The standard deviation for the number of times an odd number is rolled is 15.8
How to determine the standard deviation?The given parameters are:
Die = regular six-sided die
n = 1000
The probability of rolling an odd number is:
p = 1/2 = 0.5
The standard deviation is then calculated as;
[tex]\sigma = \sqrt{np(1 - p)[/tex]
This gives
[tex]\sigma = \sqrt{1000 * 0.5 * (1 - 0.5)[/tex]
Evaluate the products
[tex]\sigma = \sqrt{250[/tex]
Evaluate the root
[tex]\sigma = 15.8[/tex]
Hence, the standard deviation is 15.8
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Can someone please assist me with this problem
The category in the pie chart that was chosen by 1/8 of those that were surveyed is documentary.
How to illustrate the pie chart?From the pie chart, it can be seen that comedy and drama have the highest fraction as they have 1/4 each.
Therefore, the percentage of those who choose comedy or drama will be:
= (1/4 + 1/4) × 100
= 2/4 × 100
= 50%
Lastly, if 24% chose news, the others that choose others will be:
= 1/3 × 24
= 8%
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tommy starts walking from school to home at the same time that his dad starts walking home to school the both depart at 300pm tommy is walking at a speed of 1.35meters pr second and his dad is walking at a speed of 1.65 meters per second. the distance between home and school is 720 meters at what time wil they meet
Tommy and his father will meet after 2400 seconds or 40 minutes. So they will meet at 3:40 pm.
What is speed?Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance.
Given that:-
Tommy starts walking from school to home at the same time that his dad starts walking home to school they both depart at 300pm Tommy is walking at a speed of 1.35meters per second and his dad is walking at a speed of 1.65 meters per second. the distance between home and school is 720 meters at what time will they meetThe time will be calculated by using the relative speed concept.
Relative speed = Speed of father - Speed of Tommy
Relative speed = 1.65 - 1.35
Relative speed = 0.3 meter per second
Relative speed = Distance / Time
0.3 = 720 / Time
Time = 720 / 0.3
Time = 2400 seconds = 2400/ 60 = 40 minutes
We know that both departed at 3 pm they will meet at 3:40 pm.
Therefore Tommy and his father will meet after 2400 seconds or 40 minutes. So they will meet at 3:40 pm.
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Answer:
They will meet at 3:04 p.m
Step-by-step explanation:
Since they are walking toward each other, that means we should add their speed together:
speed = 1.35 m/s + 1.65 m/s
= 3 m/s
Now that we have found the speed, we can calculate the time:
time = 720 meters / 3 m/s
= 240 seconds
= 4 minutes ( 240 seconds is 4 minutes)
Each side of a hexagon is 10 inches longer than the previous side. What is the length
of the shortest side of this hexagon if its perimeter is 401 inches?
Answer:
The length of the shortest side of the pentagon would be:
40.2
Question 12 of 21
What is the domain of the exponential function shown below?
f(x) = 5.3x
Answer: All real numbers
Step-by-step explanation:
I assume you meant [tex]y=5.3^x[/tex].
In this case, the domain is the set of real numbers, as is with most standard exponential functions.
Find the midpoint of CD.
M = (¹2
X1+X2 Y1+Y2
Y₁+Y2)
2 1
C = (10,-1) and D = (-6,3)
([? ],[ ])
Answer:
Step-by-step explanation:
C=(10,-1)
D=(-6,3)
[tex]mid~point~x=\frac{10+(-6)}{2} =\frac{10-6}{2} =\frac{4}{2} =2\\y=\frac{-1+3}{2} =\frac{2}{2} =1[/tex]
mid point=(2,1)
The midpoint of line segment CD is M = (2, 1).
We have,
To find the midpoint of the line segment CD, we can use the midpoint formula:
M = ((X₁ + X₂)/2, (Y₁ + Y₂)/2)
Given C = (10, -1) and D = (-6, 3), we can substitute the values into the formula:
M = ((10 + (-6))/2, (-1 + 3)/2)
= (4/2, 2/2)
= (2, 1)
Therefore,
The midpoint of line segment CD is M = (2, 1).
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A principal of $5500 is invested in an account paying an annual rate of 7%. Find the amount in the account after 4 years if the account is compounded semiannually, quarterly, and monthly.
Answer:
Formulae is Future value, see in picture I've done example 1 for u.
The scale of a map says that 4 çm represents 5 km.
What distance on the map (in centimeters) represents an actual distance of 4
kilometers?
Answer:
3.2 km
Step-by-step explanation:
4cm÷5km=0.8 per cm to km
4km×0.8 km=3.2 km represents
Answer:
3.2 km
Step-by-step explanation:
[tex]\frac{4}{5} =\frac{x}{4}[/tex]
[tex]x=\frac{(4)(4)}{5} =\frac{16}{5} =3.2[/tex]
Hope this helps
What number am I? If you divide me by 8, the quotient is 3.
Answer:
24
Step-by-step explanation:
[tex]8 * \frac{x}{8}=3 * 8[/tex]
x = 24
Answer:
24
Step-by-step explanation:
Let the number we are looking for = [tex]x[/tex].
∴ According to the question:
[tex]x[/tex] ÷ 8 = 3
• Multiply both sides by 8:
[tex]x[/tex] = 8 x 3
[tex]x[/tex] = 24
► Math and Gymnastics
In a gymnastics competition, gymnasts compete
in events such as the balance beam, parallel bars,
vault, and floor exercise,
Leigh earned the following scores from the judges
for her balance beam routine.
9.30 9.20
Follow these steps to find Leigh's final score.
1. Order the scores from least to greatest.
9.20
9.30
9.20
9.00
Answer:
9.00,9.20,9.30
Step-by-step explanation:
Evaluate 2 p-q when p=17 and q=3.
Final answer:
The value of the expression is 31.
Step-by-step explanation:
Substitution is a process of putting the values of variable in the expression.
Given: p=17 and q=3
To find: value of 2p-q
We will substitute the values and simplify.
Putting the values of variables in the expression as
2p-q = 2x17-3 =34-3 = 31
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[tex]\large\text{Hey there!}[/tex]
[tex]\large\textbf{What does your current question look like?}[/tex]
[tex]\mathsf{2p - q}[/tex]
[tex]\large\textbf{How will we make the question easier to solve?}[/tex]
[tex]\mathsf{2p - q}[/tex]
[tex]\mathsf{= 2(17) - 3}[/tex]
[tex]\mathsf{= 34 - 3}[/tex]
[tex]\mathsf{= 31}[/tex]
[tex]\large\textbf{What is the \boxed{overall} answer?}[/tex]
[tex]\large\boxed{\mathsf{17}}\large\checkmark[/tex]
[tex]\large\text{Good luck on your assignment \& enjoy your day!}[/tex]
The graph for the first equation of a ssystem is shown in orange the second equation is 3y+30= 6x
The solution to the system of equations is: (1, -8).
How to Find the Solution to a System of Equations?The solution is the coordinate of the point where both lines of the equations meet.
Second equation: 3y + 30 = 6x, rewrote in slope-intercept form:
3y = 6x - 30
y = 6x/3 - 30/3
y = 2x - 10 --> eqn. 1
Find the slope (m) and y-intercept (b) of the first graphed equation:
Slope (m) = change in y/change in x = rise/run = -4/2 = -2
The line intersects the y-axis at y = -6, so, the y-intercept, b = -6.
The first equation would be: y = -2x - 6 ---> eqn. 2
Subtract eqn. 2 from eqn. 1 to eliminate x
y = 2x - 10 --> eqn. 1
y = -2x - 6 ---> eqn. 2
2y = 0 - 16
2y = -16
y = -16/2
y = -8
Substitute y = -8 into eqn. 1 to find x:
-8 = 2x - 10
-8 + 10 = 2x
2 = 2x
2/2 = x
1 = x
x = 1
The solution is therefore: (1, -8).
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Which choice represents the simplified exponential expression? (9^7)^4
Answer:
[tex]9^{28}[/tex]
Step-by-step explanation:
using the rule of exponents
[tex](a^{m}) ^{n}[/tex] = [tex]a^{mn}[/tex] , then
[tex](9^7)^{4}[/tex] = [tex]9^{7(4)}[/tex] = [tex]9^{28}[/tex]
Giving Brainliest to the first person who can accurately answer and explain these questions.
Answer:
It's A 48,736
Step-by-step explanation:
Answer:
48,856.11
Step-by-step explanation:
Compound interest is generally written as: [tex]A=P(1+\frac{r}{n})^{nt}[/tex] where P = principle amount, r = interest rate, n=compound periods, t = time. This is compounded continuously which can be defined as: [tex]A=Pe^{rt}[/tex]. If you're confused what e is, one of the definitions, is [tex]\lim_{x\to\infty}{(1+\frac{1}{x})^x[/tex]. This is essentially the very definition of continuous compound. It's when the amount of compounds (n in the equation) goes towards infinity. So using the previous defined equation simply plug the values into the equation.
[tex]A=(40000)e^{0.025*8}[/tex]
Multiply inside the exponent
[tex]A=(40000)*e^{0.2}[/tex]
raise e to the power of 0.2
[tex]A\approx40000*1.221[/tex]
Multiply
[tex]A=48,856.11[/tex]
What is the height of a cylinder with a volume of 384 pi cubic inches and a radius of 8 inches? Round to the nearest tenth of an inch.
inches
Answer: 1.9 inches
Step-by-step explanation:
- the equation to find the volume of a cylinder is V = π r^2 h
- so we can just change this equation around to H = V / π r^2
- so H = 384/ π 8^2 = 1.91 or 1.9
hope this helps :)
Use the vertical line test to determine whether or not the graph is a graph in which y is a function of x.
The given graph is a function.
The correct option is (B).
What is vertical line test?The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function by visually examining the number of intersections of the curve with vertical lines.
As we draw the vertical line then for one input x there is one output.
Hence, the given graph is function.
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A formula for the normal systolic blood pressure for a man age A , measured in mmHg, is given as P=0.006A2−0.02A+120 . Find the age of a man whose normal blood pressure measures 128 mmHg.
The age of the man whose normal pressure measures 128 mmHg is approximately 38 years.
How do we determine the age of the man using a quadratic equation?The quadratic formula can be used to determine the age of a man whose normal blood pressure measures 128 mmHg. This can be expressed mathematically as:
[tex]\mathbf{ \dfrac{-b \pm\sqrt{b^2 - 4ac}}{2a}}[/tex]
From the given equation:
P = 0.006A² - 0.02A + 120
where;
P = 128128 = 0.006A² - 0.02A + 120
= 0.006A² - 0.02A + 120 - 128
= 0.006A² - 0.02A - 8
where:
a = 0.006 , b = - 0.02, and c = -8[tex]\mathbf{ \dfrac{-(-0.02) \pm\sqrt{(-0.02)^2 - 4(0.006)(-8)}}{2(0.006)}}[/tex]
[tex]\mathbf{ = \dfrac{(0.02) \pm 0.43863}{0.012}}[/tex]
= 38.2195 or -34.8862
Taking the positive integer value, the age of the man whose normal pressure measures 128 mmHg is approximately 38 years.
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Let sets A and B be defined as follows.
A= {c,d,e,f}
B is the set of odd numbers greater than 5 and less than 23 (a) Find the cardinalities of A and B. n(A) = n(B)=
There are 4 elements in the set A and 8 elements in set B that is n(A) = 4 and n(B) = 8
Cardinality of a setThis is the total number of elements in a set. Given the following sets;
A = {c, d, e, f}
B = {odd numbers greater than 5 and less than 23}
B = {7,9,11,13, 15, 17, 19, 21}
Since there are 4 elements in the set A and 8 elements in set B hence n(A) = 4 and n(B) = 8
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System A
−10x−4y=0
−2x+7y=8
System B
−10x−4y=8
−2x+7y=0
1) How can we get System B from System A?
(Choice C, Checked, Correct)
CORRECT (SELECTED)
Swap only the right-hand sides of both equations
2) Based on the previous answer, are the systems equivalent? In other words, do they have the same solution?
CORRECT (SELECTED)
No
For the given systems we have:
1) Swap the right sides of both equations in system A.
2) No, the systems are not equivalent systems.
How can we get System B from System A?
The two systems are:
A:
-10x - 4y = 0
-2x + 7y = 8
B:
-10x - 4y = 8
-2x + 7y = 0
Notice that the only different thing between the systems is that the right sides are inverted. So, if we invert the right side of A, we will get system B.
2) Are the systems equivalent?
No, the systems are not equivalent because to go from system A to system B we only modified the right side of system A, the systems would be equivalent only if modifying both sides of A gave system B, but this is not the case.
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If....................
Answer:
C - 22
Step-by-step explanation:
Put in '3 ' for 'x' in both of the equations....then multiply the results together
f(3) = 3 (3)^2 - 5 = 22
g(3) = -1
22 * -1 = -22
To solve for f(3)g(3):
* We know fg(x) means we need to multiply f with g replacing all x's with the x-value given
Replace all x's with 3Solve for f(3)g(3)[tex](3(3)^{2}-5)(-2(3)+5)\\(3(9)-5)(-6+5)\\22 * -1\\-22[/tex]-22 is the answer
Hope it helps!
HELP
17x - 32y + 2.78y - 11,345x + 1/5x
Answer:
i think this is the answers
Step-by-step explanation:
-13.78xy
Question 4 of 5
Select the correct answer.
On a number line, point A is at -3.4 and point C is at 0.6. Point C divides AB in a ratio such that AC to CB is 4:7. What is the length of
AB?
O
AB = 4.2 units
AB = 11 units
AB= 2.8 units
AB= 7.6 units
Answer:
AB = 11 units
Step-by-step explanation:
a given ratio also tells us how many equally sized units there are in the whole (in this case the line).
the ratio 4:7 tells us therefore, that from the whole line 7 ratii units (of 7+4 = 11 ratio units) are on the side of CB.
4 ratio units (of the 11 ratio units) are on the side of AC.
AC is the distance between A and C.
that is
0.6 - -3.4 = 0.6 + 3.4 = 4 line units
aha ! the distance is 4 units on the number line, and the ratio tells us that AC is 4 ratio units.
so, line unit and ratio units are 1:1 the same.
that means that CB with 7 ratio units is then also 7 line units long.
so, the whole line AB is then 4 + 7 = 11 line units long.
Answer:
11 units
Step-by-step explanation:
correct on plato
Find an equation of each line given one point and the slope : (4, 8); slope 8
Step-by-step explanation:
in such a case the easiest approach might be using the point-slope form of a line equation :
y - y1 = m(x - x1)
with m being the slope, and (x1, y1) being a point on the line.
so, in our case that would be
y - 8 = 8(x - 4)
simplified this would be
y - 8 = 8x - 32
y = 8x - 24
FYI - this would be then the slope-intercept form (-24 would be the intercept point on the y-axis).
A box contains 240 lumps of sugar. Fie lumps are fitted across the box and the were three layers. How many lumps are fitted along the box?
Answer:
v240
Step-by-step explanation:
how to convert each rate to a unit rate
Answer:
If you have a rate, such as price per some number of items, and the quantity in the denominator is not 1, you can calculate unit rate or price per unit by completing the division operation: numerator divided by denominator.
Step-by-step explanation:
Find the value of 5y-3 given that -3y-8=7. Simplify your answer as much as possible. Find the value of 5y - 3 given that -3y - 8 = 7 . Simplify your answer as much as possible .
Answer:
-28
Step-by-step explanation:
Find 5y-3 , given -3y - 8 = 7.
First, we will multiply -3y - 8 = 7 by [tex]-\frac{5}{3}[/tex] to get 5y first.
[tex]-\frac{5}{3} (-3y-8)=-\frac{5}{3} (7)\\5y+\frac{40}{3} =-\frac{35}{3} \\[/tex]
Now we will get the constant on the left side of the equation to 3.
[tex]5y+\frac{40}{3} -\frac{40}{3} =-\frac{35}{3} -\frac{40}{3} \\5y=-25\\5y-3=-25-3\\5y-3=-28[/tex]
The difference of a number and 8 is the same as 38 less the number. Find the number.
Use the demoivres theorem
The value of the given complex number is -1
De'moivres theorem
Given the polar form of a complex number expressed as:
[tex](cos\theta + isin\theta)^n\\[/tex]
This can also be expressed according to the de moivre's theorem as;
[tex]=(cos\theta + isin\theta)^n\\\\=(cosn\theta+isinn\theta)[/tex]
Given the expression below;
[tex](cos\frac{\pi}{6} + isin\frac{\pi}{6} )^{18}\\(cos18\cdot\frac{\pi}{6} + isin18\cdot\frac{\pi}{6} )\\(cos3\pi + isin3\pi)\\=-1[/tex]
Hence the value of the given complex number is -1
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Solven/6 =24/36, for the unknown quantity,n.
n=192
n=144
n=108
n=4
Answer:
n = 4
Step-by-step explanation:
[tex]\frac{n}{6} =\frac{24}{36}[/tex]
cross multiply
24*6 = 144
n * 36 = 36n
144 = 36n
divide both sides by 36
n = 4
answer is D
n=4
simplify the fraction on the right to get 4/6
n/6 = 4/6
since denominators are same, you can cancel those
therefore, your answer will be n=4
Use a truth table to decide whether each argument is valid or invalid If a person is on this reality show, they must be self-absorbed. Laura is notself-absorbed. Therefore, Laura cannot be on this reality show.
The arguments are valid therefore F F →T
What is a truth table?A truth table is a mathematical table which shows the truth values for a given set of arguments and tells if the argument is valid or invalid.
Analysis:
Argument 1( P)= if a person is on this reality show(true) T
Argument 2(Q) = the person is self absorbed true(T)
Laura is not self absorbed = False(≈Q)
Laura wont be on the reality show = False(≈P)
So she can only be on the reality show if she is self absorbed else she cannot.
so F F → T
Which means that the argument is valid.
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Type the correct answer in each box. Use numerals instead of words.
What is the equation of the quadratic function shown in the graph?
The equation of the quadratic function shown in the graph y - 8 = -2(x + 1)².
How to illustrate the graph?The vertex of this parabola is (-1, 8). It opens downward, so the x² term has a negative coefficient. The zeros are (-3, 0) and (1, 0), and the y-intercept is (0, 7).
Through the vertex form of the equation of a parabola we get:
y - (8) = a(x - (-1)) + 7, or.y - 8 = a(x + 1)².
Find coefficient a by substituting the coordinates (-3, 0) in this equation:
0 - 8 = a(-3 + 1)^2, or
-8 = a(-2)² or a = -2
The desired equation is y - 8 = -2(x + 1)^2
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