The measure of angle LEP can be found using the angle addition postulate, which states that the measure of an angle formed by two adjacent angles is equal to the sum of their measures. Given that angle, LEW is 51 degrees and angle PEW is 27 degrees, we can find the measure of angle LEP by adding these two angles. Thus, the angle LEP is 78 degrees (51 + 27).
L
/ \
/ \
/ \
E-------P
W
In mathematics, an angle is a geometric figure formed by two rays sharing a common endpoint, known as the vertex of the angle. There are two main ways to label angles: by giving the angle a name, usually a lowercase letter or a Greek letter, or by using the three letters that define the angle, with the middle letter being where the angle is located. Angles are typically measured in degrees using a protractor and are defined by their measure, which is not dependent upon the lengths of the sides of the angle. Coterminal angles share terminal sides but differ in size by an integer multiple of a turn.
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Max’s first test score was a 73. His second test score was a 96. What was his percent change? Round to the nearest whole percent of necessary.
To find the percent change, we need to use the formula:
percent change = (new value - old value) / old value * 100%
In this case, Max's old value is 73 and his new value is 96. So:
percent change = (96 - 73) / 73 * 100%
percent change = 23 / 73 * 100%
percent change = 0.3151 * 100%
percent change = 31.51%
Therefore, Max's percent change is 31.51%, rounded to the nearest whole percent, it is 32%.
Which equation is represented in the graph? parabola going down from the left and passing through the point negative 3 comma 0 then going to a minimum and then going up to the right through the points 0 comma negative 6 and 2 comma 0 Group of answer choices y = x2 − x − 6
The equation represented by the graph is: y = x² - x - 6. We can solve it in the following manner.
The vertex of the parabola is at (0, -6). We can calculate it in the following manner.
Yes, the equation represented by the graph is: y = x² - x - 6
This is a quadratic equation in standard form, where the coefficient of the x² term is positive, which means that the parabola opens downwards. The equation has a y-intercept of -6 and crosses the x-axis at x = -1 and x = 3. The vertex of the parabola is at (0, -6).
A parabola is a symmetrical plane curve that results from the intersection of a cone with a plane parallel to its side. It is a type of conic section, along with circles, ellipses, and hyperbolas.
A parabola can also be defined as the graph of a quadratic equation, which is a second-degree polynomial. The general form of a quadratic equation in one variable is:
ax² + bx + c = 0
Where a, b, and c are constants and x is the variable. When graphed, a quadratic equation in one variable produces a parabolic curve. The direction and shape of the parabola depend on the sign and value of the coefficient a.
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Need help ASAP with homework
Answer:
A
Step-by-step explanation:
Since this is a rectilinear angle, we can find x:
x = 180° - 98° = 82°
true or false: in a two-tailed test, we can reject the null hypothesis on either side of the hypothesized value of the population parameter.
True. This is because a two-tailed test evaluates both the extreme lower and upper ends of the distribution, allowing for the possibility of a significant difference in either direction.
In a two-tailed test, we can reject the null hypothesis on either side of the hypothesized value of the population parameter.
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can someone solve this for me
3√2 sin π/3 (x − 2) + 4 = 7
The solution to the trigonometric equation with sine function is x = 2.5.
EquationsStarting with 3√2 sin π/3 (x − 2) + 4 = 7:
First, we can simplify 3√2 sin π/3 to 3, since sin π/3 = √3/2 and 3√2 = 3 x √2 x √2 = 3 x 2 = 6.
6(x - 2) + 4 = 7
6x - 12 + 4 = 7
6x - 8 = 7
6x = 15
x = 2.5
What is general and particular solution?A particular solution to a trigonometric equation is one that is valid for a particular value or range of values of the variable, as opposed to a general solution, which is valid for all conceivable values of the variable.
Finding the general solution, which entails locating all feasible solutions to the equation within a specific range or domain, is frequently necessary while solving trigonometric equations. In order to simplify the problem and describe the answers in a compact form that can be applied to every value of the variable, one often applies a variety of trigonometric identities and algebraic operations to get the general solution.
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are the measured mean values of vcom,1 and vcom,2 the same or different (i.e. within the experimental uncertainty)?
Based on this information, we can conclude that the measured mean values of vcom,1 and vcom,2 are not significantly different from each other and fall within the range of experimental error.
Assuming that the mean value of vcom,1 is 5.2 m/s with an experimental uncertainty of 0.1 m/s, and the mean value of vcom,2 is 5.5 m/s with an experimental uncertainty of 0.2 m/s, we can calculate the difference between the two mean values and compare it with the combined experimental uncertainty.
The difference between the two mean values is 0.3 m/s, which is greater than the combined experimental uncertainty of 0.22 m/s (calculated as the square root of (0.1² + 0.2²)). Therefore, we can conclude that the two mean values are different and outside the range of experimental error.
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The complete question is :
What is the experimental uncertainty of the mean values of vcom,1 and vcom,2, and is the difference between them significant? Can we conclude that the two mean values are the same, or are they within the range of experimental error?
An ice machine produces ice cubes that are 3/4 inch on each side. What is the volume, in cubic inches, of one ice cube produced by this ice machine? A. 37/4 B. 9/4 C. 9/16 D. 27/64
oh and explain it pls
The volume of one ice cube produced by this ice machine is 27/64 cubic inches.
What do you mean by volume of cube?The volume of a cube refers to the amount of space that is contained within the cube.A cube is a three-dimensional geometric shape that has six equal square faces and all its edges have equal length. The volume of a cube can be found by multiplying the length of its sides together, using the formula:Volume of cube = (length of side)³
The volume of a cube is given by the formula V = S³ where s is the length of one side of the cube.
In this case, the length of one side of the ice cube is 3/4 inch. Therefore, the volume of one ice cube is:
V = (3/4)³ = 27/64 cubic inches.
So, the volume of one ice cube produced by this ice machine is 27/64 cubic inches.
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The volume of one ice cube produced by this ice machine is 27/64 cubic inches. The correct option is D. 27/64.
In cubic inches, of one ice cube produced by an ice machine with each side measuring 3/4 inch.
Volume’ is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a
closed surface. The unit of volume is in cubic units such as m3, cm3, in3 etc. Volume is also termed as capacity,
sometimes.
To find the volume, use the formula for the volume of a cube:
[tex]V = side^3.[/tex]
Determine the side length, which is given as 3/4 inches.
Apply the formula for the volume of a cube:
[tex]V = (3/4)^3[/tex]
Calculate the volume by cubing the side length:
V = (3/4) × (3/4) × (3/4) = 27/64 cubic inches
The volume of one ice cube produced by this ice machine is 27/64 cubic inches.
The correct option is D. 27/64.
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what is the probability that the random variable has a value between 0.1 and 3.3?a) 0.5875 b) 0.4000 c) 0.3750 d
The probability that the random variable has a value between 0.1 and 3.3 is 0.0256. Option b is correct answer.
Since the area under the density curve represents the total probability, we need to find the area between the vertical lines at x = 0.1 and x = 3.3, and under the curve.
First, we need to find the y-coordinates of the two horizontal lines. The line passing through (0, 125) and (8, 125) is parallel to the x-axis, so it has a constant y-coordinate of 125. The line passing through (8, 0) and (8, 125) is parallel to the y-axis, so it has an undefined slope and is a vertical line.
Therefore, we do not need to find its y-coordinate.
Next, we need to find the equation of the density curve. Since it is a uniform density curve, the height of the curve is constant over its entire length.
To find the height, we need to find the total area under the curve, which is given by the rectangle formed by the vertical lines at x = 0 and x = 8, and the horizontal lines at y = 0 and y = 125.
The width of the rectangle is 8, and the height is 1/125 (since the total area is 1 and the width is 8). Therefore, the height of the curve is 1/125 over its entire length.
Now, we can find the area between the vertical lines at x = 0.1 and x = 3.3, and under the curve.
The width of this area is 3.3 - 0.1 = 3.2, and the height of the curve is 1/125. Therefore, the area is:
3.2 × (1/125) = 0.0256
Therefore, the probability that the random variable has a value between 0.1 and 3.3 is 0.0256.
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The question is -
Using the following uniform density curve,
What is the probability that the random variable has a value between 0.1 and 3.3?
A) 0.5875 B) 0.0256 C) 0.3750 D) 0.2125
PLEASE CHECK GEOMETRY WILL GIVE BRAINLIEST
Answer:
YES!!!
Step-by-step explanation:
A set of wooden blocks includes a triangular prism like the one shown below. Find the volume of the block
A triangular prism whose length is l units, and whose right triangular cross section has base b units and height h units, the volume(V) of the triangular prism 31.5 cubic inches.
Since this figure represents the triangular Prism, it is given in the figure:
Length of triangular prism is 4.5 in.
In the right triangular cross-section,
Base (b) = 2 in and the height (h) = 7 in.
Volume of triangular prism formula: - A triangular prism whose length is l units, and whose right triangular cross section has base b units and height h units, then:
Volume(V) of the right triangular prism is given by V = 1/2xbhl cubic unit
Using the above values; solve for V;
V = Axl, where A is the area of right triangle, or we can write it as:
V = 1/2bhl
⇒ V = 1/2 x 2 x 7 x 4.5 cubic inches.
On simplifying we get, V = 31.5 inches³
Hence, the volume of the triangular Prism is, 31.5 cubic inches.
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Can someone help meee?
Therefore, the equation of the line is 5x - 3y = -15 and the equation of the line passing through E(4,-3) can be expressed using the point-slope form as y = (5/7)x - (20/7).
How are coordinates determined?a) We can rewrite the provided line in the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept, to determine the slope.
y + 1 = (5/7)(x - 4) (x - 4)
y = (5/7)x - (20/7) - 1
y = (5/7)x - (27/7)
This line and the one we're looking for are parallel, thus their slopes are the same (5/7). Hence, the equation of the line passing through E(4,-3) can be expressed using the point-slope form:
y - (-3) = (5/7)(x - 4) (x - 4)
y = (5/7)x - (20/7)
How are equations determined?b) The intercept form of the equation of a line with an x-intercept of 3 and a y-intercept of 5 is:
x/(-3) + y/5 = 1
The result of multiplying both sides by -15 (the least frequent multiple of -3 and 5) is as follows:
5x - 3y = -15
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help asap will give brainliest!!!!!!
Answer: x=23
Step-by-step explanation:
Set the two equal to each other:
5x=3x+46
2x=46
x=23
HELPP PLS this is due today. Look at the picture I attatched.
Step-by-step explanation:
Because a cube has 6 sides ...and a cube has equal side lengths so the area of each side is s x s = s^2
then the total is 6 s^2
Please help asap.
The sample space for tossing a fair coin 4 times is {HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT}.
Determine P(at least 2 tails).
32.25%
37.50%
43.75%
68.75%
From the given sample space the probability of P(at least 2 tails) is 68.75%.
What is probability?Probability is a way to gauge how likely something is to happen. It is a number between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty for the occurrence. Probability is a key idea in mathematics, statistics, and many other disciplines. It is used to describe uncertain events. Many techniques, such as counting techniques, probability distributions, and simulations, can be used to determine probability. Many uses for it include risk analysis, making decisions, and statistical inference.
From the given sample space the outcomes with at least 2 tails are:
{TTTT, TTT H, TT HT, T H TT, H TTT, H HTT, HT HT, HTTH, THHT, THTH, THH H}
Now,
P(at least 2 tails) = 11/16 = 0.6875 ≈ 68.75%
Hence, from the given sample space the probability of P(at least 2 tails) is 68.75%.
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According to Lear Center Local News Archive, the average amount of time that a half-hour local TV
news broadcast devotes to U.S. foreign policy, including the war in Iraq, is 38 seconds with a standard
deviation of 8 seconds. (Time, February 28, 2005). Suppose a random sample of 35 such half-hour
news broadcasts shows that an average of 36 seconds are devoted to U.S. foreign policy. Find a 95%
confidence interval for the mean time that all half-hour local TV news broadcasts devote to U.S.
foreign policy to corroborate or refute the claim.
Round to one decimal place.
Does the confidence interval suppose the Lear Center's claim?
Step-by-step explanation:
We are given:
Sample size (n) = 35
Sample mean ($\bar{x}$) = 36 seconds
Population standard deviation ($\sigma$) = 8 seconds
Confidence level = 95%
We can find the margin of error using the formula:
Margin of Error = z*(σ/√n), where z is the z-score for the given confidence level, σ is the population standard deviation, and n is the sample size.
For a 95% confidence level, the z-score is 1.96 (from the z-table or calculator).
Putting the values in the formula, we get:
Margin of Error = 1.96*(8/√35) ≈ 2.68
The confidence interval is given by:
Lower Limit = $\bar{x}$ - Margin of Error
Upper Limit = $\bar{x}$ + Margin of Error
Substituting the values, we get:
Lower Limit = 36 - 2.68 ≈ 33.32
Upper Limit = 36 + 2.68 ≈ 38.68
Therefore, the 95% confidence interval for the mean time that all half-hour local TV news broadcasts devote to U.S. foreign policy is (33.32, 38.68).
Since the Lear Center's claim of the average time being 38 seconds falls within this interval, we can say that the sample data supports the Lear Center's claim at a 95% confidence level.
Olivia bought headphones online for $33. She used a coupon code to get a 30% discount. The website also applied a 10% processing fee to the price after the discount. How much was the processing fee? Round to the nearest cent.
Answer: $25.41
Step-by-step explanation:
I think this is right, please correct me if I'm wrong
An altitude is drawn from the vertex of an isosceles triangle, forming a right angle and two congruent triangles. As a result, the altitude cuts the base into two equal segments. The length of the altitude is 18 inches, and the length of the base is 15 inches. Find the triangle’s perimeter. Round to the nearest tenth of an inch.
Answer: 54 in
Step-by-step explanation:
Since the altitude drawn from the vertex of the isosceles triangle forms two congruent right triangles and divides the base into two equal segments, we can work with one of the right triangles to find the length of the other side of the isosceles triangle.
Let's denote the length of the altitude as a, the length of half the base as b, and the length of the other side of the isosceles triangle as c. From the problem, we know that a = 18 inches and b = 15 inches / 2 = 7.5 inches.
We can use the Pythagorean theorem to find the length of c:
a² + b² = c²
Substitute the known values:
18² + 7.5² = c²
324 + 56.25 = c²
380.25 = c²
Now, take the square root of both sides to find the length of c:
c = √380.25
c ≈ 19.5 inches
Since the isosceles triangle has two sides with equal length, the perimeter is:
Perimeter = base + 2 * c
Perimeter = 15 + 2 * 19.5
Perimeter = 15 + 39
Perimeter = 54 inches
Thus, the perimeter of the isosceles triangle is approximately 54 inches.
1. Write an equation (y = a/x) that shows this relationship. Use y as your number of tacos and x as the price 2. How many tacos would you buy if they were $2.40 each ? 3. What would the price of a taco be if you bought 16 tacos? Your answer
Answer:
The equation that shows the relationship between the number of tacos (y) and the price (x) is: y = a/x If we use y as the number of tacos and x as the price of one taco, we can substitute the given values to find a. Let's assume that you would buy 5 tacos when the price is $1.20 each. Then we have: 5 = a/(1.20) Multiplying both sides by 1.20, we get: a = 6 So the equation becomes: y = 6/x Now we can answer the other questions: 2. If the price of a taco is $2.40 each, we can substitute x = 2.40 into the equation to find y: y = 6/2.40 = 2.5 So you would buy 2.5 tacos, whichWrite an equation for the nth term of the geometric sequence 896,-448, 224,.... Find the eighth term of this sequence.
896 (-1);
Oa. an
Ob. 9, -224 (-:-1.
a
896(1)
Oc. an-896
;-7
7-1
;7
Od. a=-448 (-1):
; 3.5
The eighth term of the sequence is -14
What is common ratio?
The common ratio between consecutive terms in a geometric sequence is constant. Let's denote this common ratio by 'r'. To find 'r', we can divide any term by the preceding term,
r = -448/896 = -1/2
Now we can use the formula for the nth term of a geometric sequence,
[tex]a_n = a_1 \times p^{n - 1}[/tex]
where '
[tex]a_1[/tex] is the first term and 'n' is the index of the term we want to find.
Substituting the values we have,
[tex]a_8 = 896 (-1/2)^{8-1} \\ = 896 \times (-1/2)^{7} = -14[/tex]
Therefore, the eighth term of the sequence is -14.
So, option A is the correct answer.
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Correct question is "Write an equation for the nth term of the geometric sequence 896,-448, 224,.... Find the eighth term of this sequence.
A) -14
B) -18
C) -19
D) 18"
Quadrilateral ABCD is a parallelogram. Complete the statements to prove that AB = CD and BC = AD.
Given that ABCD is a parallelogram:
Opposite sides of a parallelogram are parallel and congruent. Therefore, AB = DC.
Diagonals of a parallelogram bisect each other. Therefore, the midpoint of AC is the same as the midpoint of BD. Let M be the midpoint of AC, and N be the midpoint of BD.
By the midpoint theorem, BM = DM and BN = AN.
Since BM = DM and BN = AN, we can conclude that quadrilateral ABCD is a parallelogram in which BC || AD and CD || AB.
Therefore, we have shown that AB = CD and BC = AD in parallelogram ABCD.
A girl bought a total of 12 fiction and non-fiction books. The fiction books cost $12 each and the non-fiction books cost $25 each. If she paid $248 altogether, how many of each kind of book did she buy? How do I write that as an expression?
Does anyone know the answer to this?
Answer:
[tex] \frac{a - 3}{a + 2} [/tex]
Step-by-step explanation:
[tex] \frac{ {a}^{2} - 7a + 12 }{ {a}^{2} - 2a - 8} = \frac{(a - 3)(a - 4)}{(a + 2)(a - 4)} = \frac{a - 3}{a + 2} [/tex]
Solve the following system of equations.
Answer:
D
Step-by-step explanation:
y = x² - 4x - 5 → (1)
y = x - 9 → (2)
substitute y = x² - 4x - 5 into (2)
x² - 4x - 5 = x - 9 ( subtract x - 9 from both sides )
x² - 5x + 4 = 0 ← in standard form
(x - 1)(x - 4) = 0 ← in factored form
equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
x - 4 = 0 ⇒ x = 4
substitute these values into (2) for corresponding values of y
x = 1 : y = 1 - 9 = - 8 ⇒ (1, - 8 )
x = 4 : y = 4 - 9 = - 5 ⇒ (4, - 5 )
- Add and subtract rational numbers: word problems ZAL
4) Khalil and Sophia weighed their pet cats. Khalil's cat weighed 18 5/6 pounds and
Sophia's cat weighed 10 1/3 pounds. How much more did Khalil's cat weigh than Sophia's
cat?
Write your answer as a fraction or as a whole or mixed number.
Khalil's cat weighed 8 1/2 pounds more than Sophia's cat.
What is rational number?In mathematics, any integer that can be written as p/q where q 0 is considered a rational number. Additionally, any fraction that has an integer denominator and numerator and a denominator that is not zero falls into the group of rational numbers.
To find out how much more Khalil's cat weighed than Sophia's cat, we need to subtract the weight of Sophia's cat from the weight of Khalil's cat.
Khalil's cat weighed 18 5/6 pounds.
Sophia's cat weighed 10 1/3 pounds.
Subtracting the weights:
18 5/6 - 10 1/3
To subtract mixed numbers, we need to find a common denominator. In this case, the least common multiple of 6 and 3 is 6. So, we can convert the fractions to have a denominator of 6:
18 5/6 - 10 1/3 = 18 5/6 - 10 2/6
Now, we can subtract the whole numbers and the fractions separately:
18 - 10 = 8
5/6 - 2/6 = 3/6
Putting it back together:
8 3/6
We can simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 3 in this case:
8 3/6 = 8 1/2
So, Khalil's cat weighed 8 1/2 pounds more than Sophia's cat.
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find lcm of (x+y,x-y)
Therefore , the solution of the given problem of expressions comes out to be (x+y) is the LCM of (x+y, x-y).
What is an expression?Utilizing shifting integers that may prove rising, minimizing, or blocking is preferable to using approximations generated at random. Sharing resources, knowledge, or answers to problems was the only way they could assist one another. An equation for a declaration of truth may contain the justifications, components, and mathematical comments for methods like additional disagreement, manufacture, and mixture.
Here,
We must factor each polynomial into its irreducible factors and then take the sum of the highest powers of each irreducible factor to determine the LCM of two polynomials.
Here are the facts:
=> x+y = (x+y)
=> x-y = -(y-x)
We don't need to include the second component separately in the LCM because it is simply the negation of the first factor.
The LCM is just (x+y) because x+y is already indivisible.
Consequently, (x+y) is the LCM of (x+y, x-y).
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the state transportation department is conducting a study on the length of green lights in a certain city. the green lights' lengths are normally distributed with a mean of 45 seconds and a standard deviation of 15 seconds. how many seconds separate the lowest 24% of the means from the highest 76% in a sampling distribution of 75 traffic lights? use the z-table below.
20.4 seconds separate the lowest 24% of the means.
How to find seconds?Look up the z-scores for the given percentages (24% and 76%) using the z-table.
For the lowest 24%, find the closest percentage in the table (0.2400) which corresponds to a z-score of -0.68.For the highest 76%, find the closest percentage in the table (0.7600) which corresponds to a z-score of 0.68.Since the green lights' lengths are normally distributed with a mean of 45 seconds and a standard deviation of 15 seconds, calculate the number of seconds corresponding to the z-scores.
For the lowest 24%, the number of seconds is 45 + (-0.68 * 15) = 45 - 10.2 = 34.8 seconds.For the highest 76%, the number of seconds is 45 + (0.68 * 15) = 45 + 10.2 = 55.2 seconds.
Now, subtract the lowest 24% of the means (34.8 seconds) from the highest 76% (55.2 seconds) to find the difference in seconds.
So, 20.4 seconds separate the lowest 24% of the means from the highest 76% in the state transportation study's sampling distribution of 75 traffic lights.
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What is the following product?
3√5-√2
06/10
O 6/200
O 6/500
O 6/100000
To find the product of this expression, we can use the distributive property:
3√5 - √2 = 3√5 * 1 - √2 * 1
= 3√5 * (√2/√2) - √2 * (3√5/3√5)
= (3√10/√2) - (3√10/5)
= 15√10/5√2 - 3√10/5
= (15 - 3√2)√10/5√2
So the product is (15 - 3√2)√10 / 5√2.
Simplifying this expression by rationalizing the denominator, we get:
= (15 - 3√2)√10 / 5√2 * √2 / √2
= (15√2 - 3 * 2)√10 / 10
= (15√2 - 6)√10 / 10
= (3√2(5 - 2√10)) / 10
Hence, the product is (3√2(5 - 2√10)) / 10.
The product of expression 3√5-√2 is ( 15√2 - 2)√10 / 10
What is Expression?An expression is combination of variables, numbers and operators.
To find the product of this expression
Apply the distributive property:
3√5 - √2 = 3√5 × 1 - √2 × 1
= 3√5 × (√2/√2) - √2 × (3√5/3√5)
= (3√10/√2) - (√10/5)
= 15√10/5√2 - √10/5
= (15 - √2)√10/5√2
So the product is (15 - √2)√10 / 5√2.
Simplifying this expression by rationalizing the denominator, we get:
= (15 - √2)√10 / 5√2 × √2 / √2
= (15√2 - 2)√10 / 10
Hence, the product of expression 3√5-√2 is ( 15√2 - 2)√10 / 10
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how do you graph 2y=-3x
helpppp
Answer:
please see the attached I put the answer.
Step-by-step explanation:
I put the steps I did, to graph it.
Six different names were put into a hat. A name is chosen 116 times and the name Grace is chosen 15 times. What is the experimental probability of the name Grace being chosen? What is the theoretical probability of the name Grace being chosen? Use pencil and paper. Explain how each probability would change if the number of names in the hat were different.
Answer:
Try this!!!
Step-by-step explanation:
Experimental Probability:
The experimental probability of an event is found by dividing the number of times the event occurs by the total number of trials. In this case, the name Grace was chosen 15 times out of 116 trials, so the experimental probability of choosing Grace is:
Experimental Probability = Number of times Grace was chosen / Total number of trials
Experimental Probability = 15 / 116
Experimental Probability = 0.1293 or approximately 12.93%
Theoretical Probability:
The theoretical probability of an event is found by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, there are six names in the hat, so the probability of choosing Grace is:
Theoretical Probability = Number of favorable outcomes / Total number of possible outcomes
Theoretical Probability = 1 / 6
Theoretical Probability = 0.1667 or approximately 16.67%
If the number of names in the hat were different, both the experimental and theoretical probabilities would change. For example, if there were only three names in the hat, the theoretical probability of choosing Grace would be 1/3 or approximately 33.33%. The experimental probability would also change based on the number of times Grace was chosen out of the total number of trials. As the number of names in the hat increases, the theoretical probability of choosing Grace decreases, and the experimental probability becomes more accurate as the number of trials increases.
Carl is covering the rectangular prism-shaped box with cloth.What is the minimum amount of cloth Carl needs to cover the entire box?
The minimum amount of cloth Carl needs to cover the entire box is 272 square inches.
Describe Prism?A prism is a three-dimensional geometric shape that consists of two identical polygonal bases that are connected by a set of parallelogram faces. The shape of the prism is determined by the shape of its bases. For example, if the bases are triangles, the prism is called a triangular prism. Similarly, if the bases are squares, the prism is called a square prism, and so on.
Prisms have a number of interesting properties. The faces that connect the bases are always parallelograms, and the opposite faces are congruent and parallel. The altitude of a prism is the perpendicular distance between its bases, and its lateral faces are all rectangles or parallelograms. The volume of a prism can be calculated by multiplying the area of its base by its altitude. The formula for the volume of a prism is V = Bh, where V is the volume, B is the area of the base, and h is the altitude.
Given:
Length of the rectangular prism, l = 12 in
Height of the rectangular prism, h = 2 in
Width of the rectangular prism, w = 8 in
Carl needs to cover the total surface area of the prism, which is minimum he needs to cover.
Total surface area of rectangular prism= 2(lh+hw+lw)
TSA= 2(12 × 2 + 2×8 + 12 × 8)
= 2(24 + 16 + 96)
= 272 square inches
Minimum cloth required = 272 square inches.
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