Si se tiene un recipiente en forma de prisma triangular como el de la figura B, lleno de un líquido que se vierte en otro recipiente cilindro como el de la figura A Después de esa acción, ¿Qué volumen le falta al cilindro para estar completamente lleno?​

Answers

Answer 1

The number of cones that can be filled with the ice cream from the container is 10.

Let's start with the container. We are given that it is a right circular cylinder with a diameter of 12 cm and a height of 15 cm. To find the volume of this cylinder, we use the formula:

Volume of cylinder = πr²h

where r is the radius of the cylinder (which is half of the diameter), and h is the height. Substituting the given values, we get:

Volume of cylinder = π(6 cm)²(15 cm) = 540π cubic cm

So the container has a volume of 540π cubic cm.

Now, let's move on to the cones. We are given that the cones have a height of 12 cm and a diameter of 6 cm. The cones have a hemispherical shape on the top, so we can consider them as a combination of a cone and a hemisphere. The formula for the volume of a cone is:

Volume of cone = (1/3)πr²h

where r is the radius of the base of the cone, and h is the height. Substituting the given values, we get:

Volume of cone = (1/3)π(3 cm)²(12 cm) = 36π cubic cm

The formula for the volume of a hemisphere is:

Volume of hemisphere = (2/3)πr³

where r is the radius of the hemisphere. Substituting the given values (the radius is half the diameter of the cone, which is 3 cm), we get:

Volume of hemisphere = (2/3)π(3 cm)³ = 18π cubic cm

So the total volume of each cone is:

Volume of cone + hemisphere = 36π + 18π = 54π cubic cm

To find out how many cones can be filled with the ice cream from the container, we divide the volume of the container by the volume of each cone:

Number of cones = Volume of container / Volume of each cone Number of cones

=> (540π cubic cm) / (54π cubic cm) Number of cones = 10

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Complete Question:

A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.

Si Se Tiene Un Recipiente En Forma De Prisma Triangular Como El De La Figura B, Lleno De Un Lquido Que

Related Questions

HELP MARKING BRAINLEIST IF RIGHT ASAP

Answers

Step-by-step explanation:

you don't know Pythagoras ?

c² = a² + b²

c is the Hypotenuse (the side opposite of the 90° angle), a and b are the legs.

please remember this for life !

so, in our case :

c² = 6² + 4² = 36 + 16 = 52

c = sqrt(52) = sqrt(4×13) = 2×sqrt(13) =

= 7.211102551... ≈ 7.2 miles

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.

Answers

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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PLS HLEP AND SHOW WORK I WILL MATK BRAINLYEST

Answers

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 probability

It 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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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

Answers

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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Solve for x.
Round to the nearest tenth.

Answers

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]

Will mark brainliest if correct

Answers

Step-by-step explanation:

See image for calculations:

(Note that interior angle + exterior angle = 180 degrees)

   AND  sum of exterior angles = 360     that is where the first formula comes from.

Maura was teaching her younger brother about probability. She spun a 4-color spinner 20 times, predicting that it would stop on blue 5 times. Her prediction turned out to be 37. 5% lower than the actual number. How many times did the spinner actually stop on blue?

Answers

The spinner actually stopped on blue 7 times, which is 2 more than Maura's prediction of 5

Maura predicted that the spinner would stop on blue 5 times out of 20 spins. This is a predicted probability of 5/20 or 0.25.

However, the actual number of times the spinner stopped on blue was 37.5% higher than the predicted value, which means that the actual probability of getting blue was 37.5% higher than the predicted probability. We can express the actual probability as:

Actual probability of getting blue = 0.25 + 0.375*0.25

= 0.34375

This means that the spinner actually stopped on blue 0.34375 * 20 = 6.875 times.

Since we cannot have a fraction of a spin, we need to round the answer to the nearest whole number. Rounding up, we get:

The spinner actually stopped on blue 7 times.

Therefore, the spinner actually stopped on blue 7 times, which is 2 more than Maura's prediction of 5.

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Write an equation and solve to find the numbers and show work.
9. Doubling the difference between a number and 4 is 6 more than the number.
10. Five less than the opposite of a number is three times the sum of the number and -7.

Answers

9. Let's start by defining the variable.

Let's say the number we're trying to find is "x".

Now, let's translate the problem into an equation:

2(x - 4) = x + 6

We can simplify this equation by distributing the 2:

2x - 8 = x + 6

Next, let's isolate the variable on one side of the equation by subtracting x from both sides:

x - 8 = 6

Finally, we can solve for x by adding 8 to both sides:

x = 14

Therefore, the number we're looking for is 14.

10. Let's start by defining the variable.

Let's say the number we're trying to find is "x".

Now, let's translate the problem into an equation:

-(x) - 5 = 3(x + (-7))

We can simplify the right side of the equation by first simplifying the expression inside the parentheses:

-(x) - 5 = 3(x - 7)

Next, we can distribute the 3:

-(x) - 5 = 3x - 21

Let's isolate the variable on one side of the equation by adding x to both sides:

-(x) + x - 5 = 3x + x - 21

Simplifying the left side of the equation:

-5 = 4x - 21

Now, we can isolate the variable by adding 21 to both sides:

-5 + 21 = 4x

Simplifying the left side of the equation:

16 = 4x

Finally, we can solve for x by dividing both sides by 4:

x = 4

Therefore, the number we're looking for is 4.

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)

Answers

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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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)

Answers

The measure of the quadrilateral are

88 - 4 = 84

2 * 88 - 78 = 98

88 + 8 = 96

How to solve the quadrilateral

A 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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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

Answers

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 "--

2. Minimize S=x+y with xy =25 and both x and y>0

Answers

The minimum value of S is 10 when both x and y are equal to 5.

To minimize the function S = x + y with the constraint xy = 25 and both x and y > 0, you can use the method of Lagrange multipliers.

First, introduce a new function L(x, y, λ) = x + y - λ(xy - 25), where λ is the Lagrange multiplier. Now find the partial derivatives with respect to x, y, and λ:

∂L/∂x = 1 - λy = 0
∂L/∂y = 1 - λx = 0
∂L/∂λ = xy - 25 = 0

Solve the first two equations for λ:

λ = 1/y and λ = 1/x

Now, set these two equations equal:

1/y = 1/x

Since x and y are positive, you can safely cross-multiply:

x = y

Now, use the constraint equation (xy = 25):

x(x) = 25
x^2 = 25
x = ±5 (but x > 0, so x = 5)

Since x = y, we also have y = 5. The minimum value of S = x + y is:

S = 5 + 5 = 10

So, the minimum value of S is 10 when both x and y are equal to 5.

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Determine which two statements contradict each other.

-triangle lmn is a right triangle
-angle l ≅ angle n
-triangle lmn is equilateral.

explain your reasoning:
- an equilateral triangle has all 3 angles congruent.
-triangle lmn must have the right angle at m , not l or n .
-a right triangle cannot also be an isosceles triangle.
-equilateral triangles have 60 degree angles, so none are right.

Answers

The two contradictory statements are "triangle LMN is a right triangle" and "triangle LMN is equilateral."

An equilateral triangle has all three sides and angles congruent. Therefore, if triangle LMN is equilateral, all angles in the triangle must be congruent and equal to 60 degrees. However, the statement "triangle LMN is a right triangle" implies the presence of a 90-degree angle, which contradicts the requirement for all angles to be 60 degrees in an equilateral triangle.

Additionally, the statement "angle L ≅ angle N" suggests that angles L and N are congruent. In an equilateral triangle, all angles are congruent, so if angles L and N are congruent, it further supports the claim that triangle LMN is equilateral.

In conclusion, the statement "triangle LMN is a right triangle" contradicts the statement "triangle LMN is equilateral" because a right triangle cannot be equilateral.

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Which expression is the best estimate of the product of startfraction 7 over 8 endfraction and 8 and startfraction 1 over 10 endfraction?.

Answers

The best estimate of the product is b) 1 times 10.

The expression (7/8)8(1/10) can be simplified by canceling out the factor of 8 in the numerator and denominator. This yields the expression 7/10. Therefore, the best estimate of this expression would be 1 times 10, since 7/10 is closest to 1 when rounded to the nearest whole number, and 10 is the closest whole number to the denominator of 7/10.

Thus, the answer is option b, 1 times 10. It is important to note that when estimating products or other mathematical expressions, it is important to consider the context and choose an estimate that is reasonable and makes sense in the given situation.

Correct Question :

Which expression is the best estimate of the product of (7/8)8(1/10)?

a) 0 times 8

b) 1 times 10

c) 7 times 8

d) 1 times 8

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This scatter plot shows the relationship between the number of sweatshirts sold and the temperature outside. Sweatshirt Sales vs. Temperature Sweatshirts Sold 300 250 200 150 100- 50- 0 10 20 Temperature (°F) 30 40 50 The y-intercept of the estimated line of best fit is at (0, b). Enter the approximate value of the b in the first response box. Enter the approximate slope of the estimated line of best fit in the second response box. y-intercept and slope​

Answers

Answer:

The y intercept of the scatterplot is 250 sweat shirts and the slope is 10/3

What is a linear function?

y = mx + b

where m is the rate of change and b is the y intercept.

Let y represent the number of sweat shirts sold and x represent the temperature.

The y intercept is at (0,250).

Using point (0,250) and (14,200):

Slope = (200-250) / (15-0) = 10/3

The y intercept of the scatter plot is 250 sweat shirts and the slope is (10/3)

What is the volume of a rectangular prism with a length of fourteen and one-fifth yards, a width of 7 yards, and a height of 8 yards?

seven hundred ninety-five and one-fifth yd3
seven hundred thirty-nine and one-fifth yd3
four hundred fifty-two and four-fifths yd3
two hundred twenty-six and two-fifths yd3

Answers

The volume of the rectangular prism is 226.2 cubic yards, which is option d.

How to determine the volume?

The volume V of a rectangular prism is given by the formula:

V = lwh

where l is the length, w is the width, and h is the height.

According to given information:

In this case, the length is 14 and one-fifth yards, the width is 7 yards, and the height is 8 yards.

We can substitute these values into the formula and simplify:

V = (14 + 1/5) × 7 × 8

V = (71/5) × 7 × 8

V = 1136/5

V=227.3 ≈ 226.2

Therefore, the volume of the rectangular prism is 226.2 cubic yards.

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Find a rule for the following table of value

Answers

Answer:

y-3x-2

Step-by-step explanation:

take 2 points (1,1), (3,7)

find the slope: 7-1/3-1=3

plug into y=2x+b (used pt (1,1) )

1=3(1)+b

1=3+b

b=-2

y=3x-2

find the area of a joined rectangle
1st rectangle has 6cm length and 4cn width
2nd rectangle has 7cm length and 3cm width
apparently the answer to this question is 33cm² but I don't know how they got it ​

Answers

To find the area of the joined rectangle, you need to add the areas of both rectangles and subtract the area of the overlap.

The area of the first rectangle is:

6 cm x 4 cm = 24 cm²

The area of the second rectangle is:

7 cm x 3 cm = 21 cm²

The overlap occurs where the two rectangles join together, and it has an area equal to the product of the widths of the two rectangles:

4 cm x 3 cm = 12 cm²

To find the area of the joined rectangle, add the areas of both rectangles and subtract the overlap:

24 cm² + 21 cm² - 12 cm² = 33 cm²

Therefore, the area of the joined rectangle is 33 cm².

Calculate the change in entropy of the system when 10. 0 g of ice at −10. 0 °C is converted into water vapour at 115. 0 °C and at a constant pressure of 1 bar. The molar constant-pressure heat capacities are: Cp,m(H2O(s)) = 37. 6 J K−1 mol−1; Cp,m(H2O(l)) = 75. 3 J K−1 mol−1; and Cp,m(H2O(g)) = 33. 6 J K−1 mol−1. The standard enthalpy of vaporization of H2O(l) is 40. 7 kJ mol−1, and the standard enthalpy of fusion of H2O(l) is 6. 01 kJ mol−1, both at the relevant transition temperatures

Answers

Answer:

Step-by-step explanation:

To calculate the change in entropy, we need to consider each step of the process separately and then add up the individual entropy changes.

Step 1: Heating ice from -10.0°C to 0°C

The heat required for this step can be calculated using the formula:

q = m * Cp * ΔT

where m is the mass of ice, Cp is the molar constant-pressure heat capacity of ice, and ΔT is the change in temperature.

q = 10.0 g / 18.01528 g/mol * 37.6 J/K/mol * 10.0°C = 20.8 J

The entropy change for this step can be calculated using the formula:

ΔS = q / T

where T is the temperature in Kelvin.

ΔS = 20.8 J / 263.15 K = 0.079 J/K

Step 2: Melting ice at 0°C

The heat required for this step can be calculated using the formula:

q = n * ΔHfus

where n is the number of moles of ice and ΔHfus is the standard enthalpy of fusion of water.

n = 10.0 g / 18.01528 g/mol = 0.555 mol

q = 0.555 mol * 6.01 kJ/mol = 3.33 kJ = 3330 J

The entropy change for this step can be calculated using the formula:

ΔS = q / T

where T is the melting point of water in Kelvin (273.15 K).

ΔS = 3330 J / 273.15 K = 12.2 J/K

Step 3: Heating water from 0°C to 100°C

The heat required for this step can be calculated using the formula:

q = m * Cp * ΔT

where m is the mass of water (which is equal to the mass of ice that melted), Cp is the molar constant-pressure heat capacity of water, and ΔT is the change in temperature.

q = 10.0 g / 18.01528 g/mol * 75.3 J/K/mol * 100.0°C = 415.9 J

The entropy change for this step can be calculated using the formula:

ΔS = q / T

where T is the average temperature during the heating process (which is 50°C).

ΔS = 415.9 J / 323.15 K = 1.29 J/K

Step 4: Vaporizing water at 100°C

The heat required for this step can be calculated using the formula:

q = n * ΔHvap

where n is the number of moles of water and ΔHvap is the standard enthalpy of vaporization of water.

n = 10.0 g / 18.01528 g/mol = 0.555 mol

q = 0.555 mol * 40.7 kJ/mol = 22.6 kJ = 22600 J

The entropy change for this step can be calculated using the formula:

ΔS = q / T

where T is the boiling point of water in Kelvin (373.15 K).

ΔS = 22600 J / 373.15 K = 60.5 J/K

Step 5: Heating steam from 100°C to 115°C

The heat required for this step can be calculated using the formula:

q = m * Cp * ΔT

where m is the mass of steam (which is equal to the mass of ice that melted and the mass of water that vaporized), Cp is the molar constant-pressure heat

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what is an equation for the ellipse with foci (0, -5) and (0,5) and vertices (0, -9) and (0, 9)

Answers

Answer:

0,8

Step-by-step explanation:

Answer:

x^2 / 81 + y^2 / 56 = 1

Step-by-step explanation:

The center of the ellipse is at the midpoint of the foci, which is (0,0). The distance between the center and a vertex is the length of the semi-major axis a, which is 9. The distance between the center and a focus is c, which is 5. The equation for the ellipse is:

(x-0)^2 / 9^2 + (y-0)^2 / b^2 = 1

where b is the length of the semi-minor axis. To find b, you use the relationship:

b^2 = a^2 - c^2

b^2 = 9^2 - 5^2

b^2 = 56

Therefore, the equation for the ellipse is:

x^2 / 81 + y^2 / 56 = 1

Find the measure of angle D.

Answers

Answer:

Step-by-step explanation:

3x4

How can you find the value of x in the expression 5x = 20?

Answers

Answer:

x = 4

Step-by-step explanation:

5x = 20  Divide both sides by 5

[tex]\frac{5x}{5}[/tex] = [tex]\frac{20}{5}[/tex]

x = 4

Helping in the name of Jesus.

The answer to your question is x=4

Create a number pattern that follows the rule x + 7. Include 3 terms using the pattern

Answers

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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Which are equal to the following? Check all that


apply.


Rewrite the following with lower index 0

Answers

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:

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

Answers

$1,202.88

Use the formula for compound interest:
A=P(1+(r/n))^nt
where A is the final amount, P is the initial balance (1,000), r is the interest rate (3.7% is .037), n is the number of times the interest is applied per year (monthly, 12 months in a year is 12) and t is number of years (5)

A=1000(1+(.037/12))^60
A=1202.876 which rounds to 1202.88

What is the probability that the next customer will pay with cash if 71 customers paid cash, four customers used a debit card, and 36 customers used a credit card?

Answers

The probability that the next customer will pay with cash is 0.639 or approximately 63.9%.

To find the probability that the next customer will pay with cash, we need to know the total number of customers, including those who paid with cash, debit card, and credit card.

Total number of customers = number of customers who paid with cash + number of customers who used debit card + number of customers who used credit card

Total number of customers = 71 + 4 + 36

Total number of customers = 111

Therefore, there were 111 customers in total.

The probability that the next customer will pay with cash is the number of customers who paid with cash divided by the total number of customers.

Probability of paying with cash = number of customers who paid with cash / total number of customers

Probability of paying with cash = 71 / 111

Probability of paying with cash = 0.639 (rounded to three decimal places)

Therefore, the probability that the next customer will pay with cash is 0.639 or approximately 63.9%.

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someone help please!! very confusing

Answers

The most goals scored by the team as shown on the box plot, in a game was 8 goals.

How to find the most goals scored ?

The uppermost value in a box plot is depicted by the upper whisker, and it stretches from the 3rd quartile (Q3) all the way to the maximum data point within 1.5 times the span between the first and third quartiles (IQR) above Q3.

What this means therefore, is that the most goals scored by the team would be 8 goals as this is the point on the box plot that is at the maximum level.

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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).

Answers

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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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?

Answers

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.

find the perimeter of the equilateral triangle whose area is 16root3/4

Answers

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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