Type the correct answer in each box. Round numbers to the nearest tenth, if necessary.
Solve the equation by filling out the table.

-0.5x − 2 = 2x−1 − 5

Answer:

The answer is C

Step-by-step explanation:

Answer: D. The interquartile range (IQR) for Town A , 15° is less than the interquartile range for town B , 20°.

Step-by-step explanation:

The interquartile range is most suitable term to compare the spread of two different data displayed by box-whisker plot.

The formula for interquartile range :-

 [tex]IQR=Q_3-Q_1[/tex]

For Town A , First quartile : [tex]Q_1=15[/tex]

Second quartile : [tex]Q_2=30[/tex]

[tex]IQR=30-15=15[/tex]

For Town B , First quartile : [tex]Q_1=20[/tex]

Second quartile : [tex]Q_2=40[/tex]

[tex]IQR=40-20=20[/tex]

Clearly , the interquartile range (IQR) for Town A , 15° is less than the interquartile range for town B , 20°.

The true statements about the result of the coin toss experiment described are :

Number of heads :__0 __ 1 __ 2 __ 3

Frequency _____ :_ 2___7___9___2

Therefore, expected Number of 3 and 0 heads are the same. And the expected number of 1 and 2 heads are almost the same.

The experiment cannot be used to model the events in the options as it only gives the number of occurence of a single event.

Hence, only statements 1 and 2 are true.

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The frequency of 0, 1, 2, and 3 heads in the experiment is 2, 7, 10, and 1 respectively. Statement 2 is the most accurate regarding long-term expectations, while statement 4 can be considered conditionally true. Statements 1 and 3 are not related to the probability outcomes of the experiment.

To complete the frequency table based on the given results, we will count the occurrences of each number of heads (0, 1, 2, or 3) in the 20 trials. The frequencies are:

Based on these results, we can discuss the truthfulness of the provided statements:

The distance of the line segment joining the points (5, 4) and (-2, 1) is found using the distance formula. Substituting the given points into the formula, we calculate the distance to be approximately 7.62 units.

The distance between two points (x1, y1) and (x2, y2) in a 2-dimensional Cartesian plane is given by the distance formula: √[(x2-x1)² + (y2-y1)²].

Substituting the given points (x1, y1) = (5, 4) and (x2, y2) = (-2, 1), we get:

Distance = √[(-2 - 5)² + (1 - 4)²] = √[( -7)² + (-3)²] = √[49 + 9] = √58 ≈ 7.62.

Therefore, the distance of the line segment joining the two points (5, 4) and (-2, 1) is approximately 7.62 units.

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Answer:

1/3 - 1/x=1/5

Step-by-step explanation:

Let the total work be "1"

                        Brody          Hudson              Brody+Hudson

  Time              3 mins            x min                       5 min

  Efficiency        1/3                   -1/x                          1/5

The efficiency of Hudson is negative as he is taking out the candies out of the bowl, since efficiency of Brody + efficiency of Hudson = efficiency of both, which means,

1/3 - 1/x = 1/5....

Answer:

-59/17 =x

Step-by-step explanation:

53=-6-17x​

Add 6 to each side

53+6=-6+6-17x​

59 = -17x

Divide each side by -17

59/-17 = -17x/-17

59/-17 = x

-59/17 =x

Answer:

x=21

y= 7

Step-by-step explanation:

x+y = 28

x = 3y

Substitute the second equation into the first

3y+y = 28

4y = 28

Divide by 4

4y/4 = 28/4

y = 7

Now we need to find x

x = 3*y

x = 3*7

x = 21

Answer:

A:  x-axis

I did a quiz and got it wrong when I choose B: y-axis.

Final answer:

The point with coordinates (0, 3) is on the y-axis, above the origin by 3 units. Therefore, the correct answer is B, the y-axis.

Explanation:

A point with the coordinates (0, 3) is located where the x-coordinate is 0 and the y-coordinate is 3. In the context of a two-dimensional Cartesian coordinate system, this means the point does not move left or right from the origin on the horizontal axis, but it moves up by 3 units on the vertical axis.

Therefore, the correct answer to the question is B, the point is located on the y-axis. It is neither on the x-axis nor in any of the four quadrants since its x-coordinate is zero. Hence, it lies directly above the origin on the y-axis.

Answer:

The answer is 192

Step-by-step explanation:

2^8 = 256

8^2 = 64

256 - 64 = 192

Remember:

2^8 is really 2*2*2*2*2*2*2*2

Remember:

8^2 is really 8*8

To find the difference, you must subtract the smaller product from the larger product.

<Hope this helps!>

Answer:

192

Step-by-step explanation:

Method 1:

2^8 - 8^2 = 2^8 - 2^6 = 2^6(2^2 - 1) = 64(3) = 192

Method 2:

2^8 - 8^2 = 256 - 64 = 192

Answer:

Obtuse and Scalene

Step-by-step explanation:

Obtuse means that it is over 90 degrees, in which there is an angle of 102 degrees.

Scalene means that all three side lengths are different.

Answer:

A. Obtuse

C. Scalene

Answer:

250, -1250

Step-by-step explanation:

Geometric Sequence is a hint to think multiplication:

What can you multiply to -2 to get 10

or what is 10/-2

I hope you said -5.

So just multiply -5 to a term to get the term right after!

So

-50(-5)=250

250(-5)=-1250

To find the total profit for both wallets sold by Efficient Homemakers Ltd., use the equation P = 40x + 25y, where x is the number of leather wallets and y is the number of canvas wallets sold.

The question involves writing a function for the total profit from selling canvas wallets and leather wallets made by Efficient Homemakers Ltd.

To calculate the total profit, we denote x as the number of leather wallets and y as the number of canvas wallets.

The company makes a profit of $40 for each leather wallet, and $25 for each canvas wallet.

Thus, the total profit P can be represented by the equation:

P = 40x + 25y

This equation represents the total profit as a function of the number of leather wallets (x) and the number of canvas wallets (y) sold.

Answer:

The radius of the circle is already there, 11cm, and the diameter is 2 times the radius, which is 22

Step-by-step explanation:

First, you look at the radius (which is half of the circle) which is 11, then you multiply that times two to get the diameter. :)

Answer: The number before the decimal

Step-by-step explanation:

The digit in the ones place is 9, in the given number 409.21.

The given number is 409.21

⇒ 400 + 00 + 9 + 2×(1/10) + 1×(1/100)

⇒ 4×100 + 0×10 + 9×1 + 2×(1/10) + 1×(1/100)

So, the digit in ones place is 9.

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Answer:

False

Step-by-step explanation:

2 = x - 8

Add 8 to each side

2+8 = x-8+8

10 = x

x=4 is not a solution

For this case we have the following equation:

[tex]2 = x-8[/tex]

If we add 8 to both sides of the equation, we have:

[tex]2 + 8 = x-8 + 8\\10 = x[/tex]

Thus, the solution of the equation is [tex]x = 10,[/tex] therefore[tex]x = 4[/tex]is not a solution of the given equation.

Answer:

[tex]x = 4[/tex] is not a solution to the given equation.

False

Answer:

$22.68

Step-by-step explanation:

21×.08= 1.68

21+1.68=22.68

Total cost =$22.68

Answer:

22.68

Step-by-step explanation:

The first step is to find the amount of tax

tax = original cost * tax rate

       = 21 * 8%

       = 21 * .08

      =1.68

Then we add the tax to the original cost to find the total cost

total cost = original cost + tax

               = 21 + 1.68

               =22.68

Answer:

The 17th term in arithmetic sequence is 68

Step-by-step explanation:

The general formula of arithmetic sequence is:

aₙ = a₁ + (n – 1)d.

We are given a₆ = 101 and a₉ = 83 and we need to find a₁₇

To find the term a₁₇ we should know a₁ and d. So we would find both

a₆ = a₁ +(6-1)d

101 = a₁ +(5)d

101 = a₁ +5d     eq(1)

and

a₉ = a₁ +(9-1)d    

83 = a₁ + 8d       eq(2)

Subtracting eq(2) from eq(1)

101 = a₁ +5d

83 = a₁ + 8d

-       -     -

__________

18 = -3d

=> d = 18/-3

=> d = -6

Putting value of d in eq(1)

101 = a₁ + 5d

101 = a₁ + 5(-3)

101 = a₁ -15

=> a₁ = 101+15

=> a₁ = 116

Now finding a₁₇:

aₙ = a₁ + (n – 1)d.

a₁₇ = 116 +(17-1)(-3)

a₁₇ = 116+(16)(-3)

a₁₇ = 116 - 48

a₁₇ = 68

So, the 17th term in arithmetic sequence is 68

Answer:

x = 11.2

Step-by-step explanation:

-5x - 12y = -8  

5x + 2y = 48

you can combine all like terms from both equations together:

0x-10y=40

simplified:

-10y=40

y=-4

now you plug in the value of y into either equation:

5x+2(-4)=48

simplify

5x-8=48

add 8

5x=56

divide by 5

x=56/5=11.2

Check the picture below.

[tex]\bf \stackrel{\textit{triangles' area}}{\cfrac{1}{2}(6)(1)+\cfrac{1}{2}(6)(1)}+\stackrel{\textit{front side}}{(6\cdot 2)}+\stackrel{\textit{left and right sides}}{(4\cdot 2)+(4\cdot 2)}\implies 3+3+12+8+8[/tex]

so namely how many times does 1¼ go into 15⅓?

let's firstly convert the mixed fractions to improper fractions and then divide.

[tex]\bf \stackrel{mixed}{1\frac{1}{4}}\implies \cfrac{1\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{5}{4}}~\hfill \stackrel{mixed}{15\frac{1}{3}}\implies \cfrac{15\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{46}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{46}{3}\div\cfrac{5}{4}\implies \cfrac{46}{3}\cdot \cfrac{4}{5}\implies \cfrac{184}{15}\implies 12\frac{4}{15}[/tex]

To perform F(g(x)), substitute g(x) into F(x) by squaring g(x) and subtracting 4. The domain of F(g(x)) is all real numbers.

The question asks us to perform the composition of two functions - f(x) and g(x). Composition is denoted by (f ∘ g)(x) and involves substituting the output of the inner function (g(x)) into the input of the outer function (f(x)). In this case, we have f(g(x)), which means we need to substitute g(x) into f(x).

First, substitute g(x) into f(x) to get f(g(x)):

f(g(x)) = (g(x))^2 - 4 = (x+2)^2 -4 = x^2 + 4x + 4 - 4 = x^2 + 4x.

The domain restriction is the set of all values that x can take. Since there are no restrictions mentioned in the question, the domain is all real numbers.

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Answer:

[tex]24\sqrt{5}\ yards[/tex]

Step-by-step explanation:

Let A1 be the area of one square and A2 be the area of second square

So,

A1 = s^2

where s is side of square

[tex]s^2=125\\\sqrt{s^2}=\sqrt{125}\\s=\sqrt{25*5}\\ s= \sqrt{5^2 * 5}\\ s= 5\sqrt{5}[/tex]

So side of one square is [tex]5\sqrt{5}[/tex]

To calculate the length of fence we need to find the perimeter of the square

So,

P1 = 4 * s

[tex]=4*5\sqrt{5} \\=20\sqrt{5}[/tex]

For second square:

[tex]A_2=s^2\\5=s^2\\\sqrt{s^2}=5\\{s}=\sqrt{5}[/tex]

The perimeter will be:

[tex]P_2 = 4*s\\=4 * \sqrt{5} \\=4\sqrt{5}[/tex]

So the total fence will be: P1+P2

[tex]= 20\sqrt{5}+4\sqrt{5} \\= 24\sqrt{5}\ yards[/tex]

Answer:

[tex]A=400\ people[/tex]

Step-by-step explanation:

we have

[tex]Q=600+\sqrt{A+41}[/tex]

where

Q -----> is the daily output

A -----> is the number of people

For Q=621

Find the value of A

substitute and solve for A

[tex]621=600+\sqrt{A+41}[/tex]

Subtract 600 both sides

[tex]621-600=\sqrt{A+41}[/tex]

[tex]21=\sqrt{A+41}[/tex]

squared both sides

[tex]21^{2} ={A+41}[/tex]

[tex]441={A+41}[/tex]

Subtract 41 both sides

[tex]441-41=A[/tex]

Rewrite

[tex]A=400\ people[/tex]

Check the picture below.

[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\ \cline{1-1} C=4.5 \end{cases}\implies 4.5=2\pi r\implies \cfrac{4.5}{2\pi }=r \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} h=8\\ r=\frac{4.5}{2\pi } \end{cases}\implies V=\pi \left( \cfrac{4.5}{2\pi } \right)^2(8)\implies V=\begin{matrix} \pi \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} \cdot \cfrac{20.25}{\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}\underset{\pi }{\begin{matrix} \pi^2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} }}(\stackrel{2}{\begin{matrix} 8 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}})[/tex]

[tex]\bf V=\cfrac{40.5}{\pi }~cm^3~\hspace{9em} \stackrel{\textit{since density is }752kg~per~cm^3}{density\implies 752\left( \cfrac{40.5}{\pi } \right)}\qquad \approx ~~9694[/tex]

Option 2 is correct. The approximate weight of the trunk of an American white oak tree with a circumference of 4.5 meters and a height of 8 meters is calculated by finding the volume of the trunk and multiplying it by the tree's density, resulting in approximately 9,694 kilograms.

To calculate the approximate weight of the trunk of an American white oak tree, we first need to estimate its volume and then multiply it by the tree's density. Since the tree trunk is cylindrical, we can use the formula for the volume of a cylinder, [tex]V = \(pi \times r^2 \times h\)[/tex], where r is the radius of the base and h is the height of the cylinder. The circumference is given by C = 2 times pi times r, so we can solve for r by rearranging the formula: [tex]\(r = \frac{C}{2 \times \\pi}\)[/tex]. With a circumference of 4.5 meters, the radius is [tex]\(r = \frac{4.5 \text{m}}{2 \times \pi}\approx 0.716m\)[/tex]. Plugging the radius and the height (8 m) into the volume formula gives V approx pi times (0.716m)^2 times 8 m approx 13.07 m^3.

Knowing the volume, we can find the mass of the trunk by multiplying the tree's volume by its density. The density of American white oak is given as 752 kilograms per cubic meter. The mass (m) is then [tex]m = V \times \ext{density} = 13.07 m^3 \times 752 \frac{kg}{m^3} \approx 9,832.64 kg.[/tex] Rounding off gives us approximately 9,694 kilograms, which is option 2 and is the closest answer provided in the question.

Answer:

The answer is 27 patients.

Step-by-step explanation:

There are 3 patients per floor. There are 9 floors.

3 x 9 = 27

There are 27 patients in all.

I hope this helped! :)

Answer:

1 hour 54 minutes

Step-by-step explanation:

1 hour and 9 minutes + 45 minutes gives your answer. However, since 45+9=54, this is convenient, since now we don't need to carry. Thus, 1 hour and 54 min is your answer.

Hope this helps!

Answer: 114 minutes or  1 hour and 54 minutes.

Step-by-step explanation:

You need to analyse the exercise.

You know that it takes 45 minutes from Helflin to Pale City.

Driving back to Alabama takes 1 hour and 9 minutes. You need to remember that there are 60 minutes in an hour, therefore, this time in minutes is:

[tex]60\ minutes+9\ minutes=69\ minutes[/tex]

To find the total time, you need to add 45 minutes and 69 minutes. Then you get:

[tex]Total=45\ minutes+69\ minutes=114\ minutes[/tex] or 1 hour and 54 minutes.

For this case we have a function of the form [tex]y = g (x)[/tex]

Where:

[tex]g (x) = x ^ 2 + 2[/tex]

We must find the value of the function when x = 3. Then we substitute:

[tex]g (3) = 3 ^ 2 + 2\\g (3) = 9 + 2\\g (3) = 11[/tex]

Thus, the value of the function when [tex]x = 3[/tex] is [tex]y = 11[/tex]

Answer:

[tex]g (3) = 11[/tex]

Option C

Answer: Third Option

[tex]g(3) = 11[/tex]

Step-by-step explanation:

We have the function  [tex]g(x) = x^2 + 2[/tex] and we must find the value of g(3).

To find g (3) we must evaluate the function g(x) for x = 3. That is, we must replace x = 3 in the function

Then

[tex]g(x) = x^2 + 2[/tex]

[tex]g(3) = (3)^2 + 2[/tex]

[tex]g(3) = 9 + 2[/tex]

[tex]g(3) = 11[/tex]

Finally the correct answer is the third option

Step-by-step explanation:

[tex]for\ 2<x\leq4-\text{the horizontal segment}\ y=2\\\\for\ 4<x<8\to y=x+3\\\\\text{put}\ x=4,\ \text{and}\ x=8\ \text{to the equation}\\\\y=4+3=7\to(4,\ 7)\\y=8+3=11\to(8,\ 11)\\\\for\ x\geq8\to y=2x\\\\\text{put}\ x=8,\ and\ x=9\ \text{to the equation}\\\\y=2(8)=16\to(8,\ 16)\\y=2(9)=18\to(9,\ 18)\\\\==========================[/tex]

[tex]<,\ >\ -\ \text{op}\text{en circle}\\\\\leq,\ \geq\ -\ \text{closed circle}[/tex]

Answer:

[tex]\frac{15}{8}[/tex]

Step-by-step explanation:

"the quotient of 1 and 2/3 " expressed mathematically is,

1 ÷ [tex]\frac{2}{3}[/tex] = [tex]\frac{3}{2}[/tex]

"divided by 4/5"

[tex]\frac{3}{2}[/tex] ÷ [tex]\frac{4}{5}[/tex]

=[tex]\frac{3}{2}[/tex] x [tex]\frac{5}{4}[/tex]

= [tex]\frac{15}{8}[/tex]

In order to get the answer to this problem you will have to go to the thousands place value and look at the number next to the place value and if the number is greater then 5 then you round up which will give you your answer.

[tex]692,119[/tex]

[tex]2,119[/tex]

[tex]1<5[/tex]

[tex]= 2000[/tex]

[tex]= 692,000[/tex]

Which means your answer is "692,000."

Hope this helps.

The value 692,119 is rounded to the nearest thousand is 692,000. The nearest thousand for the given number is 2000.

The given number is 692,119

The digit in the thousands place of the given number is 2.

The digit after 2 is 1 which is less than 5. So, the digits after the thousand place is rounded as zeros. I.e., 2119 to 2000.

Therefore, the rounded number is 692,000.

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[tex](x + 10)(x + 10) = 0\\x+10=0\\x=-10[/tex]

ANSWER

[tex]x = - 10[/tex]

EXPLANATION

We have the quadratic equation

[tex](x + 10)(x + 10) = 0[/tex]

This quadratic equation is in the factored form.

According to the zero product principle either the first factor is zero or the second is zero.

We apply the zero product principle to obtain:

[tex](x + 10) = 0 \: \: or \: \: (x + 10) = 0[/tex]

This is a repeated factor therefore,

[tex]x = - 10[/tex]

is the repeated root.