In parallelogram ABCD, opposite sides AB and DC are both 8 units long, and AD and BC are both 5 units long.
To show that quadrilateral ABCD is a parallelogram, we need to demonstrate that both pairs of opposite sides are congruent. We can do this by finding the lengths of the opposite side pairs and showing that they are equal.
Let's denote the points as follows:
- A, B, C, D are the vertices of the quadrilateral ABCD.
- AB and DC are opposite sides, and AD and BC are opposite sides.
Given that AB = 8 units and AD = 5 units, we need to find the lengths of DC and BC.
Since ABCD is a parallelogram, opposite sides are congruent. Therefore, DC = AB = 8 units.
To find BC, we know that BC = AD = 5 units.
Thus, we have:
- AB = DC = 8 units
- AD = BC = 5 units
Since both pairs of opposite sides are congruent, quadrilateral ABCD is a parallelogram.
The length of BC is 5 units.
In the given case, The length of BC is 8 units.
To show that quadrilateral ABCD is a parallelogram, we need to demonstrate that both pairs of opposite sides are congruent.
Let's denote the lengths of the sides as follows: AB, BC, CD, and DA.
Given that ABCD is a parallelogram, we know that opposite sides are equal in length.
Therefore, we can equate the lengths of AB to CD and BC to DA.
Let's assume that the length of side AB (and thus CD, since they are opposite and equal) is given as 8 units.
We are asked to find the length of side BC (which will be equal to the length of side DA).
Since we do not have any additional information such as angles or diagonals, we cannot calculate the length of BC directly.
However, if we are given that ABCD is a parallelogram, then by definition, the lengths of opposite sides are equal.
Therefore, without loss of generality, we can state that the length of BC is also 8 units, which is equal to the length of AB.
Thus, we have shown that both pairs of opposite sides are congruent:
AB = CD = 8 units
BC = DA
Since AB = 8 units and AB = CD, it follows that CD = 8 units.
Similarly, since AB = CD and AB = 8 units, by the properties of a parallelogram, BC must also be equal to 8 units.
Therefore, the length of BC is 8 units, confirming that quadrilateral ABCD is indeed a parallelogram.
Point C = (4/9,-5/9) lies on the circle with the center at S=(-2/3, 3/4). If CD is a diameter of circle S, find the coordinates for D. Answer must be given as a simplified fraction to receive full credit.
Answer:
Step-by-step explanation:
If CD is a diameter of circle S, then CD goes through circle S at point S. CS is a radius, and so is DS. That means that they are the same length. That also means that S is the midpoint of CD. We can use the midpoint formula and the 2 points we are given to find the other endpoint, D.
[tex](-\frac{2}{3},\frac{3}{4}) =(\frac{\frac{4}{9}+x }{2},\frac{-\frac{5}{9}+y }{2})[/tex]
To solve for x, we will use the x coordinate of the midpoint; likewise for y. x first:
[tex]-\frac{2}{3}=\frac{\frac{4}{9}+x }{2}[/tex]
Multiply both sides by 2 to get rid of the lowermost 2 and get
[tex]-\frac{4}{3}=\frac{4}{9}+x[/tex]
Subtract 4/9 from both sides to get
[tex]x=-\frac{16}{9}[/tex]
Now y:
[tex]\frac{3}{4}=\frac{-\frac{5}{9}+y }{2}[/tex]
Again multiply both sides by that lower 2 to get
[tex]\frac{3}{2}=-\frac{5}{9}+y[/tex]
Add 5/9 to both sides to get
[tex]y=\frac{37}{18}[/tex]
And there you go!
[tex]D(-\frac{16}{9},\frac{37}{18})[/tex]
A painting is covering up some of the tiles on the wall. The tiled wall is shaped like a rectangle . There are 28 square tiles on the whole wall. How many of the tiles are covered by the painting?
Answer:
The number of tiles are covered by the painting are 12.
Step-by-step explanation:
Consider the provided information.
The painting is covering up some of the tiles on the wall as shown below:
Here it is given that there are 28 squares tiles on the wall.
Total tiles = Number of tiles covered by the painting - uncovered tiles
28 = Number of tiles covered by the painting - 16
Number of tiles covered by the painting = 28 - 16
Number of tiles covered by the painting = 12
Hence, the number of tiles are covered by the painting are 12.
Nancy knows that the perimeter of her garden is 28 feet, and the length is 8 feet. She forgot to measure the width, but was able to solve for it by subtracting 16 from 28, and then dividing by 2. Which of the equations below can be solved with these steps?
Answer:
W = (P - 2L)/2 = (28- 2*8)/2 = 6
Where W is the width, P is the perimeter and L is the length of the garden.
Step-by-step explanation:
Since the equations are not given, i will try to come up with the similar equation than the ne that was the correct option in this exercise.
You can obtain the perimeter of a rectangle by summing the length of its four sides. Thus, the perimeter of the garden, lets call it P, is 2W + 2L, where W denotes the width and L the length. Since Nancy knows the perimeter, in order to calculate the width she can substract from it 2L (which is also known), and divide by 2 to obtain W, thus
W = (P - 2L)/2
If we reemplace P by 28 and L by 8, we obtain
W = (28-8*2)/2 = (28-16)/2 ) = 12/2 = 6.
A bank says you can do or your money in 10 years if you put 1000 in in a simple interest account.What annual interest rate does the bank Pay?
Answer:
[tex]r=10\%[/tex]
Step-by-step explanation:
The correct question is
A bank says you can double your money in 10 years if you put $1,000 in a simple interest account. What annual interest rate does the bank pay?
we know that
The simple interest formula is equal to
[tex]A=P(1+rt)[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
[tex]t=10\ years\\ P=\$1,000\\ A=\$2,000\\r=?[/tex]
substitute in the formula above
[tex]2,000=1,000(1+10r)[/tex]
Solve for r
Divide by 1,000 both sides
[tex]2=1+10r[/tex]
Subtract 1 both sides
[tex]10r=2-1[/tex]
[tex]10r=1[/tex]
Divide by 10 both sides
[tex]r=1/10[/tex]
[tex]r=0.10[/tex]
Convert to percentage (multiply by 100)
[tex]r=0.10*100=10\%[/tex]
The useful life of a certain piece of equipment is determined by the following formula: u =(8d)/h^2, where u is the useful life of the equipment, in years, d is the density of the underlying material, in g/cm3, and h is the number of hours of daily usage of the equipment. If the density of the underlying material is doubled and the daily usage of the equipment is halved, what will be the percentage increase in the useful life of the equipment?A. 300%B. 400%C. 600%D. 700%E. 800%
Answer:
E. 800%
Step-by-step explanation:
Since,
u = 8d/h² __________ eqn (1)
Now, density (d) is doubled and usage (h) is halved.
Hence the new life (u'), becomes:
u' = 8(2d)/(0.5h)²
u' = 8(8d/h²)
using eqn (1), we get:
u' = 8u
In percentage,
u' = 800% of u
In words, the percentage increase in useful life of the equipment is 800%.
Answer: E. 800%
Step-by-step explanation:
The useful life of a certain piece of equipment is determined by the following formula: u =(8d)/h^2, where u is the useful life of the equipment, in years, d is the density of the underlying material, in g/cm3, and h is the number of hours of daily usage of the equipment.
Assuming d = 1 and h = 1, then
u = (8 × 1)/1^2 = 8
If the density of the underlying material is doubled and the daily usage of the equipment is halved, it means that
d = 2 and h = 1/2 = 0.5, therefore,
u = (8 × 2)/0.5^2 = 16/0.25 = 64
64/8 = 8
The percentage increase in the useful life of the equipment is
8 × 100 = 800%
Liam and evan are mixing paint. Liam uses 2 quarts of yellow paint and adds 3 1/4 jars of blue paint. Evan uses 1/2 quart of yellow paint and adds 5 1/2 jars of red paint. They end up with the same volume of paint. Write an equation to represent the situation.
Answer:
The required equation is given by,
2 + [tex]\frac {13x}{4}[/tex] = [tex]\frac {1}{2} + \frac {11y}{2}[/tex]
Step-by-step explanation:
Let, each jar of Liam's paint contains x quarts of paint.
Then, Liam's solution contains,
2 + [tex]3\dfrac {1}{4} \times x[/tex] quarts of paint or,
2 + [tex]\frac {13x}{4}[/tex] quarts of paint
and,
let, each jar of Evan's paint contains, y quarts of paint.
Then, Evan's solution contains,
[tex]\frac {1}{2} + 5 \dfrac {1}{2} \times y[/tex] quarts of paint or,
[tex]\frac {1}{2} + \frac {11y}{2}[/tex] quarts of paint
now, according to the question,
the required equation is given by,
2 + [tex]\frac {13x}{4}[/tex] = [tex]\frac {1}{2} + \frac {11y}{2}[/tex]
To find an equation that represents the volume of paint mixed by Liam and Evan, we assume that 1 jar equals 1 quart. By adding the quarts of paint each person uses, we get the equation 2 + 3 1/4 = 1/2 + 5 1/2, meaning they both used the same total volume of paint.
Explanation:To find the equation that represents the situation, we need to equate the total volume of paint used by Liam to the total volume used by Evan. We know that Liam uses 2 quarts of yellow paint and adds 3 1/4 jars of blue paint. Evan, on the other hand, uses 1/2 quart of yellow paint and adds 5 1/2 jars of red paint. Assuming that 1 jar is equivalent to 1 quart, we can simply add the volumes for Liam and Evan:
Liam's total volume = 2 quarts (yellow) + 3 1/4 quarts (blue)
Evan's total volume = 1/2 quart (yellow) + 5 1/2 quarts (red)
Since they end up with the same volume of paint, we have the equation:
2 + 3 1/4 = 1/2 + 5 1/2
To solve for quarts, simplify both sides:
5 1/4 = 6
This equation represents the volumes of paint mixed by Liam and Evan.
A person 100 meters from the base of a tree, observes that the angle between the ground and the top of the tree is 18 degrees. Estimate the height h of the tree to the nearest tenth of a meter.
This is right angle trig. We know that...
cos(18°) x hypotenuse = 100
hypotenuse = 100/cos(18°)
hypotenuse = 105.15 meters approx.
Because they want the height of the tree we want "sin(18°) x hypotenuse".
sin(18°) x 105.15 = 32.5 meters approx.
answer: 32.5 meters approx.
The required height of the tree is 32.5 meters.
Given that,
A person 100 meters from the base of a tree, observes that the angle between the ground and the top of the tree is 18 degrees. To estimate the height h of the tree to the nearest tenth of a meter.
These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.
Here,
let the height of the tree be x, and the slant height from the foot of the person to the top of the tree be h,
according to the question,
base length = 100
cos 18 = 100 / h
h = 105.14
Now,
sin 18 = x / h
sin 18 = x / 105.14
x = 32.5 meters
Thus, the required height of the tree is 32.5 meters.
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Use a right triangle to write the following expression as an algebraic expression. Assume that x is positive and that the given inverse trigonometric function is defined for the expression in x. sin (cos^-1 14x) Show the triangle that is correct to write the given expression as an algebraic expression?
Answer:
[tex]Sin(Cos^{-1} (14x))=\sqrt{1-196x^2}[/tex]
Step-by-step explandation:
First of all, from the figure we can define the cosine and sine functions as
[tex]Cos(theta)=\frac{adjacent }{hypotenuse }[/tex]
[tex]Sin(theta)=\frac{Opposite}{hypotenuse }[/tex]
And by analogy with the statement:
[tex]14x=\frac{adjacent }{hypotenuse }[/tex]
Which can be rewritten as:
[tex]\frac{14x}{1}=\frac{adjacent }{hypotenuse }[/tex]
You have then that, for the given triangle, the values of the adjacent and hypotenuse sides, are then given by:
:
Adjacent=14x
Hypotenuse=1
And according to the Pythagorean theorem:
[tex] Opposite=\sqrt{1-(14x)^2}[/tex]
Finally, by doing:
[tex]Cos^-1(14x)=theta[/tex]
We have that:
[tex]Sin(Cos^{-1} (14x))=Sen(theta)=\frac{Opposite}{hypotenuse}=\frac{\sqrt{1-(14x)^2}}{1}=\sqrt{1-(14x)^2}[/tex]
The expression [tex]\( \sin(\cos^{-1}(14x)) \)[/tex] is equivalent to the expression [tex]\[ \sqrt{1 - 196(x)^2} \][/tex].
To express [tex]\( \sin(\cos^{-1}(14x)) \)[/tex] using a right triangle, we proceed as follows:
1. Understand the expression:
[tex]\( \cos^{-1}(14x) \)[/tex] denotes the angle [tex]\( \theta \)[/tex] such that [tex]\( \cos(\theta) = 14x \)[/tex].
We are required to find [tex]\( \sin(\theta) \)[/tex].
2. Use a right triangle:
Let's consider a right triangle where:
One of the acute angles is [tex]\( \theta \)[/tex].
Assume [tex]\( \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{14x}{1} \)[/tex]
To find the opposite side (let's call it [tex]\( \sqrt{1 - (14x)^2} \))[/tex], we use the Pythagorean identity:
[tex]\[ \sin(\theta) = \sqrt{1 - \cos^2(\theta)} = \sqrt{1 - (14x)^2} \][/tex]
[tex]\[ \sin(\cos^{-1}(14x)) = \sqrt{1 - (14x)^2} \][/tex]
[tex]\[ \sin(\cos^{-1}(14x)) = \sqrt{1 - 196(x)^2} \][/tex]
Function f(x) is positive, decreasing and concave up on the closed interval[a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the left sum, right sum, and trapezoidal rule approximations for the value of integral from a to b f(x)dx. Which one of the following statements is true?
a) Left sum < trapezoidal rule value < Right sumb) Left sum < Right sum < trapezoidal rule valuec) Right sum
Answer:
Right sum < trapezoidal rule value < Left sum
Non of the completed options are valid. Option c is incomplete but it starts correctly. If there are no more options, the answer is (c).
Step-by-step explanation:
Lets call a = x0, x1, x2, x3 and x4 = b the endpoints of the intervals in increasing order. Lets also call L the length of each subinterval. Note that b-a = 4L. Lets denote yi = f(xi) for i in {0,1,2,3,4}.
Lets compute each sum:
Left sum = x0*L + x1*L + x2*L + x3*L = (y0+y1+y2+y3)L
Similarly
Right sum = (y1+y2+y3+y4)L
and trapezoidal rule value = L((y0)/2 + y1+ y2 + y3+ (y4)/2)
Since f is decreasing, we have that y0 > y1 > y2 > y3 > y4. Therefore, y0 > y4 and, as a result, Left sum > Right sum, because the Right sum has y4 instead of y0 multiplying by L.
On the other hand, multiplying L we have (y0)/2 + y1+ y2 + y3+ (y4)/2 on the trapezoidal rule value, thus it has half of y0 and half of y4, and as a consecuence, the trapezoidal sum is between the left sum and the right sum.
The correct answer is
Right sum < trapezoidal rule value < Left sum
Answer:
answer is c, i took the test
Step-by-step explanation:
What is the perimeter of rectangle ABCDABCD? (1) The longer side of the rectangle is 2 meters shorter than its diagonal (2) The ratio of the shorter side of the rectangle to its diagonal is 13
Answer:
(1) P=4a+4
(2) P=2a+4[tex]\sqrt{42}[/tex]a
Step-by-step explanation:
Well, let us call longer side b, shorter side a and diagonal d. The perimeter of a rectangle is 2*(a+b). Let us write this formula as P=2*(a+b)
In (1) it is stated that b=a+2. Hence, the perimeter of the rectangle is P=2*(a+b). In terms of b, let us write (a+2). So P=2*(a+a+2)=4a+4.
In (2) it is stated that d/a=13 or d=13a. From Pythagorean theorem d^2=a^2+b^2. Hence, b^2=168a^2 or b=2[tex]\sqrt{42}[/tex]a. Finally, P=2*(a+b)=2*(a+2[tex]\sqrt{42}[/tex]a)=2a+4[tex]\sqrt{42}[/tex]a
Need help this and I need both them to show work
Answer:
11. ∠ABC = 96°
12. (x – 2)² + (y + 3)² = 4
Step-by-step explanation:
11. The inscribe angle (the angle inside the circle, ∠ABC) is equal to half of the outer circle.
∠ABC = 1/2∠AC
∠ABC = 1/2(192°) = 96°
12. The general equation for a circle is: (x – h)² + (y – k)² = r², where
h and k are the center of the circle (h, k), and r is the radius.
Look at the graph, the circle is centered at (2, -3), so
h=2
k=-3
and the radius of the circle is 2, so
r=2
Plug it all back into the equation:
(x – h)² + (y – k)² = r²
(x – (2))² + (y – (-3))² = (2)²
(x – 2)² + (y + 3)² = 4
Imagine that you take a road trip from A to D, but you have to do it in segments. Let’s say the distance from A to B is 145 miles; from B to C is 160 miles, and C to D is 115 miles. It takes you 6 hours to drive from A to D. What was your average speed (in miles per hour) during your trip from A to D? (Hint: How many miles did you drive from A to D? Then divide the total miles by the number of hours).
A. 50
B. 60
C. 70
D. 80
E. 90
Answer:
C
Step-by-step explanation:
The average speed can be obtained by adding the distances together and dividing by the total amount of time.
The total distance the man traveled from A to D is the addition of the distance from A to B plus the distance from B to C plus the distance from C to D. This is mathematically equal to 145 + 160 + 115 = 420 miles.
Dividing 420 miles by 6 = 70 miles per hour
Could someone help me with this exercise?
Answer:
5%: 66 2/3 mL6.5%: 133 1/3 mLStep-by-step explanation:
Let x represent the number of milliliters of 6.5% vinegar required. Then the total amount of acetic acid in the mix is ...
6.5%·x + 5%(200 -x) = 6%·200
1.5x = 200 . . . . . . . . . . . . . multiply by 100, subtract 1000
x = 200/1.5 = 133 1/3 . . . . mL of 6.5% vinegar
200-x = 66 2/3 . . . . . . . . . mL of 5% vinegar
A rocket is located on a platform that is 200 feet above a deep canyon. After launching the rocket with an initial velocity of 50 ft/sec, the platform is moved.
a.) What is the max height the rocket will reach?
b.) When will it reach the max height?
c.) When will it be 300 feet off the ground?
d.) How high will it be after 4.2 seconds?
e.) Where will the rocket be after seven seconds?
Answer:
a) Max height it will reach is 327.55 ft above the ground
b) It will reach max height after 5.1 seconds
c) It will be 300 feet off the ground at 12 seconds
d) It will be 305 ft above the ground
e) The rocket will be 247.55 ft above the ground after seven seconds
Step-by-step explanation:
a) Using the equations of kinematics:
v² = v_i² + 2 g Δy
where
v is the final velocityv_i is the initial velocityg is the acceleration due to gravityΔy is the rocket's displacementTherefore,
0² = 50² + 2(- 9.8) Δy
(the negative sign shows that the positive direction is upwards. Gravity acts downwards)
Δy = -(50)² / 2(-9.8)
Δy = 127.55 ft
Thus, the maximum height that the rocket reaches will be
200 ft + 127.55 ft
= 327.55 ft above the ground
b) Using the equations of kinematics:
Δy = [(v + v_i) / 2 ] × t
t = Δy / [(v + v_i) / 2 ]
t = 127.55 / [(0 + 50) / 2]
t = 5.1 seconds
Therefore, the rocket will reach its maximum height after 5.1 seconds.
c) Using the equations of kinematics:
t₃₀₀ = Δy / [(v + v_i) / 2 ]
t₃₀₀ = 300 / [(0 + 50) / 2]
t₃₀₀ = 12 seconds
Therefore, the rocket will reach 300 feet after 12 seconds
d) Using the equations of kinematics:
Δy = [(v + v_i) / 2 ] × t
Δy = [(0 + 50) / 2] × 4.2
Δy = 105 ft
Therefore, the rocket will be
105 ft + 200 ft
= 305 ft above the ground after 4.2 seconds
e) Using the equations of kinematics:
Δy = [(v + v_i) / 2 ] × t
Δy = [(0 + 50) / 2] × 7
Δy = 175 ft
Therefore,
175 - 127.55 = 47.55 ft
Thus, the rocket will be
47.55 ft + 200 ft
= 247.55 ft above the ground after seven seconds
What is the percent of change from 6,000 to 60?
Answer: 99% decrease
Step-by-step explanation: Since the number changes from 6,000 to 60, we know that it's decreasing. Now to find the percent decrease, we divide the amount of change by the original number.
The amount of change is the difference between 6,000 and 60 and the original number is 6,000.
6,000 - 60 is 5,940 so we are left with [tex]\frac{5,940}{6,000}[/tex] and dividing 6,000 into 5,940 gives us 0.99.
Finally, since the problem is asking us for the percent, we write 0.999 as a percent by moving the decimal point 2 places to the right to get 99%.
So when a number changes from 6,000 to 60, it has decreased by 99%.
What conic section degenerates into a line?
Parabola
Hyperbola
Circle
Ellipse
I think it's Ellipse? I'm not sure though
Some degenerate parabola cases form a single straight line, while other cases form one pair of parallel lines.
A degenerate hyperbola forms two lines that intersect at the vertex of the cone. We can rule out choice B.
A degenerate circle is a single point, so we can rule out choice C.
A degenerate ellipse is also a single point. Any circle is an ellipse (but not the other way around). We can rule out choice D.
Jack accepted a job to paint a new house. He calculated that he can complete the job in 30 hours. He hired a trainee to assist him. He has seen the trainee work and estimates that it the trainee working alone would take 45 hours to complete the job. How much time should the two of them working together need to paint the house? (Round your answer to the nearest tenth.)
Answer:
20hours
Step-by-step explanation:
Jack can complete the painting in 30hours. The fraction he can paint per hour is thus 1/30
Trainee can complete the painting in 45hours, the fraction he can paint per hour is 1/45
If they are working together, the fraction that can paint in an hour is :
1/45 + 1/30 = 5/90 = 1/18
Now we know they can paint 1/18 of the room in an hour, the number of hours needed to completely paint the room is thus 1/1/18 = 18 hours
Rounding up answer to the nearest tenth is 20hours
construct an equation for the expression: the sum of a number and itself is 8. Show the solution to the equation and prove your solution to be true through your work.
PLEASE HELP ME I'M SO BEHIND ON MY SCHOOLING NEED THE ANSWER ASAP PLEASE!!!!!!!! THANK YOU
Answer:
equation : 2x = 8
solution : x = 4
Step-by-step explanation:
let the number be x
"the sum of a number and itself "
= sum of x and x
= x + x
= 2x
"the sum of a number and itself is 8"
2x = 8
solving the equation, divide both sides by 2
2x = 8
x = 8/2
x = 4
geometry, thanks if you help me! :)
Answer:
A is a function/B is not.
Step-by-step explanation:
A, there are 1 x value for 1 y value.
B, is not a function because for 1 x value, there are 2 y values.
Answer:
See below.
Step-by-step explanation:
Graph A is a function because it passes the vertical line test. You could draw a vertical line anywhere on the graph which will only pass through the graph at one point. It is a many-to-one relation.
Graph B is not a function because some vertical lines will pass through the graph at 2 points. It is a one-to-many relation.,
One-to-one and many-to-one relations are functions but one-to-many are not functions.
Geometry Help!!!
I can’t seem to find the missing third side of the isosceles triangle.
Doesn’t have to equal 180?
This is the equation I’m doing but doesn’t give me an answer from the choices: 12.25 + 12.25 + x =180
===============================
Explanation:
Let's say we had a triangle with side lengths a,b,c.
If we know that a = 12.25 and b = 12.25, then the third side c has its length restricted in such a way that
b-a < c < b+a
This is a variation of the triangle inequality theorem.
-------------
So,
b - a < c < b + a
12.25 - 12.25 < c < 12.25 + 12.25
0 < c < 24.5
which means the third side c is between 0 inches and 24.5 inches.
The value of c cannot be 0, and it cannot be 24.5 either.
Among the answer choices given, we see that only 24.0 is the only valid option here. The other two choices are too large.
-------------
Side Note: If your teacher gave you two angles (instead of two sides) to be 12.25 degrees, and wanted the third missing angle of the triangle, then you would be correct in having 12.25+12.25+x = 180 as your first step.
You are a researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 35 bacteria reveals a sample mean of ¯ x = 80 x ¯ = 80 hours with a standard deviation of s = 4.8 s = 4.8 hours. You would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.65 hours at a 98% level of confidence. What sample size should you gather to achieve a 0.65 hour margin of error? Round your answer up to the nearest whole number.
To calculate the desired sample size with a 98% confidence level and 0.65-hour margin of error, we use the appropriate formula for sample size calculation in statistics, which leads us to a required sample size of 98 bacteria.
Explanation:In this case, we are trying to determine the appropriate sample size using statistical methodology. To calculate this, we can use the formula for the sample size which is n = (Z∗σ/E)^2. Here, 'Z' is the z-value corresponding to the desired confidence level (for 98% confidence, Z score or z-value is 2.33), σ is the standard deviation (which is 4.8 hours in this case), and 'E' is the desired margin of error (0.65 hours).
Substituting these values into the formula gives: n = (2.33∗4.8/0.65)^2. After simplifying this calculation, we get n = 97.46. However, we can't have a fractional part of a sample, so we round up to the nearest whole number which is 98. So, you would need a sample size of 98 bacteria in order to achieve a 0.65-hour margin of error at a 98% confidence level.
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If ABCD is congrunent to , pqrs, then AD is congrent to ?
Answer:
AD is congruent to RS
Step-by-step explanation:
we know that
If two figures are congruent, then its corresponding sides and its corresponding angles are congruent
In this problem
If
ABCD≅PQRS
then
Corresponding angles
∠A≅∠P
∠B≅∠Q
∠C≅∠R
∠D≅∠S
Corresponding sides
AB≅PQ
BC≅QR
CD≅RS
AD≅PS
Find the length of the curve with equation $y=\dfrac{1}{3}(x^2+2)^{3/2}$ for $1\leq x\leq 4$.
To find the length of the curve defined by $y=\dfrac{1}{3}(x^2+2)^{3/2}$ over the interval $1\leq x\leq 4$, we must integrate the square root of the sum of 1 and the square of the derivative of our function from 1 to 4.
To begin with, we want to find the derivative of our function. In other words, we need to compute $dy/dx$.
The derivative, with the Chain Rule gives us:
$y' = \dfrac{1}{3} \cdot \dfrac{3}{2} \cdot 2x \cdot (x^2+2)^{1/2}$
Simplifying gives:
$y' = x \cdot (x^2+2)^{1/2}$
Next, we substitute $y'$ into the formula for finding the length of a curve:
$L = \int_{a}^{b}\sqrt{1+(y')^2}dx$
We should note that $a = 1$ and $b = 4$ here. We substitute $y'=x \cdot (x^2+2)^{1/2}$ and obtain:
$L = \int_{1}^{4}\sqrt{1+(x \cdot (x^2+2)^{1/2})^2}dx$
We can now evaluate the integral, where we will square the entire derivative and add 1 as being under the square root.
So, finally, evaluating this integral gives us the length of the curve, which in this case is 24.
Therefore, the length of the curve $y=\dfrac{1}{3}(x^2+2)^{3/2}$ over the interval $1\leq x\leq 4$ is 24.
Learn more about Curve Length here:https://brainly.com/question/32515746
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f(m) = 2.5 + 0.12m
If Natalie paid $6.82 for one call, how many minutes long was it?
Select one:
A. 28
B. 36
C. 42
D. 45
Answer:
36 minutes long
Step-by-step explanation:
6.82 = 2.5 + 0.12m
4.32 = 0.12m
36 = m; 36 minutes long.
Answer:
B. 36.
Step-by-step explanation:
Substituting 6.82 for m:
6.82 = 2.5 + 0.12m
0.12 m = 6.82 - 2.5
0.12m = 4.32
m = 4.32 / 0.12
m = 36 minutes.
find the radius pls. help
Good morning,
Answer:
r = 4 cmStep-by-step explanation:
V = h × (base area)
= 12 × (π×r²)
then 192π = 12π×r²
Then 192 = 12×r²
Then r² = 192÷12 = 16
Then r = √16 = 4.
:)
In the past month, Josh rented one video game and six DVDs. The rental price for the video game who is $2.50. The rental price for each DVD is $3.40. What is the total amount paid josh spent on video games in this past month?
Answer:
total amount paid = $ 22.9
Step-by-step explanation:
total price = $ 2.5 + $3.4(6)= $22.9
Answer:
2.50
Step-by-step explanation:
The expression 120-15x represents how many invitations Luanne has to address after x days. The expression 120 + 15(7-x) represents the number of invitations Darius has to address after x days. After how many days do Luanne and Darius have the same sumber of invitations to address?
Answer:
not possible.
Step-by-step explanation:
number of invitations luanne has to address after x days = 120-15x
number of invitations Darius has to address after x days = 120 + 15(7-x)
so, if the number of invitations should be the same for both of them,
we have to equate their number of invitations
120-15x = 120 + 15(7-x)
subtracting 120 from both the sides,
-15x = 15(7-x) = 105 -15x
adding we 15x on both sides, we wont find any solution for x.
so, this isnt possible or the question must be wrong.
4x/ 2x + y + 2y/ 2x + y Perform the indicated operation. Be sure the answer is reduced.
Answer:
[tex]\frac{4x}{2x+y} +\frac{2y}{2x+y}=2[/tex]
Step-by-step explanation:
Given:
The expression to simplify is given as:
[tex]\frac{4x}{2x+y} +\frac{2y}{2x+y}[/tex]
Since, the denominator is same, we add the numerators and divide it by the same denominator. This gives,
[tex]\frac{4x+2y}{2x+y}[/tex]
Now, we simplify further by factoring out the common terms from the numerator and denominator if possible.
We observe that, 2 is a common factor to both [tex]4x\ and\ 2y[/tex]. So, we factor out 2 from the numerator. This gives,
[tex]\frac{2(2x+y)}{2x+y}[/tex]
Now, the term [tex]2x+y[/tex] is common in both the numerator and denominator. Hence, [tex]\frac{2x+y}{2x+y}=1[/tex]
So, the simplified form is:
[tex]=2\times \frac{2x+y}{2x+y}\\\\=2\times 1\\\\=2[/tex]
Sam makes $400 per week plus $20 commission on each new sell phone plan he sells. Write an equation to determine how many new plans she sold to earn $680 last week
Answer:
She sold 14 new plans to earn $680 last week.
Step-by-step explanation:
$400 + 20(x) = $680
Take 400 away from total cost. So, 680 - 400 = 280.
Now, divide 280 by 20, and x = 14.
The equation would be $400 + 20(14) = $680
VThe speed of sound is approximately 768768768 miles per hour. When an object travels faster than the speed of sound, it creates a sonic boom. Write an inequality that is true only for speeds (s)(s)left parenthesis, s, right parenthesis at which a moving object creates a sonic boom.
Answer:
The Inequality [tex]s > 768\ mi/hr[/tex] is true at which a moving object creates a sonic boom.
Step-by-step explanation:
Given:
Speed of Sound = 768 miles per hour
Also Given:
When an object travels faster than the speed of sound, it creates a sonic boom.
We need to find the inequality which is true only for speeds (s) at which a moving object creates a sonic boom
So We can say;
When;
[tex]s < 768\ mi/hr[/tex] ⇒ Normal sound no sonic boom (false)
[tex]s = 768\ mi/hr[/tex] ⇒ speed of sound but no sonic boom (false)
[tex]s > 768\ mi/hr[/tex] ⇒ sonic boom is created (True)
Hence The Inequality [tex]s > 768\ mi/hr[/tex] is true at which a moving object creates a sonic boom.