Answer:
Part a:
The calculate value of Z = 2.946 lies in the critical region so the null hypothesis is rejected and alternate hypothesis is accepted that population mean is greater than 50.
Part b:
The calculate value of Z = 1.17851 does not lie in the critical region so the null hypothesis is accepted that population mean is not greater than 50.
Part c:
The calculate value of Z = 2.1213 lies in the critical region so the null hypothesis is rejected and concluded that population mean is greater than 50.
Step-by-step explanation:
Data as given
H 0: μ ≤ 50 against the claim H a: μ> 50 one tailed test
Z (0.05)= ± 1.645
Sample size n= 50
Using the central limit theorem
Population Standard Deviation= σ=s=6
X= 52.5 , 51 and 51.8
Part a:
Z= x-μ/ s/ √n
Z= 52.5- 50 / 6/ √50
Z= 2.5/0.84853
z= 2.946
The calculate value of Z = 2.946 lies in the critical region so the null hypothesis is rejected and alternate hypothesis is accepted that population mean is greater than 50.
Part b:
Z= x-μ/ s/ √n
Z= 51- 50 / 6/ √50
Z= 1/0.84853
z= 1.17851
The calculate value of Z = 1.17851 does not lie in the critical region so the null hypothesis is accepted that population mean is not greater than 50.
Part c:
Z= x-μ/ s/ √n
Z= 51.8- 50 / 6/ √50
Z= 1.8/0.84853
z= 2.1213
The calculate value of Z = 2.1213 lies in the critical region so the null hypothesis is rejected and concluded that population mean is greater than 50.
What is the value of the constant in the equation that relates the hey width of the rectangle
Answer: 2
Step-by-step explanation:
as H=20 and W=10
So H=constant.(W)
H=2(10)
H=20
So constant is 2
Write the following expression in simplest radical form. Plz help
Answer:[tex]4x^{3}[/tex][tex]\sqrt[3]{25x^{2} }[/tex]
Step-by-step explanation:
help plss helppppppppppppppppppppppppppppppppppppppppp
Answer:
okkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk
Step-by-step explanation:
answer mujha nahi pata aaaaaaaaaàaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
simplify (-4 - 3n) x -8
Write an equivalent fraction to 3/7 that has a denominator of 28.
answer is
[tex] \frac{12}{28} [/tex]
5.16 = 4n What the answer
Answer:
n=1.29
Step-by-step explanation:
Is there more options?
≻───── ⋆✩⋆ ─────≺
Answer:
[tex]5.16 = 4n[/tex]
[tex]\frac{5.16}{4} = \frac{4n}{4}[/tex]
Divide Both Sides by 4[tex]n=1.29[/tex]
Hope this helps!
-Fishylikeswater
the number of cars in a parking lot are no more than 7.
Let c be the number of cars in the parking lot
Answer: 2nd one because the amount of cars is either less than 7 or equal to
Step-by-step explanation:
The formula V equals S to the third power gives the volume V of a cube with the side length S the volume of a cube that has a side length of 3 inches is__?__ inches cubed
Answer:
27
Step-by-step explanation:
The formula for the volume of a cube is given as [tex]V=s^{3}[/tex]. if s=3in, then V=27inches cubed.
Katy invests £200 000 in a savings account for 4 years. The account pays compound interest
at a rate of 1.5 % per annum.
Calculate the total amount of interest Katy will get at the end of 4 years
Answer:
212272.71
Step-by-step explanation:
we have the following equation (for interesting that compound yearly)
PV(1+i)^n
200000(1+.015)^4
212272.71
The total amount of interest Katy will get at the end of 4 years is £12,272.71
Compound interestCompound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interestCompound interest refers to the phenomenon whereby the interest associated with a bank account, loan, or investment increases exponentially—rather than linearly—over time.Compound interest (or compounding interest) is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periodsHow to solve this problem?The steps are as follow:
Given:p = £200 000
r = 1.5%
n = 4 years
Formula to find Amount (A) after 4 years will as follow:A = p(1+r/100)ⁿ
A = 200000(1+1.5/100)⁴
A = 212,272.71 £
The compound interest is given by:C.I. = A - p
C.I. = 212,272.71 - 200,000
C.I. = £12,272.71
So the total amount of interest Katy will get at the end of 4 years is £12,272.71
Learn more about Compound interest here:
https://brainly.com/question/24924853
#SPJ2
I’m so confused, how do I do this?
Answer:
x = 14
Step-by-step explanation:
These angles are vertical each other, another way of saying they are opposite each other in an X. Since these angles are vertical, they are equal!
60 = 5x - 10 | Given, from here on is basic algebra
70 = 5x | Add 10 to both sides
14 = x | Divide both sides by 5
Please I’ll do anything I’m begging
Answer:
14√2
Step-by-step explanation:
This is a 45-45-90 triangle
Because both of the angles are the same all sides, but the hypotonouse are the same
this means that the other length is 14 too
we can use a²+b²=c² to solve
14²+14²=c²
=
392=c²
√392=c
√392=14√2
7.88 as a percent student
788% gdkgdkgdkgdkgdkgdkgdk
Melanie needs to write the number eighteen and eighty-one thousandths as a decimal in her computer program.How should she write this number in standard form.
Answer:
18.081
Step-by-step explanation:
I'm pretty sure it's this.
Write the equation of the line that passes through the point (-2,7) and is parallel to the line y= -4x+1.
Answer:
y = -4x - 1
Step-by-step explanation:
Parallel lines have same slope
y = -4x + 1 {Compare y = mx + b; m ->slope; b - y-intercept}
m = -4 ; (-2 ,7)
y - y1 = m(x - x1)
y - 7 = -4(x - [-2])
y -7 = -4(x + 2)
y -7 =x *(-4) + 2*(-4)
y -7 = -4x - 8
y = -4x - 8 + 7
y = -4x - 1
Which of the following could represent the question: How many 4/9s are in 6/5 as a multiplication equation?
x*4/9=6/5
x*6/5=4/9
6/5*4/9=x
4/9*6/5=x
Answer:
Step-by-step explanation:
I am pretty sure it’s 4/9 * 6/5 = x
( I think it’s this )
In a school, 130 students are sixth graders. If 52% of the students in the school are sixth graders, how many students are there in the school?
Answer:
250
Step-by-step explanation:
52%-> 130
100%-> 250
A stapler weighs 8.82 ounces. For every 1 pound, there are 16 ounces.
How many pounds does the stapler weigh, rounded to the nearest hundredth?
Answer:
0,55
Step-by-step explanation:
1 pound= 16 ounces
8.82 ounces= 8.82/ 16= 0.55 pound
Evan is signing up for a gym membership with a one-time fee to join and then a monthly fee to remain a member. The total cost of the gym membership over tt months is given by the equation C=40t+125.C=40t+125. What is the slope of the equation and what is its interpretation in the context of the problem?
Answer:
the slope of the function is 40 which represents the monthly fee to remain a mrmber.
Step-by-step explanation:
THE SLOPE IS THE COEFFICIENT OF THE INDEPENDENT VARIABLE
C= 40t + 125
How are 4.730 and 4.73 eqivalent
Answer:
The zero means nothing, it's just being used as a placeholder, like .7 and 0.7 mean the same thing.
good luck, i hope this helps :)
4.730 and 4.73 are equivalent because 0 has no value therefore if 0 has no value and you take away the 0 than you get 4.73 and 4.73.
A tank is filled with 1000 liters of pure water. Brine containing 0.08 kg of salt per liter enters the tank at 6 liters per minute. Another brine solution containing 0.09 kg of salt per liter enters the tank at 5 liters per minute. The contents of the tank are kept thoroughly mixed and the drains from the tank at 11 liters per minute.
A. Determine the differential equation which describes this system. Let SG) denote the number of kg of salt in the tank after t minutes. Then ds/dt=_____.
B. Solve the differential equation for S(t).
Answer:
The answer is below
Step-by-step explanation:
Let s(t) represent the amount of salt in the tank at time t. Therefore:
ds / dt = (rate of salt flowing into the tank) - (rate of salt going out of the tank)
[tex]\frac{ds}{dt}=[(0.08\ kg/L*6\ L/min)+(0.09\ kg/L*5\ L/min)]-(\frac{s\ kg}{1000\ L}*11\ L/min ) \\\\\frac{ds}{dt}=(0.48\ kg/min+0.45\ kg/min)-(\frac{11s}{1000}\ kg/min )\\\\\frac{ds}{dt}=0.93\ kg/min-\frac{11s}{1000}\ kg/min \\\\\frac{ds}{dt}=\frac{930-11s}{1000}\ kg/min \\\\\frac{ds}{930-11s}=\frac{1}{1000}dt\\\\Integrating:\\\\\int\limits { \frac{ds}{930-11s}} \, ds=\int\limits {\frac{1}{1000}} \, dt\\\\-\frac{1}{11}ln(930-11s)=\frac{t}{1000}+C\\\\multiply\ through\ by\ -11:[/tex]
[tex]ln(930-11s)= - \frac{11t}{1000}+A\\\\Take \ exponential:\\\\930-11s=e^{ - \frac{11t}{1000}+A}\\\\930-11s=C_1e^{ - \frac{11t}{1000}}\\\\11s=930-C_1e^{ - \frac{11t}{1000}}\\\\s=\frac{930-C_1e^{ - \frac{11t}{1000}}}{11} \\\\To \ find\ C_1,s(0)=0.Hence:\\\\0=\frac{930-C_1e^{ - \frac{11(0)}{1000}}}{11} \\\\0=930-C_1\\\\C_1=930\\\\s(t)=\frac{930-930e^{ - \frac{11t}{1000}}}{11} \\\\s(t)=930(\frac{1-e^{ - \frac{11t}{1000}}}{11})[/tex]
A) So, the required value is [tex]1.01-\frac{11S}{1000}[/tex].
B) The required value is [tex]\frac{1010}{11} (1-e^{-11/1000t} )[/tex]
Differential Equation:A differential equation is an equation that contains one or more terms and the derivatives of one variable (i.e., dependent variable) with respect to the other variable (i.e., independent variable).
[tex]\frac{dy}{dx} =f(x)[/tex]
(A) Let [tex]S(t)[/tex] denotes the number of kg of the salt in the tank at the time [tex]t[/tex] minutes.
Then,
[tex]\frac{ds}{dt}=[/tex](rate of salt in to tank)-(rate of salt of tank)
[tex]\frac{ds}{dt}=\left ( 0.08\times 0.09\times 5 \right )-\left ( \frac{s\left (t\right )}{1000}\times 11 \right ) \\ \therefore \frac{ds}{dt}=1.01-\frac{11S}{1000}[/tex]
(B)
[tex]\frac{ds}{dt}=\frac{101}{100}-\frac{11S}{1000} \\ \Rightarrow \frac{ds}{dt}=\frac{1010-11S}{1000} \\ \Rightarrow \frac{ds}{1010-11S}=\frac{dt}{1000}[/tex]
Integrating we get,
[tex]-\frac{1}{11}I_n|1010-11S|=\frac{t}{1000}+In \ C_1 \\ \Rightarrow 1010-11S=C_1e^{-11/1000t} \\ S(t)=\frac{1010-C_1e^{-11/1000t}}{11}[/tex]
Initially, [tex]S(0)=0\\\Rightarrow C_1=1010[/tex]
Then the required solution is,
[tex]\therefore S(t)=\frac{1010}{11} (1-e^{-11/1000t} )[/tex]
Learn more about the topic of Differential Equation: https://brainly.com/question/24546081
Marley and Kaitlyn are making duct tape wallets to sell at a craft fair
to make money for summer camp. They made 20 wallets over
the weekend. The need to make 125 wallets by the end of the
week. What percent of the wallets did they make over the
weekend?
Answer:
16%
Step-by-step explanation:
20/125 = 0.16
0.16 x 100 = 16% (multiply by 100 to get a percentage)
. 32+4 X (16 X �) -2
pls help
Answer:
94
Step-by-step explanation:
Anyone 100% know dis for me I’m having a struggle
Write the equation for the inverse of the function. y=Arctan (x+pi/2)
Answer:
the answer is B
Step-by-step explanation:
I NEED HELP ASAP PLS PLS
Answer:
im not sure sorry try asking an addalt
Step-by-step explanation:
nu4
Factor the trinomial by guess and check
2c^2 - 14c+20
[tex]2c^2-14c+20=0 \\ c^2-7c+10=0 \\ (c-2)(c-5)=0 \\ c_1=2,c_2=5[/tex].
Karen purchased a DVD player on sale. The original selling price was $171.50. The sale price was $145.22. What is the first step in finding the percent markdown? Find the percent markdown.
Answer:
15% off
Step-by-step explanation:
Answer:
i need help go to my question from this brainly.com/question/25995862
Step-by-step explanation:
What are the 2 inequality’s?
Answer:
y≥-1/3+2
y≥2/3-2
Step-by-step explanation:
In a right triangle, the measures of the legs are x and x + 14 and the measure of the hypotenuse is x + 16. Find the measure of x.
Answer:
[tex]x=10[/tex]
Step-by-step explanation:
We can use the Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex]
The two legs are x and (x + 14) and the hypotenuse is (x + 16). Therefore:
[tex](x)^2+(x+14)^2=(x+16)^2[/tex]
Expand:
[tex]\displaystyle x^2+(x^2+28x+196)=x^2+32x+256[/tex]
Combine like terms:
[tex]2x^2+28x+196=x^2+32x+256[/tex]
Subtract the right from the left:
[tex](2x^2+28x+196)-(x^2+32x+256)=0[/tex]
Subtract:
[tex]x^2-4x-60=0[/tex]
Factor:
[tex](x-10)(x+4)=0[/tex]
Zero Product Property:
[tex]x-10=0\text{ or } x+4=0[/tex]
Solve:
[tex]\displaystyle x = 10 \text{ or } x = -4[/tex]
The x cannot be negative since a side cannot measure -4. So, our only answer is:
[tex]x=10[/tex]
So, the legs are 10 and 24 with the hypotenuse being 26.
A physical education department wanted a single test of upper body strength that was easy to administer. Dips on the parallel bars and pull-ups on the horizontal bar were considered good tests. One faculty member thought that both tests were not needed because the correlation between the two was probably high. To evaluate this assumption, 141 students were tested on both criteria. The faculty member let X represent dips on the parallel bars and Y represent pull-ups and calculated the following from the data:
ΣX = 3,416, ΣY = 1,899, SDX = 8.84, SDY = 4.70, ΣZXZY = 109.416.
Calculate the following:
a. The mean of each variable
b. The correlation between the two variables
c. The level of confidence and the p value reached by the coefficient
d. The predicted number of pull-ups for a student who performed 20 dips
e. The standard error of the estimate
f. The predicted range of possible pull-up scores at the 95% LOC for a student who performed 20 dips
Answer:
24.23 ; 13.47 ; 0.782 ; p value < 0.00001 ;7.45
Step-by-step explanation:
Given that :
ΣX = 3,416, ΣY = 1,899, SDX = 8.84, SDY = 4.70, ΣZXZY = 109.416
Sample size, N = 141
Mean of X:
£X / N = 3416 / 141 = 24.23
Mean of Y:
£Y / N = 1899 / 141 = 13.47
B.) Correlation between the 2 variables :
£ZXZY / N - 1
= 109.416 / 140
= 0.782
C.)
Level of significance and p value :
T = [Rsqrt(n-2)] ÷ sqrt(1 - R²)
T = [0.782 * sqrt(139)] ÷ sqrt(1-0.782^2)
T = 14.79
P value from Tscore calculator
Df = 141 - 2 = 139 ; α = 0.05
Pvalue = 0.00001
Pvalue < α ; Hence, a significant positive relationship exists.
To obtain regression model :
Slope = £ZXZY / SDX²
m = 109.416 / 8.84^2 = 1. 4
yintercept = meanY - slope*x
yintercept = 13.47 - 1.4*24.3
yintercept = - 20.55
Equation in slope intercept form:
y = mx + c
y = 1.4x - 20.55
For x = 20
y = 1.4(20) - 20.55
y = 7.45