How do I solve this?

The provided integral may be expressed as follows using the following statement as a guide: 128/3 - 31 [tex]\sqrt{17}[/tex] /3

An integral in mathematics is either a number that depicts the area underneath the graph of a function over a specific period of time or a about before, the reversed of which includes the initial result (indefinite integral). To complete the whole, an essential component is required. The term crucial is a close synonym in this context. Integrals of functional and equations are a concept in mathematics. The word "aal" is derived from Middle English, which is derived from Latin Word integralis "thinking up unity," from Latin "with, entire."

To find [tex]$\int_0^1 \frac{r^3}{\sqrt{16+r^2}} d r$[/tex]

Put [tex]$16+r^2=t^2$[/tex]

[tex]$2 r d r=2 t d t$[/tex]

[tex]$r d r=d t$[/tex]

[tex]$r=0 \Rightarrow t=4$[/tex]

[tex]$r=1 \Rightarrow t=\sqrt{17}$[/tex]

[tex]$\int_0^1 \frac{r^3}{\sqrt{16+r^2}} d r=\int_4^{\sqrt{17}} \frac{t^2-16}{t} t d t$[/tex]

[tex]$=\left[\frac{t^3}{3}-16 t\right]_4^{\sqrt{7}}$[/tex]

[tex]$=\frac{(\sqrt{17})^3}{3}-16(\sqrt{17})-\frac{(4)^3}{3}+64$[/tex]

[tex]$=\frac{128}{3}-\frac{31 \sqrt{17}}{3}$[/tex]

[tex]$\int_0^1 \frac{r^3}{\sqrt{16+r^2}} d r=\frac{128}{3}-\frac{31 \sqrt{17}}{3}$[/tex]

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Answer:

We can set up a system of equations using the information given:

x + 2y = 2830 (equation 1)

2x + y = 2540 (equation 2)

where x is the number of calories in one shake and y is the number of calories in one taco supreme.

We can use either equation to solve for one of the variables and then substitute that into the other equation.

From equation (1), x = 2830 - 2y

And substituting this into equation (2) we get

2(2830-2y) + y = 2540

Now we can solve for y.

5,660 - 4y + y = 2540

-3y = -3120

y = 1040

So, one taco supreme contains 1040 calories.

And substituting this value of y back into equation (1) we can find the number of calories in one shake:

x + 2(1040) = 2830

x = 550

So, one shake contains 550 calories.

The required number of ways to write 9 as sum of 1, 2, 4 is 96 ways.

An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are arranged in a linear or sequential order. For instance, the set A=1,6 has a permutation of 2, which is 1,6,1.

Two fours and one one Three numbers must be added up. Any one of the three spaces will accept a one before fours are used to fill the remaining slots. There are thus 3 possible arrangements for these. Thus, there are

1 + 8 + 21 + 6 + 20 + 20 + 5 + 12 + 3 = 96 ways

Thus, there are 96 ways to write 9 as sum of 1, 2, 4.

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The numbers are 4.5 and 13.5.

The ratio of two numbers = 1:3

Let the numbers be x and 3x.

After increasing each number by 9, the numbers will be x + 9 and 3x + 9.

Now, According to the question, after increasing each number by 9 the ratio becomes 3:5

Hence,         [tex]\frac{x + 9}{3x + 9}[/tex]  = [tex]\frac{3}{5}[/tex]

                  5x + 45 = 9x + 27

                  9x - 5x =  45 - 27

                     4x     = 18

                       x     = 18 / 4

                              = 4.5

if x = 4.5, then 3x = 4.5 * 3 = 13.5

So, the numbers are 4.5 and 13.5.

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There are two types of systems in mathematics: discrete systems, which are composed of distinct, separate elements, and continuous systems, which are composed of elements that are connected and can take on any value over a range.

1. Discrete systems: A system with distinct, separate elements, such as a set of integers or a graph.

2. Continuous systems: A system with elements that are connected and can take on any value over a range, such as a line or a curve.

1. Discrete systems: A discrete system is a system with distinct, separate elements. Examples include a set of integers, a graph, or a network of nodes. Discrete systems are usually studied using discrete mathematics.

2. Continuous systems: A continuous system is a system with elements that are connected and can take on any value over a range. Examples include a line, a curve, a function, or a surface. Continuous systems are usually studied using calculus.

There are two types of systems in mathematics: discrete systems, which are composed of distinct, separate elements, and continuous systems, which are composed of elements that are connected and can take on any value over a range. Discrete systems are studied using discrete mathematics, while continuous systems are studied using calculus.

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In the given scenario the pairing is natural pairing, hence the samples are dependent because there is a natural pairing between the two samples.

A pairing function in mathematics is a technique to convert two natural numbers into one natural number while maintaining their uniqueness. Insets and rational numbers share the same attributes as natural numbers, which may be shown in set theory using any pairing function.

In the given situation, the pairing between the prior drug sample and later drug sample are conducted in the same men. The results will thus, be dependent as same men will be required for the research to be conducted, and the effect of the drug before will also be taken into consideration.

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The possible number of handshakes in a group of 10 people, where each person shakes hands with everyone else once are equal to 45.

Number of people in the group = 10

Each person shakes hands with everyone else once. When n people shake hands with each other, the total number of handshakes = ⁿC₂

where C denotes the combination , is represent an arrangement of objects in different ways without care of order.

Total number of handshakes = ¹⁰C₂

= 10!/2!(10 - 2)! = 10!/2!×8!

= 10×9×8!/(2×1)8!

= (10×9)/2

= 45 handshakes.

In other words, when 10 people are shaking hands, each one will shake hands with 9 others. Then, the total possible number of handshakes in a group = 10 × 9 = 90

(but remember the point that , when A shakes hands with B, B is also shaking hands with A, i.e., we are counting one handshake twice, one from A's side and the other from B's side).

The total number of handshakes in actual way = 90/2 = 45 handshakes. Hence, the total number of handshakes in a group is 45.

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The value of (AB)² is 15.

A circle is a two-dimensional figure formed by a set of points that are at a constant or at a fixed distance (radius) from a fixed point (center) on the plane. The fixed point is called the origin or center of the circle and the fixed distance of the points from the origin is called the radius. Two circles can be called congruent if they have the same radius. Equal chords are always equidistant from the center of the circle. The perpendicular bisector of a chord passes through the center of the circle. When two circles intersect, the line connecting the intersecting points will be perpendicular to the line connecting their center points. Tangents drawn at the endpoints of the diameter are parallel to each other.

Equation of first circle:

(x - 2)² + (y + 1)² = 4²

Equation of secnd circle:

(x - 2)² + (y - 5)² = (√10)²

Solve for (x - 2)² :

(x - 2)² + (y + 1)² = 4²   ==>   (x - 2)² = 16 - (y + 1)²

(x - 2)² + (y - 5)² = (√10)²   ==>   (x - 2)² = 10 - (y - 5)²

Then,

16 - (y + 1)² = 10 - (y - 5)²

16 - (y ² + 2y + 1) = 10 - (y ² - 10y + 25)

15 - 2y - y ² = -15 + 10y - y ²

30 - 12y = 0

12y = 30

y = 30/12 = 5/2

Thus, the y coordinate of A and B is 5/2.

Then solve for x :

(x - 2)² = 16 - (5/2 + 1)²

(x - 2)² = 15/4

x - 2 = ± √(15/4) = ±√15/2

x = 2 ± √15/2

Thus, the x coordinates for either A or B are 2 +√15/2 or 2- √15/2.

The intersections points are A = (2 - √15/2, 5/2) and B = (2 + √15/2, 5/2). Thus, the squared distance between them:

(AB)² = [(2 - √15/2) - (2 + √15/2)]² + (5/2 - 5/2)²

(AB)² = (-√15)² + 0²

(AB)² = 15

Thus, the value of (AB)² is 15.

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The solution to the equations are

The number of blocks walked in 5 minutes = 4 blocks

The number of blocks walked in 30 minutes = 24 blocks

The time taken to walk 4 blocks = 5 minutes

The time taken to walk 12 blocks = 15 minutes

The time taken to walk 16 blocks = 20 minutes

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The time taken for the Scott family to walk 4 blocks = 5 minutes

So , time taken for the Scott family to walk 12 blocks = 3 x time taken for the Scott family to walk 4 blocks

Substituting the values in the equation , we get

Time taken for the Scott family to walk 12 blocks = 3 x 5 = 15 minutes

And ,

Time taken for the Scott family to walk 16 blocks = 4 x time taken for the Scott family to walk 4 blocks

Substituting the values in the equation , we get

Time taken for the Scott family to walk 16 blocks = 4 x 5 = 20 minutes

Now ,

Number of blocks walked in 5 minutes = 4 blocks

So , the number of blocks walked in 30 minutes = 6 x Number of blocks walked in 5 minutes

Substituting the values in the equation , we get

The number of blocks walked in 30 minutes = 6 x 4 = 24 blocks

Hence , the equations are solved

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Answer:

The bottom most option

Step-by-step explanation:

Lets divide 3 2/5 and 3 1/6

3 2/5 = 17/5 and 3 1/6 = 19/6

17/5/(19/6) = 17/5  x 6/19 = 102/95 = 1 7/95 or the last option.

Pls mark as brainliest for no real reason. Cheers

X=5times (root2)/2

Step-by-step explanation:

Sin45=x/5

x=5sin45

x=5 times root2/2

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A number or algebraic expression is said to be in its simplest radical form and to be an nth root if it lacks any elements that are perfect nth powers under the radical.

The term "simplest radical form" refers to the most basic representation of a number or algebraic expression. When a number or algebraic expression contains no elements that are perfect nth powers under the radical, it is said to be in its simplest radical form and be an nth root.

When all of a radical expression's perfect squares, cubes, etc. are eliminated from the radical, the radical is in its simplest form. A radical is a phrase containing a root, most frequently a square or cube root.

Simply put, simplifying a radical eliminates the need to find any more square roots, cube roots, fourth roots, etc. when expressing it in its simplest radical form. Additionally, it entails eliminating any radicals from the denominator of a fraction.

Sin45 = x/5

x = 5 sin 45

x = 5 × (√2)/2

Therefore, the value of x be x = 5 × (√2)/2

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Answer:

32

Step-by-step explanation:

[tex]8\sqrt{3}[/tex] is opposite to the 60 degree angle

The side opposite to the 60 degree angle = [tex]\sqrt{3}[/tex] times the side opposite to the 30 degree angle.

Side opposite to the 30 degree angle = 8

Leg opposite to the 30 degree angle theorem states that the side opposite to the 30 degree angle is half of the hypotenuse.

Hypotenuse = 16

In the big triangle, 16 is the side opposite to the 30 degree angle, which means it is half of the hypotenuse (big triangle).

Hypotenuse of the big triangle = x = 32

Hope this helps :)

Have a great day!

In given triangle ABC the length if BC is 7.1 .

What is trigonometric functions?

A subfield of mathematics called trigonometry is concerned with the study of triangles. It is frequently referred to as "trig" casually. In trigonometry, mathematicians look at how triangles' sides and angles relate to one another.

Here in given triangle contains 90°, So it is right triangle.

Now using tangent function then

=> tan B = [tex]\frac{opposite}{adjacent}[/tex] then

=> tan 38° = [tex]\frac{AC}{BC}[/tex]

=> BC = tan 38° × AC

=> BC = tan 38° × 9.1

=> BC = 7.1

Hence the length of the side BC is 7.1.

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The length of BC in the triangle ABC is 7.109.

Trigonometry is a branch of mathematics concerned with the study of triangles. It is commonly referred to as "trig" in a casual manner. Trigonometry examines how the sides and angles of triangles relate to one another.

Because the given triangle contains 90°, it is a right triangle.

Now, using the tangent function,

The tangent function is one of trigonometry's six primary functions.

Tan A = Opposite Side/Adjacent Side is the Tangent Formula. In terms of sine and cosine, tangent may be represented as: Tan A = Sin

then,

= tan B = opposite side / adjacent side

= tan 38° = AC/BC

= BC = 38° tan x AC

= BC = tan 38° × 9.1

= BC = 7.109

As a result, the length of the side BC is 7.109.

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The p-value is a probability and it should be between 0 and 1.

The p-value of a hypothesis test is the probability of obtaining a test statistic as extreme or more extreme than the one observed, assuming the null hypothesis is true.

In this case, the null hypothesis is that the population proportion of students who went to the movie theatre last weekend is equal to 0.2 and the alternative hypothesis is that the population proportion is greater than 0.2.

Given that the test statistic is 2.25, the p-value would be the probability of getting a test statistic as extreme or more extreme than 2.25 assuming the null hypothesis is true. Without more information, we can't give you an exact p-value, but you can use a one-sided test and find the p-value using a z-table or using software that can calculate the p-value.

It is also important to note that the p-value is a probability and it should be between 0 and 1.

Therefore,  The p-value is a probability and it should be between 0 and 1.

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On solving the provided question, we can say that unlike other shapes, which all have parallel lines, only has one parallel side.

Parallel lines in geometry are coplanar infinite lines that don't intersect anywhere. In a given three-dimensional space, parallel planes are those that never cross. Curves with a constant minimum distance between them and no points of contact or intersection are said to be parallel. Two lines that are in the same plane, equally spaced apart, and never intersect are referred to as parallel lines in geometry. Either horizontal or vertical can apply. Parallel lines can be noticed in everyday objects like railroad tracks, rows of notebooks, and pedestrian crossings.

unlike other shapes, which all have parallel sides, only has one parallel side.

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Answer:

  CD = 3/√2 in

Step-by-step explanation:

You want the measure of altitude CD in isosceles right triangle ACB with the right angle at C.

All of the isosceles right triangles in this figure are similar, and all have sides in the ratio 1 : 1 : √2.

In ∆BCD, side BC is the longest, given as 3 in. That means the other two sides of that triangle are ...

  CD = BD = CB/√2

  CD = 3/√2 in

__

Additional comment

Often, we like to rationalize the denominator of expressions involving roots. That would make the expression for CD be ...

  CD = 3/√2 = (3/2)√2 = 1.5√2

<95141404393>

In this scenario, the number of winning tickets follows a binomial distribution, since each ticket has a fixed probability of winning (1/4) and the trials (purchasing a ticket) are independent.

The probability that k out of n trials will be successful is given by the binomial probability mass function:

P(k) = (n choose k) * p^k * (1-p)^(n-k)

Where n is the number of trials (100 tickets), k is the number of successful trials (winning tickets), p is the probability of success (1/4), and (n choose k) is the binomial coefficient.

To find the probability that fewer than 20 tickets are winners we have to calculate the probability of getting 0 to 19 winning tickets.

P(x<20) = P(0) + P(1) + P(2) +...+ P(19)

using the above formula we can find the probability of getting k winning tickets

P(x<20) = P(0) + P(1) + P(2) +...+ P(19)

= (100 choose 0) * (1/4)^0 * (3/4)^100 + (100 choose 1) * (1/4)^1 * (3/4)^99 +.... + (100 choose 19) * (1/4)^19 * (3/4)^81

This can be calculated using a calculator or spreadsheet software, however, it's not possible for me to provide you with the exact answer as it involves multiple complex calculations.

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Yes, a function can have 3 roots. This means that the function has 3 values of x where the y value is equal to 0. A polynomial of degree 3 or higher can have 3 roots.

Yes, a function can have 3 roots. A root of a function is a value of x for which the y value of the function is 0. This means that when a function has 3 roots, it has 3 values of x for which the y value of the function is 0. To have 3 roots, the function must be a polynomial of degree 3 or higher. A polynomial of degree 3 is usually written in the form ax^3 + bx^2 + cx + d = 0. This equation can be solved using the quadratic formula to find the 3 roots, which will be the 3 values of x for which the y value of the function is 0. The roots of the polynomial can also be found graphically by plotting the polynomial and finding where it intersects with the x-axis. This will be the 3 roots of the function.

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$45.38 and $46.42 is the  interval can the branch manager be 95% certain that the sample mean will fall within

Using the Central Limit Theorem, the branch manager can be 95% certain that the sample mean will fall within $1.034 of the mean.

What does the Central Limit Theorem state?

It states that the sampling distribution of sample means of size n has standard deviation .

By the Empirical Rule, 95% of the sample means fall within 2 standard errors of the mean.

In this problem, we have that the standard deviation and the sample size are given as follows:

Hence the standard error is given by:

[tex]s = \frac{10.34}{\sqrt{400}} = 0.517.

Two standard errors is represented by:

2 x 0.517 = $1.034.

Hence, the branch manager can be 95% certain that the sample mean will fall within $1.034 of the mean.

$45.38 and $46.42 is the  interval can the branch manager be 95% certain that the sample mean will fall within

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Answer:

14.8%

Step-by-step explanation:

decrease = -100 * ((final - initial) / initial)

Answer:

14.8%

Step-by-step explanation:

Original fishing pole cost: $54

New fishing pole cost: $46

Using the percentage decrease formula:

[tex]\frac{Original Value - Final Value}{|Original Value|}[/tex]  ×100%

Substitute

[tex]\frac{54-46}{|46|}[/tex] ×100%

From this, you should get 14.814814814814814...

Round to nearest tenths.

Final answer: 14.8%

The distribution used to obtain the critical value in this situation is the Student's t-distribution.

Critical value is a statistical value used to determine whether a hypothesis test result is statistically significant or not. It is the value that is compared to the test statistic to determine whether the null hypothesis should be rejected or not. The critical value is determined by the level of significance chosen for the study, the sampling distribution of the test statistic, and the degrees of freedom.

The Student's t-distribution is a symmetric probability distribution that is used when the population standard deviation is unknown. It is used in situations where there is a small sample size (less than 30) and the sample is drawn from a normally distributed population. In this case, the owner is interested in developing a 90% confidence interval estimate, so the critical value will be obtained from the Student's t-distribution.

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Stratified sampling is used when the population is heterogeneous.

What is Stratified sampling?

A method of probability sampling (where all members of the population have an equal chance of being included) Population is divided into 'strata' (sub-populations) and random samples are drawn from each. This increases representativeness as a proportion of each population is represented.

The sampling method described in the study is a stratified sampling method.

In stratified sampling, the population is first divided into subgroups or strata based on some relevant characteristic, such as size in this case.

Then, a simple random sample is taken from each stratum.

In this study, the sample is chosen by separating all cars by size and selecting 10 of each size grouping, this is the definition of stratified sampling.

Stratified sampling is useful when the population is heterogeneous and you want to ensure that the sample is representative of specific subgroups within the population.

This method allows for a more precise estimation of population characteristics and can reduce sampling error.

Hence, Stratified sampling is used when the population is heterogeneous.

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Answer:

(motorboat speed is 40 km/h)

(current speed) = 10 km/h

Step-by-step explanation:

Ok, let the speed of the water current be x and the speed of the motorboat be y. Then, the speed of the motorboat upstream

against the current is (x - y)

Putting it into the equation, we get,

5h (x - y) = 150 km or

(x - y) = 30 km/h -  1

Now, downstream speed is (x + y).

Again, forming it into equation, we get,

3(x + y) = 150

x + y = 50 km/h  -   2

Adding both equations, we get,

2x = 80 km/h

x (motorboat speed is 40 km/h)

40 - y = 30 km/h

y(current speed) = 10 km/h

Answer:

still water (s): 40 mph

current rate (c): 10 mph

Step-by-step explanation:

We are given two things:

1) 5 hours to travel 150 mi upstream

2) return trip 3 hours downstream

Note that when the boat goes upstream, it must push against the current, versus when it goes downstream, the current helps the boat to move. Also keep in mind the trip is always 150 mi both ways.

With that said, lets set up the problem. First, let s be the rate of the boat in still water, and let c be the rate of the current. We must keep in mind that when the boat goes upstream, it impedes its overall speed. So our equation for that looks like:

5(s-c)=150 (use for upstream)

And downstream would look like:

3(s+c)=150 (use for downstream)

Now that we have both equations, the next step is to expand them. You should get the two following equations:

5s-5c=150 AND 3s+3c=150.

Essentially, we are going to need to solve a system of equations here. You must add them to solve. First, multiply the first equation above by 3 and get 15s-15c=450 and multiply the second one by 5 and get 15s+15c=750.

When we add them we will get the following equation as a result: 30s=1200. Now divide both sides by 30 revelaing s to be 40. Now substiute in:

3(40)+3c=150

120+3c=150

-120      -120

3c=30

c=10

The system of equations is now solved revelaing the speed of the boat in still water to be 40 and the current speed to be 10.

Answer:

Equation is 14h = 91

It solves to  h = 6.5

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

Work Shown:

h = number of hours worked

14h = amount earned at $14 per hour

14h = 91 is the equation

To solve this equation, divide both sides by 14.

14h = 91

14h/14 = 91/14

h = 6.5

She worked 6.5 hours last week.

the probability that none of the student's purchases arrive the next day

P( STUDENT) = 0.99 - 0.97 = 0.002

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

here,

the probabilities of next day orders arriving on time for each retailer are 0.99, 0.97, and 0.96,

the probability that none of the student's purchases arrive the next day

P( STUDENT) = 0.99 - 0.97 = 0.002

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Answer:

Jeffrey drove a total of 303.43 miles on Monday, Tuesday, and Wednesday.

Step-by-step explanation:

To find the total miles driven by Jeffrey on Monday, Tuesday, and Wednesday, we need to add up the total miles. The total miles driven are 146.3 + 84.13 + 73.02 = 303.43 miles.

The minimum number of 1 point foul shots that your team must make to win the game is given as follows:

20.

The expression for this problem is defined as follows:

3p + 2f + s.

In which the variables are given as follows:

The opponent made these following shots:

Hence the number of points of the opponent is given as follows:

8 x 3 + 12 x 2 + 11 = 59.

Your team made these following shots:

Hence the number of points of your team is given as follows:

10 x 3 + 8 x 2 + x = 40 + x.

The team wins when:

40 + x > 59

x > 19

Hence the minimum number is of 20, as the number of one point shots is a discrete amount.

Your basketball team made 10 three-pointers, 8 two-point field goals, and x one-point foul shots.

Your opponents made 8 three-pointers, 12 two-point field goals, 11 one-point foul shots.

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Check the picture below.

[tex]cos(Y )=\cfrac{\stackrel{adjacent}{6}}{\underset{hypotenuse}{15}}\implies cos(Y)=\cfrac{2}{5}\implies cos^{-1}[cos(Y)]=cos^{-1}\left( \cfrac{2}{5}\right) \\\\\\ Y=cos^{-1}\left( \cfrac{2}{5}\right) \implies Y\approx 66.4^o[/tex]

Make sure your calculator is in Degree mode.

Answer:

66.4

Step-by-step explanation:

Hope this helped!

Answer:

2023

Step-by-step explanation:

3 + 4x = y

y = 3 + 4(505)

y = 3 + 2020

y = 2023

I would recommend taking this bet, as the expected value of the bet is Positive.

The expected value of a bet is the sum of the product of each possible outcome and its corresponding probability. In this case, the probability of getting two heads is 0.25, and the payout for that outcome is $10. The probability of not getting two heads is 0.75, and the payout for that outcome is -$2. When you multiply each outcome by its corresponding probability and sum them together, the expected value of the bet is $1.0. Because the expected value of the bet is positive, it is  a good bet to take. It is more likely that you will gain money .

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