Answer:
A
Step-by-step explanation:
because I said so.
Answer:
the correct answer is option A
Step-by-step explanation:
(9-2)(-2)
(7)(-2)
=-14
5.4 / 113.4
Pls show work
The Office of Student Services at a large western state university maintains information on the study habits of its full-time students. Their studies indicate that the mean amount of time undergraduate students study per week is 20 hours. The hours studied follows the normal distribution with a population standard deviation of six hours. Suppose we select a random sample of 150 current students. What is the probability that the mean of this sample is between 19.25 hours and 21.0 hours
Answer:
0.8254 = 82.54% probability that the mean of this sample is between 19.25 hours and 21.0 hours
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 estabilishes 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 of 20 hours, standard deviation of 6:
This means that [tex]\mu = 20, \sigma = 6[/tex]
Sample of 150:
This means that [tex]n = 150, s = \frac{6}{\sqrt{150}}[/tex]
What is the probability that the mean of this sample is between 19.25 hours and 21.0 hours?
This is the p-value of Z when X = 21 subtracted by the p-value of Z when X = 19.5. So
X = 21
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{21 - 20}{\frac{6}{\sqrt{150}}}[/tex]
[tex]Z = 2.04[/tex]
[tex]Z = 2.04[/tex] has a p-value of 0.9793
X = 19.5
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{19.5 - 20}{\frac{6}{\sqrt{150}}}[/tex]
[tex]Z = -1.02[/tex]
[tex]Z = -1.02[/tex] has a p-value of 0.1539
0.9793 - 0.1539 = 0.8254
0.8254 = 82.54% probability that the mean of this sample is between 19.25 hours and 21.0 hours
In the school band, 5/8 of the students play a brass instrument. Only 1/5 of the students who play a brass instrument play the trumpet. What fraction of the band students play the trumpet?
9514 1404 393
Answer:
1/8
Step-by-step explanation:
1/5 of 5/8 is ...
(1/5)(5/8) = (1·5)/(5·8) = 1/8
1/8 of the band students play the trumpet.
There are 15 doughnuts.
Antoine eats a third of the
doughnuts. How much did he
eat? How many doughnuts are
left?
x + a = c , solve for x
Answer:
Step-by-step explanation:
x+a=c
x=c-a
A 15 foot ladder leans against the side of a house. The bottom of the ladder is 6 feet away from the side of the house. Find , the angle of elevation of the ladder. Round your answer to the nearest tenth of a degree.
Answer: [tex]66.42^{\circ}[/tex]
Step-by-step explanation:
Given
Length of the ladder is [tex]L=15\ ft[/tex]
Bottom of the ladder is [tex]6\ ft[/tex] away from the side of the house.
Suppose, ladder is leaning against the wall with angle of elevation [tex]\theta[/tex]
from the figure, we can write
[tex]\Rightarrow \cos \theta=\dfrac{6}{15}\\\\\Rightarrow \cos \theta=\dfrac{2}{5}\\\\\Rightarrow \theta=66.42^{\circ}[/tex]
Thus, the angle of elevation is [tex]66.42^{\circ}[/tex]
13. A car travels at a speed of 55 km/h. Find the distance travelled by the car in 12minutes 30 seconds, giving your answer in meters.
Answer:
11.46 meters
Step-by-step explanation:
12min 30sec = 12.5min
55km/h * 12.5min * 1h/60min = 11.4583333333meters
A stretch of highway has a 4% uphill grade. This means that the road rises 1 foot for every 25 feet of horizontal distance. The beginning of the highway (x = 0) has an elevation of 2,225 feet. Write an equation for this stretch of roadway ini point-slope form.
Answer:
The equation for this stretch of roadway in point-slope form is [tex]y - 2225 = 0.04x[/tex]
Step-by-step explanation:
Equation in point-slope form:
The equation of a line in point-slope form is given by:
[tex]y - y_0 = m(x - x_0)[/tex]
In which [tex](x_0,y_0)[/tex] is the point and m is the slope.
A stretch of highway has a 4% uphill grade. This means that the road rises 1 foot for every 25 feet of horizontal distance.
This means that [tex]m = 0.04[/tex]
The beginning of the highway (x = 0) has an elevation of 2,225 feet.
This means that [tex](x_0,y_0) = (0,2255)[/tex]. So
[tex]y - y_0 = m(x - x_0)[/tex]
[tex]y - 2225 = 0.04(x - 0)[/tex]
[tex]y - 2225 = 0.04x[/tex]
The equation for this stretch of roadway in point-slope form is [tex]y - 2225 = 0.04x[/tex]
What is the volume of the cone below?
A. 1022496 units 3
B. 34087 units3
C. 8527 units3
D. 51121 units3
Answer:
B. 3408π units³
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightGeometry
Volume of a Cone Formula: [tex]\displaystyle V = \frac{1}{3} \pi r^2h[/tex]
r is radiush is heightStep-by-step explanation:
Step 1: Define
Radius r = 12
Height h = 71
Step 2: Find Volume
Substitute in variables [Volume of a Cone Formula]: [tex]\displaystyle V = \frac{1}{3} \pi (12)^2(71)[/tex]Evaluate exponents: [tex]\displaystyle V = \frac{1}{3} \pi (144)(71)[/tex]Multiply: [tex]\displaystyle V = \frac{1}{3} \pi (10224)[/tex]Multiply: [tex]\displaystyle V = 3408 \pi[/tex]Here's the solution :
we know,
[tex] \boxed{volume = \frac{1}{3} \pi {r}^{2} h}[/tex]
now, let's solve
[tex]v = \dfrac{1}{3} \times \pi \times {12}^{2} \times 71[/tex][tex] \dfrac{\pi}{3} \times 144 \times 71[/tex][tex]\pi \times 48 \times 71[/tex][tex] \boxed{3408\pi \: \: \: unit {}^{3} }[/tex]Constant of Variation
Given that f(x) = 2/x² and g =(x) = 13/x²
What is the domain of the functions f and g?
a. only positive integers
b. All non zero real numbers
c. only negative integers
d. All real numbers including zero
Please select the best answer from the choices provided
Answer:
B. All non zero real numbers
Step-by-step explanation:
I calculated it logically
what fraction is equal to 50% of 1/3?
Step-by-step explanation:
50% × 1/3
= 1/2 × 1/3
= 1/6
-------
Write an equation that shows how much money they would make (y) if
they worked x hours with an hourly rate of $10
Your answer
Answer:
y=10x
Step-by-step explanation:
10 is the slope or the rate of change.
Answer:
y = 10x
Step-by-step explanation:
y is your total, 10 is your amount per hour, you multiply the hourly rate by the number of hours.
Find the equation of the line parallel to y=-11-5, that passes through the point
(4, -3). Write your answer in slope-intercept form. Do not use spaces in your
answer. Enter any fractions like a/b or-a/b.
Answer:
y=41−11x
Step-by-step explanation:
The equation of the line in the slope-intercept form is y=5−11x.
The slope of the parallel line is the same: m=−11.
So, the equation of the parallel line is y=−11x+a.
To find a, we use the fact that the line should pass through the given point: −3=(−11)⋅(4)+a.
Thus, a=41.
Therefore, the equation of the line is y=41−11x.
Answer: y=41−11x.
Answer:
y=41−11x
Step-by-step explanation:
The equation of the line in the slope-intercept form is y=5−11x.
The slope of the parallel line is the same: m=−11.
So, the equation of the parallel line is y=−11x+a.
To find a, we use the fact that the line should pass through the given point: −3=(−11)⋅(4)+a.
Thus, a=41.
Therefore, the equation of the line is y=41−11x.
15. Which best reflects a correct conversion of an equation in exponential form to logarithmic form?
Answer:
[tex]5^x = 25[/tex]
[tex]\log_525 = x[/tex]
Step-by-step explanation:
Given
Convert from exponential to logarithm
(a) to (d)
Required
Which of the options is correct
Given that:
[tex]a^b = c[/tex] --- Exponential
The logarithm form is:
[tex]b = \log_ac[/tex]
From (a) to (d), only option (c) is correct.
Because it follows the above pattern
i.e.
[tex]5^x = 25[/tex] [tex]\to[/tex][tex]\to[/tex] [tex]a^b = c[/tex]
[tex]a = 5[/tex] [tex]b = x[/tex] [tex]c = 25[/tex]
[tex]b = \log_ac[/tex] becomes
[tex]x = \log_525[/tex]
or
[tex]\log_525 = x[/tex]
Select the correct answer.
Mariah is shopping for pencils and erasers to give to her piano students. She can purchase at most 50 total items. She wants the
number of pencils purchased to be greater than the square of the number of erasers.
Create a system of inequalities to model this situation, and use it to determine how many of the solutions are viable. Which statement
is true about the solution of this system?
No part of the solution region is viable because the number of pencils and erasers purchased cannot be negative.
Part of the solution region includes a negative number of pencils purchased; therefore, not all solutions are viable for the
given situation
The entire solution region is viable.
Part of the solution region includes a negative number of erasers purchased; therefore, not all solutions are viable for
the given situation.
Answer:
D. Part of the solution region includes a negative number of erasers purchased; therefore, not all solutions are viable for the given situation.
Step-by-step explanation:
I got it right on the practice
Answer:
Part of the solution region includes a negative number of erasers purchased; therefore, not all solutions are viable for
the given situation.
A family is having a pool party built in their backyard. If the Yard is rectangular and measures 10x by 10x in the pool is circular with a radius of 2x how much of the yard will be left over after the pool is built. Write your answer in factored form
1. (100-4pi)x^2
2. 100x^2-4pi(x)^2
3. (100+4pi)x^2
4. 100x^2+4pi(x)^2
Literally have the same question on my test and i dont know if i got it right or wrong. I know it has nothing to do with this :/ im sorry.
Which of the following type of tax is NOT withheld from earnings?
Answer:
Following what?
Step-by-step explanation:
I'll go with Sales Tax
The right rectangular prism is filled with cubes that have a side length of 1/8 foot.
How many cubes does it take to fill the prism? (please just give me an exact answer.) (I WILL GIVE BRAINLIST) (please just help me)
Answer:
24
Step-by-step explanation:
To find the volume of the cube just cube one of the sides, so 1/8^3 is 1/512
Yes it's the actual volume, it didn't get smaller it's just cubic inches instead of a line.
The rectangle's volume is 1/4*3/8*1/2 which if you change them to have the same denominator it's 2/8*3/8*4/8=3/64
Now convert 3/64 to have a denominator of 512
3/64*8/8= 24/512
24/512 divided by 1/512 is 24
You can fit 24 cubes in the rectangle.
PLEASE HELP! I WILL GIVE YOU BRAINLIEST! Peter walked around a park three times. How many miles did he walk?
Answer:
20.7 miles
Step-by-step explanation:
1 + 2 = 3
1.6 + 2.3 = 3.9
3.9 + 3 = 6.9
6.9 x 3 = 20.7
William friend has 18 dogs 14 cats and 4 guinea pigs what are the ratio
Answer:
18:14:4
Step-by-step explanation:
Cats to dogs: 3 to 4 or 3/4 or 3:4 There are three cats to four dogs. Dogs to cats: 4 to 3 or 4/3 or 4:3 There are four dogs to three cats. Cats to total animals: 3 to 7 or 3/7 or 3:7 There are three cats to all the animals. Dogs to total animals: 4 to 7 or 4/7 or 4:7 There are four cats to all the animals.
What is 26 × 43 - 12=
Answer:
1106
Step-by-step explanation:
PEMDAS [the order of operations]
M[ultiplication] comes before S[ubtraction], so we should multiply first:
26 × 43 = 1118
Now, we can subtract:
1118 - 12 = 1106
you can write this equation as:
(26 × 43) - 12
if that makes more sense to you
hope this helps!! :)
Solve the system of equations.
2y+7x=−5
5y−7x=12
We can solve this by substitution method.
Look at the second equation. If we rearrange to find 7x, we can substitute in the value into the first equation.
[tex]5y-7x=12[/tex]
[tex]5y-7x-12=0[/tex]
[tex]5y-12=7x[/tex]
Therefore, [tex]7x=5y-12[/tex]
Now replace the 7x in the first equation with 5y - 12:
[tex]2y+7x=-5[/tex] (substitute in 7x = 5y - 12)
[tex]2y+(5y-12)=-5[/tex]
[tex]7y-12=-5[/tex]
[tex]7y=7[/tex]
[tex]y=1[/tex]
Now that we know y, we can find x by substituting in y = 1 into any equation we want. I will use the equation: 7x = 5y - 12
[tex]7x=5y-12[/tex] (substitute in y = 1)
[tex]7x=5(1) -12[/tex]
[tex]5x=5-12[/tex]
[tex]7x=-7[/tex]
[tex]x=-1[/tex]
__________________________________________________________
Answer:
[tex]y=1\\x=-1[/tex]
BEEN STUCK FOR A WHILE PLEASE HELP!! Find the perimeter and area for the triangle. Be sure to write the formula, and use correct measure.
Answer:
Area = 77ft²
Perimeter = 44 9/20 feets feets
Step-by-step explanation:
Area of a triangle = 1/2 * base * height
Base = 19 1/4 feets = 77/4 feets
Height = 8 feets
Area = 1/2 * 77/4 * 8
Area = (77 * 8) / 8
Area = 77 feet²
Perimeter of a triangle :
Sum of the sides
Perimeter = a + b + c
Perimeter = 19 1/4 + 10 + 15 1/5
Perimeter = 44 + (1/4 + 1/5)
Perimeter = 44 9/20 feets
if emma had 3/9 cookie's and sophia had 9/8 how much wood that be in all
what is a set of ordered pairs of real numbers ?
Answer:
order pair of real number is (2,3) is given by the first number 2 and the second number 3 Example (a,b).
A cooler is in the shape of a right rectangular prism. If the cooler is 3 1/2 feet long, 2 5/6 feet wide, and 1 foot deep, what is the volume of the cooler ?
0.002191 in scientific notation
Answer:
2.191 · [tex]10^{-3}[/tex]
Step-by-step explanation:
0.002191
2.191 · [tex]10^{-3}[/tex]
The diameter of a cylindrical construction pipe is 6ft. If the pipe is 32 long, what is its volume?
Use the value 3.14 for pie , and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
Answer:
[tex] V_{pipe} \approx 904 \: {ft}^{3} [/tex]
Step-by-step explanation:
Diameter of the pipe = 6 ft
Therefore, radius (r) = 6/2 = 3 ft
Height of pipe (h) = 32 ft
Since, pipe is cylindrical in shape.
[tex] \therefore \: V_{pipe} =\pi {r}^{2} h \\ \\ \therefore \: V_{pipe} =3.14 {(3)}^{2} (32)\\ \\ \therefore \: V_{pipe} =3.14 {(3)}^{2} (32) \\ \\ \therefore \: V_{pipe} = 904.32 \\ \\ \therefore \: V_{pipe} \approx 904 \: {ft}^{3} [/tex]
Hence, the volume of pipe in nearest whole number is 904 cubic feet.
fast brainleist on line and 40
Answer:
1/40
Step-by-step explanation:
what is the value of x in the equation 3.5x = 105
Answer:
x=30
HOPE THIS HELPS
- Todo ❤️
Step-by-step explanation:
105/3.5=30