Trent will need approximately 2.86 bottles of waterproof spray to cover his tent.
To calculate the number of bottles of waterproof spray Trent will need to cover his tent, we first need to find the surface area of the tent.
The surface area of a square-based pyramid is given by the formula:
Surface Area = Base Area + (0.5 x Perimeter of Base x Slant Height)
The base of the pyramid is a square with a side length of 14 feet, so the base area is:
Base Area = (Side Length)^2 = 14^2 = 196 square feet
To find the slant height of the pyramid, we can use the Pythagorean theorem. The slant height is the hypotenuse of a right triangle formed by one side of the base, the height of the pyramid, and the slant height. The height of the pyramid is given as 8 feet, and half the length of the base is 7 feet.
Using the Pythagorean theorem:
[tex]Slant Height^2 = (Half Base Length)^2 + Height^2[/tex]
[tex]Slant Height^2 = 7^2 + 8^2Slant Height^2 = 49 + 64Slant Height^2 = 113Slant Height ≈ √113 ≈ 10.63 feet[/tex]
Now we can calculate the surface area of the tent:
Surface Area = 196 + (0.5 x 4 x 10.63)
Surface Area = 196 + (2 x 10.63)
Surface Area = 196 + 21.26
Surface Area ≈ 217.26 square feet
Since each bottle of waterproof spray covers 76 square feet, we can divide the total surface area of the tent by the coverage of each bottle to find the number of bottles needed:
Number of Bottles = Surface Area / Coverage per Bottle
Number of Bottles = 217.26 / 76
Number of Bottles ≈ 2.86
Therefore, Trent will need approximately 2.86 bottles of waterproof spray to cover his tent. Since we can't have a fraction of a bottle, he will need to round up to the nearest whole number. Therefore, Trent will need 3 bottles of waterproof spray to fully waterproof his tent.
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Write and solve an inequality that represents the number of gigabytes of data . G . You can use to stay under your budget of $130
Answer:
Sure, here is the inequality that represents the number of gigabytes of data (G) you can use to stay under your budget of $130:
```
cost_per_gb * G <= budget
```
where:
* cost_per_gb is the cost of data per gigabyte, which is $10 in this case
* G is the number of gigabytes of data
* budget is your budget, which is $130 in this case
To solve this inequality, we can first subtract cost_per_gb from both sides of the inequality. This gives us:
```
G <= budget / cost_per_gb
```
We can then plug in the values for cost_per_gb and budget to get:
```
G <= 130 / 10
```
```
G <= 13
```
This means that you can use up to 13 gigabytes of data and still stay under your budget. If you use more than 13 gigabytes of data, you will exceed your budget.
Here is a table that shows the cost of data for different amounts of data:
```
| Amount of data (G) | Cost (\$) |
|---|---|
| 1 | 10 |
| 2 | 20 |
| 3 | 30 |
| ... | ... |
| 13 | 130 |
| 14 | 140 |
| ... | ... |
```
Step-by-step explanation:
Need help with this question. PLS helpppppp
Answer:
x = 0.39 or
x = -1.72
Step-by-step explanation:
The quadrateic formula is:
[tex]x = \frac{-b\pm\sqrt{b^2 - 4ac} }{2a}[/tex]
eq: 3x² + 4x - 2
which is of the form ax² + bx + c = 0
where a = 3, b = 4 and c = -2
sub in quadratic formuls,
[tex]x = \frac{-4\pm\sqrt{4^2 - 4(3)(-2)} }{2(3)}\\\\=\frac{-4\pm\sqrt{16 + 24} }{6}\\\\=\frac{-4\pm\sqrt{40} }{6}\\\\=\frac{-4\pm2\sqrt{10} }{6}\\\\=\frac{-2\pm\sqrt{10} }{3}\\\\=\frac{-2+\sqrt{10} }{3} \;or\;=\frac{-2-\sqrt{10} }{3}\\\\=0.39 \;or\; -1.72[/tex]
A man goes 10m North and turns left and covers 6m. He again turns left and walks 5m. Which direction is he in from starting point?
The man is in the south direction from the starting point.
Let's visualize the movements of the man step by step:
The man starts by going 10 meters north.
He then turns left (which means he is now facing west) and covers 6 meters in that direction.
Next, he turns left again (which means he is now facing south) and walks 5 meters.
To determine the final direction of the man from the starting point, we can consider the net effect of his movements.
Starting from the north, he moved 10 meters in that direction. Then, he turned left twice, which corresponds to a 180-degree turn, effectively changing his direction by 180 degrees.
Since he initially faced north and then made a 180-degree turn, he is now facing south. Therefore, the direction he is in from the starting point is "south."
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Which of the following could be the ratio between the lengths of the two legs
of a 30-60-90 triangle?
Check all that apply.
A. √2:2
B. √√3:√√3
C. √5:3
D. 1 √3
□ E. 1: √2
O F. 2:3
SUBMIT
Answer: E
Step-by-step explanation:
Triangle ABC has the following coordinates: A=(5,-5), B=(3,-3), C=(5,-3) What are the coordinates of triangle A'B'C' if it is created by dilating triangle ABC with the origin (0,0) as the center of dilation and with a scale factor of 3?
Answer:A' = (15, -15), B' = (9, -9), and C' = (15, -9)
Step-by-step explanation:
To dilate triangle ABC with a center of dilation at the origin (0,0) and a scale factor of 3, you need to multiply the coordinates of each vertex by the scale factor.
Let's calculate the coordinates of triangle A'B'C':
For point A:
x-coordinate of A' = scale factor * x-coordinate of A = 3 * 5 = 15
y-coordinate of A' = scale factor * y-coordinate of A = 3 * (-5) = -15
Therefore, A' = (15, -15)
For point B:
x-coordinate of B' = scale factor * x-coordinate of B = 3 * 3 = 9
y-coordinate of B' = scale factor * y-coordinate of B = 3 * (-3) = -9
Therefore, B' = (9, -9)
For point C:
x-coordinate of C' = scale factor * x-coordinate of C = 3 * 5 = 15
y-coordinate of C' = scale factor * y-coordinate of C = 3 * (-3) = -9
Therefore, C' = (15, -9)
Hence, the correct coordinates of triangle A'B'C' are A' = (15, -15), B' = (9, -9), and C' = (15, -9).
A student is applying to the University of Florida (UF) and Florida State (FSU).
There is a 40% chance of being accepted at FSU. If the student is accepted at FSU, the probability of being accepted at UF is 60%. If the student is not accepted at FSU there is an 90% chance of non-acceptance at UF.
What is the probability that a student is accepted at FSU or is accepted at UF?
Answer:
Hope this helps and have a nice day
Step-by-step explanation:
To find the probability that a student is accepted at FSU or accepted at UF, we can use the concept of conditional probability and the law of total probability.
Let's denote the events as follows:
A: Accepted at FSU
B: Accepted at UF
We need to find P(A or B), which can be calculated as the sum of the probabilities of each event minus the probability of their intersection:
P(A or B) = P(A) + P(B) - P(A and B)
Given the information provided, we can calculate the probabilities:
P(A) = 0.4 (40% chance of being accepted at FSU)
P(B|A) = 0.6 (60% chance of being accepted at UF if accepted at FSU)
P(B|A') = 0.9 (90% chance of non-acceptance at UF if not accepted at FSU)
P(A and B) = P(A) * P(B|A) = 0.4 * 0.6 = 0.24 (probability of being accepted at both FSU and UF)
Now we can substitute these values into the formula:
P(A or B) = P(A) + P(B) - P(A and B)
= 0.4 + (1 - 0.4) * P(B|A') - P(A and B)
= 0.4 + 0.6 * 0.9 - 0.24
= 0.4 + 0.54 - 0.24
= 0.7
Therefore, the probability that a student is accepted at FSU or accepted at UF is 0.7, or 70%.
please help!!!!!!!!!!!!!!!!!!!!!!
The systematic sample would be A. The city manager takes a list of the residents and selects every 6th resident until 54 residents are selected.
The random sample would be C. The botanist assigns each plant a different number. Using a random number table, he draws 80 of those numbers at random. Then, he selects the plants assigned to the drawn numbers. Every set of 80 plants is equally likely to be drawn using the random number table.
The cluster sample is C. The host forms groups of 13 passengers based on the passengers' ages. Then, he randomly chooses 6 groups and selects all of the passengers in these groups.
What are systematic, random and cluster samples ?A systematic sample involves selecting items from a larger population at uniform intervals. A random sample involves selecting items such that every individual item has an equal chance of being chosen.
A cluster sample involves dividing the population into distinct groups (clusters), then selecting entire clusters for inclusion in the sample.
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find x using the trigonometric function
The value of x in the diagram given in the question is 6
How do i determine the value of x?From the question given above, the following data were obtained:
Angle (θ) = 60Adjacent = 3Hypotenuse = x =?The value of x can be obtained using cos ratio.
Cos θ = Adjacent / Hypotenuse
Cos 60 = 3 / x
Cross multiply
x × Cos 60 = 3
Divide both sides by Cos 60
x = 3 / Cos 60
= 3 / 0.5
= 6
Thus, the value of x is 6
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Not sure whether to use integration by substitution or partial fractions?
Answer:
Step-by-step explanation:
I think you have to use partial fractions. Substitution won't work because the numerator is not the derivative of the denominator. I hope I am correct on this.
I have attached just the partial fractions part of the question. I did not integrate.
Dylan's mom told him that she would replace each one of his dimes with a quarter. If he uses all of his coins, determine if Dylan would then have enough money to buy a game priced at $20.98 if he must also pay an 8% sales tax.
What is -2.93(b + 12) = -11.72
What is b
(Solve two-step linear equations)
please answer i am stuck
Answer:
x intercept : -1
y intercept : 3
Step-by-step explanation:
We have 3x - y = -3 ---eq(1)
The x intercept is the value of x when y = 0 in eq(1),
⇒ 3x - 0 = -3
⇒ x = -3/3
⇒ x = -1
The y intercept is the value of y when x = 0 in eq(1),
⇒ 3(0) - y = -3
⇒ -y = -3
⇒ y = 3
Solving for Side Lengths of Right Triangles
Quiz Active
1
2 3
O
4 5
с
Which relationship in the triangle must be true?
sin(B) = sin(A)
O sin(B) = cos(90 - B)
cos(B) = sin(180 - B)
O cos(B) = cos(A)
6
B
7 8
9
10
TIME REMAINING
12:30
Answer:
6 is the sin
Step-by-step explanation:
How much is 700000 in Penny’s
Answer:
$7000
Step-by-step explanation:
700,000 dollars is equal to 70,000,000 pennies.
To convert 700,000 to pennies.
We need to multiply the number by 100, since there are 100 pennies in a dollar.
1 dollar = 100 pennies.
So, 700,000 × 100
= 70,000,000
Therefore, 700,000 is equal to 70,000,000 pennies.
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the value of tan80°×tan10°+sin70+sin 20
The value of tan(80°) × tan(10°) + sin(70°) + sin(20°) = 2.28171276
What is Trigonometry?Trigonometry is the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc). These six trigonometric functions in relation to a right triangle are displayed in the figure.
Given:
tan(80°) × tan(10°) + sin(70°) + sin(20°)
Using Trigonometric identity
sin (A · B) = sin A cos B - cos A sin B
So, tan(80°) × tan(10°) + sin(70°) + sin(20°)
[tex]\rightarrow \tan (80 \times 10)=1[/tex]
[tex]\rightarrow\sin(70^\circ+20^\circ)=1.28171276[/tex]
[tex]\rightarrow 1.28171276+1=\bold{2.28171276}[/tex]
Hence, tan(80°) × tan(10°) + sin(70°) + sin(20°) = 2.28171276
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Tacoma's population in 2000 was about 200 thousand, and has been growing by about 8% each year. If this continues, what will Tacoma's population be in 2014?
people
Answer:424000
Step-by-step explanation:
First, you need to find out what is 8 percent of 200,000 which is 16000
So now we know that every year Tacoma's population grows by 16000
Now we calculate 16000 for 14 years which is 224000
Finally, we had the original population which was 200,000, and the people who moved to Tocoma in those 14 years which is 224000
Add it together and you get 424,000
Ms. Garcia, an art teacher, is buying supplies for her next unit on ceramics. Her 25 sixth graders are making mugs, and she estimates each one will use about 3/4
of a pound of clay. She also wants to have 20 pounds of clay for her seventh graders' sculptures. If Ms. Garcia has 5 2/5 pounds of clay leftover from last year, how much more clay does she need?
Answer: 2 1/2 pounds of more clay
Step-by-step explanation:
To calculate how much more clay Ms. Garcia needs, we need to add up the clay requirements for each grade level and then subtract the amount she already has.
For the sixth graders:
Number of students: 25
Clay required per student: 3/4 pound
Total clay required for sixth graders: 25 * (3/4) = 75/4 = 18 3/4 pounds
For the seventh graders:
Clay required for sculptures: 20 pounds
Total clay required for both grade levels: 18 3/4 + 20 = 38 3/4 pounds
Clay leftover from last year: 5 2/5 pounds
To find out how much more clay Ms. Garcia needs, we subtract the clay she already has from the total required:
38 3/4 - 5 2/5 = 38 3/4 - 27/5 = 38 3/4 - 27/5 = (155 - 108 + 3)/20 = 50/20 = 5/2 = 2 1/2 pounds
Therefore, Ms. Garcia needs an additional 2 1/2 pounds of clay.
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
B
Step-by-step explanation:
SAS Similarity theorem: If two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.
Side 28 is congruent to side 11.2, whereas side 20 is congruent to side 8 and both angles are congruent. Therefore both triangles are similar.
Taking the period of daylight on a certain day to be from 5.30am to 7.00pm, calculate the periods of daylight and a darkness on that day. C.202°3°, 157°30' D. 195°, 165° A. 187°30M72°301 B. 135°, 225°
The periods of daylight and darkness on that day are approximately:
Daylight: 202.5°
Darkness: 157.5°
Hence, the correct option is:
C. 202°3°, 157°30'
To calculate the periods of daylight and darkness on a certain day, we need to find the difference between the times of sunrise and sunset.
Sunrise time: 5.30 am
Sunset time: 7.00 pm
To find the period of daylight, we subtract the sunrise time from the sunset time:
Daylight = Sunset time - Sunrise time
First, let's convert the times to a 24-hour format for easier calculation:
Sunrise time: 5.30 am = 05:30
Sunset time: 7.00 pm = 19:00
Now, let's calculate the period of daylight:
Daylight = 19:00 - 05:30
To subtract the times, we need to convert them to minutes:
Daylight = (19 * 60 + 00) - (05 * 60 + 30)
Daylight = (1140 + 00) - (330)
Daylight = 1140 - 330
Daylight = 810 minutes
To convert the period of daylight back to degrees, we can use the fact that in 24 hours (1440 minutes), the Earth completes a full rotation of 360 degrees.
Daylight (in degrees) = (Daylight / 1440) * 360
Daylight (in degrees) = (810 / 1440) * 360
Daylight (in degrees) ≈ 202.5 degrees
To find the period of darkness, we subtract the period of daylight from a full circle of 360 degrees:
Darkness = 360 - Daylight
Darkness = 360 - 202.5
Darkness ≈ 157.5 degrees
Therefore, the periods of daylight and darkness on that day are approximately:
Daylight: 202.5°
Darkness: 157.5°
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An isosceles triangle has two angles both equal to x. The third angle is 45 degrees bigger than either of these. Find the value of x.
Let's use the fact that the sum of the angles of a triangle is always 180 degrees to solve this problem. Let the two equal angles be x, then the third angle is x + 45.Let's add all the angles together:x + x + x + 45 = 180Simplifying this equation, we get:3x + 45 = 180Now, we need to isolate the variable on one side of the equation. We can do this by subtracting 45 from both sides of the equation:3x = 135Finally, we can solve for x by dividing both sides of the equation by 3:x = 45Therefore, the value of x is 45 degrees.
Answer:
45°
Step-by-step explanation:
An isosceles triangle has two angles both equal to x. The third angle is 45 degrees bigger than either of these. Find the value of x.Let's turn the question into an equation
180 = x + x + x + 45
180 - 45 = 3x
135 = 3x
x = 135 : 3
x = 45°
------------------
check
180 = 45 + 45 + 45 + 45
180 = 180
same value the answer is good
HELPPPPPP ME PLEASEEEEE!!
Answer:
Step-by-step explanation:
The quadratic formula is y=ax^2+bx+c
If we move everything to the left side of the equation,
-6x^2=-9x+7 becomes
-6x^2+9x-7=0
a=-6, b=9, c=-7, so the third answer choice
Which of the segments below is a secant?
A. XY
B. UZ
C. XO
93-(15x10)+(160:16) =
Answer:
Step-by-step explanation:
Let's calculate the expression step by step:
93 - (15 × 10) + (160 ÷ 16)
First, we perform the multiplication:
93 - 150 + (160 ÷ 16)
Next, we perform the division:
93 - 150 + 10
Finally, we perform the subtraction and addition:
-57 + 10
The result is:
-47
Therefore, 93 - (15 × 10) + (160 ÷ 16) equals -47.
Find the area of the region bounded by the graphs of f(x) = x^3 + x^2 - 6x and g(x) = 2x - x^2
The area of the region bounded by the graphs of [tex]f(x) = x^3 + x^2 - 6x[/tex] and [tex]g(x) = 2x - x^2[/tex] is 69 1/3 square units.
To find the area of the region bounded by the graphs of the functions [tex]f(x) = x^3 + x^2 - 6x[/tex] and [tex]g(x) = 2x - x^2[/tex], we need to determine the points of intersection and evaluate the definite integral.
First, let's find the points of intersection by setting f(x) equal to g(x):
[tex]x^3 + x^2 - 6x = 2x - x^2[/tex]
Rearranging the equation, we get:
[tex]x^3 + 2x^2 - 8x = 0[/tex]
Factoring out an x, we have:
[tex]x(x^2 + 2x - 8) = 0[/tex]
Using the quadratic formula, we find the solutions for [tex]x^2 + 2x - 8 = 0[/tex] to be x = -4 and x = 2. Therefore, the points of intersection are (-4, -16) and (2, 4).
To calculate the area, we integrate the difference of the two functions within the bounds of -4 to 2:
Area = ∫[from -4 to 2] (f(x) - g(x)) dx
Evaluating the definite integral, we have:
Area = ∫[-4 to 2] [(x^3 + x^2 - 6x) - (2x - x^2)] dx
= ∫[-4 to 2] (x^3 + 2x^2 - 8x) dx
Integrating each term and evaluating the integral, we find:
Area = [1/4x^4 + 2/3x^3 - 4x^2] from -4 to 2
= [(1/4)(2)^4 + (2/3)(2)^3 - 4(2)^2] - [(1/4)(-4)^4 + (2/3)(-4)^3 - 4(-4)^2]
= [4/4 + 16/3 - 16] - [16/4 + (-128/3) - 64]
= 1/3 + 128/3 - 16 + 4 - 128/3 + 64
= 1/3 + 4 + 64
= 69 1/3
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Un chavo mide 3 pulgadas + un 1/4 de pulgada y otro mide 9.045 cm que diferencia de tamaño hay entre ellos
The difference in size between the two guys is approximately -0.3108 inches, which implies that the first guy is bigger than the second guy.
To calculate the difference in size between two people, one measuring in inches and the other measuring in centimeters, we must first convert all measurements to a common unit.
Guy measures 3 inches + 1/4 inch. We can convert 1/4 inch to a decimal fraction by dividing 1 by 4, which gives us 0.25 inches. So your measurement in inches would be 3 + 0.25 = 3.25 inches.
The other guy measures 9.045 cm. To convert centimeters to inches, we use the following relationship: 1 cm = 0.3937 inches. Multiplying the measurement in centimeters by 0.3937, we get the measurement in inches: 9.045 cm * 0.3937 = 3.5608 inches (approximately).
Now we can calculate the size difference between them. We subtract the measurement of the second chavo (3.5608 inches) from the measurement of the first chavo (3.25 inches):
3.25 inches - 3.5608 inches = -0.3108 inches.
The resulting difference is -0.3108 inches. This means that the second chavo is smaller in size than the first. Since the difference is negative, it indicates that the first chavo is bigger than the second.
In summary, the difference in size between the two guys is approximately -0.3108 inches, which implies that the first guy is bigger than the second guy.
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what is the square root of the fraction, 3/25?
Answer: 0.3464 (correct upto 4 decimal places )
Step-by-step explanation:
[tex]\sqrt{3/25}[/tex]= [tex]\sqrt{3} /\sqrt{25\\}[/tex] (as the square root of 25 is 5)
=1.73205/5
=0.3464
if 3+5 equals 8 then what does 5+3 equal?
Answer:
8
Step-by-step explanation:
The table represents a logarithmic function f(x).
1 over 125 −3
1 over 25 −2
one fifth −1
1 0
5 1
25 2
125 3
Use the description and table to graph the function, and determine the domain and range of f(x). Represent the domain and range with inequality notation, interval notation, or set-builder notation. Explain your reasoning.
The graph of the logarithmic function f(x) exhibits an increasing trend as x approaches positive infinity, while it approaches negative infinity as x approaches negative infinity. The domain is (0, +∞), and the range is (-∞, +∞).
To graph the given logarithmic function f(x), we can use the information provided in the table. The table gives us various values of x and their corresponding values of f(x). We can plot these points on a graph and connect them to visualize the function.
The table shows the following points: (1, 125), (-3, 1/25), (-2, 1/5), (-1, -1), (0, 5), (1, 125), (2, 2125), and (3, 3).
When we graph these points, we observe that the function starts at (-3, 1/25) and approaches positive infinity as x approaches positive infinity. Similarly, as x approaches negative infinity, the function approaches negative infinity.
From the graph, we can determine the domain and range of the function:
Domain: The domain of a logarithmic function is all real numbers greater than 0. In this case, since the function is defined for x = 1/5 and x = 3, the domain can be expressed as x ∈ (0, +∞).
Range: The range of a logarithmic function is all real numbers. In this case, the function takes values ranging from negative infinity to positive infinity. Therefore, the range can be expressed as f(x) ∈ (-∞, +∞).
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If R = {(x, y) : x and y are integers and x^2 + y^2 = 64} is a relation, then find R.
Answer:
R = {(0, 8), (0, -8), (8, 0), (-8, 0), (6, ±2), (-6, ±2), (2, ±6), (-2, ±6)}
Step-by-step explanation:
Since [tex](\pm8)^2+0^2=64[/tex], [tex]0^2+(\pm 8)^2=64[/tex], [tex](\pm 6)^2+2^2=64[/tex], and [tex]6^2+(\pm 2)^2=64[/tex], then those are your integer solutions to find R.
Pamela had $17. She bought 7 burgers for $5.50 and 2 kilograms of orange for $5.30. Find the remaining amount she has now.
$4.20
$5
$6
$6.20
Answer:
$ 6.20 Cents
Step-by-step explanation:
17 - 5.50= 11.5
11.50 - 5.30= 6.2
Add A Zero at the end
You Get 6.20
