Two students used different methods to measure the length of their model bridge

project. One student measured the bridge length in feet using 11n−2.9. The second

student measured the bridge length in feet using 5n + 6.4 What is the value of n if

the two measurements are equal?

\( \sqrt{33 + \sqrt{4 + \sqrt{50 \cos(60°) } } } \)

\( \sqrt{33 + \sqrt{4 + \sqrt{50 \times \frac{1}{2} } } } \\ = \sqrt{33 + \sqrt{4 + \sqrt{25} } } \\ = \sqrt{33 + \sqrt{4 + 5 } } \\ = \sqrt{33 + \sqrt{9} } \\ = \sqrt{33 + 3} \\ = \sqrt{36} \\ = 6\)

Hence LHS = RHS [Proved]

Hope you could understand.

If you have any query, feel free to ask.

The highest exponent of x in F(x) is 37, which means the algebraic degree of the function is 37.

The function F(x) is a cubic function.

Here, we have,

given function is:

F(x) = α⁴⁹ * x³⁷ + α⁵² * x²⁸ + α⁸¹ * x¹³ + α²⁶ * x⁹ + α³¹ * x

To determine the algebraic degree of the given (7,7)-function F(x), we need to find the highest exponent of x in the function.

F(x) = α⁴⁹ * x³⁷ + α⁵² * x²⁸ + α⁸¹ * x¹³ + α²⁶ * x⁹ + α³¹ * x

The algebraic degree of a polynomial function corresponds to the highest exponent of the variable in the function.

Linear functions have an algebraic degree of 1, affine functions have an algebraic degree of 1 or 0, quadratic functions have an algebraic degree of 2, and cubic functions have an algebraic degree of 3.

so, we get,

The highest exponent of x in F(x) is 37, which means the algebraic degree of the function is 37.

Therefore, the function F(x) is a cubic function.

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The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input.

The collection of all potential inputs for a function is its domain. For instance, the domain of f(x)=x2 and g(x)=1/x are all real integers with the exception of x=0.

Think about the function y = f. (x). The range of the function is the range of all the y values, from least to maximum. Substitute all possible values of x into the provided expression of y to see whether it is positive, negative, or equal to other values.

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A decrease in the price of cotton can have positive effects on the affordability and availability of socks in the market, benefiting consumers by potentially offering lower prices and a wider range of choices.

If the price of cotton falls in the market for a bag of socks, it is likely to have an impact on the overall cost and availability of socks. Cotton is a common material used in the production of socks, and its price plays a significant role in determining the cost of manufacturing.

When the price of cotton falls, it reduces the cost of raw materials for sock manufacturers. As a result, manufacturers may experience lower production costs. This can lead to several outcomes:

1. Decrease in sock prices: With lower production costs, manufacturers have the option to reduce the prices of socks to attract customers. This can result in more affordable socks for consumers, making them more accessible.

2. Increase in sock supply: Lower production costs may incentivize manufacturers to increase their sock production. As a result, the supply of socks in the market could rise, leading to a greater availability of socks for consumers.

3. Potential for improved quality or additional features: Manufacturers may choose to invest the cost savings from lower cotton prices into enhancing the quality of socks or adding extra features. This can result in socks with improved durability, comfort, or design, providing more options for consumers.

It's important to note that the impact of falling cotton prices on sock prices and availability may also depend on other factors, such as production and distribution costs, market competition, and consumer demand. Additionally, the extent to which the price reduction in cotton translates into lower sock prices may vary among different brands and retailers.

Overall, a decrease in the price of cotton can have positive effects on the affordability and availability of socks in the market, benefiting consumers by potentially offering lower prices and a wider range of choices.

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The equation for the exponential function containing the points (0, 8) and (1, 32) is y = 8(4)ˣ

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

An exponential function is in the form:

y = abˣ

Where a is the initial value and b is the multiplication factor.

At point (0, 8):

8 = ab⁰

a = 8

At point (1, 32):

32 = 8b

b = 4

The equation for the exponential function containing the points (0, 8) and (1, 32) is y = 8(4)ˣ

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Answer:

A⁣⁣⁣⁣nswer i⁣⁣⁣s i⁣⁣⁣n a p⁣⁣⁣hoto.

Step-by-splanation:

Answer:

hey

Step-by-step explanation:

so i dont know

how to solve this and i cant help u

Yes, they can use the walkie-talkies to talk to each other.

The distance between them is given as 28.2 meters.

The horizontal and vertical distances should be considered when calculating the distance between their apartments using the three-dimensional form of the Pythagorean theorem.

This comes out as \(\sqrt((18^2 + 19^2 + 7^2))\), which equals \(\sqrt(798)\) square root meters, or, to the nearest tenth, 28.2 meters.

Since this distance is less than the 35-meter range of the walkie-talkies, communication should be possible between the two apartments.

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Answer:

\(y=\frac{6}{5}x-24\)

Step-by-step explanation:

\(Since\ the\ yellow\ points\ are\ \left(20,0\right)and\ \left(70,60\right)\)
\(so,\ set\ the\ equation\ of\ this\ is\ y=mx+b\)
\(\rightarrow0=m\times20+b\)
   \(60=m\times70+b\)

  \(get\ m=\frac{6}{5},b=-24\)

\(so,\ the\ slope-intercept\ form\ of\ it\ is\)
       \(y=\frac{6}{5}x-24\)
\(\left\{Substitution\ method\right\}\)

I hope this helps you

:)

The score that falls exactly in the middle of the distribution of scores after they have been ranked from highest to lowest is known as the median.

The median is a measure of central tendency that is calculated by arranging the data points in order from smallest to largest and then identifying the middle value.Therefore, it is the value that separates the highest from the lowest 50% of the data, making it an ideal measurement for skewed data.

The median is the value that is halfway between the upper and lower quartiles of a dataset when it is divided into four equal parts. This measurement is less sensitive to outliers and extreme values in comparison to the mean.

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Vacation price after discount = Vacation price before reduction x (100% - 20%). a. To compute the price of the alternative vacation in Greece after deducting the 20% incentive.

In this scenario, the trip would have cost £1800 without the rebate. We add this sum to the formula to determine the total cost after the discount:

£1800 x (100% - 20%) = £1800 x 80% = £1440

A 20% discount is applied to the trip's price, which drops to £1440.

b. We deduct £100 from the vacation's cost after the 20% incentive has been applied in order to estimate the final total price after the £100 discount coupon has been used:

£1440 - £100 = £1340

The total cost of the trip is therefore £1340.

c. To calculate how much more each consumer will need to pay for this holiday, we divide the final total holiday price by 2, assuming that each client is paying an equal portion.

£1340/2 = £670

Therefore, each person's additional expense for this vacation will be £670.

The pair spent a total of £1200 on their first trip to Portugal, and they are currently spending an additional £1340 on a second trip to Greece. Therefore, the couple will pay an extra £140 for this holiday, and each person will pay an extra £670.

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Answer:

I say B

Step-by-step explanation:

The explicit formula for the recurrence relation \(\(a_n = 3a_{n-1} + 1\) with \(a_0 = 1\) is \(a_n = 3^n - 2\)\).

To find the explicit formula, we can start by computing the first few terms of the sequence. Given that \(\(a_0 = 1\)\), we can calculate \(\(a_1 = 3a_0 + 1 = 4\), \(a_2 = 3a_1 + 1 = 13\), \(a_3 = 3a_2 + 1 = 40\)\), and so on.

By observing the pattern, we can deduce that \(\(a_n\)\) can be expressed as \(\(3^n - 2\)\). This can be proven by induction. The base case is \(\(n = 0\)\), where \(\(a_0 = 1 = 3^0 - 2\)\), which holds true. Now, assuming the formula holds for \(\(n = k\)\), we can show that it also holds for\(\(n = k+1\)\).

\(\[ a_{k+1} = 3a_k + 1 = 3(3^k - 2) + 1 = 3^{k+1} - 6 + 1 = 3^{k+1} - 5 \]\)

Thus, the explicit formula \(\(a_n = 3^n - 2\)\) satisfies the recurrence relation \(\(a_n = 3a_{n-1} + 1\)\) with the initial condition \(\(a_0 = 1\)\).

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Answer:

  100.0 feet

Step-by-step explanation:

You want to know the distance to a goalpost when the angle to the top of its 30 ft height is 16°42'.

The tangent relation is ...

  Tan = Opposite/Adjacent

Multiplying by Adjacent/Tan gives ...

  Adjacent = Opposite/Tan

In this problem, the distance to the goal can be modeled by the side "adjacent" to the acute angle 16°42' in a right triangle, and the "opposite" side will be the height of the goal.

  adjacent = 30'/tan(16°42') ≈ 99.995 ft

Rounded to the nearest tenth, the distance to the goalpost is 100.0 feet.

To determine whether to reject or fail to reject the null hypothesis, we typically rely on statistical hypothesis testing. After conducting a hypothesis test, we consider the test statistic and the corresponding p-value.

When the p-value is less than or equal to the predetermined significance level (usually denoted as α), we reject the null hypothesis. This indicates that the observed data provides sufficient evidence to support the alternative hypothesis. Conversely, when the p-value is greater than the significance level, we fail to reject the null hypothesis. In this case, we do not have enough evidence to support the alternative hypothesis.

The significance level α is predetermined and represents the probability of making a Type I error, which is the rejection of the null hypothesis when it is actually true. Commonly used significance levels include 0.05 (5%) and 0.01 (1%). The choice of the significance level depends on the specific research context and the consequences of making a Type I error.

It is important to note that failing to reject the null hypothesis does not necessarily mean that the null hypothesis is true. It simply means that the observed data does not provide enough evidence to support the alternative hypothesis. There could still be other factors or limitations in the study that contribute to the lack of significant results.

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The sample means (x1 and x2) are given as 35 and 43 respectively, we can rewrite the equation as:

(35 - μ) / (σ / sqrt(n1)) = (43 - μ) / (σ / sqrt(n2))

To determine the population mean, we need additional information such as the standard deviation of the population or the sample size. Without this information, it is not possible to calculate the population mean based solely on the given data.

The z-score is calculated as:

z = (x - μ) / (σ / sqrt(n))

where x is the sample mean, μ is the population mean, σ is the standard deviation, and n is the sample size.

In the given scenario, we know that the z-scores for both sample means are equal:

z1 = z2

(x1 - μ) / (σ / sqrt(n1)) = (x2 - μ) / (σ / sqrt(n2))

Since the sample means (x1 and x2) are given as 35 and 43 respectively, we can rewrite the equation as:

(35 - μ) / (σ / sqrt(n1)) = (43 - μ) / (σ / sqrt(n2))

Without any information about the standard deviation (σ) or the sample sizes (n1 and n2), we cannot determine the population mean (μ) in this case.

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Answer:

Not enough information.

Step-by-step explanation:

AB + BC + CD + DA = 46

In a parallelogram, opposite sides are congruent.

AB + DA + AB + DA = 46

2AB + 2DA = 46

We have two unknowns and only one equation.

There is not enough information to answer the question.

A regular linear regression model is statistically helpful in providing a good fit to the information that can be used to make precise predictions about new information agendas.

A linear regression model is useful when the explanation of a significant amount of variation of the dependent variable utilizes one or more independent variables. The usability of a linear regression model can be comprehended by examining various statistical measures for instance

R-squared value of 1 shows that all of the changes in the dependent variable are elaborated by the independent variable, Hence, an R-squared value of 0 points that none of the variations is elaborated

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To determine the number of gallons of paint needed to cover office 143, we need to know the square footage of the office.

Once we have that information, we can divide the square footage by the coverage rate per gallon to calculate the required amount of paint.

Let's assume the square footage of office 143 is 800 square feet.

Number of gallons needed = Square footage / Coverage rate per gallon

Number of gallons needed = 800 square feet / 50 square feet per gallon

Number of gallons needed = 16 gallons

Therefore, you would need approximately 16 gallons of paint to cover office 143, assuming each gallon covers 50 square feet.

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The correct statement about the function represented by the table will be option (D) It is linear function because the y-value increases by an equal difference over equal interval of x-values

The terms "linear function" in mathematics apply to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.

Given a table on which there are two column in which one column represents x values while other column represent the y values

We have to find whether the relationship between x value and y value is linear or exponential

From given table let,

y₁ = 34; y₂ = 41; y₃ = 48; y₄ = 55

x₁ = 1; x₂ = 2; x₃ = 3; x₄ = 4

If the relationship between the x value and y value is linear then the difference between two consecutive value of x value and y value would be equal

So y₂-y₁ = y₄-y₃ and x₂-x₁ = x₄-x₃

Putting the value we get difference of y value 7 and x value as 1 since it is same we can say that the relation ship between x value and y value is linear

Hence the correct statement about the function represented by the table will be option (D) It is linear function because the y-value increases by an equal difference over equal interval of x-values

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Answer:

The slope of line r is -3/4

Step-by-step explanation:

First, let's find the slope of line q. We can find the slope by finding the change in y over change in x.

\(\displaystyle{m=\dfrac{y_2-y_1}{x_2-x_1}}\)

Therefore, substitute in:

\(\displaystyle{m=\dfrac{8-4}{6-3}}\\\\\displaystyle{m=\dfrac{4}{3}}\)

Therefore, the slope of line q is 4/3. Since we want to find the slope of line r and we know by the given that line r is perpendicular to line q. By the definition of perpendicular line is \(\displaystyle{m_1m_2=-1}\).

Let \(m_1\) be slope of the line q which is 4/3. Therefore, substitute in and solve for \(m_2\) (slope of line r)

\(\displaystyle{\dfrac{4}{3}m_2=-1}\\\\\displaystyle{4m_2=-3}\\\\\displaystyle{m_2=-\dfrac{3}{4}}\)

Therefore, the slope of line r is -3/4

The solution is,  D: A package that weighs 5 pounds will cost $15 for both options.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

The customer can send a package for $5, plus an additional $2 per pound.

The cost, y, can be represented by the equation y = 5 + 2x,

where x represents the amount of pounds of the package.

Another option is that the customer can pay a one-time fee of $15 to send the box, represented by the equation y = 15.

so, we get,

2x + 5 = 15

x = 5

Hence, The solution is,  D: A package that weighs 5 pounds will cost $15 for both options.

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Answer:

D: A package that weighs 5 pounds will cost $15 for both options.

Step-by-step explanation:

2x + 5 = 15

x = 5

Thus, the person above me is correct :)

Answer:

Probability helps us to know the chances of an event occurring. The probability that the first card is an even number and the card is greater than 7 is 0.15.

Step-by-step explanation:

Probability helps us to know the chances of an event occurring.

The probability that a first card is an even number and the card is greater than 7 is

Probability = (5/10)×(3/10) = 15/100 = 0.15

Hence, the probability that the first card is an even number and the card is greater than 7 is 0.15.

Ivan Hernandez- theonetheonlyivan1 on you tube :)

Answer:

Step-by-step explanation:

outer area=

first need to find the circumference of outer diameter

= π×4.8

= 15.079644.... cm

to find the outer curved area you would then do

= 77×15.079644

(ii) =1161.13264 cm²

inner curve area

circumference= π×4

=12.5663706.... cm

77×12.5663706

(i) =967.610537 cm²

total surface area=

as the outer and inner curved areas are already found only the top and bottom surfaces need to be

= area of larger circle

=π×4.8²

=72.382294.... cm²

smaller circle

=π×4²

=50.2654824.... cm²

72.382...-50.265

=22.1168116 x 2

=44.2336232 cm²

total surface area

(iii)= 2172.9768 cm²

(round this to however many decimals you need)

I hope this is understandable and useful!

also how many marks is this for?

Answer:

Suppose those rental rates have approximately a normal distribution, with a standard deviation of. $150. ... Canada, systolic blood pressure readings have a mean of 121 and a standard deviation of 16. A reading.

Probability that a randomly selected male's systolic blood pressure will be less than 100 is 0.397.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.

According to the question

For males in a certain town, the systolic blood pressure is normally distributed with a mean of 105 and a standard deviation of 9.

Probability that a randomly selected male's systolic blood pressure will be less than 100

P(x < 100)

By using normalized normal distribution

= \(N(\frac{100-105}{9} )\)

= \(N(\frac{-5}{9} )\)      

We have N(-a) = 1 - N(a), a>0                                    

= 1 -  \(N(\frac{-5}{9} )\)      

= 1 - N(0.556)

= 1 - 0.6026

= 0.3979

≈ 0.397 (nearest thousandth)

So, probability that a randomly selected male's systolic blood pressure will be less than 100 is 0.397.

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Answer:

a = b + 6

b = 8

Step-by-step explanation:

a = b + 6

b = 8

If there were any variations in the distribution during the preparation process, the slices might have slight differences in the amount of sauce and toppings.

each slice of the 12-inch thin-crust cheese pizza would have an equal distribution of sauce and toppings. This means that each slice would have the same amount of sauce and toppings spread evenly across its surface.

Since the pizza is cut equally into eight slices, each slice would represent 1/8th of the total pizza. Therefore, each slice would have an equal portion of the sauce and toppings.

It's important to note that the exact amount of sauce and toppings on each slice would depend on the original distribution applied to the pizza before it was sliced. If the pizza was prepared with a uniform distribution of sauce and toppings across the entire pizza, then each slice would indeed have an equal amount. However, if there were any variations in the distribution during the preparation process, the slices might have slight differences in the amount of sauce and toppings.

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The proportion of a normal distribution located between z = .50 and z = -.50 will be 38.2%.

We have,

A normal distribution located between z = 0.50 and z = -0.50,

So,

Now,

From the Z-score table,

We get,

The Probability corresponding to the Z score of -0.50,

i.e.

P(-0.50 < X < 0) = 0.191,

And,

The Probability corresponding to the Z score of -0.50,

i.e.

P(0 < X < 0.50) = 0.191,

Now,

The proportion of a normal distribution,

i.e.

P(Z₁ < X < Z₂) = P(Z₁ < X < 0) + P(0 < X < Z₂)

Now,

Putting values,

i.e.

P(-0.50 < X < 0.50) = P(-0.50 < X < 0) + P(0 < X < 0.50)

Now,

Again putting values,

We get,

P(-0.50 < X < 0.50) = 0.191 + 0.191

On solving we get,

P(-0.50 < X < 0.50) = 0.382

So,

We can write as,

P(-0.50 < X < 0.50) = 38.2%

So,

The proportion of a normal distribution is 38.2%.

Hence we can say that the proportion of a normal distribution located between z = .50 and z = -.50 will be 38.2%.

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Algebraic expressions are mathematical statements made up of variables, constants, and operations, which can be simplified to -17x²+4x+5.

Given expression: -10x²+4x-7x²+5.A mathematical statement made up of variables, constants, and mathematical operations is known as an algebraic expression. It stands for a mixture of numbers and letters, where the letters are called variables and they can have various values. In algebra, relationships are represented and calculations are done using algebraic expressions.

The given expression can be simplified as:

Adding the like terms together,

we get,-10x²-7x²+4x+5

= -17x²+4x+5

Thus, the simplified expression is -17x²+4x+5.

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