Using the Central Limit Theorem, it is found that the mean of the sampling distribution is of 78 and the standard deviation is of 2.84.
What does the Central Limit Theorem state?It states 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].
In this problem, for the population, we have that [tex]\mu = 78, \sigma = 11[/tex].
Then, considering samples of n = 15, we have that the standard deviation is given by:
[tex]s = \frac{11}{\sqrt{15}} = 2.84[/tex].
More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213
sandra calculated the missing side of one of these three triangles using the pythagrean therom which triangle is it
Answer:
right angled triangle
Step-by-step explanation:
the only triangle that this formula can be used to find a side is the right angled triangle
Simplify the following variable expressions
How many solutions are there for the quadratic equation?
f(x)=5x^2+3x+2
Answer:
2
Step-by-step explanation:
[tex]5x^2 +3x +2 = 0\\\\\text{Apply the quadratic formula,}~ x=\dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\\\\text{In this case,}~a= 5, ~ b = 3~ \text{and}~ c = 2\\\\ \\x=\dfrac{-3\pm \sqrt{3^2 -4\cdot 5 \cdot 2}}{2\cdot 5}\\\\~~~=\dfrac{-3 \pm \sqrt{9-40}}{10}\\\\~~~=\dfrac{-3 \pm \sqrt{-31}}{10}\\\\~~~=\dfrac{-3 \pm i\sqrt{31}}{10}\\\\\text{So, there are 2 solutions,}~ x=\dfrac{-3 + i\sqrt{31}}{10}~ \text{and} ~x=\dfrac{-3 -i\sqrt{31}}{10}[/tex]
Another way to find the number of solutions is by looking at the highest exponent(Degree), which indicates the number of solutions.
[tex]\\ \rm\rightarrowtail 5x^2+3x+2=0[/tex]
[tex]\\ \rm\rightarrowtail x=\dfrac{-3\pm \sqrt{9-40}}{10}[/tex]
[tex]\\ \rm\rightarrowtail x=\dfrac{-3\pm\sqrt{-31}}{10}[/tex]
[tex]\\ \rm\rightarrowtail x=\dfrac{-3\pm\sqrt{31}i}{10}[/tex]
Determine
the rotation around the origin that was performed to transform the preimage on the left to its image on the right.
Answer:
-90 degrees counter clock wise
Step-by-step explanation:
it goes the opposite of a clock so it would be called -90 degrees counter clockwise, you could also say 270 degrees clockwise if the other isnt an option.
Btw the answer needs to be a fraction.
Answer:
3/4
Step-by-step explanation:
if you could just tell me what I should say in the presentation, that would be great :) thx
Answer:
we're u asking for this
What is ur statistical question
Electric guitar kits originally cost $d$ dollars online. You buy the kits on sale for $50\%$ of the original price, plus a shipping fee of $\$4.50$ per kit. After painting and assembly, you sell each guitar online for $\left(1.5d+4.5\right)$ dollars. Find your profit on each guitar sold.
let's keep in mind that Profit = Revenue - Costs.
so each guitar costs originally "d" dollars online.
you buy the kits at half price, 50% of the original price, well, the original price is "d", half "d" is just 0.5d, and there's a shipping charge of $4.50. So the Cost to get one kit alone for you is 0.5d + 4.50.
After some work, you resell the kits online for 1.5d + 4.5, so since that's the selling price that is your Revenue for one kit.
[tex]\stackrel{\textit{\Large Profit}}{\stackrel{Revenue}{(1.5d~~ + ~~4.50)}~~ - ~~\stackrel{Costs}{(0.5d~~ + ~~4.50)}}\implies 1.5d+4.5-0.5d-4.5 \\\\\\ 1.5d-0.5d+4.5-4.5\implies 1d\implies d[/tex]
A puppy weighs 4 pounds. How many ounces does the puppy weigh?
Answer:
64 ounces
Step-by-step explanation:
Since 1 lb = 16 oz, just do 4 × 16 = 64
If puppy weighs 4 pounds then the weigh in ounces is 64 ounces.
What is Unit of Measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
There are 16 ounces in a pound.
1 pound= 16 ounces.
Given that puppy weighs 4 pounds.
We have to find the wight in ounces.
To convert pounds to ounces, we need to multiply the weight in pounds by 16.
The puppy weighs 4 pounds x 16 ounces/pound
= 64 ounces
Hence, if puppy weighs 4 pounds then the weigh in ounces is 64 ounces.
To learn more on Unit of measurement click:
https://brainly.com/question/15402847
#SPJ2
Find the volume of the composite solid. Round your answer to the nearest tenth.
16 ft
6 ft
4 ft
The volume is about
cubic feet.
The volume of the composite solid is 4823.04 ft³.
Wha is volume?Volume is the amount of space or the capacity of a solid shape.
To find the volume of the composite solid, we use the formula below.
Formula:
The volume of the composite solid = Volume of the cone + volume of the cylinder.
V = πr²H+πr²h/3Where:
V = Volume of the composite solidr = Radius of the base of cylinder/ the base of the coneH = Height of the cylinderh = Height of the coneπ = PieFrom the question,
Given:
r = 16 ftH = 4 fth = 6 ftπ = 3.14Substitute these values into equation 1
V = 3.14(16²)(4)+3.14(16²)(6)/3V = 3215.36+1607.68V = 4823. 04 ft³Hence, The volume of the composite solid is 4823.04 ft³.
Learn more about volume here: brainly.com/question/1972490
Help please thank you
Answer:
[tex] = 2 \times 4 = 8 \\ = 5 \times 5 = 25 \ \\ \frac{1}{2} \times 5 \times 3 = 7.5 \\ 7.5 + 8 + 2.5 = 18[/tex]
PLEASE HELP ill like!!!!!! Its 20 points
Answer:
1. Degree= 6, trinomial
2. degree= 4, binomial
Step-by-step explanation:
1. The largest exponent is 6 making it the degree and there are three terms because (m^5n^2), (mn^2), (n^6).
2. Since (9a^2bc^2) has the more than 1 exponent, you add them and the degree is 4. There are two terms because (2a^3b), (9a^2bc^2).
helppp plsss. i have to turn this in asap
Answer:
y= 2x-5
Step-by-step explanation:
The slope formula is m=(y2-y1)/(x2-x1)
-3-1 / 1-3 = -4/-2= 2=m
The Y interception- y=mx+b using coordinates (3,1)
1=2(3)+b
1=6+b (subtracting 6 on both sides to isolate b)
-5=b
plug it in
y=2x-5
Find the perimeter.
Write your answer as a fraction or as a whole or mixed numbe
5 1 cm
10
5 cm
10
Bloc
5
cm
10
5 cm
10
Answer:
20 2/5 cm
Step-by-step explanation:
4 ( 5 1/10)
4 × 51/10
2×51/5
0.4x51
=20 2/5
310, 304, 298, ...
Find the 47th term.
Answer:
The answer is 34
Step-by-step explanation:
Given;a₁ = 310a₂ = 304a₃ = 298n = 47To Find;a₄₇ = ?Formula;aₙ = a + (n – 1) × dNow,
Common Difference (d)
d = a₂ – a₁ = 304 – 310 = -6
d = a₃ – a₂ = 298 – 304 = -6
Here, common difference is same everywhere
So,
aₙ = a + (n – 1) × d
a₄₇ = 310 + (47 – 1) × (-6)
a₄₇ = 310 + 46 × (-6)
a₄₇ = 310 – 276
a₄₇ = 34
Thus, The 47th term of this sequence is 34.
What are the new coordinates of the figure above if it is dilated by a scale factor of 4, with the origin as the center of dilation ?
A. A’ (-1,-4), B’(-4,4), C’(2,-4)
B. A’(-4,-1), B’(-4,4),C’(8,-1)
C. A’(-5,-5), B’(-5,5),C’(6,-5)
D. A’(-4,-4), B’(-4,4)C’(8,-4)
Answer:
D. A’(-4,-4), B’(-4,4)C’(8,-4)
Step-by-step explanation:
Sam rode a bull for 8 seconds.
Maddie rode a bull for 2 fewer seconds than Sam did.
How long did Maddie ride her bull?
Answer:
is it 7?
Step-by-step explanation:
if he rode for 8 seconds and it says she rode for 2 seconds FEWER are you not subtracting from 8 to get 7?
In creating a new scale for the mercury thermometer, Anders Celsius initially set the boiling point of water at _____. A. 0° b. 32° c. 100° d. 273°.
The thermometer is a device that is used to measure the temperature gradient. Anders needs to set the boiling point of water at 100° C.
What is a thermometer?
The thermometer is a device that is used to measure the temperature gradient or the temperature of a body/object.
The boiling point of water is 100°C, therefore, Anders needs to set the boiling point of water at 100° C.
Thus, Anders needs to set the boiling point of water at 100° C.
Learn more about Thermometers:
https://brainly.com/question/24189042
"Your teacher brings two bags of colored goldfish crackers to class. Bag I has 25% red crackers and Bag II has 35% red crackers. Each bag contains more than 1000 crackers. Using a paper cup, your teacher takes an SRS of 50 crackers from Bag I and a separate SRS of 40 crackers from Bag II. Let p1-p2 be the difference in the sample proportions of red crackers. " The object is to find the standard deviation. I have 0. 971. Is this correct? I would like to verify
Using the Central Limit Theorem, it is found that the standard deviation is of 0.0971.
What does the Central Limit Theorem states?It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].It also states that when two variables are subtracted, the standard deviation is the square root of the sum of the variances.In this problem, for each sample, the standard error is given by:
[tex]s_I = \sqrt{\frac{0.25(0.75)}{50}} = 0.0612[/tex]
[tex]s_{II} = \sqrt{\frac{0.35(0.65)}{40}} = 0.0754[/tex]
Hence, for the distribution of differences, it is given by:
[tex]s = \sqrt{s_I^2 + s_{II}^2} = \sqrt{0.0612^2 + 0.0754^2} = 0.0971[/tex]
More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213
( Pls help ASAP) Will give 20 points if you answer 2 questions))
Answer:
1. -3 2. y=-1
Step-by-step explanation:
what is the value of x that makes the given equation true 9+8x-4-5x=-19
Answer:
x = -8
Step-by-step explanation:
9+8x-4-5x=-19
5+8x-5x=-19
5+3x=-19
-5 =-19
3x = -24
3/3 = -24/3
x= -8
[tex] { \alpha }^{2} \beta + \alpha { \beta }^{2} [/tex]
Please solve this
Car #1 travels 288 miles in 4 hours. Car #2 travels 276 miles in 3
hours. What is the speed of car #2 in miles per hours
PLEASE HELP AURGENT
Answer:
Car 1: 72 mph
Car 2: 92 mph
Step-by-step explanation:
Car 1: 72 mph
288/4 = 72
72mph
Car 2: 92 mph
276/3
92 mph
Have an amazing day!!
Please rate and mark brainliest!!
Rachel has a coupon for 15% off any
two pairs of earrings at one of her
favorite stores. If each pair of
earrings that she purchased cost
$12.99, and the sales tax in her state
is 6.5%, then what is the total
amount she spent after using her
coupon?
Answer:
Total Payment: $23.52
Savings: $4.15
Tax: $1.44
2640 yards= ________ miles
complete each conversion
After converting yards to miles:
2640 yards = 1.5 miles
Given,
2640 yards= ________ miles
Now,
To convert to yard to miles the conversion factor is 0.000568182.
So,
1 yard ⇒ 0.000568182 miles
Multiply 2640 on both sides,
2640 yards ⇒ 1.5 miles.
Therefore 2640 yards is equivalent to 1.5 miles.
Know more about unit conversion,
https://brainly.com/question/14614674
#SPJ6
Christine went on a passenger train that traveled 80 miles in one hour. How many miles will it travel in six hours?
Answer:
480
Step-by-step explanation:
[tex]80*6[/tex] = 480
Answer:
She will travel 480 miles in 6 hours
Step-by-step explanation:
All you need to do is Multiply 80 by 6 to get an answer of 480.
Hope that helps!
PLEASE HELP !
The radius of circle L is 22cm what is the lenght of its diameter ? A. 88cm B. 44 cm C. 22cm D. 11cm
Answer:
B. 44cm
Step-by-step explanation:
d(diameter) = 2r (radius)
d = 2 X 22 cm
d = 44 cm
14x - 2x + 3
12x + 3
3 (4x + 1)
4x+ 1
1
-8
3(5x + 9)
3(5x + 9)
= 3(5x + 9)
= 5x + 9
= x+9
=x
Answer:
-1/4
Step-by-step explanation:
14x - 2x + 3 = 0
12x + 3 = 0
12x = -3
12x/12 = -3/12
x = -1/4
What is the volume of this right prism? 1200 in³ 1800 in³ 2040 in³ 3600 in³ Right triangular prism. The height of the prism is labeled as 15 in. The base of the prism is a triangle with the base labeled as 30 in., the height labeled as 8 in., and the other 2 sides of the triangle labeled as 17 in.
Please help asap!!!
Volume of right prism is 1800 in³, So option 'B' is the correct answer to the following question.
Volume of right prismWhat information do we have?
Height of the prism is labeled = 15 in.
Base of the prism is a triangle with the base = 30 in
Height labeled = 8 in
Volume of right prism = Area of base triangle × Height
Volume of right prism = (1/2)(b)(h) × Height
Volume of right prism = (1/2)(30)(8) × 15
Volume of right prism = (30)(4) × 15
Volume of right prism = 120 × 15
Volume of right prism = 1800 in³
Find more information about 'Prism'.
https://brainly.com/question/318504?referrer=searchResults
Answer:
The answer is B. 1800 [tex]in^{3}[/tex]
Step-by-step explanation:
I took the test
a 21ft ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 19ft from the base of the building. how high up the wall does the ladder reach
Answer:
According to the graph:
H^2 + 10^2 = 21^2
Solve as:
H = 18.19 feet
So the height is 18.19 feet
PLEASE HELP
One number is 4 more than another number. If the greater number is x, what is the other number?
Answer:
12
Step-by-step explanation:
it would be 12 if it is unknown so 12 because y and x are used for unknown numbers.
i hope i got it right just tell me if this is wrong, please
The expression for the smaller number is q = x - 4
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the greater number be p = x
Let the smaller number be q
If the greater number is x, then the other number must be 4 less than x.
We can express this algebraically as:
On simplifying the equation , we get
q = x - 4
Hence , the other number is x - 4.
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ2