i need help with this math problem

Answer:

/13=3.60

(a)^2+(b)^2=(c)^2

(6)^2+(3.60)^2=(c)^2

36+13=(c)^2

49=(c)^2

c= /49

c=7

Step-by-step explanation:

pythagorean theorem is (a)^2+(b)^2=(c)^2

then replace it with the given values

inverse of square is squareroot

Answer:

third side is 7 units

Step-by-step explanation:

Hi there!

the Pythagorean theorem is given as a²+b²=c², where a and b are legs (the sides that make up the right angle) and c is the hypotenuse (side that is opposite to the right angle, or in this case, the third side)

we are given the lengths of the 2 legs, and we need to find the hypotenuse

a=6

b=√13

c=unknown value

square the values of a and b, add them together, and set that to equal c squared

or in other words:

6²+(√13)²=c²

36+13=c²

(because 6*6=36; √13*√13=13)

49=c²

√49=√c²

7=c

therefore the hypotenuse is 7 units

Hope this helps!

Answer:9,000

Step-by-step explanation:

Using the given conditions that sin(20) = cos(2u) = tan(24) = 3, we can find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas. By substituting the known values into the formulas, we can determine the exact values of these trigonometric functions.

Given sin(20) = 3, we can use the double-angle formula for sine to find sin(2u).

The double-angle formula for sine is sin(2u) = 2sin(u)cos(u). We know that sin(u) = -3/5, so we can substitute this value into the formula to calculate sin(2u).

Therefore, sin(2u) = 2(-3/5)(cos(u)).

Given cos(2u) = 3, we can use the double-angle formula for cosine to find cos(2u).

The double-angle formula for cosine is cos(2u) = cos^2(u) - sin^2(u). Since we already know sin(u) = -3/5 and cos(u) can be calculated using the Pythagorean identity (cos^2(u) = 1 - sin^2(u)), we can substitute these values into the formula to determine cos(2u).

Finally, given tan(24) = 3, we can use the double-angle formula for tangent to find tan(2u).

The double-angle formula for tangent is tan(2u) = (2tan(u))/(1 - tan^2(u)). By substituting the known value of tan(24) = 3 into the formula, we can calculate the exact value of tan(2u).

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Answer:

A.P(t) = Po (1 + r)^t

P(t) = 1200( 1 + 0.024)^t

B. 1417 termites

Step-by-step explanation:

Rosanne and Jimmy are looking to purchase a house. They found one that they like, but the inspection report showed that there was a problem. The foundation has termites. The report states that the foundation of a house has 1200 termites. The termites grow at a rate of about 2.4% each day.

A. Formulate an equation in exponential form that represents the termite situation.

The formula for exponential growth or increase =

P(t) = Po (1 + r)^t

Where:

P(t) = Population growth after time t

P(o) = Initial Population = 1200 termites

r = Growth rate = 2.4% = 0.024

t = Time in days

Hence, the equation in exponential form that represents the termite situation is given as:

P(t) = 1200( 1 + 0.024)^t

B. The extermination is scheduled out for one week from the date of the report. Use your equation to determine how many termites will be in the home at the time of the extermination.

The time of extermination = 1 week

1 week = 7 days

Hence,

t = 7 days

P(t) = Po (1 + r)^t

P(7) = 1200( 1 + 0.024)⁷

P(7) = 1200(1.024)⁷

P(7) = 1416.7099449 termites

Approximately

= 1417 termites

Christine's grades for last semester were A, B, C, and C. An A is worth 4 points, a B is worth 3 points, a C is worth 2 points, and a D is worth 1 point. Her total grade points were 40 and her total credit hours were 14, resulting in a GPA of 2.86 if all courses were weighted the same.

Based on the information provided, the appropriate values in the Grade Value column for each grade are:

A: 4

B: 3

C: 2

D: 1

To calculate Christine's GPA if all courses were weighted the same, we need to first calculate her total grade points and divide by the total credit hours. The grade points for each course are calculated by multiplying the grade value by the credit hours. The table can be completed as follows

To calculate the GPA, we divide the total grade points (40) by the total credit hours (14):

GPA = 40/14 = 2.86

Therefore, if all courses were weighted the same, Christine's GPA would be 2.86.

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

" Name The goal of the first few questions will be to compute a grade point average, which is a good example of weighted grading Courses with more credit hours contribute more to the GPA than those with less Below are the grades that our friend Christine earned last semester. You'll he filling in the rest of the table as you work through Questions 14 Grade Grade Value Grade Points Course English Math Credit Hours 3.0 4.0 History Science 5.0 Totals: 1. In most GPA systems, an A is worth 4 points, a B is worth 3 points, a C2 points, and a D l point. Fill in the appropriate values in the Grade Value column. 4. What would her GPA have been if all courses were weighted the same? How did you decide"--

To estimate the mean per capita income for a major city in California with an error of at most $0.56 at the 85% confidence level, the economist needs to determine the required sample size.

To calculate the required sample size, we can use the formula: \(n = \left(\frac{{Z \cdot \sigma}}{{E}}\right)^2\), where \(n\) is the sample size, \(Z\) is the Z-score corresponding to the desired confidence level (in this case, for 85% confidence level, \(Z \approx 1.44\)), \(\sigma\) is the known standard deviation (\$6.6), and \(E\) is the desired margin of error (\$0.56). Plugging in the values, we have \(n = \left(\frac{{1.44 \cdot 6.6}}{{0.56}}\right)^2 \approx 52\). Therefore, a sample size of approximately 52 would be required to estimate the mean per capita income with an error of at most $0.56 at the 85% confidence level.

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Answer:

0.6, 3/5

Step-by-step explanation:

60%=

100% * 60/100=

1*60/100=

60/100=6/10=0.6

6/10=3/5

Answer:

y=3x+14

Step-by-step explanation:

We can use point-slope intercept form to find the equation of the line.

Equation: y-y₁=m(x-x₁)

**For a line to be perpendicular to another, its slopes must be negative reciprocals of each other. So, in our example, the slope of the new line must be \(\frac{1}{3}\).

1. Plug in provided info into the equation listed above (the coords are the values that we will put for x₁ and y₁:

    y-5=\(\frac{1}{3}\)(x-(-3))

2. Simplify:

    y-5=\(\frac{1}{3}\)(x+3)

3. Distribute & Simplify

    y-5=\(\frac{1}{3}\)x+1

3. Add 5 to both sides of the equation:

    y=\(\frac{1}{3}\)+6

The equation of the line that passes through (-3, 5) and is perpendicular to the line y=-3x-1 is y = x/3 + 20/3.

For the given question;

The equation of the perpendicular line is given as;

y=-3x-1

Compare with the standard slope intercept form.

y = mx + c

m is the slope and c is the y intercept.

Say slope m1 = -3

Then, the relation for the slopes of two perpendicular lines are-

m1 x m2 = -1

m2 = -1/m1

m2 = -1/-3 = 1/3

This, line with the slope 1/3 passes through the points;

(x1, y1) = (-3, 5)

The equation of the line is obtained as;

y - y1 = m2(x - x1)

y - 5 = (1/3)(x + 5)

y = x/3 + 20/3

Thus, the equation of the line that passes through (-3, 5) and is perpendicular to the line y=-3x-1 is y = x/3 + 20/3.

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Expected Value (E(x)):

E(x) = Σ(x * P(x))

E(x) = 1.20 + 4.00 + 3.00

E(x) = 8.20

Variance:

Variance = Σ([x - E(x)]^2 * P(x))

Variance = ([6 - 8.20]^2 * 0.20) + ([8 - 8.20]^2 * 0.50) + ([10 - 8.20]^2 * 0.30)

Variance = (4.84 * 0.20) + (0.04 * 0.50) + (1.96 * 0.30)

Variance = 0.968 + 0.020 + 0.588

Variance = 1.576

Standard Deviation:

Standard Deviation = √Variance

Standard Deviation = √1.576

Standard Deviation ≈ 1.25

Therefore, the calculations for the given discrete probability distribution are as follows:

Expected Value (E(x)) = 8.20

Variance = 1.576

Standard Deviation ≈ 1.25

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(i) The set of boundary points of S is {1}.

(ii) There are no interior points in S.

(iii) S is not an open set because it does not contain any interior points.

(iv) S is a closed set because it contains all of its boundary points.

Let's analyze the set S step by step:

(i) Boundary points of S:

A boundary point of a set is a point that is neither an interior point nor an exterior point. In this case, since S consists of the elements x = 1 - 1/n for n = 1, 2, 3, ..., we can see that as n approaches infinity, x approaches 1. So, the set of boundary points of S is {1}.

(ii) Interior points of S:

An interior point of a set is a point that has an open neighborhood contained entirely within the set.

In this case, since S is defined as x = 1 - 1/n for n = 1, 2, 3, ..., we can see that as n increases, x approaches 1.

However, for any n, we can always find another n' greater than n such that 1 - 1/n' is closer to 1.

Therefore, there are no interior points in S.

(iii) S as an open set:

An open set is a set that contains all of its interior points.

Since S has no interior points (as discussed in part ii), it cannot contain all of its interior points.

Therefore, S is not an open set.

(iv) S as a closed set:

A closed set is a set that contains all of its boundary points.

In this case, the set of boundary points of S is {1}, and this set is contained within S itself.

Therefore, S contains all of its boundary points and is considered a closed set.

In summary, the set S has a single boundary point {1}, no interior points, is not an open set, and is a closed set.

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The expression equivalent to \((x + 3)/(x^2 - 2x - 3)\)divided by \((x^2 + 2x - 3)/(x + 1)\) is option (d) x + 3/(x + 1).

To simplify the given expression, we need to divide the numerator of the first fraction by the denominator of the second fraction and vice versa.

The expression \((x + 3)/(x^2 - 2x - 3)\) divided by \((x^2 + 2x - 3)/(x + 1)\) can be rewritten as\((x + 3)/(x^2 - 2x - 3)\)multiplied by\((x + 1)/(x^2 + 2x - 3).\)

Now, let's simplify the individual fractions:

The numerator (x + 3) and denominator \((x^2 + 2x - 3)\))in the first fraction cannot be further simplified.

The numerator (x + 1) and denominator\((x^2 + 2x - 3)\) in the second fraction can also not be simplified.

When we multiply the fractions, the resulting expression is (x + 3)(x + \(1)/(x^2 - 2x - 3)(x^2 + 2x - 3).\)

By multiplying the numerator and denominator, we get \((x^2 + 4x + 3)/(x^4 - 4x^2 + 9).\)

However, this expression is not equivalent to any of the given options. It seems that none of the provided options match the simplified expression.

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Answer: Click on this: a=13.6cm,b=9.5cm and c=2.6cm for the triangle show it has a step by step way

Step-by-step explanation:

Answer: A good way to get a small standard error is to use a large sample.

Step-by-step explanation:

In order to find the small standard error, there is always need of a complete set which is called the large sample.

If tried to do a small or repeating sample, you will most likely not get an error and you could get a repetition. If you do a population sample, you wont get accurate results at all.

Therefore, a good way to get a small standard error is to use a large sample. Hope this helps!

-From a 5th Grade Honors Student

9514 1404 393

Answer:

Step-by-step explanation:

Like terms are ones with the same variable (or set of variables). Here, any x-terms are "like" terms. They are combined by adding their coefficients.

  4x +4x +4x +4x = x(4+4+4+4) = 16x

  -7x +4 +3x = x(-7+3) +4 = -4x +4

  3x +5x +8 = x(3+5) +8 = 8x +8

  4x +4x = x(4+4) = 8x

The volume of air in the spherical ball is \(\frac{4}{3}\cdot \pi\cdot 3^3\cdot 10^6\). So the option A is correct.

In the given question, we have to find the volume of air in the spherical ball.

A sphere's capacity is measured by its volume. It is the area the sphere calls home. Cubic units are used to express the volume of a sphere. The sphere has a three-dimensional, rounded shape. Its shape is defined by its three axes, which are the x, y, and z axes.

Since the cross-section of the sphere is a circle, the volume in this situation is dependent on the radius's diameter. A sphere's surface area is the area or region of its outside. The following formula can be used to determine the volume of a sphere whose radius is "r":

V = \(\frac{4}{3}\pi r^{3}\)

As given r = 3·10^2. So,

V = \(\frac{4}{3}\pi (3\cdot 10^2)^{3}\)

V = \(\frac{4}{3}\cdot \pi\cdot 3^3\cdot 10^6\)

V = \(4\cdot \pi\cdot 3^2\cdot 10^6\) cm^3

Hence, the option A is correct.

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The complete question is given below:

Answer:

The answer is y = 3x + 3.

Step-by-step explanation:

Hope it helped!

Answer:

\(z=1 \\ z=-7\)

Step-by-step explanation:

Pretty straightforward question. We have the following definite integral:

\($\int\limits^z_0 {\dfrac{1}{3}x - 1} \, dx $\)

and this integral equals to \(\dfrac{7}{6}\). We want to find the value of \(z\)

Considering the property that the integral of the sum of functions \(f\) and \(g\) equals the integral of \(f\) plus the integral of \(g\), we have

\($\int\limits^z_0 {\dfrac{1}{3}x - 1} \, dx = \int _0^z\frac{1}{3}x \, dx-\int _0^z1 \,dx$\)

Now we just have to solve each integral.

\($\int _0^z\dfrac{1}{3}x \, dx = \dfrac{1}{3}\int _0^zx \, dx = \left[\dfrac{1}{3}\cdot \dfrac{x^2}{2}\right] \Big |_0^z = \dfrac{x^2}{6} \Big |_0^z = \dfrac{z^2}{6} - \dfrac{0^2}{6} =\boxed{ \dfrac{z^2}{6}}$\)

Explanation: 1/3 is a constant, that's why we ended up calculating the integral on the given interval for \(x\). Then, for the integral of \(x\) I just calculated the antiderivative, given as \(x^n = \dfrac{x^{n+1}}{n+1}\) for \(n=1\) and the Fundamental Theorem of Calculus.

For the other integral, we just have the definite integral of a constant.

\($\int _0^z1 \,dx = 1(z-0) = \boxed{z}$\)

Therefore,

\($\int\limits^z_0 {\dfrac{1}{3}x - 1} \, dx = \dfrac{z^2}{6} + z$\)

Now we can solve

\($\dfrac{z^2}{6} + z = \dfrac{7}{6} \implies z^2+6z-7=0 \implies z = \frac{-6\pm \sqrt{6^2-4\cdot 1\cdot (-7)}}{2\cdot 1}$\)

\(z=1 \\ z=-7\)

Answer:

b) 516.2 cm³

Step-by-step explanation:

1) We can break the figure into two parts, a rectangular prism and a half cylinder.

2) The volume of the rectangular prism can be determined by multiplying 12 × 7 × 5, which is 420.

3) The equation for the volume of a cylinder is πr²h, but since this is half a cylinder, we will need to use the equation 1/2 × πr²h.

4) 1/2 × π × 3.5² × 5. The radius is 3.5, because the diameter is 7.

5) This should give us 30.625π.

6) Now we add 30.625π + 420, which is approximately 516.2.

Answer:

the answer for question no 8 is. option second...ie 17

Equations -

\( - 6p = 48\)

Divide -6p using inverse operations!

\(\frac{ - 6p}{ - 6} = p\)

\( \frac{48}{ - 6} = - 8\)

\(p = - 8\)

\( - 8 \times - 6 = 48\)

The mathematical average of the number of feet in a yard, seconds in a minutes and months in a year is 25.

In Mathematics and Geometry, the arithmetic average for any data set can be calculated by using the following formula:

Arithmetic average = [∑(x)]/n

Generally speaking, we have the following standard parameters;

∑(x) = 3 + 60 + 12

∑(x) = 75

Now, we can determine the arithmetic average as follows;

Arithmetic average = 75/3

Arithmetic average = 25.

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Answer: y = 5x + 26

Step-by-step explanation:

To find the equation of a line that is perpendicular to the given line y = -1/5x + 1 and passes through the point (-5, 1), we need to determine the slope of the perpendicular line. The given line has a slope of -1/5. Perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of the perpendicular line will be the negative reciprocal of -1/5, which is 5/1 or simply 5. Now, we have the slope (m = 5) and a point (-5, 1) that the perpendicular line passes through.

We can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Substituting the values, we get:

y - 1 = 5(x - (-5))

Simplifying further:

y - 1 = 5(x + 5)

Expanding the brackets:

y - 1 = 5x + 25

Rearranging the equation to the slope-intercept form (y = mx + b):

y = 5x + 26

Therefore, the equation of the perpendicular line that passes through the point (-5, 1) is y = 5x + 26.

Answer:

D

Step-by-step explanation:

first do what's in the parenthesis, so 2x10 is 20 and 20 divided by 2 is 10.

10 x 5 is 50

Hope this helped :)

Answer:

D. Zero is not a rational number.

Step-by-step explanation:

0 is a rational number because it has a non-zero denominator.

So, option D is wrong.

Answer:

B) True

D) False

C) True

A) True

Step-by-step explanation:

Counting numbers are 1,2,3...   The ... means the pattern continues

Whole numbers 0,1,2,3...

Integers ...-3, -2, -1, 0, 1, 2, 3....

Rational numbers:\(\frac{integer}{integer}\)

Answer:

Yes, These numbers 10, 7, and 13 can form a triangle

Step-by-step explanation:

Let us use this theorem to solve the question

∵ The numbers are 10, 7, 13

∵ 10 + 7 = 17

∵ 17 > 13

∴ The sum of 10 and 7 is greater than the 3rd number 13

∵ 10 + 13 = 23

∵ 23 > 7

∴ The sum of 10 and 13 is greater than the 3rd number 7

∵ 7 + 13 = 20

∵ 20 > 10

∴ The sum of 7 and 13 is greater than the 3rd number 10

∵ The sum of every two numbers is greater than the 3rd number

→ By using the theorem above

∴ The numbers 10, 7, and 13 can form a triangle

The work required to pump all the water over the edge of the tank is approximately 271,433.64 foot-pounds.

To calculate the work required to pump all the water over the edge of the tank, we need to consider the weight of the water in the tank and the height it is lifted.

First, let's find the volume of the water in the tank. The volume of a cone is given by the formula V = (1/3)πr²h, where r is the radius and h is the height. Plugging in the values, we have:

V = (1/3)π(3²)(12)

= (1/3)π(9)(12)

= 36π

Next, we need to find the weight of the water. The weight of an object is given by the formula W = mg, where m is the mass and g is the acceleration due to gravity. The mass of the water can be found by multiplying its volume by the density of water, which is approximately 62.4 pounds per cubic foot:

m = (36π)(62.4)

≈ 22619.47 pounds

Now, we can calculate the work done by multiplying the weight of the water by the height it is lifted. In this case, the height is 12 feet:

W = (22619.47)(12)

≈ 271433.64 foot-pounds

Therefore, the work required to pump all the water over the edge of the tank is approximately 271,433.64 foot-pounds.

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The work required to pump water out of an inverted conical tank involves calculating the pressure-volume work at infinitesimally small volumes within the tank and integrating this over the entire volume of the tank. This provides an interesting application of integral calculus in Physics.

The question requires the concept of work in Physics applied to a fluid, in this case, water lying within an inverted conical tank. Work is done when force is applied over a distance, as stated by work = force x distance. In the fluid analogy, the 'force' link is the pressure exerted on the water and the distance is the change in volume of the fluid. Therefore, work done (W) = Pressure x Change in Volume (ΔV).

In this scenario, you are required to pump out water from an inverted conical tank, hence, the work you do is against the gravitational force pulling the water downwards. To calculate the total work done, you have to consider the work done at each infinitesimally small (hence, constant pressure) strip of volume and integrate over the entire volume of the tank.

The detail of calculation would require the knowledge of integral calculus and the formula for volume of a cone. I recommend considering this as an interesting application of integrals in Physics. Also remember that the volume of a cone = 1/3πr²h, where 'r' is the radius of base and 'h' is the height of cone.

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To decide whether it is sensible for Stacy to utilize the ordinary show for the inspecting conveyance of the test extent, we got to check whether the conditions for utilizing the typical conveyance estimation are met. The conditions are:

The test estimate is expansive sufficient

The test information is autonomous

The populace is at slightest 10 times bigger than the test

The test estimate, in this case, is 50. To check whether it is expansive sufficient, ready to utilize the run the show of thumb that the test measure ought to be at the slightest 10% of the populace estimate.

Hence, based on these conditions, it is sensible for Stacy to utilize the ordinary demonstration for the inspecting conveyance of the test extent. She can accept that the testing dispersion is roughly typical with a cruel of p = 0.11 and a standard deviation of sqrt[(p(1-p))/n] = sqrt[(0.11(0.89))/50] = 0.05.

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