The volume of the glass shell of the jar is 0.0136 ft³ and its weight is 2.24 lbs. The weight and volume of the water it will displace amounts to 2.24 lbs and 0.036 ft³ respectively. Consequently, the jar will sink approximately 2.2 inches into the water.
Explanation:To begin, the volume of the glass shell of the jar will first need to be established. Given that the thickness of the glass is 3/16 inches, the outer radius of the jar is 3 inches + 3/16 inches = 3.1875 inches. To get the volume, utilise the formula for the volume of a cylinder, which is πr²h. Thus, with measurements converted to feet for the calculations (1 inch = 0.08333 foot), we have an external volume of π(0.265625 ft)² * 0.5 ft = 0.1118 ft³ and an internal volume of π(0.25 ft)² * 0.5 ft = 0.0982 ft³. Hence, the volume of glass is 0.1118 ft³ - 0.0982 ft³ = 0.0136 ft³
Next, the weight of the jar is determined by the formula mass = volume * density, so mass = 0.0136 ft³ * 165 lb/ft³ = 2.24 lbs.
To ascertain the weight of water the jar will displace, we consider the principle of buoyancy, which suggests that an object will displace a volume of fluid with a weight equal to its own weight. Thus, the weight of the water displaced is 2.24 lbs.
Then, the volume of this water is found with the formula volume = weight/density -> volume = 2.24 lbs / 62.5 lb/ft³ = 0.036 ft³.
Lastly, considering the jar will sink until the weight of the water being moved equals the weight of the jar. The volume of the water displaced equates to the submerged volume of the jar. Its depth in feet is then the volume divided by the cross-sectional area of the jar (internal radius), so the distance the jar sinks is roughly 0.036 ft³ / π(0.25 ft)² = 0.18 ft -> convert to inches = 2.2 inches.
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Carlos plots a circular planter's wall on a computer. He determines that the circle that defines the part of the planter wall that gets watered by the sprinkler is (x−10)2+(y+12)2=36.
What is the diameter, in meters, of the circular area that gets watered by the sprinkler?
You receive $1,000 to put in the bank. You place it in an account that pays 4% annual interest compounded continuously. How much will you have in 15 years? Round the answer to the nearest dollar.
While Playing Yahtzee and rolling 5 dice, Mei gets the result shown at right (the numbers are 2, 4, 4, 4, and 1). Mei decides to keep the three fours and reroll the other 2 dice. a. what is the probability that Mei will have 5 of a kind? b. What is the probability that she will have 4 of a kind? c. what is the probability that she will have exactly three 4's?
How do I find the holes of this function?
What is the difference of the two polynomials?
(7y2 + 6xy) – (–2xy + 3)
sin 4 theta
hey, how do you simplify sin 4 theta? using double angle theory?
find the geometric mean between 18 and 2,
identify the image of xyz for a composition of two 270 degree rotation and a 90 degree rotation both about point x.
Answer:
The answer is D
Step-by-step explanation:
Giving a test to a group of students, the grades and gender are summarized below. if one student was chosen at random, find the probability that the student was female. male total 39 female total 26
A rectangle is drawn on a coordinate plane. Three vertices of the rectangle are points L(−3,10) , M(6,10) , and P(−3,−6) . Point N is the fourth vertex of the rectangle. How long is the side of the rectangle connecting points M and N?
Answer:
answer 16 or 1.6
Step-by-step explanation:
A lighthouse is 15m above sea level.
The lighthouse operator sights a boat at an angle of depression of 25 degrees.
How far is the boat from the lighthouse?
Round your answer to the nearest tenth.
Answer:
41.2
Step-by-step explanation:
daniel is standing 100ft from a tower and sees a bird land on top of the tower. if the angle of elevation from daniel to the top is 84.6, how tall is the tower
Jerry lost her credit card and instead of reporting it right away, she decides to continue looking for it for a couple of days. On the second day, she makes the call and reports the card lost/stolen to the credit card company. She then logs into the account activity page of his credit card and sees a recent $500 purchase that was made by someone else. How much of this $500 charge will Jerry have to pay?
Three times the number of blue marbles exceeds twice the number of red marbles by 18 also 5 times the number of blue marbles is 2 less than 6 times the number of red marbles how many of each are there?
Will give brainliest please answer quickly
Final answer:
By creating and solving a system of equations based on the given information, we find that there are 10 blue marbles and 8 red marbles.
Explanation:
To solve this problem, we set up two equations based on the information given:
3 times the number of blue marbles (3B) exceeds 2 times the number of red marbles (2R) by 18: 3B - 2R = 18.
5 times the number of blue marbles (5B) is 2 less than 6 times the number of red marbles (6R): 5B = 6R - 2.
Now, we can solve these equations using substitution or elimination. Using substitution, solve the second equation for B:
B = ⅜(6R - 2)
Then substitute this expression for B in the first equation:
3(⅜(6R - 2)) - 2R = 18
Solve for R:
R = 8
Now substitute R back into the equation for B:
B = ⅜(6(8) - 2) = 10
Thus, there are 10 blue marbles and 8 red marbles.
Find the value of a. The diagram is not to scale. a. 36 b. 144 c. 54 d. 126 **I believe the answer is B
The value of a in the diagram is 144°.
The correct option is B.
What is a trapezoid?An open, flat object with four straight sides and one set of parallel sides is referred to as a trapezoid or trapezium. A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases.
Given:
A trapezium has parallel bases and that one of its characteristics is that the two angles on a single side are supplementary, meaning that the total of the angles on two neighboring sides is 180°.
So,
∠a = 180 - 36
∠a = 144
∠b = 180 - 113
∠b = 67
Therefore, the value of a is 144°.
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The complete question is given in the attached image.
help me please please
Answer:
11
Step-by-step explanation:
A car has a 12-volt battery. The engine has a resistance of 0.22 ohms. How many amps will be drawn from the battery when the key is turned? I (to the nearest hundredth)
Answer:
54.54 amps.Step-by-step explanation:
Amps refers to the electrical current.
We have to find the electrical current when the car has a 12-volt battery and the engine has a resistance of 0.22 ohms.
The relation between these magnitudes is
[tex]V=I\times R[/tex]
Where [tex]V[/tex] is the voltage, [tex]I[/tex] is the electrical current and [tex]R[/tex] the resistance.
We know that [tex]V=12; R=0.22[/tex]. Replacing these values in the formula and solving for [tex]I[/tex]
[tex]V=I\times R\\\frac{V}{R}=I\\ I=\frac{12}{0.22}\\ I\approx 54.54 amp[/tex]
Therefore, the answer is around 54.54 amps.
The current drawn from the battery when the key is turned is approximately 54.55 amps.
To determine the current drawn from the battery, we can use Ohm's Law, which states that the current (I) is equal to the voltage (V) divided by the resistance (R):
[tex]\[ I = \frac{V}{R} \][/tex]
Given that the voltage (V) of the battery is 12 volts and the resistance (R) of the engine is 0.22 ohms, we can plug these values into the equation:
[tex]\[ I = \frac{12 \text{ volts}}{0.22 \text{ ohms}} \][/tex]
[tex]\[ I = \frac{12}{0.22} \][/tex]
[tex]\[ I \approx 54.5454 \][/tex]
Rounding to the nearest hundredth, we get:
[tex]\[ I \approx 54.55 \text{ amps} \][/tex]
Last winter, the ratio of days with snow to days with no snow was 1.02. Write this ratio as a fraction in simplest form.
Final answer:
The ratio of 1.02 can be converted to a fraction by multiplying by 100 to get 102/100 and then simplifying to its simplest form, which is 51/50.
Explanation:
To write the ratio 1.02 as a fraction in its simplest form, we first recognize that 1.02 is the same as 1.02/1. If we want to express this as a fraction, we must remove the decimal point by multiplying both the numerator and the denominator by 100 (because there are two digits after the decimal point). This gives us 102/100. We can then simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2. Therefore, the simplified fraction is 51/50.
PLEASE HELP! What is the area of triangle BCD in exact form? 35 points!
Catie is trying to determine the height that a ladder reaches as it leans against a wall. She walks under the ladder and touches her forehead to it as shown. If her feet are 16 inches from the ladder's base, the ladder's base is 4.5 feet from the bottom of the wall, and Catie is 5 feet 6 inches tall, then come up with an estimate for how high the ladder reaches up the wall to the nearest tenth of a foot. Watch your units on this problem and show all work
To find the height the ladder reaches up the wall, set up a proportion using similar triangles and Catie's height as the ladder's height. The estimate for the ladder's height up the wall is 6.8 feet.
Given information:
Catie is 5 feet 6 inches tall.Her feet are 16 inches from the ladder's base.The ladder's base is 4.5 feet from the bottom of the wall.To find the height the ladder reaches up the wall, we can set up a proportion using similar triangles. Catie's height can be considered as the ladder's height, and the distance on the wall can be related to the ladder's base and height.
Using the information provided and performing the calculations, the estimate for the height the ladder reaches up the wall would be approximately **6.8 feet** to the nearest tenth of a foot.
Which shows one way to determine the factors of x3 – 9x2 + 5x – 45 by grouping?
Answer:
x(x2 + 5) – 9(x2 + 5)
Step-by-step explanation:
By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. if the cardboard is 17 in. long and 12 in. wide, find the dimensions of the box that will yield the maximum volume. (round your answers to two decimal places.)
1. Simplify using only positive exponents:
(2t)⁻⁶
2. Simplify using only positive exponents:
(w⁻²j⁻⁴)⁻³(j⁷j³)
3. Simplify using only positive exponents:
a²b⁻⁷c⁴
----------
a⁵b³c⁻²
4. Evaluate the expression for m = 2, t = -3, and z = 0.
z⁻ᵗ(mᵗ)ᶻ
5. Use scientific notation to rewrite the number:
a. 0.0002603 in scientific notation
b. 5.38 × 102 in standard notation
Expressions with exponents can be simplified using rules of exponents, and numbers can be converted into scientific notation by recognizing how to move the decimal point and denote magnitude with the power of ten.
To simplify expressions with exponents and convert numbers into scientific notation, we apply the rules of exponents and understand the format of scientific notation.
(2t)⁻⁶: Using the negative exponent rule, which states that a⁻⁶ = 1/a⁶, we can simplify this expression to 1/(2⁶t⁶).
(w⁻²j⁻⁴)⁻³(j⁷j³): To deal with the negative and compounded exponent, we invert and take the cube, resulting in w⁶j¹². Then, multiply the j terms together to get w⁶j¹⁵.
To simplify a²b⁻⁷c⁴ / a⁵b³c⁻², we subtract exponents when dividing like bases, resulting in a⁻³b⁻¹°c⁶.
For the expression z⁻ᵗ(mᵗ)¹, when any variables are raised to the zero power, the result is 1. Thus, the entire expression evaluates to 1 due to (mᵗ)¹ becoming 1.
Converting to scientific notation: To express 0.0002603 in scientific notation, it becomes 2.603 × 10⁻⁴. The number 5.38 × 10² in standard notation is 538.
By applying these step-by-step procedures, we can simplify expressions using positive exponents and accurately convert between standard notation and scientific notation.
How many minutes greater is the software company's median than the bank's median?
Enter your answer in the box.
PLEASE HELP ME ON THIS....
thx
The perimeters of two similar quadrilaterals are 48 cm and 60 cm, respectively. If the area of the smaller quadrilateral is 96 cm2, find the area of the larger quadrilateral.
The area of the larger quadrilateral is found by using the scale factor derived from the ratio of the perimeters of the similar quadrilaterals, which comes out to 150 cm².
The question involves finding the area of a larger quadrilateral given the perimeters of two similar quadrilaterals and the area of the smaller one. In similar figures, the ratio of their areas is the square of the ratio of their corresponding linear dimensions, such as side lengths or perimeters in this case. Since the perimeters are 48 cm and 60 cm, the ratio of the perimeters (also the scale factor) is 48/60, or 4/5. Consequently, the ratio of the areas is the square of the scale factor, which is (4/5)² or 16/25. Knowing the area of the smaller quadrilateral is 96 cm², we find the area of the larger quadrilateral by dividing the area of the smaller by the scale factor squared and then multiplying by the larger scale factor squared. This gives us (96 / (16/25)) cm² = (96 * 25/16) cm² = 150 cm².
So, the area of the larger quadrilateral is 150 cm².
The length of a shadow of a building is 32 m . the distance from the top of the building to the tip of the shadow is 38 m . find the height of the building. if necessary, round your answer to the nearest tenth.
A sum of _________ can be factored according to the pattern (a + b)(a2 - ab + b2).
Solution:
we are given with [tex] (a + b)(a^2 - ab + b^2) [/tex]
we have been asked to find the representation of the given factor as a Sum.
As we know that
[tex] (a^3+b^3)= (a + b)(a^2 - ab + b^2) [/tex]
Because
[tex] (a + b)(a^2 - ab + b^2)=a(a^2 - ab + b^2)+b(a^2 - ab + b^2)\\
\\
(a + b)(a^2 - ab + b^2)=a^3-a^2b+ab^2+ba^2-ab^2+b^3\\
\\
(a + b)(a^2 - ab + b^2)=a^3+b^3\\ [/tex]
PLEASE ANYONE
HELP
I think its 120 + 15x ≤ 360
IS that Correct!!??
Given the following linear function, identify the slope and y-intercept of the function: x= 1/6x+7