Find the surface area of this composite solid.

Answer:

a ≈ 2.2

Step-by-step explanation:

Using the Cosine rule in Δ ABC

a² = b² + c² - 2bc cos A

Here b = 3, c = 4 and A = 32° , thus

a² = 3² + 4² - (2 × 3 × 4 × cos32° )

    = 9 + 16 - 24cos32°

    = 25 - 24cos32° ( take the square root of both sides )

a = [tex]\sqrt{25-24cos32}[/tex] ≈ 2.2

Answer:

20 teachers

Step-by-step explanation:

Because if you take 100 and minus it by 29, 23, 4 and 24 you get 20.

Answer:

Step-by-step explanation:

Let X be the amount of cashews that the nutty professor will mix.

Since, the total weight of the nuts should be 35 lbs

The amount of Brazil nuts = 35 - X

Now,

[tex]6x + 5.30(35 - x) = 5.64(35)[/tex]

[tex]600x + 530(35 - x) = 564 \times 35[/tex]

[tex]600x + 18550 - 530x = 19740[/tex]

[tex]70x = 19740 - 18550[/tex]

[tex]70x = 1190[/tex]

[tex]x = \frac{1190}{70} [/tex]

[tex]x = 17[/tex]

Again,

[tex] 35 - x[/tex]

[tex]35 - 17[/tex]

[tex]18[/tex]

17 pounds of cashew and 18 pounds of Brazil nuts.

Hope this helps...

Good luck on your assignment...

Step-by-step explanation:

n = 61,647, p = 0.26, q = 0.74

μ = p = 0.26

σ = √(pq/n) = 0.00177

At 0.05 significance, z = 1.96.

0.26 ± 1.96 × 0.00177

(0.257, 0.263)

0.25 is outside of the confidence interval, so we can conclude with 95% confidence that the proportion is greater than 0.25.

Answer:

[tex]\boxed{\sf \ \ \ x = 2 \ \ and \ \ y = 5 \ \ \ }[/tex]

Step-by-step explanation:

hello, we have two equation

(1) x + 4y = 22

(2) 2x + y = 9

let's multiply (1) by 2 and subtract (2)

2x + 8y - (2x + y) = 2*22 - 9 = 44 - 9 = 35

<=> 2x + 8y -2x -y = 35

<=> 7y = 35

<=> y = 35/7 = 5

we replace this value in (1) and it comes

x + 4*5 = 22

<=> x = 22 - 20 = 2

so the solution is

x = 2 and y = 5

hope this helps

Answer:

When describing a property line drawn down the center of a creek bed

Answer:

[tex]\dfrac{1}{7}[/tex]

Step-by-step explanation:

There are 7 days in a week.

For the first person, we select one day out of the 7 days. The first person has 7 options out of the 7 days.

Let Event A be the event that the first person was born on a day of the week.

Therefore:

[tex]P(A)=\dfrac{7}{7}=1[/tex]

The second person has to be born on the same day as the first person. Therefore, the second person has 1 out of 7 days to choose from.

Let Event B be the event that the second person was born.

Therefore, the probability that the second person was born on the same day as the first person:

[tex]P(B|A)=\dfrac{1}{7}[/tex]

By the definition of Conditional Probability

[tex]P(B|A)=\dfrac{P(B \cap A)}{P(A)} \\$Therefore:\\P(B \cap A)=P(B|A)P(A)[/tex]

The probability that both were born on the same day is:

[tex]P(B \cap A)=P(B|A)P(A) = \dfrac{1}{7} X 1 \\\\= \dfrac{1}{7}[/tex]

Answer:

(a)0.5

(b)0.17

(c)0.625

(b)0.375

Step-by-step explanation:

Pr(E)=0.6​

Pr(F)=0.2

[tex]Pr(E\cap F)=0.1.[/tex]

(a)Pr (E|F )

[tex]Pr (E|F )=\dfrac{Pr(E \cap F)}{Pr(F)} \\=\dfrac{0.1}{0.2}\\\\=0.5[/tex]

(b)Pr (F|E )

[tex]Pr (F|E )=\dfrac{Pr(E \cap F)}{Pr(E)} \\=\dfrac{0.1}{0.6}\\\\=0.17[/tex]

(c)Pr (E|F')​

Pr(F')=1-P(F)

=1-0.2=0.8

[tex]Pr(E \cap F')=P(E)-P(E\cap F)\\=0.6-0.1\\=0.5[/tex]

Therefore:

[tex]Pr (E|F' )=\dfrac{Pr(E \cap F')}{Pr(F')} \\=\dfrac{0.5}{0.8}\\\\=0.625[/tex]

(d)Pr(E'|F')​

[tex]P(E'\cap F')=P(E \cup F)'\\=1-P(E \cup F)\\=1-[P(E)+P(F)-P(E\cap F)]\\=1-[0.6+0.2-0.1]\\=1-0.7\\=0.3[/tex]

Therefore:

[tex]Pr (E'|F' )=\dfrac{Pr(E' \cap F')}{Pr(F')} \\=\dfrac{0.3}{0.8}\\\\=0.375[/tex]

Answer:

5x + 10 = 25

Subtract 10 on each side to make x alone

5x = 15

divide by 5 on each side

x=3 so x=3

3x + 12 = 48

48-12=36

3x=36

divide by 3

x=12

4x + 8 = 16

4x = 8

x=2

2x + 15=25

2x=10

x=5

5x + 20 = 50

5x=30

x=6

hope this helps

1. 3

2.12

3.2

4.5

5.6

Step-by-step explanation:

Answer:

Step by step explanation

First:

Solution,

1. 5x + 10 = 25

Move constant to the R.H.S and change its sign:

5x = 25 - 10

Calculate the difference

5x = 15

Divide both sides by 5

5x/5 = 15/5

calculate

X = 3

2. 3x + 12 = 48

or, 3x = 48 - 12

or, 3x = 36

or, 3x/x = 36/3

x = 12

3. 4x + 8 = 16

or, 4x = 16 - 8

or, 4x = 8

or, 4x/x = 8/4

x = 2

4. 2x + 15 = 25

or, 2x = 25 - 15

or, 2x = 10

or, 2x/x= 10/2

x = 5

5. 5x + 20 = 50

or, 5x = 50-20

or, 5x = 30

or, 5x/x = 30/5

x = 6

Hope this helps...

Good luck on your assignment...

Answer:

Polygon is pentagon

Step-by-step explanation:

In a regular polygon each angle is equal.

In a regular polygon Each angle of polygon is given by (2n-4)90/n

where n is the number of sides of the polygon

given

An interior angle of a regular polygon has a measure of 108°.

(2n-4)90/n = 108

=> 180n - 360 = 108n

=> 180n-108n= 360

=> 72n = 360

=> n = 360/72 = 5

Thus, polygon has 5 sides

and we know that regular polygon which has 5 sides is called pentagon.

Thus, Polygon is pentagon

Answer:

the answer is b

Step-by-step explanation:

Behold the quotient of F and the product of r,s, and T:  F / (r·s·T)

The numerical of the statement the quotient of F and the product of r,s, and T is F/(r×s×T).

The number which is being divided is the dividend.

The number with which we are dividing is the divisor.

The result when a dividend is divided by the divisor is the quotient.

A remainder is the extra portion of a number when it isn't completely divisible.

Given, Are some variables F, r, s, and t.

Now, The product of r,s, and T is,

= r×s×T and the complete statement the quotient of F and the product of r,s, and T can be written as,

F/(r×s×T).

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Answer:

There are 65 dimes. There are 55 nickels.

Step-by-step explanation:

This question can be solved using a system of equations.

I am going to say that:

x is the number of dimes

y is the number of nickels.

There are a total of 120 coins in the bag

This means that x + y = 120.

The total value of the coins is $9.25.

The dime is worth $0.10 and the nickel is worth $0.05. So

0.1x + 0.05y = 9.25

System:

[tex]x + y = 120[/tex]

[tex]0.1x + 0.05y = 9.25[/tex]

From the first equation:

[tex]y = 120 - x[/tex]

Replacing in the second:

[tex]0.1x + 0.05y = 9.25[/tex]

[tex]0.1x + 0.05(120 - x) = 9.25[/tex]

[tex]0.1x + 6 - 0.05x = 9.25[/tex]

[tex]0.05x = 3.25[/tex]

[tex]x = \frac{3.25}{0.05}[/tex]

[tex]x = 65[/tex]

[tex]y = 120 - x = 120 - 65 = 55[/tex]

There are 65 dimes. There are 55 nickels.

Answer:

  [tex]\dfrac{4x^2+12x+5}{6x^2-3x}[/tex]

Step-by-step explanation:

Invert the denominator and multiply.

  [tex]\dfrac{2x+5}{3x}\div\dfrac{2x-1}{2x+1}=\dfrac{2x+5}{3x}\cdot\dfrac{2x+1}{2x-1}\\\\=\dfrac{(2x+5)(2x+1)}{(3x)(2x-1)}=\boxed{\dfrac{4x^2+12x+5}{6x^2-3x}}\qquad\text{matches choice A}[/tex]

Answer:

[tex]\frac{4x^2+12x+5}{6x^2-3x}[/tex]

Step-by-step explanation:

After using the reciprocal of the second term, the denominator will multiply out to be [tex]6x^2-3x[/tex]. There is only one option with that as the denominator so it must be the correct answer.

Step-by-step explanation:

to be honest I'm not sure how to do

Answer:

(A)Step 1; it should be m∠m + m∠n + m∠o = 180 degrees (sum of angles in a triangle)

Step-by-step explanation:

The steps followed by the student are:

Step 1: m∠m + m∠n + m∠p = 180 degrees (sum of angles of a triangle)

Step 2: m∠p + m∠o = 180 degrees (adjacent supplementary angles)

Step 3: Therefore, m∠m + m∠n + m∠o = m∠o + m∠p

Step 4: So, m∠m + m∠n = m∠p

We observe that the student made a mistake in Step 1, it should be m∠m + m∠n + m∠o = 180 degrees (sum of angles in a triangle).

p is outside the triangle, therefore it cannot form one of the angles in the triangle.

Answer:

Option (A).

Step-by-step explanation:

The function f(x) = x² + 4 is defined over the interval (-2, 2)

Total number of equal parts between this interval = 5

If the interval is divided into n equal parts, height of the right endpoint of each rectangle = [tex]\frac{5}{n}[/tex]

Height of the endpoint of the k rectangles = [tex]k.\frac{5}{n}[/tex]

Therefore, height of the endpoint of the kth rectangle = Height of first rectangle + height of k rectangles

= -2 + [tex]k.\frac{5}{n}[/tex]

Option (A). will be the answer.

The height of the right endpoint of the kth rectangle h = -2 + k (5/n)

The height is a vertical distance between two points. In the case of the triangle, the height will be the distance between the base and the top vertex of the triangle.

The function f(x) = x² + 4 is defined over the interval) (-2, 2 )

Total number of equal parts between this interval = 5

If the interval is divided into n equal parts, the height of the right endpoint of each rectangle = (5/n)

Height of the endpoint of the k rectangles = k (5/n)

The height of the endpoint of the kth rectangle:-

= Height of first rectangle + height of k rectangles

= -2   +  k (  5/n )

Therefore the height of the right endpoint of the kth rectangle h = -2 + k (5/n)

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Answer:

  Always true

Step-by-step explanation:

If you can't express the number as a ratio of integers, multiplying or dividing it by integers will not make it so you can.

If π is irrational, 2π is also irrational.

It is always true that the product of a rational and an irrational number is irrational.

Answer:

all ways true

Step-by-step explanation:

Hey there! :)

Answer:

10 miles.

Step-by-step explanation:

To solve for the diagonal side, we can simply visualize the sides of the rectangle as sides of a right triangle with the diagonal being the hypotenuse.

We can use the Pythagorean Theorem (a² + b² = c²), where:

a = length of short leg

b = length of long leg

c = length of the diagonal

Solve:

c² = a² + b²

c² = 6² + 8²

c² = 36 + 64

c² = 100

c = 10 miles. This is the length of the pedestrian route.

Answer:

Solution,

Hypotenuse (h) = R

Perpendicular (p) = 8 miles

Base (b) = 6 miles

Now,

Using Pythagoras theorem:

[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]

Plugging the values:

[tex] {r}^{2} = {(8)}^{2} + {(6)}^{2} [/tex]

Calculate:

[tex] {r}^{2} = 64 + 36[/tex]

[tex] {r}^{2} = 100[/tex]

[tex]r = \sqrt{100} [/tex]

[tex]r = 10 \: miles[/tex]

Length of route = 10 miles

Hope this helps...

Good luck on your assignment...

Answer:

4 = 4

Step-by-step explanation:

=> 2x = 4

Putting x = 2

=> 2(2) = 4

=> 4 = 4

Answer:

Solution,

X= 2

Now,

2x=4

plugging the value of X,

2*2= 4

4 = 4 ( hence it is true)

Answer:

See explanation

Step-by-step explanation:

To determine whether each of these functions is [tex]O(x^2)[/tex], we apply these theorems:

(a)Given the function: f(x)=100x+1000

The highest power of n is 1.

Therefore f(x) is O(x).

Since any O(x) function is always [tex]O(x^2)[/tex], 100x+1000 is [tex]O(x^2)[/tex].

[tex](b) f(x)=100x^ 2 + 1000[/tex]

The highest power of n is 2.

Therefore the function is [tex]O(x^2)[/tex].

Answer:

i think its 2000

Step-by-step explanation:

Answer:

A. y=-1/4x

Step-by-step explanation:

We have the information 3y=12x-9, the lines are perpendicular, and the new line passes through (-4,1). First, you want to put the original equation into slope intercept form by isolating the y, to do this we need to divide everything by 3 to get y=4x-3. The slopes of perpendicular lines are negative reciprocals so you need to find the negative reciprocal of 4, so flip it to 1/4 and multiply by -1, we get the slope of the new line as -1/4. So far we have the equation y=-1/4x+b. We are given a point on the line, (-4,1), we can plug these into the equation as x and y to solve for the y-intercept, b. You set it up as 1=-1/4(-4)+b. First you multiply to get 1=1+b, then you subtract 1 from both sides to isolate the variable and you get b=0. Then you can use b to complete your equation with y=-1/4x, or letter A.

Answer: 29,000.00

Step-by-step explanation:

Let the income=x.  22%=0.22.

So 6380/x=0.22

x=6380/0.22=29,000.00

Answer:

a) Check Explanation.

b) True. Check Explanation.

c) True. Check Explanation.

Step-by-step explanation:

a) A normal distribution is one which is characterized by four major properties.

- A normal distribution is symmetrical about the center of the distribution. That is, the variables spread out from the center in both directions in the same manner; the right side of the distribution is a mirror image of the left side of the distribution.

The center of a normal distribution is located at its peak, and 50% of the data lies above the mean, while 50% lies below.

- The mean, median and the mode are coincidental. The mean, median and mode of a normal distribution are all the same value.

- A normal distribution is unimodal, that is, has only one mode.

- The ends of the probability curve of a normal distribution never touch the x-axis, hence, it is said too be asymptotic.

b) The sampling distribution of sample means arises when random samples are drawn from the population distribution and their respective means are computed and put together to form a distribution. Hence, the curve of this sampling distribition of sample means will show how the sample means are distributed. Hence, this statement is true.

c) The Central Limit Theorem gives that if the samples are drawn randomly from a normal distribution and each sample size is considerable enough, the mean of the sampling distribution of sample means is approximately equal to the population mean. So, if the conditions stated are satisfied, then thos statement too, is true.

Hope this Helps!!!

Answer:

(7, 5.25) lies on the graph.

Step-by-step explanation:

We are given the following values

x = 4,   6,  8, 12 and corresponding y values are:

y = 3, 4.5, 6, 9

Let us consider two points (4, 6) and (6, 4.5) and try to find out the equation of line.

Equation of a line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given as:

[tex]y=mx+c[/tex]

where m is the slope.

(x,y) are the coordinates from where the line passes.

c is the y intercept.

Here,

[tex]x_{1} = 4\\x_{2} = 6\\y_{1} = 3\\y_{2} = 4.5[/tex]

Formula for slope is:

[tex]m = \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m = \dfrac{4.5-3}{6-4}\\\Rightarrow m = \dfrac{1.5}{2}\\\Rightarrow m = \dfrac{3}{4}[/tex]

Now, the equation of line becomes:

[tex]y=\dfrac{3}{4}x+c[/tex]

Putting the point (4,3) in the above equation to find c:

[tex]3=\dfrac{3}{4}\times 4+c\\\Rightarrow 3=3+c\\\Rightarrow c =0[/tex]

So, final equation of given function is:

[tex]y=\dfrac{3}{4}x[/tex]

OR

[tex]4y=3x[/tex]

As per the given options, the point (7, 5.25) satisfies the equation.

So correct answer is [tex](7, 5.25)[/tex].

Answer:

  C)  42

Step-by-step explanation:

The parallel lines divide the transversals proportionally.

  x/35 = 30/25

  x = 35(6/5) . . . . multiply by 35, reduce the fraction

  x = 42

Answer:

z = 10

Step-by-step explanation:

The value of the z-statistic is given by:

[tex]z = \frac{X - \mu}{s}[/tex]

In which:

X is the measured value.

[tex]\mu[/tex] is the expected value.

[tex]s = \frac{\sigma}{\sqrt{n}}[/tex] is the standard deviation of the sample. [tex]\sigma[/tex] is the standard deviation of the population.

In this question:

The mean length was 2.9 inches, and the population standard deviation is 0.1 inch.

This means that [tex]\mu = 2.9, \sigma = 0.1[/tex]

Random sample of 100 screws.

This means that n = 100.

To see if the batch of screws has a significantly different mean length from 3 inches, what would the value of the z-test statistic be?

3 inches, so [tex]X = 3[/tex]

[tex]s = \frac{0.1}{\sqrt{100}} = 0.01[/tex]

[tex]z = \frac{X - \mu}{s}[/tex]

[tex]z = \frac{3 - 2.9}{0.01}[/tex]

[tex]z = 10[/tex]

Answer:

-10

Step-by-step explanation:

If we first note the denominator of fraction numerator sigma over denominator square root of n end fraction equals fraction numerator 0.1 over denominator square root of 100 end fraction equals fraction numerator begin display style 0.1 end style over denominator 10 end fraction equals 0.01

Then, getting the z-score we can note it is z equals fraction numerator x with bar on top minus mu over denominator begin display style 0.01 end style end fraction equals fraction numerator 2.9 minus 3 over denominator 0.01 end fraction equals negative 10

This tells us that 2.9 is 10 standard deviations below the value of 3, which is extremely far away.

Answer:

7x+7 is obviously divisible by 7.

put in any value high enough and you can find the two three digit numbers.

Step-by-step explanation:

Two three-digit numbers divisible by 7 are 98 and 105.

Two three-digit numbers divisible by 7 are 98 and 105.To create an expression that is divisible by 7, we can use the property that the difference between two numbers is divisible by 7 if the numbers themselves are divisible by 7.

Let's represent a three-digit number divisible by 7 as "7k" where k is an integer. To find two three-digit numbers divisible by 7, we can use the following expression:

7k - 7

For example, if we substitute k = 15, we get:

7(15) - 7 = 105 - 7 = 98

So, the first three-digit number divisible by 7 is 98.

Similarly, for the second three-digit number, let's substitute k = 16:

7(16) - 7 = 112 - 7 = 105

Therefore, the two three-digit numbers divisible by 7 are 98 and 105.

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Answer:

5.35 more miles

Answer:

5.35 miles to the finish line

Step-by-step explanation:

Step one

13.1-7.75=

5.35

Answer:

Step-by-step explanation:

Let x represent the length of the side not parallel to the partition. Then the length of the side parallel to the partition is ...

  y = (300 -2x)/3

And the enclosed area is ...

  A = xy = x(300 -2x)/3 = (2/3)(x)(150 -x)

This is the equation of a parabola with x-intercepts at x=0 and x=150. The line of symmetry, hence the vertex, is located halfway between these values, at x=75.

The maximum area is enclosed when the dimensions are ...

  50 ft by 75 ft

That maximum area is 3750 square feet.

_____

Comment on the solution

The generic solution to problems of this sort is that half the fence (cost) is used in each of the orthogonal directions. Here, half the fence is 150 ft, so the long side measures 150'/2 = 75', and the short side measures 150'/3 = 50'. This remains true regardless of the number of partitions, and regardless if part or all of one side is missing (e.g. bounded by a barn or river).