If a standard deviation for binomial distribution n = 48 p = 3/5 . The standard deviation is 3.39.
What is the Standard deviation?Using this formula to determine or find the standard deviation for the binomial distribution
σ =√np(1−p)
Where:
n = 48
p = 3 / 5 or 0.6
σ = ?
Let plug in the formula so as to determine the standard deviation
σ =√ (48) (0.6) ( 1 - 0.6)
σ =√ (48) (0.6) (0.4)
σ =√ 11.52
σ = 3.39
Therefore we can conclude that 3.39 is the standard deviation.
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2. Zandile invests her Christmas bonus for R 875.00 in a bank that offers
interest rates of 9% p.a. compounded half-yearly. How much interest will she
have earned after 6 years? I want the interest
After 6 years, Zandile earns an interest of rupees 608.9 after investing her Christmas bonus for R 875.00 in a bank that offers interest rates of 9% p.a. compounded half-yearly.
What is interest?The simplest way to calculate interest is as a percentage of the principal. For instance, if you agreed to borrow $100 from a friend with 5% interest, the interest you would pay would only be 5% of $100: $100(0.05) = $5.
What is compound interest?Compound interest is when an amount receives interest on top of it each time interest is paid on the original amount. The principal (original) sum and the interest that has already accrued over the course of previous periods are used to calculate compound interest.
Here,
Principal amount= 875
Rate of interest= 9% pa
Compounding= half-yearly (2/year)
Time= 6 years
A = P(1 + r/n)ⁿᵇ
A=final amount
P=initial principal balance
r=interest rate
n=number of times interest applied per time period
b=number of time periods elapsed
A=875(1+9/6)⁶*²
A=₹1,483.90
Zandile invests her Christmas bonus of R 875.00 in a bank that offers interest rates of 9% per year compounded semi-annually, and after 6 years, she earns an interest of Rs 608.99.
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Which equation is the correct translation of the following statement?Four less than a number is nine.9 - x = 49 - 4 = xx - 4 = 94 - x = 9
Given
The statement,
Four less than a number is nine.
To find:
Which equation is the correct translation of the following statement?
Explanation:
Let x be the number.
Since four less than a number is nine.
Then,
[tex]x-4=9[/tex]Hence, the correct statement is x-4=9.
find 11/3÷2/3
The quotient is 5 and ___.
After conducting mathematical operations, we know that 11/3÷2/3 leaves a remainder of 5½.
What are mathematical operations?A function in mathematics known as an operation is one that transforms zero or more input values into a clearly defined output value. The operation's complexity is determined by its operand count. A mathematical operation is a procedure. A mathematical operation can be anything from addition to subtraction to multiplication to division to finding the root.So, 11/3÷2/3:
We need to perform the division of the given fractions as follows:(Refer to the image attached below for calculations)11/3÷2/3 = 5½Therefore, after conducting mathematical operations, we know that 11/3÷2/3 leaves a remainder of 5½.
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Ms. Banks divides 18 basketballs evenly among 3 bags. For class, she takes 2 basketballs from each bag. How many basketballs are left in one of the bags?
4 basketballs
Explanation
Step 1
Ms. Banks divides 18 basketballs evenly among 3 bag
divide the 18 basketballs by 3 bags
[tex]\frac{18\text{ basketball}}{3\text{ bags}}=6\text{ basketaball per bag}[/tex]Step 2
now, she takes 2 from each bag, so
[tex]\begin{gathered} \text{total basketball per bag=6-2} \\ \text{total basketball per bag =4} \end{gathered}[/tex]Hence, the answer is 4 basketballs.
I hope this helps you
Let x be a continuous random variable that has a normal distribution with μ = 48 and 6 = 8. Assuming -
≤0.05, find the
probability that the sample mean, x, for a random sample of 16 taken from this population will be between 49.60 and 52.20.
Round your answer to four decimal places.
The probability of the sample mean is 0.2008.
What is probability?
Probability is the quality or state of being probable the extent to which something is likely to happen or be the case.
Sol-Let x be a continuous random variable that has a normal distribution with
μ=48 and σ=8
Thus,
X~N(48,8^2/16)
The standardized value of x is obtained by :
Z= X-48/√8^2/16~N(0,1)
The probability that the sample mean x for a random sample of 16 taken from this population will be between 49.62 and 52.80 can be obtained as:
P(49.62<x<52.80)
P=(49.62-48/√8^2/16<x-48/√8^2/16<52.80-48/√8^2/16)
=P(0.81<Z<2.4)
=P(Z<2.4)-P(Z<0.81)
=0.9918-0.7910
=0.2008
There for the probability is 0.2008.
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On the graph below, which dotted line represents a reflection across the x-axis of the red-solid-line graph?5 stars for quicknessplease look at png 1 is question 2 is answer
Hello!
The rule for a reflection across the x-axis is:
[tex](x,y)=(x,-y)[/tex]Knowing it, let's write some points that the red line passes through:
(-2, 0) and (0, 4).
Now, let's use this rule and change the sign of the y coordinate:
• (-2, 0) → (-2, 0) because +0 or -0 doesn't exist.
,• (0, 4) → (0, -4)
Let's analyze it and find a line that passes through these two points:
(-2, 0) and (0, -4)
It will be the blue line.
Mr. Thomatos thinks that {3, 8} and [3, 8] represent the same set of values Is Mr. Thomatos correct? Why or why not? Explain. (giving brainliest)
Answer: its not correct because the got different perenties or groupings and they mean different meaning
Step-by-step explanation:
For each graph below, state whether it represents a function.
I need help with graph 2
Answer: No
Step-by-step explanation:
The graph fails the vertical line test, and thus the graph does not represent a function.
I need help please 5. Find the distance between C (-5, 4) and Q (2,0). A. 22 B. 33 C. 53 D. 65
Given the two points:
C (-5, 4) and Q (2, 0)
To find the distance, use the distance formula below:
[tex]d\text{ =}\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]Where,
(x1, y1) = (-5, 4)
(x2, y2) = (2, 0)
Therefore, we have:
[tex]\begin{gathered} d=\sqrt[]{(2-(-5))^2+(0-4)^2} \\ \\ \text{ =}\sqrt[]{(2+5)^2+(0-4)^2} \\ \\ \text{ =}\sqrt[]{7^2+(-4)^2} \\ \\ \text{ =}\sqrt[]{49+16} \\ \\ \text{ =}\sqrt[]{65} \end{gathered}[/tex][tex]undefined[/tex]help ................
Percentage of a number
Find a number which
its a 100% percentage
henW
When 232 is 290%
Then find
X = (100%/290)• 232
Divide 232/29 = 10% = 8 exactly
Now multiply by 10 = 10• 8 = 80
Then 100% = 80
graph the system below2x-3y=-183x+y=-5
ANSWER:
STEP-BY-STEP EXPLANATION:
We have the following system of equations:
[tex]\begin{gathered} 2x-3y=-18 \\ \\ 3x+y=-5 \end{gathered}[/tex]To graph, we calculate the intercepts in each equation to then draw the straight line corresponding to each equation, like this:
[tex]\begin{gathered} \text{ For }2x-3y=-18 \\ \\ \text{The x-intercept} \\ \\ \:2x-3\cdot 0=-18 \\ \\ x=-9\rightarrow(-9,0) \\ \\ \text{The y -intercept} \\ \\ 2\cdot0-3y=-18 \\ \\ y=6\rightarrow(0,6) \\ \\ \\ \text{For }3x+y=-5 \\ \\ \text{The x-intercept} \\ \\ 3x+0=-5 \\ \\ x=-\frac{5}{3}\rightarrow\left(-\frac{3}{5},0\right) \\ \\ \text{The y- intercept} \\ \\ \:3\cdot 0+y=-5\: \\ \\ y=-5\rightarrow(0,-5) \end{gathered}[/tex]Now we graph:
Factor: x^6-5x^4-5+x
The value of the expression x^6 -5x^4 - 5 + x when simplified is x^4(x^2 - 5) - (5 + x)
How to factor the expression?The statement is given as
Factor: x^6 -5x^4 - 5 + x
From the above expression, we have
x^6 -5x^4 - 5 + x
Group the expression in two'2
So, we have
x^6 -5x^4 - 5 + x = (x^6 - 5x^4) - (5 + x)
Factorize each group of the expression
So, we have
x^6 -5x^4 - 5 + x = x^4(x^2 - 5) - (5 + x)
The above expression cannot be further simplified
Hence, the value of x^6 -5x^4 - 5 + x is x^4(x^2 - 5) - (5 + x)
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Make x the subject of h = 4(x + 3y) + 2
Answer:
x=\frac{1}{4}(h-12y-2)x=4
Step-by-step explanation:x=\frac{1}{4}(h-12y-2)x=
4
1
(h−12y−2)
Step-by-step explanation:
We are given the equation h=4(x+3y)+2h=4(x+3y)+2 .
Simplifying for x, we get,
h=4(x+3y)+2h=4(x+3y)+2
i.e. h=4x+12y+2h=4x+12y+2
i.e. 4x=h-12y-24x=h−12y−2
i.e. x=\frac{1}{4}(h-12y-2)x=
4
1
(h−12y−2)
Thus, the equation for x is x=\frac{1}{4}(h-12y-2)x=
4
1
Solve the quadratic equation X^2+5x+6=0 using the completing the square method. Be sure to explain each step.
To complete the perfect trinomial, we add (5/2)² to the given equation and get:
[tex]x^2+5x+(\frac{5}{2})^2+6=(\frac{5}{2})^2.[/tex]Subtracting 6 we get:
[tex]x^2+5x+(\frac{5}{2})^2=\frac{25}{4}-6=\frac{1}{4}.[/tex]Therefore:
[tex](x+\frac{5}{2})^2=\frac{1}{4}.[/tex]Finally, we get:
[tex]\begin{gathered} x+\frac{5}{2}=\pm\sqrt{\frac{1}{4}}, \\ x=\pm\frac{1}{2}-\frac{5}{2}. \end{gathered}[/tex]Answer: [tex]\begin{gathered} x_=-3,\text{ or x=-2.} \\ \end{gathered}[/tex]Jae created a painting with an area of 48 square inches and a length of 6 inches. They create a second painting with an area of 64 square inches. It has the same width as the first painting. What is the length of the second painting?
Given the equation of a curve is y=5/x²The value of dy/dx= -10/27Hence, estimate the value of 5/(2.98)²
The given equation is:
[tex]y=\frac{5}{x^2}[/tex]a. Find the value of dy/dx when x=3
Start by finding the derivative:
[tex]\frac{dy}{dx}=\frac{d(\frac{5}{x^2})}{dx}[/tex]You also can express 5/x^2 as 5*x^(-2):
[tex]\frac{5}{x^2}=5x^{-2}[/tex]You know the derivative of a power is:
[tex]\frac{d}{dx}x^n=n\cdot x^{n-1}[/tex]Apply it to your case:
[tex]\frac{d}{dx}5x^{-2}=(-2)\cdot5\cdot x^{-2-1}=-10\cdot x^{-3}[/tex]And finally:
[tex]\begin{gathered} x^{-n}=\frac{1}{x^n} \\ \text{Apply it to your equation} \\ \frac{dy}{dx}=\frac{-10}{x^3} \end{gathered}[/tex][tex]\begin{gathered} \text{When x=3} \\ \frac{dy}{dx}=\frac{-10}{3^3}=\frac{-10}{27} \end{gathered}[/tex]b. Estimate the value of 5/(2.98)^2:
[tex]\begin{gathered} y=\frac{5}{x^2}=\frac{5}{2.98^2}=0.563 \\ \text{Which also means x=2.98} \\ \text{Let's find the derivative when x=2.98} \\ \frac{dy}{dx}=\frac{-10}{2.98^3}=\frac{-10}{26.46}=-0.377 \end{gathered}[/tex]Mr. Lombardo took his two children to a water park. He used the coupon shown below to buy one adult ticket. The price of admission for all three family members was $76. What was the price of each child's ticket? WORLD OF WATER | This coupon is good | for one adult ticket | to World of Water | at a price of $28.00. YOU SAVE $4.00! Use the math you already know to solve the problem. a. What ticket price do you know? How much is that ticket? Explain.
Data Input
1 Adult + 2 children
The price for all three family members
$76
Procedure
Adult ticket = $28
1 Adult + 2 children = $76
2 children = 76 - 1 adult
2 children = 76 - 28
2 children = 48
children = 48/2
children = 24
3300 dollars is placed in an account with an annual interest rate of 6.75%. To
the nearest tenth of a year, how long will it take for the account value to reach
10700 dollars?
The simple interest formula is A = P(1+r t) then the value of t =33.2210 years.
What is meant by simple interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.
The simple interest formula is equal to
A = P(1+r t)
where, A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
P = $ 3300
A = $ 10700
r = 6.75 % = 6.75 / 100 = 0.0675
substitute in the formula above
$10700 = 3300(1+0.0675 t)
simplifying the above equation, we get
Divide both sides by 3300
[tex]$\frac{3300(1+0.0675 t)}{3300}=\frac{10700}{3300}$$[/tex]
Simplifying the above equation, we get
[tex]$1+0.0675 t=\frac{107}{33}$$[/tex]
Subtract 1 from both sides
[tex]$1+0.0675 t-1=\frac{107}{33}-1$$[/tex]
Simplifying the above equation, we get
[tex]$0.0675 t=\frac{74}{33}$$[/tex]
Divide both sides by 0.0675
[tex]$\frac{0.0675 t}{0.0675}=\frac{\frac{74}{33}}{0.0675}[/tex]
[tex]$t=\frac{74}{2.2275}$[/tex]
t = 33.2210 years
Therefore, the value of t exists 33.2210 years.
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Simplify the following rational expression to determine if thegiven simplification is correct. If it is correct, select TRUE. If it isnot correct, select FALSE.6x48x556x47
The question asks us to confirm the simplification of the expression:
[tex]-\frac{48x^5}{56x^4}[/tex]Step 1: Factor the numbers
[tex]\begin{gathered} 48=8\times6 \\ 56=8\times7 \end{gathered}[/tex]Therefore, the expression becomes:
[tex]-\frac{48x^5}{56x^4}=-\frac{8\times6x^5}{8\times7x^4}[/tex]Step 2: Cancel out the common terms from the expression
[tex]-\frac{8\times6x^5}{8\times7x^4}=-\frac{6x^5}{7x^4}[/tex]Step 3: Apply the rule of exponents
[tex]\frac{x^n}{x^n}=x^{m-n}[/tex]Therefore, we have:
[tex]-\frac{6x^5}{7x^4}=\frac{6}{7}x^{5-4}=-\frac{6x}{7}[/tex]CONCLUSION
The expression simplifies to give:
[tex]-\frac{48x^5}{56x^4}=-\frac{6x}{7}[/tex]The answer is TRUE.
Red Lobster charges $30 per person plus a $100 set up fee to cater an event. Olive Garden charges $25 per person plus a $200 set up fee. PART A: How many guests, g, would both restaurants cost the SAME
There would be 20 guests for the restaurants to cost the same
What are linear equations?Linear equations are equations that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the number of guests?From the question, we have the following parameters:
Red Lobster
Rate per person = $30
Set up fee = $100
Olive Garden
Rate per person = $25
Set up fee = $200
So, the equations of the restaurants are
Red Lobster = 30g + 100
Olive Garden = 25g + 200
Where the number of guests is g
When the restaurants cost the same amount, we have
Red Lobster = Olive Garden
Substitute the known values in the above equation
So, we have
30g + 100 = 25g +200
Evaluate the like terms
5g = 100
Divide by 5
g = 20
Hence, the number of guests is 20
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Find the x-intercept and y- intercept of the function f(x) = (2x + 3)/(x ^ 2 + 3)can u draw the function of f(x) = (2x + 3)/(x ^ 2 + 3)?Need solution ^^
Answer:
• x-intercept: (-1.5, 0).
,• y-intercept: (0, 1).
Explanation:
Given the function:
[tex]f(x)=\frac{2x+3}{x^2+3}[/tex](a)x-intercept
The x-intercept is the value of x at which f(x)=0.
When f(x)=0
[tex]\begin{gathered} \frac{2x+3}{x^2+3}=0 \\ \text{ Cross multiply} \\ 2x+3=0 \\ \text{ Subtract 3 from both sides of the equation} \\ 2x+3-3=0-3 \\ 2x=-3 \\ \text{ Divide both sides of the equation by 2} \\ \frac{2x}{2}=-\frac{3}{2} \\ x=-1.5 \end{gathered}[/tex]The x-intercept is located at (-1.5, 0).
(b)y-intercept
The y-intercept is the value of f(x) at which x=0.
When x=0
[tex]\begin{gathered} f(x)=\frac{2x+3}{x^2+3} \\ f(x)=\frac{3}{3} \\ f(x)=1 \end{gathered}[/tex]The y-intercept is at (0, 1).
(c)Graph
The graph of f(x) is given below:
An item is regularly priced at $50. It is on sale for 40% off the regular price. How much (in dollars) is discounted from the regular price?Amount discounted: sX5?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
regular price = $50
discount = 40% = 0.4
Step 02:
amount discounted:
amount discounted = regular price * discount
amount discounted = $50 * 0.4 = $20
The answer is:
$20
how would I answer and what would be the answer?
Answer: (-1, 0)
The interval of decreasing refers to the interval of x-values where the graph is decreasing or going down.
If we look at the graph:
We can see that the graph starts to decrease or "go down" at values x = -1 and x=0. With this, we can conclude that the interval of decrease for the given graph is (-1, 0)
Which equation demonstrates the distributive property? Responses A 36 + 9 = 4536 + 9 = 45 B 36 + 9 = 3(12 + 3)36 + 9 = 3(12 + 3) C 36 x 9 = 9 x 3636 x 9 = 9 x 36 D (12 + 3)3 = 3(12 + 3)
The correct option is option B i.e., 36 + 9 = 3(12 + 3) is an equation representing distributive property.
What is distributive property ?
Distributive property states that the outcomes are the same whether the numbers in parenthesis are added before or after multiplication.
We know that according to the distributive property both sides must be equal such that the outcomes are same whether the numbers in parenthesis are added before or after multiplication. The expression for distributive property is given as : a(b + c) = ab + ac
So , checking the options one by one :
A) 36 + 9 = 45 ; is not an equation representing distributive property as it doesn't satisfy the criteria of a distributive property.
B) 36 + 9 = 3(12 + 3) is an equation representing distributive property as it satisfies the criteria mentioned above i.e.,
36 + 9 = 3 × 12 + 3 × 3
36 + 9 = 36 + 9
45 = 45
C) 36 x 9 = 9 x 36 is not an equation representing distributive property.
D) (12 + 3) × 3 = 3 × (12 + 3) is not an equation representing distributive property because both sides are written in the same way.
Therefore , correct option is option B i.e., 36 + 9 = 3(12 + 3) is an equation representing distributive property.
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The area of a triangle is given by A = 1/2bh, where b is the base and h is the height of the triangle
The area of the triangle with base 12 units, and height of 3 units is: B. 18.
How to Determine the Area of a Triangle?To find the area of a triangle, find the height, which is the distance from its base to its highest point, and also find the length of the base of the triangle, then apply the formula below:
Area of triangle = 1/2 × base × height
From the information given, the following are the parameters we will need to work with:
Base of the triangle = QR = 12 units
Height of the triangle = PH = 3 units
Plug in the values
Area of triangle = 1/2 × 12 × 3
Area of triangle = 36/3
Area of triangle = 18 units
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continued - calculating gross payRemember, this is money round to the nearest Penny/hundredths place. Take OT rate as 1.5 times the regular pay rate.Take the regular working hours per week as 40 hours.
Given Data:
Total working hours is = 51 hours.
Pay rate=$8.45.
OT rate=1.5 times the regular pay rate.
Regular working hours is 40 hours.
Regular pay can be determined as,
[tex]RP=40\text{ hours}\times8.45\text{ USD=338 USD}[/tex]Thus, the regular pay is $338.
The OT rate can be determined as,
[tex]\begin{gathered} OT=1.5\times8.45\text{ USD} \\ =12.675\text{ USD} \end{gathered}[/tex]Thus, the overtime rate is $ 12.68.
The overtime pay can be determined as,
[tex]\begin{gathered} OT\text{ Pay=(51-40) hours}\times12.675\text{ USD} \\ =139.425\text{ USD} \end{gathered}[/tex]Thus, the overtime pay is $139.43.
The gross pay can be determined as,
[tex]\begin{gathered} GP=RP+OT\text{ Pay} \\ =338\text{ USD+139.425 USD} \\ =447.425\text{ USD} \end{gathered}[/tex]Thus, the gross pay is $ 447.425.
What kind of transformation converts the graph of f(x) = -x - 10 into the graph of g(x)
-9x - 10?
horizontal stretch
vertical stretch
vertical shrink
horizontal shrink
=
Answer:
zeroay horizontal stretch vertical shrink
Step-by-step explanation:
1+1=2
Simplify the expression 2^5 +5^4
Therefore
[tex]2^5+5^4=657[/tex]Write a quadratic function in standard form whose graph passes through (-5,0),(0,-8),(4,0)
[tex]y = -1.25 x^{2}+ 5[/tex] is the needed quadratic function in standard form.
What is a quadratic equation?A quadratic equation is one with a single degree 2-variable and has the general form [tex]a x^{2} + bx + c = 0.[/tex] a, b, and c is the constant value, and x consists of a variable.
The quadratic equation's x-intercepts are (-5, 0). That indicated that the quadratic equation's two elements are (x + 5) and (x -0).
f(x) = a (x + 5) (x - 0) (x - 0)
= ax+5a
f(x) = [tex]ax^{2} +5x[/tex]
The quadratic equation's graph goes through (4, 0). Therefore, we must change equation 1 to read x = 4 and f(x) = 0.
0 = a × 4² + (5 × 4)
0 = a × 16 +20
a = [tex]\frac{-20}{16}[/tex]
=-1.25
The quadratic equation is known to have the form ax² + bx + c = 0.
f(x) = -1.25[tex]x^{2}[/tex] + 5x
Consider y= F(x)
∴ The required quadratic equation of function in the standard form is Y = -1.25 x² + 5x.
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Please help me solve: Part CA sign in a freight elevator states that the maximum capacity of the elevator is 2,500 pounds. Use the average weight of a box as 75 pounds and the average weight of a crate as 160 pounds to complete the following parts.If there are 13 average-weight boxes on the elevator, what is the maximum number of average-weight crates that can also be on the elevator given its maximum capacity? Please explain.
Let
x ----> number of average-weight crates
so
we have that
[tex]75(13)+160x\leq2,500[/tex]solve for x
[tex]\begin{gathered} 975+160x\leq2,500 \\ 160x\leq2,500-975 \\ 160x\leq1,525 \\ x\leq9.53 \end{gathered}[/tex]therefore
the maximum number of average-weight crates is 9