Bob is building a deck that is 26.5 feet long, and he has posts that are 6 inches square to use to build the railing. If he puts theposts 6 feet apart with one on each end, how many posts will he use?

Answer:

\(\displaystyle \frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Step-by-step explanation:

This can be solved with either the washer (easier) or the shell method (harder). For the disk/washer method, the slice is perpendicular to the axis of revolution, whereas, for the shell method, the slice is parallel to the axis of revolution.  I'll show how to do it with both:

Shell Method (Horizontal Axis)

\(\displaystyle V=2\pi\int^d_cr(y)h(y)\,dy\)

Radius: \(r(y)=2-y\) (distance from y=2 to x-axis)

Height: \(h(y)=2-(-\ln y)=2+\ln y\) (\(y=e^{-x}\) is the same as \(x=-\ln y\))

Bounds: \([c,d]=[e^{-2},1]\) (plugging x-bounds in gets you this)

Plugging in our integral, we get:

\(\displaystyle V=2\pi\int^1_{e^{-2}}(2-y)(2+\ln y)\,dy=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Washer Method (Parallel to x-axis)

\(\displaystyle V=\pi\int^b_a\biggr(R(x)^2-r(x)^2\biggr)\,dx\)

Outer Radius: \(R(x)=2-e^{-x}\) (distance between \(y=2\) and \(y=e^{-x}\))

Inner Radius: \(r(x)=2-1=1\) (distance between \(y=2\) and \(y=1\))

Bounds: \([a,b]=[0,2]\)

Plugging in our integral, we get:

\(\displaystyle V=\pi\int^2_0\biggr((2-e^{-x})^2-1^2\biggr)\,dx\\\\V=\pi\int^2_0\biggr((4-4e^{-x}+e^{-2x})-1\biggr)\,dx\\\\V=\pi\int^2_0(3-4e^{-x}+e^{-2x})\,dx\\\\V=\pi\biggr(3x+4e^{-x}-\frac{1}{2}e^{-2x}\biggr)\biggr|^2_0\\\\V=\pi\biggr[\biggr(3(2)+4e^{-2}-\frac{1}{2}e^{-2(2)}\biggr)-\biggr(3(0)+4e^{-0}-\frac{1}{2}e^{-2(0)}\biggr)\biggr]\\\\V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\biggr(4-\frac{1}{2}\biggr)\biggr]\)

\(\displaystyle V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\frac{7}{2}\biggr]\\\\V=\pi\biggr(\frac{5}{2}+4e^{-2}-\frac{1}{2}e^{-4}\biggr)\\\\V=\pi\biggr(\frac{5}{2}+\frac{4}{e^2}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4}{2e^4}+\frac{8e^2}{2e^4}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4+8e^2-1}{2e^4}\biggr)\\\\V=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Use your best judgment when deciding on what method you use when visualizing the solid, but I hope this helped!

Answer:

42 or 48

Step-by-step explanation:

It's a acute angle so it's that one or that one.

Answer:

42 degrees

Step-by-step explanation:

180-132 = 48

90 + 48 = 138

180 - 138 = 42

Answer: a × ba × c = a (bc) = 0

a × ba × c = 2019-2019 = 0

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

By trial and error.

A: 50*12-100=500, 50*15-100=650. (A is not correct)

B: 500(12-11)=500, 500(15-11)=2000. (B is not correct)

C: 300(12-12)+500=500, 300(15-12)+500=1400. (if you continue try the numbers, you will see that this is the correct answer)

D: 200(12-5)+400=1800. (D is not correct)

Answer:

5  hi

Step-by-step explanation:

Answer:

A and C

Step-by-step explanation:

i chose these bc they arwe the 2 reasonable ones

Answer:

A prime number is a number only divisible by itself and 1. To write 36 as a product of its prime factors we use a factor tree. The key thing to remember is to always circle the prime numbers. So we start with writing 36 at the top of the page. 36 is divisible by 18 and 2 so draw 2 lines from the 36 with 18 and 2 at the end of the line. 2 is prime so we circle it. 18 is divisible by 9 and 2 so we draw 2 lines from the 18 with 9 and 2 at the end. Circle the 2 as it is prime. 9 is divisible by 3 and 3 so draw 2 lines with 3 at the end of each line and circle both of them.Now the factor tree is complete, we have to write out the answer. List the circled prime numbers from smallest to largest and multiply them together - 2x2x3x3. Notice that this equation is equal to 36. To answer the second part of the question - 'giving the answer in index form' we have to rewrite our answer. An index is a number above and to the right of a base number and indicates how many times a number is multiplied by itself. Therefore 2x2 in index form is 22 and 3x3 is 32 so the final answer is 36=22x32

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

divide each number and you get 32 for all of them which gives you the slope i think

The equation of the line is y = -4/3x

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

(x, y) = (3, -4) and (0, 0)

This means that the equation can be represented as

y = Y/X * x

substitute the known values in the above equation, so, we have the following representation

y = -4/3 * x

Evaluate the product

y = -4/3x

Hence, the equation is y = -4/3x

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The altitude of the plane is 8 miles

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

we know that in the right triangle ABC

tan function is ratio of opposite side and adjacent side

tan(72°)=h/x

h=xtan(72°) ....... equation 1

In the right triangle ABD

tan(55°)=h/(x+3)

h=(x+3)tan(55°) ..... equation 2

From equation 1 and 2

xtan(72°)=(x+3)tan(55°)

xtan(72°)-xtan(55°)=3tan(55°)

x[tan(72°)-tan(55°)]=3tan(55°)

x=3tan(55°)/[tan(72°)-tan(55°)]

We have to find the value of h

h=xtan(72°)

h=[3tan(55°)*tan(72°)]/[tan(72°)-tan(55°)]

h=8 miles

Hence, the height is 8 miles of the plane.

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Answer:

48

Step-by-step explanation:

8 squarded is 64. 64-16=48

Answer:

48

Step-by-step explanation:

Since b = 8

8^2 - 16

64 - 16=48

[RevyBreeze]

Answer:

Based on the provided information, the table summarizes service times (in seconds) of dinners at a fast food restaurant. To determine the number of individuals included in the summary, we can sum up the frequencies listed in the table:

7 + 24 + 14 + 1 + 4 = 50

Therefore, there are 50 individuals included in the summary.

Regarding the exact values of all the original service times, it is not possible to determine them precisely based on the given information. The table only provides ranges of service times and their corresponding frequencies. We can determine the range within which each individual's service time falls, but we cannot determine the exact value within that range.

The number of people that like sausage or mushrooms as shown in the Vann diagram is 30.

Venn diagrams are diagrams used to visually depict sets, relationships between sets, and operations on sets

To determine the number of people that like sausage or mushrooms from the Vann diagram, we use the Formula below.

Formula:

n (S ∪ M) = n (S) + n (M) − n (S ∩ M) ................. Equation 1

Where:

From the diagram,

Given:

Substitute these values into equation 1

Hence, the people who like sausage or mushrooms is 30

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Determine the value of function at x = 0 and x = 3.

The rate of change of fuction over interval [0,3] is,

So answer is 7/3.

Answer:

see explanation

Step-by-step explanation:

(21)

using the recursive rule

a₁ = 6

a₂ = a₁ + 4 = 6 + 4 = 10

a₃ = a₂ + 4 = 10 + 4 = 14

first 3 terms are 6, 10, 14

(22)

using the recursive rule

a₁ = 26

a₂ = a₁ - 10 = 26 - 10 = 16

a₃ = a₂ - 10 = 16 - 10 = 6

first 3 terms are 26, 16 , 6

(23)

substitute n = 1, 2, 3 into the explicit formula

a₁ = - 3 × \(3^{(1-1)}\) = - 3 × \(3^{0}\) = - 3 × 1 = - 3

a₂ = - 3 × \(3^{(2-1)}\) = - 3 × \(3^{1}\) = - 3 × 3 = - 9

a₃ = - 3 × \(3^{(3-1)}\) = - 3 × 3² = - 3 × 9 = - 27

first 3 terms are - 3, - 9, - 27

(24)

substitute n = 1, 2, 3 into the explicit formula

a₁ = 2 × \((-5)^{1-1}\) = 2 × \((-5)^{0}\) = 2 × 1 = 2

a₂ = 2 × \((-5)^{2-1}\) = 2 × \((-5)^{1}\) = 2 × - 5 = - 10

a₃ = 2 × \((-5)^{3-1}\) = 2 × (- 5)² = 2 × 25 = 50

first 3 terms are 2, - 10, 50

Answer:

27.41%

Step-by-step explanation:

Data provided in the question

The staffed of Alpha company = 79%

The staffed of Beta company = 62%

Based on the above information, the relative change of staffing from Alpha to beta company is

As we know that

\(\bold {\ Relative \ change = \frac{\alpha- \beta }{\beta }}\)

\(= \frac{(79 -62)}{62} \% \\\\= \frac{17}{62} \times 100\\\\=0.2741 \times 100\\\\=27.41\ \%\)

By applying the above formula we can get the relative change and the same is to be applied so that the correct percentage could come

The reference angle for the angle with the measure 2x/3 is 54⁰

You should understand that a reference angle is the acute angle to a given angle.

The given angle is 2x/3

We should understand that since the angle has the variable x

= x + 2x/3 = 90⁰

Simplifying the fraction to have

(3x+2x)/3 = 90

Cross and multiply we have 5x=270⁰

Making x the subject

x= 270/5

x=54⁰

Therefore, the reference angle with the measure 2x/3 is = 54⁰

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Answer:

Jenn is correct, as the function has two x-intercepts, at x = -3 and x = 3.

Step-by-step explanation:

x-intercepts of a function:

The x-intercepts of a function are the values of x for which f(x) = 0.

In this question:

\(f(x) = x^2 - 9\)

x-intercepts:

\(x^2 - 9 = 0\)

\(x^2 = 9\)

\(x = \pm \sqrt{9}\)

\(x = \pm 3\)

Jenn:

Jenn is correct, as the function has two x-intercepts, at x = -3 and x = 3.

The expected number of people out of 700 to order plain vanilla ice cream flavor is given as follows:

b. 224 people.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

Out of 3 x 50 = 150 people surveyed, 17 + 15 + 16 = 48 ordered plain vanilla ice cream, hence the probability of a person ordering plain vanilla ice cream flavor is given as follows:

p = 48/150

Then, out of 700 people, the expected number of people to order the plain vanilla flavor is given as follows:

700 x 48/150 = 224 people.

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Answer:

Use the form a  cos  ( b x− c) + d  to find the amplitude, period, phase shift, and vertical shift.  

x = sin ( 1 2 θ )

y = cos ( 1 2 θ )

− π ≤ θ ≤ π ( a )

Step-by-step explanation:

There is evidence to claim that the proportion of drug and alcohol use is higher locally than nationally.

Given that a recent drug survey showed an increase in the use of drugs and alcohol among local high school seniors as compared to the national percent.

Let p1 be the proportion of local seniors and p2 national seniors.

H₀ : p₁ =  p₂

Hₐ : p₁ > p₂

(right tailed test at 5% significance level)

Group I II  

Success 69 60 129

Total 100 100 200

p 0.69 0.6 0.645

q 0.31 0.4 0.355

se 0.046249324 0.048989795 0.033836002

p diff 0.09  

Std error 0.03384  

Z 2.659574468 0  

p 0.00391  

we find that p value is 0.00391 < 0.05

Hence we reject null hypothesis. There is evidence to claim that the proportion of drug and alcohol use is higher locally than nationally.

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Answer:

The quen is as following:

ABC is a right triangle at C,

Acute angles are in the ratio 5:1, i.e. ∠BAC : ∠ABC = 5:1

If CH is an altitude to AB and CL is an angle bisector of ∠ACB, find m∠HCL.

The solution is:  m∠HCL = 30°

Step-by-step explanation:

See the attached figure.

∵The triangle is right at C   ∴∠C = 90°

∴∠A + ∠B = 90° ⇒(1)

∵ Acute angles are in the ratio 5:1, i.e. ∠BAC : ∠ABC = 5:1

∴∠A = 5 times ∠B

Substitute at (1)

∴ 5 ∠B + ∠B = 90° ⇒⇒⇒ ∴∠B = 15°  and ∠A = 75°

∵CL is an angle bisector of ∠ACB

∴ ∠ACL = 90°/2 = 45°

∵ CH is an altitude to AB ⇒ ∠CHA = 90°

At the triangle AHC:

∠ACH = 180° - (∠CHA + ∠CAH) = 180° - (90° + 75°) = 15°

∴ ∠HCL = ∠ACL - ∠ACH = 45° - 15° = 30°

Answer:

In line 2, he should have substracted 9 from both sides of the equation

Step-by-step explanation:

Answer:

(2*3+x^2)+3(234x^2)

=6+x^2+702x^2

=703x^2+6

Step-by-step explanation:

easy peasy!

The simplest form of the expression \((2x^{3}+x^{2})+3(234x^{2} )\) is \(2x^{3} +703x^{2}\).

An expression is a combination of numbers, symbols, variables, indeterminants, coefficients, fraction. It is not mostly present in equal to form and it is equated because it expresses some relationship between variables.

The given expression is \((2x^{3} +x^{2} )+3(234x^{2} )\) and we need to simplify it.

Firstly we need to multiply 3 with 234 which is with \(x^{2}\).

\((2x^{3} +x^{2} )+3(234x^{2} )\)= \((2x^{3}+x^{2} +702x^{2} )\)

Now add the coefficients of \(x^{2}\). Coefficients are the numbers that are written with the variables to show their quantity.

=\(2x^{3}+703x^{2}\)

Hence the simplified form of the expression\((2x^{3} +x^{2}) +3(234x^{2} ) is (2x^{3}+703x^{2} )\).

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The formula relating future value and present value is given as:

Where,

• FV is the future value

• PV is the present value

• r is the rate of interest

• n is the number of periods interest held.

Rewrite the rate as a decimal:

Substitute FV=8600, r=0.095, n=5 into the formula:

Simplify the equation and solve for PV:

Hence, the present value is about $5,462.96.

The order of the given fractions will be 5/3>3/2>5/6.

What exactly is a fraction?

A fraction is a mathematical term that represents a portion or part of a whole. It represents the equal parts of the whole. A fraction has two components: the numerator and the denominator. The top number is referred to as the numerator, while the bottom number is referred to as the denominator. The denominator describes the total number of equal parts in a whole, whereas the numerator defines the number of equal parts taken.

5/10, for example, is a fraction.

In this case, 5 is the numerator and 10 is the denominator.

Now,

Given fractions are 5/6 ,5/3,  3/2

lets make the denominator same

Divide and multiply fraction 2 and 3 by 2 and 3 respectively

then fractions are 5/6, 10/6, 9/6

so, the order will be 10/6>9/6>5/6 i.e. 5/3>3/2>5/6

hence,

           The order of the given  fractions will be 5/3>3/2>5/6.

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The number of adult's masks sold is 63

Let the number of children's masks be represented by x

Let the number of adult's masks be represented by y.

Based on the information given, the equation to solve the question will be:

x + y = 100 ....... i

3x + 5y = 426 ....... ii

From equation i, x = 100 - y ..... iii

Put equation iii into ii

3x + 5y = 426

3(100 - y) + 5y = 426

300 - 3y + 5y = 426

Collect like terms

-3 + 5y = 426 - 300

2y = 126

y = 126/2

y = 63

The number of adult's mask sold is 63

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Answer:

This is GP and number of terms is 10 first term is 1 ratio is 3/2

Step-by-step explanation: