Answer:
a. [tex]\mathtt{P(X \geq 25) =0.0170}[/tex] ( to four decimal places)
b. [tex]P(22.5<X<25) = 0.9043[/tex] ( to four decimal places )
c. The limits will be between the interval of ( 22.33,24.67 )
Step-by-step explanation:
Given that :
mean = 23.50
standard deviation = 5.00
sample size = 50
The objective is to calculate the following:
(a) What is the likelihood the sample mean is at least $25.00?
Let X be the random variable, the probability that the sample mean is at least 25.00 is:
[tex]P(X \geq 25) = 1 - P(\dfrac{X - \mu}{\dfrac{\sigma}{\sqrt{n}}} < \dfrac{25- 23.50}{ \dfrac{5}{\sqrt{ 50}} })[/tex]
[tex]P(X \geq 25) = 1 - P(Z< \dfrac{1.5}{ \dfrac{5}{7.07107}} })[/tex]
[tex]P(X \geq 25) = 1 - P(Z< \dfrac{1.5 \times 7.071}{ {5}})[/tex]
[tex]P(X \geq 25) = 1 - P(Z< 2.1213)[/tex]
[tex]P(X \geq 25) = 1 - P(Z< 2.12)[/tex] to two decimal places
From the normal tables :
[tex]P(X \geq 25) = 1 - 0.9830[/tex]
[tex]\mathtt{P(X \geq 25) =0.0170}[/tex] ( to four decimal places)
(b) What is the likelihood the sample mean is greater than $22.50 but less than $25.00?
[tex]P(22.5<X<25) = P(\dfrac{X-\mu}{\dfrac{\sigma}{\sqrt{n}}} <\dfrac{25-23.5}{\dfrac{5}{\sqrt{50}}} ) - P(\dfrac{X-\mu}{\dfrac{\sigma}{\sqrt{n}}} <\dfrac{22.5-23.5}{\dfrac{5}{\sqrt{50}}} )[/tex]
[tex]P(22.5<X<25) = P(Z<\dfrac{1.5}{\dfrac{5}{7.071}} ) - P(Z<\dfrac{-1}{\dfrac{5}{7.071}} )[/tex]
[tex]P(22.5<X<25) = P(Z<2.12) - (Z<-1.41 )[/tex]
[tex]P(22.5<X<25) = (0.9830 ) - (0.0787)[/tex]
[tex]P(22.5<X<25) = 0.9043[/tex] to four decimal places
(c) Within what limits will 90 percent of the sample means occur?
At 90 % confidence interval, level of significance = 1 - 0.90 = 0.10
The critical value for the [tex]z_{\alpha/2} = 0.05[/tex] = 1.65
Standard Error = [tex]\dfrac{\sigma}{\sqrt{n}}[/tex]
Standard Error = [tex]\dfrac{5}{\sqrt{50}}[/tex]
Standard Error = 0.7071
Therefore, at 90 percent of the sample means, the limits will be between the intervals of : [tex](\mu \pm z_{\alpha/2} \times S.E)[/tex]
Lower limit = ( 23.5 - (1.65×0.707) )
Lower limit = ( 23.5 - 1.16655 )
Lower limit = 22.33345
Lower limit = 22.33 (to two decimal places).
Upper Limit = ( 23.5 + (1.65*0.707) )
Upper Limit = ( 23.5 + 1.16655 )
Upper Limit = 24.66655
Upper Limit = 24.67
The limits will be between the interval of ( 22.33,24.67 )
Simplify 6.920
A.-1
B.0
C.1
D.6.92
I'm pretty sure the answer is 6.92 cause when you simplify it you'll get that exact answer
Answer:
D 6.92
Step-by-step explanation:
6.920 and 6.92 are equal
What is the reflection image of
(5,−3)across the line
y=x
Answer: The Answer is (-5,-3)
hope so my answer is correct
Step-by-step explanation:
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
Data should be analyzed using each of the following except:
A. measures of central tendency
B. shape
C. population size
D. spread
Solve : p, q, s, t, w
P:-
[tex]\\ \sf\longmapsto (x+y)^2-4x^2y^2[/tex]
[tex]\\ \sf\longmapsto x^2+2xy+y^2-4x^2y^2[/tex]
[tex]\\ \sf\longmapsto x^2+y^2-4x^2y^2+2xy[/tex]
Q:-
[tex]\\ \sf\longmapsto x^2-2(x+y)-y^2[/tex]
[tex]\\ \sf\longmapsto x^2-2x-2y-y^2[/tex]
[tex]\\ \sf\longmapsto x^2-y^2-2x-2y[/tex]
S:-
[tex]\\ \sf\longmapsto x^2-4x-21+10y-y^2[/tex]
[tex]\\ \sf\longmapsto x^2-y^2-4x+10y-21[/tex]
T:-
[tex]\\ \sf\longmapsto a^2-10a+24+6b-9b^2[/tex]
[tex]\\ \sf\longmapsto a^2-9b^2-10a+6b+24[/tex]
If x+y = nx+2 then x equals
Answer:
x+y = nx+2
⇔x-nx = 2-y
⇔x(1-n) = 2-y
⇔x = (2-y)/(1-n)
Answer:
Hello,
Step-by-step explanation:
x+y=nx+2
x-nx=2-y
x(1-n)=2-y
if 1-n ≠0 (or n≠1) then
[tex]x=\dfrac{2-y}{1-x}[/tex]
Determine which one of the following statements is true. A. Exponential growth will always exceed linear growth. B. Linear growth will always exceed quadratic growth. C. Linear growth will always exceed exponential growth. D. Quadratic growth will always exceed exponential growth.
Answer:
A. Exponential growth will always exceed linear growth.
Step-by-step explanation:
The rate of growth of a linear function is always constant, that means it remains the same for any value of x or y. For an exponential growth, the rate of change is not constant, it continues to increase as the value of x increases. Therefore since the rate of growth of an exponential growth increases as the x value increases, while that of the linear growth remain constant there would be a point in which the exponential growth will exceed linear growth.
What is the difference of the rational expressions below?
Answer:
in the pic
Step-by-step explanation:
answer A
.....
9. a) A computer can finish to download an application file in 4 minutes of 600 MB per minute, 6.1 P
(1) Find the size of the application file. 1. L
(ii) How long does it take to download the file when the download rate increase
to 800 MB per minutes?
Answer:
1) 2400MB
2) 3 minutes
Step-by-step explanation:
1) 600 MB/Min * 4 Min = 2400MB
2) at 800 MB/Min a 2400MB file will require 2400MB/800MB/Min
2400/800 = 3Min
The height of the rectangular prism is 2 m. If its volume is 72 cubic meters, what is the area of the base, in square meters?
Answer:
Base area is 36 square meters
Step-by-step explanation:
The volume of a rectangular prism is V = (height)(length)(width). We know all of these dimensions except for the area of the base, which is (length)(width).
Solving this equation for (length)(width), we get:
volume 72 m^3
(length)(width) = (area of base) = -------------- = ------------- = 36 m^2
height 2 m
1)Sheyna drive to the lake and back. It took two hours less time to get there than it did to get back. The average speed on the trip there was 60 mph. The average speed on the way back was 36 mph. How many hours did the trip there take?
Answer:
8 hours
Step-by-step explanation:
Given:
Sheyna drives to the lake with average speed of 60 mph and
[tex]v_1 = 60\ mph[/tex]
Sheyna drives back from the lake with average speed of 36 mph
[tex]v_2 = 36\ mph[/tex]
It took 2 hours less time to get there than it did to get back.
Let [tex]t_1[/tex] be the time taken to drive to lake.
Let [tex]t_2[/tex] be the time taken to drive back from lake.
[tex]t_2-t_1 = 2[/tex] hrs ..... (1)
To find:
Total time taken = ?
[tex]t_1+t_2 = ?[/tex]
Solution:
Let D be the distance to lake.
Formula for time is given as:
[tex]Time =\dfrac{Distance}{Speed }[/tex]
[tex]t_1 = \dfrac{D}{60}\ hrs[/tex]
[tex]t_2 = \dfrac{D}{36}\ hrs[/tex]
Putting in equation (1):
[tex]\dfrac{D}{36}-\dfrac{D}{60} = 2\\\Rightarrow \dfrac{5D-3D}{180} = 2\\\Rightarrow \dfrac{2D}{180} = 2\\\Rightarrow D = 180\ miles[/tex]
So,
[tex]t_1 = \dfrac{180}{60}\ hrs = 3 \ hrs[/tex]
[tex]t_2 = \dfrac{180}{36}\ hrs = 5\ hrs[/tex]
So, the answer is:
[tex]t_1+t_2 = \bold{8\ hrs}[/tex]
help me im dangered plzzzzzzzzzzzzzzzzzzzz
Answer:
A
Step-by-step explanation:
Hi!
An exponent is the same thing as just multiplying the expression by itself the number of times the exponent says. So we need to multiply 1/3 by itself three times.
1/3 * 1/3 * 1/3 = 1/27
Please help me. It’s due before 7pm
Answer:
[tex]{ \boxed{6 + a = 13 }}[/tex]
Answer:
Below
Step-by-step explanation:
Let's say that x represents the mystery number
5(x + 6) = 65
5x + 30 = 65
5x = 35
Divide both sides by 5
x = 7
We can check to see if this works
6 + 7 = 13 (the sum of 6 and x)
13 x 5 = 65
Hope this helps!
Graph y = tanx for -pi/4 ≤ x ≤ pi/4. What is the range?
Answer:
( -1, 1 )
Step-by-step explanation:
For f ( x ) = tan x ; Range = R (real no.)
Range in interval = ( -1, 1 )
Answer:
Step-by-step explanation:
The graph is below(picture)
● tan Pi/4 = 1
● tan -Pi/4 = -1
So the range is [-1;1]
Geometry, please answer question ASAP
Answer:
B.
Step-by-step explanation:
The ratio of the lengths of the sides of a 30-60-90 triangle is
1 : sqrt(3) : 2
From the 1 and 2, we see that the hypotenuse must be twice the length of the short leg.
From the 1 and sqrt(3) we see that the long leg is sqrt(3) times the length of the short leg.
Now we check for these two ratios in each choice.
A.
1 is twice 1/2. Check
sqrt(3)/2 is sqrt(3) times 2. Check
B.
10 is twice 5, not twice 5/2. This does not check.
C.
2sqrt(2) is twice sqrt(2). Check
sqrt(6) is 2sqrt(2) time sqrt(3). Check
D.
6 is twice 3. Check
3sqrt(3) is sqrt(3) times 3. Check
Answer: B.
Answer:
B
Step-by-step explanation:
Angle ratio = 30 : 60 : 90
Side ratio = x : x√3 : 2x
[tex]A) x = \frac{1}{2}\\\\ \ x\sqrt{3 } = \frac{1}{2}*\sqrt{3}=\frac{\sqrt{3}}{2} \\\\2x = 2*\frac{1}{2}=1[/tex]
True
[tex]C) x = \sqrt{2} \\\\x\sqrt{3}=\sqrt{2} *\sqrt{3} =\sqrt{2*3}=\sqrt{6}\\\\2x=2\sqrt{2} \\[/tex]
True
[tex]D) \ x = 3\\\\x\sqrt{3}=3\sqrt{3}\\\\2x = 2*3 = 6[/tex]
True
plz help me Identify the domain and range of relation ({3,-2),(8,1),(-9,2),(1,8)}
Answer:
domain { -9,1,3,8)
range{ -2,1,2,8}
Step-by-step explanation:
The domain is the inputs
Domain = 3,8,-9,1
We write them in the order from smallest to largest
domain { -9,1,3,8)
The range is the outputs
Range = -2,1,2,8
We write them in the order from smallest to largest
range{ -2,1,2,8}
Two thirds of the students in a class have pets. There are
36 students in the class. How many of the students have pets?
Roselyn is driving to visit her family, which live 150 150150 kilometers away. Her average speed is 60 6060 kilometers per hour. The car's tank has 20 2020 liters of fuel at the beginning of the drive, and its fuel efficiency is 6 66 kilometers per liter. Fuel costs 0.60 0.600, point, 60 dollars per liter. How long can Roselyn drive before she runs out of fuel?
Answer:
She can go 120 km before she runs out of fuel
It will take 2 hours.
Step-by-step explanation:
150 km is the distance
60 km/ h is the speed
The gas tank is 20 liters
We can go 6 km per liter
Fuel costs .60 dollars per liter
We need to determine how far she can go on a tank of gas
20 liters * 6 km / liter = 120 km
She can go 120 km before she runs out of fuel
120 km = 60 km/ h * x hours
Divide each side by 60
120/60 = x
2 hours
Answer:
Hopes this helps!
Step-by-step explanation:
What is the volume of this figure?
Answer:
Volume = 480 cm³
Step-by-step explanation:
Volume = lwh
*Split the shape into 3 rectangles.
Rectangle 1: 4 x 4 x 8 = 128
Rectangle 2: 14 x 4 x 4 = 224
Rectangle 3: 4 x 4 x 8 = 128
Total: 128 + 224 + 128 = 480 cm³
Answer:
480
Step-by-step explanation:
just took the quiz
HELP ASAP ILL GIVE BRAINLIST
The probability of a red candy being selected from a bowl is 0.9, and the probability of a pink frosted animal cookie being taken out of a different bowl is 0.4. What is the probability of getting both a red candy and a pink cookie?
Answer:
0.36
Step-by-step explanation:
Geometry, please answer question ASAP
Answer:
Option A
Step-by-step explanation:
first calculate side b
which is 35.8
Using 2 lengths, calculate Angle G
OPTION A :)MATH QUESTION: When 8668/25 + 4141/9 - 5533/25 is computed and written as a mixed number in simplest form, what is the fractional part of that mixed number?
Answer:
23/45
Step-by-step explanation:
8668/25 + 4141/9 - 5533/25
= 26348/45
= 585(23/45)
=23/45
La madre de rosita se ha comprado una mascarilla por un valor de 1 25 dolares al mismo tiempo se ha comprado un paquete de jabones de 2 00 dolares y luego compra un gel de alcohol en 3 00 dolares después de pagar le queda 7 65 dolares que debemos saber que tengo que hacer para obtener el resultaron
Answer:
La cantidad inicial que tenía la madre de Rosita antes, comprando los artículos es de $13.90
Step-by-step explanation:
La información dada son;
El valor de la máscara = $ 1.25
El valor del paquete de jabones = $ 2.00
El valor del gel de alcohol = $ 3.00
La cantidad que le quedaba después de pagar = $ 7.65
Por lo tanto, tenemos;
La cantidad inicial que tenía la madre de Rosita antes, comprando los artículos = La cantidad que le quedaba después de pagar + El valor del gel de alcohol + El valor del paquete de jabones + El valor de la mascarilla
Por lo tanto;
La cantidad inicial que tenía la madre de Rosita antes, comprando los artículos = $ 7.65 + $ 3.00 + $ 2.00 + $ 1.25 = $ 13.90.
Solve for x help please
Answer:
A. 5
Step-by-step explanation:
Based on the secant and tangent theorem, (4 + x)*4 = 6²
We can solve for x using the equation which describes the relationship between secant and tangents.
Thus,
[tex] (4 + x)*4 = 6^2 [/tex]
[tex] 4*4 + x*4 = 36 [/tex]
[tex] 16 + 4x = 36 [/tex]
Subtract 16 from both sides
[tex] 4x = 36 - 16 [/tex]
[tex] 4x = 20 [/tex]
Divide both sides by 4
[tex] \frac{4x}{4} = \frac{20}{4} [/tex]
[tex] x = 5 [/tex]
Line LR bisects MN at point L. Find the length of ML if MN = 152 ft.
Answer:
[tex]ML = 76\text{ feet}[/tex]
Step-by-step explanation:
Since Line LR bisects MN at point L, by the definition of bisector:
[tex]\overline{ML} \cong \overline{LN}[/tex]
We want to determine ML if MN measures 152 feet.
MN is the sum of ML and LN. Hence;
[tex]ML + LN = MN[/tex]
Since ML = LN and MN = 152:
[tex]ML + (ML) = (152)[/tex]
Simplify:
[tex]2ML = 152[/tex]
And divide. Therefore:
[tex]ML = 76\text{ feet}[/tex]
In conclusion, ML measures 76 feet.
25 POINTS!!!!!! WILL GIVE BRAINLIEST!!!!! Select all the correct answers.
Which statements regarding the implications of the central limit theorem are true?
As the number of sample means decreases, the means get closer to a standard normal distribution.
For an infinite number of samples, 99.7% of the sample means would fall within the interval .
The central limit theorem holds true only for populations that are normally distributed.
For an infinite number of samples, 95% of the sample means would fall within the interval .
The mean of the population is the same as the mean of any sample taken from the population.
If the population is normally distributed, then the mean of a sample from that population will be normally distributed.
Answer:
Step-by-step explanitions:
this is true The central limit theorem holds true only for populations that are normally distributed.
this is also true For an infinite number of samples, 95% of the sample means would fall within the interval .
As the number of sample means decreases, the means get closer to a standard normal distribution.thsis is false
It is given that m=3x+1 and y= (5/1+m^2).
Find dy/dx in terms of x.
Answer:
[tex]{ \underline{ \bf{ \frac{dy}{dx} = - \frac{30m}{ {(1 + {m}^{2}) }^{2} } }}}[/tex]
Step-by-step explanation:
[tex]{ \bf{m = 3x + 1}} \\ { \sf{ \frac{dm}{dx} = 3 }} \\ \\ { \bf{y = \frac{5}{1 + {m}^{2} } }} \\ \\ { \tt{ \frac{dy}{dm} = \frac{ - 10m}{ {(1 + {m}^{2} )}^{2} } }}[/tex]
Using chain rule:
[tex]{ \boxed{ \bf{ \frac{dy}{dx} = \frac{dy}{dm}. \frac{dm}{dx} }}}[/tex]
[tex]{ \sf{ \frac{dy}{dx} = - \frac{10m}{ {(1 + {m}^{2}) }^{2} } \times 3}} \\ \\ { \sf{ \frac{dy}{dx} = - \frac{30m}{ {(1 + {m}^{2}) }^{2} } }}[/tex]
[tex]{ \underline{ \sf{ \blue{christ \:† \: alone }}}}[/tex]
Answer:
Step-by-step explanation:
Never saw a problem presented in this way in all my years of teaching calculus. But I'm thinking that we need to sub that given expression for m into the equation for y and get everything into y in terms of x in order to find the derivative. I see no other way that makes sense. Can't find the derivative of y in terms of x if there's an m in there. Making that substitution:
[tex]y=\frac{5}{1+(3x+1)^2}[/tex] which simplifies to
[tex]y=\frac{5}{1+9x^2+6x+1}[/tex] and a bit more to
[tex]y=\frac{5}{9x^2+6x+2}[/tex] and now we're ready to find the derivative. Using the quotient rule:
[tex]y'=\frac{(9x^2+6x+2)(0)-[5(18x+6)]}{(9x^2+6x+2)^2}[/tex] which simplifies to
[tex]y'=\frac{-90x-30}{(9x^2+6x+2)^2}[/tex] or, equally:
[tex]y'=-\frac{90x+30}{(9x^2+6x+2)^2}[/tex]
the ratio of boys and girls in a 4:3.If there are 20 boys, find the number of girls.
Answer:
There are 15 girls.
Step-by-step explanation:
The ratio is 4:3, meaning there are 7 parts.
4 parts= 20 (Boys)
This means 1 part is 20 divided by 4.
1 part= 5
3 parts= Amount of girls.
3 x 5 = 15.
There are 15 girls.
Answer:
15
Step-by-step explanation:
Add:
boys : girls
4 : 3 = 7
20: ? = ?
Divide:
20 / 4 = 5
5 × 3 = 15
20: 15
So, there are 15 girls.
16. Acme car rental agency charges a fee of $29 per day plus $0.15 per
mile. Travel Ease car rental agency charges $20 per day plus $0.25 per
mile. For a one-day trip, what mileage would make the two rates equal?
Answer:
90 miles
Step-by-step explanation:
0.15x + 29 = y ---- acme car agency
0.25 x + 20 = y ---- travel ease agency
0.15x + 29 = 0.25x + 20
9 = 0.1x
x = 90
find the surface area of each figure. Round to the nearest tenth if necessary.
Answer:
Step-by-step explanation:
Base of triangle = b = 8 cm
Height of triangle = h = 6 cm
Length of rectangle = l = 6 cm
Sides of the triangle : S1 = 6 cm ; S2 = 8 cm and S3 = 10 cm
Surface area of triangular prism= bh + l *(s1+ S2 + S3)
= 8 * 6 + 6*(6+8+10)
= 48 + 6*24
= 48 + 144
= 192 square cm
Zula has a conical bird feeder with a volume of 64.3 cubic centimeters and a height of 7 centimeters. Which equation can be used to find the area of the circular lid needed to cover the bird feeder?
Answer: [tex]64.3=\frac{1}{3}(B)(7)[/tex]
Step-by-step explanation:
[tex]V=\frac{1}{3} Bh[/tex]
B is the area of the base
h is the height of the cone
[tex]V=64.3 cm^3[/tex]
[tex]h=7cm[/tex]
[tex]64.3=\frac{1}{3}(B)(7)[/tex]
[tex]192.9=(B)(7)[/tex]
[tex]B=192.9/(7)[/tex]
[tex]=27.56cm^2[/tex]