Two angles are congruent if their measure have a sum of 90 degrees *

Answer:

J

Step-by-step explanation:

It is plausible to say that one group has a higher proportion of smokers than the other.

The meaning of 95% confidence in the given interval is that there is a 95% chance that the population mean is within the interval. This means that if we were to take repeated samples and calculate confidence intervals, 95% of those intervals would contain the true population mean.

To find the difference in proportions of male and female students who smoke, we define the parameters as the difference in proportions between the two groups.

The value of the sample statistic that estimates the difference of proportions, using correct notation, would be the difference in proportions in the sample.

To find a 99% bootstrap confidence interval using percentiles, we can use a tool like Statkey. This will give us a range of values within which we can be 99% confident that the true difference in proportions lies.

To find a 95% bootstrap confidence interval using margin of error, we can use the standard error estimate from the bootstrap distribution. This will give us a range of values within which we can be 95% confident that the true difference in proportions lies.

Based on the 99% confidence interval, it is unlikely that the proportions of all male and female students who smoke are the same. The confidence interval does not include zero, suggesting a significant difference between the two groups.

Therefore, it is plausible to say that one group has a higher proportion of smokers than the other.

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Answer:

4th answer is correct

Step-by-step explanation:

First, let us make x the subject.

\(\sf \frac{x+4}{4} =\frac{y+7}{7}\)

Use cross multiplication.

\(\sf 7(x+4)=4(y+7)\)

Solve the brackets.

\(\sf 7x+28=4y+28\)

Subtract 28 from both sides.

\(\sf 7x=4y+28-28\\\\\sf7x=4y\)

Divide both sides by 7.

\(\sf x=\frac{4y}{7}\)

Now let us find the value of x/4.

To find that, replace x with (4y/7).

Let us find it now.

\(\sf \frac{x}{4} =\frac{\frac{4y}{7} }{4} \\\\\sf \frac{x}{4} =\frac{4y}{7}*\frac{1}{4} \\\\\sf \frac{x}{4} =\frac{4y}{28}\\\\\sf \frac{x}{4} =\frac{y}{7}\)

Hence, in answering the stated question, we may say that As a result, the  equation son's current age is x = 10, while the father's current age is 4x = 40.

A math equation is a process that relates two statements by using the equals sign (=) to indicate equivalence. In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula can be used to understand the link between the two sentences written on opposite sides of a letter. Frequently, the logo and the software are the same. For example, 2x - 4 = 2.

\(x + 14 = 2(x + 4)\\x + 14 = 2x + 8\sx = 6\)

As a result, the brother's current age is x = 6, while the boy's current age is x + 10 = 16.

If x is the age of the son, then the father's age is 4x. In 20 years, the son will be x + 20 years old, while the father will be 4x + 20 years old. Because the father will be double his son's age in 20 years:

\(4x + 20 = 2(x + 20)\)

Expansion and simplification:

\(4x + 20 = 2x + 40\\2x = 20\sx = 10\)

As a result, the son's current age is x = 10, while the father's current age is 4x = 40.

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Answer:

it is C. or A.

Step-by-step explanation:

hope i help

The area of the shaded region will be equal to the (area of the hexagon - area of pentagon) + (area of a square - area of equilateral triangle).

From the complete question, the area of the shaded region 1 will be:

= Area of regular hexagon - Area of regular pentagon

The shaded region 2 will be:

= Area of a square - Area of equilateral triangle

Therefore, the area of the shaded region will be equal to the (area of the hexagon - area of pentagon) + (area of a square - area of equilateral triangle).

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The number of people attending affects how much food is prepared for a catered event. The number of people attending is the explanatory variable in this scenario.

One kind of independent variable is an explanatory variable. Both words are frequently used interchangeably. This is the variable that changes as we change it or watch it change. In other words, it is a factor that a researcher has changed in an experiment.

In the given situation, the number of people attending is an explanatory variable and the amount of food prepared is a dependent variable. As the number of people attending increases, the amount of food prepared also increases. This means the effect of one variable alters the effect of another variable. The change of one variable is called an independent variable while the change that occurs because of the independent variable is a dependent variable.

Therefore, the required answer is the number of people attending.

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To evaluate the integral by reversing the order of integration, we first need to draw the region of integration. From the given limits of integration, we can see that the region is a rectangle with vertices at (0,4), (0,12), (11,4), and (11,12).

Now, we can reverse the order of integration by integrating with respect to y first, and then x. The new limits of integration will be y = 4 to y = 12 and x = 0 to x = 11e^(2y/3).

So, the new integral will be:

∫(0 to 11) ∫(4 to 12) 3y e^(2x/3) dy dx

We can evaluate this integral using integration by parts. Integrating with respect to y gives us:

∫(0 to 11) [3y^2/2 e^(2x/3)] from y = 4 to y = 12

Simplifying this expression gives us:

∫(0 to 11) [36e^(2x/3) - 6e^(8x/3)]/2 dx

Now, integrating with respect to x gives us:

[27e^(2x/3) - 9e^(8x/3)] from x = 0 to x = 11

Substituting these values and simplifying gives us the final answer:

(27e^22/3 - 9e^88/3) - (27 - 9) = 27e^22/3 - 9e^88/3 - 18

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Answer:

Therefore, the rise will be 0.95 m

Step-by-step explanation:

As the waterslide has an angle of elevation of 20 degrees.

Ф = 20°

And we have to determine the rise for a run of 2.6 m.

All we need is to use the trigonometric ratio of tan Ф

Because

As

run = 2.6 m

Ф = 20°

so

tan Ф = rise/run

tan (20) = rise/run

rise = tan (20) × 2.6

rise = 0.95 m

Therefore, the rise will be 0.95 m

Answer:

#1 Corrresponding Sides

Step-by-step explanation:

Makes the most sense

Answer: a

cooresponding sides

Step-by-step explanation:

There are 40 balloons in the package that are either red or blue.

We have,

The probability of choosing a red or blue balloon can be found by adding the probabilities of choosing a red balloon and a blue balloon:

So,

P(red or blue)

= P(red) + P(blue)

= 0.15 + 0.25

= 0.4

This means that 40% of the balloons in the package are either red or blue.

To find how many balloons are either red or blue, we can multiply the total number of balloons by the probability:

= 0.4 x 100

= 40

Thus,

There are 40 balloons in the package that are either red or blue.

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Answer:

$0.231

Step-by-step explanation:

Given data

P= $77

r= 16%

t= 6 months= 0.5 years

For simple interest

A= P(1+rt)

A=77(1+0.16*0.5)

A= 77(1+0.08)

A= 77*1.08

A= $83.16

For compound interest

A=P(1+r)^t

A= 77(1+0.16)^0.5

A= 77(1.16)^0.5

A= 77*1.077

A= $82.929

The difference is

=83.16- 82.929

=$0.231

The centre line of a control chart is calculated by computing the average (mean) of the data for every period.

In control chart analysis, the centre line represents the central tendency or average value of the process being monitored. It is typically obtained by calculating the mean of the data points collected over a specific period. The purpose of the centre line is to provide a reference point against which the process performance can be compared. Any data points falling within acceptable limits around the centre line indicate that the process is stable and under control.

The calculation of the centre line involves summing up the values of the data points and dividing it by the number of data points. This average is then plotted on the control chart as the centre line. By monitoring subsequent data points and their distance from the centre line, deviations and trends in the process can be identified. Deviations beyond the control limits may indicate special causes of variation that require investigation and corrective action. Therefore, the centre line is a critical element in control chart analysis for understanding the baseline performance of a process and detecting any shifts or changes over time.

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Answer: Slope

Step-by-step explanation:

Slope is rise over run. It can be calculated by dividing the change in y (rise) over the change in x (run).

The slope of a non vertical line passing through two points is the ratio of the rise to the run.

What is slope of a line?

The slope of a line is a measurement of its steepness and direction.The slope of a line formula computes the "vertical change" to "horizontal change" ratio between two distinct points along a line.

1. Slope of Parallel Lines :

A set of parallel lines always has the same inclination angle. Assume we possess two parallel lines l1 and l2 in the reference plane, inclined at angles θ1  and θ2 with the x-axis, respectively, such that the, θ2 = θ1.

m1 = m2

Therefore, the slopes of the two given parallel lines are equal.

2. Slope of Perpendicular Lines :

A pair of perpendicular lines always form a 90° angle. Imagine we have two perpendicular lines l2 and l1 in the coordinate plane, inclined at angles θ1 and θ2 with the x-axis, respectively, so that the provided angles follow the external angle theorem, θ2 =  θ1 + 90°

m₁ = tan θ₁

m₂ = tan (θ₁ + 90º) = - cot θ₁

m₁ × m₂ = -1

Therefore, the product of slopes of two given perpendicular lines is equal to -1

Hence , The slope of a non vertical line passing through two points is the ratio of the rise to the run.

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Answer:

Both shots good: .8(.8) = .64 = 64%

Exactly one shot good: 2(.2)(.8) = .32 = 32%

Neither shot good: .2(.2) = .04 = 4%

he required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

Let’s assume the general solution of the given differential equation is,

y=e^{mx}

By taking the derivative of this equation, we get

\(\frac{dy}{dx} = me^{mx}\\\frac{d^2y}{dx^2} = m^2e^{mx}\\\frac{d^3y}{dx^3} = m^3e^{mx}\\\frac{d^4y}{dx^4} = m^4e^{mx}\\\)

Now substitute these values in the given differential equation.

\(\frac{d^4y}{dx^4}-2\frac{d^2y}{dx^2}-8y\\=0m^4e^{mx}-2m^2e^{mx}-8e^{mx}\\=0e^{mx}(m^4-2m^2-8)=0\)

Therefore, \(m^4-2m^2-8=0\)

\((m^2-4)(m^2+2)=0\)

Therefore, the roots are, \(m = ±\sqrt{2} and m=±2\)

By applying the formula for the general solution of a differential equation, we get

General solution is, \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

Hence, the required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

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Stephanie would not be able to rescind the contract because she made a unilateral mistake, and it was not a bilateral mistake.

In contract law, a unilateral mistake occurs when one party to a contract is mistaken about a material fact related to the agreement. However, the general rule is that unilateral mistakes do not provide grounds for rescission of a contract. The reason for this is that contract law places a higher emphasis on the principle of enforceability and preventing one party from unilaterally avoiding their obligations based on their own mistake.

In this case, Stephanie's mistaken belief that the painting was directly painted by Van Gogh, rather than his student, constitutes a unilateral mistake. It is important to note that the art expert's opinion, though incorrect, did not induce Stephanie's mistake or misrepresent the nature of the painting. Stephanie made the decision to sell the painting to Charlie based on her own belief and understanding of its value.

Option d is the correct choice: No, because Stephanie made the mistake, and it was not a bilateral mistake. Stephanie's mistake was unilateral, meaning it was her own error in judgment. A bilateral mistake, on the other hand, occurs when both parties to a contract share a common misunderstanding or mistake about a material fact. In such cases, the contract may be voidable by either party since there was no true "meeting of the minds."

Moreover, the exchange of consideration further strengthens Charlie's position as a bona fide purchaser. Charlie purchased the painting for $15,000.00, and consideration is a fundamental element in the formation of a contract. Once consideration is exchanged, it signifies that the parties have entered into a binding agreement, and it may limit the grounds for rescission.

In conclusion, based on the unilateral nature of Stephanie's mistake and the presence of consideration, Stephanie would not be able to rescind the contract. Therefore, option d is the correct choice.

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Answer:

-300

Step-by-step explanation:

Step 1:  Find the amount Elmer's funds decreased after purchasing the rabbits:

Let x represent Elmer's funds.

Since Elmer bought five rabbits for $10 each, he lost $10 5 times.

x - (10 * 5)

x - 50

Thus, Elmer lost (spent) $50 for the 5 rabbits.

Step 2:  Find the amount Elmer's funds decreased after purchasing the  cupboards:

Since Elmer bought four cupboards for $70 each, he lost $70 4 times:

x - (50 + (70 * 4))

x - (50 + 280)

x - 330

Thus, after purchasing the rabbits and cupboards, Elmer lost $330.

Step 3:  Find the amount Elmer's funds increased after finding the twenty-dollar bill:

Since Elmer found a twenty-dollar bill, he gained $20

x - (330 + 20)

x - 310

Step 4:  Find the amount Elmer's funds increased after returning one rabbit:

Since Elmer returned one rabbit, he gained $10:

x - (310 + 10)

x - 300

Thus, Elmer's funds changed totally by -$300.

Putting all the information together, we have:

x - 10 - 10 - 10 - 10 - 10 - 70 - 70 - 70 - 70 + 20 + 10

x - 50 - 280 + 30

x - 330 + 30

x - $300

Answer:

it is the second one as a nucleus contains neutrons and protons

Answer:

the second one

Step-by-step explanation:

Inside the nucleus are protons and neutrons and electrons orbit the nucleus.

June has 27 coins, made up of quarters and dimes. in total, the coins are worth $4.20. Therefore, there are 10 quarters and 17 dimes she have.

Dime Coin:

A cent is a dime in US parlance, one tenth of the US dollar, and is officially called a "one cent". The name was first authorized by the Money Act of 1792.

The 10-cent coin is the smallest in diameter and the thinnest US coin in circulation, measuring 17.91 mm (0.705 inches) and 1.35 mm (0.053 inches) in diameter thickness. The obverse of the current cent features a profile of President Franklin D. Roosevelt, while the reverse depicts, from left to right, an olive branch, a torch, and an oak branch.

Quarter Coin:

The quarter (short for quarter dollar) is a United States coin denominated in 25 cents (quarter dollar). The obverse of the coin depicts George Washington in profile, and since 1998 the design of the reverse has changed frequently. In continuous production from 1796 to 1831. 955 inches (24.26 mm), 0.069 inches (1.75 mm) thick. The current version consists of two layers of cupronickel (75% copper, 25% nickel) plated on a pure copper core. The overall composition of the coin is 8.33% nickel and 91.67% copper, as the cupronickel layer accounts for 1/3 of the total weight. Its weight is 0.1823 troy ounces or 0.2000 regular Dupo ounces (5,670 grams).

We can consider that:

Let d = the number of dimes

Let q = the number of quarters

Now,

   d + q = 27                        -------------------------- (1)

⇒ d = 27 - q                      

⇒ 0.10d + 0.25q = 4.20                -------------------------- (2)    

Multiply both sides of this equation by 100 to get rid of the decimal points.

10d + 25q = 420

⇒ 10(27- q) + 25q = 420

⇒ 270 - 10q + 25q = 420

⇒ 15q = 150

⇒ q = 10

Now, Putting the value of q = 10 in equation (1) :

   d + 10 = 27

⇒ d = 27 - 10

⇒ d = 17

Therefore, there are 10 quarters and 17 dimes she have.

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The bisection method is an approximation method to find the roots of the given equation by repeatedly dividing the interval. This method will divide the interval until the resulting interval is found, which is extremely small.

To determine the number of iterations required for the bisection method, we need more information, such as the desired accuracy or the stopping criterion for the method. The bisection method works by repeatedly dividing the interval in half and checking if the function changes sign within the interval. This process continues until the desired accuracy is achieved.

Without knowing the specific stopping criterion, it is not possible to determine the exact number of iterations required. The number of iterations depends on factors such as the behavior of the function and the desired accuracy.

If you provide more information about the desired accuracy or the stopping criterion, I can assist you in determining the number of iterations required for the bisection method.

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Answer:

the value of x is twenty nine

a) the population cannot be negative, the limiting population is 4300.

b)the population is increasing when 0 < p < 4300 and decreases when p > 4300.

c)the equilibrium solutions are p = 0 and p = 4300.

(a) To determine when the population is increasing or decreasing, we need to look at the sign of dp/dt.

\(\frac{dp}{dt} = 1.2p(1 - \frac{p}{4300})\)

For dp/dt to be positive (i.e. population is increasing),

we need\(1 - \frac{p}{4300} > 0, or \ p < 4300.\)

For dp/dt to be negative (i.e. population is decreasing),

we need\(1 - \frac{p}{4300} < 0, or p > 4300.\)

Therefore, the population is increasing when 0 < p < 4300 and decreases when p > 4300.

(b) To find the limiting population, we need to find the value of p as t approaches infinity.

As t approaches infinity,\(\frac{dp}{dt}\)approaches 0. Therefore, we can set \(\frac{dp}{dt}\) = 0 and solve for p.

0 = 1.2p(1 - p/4300)

Simplifying, we get:

0 = p(1 - p/4300)

So, either p = 0 or 1 - p/4300 = 0.

Solving for p, we get:

p = 0 or p = 4300.

Since the population cannot be negative, the limiting population is 4300.

(c) Equilibrium solutions occur when\(dp/dt = 0.\)We already found the equilibrium solutions in part (b): p = 0 and p = 4300.

Therefore, the equilibrium solutions are p = 0 and p = 4300.

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a)  The population is increasing when 0 < p < 4300, and  decreasing when p > 4300.

b)  The population cannot be negative, the limiting population is 4300.

c)  these are the equilibrium solutions.  At p = 0, the population is not

increasing or decreasing, and at p = 4300,  the population is decreasing

but not changing in size.

(a) To determine when the population is increasing or decreasing, we

need to find the sign of dp/dt. We have:

dp/dt = 1.2p(1 - p/4300)

This expression is positive when 1 - p/4300 > 0, i.e., when p < 4300, and

negative when 1 - p/4300 < 0, i.e., when p > 4300.

Therefore, the population is increasing when 0 < p < 4300, and

decreasing when p > 4300.

(b) To find the limiting population, we need to solve for p as t approaches infinity. To do this, we set dp/dt = 0 and solve for p:

1.2p(1 - p/4300) = 0

This equation has two solutions: p = 0 and p = 4300. Since the population cannot be negative, the limiting population is 4300.

(c) To find the equilibrium solutions, we need to solve for p when dp/dt = 0. We already found that the only solutions to dp/dt = 0 are p = 0 and

p = 4300.

Therefore, these are the equilibrium solutions.

At p = 0, the population is not increasing or decreasing, and at p = 4300,

the population is decreasing but not changing in size.

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Step-by-step explanation:

\(2xy^2 + 8y\)

2y is the common factor so:

\(2y(xy + 4)\)

Therefore, the expression that Tesha wrote is most likely option. \(C: (5 *6 + 2 *3)/(3*2*3).\)

An equation is a mathematical statement that shows the equality of two expressions or values. It contains an equal's sign (=) which separates the two expressions that are equal to each other. Equations can be simple or complex and can involve one or more variables, which are typically represented by letters. Equations are used extensively in mathematics, science, engineering, and many other fields to model and solve problems. Solving an equation involves finding the values of the variables that make the equation true.

To solve this problem, we need to simplify the expression.\((20 + 4) /12\):

\((20 + 4) / 12 = 24 / 12 = 2\)

So, the expression that Tesha wrote must also simplify to 2. Let's check each of the options:

A. \(36 / 3 *5 = 12 * 5 = 60\), which is not equivalent to 2. So, option A is not the correct one.

B. \((3 * 3 * 3) / 3 * 1 = 27 / 3 *1 = 9 * 1 = 9\), which is not equivalent to 2. So option B is not the correct one.

C. \((5 * 6 + 2 * 3) / (3 * 2 * 3) = (30 + 6) / 18 = 36 / 18 = 2\), which is equivalent to 2. So, option C is the correct one.

D. \((8 * 5 *2) / (10 * 2) = 80 /20 = 4\), which is not equivalent to 2. So option D is not the correct one.

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Answer:

5 1/3

Step-by-step explanation:

Answer:

-7 2/3

Step-by-step explanation:

-5 1/3 - 2 1/3 =

-16/3 - 7/3 = -23/3

-23/3 can be left improper or mixed,

-7 2/3

Answer:

C. a quantity used as a standard measurement

Step-by-step explanation:

A unit is a universally acceptable system of measurement. The system is majorly referred to as the international standard of units i.e (SI) units.

Since physical quantities could be categorize as either fundamental or derived. The use of units in measurement is very essential, because it relates the magnitude measured to the physical quantity.

The units of measurement tells what physical quantity has been measured.

inequation something like that

Answer:

(6-2)/4

Step-by-step explanation:

Make sure you have the parenthesis

Answer:

x=1

Step-by-step explanation: