Answer:
8
Step-by-step explanation:
4 + 2 (5 - 3) = 8
hope this helps :))
Given AD = BC and AD || BC Prove: ABCD is a paralleologram
The response to the given question would be that As a result, we have demonstrated that ABCD's opposing sides are parallel, proving that ABCD is a parallelogram.
What is parallelograms?A simple quadrilateral with two sets of parallel sides is known as a parallelogram in Euclidean geometry. Both sets of opposite sides are parallel and equal in a particular type of quadrilateral known as a parallelogram.
We must demonstrate that the opposing sides of ABCD's parallelogram are parallel.
CBA = DAB (Alternate interior angles)
Alternative interior angles (ABD = BAC; ADC = CBD) (Alternate interior angles)
DCA = ACD (Alternate interior angles)
Considering that AD = BC, we also have:
A + B Equals A + C. (Also on both sides)
AD = BC
Think about the two pairs of sides that are diagonally opposed: AB and CD and AD and BC.
We have these for AB and CD:
Interior angles of a quadrilateral: DAB + ABD + BCD + CDA = 180°; CBA + BAC + ADC + DCA = 180°. (Substituting corresponding angles)
We may insert them in and simplify to get: since DAB = CBA and ABD = BAC.
BCD = ADC
As a result of having the same transversal CD and equal alternative interior angles, AD and BC are also parallel. As a result, we have demonstrated that ABCD's opposing sides are parallel, proving that ABCD is a parallelogram.
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In a certain weather forecast, the chances of a thunderstorm are stated as "4 in 19." Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.
It’s not 0.210 or 0.21052632 ik you need to do 4 divided by 19
So, by resolving the given, we obtain the result: The probability value for probability this ranges from 0 to 1 inclusive.
What is probability?Calculating the chance that an event will occur or a statement will be true is the subject of probability theory, a branch of mathematics. A risk is a number between 0 and 1, where 1 denotes certainty and a probability of about 0 denotes the likelihood that an event will occur. The likelihood that an event will take place is mathematically expressed as probability. Probabilities can also be expressed as percentages ranging from 0% to 100% or as integers between 0 and 1. the proportion of equally plausible possibilities that actually happen in relation to all possible outcomes when a certain event occurs.
It is necessary to divide the number of desired outcomes by the total number of potential outcomes in order to describe the specified degree of possibility as a probability value between 0 and 1 inclusive.
When the likelihood of a thunderstorm is expressed as "4 in 19," it suggests that out of the 19 potential outcomes, 4 of them (a thunderstorm) are desirable (weather conditions).
Hence, the likelihood of a thunderstorm is represented as:
4/19
The probability value for this ranges from 0 to 1 inclusive.
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3.1 divided by 992
I don’t know this questin
Answer:
Step-by-step explanation:
0.003125
Answer:0.003125
When dividing by a bigger number to turn it to a decimals with 0s because it will always help and also use the simple way of division writing it down ex. 3.1 I 992 and put it in as many times as possible
explain what we mean by marginal cost
Marginal cost refers to the additional cost of producing one more unit of a product or service.
What is Marginal Cost?Marginal cost is the cost of producing one additional unit of a good or service.
In math, marginal cost refers to the additional cost of producing one more unit of a product or service. It is calculated by taking the change in total cost divided by the change in quantity produced.
Marginal cost is an important concept in economics and is used to determine the optimal level of production to maximize profits.
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A net of a building block is shown below what is the total surface area of the building block
The total surface area of the building block is therefore (4×l×w) + (2×(b×h)/2), which is equal to (2×l×w) + bh.
What is surface area?Surface area is the total exposed area of a three-dimensional object, including the object's base area and lateral area. It is the area of the surface or outer boundary of an object and is measured in units squared such as square meters or square centimeters. Surface area is an important concept in mathematics, physics, and engineering, as it is used to calculate the amount of material needed to construct an object.
The total surface area of the building block can be found by adding the area of the six faces of the block together. To calculate the surface area of the block, we first need to find the area of each face. The six faces of the building block are four rectangular faces and two triangular faces. The area of each rectangular face can be found using the formula A=l×w, where l is the length and w is the width. The area of each triangular face can be found using the formula A=(b×h)/2, where b is the base and h is the height.
By adding the area of each face together, the total surface area of the building block can be found. The total surface area is equal to the sum of the four rectangular faces plus the two triangular faces. The total surface area of the building block is therefore (4×l×w) + (2×(b×h)/2), which is equal to (2×l×w) + bh.
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Review the graph of function g(x). On a coordinate plane, a curve starts at closed circle (4, negative 4), curves up to (3, negative 3), and curves down to (negative 1, negative 8), and then curves up through (negative 3, 4). A curve starts at open circle (4, 2) and curves up through (8, 5). What are Limit of g (x) as x approaches 4 negative and Limit of g (x) as x approaches 4 plus, if they exist? Limit of g (x) = 2 as x approaches 4 negative and limit of g (x) = negative 4 as x approaches 4 plus Limit of g (x) = negative 4 as x approaches 4 negative and limit of g (x) = negative 2 as x approaches 4 plus Limit of g (x) = negative 4 as x approaches 4 negative and limit of g (x) D N E as x approaches 4 plus Limit of g (x) D N E as x approaches 4 negative and limit of g (x) = negative 4 as x approaches 4 plus
The lateral limits of the function g(x) at x = 4 are given as follows:
[tex]\lim_{x \rightarrow 4^-} g(x) = -4, \lim_{x \rightarrow 4^+} g(x) = 2[/tex]
How to calculate the lateral limits?
To obtain lateral limits, we need to take the limit of a function as it approaches a point from the left-hand side and the right-hand side separately.
If the two limits are equal, then this is the limit of the function, while if the lateral limits are different, then the limit of the function does not exist for the value of x.
On a coordinate plane, a curve starts at closed circle (4, negative 4), curves up to (3, negative 3), and curves down to (negative 1, negative 8), and then curves up through (negative 3, 4), hence the lateral limit to the left of x = 4, where x is less than 4, is given as follows:
[tex]\lim_{x \rightarrow 4^-} g(x) = -4[/tex]
A curve starts at open circle (4, 2) and curves up through (8, 5), hence the lateral limit to the right of x = 4, where x is greater than 4, is given as follows:
[tex]\lim_{x \rightarrow 4^+} g(x) = 2[/tex]
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Please help asap!
Bob's gift shop sold a record number of cards for Mother's Day. One salesman sold 29 cards, which was 10% of the cards sold for Mother's Day. How many cards were sold for Mother's Day?
The total number of cards sold for Mother's Day is 290 cards.
What is the proportions?
Proportion is a mathematical concept that expresses the equality of two ratios. Two ratios are said to be proportional if they have the same relative size or relationship.
Let x be the total number of cards sold for Mother's Day. We know that one salesman sold 29 cards, which is 10% of the total number of cards sold. Using this information, we can set up the following proportion:
(10/100) * x = 29
Simplifying, we get:
x = 290
Hence, the total number of cards sold for Mother's Day is 290 cards.
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P(A) = 0.2, P(B) = 0.4, P(A U B) = 0.5, P(A n B) = ?
The probability of both independent events A and B happening together is P(A n B) = 0.1.
What is meant by probability?
An event's probability is a numerical representation of how likely it is that the event will take place. In mathematical notation, it is written as a number between 0 and 1, or as a percentage between 0% and 100%. The higher an event's probability, the more likely it is to occur. In a sample space, there is a probability of 1 for each event. The probability formula states that the ratio between the number of favourable outcomes and the total number of outcomes determines the likelihood that an event will occur. Sets are used in the terminology of probability theory. A set is a grouping of various things.
Given,
Probability of A, P(A) = 0.2
Probability of B, P(B) = 0.4
P(A U B) = 0.5
We are asked to find P(A n B)
Now we know,
P(A U B) = P(A) + P(B) - P(A n B)
Then,
P(A n B) = P(A) + P(B) - P(A U B) = 0.2 + 0.4 - 0.5 = 0.1
Therefore the probability of both independent events A and B happening together is P(A n B) = 0.1.
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Summarize in your own words a quantity in the life-science that is modelled by a function of time. For your function, if you knew some values of its derivative, what would those values be telling you about your model? Be specific (don’t just say “rate-of-change”).
One example of a quantity in the life sciences that is modeled by a function of time is the population size of a species.
How can this be modeled?This can be modeled using a differential equation, where the rate of change of the population size is proportional to the current population size.
If we knew the values of the derivative of this function (i.e., the first derivative), we would be able to make inferences about the growth or decline of the population.
A positive derivative value would indicate that the population is growing, while a negative derivative value would indicate that the population is declining. The magnitude of the derivative would also give us information about the rate of growth or decline of the population. If the derivative is large, the population is changing quickly, while a small derivative indicates slower change.
If we had information about the second derivative of the function (i.e., the rate of change of the derivative), we would be able to make further inferences about the behavior of the population.
A positive second derivative value would indicate that the population is accelerating in its growth, while a negative second derivative value would indicate that the population is decelerating in its growth. This information could be useful in predicting future trends in population size and in making decisions about conservation efforts or resource management.
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Select ALL the correct answers. Which of the following statements are true about the equation below? The solutions are . The solutions are . The extreme value is at the point (7,-3). The graph of the quadratic equation has a minimum value. The extreme value is at the point (3,-7). The graph of the quadratic equation has a maximum value.
None of the statements (1) to (6) are true about the equation [tex]x^2-6x+2=0[/tex].
What does a math quadratic equation mean?Definitions: x ax2 + bx + c = 0 is a quadratic equation, which is a 2nd polynomial formula in a variable. a 0. It has at least 1 solution since it is a 2nd polynomial equation, which is guaranteed by the algebraic theorem. The solution might be simple or difficult.
None of the statements (1) to (6) are true about the equation. [tex]x^2-6x+2=0[/tex].
Reason why:
(1) The coefficient of the [tex]x^2[/tex] term is positive, so the graph of the quadratic equation is a parabola that opens upward. Therefore, it does not have a minimum value, but instead has a minimum point.
(2) The coordinates of the minimum point can be found using the formula x = -b/2a, which gives x = 6/2 = 3. Substituting x = 3 into the equation gives y = 2, so the minimum point is (3, 2).
(3) The point (7,-3) is not on the graph of the equation.
(4) The solutions to the equation are given by the quadratic formula x = [tex][6\± \sqrt{(6^2 - 4(1)(2))]}/2 = [6\± \sqrt{(28)]}/2 = 3\± \sqrt{7}[/tex]. So, statement (4) is partially correct, but the value of -3 is incorrect.
(5) Statement (5) is correct, as the solutions to the equation are x = [tex]3\±\sqrt7}[/tex].
(6) The graph of the quadratic equation has a minimum value, not a maximum value.
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Complete question is: Which of the following statements are true about the equation below?
x^2-6x+2=0
( 1 ) The graph of the quadratic equation has a minimum value.
( 2 ) The extreme value is at the point (3,-7).
( 3 ) The extreme value is at the point (7,-3).
( 4 ) The solutions are x = -3 + or - the square root of 7 .
( 5 ) The solutions arex = 3 + or - the square root of 7.
( 6 ) The graph of the quadratic equation has a maximum value.
(100 POINTS AND BRAINLYEST)
(SOLVE ALL)
24.2 miles above
2. The line of site to the horizon would be tangent to the Earth’s surface. What kind of angle is formed between the radius of the Earth and the line of site? (1 point)
3. You will be setting up a right triangle to solve this problem using the radius of the Earth (3,959 miles), the distance to the horizon (which is unknown), and the altitude of Felix. Sketch and image of this scenario. Include distances on the right triangle. (3 points)
4. Use the Pythagorean Theorem to find the distance from Felix in the image to the horizon. (3 points)
5. Standing on the ground, the surface of the Earth appears to be flat. How far would a person on the ground have to travel to get a point on the horizon that Felix could see. Sketch a right triangle of this scenario using the altitude of Felix, the distance to the horizon, and the distance on the ground to the horizon (which is unknown). Include distances on the right triangle. Use the Pythagorean Theorem to find the missing side of the triangle. (5 points)
6. Use the answer from number 5 to determine the central angle of the Earth that Felix is viewing from his altitude. Treat the answer from number 5 like an arc length. You will need to use the radius of the Earth in this problem. Answer in radians or degrees. (2 points)
The analysis of the distances and angles viewed by Felix are presented as follows;
2. The angle formed is a right angle
3. Please find the drawing of the scenario created with MS Word
4. The distance obtained using Pythagorean Theorem is about 438.53 miles
5. The distance the person travels is about 437.86 miles
6. The central angle Felix is viewing from his altitude is about 6.34°
What is the Pythagorean Theorem?The Pythagorean Theorem states that the square of the hypotenuse side of a right triangle is equivalent to the sum of the squares of the legs of the right triangle.
2. The angle formed by a tangent to a spherical surface, such as the Earth's approximately spherical surface and the radius of the sphere is a right angle.
Therefore;
The angle formed between the radius of the Earth and the tangential line of sight is a right angle3. The possible elevation of Felix above the Earth's surface, obtained from a similar question is; 24.214 miles
Therefore;
The legs of the right triangle are the radius of the Earth and the distance from Felix's to the point on the horizon.
The hypotenuse sum of Felix's altitude and the radius of the Earth
Please find attached the drawing of the scenario created with MS Word
4. Pythagorean Theorem indicates that the distance from Felix to the image on the horizon, d, can be obtained as follows;
d = √((3,959 + 24.214)² - 3,959²) ≈ 438.53
The distance from Felix to the image on the horizon is about 438.53 miles
5. The distance the person has to travel can be found as follows;
The surface of the Earth is assumed to be flat
The distance to the horizon from Felix is about 438.53 miles
The distance, l, the person on the ground has to travel is therefore;
l = √(438.53² - 24.214²) ≈ 437.86
The distance the person on the ground has to travel to get to a point on the horizon Felix could see is about 437.86 miles6. The central angle, θ, of the Earth that Felix is viewing, with an arc length of 437.86 miles can be found using the formula for finding the arc length of a sector of a circle as follows;
θ/360 × 2 × π × 3,959 ≈ 437.86
θ ≈ 437.86 × 360/(3,959 × 2 × π) ≈ 6.34°
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A grocer wants to mix two kinds of coffee. One kind sells for $0.90
per pound, and the other sells for $2.40
per pound. He wants to mix a total of 28
pounds and sell it for $1.45
per pound. How many pounds of each kind should he use in the new mix? (Round off the answers to the nearest hundredth.)
In order to create a 28-pound blend that he can sell for $1.45 per pound, the grocer should combine approximately 17.73 pounds of the less costly coffee and 10.27 pounds of the more expensive coffee.
How many pounds of each kind should he use in the new mix?Let's designate the quantity of the less expensive coffee X and the more expensive coffee Y. Since we are aware that the grocer wishes to combine 28 pounds altogether, we can write:
x + y = 28
The total profit from selling the mixture would be: 28($1.45) = $40.60 because we also know that he intends to sell it for $1.45 per pound.
The costs and quantities of the two varieties of coffee can be used to create a new equation.
0.9x + 2.4y = $40.60
With two variables in each equation, we now have two equations that we can solve by substitution or elimination. Use of substitution
28 + y = x - 0.9x + 2.4y = 40.60
0.9x + 2.4(28 - x) = $40.60
0.9x + 67.2 - 2.4x = $40.60\s-1.5x = -$26.60\sx = 17.73
We can apply the first equation to determine y now that we know x: x + y = 28.
17.73 + y = 28 \sy = 10.27
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Please help as fast as possible! I know that’s what everyone asks but seriously I’ll give you points
Answer:
Number 2 and number 1
Step-by-step explanation:
youre all good
What are all possible values of x that satisfy the inequality x3−8≥1?
By answering the above question, we may state that Therefore, all possible values of x that satisfy the inequality [tex]x^3[/tex] - 8 ≥ 1 are x ≥ 2.08.
What is inequality?A connection between two expressions or values that is not equal in mathematics is referred to as an inequality. Hence, inequity results from imbalance. In mathematics, an inequality establishes the connection between two non-equal numbers. Egality and inequality are not the same. Use the not equal symbol most frequently when two values are not equal (). Values of any size can be contrasted using a variety of inequalities. By changing the two sides until just the variables are left, many straightforward inequalities may be solved. Nonetheless, a variety of factors support inequality: Both sides' negative values are split or added. Exchange the left and the right.
[tex]x^3[/tex] - 8 ≥ 1
[tex]x^3[/tex] ≥ 9
Taking the cube root of both sides, we get:
x ≥ ∛9
Since ∛9 ≈ 2.08, the solution to the inequality is:
x ≥ 2.08
Therefore, all possible values of x that satisfy the inequality [tex]x^3[/tex] - 8 ≥ 1 are x ≥ 2.08.
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What would the hypotenuse have to be if the legs of a right triangle are 9 and 5?
Answer:
Roughly 10.30
Step-by-step explanation:
Use Pythagorean theorem:
[tex]c^2 = a^2 + b^2[/tex]
Where [tex]c[/tex] is your hypotenuse
So:
[tex]c^2 = (9)^2 + (5)^2[/tex]
[tex]c= \sqrt{106}[/tex]
[tex]c[/tex] ≈ [tex]10.30[/tex]
Answer:10.3
Step-by-step explanation:
Does this represent a function yes or no because??????????
Answer:
Step-by-step explanation: It is a function. Because one input goes to exact one output.
What does each expression or equation represent in this situation? (What does the notation mean in English?)
The cost of apples when the number of apples bought is n can be found using the function:
C(n) = 0.9n
What is a function?
A mathematical statement or rule that establishes the link between an independent variable and a dependent variable is called a function. Relationships called functions provide an output for each input. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Often, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range.
Assuming the question is the one given below.
Given a function C which gives the cost of buying the n apples in dollars.
The first expression given is:
1) C(5) = 4.50
The input of the function is 5 and the output is 4.50.
This means that when the number of apples is 5 the total cost is $4.50.
Let us assume the general equation of the function as below:
C(n) = kn
When n = 5
C(5) = 5k = 4.50
k = 4.50/5 = 0.9
Hence the function is C(n) = 0.9n
2) We found the function as C(n) = 0.9n
C(2) means the cost when the number of apples is 2.
C(2) = 0.9 * 2 = $1.8
Therefore the cost of apples when the number of apples bought is n can be found using the function:
C(n) = 0.9n
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I need help anyone please ?!!!!!!!
Answer:its a
Step-by-step explanation:you did it wrong
In 8, substitute each given value of the variable to find which, if any,
is a solution of the inequality.
8. y> 23
y = 20, 23, 25.1, 35
Answer:
Substituting the given values of y in the inequality y > 23:
When y = 20, 20 is not greater than 23, so it's not a solution.
When y = 23, 23 is not greater than 23, so it's not a solution (it's equal).
When y = 25.1, 25.1 is greater than 23, so it's a solution.
When y = 35, 35 is greater than 23, so it's also a solution.
Therefore, the solutions of the inequality are y = 25.1 and y = 35.
11. Jenn bought 4 identical book
bags online for a total cost of
$95.65 including a flat ate of
$4.99 for shipping. Write an
equation to find the cost of each
book bag, b.
Answer:
Step-by-step explanation:
Let x be the cost of each book bag. Then, we can set up the following equation based on the information given:
4x + 4.99 = 95.65
Here, 4x represents the cost of the four identical book bags, and 4.99 is the flat rate for shipping. We add them up to get the total cost of $95.65.
To solve for x, we can first subtract 4.99 from both sides of the equation to isolate the term 4x on the left-hand side:
4x = 90.66
Then, we can divide both sides of the equation by 4 to solve for x:
x = 22.67
Therefore, each book bag costs $22.67.
D
Incorrect
Your answer is incorrect.
This year Keisha watched 50 movies. She thought that 46 of them were very good. Of the movies she watched, what percentage did she rate as very good?
Keisha rated 92% of the movies she watched as very good.
How to find the percentage of movies that Keisha rated as very good.To find the percentage of movies that Keisha rated as very good, we can use the formula:
Percentage = (Number of movies rated as very good / Total number of movies watched) x 100%
Plugging in the values we have:
Percentage = (46 / 50) x 100%
Percentage = 92%
Therefore, Keisha rated 92% of the movies she watched as very good.
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The quality control manager at a computer manufacturing company believes that the mean life of a computer is 83 months, with a standard deviation of 9 months.
If he is correct, what is the probability that the mean of a sample of 78 computers would differ from the population mean by less than 0.4 months? Round your answer to four decimal places.
The probability that the mean of a sample of 78 computers would differ from the population mean by less than 0.4 months is:
P (μ-0.4 <x<μ +0.4) = P (-0.39<x<0.39) = 0.3035
What do you mean by probability?By simply dividing the favourable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favourable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1. Moreover, the proportion of positive outcomes cannot be negative.
Here we have,
μ = 83,0 = 9, n = 78
Since sample size is large so we can assume normal distribution using CLT.
The z-score for x= μ-0.4 is
z=(μ-0.4-μ)/o/√n
=-0.4/9/√78
= -0.39
The z-score for x= μ +0.4 is
z=(μ+0.4-μ)/σ/√n
= 0.4/9/√78
= 0.39
The probability that the mean of a sample of 78 computers would differ from the population mean by less than 0.4 months is:
P (μ-0.4 <x<μ +0.4) = P (-0.39<x<0.39) = 0.3035.
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Write the equation of the trigonometric graph. Use a positive coefficient on cosine for this activity.
The required equation of the trigonometric graph is y = 2cos[(π/8)(x-2)-2] which represents the cosine function.
What is the cosine function?The cosine function has a range of values between -1 and 1, and it is a periodic function that repeats every 2π radians or 360 degrees.
The graph of the cosine function is a wave-like curve that oscillates between -1 and 1, with a period of 2π radians or 360 degrees.
As we can see, the function's behavior repeats itself. In terms of the form of the function, we may select any interval of length 2π and the following interval of length 2π will be equal to the previous one.
Here, y = 2cos[(π/8)(x-2)-2]
Thus, the equation of the trigonometric graph is y = 2cos[(π/8)(x-2)-2] which represents the cosine function.
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help!! Find the missing length and round it to the nearest tenth.
The length of the hypotenuse is approximately 6.7.
What is the Pythagorean theorem and how is it used to find the hypotenuse of a right triangle?
The Pythagorean theorem is a fundamental relationship in Euclidean geometry that relates the lengths of the sides of a right triangle. It states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Mathematically, the Pythagorean theorem can be expressed as:
[tex]c^2 = a^2+ b^2[/tex]
where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.
Finding the missing length :
In the given problem, we are given the lengths of two sides of a right triangle, which are 3 and 6. We can use these values to find the length of the hypotenuse using the Pythagorean theorem:
[tex]h^2 = 3^2+ 6^2[/tex]
[tex]h^2 = 9 + 36[/tex]
[tex]h^2 = 45[/tex]
Taking the square root of both sides gives:
[tex]h = \sqrt{45}[/tex]
Using a calculator, we can simplify this to:
[tex]h \approx 6.7[/tex] (rounded to the nearest tenth)
Therefore, the value of the hypotenuse of the right triangle with sides 3 and 6 is approximately 6.7.
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36 letters in 6 minutes
Answer:
36 divided by 6 = 6
Step-by-step explanation:
Nora left her house and drove to the store. She stopped and went inside. From there,
she drove in the same direction until she got to the bank. She stopped and went
inside the bank. Then she drove home. The graph below shows the number of blocks
away from home Nora x is a minutes after she left her house, until she got back home.
Distance (Blocks from Home)
How long was Nora in the bank?
Answer:
7 minutes
Step-by-step explanation:
It is 7 minutes because the bank it the top straight line and it elapses for 7 minutes
Q+9p when q = 18 and p = 4
Answer: 48
Step-by-step explanation: 9p p=4 9*4=36 +18 = 48
In 50 words or fewer, describe the relationship between the volumes of a cylinder
and a cone that have the same size base and equal heights.
These figures have curved surfaces, not flat faces. A cylinder is similar to a prism, but its two bases are circles, not polygons. Also, the sides of a cylinder are curved, not flat. A cone has one circular base and a vertex that is not on the base.
When a cone and cylinder have the same height and radius the cone will fit inside the cylinder. The volume of the cone will be one-third that of the cylinder. If the radius or height are different, then there is no relationship between them.
Tic-tac-toe: In the game of tic-tac-toe, if all moves are performed randomly the probability that the game will end in a draw is 0.127. How is 0.127 figured in this problem?
There are 5 methods to determine which player has less pieces, 5! ways probability to arrange the Xs, and 4! ways to order the Os, for a total of 5 x 5 x 4! = 28,800 possible games.
What is probability?Calculating the chance that an event will occur or a statement will be true is the subject of probability theory, a branch of mathematics. A risk is a number between 0 and 1, where 1 denotes certainty and a probability of about 0 denotes the likelihood that an event will occur. The likelihood that an event will take place is mathematically expressed as probability. Probabilities can also be expressed as percentages ranging from 0% to 100% or as integers between 0 and 1. the proportion of equally plausible possibilities that actually happen in relation to all possible outcomes when a certain event occurs.
Case 1: There are 5 Xs and 4 Os on the board, and there is a one-point difference in the number of Xs and Os. In this situation, starting with the player who has less pieces on the board, we must alternately put the Xs and Os in the squares. There are 5 methods to determine which player has less pieces, 5! ways to arrange the Xs, and 4! ways to order the Os, for a total of 5 x 5 x 4! = 28,800 possible games.
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4.3 GRE scores, Part I. Sophia who took the Graduate Record Examination (GRE) scored 160 on the Verbal Reasoning section and 157 on the Quantitative Reasoning section. The mean score for Verbal Reasoning section for all test takers was 151 with a standard deviation of 7, and the mean score for the Quantitative Reasoning was 153 with a standard deviation of 7.67. Suppose that both distributions are nearly normal.
(a) Write down the short-hand for these two normal distributions.
(b) What is Sophia’s Z-score on the Verbal Reasoning section? On the Quantitative Reasoning section? Draw a standard normal distribution curve and mark these two Z-scores.
(c) What do these Z-scores tell you?
(d) Relative to others, which section did she do better on?
(e) Find her percentile scores for the two exams.
(f) What percent of the test takers did better than her on the Verbal Reasoning section? On the Quantitative Reasoning section?
The normal distribution is N(151, 7), the z-score for verbal and quantitative reasoning are 1.29 and 0.52 respectively.
What is the short-hand for these two normal distribution(a) The shorthand for the normal distribution of the Verbal Reasoning section is N(151, 7), where 151 is the mean score and 7 is the standard deviation. The shorthand for the normal distribution of the Quantitative Reasoning section is N(153, 7.67), where 153 is the mean score and 7.67 is the standard deviation.
(b) Sophia’s Z-score on the Verbal Reasoning section is (160-151)/7 = 1.29. Her Z-score on the Quantitative Reasoning section is (157-153)/7.67 = 0.52.
(c) The Z-scores represent how many standard deviations above or below the mean Sophia’s scores are. A Z-score of 1.29 on the Verbal Reasoning section means Sophia’s score is 1.29 standard deviations above the mean score of all test takers. A Z-score of 0.52 on the Quantitative Reasoning section means Sophia’s score is 0.52 standard deviations above the mean score of all test takers.
(d) Sophia did better on the Verbal Reasoning section because her Z-score is higher for that section.
(e) To find the percentile scores, we use the standard normal distribution table. Sophia’s percentile score on the Verbal Reasoning section is the percentage of test takers who scored lower than her. Using the Z-score of 1.29 and the table, we find that her percentile score is approximately 90.7%. Her percentile score on the Quantitative Reasoning section is the percentage of test takers who scored lower than her. Using the Z-score of 0.52 and the table, we find that her percentile score is approximately 69.4%.
(f) To find the percentage of test takers who did better than Sophia on each section, we can use the standard normal distribution table again. For the Verbal Reasoning section, we need to find the area to the right of Sophia’s Z-score of 1.29. Using the table, we find that this area is approximately 9.3%. Therefore, approximately 9.3% of test takers did better than Sophia on the Verbal Reasoning section. For the Quantitative Reasoning section, we need to find the area to the right of Sophia’s Z-score of 0.52. Using the table, we find that this area is approximately 30.4%. Therefore, approximately 30.4% of test takers did better than Sophia on the Quantitative Reasoning section.
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