Find the geometric mean of 5 and 320.

A. 35
B. 40
C. 45
D. 50

the area of the triangle shown is  14 square inches

It is important to note that the formula that is used for calculating the area of a triangle is expressed with the equation;

A = 1/2bh

Such that the given parameters of the equation are;

From the information given, we have that;

b = 3 + h = 3 + 4 = 7 inches

h = 4 inches

Now, substitute the values, we get;

Area = 1/2 (7)(4)

multiply the value and expand the bracket

Area = 1/2(28)

divide the values

Area = 14 square inches

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Answer: c=60

Step-by-step explanation: Based on the given conditions, formulate::

15/c= 6/24

By setting up and solving a proportion that represents the ratio of blue counters to total counters in two different scenarios, we find that an estimate for the total number of counters in the bag is 60.

We can set up a proportion to solve this problem. In this case, the counters represent the total numbers in different situations. Initially, there are 15 blue counters out of an unknown total 'x'. Meanwhile, Hussain picked 6 blue counters out of 24. As these are similar situations (picking blue counters out of a total), we can express this as a proportion as follows: 15/x = 6/24 .

To solve this proportion, simply cross multiply and solve for x: 15*24 = 6*x. Simplify this to 360 = 6x. Diving both sides by 6 gives the value of x as 60.

So an estimate for the total number of counters in the bag, or 'x', is 60.

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Answer:

The center is (9, -4), and the radius is

√36 = 6.

The locations of the angles in the right triangle, and the number pairs indicates that we get;

A right triangle is a triangle that has one 90° interior angle.

1. The three similar triangles are; ΔMKJ, ΔMLK, and ΔKLJ

2. The three similar triangles are; ΔXZW, ΔXYZ, ΔZYW

3. The area of the triangle is; (1/2) × 8 × 6 = 24, which indicates;

(1/2) × 10 × x = 24

x = 24/((1/2) × 10) = 4.8

x = 4.8

4. The area of the triangle is; (1/2) × 21 × 20 = 210, which indicates;

(1/2) × 29 × x = 210

x = 210/((1/2) × 29) = 420/29 = 14 14/29

x = 14 14/29

5. The area of the triangle is; (1/2) × 20 × 48 = 480, which indicates;

(1/2) × 52 × x = 480

x = 480/((1/2) × 52) = 240/13 = 18 6/13

x = 18 6/13

6. The area of the triangle is; (1/2) × 13.2 × 22.4 = 147.84, which indicates;

(1/2) × 26 × x = 147.84

x = 147.84/((1/2) × 26) = 3696/325 = 11 121/325

x = 11 121/325

The geometric mean of a pair of numbers can be obtained as follows;

7. The geometric mean is; √(16 × 27) = √(432)

√(432) = 12·√3

8. The geometric mean is; √(5 × 36) = √(180)

√(180) = 6·√5

9. The geometric mean of the number is; √(24 × 32) = √(768)

√(768) = 16·√3

10. The geometric mean of the numbers is; √(8 × 48) = √(384)

√(384) = 8·√6

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Answer:

Step-by-step explanation:

17.5

Answer: 280

Step-by-step explanation:

The products of each pair of numbers are:

1 x 33 = 33

4 x 30 = 120

8 x 26 = 208

14 x 20 = 280

b. To find the pair of numbers that will produce the largest possible product, we need to look for the pair with the closest product to 340 (the square of 17, which is the average of the two numbers).

The pair of numbers with the closest product to 340 is 14 and 20, whose product is 280. Therefore, the pair of numbers that will produce the largest possible product is 14 and 20, and the product is 280.

The height of the pole is approximately 10.2 yards tall.

Let's use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse (the longest side).

In this case, the pole is the vertical side of the right triangle, the ground is the horizontal side, and the rope is the hypotenuse. Let's call the height of the pole "h". Then we have:

h² + 11² = 15²

Simplifying:

h² + 121 = 225

Subtracting 121 from both sides:

h² = 104

Taking the square root of both sides:

h = √104

Simplifying:

h ≈ 10.2

Therefore, the pole is approximately 10.2 yards tall.

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Answer:

Step-by-step explanation:

Perimeter: 34 yd

Area: 37 yd²

Answer:

x = 4[tex]\sqrt{3}[/tex]

Step-by-step explanation:

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , then

x² + 4² = 8²

x² + 16 = 64 ( subtract 16 from both sides )

x² = 48 ( take square root of both sides )

x = [tex]\sqrt{48}[/tex] = [tex]\sqrt{16(3)}[/tex] = [tex]\sqrt{16}[/tex] × [tex]\sqrt{3}[/tex] = 4[tex]\sqrt{3}[/tex]

Answer: 96

Step-by-step explanation: There are 16 cups in each gallon. To get how many there are in 6 gallons you would need to multiply 6 and 16.

6*16=96

or

16+16+16+16+16+16= 96

The vector v+w has a magnitude of 2√2 and its direction is along the positive x-axis.

What is meant by vector?

A vector is a quantity that has both magnitude and direction. It is represented as an arrow with its length representing the magnitude and its direction representing the direction of the quantity.

What is meant by the x-axis?

The x-axis is the horizontal line on a coordinate plane that is used as a reference for plotting and describing the positions of points in two-dimensional space. It is often referred to as the "horizontal axis" or the "abscissa".

According to the given information

Here the vector v has a magnitude of 2 and a direction of 45° so the components of vector v are:

v_x = 2 cos 45° = √2

v_y = 2 sin 45° = √2

Vector w has a magnitude of 2 and a direction of 45° South of East. This means that the angle between vector w and the positive x-axis is 45°, and the angle between vector w and the negative y-axis is 45°. Therefore, the components of vector w are:

w_x = 2 cos 45° = √2

w_y = -2 sin 45° = -√2

Now we can add the components of vectors v and w to find the components of the vector v+w:

(v+w)_x = v_x + w_x = √2 + √2 = 2√2

(v+w)_y = v_y + w_y = √2 - √2 = 0

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Step-by-step explanation:

when we are supposed to find each degrees of a certain angle on an equilateral triangle all we have to know is that a triangle is equal to 180° there for each angle or each line is equal to 180° / 3

The right circular cylindrical tank which is 5 m long and 13 m in diameter holds about 663,325 liters of liquid approximately.

The formula to find the volume of a right cylindrical tank is

V = πr²h, where 'r' is the radius and 'h' is the height.

Given that, the height is 5 m and the diameter is 13 m.

Radius = Diameter/2.

Radius = 13/2 = 6.5 m.

We know that, π = 3.14.

Now, we can substitute the values in the formula.

V = 3.14×(6.5)²×5.

V = 3.14×6.5×6.5×5

V = 663.325 cubic meters.

Now, we have to convert cubic meters into liters.

We need to multiply by 1000 as a thousand liters are in one cubic meter.

663.325×1000 = 663,325.

Therefore, the tank holds about 663,325 liters of liquid approximately.

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Answer:

We can use the formula for compound interest to calculate the amount of interest Brian will earn:

A = P (1 + r/n)^(nt)

where:

A = the total amount after 7 years

P = the principal amount ($9,411)

r = the annual interest rate (3.48%)

n = the number of times the interest is compounded per year (52 weeks in a year, so n = 52)

t = the number of years (7)

Plugging in the values, we get:

A = $9,411 (1 + 0.0348/52)^(52*7)

A = $9,411 (1.0006692302021135)^364

A = $12,471.36

To find the amount of interest earned, we can subtract the principal amount from the total amount:

Interest = $12,471.36 - $9,411 = $3,060.36

Therefore, Brian will earn $3,060.36 in interest after 7 years. Rounded to the nearest cent, this is $3,060.37.

Answer:

If a sample of 99 students is taken from a population of 352 students, the population variance, σ2, is the variance of the entire population, which includes all 352 students. Therefore, the answer is (B) 352.

It's worth noting that the sample of 99 students could be used to estimate the population variance if certain assumptions are met and appropriate statistical methods are used. However, the question specifically asks for the population variance, which refers to the variance of the entire population, not just the sample.

Answer:

If a sample of 99 students is taken from a population of 352 students, the population variance, σ2, is the variance of the heights of all 352 students in the population.

Therefore, the answer is B. 352.

Answer:

The salary of a paramedic can vary depending on several factors such as location, experience, and employer. According to the Bureau of Labor Statistics, the median annual wage for paramedics and EMTs was $36,650 in May 2020.

Assuming a constant annual income of $36,650 over 30 years, the estimated total income for a paramedic would be:

$36,650 x 30 = $1,099,500

However, it is important to note that this is just an estimate and does not take into account potential salary increases, promotions, or changes in the job market.

the cost of day old donuts after the discount is $4.95.

         A discount is a decrease in the cost of a good or service. Discount is the reduction in the price of goods or services offered by shopkeepers at the marked price.

       Discounts are offers or rebates made to customers on the marked-down prices of goods. We come across phrases like cost price, tagged price, discount, and selling price when making a purchase. Shop owners give discounts to customers to encourage product sales. Let's examine the connections between these concepts.

       The formula to calculate the discount is:

Discount = List Price - Selling Price

Discount (%) = (Discount/List Price) × 100

the discount is 40% ⇒0.4

customer buys 3 donuts.

price of 1 donut = $2.75

total cost for 3 donuts= $2.75 x 3 = $8.25

discount for 1 donut= [tex]\frac{0.4}{100}* 2.75[/tex]=$1.1

so, for 3 donuts discount = $1.1 x 3 = $3.3

therefore the final price to be paid by customer is

                    =$8.25-$3.3

                    =$4.95

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Answer:

2.75

Step-by-step explanation:

When you put that equation into a calculator, you get 2.75.

Answer:

Step-by-step explanation:

To solve for x in the equation 11=4x, we need to isolate x on one side of the equation.

We can start by dividing both sides of the equation by 4:

11/4 = (4x)/4

Simplifying the right side of the equation, we get:

11/4 = x

Therefore, x = 11/4 or 2.75.

The number 2 is the one for which the theoretical probability matches the experimental probability.

To determine which number has a theoretical probability that matches the experimental probability, we need to calculate both the theoretical and experimental probabilities for each of the four numbers.

The theoretical probability of spinning any one of the four numbers is 1/4, or 0.25. This is because there are four equally likely outcomes, and each outcome has a probability of 1/4.

To calculate the experimental probability, we need to count the number of times each number was spun and divide by the total number of spins. Here are the results:

- Number 1 was spun 9 times out of 28 spins, so its experimental probability is 9/28, or approximately 0.321.

- Number 2 was spun 7 times out of 28 spins, so its experimental probability is 7/28, or approximately 0.250.

- Number 3 was spun 6 times out of 28 spins, so its experimental probability is 6/28, or approximately 0.214.

- Number 4 was spun 6 times out of 28 spins, so its experimental probability is 6/28, or approximately 0.214.

To find the number that has a theoretical probability that matches the experimental probability, we can compare the theoretical probability to each of the experimental probabilities. The number that has an experimental probability that is closest to the theoretical probability of 0.25 is number 2, which has an experimental probability of approximately 0.250.

Therefore, the number 2 is the one for which the theoretical probability matches the experimental probability.

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Answer:

sorry I just wanted points

Answer: 2

Step-by-step explanation:

We can simplify the given logarithmic expression using the logarithmic property that states:

log a base b - log c base b = log (a/c) base b

Using this property, we can rewrite the expression as follows:

log 16 base 2 - log 4 base 2 = log (16/4) base 2

Simplifying the numerator of the logarithm, we get:

log (16/4) base 2 = log 4 base 2

Now, we can evaluate the logarithm using the definition of logarithm, which states that:

log b base a = x if and only if a = b^x

In this case, we have:

log 4 base 2 = x if and only if 2^x = 4

We know that 2 raised to what power gives 4? It is 2, because 2^2 = 4.

Therefore, we have:

log 4 base 2 = 2

Hence, the value of the given logarithmic expression is 2.

The C-intercept of the equation means that she will have to pay $15 per day for renting the car.

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

C=0.32m+15

In the equation C=0.32m+15, the C-intercept represents the fixed cost of renting a car per day, which is $15 in this case.

This means that regardless of how many miles Janelle drives, she will have to pay $15 per day for renting the car.

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The vector (3, 8, 1) provides the system's solution.

As a result, the system's vector solution is (3, 8, 1).

A sort of data structure used in computer programming is the vector. It is a collection of data objects that can be any type, such as strings, numbers, or even other vectors. The storage and manipulation of collections of data elements, such as a list of numbers, words, or other data elements, is done using vector data structures. Sorting, searching, and data manipulation can all be done with vector data structures.

The matrix equation Axequalsb's augmented matrix for the linear system is as follows:

[tex]\left[\begin{array}{ccc}1&-2&4\\7&-4&3\\-6&2&5\\-3&16&-29\end{array}\right][/tex]

Part - 2:

Step 1: Write the system's solution as a vector after solving it.

We must first reduce the augmented matrix to its reduced row-echelon form in order to solve this system.

[tex]\left[\begin{array}{ccc}1&0&0\\0&1&0\\-5&2&0\\-3&8&1\end{array}\right][/tex]

Step 2: We can now quickly find solutions for the unknowns.

[tex]x_1[/tex] equals

3

[tex]x_2[/tex] equals

8

[tex]x_3[/tex] equals

1

Step 3:

The vector (3, 8, 1) provides the system's solution.

As a result, the system's vector solution is (3, 8, 1).

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the perimeter of the polygon is: [tex]5 + 5 + 6 = 16[/tex]  So, the perimeter of the polygon with vertices at   [tex](1, 2), (4, 6),[/tex] and  [tex](7, 2)[/tex] is [tex]16[/tex]  units.

To find the perimeter of the polygon with vertices at   [tex](1, 2), (4, 6),[/tex] and  [tex](7, 2),[/tex] we need to find the length of each side of the polygon and add them up.

Using the distance formula, we can find the length of each side:

The length of the side connecting (1, 2) and (4, 6) is:

[tex]\sqrt((4-1)^2 + (6-2)^2) = \sqrt(3^2 + 4^2) = 5[/tex]

The length of the side connecting [tex](4, 6) and (7, 2) is:\sqrt((7-4)^2 + (2-6)^2) = \sqrt(3^2 + (-4)^2) = 5[/tex]

The length of the side connecting [tex](7, 2) and (1, 2) \ is:\ \sqrt((1-7)^2 + (2-2)^2) = \sqrt((-6)^2 + 0^2) = 6[/tex]

Therefore, the perimeter of the polygon is:  [tex]5 + 5 + 6 = 16[/tex] So, the perimeter of the polygon with vertices at [tex](1, 2), (4, 6),[/tex] and [tex](7, 2) \ is \ 16[/tex] units.

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According to the information, the probability of missing the first penalty but scoring the second penalty is 3/16.

The probability of missing the first penalty is 1/4, and the probability of scoring the second penalty given that she missed the first one is 3/4. Therefore, the probability of missing the first penalty but scoring the second penalty is:

(1/4) * (3/4) = 3/16

So the probability is 3/16, or 0.1875 as a decimal, or 18.75% as a percentage, in its simplest form.

According to the above, the three diagrams would be like this:

      ------- Score (3/4)

     |

------|

     |------- Score (3/4)

     |

     ------- Miss (1/4)

             |

             ------- Score (3/4)

             |

             ------- Miss (1/4)

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Answer:

  (a)  52°

  (b)  128°

Step-by-step explanation:

You want the angle whose sine is 0.79 (a) in the interval [0, 90°], and (b) in the interval [90°, 180°].

The inverse sine function is used to find the angle when its sine is known.

  sin(x) = 0.79

  x = arcsin(0.79) ≈ 52°

x ≈ 52° in the domain 0 ≤ x ≤ 90°.

The sine function is symmetrical about x = 90°, so other angles for which sin(x) = 0.79 can be found as 180° -x.

  180° -52° = 128°

x = 128° in the domain 90° ≤ x ≤ 180°.

__

Additional comment

The attachment shows the angles and that their sine is 0.79. Note that the calculator is set to Degrees mode.

<95141404393>

x = 5.5

we can solve this by using tanø formula i.e p/b

Answer: 105m

Step-by-step explanation:

Hope this helps! :)

There are 25  persons who actually voted, the 95% confidence interval for the population of registered voters who voted in the most recent school board election is 0.2±0.07 that is (0.13, 0.27).

In statistics, a confidence interval, means  the probability which a population parameter will fall between a set of values for a certain proportion of times. Confidence intervals measure the degree of uncertainty or certainty in a sampling method. There are various types of confidence interval such as 90%, 95%, 99% etc.

A certain randomly selected sample of 125 registered voters showed that 20% of them voted in the most recent school board election.

So in 125persons the persons who actually voted are

                (125×20)/100

              = 2500/100

              = 25

For 95% confidence interval the z value is 1.96.

If we take p as probability of success that is the persons who actually voted then 1-p denotes the probability of failure.

p= 25/125= 1/5 = 0.2          n= 125

1-p= 1-(1/5)

    = 1-0.2= 0.8

The formula for confidence interval is

p± z√{p(1-p)/n}

0.2 ±1.96√{(0.2×0.8)/125}

= 0.2 ± 1.96√(0.16/125)

= 0.2± 1.96 ×0.035777

= 0.2±0.07012

Hence , the 95% confidence interval for the population of registered voters who voted in the most recent school board election is 0.2±0.07

that is (0.13, 0.27).

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