The value of x in terms of l is.
[tex]x=\sqrt{5l^{2} }[/tex]
What is Pythagoras Theorem?A fundamental relationship in Euclidean geometry between a right triangle's three sides is known as the Pythagorean theorem, or Pythagoras' theorem. The area of the square whose side is the hypotenuse is said to be equal to the total of the areas of the squares on the other two sides.
given data:length = [tex]l[/tex]
width= [tex]2l[/tex]
diagonal = [tex]x[/tex]
We would get a right angle triangle if we were to cut a part across the diagonal. The Pythagoras Theorem can be used to solve the right angle triangle.
[tex]x^{2} =a^{2} +b^{2}[/tex]
using this formula substituting the value:
[tex]x^{2} =l^{2} +2l^{2}[/tex]
[tex]x^{2} =l^{2} +4l^{2} \\x^{2} =5l^{2} \\x=\sqrt{5l^{2}} \\[/tex]
from the above calculation we have:
[tex]x=\sqrt{5l^{2} }[/tex]
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Cost of 4 tables and 3 chairs is $225 and 3 tables and 4
chairs cost $195. Find the cost of 2 chairs and 1 table.
The cost of 2 chairs is = $30
The cost of 1 table = $60
Step-by-step explanation:
Let a table represent x
A chair represents y
4x + 3y = 225.......eq 1
3x + 4y = 195........eq 2
Use elimination method
x - y = 30
x= 30 + y...... Eq 3
Substitute the value of x into equation 1
4(30+ y) + 3y= 225
120 + 4y + 3y= 225
7y + 120= 225
7y= 225-120
7y= 105
y= 15
Substitute the value of y in eq 2
3x + 15 = 195
3x= 195-15
3x= 180
x= 60
Therefore, the cost of 2 chairs is 15 * 2= $30
The cost of 1 table = $60
Answer:
65
Step-by-step explanation:
How many roots does the polynomial….
Answer:
(a) 3
Step-by-step explanation:
The fundamental theorem of algebra tells you a polynomial has a number of roots equal to its degree.
RootsThe degree of a polynomial is the largest exponent of the variable. Here, the degree is 3. That means there are three roots.
In general, the roots of a polynomial with real coefficients will be real or pairs of complex roots. The attached graph shows the roots of this cubic function are all real (and irrational).
(1)[3 Pts] The probability of producing a high-quality color print is 0.10. How many prints do you have to produce so that the probability of producing at least one quality print is larger than 0.90
The number of prints that the probability of producing at least one quality print is 22.
Given that the probability of producing a high-quality color print is 0.10.
The binomial distribution summarizes the number of trials or observations when each trial has an equal chance of reaching a certain value. The binomial distribution determines the probability of observing a particular number of positive results in a defined number of tests.
Probability of high-quality color print (P) = 0.1
Probability of producing not high-quality color print (1-P) = 0.9
Assume the no. of prints to produce 'n' and these are produced independently say 'x' be the no. of producing quality prints, which follows a binomial distribution.
The probability function of binomial distribution is
[tex]P(X=x)\left(\begin{array}{l}n\\ x\end{array}\right)P^x(1-P)^{n-x},x=0,1,2,.....,n[/tex]
Given that
P(X≥1)≥0.90
1-P(X=0)≥0.90
1-(1-P)ⁿ≥0.90
1-(0.90)ⁿ≥0.90
(0.90)ⁿ≥0.10
Now, taking log of both sides, we get
nlog(0.90)≥log(0.10)
n(0.1053)≥2.3025
n≥21.86
n≈22
Hence, the probability of producing a high-quality color print is 0.10 and the number of prints to produce so that the probability of producing at least one quality print is larger than 0.90 is 22.
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(05.02 MC)
Solve 2 log x = log 64.
Ox= 1.8
Ox=8
Ox= 32
Ox = 128
Answer:
x = 8
Step-by-step explanation:
[tex]2logx=log64\\logx^2=log64[/tex]
now that both sides has log, you can remove them and leave it as:
[tex]x^{2} =64\\[/tex]
take the square root of both sides:
[tex]x = [8, -8]\\x = 8[/tex]
logarithmic equations can't have negative solutions, plus -8 isn't an option
i hope this helped!
explain how the following problem could be solved. then, solve the problem. a full-grown dog is about one-eighth as heavy as a cow. together, they weigh 360 kg.
The problem could be solved using the linear equation in one variable, x/8 + x = 360, where x kg is the weight of a cow.
The weight of the cow, on solving the equation, is found to be 320 kg.
The weight of the full-grown dog = (1/8)*320 kg = 40 kg.
We assume the weight of the cow to be x kg.
The weight of a full-grown dog is given to be one-eight of a cow, that is, the weight of a full-grown dog = (1/8)*x = x/8 kg.
Thus, the sum of the weights of the full-grown dog and the cow = x/8 + x kg.
But, we are given that together, they weigh 360 kg.
This can be shown as the linear equation in the one variable:
x/8 + x = 360.
Thus, the problem could be solved using the linear equation in one variable, x/8 + x = 360, where x kg is the weight of a cow.
To solve the problem, we solve the equation as follows:
x/8 + x = 360,
or, (9/8)x = 360 {Simplifying},
or, x = 360*8/9 {Cross-Multiplying},
or, = 320.
Thus, the weight of the cow, on solving the equation, is found to be 320 kg.
The weight of the full-grown dog = (1/8)*320 kg = 40 kg.
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There are 15 players on a volleyball team. Only 6 players can be on the court for a game. How many different groups of players of 6 players can the coach make, if the position does not matter?
Using the combination formula, the coach can make 5,005 different groups.
The position does not matter, hence the combination formula is used.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, 6 students are taken from a set of 15, hence the number of groups is:
[tex]C_{15,6} = \frac{15!}{6!9!} = 5005[/tex]
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How many different 2-digit numbers are there with the following property: it is evan and its digits are distinct?
By counting all the even 2-digit numbers between 10 and 100, there are 41 even and distinct digits.
What is an even number?An even number can be defined as a type of number which is divisible by two (2) without any remainder.
How to determine this 2-digit number?Since this 2-digit numbers are even and its digits are distinct, we can infer and logically deduce the following points:
They are between 10 and 100.They are not repeated.They must contain two digits only.By counting all the even 2-digit numbers between 10 and 100, there are 41 even and distinct digits.
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What is the domain and range of each function?
FIRST PERSON TO ANSWER GETS BRAINLIEST OR 5 STARS :D
A) f(x) = −2x
Domain:
Range:
g(x) = ½x2 + 5
Domain:
Range:
Answer:
Greetings!A) Domain: x∈R or in interval notation (- ∞, ∞)
Range: x∈R or in interval notation (- ∞, ∞)
Thus, they both the domain & the range of the first function are the same.
B) Domain: x∈R or in interval notation (- ∞, ∞)
Range: [-5,∞)
Using it's concepts, the domain and the range of the functions are given as follows:
a) Both all real numbers.
b) Domain all real numbers, range [tex]y \geq 5[/tex].
What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input.The range of a function is the set that contains all the values of the output.In this problem, neither function has any impediment, such as an even root or denominator, hence the domain is all real numbers. As for the range, a linear function assumes all real values, while a concave up quadratic function assumes values of the vertex, in this case y = 5, and greater, hence the range of the second function is [tex]y \geq 5[/tex].
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PLEASE HELP quickly
Answer:
C. Radius or diameter must be known.
Step-by-step explanation:
The radius or diameter must be known so you can use the formula.
Hope this helps!
There are 24 students in a class. if 16 are boys, what fraction of the students are boys?
Answer:
2/3 is the fraction of students who are boys.
Step-by-step explanation:
First of all, a fraction consists of two parts: The denominator and the numerator. The denominator is the whole, while the number is a part of the whole (and sometimes above).
1. Since in your question, there are 24 students in total in the class, the denominator will be 24.
2. You said that 16 of them are boys, so 16 is the numerator.
3. In a fraction, it will be 16/24.
4. 16/24 can be simplified into 2/3 since both 16 and 24 can be divided by 8.
So our final answer is 2/3.
PLEASE HELP WILL GIVE YOU ALOT OF POINTS
Rebecca filled 28 glasses with orange juice for a camp breakfast. if each glass holds 1 cup of juice, how many quarts of orange juice did rebecca use?
The number of quarts of orange juice did Rebecca use is 7
Given that 28 glasses with orange juice are filled for a camp breakfast
Each glass holds 1 cup of juice
We need to find the number of quarts of orange juice did Rebecca use
We know that a quarts has 4 cups
We need to calculate the quarts from 28 glasses
Let the number of the quarts be x
So the equation formed is
4x = 28
Where x is number of quarts and 28 are the number of glasses
x = 7
Hence the number of quarts is 7
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True or False: Both equations have 'no solutions'.
15x +4-2x = 3(6x + 5)
(2x-8)=(8x+36)
Answer:
False
Step-by-step explanation:
They both have 1 solution
15x + 4 = 3(6x +5)
15x +4 = 18x + 15 Multiple everything in the parentheses by 3.
4 = 3x + 15 Subtract 15 x from both sides
-11 = 3x Subtract 15 from both sides
-11/3 = x Divide both sides by 3
There is only one solution for this equation.
2x -8 = 8x + 36
-8 = 6x + 36 Subtract 2x from both sides
--44 = 6x Subtract 36 from both sides
-44/6 = x Divide both sides by 6.
There is only one solution for this equation.
Answer:
false
Step-by-step explanation:
They both have solutions
An allergy medication is successful in treating 60% of all patients who use it. The medication is given to 200 patients. Let X
The mean is μ=140.
The standard deviation is σ = 6.4807.
The probability that X (number of successful treatments) is 128 or less is 0.0322.
What is normal distribution curve?In statistics, a normal distribution's probability density function is represented by a symmetrical bell-shaped curve. The likelihood that the random variable will fall between two values that define a vertical portion of the curve is represented by the area of the section.
According to the question,
An allergy medication is successful in treating 70%
The medication is given to 200 patients.
Thus,
The random variable X is a binomial random variable with n = 200 (there were 200 patients).
The probability that a medication is successful in treating a randomly selected patient is 0.7.
p = 0.7 (the medication was successful in 70% cases).
Step 1: Use the formulas for mean and standard deviation of a binomial random variable X.
[tex]\begin{gathered}\mu=E(X)=n \cdot p \\\sigma=\sqrt{n \cdot p \cdot(1-p)}\end{gathered}[/tex]
Substitute values of 'n' and 'p' to get the result,
[tex]\begin{gathered}\mu=200 \cdot 0.7=140 \\\sigma=\sqrt{200 \cdot 0.7 \cdot 0.3}=\sqrt{42}=6.4807 .\end{gathered}[/tex]
Thus, the mean is obtained as 140.
The standard deviation is 6.4807.
Step 2: find P(X≤128)
As a result, the prerequisites for a normal approximation to the binomial distribution are satisfied.
[tex]$n \cdot p=200 \cdot 0.7=140 \geq 10$$$n \cdot(1-p)=200 \cdot 0.3=60 \geq 10 .$$[/tex]
[tex]\begin{aligned}P(X \leq 128) & \approx P\left(Z \leq \frac{128-n \cdot p}{\sqrt{n \cdot p \cdot(1-p)}}\right)=P\left(Z \leq \frac{128-200 \cdot 0.7}{\sqrt{200 \cdot 0.7 \cdot(1-0.7)}}\right) \\&=P(Z \leq-1.85)=0.0322\end{aligned}[/tex]
Therefore, the probability that X is 128 or less. is 0.0322.
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The complete question is-
An allergy medication is successful in treating 70% of all patients who use it. The medication is given to 200 patients. Let X = number of successful treatments. What are the mean and standard deviation of X? Use the normal curve to approximate the probability that X is 128 or less.
Solve the system of equations 4x+5y=-14 and -5x-8y=10 by combining the equations.
The solution of the system is:
x = 62/7
y = 30/7
How to solve the system of equations?
Here we have the system:
4x + 5y = -14
-5x - 8y = 10
To solve it by combining the equations, we need to try to remove one of the variables.
If we take the sum of 5 times the first equation and 4 times the second equation we get:
5*(4x + 5y) + 4*(-5x - 8y) = 5*(-14) + 4*10
If we simplify that we get:
20x + 25y - 20x - 32y = -30
-7y = -30
Now we can solve that for y:
y = -30/-7 = 30/7
Now to get the value of x, we can replace the value of y in any of the given equations:
Using the first one:
4x + 5y = -14
x = (-14 - 5y)/4
x = (-14 - 5*30/7)/4 = (-98/7 - 150/7)/4 = 248/28 = 124/14 = 62/7
The solution of the system is:
x = 62/7
y = 30/7
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An arc of length 8 in. is intersected by a central angle in a circle with a radius of 3 in. What is the measure of the angle
Answer: [tex]\theta=\frac{8}{3} \text{ radians}[/tex]
Step-by-step explanation:
[tex]8=3\theta\\\\\theta=\frac{8}{3} \text{ radians}[/tex]
What is the simplified form of startroot startfraction 48 over 192 endfraction endroot?
By the use of factor decomposition and algebra properties, we conclude that the rational number 48/192 is equal to the rational number 1/4.
How to simplify rational numbers
In this question we should simplify a rational number into its simplest form based on two facts. First, that all natural numbers except 1 and the prime numbers are products of prime numbers and, second, the simplification of the fraction can be done by using the following algebra property:
(a · c)/(b · c) = a/b, where a, b, c are natural numbers. (1)
Along with power properties.
Now we proceed to simplify the rational number:
48/192 = (2⁴ × 3) / (2⁶ × 3)
48/192 = 1 / 2²
48/192 = 1 / 4
By the use of factor decomposition and algebra properties, we conclude that the rational number 48/192 is equal to the rational number 1/4.
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Answer:
4
Step-by-step explanation:
The ratio of dogs to cats is 3 to 8. if there are 294 dogs, how many cats are there?
Answer:
784 cats Yikes !
Step-by-step explanation:
d/c = 3/8
3/8 = 294/c
c = 294 * 8/3 = 784 cats
Solve for x sim b (10, 0.75) for x = 5
The value of [tex]x \sim B (10, 0.75)[/tex] for x = 5 is 0.06
How to solve the probability?The expression is given as:
[tex]x \sim B (10, 0.75)[/tex]
This means that:
n = 10
p = 0.75
The probability is then calculated as
[tex]P(x)= ^nC_x * p^x *(1 - p)^{n-x[/tex]
This gives
[tex]P(5)= ^{10}C_5 * 0.75^5 *(1 - 0.75)^5[/tex]
Evaluate the combination expression
[tex]P(5)= 252 * 0.75^5 *0.25^5[/tex]
Evaluate
P(5)= 0.06
Hence, the value of [tex]x \sim B (10, 0.75)[/tex] for x = 5 is 0.06
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Find the volume of the composite figure. Round to the nearest tenth if necessary.
The volume of the given composite solid is 375 m³
Volume of composite solidFrom the question, we are to determine the volume of the composite solid
The volume of the composite solid = Volume of the cuboid + Volume of the triangular prism
Thus,
Volume of the composite solid = (5 × 5 × 13) + 1/2(5 × 4 × 5)
Volume of the composite solid = 325 + 50
Volume of the composite solid = 375 m³
Hence, the volume of the given composite solid is 375 m³
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The lateral surface area of cone A is exactly 1/2 the lateral surface area of the cylinder B.
A. True
B. False
The statement, "the lateral surface area of cone A is exactly half of that of cylinder B" is: A. True.
What is the Lateral Surface Area of a Cone and a Cylinder?Lateral surface area of cone = πrl
Lateral surface area of cylinder = 2πrh
Lateral surface area of cone A = πrl = πrh
Lateral surface area of cylinder B = 2πrh
This means the lateral surface area of cylinder B is twice that of cone A. Thus, lateral surface area of cone A is exactly half of that of cylinder B.
The answer is: A. True.
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Rearrange the equation so q is the independent variable.
-7q+12r=3q-4r
Rearranging the equation so q is the independent variable is; q = -1.6r
How to change the subject of a subject?We are given the expression;
-7q + 12r = 3q - 4r
Since we want to make q the subject, let us rearrange the equation with variables having q on the left and others on the right side to get;
-7q - 3q = -4r - 12r
-10q = -16r
q = 16r/10
q = -1.6r
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PLEASE HELP IM STUCK
Answer:
-3
Step-by-step explanation:
look at the hint: slope (most call it gradient) = change in y/change in x
so you take 2 x and y variables and subtract
15 - 9 = 6 ← change in y
0 - 2 = -2 ← change in x
slope (gradient) = 6/-2
slope (gradient) = -3
A research center poll showed that 85% of people believe that it is morally wrong to not report all income on tax returns. What is the probability that someone does not have this belief? The probability that someone does not believe that it is morally wrong to not report all income on tax returns is (Type an integer or a decimal.)
The probability that someone does not believe that it is morally wrong to not report all income on tax returns is = 0.15
For given question,
A research center poll showed that 85 percent of people believe that it is morally wrong to not report all income on tax returns.
so, the probability that someone have this belief is P = 0.85
We know that in probability,
p = 1 - q
where;
p is probability of success
q is probability of failure.
Thus the probability that someone does not have this belief would be,
= 1 - P
= 1 - 0.85
= 0.15
Therefore, the probability that someone does not believe that it is morally wrong to not report all income on tax returns is = 0.15
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Triangle JKL is graphed on the coordinate plane. -5 -4 -3 y B MD N In L 2 4 5 X What are the coordinates of its image, JKL, if this triangle is dilated by a factor of 5 with respect to the origin? O J(2, 7), K (8, 7), and L'(5, 1) O J'(-5, 2), K'(5, 2), and L'(0, -5) O J'(-3, 2), K'(8, 2), and L'(0, -9) O J'(-15, 10), K'(15, 10), and L'(0, -20)
The coordinate of the image of JKL when dilated by a factor of 5 with respect to the origin is J'(-15, 10), K'(15, 10) and L'(0, 20).
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.
Translation is the movement of a point either up, left, right or down in the coordinate plane.
Let us assume that triangle JKL has vertices at J(-3, 2), K(3, 2) and L(0, 4).
The coordinate of the image of JKL when dilated by a factor of 5 with respect to the origin is J'(-15, 10), K'(15, 10) and L'(0, 20).
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the price for 5/6 l of liquid x is $80. what is the price per litre of liquid x
Answer:
$96.
Step-by-step explanation:
5/6 costs 80
Multiply both parts by 6/5:
5/6 * 6/5 ( = 1 ) costs 80 * 6/5
= 16 * 6
= $96.
The quadratic parent function has been reflected down, stretched vertically by a factor of 1/3
1a) f(x) = -1/3(x + 12)² + 9
1b) f(x) = -1/3x² - 8x - 39
Lets simplify it,
Expand by FOIL (First Outside Inside Last)
Standard Form: ax² + bx + c = 0
Transformations Graph: f(x) = a(bx - c)² + d
Reflected down and vertically stretched by 1/3: a = -1/3
Shifted vertically by 9 units: d = 9
Shifted horizontally by -12 units: c = -12
Vertex Form:
f(x) = a(bx - c)² + d
f(x) = -1/3(x + 12)² + 9
Standard Form:
f(x) = -1/3(x + 12)² + 9
f(x) = -1/3(x² + 24x + 144) + 9
f(x) = -1/3x² - 8x - 48 + 9
f(x) = -1/3x² - 8x - 39
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.For a field trip, 6 students rode in cars and the rest filled 8 buses. How many students were in each bus if 326 students were on the trip?
Let s represent the number of students on each bus.
Equation:
Answer:
Answer:
(326-6) ÷ 8 = s
40 = s
Step-by-step explanation:
Write the slope-intercept form of the equation that passes through the point (4,-6) and is parallel to the line y = -3/4x - 5
The equation that runs through the location (4,-6) has the slope-intercept form, [tex]y=-\frac{3}{4}x-3[/tex] .
Formation of the equationA line's equation written in the slope-intercept form:
y=mx+b
where m= slope & b= y-intercept
The slope of two parallel lines is equal.
Currently, we know the line's equation:
[tex]y=-\frac{3}{4} x-5[/tex]
here, slope, m= [tex]-\frac{3}{4}[/tex]
A line equation is created by adding the slope's value and the point's coordinates (4, -6):
[tex]-6=-\frac{3}{4}(4)+b[/tex]
⇒ -6=-3 +b [adding 3 to both sides]
⇒-3=b
⇒b= -3
Hence the solution is [tex]y=-\frac{3}{4}x-3[/tex] .
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Devon made a mosaic in art class with different-shaped tiles. She started by putting 2 rows of t triangle tiles at the top of the mosaic and 2 rows of c circle tiles at the bottom. She finished by putting 20 square tiles in between the triangle and circle tiles.
The expressions that represent number of tiles that Devon used on her mosaic:
A. 20 + 2t + 2c
D. 20 + t + t + c + c
What is an expression?An expression refers to a mathematical equation which shows the relationship between two or more numerical quantities or variables.
For the expressions that represent number of tiles that Devon used on her mosaic:
Let the triangle tiles be t.Let the circle tiles be c.Two rows of t triangle tiles = t + t = 2t.Two rows of c circle tiles = c + c = 2t.Mathematically, the expression is given by:
Total tiles = 20 + t + t + c + c
Total tiles = 20 + 2t + 2c.
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Complete Question:
Devon made a mosaic in art class with different-shaped tiles. She started by putting 2 rows of t triangle tiles at the top of the mosaic and 2 rows of c circle tiles at the bottom. She finished by putting 20 square tiles in between the triangle and circle tiles.
Pick all the expressions that represent how many tiles Devon used on her mosaic.
A. 20 + 2t + 2c
B. 20 + 4 ( t + c )
C. 2 ( 20 + t + c )
D. 20 + t + t + c + c