10.3 Surface Area of Triangular Prisms.
Please help with these 6 answers in photo

Answer:

No solutions

Step-by-step explanation:

i have a feeling it's "no solutions". looking at the equations, the only thing that's different is the y intercepts (one being +1 and the other +7). that tells me they are parallel, so they'll never touch each other

The equation that represents this function is y = -3x + 8

From the question, we have the following parameters that can be used in our computation:

X: 0,5,10,15

Y: 8,-7,-22,-37

A linear relation is represented as

y = mx + c

Where

c = y when x = 0

Using the above as a guide, we have the following:

c = 8

So, we have

y = mx + 8

Using the points on the table, we have

5m + 8 = -7

This gives

5m = -15

m = -3

So, the function is

y = -3x + 8

Hence, the function is y = -3x + 8

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The result are Blank #1: 65°, Blank #2: 115°, Blank #3: 65°, Blank #4: 115°

Vertical angles are pairs of angles that are formed by two intersecting lines or two intersecting line segments. These angles are opposite each other and are located at the opposite corners of the intersection.

Vertical angles, ∠BAD = ∠CAE

it means (x+75)° = (3x-5)°

so, x = 40°

1. ∠BAC = 180° - (x+75)° = 180 - (40 + 75) = 65°

2. ∠CAE = (3x-5)° = 3×40 - 5 = 115°

3. ∠DAE = ∠BAC = 65°

4. ∠BAD = (x+75)° = 40+75 = 115°

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Based on the information in the graph, it can be inferred that the amount of prize money in year 10 of the contest would be $11,790 (option A).

To predict the amount of prize money in year 10 of the contest we must take into account the information of the image. As can be seen from year 1 to year 8, the amount of prize money has not had a very radical variation, but has remained in a range between 6,000 and 12,000.

Based on the foregoing, it could be inferred that for year 10 the amount of prize money does not fall outside these ranges. Then we could affirm that in year 10 the amount of prize money will be $11,790 because it is within the range in which this value has fluctuated.

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The equation of the hyperbola with the given foci and vertices is (x - 3)² - (y - 1)² = 64

Hyperbola is a type of conic section, which is a curve formed by the intersection of a cone with a plane. It is similar to a circle, but with two separate halves that are mirror images of each other. These two halves are called branches, and the point where they intersect is the vertex. The hyperbola is characterized by its two foci, which are points that lie on the inside of the structure.

The equation of a hyperbola with foci (h, k) and (h, l) and vertices (m, n) and (p, n) is given by:
((x - h)² / (m - h)²) - ((y - n)² / (k - n)²) = 1
In this case, h = 3, k = 11, l = -9, m = 11, and n = 1. Plugging these values into the equation, we get:
((x - 3)² / (11 - 3)²) - ((y - 1)² / (11 - 1)²) = 1
Simplifying, we get:
(x - 3)² - (y - 1)² = 8²
Therefore, the equation of the hyperbola with the given foci and vertices is: (x - 3)² - (y - 1)² = 64.

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Answer:

$14500

Step-by-step explanation:

$10 per unit means 1 unit is equivalent to 10 dollars.

∴Unit multiplier = [tex]\frac{10 dollars}{unit}[/tex]

$5 per unit means 1 unit is equivalent to 5 dollars

∴Unit multiplier = [tex]\frac{5 dollars}{unit}[/tex]

Remaining units = 1000 - 100 = 900 units

The unit multipliers are arranged in such a way that the "units” in the numerator and denominator will cancel each other out leaving us with “dollars” in the numerator. Our answer should be expressed in dollars
since the question requires us to calculate the bill

Bill of the House = Charge of first 100 units + Charge of remaining units

                            = (1000 units)([tex]\frac{10dollars}{unit}[/tex]) + [(900)units][[tex]\frac{5dollars}{unit}[/tex]]

                            = $10000 + $4500

                            = $14500

Answer:

[tex](4 \times 3) - (2 + 9)[/tex]

The range, which is the distance between the smallest and greatest linear equation values in the data,  does not take into account the distribution of the data within that range.

In algebra, a linear equation refers to one with its form y=mx+b. B is the gradient, and m is the esta. The preceding clause is commonly referred to as a "linear function with two variables" so even though y and x are variables. Bivariate linear equations are linear equations with two variables. There are several linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation seems to have the structure y=mx+b, where m is the slope and b is the y-intercept, it is said to be linear. When a measurement seems to have the formula y=mx+b, both with m identifying its slope and b denoting the y-intercept, it is said to be linear.

Because it has a lower IQR, Fast Chicken can more consistently estimate their wait time (Interquartile Range). In this case, the IQR is the range of the middle 50% of the data, which is the distance between the first and third quartiles.

Super Fast Food, on the other hand, has a higher IQR, indicating that the data is more dispersed. This means that customers report a wider range of wait times, making it more difficult to estimate a consistent wait time. The range, which is the distance between the smallest and greatest values in the data, is not as useful for measuring consistency in this case because it does not take into account the distribution of the data within that range.

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Answer:

32

Step-by-step explanation:

given that there are 128 fluid ounces in a gallon and she would have drank 3 gallons which is 384 ounces then divide

384 divided by 12 = 32

Answer:

a)0.25

b)0.063

c)0.313

d)Yes​, because the probability that 3 or more of the selected adults believe in reincarnation is greater than 0.05.

Step-by-step explanation:

Probability nation is that adult believe in reincarnation

Therefore,

Using binomial distribution

Where

a) When r=3

The probability that exactly 3 of the 4 adults believe in reincarnation is  

0.25

b) Now,

The probability that all of the selected adults believe in reincarnation is  

. 0.063

c) In this case atleast 3 will believe therefore

The probability that at least 3 of the selected adults believe in reincarnation is  0.313

d)Yes​, because the probability that 3 or more of the selected adults believe in reincarnation is greater than 0.05 i.e 0.313.

Answer:

Step-by-step explanation:

To find the cost per hour of bike use at Cheng's Bike Rentals, we need to divide the total cost of renting the bike by the number of hours it was rented for.

If it costs $22 to rent a bike for 4 hours, then the cost per hour is:

$22 / 4 hours = $5.50/hour

Therefore, it costs $5.50 per hour of bike use at Cheng's Bike Rentals.

Answer:  2/3

Step-by-step explanation:

3/8 * .25/X

3X = 2

X = 2/3

A triangle is a geometrical shape that is formed by three straight lines connecting three non-collinear points. The three points are called the vertices of the triangle, and the lines connecting them are called sides or edges.

To prove that triangle QRS is similar to triangle TUV, we need to show that their corresponding angles are equal and their corresponding sides are proportional.

Let's start by identifying the corresponding angles:

Now, let's look at the corresponding sides:

To prove that the triangles are similar, we need to show that the ratios of the corresponding sides are equal:

QS/TV = RS/UV (given)

QS/TV = 3/3 (since QR=3TU)

QS/TV = 1

RS/UV = 3/3 (since QR=3TU)

RS/UV = 1

Since the ratios of the corresponding sides are equal, the triangles are similar. Therefore, we can conclude that triangle QRS ~ triangle TUV.

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Answer:

two are supplementary. the measure of one of these angles is 12 degrees less than one-third the measure of the other.what is the measure of each angle

Let's call the measures of the two angles x and y, where x is the larger angle. We know that the two angles are supplementary, which means they add up to 180 degrees:

x + y = 180

We also know that one of the angles (let's say y) is 12 degrees less than one-third the measure of the other angle (x):

y = (1/3)x - 12

Now we can substitute the second equation into the first equation to solve for x:

x + (1/3)x - 12 = 180

Multiplying both sides by 3 to get rid of the fraction, we have:

3x + x - 36 = 540

Combining like terms, we get:

4x - 36 = 540

Adding 36 to both sides, we get:

4x = 576

Dividing both sides by 4, we get:

x = 144

Now we can use the first equation to solve for y:

144 + y = 180

Subtracting 144 from both sides, we get:

y = 36

Therefore, the measures of the two angles are 144 degrees and 36 degrees.

Hence, in answering the stated question, we may say that As a result, we  angles have demonstrated that angle PQR equals angle PQS, assuming that angle article equals angle pqs and QS = PR.

An angle is a shape in Euclidean geometry that is comprised of two rays, known as such angle's flanks, that meet at a central location known as the angle's set of vertices. Two rays might combine to generate an angle there in plane in which they are located. An angle is formed when two planes collide. They are known as dihedral angles. In plane geometry, an angle is a potential configuration between two rays and lines that meet a termination. The English name "angle" is derived from the Latin phrase "angulus," which means "horn." The apex is the point at where the two rays, also known also as angle's sides, converge.  

It is difficult to propose a specific solution without a diagram or a comprehensive description of the figure. But, based on the facts provided, we can apply the following argument to demonstrate that angle PQR equals angle PQS.

Assuming that angle article equals angle pqs and QS = PR.

To demonstrate: angle PQR = PQS angle.

We know that angle pqs = angle article. This signifies that the two angles are parallel.

We also understand that QS Equals PR. That is, these two line segments are congruent.

As a result, angle PQR equals angle PQS.

As a result, we have demonstrated that angle PQR equals angle PQS, assuming that angle article equals angle pqs and QS = PR.

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In response to the stated question, we can state that The odds of equation drawing a bronze star the second time are 9/32.

An equation is a mathematical assertion that establishes the equality of two expressions that are joined together by the equals sign ('='). For example, 2x – 5 = 13. 2x-5 and 13 are examples of expressions. The letter '=' connects the two expressions. A mathematical formula is called an equation if it contains two algebraic expressions on either side of the equal sign (=). It shows how the right and left formulas are equivalent to one another. Any formula will result in L.H.S. = R.H.S. (left side = right side).

There are 12-3=9 bronze stars remaining in the bag if none of the three stars that were removed were bronze.

12 + 12 + 12 + 3 = 33 stars are still in the bag.

There are now 33-1=32 stars in the bag after drawing one star out of it without replacing it.

The following formula can be used to determine the likelihood of drawing a bronze star a second time:

Bronze stars remaining in the bag divided by the total number of stars in the bag is 9/32 for P(drawing a bronze star).

The odds of drawing a bronze star the second time are 9/32.

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683 rounded to the nearest hundred is 700

2329 rounded to the nearest hundred is 2300

The product of the rounded numbers is 1,610,000.

From the question, we are to round the given numbers to the nearest hundred and determine the product of the rounded numbers.

The given numbers are 683 and 2329.

Rounding 683 and 2329 to the nearest hundred gives:

683 rounded to the nearest hundred is 700

2329 rounded to the nearest hundred is 2300

Now, we will determine the product of these rounded numbers.

That is,

The product of 700 and 2300

700 × 2300 = 1610000

Hence, the product of the rounded numbers is 1,610,000.

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Answer:

  0.3176523

Step-by-step explanation:

You want the probability of exactly 5 successes in 7 trials of a binomial experiment in which the probability of success is 70%.

The desired probability is the product of the probability of 5 success and 2 failures, multiplied by the number of ways that result might occur.

  P(x=5) = 7C5·(0.7^5)(1 -0.7)^2 = 0.3176523

The probability of exactly 5 successes is 0.3176523.

__

Additional comment

Any of a number of probability calculators can tell you this probability. Spreadsheets have appropriate functions built in as well.

[tex]\blue{\huge {\mathrm{PROBABILITY}}}[/tex]

[tex]\\[/tex]

[tex]{===========================================}[/tex]

[tex]{\underline{\huge \mathbb{Q}{\large \mathrm {UESTION : }}}}[/tex]

[tex]{===========================================}[/tex]

[tex] {\underline{\huge \mathbb{A} {\large \mathrm {NSWER : }}}} [/tex]

[tex]{===========================================}[/tex]

[tex] {\underline{\huge \mathbb{S} {\large \mathrm {OLUTION : }}}} [/tex]

We can use the binomial probability formula to find the probability of exactly 5 successes in 7 trials:

[tex]\sf P(5\: successes\: in\: 7\: trials) = (7\: choose\: 5) (0.7)^5 (0.3)^2[/tex]

where:

Plugging in these values, we get:

[tex]\begin{aligned}\sf P(5\: successes\: in\: 7\: trials)& =\sf 21 (0.7)^5 (0.3)^2\\& =\bold{ 0.3176523}\end{aligned}[/tex]

Therefore, the probability of exactly 5 successes in 7 trials of a binomial experiment in which the probability of success is 70% is 0.3176523.

[tex]{===========================================}[/tex]

[tex]- \large\sf\copyright \: \large\tt{AriesLaveau}\large\qquad\qquad\qquad\tt 04/01/2023[/tex]

Answer: x = 50, m∠N = 50°

Step-by-step explanation:

x = 50, m∠N = 50°

Since ∠M and ∠N are supplementary, the two angles add up to 180°. Therefore, m∠N = 180° - 37° = 143°. Because m∠N = 13x, we can solve for x by dividing both sides by 13, which gives x = 50. Therefore, m∠N = 13x = 13(50) = 50°.

The ordered pair solutions for the system of equations are (-2, 5) and (1, 2).

To determine if an ordered pair is a solution to two systems of equations, substitute the values ​​of the variables into each equation. If an ordered pair makes both equations true, it is the solution of the system. 

To find the ordered pair solutions for the system of equations, we need to solve the two equations simultaneously.

f(x) = x² + 1 ...(1)

f(x) = -x + 3 ...(2)

Setting the two equations equal to each other, we get:

x² + 1 = -x + 3

Rearranging this equation, we get:

x² + x - 2 = 0

Factoring this quadratic equation, we get:

(x + 2)(x - 1) = 0

Therefore, the solutions for x are x = -2 and x = 1.

Substituting these values of x into either equation (1) or (2), we get:

For x = -2: f(-2) = (-2)² + 1 = 5, and f(-2) = -(-2) + 3 = 5.

For x = 1: f(1) = 1² + 1 = 2, and f(1) = -1 + 3 = 2.

Therefore, the ordered pair solutions for the system of equations are (-2, 5) and (1, 2).

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The correct answer is "The extreme value theorem applies, and f(x) has both a minimum and a maximum."

What is the extreme value theorem?

The extreme value theorem states that if a function is continuous on a closed interval, then it must have both a maximum and a minimum value on that interval. To determine whether the extreme value theorem applies to the graph of f(x), we need to check if the function is continuous on a closed interval and whether it has a highest and lowest point within that interval.

Looking at the graph of f(x), we can see that the function is continuous on the closed interval [-3, 3] since it has no breaks or jumps. Additionally, the graph has the highest point at (1, 2) and the lowest point at (-3,-2). Therefore, we can conclude that the extreme value theorem applies and that f(x) has both a minimum and a maximum value on the interval [-3, 3].

Therefore, the correct answer is (a) "The extreme value theorem applies, and f(x) has both a minimum and a maximum."

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Answer:

x = 3

y = 7

Step-by-step explanation:

3x - y = 2                                  Y = 2x - 1

3x - 2x - 1 = 2

x - 1 = 2

x = 3

Now put 3 in for x and solve for y

3(3) - y = 2

9 - y = 2

- y = -7

y = 7

Let's check

3(3) - 7 = 2

9 - 7 = 2

2 =2

So, x = 3 and y = 7 is the correct answer.

Hence, in response to the provided question, we can say that As a result,  exponents [tex]/sqrt(196y^8)[/tex] simplifies to [tex]14y^4[/tex].

Exponentiation, sometimes known as "raising b to the nth power," is a substitution cipher that includes two numbers: a base quantity, b, and an argument, meaning power, n. Exponents represent the number of times a value has been increased by itself. As an example, 2-3 (represented as 23) represents: 2 x 2 x 2 = 8. 2 + 3 = 6 does not equal 23. Remember that an integer multiplied by one equals itself. Exponents are a method for expressing large numbers as powers. The amount that represents however many times a statistic has already been amplified by itself is called the exponent. As an example, multiplying 6 by 4 yields 6 x 6 x 6.

Using exponent principles and the square root of perfect squares, we may simplify sqrt(196y8) as follows:

[tex]\sqrt(196y8) = \sqrt((142*(y4)2) [since 196 = 142 and (y4)2 = y8]\\\sqrt(142) * \sqrt((y4)2) [using the \sqrt(ab) = \sqrt(a) * \sqrt(b) rule]\\= 14y^4[/tex]

As a result, [tex]/sqrt(196y^8)[/tex] simplifies to [tex]14y^4[/tex].

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The answer of the question based on the players can fill their water bottles with the sports drink before the cooler is empty is 15 players.

An amount may refer to quantity of something that can be measured, such as amount of substance or amount of  the time.

The cooler can hold 5 1/2 gallons of sports drink, and Coach Walker fills 3/4 of it, which means he fills:

5 1/2 gallons * 3/4 = (5 * 2/2 + 1/2) * 3/4 = 15/4 gallons

We know that 1 gallon equals 8 pints, so we can convert the 15/4 gallons to pints:

15/4 gallons * 8 pints/gallon = 30 pints

Therefore, there are 30 pints of sports drink in the cooler. Assuming each player's water bottle can hold 2 pints of sports drink, we can find how many players can fill their bottles before the cooler is empty by dividing the total amount of sports drink by the amount used by each player:

30 pints / 2 pints/player = 15 players

Therefore, 15 players can fill their water bottles with the sports drink before the cooler is empty.

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Answer:

So g would be 15.

S thus measures around 2.77 centimetres in length.

The law of sines is frequently used to find the elusive side or angle of a triangle. This law can be used if precise triangle measurement combinations are given. ASA The objective is to identify the unknown side given two angles and an included side.

The Law of Sines can be used to determine the length of side s: s/sin(mS) = q/sin(mQ).

replacing the specified values:

s/sin(10°) = 3.9/sin(74°)

s ≈ sin(10°) × 3.9 ÷ sin(74°)

s ≈ 0.684 × 3.9 ÷ 0.961

s ≈ 2.77 cm (rounded to the nearest 10th)

S thus measures around 2.77 centimetres in length.

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The normal probability plot is a useful tool for assessing the normality of a sample of data. By plotting the sample values against the quantiles of a normal distribution, one can quickly determine whether the data could have come from a population that is normally distributed.

Sample data is a subset of data taken from a larger population. It is used to estimate the characteristics of the larger population. Sample data is usually collected using a variety of methods such as surveys, experiments, and simulations. It is important to select a sample that accurately represents the population in order to draw reliable conclusions.

A normal probability plot is a graphical tool used to assess whether or not a sample of data could have come from a population that is normally distributed. The data is plotted on a graph, with the x-axis representing the sample values and the y-axis representing the quantiles of a normal distribution. If the points form a straight line, then the population is normally distributed.

In this situation, the sample data being studied is the wall thickness of O-rings. To create the normal probability plot, each sample value should first be converted to a standard normal deviate, which can be found using the standard normal distribution table. The standard normal deviate is then plotted against the sample values, and the points are connected to form a line. If the line is straight, then it can be concluded that the sample data could have come from a population that is normally distributed. If the line is curved, then the data does not fit the normal distribution.

The normal probability plot is a useful tool for assessing the normality of a sample of data. By plotting the sample values against the quantiles of a normal distribution, one can quickly determine whether the data could have come from a population that is normally distributed.

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Number line  that represents the solution to |x − 21| < 3 is C.

Tο sοlve the inequality |x - 21| < 3, we need tο find all the values οf x that are less than 3 units away frοm 21 οn the number line.

Starting frοm 21, we can cοunt 3 units tο the left and 3 units tο the right tο find the interval οf values that satisfy the inequality:

| x - 21 | < 3 can be written as -3 < x - 21 < 3

Adding 21 tο all parts οf the inequality gives:

18 < x < 24

Therefοre, the sοlutiοn tο the inequality is the interval οf values between 18 and 24, excluding the endpοints.

Lοοking at the answer chοices, we can see that οptiοn C represents this interval οf values:

A:

B:

C: |----|----|----|----|----|----|

18 19 20 21 22 23 24

D:

Therefore, the correct answer is C.

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The probability that a randomly selected adult has an IQ between 93 and 117 is approximately 0.6827 or 68.27%.

What is probability?

Probability is a branch of mathematics that deals with the study of random events and their outcomes. It is the measure of the likelihood of an event occurring, expressed as a number between 0 and 1.

To find the probability that a randomly selected adult has an IQ between 93 and 117, we need to standardize the distribution using the z-score formula, and then find the area under the normal distribution curve between those two z-scores.

The z-score formula is:

z = (x - μ) / σ

where x is the IQ score we are interested in, μ is the mean IQ score, and σ is the standard deviation of IQ scores.

For the lower bound of 93, the z-score is:

z = (93 - 105) / 20 = -0.6

For the upper bound of 117, the z-score is:

z = (117 - 105) / 20 = 0.6

Now, we need to find the area under the normal distribution curve between these two z-scores. We can use a standard normal distribution table or a calculator to find this probability. Using a calculator, we can use the normalcdf function:

normalcdf(-0.6, 0.6, 0, 1)

This gives us a probability of 0.6827.

Therefore, the probability that a randomly selected adult has an IQ between 93 and 117 is approximately 0.6827 or 68.27%.

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The only expression that does not belong to the other 3 is the one that is a  binomial.

A monomial is defined as an algebraic expression that has only one non- zero term. Examples of a monomial expression are x, 7xy²

A binomial is defined as an algebraic expression that has two non-zero terms. Examples of a binomial expression: x² + 2y

A trinomial is defined as an algebraic expression that possesses three non-zero terms. Examples of a trinomial expression: a + b + c

A polynomial is defined as an algebraic expression that has one, two or more terms.

The only expression that does not belong to the other 3 is (b - 2⁻¹) because it is the only binomial.

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