How many cubic feet of space is there in a warehouse that is 610 feet wide by 140 feet deep and has an 18 foot ceiling?
Final answer:
The warehouse has a volume of 252,000 cubic feet, calculated using the corrected dimensions of 140 feet in length, 100 feet in width, and an 18-foot ceiling.
Explanation:
To calculate the volume of a warehouse, we use the formula for the volume of a rectangular prism, which is length × width × height. However, the question contains a typo about the width of the warehouse.
We are informed that the correct width is 100 feet, not 610 feet.
Given the corrected dimensions (140 feet by 100 feet with an 18 foot ceiling), we can now calculate the volume of the warehouse.
Volume = length × width × height
= 140 feet × 100 feet × 18 feet
= 252,000 cubic feet.
Therefore, the warehouse has a volume of 252,000 cubic feet of space.
In science class, Savannah measures the temperature of a liquid to be 50∘ Celsius. Her teacher wants her to convert the temperature to degrees Fahrenheit. What is the temperature of Savannah's liquid to the nearest degree Fahrenheit
Final answer:
To convert the temperature of Savannah's liquid from Celsius to Fahrenheit, use the equation °F = (°C × 9/5) + 32. Savannah's temperature in Celsius is 50°, so her temperature in Fahrenheit is 122°F.
Explanation:
To convert the temperature from Celsius to Fahrenheit, you can use the equation:
°F = (°C × 9/5) + 32.
In this case, Savannah's temperature in Celsius is 50°. Using the equation, we can calculate her temperature in Fahrenheit as:
°F = (50 × 9/5) + 32 = 122°F.
Therefore, the temperature of Savannah's liquid to the nearest degree Fahrenheit is 122°F.
Savannah's liquid, initially measured at 50°C, converts to 122°F using the formula F = C x (9/5) + 32.
Explanation:Converting Celsius to FahrenheitTo convert the temperature from degrees Celsius to degrees Fahrenheit, we use the conversion formula: F = \( C \times \frac{9}{5} + 32 \), where F is the temperature in degrees Fahrenheit and C is the temperature in degrees Celsius.
In Savannah's case, she measured the temperature as 50°C. Applying the conversion formula:
First, multiply the Celsius temperature by \( \frac{9}{5} \)50 \times \frac{9}{5} = 90Then, add 32 to this result to find the Fahrenheit temperature.90 + 32 = 122Therefore, the temperature of Savannah's liquid to the nearest degree Fahrenheit is 122°F.
You are required to take five courses, one each in humanities, sociology, science, math, and music. you have a choice of 2 humanities courses, 2 sociology courses, 6 science courses, 6 math courses, and 8 music courses. how many different sets of five courses are possible?
By multiplying the course options together for Humanities, Sociology, Science, Math and Music (2*2*6*6*8), we found that there are a total of 576 different sets of five courses.
Explanation:To answer this question, we have to calculate the number of different sets of five courses. This can be done by multiplying the number of choices available for each requirement. So, if you have 2 humanities courses, 2 sociology courses, 6 science courses, 6 math courses, and 8 music courses to decide from, the calculation would be as follows:
We then multiply these options together (2*2*6*6*8) to get the total number of different sets of courses possible, which is 576.
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To find the total number of different sets of five courses, multiply the number of choices for each course category: 2 (Humanities) × 2 (Sociology) × 6 (Science) × 6 (Math) × 8 (Music). This results in 1152 different sets of five courses.
To determine the number of different sets of five courses possible, we need to consider the choices available for each category:
- Humanities: 2 choices
- Sociology: 2 choices
- Science: 6 choices
- Math: 6 choices
- Music: 8 choices
The total number of different sets of five courses can be found by multiplying the number of choices in each category together. Here is the calculation:
2 × 2 × 6 × 6 × 8
Let's calculate this step-by-step:
1. 2 × 2 = 4
2. 4 × 6 = 24
3. 24 × 6 = 144
4. 144 × 8 = 1152
Therefore, the number of different sets of five courses possible is: 1152
PLEASE HELP 50 POINTS
A sports club rewards teams based on overall points earned in a season. The data for points are shown in the table, where Low represents the fewest points scored and High represents the highest points scored by a single team member.
Team Low High Range Mean Median IQR σ
Team A 22 58 36 42.1 44 18.25 10.35
Team B 38 49 11 43.9 44.5 3.5 2.97
Team C 27 36 9 31.8 32 3.75 2.55
Part A: If the club wants to award the team that has the most consistent scoring among its team members, which team should it choose and why? Justify your answer mathematically. (5 points)
Part B: If the club wants to award the team with the highest average score, which team should it choose and why? Justify your answer mathematically. (5 points)
What equation results from completing the square and then factoring? x2 + 6x = 13
To the nearest degree what is the measure of each exterior angle of a regular hexagon ?
a.60°
b.45°
c.30°
d.51°
Answer:
A
Step-by-step explanation:
The sum of measures of all the exterior angles of ANY POLYGON is 360°.
The measure of each exterior angle of ANY POLYGON is [tex]\frac{360}{n}[/tex]
where [tex]n[/tex] is the number of sides of the polygon
A hexagon has 6 sides, thus the measure of each exterior angle of a hexagon is:
[tex]\frac{360}{6}=60[/tex] degrees
Answer choice A is correct.
Determine the factors of 15x2 + 3xy + 10x + 2y. (4 points)
(3x + 2)(5x + y)
(5x + y)(2x + 3)
(3x + y)(5x + 2)
(5x + 3)(2x + y)
Answer:
the answer is the first option : A
Step-by-step explanation:
What reference angle in the first quadrant corresponds to theta = -120? Answer in radians.
Answer:
Answer: Reference angle is π/3 Radians
Step-by-step explanation:
Express the number as a ratio of integers. 7.5336
WILL GIVE BRAINLIEST PLEASE HELP!!
What is the fifth term of the recursive formula an=2an-1 with the first term of 3?
A.
7
B.
17
C.
33
D.
65
How many square meters are in 350 square centimeters?
To convert 350 square centimeters to square meters, divide by the conversion factor that 1 square meter equals 10,000 square centimeters, resulting in 0.035 square meters.
Explanation:To convert 350 square centimeters to square meters, we should remember that 1 square meter is equal to 10,000 square centimeters because 1 meter is equal to 100 centimeters and for area, we need to square that conversion (100 cm × 100 cm).
We start with the given quantity of 350 square centimeters. Then, we use the conversion factor 1 square meter is 10,000 square centimeters to perform the calculation, which gives us:
350 cm² × (1 m² / 10,000 cm²) = 0.035 m².
Therefore, 350 square centimeters is equal to 0.035 square meters.
Use the equation and type the ordered-pairs.
y = log 3 x
{(1/3,____,)(1,___), (3,___),(9,____),(27,____),(81,___)}
Answer:
[tex]{(1/3, 0) , ( 1, 0.477), (3, 0.954), (9, 1.43), (27, 1.90), (81, 2.385)}\\[/tex]
Step-by-step explanation:
Here the "X" Values are given, thus the corresponding "Y" values will be
[tex]Y = log (3 X)\\a) X = \frac{1}{1} , Y = log (3 * \frac{1}{3} ) = log (1) = 0\\b) X = 1, Y = log (3*1) = log (3) = 0.477\\c) X = 3, Y = log (3*3) = log (9) = 0.954\\d) X = 9, Y = log (3*9) = log (27) = 1.43\\e) X = 27, Y = log (3* 27) = log (81) = 1.90\\f) X = 81, Y = log (3 * 81) = log (243) = 2.385\\[/tex]
So the pattern would be
[tex]{(1/3, 0) , ( 1, 0.477), (3, 0.954), (9, 1.43), (27, 1.90), (81, 2.385)}\\[/tex]
please help, show me the steps
Find the period of the function. y = 5 cos one divided by twox
Please Help!! Find the measure of angle 2. Image Attached
opposite angles = 180 degrees
180-111 = 69
angle 2 = 69 degrees
linear function graph express in slope intercept form
midpoint of 4 – 3i and –2 + 7i please help!!!!!
An electronic device that previously sold for $21 has been reduced to 17.43. the price reduction, rounded to the nearest whole percent is
The price reduction, rounded to the nearest whole percent is [tex]17[/tex]%.
What is whole number?
The whole numbers are the part of the number system which includes all the positive integers from 0 to infinity. These numbers exist in the number line.
What is Percentage?
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
According to question, an electronic device that previously sold for $[tex]21[/tex] has been reduced to [tex]17.43[/tex]
We have to find the price reduction, rounded to the nearest whole percent .
So percentage reduction
[tex]=\frac{21-17.43}{21}[/tex]×[tex]100[/tex]%
[tex]=0.17[/tex]×[tex]100[/tex]%
[tex]=17[/tex]%
Hence, price reduction, rounded to the nearest whole percent is [tex]17[/tex]%.
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Find 3 consecutive even intergers if the sum is 108
the ratio of the corresponding side of two regular polygons is 3:4 the area of the larger polygon is 320 m squared what is the area of the smaller polygon?
The area of the smaller polygon with a side ratio of 3:4 is 180 m2 for the smaller polygon.
When dealing with the areas of similar polygons, if the ratio of corresponding sides is given, such as 3:4 in this case, the ratio of their areas is the square of the ratio of their sides. This is because the area is a two-dimensional measure, so each dimension is scaled by the ratio.
Given that the area of the larger polygon is 320 , we establish that the scale factor is 3 for the smaller polygon and 4 for the larger one.
To find the area of the smaller polygon, we use the fact that the ratio of the areas is (3/4)2 = 9/16.
This means that the area of the smaller polygon is 9/16 times the area of the larger polygon. Therefore, focusing on the comparison of areas, we calculate:
Area of smaller polygon = (9/16) x Area of larger polygon
= (9/16) x 320
Area of smaller polygon = 180
Find the volume of a sphere that has a surface area of 16 sq. in.
A. (32/3) cubic inches
B.8 cubic inches
C.(4/3) cubic inches
Answer:
A is the answer
help me create an extraneous radical equation please using this model!! :) thank you.
[tex]a \sqrt{x}+b + c = d[/tex]
I don't need you to solve it, just help me pick numbers for variable a, b, c, and d to create an extraneous solutuion
If f(x)=x-7 and g(x)=x^3, what is G(f(x))?
A. x^3+x-7
B. x^3(x-7)
C. X^3-7
D. (x-7)^3
Answer:
D. [tex](x-7)^3[/tex]
Step-by-step explanation:
Given functions are,
[tex]f(x) = x-7-----(1)[/tex]
[tex]g(x)=x^3-----(2)[/tex]
Now,
[tex]g(f(x))=g(x-7)[/tex] ( From equation (1) ),
[tex]=(x-7)^3[/tex] ( From equation (2) ),
[tex]\implies g(f(x)) = (x-7)^3[/tex]
Hence, Option D is correct.
andy states, " if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram."
A.True
B.False
The statement "If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram." is True .
What is parallelogram?"It is a quadrilateral whose opposite sides are parallel and equal in length."
What is diagonal?"It is a straight line that connects the opposite corners of a polygon through its vertices."
According to the question
The statement states that
"if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram."
Now ,
As per properties of parallelogram
In any quadrilateral the two diagonals bisect each other is a parallelogram .
Hence, The statement is True .
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A sample of size 40 is taken from an infinite population whose mean and standard deviation are 68 and 12 respectively. the probability that the sample mean is larger than 70 equals:
To solve this problem, we can use the z statistic to find for the probability. The formula for z score is:
z = (x – u) / s
Where,
u = the sample mean = 68
s = standard deviation of the samples = 12
x = sample value = 70
In this case, what is asked is the probability that the sample mean is larger than 70, therefore this corresponds to the right of z on the graph of normal distribution.
z = (70 – 68) / 12
z = 2 / 12
z = 0.17
Therefore finding for P at z ≥ 0.17 using the standard distribution tables:
P (z = 0.17) = 0.5675
But this is not the answer yet since this is the P to the left of z. Therefore the correct one is:
P (z ≥ 0.17) = 1 - 0.5675
P (z ≥ 0.17) = 0.4325 = 43.25%
The probability that the sample mean is larger than 70 is 43.25%
The probability that the sample mean is larger than 70 for a sample size of 40 from a population with a mean of 68 and standard deviation of 12 is approximately 14.69%.
To determine this probability, we can use the Central Limit Theorem (CLT), which states that the distribution of sample means will be approximately normal if the sample size is large enough (n ≥ 30 is a common benchmark).
The standard error of the mean is calculated using the formula:
SE = σ / √n
Where σ is the population standard deviation and n is the sample size.
In this case:
σ = 12
n = 40
Therefore,
SE = 12 / √40 ≈ 1.8974
The z-score is calculated using the formula:
z = (M - μ) / SE
Where M is the sample mean,
μ is the population mean,
SE is the standard error.
Given,
μ = 68
M = 70
Therefore,
z = (70 - 68) / 1.8974 ≈ 1.054
Using the z-table, we find the probability that a z-score is less than 1.054 is approximately 0.8531.
However, we need the probability that the sample mean is greater than 70, so we subtract this from 1,
1 - 0.8531 ≈ 0.1469
Thus, the probability that the sample mean is larger than 70 is approximately 0.1469, or 14.69%.
geometry. helppp!!! please explain this
What is the value of 10 C 2
What is the next number in the sequence 5 10 3 15 20 13 25 30?
Foe the AP given by a1,a2,......,an,...with non zero common difference, the equation satisfied are
Four students get 90s on a test, three get 70s, 2 get 60s and one gets an 80. what is the mean test score in this group?
Final answer:
The mean test score for the group is calculated by summing the products of each unique score and the number of students who received it, then dividing by the total number of students. In this case, the mean test score is 77.
Explanation:
To calculate the mean test score for the group, you multiply each score by the number of students who received it, then sum all those products, and finally divide by the total number of students. Four students scoring 90 would contribute 4 x 90 = 360 to the total sum. Three students scoring 70 contribute 3 x 70 = 210. Two students scoring 60 contribute 2 x 60 = 120. One student scoring 80 adds 80 to the sum. The total sum of all scores is 360 + 210 + 120 + 80 = 770. Since there are a total of 10 students (4 + 3 + 2 + 1), the mean score is calculated as 770 ÷ 10 = 77. Therefore, the mean test score in this group is 77.