Choose the equation of the lemniscate with the domain pi/2
r² = -25sin(28)
r² = 25sin(28)
r² = -25cos(28)
r² = 25cos(28)

Answer:

-4x=4

Step-by-step explanation:

-4x+7=11 subtract 7 add to the 11 answer-4x=4

Answer:

x=-1

Step-by-step explanation:

Move all terms not containing  x  to the right side of the equation.

Subtract 7 from both sides of the equation

-4x=11-7

Subtract 7 from 11

-4x=4

Divide each term and simplify

x=-1.

Hope this helps :)

Plz mark brainiest!

A sphere is a collection of points that are equally spaced apart from a fixed point. A sphere is a perfectly round geometrical object in three dimensions with equal distances between each point on its surface and its centre.

Any point on the sphere will always be a bbfrom the fixed b, giving the object a three-dimensional shape. The radius of the sphere, which is a bfigure, defines its surface. It is important to remember that the idea of equal distances from a fixed point can be applied to higher dimensions, where the resulting form is known as a hypersphere.

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a) The 90% confidence interval for the population proportion is approximately (0.7777, 0.8423).

b) The 95% confidence interval for the population proportion is approximately (0.7737, 0.8463).

To calculate the confidence intervals for the population proportion, we can use the formula:

Confidence Interval = sample proportion ± margin of error

The margin of error can be calculated using the formula:

Margin of Error = critical value * standard error

where the critical value is determined based on the desired confidence level and the standard error is calculated as:

Standard Error = \(\sqrt{((p * (1 - p)) / n)}\)

Given that the sample proportion (p) is 0.81 and the sample size (n) is 500, we can calculate the confidence intervals.

a. 90% Confidence Interval:

To find the critical value for a 90% confidence interval, we need to determine the z-score associated with the desired confidence level. The z-score can be found using a standard normal distribution table or calculator. For a 90% confidence level, the critical value is approximately 1.645.

Margin of Error = \(1.645 * \sqrt{(0.81 * (1 - 0.81)) / 500)}\)

≈ 0.0323

Confidence Interval = 0.81 ± 0.0323

≈ (0.7777, 0.8423)

Therefore, the 90% confidence interval for the population proportion is approximately (0.7777, 0.8423).

b. 95% Confidence Interval:

For a 95% confidence level, the critical value is approximately 1.96.

Margin of Error = \(1.96 * \sqrt{(0.81 * (1 - 0.81)) / 500)}\)

≈ 0.0363

Confidence Interval = 0.81 ± 0.0363

≈ (0.7737, 0.8463)

Thus, the 95% confidence interval for the population proportion is approximately (0.7737, 0.8463).

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Answer:

  2

Step-by-step explanation:

You want to know the z-score of an x-value that is two standard deviations to the right of the mean.

The z-score is the number of standard deviations a value is to the right of the mean.

If x=30 is 2 standard deviations to the right of the mean, the z-score is 2.

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Answer:

90 + 90

Step-by-step explanation:

Answer: \(\frac{-2}{1}\)

Step-by-step explanation:

In the equation y=-2x +3, we can use y=mx+b to help find the slope. m is the slope, and in this case, it is -2, which is the same as \(\frac{-2}{1}\). The slope has a rise of -2, and a run of 1.

Answer:

3. This would be third person view

4. Tyrone's mother and Tyrone himself

Step-by-step explanation:

3. Explanation: "Tyrone will be so surprised," she thought. "He has no

idea that we have a puppy waiting for him at Grandma's

house." This is third person view because it says "thought" and whilst it is her view point, Tyrone wondered to himself - Tyrone saw his mother smiling to herself and wondered what she was thinking.- therefore, causing it to be third person point of view.

Answer:

60 km/h

Step-by-step explanation:

Average speed is total distance over total time.

Total distance: 30 + 0 + 150 = 180 km.

Total time: 0.75 + 0.25 + 2 = 3 hrs.

180/3 = 60/1

Answer:

  see the attached graph

Step-by-step explanation:

You want to graph these inequalities and identify their solution space.

The boundary line associated with the solution of an inequality is found by replacing the inequality symbol with an equal sign. Here, that means the boundary lines are given by the equations ...

These lines can be plotted by finding their x- and y-intercepts, then drawing the line through those points. In each case, the intercept is found by setting the other variable to zero and solving the resulting equation.

x-intercept of x+y=8:  x = 8, or point (8, 0)

y-intercept of x+y=8:  y = 8, or point (0, 8)

The inequality symbol for this inequality is "less than or equal to", so the boundary line is included in the solution set. That means the line is drawn as a solid (not dashed) line.

When we look at one of the variables with a positive coefficient, we see ...

  x ≤ ... — shading is to the left of the boundary line

or

  y ≤ ... — shading is below the boundary line

The solution space for this inequality is shown in blue in the attached graph.

The x- and y-intercepts are found the same way as above. They are ...

  x-intercept:  x = 2, or point (2, 0)

  y-intercept:  y = -2, or point (0, -2)

The boundary line is solid, and shading is to its left:

  x ≤ ...

The solution space for this inequality is shown in red in the attached graph.

The solutions of the set of inequalities are all the points on the graph where the shaded areas overlap. This is the left quadrant defined by the X where the lines cross.

__

Additional comment

To summarize the "step-by-step", you want to ...

In this process, you make use of your knowledge of plotting points and lines. You also make use of your understanding of "greater than" or "less than" relationships in the x- and y-directions on a graph.

The value of the a is 2.

What is the fraction?

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many parts of a particular size there are when used in conversational English.

We have,

8⁻¹ / 4⁻¹ - a⁻¹ = 1

By simplifying the given equation we get,

8⁻¹ - a⁻¹ = 1 * 4⁻¹

By further calculating the equation,

1/8 - 1/a = 1/4

4(1/8 - 1/a) = 1

4/8 - 4/a = 1

1/2 - 4/a = 1

4/a = 1/2

1/a = 4/2

a = 2/4

a = 2

Hence, the value of the a is 2.

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The random variable "the number of cups of coffee sold in a cafeteria during lunch" is discrete.

This is because the variable can only take on integer values, such as 0, 1, 2, 3, and so on. It is not possible to sell a fraction of a cup of coffee, which is what would make it a continuous variable.

A discrete random variable has a finite or countably infinite number of possible outcomes, and each outcome has a non-zero probability.

In contrast, a continuous random variable can take on any value within a certain range, and the probabilities are described by a probability density function.

In this case, since the number of cups of coffee sold can only take on whole number values, it is a discrete random variable.

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The cost of 5 pairs of shoes is 108.78 dollars.

The cost of 3 pairs of shoes is $65.27. At this price, the cost of 5 pairs of shoes can be calculated as follows:

Let's find the cost of each pair of shoes before we can get the cost of 5 pairs of shoes.

Therefore,

3 pairs of shoe = 65.27 dollars

1 pair of shoes = ?

cross multiply

cost of each pair = 65.27 / 3

cost of each pair = 21.76 dollars

Therefore, the cost of 5 pairs of shoes can be found as follows:

cost of 5 pairs of shoes = 21.76 × 5

cost of 5 pairs of shoes = 108.783333333

Therefore,

cost of 5 pairs of shoes = 108.78 dollars

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The list of all the positive common divisors of 48 and 60 is:1, 2, 3, 4, 6, 12.

To find all the common divisors of 48 and 60, we need to first list the divisors of both numbers. So let's list out the divisors of both 48 and 60.

Divisors of 48:1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Divisors of 60:1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Now, we can identify the common divisors by comparing the two lists. The common divisors of 48 and 60 are:1, 2, 3, 4, 6, 12

In division, we divide a number by any other number to get another number as a result. So, the number which is getting divided here is called the dividend. The number which divides a given number is the divisor.

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The probability that the sample mean will be within plus minus 2 of the population mean if the sample size is n = 100 between z-scores of 0 and 2.5 using a z-table.

The standard deviation of the sample distribution, commonly known as the standard error, can be computed using the formula given that the population mean is 100 and the standard deviation is 16:

Standard Error = Standard Deviation / sqrt(sample size)

Let's determine the likelihoods for sample sizes of n = 100 and n = 400:

For n = 100:

Standard Error = 16 / sqrt(100) = 16 / 10 = 1.6

We can determine the z-scores for the upper and lower boundaries to establish the likelihood that the sample mean will be within plus or minus 2 of the population mean:

Lower Bound z-score = (Sample Mean - Population Mean) / Standard Error

Lower Bound z-score = (100 - 100) / 1.6

Lower Bound z-score = 0

Upper Bound z-score = (Sample Mean - Population Mean) / Standard Error

Upper Bound z-score = (104 - 100) / 1.6

Upper Bound z-score = 4 / 1.6

Upper Bound z-score = 2.5

We can calculate the region under the normal distribution curve between z-scores of 0 and 2.5 using a z-table or statistical software. This shows the likelihood that the sample mean will be within +/- 2 standard deviations of the population mean.

For n = 400:

Standard Error = 16/√400

Standard Error = 16/20

Standard Error = 0.8

We determine the z-scores by following the same procedure as above:

Lower Bound z-score = (Sample Mean - Population Mean) / Standard Error

Lower Bound z-score = (100 - 100) / 0.8

Lower Bound z-score = 0

Upper Bound z-score = (Sample Mean - Population Mean) / Standard Error

Upper Bound z-score = (104 - 100) / 0.8

Upper Bound z-score = 4 / 0.8

Upper Bound z-score = 5

Once more, we may determine the region under the normal distribution curve between z-scores of 0 and 5 using a z-table or statistical software.

A larger sample size, like n = 400, has the benefit of a lower standard error. The sampling distribution of the sample mean will be more constrained and more closely resemble the population mean if the standard error is less.

As a result, there is a larger likelihood that the sample mean will be within +/- 2 of the population mean. In other words, the estimate of the population mean gets more accurate and dependable as the sample size grows.

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Answer:

This year, Juanita will have to use $75.

Step-by-step explanation:

Because if 2 shirts is $15, 4 shirts will be $30. $45 is $15 more than $30, so the increase is $15. 2*4 is 8, so that will make it 15*4=60. 60+15=75.

Answer:

60

Step-by-step explanation:

Answer:

\(\displaystyle 3x - y = 19\:or\:y = 3x - 19\)

Step-by-step explanation:

Plug the information into the Slope-Intercept Formula:

\(\displaystyle 5 = 3[8] + b \hookrightarrow 5 = 24 + b; -19 = b \\ \\ y = 3x - 19\)

Suppose you need to write this equation in standard form. You would follow these procedures:

y = 3x - 19

- 3x - 3x

__________

\(\displaystyle -3x + y = -19\)

*Now, you can leave the standard equation like this, but UNIVERSALLY, the A-term is positive, so you must multiply the negative out as well.

\(\displaystyle \boxed{3x - y = 19}\)

I am joyous to assist you at any time.

The size of the square footing, considering the given factors and Teng's equation, is 368.69 meters for each side length.

To determine the size of the square footing, we can use Teng's equation, which relates the applied load, allowable settlement, and dimensions of the footing. Teng's equation is given by:

A = (N * Q * FOS) / (P * S)

Where:

A = Area of the footing

N = Factor related to soil characteristics (given as 11)

Q = Applied load on the footing (given as 1500 kN)

FOS = Factor of safety (given as 2.5)

P = Allowable settlement (given as 45 mm, which is 0.045 m)

S = Depth of footing (given as 3 m)

Substituting the given values into the equation, we have:

A = (11 * 1500 * 2.5) / (0.045 * 3)

Simplifying the expression:

A = 55000 / 0.405

A = 135802.47 square meters (approximately)

Since a square footing has equal dimensions for length and width, we can find the side length of the square footing by taking the square root of the calculated area:

Side length = √135802.47

Side length ≈ 368.69 meters

Therefore, the size of the square footing, considering the given factors and Teng's equation, is approximately 368.69 meters for each side length.

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To find the minimum number of 10-foot boards that Paul should buy, we need to determine the total length of lumber he needs and then divide it by the length of each board.

Paul needs 8 pieces of lumber, each 38 inches long. To convert the length to feet, we divide 38 by 12 (since there are 12 inches in a foot):

38 inches ÷ 12 = 3.17 feet (approximately)

Now, we can find the total length of lumber needed:

8 pieces × 3.17 feet = 25.36 feet (approximately)

Next, we divide the total length by the length of each board:

25.36 feet ÷ 10 feet = 2.54 (approximately)

Since we can't buy a fraction of a board, we round up to the nearest whole number.

Therefore, Paul should buy at least 3 boards to have enough lumber for the bookcase.

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Answer:

Step-by-step explanation:

= 8^7 = 2^21

Answer:

\(8^{7}\) hopefully this helps

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

You have a total of 6 outcomes (1,2,3,4,5,6).  That is your numerator.  Out of those numbers, you only want 2 of them (4 or 5), so the fractions would be 2/6 or 1/3 which can also be written 1:3

Answer:

3. is a functions and 4 isnt

Step-by-step explanation:

(b) To prove the equivalence of x ∧ (¬y ↔ z) and ((x → y) ∨ ¬z) → (x ∧ ¬(y → z) and (x ∨ y ∨ ¬z) ∧ (¬x ∨ y ∨ z) ⇐⇒ ¬y → (x ↔ z), we can use the following equivalence laws:

Implication Elimination (→E), Implication Introduction (→I) ,De Morgan's Laws (DeM) ,Double Negation (DN) ,Commutation (Comm), Association (Assoc) ,Distributive Laws (Dist)

By applying these laws step by step, we can simplify both sides of the equation and show that they are equivalent.

To prove the equivalence of two logical expressions, we manipulate each side using logical equivalence laws until they are in the same form. In this case, we start with the left-hand side (LHS) and the right-hand side (RHS) of the equation and apply the laws to simplify them.

By using laws such as De Morgan's Laws to expand and distribute the negation, Commutation and Association to rearrange terms, and Implication Introduction and Elimination to handle implications, we can transform both sides of the equation into equivalent forms.

The step-by-step process involves applying the laws to manipulate the expressions, simplifying them, and making them match. The end goal is to show that the LHS and RHS of the equation are equivalent, meaning they have the same truth value for all possible truth assignments to the variables involved.

By carefully applying the equivalence laws, the proof demonstrates that the original statement is valid and that the LHS and RHS of the equation are equivalent logical expressions.

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If z = xy⁷ − x²y, x = t² + 1, y = t² − 1, then using chain rule the value of dz/dt = 2t(y⁷ + xy⁶(dy/dx) - 2xy - x²(dy/dx)) + 2t(xy⁷ + 7xy⁶ - x²)

To find dz/dt using the chain rule, we need to differentiate z with respect to t while considering the relationship between z, x, y, and t.

Given:

z = xy⁷ − x²y

x = t² + 1

y = t² − 1

We can start by finding dz/dx and dz/dy separately and then use the chain rule to combine them to find dz/dt.

First, let's find dz/dx:

Differentiating z with respect to x, keeping y constant:

dz/dx = (d/dx)(xy⁷) - (d/dx)(x²y)

Using the product rule for differentiation:

dz/dx = y⁷ + xy⁶(dy/dx) - 2xy - x²(dy/dx)

Next, let's find dz/dy:

Differentiating z with respect to y, keeping x constant:

dz/dy = (d/dy)(xy⁷) - (d/dy)(x²y)

Using the product rule again:

dz/dy = x(y⁷ + 7y⁶(dy/dy)) - x²

Since dy/dy = 1, we can simplify dz/dy as:

dz/dy = xy⁷ + 7xy⁶ - x²

Now, let's use the chain rule to find dz/dt:

dz/dt = (dz/dx)(dx/dt) + (dz/dy)(dy/dt)

Substituting the expressions we found earlier for dz/dx and dz/dy, and using dx/dt = 2t and dy/dt = 2t:

dz/dt = (y⁷ + xy⁶(dy/dx) - 2xy - x²(dy/dx))(2t) + (xy⁷ + 7xy⁶ - x²)(2t)

Simplifying this expression gives us dz/dt in terms of t, x, and y:

dz/dt = 2t(y⁷ + xy⁶(dy/dx) - 2xy - x²(dy/dx)) + 2t(xy⁷ + 7xy⁶ - x²)

This is the complete calculation for finding dz/dt using the chain rule.

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Complete question is:

Use the chain rule to find dz/dt. z = xy⁷ − x²y, x = t² + 1, y = t² − 1

Answer:

B.   3,158

Step-by-step explanation:

h(x) = -49x − 125

Let x = -67

h(-67) = -49(-67) − 125

          =3283-125

          = 3158

Answer:

Answer B

Step-by-step explanation:

To find the value of h(-67) for the function h(x) = -49x - 125,

we substitute -67 for x in the function and evaluate it.

h ( - 67 ) = - 49 ( - 67 ) - 125

Now we can simplify the expression:

h ( -67 ) = 3283 - 125

h ( -67 ) = 3158

The time is needed between injections is 3.6 hours, i.e., the drug is to be injected again when the number of milligrams reaches 6 mg.

We have the exponential function of number of milligrams D (ht) of a certain drug that is in a patient's bloodstream h hours after the drug is injected is

\(D(h)=25 {e}^{ - 0.4 h}\)

We have to solve for h (the numbers of hours) that would have passed when the D(h) (the amount of medication in the patient's bloodstream) equals 6 mg in order to know when the patient needs to be injected again.

\(6 = 25 {e}^{ - 0.4h} \)

\( \frac{6}{25} = \frac{25}{25} {e}^{ - 0.4h} \)

\(0.24= {e}^{ - 0.4h} \)

Taking logarithm both sides of above equation , we get,

\( \ln(0.24) = \ln( {e}^{ - 0.4h)} \)

Using the properties of natural logarithm,

\( \ln(0.24) = - 0.4h\)

\( - 1.427116356 = - 0.4h\)

\(h = \frac{1.42711635}{0.4} = 3.56779089\)

=> h = 3. 6

So, after 3.6 hours, the patient needs to be injected again.

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The type of loan that Brady most likely getting  is option (a) conventional loan

Conventional loans are typically not guaranteed or insured by the government and often require a higher down payment compared to government-backed loans such as FHA or VA loans. The down payment requirement of $5,250, which is 3.5% of the purchase price, is lower than the typical down payment requirement for a conventional loan, which is usually around 5% to 20% of the purchase price.

ARM (Adjustable Rate Mortgage) loans have interest rates that can change over time, which can make them riskier for borrowers. FHA (Federal Housing Administration) loans are government-backed loans that typically require a lower down payment than conventional loans, but they also require mortgage insurance premiums.

VA (Veterans Affairs) loans are available only to veterans and offer favorable terms such as no down payment requirement, but not everyone is eligible for them. Fixed-rate loans have a fixed interest rate for the life of the loan, but the down payment amount does not indicate the loan type.

Therefore, the correct option is (a) Conventional loan

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