please solve step by step

Rose curves are characterized by equations of the form r = a cos (nθ) or r = a sin (nθ), a ≠ 0. If n ≠ 0 is even, the rose has 2n petals; if n ≠ ± 1 is odd, the rose has n petals.

This means that the number of petals of a rose curve depends on the value of n in the equation. If n is even, the number of petals is 2n, and if n is odd, the number of petals is n.

The value of a determines the size of the rose curve. If a is large, the curve will be large, and if a is small, the curve will be small. The cosine or sine function determines the shape of the rose curve.

The cosine function results in a rose curve that is symmetrical about the x-axis, while the sine function results in a rose curve that is symmetrical about the y-axis.

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--The given question is incomplete; the complete question is

"Complete the sentence below.

Rose curves are characterized by equations of the form r = a cos (nθ) or r = a sin (nθ), a ≠ 0. If n ≠ 0 is even, the rose has___ petals; if n ≠ ± 1 is odd, the rose has____ petals."--

The function F(x) has a derivative f'(x) = sin(x) - xcos (x). This is accomplished by employing the chain rule and the basic calculus theorem.

The calculus fundamental theorem can be used to derive the derivative of f(x).

Let x1sin(t)dt equal F(x). The fundamental theorem of calculus states that F'(x) = sin (x).

Let g(x) now equal x. The chain rule then states that f'(x) = g' (x) F'(x)= g'(x)sin(x)=cos (x).

Therefore, f'(x) = sin(x) - xcos is the derivative of f(x) (x).

F(x) has a derivative f'(x) = sin(x) - xcos (x). Applying the chain rule and the calculus's fundamental theorem will get this result. The integrand assessed at the integral's upper limit is equivalent to the derivative of a definite integral, according to the calculus fundamental theorem. According to the chain rule, the derivative of a function made up of two functions is equal to the sum of the derivatives of the inner and outer functions. The inner function in this instance is sin(t), while the outer function is x. Thus, by using the chain rule and the fundamental theorem of calculus, we can determine that f'(x) = sin(x) - xcos (x)

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The solution to the equation is x = 27

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

√2x+10 -6=2

Add 6 to both sides of the equation

This gives

√2x+10 = 8

Square both sides

So, we have the following representation

2x + 10 = 64

Subtract 10 from both sides

2x = 54

Divide by 2

x = 27

Hence, the solution is 27

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Answer:

d=rt, d/r=t, and r=d/t

Step-by-step explanation:

d=rt is a correct option, so we can use this to solve for others

if you isolate t, d/r=t is also correct

isolate r to get r=d/t

Answer:

Jimmy spent 4/25 of his $5,000 budget on hotel accommodation, which is equal to $2,000. He spent 3/20 of his budget on airfare, which is equal to $1,500, 1/10 of his budget on shopping, which is equal to $500, and 1/5 of his budget on the remainder, which is equal to $1,000. This means that Jimmy spent $2,000 on hotel accommodation, which is $500 more than he spent on food.

Answer:

the answer to this question is 6:00

The number of patients before 2 hours is 40,000.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics.

As per the given data:

The growth rate of covid patients is given and number of patients at 8:00 am is 44,100.

We have to find out what was the number before 2 hours.

Growth rate (G) = 5% per hour.

Number of patients at 8 : 00 AM = 44,100

Let's assume the number of patients 2 hours before is P.

Patients after two hours:

P(1 + G/100)^2

= P(1 + 5/100)^2

= P(1.05)^2

= 1.1025P

From the given data:

1.1025P = 44,100

P = 40,000

The number of patients before 2 hours is 40,000.

Hence, The number of patients before 2 hours is 40,000.

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1. The 08 08 bus takes 89 minutes to go from Birmingham to Coventry

2. The latest time Chris have to leave his house is 7:26

The bus time table shows that only two buses will leave can meet up with Chris resuming time. The bus 7:05 and the bus that leave by 7: 33

Calculating the latest time Chris could leave his home is by taking the second bus.

7 minutes to walk from his house to his bus stop. Therefore the 7minutes is deducted from the starting time of the second bus.

7:33-7minutes = 7: 26 am

Therefore the latest time he should leave home to meet up with 9:30 am resuming is 7:26 am

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Answer:

y = 17

Step-by-step explanation:

the absolute value always gives a positive value , that is

| - a | = | a | = a

given

y = | x | + 10 ( substitute x = - 7 into the equation )

y = | - 7 | + 10 = | 7 | + 10 = 7 + 10 = 17

Answer:

wow this is highschool

Step-by-step explanation:

I'm still in ms so I can't help sozz

Answer: 1.75

Step-by-step explanation:

Add the number of cars (3+4+1) which would give you 8.

Then multiply the number of students in one car by the the number of cars in each row (1x3, 2x4, 3x1) which would give you 3, 8 and 3.

Then you add all 3 numbers together to give you 14.

You then do 14/8 which would give you 1.75

Answer:

a) Since the question is asking for a disjunction, involving an or, this means that the answer to the question can be either solution, not both.

b) Conjunction involves an "and" so it means both answers

Step-by-step explanation:

Using the component method of vector addition, the resultant of the given three vectors is 63.803 km at an angle of -86.6° from the positive x-axis.

We must divide each vector into its x- and y-components in order to use the component method to obtain the resultant of the given vectors.

The resultant vector can then be obtained by adding the x- and y-components together.

Vector a = 56 km, east

The x-component of vector a = 56 km

The y-component of vector a = 0 km

Vector b = 11 km, 22° south of east

To find the x-component, we can use trigonometry:

x-component = 11 km * cos(22°) = 10.213 km

To find the y-component, we can use trigonometry:

y-component = 11 km * sin(22°) = -4.282 km

Vector c = 88 km, 44° west of south

To find the x-component, we can use trigonometry:

x-component = 88 km * sin(44°) = -61.578 km

To find the y-component, we can use trigonometry:

y-component = 88 km * cos(44°) = -59.229 km

x-component: 56 km + 10.213 km + (-61.578 km) = 4.635 km (east is positive)

y-component: 0 km + (-4.282 km) + (-59.229 km) = -63.511 km (north is positive)

Resultant = sqrt((4.635 km)^2 + (-63.511 km)^2) ≈ 63.803 km

The direction of the resultant vector can be found using the inverse tangent function:

angle = atan(-63.511 km / 4.635 km) ≈ -86.6°

Thus, the resultant vector is approximately 63.803 km at an angle of -86.6° from the positive x-axis.

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To compute the median of three sets of scores, we need to arrange the scores in order from smallest to largest and then select the middle score.

Mean, median and mode are measures of central tendency and are used to describe the central value of a set of data. The mean is the average of all the values in the set, the median is the middle value and the mode is the most frequently occurring value.

To compute the mean of three sets of scores, we need to sum up all the scores and divide by the total number of scores. This can be represented by the formula:

Mean = (Score1 + Score2 + Score3) / 3

To compute the median of three sets of scores, we need to arrange the scores in order from smallest to largest and then select the middle score. This can be represented by the formula:

Median = (Score2 + Score3) / 2

To compute the mode of three sets of scores, we need to identify the score that occurs the most frequently. This can be represented by the formula:

Mode = Most Frequently Occurring Score

For example, if the three scores are 3, 7, and 4, then the mean is (3 + 7 + 4) / 3 = 4.67, the median is (3 + 4) / 2 = 3.

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The volume of the solid can be calculated by integrating the area of the cross section over the entire height of the solid.

The washer method is a way to calculate the volume of a solid that is created when a region is rotated about a certain line.

Here you find the area of this cross section, and multiply it by the circumference of a circle with the same radius as the cross section.

To use the washer method to find the volume of the solid created when the region bounded by

=> y = 12x², y=0, and x=2 is rotated about the line y=3,

we first need to find the cross section of the solid at different heights along the line of rotation.

To do this, we need to find the points where the plane perpendicular to the line of rotation intersects the original region. This is done by finding where the equation of the plane and the equation of the original region intersect.

Next, we find the area of the cross section and multiply it by the circumference of a circle with the same radius.

Finally, we add up all of these washer volumes to find the total volume of the solid.

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Binomials include formulas such as a + b, x - y, etc. For the expansion of a binomial raised to exponents 2 and 3, we have a set of algebraic identities. Examples are (a + b)2 = a2 + 2ab + b2.

Let us review the definition of a "binomial" before understanding the formulas for binomial expansion. An expression in algebra with two terms is called a binomial.

Binomials include formulas such as a + b, x - y, etc. For the expansion of a binomial raised to exponents 2 and 3, we have a set of algebraic identities. Examples are (a + b)2 = a2 + 2ab + b2.

However, what happens if the exponents are larger numbers? The expansion can be difficult to locate manually.

This procedure is made simpler using the binomial expansion formula. Learn the formula for the binomial expansion and a few examples with solutions.

The expansion of (a + b)3 can be found in Example 1.

Solution:

The sum of (a plus b)3

by applying the binomial expansion formula,

(x + y)n = nC 0 xn y0 + nC 1 xn-1 y1 + nC 2 xn-2 y2 + nC 3 xn-3 y3 +... + nC n 1 x yn-1 + nC n x0yn

(a + b)

3 = 3C

0  a3 + 3C

1  a(3 - 1) (3 - 1) b + 3C

2  a(3 - 2) (3 - 2) b2 + 3C

3  a(3 - 3) b3

= ( 3! / [(3-0)!0!] ) a3 + ( 3! / [(3-1)!1!] ) a(3 - 1) (3 - 1) b + ( 3! / [(3-2)!2!] ) a(3 - 2) (3 - 2) b2 + ( 3! / [(3-3)!3!] ) a(3 - 3) b3

= (a3 first) + (a2 second) + (a1 second) + (a0 third)

= a3 + 3 a2, b + 3 a b2, and b3

(A + B)3 = A3 + 3 A2 B + 3 A B 2 + B3.

The Complete Question.

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The heart rate is in beats per minute at rest and while running 72 times each minute.

150 times/minute friend's heartbeat in 3 minutes while running than while at rest

Part 1

When at rest, 18 times in 15 seconds.

1 second equals 18/15

= 1.2 cycles per second

1 minute equals 1.2x60

72 times each minute.

Part 2

10 seconds of running, 25 times.

1 second equals 25/10

= 2.5 seconds/minute

1 minute equals 2.5 x 60

150 times each minute.

Part 3

At rest, in 3 minutes, 72 x 3 = 216

Running for 3 minutes equals 150 x 3 = 450.

How many more times in three minutes does your friend's heart pulse while they are exercising than when they are not?

Response: 450 - 216

= 234 times

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Answer:

13 7/12

Step-by-step explanation:

5+7+13

4/12+3/12+7/12

The value of 845 divided by 3 will be 281 R 2.

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

In this case, 845 divided by 3 will be:

= 845 / 3

= 281 2/3

Therefore, 845 ÷ 3 = 281 R 2.

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Answer:

-2

Step-by-step explanation:

Δy =4- (-8) =12

Δx = -4 -2 = -6

12/(-6) =-2

The total number of micrograms present in the 65.3 kilograms is equal to 65,300,000,000 micrograms.

Conversion of units from kilogram to grams is :

1 kilogram = 1,000 grams

Conversion of units from grams to micrograms is :

1 grams  = 1,000,000 micrograms

⇒ 1 kilogram = ( 1,000 × 1,000,000 ) micrograms

⇒1 kilograms = 1,000,000,000 micrograms

Substitute the required value for the converting kilogram to micrograms we get,

⇒ 65.3 kilograms = ( 65.3 × 1,000,000,000 ) micrograms

⇒65.3 kilograms = 65,300,000,000 micrograms

Therefore, the total quantity of micrograms in 65.3 kilograms is equal to 65,300,000,000 micrograms.

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Answer:

The equation 2n + 1 = 157 represents the situation where the sum of two consecutive numbers is 157.

To find the first number, we can start by subtracting 1 from both sides of the equation:

2n = 156

Then we can divide both sides by 2:

n = 78

So the first number is 78, which corresponds to the answer choice B.

Step-by-step explanation:

the second, third, sixth, eighth, and tenth expressions did not properly express propositions because they cannot be proven true or false.

1. Yes

2. No

3. No

4. Yes

5. Yes

6. No

7. Yes

8. No

9. Yes

10. No

Propositions are statements that can be either true or false. Of the ten expressions provided, seven of them properly expressed propositions. The first expression, "Mike likes beer," is a proposition because it is a statement that can be proven true or false. The fourth expression, "An isosceles right triangle has two interior angles that are 45 degrees each and one interior angle that is 90 degrees," is also a proposition because it is a statement that can be proven true or false. The fifth expression, "Do you want another beer?," is a proposition because it is asking a question that can be answered with either a yes or a no. The ninth expression, "George Washington was not the first president of the United States," is a proposition because it is a statement that can be proven true or false. However, the second, third, sixth, eighth, and tenth expressions did not properly express propositions because they cannot be proven true or false.

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The lowest term of rational expression is 4z⁶/3

What is rational expression?

A rational expression is simply a quotient of two polynomials. Or in other words, it is a fraction whose numerator and denominator are polynomials.

Rational expressions look like fractions that have variables in their denominators (and often numerators too). For example, x 2 x + 3 \dfrac{x^2}{x+3} x+3x2 ​start fraction, x, squared, divided by, x, plus, 3, end fraction is a rational expression.

To write a rational expression in lowest terms, we must first find all common factors (constants, variables, or polynomials) or the numerator and the denominator. Thus, we must factor the numerator and the denominator. Once the numerator and the denominator have been factored, cross out any common factors.

A) The expression is undefined when x=10 or x=-5 because the denominator would be equal to zero, which is undefined in mathematics.

B) The rational expression 8z³/20z⁶ can be simplified to 2z³/5z⁶. The expression can be further simplified by dividing both the numerator and denominator by z³, giving us 2/5z³.

C) The expression 12-4/5y-36 is undefined when y=-9 or y=4 because the denominator would be equal to zero, which is undefined in mathematics.

D) The expression (99-3333)/2535 cannot be simplified as the numerator and denominator are prime numbers and cannot be further reduced.

So, the answer is:

A) x=10, x=-5

B) 2/5z³

C) y=-9, y=4

D) cannot simplify

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Answer:

[tex]m\angle A = 44\textdegree, a = 13.9, b = 18.0[/tex]

Step-by-step explanation:

Step 1: Solve for the Missing Angle

The measures of all of the interior angles of a triangle will always add up to [tex]180\textdegree[/tex]. Therefore,

[tex]m\angle A = 180\textdegree - (m\angle B + m\angle C) = 180\textdegree - (64\textdegree + 72\textdegree) = 44\textdegree[/tex]

Step 2: Solve for the Missing Sides

When we are given the side lengths and angle measures of a triangle, we can use either the Law of Sines or the Law of Cosines to solve for the rest of the triangle.

The Law of Sines is as follows: [tex]\frac{sinA}{a} = \frac{sinB}{b} = \frac{sinC}{c}[/tex]

The Law of Cosines is as follows: [tex]c^{2} = a^{2} +b^{2} -2abcosC[/tex] (you can exchange c for a or b, respectively)

In this case, we are only given 1 side length and all 3 angle measures, so it would be more appropriate to use the Law of Sines as we need at least 2 side lengths to use the Law of Cosines.

Now that we know which formula to use, let's start by solving for [tex]a[/tex], using the given values of [tex]c=19[/tex], [tex]\angle A = 44\textdegree[/tex], and [tex]\angle C = 72\textdegree[/tex].

Substituting these values in, we get:

[tex]\frac{sinA}{a} = \frac{sinC}{c} \\ \frac{sin44\textdegree}{a} = \frac{sin72\textdegree}{19}\\a=\frac{19sin44\textdegree}{sin72\textdegree} \approx \bf 13.9[/tex]

Repeating this process for [tex]b[/tex], this time using [tex]\angle B = 64\textdegree[/tex], we get:

[tex]\frac{sinB}{b} = \frac{sinC}{c} \\ \frac{sin64\textdegree}{b} = \frac{sin72\textdegree}{19}\\b=\frac{19sin64\textdegree}{sin72\textdegree} \approx \bf 18.0[/tex]

The percentage of buyers who paid more than $1790 is 2.275%.

The percentage of buyers who paid between $1505 and $1695 is 68.29%

The  percentage of buyers who paid between $1600 and $1885 is 15.73%

The relationship between a value and a set of values' mean is described by the statistical measurement known as the Z-score. Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score.

Given:

Let X be a random variable representing the prices paid for a particular model of HD television.

It is provided that X follows a normal distribution with mean, μ = $1600 and standard deviation, σ = $95.

1. P(X> 1790)

= P( Z> (1790- 1600)/ 95)

= P(Z> 2)

= 1- P(z< 2)

= 1- 0.97725

= 0.02275

= 2.275%

2. P( 1505 < X < 1695)

= P( -1 < Z < 1)

= 0.68269

3.  P( 1600 < X < 1885)

= P( 1 < Z < 3)

= P( Z< 3 ) - P(Z < 1)

= 0.99865 - 0.84134

= 0.15731

4. P( 1410 < X < 1600)

= P( - 2 < Z < 0)

= P( Z< 0 ) - P(Z < -2)

= 0.5 - 0.02275

= 0.47725

5. P (X> 1885)

= P( Z> 3)

= 1- P(Z<3)

= 0.0013

= 0.13%

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Drake uses 9/4 cup of sugar to make 9 mug of brownie. Then the amount of sugar needed to make one brownie is 1/4 cup of sugar.

Determine how much sugar is needed

These are the specified parameters:

9/4 cup of sugar to make 9 mug of brownie.

Determine much sugar to make one brownie

Lots of sugar = cup of sugar : mug of brownie

                      = 9/4 : 9

                      = 9/4 × 1/9

                       = 1/4

So the amount of sugar needed to make one brownie is 1/4 cup of sugar.

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Based on the information given, the old oak tree is 1 order of magnitude or ten times bigger in comparison to the younger oak tree.

In mathematics and related areas, the orders of magnitude compare two items or variables using 10 as a reference. In this way, if the value is 10 times bigger than another the order of magnitude is 1 (one zero), but if one value is 100 times bigger then the order of magnitude is 2(100 or 2 zeros).

1012 / 92 = 11 which means the order of magnitude is 1

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