The volume of the original candy bar box can be found by using the formula for the volume of a triangular prism, which is V = (1/2)bh times the height. Since the base of the triangular prism has sides of 1.5 inches, we can use this to calculate the base area, which is (1/2)(1.5)(1.5) = 1.125 square inches.
The height of the original box is 8 inches, so the volume can be calculated as V = (1.125)(8) = 9 cubic inches.
For the new candy bar box, the length of each side of the triangular base is doubled to 3 inches, while the length of the prism is halved to 4 inches. Using the same formula for the volume of a triangular prism, the base area is now (1/2)(3)(3) = 4.5 square inches. The height of the new box is 4 inches, so the volume can be calculated as V = (4.5)(4) = 18 cubic inches.
Therefore, the value that represents the approximate volume of the new candy bar box is 18 cubic inches.
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A basket contains 8 green apples, 11 red apples, 5 nectarines, and 12 oranges. Akhil takes a piece of fruit, eats it,
then grabs another. What is the P(two oranges)?
The probability of Akhil picking two oranges is 11/105 OR 10.476%.
To find the probability of Akhil picking two oranges, we need to consider the total number of fruits and the number of oranges in the basket.
The total number of fruits is 8 green apples + 11 red apples + 5 nectarines + 12 oranges = 36 fruits.
The probability of picking the first orange is 12 oranges / 36 fruits = 1/3.
After eating the first orange, there are now 35 fruits left and 11 oranges.
The probability of picking the second orange is 11 oranges / 35 fruits.
So, the probability of Akhil picking two oranges (P(two oranges)) is the product of the individual probabilities: (1/3) * (11/35) = 11/105.
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The table shows the number of different categories of books that Mrs. Hoover, the librarian, sold at the book fair on Thursday.
If Mrs. Hoover sells 50 books at the book fair on Friday, which prediction for Friday is NOT supported by the data in the table?
A The difference between the number of sports and trivia books sold and the number of arts and crafts books sold on Friday will be 12.
B The number of non-fiction books sold on Friday will be two-and-a-half times the number of arts and crafts books sold on Friday.
C The combined Friday sales for non-fiction books and novels will be 30 books.
D The number of novels sold on Friday will be 10 times the number of non-fiction books sold on Friday.
The prediction that is not supported by the data is option B: "The number of non-fiction books sold on Friday will be two-and-a-half times the number of arts and crafts books sold on Friday."
How to explain the dataWe can see from the table that on Thursday, 7 sports and trivia books and 19 arts and crafts books were sold, for a difference of 12.
On Thursday, 13 non-fiction books and 19 arts and crafts books were sold. If we assume that the same ratio will hold on Friday, then we can predict that the number of non-fiction books sold will be (19/2)*2.5 = 23.75, which is not a whole number. Therefore, this prediction is not supported by the data.
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Afia visits the shopping mall on tuesday to purchase some groceries. if she goes back after 295 days, what day did she visit the shopping mall again
Afia visits the shopping mall on Tuesday to purchase some groceries. if she goes back after 295 days, she visits the shopping mall again on a Wednesday.
To find out what day Afia visited the shopping mall again, we can divide 295 by 7 because there are 7 days in a week. we need to find out how many full weeks have passed and how many days.
= 295/ 7 = 42.1
The 295 divided by 7 is 42 with a remainder of 1 or we can write as that 42 full weeks and 1 day have passed.
When 42 weeks have passed that day will be Tuesday and the 1 day after Tuesday is Wednesday.
Therefore, Afia visited the shopping mall again on a Wednesday.
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PLS HLEP AND SHOW WORK I WILL MATK BRAINLYEST
Based on the information, statement (A) False is correct.
The probability of being female and working part-time only in the summer is 0.336, which is not equal to 0.42.
How to calculate the probabilityIt should be noted that since the proportion of females who work part-time only in the summer (84%) is greater than the overall proportion of students who work part-time only in the summer (80%), we can conclude that gender and working part-time only in the summer are dependent. This means that knowing someone's gender gives us information about the likelihood that they work part-time only in the summer.
Therefore, statement (A) False is correct.
The probability will be:
0.80 x 0.50 x 0.84 = 0.336
The probability of being female and working part-time only in the summer is 0.336, which is not equal to 0.42.
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Determine whether the geometric series is convergent or divergent. If it is convergent, find the sum. (If the quantity diverges, enter DIVERGES.) 00 7 80 3| n n = 1
|r| = 7/80 < 1, the series is convergent. The sum = 0/(1-7/80) = 0. the sum of the geometric series is 0.
The geometric series with first term 0 and common ratio 7/80 is given by 0, 7/80, (7/80)², (7/80)³, ... In general, the nth term is (7/80)ⁿ⁻¹.
To determine whether this series is convergent or divergent, we can use the formula for the sum of an infinite geometric series:
sum = a/(1-r)
where a is the first term and r is the common ratio. In this case, a = 0 and r = 7/80.
If |r| < 1, then the series converges to the sum given by the above formula. If |r| ≥ 1, then the series diverges.
In this case, |r| = 7/80 < 1, so the series is convergent. The sum is given by:
sum = 0/(1-7/80) = 0
Therefore, the sum of the geometric series is 0.
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The arable land area of a commune is about 81. 5 ha. This year's summer-autumn crop, this commune intends to use 57 of these areas to grow rice. Calculate the area of the commune's summer-autumn rice crop (use a handheld calculator and then round the result to the third decimal place)
The area of the commune's summer-autumn rice crop is approximately 570,041.902 square meters. ( rounded to the third decimal place)
To calculate the area of the commune's summer-autumn rice crop, we need to multiply the total area of the commune by the percentage of the area used to grow rice.
First, we need to convert the area from hectares to square meters since the percentage is based on the total land area in square meters.
1 hectare = 10,000 square meters
So, 81.5 hectares = 81.5 x 10,000 = 815,000 square meters
Next, we can calculate the area of the rice crop:
57/81.5 = 0.699386503
0.699386503 x 815,000 = 570,041.902 square meters
Rounding to the third decimal place, the area of the commune's summer-autumn rice crop is approximately 570,041.902 square meters.
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Find an equivalent expression for the missing side length of the rectangle.
then find the missing side length when x = 3. round to the nearest tenth of
an inch.
8x in.
2x in.
? in.
expression: 4
length:
6
in.
answer 1:
4
answer 2:
6
The missing side length of the rectangle is 7.75 inches when x is equal to 3. This is obtained by using the Pythagorean theorem to solve for the length of the other side, which is approximately 6.3 inches.
Using the Pythagorean theorem, we can find the missing side length of the rectangle
a² + b² = c²
where c is the length of the diagonal and a and b are the lengths of the sides.
Plugging in the values given, we get
(2x)² + b² = (8x)²
4x² + b² = 64x²
b² = 60x²
b = √(60x²) = √(60)x
When x = 3, the missing side length is
b = √(60)(3) = 7.75 in. (rounded to the nearest tenth of an inch)
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--The given question is incomplete, the complete question is given
"Find an equivalent expression for the missing side length of the rectangle.
then find the missing side length when x = 3. round to the nearest tenth of an inch.
8x in. is a diagonal of rectangle
2x in. is one side of rectangle
? in. is other side at base "--
A random sample of American adults was asked whether or not they smoked cigarettes. Those who responded affirmatively were asked how many cigarettes they smoked per day. Assuming that there are 50 million American adults who smoke, estimate with 95%% confidence the number of cigarettes smoked per day in the United States.
We estimate with 95% confidence that the number of cigarettes smoked per day in the United States is between 14.38 and 15.62 million.
To estimate the number of cigarettes smoked per day in the United States, we need to use the following formula for a confidence interval:
sample statistic +/- z* (standard error of the statistic)
where the sample statistic is the mean number of cigarettes smoked per day, z* is the critical value from the standard normal distribution for the desired confidence level, and the standard error of the mean is given by:
standard deviation / sqrt(sample size)
We do not have the sample mean or standard deviation directly, but we can estimate them from the sample of American adults who smoke.
Let's assume that the sample size is n = 1000, and that the sample mean and standard deviation of cigarettes smoked per day are 15 and 10, respectively. Then the standard error of the mean is:
standard error = 10 / sqrt(1000) = 0.316
To find the critical value of z* for a 95% confidence level, we look up the value in the standard normal distribution table or use a calculator. For a two-tailed test with alpha = 0.05, the critical value is approximately 1.96.
Thus, the 95% confidence interval for the mean number of cigarettes smoked per day in the United States is:
15 +/- 1.96*0.316 = (14.38, 15.62)
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Marci described the light from the sun as a line that starts at the sun and continues on forever.wich geometric term best describes marcis description of the sun's light
The geometric term best describes Marci's description of the sun's light is ray
What is a ray?A ray is a line that extends eternally in one direction from a point in geometry, in this case the sun.
It symbolizes a straight journey without any turning points.
As the sun's light propagates in a straight line throughout space without end, Marci's description fits the definition of a ray.
To explain Marci's depiction of the sun's light as a line that originates at the sun and never ends is to use the geometric term "ray."
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Answer: Ray
Step-by-step explanation:
A ray continues but may have a segment near the stopping point
a researcher is interested in the disappearance of spotted owls from northwestern forests. she studies 10 breeding pairs of spotted owls in cascade national park for one year. the 10 breeding pairs are the: group of answer choices selected sample snowball sample stratified sample target population
The 10 breeding pairs of spotted owls in Cascade National Park studied by the researcher represent a selected sample. So, the correct answer is A)
The 10 breeding pairs of spotted owls represent a selected sample.
A sample is a subset of a larger population that is chosen for research or study purposes. In this case, the researcher is interested in studying the disappearance of spotted owls from northwestern forests, but it would be impractical to study the entire population of spotted owls in the region.
Therefore, the researcher selected a smaller group of 10 breeding pairs in Cascade National Park as a representative sample to study over the course of one year. The selected sample may help the researcher to draw conclusions about the population of spotted owls in the region. So, the correct option is A).
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--The given question is incomplete, the complete question is given
" a researcher is interested in the disappearance of spotted owls from northwestern forests. she studies 10 breeding pairs of spotted owls in cascade national park for one year. the 10 breeding pairs are the: group of answer choices
selected sample
snowball sample
stratified sample
target population"--
The force on a particle is described by 8x^3-5 at a point s along the z-axis. Find the work done in moving the particle from the origin to x = 4.
The work done in moving the particle from the origin to x = 4 under the influence of the force F (x) = 8[tex]x^3[/tex]-5 is 492 units of work.
The work done in moving a particle along a path under the influence of a force, we use the work-energy principle.
This principle states that the work done on a particle by a force is equal to the change in the particle's kinetic energy.
Mathematically this can be expressed as:
W = ΔK
Where
W is the work done,
ΔK is the change in kinetic energy and
Both are scalar quantities.
The work done by a force on a particle along a path is given by the line integral:
W = ∫ C F · ds
Where,
C is the path,
F is the force,
ds is the differential displacement along the path and denotes the dot product.
In the case where the force is a function of position only (i.e., F = F(x,y,z)), we can evaluate the line integral using the parametric equations for the path.
If the path is given by the parameterization r(t) = <x(t), y(t), z(t)>, then we have:
W = ∫ [tex]a^b[/tex] F(r(t)) · r'(t) dt
The work done in moving the particle from the origin to a final position at x = 4. We can evaluate the work done using the definite integral of the force from x = 0 to x = 4, as shown in the solution.
The initial kinetic energy is zero.
The work done by the force in moving the particle from x = 0 to x = 4 is given by the definite integral:
W = ∫ F(x) dx
Substituting the given expression for the force, we have:
W = ∫0 (8x - 5) dx
Integrating with respect to x, we have:
W = [(2x - 5x)]_0
W = (2(4) - 5(4)) - (2(0) - 5(0))
W = 512 - 20
W = 492
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If the circumference of a circle is 50. 4 ft, what is its area? (Use π = 3. 14) *
2 points
50. 24 sq ft
113. 04 sq ft
202. 24 sq ft
314 sq ft
If the circumference of a circle is 50. 4 ft, its area is 202.24 sq ft. Correct option is C: 202.24 sq ft.
The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle. We are given that the circumference is 50.4 ft, so we can solve for the radius:
50.4 = 2πr
r = 50.4 / (2π)
r ≈ 8.02 ft
Now we can use the formula for the area of a circle: A = πr²
A = 3.14 * (8.02)²
A ≈ 202.24 sq ft
Therefore, the answer is option C: 202.24 sq ft.
Alternatively, to find the area of a circle with a circumference of 50.4 ft, we will first find the radius using the formula for circumference (C = 2πr) and then use the formula for the area of a circle (A = πr²). Using π = 3.14:
Solve for the radius (r):
C = 2πr
50.4 = 2(3.14)r
r = 50.4 / (2 * 3.14)
r ≈ 8 ft
Calculate the area (A):
A = πr²
A = 3.14 * (8²)
A = 3.14 * 64
A ≈ 201.06 sq ft
The closest answer among the options provided is 202.24 sq ft. Correct option is C: 202.24 sq ft.
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A pack of 24 crayons costs the manufacturer $0.05 to make and is sold to the stores for $0.25. the stores sell the crayons for $0.50 during back to school week.
1.an equation that represents the mark up cost by the manufacturer is
a.p(c)=2c
b.p(c)=5c
c.p(c)=10c
2.an equation that represents the store mark up cost is
a.s(p)=2p
b.s(p)=5p
c.s(p)=10p
3.a composition of these two functions is
a.s(p(c))=2c
b.s(p(c))=10c
c.s(p(c))=5c
4.it represents
a.the total markup from cost to sales price
b.how much the store profits from the sale
c.how much money the manufacturer makes
a. s(p)=2p b. p(c)=5c c. s(p(c))=5c a. The total markup from cost to sales price.
How are the mark-up costs and profits determined in the pricing of the crayons?The equation that represents the mark-up cost by the manufacturer is c. p(c) = 10c. This equation implies that the manufacturer adds a mark-up of 10 times the cost to determine the selling price of the crayons.The equation that represents the store mark-up cost is b. s(p) = 5p. This equation implies that the store adds a mark-up of 5 times the cost price (or the price they purchase from the manufacturer) to determine the selling price during back-to-school week.The composition of these two functions is c. s(p(c)) = 5c. This equation represents that the store applies their mark-up (5 times the cost) to the manufacturer's selling price (10 times the cost) to determine the final selling price of the crayons.It represents a. the total mark-up from cost to sales price. This composition equation shows how both the manufacturer and the store contribute to the mark-up, resulting in the final selling price of the crayons. It accounts for the mark-up at each stage of the distribution process, from the manufacturer to the store.Learn more about manufacturer
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Solve for x.
Round to the nearest tenth.
Answer:
x = 65°
Step-by-step explanation:
The upper angle of the triangle is inscribed, so it is equal to half the size of the arc
Let's call this angle α:
[tex] \alpha = \frac{100°}{2} = 50°[/tex]
Since the given triangle is isosceles, the remaining angles are equal (don't forget, that a triangle's sum of all its angles is equal to 180°):
[tex]2x + 50° = 180°[/tex]
[tex]2x = 180° - 50°[/tex]
[tex]2x = 130°[/tex]
Divide both sides of the equation by 2 to make x the subject:
[tex]x = 65°[/tex]
Create a number pattern that follows the rule x + 7. Include 3 terms using the pattern
The number pattern that follows the rule x + 7, including 3 terms using the pattern, is: 8, 15, 22.
To do this, let's start with an initial value for x, and then generate the next two terms using the given pattern.
Step 1: Choose an initial value for x. Let's say x = 1.
Step 2: Apply the rule x + 7 to find the first term: 1 + 7 = 8.
Step 3: For the second term, use the first term as the new x: 8 + 7 = 15.
Step 4: For the third term, use the second term as the new x: 15 + 7 = 22.
So, the number pattern that follows the rule x + 7, including 3 terms using the pattern, is: 8, 15, 22.
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What would the balance be after 5 years if you deposited $1,000 in an account compounded monthly if the interest rate is 3. 7%?
$5,000. 00
$1,199. 21
$1,185. 00
$1,202. 88
Lawrence bought his condominium for
$100,900. During the past 2 years, its
value increased 8%. What is the current
value of Lawrence's condominium?
Answer: $108,972
Step-by-step explanation:
To find the current value of Lawrence's condominium, we need to calculate the 8% increase in value over the past 2 years.
First, find the increase in value:
$100,900 * 0.08 = $8,072
Next, add this increase to the original price:
$100,900 + $8,072 = $108,972
So, the current value of Lawrence's condominium is $108,972.
2. Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. Show
your work.
Answer:
(x-4)
(2x-78)
(x+8)
The measure of the quadrilateral are
88 - 4 = 84
2 * 88 - 78 = 98
88 + 8 = 96
How to solve the quadrilateralA quadrilateral is a polygon with four sides and four vertices (corners). There are many different types of quadrilaterals, including squares, rectangles, parallelograms, trapezoids, and kites. The angles and sides of a quadrilateral can vary depending on its specific type, but the sum of the internal angles of any quadrilateral is always 360 degrees.
x - 4 + x + 8 = 180
we have to find the value of x
x = 88
The angles would be
88 - 4 = 84
2 * 88 - 78 =
88 + 8 = 98
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A line has a slope of – 7 and passes through the point (2,7). Write its equation in slope-intercept form.
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{7})\hspace{10em} \stackrel{slope}{m} ~=~ - 7 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{- 7}(x-\stackrel{x_1}{2}) \\\\\\ y-7=-7x+14\implies {\Large \begin{array}{llll} y=-7x+21 \end{array}}[/tex]
Randy is planning to drive from New Jersey to Florida. Every time Randy stops
for gas, he records the distance he traveled in miles and the total number of gallons
Lised. Assume that the number of miles driven is proportional to the number of
Dallons consumed in order to complete the table.
The missing values of the table representing the number of miles driven is proportional to the number of gallons consumed are,
Gallons consumed : 2 4 7 8 10 12
Miles driven : 54 108 189 216 270 324
Let us consider 'x' represents the number of miles driven .
And 'y' represents the number of gallons consumed .
Number of miles driven is proportional to the number of gallons consumed.
⇒ ( x₁ / x₂ ) = ( y₁ / y₂ )
⇒ ( 2/ 4) = ( 54 / y₂ )
⇒y₂ = ( 54 × 4 ) / 2
⇒y₂ = 108.
⇒ ( x₁ / x₃ ) = ( y₁ / y₃ )
⇒ ( 2/ x₃) = ( 54 / 189)
⇒x₃ = ( 189 × 2 ) / 54
⇒x₃= 7
⇒ ( x₁ / x₅ ) = ( y₁ / y₅ )
⇒ ( 2/ 10) = ( 54 / y₅ )
⇒y₅ = ( 54 × 10 ) / 2
⇒y₅ = 270.
⇒ ( x₁ / x₆ ) = ( y₁ / y₆ )
⇒ ( 2/ 12) = ( 54 / y₆ )
⇒y₆ = ( 54 × 12 ) / 2
⇒y₆ = 324
Therefore, using the proportional relation between miles driven and gallons consumed the value of the table are,
Gallons consumed : 2 4 7 8 10 12
Miles driven : 54 108 189 216 270 324
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The above question is incomplete, the complete question is:
Randy is planning to drive from New Jersey to Florida. Every time Randy stops for gas, he records the distance he traveled in miles and the total number of gallons used. Assume that the number of miles driven is proportional to the number of gallons consumed in order to complete the table.
Gallons consumed : 2 4 8 10 12
Miles driven : 54 189 216
Determine where the absolute extrema of f(x)= 4x/ x²+1 on the interval [-4,0] occur. 1. The absolute maximum occurs at x= 2. The absolute minimum occurs at x =
The absolute maximum of f(x) = 4x / (x² + 1) on the interval [-4,0] occurs at x = 2 and the absolute minimum occurs at x = -4.
To find the absolute extrema, we first find the critical points by setting the derivative of f(x) equal to zero:
f'(x) = (4(x² + 1) - 8x²) / (x² + 1)² = 0
Simplifying, we get:
4 - 4x² = 0
x² = 1
x = ±1
Since x = -4 and x = 0 are also endpoints of the interval, we evaluate f(x) at these five points:
f(-4) = -8/17
f(-1) = -4/5
f(0) = 0
f(1) = 4/5
f(2) = 8/5
Thus, the absolute maximum occurs at x = 2, where f(x) = 8/5, and the absolute minimum occurs at x = -4, where f(x) = -8/17.
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16 workers will build a house; they can do so in 144 days. if all workers work a the same rate, how many more workers would be needed to build the same house in 96 days
To build a house in 96 days, more workers are required such that the total number of workers becomes 24.
Let W be the number of workers required to build the house in 96 days. Using the work formula, we can write:
(16 workers) x (144 days) = (W workers) x (96 days)
Simplifying the equation, we get:
W = (16 workers x 144 days) / 96 days = 24 workers
Therefore, to build the house in 96 days, 24 workers are required, which is 8 more workers than the original 16. This is because, to complete the work in a shorter time, more workers are needed to contribute their efforts to the work.
The total work done by all the workers remains constant, so if we decrease the time taken to complete the work, we need to increase the number of workers to maintain the same work rate.
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Which are equal to the following? Check all that
apply.
Rewrite the following with lower index 0
To rewrite a given expression with lower index 0, which involves changing the subscript of any variable or quantity to 0.
How to rewrite with lower index 0?To rewrite a given expression with lower index 0. This involves changing the subscript of any variable or quantity that is written with a different index to 0. This is a common practice in mathematics and science when dealing with sequences or series of values.
By setting the lower index to 0, the sequence or series starts with the first element, which is often easier to work with and more intuitive than starting with another index.
In many cases, the values of the sequence or series may not change, but the notation becomes more consistent and easier to manipulate.
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Answer:
here sorry I'm late
Step-by-step explanation:
How can you use your knowledge of evaluating expressions involving square roots to
identify and correct an error in calculating the period of a pendulum?
the period of a pendulum is the time in seconds) it takes the pendulum to swing back
and forth. the period t is represented by t = 1.1vi, where l is the length of the
pendulum (in feet).
To use our knowledge of evaluating expressions involving square roots to identify and correct an error in calculating the period of a pendulum, we should first ensure that the formula mentioned (t = 1.1vi) is accurate.
The correct formula for the period of a pendulum is t = 2π√(l/g), where l is the length of the pendulum (in feet) and g is the acceleration due to gravity (approximately 32.2 ft/s²).
When evaluating the period t, make sure to use the correct formula and follow these steps:
1. Substitute the given length of the pendulum (l) into the formula.
2. Divide the length by the acceleration due to gravity (g).
3. Calculate the square root of the result.
4. Multiply the square root by 2π.
By correctly evaluating the expression and ensuring you've used the accurate formula, you'll be able to identify and correct any errors in calculating the period of a pendulum.
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Edna gasta la mitad de su salario en el pago de renta, utilidades y
comida. Si į de esos gastos se va en renta, ¿qué fracción de su salario
se va en renta? Halla su salario mensual considerando que su renta
mensual es de $150. 0.
Entonces, 1/8 de su salario se va en renta, y su salario mensual es de $1200.
Entiendo que deseas saber qué fracción del salario de Edna se va en renta y cuál es su salario mensual si su renta mensual es de $150. Para resolver esto, seguiré estos pasos:
1. Sabemos que Edna gasta la mitad de su salario en renta, utilidades y comida. Esto se puede expresar como 1/2 de su salario.
2. Se nos dice que 1/4 de esos gastos se va en renta. Entonces, para encontrar la fracción de su salario que se va en renta, multiplicamos 1/2 (gastos totales) por 1/4 (fracción de gastos en renta): (1/2) * (1/4) = 1/8.
3. Ahora sabemos que 1/8 de su salario se va en renta. Para hallar su salario mensual, utilizaremos la renta mensual de $150.
4. Si 1/8 de su salario equivale a $150, podemos resolver su salario (S) utilizando la siguiente ecuación: (1/8)S = 150.
5. Para encontrar S, multiplicamos ambos lados de la ecuación por 8: S = 150 * 8.
6. Finalmente, calculamos el valor: S = 1200.
Entonces, 1/8 de su salario se va en renta, y su salario mensual es de $1200.
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Statistics from Cornell's Northeast regional Climate Center indicate that Ithaca, NY, gets an average of 36. 1 inches of rain each year with a
standard deviation of 5. 2 inches,
My friend stayed in Ithaca, NY there for 10 years, she said that the average while she was there was less than 34 inches. What is her vscore for
the 10 years?
(Round to the thousandth place) (Use a Standard Deviation that is rounded to the thousandth place)
Rounded to the thousandth place, your friend's z-score for the 10 years is approximately -0.404.
To calculate your friend's z-score for the 10 years she stayed in Ithaca, NY, you can use the following formula:
z = (X - μ) / σ
where:
- z is the z-score
- X is the sample mean (in this case, 34 inches)
- μ is the population mean (in this case, 36.1 inches)
- σ is the standard deviation of the population (in this case, 5.2 inches, rounded to 5.200 for thousandth place)
Plugging in the values:
z = (34 - 36.1) / 5.200
z = -2.1 / 5.200
z = -0.404
Therefore, your friend's z-score for the 10 years is approximately -0.404, rounded to the thousandth place.
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What is the length of the line?
A. 9
B. 8
C. squared 45
D. squared 27
Answer:
C) [tex]\sf \sqrt{45}[/tex]
Step-by-step explanation:
Pythagorean theorem:
AB = 6 units
BC = 3 units
AC is hypotenuse and AB is the base and BC is the altitude.
Hypotenuse² = base² + altitude²
AC² = AB² + BC²
[tex]\sf = 6^2 + 3^2\\\\ = 36 + 9\\\\ = 45[/tex]
[tex]\sf AC= \sqrt{45}[/tex]
find the perimeter of the equilateral triangle whose area is 16root3/4
The perimeter of this equilateral triangle is equal to 12 units.
How to calculate the area of an equilateral triangle?In Mathematics and Geometry, the area of an equilateral triangle can be calculated by using this formula:
Area of an equilateral triangle, A = √3/4 × a²
Where:
a represent the side lengths of an equilateral triangle.
By substituting the given parameters or dimensions into the formula for the area of an equilateral triangle, we have the following;
16 √3/4 = √3/4 × a²
a² = 16
a = 4 units.
In Mathematics and Geometry, the perimeter of an equilateral triangle can be calculated by using this mathematical equation:
Perimeter of an equilateral triangle, P = 3a
Perimeter of an equilateral triangle, P = 3(4)
Perimeter of an equilateral triangle, P = 12 units.
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f(x)=1/2x^4+2x^3 is concave up when f”(x) is
The function f(x) = (¹/₂)x⁴ +2x³ is concave up when f''(x) > 0, which is true when x > 0 or x < -2.
What is the concavity of the function?The concavity of a function is determined by taking the second derivative.
f'(x) = 2x³ + 6x²
f''(x) = 6x² + 12x
To find out when f(x) is concave up, we need to determine when f''(x) is positive;
f''(x) > 0
6x² + 12x > 0
6x(x + 2) > 0
When x > 0, both factors are positive, and the inequality is true.
When x < -2, both factors are negative, and the inequality is true.
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A worker in a computer factory compared these measurements. 43 5 3 101 1,000' 10' 100 10,000 Which of the following lists the measurements in order from least to greatest? 101 3 43 5 10,000' 100' 1,000' 10 B 101 43 35 10,000 1,000 100' 10 5 3 43 101 10' 100 1,000 10,000 3 5 43 101 100' 10' 1,000 10,000 D
we can combine the two lists to get the complete order from least to greatest: [tex]3, 5, 10, 43, 101, 100', 1,000', 10,000'.[/tex]Thus, option B is correct.
What is the order from least to greatest?To order these measurements from least to greatest, we need to compare their magnitudes. We can group the measurements into two categories: those that are integers (whole numbers) and those that are in feet (measuring length).
Starting with the integers, we can see that 3 is the smallest and 10,000 is the largest. So, the integers can be ordered as follows: [tex]3, 5, 10, 43, 101, 10,000.[/tex]
Next, we can order the measurements in feet. 100', 1,000', and 10,000' represent increasing lengths, so they can be ordered as follows: [tex]100', 1,000', 10,000'.[/tex]
Therefore, Finally, we can combine the two lists to get the complete order from least to greatest: [tex]3, 5, 10, 43, 101, 100', 1,000', 10,000'.[/tex]
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