sketch the region in the plane consisitng of points whose polar coordinates satisfy the given conditions. 1

Answer:

  1856 ft²

Step-by-step explanation:

You want the surface area of an isosceles triangular prism 23 ft long with a triangle base of 24 ft and a height of 16 ft.

The area of the two triangles is ...

  A = 2 × 1/2bh = bh

  A = (24 ft)(16 ft) = 384 ft²

The area of the three rectangular sides is ...

  A = LW

  A = (24 ft + 20 ft + 20 ft)(23 ft) = 64·23 ft² = 1472 ft²

The surface area of the prism is the sum of the base area and the lateral area:

  A = 384 ft² +1472 ft² = 1856 ft²

The surface area of the prism is 1856 square feet.

__

Additional comment

We recognize each of the smaller right triangles that make up one base is a 3-4-5 right triangle with a scale factor of 4 ft. That makes the hypotenuse exactly 20 ft, as shown in the diagram.

The lateral area is effectively the product of the prism length (23 ft) and the perimeter of the triangular base.

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the sample proportion (p^) is 0.4 or 40%.

To calculate the sample proportion (p^) for the number of Mizzou students with brown eyes, use the following formula:

A set is a collection of objects or groups of objects. These objects are often called elements or members of a set. For example, a group of players in a cricket team is a set.

p = (number of students with brown eyes) / (total number of students in the sample)

In this case, there are 24 students with brown eyes out of a sample of 60 students. Therefore, the numerical value of the statistic p^ is:

\(p = \frac{24} { 60} = 0.4\)

So, the sample proportion (p^) is 0.4 or 40%.

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The numerical value of the statistic p^ for the random sample of 60 Mizzou students is 0.4, meaning 40% of the

sampled students have brown eyes.

To find the numerical value of the statistic p^ (sample proportion) for the given problem, you should follow these steps:

Identify the total number of students (n) in the sample, which is 60.

Identify the number of students with brown eyes (x), which is 24.

Calculate the sample proportion (p^) using the formula: p^ = x/n

Applying the formula:

p^ = 24/60

p^ = 0.4

So, the numerical value of the statistic p^ for the random sample of 60 Mizzou students is 0.4, meaning 40% of the

sampled students have brown eyes.

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Answer:? Okkkkk

Step-by-step explanation:

Lol

To evaluate this triple integral, we need to set up the bounds for each variable. Since the solid tetrahedron is defined by the vertices (0,0,0), (2,0,0), (0,2,0), and (0,0,2), we know that:


∫(from 0 to 2) ∫(from 0 to 2-x) ∫(from 0 to 2-x-y) y^2 dz dy dx

Now, integrate with respect to z:

= ∫(from 0 to 2) ∫(from 0 to 2-x) y^2(2-x-y) dy dx

Next,  with respect to y:

= ∫(from 0 to 2) [-y^3/3 + xy^2 - y^2x/2] (from 0 to 2-x) dx

= ∫(from 0 to 2) [-8x^3/3 + 4x^4/3] dx

Finally, integrate with respect to x:

= [-2x^4/3 + x^5/3] (from 0 to 2)

= [-16/3 + 32/3] - 0

= 16/3

So, the triple integral evaluates to 16/3.

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Answer:

a=2/5

Step-by-step explanation:

1.7((2)/(5))+0.3((2)/(5)) = 0.8=80/100=4/5

Answer:

the answer is a=2/5

Step-by-step explanation:

combine like terms 1.7+0.3=2

get the varliable alone 2/4/5

answer 2/5

The interval of completion times containing the middle 95% of test-takers is approximately [40, 74].

We are given the mean μ = 57 and the standard deviation σ = 8 of the length of time needed to complete a certain test, which is normally distributed.A) We need to find the percent of people that take between 49 and 65 minutes to complete the exam.To find this, we can use the z-score formula as follows;z = (x - μ) / σ, where x = completion time= 49 minutesz1 = (49 - 57) / 8= -1z2 = (65 - 57) / 8= 1

Now, we need to find the area under the normal curve between these z-scores as shown in the figure below;z1 = -1, z2 = 1We can see that the area under the normal curve between -1 and 1 is approximately 0.6826. Therefore, the percent of people that take between 49 and 65 minutes to complete the exam is 68.26%.B) We need to find the interval of completion times containing the middle 95% of test-takers.To find this, we need to find the z-scores corresponding to the middle 95% of test-takers from the normal distribution table or calculator.

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2.1 The volume in ml of one can of cold drink is 83 ml.

2.2 The height of the cooler bag is 18 cm.

2.3 The volume in ml of the cooler bag if the breadth of the bag is 12 cm and the length 18 cm is 3,888 ml.

2.4 The circumference of the can is 18.84 cm.

In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

By substituting the given side lengths into the volume of a cylinder formula, we have the following;

Volume of can = 3.14 × (6/2)² × 8.84

Volume of can = 83.27 cm³.

Note: 1 cm³ = 1 ml

Volume of can in ml = 83.27 ≈ 83 ml.

Part 2.2.

For the height of the cooler bag, we have:

Height of cooler bag = 2 × height of can

Height of cooler bag = 2 × 8.84

Height of cooler bag = 17.68 ≈ 18 cm.

Part 2.3

Volume of cooler bag = length × breadth × height

Volume of cooler bag = 18 × 12 × 18

Volume of cooler bag = 3,888 ml.

Part 2.4

The circumference of the can is given by:

Circumference of circle = 2πr

Circumference of can = 2 × 3.14 × 3

Circumference of can = 18.84 cm.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The measure of each marked angle is 60 degrees for the given figure, which are alternate exterior angles.

The angles are given as:

∠1 = 10x-20 and ∠2 = 7x+4

As we know that alternate exterior angles are described as the pair of angles formed on the outer side of the parallel lines and on opposite sides of the transversal when two parallel lines are crossed by a transversal.

By alternate exterior angles, it can be written as:

∠1 = ∠2

10x-20 = 7x+4

10x -7x = 4 + 20

3x = 24

x = 24/3

x = 3

From given angles:

80 - 20 = 60

56 + 4 = 60

Thus, the measure of each marked angle is 60 degrees.

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Answer:

w=19

Step-by-step explanation:    

Answer:

Mr.Green washed the most laundry with .375 of it done

what remains is .291

Step-by-step explanation:

3/8 or 3 divided by 8 is .375

1/3= .3333 repeating or rounded to .334

.375+.334= .709

1.000 - .709= .291

hopes this helps

Answer:

1. Mr. Green washed more laundry 2. 7/24 of the laundry still needs to be washed

Step-by-step explanation:

If you find a common denominator you can compare them. I used the common denomiator of 24. Next, you need to change both fractions so that they have the same denominator. To do that we have to multiply both the numerator and denominator of 3/8 by 3. When you do that, you end up with 9/24. Then you have to do the same for 1/3 but this time multiplying the numerator and the denominator by 8. That will leave us with 9/24 and 8/24 which proves that Mr. Green did more laundry.

For the second question, we will need to add the two amounts of laundry already washed and then find out how much remains from there. We can use the fractions that already have a common denominator from the explanation above. Now we have to add 9/24 and 8/24 together. Once we add them together, we will get 17/24 which is how much laundry is already done. Now, we need to take the remaining amount from 17/24 which is 7/24, and that represents how much laundry sitll needs to be washed.

(sorry if this is confusing but I hope it helped!)

The expected value of the continuous random variable V is 5. The expected value of V is 5, indicating that, on average, we expect the value of V to be around 5.

To calculate the expected value of a continuous random variable V with a given probability density function (PDF), we integrate the product of V and the PDF over its entire range.

The PDF of V is defined as:

f(v) = 6/24 = 0.25 for 3 ≤ v ≤ 7, and 0 otherwise.

The expected value of V, denoted as E(V), can be calculated as:

E(V) = ∫v * f(v) dv

To find the expected value, we integrate v * f(v) over the range where the PDF is non-zero, which is 3 to 7.

E(V) = ∫v * (0.25) dv, with the limits of integration from 3 to 7.

E(V) = (0.25) * ∫v dv, with the limits of integration from 3 to 7.

E(V) = (0.25) * [(v^2) / 2] evaluated from 3 to 7.

E(V) = (0.25) * [(7^2 / 2) - (3^2 / 2)].

E(V) = (0.25) * [(49 / 2) - (9 / 2)].

E(V) = (0.25) * (40 / 2).

E(V) = (0.25) * 20.

E(V) = 5.

Therefore, the expected value of the continuous random variable V is 5.

The expected value represents the average value or mean of the random variable V. It is the weighted average of all possible values of V, with each value weighted by its corresponding probability. In this case, the expected value of V is 5, indicating that, on average, we expect the value of V to be around 5.

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Answer:

-272

Step-by-step explanation:

Answer:

1:15 pm

Given:

-the turkey weighs 11.25 pounds

-it takes 12 min to cook a pound of turkey

-dinner is at 3:00 pm

Step by step:

(number of minutes) x (number of pounds)

Round 11.25 to 11

12x11= 132

0.25 pounds is 12/4 (0.25 is 1/4 of a whole)= 3

132+3= 135

It takes 135 minutes to cook a turkey,

135 min = 2.25 hours (2 hours and 15 minutes)

1:15 pm you need to start cooking.

The volume of pentagonal prism B, the image, is 448 cubic in.

The volume of a prism is directly proportional to the cube of the scale factor. Therefore, if prism B is the image of prism A after dilation by a scale factor of 2, the volume of prism B will be 2³ = 8 times the volume of prism A.

Given that the volume of prism A is 56 in³. Then the volume of prism B is calculated as,

=> Volume of prism A × (Scale factor)³

=> 56 in³ × 8

=> 448 in³

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The numerical probability of Flora picking out a blue sock is 1 out of 6, or approximately 0.1667, or 16.67%.

To calculate the numerical probability of Flora picking out a blue sock, we need to consider the total number of socks and the number of blue socks in the drawer.

Given:

Total number of socks = 12

Number of red socks = 9

Number of blue socks = 2

Number of green socks = 1

The probability of Flora picking a blue sock can be calculated as the ratio of the number of blue socks to the total number of socks:

Probability of picking a blue sock = Number of blue socks / Total number of socks

Probability of picking a blue sock = 2 / 12

Simplifying the fraction, we get:

Probability of picking a blue sock = 1 / 6

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Answer:

\(50\)

Step-by-step explanation:

Let \(x =\) blank (for convenience)

\(20\%x=10\)

\(0.2x=10\) (change \(20\%\) into its decimal form)

\(x = 10\div 0.2\) (divide \(0.2\) on both sides)

\(x=50\)

∴ Blank = 50

Hope this helps :)

Answer:

65° or 115°

Step-by-step explanation:

there is no picture but if

mEDB looks like mCDB then its 65°

but if they dont look alike then

180-65=115

straight line is 180°

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Answer:

D

Step-by-step explanation:

P prime of t indicates a rate of change

The required expression that gives the rate of the population of the city will be changing at time t=5 is D) P'5. Option D is correct.

Given that,
A city planner developed the function P to model the population of a city over the next 25 years, where P(t) is the projected population of the city t years from now.

Rate of change is defined as the change in value with rest to the time is called rate of change.

Here,
The rate of the population expression at t = 5 is given by the differentiation of the expression at t = 5 because differentiation represents the rate for the given equation of population. i.e.
P'5

Thus, the required expression that gives the rate of the population of the city will be changing at time t=5 is D) P'5. Option D is correct.

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The volume of 11 gallons is 50 litres.

The volume of 40 litres is 8.8 litres.

The capacity of the tank in gallons is 26.7 gallons

The graph of a proportional relationship is always a straight line through the origin.

Therefore, the graph is a relationship between the variables volumes in litres and gallons. The litres is on the y axis while the gallons is on the x axis.

Hence, let's use the graph to convert the volumes.

11 gallons = 50 litres

40 litres = 8.8 litres

A tank has a volume of 120, 000 cm cube.

1 litre  = 1000 cm³

The capacity of the tank in gallons can be found as follows:

1000 cm³ = 1 litres

120,000 cm³= ?

volume in litres = 120,000 / 1000

volume in litres = 120 litres

From the graph,

36 litres = 8 gallons

120 litres = ?

cross multiply

volume in gallons = 120 × 8  / 36

volume in gallons = 960 / 36

volume in gallons = 26.6666666667

Therefore, the capacity of the tank in gallons is 26.7 gallons

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Answer:

  a) 50 L

  b) 8.8 gal

  c) 26.4 gal

Step-by-step explanation:

Given a graph showing the relationship between (imperial) gallons and litres, you want equivalents for 11 gallons, 50 litres, and 120000 cm³.

You have correctly read the graph, which tells you 11 gallons is about 50 litres.

You have correctly read the graph, which tells you 40 litres is about 8.8 gallons.

You are told that 1000 cm³ is 1 litre, so 120,000 cm³ will be 120 litres.

You notice this is 3 times the volume of the previous question:

  120 L = 3×(40 L) = 3×(8.8 gal) = 26.4 gal

120000 cm³ is about 26.4 gallons.

__

Additional comment

A more precise conversion of 120000 cm³ is 26.3963097959... gallons. The decimal has a very long repeat.

The amount of chicken meat required by the lion to meet his protein diet is 6.66 ounces.

A 120-pound lion need 50 gram of protein a day.

The protein provided by the 4-ounce chicken is 30 grams.

By using unitary method,

We can write,

4 ounce chicken = 30 grams protein

4/30 ounce chicken = 1 grams protein

Now, the required amount of protein is 50 grams.

So, the chicken meat needed is,

50 grams = 4/30 x 50 ounces

50 grams protein = 6.66 ounces.

So, a total of 6.66 ounces of chicken meat is required.

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The correct answer is Option B. There'll be 70 kg/ha organic carbon would be saved annually by using reduced tillage.

Reduced tillage, also known as conservation tillage, is a practice that minimizes the disturbance of the soil and helps to maintain organic carbon in the soil. This practice can help to improve soil health, reduce erosion, and increase water retention.
One study found that reduced tillage can increase organic carbon levels in the soil by 70 kg/ha (kilograms per hectare) per year. This is equivalent to 70,000 g/ha (grams per hectare) per year. Therefore, the correct answer is option B. 70 kg/ha.
In conclusion, reduced tillage can help to increase organic carbon levels in the soil, leading to improved soil health and other benefits. The amount of organic carbon saved annually by using reduced tillage is 70 kg/ha.

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56/120

Step-by-step explanation:

The body masses of the two children in terms of their father's body mass, x, are:

First child's body mass = 5x/6 kg

Second child's body mass = 4x/5 kg

To express the body mass of the man's two children in terms of their father's body mass, we can use the given ratios.

Let the body mass of the man be x kg.

The first child's body mass is five-sixths of their father's body mass:

Body mass of the first child = (5/6) * x

= 5x/6 kg.

The second child's body mass is four-fifths of their father's body mass:

Body mass of the second child = (4/5) * x

= 4x/5 kg.

Therefore, the body masses of the two children in terms of their father's body mass, x, are:

First child's body mass = 5x/6 kg

Second child's body mass = 4x/5 kg

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Answer:

Step-by-step explanation:

The first option is correct because the expression \(5t+4y\) has a coefficient of 5.

Important information:

In the product of a variable and a constant, the constant number is called the coefficient.

For example, 4 is the coefficient of x in 4x.

The coefficients of \(5t+4y\) are 5 and 4.

The coefficients of \(2x+3y\) are 2 and 3.

The expression 0 has no coefficient.

The coefficient of \(3x+2\) is 3.

Therefore, the first option is correct.

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The Slope of line is 10

the equation of line is y = 10x + 4.

The equation of a line is a formula that describes the relationship between the x and y coordinates of points on the line. The most commonly used form of the equation of a line is the slope-intercept form: y = mx + b

First make a chart for x and y values from the given graph;

Study time in hours (x) =  60    75    70     80    90    80   100   95   100

Grade % (y) =                       1       1       2       2      2       3      3      4      4

We know that the line equation, y = mx + b

Slope (m) = \(\frac{y_{2} -y_{1}}{x_{2} -x_{1}}\)

Take any two values from chart, (2, 80) and (4, 100)

Put the values then, m = \(\frac{100-80}{4-2}} = \frac{20}{2} = 10\)

m = 10

Therefore, the Slope of line is 10.

So, equation for (2, 80) is: y = mx + b

80 = 10 × 2 + b

b = 4

put the values in above line equation; y = 10x + 4

Therefore, the equation of line is y = 10x + 4

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Answer:

166.5

Step-by-step explanation:

The can contains 15.7 g of sugar per 100 mL. So if the can holds 330 mL of soft drink, then overall it contains

(15.7 g) / (100 mL) × (330 mL) = 51.81 g

of sugar, and this is

(51.81 g) / (90 g) ≈ 0.575667 ≈ 57.6%

so Tom's friend is correct.

Answer:

The highest common factor is 5

Step-by-step explanation:

3x5=15  4x5=20

Answer:

answer is 5

Step-by-step explanation:

See image below, This is a good website  called Cue math explaining.  

https://www.cuemath.com/questions/gcf-of-15-and-20/

The sprinter's speed before he increased it was 8.2 miles per hour.

To find the sprinter's speed before he increased it, we can use the following steps:
Step 1: Identify the final speed and the increase in speed.
The sprinter's top speed is 23 miles per hour, and he increased his speed by 14.8 miles per hour.
Step 2: Subtract the increase in speed from the final speed.
We can determine the sprinter's initial speed by subtracting the increase in speed (14.8 miles per hour) from the final speed (23 miles per hour).
Initial speed = Final speed - Increase in speed
Initial speed = 23 miles per hour - 14.8 miles per hour
Step 3: Calculate the initial speed.
Now, we can perform the subtraction:
Initial speed = 8.2 miles per hour
So, the sprinter's speed before he increased it was 8.2 miles per hour.

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The sprinter's speed before he increased his speed was approximately 8.2 miles per hour. The correct option is D

We need to subtract the increase in speed from his top speed.

Assume that "x" miles per hour represents the sprinter's initial speed (before to the increase).

The sprinter improved his speed by 14.8 miles per hour, as indicated by the information, to reach a top speed of 23 miles per hour. This can be said as follows:

x + 14.8 = 23

To find the value of "x," we can solve this equation:

x = 23 - 14.8

x ≈ 8.2

Therefore, the sprinter's speed before he increased his speed was approximately 8.2 miles per hour.

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