Lillian is trying to determine how people feel about the new act Congress is trying to put through. Which question would be the MOST appropriate for her survey?
A) How do you feel about the new Act Congress is trying to pass?
B) How do you feel about Congress spending billions of dollars on this new Act?
C) Which is better Congress passing this new Act or trying to erase national debt?
D) How do you feel about Congress raising federal taxes in order for the Act to be financed?

[tex]\bf \qquad \qquad \textit{joint compound proportional variation} \\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with \underline{z}} \end{array}\implies y=\cfrac{kx}{z}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{W varies jointly as its width, squared heght and inversely with length}}{W=\cfrac{wh^2}{L}}[/tex]

[tex]\bf \textit{now we also know that }~~ \begin{cases} w=\frac{1}{4}\\ h=\frac{1}{3}\\ L=12\\ W=30 \end{cases}\implies 30=\cfrac{~~k\frac{1}{4}\left( \frac{1}{3} \right)^2~~}{12} \\\\\\ 360=\cfrac{k}{36}\implies 12960=k~\hfill \boxed{W=\cfrac{12960wh^2}{L}}[/tex]

[tex]\bf \textit{when } \begin{cases} w=\frac{1}{4}\\ h=\frac{1}{2}\\ L=12 \end{cases}\textit{ what is \underline{W}?}\qquad W=\cfrac{12960\left( \frac{1}{4} \right)\left(\frac{1}{2} \right)^2}{12} \\\\\\ W=1080\left( \cfrac{1}{4} \right)\left( \cfrac{1}{4} \right)\implies W=1080\cdot \cfrac{1}{16}\implies W=\cfrac{135}{2}\implies W=67\frac{1}{2}[/tex]

Using the joint variation, A similar beam can support [tex]67 \frac{1}{2}[/tex] feet if the beam is one-fourth foot wide and half a foot high, and 12 feet long.

What is Proportion

A proportion is an equation stating that two rational expressions are equal. Simple proportions can be solved by applying the cross products rule.

If [tex]\frac{a}{b} = \frac{c}{d}[/tex] then ab = bc.

What is Direct variation?

The phrase “ y varies directly as x” or “ y is directly proportional to x” means that as x gets bigger, so does y, and as x gets smaller, so does y. That concept can be translated in two ways.

[tex]\frac{y}{x} = k[/tex] for some constant k.

The k is called the constant of proportionality. This translation is used when the constant is the desired result.

What is Inverse Proportion?

According to the expressions "y varies inversely as x" and "y is inversely proportionate to x," y decreases as x increases or vice versa. There are two translations for this idea. For any constant k, referred to as the constant of proportionality, yx = k. If the constant is wanted, use this translation.

What is Joint Variation?

Joint variation is the term used to describe when one variable changes as the sum of other variables. There are two translations for the phrase "y fluctuates concurrently as x and z."

So, In the given question:

Weight that a rectangular beam can support varies jointly as its width and the square of its height and inversely as its length;

It is in joint proportion;

[tex]\begin{aligned}&\mathbf{W}=\frac{\mathbf{w h}^2}{\mathbf{L}} \\&\left\{\begin{array}{l}w=\frac{1}{4} \\h=\frac{1}{3} \\L=12 \\W=30\end{array} \quad \Longrightarrow 30=\frac{\mathbf{k} \frac{1}{4}\left(\frac{1}{3}\right)^2}{12}\right.\end{aligned}[/tex]

[tex]360=\frac{\mathrm{k}}{36} \Longrightarrow 12960=\mathrm{k}[/tex]

Now,

[tex]\text { when }\left\{\begin{array}{l}w=\frac{1}{4} \\h=\frac{1}{2} \\L=12\end{array}\right.[/tex]

[tex]W=\frac{12960\left(\frac{1}{4}\right)\left(\frac{1}{2}\right)^2}{12}[/tex]

[tex]W=1080\left(\frac{1}{4}\right)\left(\frac{1}{4}\right) \\\Longrightarrow W=1080 \cdot \frac{1}{16}[/tex]

[tex]\\\Longrightarrow\mathrm{W}=\frac{135}{2} \\\Longrightarrow \mathrm{W}=67 \frac{1}{2}[/tex]

Hence, A similar beam can support [tex]67 \frac{1}{2}[/tex] feet if the beam is one-fourth foot wide and a half a foot high, and 12 feet long.

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Answer:

D. -2x+3y=12

Step-by-step explanation:

ANSWER

D. -2x+3y=12

EXPLANATION

The given line passes through:

(0,4) and (-6,0)

These are the x and y intercepts.

The equation is given by :

[tex] \frac{x}{a} + \frac{y}{b} = 1[/tex]

where a= -6 is the x-intercept and b=4 is the y-intercept.

We substitute the values to get,

[tex]\frac{x}{ - 6} + \frac{y}{4} = 1[/tex]

Multiply through by 12,

[tex]\frac{x}{ - 6} \times 12 + \frac{y}{4} \times 12 = 1 \times 12[/tex]

[tex] - 2x + 3y = 12[/tex]

The correct answer is D .

Answer:

The measure of angle BCD is [tex]35\°[/tex]

Step-by-step explanation:

we know that

The measurement of the outer angle is the semi-difference of the arcs it encompasses.

so

[tex]m<BCD=\frac{1}{2}(120\°-50\°)=35\°[/tex]

Answer:

4     5

8     10

20    25

5,20

Step-by-step explanation:

Answer:

f(x) = (x + 4)² - 13

Step-by-step explanation:

You will have to "complete the square [½B]²" to figure this out. Here is how you would set it up:

(x + 4)² → x² + 8x + 16

x² + 8x + 16 - 13 → x² + 8x + 3 [TA DA!]

We know that our vertex formula is correct. Additionally, that -h gives you the OPPOSITE terms of what they really are, and k gives you the EXACT terms of what they really are. Therefore, your vertex is [-4, -13].

I am joyous to assist you anytime.

ANSWER

[tex]48 {x}^{4} + 60{x}^{2} {y}^{3} + 56 {y}^{6}[/tex]

EXPLANATION

We want expand:

[tex](12x^2+8y^3)(4x^2+7y^3)[/tex]

We expand using the distributive to obtain:

[tex]12 {x}^{2} (4 {x}^{2} + 7 {y}^{3} ) + 8 {y}^{3} (4 {x}^{2} + 7 {y}^{3} )[/tex]

[tex]48 {x}^{4} + 28 {x}^{2} {y}^{3} + 32{x}^{2} {y}^{3} + 56 {y}^{6}[/tex]

Simplify further by combining the two terms in the middle:

[tex]48 {x}^{4} + 60{x}^{2} {y}^{3} + 56 {y}^{6}[/tex]

Answer:

[tex]48 {x}^{4}  + 60{x}^{2} {y}^{3} +  56 {y}^{6}[/tex]

Step-by-step explanation:

Answer: 12.5 tomatoes

Step-by-step explanation:

You know that the recipe for 4 servings requires 5 tomatoes and you want to make chili for 10 servings. Therefore, to calculate the amount of tomatoes required for this, you should use the following conversion factor:

[tex]\frac{5\ tomatoes}{4\ servings}[/tex]

Now multiply the conversion factor by the 10 servings:

[tex]=(10\ servings)(\frac{5\ tomatoes}{4\ servings})\\=12.5\ tomatoes[/tex]

Therefore, you will use 12.5 tomatoes to make 10 servings.

Answer:

Tomatoes for 10-servings = 12.5

Step-by-step explanation:

Given

Number of tomatoes for 4 servings = 5

So we can calculate the number of tomatoes for one serving by dividing the serving by number of tomatoes.

So,

Number of tomato for one serving = 5/4

= 1.25

Now we can calculate the number of tomatoes for 10 servings

Number of tomatoes for 10 servings = Number of tomatoes for one serving * 10

= 1.25 * 10

= 12.5 tomatoes

Answer:

7

Step-by-step explanation:

The given algebraic expression is;

[tex]-x^2-6y+13x+7[/tex]

This is an algebraic expression in x and y.

Any term that is independent  of these two variables is called the constant term.

The term '7' is independent  of these variables.

Hence the constant term is 7.

About $290.83.

Hope this helps!

The police officer will earn approximately $290.83 more each month in his second year, as his annual salary will raise from $26,400 to $29,890.

In this scenario, we are dealing with a salary raise and how it affects the overall monthly income. The first year, the police officer is earning $2,200 per month, which translates to an annual salary of $26,400 (since there are 12 months in a year, you can simply multiply the monthly income by 12 to find this). The second year, his annual salary will be raised to $29,890.

To see how much more they will be making a month, subtract the first year's annual salary from the second year's total ($29,890 - $26,400 = $3,490). This is the total raise for the year, but we want to find out how much more the officer will be making a month. Since the raise is distributed over 12 months, simply divide this total by 12 to get the answer. $3,490 ÷ 12 = approximately $290.83. So, the police officer will be making around $290.83 more each month in the second year.

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Answer:

On second day: 500 cm^3

On third day: 250 cm^3

Step-by-step explanation:

Let x be the initial amount of helium gas in the balloon.

As it is mentioned in the question that the balloon loses half of it's gas in one day. So after one day the gas will be half of the current volume. And to calculate the volume of gas the next day, the reduced volume will be divided by two.

So,

x = 1000 cm^3

Volume on second day,

x1 = 1000/2

=> 500 cm^3

Volume of gas on third day

x2 = x1/2

=> 500/2

=> 250 cm^3

Answer:

the answer is 500cm^3 and 250cm^3

Step-by-step explanation:

This is the correct answer to your question.

Answer:

(6.08,170.54)

Explanation:

It goes 6 to the left and 1 up

Using Pythagorean theorem= 1/6=tan(angle)

Inverse tan 1/6= angle

= 9.46 degrees

180-9.46= 170.54 degrees is the angle

1^2+(-6)^2=h^2

1+36=h^2

h= square root of 37

h= 6.08

Hope you get it!

Answer:

100

Step-by-step explanation:

"What number" means a variable, like x.

"Is" means equals.

"Less than" means subtracted from.

Percent means out of 100.

"Of" means multiplication.

x = (150/100) 80 - 20

x = 120 - 20

x = 100

The answer is:

{-5<x<5}

To solve the problem, we need to remember how Absolute Value Functions behave, when we have this type of function, related to an inequality, the solution will be between two values.

We are given the inequality:

[tex]|x|<5[/tex]

So, we know that "x" will be between -5 and 5:

[tex]-5<x<5[/tex]

Hence, the solution of the given inequality will be:

(-5,5) or {-5<x<5}

Have a nice day!

Answer:

{x|-5 < x < 5}

Step-by-step explanation:

I got the answer right.

Answer:

logbase13(169)=2

Step-by-step explanation:

Convert the exponential equation to a logarithmic equation using the logarithm base (13)of the left side (169) equals the exponent (2).

In the logarithimic form we have the equation as [tex]log_{13} 169 = 2[/tex].

We must note that we can write either in the logarithmic form or in the index form.

In this case, we have written in the index form as [tex]169=13^2[/tex]. In the logarithimic form we have the equation as [tex]log_{13}169 = 2[/tex].

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Answer:

hello :

the axis of symmetry  is the line wher an equation is : x =2

the vertex is : (  2 ; 5 )

Step-by-step explanation:

write this expression in the vertex form :

y=-x²-4x+1​

y = - ((x² +4x +4) -4) +1

y = - (x -2)²+5

the axis of symmetry  is the line wher an equation is : x =2

the vertex is : (  2 ; 5 )

Answer:

[tex]\left[\begin{array}{cc}-\frac{1}{2}&\frac{1}{6}\\-\frac{1}{2}&\frac{1}{3}\\\end{array}\right][/tex]

Step-by-step explanation:

If a 2x2 matrix is given as:

[tex]\left[\begin{array}{cc}a&b\\c&d\\\end{array}\right][/tex]

The inverse is:

[tex]\frac{1}{ad-bc}\left[\begin{array}{cc}d&-b\\-c&a\\\end{array}\right][/tex]

Our matrix given is:

[tex]\left[\begin{array}{cc}-4&2\\-6&6\\\end{array}\right][/tex]

Using the formula, let's find the inverse:

[tex]\frac{1}{ad-bc}\left[\begin{array}{cc}d&-b\\-c&a\\\end{array}\right]\\=\frac{1}{(-4)(6)-(-6)(2)}\left[\begin{array}{cc}6&-2\\6&-4\\\end{array}\right]\\=\frac{1}{-12}\left[\begin{array}{cc}6&-2\\6&-4\\\end{array}\right]\\=\left[\begin{array}{cc}-\frac{1}{2}&\frac{1}{6}\\-\frac{1}{2}&\frac{1}{3}\\\end{array}\right][/tex]

The 7 is in the 10 thousandth place of the number 472,085

That means is has the value of 70,000

Answer:

70,000

Step-by-step explanation:

The 7 is in the 10,000 place so therefore it would be 7 multiplied by 10,000

Answer:

C

Step-by-step explanation:

The central angle is 20% of 360°, that is

central angle = [tex]\frac{20}{100}[/tex] × 360° = 0.2 × 360° = 72° → C

Answer:

Find the measure of the central angle that you would draw to represent 20% in a circle graph.

A. 18°

B. 60°

C. 72°

D. 20°

Step-by-step explanation:

The central angle is 20% of 360°

20 % of 360 = 72°

Hey there!

First, the minus sign is equal to -1 (in this case)

Now, let's distribute -1 by multiplying it times 5 and -3v:

-5+3v

or

3v-5

Both expressions are equivalent (equal to each other)

Hence, the answer is

[tex]\boxed{\boxed{\bold{3v-5}}}[/tex]

Hope everything is clear.

Let me know if you have any other questions.

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To simplify the expression -(5-3v) using the distributive property, distribute the negative sign to each term inside the parentheses and combine like terms.

To simplify the expression -(5-3v) using the distributive property, we need to distribute the negative sign to each term inside the parentheses. This means we will multiply -1 by both 5 and -3v.

The distributive property states that for any numbers a, b, and c, a(b + c) is equal to ab + ac. Applying this property to our expression, we get -(5) - (-3v), which simplifies to -5 + 3v.

Therefore, the simplified expression is -5 + 3v.

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Answer:

its c

Step-by-step explanation:

Answer: Option C.

Step-by-step explanation:

The surface area of the right triangular will be the sum of all its faces.

You can observe in the figure that the faces of the right triangular prism are: Two equal right triangles and three different rectangles.

The formula for calculate the area of a triangle is:

  [tex]A=\frac{bh}{2}[/tex]

Where "b" is the base and "h" is the height.

The formula for calculate the area of a rectangle is:

  [tex]A=lw[/tex]

Where "l" is the length and "w" is the width.

Then, the surface area of the right triangular prism is:

[tex]SA=\frac{ba}{2}+\frac{ba}{2}+dc+db+da\\\\SA=2(\frac{ba}{2})+d(c+b+a)\\\\SA=2(\frac{4cm*3cm}{y})+8cm(5cm+4cm+3cm)\\\\SA=108cm^2[/tex]

Answer:

c. 216 inches

Step-by-step explanation:

6*6=36

Root 6 times root 6=6

36 times 6 is 216

Answer:

Area of square= 216 square inches

Perimeter  of square [tex]= 24\sqrt{6}[/tex] inches.

Step-by-step explanation:

Given that length of the side of the square = [tex]6\sqrt{6}[/tex] inches.

Now we need to find area of the rectangle. So apply the formula  area of rectangle

[tex]Area of square= (side)^2[/tex]

[tex]Area of square= (6\sqrt{6})^2[/tex]

[tex]Area of square= 6^2(\sqrt{6})^2[/tex]

[tex]Area of square= 36(6)[/tex]

Area of square= 216 square inches

Similarly

[tex]Perimeter of square= 4(side)[/tex]

[tex]Perimeter  of square= 4(6\sqrt{6})[/tex]

Perimeter  of square [tex]= 24\sqrt{6}[/tex] inches.

Answer:

x= 4-7i  x= 4+ 7i

Step-by-step explanation:

step 1 : make equation = 0

[tex]x^{2}[/tex] - 8x + 65 = 0

step 2 : solve for x [ using the quadratic equation]

ie :     x = -b ± [tex]\sqrt{b^{2}-4ac}[/tex] / 2a

so it will look like this

x= -(-8) ± [tex]\sqrt{(-8)^{2} - 4(1)(65)}[/tex] /2(1)

when you simplify you wont be able to root the -196 so you will have to separate the roots

x = 8 ±( [tex]\sqrt{-1}[/tex] )( [tex]\sqrt{196}[/tex]) / 2

now there is a rule for negative roots whereby  [tex]\sqrt{-1}[/tex] is equivalent to i so now you will change [tex]\sqrt{-1}[/tex] into i

Simplify [tex]\sqrt{196}[/tex]

which will give you 14

now place all the new values into the formula

8 ± 14i /2

you can then further simplify to  

4 ± 7i

step 3 : separate

this will give you the final answer of

x= 4 + 7i   x= 4- 7i

Answer:

x = 4+7i and x=4-7i

Step-by-step explanation:

I just did the test

The correct answers are 5, 10, and 15. I'm doing the same subject and I got a 100 on a question similar. Good luck!

Answer:

5, 10, and 15

Step-by-step explanation:

Answer:

the means absolute deviation is 1.8

the striking deviation is 7

(it is because the data point on the far right of the graph)

Step-by-step explanation:

calculate the absolute deviation:

1.  calculate the mean (add all numbers and divide by 10) = 2.6

2.  find the absolute value of each

2.6 - 0 = 2.6

2.6 - 1 = 1.6 (you have 1's 4 times so each one will be 1.6)

2.6 - 3 = 0.4

2.6 - 4 = 1.4 (you have 4's 3 times)

2.6 - 7 = 4.4

3.  Then add all of those values together

2.6 + 1.6 + 1.6 + 1.6 +  1.6 + 0.4 + 1.4 + 1.4 + 1.4 + 7.4 = 18

4.  find the mean of the difference

18/10 = 1.8

Answer:

1.8 and 7, just like the other person said<3

Step-by-step explanation:

Answer:

The correct answer is option A.  1

Step-by-step explanation:

Points to remember

An element in a matrix is represented by Eₐₓ

It means that the element in ath row and xth column

From the figure we can see that a 4 x 4 matrix.

To find element a₃₃

From the given matrix we get a₃₃

a₃₃ means element in 3rd row and 3rd column

Here a₃₃ = 1

Therefore the correct answer is option A.  1

38 green is d mode of the data

Answer:

Median = 18

Step-by-step explanation:

The median is the middle number if the elements (prices)  are arranged from least to greatest.

let's arrange the prices of watches from least to greatest:

12, 15, 16, 16, 20, 22, 24 27

Since there are even number of numbers (8), the median is the value between 4th and 5th numbers.

4th number is 16

5th number is 20

We need the value between 16 and 20. We get that by adding these 2 and dividing by 2:

16 + 20 = 36

36/2 = 18

THus, median = 18

Answer:

522 [tex]m^2[/tex]

Step-by-step explanation:

To find the surface area, we can find the area of each shape in the net.

There are 2 identical triangles and 3 different rectangles. Then we can add all of these areas together

[tex]2(\frac{1}{2} (9)(14))=126\\\\(10)(14)=140\\\\(10)(16.6)=166\\\\(9)(10)=90\\\\126+140+166+90=522[/tex]

Answer:

Step-by-step explanation:

In this problem, you have to work sort of backwards.

The mean is 2.3 and there are 6 numbers [including this missing one] so multiply 2.3 by 6.

2.3 x 6 = 13.8

Now, subtract the 5 values you know from 13.8

13.8 - 2.3 - 4.1 - 1.2 - 1 - 0.5 = 4.7

Thus, the missing value is 4.7

I hope this helps!

It would be 170.1

Steps:

Each triangle side: 10 × 9 = 90 × 0.50 = 45

Since there are three sides: 45 × 3 = 135

Bottom triangle: 9 × 7.8 = 35.1

135 + 35.1= 170.1

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Answer:

170.11

Step-by-step explanation:

Question

Find the surface area of the regular pyramid.

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Find the surface area of the regular pyramid.

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Find the surface area of the regular pyramid.

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Find the surface area of the regular pyramid.

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