In the given right triangle the length of side a is approximately 9.92 units.
Define the right triangle.A right triangle is a variety of triangles with a 90-degree angle (a right angle). The junction of the triangle's two legs, or the sides that meet at a right angle, creates this angle. The hypotenuse, which is always located opposite the right angle, is the third side of a right triangle.
A key characteristic of right triangles is the Pythagorean theorem, which asserts that the square of the hypotenuse is equal to the sum of the squares of the two legs of a right triangle.
We can use the trigonometric ratios of sine, cosine, and tangent to solve for the missing side of a right triangle. Since we are given the measure of one acute angle and the length of the side opposite that angle, we can use the tangent ratio:
tan A = opposite/adjacent
tan 51° = a/8
Multiplying both sides by 8:
a = 8 tan 51°
Using a calculator, we find that:
a ≈ 9.92
Therefore, the length of side a is approximately 9.92 units.
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Circumference of circle is 94 CM find its radius
Answer:
R=47/pi
Step-by-step explanation:
If the of circumference of the circle is 94 cm, the diameter is 94/pi makin the radius 47/pi.
Salmon needs to buy plastic forks. Brian a has a box of 42 forks for a $1.49 round to the nearest cent. How much each fork is?
Answer:
Step-by-step explanation:
$1.49 = 149 cents
149 / 42 = ~4
4 cents per fork
what is y2x+x2y? i need answer now
Answer:
are you trying to find the derivative if so the answer will be 0
Step-by-step explanation:
You are a driver of a dump truck with a trailer (dump bin) that is 21 feet long, 8 feet wide, and 6 feet tall. Daily, you haul full loads of dirt from one location to another. The dump bin can hold dirt equivalent to 1.2 times its capacity.
What is the minimum number of trips needed to haul 20,000 cubic feet of dirt?
A 16
B 17
C 19
D 20
E 24
The minimum number of trips needed to haul 20,000 cubic feet of dirt is B) 17.
What is capacity?
The ability to hold or contain something. The maximum amount or number that can be contained in a room's seating capacity.
The capacity of the dump bin is:
21 feet (length) x 8 feet (width) x 6 feet (height) = 1,008 cubic feet
The dump bin can hold dirt equivalent to 1.2 times its capacity, which is:
1.2 x 1,008 cubic feet = 1,209.6 cubic feet
To haul 20,000 cubic feet of dirt, you need:
20,000 cubic feet / 1,209.6 cubic feet per load = 16.52 loads
Since you can't have a fraction of a load, you need to round up to the nearest whole number, which is 17 loads.
Therefore, the minimum number of trips needed to haul 20,000 cubic feet of dirt is B) 17.
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A restaurant has 8 quarts of pudding. They serve the pudding in cups that hold 1/6 of a quart. How many cups of pudding could be made?
Therefore , the solution of the given problem of fraction comes out to be the restaurant could make 48 cups of pudding from the 8 quarts they have.
Fraction : What is it ?An whole can be represented by any set of related sums or fractions. In standard English, a percentage is used to represent the quantity of a specific size. 8, 3/4. Also wholes are fractions. Numbers are expressed in mathematics using the ratio of it's own portion to the bottom. These fractions are all made up of basic numbers. Due to variances in actual percentage calculations, numerators, and numerators, a difficult fraction contains a fraction. A measurement that reflects a portion of the whole is a percentage.
Here,
There are different ways to approach this problem, but one possible method is to use unit conversions to find how many cups are in 8 quarts, and then divide by 1/6 of a quart per cup.
1 quart = 4 cups (by definition of quart)
Therefore, 8 quarts = 8 x 4 cups = 32 cups
1/6 of a quart = 1/6 x 4 cups = 2/3 cups
Therefore, the number of cups of pudding that could be made is:
32 cups / (2/3 cups) = 48 cups
Therefore, the restaurant could make 48 cups of pudding from the 8 quarts they have.
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Select the correct answer from each drop-down menu. Graph shows a four-sided polygon is plotted on a coordinate plane at A (3, 4), B (5, 3), C (3, 2), and D (1, 3). Polygon ABCD is plotted on a coordinate plane. If the polygon translates 3 units to the left and 1 unit down, the length of diagonal A ′ C ′ ¯ is units. If the polygon translates 3 units further to the left and four units down, the length of diagonal A ′ C ′ ¯ . Reset Next
Therefore, the length of diagonal A'C' is also 2 units after the polygon translates 3 units further to the left and 4 units down.
What is a polygonal example?A polygon is any form having three sides. Although a circle is curved and devoid of sides and angles, it is not categorised as a polygon even if it is a plane figure.
If the polygon translates 3 units to the left and 1 unit down, the coordinates of the new vertices would be:
A' (0, 3)
B' (2, 2)
C' (0, 1)
D' (-2, 2)
To find the length of diagonal AC, we can use the distance formula:
AC = √[(3-3)^2 + (2-4)^2] ≈ 2 units
If the polygon translates 3 units further to the left and 4 units down, the coordinates of the new vertices would be:
A'' (-3, -1)
B'' (-1, -2)
C'' (-3, -3)
D'' (-5, -2)
To find the length of diagonal A'C', we can use the distance formula:
A'C' = √[(0-0)^2 + (1-3)^2] ≈ 2 units
Therefore, the length of diagonal A'C' is also 2 units after the polygon translates 3 units further to the left and 4 units down.
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Compare the investment below to an investment of the same principal at the same rate compounded annually. principal: $1,000, annual interest: 3%, interest periods: 4 , number of years: 15
The investment with annual compounding yields a higher future value of $1,520.10 compared to $1,489.36 for the given investment method.
What is compounding?The process through which an investment earns returns on both the principal and the accrued interest over time is known as compounding. To put it another way, it is the reinvestment of interest income into an investment that enables the investment to increase exponentially over time.
Compounding works on the basic premise that interest earned on an investment is added to the principal amount. The interest is then calculated using the new, higher principal amount during the subsequent interest period, yielding even more interest. When the money generated is reinvested and grows over time, this cycle keeps repeating, increasing the investment's value more swiftly.
The investment given has a principal of $1,000, an annual interest rate of 3%, and interest periods of 4 per year. The investment is held for 15 years. To compare this investment to one with the same principal and annual interest rate compounded annually, we need to calculate the future value of the investment using both methods and compare the results.
Using the given investment method, we can calculate the future value as follows:
FV = P(1 + r/n)^(nt)
FV = 1000(1 + 0.03/4)^(4*15)
FV = $1,489.36
Using annual compounding, we can calculate the future value as:
FV = P(1 + r)^t
FV = 1000(1 + 0.03)^15
FV = $1,520.10
So, the investment with annual compounding yields a higher future value of $1,520.10 compared to $1,489.36 for the given investment method. This difference occurs because compounding more frequently leads to more frequent accumulation of interest, resulting in a higher final amount.
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Aldo and Lena are standing on a riverbank 220 meters apart at points A and B respectively (see the figure below). They want to know the distance from Aldo to a house located across the river at point C. Aldo measures angle A to be 51 and Lena measures angle B to be 65. What is the distance from Aldo to the house? Round your answer to the nearest tenth of a meter.
When Aldo and Lena are standing on a riverside 220 meters apart at certain points, the distance between Lena and the home is 240.8 meters.
what is distance ?Displacement is the overall, purposeless movement of an object. Speed can be characterized as the amount of area an object has covered, disregarding of the origin or ending location. Distance has characterized by the extent or size of the distance between two places. The gap between adjacent positions and the distance moved between them are not exactly the same thing, it should be emphasized. The travelled is the entire length of a path that join different places. Distance is the average trip distance of a body. It is also known as distance. For instance, OP = 360 m would indicate the length of the path for an object traveling from 0 ° to point P.
given
BC/sin 53 = 250/sin 56
BC = 250 * sin 53 /sin 56
=240.8 m
When Aldo and Lena are standing on a riverside 220 meters apart at certain points, the distance between Lena and the home is 240.8 meters.
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A group of students have been surveyed to determine if they prefer to work in groups or individually for projects. There are 8 students who prefer to work in groups for every 10 students who prefer to work individually. If there were 2,200 students who prefer to work in groups, how many students were surveyed in total?
A right triangle has a base, b
, that is 6
inches. The area of the triangle, with h
representing the height, is given by the expression
Answer:
Below
Step-by-step explanation:
See the image below :
Area of the ENTIRE rectangle would be: Area = Base * Height
I think you can see that the triangle is 1/2 of the rectangle. so the
Area of the right triangle would be: Area = 1/2 * base * height
Please help!! If a rock is thrown upward on an exoplanet of a nearby star with initial velocity of 20, its height in
meters t seconds later is given by y = 20t - 1.87t².
To determine the height of the rock at a specific time, we need to substitute the time value into the equation y = 20t - 1.87t². For example, to find the height of the rock after 3 seconds, we substitute t = 3 into the equation:
y = 20(3) - 1.87(3)²
y = 60 - 16.83
y = 43.17
Therefore, the height of the rock after 3 seconds is 43.17 meters.
The television show Pretty Betty has been successful for many years. That show recently had a share of 26, meaning that among the TV sets in use, 26% were tuned to Pretty Betty. Assume that an advertiser wants to verify that 26% share value by conducting its own survey, and a pilot survey begins with 14 households have TV sets in use at the time of a Pretty Betty broadcast.
Find the probability that none of the households are tuned to Pretty Betty.
P(none) = Find the probability that at least one household is tuned to Pretty Betty.
P(at least one) = Find the probability that at most one household is tuned to Pretty Betty. P(at most one) = If at most one household is tuned to Pretty Betty, does it appear that the 26% share value is wrong? (Hint: Is the occurrence of at most one household tuned to Pretty Betty unusual?) yes, it is wrong no, it is not wrong
This means that if at most one household is tuned to Pretty Betty, it is not unusual and does not necessarily indicate that the 26% share value is wrong.
What is probability ?
Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.
This is a binomial distribution problem, where the probability of success (a household tuned to Pretty Betty) is p = 0.26 and the number of trials is n = 14.
The probability that none of the households are tuned to Pretty Betty is:
P(none) = (1 - p)ⁿ = (1 - 0.26)¹⁴≈ 0.031
The probability that at least one household is tuned to Pretty Betty is:
P(at least one) = 1 - P(none) = 1 - 0.031 ≈ 0.969
The probability that at most one household is tuned to Pretty Betty is:
P(at most one) = [tex]P(0) + P(1) = (1 - p)^n + np(1 - p)^{(n-1)[/tex] ≈ 0.500
However, if more than one household is tuned to Pretty Betty, it may indicate that the share value is inaccurate.
Therefore, This means that if at most one household is tuned to Pretty Betty, it is not unusual and does not necessarily indicate that the 26% share value is wrong.
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Suppose that 37% of people have dogs. If two people are randomly chosen, what is the probability that they both have a dog?
Answer:
0.1369
Step-by-step explanation:
(37/100)^2=0.1369
Help asap, I need this done I will mark brainliest!!!
Answer:
A≈50.27in²
Step-by-step explanation:
A=πr2=π·42≈50.26548in²
help solve feasible regions and optimization
The inequalities solution is given below as
(5,8)-44 -25What is the inequalities solution?[tex]8 x-y \leq 32 \\\\&-3 x+5 y \leq 25 \\\\& \Rightarrow {[8 x-y \leq 32] \times 5 } \\\\& {[-3 x+5 y \leq 25] \times 1 } \\\\& \Rightarrow 40 x-5 y \leq 160 \\\\&-3 x+5 y \leq 25 \\\\& 37 x \leq 185 \\\\& x \leq \frac{185}{37} \leq 5[/tex]
substitute $x=5$ into eqn(11)
[tex]-3 x+5 y \leq 25\\\\$-3(5)+5 y \leq 25\\\\& -15+5 y \leq 25 \\\\\& 5 y \leq 25+15 \\\\& 5 y \leq 450 \\\\& y \leq \frac{40}{5} \\\\& -y \leq 8 \\\\[/tex]
(5,8)
z=-4 x+5 y
[tex]& \frac{\partial z}{\partial x}=-4(i)-5 y \\[/tex]
=-4-5 y
when y=8
[tex]\frac{\partial z}{\partial x} & =-4-5(8)[/tex]
=-4-40
=-4-40
=-44
[tex]& \frac{\partial z}{\partial y}=-4 x-5(i) \\[/tex]
when x=5
[tex]\frac{\partial z}{\partial y}=-4 x-5 \\[/tex]
[tex]\frac{\partial z}{\partial y} & =-4(5)-5 \\[/tex]
=-20-5
=-25
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Some values of f(x) are given in the table. Find the value of f-¹ (6).
Using the table and definition of inverse functions we will get:
f ⁻¹ (6) = 10.
How to find the value of f ⁻¹ (6)?Remember how inverse functions work, we know that for two inverse functions f(x) and f ⁻¹ (x)?
if f(x) =y
Then:
f ⁻¹ (y) = x
So now we want to find f ⁻¹ (6), then if:
f ⁻¹ (6) = k
f(k) = 6
Looking at the table we can see that f(10) = 6, then f ⁻¹ (6) = 10.
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write a function that decreases by 12% every time x increases by 1.
A function that decreases by 12% every time x increases by 1 is,
y = 100(1 -0.12)ˣ.
What is exponential decay?An exponential function's curve is created by a pattern of data called exponential decay, which exhibits higher decreases over time.
The exponential decay function:
Aₙ = A₀(1-r)ˣ, where y = Final amount, A₀ = Initial amount, r = Rate of decay in decimal form, x = Time.
An exponential decay function is represented by the following equation,
y = a(1 -r)ˣ.
Here, a = 100.
And the function decreases by 12%.
So,
100 - 12 = 88
In decimals, 88 = 0.88.
So, y = 100(1 -0.12)ˣ.
Therefore, the function is y = 100(1 -0.12)ˣ.
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What is the value of n in the figure?
Answer:
n = 14
Step-by-step explanation:
Theorem:
In a triangle, the measure of an exterior angle equals the sum of the measures of the two remote interior angles.
12n - 8 = 8n - 4 + 52
4n = 56
n = 14
I would really appreciate help, it's due very soon.
Answer:
Area = 380 square inch
Volume = 697 cubic inch
Step-by-step explanation:
Diameter = 11
=> radius = 11/2 = 5.5
A = 4πr^2 =4·π·(5.5^2) ≈ 380 square inch
V=4/3πr^3=4/3·π·(5.5^3) ≈ 697 cubic inch
2. Determine la mediana y los valores correspondientes al primer y tercer cuartiles en los siguientes datos.5.24 6.02 6.67 7.30 7.59 7.99 8.03 8.35 8.81 9.45 9.61 10.37 10.39 11.86 12.22 12.71 13.07 13.59 13.89 15.42
The average is 9.99, the very first percentile is 8.01, as well as the upper quartile is 13.33 as a result.
The 4 quartiles are what?From smallest to highest number, 25% is the first quartile. Second quartile: 25.1% to 50% (till median) 51% to 75%, third quartile (above the median) 25% of the biggest values are in the fourth quartile.
The data must first be arranged in ascending order before we can calculate the median or quartiles of the provided data:
5.24, 6.02, 6.67, 7.30, 7.59, 7.99, 8.03, 8.35, 8.81, 9.45, 9.61, 10.37, 10.39, 11.86, 12.22, 12.71, 13.07, 13.59, 13.89, 15.42
There are a total of 20 data points, and the median is calculated as that of the average of a 10th and 11th pieces of data:
(9.61 + 10.37) / 2 = 9.99; median
The very first quartile (Q1) must be determined in order to determine.
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Give some
Unit transformation questions.
Answer:
Examples below
Step-by-step explanation:
How many milliseconds are in 3.25 days?
How many grams are in 12.6 ounces ?
How many meters are in 2 3/4 miles ?
A laptop computer that you want to purchase was originally priced at $750. You will receive a 20% student
discount, and the sales tax rate is 8%. How much money will you pay for the laptop? Round to the nearest cent
if needed.
The amount paid with discount for the laptop is $ 660.
What is discount?Discount is the amount of money removed from the price of an object being sold.
What is amount paid?Amount paid is the total cost of an item.
How to find how much you will pay for the laptop?Since laptop computer that you want to purchase was originally priced at $750. You will receive a 20% student discount, and the sales tax rate is 8%.
First, we need to know how much discount is given.
Since there is a 20 % discount, the amount of discount removed is 20% × $750 = 0.2 × % 750 = $ 150
Also, there is a sales tax rate of 8%. So, the amount of sales tax added is 8% × $750 = 0.08 × $ 750 = $ 60
So, the total amount paid is T = price - discount + tax
= $ 750 - $ 150 + $ 60
= $ 660
So, the amount paid is $ 660.
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Find the perimeter of the triangle whose vertices are (−4,−2)
, (2,−2)
, and (2,6)
. Write the exact answer. Do not round.
The perimeter of the triangle is 24 units.
what is perimeter ?
Perimeter is the total distance around the boundary of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape. For example, the perimeter of a rectangle is found by adding the length of all four sides, while the perimeter of a circle is the distance around the circle. Perimeter is typically measured in units such as centimeters, meters, feet, or miles.
Given by the question:
To find the perimeter of the triangle, we need to find the distance between each pair of vertices and then add them up.
Distance between (-4, -2) and (2, -2):
[tex]d = sqrt[(2-(-4))^2 + (-2-(-2))^2] = sqrt[6^2 + 0^2] = 6[/tex]
Distance between (2, -2) and (2, 6):
[tex]d = sqrt[(6-(-2))^2 + (2-2)^2] = sqrt[8^2] = 8[/tex]
Distance between (2, 6) and (-4, -2):
[tex]d = sqrt[(-4-2)^2 + (-2-6)^2] = sqrt[(-6)^2 + (-8)^2] = sqrt[36 + 64] = sqrt[100][/tex]= 10
Now we add up the distances:
Perimeter = 6 + 8 + 10 = 24
Therefore, the perimeter of the triangle is 24.
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1. Assignment 1: By using the general equation N₁ = N x 2" where Nt is
the number of cells at given time (in minutes) and No is the initial
number of cells, and "n" is the number of generations at that point
(number of cell division), calculate how many cells you will have in
30, 60, 90, and 120 minutes if your bacteria has a generation time of
30 minutes and you start with 100 cells at O time.
Answer:
Step-by-step explanation:
If the generation time of bacteria is 30 minutes, it means that in every 30 minutes, the number of cells will double. Let No = 100 be the initial number of cells, and n be the number of generations at that point.
Using the given formula N1 = N x 2^n, we can find the number of cells at any given time t, in minutes.
For t = 30 minutes:
The number of generations in 30 minutes is 1 (since generation time is also 30 minutes)
N1 = 100 x 2^1 = 200 cells
For t = 60 minutes:
The number of generations in 60 minutes is 2 (since generation time is 30 minutes)
N1 = 100 x 2^2 = 400 cells
For t = 90 minutes:
The number of generations in 90 minutes is 3 (since generation time is 30 minutes)
N1 = 100 x 2^3 = 800 cells
For t = 120 minutes:
The number of generations in 120 minutes is 4 (since generation time is 30 minutes)
N1 = 100 x 2^4 = 1600 cells
Therefore, after 30 minutes, the number of cells will be 200, after 60 minutes it will be 400, after 90 minutes it will be 800, and after 120 minutes it will be 1600.
Macy has 27 red stickers and 33 blue stickers. She gives away 50
stickers. How many stickers does she have left? Choose the two
operations needed to solve the problem.
First add, then subtract
First add, then divide
First multiply, then subtract
Answer:
First add, then subtract
10
Step-by-step explanation:
First subtract, then determine the result:
27 + 33 = 60
60 - 50 = 10
Macy has 10 stickers left.
The operations needed to solve the problem are:
First add, then subtract.
Morgan has 46 m of fencing to build a four-sided fence around a rectangular plot of land. The area of the land is 130 square meters. Solve for the dimensions (length and width) of the field.
Answer:
So we have two possible values for the width: W = 16 or W = 7.5.
If W = 16, then L = 130/16 ≈ 8.125. This gives us a perimeter of 2(8.125) + 2(16) = 48.25, which is too much fencing.
If W = 7.5, then L = 130/7.5 ≈ 17.333. This gives us a perimeter of 2(17.333) + 2(7.5) ≈ 46.666, which is close enough to 46. Therefore, the dimensions of the field are approximately L = 17.333 m and W = 7.5 m.
Step-by-step explanation:
Let the length of the rectangular plot be L, and let the width be W. Then we have:
The perimeter of the plot is 2L + 2W, and this must equal the length of fencing that Morgan has, which is 46 m. So we have the equation:
2L + 2W = 46
The area of the plot is LW, and we know that this equals 130 square meters. So we have the equation:
LW = 130
We can solve for one variable in terms of the other from the second equation, so let's solve for L:
L = 130/W
Now we can substitute this expression for L into the first equation:
2(130/W) + 2W = 46
Simplifying this equation, we get:
260/W + 2W = 46
260 + 2W^2 = 46W
2W^2 - 46W + 260 = 0
Dividing by 2, we get:
W^2 - 23W + 130 = 0
This is a quadratic equation that we can solve using the quadratic formula:
W = [23 ± √(23^2 - 4(1)(130))] / (2(1))
W = [23 ± 9] / 2
So we have two possible values for the width: W = 16 or W = 7.5.
If W = 16, then L = 130/16 ≈ 8.125. This gives us a perimeter of 2(8.125) + 2(16) = 48.25, which is too much fencing.
If W = 7.5, then L = 130/7.5 ≈ 17.333. This gives us a perimeter of 2(17.333) + 2(7.5) ≈ 46.666, which is close enough to 46. Therefore, the dimensions of the field are approximately L = 17.333 m and W = 7.5 m.
Answer:
Length = 13
Width = 10
Step-by-step explanation:
Let L = length and W = width of the plot
The area is given by LW and is given as 130 square meters
LW = 130 (1)
The perimeter = 2(L + W) and given as 46 meters(length of fencing)
2(L + W) = 46
L+W = 23 (2)
In equation 1, isolate L by dividing both sides by W
LW/W = 130/W
L = 130/W
Substitute this value for L in equation (2)
L + W = 23
130/W + W = 23
Multiply throughout by W:
130/W x W + W x W = 23x W
130 + W² = 23W
Subtract 130W from both sides:
130 + W² - 23W= 0
Rewrite as
W² - 23W + 130 = 0
This is a quadratic equation which can be solved by factoring
Factoring W² - 23W + 130 = 0
(W - 13)(W-10) = 0
This means W = 13 or W = 10
If W = 13, L = 130/W = 120/13 = 10
If W = 10, L = 130/W= 130/10 = 13
So the possible values for L, W are
L = 13, W = 10
or
L = 10, W =13
Choosing the larger value for L gives us:
L = 13, W = 10
8 The River Indus is about 3200 km long. a The Mississippi is about 19% longer than the Indus. How long is the Mississippi? b The Rhine is about 62% shorter than the Indus. How long is the Rhine?
Answer:
the Rhine River is approximately 1216 km long
Step-by-step explanation:
a) If the Mississippi River is 19% longer than the Indus River, we can find its length by multiplying the length of the Indus River by 1.19:
Length of Mississippi River = 3200 km x 1.19 = 3808 km
Therefore, the Mississippi River is approximately 3808 km long.
b) If the Rhine River is 62% shorter than the Indus River, we can find its length by multiplying the length of the Indus River by 0.38 (100% - 62% = 38%):
Length of Rhine River = 3200 km x 0.38 = 1216 km
Therefore, the Rhine River is approximately 1216 km long.
While on a hike, Vera reached the peak of a mountain 3,000 feet above sea level. If she climbed down the mountain at a steady rate of five feet per minute, find her location after three hours.
Vera's location after three hours is thus 2,100 feet above sea level.
What is division?Division is a basic arithmetic operation used to find how many times one number (the divisor) is contained within another number (the dividend). The result of a division operation is the quotient. Division is often represented using the symbol "÷" or "/". Sometimes division results in a remainder, which is the amount left over after dividing as much as possible. Division is one of the four basic arithmetic operations, along with addition, subtraction, and multiplication. It is used in a wide variety of mathematical and real-world contexts, such as sharing equally, calculating rates, and solving equations.
Here,
To find Vera's location after three hours of climbing down the mountain, we first need to convert three hours into minutes. There are 60 minutes in one hour, so three hours is:
3 hours x 60 minutes/hour = 180 minutes
Vera descends at a rate of five feet per minute, so after 180 minutes, she will have descended:
180 minutes x 5 feet/minute = 900 feet
3,000 - 900 = 2,100
Therefore, Vera's location after three hours is 2,100 feet above sea level.
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Please i need help due in 25 minutess
The evaluation of the two more bids Bruno received, and the equations, table and graph obtained from the bids are as follows;
The variables used for the bids are;x = The number of books
y = The total charge based on the pricing
The equations are;
Bid 7: y = 15·x + 3
Bid 8: y = 10·x + 40
Please find the completed table in the following explanation part
Part B;
Please find attached the graph of the two equations, created with MS Excel
What is an equation?An equation is a mathematical statement indicating that the quantity, magnitude or values of two expressions are the same.
The amount Bid 7 charges per book = $15
Amount paid upfront for Bid 7 = $5
Amount Bid 8 charges upfront = $40
Amount Bid 8 charges per book = $10
The variables are;
x = The amount charged per booky = The total amount paidThe equations are;
Bid 7: y = 15·x + 5Bid 8: y = 10·x + 40The table of values can be presented as follows;
Bid 7 [tex]{}[/tex] Bid 8
x [tex]{}[/tex] y = 15·x + 5 y = 10·x + 40
0 [tex]{}[/tex] 5 [tex]{}[/tex] 40
3 [tex]{}[/tex] 50 [tex]{}[/tex] 70
5 [tex]{}[/tex] 80 [tex]{}[/tex] 90
7 [tex]{}[/tex] 110 [tex]{}[/tex] 110
10 [tex]{}[/tex] 155 [tex]{}[/tex] 140
Part B;
Please find attached the required graph of the two equations, showing the legend and the scale for the x and y axis created with MS Excel.
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In a random sample of 100 students from a large high school, 37 regularly bring a reusable water bottle from home. Which of the following gives the correct value and interpretation of the standard error of the sample proportion? (a) In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home will be at most 0.095 from the true proportion. (b) In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home will be at most 0.048 from the true proportion. is ne (c) In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home typically varies by about 0.095 from the true proportion.
(d) In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home typically varies by about 0.048 from the true proportion (e) There is not enough information to calculate the standard error.
The standard error tells us how much we can expect the sample proportion to vary from the true proportion in repeated samples of the same size. Option (d) correctly states that "In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home typically varies by about 0.048 from the true proportion." This means that if we were to take many samples of 100 students from the same school and calculate the proportion of students who bring a reusable water bottle from home in each sample, about 95% of the sample proportions would fall within +/-0.048 of the true proportion.
What is the best interpretation of the standard errorThe correct option is (d) "In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home typically varies by about 0.048 from the true proportion."
The standard error of the sample proportion can be calculated using the formula:
SE = √[p*(1-p) / n]
where p is the sample proportion and n is the sample size.
In this case, the sample proportion is 37/100 = 0.37 and the sample size is 100. Plugging in these values, we get:
SE = sqrt[0.37*(1-0.37) / 100] = 0.048
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