / 4a + c
In this case, a = 2, b = -16, and c = 800. Substituting these values into the formula, we get:
x = -(-16) / 2(2) = 4
f(x) = -(-16)^2 / 4(2) + 800 = 848
Therefore, the minimum height of the satellite during the given time period is 848 kilometers, and it occurs after 4 hours of flight time.
solve for x in the triangle. round your answer to the nearest tenth.
Answers
Answer:
3.7
Step-by-step explanation:
Hypotenuse is 5
Adjacent is unknown x
Cos 42 = adjacent / hypotenuse
Co's 42 = x/ 5
0.74 = x/5
Multiply both sides by 5
3.7 = x
the figure shown is composed of two parallelograms. find x. justify your answer
Answers
Answer:
to find x u will do : 61+132+x=1290
x=1290-193
x=1097
Which equation is true when x = 3?
Group of answer choices
8x = 28
x - 19 = 16
28 + x = 25
x/3 = 1
Answers
The equation that is true when x is equal to 3 is (x/3) = 1. By substituting the given x value and simplifying the equation we can solve.
What is division?Division is a mathematical operation that is used to split a quantity or value into equal parts or groups. It is one of the four basic arithmetic operations, along with addition, subtraction, and multiplication.
According to question:The equation that is true when x = 3 is:
x/3 = 1
Substituting x = 3, we get:
3/3 = 1
Which is true, since 3 divided by 3 is equal to 1.
The other equations:
8x = 28: If we substitute x = 3, we get 8(3) = 24, which is not equal to 28, so this equation is not true when x = 3.x - 19 = 16: If we substitute x = 3, we get 3 - 19 = -16, which is not equal to 16, so this equation is not true when x = 3.28 + x = 25: If we substitute x = 3, we get 28 + 3 = 31, which is not equal to 25, so this equation is not true when x = 3.To know more about division visit:
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Select all equations that are equivalent to
5 - (6 - 2x) = (3x+4)/2
-1 + 2x = (3x+4)/2
30 - 10x = (3x+4)/2
5-(6 - 2x) = 3/2x+2
5- (6 – 2x) = 3x+4
- 2 + 4x = 3x + 4
Answers
The equations that are equivalent to 5 - (6 - 2x) = (3x+4)/2 are -1 + 2x = (3x+4)/2; and 30 - 10x = (3x+4)/2 .
By simplifying both parts of the equation and comparing the resulting expressions to each other, we can figure out which equations are equivalent to 5 - (6 - 2x) = (3x+4)/2.
5 - (6 - 2x) = (3x+4)/2
5 - 6 + 2x = 3x/2 + 2
2x - 1 = 3x/2 + 2
To get rid of the fraction, multiply both parts by two.
4x - 2 = 3x + 4
Adding 2 to both ends and subtracting 3 times:
x = 6
Let's verify which of the provided equations is equal to x = 6 now.
-1 + 2x = (3x+4)/2, where x = 6 results in:
-1 + 2(6) = (3(6) + 4)/2 \s11 = 11
The initial equation and this one are equivalent, and both are correct.
When we change x to 6, we obtain the following equation: 30 - 10(6) = (3(6) + 4)/2 -30 = -30.
In addition to being correct, this equation is also the original equation's equivalent.
If we substitute 6 for x, we obtain the following equation: 5-(6 - 2(6)) = 3/2(6)+2 1 = 8
This equation is false and does not have the same value as the initial equation.
When we replace x with 6, we obtain the formula 5- (6 - 2(6)) = 3(6)+4
3 = 22
Additionally, this equation is false and is not equal to the initial equation.
2 + 4x = 3x + 4:
When x = 6 is substituted, the result is: -2 + 4(6) = 3(6) + 4 (20) = 22.
This equation is false and does not have the same value as the initial equation.
As a result, the formulae corresponding to 5 - (6 - 2x) = (3x+4)/2 are: -1 + 2x = (3x+4)/2 30 - 10x = (3x+4)/2
A) -1 + 2x = (3x+4)/2; and C) 30 - 10x = (3x+4)/2 are the solutions.
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Carlos tomo 1/5 litros de agua a las 8. 00 am; 3/4 litros de agua a las 12. 12:00 AM. Y7/20 litros de agua a las 5:00 pm. Cuantos litros de agua tomo en total durante el dia
Answers
The total amount of water Carlos drank throughout the day is 2.65 liters.
In order to calculate the total amount of water Carlos drank throughout the day, we must add all the amounts that he drank. The total amount of water Carlos drank during the day is equal to:
1/5 liters + 3/4 liters + 7/20 liters
This can be expressed in fraction form as:
[tex]\frac{19}{20} + \frac{27}{20} + \frac{7}{20} = \frac{53}{20}[/tex]
= 2.65 liters
Therefore, Carlos drank a total of 2.65 liters of water throughout the day.
To calculate this, we can use the addition of fractions formula. This formula states that to add two fractions, we must find the least common denominator of the two fractions, and then add the numerators of the two fractions.
In this case, the least common denominator of the three fractions is 20. This is because all three fractions have a denominator of 20, and 20 is the smallest number that can be divided by both 5 and 4.
Once we have the least common denominator, we can add the numerators of the fractions. For the first fraction, 1/5, the numerator would be 1, for the second fraction, 3/4, the numerator would be 3, and for the third fraction, 7/20, the numerator would be 7.
Therefore, the addition of fractions formula would look like this:
[tex]\frac{1 + 3 + 7}{20}\\\\ = \frac{11}{20}\\\\ = 2.65 liters[/tex]
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Type your answers into the boxes. Complete the following questions. 4+7 x6= 12 + 9 x3 -1 =
Answers
4 + 7×6 = 4 + 42 = 46
12 + 9×3 - 1 = 12 + 27 - 1 =39 - 1 = 38
Please ASAP Help
Will mark brainlest due at 12:00
Answers
Answer: (-6,-4)
Step-by-step explanation:
Midpoint formula
(x,y) midpoint= ((x1+x2)/2, (y1+y2)/2)
X: (0-12)/2=-6
Y: (0-8)/2=-4
(-6,-4)
Answer:
A
Step-by-step explanation:
lucky for u, finding the midpoint is really easy to learn and master
alright so first you take a look at both points. we got:
- (0,0)
- (12,8)
we need to add the x coordinates
0+12 = 12
then divide by 2
12/2 = 6
6 the x coordinate for our segment midpoint
now we need to add the y coordinates
0+8 = 8
divide by 2
8/2 = 4
4 is the y coordinate for our segment midpoint
How now we combine the x value and y value to create a coordinate:
(6,4)
That matches choice A
please help will give brainistFor two programs that total 1073 students, the type of student for two majors is as follows. Undergraduate Graduate History Science 390 422 73 188 Find the probability a student is a science major, given they are a graduate student. P(AnB) P(B|A) = P(A) P(science | graduate) = [?] Round to the nearest hundredth. I Enter
Answers
The probability that a student is a science major, given they are a graduate student is given as follows:
P(science|graduate) = 0.7203 = 72.03%.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The outcomes for this problem are given as follows:
Desired outcomes: graduate science students -> 188 from the table.Total outcomes: graduate students: 73 + 188 = 261 students.Hence the probability that a student is a science major, given they are a graduate student is obtained as follows:
P(science|graduate) = 188/261
P(science|graduate) = 0.7203 = 72.03%.
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Answer:
0.72
Step-by-step explanation:
describe the complement of the given event. 71% of a person's credit card purchases are seventy dollars or more.
Answers
The complement of the given event is that 29% of the person's credit card purchases are less than seventy dollars.
To describe the complement of the given event, we need to first understand what complement means in probability theory. The complement of an event is the set of outcomes that are not included in the event.
So, the given event is that 71% of a person's credit card purchases are seventy dollars or more. This means that 100% - 71% = 29% of the person's credit card purchases are less than seventy dollars. This is the complement of the given event.
Hence, the complement of the given event is that 29% of the person's credit card purchases are less than seventy dollars.
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Find the first 4 terms of the infinite geometric series if
S=33/4
r=1/3
Answers
The first four terms of the infinite geometric series are 11/2, 11/6, 11/18, and 11/54.
What are the first 4 terms of the infinite geometric series?We can use the formula for the sum of an infinite geometric series to find the value of the first term:
S = a / (1 - r)
Where S is the sum of the infinite geometric series, a is the first term, and r is the common ratio.
Given that:
S=33/4
r=1/3
Substituting the given values:
33/4 = a / (1 - 1/3)
33/4 = a / (2/3)
a = (33/4) × (2/3) = 11/2
Now that we know the first term, we can use the formula for the nth term of a geometric series to find the first four terms:
an = a × r^(n-1)
Where an is the nth term, a is the first term, r is the common ratio, and n is the number of the term we want to find.
So the first four terms are:
a1 = 11/2
a2 = 11/2 × 1/3 = 11/6
a3 = 11/6 × 1/3 = 11/18
a4 = 11/18 × 1/3 = 11/54
Therefore, the first four terms are 11/2, 11/6, 11/18, and 11/54.
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56 is 69% of what number? Round your answer to the nearest hundredth if necessary.
Incorrect answer:124
Answers
Answer:
Approximately 81.159
Step-by-step explanation:
First, set up the equation
56 = (0.69)(x)
^ is 69% of a number
Divide each side by 0.69 to simplify
56 / 0.69 = x
x ≈ 81.159420...
How do I solve this, steps please!
2(x-1)(x+1) / x^2 -x-20
Answers
The expressiοn 2(x-1)(x+1)/(-x-20) can be written as 2(x+1)/(x-5).
What is Algebraic expressiοn ?Algebraic expressiοn can be defined as cοmbinatiοn οf variables and cοnstants.
Tο simplify the expressiοn 2(x-1)(x+1)/(-x-20), yοu can fοllοw these steps,
Factοr the denοminatοr, (-x-20), tο get (x-5)(x+4).
Rewrite the numeratοr as 2(-1).
Substitute the factοred denοminatοr frοm step 1 intο the expressiοn, giving 2(-1)/[(x-5)(x+4)].
Factοr the numeratοr, 2(x-1)(x+1), and cancel οut the cοmmοn factοr οf (x-1) frοm the numeratοr and denοminatοr.
sο we get as, The final simplified expressiοn is 2(x+1)/(x-5).
Therefοre, The final simplified expressiοn is 2(x+1)/(x-5).
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We can describe 12x - 8 as an expression. It can also be written as 4(3x– 2) 4 and 3x–2 are both of 12x-8
Answers
Hence, in respοnse tο the prοvided questiοn, we can say that 12x - 8 can functiοn be factοred οut as 4(3x - 2), where 4 is a cοmmοn factοr οf 12 and 8, and (3x - 2) is the expressiοn that remains after factοring οut 4.
What is functiοn?Mathematicians research numbers and their variants, equatiοn and related structures, οbjects and their lοcatiοns, and prοspective lοcatiοns fοr these things. The term "mοdule" is used tο describe the cοnnectiοn that exists in between set οf inputs, each οf which has a cοrrespοnding οutput. A functiοn is an input-οutput cοnnectiοn in which each inputs results in sοmething like a single, distinct return. A dοmain, cοdοmain, οr scοpe is assigned tο each functiοn. Functiοns are usually denοted by the letter f. (x). An x is used fοr entry. On capabilities, οne-tο-οne capabilities, multiple prοwess, in capabilities, and οn capabilities are the fοur majοr types οf accessible functiοns.
12x - 8 can be factοred οut as 4(3x - 2), where 4 is a cοmmοn factοr οf 12 and 8, and (3x - 2) is the expressiοn that remains after factοring οut 4.
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Complete question:
We can describe 12x-8 as an expression.
It can also be written as 4(3x-2)
4(3x-2) is a ___ of 12x-8.
What is the blank?
Steve is buying meat for a barbecue. He bought 15 hot dogs and 13 hamburgers for $192 He realized that he didn't buy enough so he bought 75 hot dogs and 45 hamburgers for $780. How much is 1 hot dog or one hamburger
Answers
1 hot dog costs amount $8.00 and 1 hamburger costs $10.80.
Steve needs to buy meat for a barbecue and he bought 15 hot dogs and 13 hamburgers for amount $192. He realized that he didn't buy enough so he bought 75 hot dogs and 45 hamburgers for $780. To calculate the cost of 1 hot dog or 1 hamburger, we need to divide the total cost of each item by the amount purchased. For the hot dogs, we divide $780 by 75, which gives us $8.00. For the hamburgers, we divide $780 by 45, which gives us $10.80. Therefore, the cost of 1 hot dog or 1 hamburger is $8.00 and $10.80 respectively.
Hot Dogs : ($192 + $780) / (15 + 75) = $8.00
Hamburgers : ($192 + $780) / (13 + 45) = $10.80
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