Answer:
Since the second box has inside dimensions four times those of the first box, its volume is $(4a)^3 = 64a^3$ times as much as the volume of the first box, whose volume is $a^3$. Therefore, the answer is (D) 64.
Use the remainder theorem and synthetic division to find the value of
f(3) if f(3) = x^3 - 6x^2 + 13x - 11
SHOW THE STEPS OF THE SYNTHETIC DIVISION!
The quotient is x² - 3 - 4 and remainder is 1.
So, The value of f (3) is, 1
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
The value of f(3) is told by the remainder theorem to be the remainder from division of f(x) by (x -3). That division is shown in the attachment. The remainder is 1, hence we have;
⇒ f(3) = 1
The number at upper left in the synthetic division table is the value of x for which we are evaluating f(x).
When the polynomial is written in Horner Form:
⇒ f(x) = ((x -6)x +13)x -11
Here, the coefficient of x at each point in the evaluation is the same as the number on the bottom row of the synthetic division. The result of the evaluation is the same as the remainder from the division.
Now, Add the obtained result to the next coefficient of the dividend and write down the sum as;
3 | 1 - 6 13 - 11
3 - 9 3x4 = 12
-----------------------
1 - 3 4 (- 11) + 12 = 1
Thus, We have complete table and have obtained the resulting coefficient are,
1 , - 3, 4, 1
Thus, The quotient is x² - 3 - 4 and remainder is 1.
So, The value of f (3) is, 1
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the waiting time, in hours, between successive speedersspotted by a radar unit is a continuous random variable wthcumulative distribution function
F(x)=
Find probability of waiting less than 12 min. betweensuccessive speeders?
a) using the cumulative distribution function of X
b) using the probability density function of X
The probability of waiting less than 12 minutes between successive speeders is 0.02.
The time elapsed between successive speeders detected by a radar unit is a random variable with a cumulative distribution function:
F(x) = 0 when x = 0.
x/10, for 0 x ten 1, for x ten
a) Using the cumulative distribution function, to calculate the probability of waiting less than 12 minutes (0.2 hours) between successive speeders: F(0.2):
F(0.2) = 0.2/10 = 0.02
So, the probability of waiting less than 12 minutes between speeders is 0.02.
b) Using the probability density function, we can differentiate the cumulative distribution function with respect to x to find the probability:
For x = 0, f(x) = dF(x)/dx = 0.
1/10 for 0 x 10 0, 0 for x 10
The area under the probability density function up to x=0.2 represents the probability of waiting less than 12 minutes:
P(0 < w < 0.2) = ∫0.2 0 f(x) (x) dx = ∫0.2 0 (1/10) dx = (1/10) * [x] 0.2 = 0.02
Using either the cumulative distribution function or the probability density function, the probability of waiting less than 12 minutes between successive speeders is 0.02.
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Find the equation of the plane that passes through the line of intersection of the planes 2x−3y−z+1=0
and 3x+5y−4z+2=0, and that also passes through the point (3,−1,2)
The equation of the plane that passes through the line of intersection of the two planes and passes through the point (3,-1,2) is x - 2y + 7z - 17 = 0 .
The Plane we want to find passes through the line of intersection of the planes, so it is perpendicular to the normal vectors of both planes.
The Normal Vector of the plane 2x - 3y - z + 1 = 0 is (2, -3, -1), and
the normal vector of the plane 3x + 5y - 4z + 2 = 0 is (3, 5, -4).
The cross product of these two vectors gives a vector which is perpendicular to both of them, and
hence , it lies along the line of intersection of the two planes:
the cross product of (2, -3, -1) x (3, 5, -4) is = (-7, -2, 1) ;
The vector (-7, -2, 1) is the direction vector of the line of intersection.
Now to find the equation of the plane that passes through the point (3, -1, 2) and is perpendicular to this direction vector.
we let , equation of the plane be ax + by + cz + d = 0. We know that the point (3, -1, 2) lies on the plane, so we have:
⇒ a(3) + b(-1) + c(2) + d = 0 ;
⇒ 3a - b + 2c + d = 0 ;
We also know that the plane is perpendicular to the direction vector (-7, -2, 1), so we have:
⇒ a(-7) + b(-2) + c(1) = 0 ;
⇒ -7a - 2b + c = 0 ;
Let say a = 1. Then we have :
⇒ a = 1
⇒ -7a - 2b + c = 0
⇒ 3a - b + 2c + d = 0
Substituting a = 1 into the first equation gives:
⇒ -7 - 2b + c = 0 ;
Solving for c in terms of b gives:
⇒ c = 2b + 7
Simplifying ,
we get ;
⇒ 3 - b + 2(2b + 7) + d = 0 ;
Solving for d in terms of b gives: ⇒ d = -2b - 17 ;
Therefore, the equation of the plane is x - 2y + 7z - 17 = 0 .
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The scores of a certain population on the Wechsler Intelligence Scale for Children (WISC) are thought to be Normally distributed with mean μ and standard deviation σ = 10. A simple random sample of 25 children from this population is taken and each is given the WISC. The mean of the 25 scores is = 104.32.
Based on these data, a 95% confidence interval for μ is
104.32 ± 0.78.
104.32 ± 3.29.
104.32 ± 3.92.
104.32 ± 19.60
If the scores of a certain population are Normally Distributed , and the mean is 104.32 , then the 95% confidence interval is (b) 104.32 ± 3.29 .
The Scores of the population of WISC are Normally Distributed ;
and the Mean(μ) of the 25 scores is = 104.32 ;
the standard deviation(σ) for the population is = 10 ;
the sample size(n) = 25 ;
For the 95% confidence, critical value is = 1.96 ;
So, Confidence interval is written as = μ ± 1.96(σ/√n)
Substituting the required values ,
we get ;
⇒ 104.32 ± 1.96(10/√25)
⇒ 104.32 ± 1.96×2
⇒ 104.32 ± 3.92
Therefore , the required 95% confidence interval is (104.32 ± 3.92) .
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The given question is incomplete , the complete question is
The scores of a certain population on the Wechsler Intelligence Scale for Children (WISC) are thought to be Normally distributed with mean μ and standard deviation σ = 10. A simple random sample of 25 children from this population is taken and each is given the WISC. The mean of the 25 scores is = 104.32.
Based on these data, a 95% confidence interval for μ is
(a) 104.32 ± 0.78.
(b) 104.32 ± 3.29.
(c) 104.32 ± 3.92.
(d) 104.32 ± 19.60
¿ Como despejar B en esta variable
The simplified form of the expression (4 - a²b³)/5 = (9 - 3b³)/7 is
b³(15 - 7a²) = 17.
What is an equation?An equation is written in the form of variables and constants separated by the operation of multiplication and division,
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
Given, An equation (4 - a²b³)/5 = (9 - 3b³)/7, in variables 'a' and 'b'.
7(4 - a²b³) = 5(9 - 3b³).
28 - 7a²b³ = 45 - 15b³.
15b³ - 7a²b³ = 45 - 28.
b³(15 - 7a²) = 17.
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jenny made $126 in 9 hours of work at the same rate how many hours would she have to work to make 252
Help please I’m dying and it is dew tomorrow and I have no clue what it could be
The effect on the graph for the given function if the slope of the function is changed to -10 include the following: D. the line is less steep.
The effect on the graph for the given function if the y-intercept of the function is changed to a smaller positive number is: C. the line shifts down.
What is a slope?In Mathematics, a slope is sometimes referred to as rate of change and it is typically used to describe both the direction, ratio, and steepness of the function of a straight line based on its coordinates or points.
Generally speaking, a slope simply refers to a measure of the steepness of a straight line. This ultimately implies that, the higher the slope of a line, the more steep it is and vice-versa.
Based on the information provided about this function y = 8 - 2x, we can logically deduce that the line would be shifted downward when its y-intercept is changed to a smaller positive number.
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Find, using the method of volumes by SLICES, the volume of a pyramid of height h with an equilateral triangle base with side a.
The volume of the pyramid of height h with an equilateral triangle base with side a, by using the method of volumes by SLICES is V = a²h/3.
We can use the method of volumes by slices to find the volume of the pyramid.
Consider a slice of the pyramid that is perpendicular to the base and at a distance x from the apex. This slice has a cross-sectional area of a square with side length (base of pyramid) s, We can use the Pythagorean theorem to find that the
Height of the slice is [tex]\sqrt{(a^2 - (a/2)^2 - x^2)} = \sqrt{(3a^2/4 - x^2).[/tex]
Therefore, the volume of the slice is given by the product of its cross-sectional area and height:
dV = s^2 dh = (a^2 - 4x^2)/4 dh
To find the total volume of the pyramid,
we integrate dV from x=0 to x=h:
V = ∫₀ʰ (a²-4x²)/4 dx
Simplifying the integrand, we get:
V = (1/4) ∫₀ʰ (a² - 4x²) dx
V = (1/4) [a²x - (4x³)/3] from x=0 to x=h
V = (1/4) [a²h - (4h³)/3]
V = a²h/3
Therefore, the volume of the pyramid is V = a²h/3.
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mack is selling beaded necklaces and beaded wristbands at the craft market. a. a necklace requires 40 minutes to make. b. a wristband requires 25 minutes to make. c. mack has 360 minutes to make the necklaces and wristbands. additionally, a. mack wants to make no more than 12 items. b. when mack sells the necklaces and wristbands at the craft market, he will make $3.00 profit per necklace and $2.00 profit per wristband. let x = the number of necklaces mack maker.
Let y = the number of wristbands mack makes.
Mack should make 4 necklaces and 8 wristbands to maximize his profit while staying within his time and quantity constraints.
His profit would be:
Profit = 3(4) + 2(8) = $20.
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously are called simultaneous equations. And the simultaneous equation is the system of equations.
From the information given, we know:
a) Necklace requires 40 minutes to make.
Let x be the number of necklaces made, then the total time spent on necklaces is 40x.
b) Wristband requires 25 minutes to make.
Let y be the number of wristbands made, then the total time spent on wristbands is 25y.
c) Mack has a total of 360 minutes to make necklaces and wristbands. Therefore, the equation for time is:
40x + 25y = 360
d) Mack wants to make no more than 12 items, so we have the inequality:
x + y ≤ 12
e) Mack makes a profit of $3.00 per necklace and $2.00 per wristband. Therefore, the equation for profit is:
Profit = 3x + 2y
Now we have the following system of equations:
40x + 25y = 360
x + y ≤ 12
Profit = 3x + 2y
From equation (2), we have y = 12 - x.
Substitute y = 12 - x into equations (1) and (3):
40x + 25(12 - x) = 360
Profit = 3x + 2(12 - x)
Simplify and solve for x:
40x + 300 - 25x = 360
15x = 60
x = 4
Substitute x = 4 into equation (2) to find y:
y = 12 - x = 12 - 4 = 8
Therefore, His profit would be, Profit = 3(4) + 2(8) = $20.
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A shipment of 1500 washers contains 400 defective and 1100 non-defective washers. Two hundred washers are chosen at random (without replacement) and classified as defective or non-defective_ a) What is the probability that exactly 90 defective washers are found? (Do NOT compute out:) b) What is the probability that at least 2 defective items are found? (Do NOT compute out:)
The probability that exactly 90 defective washers are found is (400 choose 90) * (1100 choose 110) / (1500 choose 200). and the probability that at least 2 defective items are found is (400 choose 1) * (1100 choose 199) / (1500 choose 200).
Let X be the number of defective washers in a sample of 200 washers.
We can model X as a hypergeometric distribution with parameters N = 1500 (total number of washers), K = 400 (total number of defective washers), and n = 200 (sample size).
a) The probability of finding exactly 90 defective washers is:
P(X = 90) = (400 choose 90) * (1100 choose 110) / (1500 choose 200)
This is because we need to choose 90 defective washers from the 400 defective washers, and 110 non-defective washers from the 1100 non-defective washers, out of the total of 200 washers chosen.
b) The probability of finding at least 2 defective items can be calculated as the complement of the probability of finding 0 or 1 defective item in the sample:
P(X >= 2) = 1 - P(X = 0) - P(X = 1)
To compute P(X = 0), we need to choose 0 defective washers from the 400 defective washers, and 200 non-defective washers from the 1100 non-defective washers, out of the total of 1500 washers:
P(X = 0) = (400 choose 0) * (1100 choose 200) / (1500 choose 200)
To compute P(X = 1), we need to choose 1 defective washer from the 400 defective washers, and 199 non-defective washers from the 1100 non-defective washers, out of the total of 1500 washers:
P(X = 1) = (400 choose 1) * (1100 choose 199) / (1500 choose 200)
Once we have computed P(X = 0) and P(X = 1), we can substitute these values into the expression for P(X >= 2) to obtain the desired probability.
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A tower made of wooden blocks measures114 feet high. Then a block is added that increases the height of the tower by 8 inches.
What is the final height of the block tower?
Depends how the answer "should" be formatted but 114 2/3 feet should do the trick
The displacement (in meters) of a particle moving in a straight line is given by the equation of motions = 4/t2, where t is measured in seconds. Find the velocity of the particle at times t = a, t = 1, t = 2, and t = 3(a) Find the average velocity during each time period. (i) [1, 2] cm/s (ii) [1, 1.1] cm/s
(b) Estimate the instantaneous velocity of the particle when t = 1. cm/s
The velocity of the particle at times t = a, t = 1, t = 2, and t = 3 are:
a) 4/a^2 m/s, 4 m/s, 1 m/s, 4/9 m/s.
b) The instantaneous velocity of the particle when t=1 is 4 m/s.
To find the velocity, we need to take the derivative of the displacement function with respect to time. The derivative of s = 4/t^2 is ds/dt = -8/t^3. So, the velocity of the particle at time t is given by v = ds/dt = -8/t^3.
For t = a, the velocity is v = -8/a^3 m/s. For t = 1, the velocity is v = -8 m/s. For t = 2, the velocity is v = -2 m/s. For t = 3, the velocity is v = -8/27 m/s.
To find the average velocity during the time period [1, 2], we need to find the displacement at t = 2 and t = 1, then calculate the change in displacement divided by the time interval: (4/4 - 4/1)/1 = 0 cm/s. To find the average velocity during the time period [1, 1.1], we need to find the displacement at t = 1.1 and t = 1, then calculate the change in displacement divided by the time interval: (4/1.1^2 - 4/1)/0.1 = -19.60 cm/s.
To estimate the instantaneous velocity of the particle at t = 1, we can plug in t = 1 to the derivative we found earlier: v = -8/1^3 = -8 m/s. Therefore, the instantaneous velocity of the particle when t = 1 is 4 m/s.
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A box contains 24 tiles. Each tile has certain properties:
Each tile is made of wood or plastic.
Each tile is red, yellow, or blue.
Each tile is a triangle, square, pentagon, or circle.
There is exactly one tile for each combination of properties. For example, there is one red circle that is made of wood.
Steve chooses one tile, and Ellen chooses a different tile.
What is the probability that both tiles are red?
Answer: 12
Step-by-step explanation:
use fractions from the number lines in problem 1 complete the sentence. use words, pictures, or numbers to explain how you made that comparison
Based on the data, we can infer that the following numbers fill in the blanks: 100 is greater than 10.
How to fill in the blanks?To fill in the blanks we must carefully read the information in the fragment. Once we understand this information we can select the two numbers that meet the rule mentioned in the statement.
According to the above, a correct statement would be:
100 is greater than 10.Additionally, we could put other values that comply with this rule, for example:
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What values of x
and y
satisfy the system {y=−2x+3
{y=5x−4?
Enter your answer as an ordered pair, like this: (42, 53)
If there is no solution, enter "no"; if there are infinitely many solutions, enter "inf."
The solution to the system of equation y = -2x + 3 and y = 5x - 4 is (1,1).
What is the solution to the system of equation?Given the system of equation in the question;
y = -2x + 3
y = 5x - 4
To solve the system of equation, plug equation one to into equation two and solve for x.
y = 5x - 4
Plug in y = -2x + 3
-2x + 3 = 5x - 4
Solve for x
-2x - 5x = - 4 - 3
-7x = -7
x = -7 / -7
x = 1
Now, plug x = 1 into equation one and solve for x.
y = -2x + 3
Plug in x = 1
y = -2( 1 ) + 3
y = -2 + 3
y = 1
Therefore, the value of x is 1 and y is also 1.
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what is the value of the expression shown below when x=7? 3x^2 - 2x+3
The expression value of 3x^2 - 2x+3 is 6x^2 - 13x + 6
What is expression value?Value of an Expression The value of the expression is the result of the calculation described by this expression when the variables and constants in it are assigned values. Letters can be used to represent numbers in an algebraic expression.
Apply the distributive property:
→ 3x (2 - 3) - 2 (2x - 3)
Apply the distributive property:
→ 3x (2x) + 3x ⋅ -3 - 2 (2x - 3)
Apply the distributive property:
→ 3x (2x) + 3x ⋅ -3 - 2 (2x) - 2 ⋅ -3
Simplify each term:
→ 6x^2 - 9x - 4x + 6x
Subtract 4x from -9x
→ 6x^ - 13x + 6
Therefore, the expression value of 3x^2 - 2x+3 is 6x^2 - 13x + 6
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The value of the expression given is 136.
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
Given expression is,
3x² - 2x + 3
We have to find the value of the expression when x = 7.
Substitute x = 7.
(3 × 7²) - (2 × 7) + 3 = (3 × 49) - 14 + 3
= 147 - 14 + 3
= 136
Hence the value of the expression is 136.
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each area to its corresponding radius or diameter of the circle.(All areas are approximate.)
area: 221.5584 square units
area: 78.5 square units
area: 452.16 square units
area: 36.2984 square units
area: 314 square units
area: 886.2336 square units
radius: 12 units
arrowBoth
diameter: 16.8 units
arrowBoth
radius: 3.4 units
arrowBoth
diameter: 10 units
arrowBoth
The areas, diameters, and radii can be grouped as follows:
1. Area: 221.5584 square units
Diameter: 16. 8 units
Radius: 8.4 units
2. Area: 78.5 square units
Diameter: 10 units
Radius: 5 units
3. Area: 452.16 square units
Diameter: 24 units
Radius: 12 units
4. Area: 36.2984 square units
Diameter: 6.8 units
Radius: 3.4 units
5. Area: 314 square units
Diameter: 20 units
Radius: 10 units
6. Area: 886.2336 square units
Diameter: 33.6 units
Radius: 16.8 units
How to calculate the diameter and radiusFirst, we are given the area of the circles. Next, we need to note the formula of the area of a circle and this is: πr²
To get the radius, we can use the formula: √(A/π)
For the first case, we have:
Area = 221.5584 square units
Thus, radius = √(221.5584/3.14)
= 8.4
Since diameter is = 2r, then diameter in this case
= 16.8 units.
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Charlotte and Pablo are each making purple paint by mixing blue
paint and red paint. Charlotte uses 1 cup of red paint for every
2 cups of blue paint. Pablo uses 2 cups of red paint for every
3 cups of blue paint. Whose paint is a bluer shade of purple?
Answer:
Charlotte's mix has a bluer shade of purple
Step-by-step explanation:
Since we are asked whose paint is a bluer shade it would be easier to express the ratios of the paint mix as blue:red
Charlotte: 1 cup red for every 2 cups blue ==> 2 cups blue for every 1 cup red
This can be expressed as the ratio
[tex]\dfrac{ 2 \;blue}{1\;red} = \dfrac{2}{1} = 2[/tex]
[tex]-------------------[/tex]
Pablo : 2 cups red for every 3 cups blue ==> 3 cups blue for every 2 cups red
The ratio of blue to red
= [tex]\dfrac{3 \;blue}{2\;red} = \dfrac{3}{2} = 1\dfrac{1}{2} \;\; (or\; 1.5)[/tex]
Since
[tex]2 > 1\dfrac{1}{2} \;\;\;(or\; 2 > 1.5)[/tex]
Charlotte's mix has a bluer shade of purple
It takes 6 hours to travel 372 miles. How long
will it take to travel 279 miles?
The time to travel 279 miles is 4.5 hours
How to determine the time takenWe can use the formula:
time = distance ÷ speed
To find the time it will take to travel 279 miles, given that it takes 6 hours to travel 372 miles.
The speed is constant, so we can find it by dividing the distance by the time for the first trip:
speed = distance ÷ time = 372 miles ÷ 6 hours = 62 miles/hour
Now we can use the speed to find the time it will take to travel 279 miles:
time = distance ÷ speed = 279 miles ÷ 62 miles/hour ≈ 4.5 hours
Hence, it will take approximately 4.5 hours to travel 279 miles at this speed.
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convert the binary fractional number 0.000112 to a decimal representation. you can use fractions or floating point values, but your answer must be precise. you can use expressions if that's useful.
The decimal representation of the given binary fractional number 0.000112 is 0.109375.
Binary numbers are composed of only 0s and 1s, while decimal numbers are composed of 0-9. Additionally, binary numbers follow a different place value system, where each digit represents a power of 2 rather than a power of 10.
Now, let's focus on the given problem - converting a binary fractional number 0.000112 to a decimal representation. We can use the following formula to convert any binary fraction to decimal:
(decimal equivalent) = (binary digit 1/2¹) + (binary digit 2/2²) + (binary digit 3/2³) + ...
Using this formula, we can start by breaking down the given binary fraction 0.000112 into its individual binary digits:
0.000112 = 0/2¹ + 0/2² + 0/2³ + 1/2⁴ + 1/2⁵ + 1/2⁶
Now, we can simply evaluate each term in the equation and add them up to get the decimal equivalent:
0/2¹ = 0
0/2² = 0
0/2³ = 0
1/2⁴ = 0.0625
1/2⁵ = 0.03125
1/2⁶ = 0.015625
(decimal equivalent) = 0 + 0 + 0 + 0.0625 + 0.03125 + 0.015625 = 0.109375
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(x − 3)(x² - 7x - 2)
Answer:
[tex]\huge\boxed{\sf x\³ - 10x\² + 19x + 6}[/tex]
Step-by-step explanation:
Given expression:= (x - 3)(x² - 7x - 2)
Distribute= x(x² - 7x - 2) - 3(x² - 7x - 2)
= x³ - 7x² - 2x - 3x² + 21x + 6
Combine like terms= x³ - 7x² - 3x² - 2x + 21x + 6
= x³ - 10x² + 19x + 6[tex]\rule[225]{225}{2}[/tex]
Albinism in humans is autosomal and fully recessive to normal color. A couple, who are both normal, have a daughter who is albino and a son who is normal. The couple wants to have 3 more children. What is the probability that they will have 3 normal girls?
The probability that the couple will have 3 normal girls is approximately 0.422
Since both parents are normal, they both have to be heterozygous carriers for the recessive allele that causes albinism. We can represent the normal allele with the letter N and the albino allele with the letter n. Then, we can write the genotypes of the parents as Nn x Nn.
The daughter is albino, so her genotype must be nn. The son is normal, so his genotype must be Nn.
We want to find the probability that the couple will have 3 normal girls. We can use the multiplication rule of probability to find this probability:
P(3 normal girls) = P(normal girl) x P(normal girl) x P(normal girl)
The probability of having a normal girl is 3/4 since there are three possible genotypes that result in a normal phenotype (NN, Nn, Nn) out of a total of four possible genotypes. The probability of having a normal boy is also 3/4, for the same reason.
Therefore, the probability of having 3 normal children (in this case, girls) is:
P(3 normal girls) = (3/4) x (3/4) x (3/4) = 27/64 ≈ 0.422
So, the probability that the couple will have 3 normal girls is approximately 0.422, or about 42.2%.
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Help me pls asap …..
Based on the information, it can be inferred that the volume of a cube with a side length of 30 cm is 27,000cm³ and the area would be 90cm².
How to calculate the volume and area of the cube?To calculate the volume and area of the cube we must perform the following mathematical procedures:
Volume:
We must multiply side * base * depth = volume.
30cm * 30cm * 30cm = 27,000cm³Area:
We must multiply the base by the side
30cm * 30cm = 90cm²According to the above, the area and volume of this cube would be 90cm² and 27,000cm³ respectively.
Note: This question is incomplete. Here is the complete information:
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5. without solving, identify 3 equations that you think would be the least difficult to solve and 3 equations that you think would be the most difficult to solve. Explain you reasoning.
Three equations that you think would be the least difficult to solve are,
∛(t + 4) = 3
∛ (r³ - 19) = 2
4 + ∛- m + 4 = 6
And, 3 equations that you think would be the most difficult to solve are,
∛z + 9 = 0
6 - ∛b = 0
∛2n + 3 = - 5
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Now, By all the expressions;
Some expression gives easily real solution after solving.
But here some expression have complex solution after solving and tough to solve.
Thus, By all the expressions,
Three equations that you think would be the least difficult to solve are,
∛(t + 4) = 3
∛ (r³ - 19) = 2
4 + ∛- m + 4 = 6
And, 3 equations that you think would be the most difficult to solve are,
∛z + 9 = 0
6 - ∛b = 0
∛2n + 3 = - 5
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What is the length of XZ? Step by step.
The measure of XZ is equivalent to 24. Option C is correct
Solving similar trianglesThe given triangles in question are similar in nature. For every similar triangles, the ratio of the similar sides of the triangle is equal to a constant as shown:
k+3/36 = k+5/44
Cross multiply and expand
36(k + 5) = 44(k + 3)
36k + 180 = 44k + 132
36k - 44k = 132-180|
-8k = -48
k = 6
For the measure of XZ
k/XZ = k+5/44
6/XZ = 11/44
6/XZ = 1/4
XZ = 24
Hence the measure of XZ from the given diagram is equivalent to 24
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help please
i give brainliest
Suppose a basketball player makes 55.3% of shots and that the probability of making each shot is independent. If the basketball player attempts 6 shots, what is the probability of making at least one shot?
There is a probability of 98.1% or around 0.98 of making at least one shot.
We can solve this problem using the binomial distribution. Let X be the number of shots the basketball player makes out of 6 attempts. Then X follows a binomial distribution with parameters n = 6 (number of trials) and p = 0.553 (probability of success).
The probability of making at least one shot can be calculated as the complement of the probability of missing all six shots. That is:
P(X ≥ 1) = 1 - P(X = 0)
Using the binomial probability formula, we can calculate P(X = 0) as:
P(X = 0) = (6 choose 0) * (0.553)^0 * (1 - 0.553)^(6-0) = 0.019
where (6 choose 0) = 1 is the number of ways to choose 0 shots out of 6.
Therefore,
P(X ≥ 1) = 1 - P(X = 0) = 1 - 0.019 = 0.981
So the probability of making at least one shot is approximately 0.981 or 98.1%.
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evaluate the following: f open parentheses x close parentheses equals 3 x squared minus 2 x plus 1 comma space e v a l u a t e space f open parentheses negative 1 close parentheses
The value of the function f(x) = 3x^2 - 2x + 1 at x = -1, will be 6
In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.
Algebraic expressions are expressions that are made up of variables and constants. Any value can be assigned to a variable. The value of an expression changes depending on the values assigned to the variables it includes. There are an unlimited number of points on a number line.
To evaluate the function f(x) = 3x^2 - 2x + 1 at x = -1,
we simply substitute -1 for x in the expression:
f(-1) = 3(-1)^2 - 2(-1) + 1
= 3(1) + 2 + 1
= 6
Therefore, f(-1) = 6.
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Find the sum and express it in simplest form.
(-3n³-3n²) + (8n³ + 6n² - 4)
Answer:
= 5n³ + 3n² - 4
Step-by-step explanation:
(-3n³-3n²) + (8n³ + 6n² - 4)
= -3n³-3n²+8n³+6n²-4
= -3n³+8n³-3n²+6n²-4
= 5n³+3n²-4.
Please solve quickly! Within 30 minutes would be great!
Please solve for the variable indicated.
A=1/2bh(h+b), solve for h
If you could break it down step by step that would be super helpful! I’m very confused. Thank you!
The equation solved for the variable h is h = [tex]\sqrt[]{\frac{2A -b^2}{b} }[/tex]
How to determine the subject of formulaTo solve for a variable in a given equation is to make it the subject of formula.
The variable is made to stand alone on one end of the equality sign.
We have the equation given as;
A=1/2bh(h+b)
First, cross multiply
2A = bh(h+b)
2A = bh² + b²
collect like terms
2A - b² = bh²
Now divide by the coefficient of h²
h² = 2A - b²/b
Find the square root of both sides
h = [tex]\sqrt[]{\frac{2A -b^2}{b} }[/tex]
Hence, the equation is h = [tex]\sqrt[]{\frac{2A -b^2}{b} }[/tex]
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