Answer:
3.44 cm
Step-by-step explanation:
When the pendulum is at its lowest point, the vertical length of the pendulum is L.
When the pendulum is at its highest point, the vertical length of the pendulum is L cos θ.
So the height difference of the pendulum between its lowest and highest points is h = L − L cos θ.
The pendulum swings 72° from right to left, or 36° from the vertical.
The length of the pendulum is 18 cm.
So the height is:
h = L − L cos θ
h = 18 − 18 cos 36°
h = 3.44
The graphs below have the same shape. What is the equation of the blue graph?
g(x) =
A. g(x) = (x + 3)2 + 1
B. g(x) = (x - 3)2 + 1
C. g(x) = (x - 3)2 - 1
D. g(x) = (x + 3)2 - 1
Explanation:
The vertex of a parabola is either the highest point or the lowest point, depending on how the parabola is oriented. In this case, it is the lowest point.
For the red f(x) curve, we see the vertex is (0,0)
The blue g(x) curve has its vertex at (3,1)
In general, the vertex is represented by (h,k)
For the blue curve, (h,k) = (3,1) so h = 3 and k = 1 pair up together
We will plug those values along with a = 1 into the vertex form below
y = a(x-h)^2 + k
y = 1(x-3)^2 + 1
y = (x-3)^2 + 1
The blue curve is the result of shifting the red curve 3 units to the right and 1 unit up. No vertical stretching or compressing has been applied, which is why a = 1 stays the same.
Pretty confused on finding the missing line segment. Please help.
Answer:
Option (1). 17
Step-by-step explanation:
Length of a segment having coordinates (x₁, y₁) and (x₂, y₂) is given by the formula,
d = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Coordinates of points A and C are (4, 3) and (19, 11).
To get the length of segment AC we will substitute the coordinates in the formula,
AC = [tex]\sqrt{(19-4)^2+(11-3)^2}[/tex]
= [tex]\sqrt{(15)^2+8^2}[/tex]
= [tex]\sqrt{225+64}[/tex]
= [tex]\sqrt{289}[/tex]
= 17
Therefore, length of segment AC = 17 units.
Option (1) will be the answer.
A chemist begins with 120 mL of a radioactive substance that decays exponentially. After 24 hours, only 30 mL of the substance remain. How many mL will remain after 48 hours? 12.5 mL 7.5 mL 4.5 mL 9.5 mL
Answer:
7.5 mL
Step-by-step explanation:
If it decays exponentially then you divide the previous number by 4 to get the next number and 30 divided by 4 is 7.5mL.
Determine the measure of the unknown angles.
PLEASE HELP!!! ASAP!!
(Picture included)
(V.O.A) means vertically opposite angle.
Find the value of x for which the lines l and m are parallel. Choices are in the attachment.. (disregard the filled in answer)
You chose the correct answer.
======================================================
Explanation:
Lines M and L are only parallel if and only if the corresponding angles are congruent.
The angles 127 and (9x+10) degrees are corresponding angles. They are both on the same side of the transversal, and they are to the right of each parallel line.
Set the two angle expressions equal to one another. Solve for x
9x+10 = 127
9x = 127-10
9x = 117
x = 117/9
x = 13
Answer:
x=13
Step-by-step explanation:
For the lines to be parallel, the angles would be equal
127 = 9x+10
Subtract 10 from each side
127 -10 = 9x+10-10
117 = 9x
Divide each side by 9
117/9 = 9x/9
13 =x
The volume of a cylinder is 2,200 pie cubic inches. The diameter of the circular base is 10 inches. What is the height of the cylinder
Answer:
Step-by-step explanation:
H = V/ pie r^2
H = [tex]\frac{2200pie}{Pie 5^2}[/tex]
R= 5 because the radius is half the diameter
Pies cancel out leaving you with:
H = 2200/5^2
H = 2200/25
H = 88
Hope this helps :)
Find the lower bound for the following lengths:
a) 40 cm measured to the nearest cm.
b) 82.8 cm measured to the nearest tenth of a cm.
Answer:
a) Lower bound = 39.5
b) Lower bound = 82.75
New packaging for fruit snacks contains 10% less weight than the original packaging. If the new package costs 15% more than the original package, by what fraction did the unit price increase? Express your answer as a common fraction.
Answer:
5/18
Step-by-step explanation:
Let's say the original packaging was 1 lb of packaging for $1.
The cost was $1/lb.
Then the weight went down by 10% and the price went up by 15%.
Now 0.9 lb of packaging cost $1.15.
The new unit cost is $1.15/(0.9 lb)
The difference is
$1.15/(0.9 lb) - $1/lb =
= $1.15/(0.9 lb) - $0.9/(0.9 lb)
= $0.25/(0.9 lb)
=$25/(90 lb) = $5/(18 lb)
The price went up by 5/18.
A medical researcher is studying the effects of a drug on blood pressure. Subjects in the study have their blood pressure taken at the beginning of the study. After being on the medication for 4 weeks, their blood pressure is taken again. The change in blood pressure is recorded and used in doing the hypothesis test. Change: Final Blood Pressure - Initial Blood Pressure The researcher wants to know if there is evidence that the drug increases blood pressure. At the end of 4 weeks, 32 subjects in the study had an average change in blood pressure of 2.5 with a standard deviation of 4.8. Find the p -value for the hypothesis test.
Answer:
The p -value for the hypothesis test is 0.003.
Step-by-step explanation:
In this case, a paired t-test would be used to determine whether the drug increases blood pressure.
The hypothesis can be defined as follows:
H₀: The drug has no effect on blood pressure, i.e. d = 0.
Hₐ: The drug increases blood pressure, i.e. d > 0.
The information provided is:
[tex]n=32\\\bar d=2.5\\S_{d}=4.8[/tex]
The test statistic is:
[tex]t=\frac{\bar d}{S_{d}/\sqrt{n}}[/tex]
[tex]=\frac{2.5}{4.8/\sqrt{32}}\\\\=2.9463\\\\\approx 2.95[/tex]
The degrees of freedom of the test is:
[tex]df=n-1=32-1=31[/tex]
The p-value of the test is:
[tex]p-value=P(t_{31}>2.95)=0.003[/tex]
*Use a t-table.
Thus, the p -value for the hypothesis test is 0.003.
A t-test is an inferential statistic that is used to see if there is a significant difference in the means. The p-value for the hypothesis test is 0.003.
What is a t-test?A t-test is an inferential statistic that is used to see if there is a significant difference in the means of two groups that are connected in some way.
As it is given that 32(n) subjects in the study had an average change in blood pressure of 2.5([tex]\bar d[/tex]) with a standard deviation of 4.8([tex]S_d[/tex]).
Now, in order to solve the problem we need to use t-test, the test will determine whether the blood pressure increases or not under the influence of the drug.
The hypothesis for the test can be defined as:
H₀: The drug has no effect on blood pressure, therefore, d = 0.
Hₐ: The drug has increased blood pressure, therefore, d>0.
The test static is:
[tex]t = \dfrac{\bar d}{\dfrac{S_d}{\sqrt n}}\\\\\\t = \dfrac{2.5}{\dfrac{4.8}{32}} = 2.946 \approx 2.95[/tex]
Further, the degree of freedom of the test can be written as,
[tex]d_f=n-1 = 32-1=31[/tex]
Thus, the p-value of the test is:
[tex]p-value = P(t_{31} > 2.95)\\\\\text{Using the t-table}\\\\p-value = 0.003[/tex]
Hence, the p-value for the hypothesis test is 0.003.
Learn more about T-test:
https://brainly.com/question/1189751
I'm a survey of 200 employees, 65% agreed that the management of the cafeteria should be changed. If the confidence interval is 95%, the margin of error for this survey is %, and the maximu
Answer:
Step-by-step explanation:
Confidence interval for population proportion is expressed as
Sample proportion ± margin of error
Margin of error = z × √pq/n
Where
z represents the z score corresponding to the confidence level
p = sample proportion. It also means probability of success
q = probability of failure
q = 1 - p
From the information given,
Sample proportion, p = 65/100 = 0.65
q = 1 - 0.65 = 0.35
n = 200
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.025 = 0.975
The z score corresponding to the area on the z table is 1.96. Thus, the z score for a confidence level of 95% is 1.96
Margin of error = 1.96√(0.65)(0.35)/200
Margin of error = 0.066 = 6.6%
The maximum boundary of the interval is
0.65 + 0.066 = 0.716
Dos familias asisten a un sitio de comidas rápidas de la ciudad, una de ellas pide 4 perros calientes y 3 hamburguesas y pagan 43000 pesos, la otra familia, piden 5 perros calientes y 1 hamburguesa y pagan 34500 pesos, se desea saber ¿cuál es el valor de cada perro y de cada hamburguesa?.
Answer:
Cada perro caliente cuesta 5,500 pesos y cada hamburguesa cuesta 7,000 pesos.
Step-by-step explanation:
Sea x el precio de los perros calientes y y el precio de las hamburguesas.
Escribiendo los datos de la primera familia en forma de ecuación tenemos:
[tex]4x+3y=43,000[/tex] (4 perros calientes y 3 hamburguesas cuestan 43,000 pesos)
Escribiendo los datos de la segunda familia:
[tex]5x+y=34500[/tex] (5 perros calientes y 1 hamburguesa cuestan 34,500 pesos)
Vamos a resolver este sistema de ecuaciones por el método de suma y resta:
[tex]4x+3y=43,000\\5x+y= 34,500[/tex]
Multiplicando la segunda ecuación por -3 y sumando ambas tenemos:
[tex]4x+3y=43,000\\-15x-3y= -103,500\\\\-11x=-60,500\\x=-60,500/-11\\x= 5,500[/tex]
Por lo tanto, un perro caliente cuesta 5,500 pesos.
Ahora sustituimos este valor en nuestra segunda ecuación para encontrar el precio de las hamburguesas:
[tex]5x+y=34500\\5(5,500)+y=34,500\\27,500 +y=34,500\\y=34,500-27,500\\y=7,000[/tex]
Por lo tanto, las hamburguesas cuestan 7,000 pesos cada una
Can you guys please help me? I don't really get what it is asking us to do.
The correct answer is 160
And u have to do the question correctly...
Cuz I told u the answer......
Hope this helps......
find the difference between the endpoints of the interval on the y-axis. (1) [y-value at x=p] - (2) [y-value at x=p+k]
I know you don't need this anymore but for the ones who do this is the answer.........Look at the graph and trust it. Yes, I know it says to substitute and you can following the last page on part a) Doing what they do in the tables and it will get you the same answer as if you'd just look at the graph.
The answer for the y- value at x=p IS 8. and the answer for the y-value at x=p+k IS 5. So go ahead and write that down if you haven't already!
For step2 Find the difference between the endpoints of the interval on the y-axis. The answer to your question, Is and always will be 3! The difference is 3 because you subtract 3 from 8 and you get 5.
If you didn't read clearer, I'll write it for you again, The length interval is K, it is the length between p and p+k.
For the following questions, does your answer to step 2 depend on p, well I suppose. This is why....The answer does depend on p because we are dealing with a slope. if you move up or down the slope it will not be the same.
For the question..... Is the difference between the y-values the same regardless of where the interval starts? The answer is yes!!! And No!!! But WRITE YES! Why? Because if the interval moves as a whole the difference between the y-values is the same! Try it for yourself. Move K back two x-values and the difference for the y-values will be the same, IT WILL STILL BE THREE.
Hope you understood!
And for part one the answer on part c (-2). It depends on K.
PLEASE HELP!
Evaluate the following using exact radian measure. Show all of your work.
[tex]cot { }^{ - 1} ( - \frac{1}{ \sqrt{3} } )[/tex]
Answer:
PEMDAS DAT
Step-by-step explanation:
Rationalize the denominator of 2/√3−1 Please give step by step answer
Answer:
√3 + 1
Step-by-step explanation:
Step below are self-explanatory
2/(√3−1)= 2×(√3 + 1)/(√3 - 1)×(√3 + 1) = multiplied both sides by √3 + 12×(√3 + 1)/(√3² - 1²)= used (a+b)(a-b)= a² - b² formula2×(√3 + 1)/(3 - 1)=2×(√3 + 1)/2= cancelled like terms√3 + 1.Resolva as equações, sendo U = Q (separe as respostas por vírgulas). A) 3y - 2 = - y + 4 B) 5 - 4x = x + 3 + 2x C) - 12 - 9x = - 4 - 12x D) - x - 6 + 3x = -2x + 8x + 15
Answer:
[tex](A) y=1.5[/tex]
[tex](B)x=\dfrac27[/tex]
[tex](C)x=2\dfrac23[/tex]
[tex](D)x=-5.25[/tex]
Step-by-step explanation:
(A)
[tex]3y - 2 = - y + 4\\3y+y=4+2\\4y=6\\y=\dfrac64\\\\y=1.5[/tex]
(B)
[tex]5 - 4x = x + 3 + 2x\\5 - 4x = 3 +3x\\5-3=3x+4x\\7x=2\\x=\dfrac27[/tex]
(C)
[tex]-12 - 9x = - 4 - 12x\\-9x+12x=-4+12\\3x=8\\x=\dfrac83\\\\x=2\dfrac23[/tex]
(D)[tex]- x - 6 + 3x = -2x + 8x + 15[/tex]
[tex]2x-6 = 6x + 15\\2x-6x=15+6\\-4x=21\\x=\dfrac{21}{-4} \\\\x=-5.25[/tex]
find the solution(s) to (x + 3)^2=49
Answer:
x = 4
x = -10
Step-by-step explanation:
(x + 3)² = 49
Take the square root of both sides.
x + 3 = ±7
The equation is x + 3 = 7 or x + 3 = -7.
x + 3 = 7
Subtract 3 on both sides.
x = 4
x + 3 = -7
Subtract 3 on both sides.
x = -10
Answer:
x₁ = -10
x₂ = 4
Step-by-step explanation:
(x + 3)² = 49
x + 3 = ± 7
x + 3 = -7 → x = -10
x + 3 = 7 → x = 4
Hope this helps! :)
Can anyone help with this?
Answer:
115/5 23 so 20% =23 23x4 =92
Which statement best describes the function below : F(x)=2x^2-3x+1
Answer:
it is a many to one function:)
Step-by-step explanation:
The statement which best describes the function F(x)=2x^2-3x+1 is it is a many to one function.
How do you find the piecewise function?
A piecewise function is a function built from pieces of different functions over different intervals. For example, we can make a piecewise function f(x) where f(x) = -9 when -9 < x ≤ -5, f(x) = 6 when -5 < x ≤ -1, and f(x) = -7 when -1 <x ≤ 9.
What is a function example?f(x) = x2 shows us that function "f" takes "x" and squares it. Example: with f(x) = x2: an input of 4. becomes an output of 16.
Learn more about piecewise function at https://brainly.com/question/27262465
#SPJ2
x+2y=-6 solve for x?
Answer:
Step-by-step explanation:
x
+
2
y
=
6
Subtract
x
from both sides of the equation.
2
y
=
6
−
x
Divide each term by
2
and simplify.
Tap for more steps...
y
=
3
−
x
2
Answer:
x=2y-6
Step-by-step explanation:
To solve for x, we need to have one more equation, as there are two variables; x and y. But, we can still get it to this point.
First, we need to get x on to one side.
x=-2y-6
That is all we can do from here.
If you provide another corresponding equation, we can solve for x.
Hope this provides some guidance!!
~gloriouspurpose~
James earned $816 each year. He earned x dollars less per month than Matt, who earned $80 per month. Equation: 12(80 – x) = 816 x = 12; monthly earnings = $68
Answer:
see below
Step-by-step explanation:
12(80 – x) = 816
Divide each side by 12
80-x = 816 /12
80-x = 68
Subtract 80 from each side
80-x-80 = 68-80
-x = -12
Multiply each side by -1
x = 12
James earned 80-12 = 68
Answer:
Which strategies will verify that the value for x is correct? Check all that apply.
Substitute 12 for x in the equation.
Multiply $68 by 12 months.
Step-by-step explanation:
B and C
the second and third one.
PLEASE HELP! The composite figure is made up of a cone and a half sphere. The radius of the half sphere is 6 cm. What is the volume of the composite figure? Use 3.14 for Pi. Round to the nearest hundredth.
Answer:
904.32 cm^3
Step-by-step explanation:
V = (1/3)(pi)r^2h + (1/2)(4/3)(pi)r^3
V = (1/3)(3.14)(6 cm)^2(12 cm) + (1/2)(4/3)(3.14)(6 cm)^3
V = 904.32 cm^3
The volume of the figure would be the combination of the volume of the cone and the hemisphere that is 904.32 cm^3.
How to find volume of a right circular cone?Suppose that the radius of the considered right circular cone be 'r' units.
And let its height be 'h' units.
Then, its volume is given as:
[tex]V = \dfrac{1}{3} \pi r^3 h \: \rm unit^3[/tex]
Right circular cone is the cone in which the line joining the peak of the cone to the center of the base of the circle is perpendicular to the surface of its base.
The composite figure is made up of a cone and a half-sphere.
The radius of the half-sphere is 6 cm.
The volume of the figure would be the combination of the volume of the cone and the hemisphere.
The volume of the figure is
[tex]V = (1/3)(\pi)r^2h + (1/2)(4/3)(\pi)r^3\\V = (1/3)(3.14)(6 cm)^2(12 cm) + (1/2)(4/3)(3.14)(6 cm)^3\\V = 904.32 cm^3[/tex]
Learn more about the volume of cone here:
https://brainly.com/question/26093363
#SPJ2
Please answer this question in two minutes
Answer:
t = 8; u = 14.
Step-by-step explanation:
If the two triangles are to be congruent, their side lengths and angles must be equal.
In this case, segment RQ corresponds with segment HI, and segment QS corresponds to segment IJ.
Since they are equal, we know that...
3u = u + 28
and
16t - 32 = 12t
Solve for both!
3u = u + 28
2u = 28
u = 14
16t - 32 = 12t
4t = 32
t = 8
So, t = 8 and u = 14.
Hope this helps!
Answer他媽的你你一個愚蠢的屁股妓女，你需要做你贏了他媽的作業傻瓜屁股
Step-by-step explanation:
A square with a length of 14 cm is scaled up
to create an image, using a scale factor of 3.25.
What is the area of the image?
Answer:
The area of the image is 2,070.25 cm^2
Step-by-step explanation:
The first thing we do here is to scale up the square using the factor given.
Thus, for a length of 14 cm scaled up by 3.25, the new length becomes 14 * 3.25 = 45.5 cm
Mathematically, the area of the square is L^2
where L in this case is 45.5 cm
The area of the scaled up square would be 45.5 * 45.5 = 2,070.25 cm^2
2+2 what does it 1+!
Answer:
4 AND 2
Step-by-step explanation:
Answer:
Hello!
______________________
This question is very easy.
2 + 2 = 4
1 + 1 = 2
Step-by-step explanation: Add.
Hope this helped you!
Question 10 PLEASE HELP find the slope of the line described by: x-7y=-6
Answer:
slope m=1/7
Step-by-step explanation:
x-7y=-6
-7y=-x-6
y=-x/-7 -6/-7
y=1/7 x+6/7
Help please I don’t get it :( .
Here are the Ramps from screen 3 that make a smooth slide , why do you think these Ramps lead to a smooth ride ?
Answer:
yeah me either sorry homie I just dont get this work at all im just being there for your mental support lol
Consider the following 8 numbers, where one labelled x is unknown.
11, 1, 34, x, 41, 10, 47, 2
Given that the range of the numbers is 67,
work out 2 values of x.
Answer:
x=-20 or x=68
Step-by-step explanation:
you can either make it so 47 remains the largest number and so take 67 from 47 (=-20) or you can leave 1 as the smallest number and add 67 to 1 (=68)
ASAP plaase ABCD is a square. The length of each side of the square ABCD is___units, and the length of its diagonal is about_____units. First options:9, 14, 28 Second options:14, 18.6, 19.8
Answer:
length is 14
diagonal is 19.8
Step-by-step explanation:
To find the length of the side of the square, what we need to do is to use the height 12 in each triangle to find the length of the adjacent in each triangle and add together.
Mathematically we can find the length of this adjacent using the Pythagoras theorem which states that the square of the hypotenuse equals sum of the squares of the two other sides.
Applying this to each of the 2 triangles but summing the answer;
The length l is as follows;
Let’s call the adjacent fir each side of the triangle a and b but the addition being l
a^2 = 15^2 - 12^2 = 225-144 = 81
a^2 = 81
a = 9
b^2 = 13^2 -12^2
b^2 = 169-144
b^2 = 25
b = 5
l = a + b = 9 + 5 = 14
The diagonal can also be calculated using pythagoras’
d^2 = 14^2 + 14^2
d^2= 196 + 196
d^2 = 392
d = √(392)
d = 14√2 = 19.8
Two pathways meet at 30° to each other. One pathway has lighting and the other does not.
The distance between successive lights on the lighted pathway is 5 metres. Each light has a
range of effective illumination of 6 metres.
What length of the pathway without lights is illuminated by the pathway with lights?
Answer:
12 meters
Step-by-step explanation:
Draw a picture of the two pathways 30° apart. Add a circle representing the illumination of the light on one of the pathways. Draw a line from the center of the circle to the last point where it intersects the pathway without lights.
This forms a triangle. One leg is x, the length of the pathway without lights. Another leg is 5n, where n is an integer. This represents how far the light is from where the pathways meet. The third and final leg is 6, the radius of the illumination.
Use law of cosine to solve:
6² = x² + (5n)² − 2x(5n) cos 30°
36 = x² + 25n² − 5√3 xn
0 = x² − 5√3 xn + 25n² − 36
In order to have a solution, the discriminant must be greater than or equal to 0.
b² − 4ac ≥ 0
(-5√3 n)² − 4(1)(25n² − 36) ≥ 0
75n² − 100n² + 144 ≥ 0
144 − 25n² ≥ 0
144 ≥ 25n²
144/25 ≥ n²
12/5 ≥ n
So n must be an integer less than 12/5, or 2.4. Therefore, the largest value of n is 2. Substituting:
0 = x² − 5√3 x(2) + 25(2)² − 36
0 = x² − 10√3 x + 64
Solve with quadratic formula:
x = [ 10√3 ± √(300 − 4(1)(64)) ] / 2(1)
x = (10√3 ± √44) / 2
x = 5√3 ± √11
x ≈ 5.34 or 11.98
We want the larger value of x. So approximately 12 meters of the pathway without lights is illuminated.