find the missing side of the triangle please

Answer:

Step-by-step explanation:

The integer is 45, since integers are only whole numbers and they're negative counterparts, so even if the fraction or decimal is negative, it is not an integer because it's not a whole number. Hope that helps!

Answer:

\(45/9\\45\\14/2\)

Step-by-step explanation:

An integer is a number that can be written without a fractional component.

\(-92.67=-278/3\)

\(-6/7=-6/7\)

\(45/9=5\)

\(45=45\)

\(14/2=7\)

A researcher generates a random sample of 50 college students from a nearby university using a random number generator. The researcher is utilizing a sample survey.

What is a sample survey?

A sample survey is a process that helps researchers to study a small part of a large population to generalize and make predictions about the entire population. It involves the selection of a smaller group of individuals from a larger population of interest, and the results obtained from this selected group are then used to draw inferences or generalizations about the population.

For instance, in this case, the researcher is only interested in 50 college students, but it would be impractical to study the entire student body at the university. Therefore, the researcher utilized a sample survey to select a random sample of 50 college students from a nearby university using a random number generator.

The sample survey method is generally considered more cost-effective and practical than other research methods such as a census, which involves studying an entire population.

Therefore, in conclusion, the researcher is utilizing a sample survey.

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The expression states that for every linear polynomial p with real coefficients and a nonzero coefficient of x, there is exactly one real root r.

For all linear polynomials with real coefficients and a nonzero coefficient of x, there exists exactly one real root. This can be expressed using the universal quantifier "for all" and the existential quantifier "there exists", connected by the logical connective "and". Additionally, the statement "exactly one real root" can be expressed using the quantifier "there exists" and the logical connective "and".

Using quantifiers and logical connectives, we can express the given fact as follows:

∀p ∃!r ((isLinearPolynomial(p) ∧ hasRealCoefficients(p) ∧ coefficientOfX(p) ≠ 0) → hasRealRoot(p, r))

Explanation:

- ∀p: For every polynomial p
- ∃!r: There exists exactly one real root r
- isLinearPolynomial(p): p is a linear polynomial (degree 1)
- hasRealCoefficients(p): p has real coefficients
- coefficientOfX(p) ≠ 0: The coefficient of x in p is nonzero
- hasRealRoot(p, r): p has a real root r

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$ 410

hi there !

80% ................. $328

100% .................$ x

x = 100×328/80

= 32800/80

= $ 410

Good luck !

Answer:

y = -1.0

Step-by-step explanation:

Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operations, and =

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

First, add 4y and subtract 14 from both sides:

1y (+4y) + 14 (-14) = -4y (+4y) + 9 (-14)

1y + 4y = 9 - 14

Combine like terms:

5y = -5

Isolate the variable, y. Divide 5 from both sides:

(5y)/5 = (-5)/5

y = -5/5

y = -1

y = -1 is your answer.

~

The expression to represent the amount of money Dion spent on fruit is 3x + 2y.

The amount of money Dion spent is $6.15

Expression are numbers, symbols and operators grouped together that show the value of something.

Dion bought 3 pounds of oranges and 2 pounds of grapefruit.

The expression to represents the amount of money Dion spent on fruit is as follows:

let

x = cost of each pounds of oranges

y = cost of each pounds of grapefruit

Therefore,

total cost = 3x + 2y

Let's evaluate the expression

total cost = 3(0.99) + 2(1.59)

total cost = 2.97 + 3.18

total cost = 6.15 dollars

Therefore, Dion spent $6.15

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Answer:

Step-by-step explanation:

\(\sqrt{(-3-4)^2+(-7-3)^2\)

\(\sqrt{(-7)^2+(-10)^2\)

\(\sqrt{49+100\)

\(\sqrt{149\)

a) The utility depends on both health (H) and consumption of other goods (X).

b) The coefficient is negative, indicating a negative relationship between two variables.

c) Health (H) is greater than zero, suggesting a positive value for health.

d) Health (H) is a function of a variable denoted as 'm'.

e) The variable 'm' is greater than zero and the coefficient is negative.

f) The product of two variables, 'm' and 'm', is negative.

a) The expression in (a) is reasonable as it acknowledges that utility is influenced by both health and consumption of other goods. It recognizes that happiness or satisfaction is derived not only from health but also from other aspects of life.

b) The expression in (b) suggests a negative coefficient and a negative relationship between the variables. This could imply that an increase in one variable leads to a decrease in the other. The reasonableness of this relationship would depend on the specific variables involved and the context of the theoretical framework.

c) The expression in (c) states that health (H) is greater than zero, which is reasonable as health is generally considered a positive attribute that contributes to well-being.

d) The expression in (d) indicates that health (H) is a function of a variable denoted as 'm'. The specific nature of the function or the relationship between 'm' and health is not provided, making it difficult to assess its reasonableness without further information.

e) The expression in (e) states that the variable 'm' is greater than zero and the coefficient is negative. This implies that an increase in 'm' leads to a decrease in some other variable. The reasonableness of this relationship depends on the specific variables involved and the theoretical context.

f) The expression in (f) suggests that the product of two variables, 'm' and 'm', is negative. This implies that either 'm' or 'm' (or both) are negative. The reasonableness of this expression would depend on the meaning and interpretation of the variables involved in the theoretical framework.

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The first differential equation has a third-order derivative of y and the second differential equation has a fifth-order derivative of y.

The order of a differential equation refers to the highest derivative present in the equation. In the first differential equation, y' represents the first derivative of y, while y'' represents the second derivative of y. However, there is no term explicitly representing the third derivative of y, so the order of this equation is 0.

The second differential equation involves multiple derivatives. The term "dy/dx" represents the first derivative of y, "cos y" represents the function of y, and "x^3" represents the third power of x. The equation also includes various differentiation operators, such as dx^5/dx^3. When simplified, we find that the highest derivative present is the fifth derivative of y, represented as "d^5y/dx^5". Therefore, the order of this differential equation is 5.

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The number of units x =  1500 units produce a maximum revenue r found using the given function.

To find the number of units x that produces a maximum revenue r, we need to differentiate the given revenue function with respect to x.

Then equate the derivative to zero to find the critical points which will be the maximum or minimum point for the function.

r = 180x² - 0.08x³

Let's differentiate the above revenue function with respect to x.

Using the Power Rule and the Chain Rule, we get:

dr/dx = d/dx [180x² - 0.08x³]

dr/dx = 360x - 0.24x²

To find the critical points, we need to solve the equation 360x - 0.24x² = 0

Factorizing x from the above equation, we get:x (360 - 0.24x) = 0x = 0 or 360 - 0.24x = 0

Solving for x, we get:x = 0 or x = 1500

We need to verify whether these critical points correspond to a maximum or minimum value of the function.To find out, we'll take the second derivative of the revenue function.

Using the Power Rule and the Chain Rule, we get:

d²r/dx² = d/dx [360x - 0.24x²]d²r/dx²

= 360 - 0.48x

The second derivative test states that if d²r/dx² > 0, the function has a minimum at that point; and if d²r/dx² < 0, the function has a maximum at that point.

At x = 0, d²r/dx² = 360 which is greater than 0, therefore, the function has a minimum value at x = 0.

At x = 1500, d²r/dx² = 360 - 0.48(1500)  = -360 which is less than 0, therefore, the function has a maximum value at x = 1500.

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Answer:

1) 5/8

\(\frac{5}{8} rad = 35.809\textdegree\)  or (atau)   \(\frac{5}{8} \pi rad = 112.5\textdegree\)

2) a. 75°  b. 132°

\(75\textdegree = 1.308\) \(rad\)   or (atau)    \(75\textdegree = 0.41\overline{6}\) \(\pi\) \(rad\)

\(132\textdegree = 2.303\) \(rad\)  or (atau)    \(132\textdegree = 0.7\overline{3}\) \(\pi\) \(rad\)

The obtained graph is having is passes though the point (0,3.74 )on y-axis and (123,0) on the x-axis. None of the option is correct.

A function is a statement, rule, or law that specifies the connection between two variables. Functions are common in mathematics and are required for the formulation of physical connections.

The given equation of the function is;

\(y = -(x+2)^{1/3}+5\)

Hence,the obtained graph is having is passes though the point (0,3.74 )on y-axis and (123,0) on the x-axis.

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Answer:

The function f(x) = sqrt(x - 2) + 3 represents a square root function that is shifted 2 units to the right and 3 units up from the parent function f(x) = sqrt(x).

The endpoint of the function occurs when the radicand (x - 2) is equal to zero, which means x = 2. So, the function has an endpoint at (2, 3).

Since the function involves a square root, the value of y cannot be negative. Therefore, the function is increasing to the right.

The correct graph that represents the function f(x) = sqrt(x - 2) + 3 is the one that shows a curve with an endpoint at (2, 3) that increases to the right.

Therefore, the answer is: The graph shows a curve with an endpoint at 2 comma 3 that increases to the right. A.

The average length of a Major League Baseball game increased by 30 minutes from 1970 to 2018. The relative change in game times is calculated to the nearest whole percent.

To calculate the absolute change in Major League Baseball game times from 1970 to 2018, we subtract the initial value (150 minutes) from the final value (180 minutes):

Absolute change = 180 minutes - 150 minutes = 30 minutes

Therefore, the absolute change in game times is 30 minutes.

To determine the relative change, we divide the absolute change by the initial value and multiply by 100:

Relative change = (30 minutes / 150 minutes) * 100

Relative change = 0.2 * 100 = 20%

Therefore, the relative change in Major League Baseball game times from 1970 to 2018 is 20%, rounded to the nearest whole percent.

In this problem, the main words to focus on are "average length," "Major League Baseball game," "1970," "2018," "absolute change," and "relative change." By subtracting the initial value from the final value, we calculate the absolute change, while the relative change is determined by dividing the absolute change by the initial value and multiplying by 100.

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An significance level of 0.05 to compare the p-value against for decision-making regarding the null hypothesis.

The proportion of gun owners went up between 2015 and 2020 a two-proportion z-test.

Null hypothesis (H₀): The proportion of gun owners is the same in 2015 and 2020.

Alternative hypothesis (H₁): The proportion of gun owners increased between 2015 and 2020.

For the two-proportion z-test, the test statistic is given by,

z = (p₁ - p₂) / √(p(1 - p) × (1/n₁ + 1/n₂))

where:

p₁ and p₂ are the sample proportions of gun owners in 2015 and 2020, respectively.

p is the pooled sample proportion, calculated as (x₁ + x₂) / (n₁ + n₂), where x₁ and x₂ are the number of gun owners in 2015 and 2020, and n₁ and n₂ are the corresponding sample sizes.

The test statistic (z-score), it to calculate the p-value. The p-value is the probability of obtaining a test statistic as extreme as the observed one, assuming the null hypothesis is true.

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The price per T-shirt should be at least $15 to achieve a profit of $250.

To calculate the price per T-shirt that will yield a profit of at least $250, we need to consider the cost of production, the desired profit, and the number of shirts to be sold.

Given that the cost to make each T-shirt is $10, and we want to sell 50 shirts, the total cost of production would be 10 * 50 = $500.

Now, let's calculate the minimum revenue needed to achieve a profit of $250. We add the desired profit to the total cost of production: $500 + $250 = $750.

Finally, to determine the price per T-shirt, we divide the total revenue by the number of shirts: $750 ÷ 50 = $15.

Therefore, to make a profit of at least $250, the price per T-shirt should be set at $15.

By selling each T-shirt for $15, the total revenue would be $15 * 50 = $750. From this revenue, we subtract the total production cost of $500 to calculate the profit, which amounts to $750 - $500 = $250. Thus, by charging $15 per T-shirt, the desired profit of $250 is achieved.

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Answer:

4^6 / 5^6

Step-by-step explanation:

We know that (a/b) ^c = a^c / b^c

(4/5) ^6 = 4^6 / 5^6

=======================================================

Explanation:

The rule is

\(\left(\frac{a}{b}\right)^c = \frac{a^c}{b^c}\)

Basically we raise each part of the fraction to the outer exponent. In this case, a = 4, b = 5 and c = 6.

---------------------------------

The outer exponent c = 6 tells us how many copies of (a/b) we are multiplying together. So we are multiplying 6 copies of (4/5) together like so

\(\left(\frac{4}{5}\right)^6 = \left(\frac{4}{5}\right)*\left(\frac{4}{5}\right)*\left(\frac{4}{5}\right)*\left(\frac{4}{5}\right)*\left(\frac{4}{5}\right)*\left(\frac{4}{5}\right)\\\\\left(\frac{4}{5}\right)^6 = \frac{4*4*4*4*4*4}{5*5*5*5*5}\\\\\left(\frac{4}{5}\right)^6 = \frac{4^6}{5^6}\\\)

For larger values of c, it's easiest to use the formula directly instead of expand things out like what is shown above. I recommend trying out small values of c such as c = 2 or c = 3.

Answer:

\(y = \frac{6}{5} x-\frac{7}{5}\)

Step-by-step explanation:

6x - 5y = 7 is in standard form

-5y = -6x + 7

divide all terms by -5

\(y = \frac{6}{5} x-\frac{7}{5}\)

We can factorize the quadratic as

\(3x^2 + 4x - 12 = 3 (x - r) (x - s)\)

and expand the right side to get

\(3x^2 + 4x - 12 = 3x^2 - 3(r + s) x + 3rs\)

\(\implies r + s = -\dfrac43 \text{ and } rs = -4\)

Then we find

\((r + s)^2 = r^2 + 2rs + s^2 \implies r^2 + s^2 = \left(-\dfrac43\right)^2 - 2(-4) = \boxed{\dfrac{88}9}\)

The z score associated with the highest 10% is closest to: option (c) 1.28

-To find the z score associated with the highest 10%, first determine the percentage that corresponds to the lower 90%, since the z score table typically represents the area to the left of the z score.

- Look up the 0.90 (90%) in a standard normal distribution  (z score) table, which will give you the corresponding z score.

-The z score closest to 0.90 in the table is 1.28, which corresponds to the highest 10% of values.

Therefore, the z score associated with the highest 10% is closest to 1.28.

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Answer:

y=1

Step-by-step explanation:

Let's solve your equation step-by-step.

5(2y−3)−4y=8−2y−15

Step 1: Simplify both sides of the equation.

5(2y−3)−4y=8−2y−15

(5)(2y)+(5)(−3)+−4y=8+−2y+−15(Distribute)

10y+−15+−4y=8+−2y+−15

(10y+−4y)+(−15)=(−2y)+(8+−15)(Combine Like Terms)

6y+−15=−2y+−7

6y−15=−2y−7

Step 2: Add 2y to both sides.

6y−15+2y=−2y−7+2y

8y−15=−7

Step 3: Add 15 to both sides.

8y−15+15=−7+15

8y=8

Step 4: Divide both sides by 8.

The value of y is 1

Given the equation 5(2Y - 3) – 4y = 8 – 2y - 15

Expand

10Y - 15– 4y = 8 – 2y - 15

6y - 15 = -7 - 2y

Collect the like terms

6y + 2y = -7 + 15

8y = 8

Divide both sides by 8

8y/8 = 8/8

y = 1

Hence the value y of is 1

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csc(x)/[1+cot^2(x)] simplifies to sin(x).

We can simplify csc(x)/[1+cot^2(x)] as follows:

csc(x) = 1/sin(x) [Reciprocal identity]

cot^2(x) = cos^2(x)/sin^2(x) [Definition of cotangent]

1 + cot^2(x) = (sin^2(x) + cos^2(x))/sin^2(x) = 1/sin^2(x) [Pythagorean identity]

Substituting these identities into the expression, we get:

csc(x)/[1+cot^2(x)] = (1/sin(x)) / [1/sin^2(x)] = sin(x)

Therefore, csc(x)/[1+cot^2(x)] simplifies to sin(x).

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Answer:

x² + 34x + 104 = 0

x² + 34x = -104

x² + 34x + ((1/2)(34))² = -104 + ((1/2)(34))²

x² + 34x + 17² = -104 + 17²

x² + 34x + 289 = 185

(x + 17)² = 185

x + 17 = +√185

x = -17 + √185

Answer:

\(12\sqrt{3} \) feet

Step-by-step explanation:

In a 30-60-90 triangle, the ratios of the side lengths of the triangle is \(1:\sqrt{3} :2\)

Where 1 is the shortest leg, root(3) is the longer leg, and 2 is the hypotenuse.

First we can set x equals to the length of the original pole, and so the shorter leg has a length of x/3 and using the ratio of side lengths, we can find that:

\(\frac{x}{3} * \sqrt{3} = \frac{\sqrt{3} x}{3} = 12\)

Solving for x, we find that

\(x=\frac{36}{\sqrt{3} } = \frac{36 * \sqrt{3} }{\sqrt{3} * \sqrt{3} } = \frac{36 \sqrt{3} }{3} = 12\sqrt{3} \)

So the length of the original pole would be \(12\sqrt{3} \) feet

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Answer:

Hanna

Step-by-step explanation:

In order to find out how fast Thomas has drove as compared to Hanma we have to compare the speed of each other,

Speed of Hanna = 50mph (as given in ur question)

Speed of Thomas

Since the unit of time of the distance traveled by Thomas is not same as that of Hanna we have to convert the minutes into hour,

Distance traveled = 12miles

Time taken = 15minutes

Speed = 12miles/15mim

Converting minutes into hours we have to multiply by a number whose product will be 60 and that will 4

that is 15 times 4 is 60. But to make the ratio equal

we have to multiply the distance too by 4.

= 12*4/15*4

=48 miles/60minutes

=48miles/1hour

=48mph

Comparing both speeds

Speed of Hanna compared to Speed of Thomas,

50mph > 48mph

Hence, Hanna has the faster speed.

Total 20 number cases should the manager order each month to server an average of 240 vashes of flowers.

Manager of a flower shop determines that an average of 240 vases of flowers is sold each month.

3 cases contain 36 vases.

so 1 case will contain 36/3 vases.

1 case will contain  = 12 vases.

How many cases of vases should the manager order each month.

Given is that 240 vashes of flowers each month is sold.

according to 12 vashes per case we need 20  cases to cover 240 vashes of flowers each month.

12* 20  = 240.

We need 20 cases here.

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Answer:

Option C: x=3 and y= -6 is the correct answer.

Step-by-step explanation:

Given that:

x - 2y = 15     Eqn 1

2x+4y = -18    Eqn 2

Multiplying Eqn 1 by 2

2(x-2y=15)

2x-4y=30    Eqn 3

Adding Eqn 2 and Eqn 3,

(2x+4y)+(2x-4y)=-18+30

2x+4y+2x-4y=12

4x=12

Dividing both sides by 4

\(\frac{4x}{4}=\frac{12}{4}\\x=3\)

Putting x=3 in Eqn 2

2(3)+4y=-18

6+4y=-18

4y= -18-6

4y= -24

Dividing both sides by 4

\(\frac{4y}{4}=\frac{-24}{4}\\y=-6\)

Hence,

Option C: x=3 and y= -6 is the correct answer.

Answer: 1/4 pound (lb) is equal to 4 ounces (oz).

This is because there are 16 ounces in one pound, so you can divide a pound into 16 equal parts, and each part is one ounce. Similarly, you can divide a pound into 4 equal parts , and each part is 1/4 pound. So in order to convert 1/4 pound to ounces, you can multiply 1/4 by 16.

1/4 lb * 16 oz/lb = 4 oz

When converting units, you are essentially multiplying or dividing by a conversion factor. In this case, the conversion factor is 16 oz/lb which tells you that there are 16 ounces in one pound. This factor allows you to convert between pounds and ounces by multiplying or dividing by it.

It's important to pay attention to the units in the conversion factor when using them. Here, the numerator and denominator of the conversion factor have the same unit, but it's not always the case. And the conversion factor helps to cancel out the unwanted unit and yield the desired unit in the end.

Step-by-step explanation:

Answer:

69.825

Step-by-step explanation:

Answer:

1000

Step-by-step explanation:

b.) 23.4x13.9/0.18= 1000