Convert the rectangular coordinates to polar coordinates. (-1,√3)

Answer:

17

Step-by-step explanation:

4 × 5 - 3² x 2 ÷ 6

20 - 3² × 2 ÷ 6

20 - 9 × 2 ÷ 6

20 - 18 ÷ 6

20 - 3 = 17

HOPE THIS HELPS AND HAVE A NICE DAY <3

The number of children who like both pistachio and chocolate ice cream is 73.

Here we have to find at least one kind of ice cream liked by the children.

It is given that the total number of children is 395. The number of children who don't like any ice cream is 170.

So we get the number of students who like one or both the ice cream is 395 - 170 = 225.

Here it is provided that 123 children like pistachio ice cream and 175 children like chocolate ice cream.

So the total number of children who like pistachio and chocolate ice cream is 175+ 123 = 298. Which cannot be greater than 225.

So the number of children who like both ice creams is 298 - 225 = 73.

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Answer:

The distance between C and D is 4.2768 inches.

Step-by-step explanation:

As from A to B the distance is 5.625 inches and actual is 1688 miles

so,

1 mile = 5.625/1688 = 0.0033 inches

So, the distance between C and D is 1296 miles

= 1296 x 0.0033 inches = 4.2768 inches  

The maximum money supply with a 5% reserve requirement and a $400 initial deposit is $8,000.

To calculate the maximum total amount of money that will be in the money supply, we need to consider the money multiplier effect based on the reserve requirement.

The money multiplier is given by the formula: MM = 1 / reserve requirement.

Given that the reserve requirement is 5% (rr = 0.05), the money multiplier is MM = 1 / 0.05 = 20.

The initial deposit is $400.

To calculate the maximum total amount of money in the money supply, we multiply the initial deposit by the money multiplier:

Maximum Money Supply = Initial Deposit * Money Multiplier

= $400 * 20

= $8,000.

Therefore, the maximum total amount of money that will be in the money supply is $8,000 when the reserve requirement is 5% and all currency is deposited in banks with no excess reserves.

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Problem

Solution

for this case we can see that

AB = DC

And we have also that

BO= CO

We also can see that:

< AOB = < COD

And the best answer for this case is:

B. side- side -side

Your answer: (D) Regions with a higher percentage of seat belt usage tend to have lower numbers of highway deaths due to failure to wear seat belts.

In this context, "negative" means that there is an inverse relationship between the number of highway deaths due to failure to wear seat belts and the percentage of seat belt usage. Option (B) correctly states that the correlation is negative. Option (C) is incorrect because it suggests a comparison between two regions.

whereas the regression equation predicts the number of deaths based on seat belt usage within a given region. Option (D) is correct and states that regions with higher seat belt usage tend to have lower numbers of deaths. Option (A) and (E) are incorrect because they do not accurately describe the negative association between the variables.

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Hii!

_________________________________________________________

\(\leadsto\parallel\boldsymbol{Answer.}\parallel\gets\)

   Slope = 4

__________________________________________________________

\(\leadsto\parallel\boldsymbol{Explanation.}\parallel\gets\)

USE the slope formula.

\(\sf \cfrac{y2-y1}{x2-x1}}\)

SUBSTITUTE the values.

\(\sf \cfrac{6-2}{4-3}}\)

\(\sf \cfrac{4}{1}}\)

SIMPLIFY.

\(\sf 4}\)

________________________________________________________

Hope that this helped! Best wishes.

\(\textsl{Reach far. Aim high. Dream big.}\)

\(\boldsymbol{-Greetings!-}\)

________________________________________________________

The perimeter of triangle ABC is 3 cm.

Given:- AB is congruent to segment AC  

AB= AC= 1/2x + 1/4

BC= 5/2-x

Perimeter of a triangle = Sum of all sides

                                      = (1/2x + 1/4) + (1/2x + 1/4) + (5/2-x)

                                      = 1/2x +1/2x -x +1/4+1/4+5/2

                                      = 3 cm

Therefore, the perimeter of triangle ABC is 3 cm.

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Answer:

i think ..................

Step-by-step explanation:

society idsbwj ja

The value of the limit is 12.

A limit in mathematics is a point at which a function approaches the output for the specified input values. Calculus and mathematical analysis depend on limits, which are also used to determine integrals, derivatives, and continuity.

It is employed in the analysis process and constantly considers how the function will behave at a specific moment.

We can expand the cube:

(2+h)³ = 8+12h +6h²+ h³

Plugging this in,

lim (h->0)8+12h +6h²+ h³-8 / h = lim (h->0) 12h +6h²+ h³ / h

=> lim (h->0) (12h +6h+ h²) = 12

The idea of the limit of a topological net broadens the definition of the limit of a sequence and relates it to the limit and direct limit in theory category. In general, there are two sorts of integrals: definite integrals and indefinite integrals. The upper limit and lower limit for definite integrals are correctly specified.

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When an object receives an applied net force, the velocity versus time graph will show a change in velocity over time. Therefore, the velocity versus time graph is a useful tool for analyzing the effects of net force on an object's motion.

When an object receives an applied net force, its velocity versus time graph will show the following characteristics:

1. A non-zero slope: The slope of the velocity vs. time graph represents the acceleration of the object. Since a net force is applied, the object will experience acceleration, and the graph will have a non-zero slope.

2. Linear relationship: If the net force applied is constant, the acceleration will also be constant. This results in a linear relationship between velocity and time on the graph. The slope of the graph will indicate the acceleration of the object, which is directly proportional to the net force applied. As the net force increases, the acceleration and slope of the graph will also increase.

3. Positive or negative slope: The direction of the slope depends on the direction of the applied force. If the net force is in the same direction as the object's initial velocity, the slope will be positive, indicating an increase in velocity. If the force is in the opposite direction, the slope will be negative, indicating a decrease in velocity.

In summary, the velocity vs. time graph of an object receiving an applied net force will have a linear relationship with a non-zero slope, which can be either positive or negative depending on the direction of the force.

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ST = ST (Common)

RT = TQ (Given)

∠ RTS = ∠ SQT (Both 90°)

So, ∆ RTS ≅ ∆ QTS (By SAS congruency rule)

So, RS = QS (By C.P.C.T.)

=> 2x + 8 = 8x - 4

=> 8 + 4 = 8x - 2x

=> 12 = 6x

=> 12/6 = x

=> 2 = x

SR = 2x + 8 (Given)

=> SR = 2(2) + 8 (Putting the value of x)

=> SR = 4 + 8

=> SR = 12

Answer:

Step-by-step explanation:

Answer: A.

Step-by-step explanation: Think of present tense, past tense, future tense

Answer:

A

Step-by-step explanation:

Answer:

3 things :)

Step-by-step explanation:

#1. I have reported these websites to many brainly users and I hope they all stay safe.

#2. As you can see in the model there are 10+ (positives) and -4 (negatives)

and when you subtract the positives and the negatives (10 -4) you would get 6

#3. The equation that represents the model would be when you divide the negative and the positive in this case -4/10 which would equal -2/5

Step-by-step explanation:

first, distribute 7 to 6m (this means 7 • 6m)

7 • 6m = 42m

then distribute 7 to 7 (which is 7 • 7)

7 • 7 = 49

your simplified expression is 42m + 49. i hope this helps! have a great day <3

An infinite geometric series is one in which each term is equal to the preceding term multiplied by a fixed non-zero number, known as the common ratio.

The first term is called a1, and the common ratio is represented by r.In this particular question, we are required to find the value of a1 and r for an infinite geometric series. The partial sum S2 will also need to be found.For a geometric sequence that is infinite, the formula for the partial sum, Sn, is:Sn = a1 / (1-r), where a1 is the first term and r is the common ratio.To solve for a1, it is necessary to know two other variables: the common ratio r and the value of the first term a1. S2 is the sum of the first two terms, so: S2 = a1 + arTo find S2, we must first determine a1 and r. a1 is the first term in the sequence, and r is the common ratio. We can obtain both a1 and r by dividing the second term by the first term.The formula is:r = (ar/a1) = a2/a1 Substitute the value of r and a1 into the formula for S2 to obtain the result: S2 = a1 + ar = a1 + a1r = a1(1+r) Therefore, the value of a1 is a constant number that will appear in the series, and the common ratio, r, will be multiplied by this number to obtain the next value in the series.

So, a1 is the first term, and r is the common ratio of the infinite geometric series. S2, the sum of the first two terms, is found by using the formula S2 = a1 + ar where a1 is the first term and r is the common ratio.

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X is a connected set but not a path-connected set. X={x,0xe[0,1}U{1/nyneN,ye{0,1]}U{0,1}.

To prove that X is connected, let us assume that X can be divided into two disjoint non-empty open sets A and B. Since X is the union of different points, any point in X will be in either A or B. Let us take an arbitrary point p in A. Since A is open, there is an open ball centered at p that is contained in A. Because B is disjoint from A, it follows that every point in this ball is also in A. By a similar argument, any point in B must have a ball centered at that point that is entirely contained in B. Thus, X must be either in A or B and hence, cannot be divided into two disjoint non-empty open sets. However, X is not path-connected since there is no path between points in [0,1] x {0} and {1} x {1}. Thus, it is connected but not path-connected.

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Answer:

10.3

Step-by-step explanation:

Answer:

10.3 is already rounded to the nearest tenth.

Step-by-step explanation:

Where the 3 is is the tenths place.

Systematic sampling offers several advantages. It is relatively easy to implement and eliminates bias that may arise from the subjective selection of participants.

The sampling method described in the scenario is called systematic sampling.

Systematic sampling involves selecting every nth element from a population after randomly selecting a starting point. In this case, the store manager randomly chooses a shopper entering the store as the starting point and then proceeds to interview every 20th person after that initial selection.

Systematic sampling offers several advantages. It is relatively easy to implement and eliminates bias that may arise from the subjective selection of participants. By ensuring a regular interval between selections, systematic sampling provides a representative sample from the population.

However, it's important to note that systematic sampling can introduce a form of bias if there is any periodicity or pattern in the population. For example, if the store experiences a peak in customer traffic during specific time periods, the systematic sampling method might overrepresent or underrepresent certain groups of shoppers.

To minimize this potential bias, the store manager could randomly select the starting point for the systematic sampling at different times of the day or on different days of the week. This would help ensure a more representative sample and reduce the impact of any inherent patterns or periodicities in customer behavior.

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Answer: To prove that triangles △ABC and △DEF are similar, we would use the AA Similarity Postulate. This postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. In other words, if the corresponding angles of two triangles are congruent, then the triangles are similar.

Step-by-step explanation:

The width of the original piece of sheet metal is (w^2 - l^2)/(3w + 3l), and the length is (l^2 - w^2)/(3w + 3l).

To solve this problem, we can use the formula for the volume of a rectangular box, which is V = lwh, where l is the length, w is the width, and h is the height.

First, let's find the height of the box. Since we cut squares from each corner, the height of the box is the length of the square that was cut out. Let's call this length x.

The width of the box is the original width minus the lengths of the two squares that were cut out, which is w - 2x.

Similarly, the length of the box is the original length minus the lengths of the two squares that were cut out, which is l - 2x.

Now we can write the volume of the box in terms of x, w, and l:

V = (w - 2x)(l - 2x)(x)

Expanding this expression, we get:

V = x(4wl - 4wx - 4lx + 8x^2)

Simplifying further:

V = 4x^3 - 4wx^2 - 4lx^2 + 4wlx

To find the dimensions of the original piece of sheet metal, we need to maximize this volume. We can do this by taking the derivative of the volume with respect to x and setting it equal to zero:

dV/dx = 12x^2 - 8wx - 8lx + 4wl = 0

Solving for x, we get:

x = (2wl)/(3w + 3l)

Now we can use this value of x to find the width and length of the original piece of sheet metal:

w - 2x = w - 2(2wl)/(3w + 3l) = (w^2 - l^2)/(3w + 3l)

l - 2x = l - 2(2wl)/(3w + 3l) = (l^2 - w^2)/(3w + 3l)

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Answer:

75

Step-by-step explanation:

(0.45)(30) = (0.18)x

x = (0.45)(30) / (0.18)

x = 13.5 / 0.18 = 75

Check the answer:

(0.45)(30) = (0.18)(75)

13.5 = 13.5   answer is correct!

Answer:

Step-by-step explanation:

45% of 30 = 18% of some number

In this kind of questions, we usually assume the missing number as as something

Let the number be x

So assuming the number is x, the equation will be as follows:

45% of 30 is equal to 18% of x

45/ 100 * 30 = 18/100 * x

This means that 0.45 *30= 0.18 * x

Therefore, 13.5 = 0.18 x

Thus X = 13.5 / 0.18

Which is equal to 75

Thus 45% of 30 is equal to 18% of 75

Proving the above situation as follows:

45% OF 30 = 13.5

And 18% of 75 = 13.5

Thus both equations are equal.

Solution =75

The sum of the infinite geometric series is -18.

An infinite geometric series refers to the sum of an infinite geometric sequence. The series does not have a last term. The general formula for finding the sum of an infinite geometric series is given by

s = a⁄1-r

where s is the sum, a is the first term of the series, and r is the common ratio.

Based on the infinite geometric sequence described by An= 18(2)^n-1, a = 18 and r = 2.

Hence, substituting the values in the general formula:

s = 18⁄1-2 = -18

The sum of the infinite geometric series related to the given infinite geometric sequence is -18.

Note: The question is incomplete. The complete question probably is: Find the sum, if it exists, of the infinite geometric series related to the infinite geometric sequence described by An= 18(2)^n-1

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The statement "if the dot product of two nonzero vectors is zero, the vectors must be perpendicular to each other" is true. The dot product of two vectors is zero if and only if the vectors are perpendicular.

The dot product of two vectors is defined as the product of their magnitudes and the cosine of the angle between them. When the dot product is zero, it means that the cosine of the angle between the vectors is zero, which occurs when the vectors are perpendicular.

In other words, the dot product being zero indicates that the vectors are at a 90-degree angle to each other, supporting the statement that they are perpendicular.

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Answer:

for the 2 blank it is "22, 20.25"

Step-by-step explanation:

because each of them are subtracting by 1.75

To find the probability that a plant chosen at random will be between and cm tall, we need to use the normal distribution formula. We know that the mean height of the plant is cm and the standard deviation is cm.

First, we need to standardize the values of and by subtracting the mean and dividing by the standard deviation:

Z1 = ( - ) / = ( - ) /
Z2 = ( - ) / = ( - ) /

Next, we use a standard normal distribution table or calculator to find the area under the curve between these two Z-values. This area represents the probability that a plant chosen at random will have a height between and cm.

Alternatively, we can use the normal distribution function on a calculator or software to find the probability directly. The formula for the normal distribution function is:

P( < X < ) = 1/2[erf(( - )/sqrt(2)) - erf(( - )/sqrt(2))]

where erf is the error function.

Using either method, we can find that the probability that a plant chosen at random will be between and cm tall is approximately %.

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Value of expression 1 + 1 = 2

Addition is the process of adding two or more items together. In math, addition is the method of calculating the sum of two or more numbers.

Given expression,

1 + 1

+ is sign of Addition, Adding the numbers,

1 + 1 = 2

Hence, 2 is the value of expression 1 + 1.

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By using the point-slope form, the equation of a line that passes through the point (-14, 6) with slope -7/4 is equal to y = -7x/4 + 30.5.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

From the information provided above, we have the following slope and data points on the line:

At data point (-14, 6), a linear equation of this line can be calculated in point-slope form as follows:

y - y₁ = m(x - x₁)

y - 6 = -7/4(x - (-14))

y - 6 = -7/4(x + 14)

y = -7x/4 + 24.5 + 6

y = -7x/4 + 30.5

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Answer:

\(60 \ \text{m}^{2}\)

Step-by-step explanation:

We are given the base, which is 15 meters. When we increase the base, we will obtain the height, which is 8 meters. Now, let's substitute the base and the height in the formula to find the area of the triangle.

\(\rightarrow \dfrac{1}{2} \times 15 \times 8\)

\(\rightarrow 15 \times 4\)

\(\rightarrow 60 \ \text{m}^{2}\)

Thus, the area of the triangle is \(\bold{60 \ \text{m}^{2}}\).

Options b, d, and e are the true statements about the substitution method.

b. It is useful to solve the integral ∫2x sin x^2 dx.

d. It utilizes the formula ∫ f(u(x))u'(x) dx = ∫ f(u) du.

e. It is based on the chain rule for derivatives.

The true statements about the substitution method are:

b. It is useful to solve the integral ∫2x sin x^2 dx.

The substitution method is commonly used to simplify integrals and make them easier to evaluate. It can be applied to various types of integrals, including the given example.

d. It utilizes the formula ∫ f(u(x))u'(x) dx = ∫ f(u) du.

The substitution method involves making a substitution in the integral by introducing a new variable. This formula represents the fundamental principle of substitution, where the derivative of the substituted function appears in the integral.

e. It is based on the chain rule for derivatives.

The substitution method is based on the chain rule of derivatives. By making an appropriate substitution, the integral can be transformed into a new form that corresponds to a derivative of a simpler function.

Therefore, options b, d, and e are the true statements about the substitution method.

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