The dimensions of each half rectangular brick are, length 15 cm, and height 10 cm.
What are the dimensions of the brick?Let the original dimensions of the rectangular brick be length L, breadth B, and height H.
According to the problem statement, each dimension of the original brick is 5 cm larger than the desired dimensions of each half brick.
Therefore, the dimensions of each half brick are;
(L-5)/2, (B-5)/2, and (H-5)/2.
Since the two half bricks have identical dimensions, we have:
(L-5)/2 = (B-5)/2 = (H-5)/2
Simplifying this equation, we get:
L-5 = B-5 = H-5
Therefore, L = B = H + 5.
Now, the volume of the original brick is L x B x H, and the volume of each half brick is [(L-5)/2] x [(B-5)/2] x [(H-5)/2].
Since the two half bricks have the same dimensions, their volumes are equal. Thus, we have:
(L-5)/2 x (B-5)/2 x (H-5)/2 = (L x B x H)/2
Substituting L = B = H + 5, we get:
(H+5-5)/2 x (H+5-5)/2 x (H-5)/2 = (H x H x (H+5))/2
Simplifying this equation, we get:
(H+5)/2 x (H-5)/2 x H/2 = (H x H x (H+5))/2
Cancelling out the factor of 1/2, we get:
(H+5)(H-5)H = H x H x (H+5)
Simplifying this equation, we get:
H³ - 125H = H³ + 5H²
Subtracting H³ from both sides, we get:
-125H = 5H²
Dividing both sides by 5H, we get:
H = -25 or H = 0
Since H represents the height of the brick, it must be positive. Therefore, we have H = 0, which implies that the original brick has zero height. This is not a valid solution, so we reject it.
Therefore, the only valid solution is:
H = 25 cm
Substituting this value of H in the equation L = B = H + 5, we get:
L = B = 30 cm
Therefore, the dimensions of the original brick are:
Length = L + 5 = 35 cm
Breadth = B + 5 = 35 cm
Height = H + 5 = 30 cm
And the dimensions of each half brick are:
Length = Breadth = 15 cm
Height = 10 cm
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Find the volume of the solid where the cone and half sphere are hollow. Use 3.14 for π.
The Answer: 758.83 in³
Step-by-step explanation:
Volume of Solids
The volume of the solid is 758.83 in³
Step-by-step explanation:
Given that the cone and half sphere is hollow
The volume of the cone =
The Volume of the sphere =
So the Volume of the half sphere =
The volume of solid = volume of cone + volume of the half sphere
Given
height h = 19 in
radius r = 5 in
=
= 1/3 × 3.14 × 5 × 5 × 19
= 497.16 in³
= 2/3 × 3.14 × 5 × 5 × 5
= 261.67 in³
V = 497.16 in³ + 261.67 in³
= 758.83 in³
Hence the volume of the solid is 758.83 in³
Volume of Solids
The volume of the solid is 2813 in³
Step-by-step explanation:
Given that the cone and half sphere is hollow
The volume of the cone [tex]=1/3\pi r^2h[/tex]
The Volume of the sphere [tex]=4/3\pi r^3[/tex]
So the Volume of the half sphere [tex]=2/3\pi r^3[/tex]
The volume of solid = volume of cone + volume of the half sphere
[tex]V=V_1+V_2[/tex]
Given
height h = 26 in
radius r = 8 in
[tex]V_1=1/3\pi r^2h[/tex]
[tex]= 1/3 \times 3.14 \times 8 \times 8\times 26[/tex]
[tex]=1741.65 \ in^3[/tex]
[tex]V_2=2/3\pi r^3[/tex]
[tex]= 2/3 \times 3.14 \times 8 \times 8\times 8[/tex]
[tex]= 1071.78 \ in^3[/tex]
[tex]V = 1741.65 \ in^3 + 1071.78 \ in^3[/tex]
[tex]2813 \ in^3[/tex]
Hence the volume of the solid is 2813 in³
Please help me! I give brainly and points
Answer:
3.5 seconds
Step-by-step explanation:
h(t) = 112t - 16t^2
we can re-write it: h(t) = -16t^2 + 112t
with a = -16 and b = 112
the formula -b/(2a) corresponds to x-coordinate of the maximum.
-112/(2 x -16) = 3.5
I need help Please I dare you to a star :)
The area of a parallelogram can be found by multiplying the base by the height
Area of a parallelogramThe formula for the area of a parallelogram is shown:
A = b × h
where A is the area, b is the base, and h is the height of the parallelogram.
Note that the base and the height must be perpendicular to each other.
1) A = 1/2bh
= 0.5 * 13/6 * 24
= 26 ft^2
1)A = bh
= 15/4 * 14/5
10.5 ft^2
3) 8/3 * x = 24
x = 24 * 3/8
x = 9 ft
4) x * 4/5 = 10
x = 10 * 5/4
= 12.5 ft
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The area of this triangle is equal to 26 yd².
The area of this parallelogram is equal to 21 ft² or 10 1/2 ft².
The base of this parallelogram as a fraction is 72/8 feet.
The base of this rectangle is 25/2 cm or 12 1/2 cm.
How to calculate the area of a triangle?In Mathematics and Geometry, the area of a triangle can be calculated by using the following formula:
Area = 1/2 × base × height
Area = 1/2 × 24 × 2 1/6
Area = 12 × 13/6
Area = 156/6
Area = 26 yd²
How to calculate the area of this parallelogram?In Mathematics and Geometry, the area of a parallelogram can be calculated by using the following formula:
Area of a parallelogram = base × height
Area of a parallelogram = 2 4/5 × 3 3/4
Area of a parallelogram = 14/5 × 15/4
Area of a parallelogram = 7 × 3/2
Area of a parallelogram = 21/2 = 10 1/2 ft²
24 = base × 2 2/3
24 = base × 8/3
Base = 72/8
Base = 9 feet.
For the base of the rectangle, we have:
Area of rectangle = length × breadth
10 = 4/5 × breadth
Breadth = 50/4
Breadth = 25/2 = 12 1/2 cm.
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How to determine the inventory cost by the average cost methods for FIFO and LIFO?
FIFO Method:
1. Determine the cost of the oldest inventory items available for sale (i.e., the items purchased first.
2.Multiply the cost per item by the number of items sold to determine the COGS.
3.Subtract the COGS from the total cost of the oldest inventory items to determine the value of the last inventory.
LIFO Method: The only difference between FIFO and LIFO method is that in LIFO method, newest inventory cost and value are determined in the first and last step respectively.
What is average cost method?The average cost method is a way of determining the cost of inventory by taking the average of the cost of each item in the inventory. FIFO and LIFO are two other methods of determining the cost of inventory.
Average Cost Method:
Determine the total cost of all inventory items available for sale.
Determine the total number of inventory items available for sale.
Divide the total cost of inventory by the total number of items to get the average cost per item.
Multiply the average cost per item by the number of items sold to determine the cost of goods sold (COGS).
Subtract the COGS from the total cost of inventory to determine the value of the ending inventory.
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Find the value of c in the right triangle below. Round your answer to the nearest whole number if necessary.
Using Pythagoras theorem, the value of c is √193.
What is Pythagoras' theorem?
A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Here, we have
Given: the right triangle and given sides.
We have to find the value of c.
We apply here Pythagoras theorem and we get
a² + b² = c²
a = 7
b = 12
c = ?
(7)² + (12)² = c²
49 + 144 = c²
193 = c²
c = √193
Hence, the value of c is √193.
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At a pancake breakfast, there are a total of 150 pancakes.
Some are blueberry, some are plain, some are chocolate chip.
Two-thirds of the blueberry ones are eaten.
Four-fifths of the plain ones are eaten.
Half of the chocolate chip ones are eaten.
Now there are an equal number of each type of pancake.
How many of each type of pancake was there to begin with?
Applying equations, the number of each type of pancake are originally: 81 blueberry pancakes, 27 plain pancakes, and 42 chocolate chip pancakes.
How to Solve Word Problems Using Equations?Let's use the following variables to represent the number of each type of pancake:
Let x be the number of blueberry pancakes.Let y be the number of plain pancakes.Let z be the number of chocolate chip pancakes.From the problem statement, we know that:
x + y + z = 150 (total number of pancakes)
1/3 x blueberry pancakes are left
4/5 y plain pancakes are left
1/2 z chocolate chip pancakes are left
There are now an equal number of each type of pancake
From the last statement, we can set up the following equations:
1/3 x = y = 1/2 z
Multiplying all sides of each equation by the least common multiple of the denominators, we get:
2x = 6y = 3z
Dividing all sides of each equation by 2, we get:
x = 3y = 3/2 z
Now we can use the equation x + y + z = 150 to substitute for x in terms of y and z:
3y + y + 2/3(3/2z) = 150
Simplifying and solving for z, we get:
5z = 270
z = 54
Substituting z = 54 into x = 3/2 z, we get:
x = 81
Substituting z = 54 into y = x/3, we get:
y = 27
Therefore, there were originally 81 blueberry pancakes, 27 plain pancakes, and 42 chocolate chip pancakes.
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Around 2015, there were about 23 million people aged 13-17 living in the United States. Each one viewed an average of 800 text messages per month. Using the
average amount of text messages per person for each person, how many text messages were sent in the United states per month by this group?
Show your work using powers of 10 and express your answer in scientific notation.
Answer:
Step-by-step explanation:
To find the total number of text messages sent per month by the 23 million people aged 13-17 in the United States, we can multiply the average number of text messages per person (800) by the number of people (23,000,000):
Total number of text messages = 800 text messages/person/month x 23,000,000 people
Total number of text messages = 18,400,000,000 text messages/month
To express this number in scientific notation, we can move the decimal point 10 places to the left, since there are 10 digits to the right of the decimal point:
Total number of text messages = 1.84 x 10^10 text messages/month
Therefore, the total number of text messages sent per month by the 23 million people aged 13-17 in the United States is approximately 1.84 x 10^10 text messages.
I need help with this please
Answer:
180 cubic centimeters
Step-by-step explanation:
How can we find the volume of a box?We can find the volume of a box by multiplying the dimensions of the box together.
In other words
Volume = length × width × height
Finding the volume of the boxGiven dimensions
length = 6 cmheight = 10 cm width = 3 cmBy plugging these given dimensions into the formula we acquire
Volume = 6 × 10 × 3
==> multiply 10 and 6
Volume = 60 × 3
==> multiply 60 and 3
Volume = 180
The volume of the box is 180 cubic centimeters.
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An item is regularly priced at $53. Joe bought it on sale for 10% off the regular price. How much did Joe pay?
Answer:
$47.7
Step-by-step explanation:
You first have to find how much of 53 is 10%: 53/10 = 5.3 53-5.3= 47.7
Kim works from 6 to 11 on Friday and Saturday evenings at Lombardi's Italian Restaurant. She gets $5.75 an hour plus tips. Her tips were $27.35 on Friday and $32. 10 on Saturday. How much did she earn for the 2 nights' work?
How much did she average per hour?
therefore , Kim earn Average is: $11.70(rounded) per hour
Total for two nights:$116.95
Friday, total earning:
(11 - 6)*$5.75 + $27.35
5×$5.75+$27.35
= $56.1
Saturday, total earning:
(11 - 6)*$5.75 + $32.10
5×$5.75+$32.10
= $60.85
Total for the two nights is:
$56.1 + $60.85 = $116.95
Define average per hour?
The term "hourly average" refers to the average result obtained from ongoing monitoring over each 60-minute interval. An arithmetic average of all entire 15-minute data blocks for a clock hour is referred to as the hourly average.
Average per hour is:
$116.95/(5 + 5)
= $116.95 / 10
= $11.70(rounded)
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Convert 2 3/4 to a decimal order
to make the same shade of green how much yellow paint does andre need if he uses 8 cups of blue paint?
How much blue paint does Andre need if she uses 15 cups of yellow paint?
Andre makes green paint by mixing 5 cups οf yellοw paint with 2 cups οf blue paint.
Tο make the same shade οf green, Andre needs 20 cups yellοw paint if he uses 8 cups οf blue paint.
Andre needs 6 cups blue paint if she uses 15 cups οf yellοw paint.
What dο yοu mean by paint?Any cοlοred liquid, liquefiable, οr sοlid mastic substance that fοrms intο a film when applied tο a surface in a thin layer is referred tο as paint. It can be used tο give texture, cοlοr, οr prοtectiοn, amοng οther things. There are numerοus types and shades οf paint that can be prοduced. Mοst paint kinds eventually sοlidify, but they are nοrmally kept, purchased, and applied as liquids. The bulk οf paints are either οil- οr water-based, and each has unique characteristics.
Andre makes green paint by mixing 5 cups οf yellοw paint with 2 cups οf blue paint.
Suppοse tο make the same shade οf green, he uses 8 cups οf blue paint and x cups οf yellοw paint.
Then, yellοw/blue= 5/2= x/8
Or, 2x= 5*8
Or, x= 40/2
Or, x=20
Sο tο make the same shade οf green, Andre needs 20 cups yellοw paint if he uses 8 cups οf blue paint.
Suppοse Andre needs y cups blue paint if she uses 15 cups οf yellοw paint.
Yellοw/blue= 5/2= 15/y
Or, 5y= 15*2
Or, y= 30/5
Or, y=6
Sο Andre needs 6 cups blue paint if she uses 15 cups οf yellοw paint.
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David earns $416 in eight hours. How much does he earn in 2.8 hours
Answer:
per hour he earns 416/8= 52$
in 2.8 hours he will earn = 52×2.8= 145.6$
Step-by-step explanation:
i hope you find it helpful, have a nice day
The first thing we must know is how much David earns per hour.
$416 ÷ 8 hrs = $52/hr
$52/hr x 2.8hrs = $145.6
David earns $145.6 in 2.8 hours.
Does anyone know this answer??
Answer:
h ≈ 19 m
Step-by-step explanation:
using the tangent ratio in the right triangle
tan43° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{h}{20}[/tex] ( multiply both sides by 20 )
20 × tan43° = h , then
h ≈ 19 m ( to the nearest whole number )
IS THIS CORRECT I NEED TO KNOW?
Answer:
A' (0, 0 )
Step-by-step explanation:
a translation of 5 units right adds 5 to the x- coordinate
a translation of 2 units down subtracts 2 from the y- coordinate
A (- 5, 2 ) → A' (- 5 + 5, 2 - 2 ) → A' (0, 0 )
(NEED HELP PLS)
The piecewise function of this graph is given below. What is the missing piece to this piecewise function? Enter the sub function and it’s domain separated by a comma.
hi i also need help me toppers
Round to the nearest hundred
To the nearest hundredths place: 29.03 kg
The county fair charges $10 admission and $2 per ride. What is the cost for one admission and r rides
The total cost for one admission and r rides is $10 for admission and $2 multiplied by r for the rides, which can be expressed as the formula: Cost = $10 + $2r.
The problem statement provides two pieces of information: the admission cost and the ride cost. We are asked to find the total cost for one admission and r rides.
The admission cost is straightforward - it is a fixed cost of $10. This means that regardless of how many rides you go on, you will always pay $10 just to get into the fair.
The ride cost is based on the number of rides you go on. Each ride costs $2, so if you go on r rides, you will pay $2 multiplied by r, or 2r, for the ride portion of the cost.
To find the total cost for one admission and r rides, we simply add the admission cost of $10 to the ride cost of 2r, which gives us the formula:
Cost = $10 + $2r
This formula tells us that the cost of one admission and r rides is equal to $10 plus $2 multiplied by the number of rides (r) that the person goes on.
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Jack has to fill 50 water bottles for the soccer team. Each bottle holds
500 milliliters of water. How many liters of water does James need in all?
Answer: 10
Step-by-step explanation:
500 divided 50
4.0 = (0.40+ x)²/(0.15 - x)^2
solve for x
Answer:
-0.03334
Step-by-step explanation:
i just graphed it and looked at were y=4 and gave you the x value
:)
Answer:
x1 = -0.0333333, x2=0.7
Here is a triangular prism. Find the volume and surface area.
Answer:
125cm²
Step-by-step explanation:
Ms. Munoz had students in two class periods write essays for a diagnostic test. The following dot plots show the scores from each class. Each dot represents a different student's score. 1 .II. 1 2 First period essay scores 000 ng dot plots 3 000000000 000000 5 2 3 4 Second period essay scores 5 Complete the comparison of the typical essay scores. In general, the students in Select class period ✓ had higher scores, with Select typical score v on the essay
Based on the dot plots, it can be concluded the students in the second period had higher scores with a typical score of 3 on the essay.
What do the dot plots show?The dot plots show the scores Ms. Munoz students got on their essays for two different periods. In these plots, we can observe that in the first period the scores were between 1 and 4, while in the second period, the scores were between 2 and 5.
This shows the scores were higher in the second period, moreover, the typical or the most common score was 3.
Note: This question is incomplete; below I attach the missing information.
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Open the image and answer the question
Answer:
[tex] {≈225.4 \: m}^{2} [/tex]
[tex] {≈248.2 \: m}^{2} [/tex]
Step-by-step explanation:
(My first few steps are in the photo I've added)
Now, we can find the area of the first cutout:
[tex]s(cutout1) = \frac{\pi \times {r}^{2} \times \alpha }{360°} = \frac{\pi \times {18}^{2} \times 114°}{360°} = \frac{36963\pi}{360°} = 102.6\pi[/tex]
We can also find the altitude of the first triangle using trigonometry:
[tex] \sin(∠obd) = \frac{od}{ob} [/tex]
We also need to find AB by using the Pythagorean theorem:
[tex] {ad}^{2} = {ao}^{2} - {od}^{2} = {18}^{2} - {5.56}^{2} = 293.0864[/tex]
[tex]ad > 0[/tex]
[tex]ad = \sqrt{293.0864} ≈ 17.12[/tex]
[tex]ab = 2 \times 17.12 = 34.24[/tex]
[tex]h1 = od = ob \times \sin(∠obd) = 18 \times \sin(18°)≈5.56[/tex]
Then, we can find the area of the 1st triangle:
[tex]s (1triangle)= \frac{1}{2} \times 5.56 \times 34.24 ≈95.19[/tex]
And we can also find the area 1:
[tex]area1 = s(cutout1) - s(triangle1) = 102.6\pi - 95.19≈225.25[/tex]
Now let's do the same thing with the second area:
[tex]s(cutout2) = \frac{\pi \times {r}^{2} \times \alpha }{360°} = \frac{\pi \times {18}^{2} \times 131°}{360°} = \frac{42444\pi}{360°} =117.9 \pi[/tex]
[tex] \sin(∠obe) = \frac{oe}{oc} [/tex]
[tex]h2 = oe = oc \times \sin(∠obe) = 18 \times \sin(24.5°)≈7.46[/tex]
[tex] {be}^{2} = {bo}^{2} - {oe}^{2} = {18}^{2} - {7.46}^{2} = 268.3484[/tex]
[tex]be > 0[/tex]
[tex]be = \sqrt{268.3484} ≈16.38[/tex]
[tex]bc = 2 \times 16.38 = 32.76[/tex]
[tex]s(triangle2) = \frac{1}{2} \times 7.46 \times 32.76 = 122.19[/tex]
[tex]area2 = s(cutout2) - s(triangle2) = 117.9\pi - 122.19≈248.2[/tex]
I don't know if I got this right, though...
The area of the shaded segments in the circle is 422.5 square meters
Calculating the area of the shaded segmentsGiven that
Radius = 18 meters
Angles = 114 degrees and 131 degrees
The area of the shaded segments is the sum of the area of the individual segments and this is calculated as
Segment area = (½) × r² × [(π/180) θ – sin θ]
Using the above, we have
Shaded segments = (½) × 18² × [(114π/180) – sin (114)] + (½) × 18² × [(131π/180) – sin (131)]
Evaluate
Shaded segments = 422.5 square meters
Hence, the shaded segments is 422.5 square meters
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HELP ASAP WILL GIVE BRAINLYEST AND 45 POINTS
Applying the angle relationships, the measures are: 1. m<A = 18°; m<B = 40°; 2. m<A = 9°; m<B = 43°; 3. m<C = 123°; m<D = 158°; 4. m<C = 131°; m<D = 160°
How to Apply Angle Relationship?The position of the angle relationships in the image shown will determine the measures of the angles involved.
Therefore, we have the following for Figure A:
1. m<D = 162°; m<C = 122°
m<A = 180 - 162 = 18° [the angle relationship is linear pair]
m<B = 180 - 122 - 18 = 40° [triangle sum theorem]
2. m<D = 171°; m<C = 128°
m<A = 180 - 171 = 9° [the angle relationship is linear pair]
m<B = 180 - 128 - 9 = 43° [triangle sum theorem]
3. m<A = 22°; m<B = 35°
m<C = 180 - 22 - 35 = 123° [triangle sum theorem]
m<D = 180 - 22 = 158° [the angle relationship is linear pair]
4. m<A = 20°; m<B = 29°
m<C = 180 - 20 - 29 = 131° [triangle sum theorem]
m<D = 180 - 20 = 160° [the angle relationship is linear pair]
Therefore, we have the following for Figure B:
9. m<A = 65° [given]
m<B = 180 - 65 = 115° [linear pair]
m<C = 65° [corresponding angles]
m<D = m<B [corresponding angles]
m<D = 115°
m<E = m<C = 65° [vertical angles]
m<F = 180 - 65 - 90 = 25
10. m<A = 70° [given]
m<B = 180 - 70 = 110° [linear pair]
m<C = 70° [corresponding angles]
m<D = m<B [corresponding angles]
m<D = 110°
m<E = m<C = 70° [vertical angles]
m<F = 180 - 70 - 90 = 20
11. m<F = 22° [given]
m<E = 180 - 90 - 22 = 68°
m<E = m<C = 68° [vertical angles]
m<A = m<C = 68° [corresponding angles]
m<B = 180 - 68 = 112° [linear pair]
m<D = m<B = 112° [corresponding angles]
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A delivery truck is transporting boxes of two sizes: large and small. The combined weight of a large box and a small box is 65 pounds. The truck is
transporting 60 large boxes and 50 small boxes. If the truck is carrying a total of 3750 pounds in boxes, how much does each type of box weigh?
Answer:
Large box = 50 pounds
Small box = 15 pounds
Step-by-step explanation:
Because there are 50 small boxes, the truck is carrying 50 combined large and small boxes. That means the area of those boxes are 50 * 65 = 3250 pounds. There are 10 large boxes left. 3750-3250 = 500. The weight of 10 large boxes is 500 pounds, which means 1 large box is 500/10 which is 50 pounds.
If a large box is 50 pounds, and the combined weight is 65 pounds, 65-50 = 15 pounds for a small box.
help for math (geometry)
Lisa stands at the window of a bulding looking for her lost cat.she spots her cat 58.5 m away from building.if the window is 12.6m high what is the ngle of depression from lisa line of sight to the car?draw a picture and show ur work (geometry)
Therefore, the angle of depression from Lisa's line of sight to the cat is approximately 12.21 degrees.
What is angle?An angle is a geometric figure formed by two rays (or line segments) that share a common endpoint, called the vertex. The rays are also called the sides or legs of the angle. Angles are usually measured in degrees, with a full circle measuring 360 degrees. Angles are used to describe the direction of an object, the orientation of a shape, or the position of a line. They are also used in trigonometry to calculate distances and heights in triangles, and in many other areas of mathematics and science.
Here,
In the diagram above, we have Lisa standing at point L and looking out the window of the building at her lost cat at point C, which is 58.5 meters away from the building. The height of the window from the ground is 12.6 meters. Let's call the angle of depression from Lisa's line of sight to the cat as ∠WLC. To find this angle, we need to use the tangent function, which relates the opposite side (12.6 meters) and adjacent side (58.5 meters) of ∠WLC.
tan ∠WLC = opposite / adjacent
tan ∠WLC = 12.6 / 58.5
Using a calculator, we get:
∠WLC = tan⁻¹(12.6 / 58.5)
∠WLC ≈ 12.21 degrees
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help i only need 8 show work
The height of the flagpole is approximately 68.53 feet.
What is trigonometric equations ?Trigonometric equations are equations that involve trigonometric functions such as sine, cosine, tangent, and their reciprocals. These equations typically involve finding the values of the angles or sides of a right-angled triangle or periodic functions that repeat themselves after certain intervals.
According to given information:This problem involves finding the height of a flagpole using trigonometry. The surveyor measures the angle of elevation from the tripod to the top of the pole and knows the distance from the base of the pole to the tripod. By using the tangent function and the given angle, we can set up an equation that relates the height of the pole to the distance and the angle. We simplify the equation and solve for the unknown height, which gives us an approximate value of 68.53 feet.
the height of the flagpole, we can use trigonometry. Let's call the height of the flagpole "h".
Using the tangent function, we can set up the following equation:
tan(26) = h / (150 + 3)
The 3 feet is added to the distance because the tripod is 3 feet tall.
Simplifying this equation, we get:
tan(26) = h / 153
To solve for "h", we can multiply both sides by 153:
h = tan(26) * 153
Using a calculator, we can evaluate the right side of the equation to get:
h ≈ 68.53
Therefore, the height of the flagpole is approximately 68.53 feet.
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Find how many years it would take for an investment of $4500 to grow to $8800 at an annual interest rate of 6.8% compounded daily
Answer:
6.92 years
Step-by-step explanation:
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the final amount (in this case, $8800)
P = the initial investment (in this case, $4500)
r = the annual interest rate (in decimal form, so 6.8% = 0.068)
n = the number of times the interest is compounded per year (in this case, daily, so n = 365)
t = the number of years
We want to solve for t, so we can rearrange the formula as follows:
t = (ln(A/P)) / (n ln(1 + r/n))
where ln is the natural logarithm.
Plugging in the given values, we get:
t = (ln(8800/4500)) / (365 ln(1 + 0.068/365))
t ≈ 6.92
Therefore, it would take about 6.92 years (or about 7 years) for the investment to grow to $8800 at an annual interest rate of 6.8% compounded daily.
One 12 ounce can of soda has 150 calories. If Josiah drinks the big 28 ounce size from the local mini-mart, how many calories does he get?
What is the probability of Meikel wearing khakis and sandals?please help!!!ALL I ASK!!please anybody.. :)
Answer:
The probability of Meikel wearing khakis and sandals is
Step-by-step explanation:
3 ÷ 12 which should give us
1/4