Answer: We are given a right triangle where the two legs have lengths 2 and 4, and we need to find the length of the hypotenuse (which is denoted by x in the question). We can use the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. That is,
hypotenuse^2 = leg1^2 + leg2^2
Plugging in the values we know, we get:
x^2 = 2^2 + 4^2
Simplifying the right-hand side, we get:
x^2 = 4 + 16
x^2 = 20
Taking the square root of both sides (and noting that x must be positive since it is a length), we get:
x = sqrt(20) = 2sqrt(5)
Therefore, the length of the hypotenuse is 2sqrt(5).
Step-by-step explanation:
if a=-3 what’s a squared
Answer:
a^2=9
Step-by-step explanation:
there is a rule that states that if you multiply - with - it becomes + so a number squared just means that the number multiplies with itself so -3*-3=+9 or 9 (any number with + can be written as the number without the +sign, for ex. +1 is the same as 1)
Kareem is considering buying a guitar priced at $179.99 He has $200 cash with him. Predict whether he has enough money.
The current HST rate is 13%
a) Round the price of the guitar to a convenient amount:
b) What is 10% of the rounded price
c) What is 1% of the rounded price
d) How many 1%s do you need?
e) What is the estimated tax?
f) Add the estimated tax to the rounded price.
Does Kareem have enough money with him? YES OR NO
If Kareem is considering buying a guitar priced at $179.99 He has $200 cash with him.
a) The guitar to a convenient amount is $180.
b) 10% of the rounded price is $18.
c) 1% of the rounded price is $1.80
d) 13 1%s is needed
e) The estimated tax is $23.40
f)The estimated tax to the rounded price is $203.40.
g) No Kareem does not enough money with him.
What is 10% of the rounded price?a) Let's round the price of the guitar to the nearest dollar for convenience. $179.99 rounds up to $180.
b) 10% of $180:
$180× 10% =$18
c) 1% of $180:
180× 1% = $1.80
d) How many 1%s do you need?
To find out how many 1%s we need, we can divide the estimated tax rate of 13% by 1%:
13 ÷ 1 = 13
So we need 13 1%s.
e) To find the estimated tax, we can multiply the rounded price by the tax rate of 13%:
$180 x 0.13 = $23.40
f) Add the estimated tax to the rounded price:
$180 + $23.40 = $203.40
Since Kareem has $200 cash with him, he does not have enough money to buy the guitar. Therefore, the answer is NO, he does not have enough money.
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Express the number 78.263 using ones, tenths, and thousandth so
Answer:
70 + 8 + 0.2 + 0.06 + 0.003
Step-by-step explanation:
Expressing the number means to be written based on the place values.
Therefore:
7 = tens place value (70)
8 = ones place value (8)
. = decimal point (.)
2 = tenths place value (0.2)
6 = hundredths place value (0.06)
3 = thousandths place value (0.003)
~
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4. Claire jogs around an oval track and is able to complete one lap in 5 minutes.
If she jogs at the same pace for 42 minutes, how many laps would she be able
to jog? Write an inequality and find the number of whole laps Claire completes.
The inequality that represent how many laps she can do is "number of laps < 8.4".
Claire can jog a maximum of 8 laps in 42 minutes.
What number of whole laps did Claire completes?Since Claire can jog one lap in 5 minutes, we can use division to find how many laps she can complete in 42 minutes:
= 42 minutes / 5 minutes per lap
= 8.4 laps
However, since Claire cannot jog a fractional number of laps, we need to round down to the nearest whole number of laps. This is because she will have only completed a fraction of a lap by the time she reaches the end of the 42 minutes, and we want to know how many whole laps she completes. Therefore, we can write the inequality as "number of laps < 8.4".
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Identify AB as a major arc, minor arc, or semicircle.
o Major arc
• Minor arc
O Semicircle
Find the measure of the arc.
AB=
AB can be identified to be, based on the circle, to be a A. Major arc.
The measure of the arc would be 226 degrees.
How to find the measure of the arc ?A major arc is an arc on a circle that is greater than 180 degrees, or half the circumference of the circle. A major arc is also known as a large arc. It extends from one endpoint of a minor arc to the other endpoint of the same arc, passing through the center of the circle.
AB is a major arc because it is larger than half of the circle which means it is greater than 180s degrees.
The measure of arc AB is:
= Half a circle angle + arc CB
= 180 + 46
= 226 degrees
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Three rods measure 20 cm, 41 cm and 44 cm. If the same length is cut off each piece, the
remaining lengths can be formed into a right triangle.
a) Sketch and label a diagram with expressions for the side lengths.
b) Write an equation to model the situation.
c) What length is cut off?
d) What are the dimensions of the right triangle?
|<---- 20 cm ---->|
| |
+------------------+
|<---- 41 cm ---->|
| |
+------------------+
|<---- 44 cm ---->|
| |
+------------------+
After x is cut off each rod, the remaining lengths can be arranged to form a right triangle, as shown below:
+---------(44-x)--------+
| |
| |
| |
| |
| |
| |
(20-x) | | (41-x)
+-----------+------------------------+
| x |
b) To model the situation, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. In this case, we have:
(20-x)^2 + (41-x)^2 = (44-x)^2
c) To find the length that is cut off, we can solve the equation from part (b) for x. First, we can simplify the equation by expanding the squares:
400 - 40x + x^2 + 1681 - 82x + x^2 = 1936 - 88x + x^2
Simplifying further, we get:
2x^2 - 18x - 855 = 0
We can solve for x by using the quadratic formula:
x = [18 ± sqrt(18^2 + 4(2)(855))] / (2(2))
x = [18 ± sqrt(7404)] / 4
x ≈ 16.98 or x ≈ -24.98
Since x represents a length that is cut off each rod, it must be positive. Therefore, we can discard the negative solution and conclude that the length that is cut off is approximately 16.98 cm.
d) Using the length that is cut off, we can find the dimensions of the right triangle by substituting x = 16.98 into the expressions for the remaining lengths. We get:
(20 - 16.98) = 3.02 cm
(41 - 16.98) = 24.02 cm
(44 - 16.98) = 27.02 cm
Therefore, the dimensions of the right triangle are 3.02 cm, 24.02 cm, and 27.02 cm.
Tan^2a-cosec^2a+1=0 value of pie
the solutions for a are:
a = n×π, π/4, or 7π/4, where n is any integer.
define integerAn integer is a whole number that can be positive, negative, or zero, but does not include fractions or decimals.
tan²(a) - csc²(a) + 1 = 0
tan²(a) - (1/sin²(a)) + 1 = 0
(tan²(a)sin²(a) - 1 + sin²(a))/sin²(a) = 0
Simplifying the numerator:
(tan²(a) - 1)sin²(a) = 0
Using the identity tan^2(a) = sec²(a) - 1:
(sec²(a) - 2)sin²(a) = 0
Expanding and simplifying:
sec²(a)sin²(a) - 2sin²(a) = 0
sin²(a)(sec^2(a) - 2) = 0
So either sin²(a) = 0 or sec²(a) - 2 = 0.
If sin²(a) = 0, then a is an integer multiple of pi (i.e., a = n×π for some integer n).
If sec²(a) - 2 = 0, then sec²(a) = 2,
cos(a) = ±√(2)/2
So a can be π/4 or 7π/4.
Therefore, the solutions for a are:
a = n×π, π/4, or 7π/4, where n is any integer.
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The Singh family ordered a large pizza with a diameter of 20 inches for dinner. If one of the members of the family ate one eighth of the pizza, how many square inches of pizza are remaining? Use 3.14 for π.
274.75 square inches
39.25 square inches
314 square inches
157 square inches
274.75 square inches of pizza are remaining. Option A is the correct option.
What is π in math?
The ratio of a circle's diameter to its circumference, or "pi," is a mathematical constant that is roughly equal to 3.14159 (/pa/; also written as "pi"). Numerous mathematical and physics formulas contain the number. It is an irrational number, meaning that although fractions like 22/7 are frequently used to approximate it, it cannot be expressed exactly as a ratio of two integers.
Given that, the diameter of large pizza is 20 inches.
The radius of a circular shape is half of the diameter.
The radius of the pizza is (20 inches)/2 = 10 inches.
Area of a circular shape is ∏r² .
The area of the pizza is 3.14×10² = 314 in²
The total part of the pizza is considered as 1.
One-eighth of the pizza is eaten, and the remaining portion is (1-1/8) = 7/8.
The area of remaining pizza is
314 in² × (7/8)
= 274.75 square inches
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PLEASEEEE HURRY!!!!!!!
For the equation: 2(x - 7) = 3 - 7x + 5 + 8 + 7x + 11 , the right side of the equation can be simplified by combining like terms.
Simplify the right side of the equation:
The left side of the equation can be simplified using the Distributive Property.
Simplify the left side of the equation:
Answer:
2x-14=27
Step-by-step explanation:
Right Side) Combine like terms
Step 1) 3+5+8+11=27
Step 2) -7x+7x=0
Right side: 27
Left Side) Distribute
2*x=2x
2*(-7)=-14
Answer : 2x-14=27
A sealed, inflated balloon is placed into a flask of liquid nitrogen at a temperature of 77 k. The ballon begins to shrink and shrivel up. Use gas particle motion to explain why.
This causes the volume of the balloon to decrease, leading to an increase in the number of collisions between gas particles and the inside surface of the balloon, and causing the balloon to shrink and shrivel up.
What is temperature?Temperature is a measure of the average kinetic energy of the particles in a substance or system. In other words, it is a measure of how hot or cold something is relative to a standard reference point. The SI unit of temperature is the kelvin (K), but temperature is often measured in degrees Celsius (°C) or Fahrenheit (°F) in everyday life. Temperature plays a crucial role in many natural and man-made processes, and is a key factor in determining the behavior of matter at different states.
Here,
When a sealed, inflated balloon is placed into a flask of liquid nitrogen at a temperature of 77 K, the gas particles inside the balloon lose thermal energy and slow down. As the temperature drops, the average kinetic energy of the gas particles decreases, causing them to move slower and collide less frequently. This results in a decrease in pressure inside the balloon.
According to the Ideal Gas Law, PV = nRT, where P is the pressure of the gas, V is its volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin. As the pressure inside the balloon decreases, its volume also decreases, since the number of moles of gas and the gas constant remain constant.
Since the balloon is sealed, the gas particles cannot escape, so they continue to collide with each other and the inside surface of the balloon. As the volume of the balloon decreases, the gas particles become more crowded, increasing the number of collisions between them. This leads to a decrease in the distance between the gas particles and the inside surface of the balloon, causing the balloon to shrink and shrivel up.
In summary, when a sealed, inflated balloon is placed into a flask of liquid nitrogen at a temperature of 77 K, the gas particles inside the balloon lose thermal energy, slow down, and collide less frequently, resulting in a decrease in pressure inside the balloon.
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A basketball player has a 70% accuracy rate for making free throws. Mark thought that each attempt was independent and the probability stayed at 70% for this player.
During a game, this player was fouled and given the chance to take two free throws.
P left parenthesis X equals k right parenthesis equals left parenthesis 1 minus p right parenthesis to the power of k minus 1 end exponent p
Using the geometric distribution formula, what is the probability that this player misses his first free throw, but makes the second one? Answer choices are rounded to the hundredths place.
If a basketball player has a 70% accuracy rate for making free throws. The probability that this player misses his first free throw, but makes the second one is 0.21.
How to find the probability?The probability of making a free throw is 0.7, so the probability of missing a free throw is 0.3.
Let X be the number of trials (free throws) until the first success (a made free throw). Since we want to know the probability of missing the first free throw and making the second one, we want to find P(X = 2).
Using the geometric distribution formula, we have:
P(X = 2) = (1 - p)^(k-1) * p
where:
p is the probability of success (making a free throw)
k is the number of trials (2 in this case), and (1 - p)^(k-1) is the probability of having k-1 failures (missing the first free throw) followed by one success (making the second free throw).
Plugging in the values, we get:
P(X = 2) = (1 - 0.7)^(2-1) * 0.7
= 0.3 * 0.7
= 0.21
Therefore, the probability is 0.21 (rounded to the hundredths place).
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The area of a square is represented by the formula A = s². When that square is cut by a diagonal, two isosceles triangles are formed. the area of one of the returning triangles is A= 1/2s².Suppose the side of the original square is 10 cm. Find the area of one of the triangles.
Using the given formula [A = 1/2s²], we know that the area of one of the triangles is (C) 50 cm².
What is the area?A patch's area on a surface determines how big it is.
Whereas a plane region or area refers to the area of a shape or planar lamina, a surface region or plane area refers to the area of an open surface or the boundary of a three-dimensional object.
A plane figure's area is the space that its perimeter encompasses.
The area of a closed figure is the total number of unit squares covering its surface.
The area is measured in square units like cm² and m².
So, we know that the area of the triangle is now:
A = 1/2s²
The side of the square is: 10 cm
Then, the area of the one triangle is:
A = 1/2s²
A = 1/2*10²
A = 1/2*100
A = 50 cm²
Therefore, using the given formula [A = 1/2s²], we know that the area of one of the triangles is (C) 50 cm².
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1. You have started a podcast and the number of people who listened to you the first month
was 150, but over the next several months your viewership numbers have increased by
40% a month.
you have
how
a. Write the 40% growth as one decimal. (should it be smaller or larger than 1?)
b. Make a table of the number of listeners over the first 5 months of your podcast.
(a) The 40% grοwth in decimal is 0.4.
(b) 1st mοnth 2nd mοnth 3rd mοnth 4th mοnth 5th mοnth
150 210 294 412 577
What is percentage?A percentage is a number οr ratiο that can be expressed as a fractiοn οf 100 in mathematics. If we need tο calculate a percentage οf a number, we shοuld divide it by its entirety and then multiply it by 100. The percentage, therefοre, refers tο a part per hundred. Per 100 is what the wοrd percent means. The letter "%" stands fοr it.
The given percentage is 40%.
Cοnvert it fractiοn 40 × 1/100
Cοnvert it decimal fοrm:
= 0.4
First mοnth:
The number οf listeners is 150.
Secοnd mοnth:
The number οf listeners is
150 + (150×0.4)
=150 + 60
= 210
Third mοnth:
The number οf listeners is
210 + (210×0.4)
=210 + 84
= 294
Fοurth mοnth:
The number οf listeners is
294 + (294×0.4)
=294 + 117.6
= 411.6
≈ 412
Fifth mοnth:
The number οf listeners is
412 + (412×0.4)
=412 + 164.8
= 576.8
≈ 577
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The length of a rectangular room is 5 feet longer than twice the width. If the room's perimeter is 178 feet, what are the room's dimensions?
Answer: Let's begin by assigning variables to represent the dimensions of the room. Let's use "l" to represent the length and "w" to represent the width.
We know that the length of the room is 5 feet longer than twice the width, so we can write an equation:
l = 2w + 5
We also know that the perimeter of the room is 178 feet. The formula for the perimeter of a rectangle is:
perimeter = 2(length + width)
Substituting the equation we found for the length, we get:
178 = 2(2w+5 + w)
Simplifying, we can combine like terms and solve for w:
178 = 2(3w+5)
89 = 3w+5
84 = 3w
w = 28
Now that we know the width is 28 feet, we can use the equation for the length to find the length:
l = 2w+5 = 2(28)+5 = 61
Therefore, the dimensions of the room are 61 feet by 28 feet.
Step-by-step explanation:
CAN SOMEONE HELP WITH THIS QUESTION?✨
As a result, when the camera and the rocket are 4255 feet apart, the rate trigonometry of change in the angle of elevation after launch is roughly -0.15807 radians/foot.
what is trigonometry?Trigonometry is the field of mathematics that explores the connection between triangle side lengths and angles. The issue first originated in the Hellenistic era, during the third century BC, as a result of the use of geometry in astronomical investigations. The subject of mathematics known as exact techniques is concerned with certain trigonometric functions and their possible applications in calculations. Trigonometry contains six commonly used trigonometric functions. Their separate names and acronyms are sine, cosine, tangent, cotangent, secant, and cosecant (csc). Trigonometry is the study of triangle characteristics, particularly those of right triangles. As a result, geometry is the study of the properties of all geometric forms.
Where is the camera's angle of elevation and c is the rocket's height above ground level.
We may express the angle of elevation using the given formula as:
r θ = tan⁻¹(c/2000)
c2 + x2 = d2, where d = 4255 ft 2c(dc/dx) + 2x = 0, and dc/dx = -x/c.
When we multiply c by 2000 tan() and x by (d2 - 20002) (since x is the horizontal distance between the camera and the rocket), we get: dc/dx = -(d2 - 20002) / (2000 tan())
tan1(0.02d/2000) = tan1(d/100000)
dc/dx = -(d2 - 20002) / (2000 tan(tan1(d/100000)) = -(d2 - 20002) / (2000 tan(tan1(d/100000)) = -0.005(d2 - 20002) / d
dc/dx = -0.005(42552 - 20002) / 4255 -0.15807 radians per foot
As a result, when the camera and the rocket are 4255 feet apart, the rate of change in the angle of elevation after launch is roughly -0.15807 radians/foot.
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Please help!! Correct answer gets brainliest
Answer:
Its both box A and B, Answer D
Step-by-step explanation:
Box A has a volume of 14
Box B has a volume of 15
Answer:
D. Both box A and box B
Hope this helps!
Step-by-step explanation:
Volume = L * W * H
The pillows have a volume of 13.5
Box A has a volume of 14
Box B has a volume of 15
Both boxes can hold the pillows.
A single card is drawn from a deck of 52 cards. What are the odds in favor of drawing a 7?
The odds in favor of drawing a 7 are 1 to 12.
What is probability?
Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
There are four 7s in a deck of 52 cards, so the probability of drawing a 7 is 4/52, which simplifies to 1/13. The odds in favor of drawing a 7 are the ratio of the probability of drawing a 7 to the probability of not drawing a 7, which is:
(1/13) : (12/13
We can simplify this ratio by dividing both terms by the greatest common factor, which is 1:
(1/13) : (12/13) = 1 : 12
Therefore, the odds in favor of drawing a 7 are 1 to 12.
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CONVERT 25 DEGREES CELECIOUS TO TO FERENHEIGHT SHOW THE CONVERSION STEPS.
Answer:
Step-by-step explanation:
The formula to convert Celsius to Fahrenheit is given by °F = °C × (9/5) + 32F = [ C × (9/5) + 32 ] Given that, C = 25F = 25 × (9/5) + 32F = 45 + 32F = 77Thus, 25° C is equivalent to 77° F.
|x-y|+4
X=-1 Y=3
Please help
Solve with steps
Step-by-step explanation:
it is 8 bcs -1 - 3 = -4 turn it to 4 and +4
100 POINTS NEED HELP ASAP
Answer:
Step-by-step explanation:
we would cut it into small pieces and find their area,
Add three segments:
PH, HK and LNThis will give us the following shapes:
Semicircle with diameter PH,Triangle HKJ,Triangle LMN,Rectangle ONKH.You may find each area and add up to get the total area.
Question
If the end behavior is decreasing to the left, what might be true about the function? Select all that apply.
Select all that apply:
The degree is even and the leading coefficient is positive.
The degree is even and the leading coefficient is negative.
The degree is odd and the leading coefficient is positive.
The degree is odd and the leading coefficient is negative.
FEEDBACK
MORE INSTRUCTI
If the function is increasing to the left and falls to the right,
Leading coefficient of the function will be negative and the degree of the function will be Odd.
What is a polynomial's leading coefficient?
The term in a polynomial that has the highest power of x is the leading term. For instance, the leading term in the equation 7+x3x2 is 3x2. The coefficient of the first term is referred to as a polynomial's leading coefficient. The leading coefficient in the aforementioned example is 3.
Leading coefficient of the function will be negative and the degree of the function will be Odd.
Similarly, if the function is increasing to the right and falls to the left,
Leading coefficient of the function will be positive and the degree of the function will be Odd.
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PLEASE PLEASE PLEASE HELP!
Answer:
w-4
Step-by-step explanation:
Suppose we going to find⊕
(4-w)÷(-w-9 ) =⊕÷(w+9 )
⇒(4-w) ÷ -(w+9) =⊕÷(w+9)
cross-multiply we will get
∴ ⊕={(4-w)×(w+9)}÷-(w+9)
= -(4-w) after cancelling ( w+9)
therefore our answer is ( w-4 )
A cancer research walk is being held at two different parks in the city. Ace Park measures 75m long and 40m wide. Lewis Park measures 90m long and
30m wide. Jay walked two rounds around Ace Park. Sandra walked two rounds around Lewis Park. Who walked longer and by how much?
Answer:
Sandra walked longer by 240 - 230 = 10 meters.
Step-by-step explanation:
To find out who walked longer and by how much, we need to calculate the distance walked by each person.
For Jay who walked two rounds around Ace Park, the distance walked is:
Distance = 2 × (length + width) = 2 × (75 + 40) = 230 meters
For Sandra who walked two rounds around Lewis Park, the distance walked is:
Distance = 2 × (length + width) = 2 × (90 + 30) = 240 meters
Therefore, Sandra walked longer by 240 - 230 = 10 meters.
ALGEBRA In AXYZ, m Z-113 and m X-28°. What is m Y?
The angle Y measures 39 degrees. According to the given question.
How to find angle in triangle ?
To find the measure of an angle in a triangle, you need to know the measures of the other two angles in the triangle. Since the sum of all angles in a triangle is always 180 degrees, you can use this fact to calculate the measure of the third angle.
There are a few different methods we can use to find the measure of an angle in a triangle:
Subtract the measures of the other two angles from 180 degrees. This works for any triangle, regardless of its shape or size.
Use the fact that the angles opposite equal sides of a triangle are equal. This is known as the "angle-side-angle" (ASA) theorem. For example, if you know the lengths of two sides of a triangle and the angle between them, you can use the Law of Cosines to find the third side and then use the Law of Sines to find the opposite angle.
Use the fact that the angles in a right triangle are related by the Pythagorean Theorem. If you know the lengths of two sides of a right triangle, you can use the Pythagorean Theorem to find the length of the third side, and then use trigonometric ratios (sine, cosine, tangent) to find the measure of the angle opposite the known side.
Use the fact that the angles in an equilateral triangle are all equal. If you know that a triangle is equilateral, you can simply divide 180 degrees by 3 to find the measure of each angle.
In a triangle, the sum of all angles is always 180 degrees. Therefore, we can use this fact to find the measure of angle Y:
angle Z + angle X + angle Y = 180 degrees
Substituting the given values:
113 degrees + 28 degrees + angle Y = 180 degrees
Simplifying and solving for angle Y:
141 degrees + angle Y = 180 degrees
angle Y = 180 degrees - 141 degrees
angle Y = 39 degrees
Therefore, angle Y measures 39 degrees.
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Your complete question is :-ALGEBRA In Triangle XYZ, angle Z=113 and angle X=28°. What is angle Y?
A mobile base station (BS) in an urban environment has a power measurement of 25 µW at 325 m. If the propagation follows an inverse 4th power law (Section 3.2.2), what is a reasonable power value, in µW, to assume 1.3 km from the BS?
Give your answer in scientific notation to two decimal places.
Hence, 1.56 W (or, in scientific notation, 1.56 x 10-6 W or 1.56E-06 W) to equation two decimal places is a fair power figure to assume at a distance of 1.3 km from the BS.
What is equation?A mathematical equation is a process that links two statements and indicates equality using the equals sign (=). A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the equal sign separates the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula may be used to understand the link between the two sentences that are written on opposite sides of a letter. Frequently, the logo and the particular software are identical. like in 2x - 4 = 2, for example.
The received power at a distance d is determined by:
Pr is equal to Pt, Gt, Gr, and (/4d)2.
where:
The transmitted power is Pt.
The transmitter antenna gain is Gt.
the receiver antenna gain, or Gr.
is the signal's wavelength.
Pr2 = (d1/d2)4 * Pr1
where:
At a distance of 325 m, Pr1 is the received power, which is specified as 25 W.
d1 is 325 metros away, while d2 is 1.3 kilometres away (i.e., 1300 m)
Inputting the values provided yields:
Pr2 = 25 W * (325/1300 m)4 = 25 W * 0.0625 = 1.5625 W
Hence, 1.56 W (or, in scientific notation, 1.56 x 10-6 W or 1.56E-06 W) to two decimal places is a fair power figure to assume at a distance of 1.3 km from the BS.
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Mary Jo spends $2,300 to buy stock in two companies. She pays $19 a share to one of the companies and $24 a share to the other. If she ends up with a total of 100 shares, how many shares did she buy at $19 a share and how many did she buy at $24 a share?
She bought ____ shares at $19 and ___ shares at $24.
Answer:
Mary Jo bought 20 shares at $19 a share and 80 shares at $24 a share.
Step-by-step explanation:
Let's use algebra to solve the problem. Let x be the number of shares Mary Jo buys at $19 a share, and y be the number of shares she buys at $24 a share.
We know that Mary Jo spends a total of $2,300, so we can write the equation:
19x + 24y = 2300
We also know that she ends up with a total of 100 shares, so we can write the equation:
x + y = 100
Now we have two equations with two variables, which we can solve using substitution or elimination.
Let's use substitution. Solve the second equation for x:
x = 100 - y
Substitute this expression for x in the first equation:
19(100 - y) + 24y = 2300
Simplify and solve for y:
1900 - 19y + 24y = 2300
5y = 400
y = 80
So Mary Jo bought 80 shares at $24 a share.
To find the number of shares she bought at $19 a share, substitute y = 80 in the second equation:
x + 80 = 100
x = 20
Therefore, Mary Jo bought 20 shares at $19 a share.
In summary, Mary Jo bought 20 shares at $19 a share and 80 shares at $24 a share.
Find the amount of interest earned by depositing $220 into an account that earns 4% interest for one year.
O $880
$55
O $8.80
O $5500
Answer:
To find the amount of interest earned by depositing $220 into an account that earns 4% interest for one year, we can use the simple interest formula:
Interest = Principal * Rate * Time
Where:
Principal = $220 (the amount deposited)
Rate = 4% (expressed as a decimal, so 0.04)
Time = 1 year
Plugging in these values, we get:
Interest = $220 * 0.04 * 1
Interest = $8.80
Therefore, the amount of interest earned by depositing $220 into an account that earns 4% interest for one year is $8.80.
9. Conrad aims to save money to travel to Puerto Rico in order to work on a team that studies ancient cities there. What is this an example of?
A. Quantitative value
OB. Priority
OC. Poverty
O D. Value
The answer is D. Value. A value is something that a person considers important or desirable in life. It can be a principle, a goal, a belief, or an attitude that guides one’s choices and actions. Conrad’s aim to save money to travel to Puerto Rico and work on a team that studies ancient cities there is an example of his value because it shows what he cares about and what motivates him.
A quantitative value is a value that can be measured or expressed numerically, such as income, height, weight, etc. A priority is something that is more important than other things and needs attention first. Poverty is the state of being extremely poor. None of these terms describe Conrad’s aim accurately.
Conrad’s aim to travel to Puerto Rico and work on a team that studies ancient cities there is not a priority because it is not something that he needs to do urgently or immediately. It is also not something that depends on external factors or demands. It is his value because it reflects his interest, passion, and motivation in life. It is something that he would pursue even if it was difficult or challenging.
Or maybe if it's priority then I'm sorry.
5^-3 * 27* 125 / 3^-2 * 81^2 * 9
classifying parallelegrams
The quadrilateral in the diagram is a rectangle, which is a special type of parallelogram.
Are a parallelogram's four angles of equal measure?No, a parallelogram does not have equal angles on all sides. The opposite angles of a parallelogram are equal, and the consecutive (adjacent) angles are supplementary, according to two fundamental theorems about parallelograms' angles.
There is a quadrilateral with four sides in the provided diagram. It is a parallelogram because the opposite sides are parallel and congruent, and the opposite angles are congruent.
We can also deduce that it is a rectangle because all angles are right angles (90 degrees).
As a result, the diagram's quadrilateral is a rectangle, a particular kind of parallelogram.
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