Answer:
H0 : μ = 91000
H1 : μ ≠ 91000
Test statistic = - 2.594
Pvalue = 0.016
|Tcritical | = 2.064
Reject H0. We can conclude that the mean annual administrator salary in Ohio differs significantly from the national mean annual salary.
Reject H0. We can conclude that the mean annual administrator salary in Ohio differs significantly from the national mean annual salary.
Step-by-step explanation:
The hypothesis :
H0 : μ = 91000
H1 : μ ≠ 91000
From the data given :
77600 76000 90700 97200 90700
101800 78700 81300 84200 97600
77500 75700 89400 84300 78700
84600 87700 103400 83800 101300
94700 69200 95400 61500 68800
Using calculator :
Sample mean, xbar = 85272
Sample standard deviation, s = 11039.23
Sample size, n = 25
The test statistic :
(xbar - μ) ÷ (s/√(n))
(85272 - 91000) / (11039.23/√(25)
Test statistic = - 5728 / 2207.846
Test statistic = - 2.594
The Pvalue : df = n - 1 = 25 - 1 = 24
Pvalue(-2.594, 24) = 0.0159
Decision region :
Reject H0 ; If Pvalue < α ;
α = 0.05
Using the critical value :
Decision region :
Reject H0 ; If Test statistic > |Tcritical;
Tcritical value at df = 24 ; α = 0.05 ;
|Tcritical | = 2.064
Hence,
We Reject H0 ; Since, |Test statistic| > |Tcritical|and conclude that mean salary depends differs
find the coefficient of the third term of (x+2)^5
Answer:
40
Step-by-step explanation:
(x+2)^5 use binomial theorem :
(a+b)^n = (n choose 0)*a^n*b^0 + (n choose 1)*a^(n-1)*b^1 + (n choose 2)*a^(n-2)*b^2) + ... + (n choose (n-1)*a^1*b^(n-1) + ( n choose n)*a^0*b^n
this seems like a lot but to break it down, notice how the exponent on 'a' decreases as the exponent on 'b' gets bigger.
also, the 'choose' formula is :
(n choose r ) = n!/ (n-r)!r!
now plug in your values
(x+2)^5 =
(5 choose 0)*x^5*2^0 + (5choose 1)*x^4*2^1 + (5 choose 2)*x^3*x^2 + (5 choose 3)*x^2*2^3 + (5 choose 4)*x^1*2^4 + (5 choose 5)*x^0*x^5
we only need the third term so we will solve for this :
(5 choose 2)*x^3*x^2
5 choose 2 = 5!/ (5-2)!2! = 5!/ 3!2! = 10
x^3 * 2^2 = 4x^3
10*4x^3 = 40x^3
Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. P(X > 3), n = 5, p = 0.2
Answer:
0.0064
0.00032
Step-by-step explanation:
Given the details:
P(X > 3), n = 5, p = 0.2
The binomial distribution is related using the formula:
P(x = x) = nCx * p^x * q^(n-x)
q = 1 - p = 1 - 0.2 = 0.8
P(X > 3) = p(x = 4) + p(x = 5)
P(x = 4) = 5C4 * 0.2^4 * 0.8^1 = 5 * 0.2^4 * 0.8^1 = 0.0064
P(x = 5) = 5C5 * 0.2^5 * 0.8^0 = 1 * 0.2^5 * 0.8^0 = 0.00032
100 mice eat 100 cakes. If each big mouse eats 3 cakes, and 3 baby mice eat 1 cake, how many big mice and baby mice are there?
Find the missing side. Round your answer to the nearest tenth
Answer:
x = 24.8
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
Sin theta = opp / hypotenuse
sin 75 = 24 /x
x sin 75 = 24
x = 24/ sin 75
x=24.84662
Rounding to the nearest tenth
x = 24.8
1. Define the following: Odds ratio Relative risk 2. Describe how to calculate the Odds ratio and provde the formula. 3. Describe how to calculate the Relative Risk and provide the formula.
Answer and Explanation:
Odds ratio is the odds that an outcome would happen given a level of exposure in comparison to the occurrence of that outcome without exposure. Odds ratio is calculated by dividing odds of event occurring with exposure(the first group) by odds of event(usually disease) occurring without exposure. Odds is different from probability(denoted p/1-p). While probability is the number of favorable events divided by total number of events, odds is number of favorable events/number of unfavorable events.
Relative risk, also measuring relationship between exposure and outcome, is the ratio of the probability that an outcome would occur without exposure and probability that an outcome would occur with exposure.
Is the following shape a square? How do you know?
.8
C.
A
0
O A. No, the opposite sides are not parallel.
B. Yes, the opposite sides are parallel, and all sides are the same
length
O C. No, the sides are not congruent.
D. Yes, the adjacent sides are perpendicular, and all sides are the
same length
state the hundred thousands place for 7,832,906,215
Answer:
Step-by-step explanation:
6 is the thousands place
0 (right next to it) is the 10 thousands place
9 is the hundred thousands place. There is only 1 nine present so the answer is unique.
• The difference between a polynomial or rational equation and polynomial or rational inequality
Answer:
An equation has an equal sign between two expressions, while an inequality has a ≤ or ≥ sign.
Explain why a + b = d.
B
lbº
aº
dº
A
С C
What is the length of segment AC?
Answer:
10 units
Step-by-step explanation:
Point A (3,-1)
Point B (-5,5)
Distance between them,
√{(-5-3)²+(5-(-1))²}
= √{(-8)²+6²}
= √(64+36)
= √100
= 10 units
A waste management company is designing a rectangular construction dumpster that will be twice as long as it is wide and must hold 10 yd3 of debris. Find the dimensions of the dumpster that will minimize its surface area.
Answer:
The dimensions are:
l = 2*1.96 = 3.92 yd
h = 5/(1.96)² = 1.30 yd
w = 1.96 yd
Step-by-step explanation:
The volume is given by:
[tex]V=l*w*h[/tex]
Where:
l is the longw the wide h the heightWe know that l = 2w, so we have:
[tex]V=2w^{2}*h[/tex]
[tex]10=2w^{2}*h[/tex]
[tex]5=w^{2}*h[/tex] (2)
Now, the surface of this parallelepiped is:
[tex]S=2wh+2lh+lw[/tex]
Using l = 2w:
[tex]S=2wh+4wh+2w^{2}[/tex]
Using (2) we obtain the surface equation in terms of w.
[tex]S=2w\frac{5}{w^{2}}+4w\frac{5}{w^{2}}+2w^{2}[/tex]
[tex]S=2\frac{5}{w}+4\frac{5}{w}+2w^{2}[/tex]
We need to take the derivative with respect to w to minimize the surface area.
[tex]S=2\frac{5}{w}+4\frac{5}{w}+2w^{2}[/tex]
[tex]S=\frac{30}{w}+2w^{2}[/tex]
[tex]\frac{dS}{dw}=-\frac{30}{w^{2}}+4w[/tex]
Now, let's equal it to zero.
[tex]0=-\frac{30}{w^{2}}+4w[/tex]
[tex]\frac{30}{w^{2}}=4w[/tex]
[tex]w^{3}=\frac{30}{4}[/tex]
[tex]w=1.96\: yd[/tex]
So, l = 2*1.96 = 3.92 yd and h = 5/(1.96)² = 1.30 yd
Therefore, the dimensions are:
l = 2*1.96 = 3.92 yd
h = 5/(1.96)² = 1.30 yd
w = 1.96 yd
I hope it helps you!
Find the area of a rectangle whose length is 14cm and breadth is 6cm
Answer:
Ellos dan las pistas de algunos problemas se pueden resolver de forma automática, los valores numéricos tienen ninguna importancia en los distintos ejemplos.
Traza 1
Uno de los lados de un rectángulo es 20 cm de largo; un segundo lado del rectángulo es de 0,85 m de largo. Calcular el perímetro y el área del rectángulo.
Traza 2
Calcular el área de un rectángulo cuyas dimensiones son 85 cm de largo y 20 cm respectivamente.
Traza 3
La base de un rectángulo es 20 cm de largo; la área es de 300 cm². Calcular la altura del rectángulo.
Traza 4
La altura de un rectángulo es 15 cm de largo; la área es de 300 cm². Calcula la base del rectángulo.
Traza 5
Un rectángulo tiene la altura que es de 3/8 de la base; la suma de las longitudes de los dos segmentos es 44 cm. Determinar el área del rectángulo y el perímetro.
Traza 6
La base de un rectángulo es de 0,40 m de largo; La altura del rectángulo es 30 cm. Calcular la diagonal.
Traza 7
Un tamaño de un rectángulo es un medio del lado de un cuadrado que tiene el perímetro de 20 cm. Sabiendo que los dos polígonos tienen el mismo perímetro, calcula la medida del tamaño del rectángulo.
Traza 8
La diagonal de un rectángulo es de 50 cm; la base es de 3/4 de la altura. Calcular el perímetro y el área del rectángulo.
Traza 9
La diagonal de un rectángulo mide 50 cm; ella es 5/3 de altura. Calcular el perímetro y el área del rectángulo.
Traza 10
Una mesa rectangular tiene lados de 180 cm y 90 cm respectivamente. Cuál es el perímetro y el área de un mantel que cuelga de 20 cm alrededor de la mesa?
Traza 11
Calcular el área de un rectángulo que tiene la altura 10 cm de largo, sabiendo que la medida de la base es el doble de la altura.
Traza 12
La diferencia entre el tamaño de un rectángulo es 12 cm y una es el triple de la otra. Calcular el área del rectángulo
Traza 13
La suma entre el tamaño de un rectángulo es 12 cm y una es el triple de la otra. Calcular el área del rectángulo
Traza 14
La suma de la base y la altura de un rectángulo es 50 cm; la base es superior a la altura de 4 cm. Calcular el área del rectángulo.
Traza 15
El semi-perímetro de un rectángulo es 32 cm y una dimensión es de 3/5 de la otra. Calcular el área del rectángulo.
Traza 16
El semi-perímetro de un rectángulo es 30 cm y una dimensión es igual a los sus 2/5. Calcular el área del rectángulo.
Traza 17
Un rectángulo tiene una base de 20 cm y una altura igual a 2/5 de la base. Calcular el perímetro y el área del rectángulo.
Traza 18
Un rectángulo tiene el área de 600 cm² y la base es 20 cm de largo. Cuál es su perímetro ?
Traza 19
Un rectángulo tiene un perímetro de 100 cm y la base es 30 cm de largo. Calcula su área.
Traza 20
Un rectángulo tiene un perímetro de 120 cm. Sabiendo que un tamaño es tres veces la otra, calcula el área del rectángulo.
Traza 21
La diferencia entre el tamaño de un rectángulo es 10 dm. Sabiendo que el perímetro es 100 dm, calcula el área del rectángulo.
Traza 22
Un rectángulo tiene un perímetro de 100 cm. Calcula su área sabiendo que la medida de la base es superior a la de la altura de 10 cm.
Traza 23
En el perímetro de un rectángulo es de 100 cm y la altura es de 20 cm de largo. Calcular el perímetro de un rectángulo equivalente a el mismo y que tiene su base de 40 cm de largo.
Traza 24
Un rectángulo es formado por dos cuadrados congruentes que tienen cada uno el perímetro de 24 cm. Calcular el perímetro y el área del rectángulo.
Traza 25
Un rectángulo es formado por tres cuadrados congruentes con cada lado 20 cm de largo. Calcular el perímetro y el área del rectángulo.
Traza 26
Un rectángulo es formado por dos cuadrados congruentes. Sabiendo que el perímetro del rectángulo es de 180 cm, calcular su área.
Traza 27
Un rectángulo y un cuadrado tienen el mismo perímetro. El lado de un cuadrado de 45 cm y las dimensiones del rectángulo son una 1/2 de la otra. Calcular el área del rectángulo.
Traza 28
Dos rectángulos son equivalentes. Sabiendo que las dimensiones de el primero miden respectivamente 30 cm y 20 cm, y que la base del segundo rectángulo es 40 cm de largo, calcula la diferencia entre los dos perímetros.
Traza 29
Calcular el perímetro de la figura y el área de la parte interior con la obtención de las medidas a partir del dibujo:
Traza 30
Calcular el perímetro de la figura y el área de la parte interior con la obtención de las medidas a partir del dibujo:
Traza 31
Un constructor ha comprado un terreno que tiene la planta mostrada en el dibujo y las dimensiones en metros se indican en la figura. Calcula el área y el perímetro de la tierra.
Traza 32
Una parcela de tierra tiene una forma rectangular con unas dimensiones de 50 m y de 30 m de largo. En el interior se ha construido una casa que ocupa una superficie rectangular de longitud 20 m y de 8 m de ancho. Calcular el área de la tierra permanecida libre.
Traza 33
Step-by-step explanation:
Answer:
A= 84cm
Step-by-step explanation:
length x width= area
plug in the given information.
14cm x 6cm = A
A=84
with a length of 14cm and a width of 6cm multiply them for an area of 84cm.
the expression -6x-7(4+3) is equivalent to?
Answer:
x(12y+4)
2 0 l e t t e r s
Sam can mow a lawn in 40 minutes. Melissa can mow the same lawn in 80 minutes. How long does it take for both Sam and Melissa to mow the lawn if they are working together?
Answer:
It will take them both 24 minutes to mow the lawn if they are working together.
Step-by-step explanation:
Given that Sam can mow a lawn in 40 minutes, and Melissa can mow the same lawn in 80 minutes, to determine how long does it take for both Sam and Melissa to mow the lawn if they are working together, the following calculation must be performed:
1/40 + 1/60 = 1 / X
3X + 2X = 120
X = 120/5
X = 24
Thus, it will take them both 24 minutes to mow the lawn if they are working together.
!!! HELP ASAP !!! I almost got the problem but the problem was the rounding. I believe I rounded right but it is still incorrect. Can someone please help me on the rounding portion of the question? Thank you for your help!!!
Given limit f(x) = 4 as x approaches 0. What is limit 1/4[f(x)]^4 as x approaches 0?
Answer:
[tex]\displaystyle 64[/tex]
General Formulas and Concepts:
Calculus
Limits
Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]
Limit Rule [Variable Direct Substitution Exponential]: [tex]\displaystyle \lim_{x \to c} x^n = c^n[/tex]
Limit Property [Multiplied Constant]: [tex]\displaystyle \lim_{x \to c} bf(x) = b \lim_{x \to c} f(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \lim_{x \to 0} f(x) = 4[/tex]
Step 2: Solve
Rewrite [Limit Property - Multiplied Constant]: [tex]\displaystyle \lim_{x \to 0} \frac{1}{4}[f(x)]^4 = \frac{1}{4} \lim_{x \to 0} [f(x)]^4[/tex]Evaluate limit [Limit Rule - Variable Direct Substitution Exponential]: [tex]\displaystyle \lim_{x \to 0} \frac{1}{4}[f(x)]^4 = \frac{1}{4}(4^4)[/tex]Simplify: [tex]\displaystyle \lim_{x \to 0} \frac{1}{4}[f(x)]^4 = 64[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
Book: College Calculus 10e
Answer: C. 64
Step-by-step explanation:
Edge 100%
what is the image of ( 4, -8 ) after a dilation by a scale factor of 1/4 centered at the origin ?
what we know?:
* scale factor of 1/4
* the point (4, -8)
all we have to do is put 4/4 (because we are dilating by 1/4)
4/4= 1
same for the other one: -8/4= -2
FINAL ANSWER: (1, -2)
Does anyone know how to take the fuzzy stuff off
Answer:
???
Step-by-step explanation:
The circumference of a
square orchard is 1600
meters. How many square
meters does the orchard
cover? How many hectares?
Answer:
A square is 4 even sides.
the circumference around the square area is 1600 meters. This means that each side is 400 meters.
Square meters is the area of the square.
400 x 400 = 160000 m^2
To get to Hectares, you divide the squared measurement by 10,000.
Answer:
160000m^2 = 16ha
Step-by-step explanation:
Bit of a nit pick first the word is perimeter not circumference circumference only applies to circles. 1600/4=400 (divide by 4 because a square has 4 sides) 400^2=160000 (A=L*H the length and height are the same so you square it) 160000/10000=16 (1 hectare = 10000m^2), Hope this helps. :)
Kezang was 5 times as old as his son 10 years ago. After 8 years, Kezang will be twice as
old as his son. What are their present age
Find all the zeros of f(x).
f(x) = 2x3 + 7x2 - 28x + 12
Arrange your answers from smallest to largest. If
there is a double root, list it twice.
Plz help!
Answer:
The zeroes are -6, 1/2 and 2.
Step-by-step explanation:
f(x) = 2x3 + 7x2 - 28x + 12 = 0
From the first and last coefficient 2 and 12, one guess for a zero is x = 2.
So substituting x = 2:
f(2) = 16+ 28 - 56 + 12 = 0
So x = 2 is a zero and x - 2 is a factor of f(x)
Performing long division:
x - 2)2x3 + 7x2 - 28x + 12( 2x2 + 11x - 6 <------- Quotient
2x3 - 4x2
11x2 - 28x
11x2 - 22x
- 6x + 12
-6x + 12
.............
Now we solve
2x2 + 11x - 6 = 0
(2x - 1)(x + 6) = 0
2x - 1 = 0 or x + 6 = 0, so:
x = 1/2, x = -6.
Answer: -6, 1/2, 2.
Step-by-step explanation:
{(x) = 2x3 + 7x2 - 28x + 12 = 0
From the first and last coefficient 2 and 12, one
guess for a zero is x=2.
So substituting x=2:
{(2) = 16+ 28 - 56 + 12 = 0
So x = 2 is a zero and x - 2 is a factor of f(x)
Performing long division:
X - 2)2x3 + 7x2 - 28x + 12(2x2 + 11x - 6 <
Quotient
38)
A man completes a job in 5 days working 8 hours a day. How many days will he take to complete the same job working 2 hours overtime per day in addition?
Answer:
dbcjchdiskcnbcksksnnckdkxnn
One angle measures 27° more than 2 times another. If the two angles are complementary, find the measures of the angles.
A. 21°; 69°
B. 26°; 64°
C. 31°; 59°
D. 23°; 67°
Answer:
A. 21°, 69°
Step-by-step explanation:
If you work by process of elimination all you have to do is take 27 away from the bigger degree of the two and see if it is 2x as much as the smaller degree.
Ex.
1. 69°-27°= 42°, which is 2x as many as 21°.
Male bluethroats have a complex song which is thought to be used to attract female birds. Let x denote the duration of a randomly selected song (in seconds) from a male bluethroat. The authors of research on bluethroat song report the mean song duration is 13.8 seconds and the standard deviation of song durations is 11.8 seconds. The authors also noted that the song length distribution is not normal.
Required:
a. Let = average song duration (in seconds) for a sample of 36 male bluethroat songs. Is this distribution of the sample mean song duration " normally distributed" ?
b. Find the probability that a sample of 36 male bluethroat songs will have a mean duration greater than 12 seconds. Draw, label, and shade a graph to illustrate your result.
Answer:
a) Sample size larger than 30, so by the Central Limit Theorem, yes.
b) 0.8199 = 81.99% probability that a sample of 36 male bluethroat songs will have a mean duration greater than 12 seconds. The sketch is given at the end.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean song duration is 13.8 seconds and the standard deviation of song durations is 11.8 seconds.
This means that [tex]\mu = 13.8, \sigma = 11.8[/tex]
Sample of 36
This means that [tex]n = 36, s = \frac{11.8}{\sqrt{36}} = 1.9667[/tex]
a. Let = average song duration (in seconds) for a sample of 36 male bluethroat songs. Is this distribution of the sample mean song duration " normally distributed" ?
Sample size larger than 30, so by the Central Limit Theorem, yes.
b. Find the probability that a sample of 36 male bluethroat songs will have a mean duration greater than 12 seconds. Draw, label, and shade a graph to illustrate your result.
This is 1 subtracted by the p-value of Z when X = 12. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{12 - 13.8}{1.9667}[/tex]
[tex]Z = -0.915[/tex]
[tex]Z = -0.915[/tex] has a p-value of 0.1801.
1 - 0.1801 = 0.8199
0.8199 = 81.99% probability that a sample of 36 male bluethroat songs will have a mean duration greater than 12 seconds.
Sketch:
Does the picture below indicate that:
ZJAC ZDBE?
С DA
J
939
A
B
→E
Yes
No
Pls help
Answer:
No
Step-by-step explanation:
The measure of <JAC is shown to be 93°.
The little square symbol inside <DBE shows that <DBE is a right angle.
The measure of a right angle is 90°.
m<DBE = 90°
Congruent angles are angles with equal measures.
Since the measures of angles JAC and DBE are different, they are not congruent.
Answer: No
Question 5 of 25
Find the common ratio for this geometric sequence.
0.7, 2.1, 6.3, 18.9,...
O A. 1.4
O B. 3
O C.-3
D. 0.33
SUBMIT
Answer:
3
Step-by-step explanation:
common ratio
2.1/0.7=3
6.3/2.1=3
18.9/6.3=3
therefore common ratio is equal to 3
a river generates a spring flood about 40% of the time. Based on these records, what is the chance that it will flood for at least three years in a row sometime during the next five years
PLEASEEEE HELPPPPPPP!!!!!
To find S or T add them together:
3/5 + 1/3
Rewrite the fractions to have a common denominator
9/15 + 5/15 = 14/15
Answer: 14/15
Step-by-step explanation:
Here is your answer . Hope it helps.
Does this graph represent a function?
Answer:
I think it's a function
Step-by-step explanation:
as you can see in the picture curve drawn in a graph represents a function, if every vertical line intersects the curve in at most one point. So I think its a function.
Answer:
yes
Step-by-step explanation:
it's a cubic function having maximum and minimum turning points
it has a point of inflation, y - intercept and x-intercept
he solutions to the inequality y > −3x + 2 are shaded on the graph. Which point is a solution? (0, 2) (2, 0) (1, −2) (−2, 1)
Answer:
The Answer Is Point B (2,0)
Step-by-step explanation:
