Find the principal (positive) square root of 15. If necessary, round the answer
to the nearest hundredth (two decimal places).

To solve this problem, we will use the following formula for the surface area of a square pyramid:

where BA= base area, and A_t is the area of one of the lateral triangles.

Now, we are given that:

Recall that the area of a square is given by the following formula:

We are given that the side of the base is 5 cm long, therefore, the base area is:

Finally, we get that:

Answer:

Answer:

The answer depends on the shape of the trapezoid...

Step-by-step explanation:

A trapezoid is a 4-sided flat shape with straight sides that has a pair of opposite sides parallel. (trapezium)

Area = (a+b/2) * h

IF the sides are a = 3 ,b = 3 and height  = 4

THEREFORE:

(3+3/2) * 4

6/2 * 4

3 * 4

12

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Answer:

4000 miles

Step-by-step explanation:

320x1.5=480

(320x5)+(480x5)=4000

4000 miles

Answer:

\(4,000\text{ miles}\)

Step-by-step explanation:

Let's say that the two planes travel at point \(p\). Without loss of generality, let's say that the first plane travels left and the second plane travels right.

Distance is given by \(d=rt\), where \(r\) is rate or speed and \(t\) is time.

If the first plane travels at a speed of 320 mph and the second plane travels 1.5 times this, the second plane must travel \(320\cdot 1.5=480\) mph.

Using \(d=rt\), the first plane must travel:

\(d=320\cdot 5=1600\) miles

The second plane must travel:

\(d=480 \cdot 5=2400\) miles

However, these are the planes' respective distances from point \(p\). Since they travelled in opposite directions, the total distance between them is equal to \(1600+2400=\boxed{4,000\text{ miles}}\)

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Domain :

\(x \leqslant - 1\)

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Range :

\(y \geqslant 0\)

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Thus the correct answer is (( B )) .

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

Answer:

d

Step-by-step explanation:

range means y values so automatically a and b aren't right

there's no limits for y since it's linear, so it's D

that R sign basically means "all real numbers"

We are asked to determine the area of a triangle given two sides and the angle in-between. To do that we will use the following formula:

Where "a" and "b" are the sides of the triangle and "theta" is the angle in-between. Replacing the values we get:

Solving the operations:

Therefore, the area is 27.70 square centimeters.

Based on the sample response given, the statements included in the explanation on the horizontal line test are:

The horizontal line test is used to not only find out if a graph has an inverse function, but also if that inverse is also a function itself.

To pass the horizontal line test, the function has to be one-to-one which means that a horizontal line can intersect the graphed function at one point in all places. If this happens, then there is an inverse and the inverse itself is a function.

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Answer:

Jayden is running faster

Answer:

\(\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}\)

The angle of elevation depends on the heights of the objects and the distance between them. Can you please provide more details or clarify your question?

Elevation angle, also known as the angle of elevation, is the angle between an observer's line of sight and a horizontal reference line or plane. It is commonly used in geometry, trigonometry, and navigation to describe the angle at which an object is observed from a certain point. The elevation angle is measured in degrees, and it is typically positive when the observer's line of sight is directed upwards from the horizontal plane and negative when it is directed downwards. The elevation angle is often used in applications such as surveying, astronomy, and aviation to determine the height or altitude of an object or to calculate the distance between two points.

I cannot answer this question without more context or information about the specific boy and lighthouse in question.

The angle of elevation depends on the heights of the objects and the distance between them. Can you please provide more details or clarify your question?

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The length of the line segment that connects points at (5, 4) and (−3, −1) is found to be 9.43 units.

Using the formula obtained from Pythagoras' theorem, distance can be computed.

The distance formula in coordinate geometry is:

(P, Q) = √ (x2 – x1)² + (y2 – y1)².

Given points: (5, 4) and (−3, −1)

d = √ (-3 - 5)² + (4 + 1)²

d = √ 64 + 25

d = √ 89

d = 9.43

Thus, the length of the line segment that connects points at (5, 4) and (−3, −1) is found to be 9.43 units.

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It took Emily 33.4 minutes to make dinner.

A mixed number is a kind of fraction that also has a proper fraction and a whole number. The number of whole units is represented by the whole number, and the fraction of a unit is represented by the proper fraction.

To solve the problem, we have to convert the mixed number  \(9 \frac{1}{10}\)   to a decimal number:

⇒ \(9 \frac{1}{10} = 9 +\frac{1}{10} = \frac{(9*10)+1}{10}\)

⇒ \(\frac{91}{10}\)  =  9.1

This means that Emily finished making dinner 9.1 minutes sooner than the cake.

To find out how long it took Emily to make dinner, we can subtract 9.1 from the cake baking time:

⇒ 42.5 - 9.1 = 33.4 minutes

Therefore, it took Emily 33.4 minutes to make dinner.

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Answer:

u = 0

Step-by-step explanation:

hedh djsf

fjdg

ggf

The value of m + n is given as follows:

A. 18.

The exponential expression for this problem is defined as follows:

\((x^5y^6)^{\frac{1}{5}}(x^3y^4}^{\frac{1}{4}}\)

Applying the power of power rule, we have that the exponents are given as follows:

Then the values of m and n are given as follows:

m = 7, n = 11.

Thus the sum is given as follows:

m + n = 7 + 11 = 18.

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1.Identify the fractions. Using the distributive property, you’ll eventually turn them into integers.

2.For all fractions, find the lowest common multiple (LCM) -- the smallest number that both denominators can fit neatly into. This will allow you to add fractions.

3.Multiply every term in the equation by the LCM.

4.Isolate variables adding or subtracting like terms on both sides of the equals sign.

5.Combine like terms.

6.Solve the equation and simplify, if needed.

The rate that is equivalent to the rate at which John drove to San Antonio is 60 miles per hour

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

John drove from here to San Antonio which is 180 miles away in 3 hours.

This means that

Distance = 180 miles

Time = 3 hours

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

Speed = Distance/Time

Substitute the known values in the above equation, so, we have the following representation

Speed = 180/3

Evaluate

Speed = 60

Hence. the rate that is equivalent to the rate at which John drove to San Antonio is 60 miles per hour

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Answer:  x = -3/2

Step-by-step explanation:

Answer:

-9

Step-by-step explanation:

Here we use the slope formula: m= y2-y1/x2-x1. We simply plug in the numbers we know: -1/10 = -5+6/t-1. Then we solve for t. Multiply both sides by (t-1) so -1/10 (t-1)= 1. Then multiply both sides by -1/10 so t-1= -10 and then add one to both sides so t=-9.

A study based on a population sample that includes 2000 respondents would be the most reliable out of the given options.

In statistical analysis, the reliability of a study depends on the representativeness and size of the sample.

A larger sample size generally provides more reliable results as it reduces the sampling error and increases the precision of the estimates.

Given that the population contains 20,000 people, we need to consider which number of respondents would yield the most reliable study.

Option A: 200 respondents

This represents only 1% of the population.

While it is better than having just 2 respondents, it may not be sufficient to accurately capture the characteristics of the entire population.

Option B: 20 respondents

This represents only 0.1% of the population.

With such a small sample size, the study would likely suffer from a high sampling error and may not provide reliable results.

Option C: 2000 respondents

This represents 10% of the population.

While it is a larger sample size compared to the previous options, it still only captures a fraction of the population.

The study may provide reasonably reliable results, but there is room for potential sampling error.

Option D: 2 respondents

This represents an extremely small sample size, accounting for only 0.01% of the population.

With such a small sample, the study would be highly susceptible to sampling bias and would likely yield unreliable results.

Based on the options provided, option C with 2000 respondents would be the most reliable study.

Although it does not include the entire population, a sample size of 2000 respondents provides a larger representation of the population and reduces the potential for sampling error.

However, it's important to note that the reliability of a study depends not only on sample size but also on the sampling method, data collection techniques, and other factors that ensure representativeness.

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Answer:

35/42 = b/7    and b= 35/6

Step-by-step explanation:

Our base is unkhown so it will be the variable in our equation :

so b is 35/6 cm

Answer:

  8

Step-by-step explanation:

You want to know the measure of segment XY if ∆XYZ ≅ ∆MNL and MN = 8.

Segment XY is named using the first two vertices listed in the name of ∆XYZ. That means the segment is the same length as the one named by the first two vertices listed in the name of congruent ∆MNL, segment MN.

Segment MN is given as 8 units long. Segment XY is congruent, so is also 8 units long.

  XY = 8 units

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Answer:

7, 2, -3, -8

Step-by-step explanation:

y = -5x + 2  Substitute in -1 for x

y = -5(-1) + 2

y = 5 + 2

y = 7

y = -5x + 2  Substitute in 0 for x

y = -5(0) + 2

y = 0 + 2

y = 2

y = -5 + 2 substitutes in 1 for x

y = -5(1) + 2

y = -5 + 2

y = -3

y = -5x + 2  Substitute in 2 for x

y = -5(2) + 2

y = -10 + 2

y = -8

Helping in the name of Jesus.

Answer:

\(P(Dogs) = 0.2025\)

Step-by-step explanation:

Given

\(Proportion, p = 45\%\)

Required

Probability of two people having dog

First, we have to convert the given parameter to decimal

\(p = \frac{45}{100}\)

\(p = 0.45\)

Let P(Dogs) represent the required probability;

This is calculated as thus;

P(Dogs) = Probability of first person having a dog * Probability of second person having a dog

\(P(Dogs) = p * p\)

\(P(Dogs) = 0.45 * 0.45\)

\(P(Dogs) = 0.45^2\)

\(P(Dogs) = 0.2025\)

Hence, the probability of 2 people having a dog is \(P(Dogs) = 0.2025\)

Required correct functions are f(x)=5x⁶, f(x)=10x⁴+6x³−7x²+9, f(x)=7x⁸−9x⁶−12x+46

What is function?

In mathematics, a function is a rule that assigns a unique output (value) for each input (value) in a given domain. A function can be thought of as a machine that takes in a number (or other mathematical object) as input and produces another number (or object) as output.

Functions are commonly denoted using notation such as f(x) or g(y), where f and g represent the function and x and y represent the input values. The domain of a function is the set of all possible input values, while the range is the set of all possible output values.

Here,

The functions that are increasing in value as they approach both negative and positive infinity are the ones that have a positive leading coefficient and an even degree or a negative leading coefficient and an odd degree.

Therefore, the functions that meet these conditions are:

f(x)=5x⁶(even degree, positive leading coefficient)

f(x)=10x⁴+6x³−7x²+9 (even degree, positive leading coefficient)

f(x)=7x⁸−9x⁶−12x+46 (even degree, positive leading coefficient)

Therefore, the correct answers are:

f(x)=5x⁶

f(x)=10x⁴+6x³−7x²+9

f(x)=7x⁸−9x⁶−12x+46

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Answer:

2640 miles/day

Step-by-step explanation:

There are 24 hours in a day, so 110*24 = 2640.

Answer:

A. To convert pounds to kilograms, we need to multiply by 0.453592. Therefore, the fish from region A weighs about 130 kg (286 x 0.453592), rounded to the nearest whole number.

B. Similarly, the fish from region B weighs about 279 kg (614 x 0.453592), rounded to the nearest whole number.

Evaluate- (x - 1) (3x² + x - 6)

______________

x + 1

Expand- 3x³- 2x² - 7x + 6

_____________

x + 1

Factor- (x -1) (x - ✔73 -1 ) (x - ✔73 - 1)

_____ ______

6 6

_________________________

x + 1

Answer:

y = 5x - 28

Step-by-step explanation:

y - y1 = m(x - x1)

y - 7 = 5(x - 7)

y - 7 = 5x - 35

add 7 to both sides to get rid of - 7 --> y = 5x -35 + 7

The ladder will reach a Height of approximately 43.46 meters on the building.

To find out how high on the building the ladder will reach, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the ladder forms a right triangle with the ground and the building. The base of the ladder is 7 meters, the height of the building is what we need to find, and the length of the ladder is given as 44 meters.

Using the Pythagorean theorem, we can set up the equation:

(Height of the building)^2 + 7^2 = 44^2

Simplifying the equation, we have:

(Height of the building)^2 + 49 = 1936

Subtracting 49 from both sides, we get:

(Height of the building)^2 = 1887

To find the height of the building, we take the square root of both sides:

Height of the building = √1887

Calculating the square root of 1887, we find that the height of the building is approximately 43.46 meters.

Therefore, the ladder will reach a height of approximately 43.46 meters on the building.

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The y-intercept of the linear model is 211,400, which represents the estimated number of automobiles in the town in the year 2015 (when the independent variable is zero).

To find the y-intercept of the linear model, we need to determine the value of the dependent variable (the number of automobiles) when the independent variable (the number of years since 2015) is equal to zero.

Let's first find the slope of the line, which represents the rate of change of the number of automobiles per year:

slope = (change in number of automobiles) / (change in number of years)

slope = (2420 - 1890) / (2020 - 2015) = 106 automobiles per year

Now we can use the point-slope form of a linear equation to find the y-intercept:

y - y1 = m(x - x1)

where y1 is the value of the dependent variable when the independent variable is x1. In this case, x1 = 2015, y1 = 1890, and m = 106 (the slope we just calculated).

y - 1890 = 106(x - 2015)

To find the y-intercept, we can set x = 0:

y - 1890 = 106(0 - 2015)

y - 1890 = -213,290

y = 211,400

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