Answers
The Volume of Trapezoidal prism is 420 cm².
From the given figure we can write the dimension of the prism as
a = 5, b=15, c= 15, d= 15
h= 7 and l = 6 cm
Now, Volume of Trapezoidal prism
= 1/2 (a+b) x h x l
= 1/2 (5+15) x 7 x 6
= 1/2 x 20 x 42
= 10 x 42
= 420 cm²
Thus, the Volume of Trapezoidal prism is 420 cm².
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Related Questions
A mail distribution center processes as
many as 175,000 pieces of mail each day.
The mail is sent via ground and air. Each
land carrier takes 1500 pieces per load
and each air carrier 1250 pieces per
load. The loading equipment is able to
handle as many as 200 loads per day.
Let x be the number of loads by land carriers
and y the number of loads by air carriers. Which
system of inequalities represents this situation?
Click on the correct answer.
1500x + 1250y≥ 175,000 x+y≥200
1250x + 1500y ≥ 175,000 x+y≤ 200
1500x + 1250y≤ 175,000 x+y≤ 200
1250x + 1500y≤ 175,000 x+y≤ 200
Answers
The correct system of inequalities is 1500x + 1250y ≥ 175,000 and x + y ≥ 200, option A is correct.
We have two carriers: land carriers and air carriers.
The land carriers can transport 1500 pieces of mail per load, and the air carriers can transport 1250 pieces of mail per load.
The loading equipment at the distribution center can handle up to 200 loads per day.
To represent this situation using a system of inequalities, we can define the variables x and y as the number of loads by land carriers and air carriers, respectively.
The first inequality, 1500x + 1250y ≥ 175,000, represents the total number of pieces of mail transported per day.
The second inequality, x + y ≥ 200, represents the total number of loads.
Hence, the correct system of inequalities is 1500x + 1250y ≥ 175,000 and x + y ≥ 200.
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[tex]3^a = 9^b = 27^c[/tex] and a, b, and c don’t equal 0, what is [tex]\frac{a}{b} + \frac{b}{c} + \frac{c}{a}[/tex]
Answers
To solve the expression [tex]\large\sf\:\frac{a}{b} + \frac{b}{c} + \frac{c}{a}\\[/tex] given the conditions [tex]\large\sf\:3^a = 9^b = 27^c\\[/tex], we can use logarithmic properties and the fact that [tex]\large\sf\:3^2 = 9\\[/tex] and [tex]\large\sf\:3^3 = 27\\[/tex].
Let's start by finding the values of a, b, and c using logarithmic properties:
Taking the logarithm of both sides of [tex]\large\sf\:3^a = 9^b\\[/tex], we get:
[tex]\large\sf\:\log_3(3^a) = \log_3(9^b)\\[/tex]
Applying the power rule of logarithms, we can bring down the exponents:
[tex]\large\sf\:a\log_3(3) = b\log_3(9)\\[/tex]
Since [tex]\large\sf\:\log_3(3) = 1[/tex] and [tex]\large\log_3(9) = 2\\[/tex], we simplify to:
[tex]\large\sf\:a = 2b\\[/tex] ---- (1)
Similarly, taking the logarithm of both sides of [tex]\sf\:9^b = 27^c\\[/tex], we get:
[tex]\large\sf\:b\log_3(9) = c\log_3(27)\\[/tex]
Using the values of [tex]\sf\:\log_3(9)\\[/tex] and [tex]\sf\:\log_3(27)\\[/tex] as before, we have:
[tex]\large\sf\:b(2) = c(3)\\[/tex]
Simplifying, we get:
[tex]\large\sf\:2b = 3c\\[/tex] ---- (2)
Now, let's substitute the value of b from equation (1) into equation (2):
[tex]\large\sf\:2(2b) = 3c\\[/tex]
[tex]\large\sf\:4b = 3c\\[/tex]
Rearranging, we find:
[tex]\large\sf\:c = \frac{4b}{3}\\[/tex] ---- (3)
We now have expressions for a, b, and c in terms of b. Let's substitute these into the expression [tex]\large\sf\:\frac{a}{b} + \frac{b}{c} + \frac{c}{a}\\[/tex]:
[tex]\large\sf\:\frac{a}{b} + \frac{b}{c} + \frac{c}{a} = \frac{2b}{b} + \frac{b}{\frac{4b}{3}} + \frac{\frac{4b}{3}}{2b}\\[/tex]
Simplifying further, we get:
[tex]\large\sf\:\frac{2}{1} + \frac{3}{4} + \frac{2}{3}\\[/tex]
Finding the common denominator and combining the fractions, we have:
[tex]\large\sf\:\frac{24}{12} + \frac{9}{12} + \frac{8}{12}\\[/tex]
Adding the fractions together, we obtain:
[tex]\large\sf\:\frac{24 + 9 + 8}{12} = \frac{41}{12}\\[/tex]
Therefore, [tex]\large\sf\:\frac{a}{b} + \frac{b}{c} + \frac{c}{a} = \frac{41}{12}\\[/tex].
NEED HELP ASAP WILL GIVE BRAINLIEST HELP!
Answers
Answer:
The correct answer is 2.
The graph below shows a company's profit f(x), in dollars, depending on the price of pens x, in dollars, sold by the company:
Graph of quadratic function f of x having x intercepts at ordered pairs 0, 0 and 6, 0. The vertex is at 3, 120.
Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit?
Part B: What is an approximate average rate of change of the graph from x = 3 to x = 5, and what does this rate represent?
Part C: Describe the constraints of the domain.
Answers
The Domain of the function would be the interval [0, 6].The increasing interval represents the point where the company is pricing the pens appropriately, resulting in increasing profit.Average rate of change = (f(5) - 120) / (5 - 3)
Part A:
The x-intercepts of the graph, located at the ordered pairs (0, 0) and (6, 0), represent the points where the profit function intersects the x-axis. In the context of the problem, these x-intercepts indicate the price values at which the company sells pens, resulting in zero profit. When the price is $0, the company does not make any profit, and when the price is $6, the company also does not make any profit. The x-intercepts represent the break-even points where the company covers its costs but does not generate any profit.
The maximum value of the graph, located at the vertex (3, 120), represents the peak profit achieved by the company. The vertex is the highest point on the graph and indicates the optimal price at which the company can maximize its profit. In this case, when the price of pens is $3, the company achieves a maximum profit of $120.
Regarding the intervals of increasing and decreasing profit, the function is decreasing to the left of the vertex (3, 120) and increasing to the right of the vertex. This means that for prices less than $3, the profit decreases, and for prices greater than $3, the profit increases. The decreasing interval represents the point where the company is pricing the pens too low, resulting in decreasing profit. The increasing interval represents the point where the company is pricing the pens appropriately, resulting in increasing profit.
Part B:
To find the approximate average rate of change of the graph from x = 3 to x = 5, we need to calculate the slope of the line segment connecting the two points. The average rate of change represents the average amount by which the profit changes per unit increase in price over the given interval.
Using the coordinates (3, 120) and (5, f(5)) on the graph, we can determine the change in profit and price:
Change in profit = f(5) - 120
Change in price = 5 - 3
Substituting the values of the points into the equation, we can calculate the approximate average rate of change:
Average rate of change = (f(5) - 120) / (5 - 3)
Part C:
The constraints of the domain refer to the limitations or restrictions on the values that x (the price of pens) can take. Based on the given information, the x-intercepts of the graph are at (0, 0) and (6, 0), indicating that the price cannot be negative or exceed $6. Therefore, the domain of the function would be the interval [0, 6]. The constraint is that the price of the pens must be within this range for the profit function to be applicable.
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Note the full question may be :
A bakery sells cupcakes for $2 each. The bakery's total revenue from selling cupcakes is given by the function R(x) = 2x, where x represents the number of cupcakes sold.
Part A: What does the x-intercept of the graph of R(x) represent? Explain its significance in the context of the bakery's revenue.
Part B: What is the slope of the graph of R(x)? Interpret the meaning of this slope in terms of the bakery's revenue and the price of cupcakes.
Part C: If the bakery wants to maximize its revenue, what should be the ideal number of cupcakes to sell? Explain your answer based on the graph of R(x).
PLEASE HURRY!
The box plot shows the times for sprinters on a track team.
A horizontal number line starting at 40 with tick marks every one unit up to 59. The values of 42, 44, 50, 54, and 56 are all marked by the box plot. The graph is titled Sprinters' Run Times, and the line is labeled Time in Seconds.
Which of the following is the five-number summary for this data?
Min = 42, Q1 = 44, Median = 50, Q3 = 54, Max = 56
Min = 41, Q1 = 43, Median = 49.5, Q3 = 56, Max = 58
Min = 44, Q1 = 48, Median = 50.5, Q3 = 53, Max = 56
Min = 42, Q1 = 45, Median = 49, Q3 = 56, Max = 58
Answers
Min = 42, Q1 = 44, Median = 50, Q3 = 54, Max = 56
This is determined based on the given values marked on the box plot. The minimum value is 42, the lower quartile (Q1) is 44, the median is 50, the upper quartile (Q3) is 54, and the maximum value is 56.
In the figure below, S is the center of the circle. Suppose that JK = 16, MP= 8, LP = 2x + 4, and PS= 3.5. Find the
following.
Answers
The measure for NS is 3.5 cm and the value of x is 2.
We have,
JK = 16, MP= 8, LP = 2x + 4, and PS= 3.5.
Since PS is perpendicular to ML then
MP = LP
So, 8 = 2x+ 4
2x = 8-4
2x= 4
x= 4/2
x= 2
Now, ML = MP + PL = 16
and, JK = ML= 16
Then, NS = PS
NS = PS = 3.5 cm
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Julle is selling candy bare to raise money for new band uniforms. Candy bar x sells for $2 and candy bar y sells for $3. The number of y candy bare Julla sells must be greater than or equal to three times the number of x candy bars she sells. She has at most 36 candy bars to sell. What is the maximum revenue she can make?
Answers
Answer:
n this question, you are asked how much the maximum revenue. Since candy Y sold for a higher price than candy X, that means you have to sell candy Y as much as possible.The number of candy Y must be >= 3 times candy X. Since this won't limit candy Y selling, then you can convert all 36 candy into candy Y and 0 candy X36 candy (Y) >= 0 candy(X) ----> the requirement is met.The revenue would be 36 candy Y * $3/candy Y= $108
Step-by-step explanation:
Results:
1. Machine A costs the most but offers the highest increase in coffee output. Operating the machine can be difficult, so employees will need training.
2. Machine B costs $100 less than machine A, produces acceptable coffee output, and is simple to use. No training is required.
3. Machine C costs the least, produces slightly less than the current machine, and is simple to use. No training is required.
11
Select the correct answer from each drop-down menu.
Complete the sentence to tell why the writer has created this proposal.
The writer has written the proposal to
A) determine which kind of coffee most people like
B) compare different coffee makers before making a purchase
C) analyze the budget for buying a new coffee maker
Answers
Answer:
Step-by-step explanation:
imagine copy and pasting your question.
Which of the following statements are true? Check all of the boxes that apply.
f(x) = 2√x has the same domain and range as f(x)=√x
f(x) = -2√x has the same domain and range as f(x)=√x
f(x) = -√x has the same domain as f (x)=√x, but a different range.
f(x)=√x has the same domain as f(x)=√x, but a different range
0 0 0 0
DONE ✔
Intro
15 of 19
Answers
The correct statements regarding the domain and the range of the functions are given as follows:
f(x) = 2√x has the same domain and range as f(x)=√xf(x) = -√x has the same domain as f (x)=√x, but a different range.How to obtain the domain and range of a function?The domain of a function is defined as the set containing all the values assumed by the independent variable x of the function, which are also all the input values assumed by the function.The range of a function is defined as the set containing all the values assumed by the dependent variable y of the function, which are also all the output values assumed by the function.For the square root function, we have that:
The domain is x >= 0.The range is y >= 0.Hence if we multiply the function by a negative number, the domain of the function remains constant, but the range is changed.
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3500pounds is placed into a savings account that pays interest at arate of 1.5% compounded annually.
Calculate the total compound amount at the end six years of investment, rounded to 2 decimal places.
Answers
Answer:
$3827.00
Step-by-step explanation:
To calculate the total compound amount at the end of six years with an interest rate of 1.5% compounded annually, we can use the formula for compound interest:
A = P * (1 + r/n)^(n*t)
Where:
A = Total compound amount
P = Principal amount (initial investment)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years
In this case:
P = $3500
r = 1.5% = 0.015 (as a decimal)
n = 1 (compounded annually)
t = 6 years
Substituting these values into the formula, we have:
A = 3500 * (1 + 0.015/1)^(1*6)
Calculating this expression, we get:
A ≈ 3500 * (1.015)^6 ≈ 3500 * 1.093717 ≈ 3827.00
Rounding the total compound amount to 2 decimal places, the final value is approximately $3827.00
What is the area of the rhombus? 25 mm2 33 mm2 50 mm2 100 mm2
Answers
The area of the rhombus is 100 mm². The Option D.
What is the area of the rhombus?To get area of a rhombus, we will use the formula: Area = (d₁ * d₂) / 2 where d₁ and d₂ are the lengths of the diagonals.
Given that the horizontal diagonal length is 25 millimeters (d₁ = 25 mm) and the vertical diagonal length is 8 millimeters (d₂ = 8 mm.
We will substitute values into the formula:
Area = (25 mm * 8 mm) / 2
Area = 200 mm² / 2
Area = 100 mm².
Full question:
A rhombus with horizontal diagonal length 25 millimeters and vertical diagonal length 8 millimeters. what is the area of the rhombus? 25 mm2 33 mm2 50 mm2 100 mm2
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Find the missing angle and side measures of Delta*ABC , given that
m angle A = 50 deg , m angle C = 90 deg , and CB = 16
Answers
The missing angle is <B= 40 degree and missing side length is AB = 12.25 and AC = 19.068.
To find the missing angle and side measures of ΔABC, we can use the properties of a triangle.
Given:
∠A = 50°
∠C = 90°
CB = 16
We can start by finding the measure of ∠B:
∠A + ∠B + ∠C = 180° (Sum of angles in a triangle)
50° + ∠B + 90° = 180°
∠B + 140° = 180°
∠B = 180° - 140°
∠B = 40°
Now, using Sine law
CB/ sin A = AB / sin C
16 / sin 50 = AB / sin 90
16 / 0.766044 = AB
AB = 12.25
Again 12.25 = AC/ sin B
12.25 = AC / sin 40
AC = 19.068
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Use the given proof to answer the question below:
Given ABCD is a parallelogram.
Prove: ADCB
D
A
1
2
3
4
S
6
Statements
ABCD is a parallelogram
ABI CD and AD IBC
and
AC = AC
ADCA ABAC
AD CB
Which of the options below complete the proof?
A. Statement 3: LBACZCAD and ZBCA LDCA
Reason 5: A.A.S. Postulate
B. Statement 3: LBACCAD and ZBCA = LDCA
Reason 5: A.S.A Postulate
C. Statement 3: LBAC LDCA and LBCA LDAC
Reason 5: A.A.S. Postulate
D. Statement 3: ZBAC LDCA and LBCA LDAC
Reason 5: A.S.A Postulate
Reasons
Given
Definition of parallelogram
Alternate interior angles theorem
Reflexive property
C.P.C.T.C.
Answers
The correct option is D.
Given that ABCD is a parallelogram, we need to prove AD ≅ CB.
So,
Properties of a parallelogram =
Opposite sides are parallel.
Opposite sides are congruent.
Opposite angles are congruent.
Statement Reason
1. ABCD is a parallelogram Given
2. AB║CD and AD║BC Definition of parallelogram
3. ∠BAC ≅ ∠DCA and ∠BCA ≅ ∠DAC Alternate interior angles theorem
4. AC ≅ AC Reflexive property
5. ΔBAC ≅ ΔDCA A.S.A Postulate
6. AD ≅ CB CPCTC
Hence the correct option is D.
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A dance team is made up of 9 girls and 3 boys. Two of the girls and 1 of the boys are also on the debate team. What percent of the dance team is also on the debate team? Enter your answer in the box.
Answers
Answer:
25%
Step-by-step explanation:
9+3=12 dance people total
divide 3 by 12 to determine debate members over dance members
=.25 or 25%
the expression 2x+4 is equal to what for x = 3
Answers
Answer:10
Step-by-step explanation: You plug in 3 for x so you get the equation 2(3)+4
Which becomes 6+4
Which equals 10
Find the values of m and n. Give the answer in simplest radical form.
PLS HELP ASAPP!!!!!!
Answers
The values of the side m and n for the right triangle are 36 and 12√3 respectively using the trigonometric ratio of sine
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
recall that sin60° = √3/2 and sin30° = 1/2
sin 60° = m/(24√3) {opposite/hypotenuse}
√3/2 = m/(24√3)
m = (24√3 × √3)/2 {cross multiplication}
m = 12 × 3
m = 36
sin 30° = n/(24√3)
1/2 = n/(24√3)
n = 24√3/2 {cross multiplication}
n = 12√3
Therefore, the values of the side m and n for the right triangle are 36 and 12√3 respectively using the trigonometric ratio of sine
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23 POINTS PLS HELPPP!!!
Use the Law of Sines to find the length of side b in ABC. Round to the nearest tenth. Show your work.
Consider
ABC.
B
28°
112°
37
Answers
Angle C of the triangle measures 40°.
Side AC = 18.84
Side AB= 25.79
Given triangle,
∠A = 112°
∠B = 28°
BC = 37
Now,
Sum of all the interior angles of triangle is 180.
So,
∠A + ∠B +∠C = 180°
112° + 28° + ∠C = 180°
∠C = 40°
Now,
According to sine rule,
Ratio of side length to the sine of the opposite angle is equal.
Thus,
a/SinA = b/SinB = c/SinC
Let,
BC = a
AC = b
AB = c
So,
a/Sin112 = b/Sin28 = c/Sin40
37/0.921 = b/0.469 = C/0.642
Solving,
AB = c = 25.79
AC = b = 18.84
Thus with the properties of triangle side length and angles can be calculated.
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In the incidence matrix for this figure, what would be the element in row 1 column 5?
Answers
In the incidence matrix, the element in row 1 column 5 is determined as 1.
What is the element in row 1 and column 5?The element in row 1 column 5 is calculated as follows;
In an incidence matrix, the rows represent the vertices of the graph, and the columns represent the edges.
Since vertex 1 and vertex 5 are adjacent to each other, the value of the element in row 1 column 5 will be 1, indicating that there is a connection between vertex 1 and vertex 5.
Had it been they are not adjacent, the element would have been 0. Since there will be no connection between them in the polygon.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
The value of x in the given right triangle HJK include the following: C. 10.
What is a 30-60-90 triangle?In Mathematics and Geometry, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the side lengths are in the ratio 1:√3:2.
This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side):
Hypotenuse, x = 5 × 2
Hypotenuse, x = 10.
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Write equivalent fractions for 2 2/3 and 2 1/4 using a common denominator please hurry
Answers
The equivalent fractions for the mixed numbers, with the same denominator, are given as follows:
32/12 and 27/12.
How to obtain the equivalent fractions?The mixed numbers in the context of this problem are given as follows:
2 and 2/3.2 and 1/4.The fractions that represent each number are given as follows:
2 + 2/3 = 6/3 + 2/3 = 8/3.2 + 1/4 = 8/4 + 1/4 = 9/4.The least common factor of 3 and 4 is given as follows:
3 x 4 = 12.
Hence the equivalent fractions are given as follows:
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can someone answer the ones i got wrong please
Answers
When a student is selected at random, the solution for the various possible outcome would be given below as follows:
p(pass or did not study)=0.409
p(pass or did study)=0.312
p(fail and pass)= 0.201
p(pass or fail)= 1
How to calculate the possible outcome of the following given event?The formula that is used to calculate probability = possible outcome/sample space.
The total number of scores of the statistics students = 93
For p(pass or did not study):
possible outcome = 38
sample size = 93
probability = 38/93 = 0.409
For p(pass or did study):
possible outcome = 29
sample size = 93
probability = 29/93 = 0.312
For p(fail and pass):
p(fail) = 26/93
p(pass) = 67/93
probability = 26/93× 67/93
= 1742/8649
= 0.201
For p(pass or fail);
P(pass) = 67/93
P(fail) = 26/93
Probability of pass or fail = 67/93+26/93
= 93/93 = 1
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April can buy a package of 10 folders for $1.20 or a package of 8 folders for $1.12. What is the unit price, per folder, in each package?
Each folder in the package of 10 costs $
Each folder in the package of 8 costs $
Answers
Answer:
Step-by-step explanation:
For the package of 10 folders: Unit price = $1.20 / 10 = $0.12 For the package of 8 folders: Unit price = $1.12 / 8 = $0.14
When applied mathematically - 1.20 / 10 = $0.12 (each folder)
1.12 / 8 = $0.14
May I please get a little help with this question? Thank you so much.
Answers
The y-intercept of the function is (0, c)
The coefficients b determine the horizontal shift of the parabola compared to the parent function
If a is negative, the parabola opens downward
The y-intercept of the function is (0, c).
This means that when x = 0, the y-value is equal to c.
The constant term c represents the y-coordinate of the point where the parabola intersects the y-axis.
The coefficient b determines the horizontal shift of the parabola compared to the parent function.
The value of b affects the position of the vertex and determines if the parabola is shifted to the left or right.
A positive value of b shifts the parabola to the left, while a negative value of b shifts it to the right.
If a is negative, the parabola opens downward.
The coefficient a determines the shape of the parabola.
If a is positive, the parabola opens upward, and if a is negative, the parabola opens downward. The sign of a determines the direction in which the parabola faces.
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33 + 78 + 23 + 21 + 98 + 32 = ???
Answers
Answer:
The sum of 33, 78, 23, 21, 98, and 32 is 325.
Find probability between 240 and 300 apples.
Answers
Answer:
47.5% (rounds to 48%)
Step-by-step explanation:
You want the probability that a tree has between 240 and 300 apples, given the distribution of numbers of apples is normal with mean 300 and standard deviation 30.
CenterThe given diagram shows the center 95% of numbers of apples lies between 240 and 360. The number between 240 and 300 is half that symmetical distribution, so is ...
95%/2 = 47.5%
The probability a tree will have between 240 and 300 apples is about 47.5%.
__
Additional comment
The figure "95%" is an approximation. A closer value is 95.45%. Hence, a closer value to the probability is 47.7%.
No rounding requirement is shown. To the nearest whole percentage point, the probability would be 48%.
<95141404393>
You empty a 2-liter bottle every 8 seconds into tanks that hold 50 gallons. How long will it take you to fill 11 tanks? (3.8 l = 1 gallon)(Convert 11 tanks to hours)
Answers
It will take approximately 2.32 hours to fill 11 tanks.
First, we need to convert the capacity of the tanks from gallons to liters, as the rate at which we empty the bottle is given in liters. Since 1 gallon is equal to 3.8 liters, the capacity of each tank is 50 gallons * 3.8 liters/gallon = 190 liters.
Now, let's calculate the time it takes to fill one tank:
The bottle is emptied at a rate of 2 liters every 8 seconds. To find the time it takes to fill one tank, we divide the capacity of the tank (190 liters) by the rate at which we empty the bottle (2 liters/8 seconds):
Time for one tank = 190 liters / (2 liters/8 seconds) = 190 liters * (8 seconds/2 liters) = 760 seconds.
Next, we need to find the total time required to fill 11 tanks. Since each tank takes 760 seconds to fill, we multiply this by 11 to account for the 11 tanks:
Total time to fill 11 tanks = 760 seconds/tank * 11 tanks = 8,360 seconds.
Finally, we convert the total time from seconds to hours. There are 60 seconds in a minute and 60 minutes in an hour, so:
Total time to fill 11 tanks = 8,360 seconds * (1 minute/60 seconds) * (1 hour/60 minutes) = 2.32 hours (rounded to two decimal places).
Therefore, it will take approximately 2.32 hours to fill 11 tanks.
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Which statements are true of the graph of h(x) = 3√x-4? Check all that apply.
The domain of h(x) is the set of all real numbers.
The range of h(x) is the set of all real numbers.
For all points (x, h(x)), h(x) exists if and only if x - 4
2
O The graph of h(x) is a translation of f(x) down 4 units.
O The graph of h(x) intercepts the x-axis at (4, 0).
Answers
The true statements about the graph of h(x) = ∛(x-4) are:
The domain of h(x) is the set of all real numbers.
For all points (x, h(x)), h(x) exists if and only if x - 4≥0
The graph of h(x) intercepts the x-axis at (4, 0).
The domain of h(x) is the set of all real numbers since there are no restrictions on the input variable x.
For all points (x, h(x)), h(x) exists if and only if x - 4 ≥ 0. This is because the cube root function is only defined for non-negative values, and the expression inside the cube root, x - 4, must be non-negative for h(x) to exist.
The graph of h(x) intercepts the x-axis at (4, 0) since plugging in x = 4 into the equation gives h(4) = ∛(4-4) = ∛0 = 0. This means that the point (4, 0) lies on the graph.
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subtract 8.263 from 13.48.
Answers
Answer:
13.48 - 8.263 = 5.217
Answer:5.217
Step-by-step explanation: caculate it
50 Points! Multiple choice geometry question. Photo attached. Thank you!
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The distance between the side AB are 314.2 ft.
In a triangle ABC AC = 200 ft, m ∠A = 72°, and m ∠B = 37°. we need to find the measure of the side AB,
So,
Using sine law.
Sin A / CB = Sin B / AC = Sin C / AB
Using the angle sum property of a triangle we find the value of angle C,
∠C = 180° - (∠A + ∠B)
∠C = 180° - (72° + 37°)
∠C = 180° - 109°
∠C = 71°
So,
Sin 37° / 200 = Sin 71° / AB
AB = 200 / Sin 37° × Sin 71°
AB = 314.2 ft
Hence the distance between the side AB are 314.2 ft.
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Dakota is a quality control manager for a manufacturing plant that produces batteries for tablet computers. Based on prior history, Dakota knows that 0.6% of all tablet computer batteries produced are defective. He selects a random sample of n=1,200 tablet computer batteries from a recently produced lot and tests each battery to determine whether it is defective. What is the probability that Dakota finds 5 or fewer defective batteries? Use a TI-83, TI-83 plus, or TI-84 calculator to find the probability.
Round your answer to four decimal places.
Answers
Using binomial probability, the probability is 0.8897
What is the probability that Dakota finds 5 or fewer defective batteries?Using binomial probability formula, we can determine the number of defective batteries
In this case, n = 1,200 (the sample size) and p = 0.006 (the probability of finding a defective battery).
We want to find the probability of finding 5 or fewer defective batteries, which is equivalent to finding the cumulative probability up to 5.
Let's calculate this probability:
P(X ≤ 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)
Using the binomial probability formula:
[tex]P(X = k) = C(n, k) * p^k * (1 - p)^(^n ^- ^k^)[/tex]
where C(n, k) represents the number of combinations of n items taken k at a time.
Plugging the values and solving;
P(X ≤ 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) =
[tex]C(1200, 0) * 0.006^0 * (1 - 0.006)^(^1^2^0^0 ^- ^0^)\\+ C(1200, 1) * 0.006^1 * (1 - 0.006)^(^1^2^0^0 ^- ^1^)\\+ C(1200, 2) * 0.006^2 * (1 - 0.006)^(1^2^0^0 ^- ^2^)\\+ C(1200, 3) * 0.006^3 * (1 - 0.006)^(^1^2^0^0 ^- ^3)\\+ C(1200, 4) * 0.006^4 * (1 - 0.006)^(^1^2^0^0 ^- ^4)\\+ C(1200, 5) * 0.006^5 * (1 - 0.006)^(^1^2^0^0 ^- ^5^)[/tex]
To calculate these probabilities, we need to use a combination formula to determine the number of combinations. The combination formula is given by:
C(n, k) = n! / (k! * (n - k)!)
Now let's calculate the probability:
[tex]P(X \leq 5) = \\C(1200, 0) * 0.006^0 * (1 - 0.006)^(^1^2^0^0 ^- ^0^)\\+ C(1200, 1) * 0.006^1 * (1 - 0.006)^(^1^2^0^0 ^- ^1^)\\+ C(1200, 2) * 0.006^2 * (1 - 0.006)^(^1^2^0^0 ^- ^2^)\\+ C(1200, 3) * 0.006^3 * (1 - 0.006)^(^1^2^0^0 ^- ^3^)\\+ C(1200, 4) * 0.006^4 * (1 - 0.006)^(^1^2^0^0 ^- ^4^)\\+ C(1200, 5) * 0.006^5 * (1 - 0.006)^(^1^2^0^0 ^- ^5^)[/tex]
Using a calculator or statistical software to perform the calculations, we find that the probability is approximately 0.8897 when rounded to four decimal places
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