Answer:
(4b - a)²(x + y)
Step-by-step explanation:
x(4b - a)² + y(4b - a)² ← factor out (4b - a)² from each term
= (4b - a)²(x + y)
A population has a mean of 128 and a standard deviation of 32. Suppose a sample of 64 is selected. What is the probability that the sample mean will be within +- 5 of the population mean?
The probability that the sample mean will be within +- 5 of the population mean is 0.7888.
What will the probability be?In this case, within 5 will be:
= 128 ± 5 = 123, 133
The probability will be:
P(123 < x < 133)
= P(123 - 128))4 =(133 - 128)/4
= P(-1.25< Z < 1.25 )
= P(Z < 1.25) - P(Z < -1.25 )
Using z table,
= 0.8944 - 0.1056
= 0.7888
The probability is 0.7888.
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What is the slope of the line represented by the equation y = 4/5x-3?
A. -3
B. -1/
C. //
D. 3
Hurry!!!!
Translate the following phrase to a mathematical expression. Then, evaluate the expression for n = 5.
the quotient of twenty and a number
A. n ÷ 20; 4
B. 20 - n = 15
C. 20 ÷ n ; 4
D. 20 n ; 100
The mathematical expression is 20÷n and the value of the expression at n=5 is 4.
We are given a phrase and we have to convert it into a mathematical expression. The phrase is given below :
P = "the quotient of twenty and a number"
An expression or mathematical expression is a finite collection of symbols that are well-formed according to context-dependent norms. In mathematics, an expression is a statement that involves at least two distinct numbers (known or unknown) and at least one operation. The mathematical expression equivalent to the above phrase is 20/n.
We now need to evaluate the mathematical expression for n = 5.
20/5 = 4
The value is 4.
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Which of the following shows the prime factorization of 36 using exponential notation?
O2.3²
O 6²
O 4.9
O 2².3²
(B) 6² shows the prime factorization of 36 using exponential notation.
What is exponential notation?Very large or very small numbers can be written and handled more easily by using exponential notation. A number is typically expressed in exponential notation as a coefficient between one and ten times an integral power of ten, the exponent.For instance, Since the number 7 has been multiplied by itself three times, the exponent, in this case, is three. Since 343 is equal to 7³, we can write it as "7 to the power of 3" or "343 is equal to 7³."So, the prime factorization of 36:
36/6 = 66/6 = 1And we know that: 6 × 6 = 36 ⇒ 6² = 36
Then, the prime factorization of 36 using exponential notation will be 6².
Therefore, (B) 6² shows the prime factorization of 36 using exponential notation.
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The correct question is given below:
Which of the following shows the prime factorization of 36 using exponential notation?
A. 2.3²
B. 6²
C. 4.9
D. 2².3²
Help me please show your work please
The fewest number of miles he can drive each day is option a which is 343.
What is basic division?The mathematical technique used to divide big numbers into more manageable groups or portions in mathematics is called long division. Making a difficulty into manageable, straightforward steps is beneficial. There are remainders, quotients, dividends, and divisors in long divisions. The dividend, which is the big number divided by the divisor in a long division problem, is the problem's large number. The excess amount that cannot be divided is referred to as the residue, and the quotient is the outcome of the division. Compared to multiplication, division is the opposite. When you divide 12 into three equal groups, you get four in each group if three groups of four add up to 12, which they do when you multiply. Determine how many equal groups are created by splitting the population.
Total miles = 1375
Number days = 4
1 day = 1375/4
= 343.75
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ive done this question so many times and I just cant seem to get it can you please help me figure this out
Explanation
to figure out this, we need to check every option
[tex]\begin{gathered} V=\frac{1}{3}Bh \\ \end{gathered}[/tex]Step 1
[tex]\begin{gathered} B=50 \\ h=10 \end{gathered}[/tex]replace.
[tex]\begin{gathered} V=\frac{1}{3}Bh \\ V=\frac{1}{3}\cdot50\cdot10 \\ V=166.66 \end{gathered}[/tex]Step 2
[tex]\begin{gathered} B=50 \\ h=30 \end{gathered}[/tex]
replace
[tex]\begin{gathered} V=\frac{1}{3}Bh \\ V=\frac{1}{3}\cdot50\cdot30 \\ V=500 \end{gathered}[/tex]Step 3
[tex]\begin{gathered} B=100 \\ h=10 \end{gathered}[/tex]
replace
[tex]\begin{gathered} V=\frac{1}{3}Bh \\ V=\frac{1}{3}\cdot100\cdot10 \\ V=\frac{1000}{3}=\frac{999}{3}+\frac{1}{3}=333\text{ }\frac{1}{3} \\ V=333\text{ }\frac{1}{3} \end{gathered}[/tex]so, the answer is
[tex]B=100cm^2\text{ h=10 cm}[/tex]I hope this helps you
Zion has an 80:1 scale-drawing of the floor plan of his grandmother’s house. On the floor plan, the dimensions of his grandmother’s rectangular living room are 1 inches by 2 inches. 8721 What is the area of his grandmother’s real living room in square feet?
1) Gathering the data
80:1 scale
On the floor plan : width: 1 inch x 2 inches
2) Let's find the real area of the living room by setting a proportion:
Since on the fo
Find the area of the circle. Use 3.14 or 22/7 fir Pi
ANSWER
132.7 km^2 option B
EXPLANATION
Step 1: Formula for Area of a Circle
[tex]\text{Area of a circle = }\pi r^2[/tex]where radius r = diameter/2
r = 13/2
r = 6.5km
Step 2: Substitute the values of r = 6.5 and pi = 3.14
[tex]\begin{gathered} \text{Area = }\pi r^2 \\ \text{ = 3.14 }\times6.5^2 \\ \text{ = 3.14 }\times\text{ 42.25} \\ \text{ = }132.665\text{ }=\text{ 132.7 }km^2\text{ (to nearest tenth)} \\ \end{gathered}[/tex]Hence, the area of the circle with radius 6.5km is 132.7km^2 (to the nearest tenth).
An investigation of a number of automobile accidents revealed the following information:15 accidents involved alcohol and excessive speed27 accidents involved alcohol.13 accidents involved excessive speed but not alcohol22 accidents involved neither alcohol nor excessive speedHow many accidents were investigated? ** note: Let the universal set U be the set of all automobile accidents. Use the information provided to create a Venn diagram containing 2 subsets. Let A be the set of accidents involving alcohol and S be the set of accidents involving excessive speed. **
To solve this type of question we should use the Venn diagram
Let me draw it and show you where we will put each number given
Since there are 15 accidents involved alcohol and excessive speed
Then we should put 15 in the common part of the 2 circles
Since there are 27 accidents involved alcohol
That means 27 = alcohol only + alcohol and excessive speed
Then to find alcohol only we should subtract 15 from 27 to get the number of alcohol only
27 - 15 = 12
Since there are 13 accidents involved excessive speed but not alcohol
That means the excessive speed only is 13
Let us put it in the Venn diagram
Since there are 22 accidents involved neither alcohol nor excessive speed
That means we will put this number outside the circles inside the rectangle
To find the total number of accidents we will add all the numbers in the figure
[tex]\begin{gathered} T_{acc}=12+15+13+22 \\ T_{acc}=62 \end{gathered}[/tex]Then there are 62 accidents in this investigated
True or False? if false. correct the statement
1. if a number is in integer. then the number is alse rational
2. if a number is real. then it is alse rational
3. 3.456 is an irrational number
4. √11 is a real number
5. zero is an natural number
6. 9 is an integer
7. if a number is natural. then it alse whole
The True statements are,
If a number is in integer, then the number is else rational,√11 is a real numberzero is an natural number9 is an integerIf a number is natural. then it else whole.The False statements are,
If a number is real. then it is else rational3.456 is an irrational numberWhat is a Rational number :Any number that can be written as a ratio (or fraction) of two integers is a rational number.
A rational number is a number that is in the form of p/q, where p and q are integers, and q is not equal to 0. Some of the examples of rational numbers include 1/3, 2/4, 1/5, 9/3, and so on.
What is a Irrational number :An irrational number is a type of real number which cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio. If N is irrational, then N is not equal to p/q where p and q are integers and q is not equal to 0. Example: √2, √3, √5, √11, √21, π(Pi) are all irrational.
What is a Real numbers :Real numbers are numbers that include both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5) and irrational numbers such as √3, π(22/7), etc., are all real numbers.
Real numbers ⇒ Rational , Irrational numbers
Rational numbers ⇒ Integer, Fraction
Based on the given statement,
(1) . If a number is in integer. then the number is else rational. [ TRUE ]
The rational numbers are include integers.
So, this statement is True.
(2) . If a number is real. then it is else rational. [ False ]
The real numbers are include rational and irrational numbers.
So, this statement is False.
(3) . 3.456 is an irrational number. [ FALSE ]
= 3.456
= 3456/1000
So, it is rational number.
Then, it is not irrational number. So, this statement is False.
(4) . √11 is a real number. [ TRUE ]
This statement is True, because √11 is real number.
(5) . zero is an natural number. [ TRUE ]
This statement is True, because zero is natural number.
(6) . 9 is an integer. [ TRUE ]
We can write,
= 9
= 3*3
So, this statement is true, because 9 is an integer.
(7) . If a number is natural. then it else whole. [ TRUE ]
This statement is true, because natural means the whole larger than zero, like 0 , 1 , 2 , ........
So, this statement is True.
Therefore,
The True statements are,
If a number is in integer, then the number is else rational,√11 is a real numberzero is an natural number9 is an integerIf a number is natural. then it else whole.The False statements are,
If a number is real. then it is else rational3.456 is an irrational numberTo learn more about information visit Irrational problems :
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find the lateral area, surface area, and volume of the following figure. leave answer in simplest radical form or in terms of pi. round to the nearest tenth. Solve for the lateral surface area
Given:
The dimensions of the rectangular prism :
length(l)= 5 in
width (w) = 2 in
height (h) = 3 in
The formula for the lateral surface area L.A of a rectangular prism is:
[tex]L.A\text{ = 2\lparen l + w\rparen h}[/tex]Substituting the given values into the formula:
[tex]\begin{gathered} L.A\text{ = 2}\times\text{ \lparen5 + 2\rparen }\times\text{ 3} \\ =\text{ 42 in}^2 \end{gathered}[/tex]Answer: 42 square inch
Pigeons once used to be welcome at Trafalgar Square and the public were encouraged to feed them. This gave a good opportunity to estimate the pigeon population in London. At one point 84 pigeons were caught and tagged. Two days later, 120 pigeons were caught in Trafalgar Square and it was found that 3 of the pigeons were tagged. Approximately how many pigeons were there in London?
A total of 201 pigeons are there in London as determined by set theory.
What is Set Theory?
The area of mathematical logic known as set theory examines sets, which are essentially collections of objects.Set theory is an area of mathematics that primarily deals with objects that are pertinent to mathematics as a whole, despite the fact that any form of an object can be gathered into a set.The pigeon caught in the first attempt=84
No. of them tagged=84
⇒Set A=84
Pigeon caught in second attempt =120
⇒Set B=120
No. of them found tagged=3
No. of Pigeons in London = Set A∪Set B-3
84+120-3=201
A total of 201 pigeons are there in London as determined by set theory.
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Find the zeros of the function ƒ(x) = x2 + 2x – 3.
In order to determine the zeros of this function, the steps are:
1. Assume f(x) = 0. Hence, the equation becomes:
[tex]0=x^2+2x-3[/tex]2. Factor the quadratic function by finding some factors of -3 that sums to the middle term 2.
a. -3 and 1 → -2
b. -1 and 3 → 2
So, the factors of -3 that sums to 2 are -1 and 3.
So, the quadratic equation can be factored into:
[tex]0=(x-1)(x+3)[/tex]3. Equate each factor to zero and solve for x.
[tex]\begin{gathered} x-1=0\Rightarrow x=1 \\ x+3=0\Rightarrow x=-3 \end{gathered}[/tex]Therefore, the zeroes of the function are at (-3, 0) and (1, 0). (Option C)
5/9 + 3/9 in decimals
Answer:
0.8 *repeating
Step-by-step explanation:
5/9 + 3/9 = 8/9!
8/9 as a decimal is 0.888888888 (repeating forever)
Raina pays $3.84 for a bag of 16 tangerines. find the unit price in dollars per Tangerine. If necessary, round your answer to the nearest cent.
A hacker is trying to guess someone’s password. The hacker knows (somehow) that the password is ) digits long, and that each digit could be a number between 0 and 4 assume that the hacker makes random guesses.
What is the probability that the hacker guesses the password on his first try?
Step-by-step explanation:
easy the hacker got the password by hacking maybe he is bot so he gusss it but if he guss it he may got brainlist answer mark me ok so he got 2312
Help mee pleasee!!
thank you <3
Equation of line passing through two points (-2,11) and (1,-4) is f(x)=
What is equation of line?y=mx+b is the equation of line where m is the slope and b is the y intercept.
Since slope of line passing through two points (x₁, y₁) and (x₂, y₂)
m=y₂-y₁/x₂-x₁
slope of line passing through two points (-2,11) and (1,-4)
y₂=-4,y₁=11, x₂=1, and x₁=-2
m=-4-11/1-(-2)
m=-15/1+2
m=-15/3
m=-5
Therefore, the slope of the line is -3.
Now use the slope and either of the two points to find the y-intercept.
y=mx+b for (-2, 11)
11=-3(-2)+b
11=6+b
11-6=b
5=b
Hence equation of line will be
y=-3x+5
f(x)=-3x+5
Therefore equation of line passing through two points (-2,11) and (1,-4) is f(x)=-3x+5
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For the polynomial Ax) = x² – x4 + 2x3 – 13 as x + f(x) +00 A. True O B. False
Notice that the degree of the polynomial is even (4), also the leading coefficient is negative (-1). Therefore:
[tex]x\rightarrow\infty,f(x)\rightarrow-\infty.[/tex]Answer: Option B) False.
how much money will be in a bank after three years if nine dollars is deposited adding interest rate of 5% compounded annually? Round to the nearest cent.
ANSWER
[tex]10.45[/tex]EXPLANATION
Given;
[tex]\begin{gathered} p=9 \\ I=5 \\ t=3 \end{gathered}[/tex]Recall, the compound interest formula;
[tex]A=P\cdot \left(1+\frac{r}{n}\right)^{nt}[/tex]Substituting the values into the formula;
[tex]\begin{gathered} A=P\cdot \left(1+\frac{r}{n}\right)^{nt} \\ =9\left(1+\frac{5\%\:}{12}\right)^{12\cdot\:3} \\ =9\left(1+\frac{0.05}{12}\right)^{12\cdot\:3} \\ =9(1+0.00416)^{36} \\ =9\times1.16147 \\ =10.45325 \\ \cong10.45 \end{gathered}[/tex]Therefore, the amount in the bank account after 3 years will be $10.45
31.What is the surface area of the cylinder?
Hello there. To solve this question, we'll have to remember some properties about cylinders.
We want to determine the surface area of the following cylinder:
In this case, the surface area comprehends the bottom, the top and the lateral area of the cylinder.
For a cylinder with height h and radius R, it is easy to show that
By redrawing the cylinder as the following figures:
Notice the 2pi * R came from the measure of the circumference of the top and bottom circles.
The area of the circles are given as
[tex]\pi\cdot R^2[/tex]And the area of the rectangle is
[tex]2\pi Rh[/tex]So the surface area of this cylinder is given as
[tex]2\pi R^2+2\pi Rh[/tex]Plugging the values R = h = 1.5 m, we'll get
[tex]2\pi\cdot1.5\cdot(1.5+1.5)=9\pi\approx28.27\text{ m}^2[/tex]In this case, the answer is 9pi and it is contained in the 4th option.
Triangle A(1, 2), B(3, 2), C(2, 4) is rotated 90
degrees around the origin. What are the
coordinates of A'B'C'?
The coordinates of the transformed figure are: A ’(-1, -2), B ’(-3, -2), C ’(-2, 4)
When a shape is rotated, it must be rotated through a point, here itis rotated around the origin
The coordinates of the triangle is given as:
A(1, 2), B(3, 2), C(2, 4) is rotated 90 degree
The rule of 90 degrees clockwise rotation is:
x, y = -x, -y
So, we have:
A(1, 2) which becomes (-1, -2)
B(3, 2), which becomes (-3, -2)
C(2, 4) which becomes (-2, -4)
Hence, the coordinates of the transformed figure are:
A ’(-1, -2), B ’(-3, -2), C ’(-2, 4)
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Solve the inequality />
d > 105
Explanations:The given inequality is:
[tex]\frac{d}{7}>\text{ 15}[/tex]Multiply both sides by 7:
[tex]7\text{ }\times\frac{d}{7}>\text{ 15}\times7[/tex][tex]d\text{ > }105[/tex]need help for answer:10n=1/4+3/20n
Answer:
5/197
Step-by-step explanation:
Please look at the image below!
Answer: n=5/197
Step-by-step explanation:
help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeeee
thank you
The domain and range for the relation is [-∞, ∞] and [0,-3], and both of them can be described by interval notation .
Since the graph given to us present a relation or a function, The domain and range of a function are the set of all the inputs and yield a function that can grant separately. The domain and range are vital viewpoints of a function. The domain takes all the conceivable input values from the set of real numbers and the range takes all the yield values of the function. In simple words, the domain is the set of all "x" values and the range is the set of all "y" values in a set of ordered sets and the requested sets are composed as in the form (x, y) or [x,y]
for the given the points are : (0,-3),(1,-3),(2,-3),(3,-3),(4,-3),(5,-3),(-1,-3)(-2,-3),(-3,-3),(-4,-3),(-5,-3)
so the domain set is ={-5,-4,-3,-2,-1,0,1,2,3,4,5}
and the range set is ={0,-3,-4,-5,-6,-7,-8}
so the domain and range is [-∞, ∞] and [0,-3]
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Consider the function f(x)=cos(0.9x).How much does x have to increase by for 0.9x to increase by 2π?What is the period of f?Consider the function g(x)=sin(5πx).How much does x have to increase by for 5πx to increase by 2π?What is the period of g?
Let Δx be an increase in the variable such that 0.9x increases by 2π. Then:
[tex]\begin{gathered} 0.9(x+\Delta x)-0.9x=2\pi \\ \Rightarrow0.9x+0.9\Delta x-0.9x=2\pi \\ \Rightarrow0.9\Delta x=2\pi \\ \Rightarrow\Delta x=\frac{2\pi}{0.9} \\ \therefore\Delta x=\frac{20\pi}{9} \end{gathered}[/tex]The period of a function f is a quantity T such that for every x, then:
[tex]f(x)=f(x+T)[/tex]The cosine function has a period of 2π over its argument. In this case, we know that:
[tex]f(x)=\cos (0.9x)[/tex]The argument of cosine is 0.9x and we already know that for an increase of 20π/9 in x, there is an increase of 2π in 0.9x. Therefore:
[tex]\begin{gathered} f(x+\frac{20\pi}{9})=\cos (0.9(x+\frac{20\pi}{9})) \\ =\cos (0.9x+0.9\cdot\frac{20\pi}{9}) \\ =\cos (0.9x+2\pi) \\ =\cos (0.9x) \\ =f(x) \end{gathered}[/tex]Then, for every x we know that:
[tex]f(x+\frac{20\pi}{9})=f(x)[/tex]Therefore, the period of f is:
[tex]\frac{20\pi}{9}[/tex]Following a similar process, we can find the period of the function g. Since we know that the period of the sine function is also 2π.
[tex]\begin{gathered} 5\pi\Delta x=2\pi \\ \Rightarrow\Delta x=\frac{2\pi}{5\pi} \\ \therefore\Delta x=\frac{2}{5} \end{gathered}[/tex]Therefore, the period of g is:
[tex]\frac{2}{5}[/tex]Write the percent as decimal 5.3%
Given:-
[tex]5.3\%[/tex]To convert the given percentage as decimal.
So now we simplify,
[tex]5.3\%=\frac{5.3}{100}=0.053[/tex]So the required decimal number is 0.053
A triangle has sides with lengths of 10 miles, 12 miles, and 17 miles. Is it a right triangle? yes no
you can solve a triangle if you have the 3 sides
using these formulas
[tex]\begin{gathered} \cos A=\frac{b^2+c^2-a^2}{2bc} \\ \\ \cos B=\frac{a^2+c^2-b^2}{2ac} \end{gathered}[/tex]So
[tex]\begin{gathered} \cos A=\frac{10^2+12^2-17^2}{2(10)(12)} \\ \cos A=\frac{-45}{240} \\ A=\cos ^{-1}(\frac{-45}{240}) \\ A=100.8 \end{gathered}[/tex][tex]undefined[/tex]the sum of all the angles must equal 180
[tex]\begin{gathered} A+B+C=180 \\ 100.8+35.29+C=180 \\ C=180-35.29-100.8 \\ C=43.41 \end{gathered}[/tex]a rigth triangle have an angle of 90°, so this triangle isn't rigth
9 1 point Jonah has 20 nickels and dimes. In total, he has $1.75. Use question 7 to find out how many dimes Jo Type your answer... Previous
Answer:
Jonah has 15 dimes.
Step by step explanation:
Since question 7, tells us that we have to use the following equations to solve the system:
Let x be the nickels
Let y be the dimes
[tex]\begin{gathered} x+y=20\text{ (1)} \\ .05x+.10y=1.75\text{ (2)} \end{gathered}[/tex]We can use the substitution method to solve the system, isolate y in equation (1), and then plug it into equation (2)
[tex]y=20-x\text{ (1)}[/tex][tex]\begin{gathered} .05x+.10(20-x)=1.75 \\ \end{gathered}[/tex]Now, solve for x.
[tex]\begin{gathered} .05x+2-.10x=1.75. \\ -.05x=1.75-2 \\ -.05x=-0.25 \\ x=\frac{-0.25}{-0.05} \\ x=5 \end{gathered}[/tex]That means Jonah has 5 Nickels. Now to solve for y(dimes), substitute x=5 into equation (1)
[tex]\begin{gathered} y=20-x \\ y=20-5 \\ y=15 \end{gathered}[/tex]Jonah has 15 dimes.
hey, I would like to know how to this problem
Given:
Graph is given.
Insecting point of two lines is (1,2.5)
[tex]\text{Solution : (1,2.5)}[/tex]Four movie tickets cost $50. How much will six movie tickets cost?
Answer:
300
Step-by-step explanation:
just do 50 times 6 bro
