Answer:
6
Step-by-step explanation:
8 cube root is 2
there are 3 different lengths
3x2=6
Provide an appropriate response.
Find the area of the shaded region. The graph depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test).
Answer:
A) 0.7938---------------------------
Givenμ = 100, σ = 15Find the area between x = 85 and x = 125.
Find z-scores for each endz = (x - μ)/σz₁ = (85 - 100)/15 = - 15/15 = - 1z₂ = (125 - 100)/15 = 25/15 ≈ 1.67Find the corresponding probabilities from z-score tablez₁ = 0.1587z₂ = 0.9525Find the differencez₂ - z₁ = 0.9525 - 0.1587 = 0.7938The matching choice is A
Answer:
0.7938
Step-by-step explanation:
The given graph is a normal distribution curve.
If a continuous random variable X is normally distributed with mean μ and variance σ²:
[tex]\boxed{X \sim \textsf{N}(\mu,\sigma^2)}[/tex]
Given:
mean μ = 100standard deviation σ = 15[tex]\text{If \; $X \sim \textsf{N}(100,15^2)$,\;\;find\;\;P$(85\leq X\leq 125)$\;\;to\;3\;s.f.}[/tex]
Therefore, we need to find the area to the left of x = 125 and subtract the area to the left of x = 85.
Method 1
Using a calculator:
[tex]\begin{aligned}\implies \text{P}(85\leq X\leq 125)&= \text{P}(X\leq 125)-\text{P}(X < 85)\\&=0.9522096477-0.1586552539 \\&=0.7935543938\\&\approx0.7938\end{aligned}[/tex]
Method 2
Converting to the z-distribution.
[tex]\boxed{\text{If\;\;$X \sim$N$(\mu,\sigma^2)$\;\;then\;\;$\dfrac{X-\mu}{\sigma}=Z$, \quad where $Z \sim$N$(0,1)$}}[/tex]
[tex]x=85 \implies Z_1=\dfrac{85-100}{15}=-1[/tex]
[tex]x=125 \implies Z_2=\dfrac{125-100}{15}=1.67[/tex]
Using the z-tables to find the corresponding probabilities (see attachments).
[tex]\begin{aligned}\implies \text{P}(-1\leq Z\leq 1.67)&= \text{P}(Z\leq 1.67)-\text{P}(Z < -1)\\&=0.9525-0.1587\\&=0.7938\end{aligned}[/tex]
A lamina occupies the region inside the circle x2 + y2 = 18y but outside the circle x2 + y2 = 81. Find the center of mass if the density at any point is inversely proportional to its distance from the origin.
If the density at any place is inversely proportional to its distance from the origin, locate the center of mass as (0,4.5).
Given that,
The area inside the circle where x² + y² = 18y and outside the circle where x² + y² = 81 is occupied by a lamina.
We have to find if the density at any place is inversely proportional to its distance from the origin, locate the center of mass.
We know that,
Take the equation
x² + y² = 18y
x² + y² - 18y=0
Adding and subtracting 9².
x² + y² - 18y+ 9²-9²=0
x² + y² - 18y+ 9²=9²
x² + (y-9)²=9²
Which is a circle of radius 9 and center (0,9), And now the second equation
Now,
x²+y²=81
Which is a circle with radius 9 and center (0,0).
We can plot the curves in the picture we can see.
The density will be evenly distributed around the lines x=0 and y=4.5, which are the lines of symmetry, in a more complicated scenario where we would need to utilize integration to identify the Center of Mass.
Therefore, if the density at any place is inversely proportional to its distance from the origin, locate the center of mass as (0,4.5).
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using the gcf you found in part b, rewrite 56+96 as two factors. one factor is the gcf and the other is the sum of two numbers that do not have a common factor. show your work. (4 points)
If the one factor is the gcf and the other is the sum of two numbers that do not have a common factor, then the expression will be 8(7 + 12)
The expression is given by
56 + 96
First we have to find the GCF of the numbers
Prime factorization
56 = 2×2×2×7
96 = 2×2×2×2×2×3
The GCF(56, 96) = 8
Write the expression using the GCF
56 + 96 = 8(7) + 8(12)
Here we have to apply the distributive property
AB + AC = A(B + C)
Then,
8(7) + 8(12) = 8 (7 + 12)
Hence, if the one factor is the gcf and the other is the sum of two numbers that do not have a common factor, then the expression will be 8(7 + 12)
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there are 10 marbles in the bag 2 yellow 3 pink and 5 blue what is the probability of drawing two pink ones if the first marble was not put back before the 2nd drawing
The probability of drawing two pink ones if the first marble was not put back before the 2nd drawing is 2/9.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
We are given that there are 10 marbles in the bag 2 yellow 3 pink and 5 blue.
First, we need to find the probability of drawing a blue marble on the first draw.
Since there are 5 blue marbles and 10 total, then the probability is;
5⁄10, or 1/2.
Now, we no longer have that blue marble, there are 4 blue marbles and 9 total.
The chances of drawing a blue marble are; 4/9.
Therefore, the chance that both marbles drawn are blue is the chance that the first one is blue times the chance that the second one is blue.
1/2 x 4/9 = 4/18 = 2/9
Hence, the probability of drawing two pink ones if the first marble was not put back before the 2nd drawing is 2/9.
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T/F study unit 7.1 the dynamic nature of memory match each term to the corresponding process. drag each item on the left to its matching item on the right. retrieval storage memory encoding
The matching terms and processes are;
1. The nervous system's ability to acquire, retain, and retrieve information- memory
2. Remembering stored information- retrieval
3. Processing information for storage- encoding
4. Retention of information- storage
Given,
The nervous system's capacity for information acquisition, storage, and retrieval is known as memory. Information is processed for storage by encoding, whereas information is remembered from storage through retrieval. Information is retained through storage.
Memory is the process of storing and recalling previously acquired information. The act of storing involves adding new information to the memory, which the brain alters for improved storage. It is easier for the brain to access and bring into conscious mind information that has been encoded.
Information is stored so that it will last throughout time. Modern memory psychology distinguishes between two basic types of memory storage: short-term memory and long-term memory.
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Given question is incomplete. Completed question is here;
Match the terms with their corresponding processes.
a. memory
b. encoding
c. retrieval
d. storage
1. the nervous system's ability to acquire, retain, and retrieve information
2. remembering stored information
3. processing information for storage
4. retention of information
What is the ratio of the number of days in the week that do not begin with the letter "T" to the number of days in the week that do begin with the letter "T"? (1 point)
a
7 over 2
b
2:5
c
2 to 7
d
5 over 2
Answer:
i believe it is b)
the no. of days beginning with T (2)
the no. of days not starting with T (5)
What are the different types of cubicles?.
5 types of cubical are: dedicated, Private office, L-shaped, circular, High walled cubicles
Dedicated Cubicles: A professional cubicle is typically mid-sized and can combine various cubicle designs to improve output across a wide range of vocations.Cubicles for private offices: For some people, private office cubicles are the best option. These types of cubicles are typically designed for executive cubicles rather than the plainer designs used for the majority of workers employing drywall and flat materials."L" shaped: These sectional or "L" shaped cubicles can greatly influence the number of diverse looks your cubicle collection can take on. Of course, this view is superior to cubicle stations with three or four sides everywhere.Circular Cubicles: A circular cubicle is another novel feature of the workplace. These can introduce a fresher perspective that is fashionable, a sight that is not typically present in the majority of offices today.High-Walled Cubicles: The majority of workstations kinds can be categorized according to the heights of their panels and walls, which directly affects the amount of employee privacy your business will provide.
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What is the solution to the system of equations y =- 5x 3?.
The solution of equation is y = -15, x = 1 .The equation used to obtain the value of y and x is y = -15x.
What is Equations ?
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.
We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign. It will be regarded as a phrase.
The given equation is: y= -5x3
or y= -15x
or y\x=-15
Divide with 1 both side
y/x = -15/1
Then y = -15 , x = 1
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Answer: (5,28)
Step-by-step explanation:
(10 points) suppose two fair dice are rolled. find each probability of getting (a) a sum of 5 or sum of 7 (b) the first die shows a 3 or the sum of the result is 6 or 8
The required probability of a sum of 5 or sum of 7 and the first die shows a 3 or the sum of the result is 6 or 8 are 5/18 and 1/18 receptively.
What is probability?Probability is just the way that logical something is to occur. Whenever we're uncertain about the result of an occasion, we can discuss the probabilities of specific results — how likely they are. The investigation of occasions administered by likelihood is called statistics.
According to given data:Two fair dice are thrown then the number of possible way is 6×6 = 36
a) a sum of 5 or sum of 7 :-
The total possible way for dice occurs sum 5 or sum 7 is (1, 4), (2, 3), (3, 2), (4, 1), (1, 6), (2, 4), (3, 4), (4, 3), (5, 2), (6, 1).
So, the total number possible way for dice occurs sum 5 or sum 7 = 10.
Probability = 10/36 = 5/18
Hence, the probability is 5/18.
b) The first dice shows 3 or the sum of the result is 6 or 8 :-
As, first dice shows 3 we have fixed 3 in first dice or results sum is 6 or 8 then second dice possibilities only consist two number either 3 or 5,
So, total possible ways for first dice shows 3 or sum of result is 6 or 8 is (3, 3), (3, 5).
There are only two ways,
Therefore, probability = 2/36 = 1/18
Hence, the probability is 1/18.
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I will give brainlest
Answer:
[tex]\huge\boxed{\sf r = 1/4}[/tex]
Step-by-step explanation:
Given that,y = rx -------------------(1)
From the table,
x = 8 when y = 2
Put in the above equation.
2 = r(8)
Divide 8 to both sides
2/8 = r
r = 2/8
r = 1/4
[tex]\rule[225]{225}{2}[/tex]
a city has 9 coffee shops. 3 starbucks, 2 caribou coffees, and 4 crazy mocho coffee. if a person selects on shop at random to buy a cup of coffee, find the probability that it is either a starbucks or crazy mocho coffee.
Answer:
7/9
Step-by-step explanation:
total: 3+2+4
starbucks or crazy mocho: 3+4
(3+4)/(3+2+4)=7/9
What is the sum of all positive integers that have twice as many digits when written in base $2$ as they have when written in base $3$? Express your answer in base $10$.
2 in base 10 =10 in base 2 = 2 in base 3
8 in base 10 =1000 in base 2 = 22 in base 3.
2 + 8 = 10 the sum of positive integers.
The least common multiple of $1!+2!$, $2!+3!$, $3!+4!$, $4!+5!$, $5!+6!$, $6!+7!$, $7!+8!$, and $8!+9!$ can be expressed in the form $a\cdot b!$, where $a$ and $b$ are integers and $b$ is as large as possible. What is $a+b$?
LCM[1!+2!, 2!+3!, 3!+4!, 4!+5!, 5!+6!, 6!+7!, 7!+8!, 8!+9!] =3,628,800. This can be written as:
1. 10! = 1 + 10 = 11, which is a + b
Sum of all positive integers having twice as many digits when written in base $2$ as they have when written is base $3$ is 10.
This is because the only two integers which fits the constraint are 2 and 8,
2 in base 10 =10 in base 2 = 2 in base 3
8 in base 10 =1000 in base 2 = 22 in base 3.
The result of the expression $a+b$ is 11
This is because the LCM of [1!+2!, 2!+3!, 3!+4!, 4!+5!, 5!+6!, 6!+7!, 7!+8!, 8!+9!] =3,628,800
Which can be written as : 1. 10! = 1 + 10 = 11
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OThe sum of two numbers is 38. When 8
is added to twice one of the numbers, the
result is 5 times the other number. Find the
two numbers.
The two numbers are 12 and 26.
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
Let x and y be the 2 numbers
x+y=38........(1)
8+2x=5y.......(2)
(1) => x=38-y
8+2(38-y)=5y
8+76-2y=5y
84=5y+2y=7y
y=84/7 = 12
when y=12, x=38-y = 38 - 12 = 26
So, the two numbers are 12 and 26.
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What kind of line is used when the inequality symbol is ≥ or ≤?.
The kind of line is used when the inequality symbol is ≥ or ≤ is solid line
If the original inequality is ≤ or ≥, the boundary line is drawn as a solid line, since the points on the line will make the original inequality true.
The kind of line is used when the inequality symbol is ≥ or ≤ is solid line
But in case of < or > symbol, the line used is dotted line.
A solution of an inequality is a number which when substituted for the variable makes the inequality a true statement.
Therefore, The kind of line is used when the inequality symbol is ≥ or ≤ is solid line
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What is the angle of each side of a circle?.
The central angle states the property of the center of the circle, So It is called the central angle.
What is a Central Angle?
The central angle is the angle that a circle's arc occupies in its center. The arms of the central angle are formed by the radius vectors. In other words, it's an angle whose vertex is the center of a circle and whose arms, which have the circle's two radii as their arms, cross at two separate positions. These two points make an arc when they are combined. The angle that this arc at the circle's center subtends is known as the central angle.
An arc's angle at the circle's center is twice as large as its angle at any other point along the circle's circumference. the angle subtended by the arc in the opposite segment of the circle is twice as large as the angle at the center of the circle.
Hence,
The central angle states the property of the center of the circle, So It is called the central angle.
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the width of a rectangular patio is increased by 10 % 10%. its length is increased by 20 % 20%. by what percentage has its area increased?
Answer: 32%
Step-by-step explanation:
Let's set the original dimensions of the rectangular patio as:
width = wlength = lThat'll set the original area(a) of the patio as a = w · l.
The new dimensions of the patio can be calculated as:
width = w + 0.1w = 1.1wlength = l + 0.2l = 1.2lThe new area can then be calculated as 1.1w · 1.2l = 1.32 · w · l = 1.32a
Using the two areas, the percent increase can be calculated as:
[tex]\frac{1.32a-a}{a}*100 =\frac{1.32-1}{1}*100 =0.32*100=32[/tex]
How will the solution of the system Y 2x two thirds and Y 2x one third change if the inequality sign on both inequalities is reversed to?.
The system of inequalities did not have any solution, but after reversing the sign we will get a solution of the system of inequalities.
The inequalities are : y > 2x + 2/3 and y < 2x + 1/3
There is no intersection and no solution to the system since the region above the line y = 2x + 2/3 and the region below the line y = 2x + 1/3, respectively, are the solutions to the inequality y > 2x + 2/3 and y <2x + 1/3, respectively.
Now when the signs are changed we get:
y < 2x + 2/3 and y > 2x + 1/3
The region below the line y = 2x + 2/3 is the solution of the inequality
y= 2x + 2/3, and the region above the line y = 2x + 1/3 is the solution of the inequality y > 2x + 1/3. This implies that the area between the two lines is where the system's solution lies.
Disclaimer: The complete question is :
How will the solution of the system y>2x+2/3 and y<2x+1/3 change if the inequality sign on both inequalities is reversed to y<2x+2/3 and y>2x+1/3?
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Answer:
There is no solution to the system in its original form. There are no points in common. If the signs are reversed, the system has an intersection with an infinite number of solutions.
Step-by-step explanation:
Sample answer
Type the correct answer in the box. Use numerals instead of words. A regular pentagonal prism has a volume of 2,850 cubic millimeters. What is the height of the prism? a regular pentagonal prism with height labeled h. The pentagonal base has side edge labeled 12 millimeters. Apothem from center to a base edge is labeled 5 millimeters. The height of the prism is millimeters.
The required height of given regular pentagonal prism is 19 millimeters.
What is the volume of regular pentagonal prism ?We work out the volume of a pentagonal crystal utilizing the recipe is V = 5/2abh where this equation is additionally perceived as V = [1/2 × 5 × base length × apothem] × level of the crystal. The qualities are placed in the recipe and compose the response so got in cubic units.
According to question:We have,
volume of regular pentagonal prism = 2850 cubic millimeters.The pentagonal base has side edge labeled 12 millimeters.Apothem from center to a base edge is labeled 5 millimetersThen
V = 5/2abh
2850 =( 5×12×h)×5/2
h = 19 millimeters
Thus, required height of the pentagonal prism is 19 millimeters.
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Answer:
19 millimeters
Step-by-step explanation:
i took the test and got right hope this helps :)
Which expression can be used to show a roster of twenty-four players divided into four teams?.
A roster of twenty-four players divided into four teams can be represented by the expression 24/4.
Given
24 players total
(4) teams total.
This can be expression as = 24 / 4.
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use cross products to determine whether the ratios and form a proportion. do they form a proportion?
No , they do not form a proportion because 77 and 60 are not equal
Hence , not form proportion
Set up a proportion as 4/7 = 11/15
Cross multiply:
7×11
4×15
You should get 77 and 60 for the products. Since the products don't equal each other, they are not proportional.
complete question is
use cross products to determine whether the ratios 4/7 and 11/15 form a proportion. Do they form a proportion? Explain your steps and your conclusion
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Which equation represents the line that passes through (- 6 7 and (- 3 6 )?.
Answer:
y = -1/3 x + 5
Step-by-step explanation:
To write the equation, you need the slope and the y-intercept to write the equation in the slope intercept form. You did not state what form, so this is the form that I will use.
y = mx + b M is the slope and b is the y intercept.
The slope is the change in y over the change in x. For the two points we can find the change in y by using the numbers 6 and 7. We can find the change in x by using the numbers - and -6,
[tex]\frac{6-7}{-3 - -3}[/tex] = [tex]\frac{-1}{-3+6}[/tex] = [tex]\frac{-1}{3}[/tex] This is the slope.
To find the y intercept (b) we will use one point and the slope. It does not matter which point that you use. I am going to use the point (-3,6).
slope (m) = [tex]\frac{-1}{3}[/tex]
x = -3
y = 6 Plug these into the equation and solve for b.
y = mx + b
6 = ([tex]\frac{-1}{3}[/tex]) (-3) + b
6 = 1 + b Subtract 1 from both sides.
5 = b
y = [tex]\frac{-1}{3}[/tex]x + 5
how does the mitochondria aids the process of protein synthesis?
Mitochondria use proteins to break down sugars and produce cellular energy in the form of ATP.
The school cook ordered p packages of hot dog buns for the year-end picnic. Each package contains 8 buns. Write an expression that shows how many hot dog buns were ordered.
The school cook ordered p packages of hot dog buns for the year-end picnic. Each package contains 8 buns. Write an expression that shows how many hot dog buns were ordered.
order = 8p
For a continuous random variable x, the probability density function f(x) represents.
The probability density function f(x) represents the probability at a given value of x.
In a distribution, the notation f(x) is the equivalent to the probability of event x, that is:
[tex]f(x) = P(X = x)[/tex]
The area under the curve is given by the cumulative distribution, which is given by:
[tex]P(X\leq x) = \int\limits^x_0f(x)dx[/tex]
Thus it is not f(x).
And f(x) can also be the height of the relative frequency function, but not of the function itself.
Hence the answer is the probability density function f(x) represents the probability at a given value of x.
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I went into a store with a 70% off sign on the door. I found a pair of pants that were originally $49.99 for $30.00 I didn't think this was 70% off so I had to make sure. What were the real percentage off?
Answer:
The sale price is 39.99 % off
Step-by-step explanation:
To find the percentage off,
take 49.99 - 30.00 = 19.99
Then divide by 49.99
19.99/49.99
39.9879976
The sale price is 39.99 % off
2(x - 2) = -2
solve for x.
Answer:
x = 1
Step-by-step explanation:
2(x - 2)= -2
2x - 4 = -2
2x = 2
x = 1
Answer:
x = 1
Step-by-step explanation:
2(x - 2) = -2
Solve for x
Divide each side by 2
2/2(x - 2) = -2/2
x-2 = -1
Add 2 to each side
x - 2+2 = -1+2
x = 1
Please Help, I need to get a 100%
Answer:
C
Step-by-step explanation:
Denominator can't be 0
Therefore, [tex]x-7\neq 0[/tex]
Adding 7 to both sides gives [tex]x\neq 7[/tex]
Only C corresponds to our answer.
Is 15 a multiple or factor of 5?.
Answer:
Multiple
Step-by-step explanation:
A multiple of 5 is anything that it can multiply into. For example: 5, 10, 15, 20, 25 and so on.
A factor is a number that divides into your number and leaves no remainder. An example of this is 2 is a factor of 4. 15 is not a factor of 5 because it cannot divide evenly. The only factors of 5 are 1 and 5.
the histograms show the results of three simulations of a sampling distribution of a sample mean. for each simulation, 1,500 samples of size n were selected from the same population and the sample mean was recorded. the value of n was different for each of the three simulations.
The histograms show the results of three simulations of a sampling distribution of a sample mean. Arranging from the least value of n to the naximum value, the order is A, C, B.
A histogram is a bar graph-like representation of data that groups a range of classes into columns along the horizontal x-axis. The vertical y-axis represents the number count or percentage of occurrences in the data for each column. Columns can be used to visualized as patterns of data distributions.
Lesser the value of n larger the variablity.
Arranging from the least value of n to the naximum value, the order is A, C, B
Therefore, The histograms show the results of three simulations of a sampling distribution of a sample mean. Arranging from the least value of n to the naximum value, the order is A, C, B.
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A new car is purchased for 23700 dollars. The value of the car depreciates at 15% per year. If you wanted to know the value of the car after 10 years which function would give you that information?.
The value of the car after 10 years is 4668.9 dollars
What is depreciation?Depreciation is the reduction in the value of an asset or commodity over time and such valued reductions are reflected in the balance sheet at the year ended.
According to the given information:
Prize of the new car purchased P = 23700 dollars
the rate at which the value of a car depreciates R = 15% per year
Now, the value of the car after 10 years could be determined by the formula
Amount = P[tex](1-r)^{t}[/tex]
P = 23700 dollars R = 15% per year t = 10 years
Substituting all the values in the above formula:
Amount = [tex]23700(1-0.15)^{10}[/tex]
= [tex]23700(0.85)^{10}[/tex]
= 23700×0.197
= 4668.9 dollars
The value of the car after 10 years is 4668.9 dollars
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