Answer:
x=6
Step-by-step explanation:
sqrt (2x-3) = sqrt (3x-9)
Square each side
(sqrt (2x-3))^2 = (sqrt (3x-9))^2
2x-3 = 3x-9
Subtract 2x from each side
2x-3-2x = 3x-2x-9
-3 = x-9
Add 9 to each side
-3+9 = x-9+9
6 =x
Check solution
sqrt (2*6-3) = sqrt (3*6-9)
sqrt (9) = sqrt (9)
3=3
Solution is valid
sqrt (2x-3) = sqrt (3x-9)
Square each side
(sqrt (2x-3))^2 = (sqrt (3x-9))^2
2x-3 = 3x-9
Subtract 2x from each side
2x-3-2x = 3x-2x-9
-3 = x-9
Add 9 to each side
-3+9 = x-9+9
6 =x
sqrt (2*6-3) = sqrt (3*6-9)
sqrt (9) = sqrt (9)
3=3
Therefore ans x = 6
Answered by Gauthmath must click thanks and mark brainliest
ASAP HELP: If a sample proportion is 0.55, which range of possible values best describes an estimate for the population parameter?
A. (0.55, 0.6)
B. (0.4, 0.7)
C. (0.4, 0.69)
D. (0.5, 0.59)
Answer:
B.(0.4,0.7)
Step-by-step explanation:
We are given that
Sample proportion
[tex]\hat{p}=0.55[/tex]
We have to find the range of possible values which describes best an estimate for the population parameter.
Estimate for the population parameter
[tex]\hat{p}\pm Z(SE)[/tex]
A.(0.55,0.6)
Difference between 0.55 and 0.55=0
Difference between 0.55 and 0.6=0.05
Difference between 0.55 and 0.55 is not equal to difference between 0.55 and 0.6.
Hence, option A is wrong.
B.(0.4,0.7)
Difference between 0.55 and 0.4=0.15
Difference between 0.55 and 0.7=0.15
Difference between 0.55 and 0.4 is equal to difference between 0.55 and 0.7.
Hence, option B is correct.
C. (0.4,0.69)
Difference between 0.55 and 0.4=0.15
Difference between 0.55 and 0.69=0.14
Difference between 0.55 and 0.4 is not equal to difference between 0.55 and 0.69.
Hence, option C is not correct.
D.(0.5,0.59)
Difference between 0.55 and 0.5=0.05
Difference between 0.55 and 0.59=0.04
Difference between 0.55 and 0.5 is not equal to difference between 0.55 and 0.59.
Hence, option D is not correct.
what describes shoe size?
a. natural number
b. integer
c. rational number
d. real number
Write a linear equation representing the information shown in the table.
A) y = –2∕5x – 5
B) y = –5∕2x – 5
C) y = 5∕2x – 5
D) y = 2∕5x – 5
Answer: C
Step-by-step explanation:
There are many ways to find the linear equation that matches the table, but let's do it so that we find the slope and y-intercept.
Based on the first entry (0,-5), we know that the y-intercept is -5.
To find slope, we take any two points and plug them into this [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]. We'll use the first two points.
[tex]m=\frac{0-(-5)}{2-0} =\frac{5}{2}[/tex]
Now, we know the slope is [tex]\frac{5}{2}[/tex].
The only equation that has the same slope and y-intercept that we found is C.
Rudy Banks has won $5000 to attend university. If he invests the money in an
account at 12% per annum, compounded monthly, how much can he draw monthly
for the next 3 years?
Answer:
$7153.84
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Compounded Interest Rate Formula: [tex]\displaystyle A = P(1 + \frac{r}{n})^{nt}[/tex]
P is principle amountr is raten is compound ratet is timeStep-by-step explanation:
Step 1: Define
Identify variables
P = 5000
r = 12% = 0.12
n = 12
t = 3
Step 2: Find Interest
Substitute in variables [Compounded Interest Rate Formula]: [tex]\displaystyle A = 5000(1 + \frac{0.12}{12})^{12(3)}[/tex][Exponents] Multiply: [tex]\displaystyle A = 5000(1 + \frac{0.12}{12})^{36}[/tex](Parenthesis) Add: [tex]\displaystyle A = 5000(1.01)^{36}[/tex]Evaluate exponents: [tex]\displaystyle A = 5000(1.43077)[/tex]Multiply: [tex]\displaystyle A = 7153.84[/tex]CHOOSE THE EQUIVALENT STATEMENT.
If a parallelogram has congruent diagonals, then it is a rectangle.
A. If a parallelogram is not a rectangle, then it does not have congruent diagonals.
B. If parallelogram does not have congruent diagonals, then it is a rectangle.
C. If a parallelogram is a rectangle, then it does not have congruent diagonals.
Answer: A. If a parallelogram is not a rectangle, then it does not have congruent diagonals.
The radius of a sphere is 3 inches. Which represents the volume of the sphere?
A) 120 cubic inches
B) 367 cubic inches
C) 647 cubic inches
D) 817 cubic inches
The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $16 and $30 per share.
What is the probability that the stock price will be:_______
a) More than $25? (Round your answer to 4 decimal places.)
b) Less than or equal to $18? (Round your answer to 4 decimal places.)
Answer:
a) 0.3571 = 35.71% probability that the stock price will be more than $25.
b) 0.1429 = 14.29% probability that the stock price will be less than or equal to $18.
Step-by-step explanation:
Uniform probability distribution:
An uniform distribution has two bounds, a and b.
The probability of finding a value of at lower than x is:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
The probability of finding a value between c and d is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
The probability of finding a value above x is:
[tex]P(X > x) = \frac{b - x}{b - a}[/tex]
Uniformly distributed between $16 and $30 per share.
This means that [tex]a = 16, b = 30[/tex]
a) More than $25?
[tex]P(X > x) = \frac{30 - 25}{30 - 16} = 0.3571[/tex]
0.3571 = 35.71% probability that the stock price will be more than $25.
b) Less than or equal to $18?
[tex]P(X < 18) = \frac{18 - 16}{30 - 16} = 0.1429[/tex]
0.1429 = 14.29% probability that the stock price will be less than or equal to $18.
Subtract.
8 over 9 minus 1 over 3
Answer:
5 over 9
Step-by-step explanation:
multiplayer both sides of the second fraction by 3, then you have 3 over 9. So the problem becomes 8-3=5
Write an expression (or equation) that represents the number of square feet
of wallpaper you will need if the height of the family room is x feet, with a
length and width that are each 3 times the height of the room. The family
room has 1 door, which is 3 feet wide and 7 feet tall.
Answer: Given
room height is x feet
room length is 3x feet
room width is 3x feet
a door 3 ft wide by 7 ft tall
Find
The net area of the wall, excluding the door
Solution
The area of the wall, including the door, is the room perimeter multiplied by the height of the room. The room perimeter is the sum of the lengths of the four walls.
... gross wall area = (3x +3x +3x +3x)·x = 12x²
The area of the door is the product of its height and width.
... door area = (7 t)×(3 ft) = 21 ft²
Then the net wall area, exclusive of the door is ...
... net wall area = gross wall area - door area
... net wall area = 12x² -21 . . . . square feet
An election ballot asks voters to select three city commissioners from a group of six candidates. If your aunt and father are running, what is the probability that either your aunt or your father will become a city commissioner
Answer:
0.8 = 80% probability that either your aunt or your father will become a city commissioner.
Step-by-step explanation:
The candidates are chosen from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
6 candidates, which means that [tex]N = 6[/tex]
2 are the aunt and father, which means that [tex]k = 2[/tex]
3 are chosen, which means that [tex]n = 3[/tex]
What is the probability that either your aunt or your father will become a city commissioner?
Probability of at least one of them being chosen, which is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 0) = h(0,6,3,2) = \frac{C_{2,0}*C_{4,3}}{C_{6,3}} = 0.2[/tex]
Then
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.2 = 0.8[/tex]
0.8 = 80% probability that either your aunt or your father will become a city commissioner.
find the missing variables
The triangle on the image is a right triangle which means we can use trigonometry to untangle its mysteries.
We have a side an and angle from that we can compute anything.
We will first compute x, we do so by taking the cosine of an angle,
[tex]\cos(45)=\frac{5\sqrt{2}}{x}[/tex]
[tex]x=\frac{5\sqrt{2}}{\cos(45)}=\frac{5\sqrt{2}}{\frac{\sqrt{2}}{2}}=\frac{10\sqrt{2}}{\sqrt{2}}=\boxed{10}[/tex]
Then we can also compute y, simply by using pythagorean theorem,
[tex]10^2=y^2+(5\sqrt{2})^2[/tex]
[tex]y=\pm\sqrt{100-50}=\pm\sqrt{50}=\boxed{5\sqrt{2}}[/tex].
So triangle has sides [tex]5\sqrt{2},5\sqrt{2},10[/tex] which is also known as equilateral triangle.
Hope this helps :)
Which of the following rational functions is graphed below?
Answer:
D. F(x) = [tex]\frac{1}{(x+4)}^{2}[/tex]
Use the information below to complete the problem: p(x) = (1)/(x + 1)
and q(x) = (1)/(x - 1)
Perform the operation and show that it results in another rational expression.
p(x) - q(x)
Given:
The functions are:
[tex]p(x)=\dfrac{1}{x+1}[/tex]
[tex]q(x)=\dfrac{1}{x-1}[/tex]
To find:
The rational expression for [tex]p(x)-q(x)[/tex].
Solution:
We have,
[tex]p(x)=\dfrac{1}{x+1}[/tex]
[tex]q(x)=\dfrac{1}{x-1}[/tex]
Now,
[tex]p(x)-q(x)=\dfrac{1}{x+1}-\dfrac{1}{x-1}[/tex]
[tex]p(x)-q(x)=\dfrac{(x-1)-(x+1)}{(x+1)(x-1)}[/tex]
[tex]p(x)-q(x)=\dfrac{x-1-x-1}{x^2-1^2}[/tex] [tex][\because a^2-b^2=(a-b)(a+b)][/tex]
[tex]p(x)-q(x)=\dfrac{-2}{x^2-1}[/tex]
Therefore, the required rational expression for [tex]p(x)-q(x)[/tex] is [tex]\dfrac{-2}{x^2-1}[/tex].
Help please:))
2. When shipping ice cream, melting is understandably a big concern. You will notice that ice cream is not generally packaged in a cube-shaped container. A standard container of ice cream contains 1 L, or 1000 cm3 of ice cream,
a. What would be the optimal dimensions (radius and height) to minimize surface area?
b. What would the surface area be?
C. Suggest at least two reasons why this is different from the ice cream packaging that you see in the stores.
Answer:
a) Because this asks about the radius and height, I assume that we are talking about a cylinder shape.
Remember that for a cylinder of radius R and height H the volume is:
V = pi*R^2*H
And the surface will be:
S = 2*pi*R*H + pi*R^2
where pi = 3.14
Here we know that the volume is 1000cm^3, then:
1000cm^3 = pi*R^2*H
We can rewrite this as:
(1000cm^3)/pi = R^2*H
Now we can isolate H to get:
H = (1000cm^3)/(pi*R^2)
Replacing that in the surface equation, we get:
S = 2*pi*R*H + pi*R^2
S = 2*pi*R*(1000cm^3)/(pi*R^2) + pi*R^2
S = 2*(1000cm^3)/R + pi*R^2
So we want to minimize this.
Then we need to find the zeros of S'
S' = dS/dR = -(2000cm^3)/R^2 + 2*pi*R = 0
So we want to find R such that:
2*pi*R = (2000cm^3)/R^2
2*pi*R^3 = 2000cm^3
R^3 = (2000cm^3/2*3.14)
R = ∛(2000cm^3/2*3.14) = 6.83 cm
The radius that minimizes the surface is R = 6.83 cm
With the equation:
H = (1000cm^3)/(pi*R^2)
We can find the height:
H = (1000cm^3)/(3.14*(6.83 cm)^2) = 6.83 cm
(so the height is equal to the radius)
b) The surface equation is:
S = 2*pi*R*H + pi*R^2
replacing the values of H and R we get:
S = 2*3.14*(6.83 cm)*(6.83 cm) + 3.14*(6.83 cm)^2 = 439.43 cm^2
c) Because if we pack cylinders, there is a lot of space between the cylinders, so when you store it, there will be a lot of space that is not used and that can't be used for other things.
Similarly for transport problems, for that dead space, you would need more trucks to transport your ice cream packages.
A survey of North Albion students found that they favoured Avengers: EndGame to Black Panther to Mulan in a ratio of 8:7:3. If 754 students were surveyed, how many preferred each movie?
Answer:
Avengers: Endgame ≈ 335
Black Panther ≈ 293
Mulan ≈ 126
Step-by-step explanation:
8+7+3=18
754/18 = 41.88888889
8*41.88888889 ≈ 335
7*41.88888889 ≈ 293
3*41.88888889 ≈ 126
335+293+126=764
The maximum and minimum values of a quadratic function are called as_______of the function.
Determine the number positive real zeros of the polynomial below. (Type answer in as a whole number)f(x)=x^5+3x^2-4x+2
Answer:
The number of positive real zeros is 2 or 0
Step-by-step explanation:
Given
[tex]f(x)=x^5+3x^2-4x+2[/tex]
Required
Number of positive real zeros
Using Descartes rule of signs;
We write out the signs in front of each term;
Sign = + + - +
Count the number of times the sign alternate; i.e. from positive to negative and from negative to positive
From positive to negative, we have: 1 (i.e. + - )
From negative to positive, we have: 1 (i.e. - +)
Add up the count
[tex]count = 1+1[/tex]
[tex]count = 2[/tex]
Hence, the number of positive real zeros is 2 or 0
Ophelia is making homemade spaghetti sauce by combining 48 oz of tomato paste with 6 cups of water.how many ounces of tomatoes paste are needed for every cup of water show your work.
Answer:
8 ounces of tomato paste for each cup of water.
Step-by-step explanation:
Just divide 48 / 6 to get 8 oz of tomato paste per cup of water.
Hope this helps!
Work Shown:
48 oz of tomato paste = 6 cups of water
48/6 oz of tomato paste = 6/6 cups of water
8 oz of tomato paste = 1 cup of water
In short, we divide both values by 6 so that the "6 cups" becomes "1 cup". We can say the unit rate is 8 oz of tomato paste per cup of water.
Find the work done by the force field F= on a particle that moves along the cubic y=x[tex]x^{3}[/tex] from (2,3) to (4,4).
Answer:
2 4 because I tookt the test
Find the lateral surface area and volume of the solid object.
Answer:
See answers below
Step-by-step explanation:
Lateral surface area of a cone is expressed as:
L = πr√h²+r²
Given that
r = 11.5/2 = 5.75cm
h=16.6cm
L = 3.14(5.75)√16.6²+5.75²
L = 18.055√275.56+33.0625
L = 18.055*17.56
L=317.0458cm²
Volume = 1/3πr²h
Volume = 1/3π(5.75)²(16.6)
Volume = 1,723.34975/3
Volume = 574.45cm³
compound interest on a sum of money for 2 years compounded annually is Rs 8034 simple interest on the same sum for the same period and at the same rate is Rs 7800 find the sum and the rate of interest
Here, we want to find the interest rate and principal
The interest rate, r = 6% and the principal, P = Rs 65,000
Compound interest:
A = P(1 + r/n)^t
Simple interest :
I = P * r * t
Simple interest for 2 years = Rs 7800
Simple interest for 1 year = Rs 7800 / 2
= Rs 3900
Compound interest for 2 years = Rs 8034
Compound interest for the second year = Rs 8034 - Rs 3900
= Rs 4134
Interest on Rs 3900 = Rs 4134 - Rs 3900
= Rs 234
Therefore,
Interest rate, r = 234/3900 × 100
= 0.06 × 100
r = 6%
Recall,
Simple interest :
I = P * r * t
Then,
P = I / r * t
= 3900 / 6% * 1
= 3900 / 0.06
= 65,000
P = Rs 65,000
https://brainly.in/question/1489411
al calls every 3 days, lee every 4 days, and pat every 6 day. Once every ? days, all three will call on the same day
Answer:
12
Step-by-step explanation:
Find the LCM (Least Common Multiple) of the three numbers.
We could multiply 3 x 4 x 6 to get 72, but there is a smaller multiple, 12.
6 x 2 = 12
4 x 3 = 12
3 x 4 = 12
Hope this helps!
Is 1 2/6 a rational number?
Answer:
Yes, it is rational number.
Step-by-step explanation:
A rational number is any integer, fraction, terminating decimal, or repeating decimal.
Hope it is helpful.....wrote the terms below.
–8, –4, 0, 4, 8, 12
What do these terms represent?
an arithmetic series
an arithmetic sequence
a geometric series
a geometric sequence
Answer:
an arithmetic sequence
Step-by-step explanation:
an arithmetic series is wrong also heres an example i found of an arithmetic sequence
The terms in the given sequence represents an arithmetic sequence.
What is Arithmetic Sequence?Arithmetic sequence is a sequence of numbers where the numbers are arranged ion a definite order such that the difference of two consecutive numbers is a constant. This constant of difference is called common difference which is commonly denoted by the letter 'd'.
Given sequence of numbers is,
-8, -4, 0, 4, 8, 12, ......
We have to find which sequence does it represent.
This is not a series since they are not represented as the sum.
If the sequence is a geometric sequence, then the ratio of consecutive numbers will be same.
If it is arithmetic sequence, then the difference of consecutive numbers will be same.
Here, ratio is not same.
Difference are same.
-4 - -8 = 4, 0 - -4 = 4, 4 - 0 = 4, 8 - 4 = 4, ........
Common difference is 4.
Hence it is an arithmetic sequence.
Learn more about arithmetic Sequence here :
https://brainly.com/question/15412619
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faith is 16 years older than precoius in 10 years time. faith will be double Precious age. How old is precious?
Answer:
6 years old
Step-by-step explanation:
Let [tex]f[/tex] represent Faith's current age and let [tex]p[/tex] represent Precious's current age.
Faith is 16 years older than Precious:
[tex]f=p+16[/tex]
In 10 years' time, Faith will be double Precious's age:
[tex]f+10=2(p+10)[/tex]
We can substitute the top equation into the bottom equation:
[tex](p+16)+10=2(p+10)[/tex]
We can combine like terms on the left side and expand out the right side:
[tex]p+26=2p+20[/tex]
We can subtract p from both sides, and then subtract 20 from both sides to get:
[tex]6=p[/tex]
This means Precious is 6 years old.
Rubin grew 9 tomatoes with 6 seed packs. How many seed packs does Rubin need to have a total of 21 tomatoes in his garden?
Answer: 14 seed packs
Step-by-step explanation:
You'd divide the 9 tomatoes by the 6 seed packs that were necessary to grow them, resulting in 1.5 tomatoes per seed pack. Divide 21 by this 1.5 to find the number of seed packs needed to grow 21 tomatoes, which would be 14.
A solid oblique pyramid has a square base with edges measuring x cm. The height of the pyramid is (x + 2) cm.
A solid oblique pyramid has a square base with edges measuring x centimeters. The height is (x + 2) centimeters.
Which expression represents the volume of the pyramid?
StartFraction x cubed + 2 x squared Over 3 EndFraction cm3
StartFraction x squared + 2 x squared Over 2 EndFraction cm3
StartFraction x cubed Over 3 EndFraction cm3
StartFraction x cubed + 2 x squared Over 2 EndFraction cm3
Answer:
Hello,
Answer A StartFraction x cubed + 2 x squared Over 3 EndFraction cm3
Step-by-step explanation:
[tex]V=x^2*\dfrac{x+2}{3} \\\\\boxed{V=\dfrac{x^3+2x^2}{3} }\\[/tex]
the third of the sum of the cube of x and double of the square of x ( cm³)
The Volume of pyramid with a square base of side x cm and height of (x + 2) cm is (x³ + 2x²) / 3
What is volume?
Volume is the amount of space occupied by a three dimensional shape or object.
Area of the square base = x * x = x² cm²
Volume of pyramid = (1/3) * area of base * height = (1/3) * x² * (x + 2)
Volume of pyramid = (x³ + 2x²) / 3
The Volume of pyramid with a square base of side x cm and height of (x + 2) cm is (x³ + 2x²) / 3
Find out more on volume at: https://brainly.com/question/12410983
Answer this please~!!!!
Answer:
12
Step-by-step explanation:
113.04=3.14 x 3^2 x h/3
A company is reviewing tornado damage claims under a farm insurance policy. Let X be the portion of a claim representing damage to the house and let Y be the portion of the same claim representing damage to the rest of the property. The joint density function of X and Y is Determine the probability that the portion of a claim representing damage to the house is less than 0.2.
Answer:
Please find the complete question in the attachment.
Step-by-step explanation:
The likelihood of the part of claims that is less than 0.05 for all the houses is calculated as:
[tex]P(X < 0.05) = int^{0.05}_{0} int^{1-x}_{0} f(x,y) \ dy\ dx\\\\[/tex]
[tex]= \int^{0.05}_{0} \int^{1-x}_{0} 6(1-x-y) \ dy\ dx\\\\= \int^{0.05}_{0} 6((1-x)-x(1-x)-\frac{(1-x)^2}{2}) \ dx\\\\ = \int^{0.05}_{0} 6(1-2x+x^2-0.5-0.5x^2+x) \ dx\\\\= \int^{0.05}_{0} 6(0.5x^2-x+0.5) \ dx\\\\= 6(0.5\times \frac{0.05^3}{3} -\frac{0.05^2}{2}+0.5 \times 0.05 )\\\\ =0.1426\\\\[/tex]
Given the exchange rate as K1: HK$1.353, calculate Hong Kong dollar equivalent of K70
Answer:
The Hong Kong dollar equivalent of K70 is HK $ 94.71.
Step-by-step explanation:
Given the exchange rate as K1: HK $ 1,353, to calculate Hong Kong dollar equivalent of K70 the following calculation must be performed:
1,353 x 70 = X
94.71 = X
Therefore, the Hong Kong dollar equivalent of K70 is HK $ 94.71.
