Using the t-distribution, it is found that since the p-value is greater than 0.01, there is no evidence that the new machine should be rejected at the 0.01 significance level.
What are the hypothesis tested?At the null hypothesis, it is tested if the average is not less than 25, that is:
[tex]H_0: \mu \geq 25[/tex]
At the alternative hypothesis, it is tested if the average is less than 25, that is:
[tex]H_1: \mu < 25[/tex]
What is the test statistic?The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.Considering the situation described, the values of the parameters are given as follows:
[tex]\overline{x} = 24.97, \mu = 25, s = 2.16, n = 10[/tex]
Hence the test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{24.97 - 25}{\frac{2.16}{\sqrt{10}}}[/tex]
t = -0.04
What is the p-value and the conclusion?Using a t-distribution calculator, for a left-tailed test, as we are testing if the mean is less than a value, with 10 - 1 = 9 df and t = -0.04, the p-value is of 0.4844.
Since the p-value is greater than 0.01, there is no evidence that the new machine should be rejected at the 0.01 significance level.
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Simplify the expression cos (tan-1(x/2)).
\cos (\tan \left( -1\right) (\frac{x}{2}))
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Combine multiplied terms into a single fraction
\cos (\tan \left( -1\right) \cdot \frac{x}{2})
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\cos (\frac{\tan \left( -1\right) x}{2})
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Solution
\cos \left( \frac{\tan \left( -1\right) x}{2}\right)
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Answer:
Step-by-step explanation:
[tex]cos(tan^{-1}(\frac{x}{2} ))\\put~tan^{-1}(\frac{x}{2} )=t\\\frac{x}{2} =tan~t\\sec^2t-tan^2t=1\\sec^2t=1+tan^2t=1+(\frac{x}{2} )^2=\frac{x^2+4}{4} \\sec~t=\pm\frac{\sqrt{x^2+4}}{2} \\cos ~t=\pm\frac{2}{\sqrt{x^2+4}} \\hence~cos(tan^{-1}(\frac{x}{2} ))=cos~t=\pm\frac{2}{\sqrt{x^2+4}}[/tex]
What is the equation of the circle that has its center at -26,120 and passed through the origin
well, first off let's check those two points, we know it's centerd at (-26 , 120) and we also know it passes through (0 , 0), so the distance between those two points is its radius
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{-26}~,~\stackrel{y_2}{120})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{radius}{r}=\sqrt{(~~-26 - 0~~)^2 + (~~120 - 0~~)^2} \implies r=\sqrt{(-26)^2 + (120 )^2} \\\\\\ r=\sqrt{( -26 )^2 + ( 120 )^2} \implies r=\sqrt{ 676 + 14400 } \implies r=\sqrt{ 15076 } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{-26}{h}~~,~~\underset{120}{k})}\qquad \stackrel{radius}{\underset{\sqrt{15076}}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - (-26) ~~ )^2 ~~ + ~~ ( ~~ y-120 ~~ )^2~~ = ~~(\sqrt{15076})^2 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (x+26)^2+(y-120)^2 = 15076~\hfill[/tex]
In 5-card poker, the number of outcomes favorable to an event E is given in the table. Find the
probability of being dealt four of a kind or a a straight.
The probability of being dealt four of a kind or a straight is
(Round to 6 decimal places.)
Event E
Royal flush
Straight flush
Four of a kind
Full house
Flush
Straight
Three of a kind
Two pairs
One pair
No pair
Total
# of Outcomes Favorable to E
4
36
624
3744
5108
10,200
54,912
123,552
1,098,240
1,302,540
2,598,960
The probability of being dealt four of a kind or a straight is 0.00416 or 0.416%.
What is probability?It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
It is given that:
In 5-card poker, find the probability of being dealt the following hand. Refer to the table.
From the table:
Total number of outcomes = 2598960
Total number of favorable outcomes = 624 + 10200 = 10824
The probability of being dealt four of a kind or a straight
P = 10824/2598960
P = 0.00416
In percentage:
P = 0.416%
Thus, the probability of being dealt four of a kind or a straight is 0.00416 or 0.416%.
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Prove that :-
(sinA + secA)² + (cosA + cosecA)² = 1 + secAcosecA
May this answers be helps you to solve
About 5% of the population has a particular genetic mutation. 300 people are randomly selected.
Find the standard deviation for the number of people with the genetic mutation in such groups of 300. Round your answer to two decimal places.
The standard deviation for the number of people with the genetic mutation is 3.77
How to determine the standard deviation?The given parameters are:
Sample size, n = 300
Proportion that has the particular genetic mutation, p = 5%
The standard deviation for the number of people with the genetic mutation is calculated as:
Standard deviation = √np(1 - p)
Substitute the known values in the above equation
Standard deviation = √300 * 5% * (1 - 5%)
Evaluate the product
Standard deviation = √14.25
Evaluate the exponent
Standard deviation = 3.77
Hence, the standard deviation for the number of people with the genetic mutation is 3.77
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If P(A)=12, P(A B)=16, and P(A B)=23, what is P(B)?
1/4
2/3
1/2
1/3
Answer:
P(B) 7
Step-by-step explanation:
The answer is P (B)
Si al invertir $60.000 se pierde un 8% ¿A cuánto asciende la pérdida?
Trabajando con porcentajes, concluimos que la pérdida es de $4800.
¿A cuánto asciende la pérdida?
Sabemos que la inversión inicial es de $60000, y de esta cantidad, se pierde un 8%.
Entonces la pérdida va a ser el 8% de $60000.
Podemos escribir las relaciones:
$60000 = 100%
x = 8%
Queremos resolver esto para x, tomando el cociente entre esas relaciones y resolviendo para x obtenemos:
x = $60000*(8%/100%) = $60000*0.08 = $4800
Así, concluimos que la pérdida es de $4800.
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Find the distance between each pair of points. Round your answer to the nearest tenth if necessary
(IMAGE)
three varieties of coffee -coffee A coffee B and coffee C are combined and roasted yield a 54 lb batch of coffee beans. twice as many pounds of coffee C which is retails for $10.39 per pound are needed as coffee a which sells for $15.21 per pound coffee b retails for $13.21 per pound. how many pounds of each coffee should be used in a blend that sells for $12.61 per pound?
8.9 pounds of coffee A, 27.3 pounds of coffee B and 17.8 pounds of coffee C are need to make a blend that sells for $12.61 per pound.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent coffee A, y represent coffee B and z represent coffee C, hence:
x + y + z = 54 (1)
Also:
2x = z (2)
And:
15.21x + 13.21y + 10.39z = 12.61(54) (3)
x = 8.9, y = 27.3 and z = 17.8
8.9 pounds of coffee A, 27.3 pounds of coffee B and 17.8 pounds of coffee C are need to make a blend that sells for $12.61 per pound.]
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In a football tournament, each team played exactly 19 games. Teams get three points for everyone and one point for every time. At the end of the tournament, team Olympus got a total of 28 points. How many could team Olympus have tied?
We can actually deduce here that when the tournament ended, team Olympus have tied for 13, 10, 7, 4, 1 times.
What is inequality?In Mathematics, inequality is used to express or show quantities that are less than, greater than, greater than or equal to, less than or equal to.
The following can be seen in inequality expressions:
≤≥ ><≠Looking at the question, we can see that each team plays exactly 19 games.
Every win (w) = 3
Every tie (t)= 1
Every loose = 0
But Olympus got a total of 28 points
Thus: 3w + t = 28 ---------(1)
Note that each team plays 19 games
Thus, T + W ≤ 19 --------------(2)
and T , W ≥ 0
Looking at equation (1) and (2)
=> 2W ≥ 9
=> W ≥ 4.5
( match can be won in integers only )
=> W ≥ 5
W - 5, 6, 7, 8, 9
T - 13, 10, 7, 4, 1
Loose - 1, 3, 5, 7, 9
Thus, team Olympus have tied for 13, 10, 7, 4, 1 times.
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The volume of a rectangular prism is given by the following function:
V(x) = 2x³ + x² - 16 - 15
The length of the rectangular prism is (x − 3) and the width is (2x + 5). What is the height?
[tex]v(x) = wlh \\ 2x {}^{3} + {x}^{2} - 16 x- 15 =(2x + 5)(x - 3)h \\ h = \frac{2x {}^{3} + x {}^{2} - 16x - 15 }{2x {}^{2} - x - 15 } \\ using \: long \: divison \\ h = x + 1[/tex]
Which pair of words describe this system of equations
3y=9x-6
2y-6x=4
The pair of words that describe the given system of equations is: consistent and dependent.
A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.
It demonstrates the equality of the relationship between the expressions written on the left and the right.
Given equations:
3y=9x-6
2y-6x=4
The first equation can be simplified and written as: y=3x-2
Similarly, the second equation can be written as: y-3x=2
It can be seen that the two equations are the same. Thus, the given system of equations is consistent and dependent.
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A poster is 15 inches wide by 24 inches tall. A smaller version of the same poster is created using a scale factor of 2/3. What is the area of the smaller poster
The area of the small poster is 160 inches square
How to determine the area
From the information given, we have the poster to take the form of a rectangle
The formula for area of a rectangle is;
Area = length × width
For the smaller poster created using a scale of factor 2/3
Length = 2/ 3 × 24
Length = 16 inches
Width = 2/ 3 × 15
Width = 10 inches
Substitute into the formula
Area = 16 × 10
Area = 160 inches square
Thus, the area of the small poster is 160 inches square
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Complete the equivalent fraction 3/5 = ?/10
Answer:
Step-by-step explanation:
3/5 = x/10
5x = 30
x = 6
6/10
Hey there!
Original equation:
3/5 = ?/10
Convert to:
3/5 = x/10
Cross multiply the numbers:
3 * 10 = 5 * x
Simplify it:
3 * 10 = 5 * x
30 = 5x
5x = 30
Divide 5 to both sides:
5x/5 = 30/5
Simplify it:
x = 30/5
x = 6
Therefore, your mystery number should be: 6
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
The sum of three numbers is 100. The second number is 2 times the third. The third number is 8 less than the first. What are the numbers?
Answer:
Step-by-step explanation:x+y+z=100(let x ,y,z represent the first second and third numbers respectively)
Therefore,y=2z
z=x-8
y=2x-16
substituting the values of x,y and z into the question,we have
x+(2x-16)+(x-8)=100
Simplifying,we have
4x-24=100
adding 24 to both sides of the equation,
4x=100+24
4x=124
dividing both sides of the equation by the co-efficient of x,we have
4x/4=124/4
4.31=124
therefore,x=31.
The perimeter of a rectangular field is 282 yards. If the width of the field is 52 yards, what is its length?
Answer: 89 yards
Step-by-step explanation: The perimeter is all the sides added up together. Since the width of the field is 52, the two sides are 52 yards which in total is 104 yards. 282- 104 = 178 yards. The length is 178/2 yards which is 89 yards.
Answer:
75
Step-by-step explanation:
math
Sarah is spending the day at a state fair. While at the fair, she can play games or ride rides. When Sarah arrives at the fair, she purchases 15 tickets and wants to use all of the tickets that she purchases. Playing a game at the fair requires three tickets, and riding a ride at the fair requires six tickets. To make her trip to the fair worthwhile, Sarah decides she must participate in seven activities at the fair.
Sarah requires the purchase of additional 12 tickets to ensure her participation in the seven activities at the fair.
How are the additional (missing) tickets determined?The additional tickets required by Sarah can be determined as follows:
Number of tickets purchased initially = 15
Number of tickets for playing a game = 3
Number of tickets for riding a ride = 6
Sarah can play five (5) games with 15 tickets (15/3).
Sarah can then purchase 12 additional tickets (6 x 2).
The later action enables Sarah to participate in 5 games and 2 rides, making it a total of 7 activities.
Thus, by purchasing additional 12 tickets, Sarah can participate in 5 games and 2 rides, making it a total of 7 activities.
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Question Completion:How many more tickets does Sarah require to ensure her participation in the seven activities at the fair?
QUESTION IS DOW BELOW 5 POINTS EACH PLEASE HELP PLEASE HELP PLEASE HELP
WILL GIVE BRAINLIEST FOR ACCURATE ANWSER
The length of segment XY is 52 units and the length of segment HD is 26 units
How to determine the lengths?Secant lines (a)
To do this, we make use of the following intersecting secant theorem
VZ * VW = VY * VX
Substitute the known values in the above equation
12 * 40 = VY * 8
Divide by 8
12 * 5 = VY
Evaluate the product
VY = 60
The length VX is
XY = VY - VX
Substitute the known values in the above equation
XY = 60 - 8
Evaluate
XY = 52
Hence, the length of segment XY is 52 units
Secant lines (b)
To do this, we make use of the following intersecting secant theorem
GH^2 = HC * HD
Substitute the known values in the above equation
13^2 = 6.5 * HD
Divide by 6.5
13^2/6.5 = HD
Evaluate the quotient
26 = HD
The length HD is
HD = 26
Hence, the length of segment HD is 26 units
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How do I graph the following set {x is an even number, -1≤x<12}
Step-by-step explanation:
Use this sort of layout, but where x will be an odd number, do not shade it. there should be a pattern of shaded segments followed by unshaded segments repeating
What is the sum of ∞Σn=1 2(1/5)^n-1? s=1/5 s=2/5 s=5/3 s=5/2
The sum of the sum notation ∞Σn=1 2(1/5)^n-1 is S= 5/2
How to determine the sum of the notation?The sum notation is given as:
∞Σn=1 2(1/5)^n-1
The above notation is a geometric sequence with the following parameters
Initial value, a = 2Common ratio, r = 1/5The sum is then calculated as
S = a/(1 - r)
The equation becomes
S = 2/(1 - 1/5)
Evaluate the difference
S = 2/(4/5)
Express the equation as products
S = 2 * 5/4
Solve the expression
S= 5/2
Hence, the sum of the sum notation ∞Σn=1 2(1/5)^n-1 is S= 5/2
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Answer:
S = 5/2
Thank me later
Given: m space measured angle space C space equals space 76, a = 20, and b = 13. What is the length of c to the nearest tenth?
Based on the given parameters, the length of c is 8.0 units
How to determine the side length of c?The given parameters are
Angle c = 76 degrees
Side a = 20
Side b = 13
The length of c is then calculated using the following law of sines
c^2 = a^2 + b^2 - 2absin(C)
Substitute the known values in the above equation
So, we have
c^2 = 20^2 + 13^2 - 2 * 20 * 13 * sin(76)
Express 20^2 as 400
c^2 = 400 + 13^2 - 2 * 20 * 13 * sin(76)
Express 13^2 as 169
c^2 = 400 + 169 - 2 * 20 * 13 * sin(76)
Evaluate the product and sin(76)
c^2 = 400 + 169 - 520 * 0.9703
Evaluate the product
c^2 = 400 + 169 - 504.55
Evaluate the exponents
c^2 = 400 + 169 - 504.55
So, we have
c^2 = 64.45
Evaluate the square root
c = 8.0
Hence, the length of c is 8.0 units
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Evaluate the function f(x) = –2x2 – 3x + 5 for the input value –3.
−22
–4
2
32
Hi there,
please see below for solution steps :
‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
Evaluate by substituting :
[tex]\begin{gathered} \boldsymbol{f(x)=-2x^2-3x+5; \ evaluate \ when \ x=-3} \\\boldsymbol{Write \ -3 \ everywhere \ you \ see \ and \ x :}\\\boldsymbol{f(-3)=-2(-3)^2-3(-3)+5}\\\boldsymbol{Evaluate \ using \ Order \ of \ Operations :}\\\boldsymbol{f(-3)=-2(9)+9+5= > -18+9+5= > -18+14= > -4}\end{gathered}[/tex]
Therefore, the answer is [tex]\LARGE\textbf{-4}[/tex].
I hope the answer - and steps - made sense to you !!
Happy Learning !!
‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
ill give you brainliest :)
Following the instructions for the inequalities gives the following results:
1. 4<7, both sides multiplied by 7
= 28<49, both sides multiplied by 6
= 168<294, both sides multiplied by 3
= 504<882, both sides multiplied by 10
= 5,040<8,820
2. 11>2, add 5 to both sides
= 16>3, add 3 to both sides
= 19>9, add -4
= 15>5
3. -4<-2, subtract 6
= -10<-8, subtract 8
= -18<-16, subtract 2
= -20<-18
4. -8<8, divide by -4
= 2>-2, divide by -2
= -1<1
5. The inequalities remain correct at the end because the same mathematical operations are performed on both sides simultaneously.
What are inequalities?Inequality is a relationship of a non-equal comparison between two numbers or algebraic expressions.
Inequality can be represented as greater than, greater than or equal to, less than, or less than or equal to.
Thus, the rules for inequalities show that if one adds to, subtracts from, multiplies by, or divides by the same number on both sides of an inequality, the inequality remains true.
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1+1-1(2)+1=?
A,0
B,1
C,2
D,3
Answer:
B. 1
Step-by-step explanation:
-1*2 = -2
-2+1 = -1
-1+1 = 0
0+1 = 1
Is
7 3
a proper, an improper, a mixed number, or a decimal fraction?
a proper fraction
an improper fraction
a mixed number
a decimal number
Answer: an improper fraction
Step-by-step explanation: An improper fraction is a fraction that is larger than 1 7/3 is larger than one because 7, the numerator is larger than the denominator so 7/3 is an improper fraction
Let r(x)=x^2 - x + 14. Find all values of a such that r(a) = 20.
Answer:
a=–2, 3
Step-by-step explanation:
r(a)=20
a²–a+14=20===> a²–a–6=0===> (a–3)(a+2)
Someone please help me with this question
Answer: Neither
Step-by-step explanation:
It is not an angle of the quadrilateral, so it is not an interior angle.
It does not form a linear pair with any interior angle of the quadrilateral, so it is not an exterior angle.
NO LINKS!! Please help me with this problem
Information : The given hyperbola is a horizontal hylerbola with its centre (3 , -5) and one of its focus at (9 , -5) and vertex at (7 , -5) and as we can see that the focus and vertex have same y - coordinates, it must have its Transverse axis on line y = - 5.
Now,
it's vertex is given, I.e (7 , -5)
so, length of semi transverse axis will be equal to distance of vertex from centre, i.e
a = 7 - 3 = 4 unitsNow, it's focus can be represented as ;
[tex]\qquad \sf \dashrightarrow \: (3 + ae, - 5 )[/tex]
so,
ae + 3 = 9and we know, a = 4
[tex]\qquad \sf \dashrightarrow \: 4e + 3 = 9[/tex]
[tex]\qquad \sf \dashrightarrow \: 4e = 6[/tex]
[tex]\qquad \sf \dashrightarrow \: e = \cfrac{3}{2} [/tex]
Now, let's find the measure of semi - conjugate axis (b)
[tex]\qquad \sf \dashrightarrow \: {b}^{2} = {a}^{2} ( {e}^{2} - 1)[/tex]
[tex]\qquad \sf \dashrightarrow \: {b}^{2} = 16( \frac{9}{4} - 1)[/tex]
[tex]\qquad \sf \dashrightarrow \: {b}^{2} = 16( \frac{9 - 4}{4} )[/tex]
[tex]\qquad \sf \dashrightarrow \: {b}^{2} = 16( \frac{5}{4} )[/tex]
[tex]\qquad \sf \dashrightarrow \: {b}^{2} = 20[/tex]
[tex]\qquad \sf \dashrightarrow \: b = \sqrt{20} [/tex]
So, it's time to write the equation of hyperbola, as we already have the values of a and b ~
[tex]\qquad \sf \dashrightarrow \: \cfrac{ {(x - h)}^{2} }{ {a}^{2} } - \cfrac{( {y - k)}^{2} }{ {b}^{2} } = 1[/tex]
[ plug in the values, and h = x - coordinate of centre, and k = y - coordinate of centre ]
[tex]\qquad \sf \dashrightarrow \: \cfrac{ ({x-3)}^{2} }{ {16}^{} } - \dfrac{ {(y+5)}^{2} }{ { {20} }^{} } = 1[/tex]
Hello and Good Morning/Afternoon:
Let's solve this problem step-by-step:
Let's find the format of the standard form of hyperbole:
[tex]\hookrightarrow \frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2} =1[/tex]
(h,k): hyperbole center ⇒(3,-5)Let's find the value of a, b:
value of a: distance between vertex (7, -5) and center (3, -5)[tex]a = \sqrt{(7-3)^2+(-5--5)^2} =\sqrt{16} =4[/tex]
value of b: [tex]\sqrt{c^2-a^2}[/tex]⇒value of c: distance between focus (9, -5) and center (3, -5)
[tex]c = \sqrt{(3-9)^2+(-5--5)^2}=\sqrt{36} =6[/tex]
⇒ therefore:
[tex]b = \sqrt{c^2-a^2} =\sqrt{6^2-4^2}=\sqrt{20}[/tex]
Let's plug everything into our standard form of the equation:
[tex]\frac{(x-3)^2}{4^2} -\frac{(y--5)^2}{(\sqrt{20})^2 } =1\\\frac{(x-3)^2}{16} -\frac{(y+5)^2}{20 } =1[/tex] <== Answer
Hope that helps!
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find the slope of the line that passes through each pair of points a. (-4, 5), (1, 1)
ASAP HELP ME WITH THIS QUESTIONN
Answer:
inductive reasoning
Step-by-step explanation: