Which equation can be used to solve for b?

Triangle A B C is shown. Angle B C A is a right angle and angle C A B is 30 degrees. The length of side B C is 5 centimeters, the length of B A is 10 centimeters, and the length of C A is b.

tan(30o) = StartFraction 5 Over b EndFraction
tan(30o) = StartFraction b Over 5 EndFraction
tan(30o) = StartFraction 10 Over b EndFraction
tan(30o) =
Mark this and return

Answer:

2 hours

Step-by-step explanation:

1 hour from before she does her soccer practice and another 1 hour after her soccer practice so it's going to be

1+1=2

Answer: she works on her homework in total for 2 hours.

Step-by-step explanation: 1+1=2, 60 minutes are in 1 hour, 60+60=120 minutes= 2 hours

The value of N is 90 and the value of F is 80 degrees

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

Similar Polygons

This means that

Angle N = Angle J

So, we have

Angle N = 90 degrees

Here, we have

F = K

So, we have

Angle F = 80 degrees

To do this, we use the following ratio

x : 12 = 9 : 18

So, we have

x/12 = 9/18

Evaluate

x = 6

To do this, we use the following ratio

y : 18 = 10 : 12

So, we have

y/18 = 10/12

Evaluate

y = 15

Here, we have

Given ratio = 6 : 7

This means that

The ratio of the perimeter is 6 : 7

Here, we have

Ratio = 5 : 2

So, we have

JKL : 35 = 5 : 2

This gives

JKL : 35 = 35 : 14

Hence, the perimeter is 35 units

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The booster club's lowest ticket price at which it can generate $3,600 in income is $20.

Its core idea is thought to be the figure is probably smallest equivalent fraction. Where to calculate the simplest form. Look for matching parameters in the denominator but also numerator. A uneven number can be checked to discover if it is a mathematical concept. A statement having two collinear and an equal sign in the middle is referred to as a mathematical model. Every variable's degrees are listed in lowest to highest in the general form of any equation. The model for a linear equation is x + b = 0. The general form of a two-variable linear equation is an x + b y + c = 0. (or something similar). Either conditional calculations or identities are categories for equations. An identity holds true for any real worth of the variables.

given

ticket price = p

total to make $3,600

the equation = 3600 = p(–4p+260) is the correct expression

lowest ticket price = 3600 = p(–4p+260)

= 3600 = -4p2 + 260p

= 4p2-260p + 3600

= 2p2 -130p + 1800

p2 - 65p + 900

(p-20 )(p-45)

p = 20

The booster club's lowest ticket price at which it can generate $3,600 in income is $20.

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The amount of money that will be used to drive only one mile by the different vehicles given above such as Deswagon and DesMobile would be =$57.35 and $56.78 respectively.

The total mileage that can be covered by Deswagon = 490miles.

The total cost of gas for the Deswagon = $28,100

Therefore the amount that will be paid for only one mile = X.

That is , 490 miles = $28,100

1 mile = ×

make X the subject of formula;

X = 28,100/490

= $57.35.

The total mileage that can be covered by DesMobile = 575miles.

The total cost of gas for the DesMobile = $32,650.

Therefore the amount that will be paid for only one mile = X.

That, 575 miles = $32,650

1 mile = X

Make X the subject of formula;

X = 32,650/575

X = $56.78.

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The weight of 1 gallon water is 10 pounds and the weight of 1 litre of water is 1 kilogram.

Also, one kilogram is approximately equal to 2.2046226218 lbs.

One US gallon is equal to 3.785411784 liter.

A gallon is a unit of volume in imperial units and US standard units. Three different versions are currently in use:

imperial gallon (imp gallon), defined as

.5

609 liters, is or was used in Great Britain, Ireland, Canada, Australia, New Zealand and some Caribbean countries;

US gallons (US gallon), defined as 3.785

1178

L,[1] (231 cubic meters), used in the United States and some Latin American and Caribbean countries; and

US dry gallons ("usdrygal"), defined as 1⁄8 US Bushel (exactly

.

0

88377086 L).

There are two pints in a liter and four liters in a gallon. Different sized pints correspond to different sized imperial and US gallons.

The IEEE standard symbol for both US (liquid) and imperial gallons is gal [2], different from gal (symbol: Gal), the CGS unit of acceleration.

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CJ's rectangular prism will require more material to construct since it has a larger surface area than Torey's prism.

To compare the amount of material required to construct the two rectangular prisms, we need to calculate the surface area of each prism. The surface area of a rectangular prism is given by the formula:

Surface area = 2lw + 2lh + 2wh

where l, w, and h are the length, width, and height of the rectangular prism.

For CJ's prism, we have:

l = 7 cm, w = 4 cm, h = 12 cm

So the surface area of CJ's prism is:

Surface area of CJ's prism = 2(7 cm x 4 cm) + 2(7 cm x 12 cm) + 2(4 cm x 12 cm)

= 56 cm² + 168 cm² + 96 cm²

= 320 cm²

For Torey's prism, we have:

l = 10 cm, w = 6 cm, h = 3 cm

So the surface area of Torey's prism is = 2(10 cm x 6 cm) + 2(10 cm x 3 cm) + 2(6 cm x 3 cm)

= 120 cm² + 60 cm² + 36 cm²

= 216 cm²

Therefore, CJ's rectangular prism will require more material to construct since it has a larger surface area than Torey's prism.

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The number of rational zeroes in f(x) = 4x⁴ - x³ + 3x² - 4x - 6 is 12.

The rational root theorem explains how a polynomial's roots and coefficients are related. It explains the kind of rational roots that the polynomial might have in particular.

According to the rational root theorem, the possible roots of a polynomial of degree three and above are,

± (coefficient of the last term)/(coefficient of the first terms).

Given, A polynomial function f(x) = 4x⁴ - x³ + 3x² - 4x - 6.

Now, The rational roots are ± (a₄)/(a₀).

= (± 1, ± 2, ± 3, ± 6)/(± 1, ± 2, ± 4).

Therefore, The possible number of rational zeroes is 4×3 = 12.

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The proof for the given statements is as follows:

Statements:

1. overline AB || overline PQ

2. overline AP || overline BQ

3. overline BP || overline CQ

Reasons:

1. Since AB || PO, then AB || PQ

2. Since AP || BQ and AB || PQ, then AP || BQ

3. Since BP || CQ and AB || PQ, then BP || CQ

Therefore, by the properties of parallel lines, we can conclude that angle ABP congruent to angle BCQ and angle BAP congruent to angle CBO. Since angles ABP and BCQ are congruent, and angles BAP and CBO are congruent, this implies that angle ABP is congruent to angle QPB, and angle CBQ is congruent to angle PQB.

By the definition of similar triangles, two triangles are said to be similar if their corresponding angles are congruent. Therefore, triangle ABP is similar to triangle QPB, which is similar to triangle BCQ, proving the statement.

The probability of getting at least one head in two flips of a coin is 3/4 or 0.75, which means that there is a 75% chance of getting at least one head in two flips of a coin.

To find the probability of at least one head in two flips of a coin, we can use the complement rule. The complement of the event "at least one head" is "no heads."

The probability of getting no heads in two flips of a coin is (1/2) x (1/2) = 1/4.

Therefore, the probability of getting at least one head in two flips of a coin is:

1 - (probability of no heads) = 1 - 1/4 = 3/4

The probability of getting at least one head in two flips of a coin is 3/4 or 0.75, which means that there is a 75% chance of getting at least one head in two flips of a coin.

In other words, if you flip a coin twice, the probability of getting at least one head is relatively high, and you are more likely to get at least one head than to get no heads at all.

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(a) The fraction of his money spend on a book is 12/40 = 3/10

Money spent on books

3/5 = x/2

3/5 = 40/2

Hence, at a fraction of money is 12/40 = 3/10

(b) Roy has money at first is $40

Roy spent money on game boys = 1/2

He spent money on books = 3/5

Let Roy has money = x

Money on game boys

= 1/2 of x = x/2

Money spent on books

= 3/5 = x/2

= 3x/10

= x/2 - 3x/10

= 5x/10 - 3x/10

= 2x/10

But the remaining money = $8

= x/5 = 8

= x = 40

Therefore, Roy has money at first = $ 40

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"Poke the bear" in cybersecurity refers to intentionally triggering a potential threat in order to test an organization's security systems and identify vulnerabilities.

In cybersecurity, "Poke the bear" means intentionally attempting to trigger a potential cyber threat in order to test an organization's security systems and identify vulnerabilities. This may involve actions such as sending a phishing email to see if employees fall for it, or attempting to breach a system in order to determine how strong its defenses are.

By proactively identifying weaknesses in their security systems, organizations can take steps to improve their cybersecurity posture and reduce the risk of a successful attack. However, "Poking the bear" should be done carefully and ethically, with appropriate permissions and safeguards in place.

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Reena's original speed as compared to her new speed concludes that Reena arrived at her destination in her planned amount of time which is 20 hours.

What is speed?

The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.

Reena's original plan was to drive for 20 hours at an average speed of 50 mph, which means that she would have covered a distance of -

Distance = Speed x Time

Distance = 50 mph x 20 hours

Distance = 1000 miles

Now calculate the distance that Reena actually traveled.

She drove at an average speed of 60 mph for the first 5 hours, covering a distance of -

Distance1 = Speed1 x Time1

Distance1 = 60 mph x 5 hours

Distance1 = 300 miles

For the remaining 15 hours of the journey, she drove at an average speed of 50 mph, covering a distance of -

Distance2 = Speed2 x Time2

Distance2 = 50 mph x 15 hours

Distance2 = 750 miles

The total distance that Reena traveled is the sum of the two distances -

Total Distance = Distance1 + Distance2

Total Distance = 300 miles + 750 miles

Total Distance = 1050 miles

Reena actually traveled 1050 miles to reach Chicago, which is 50 miles more than her planned distance of 1000 miles.

To calculate how much earlier Reena arrived in Chicago than she originally planned, we need to compare the time it took her to travel the two distances -

Time1 = Distance1 / Speed1

Time1 = 300 miles / 60 mph

Time1 = 5 hours

Time2 = Distance2 / Speed2

Time2 = 750 miles / 50 mph

Time2 = 15 hours

Total Time = Time1 + Time2

Total Time = 5 hours + 15 hours

Total Time = 20 hours

Reena arrived in Chicago in 20 hours, which was exactly the same as her original plan.

Therefore, she did not arrive earlier than planned.

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In case of measurement, 300 mm is equivalent to 11.811 inches.

Measurement is a critical aspect of our daily lives as it helps us quantify things and understand the world around us.

When it comes to converting units of measurement, it is essential to understand the basic conversions. One such conversion is between millimeters (mm) and inches (in).

To convert millimeters to inches, we need to know the conversion factor, which is 1 mm = 0.0393701 in. This means that if we have a measurement of 300 mm and we want to know its equivalent in inches, we simply multiply 300 by the conversion factor:

300 mm x 0.0393701 in/mm = 11.811 inches (rounded to the nearest thousandth)

It is essential to remember that understanding conversions between units of measurement is crucial in many fields such as engineering, science, and medicine. Being able to convert units accurately can prevent errors and ensure precise calculations.

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The object has a mass of 5.76 kg.

We may represent "m" in terms of "e" (energy) and "v" (speed) using the kinetic energy formula, assuming that "m" relates to the mass of the object:

The energy an object possesses as a result of its motion is known as kinetic energy. It is described as the energy that a moving object contains as a result of its motion, which is dependent on the mass and velocity of the object.

The formula for calculating an object's kinetic energy is KE = 1/2 * m * v2.

To solve for "m," we can rearrange this formula:

m = 2 x KE /

We obtain the following by substituting the given values:

m = 2 x 1800 / 25

m = 2 x 1800 J / 625

m= 5.76 (rounded to two decimal places)

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Answer:

Step-by-step explanation:

To solve for x in the equation:

x - 2/5 = 1/5

We can start by isolating x on one side of the equation. We can do this by adding 2/5 to both sides:

x - 2/5 + 2/5 = 1/5 + 2/5

Simplifying, we get:

x = 3/5

Therefore, the solution is:

x = 3/5

To convert ml to kg we have to find the density of the liquid or the body first.

The density of the body is defined as the mass of the body per unit volume of the body.

The density of the body is the only link between  mass and the volume of the body. As we know that volume and mass have different unit I.e. mass have Kg and volume have ml.

So, what we do is,

Density = Mass/volume

Now, we can inter convert them to our requirement.

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Answer:

This is an obtuse triangle.

Step-by-step explanation:

Sure that are 2 acute angle but it is not acute, if it was acute, then it would have 3 acute angles. It might look like a right triangle, but the angle on the bottom left is actually past 90º. So it is an obtuse triangle. Hope this helped! Have a good day!

The greatest common factor (GCF) of 42, 126, and 210 is 42.

To find the GCF, you can use several methods such as prime factorization or the Euclidean algorithm. One way to find the GCF using prime factorization is to express each number as a product of its prime factors:

42 = 2 × 3 × 7

126 = 2 × 3² × 7

210 = 2 × 3 × 5 × 7

Then, identify the common prime factors and their smallest exponent across all three numbers. In this case, the common prime factors are 2, 3, and 7. The smallest exponent of 2 is 1, the smallest exponent of 3 is 1, and the smallest exponent of 7 is 1. Therefore, the GCF is

= 2 × 3 × 7

= 42

Another method to find the GCF is the Euclidean algorithm, which involves finding the remainder of dividing the larger number by the smaller number repeatedly until the remainder is zero. The GCF is the last nonzero remainder. However, in this case, the prime factorization method is simpler and quicker.

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The image point of (-7, 5) after the translation is (-2, 9).

What is the translation in the coordinate system?

A translation in the Cartesian plane can be described by a rule that indicates how to move each point of a figure to its image under the translation. The rule is usually given as a pair of numbers (a, b), where a is the horizontal distance to move each point (positive to the right, negative to the left), and b is the vertical distance to move each point

To find the image point of the point (-7, 5) after a translation right 5 units and up 4 units, we need to add 5 to the x-coordinate and add 4 to the y-coordinate.

The new x-coordinate will be -7 + 5 = -2, since we're moving the point to the right 5 units.

The new y-coordinate will be 5 + 4 = 9, since we're moving the point up 4 units.

Hence, the image point of (-7, 5) after the translation is (-2, 9).

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Both the 100kg of water and 100kg of paint weigh the same, since they both have a mass of 100kg.

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

A  cup of water is lighter than a cup of paint

The initial comparison of a cup of water being lighter than a cup of paint cannot be used regarding the weight or mass of 100kg of either substance.

In this case, since both 100kg of water and 100kg of paint have the same mass,

They would also have the same weight if they were located in the same place with the same gravitational force acting upon them.

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Answer:

12.598

Step-by-step explanation:

divide the length value by 2.54

The derivative of cubed root X is:

  [tex]\frac{1}{3\sqrt[3]{X^{2} } }[/tex]

To find the derivative of cubed root X, we can use the power rule. The power rule states that the derivative of Xⁿ is nX⁽ⁿ⁻¹⁾. In this case, the cubed root of X can be written as X^(1/3).

Using the power rule, we can find the derivative:

[tex]\frac{d}{dx} (X^{1/3} )= \frac{1}{3} (X^{(1/3) - 1})[/tex]

Simplifying the exponent gives us:

[tex]\frac{d}{dx} (X^{(1/3)}) = \frac{1}{3}X^{-2/3}[/tex]

Finally, we can rewrite the expression to get rid of the negative exponent:


[tex]\frac{d}dx}(X^{(1/3)}) = \frac{1}{3\sqrt[3]{X^{2} } }[/tex]

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The inverse function of the given function which gives the value of the number of days when the population of bacteria is known is:

f ⁻¹(x) = log₁.₆(1.6x - 32)

What is an inverse function?

A function takes in values, applies specific operations to them, and produces an output. The inverse function acts, agrees with the outcome, and returns to the initial function. The output of a function is returned by the inverse function, which also returns the initial value. A function that can reverse into another function is known as an inverse function or anti function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y.

The given function is:

[tex]f(x) = 1.6^{x-1} + 20\\[/tex]

[tex]y = 1.6^{x-1} + 20\\[/tex]

Now we are asked to find the inverse of this function.

That is, we have to write x in terms of y.

And then substitute the y back with x, to write as an inverse function

f ⁻¹(x).

[tex]y = 1.6^{x-1} + 20\\[/tex]

y - 20 = [tex]1.6^{x-1}[/tex]

y-20 = 1.6ˣ / 1.6

1.6y - 1.6 * 20 = 1.6ˣ

1.6y - 32 = 1.6ˣ

x = log₁.₆(1.6y - 32)

Therefore the inverse function of the given function which gives the value of the number of days when the population of bacteria is known is:

f ⁻¹(x) = log₁.₆(1.6x - 32)

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Answer:

surface area = 578^2

Step-by-step explanation:

SA of cylinder = 2πr^2+2πrh

r = radius (8)

h = height (7)

= 2 x π x 6^2 + 2 x π x 8 x 7

= 578.053

a) The probability of finding oil is 0.70, or 70%.

b) The new probability of finding oil is the sum of the probabilities of finding high-quality oil and medium-quality oil, which is  1.00 or 100% .

(a) The probability of finding oil is the sum of the probabilities of finding high-quality oil and medium-quality oil, since both of these outcomes are considered positive for the oil company:

P(find oil) = P(high-quality oil) + P(medium-quality oil) = 0.50 + 0.20 = 0.70

Therefore, the probability of finding oil is 0.70, or 70%.

(b) To interpret the soil test, we can use Bayes' theorem:

P(Ai | S) = P(S | Ai) * P(Ai) / P(S)

where P(Ai | S) is the updated probability of finding oil given the soil test, P(S | Ai) is the probability of observing the soil test result given that there is oil of the corresponding quality, P(Ai) is the prior probability of finding oil of the corresponding quality, and P(S) is the probability of observing the soil test result regardless of the presence of oil.

Using the given probabilities, we can calculate:

P(S) = P(high-quality oil) * P(S | high-quality oil) + P(medium-quality oil) * P(S | medium-quality oil) + P(no oil) * P(S | no oil)

= 0.50 * 0.20 + 0.20 * 0.80 + 0.30 * 0.20

= 0.26

Now we can calculate the updated probabilities for each quality of oil:

P(high-quality oil | S) = P(S | high-quality oil) * P(high-quality oil) / P(S)

= 0.20 * 0.50 / 0.26

= 0.3846 or 0.38 (rounded to two decimal places)

P(medium-quality oil | S) = P(S | medium-quality oil) * P(medium-quality oil) / P(S)

= 0.80 * 0.20 / 0.26

= 0.6154 or 0.62 (rounded to two decimal places)

P(no oil | S) = P(S | no oil) * P(no oil) / P(S)

= 0.20 * 0.30 / 0.26

= 0.2308 or 0.23 (rounded to two decimal places)

The oil company should interpret the soil test as providing evidence for the presence of medium-quality oil, since the updated probability for this outcome is higher than the updated probability for high-quality oil. The revised probabilities for finding oil are:

P(find high-quality oil | S) = P(high-quality oil | S) = 0.38

P(find medium-quality oil | S) = P(medium-quality oil | S) = 0.62

P(find no oil | S) = P(no oil | S) = 0.23

Therefore, the new probability of finding oil is the sum of the probabilities of finding high-quality oil and medium-quality oil, which is:

P(find oil | S) = P(find high-quality oil | S) + P(find medium-quality oil | S)

= 0.38 + 0.62

= 1.00 or 100% (rounded to two decimal places)

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On solving the provided question, we can say that the perimeter can be calculated by add all lengths of the figure =  5.6 + 8+5.6+4.5+3.5 = 27.2units

A limit is a closed route that surrounds, delimits, or includes a two-dimensional form or a one-dimension length. The outermost part of a circle or an ellipse is called the perimeter. The perimeter calculation has several real-world applications. A shape's perimeter is the measurement of its edge's radius. Discover how to determine the circle by adding together the lengths of both the sides of irregular configurations. The perimeter of any form may be calculated by multiplying its side lengths. An object's perimeter is the region that surrounds it. A good illustration of this at your house is a closed-off garden. Its perimeter is the space around something. For a 50 by 50 foot yard, a 200 foot barrier will be required.

the perimeter can be calculated by add all lengths of the figure =

5.6 + 8+5.6+4.5+3.5 = 27.2units

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The population of Blueville in 2012 from the exponential function is;

⇒ 9000

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Here, We are given the equation of the function as;

⇒ f (x) = 9000(0.985)ⁿ

where;

x is the number of years since 2012

Thus, In the year 2012, it means that n will be 0,

Hence, As number of years is 0 by then we get;

f(0) = 9000(0.985)⁰

f(0) = 9000 * 1

f(0) = 9000

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The total area under the frequency polygon for a continuous random variable equals 1 is True.

A frequency polygon is very similar to a histogram, which is used to compare data sets or to depict a cumulative frequency distribution. A line graph is used to show quantitative data.

Statistics is concerned with the collecting of facts and information for a certain goal. The computation of each run for each ball in cricket provides game statistics. Tables, graphs, pie charts, bar graphs, histograms, polygons, and other graphical representations of statistical data are employed.

Frequency polygons are a visually appealing way of expressing quantitative data and frequency distributions. Let's look at how to draw a frequency polygon.

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Answer:

30^

Step-by-step explanation:

To write 0.3 as a percent, multiply 0.3 by 100. Append % symbol in the product obtained. So, 0.3 as a percent is 30 %. We can write in just two steps to calculate any decimal into a percent.