A 10-ft bar of I-beam weighs 201 lb. What is the weight of a 6-ft length?

Answer:

45 coaches

Step-by-step explanation:

11:3 = 165:45

Answer:45

Step-by-step explanation:

Answer:

Step-by-step explanation:

the answer in simplest form is 4/3.

Answer: 1.) -24

2.) 96

3.) 8

Step-by-step explanation:

1.) A negative number multiplied times a positive number will automatically equal a negative answer. Ex: (-9) (5) = -45

2.) A negative number multiplied times a negative number will autimatically equal a positive answer. Ex: (-4) (-5) = 20

3.) This is the same as the statement above, but all you're doing this time is dividing. A negative number divided by a negative number will equal a positive number. Ex: -36 ÷ (-9) = 4

Answer:

The lowest score on the final exam that would qualify a student for an​ A is 80.

The lowest score on the final exam that would qualify a student for a B is 74.68.

The lowest score on the final exam that would qualify a student for a C is 67.33.

The lowest score on the final exam that would qualify a student for a​ D is 62.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Mean of 71 and a standard deviation of 7.

This means that \(\mu = 71, \sigma = 7\)

Grades are assigned such that the top​ 10% receive​ A's, the next​ 20% received​ B's, the middle​ 40% receive​ C's, the next​ 20% receive​ D's, and the bottom​ 10% receive​ F's.

This means that:

90th percentile and above: A

70th percentile and below 90th: B

30th percentile to the 70th percentile: C

10th percentile to the 30th: D

Lowest score for an A:

Top 10% receive A, which means that the lowest score that would qualify a student for an A is the 100 - 10 = 90th percentile, which is X when Z has a pvalue of 0.9, so X when Z = 1.28.

\(Z = \frac{X - \mu}{\sigma}\)

\(1.28 = \frac{X - 71}{7}\)

\(X - 71 = 7*1.28\)

\(X = 80\)

The lowest score on the final exam that would qualify a student for an​ A is 80.

Lowest score for a B:

70th percentile, which is X when Z has a pvalue of 0.7, so X when Z = 0.525.

\(Z = \frac{X - \mu}{\sigma}\)

\(0.525 = \frac{X - 71}{7}\)

\(X - 71 = 7*0.525\)

\(X = 74.68\)

The lowest score on the final exam that would qualify a student for a B is 74.68.

Lowest score for a C:

30th percentile, which is X when Z has a pvalue of 0.3, so X when Z = -0.525.

\(Z = \frac{X - \mu}{\sigma}\)

\(-0.525 = \frac{X - 71}{7}\)

\(X - 71 = 7*(-0.525)\)

\(X = 67.33\)

The lowest score on the final exam that would qualify a student for a C is 67.33.

Lowest score for a D:

10th percentile, which is X when Z has a pvalue of 0.1, so X when Z = -1.28.

\(Z = \frac{X - \mu}{\sigma}\)

\(-1.28 = \frac{X - 71}{7}\)

\(X - 71 = 7*(-1.28)\)

\(X = 62\)

The lowest score on the final exam that would qualify a student for a​ D is 62.

Answer:

See attachment for graph

Step-by-step explanation:

Given

\(y = x^2 - 3\)

Required

The graph of the equation

First, we determine the range of y

\(x = -3\)

\(y = x^2 - 3 \to y = (-3)^2 - 3 = 6\)

\((-3,6)\)

\(x = -2\)

\(y = (-2)^2 - 3 = 1\)

\((-2,1)\)

\(x = -1\)

\(y = (-1)^2 - 3 = -2\)

\((-1,-2)\)

\(x=0\)

\(y = 0^2 - 3 = -3\)

\((0,-3)\)

\(x = 1\)

\(y= 1^2 - 3 = -2\)

\((1,-2)\)

\(x = 2\)

\(y =2^2 - 3 = 1\)

\((2,1)\)

\(x = 3\)

\(y = 3^2 - 3 = 6\)

\((3,6)\)

See attachment for graph

The solution is Option A.

Yes , The measure of angle 1 and angle 2 are same because they intercept the same arc of the circle

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The perimeter of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle

Given data ,

From the circle , the four angles are 1 , 2 , 3 , and 4

And , from the circle theorem

In a circle, the measures of the angles subtended by the same arc on the circumference of the circle are equal

So , from the circle , we can see that

∠1 and ∠2 are subtended by the same arc AB at points C and D respectively

And , the points C and D lies on the circumference of the circle

So , the measures of the angle must be equal

Hence , The angles ∠1 and ∠2 have equal measures because they intercept the same arc of the circle

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Answer:

(d) -12

Step-by-step explanation:

3a = _____

a = -4

3(-4) = ___

3(-4) = -12

The answer is (d) -12

Answer: 80

Step-by-step explanation: Let x be the total number of people at the party.

According to the problem, the number of people who ate chicken wings was 14 less than 3/5 of the total number of people, so we can write:

34 = (3/5)x - 14

To solve for x, we can first add 14 to both sides of the equation:

34 + 14 = (3/5)x

48 = (3/5)x

Then we can multiply both sides by 5/3:

(5/3) * 48 = x

80 = x

Therefore, the number of people at the party was 80.

To write a one-step equation with the same solution, we can simply write:

x = 80

This is a one-step equation because the solution is obtained in just one step by assigning the value 80 to the variable x.

Ahem, here goes, my attempt at a minute-long rap in praise of the parallelogram:

Yo, listen up, the parallelogram is where it's at,

A shape so brilliant, the angles are sat.

Parallel sides that never converge,

Internal angles that never diverge.

Each side an equal length,

A geometry prodigy's dream length.

The diagonals intersect, another line through the middle they meet,

Creating symmetry so neat.

A rectangle it could be,

But it's oblong, not square, can't you see?

With depth and width in perfect balance we see,

A two-dimensional form of complexity.

While the square is simple, the parallelogram is hip,

A mathematical masterpiece, skip, skip, skip!

four right angles keep the shape so tight,

Parallel lines dominate left and right.

Rotated or reflected without a care,

Its structural integrity beyond compare.

triangles form at each corner you'll note,

Acute or obtuse, depends on the protractor's groove.

A versatile shape with reason and purpose galore,

The parallelogram, simply, carries the floor.

From geometry to art, its angles they intrigue,

As a basis for patterns, its potential we can truly plug.

A forgotten form that deserves more acclaim,

Put the parallelogram on geometry's game!

This shape so underrated, rarely appreciated it seems,

But with logic and virtue, strong foundations it gleams.

The parallelogram, the parallelogram, Hooray!

This is why the parallelogram is the best shape, I say!

Answer:

B: 9

Step-by-step explanation:

The prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, and 23.

Answer:

what do you need help with

Answer:

what do you need help with?

Step-by-step explanation:

Given:

The admission fee at an amusement park is $4.25 for children and $7.20 for adults.

Let the number of children = x

Let the number of adults = y

On a certain day, 333 people entered the park

so, we have the following equation:

And, the admission fees collected totaled $1843

so, the equation will be:

We will solve the equations (1) and (2)

From equation (1):

substitute with (x) from equation (3) into equation (2):

solve the equation to find y:

Substitute with (y) into equation (3) to find the value of (x):

So, the answer will be:

The number of children = x = 188

The number of adults = y = 145

The distance between the points B and C is 12m

Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²). This formula is used to find the distance between any two points on a coordinate plane or x-y plane.

for the coordinates B (-14,-5) and C(-14, 7), then x1 = -14 ,x-2= -14 , y1= -5 and y2= 7

therefore d =√((x2 – x1)² + (y2 – y1)²) = √((-14– -14)² + (-5 – 7)²)

d=√((0)² + 12²)

d=√144

d= 12m

therefore the distance between the points B and C is 12m.

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Decompose each given F(s) into partial fractions.

\(F(s) = \dfrac{s+1}{s(s-1)(s-3)}\)

has partial fraction decomposition

\(\dfrac{s+1}{s(s-1)(s-3)} = \dfrac as + \dfrac b{s-1} + \dfrac c{s-3}\)

Combine the rational terms on the right and solve for the coefficients:

\(\dfrac{s+1}{s(s-1)(s-3)} = \dfrac{a(s-1)(s-3) + b s(s-3) + c s(s-1)}{s (s-1) (s-3)}\)

\(1 = a(s-1)(s-3) + bs(s-3) + c s(s-1)\)

\(1 = 3 a + (-4 a - 3 b - c) s + (a + b + c) s^2\)

\(\begin{cases}3a=1 \\ -4a-3b-c = 0 \\ a+b+c=0 \end{cases} \implies a=\dfrac13, b=-\dfrac12, c=\dfrac16\)

Then

\(F(s) = \dfrac13 \times \dfrac1s - \dfrac12 \times \dfrac1{s-1} + \dfrac16 \times \dfrac1{s-3}\)

Using the frequency-shifting property, the inverse transform is

\(\boxed{f(t) = \dfrac13 - \dfrac{e^t}2 + \dfrac{e^{3t}}6}\)

The other transform can be dealt with in the same manner.

\(F(s) = \dfrac1{(s-1)(s-2)(s-3)} = \dfrac a{s-1} + \dfrac b{s-2} + \dfrac c{s-3}\)

\(\implies 1 = a(s-2)(s-3) + b(s-1)(s-3) + c(s-1)(s-2)\)

\(\implies 1 = 6 a + 3 b + 2 c + (-5 a - 4 b - 3 c) s + (a + b + c) s^2\)

\(\implies \begin{cases}6 a + 3 b + 2 c=1 \\ -5a-4b-3c = 0 \\ a+b+c=0\end{cases} \implies a=\dfrac12, b=-1, c=\dfrac12\)

\(\implies F(s) = \dfrac12 \times \dfrac1{s-1} - \dfrac1{s-2} + \dfrac12 \times \dfrac1{s-3}\)

\(\implies \boxed{f(t) = \dfrac{e^t}2 - e^{2t} + \dfrac{e^{3t}}2}\)

Answer:

multiply length with breadth which is 34 *42

Answer:1'428 sq ft because you multiply 34x42 witch= to 1,428

Using simultaneous equation, the solution to the system of linear equations are 1223 $10 tickets, 1332 $20 tickets, and 763 $30 tickets were sold.

Let's solve the problem step by step.

Let:

x = number of $10 tickets sold

y = number of $20 tickets sold

z = number of $30 tickets sold

From the given information, we can form the following equations:

Equation 1: x + y + z = 3318 (Total number of tickets sold)

Equation 2: y = x + 109 (109 more $20 tickets than $10 tickets were sold)

Equation 3: 10x + 20y + 30z = 61760 (Total sales from ticket sales)

We can use these three equations to solve for the values of x, y, and z.

First, let's substitute Equation 2 into Equation 1:

x + (x + 109) + z = 3318

2x + 109 + z = 3318

2x + z = 3209 (Equation 4)

Now, let's substitute the value of y from Equation 2 into Equation 3:

10x + 20(x + 109) + 30z = 61760

10x + 20x + 2180 + 30z = 61760

30x + 30z = 59580

x + z = 1986 (Equation 5)

We now have a system of equations (Equations 4 and 5) with two variables (x and z). We can solve this system to find the values of x and z.

Multiplying Equation 4 by 30, and Equation 5 by 2, we get:

60x + 30z = 96270 (Equation 6)

2x + 2z = 3972 (Equation 7)

Now, subtract Equation 7 from Equation 6:

(60x + 30z) - (2x + 2z) = 96270 - 3972

58x + 28z = 92298

Simplifying, we have:

29x + 14z = 46149 (Equation 8)

Now, we can solve Equations 5 and 8 simultaneously:

x + z = 1986 (Equation 5)

29x + 14z = 46149 (Equation 8)

Multiplying Equation 5 by 14, and Equation 8 by 1, we get:

14x + 14z = 27804 (Equation 9)

29x + 14z = 46149 (Equation 8)

Now, subtract Equation 9 from Equation 8:

(29x + 14z) - (14x + 14z) = 46149 - 27804

15x = 18345

Divide both sides of the equation by 15:

x = 18345 / 15

x = 1223

Substituting the value of x into Equation 5, we can find z:

1223 + z = 1986

z = 1986 - 1223

z = 763

Now that we have the values of x and z, we can substitute them back into Equation 1 to find y:

1223 + y + 763 = 3318

y + 1986 = 3318

y = 3318 - 1986

y = 1332

Therefore, the solution to the problem is:

x = 1223 (number of $10 tickets sold)

y = 1332 (number of $20 tickets sold)

z = 763 (number of $30 tickets sold)

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The length of the rectangle is twice its width. If its perimeter is 7 1/3 cm, its length will be 22/9 cm, and the width is 11/9 cm.

Let's assume the width of the rectangle is "b" cm.

According to the given information, the length of the rectangle is twice its width, so the length would be "2b" cm.

The formula for the perimeter of a rectangle is given by:

Perimeter = 2 * (length + width)

Substituting the given perimeter value, we have:

7 1/3 cm = 2 * (2b + b)

To simplify the calculation, let's convert 7 1/3 to an improper fraction:

7 1/3 = (3*7 + 1)/3 = 22/3

Rewriting the equation:

22/3 = 2 * (3b)

Simplifying further:

22/3 = 6b

To solve for "b," we can divide both sides by 6:

b = (22/3) / 6 = 22/18 = 11/9 cm

Therefore, the width of the rectangle is 11/9 cm.

To find the length, we can substitute the width back into the equation:

Length = 2b = 2 * (11/9) = 22/9 cm

So, the length of the rectangle is 22/9 cm, and the width is 11/9 cm.

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Answer:

2 forms

Step-by-step explanation:

hope this helps <3

\( \sf \longrightarrow \: \frac{8}{5} \div 6 \\ \)

\( \sf \longrightarrow \: \frac{5}{8} \times 6 \\ \)

\( \sf \longrightarrow \: \frac{5 \times 6}{8} \\ \)

\( \sf \longrightarrow \: \frac{30}{8} \\ \)

\( \sf \longrightarrow \: \frac{8}{30} \\ \)

\( \sf \longrightarrow \: 0.26 \\ \)

_____________________________

Answer:

\({ \tt{16 {b}^{2} c {}^{12} - 0.25 }}\)

» Change the decimal to a fraction:

\( = { \tt{ {16b}^{2} {c}^{12} - \frac{1}{4} }} \\ \)

» Change the other degrees to indices;

\( = { \tt{ \blue{( {4}^{2}) }} {b}^{2} {c}^{12} - \frac{1}{ \red{( {2}^{2} )}} } \\ \\ = { \tt{ {(4bc {}^{6} )}^{2} - \frac{1}{4} }}\)

» Factorize:

\( = { \tt{4}^{2} \{ ( {bc}^{6} ) {}^{2} - \frac{1}{4} \}} \\ \\ { \boxed{ \tt{ = 16 \{ { \blue{{(bc}^{6}) {}^{2} - \frac{1}{4} } \}}}}}\)

Answer:

\(y=x^3-12x^2+48x-58\)

Step-by-step explanation:

Transformation Rules

\(f(x+a)=f(x) \: \textsf{translated}\:a\:\textsf{units left}\)

\(f(x-a)=f(x) \: \textsf{translated}\:a\:\textsf{units right}\)

Given equation: \(y=x^3+6\)

If the graph of the equation is translated 4 units to the right, then we replace \(x\) with \((x-4)\):

\(\implies y=(x-4)^3+6\)

\(\implies y=(x-4)(x-4)(x-4)+6\)

\(\implies y=(x-4)(x^2-8x+16)+6\)

\(\implies y=x^3-8x^2+16x-4x^2+32x-64+6\)

\(\implies y=x^3-12x^2+48x-58\)

Answer:

Step-by-step explanation:

Given

Translating 4 units right

First, let's define rational and irrational numbers.

Rational numbers. Are those numbers that can be expressed as the ratio of 2 integers.

Irrational numbers. These numbers are the opposite of rational numbers, they can't be expressed at the ratio of 2 integers abd their decimal numbers are infinite.

Now, addressing the question, to order rational and irrational numbers we must take a close look th the decimal numbers given for the rational number.

For example, say that we are comparing 9.43 and \(\sqrt{89} \\\). Let's convert the numbers to their decimal form to easily compare them.

9.43 is already a decimal.

\(\sqrt{89} =9.433981132\).

Based of the obtained values, the greatest number of these 2 is, clearly, \(\sqrt{89} \\\). In case we are comparing these same 2 numbers, and we are only given the decimal form of \(\sqrt{89} \\\) as 9.43, we can still affirm that \(\sqrt{89} \\\) is the greatest number, because it's irrational, it has more decimal numbers that are greater than those on 9.43, which only has 2.

The way to compare and order rational and irrational numbers is to convert all the numbers to their decimal form and see who has the greater value. It's important to always keep in mind that irrational numbers have infinite decimal figures. If we have the exact same decimal figures for an irrational and a rational number, the irrational number will always be greater since it has infinite decimal places.

Answer:

Barts total cost is (c)213.36

Step-by-step explanation:

First, you subtract 6% from $219

=204.92

add shipping,

+7.50

=213.36

Hope this helps <3

Answer:

C. $213.36

Step-by-step explanation:

The original price is $219 and the discount is 6% which is equal to $13.14

$219 - $13.14 + $7.50 (shipping cost) = $213.36

Answer:

B

Step-by-step explanation:

A vertex is where two lines intersect

Answer:

The  probability is  \(P(0.35 <X < 0.55) = 0.9921772\)

Step-by-step explanation:

From the question we are told that

  The sample size is  n =  175

   The population proportion is  p =  0.45

Generally the mean of the sampling distribution is  \(\mu_{x} = 0.45\)

 Generally the standard deviation is mathematically represented as  

        \(\sigma_{x} = \sqrt{\frac{p (1-p)}{n} }\)

=>      \(\sigma_{x} = \sqrt{\frac{0.45 (1-0.45)}{175} }\)

=>      \(\sigma_{x} = 0.0376\)

Generally the probability of  that the sample proportion of orange candies will be between 0.35 and  0.55 is  

      \(P(0.35 < X < 0.55) = P( \frac{0.35 - 0.45}{0.0376} < \frac{X -\mu_{x}}{\sigma_{x}} < \frac{0.55 - 0.45}{0.0376} )\)

=>   \(P(0.35 <X < 0.55) = P( -2.696 < \frac{X -\mu_{x}}{\sigma_{x}} < 2.6595 )\)

Generally \(\frac{X - \mu_{x}}{\sigma_{x}} = Z (The \ standardized \ value \ of X)\)

So

    \(P(0.35 <X < 0.55) = P( -2.6596 < Z< 2.6595 )\)

=>  \(P(0.35 <X < 0.55) =P( Z< 2.6595 ) - P( Z < -2.6596 )\)

From the z-table  

    \(P( Z< 2.6595 ) = 0.99609\)

and

    \(P( Z< - 2.6595 ) = 0.0039128\)

So

   \(P(0.35 <X < 0.55) =0.99609 - 0.0039128\)

=> \(P(0.35 <X < 0.55) = 0.9921772\)

The required value of trigonometric ratios is,

sin 45° = 1/\(\sqrt{2}\)

cos 30 = \(\sqrt{3}\)/2

tan 60 = 1/  √3

We know that,

Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.

Therefore,

sin 45° = 1/\(\sqrt{2}\)

cos 30 = \(\sqrt{3}\)/2

tan 60 = 1/  √3

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Step-by-step explanation:

Since you didn't actually ask a question, I'm just going to explain how to get rid of the radicals.

When it comes to radical equations like these, you can usually square both sides to get rid of the radical.

The reason this works is because the "square root" of something is the same as that something raised to the power of 1/2. And when you raise a power to a power, you multiply the two together; which reduces the 1/2 and gets rid of the root. (This is actually true for any root. If you wanted to get rid of a cube root you could cube both sides. If you had a 20th root, you could raise both sides to the power of 20.)

From here you'll either have your answer or perhaps need to continue solving. My work is in the attachment, comment with any questions.

In order to create 728 millilitres of the medication, 273 millilitres of component A are required.

A compound in chemistry is a material comprised of two or more separate chemical elements mixed together in a certain proportion. Chemical connections that are challenging to break are created when the elements interact with one another.

Compound A:Compound B ratio in the medication is 3:5. In other words, there are 3 millilitres of compound A and 5 millilitres of compound B for every 3+5=8 millilitres of the medicine.

We may set up a percentage using the ratio of compound A to the total volume of the medicine to determine how much compound A is required to make 728 millilitres of the drug:

3 ml x 3 ml x 3 ml

-------- = ----------

728 ml total, 8 ml overall

If we cross-multiply, we obtain:

8(x) = 3(728)

To find x, we use the formula x = 3(728)/8 = 273

In order to create 728 millilitres of the medication, 273 millilitres of component A are required.

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273 milliliters of compound A are needed to make 728 milliliters of the drug.

What are proportions?

In mathematics, a proportion is a statement that two ratios are equal. It expresses the relationship between two or more quantities that are directly proportional to each other. A proportion can be represented as an equation of the form:

a/b = c/d

To determine the amount of compound A needed to make 728 milliliters of the drug, we need to use the given ratio of 3 milliliters of compound A to 5 milliliters of compound B.

Let's start by finding the ratio of compound A to the total amount of ingredients (A+B) in the drug:

3 : (3+5) or 3:8

This means that for every 8 milliliters of the drug, 3 milliliters of compound A are used.

To find out how many milliliters of compound A are needed for 728 milliliters of the drug, we can set up a proportion:

3/8 = x/728

where x represents the amount of compound A needed.

To solve for x, we can cross-multiply:

8x = 3*728

8x = 2184

x = 273

Therefore, 273 milliliters of compound A are needed to make 728 milliliters of the drug.

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