A rectangular sheet of steel is being cut so that the length is four times the width the perimeter of the sheet must be less than 100 inches . Which inequality can be used to find all possible lengths,l.of the steel sheet

Answer:

3 - b=12

4- b=14.1

Step-by-step explanation:

Area of the bookshelf=864 square inches

the book shelf is a rectangular prism

if we have height=4b, width=3b, length=b

then the area=length * width

A=(l*w)*2 ( we have 2 shelves)

864=(b*3b)*2

864=6b²

b²=864/6=144

b=√144= 12 inches

4- to cover the sides :

(height * length)*2   ( we have 2 sides)

(4b*b)×2=1600

8b²=1600

b²=1600/8=200

b=√200=14.1

Answer:

Question #3:  b = 12 in

Question #4:  b = 14.1 in

Step-by-step explanation:

Please see in the image attached the actual proportions that the furniture manufacturer uses to build the furniture in question:

Height = 4 b

Width = 3 b

Depth = b

So for question #3, given that the customer wants a total surface of the shaded shelves to be 864 [tex]in^2[/tex]

we can write that one wants twice the area of each rectangle of width 3 b and depth b to total 864:

[tex]2\,(3b\,*\,b)=864\\6 b^2=864\\b^2=864/6\\b^2=144\\b=12\,\,in[/tex]

Question # 4:

The total lateral surface to be covered by the silk is 1600 [tex]in^2[/tex], therefore if we consider the surface of each lateral plank as:

Area of each lateral plank :

[tex](4b)\,(b) = 4\,b^2[/tex]

Then twice these is: [tex]8\, b^2[/tex]

So we can solve for be requesting that these total surface equal the amount of silk:

[tex]8\,b^2=1600\\b^2=1600/8\\b^2=200\\b=\sqrt{200} \\b\approx 14.1421\,\,in[/tex]

which rounded to the nearest tenth of an inch gives:

[tex]b\approx 14.1\,\,in[/tex]

Answer:

The correct option is;

y < x - 2, and y > x + 1

Step-by-step explanation:

The given graph of inequalities is made up of parallel lines. Therefore, the slope of the inequalities are equal

By examination of the graph, the common slope = (Increase in y-value)/(Corresponding increase in x-value) = (0 - 1)/(-1 - 0) = 1

Therefore, the slope = 1

We note that the there are three different colored regions, therefore, the different colored regions opposite to each inequalities should be the areas of interest

The y-intercept for the upper bounding linear inequality, (y >) is 1

The y-intercept for the lower bounding linear inequality, (y <) is -2

The two inequalities are y > x + 1 and y < x - 2

The correct option is y < x - 2, and y > x + 1.

The system of linear inequalities is represented by  the graph is y> x-2 and y < x + 1

Inequalities is an expression that shows the non equal comparison of two or more variables and numbers.

Given that:

The system of linear inequalities is represented by  the graph is y> x-2 and y < x + 1

Find out more on linear inequalities at: https://brainly.com/question/21103162

Answer:

The correct option is;

B. N'(1, 0), U'(3, 5), L'(5, 2), H'(3, -2)

Step-by-step explanation:

The coordinates of the pre-image are given as follows;

H(1, -5), N(-1, -3), U(1, 2), and L(3, -1)

The required transformation is T₍₂, ₃₎,which is a translation of (two) 2 units right and an additional  translation of (three) 3 units up, which gives the coordinates of the image as follows;

N(-1, -3) transformed by N(-1 + 2, -3 + 3)  [tex]\overset{T_{(2,\, 3)}}{\rightarrow}[/tex] N'(1, 0)

U(1, 2) transformed by U(1 + 2, 2 + 3)  [tex]\overset{T_{(2,\, 3)}}{\rightarrow}[/tex] U'(3, 5)

L(3, -1) transformed by L(3 + 2, -1 + 3)  [tex]\overset{T_{(2,\, 3)}}{\rightarrow}[/tex] L'(5, 2)

H(1, -5) transformed by H(1 + 2, -5 + 3)  [tex]\overset{T_{(2,\, 3)}}{\rightarrow}[/tex] H'(3, -2)

The coordinates of the vertices of the given figure after the given transformation, T₍₂, ₃₎, are N'(1, 0), U'(3, 5), L'(5, 2), and H'(3, -2).

Therefore, the correct option is N'(1, 0), U'(3, 5), L'(5, 2), H'(3, -2).

Answer:

x= 36 km

Step-by-step explanation:

Vince went on a 3 day hiking trip. Each day, he walked 3/4 the distance that he walked the day before. He walked 83.25 kilometers total in the trip. How far did Vince walk on the 1st day of the trip?

Assume vince walked x km on the first day .

The following equation can be formed

x + 3/4 x + (3/4)^2 x = 83.25

x + 0.75x + 0.5625x = 83.25

Add the like terms

2.3125x = 83.25

Divide both sides by 2.3125

x = 36 km.

Answer:

36

Step-by-step explanation:

Answer:

Step-by-step explanation:

Area of a rectangle = Length * Width

Given parameters

Area A = 8x2 – 10x – 12

Length of the rectangle = 4x+3

Required

Width of the rectangle.

Substituting the given parameters into the formula

8x2 – 10x – 12  = (4x+3)*width

width = 8x2 – 10x – 12 /4x+3

S

Factorizing the numerator

8x² – 10x – 12

= 2(4x²-5x-6)

= 2(4x²-8x+3x-6)

= 2(4x(x-2)+3(x-2))

= 2(4x+3)(x-2)

Width = 2(4x+3)(x-2)/4x+3

Width = 2(x-2)

Width = 2x-4

Hence the width of the rectangle is 2x-4

Answer:

n/2>8

Step-by-step explanation:

Half of N is N/2

And if 8 is less that half of N or N/2

then

N/2 has to be greater than 8

N/2>8

The statements that can be used to describe the reasoning used to determine if Kelsey’s inequality is correct include:

It should be noted that the inequality symbol is incorrect because she can spend up to and including $65.

Based on the information given, the correct expression that can be used to solve the question should be:

65 - (5.50b + 7.5)

In conclusion, the correct options are B and C.

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Answer:

B and C

Step-by-step explanation:

Answer:

117.79

Step-by-step explanation:

[tex](-3+5,10-7)=(2,3)[/tex]

Hey there! I'm happy to help!

When building equations, the word "is" means "equals".

First, we have the sum of a number and six. You can use any letter to represent the number. I will use n.

(n+6)

We see that this is multiplied by 5. We can just put the 5 next to the parentheses. This shows multiplication.

5(n+6)

Is 48

5(n+6)=48

Have a wonderful day! :D

Answer:

14)  answer is 4

15) proved

Step-by-step explanation:

x=7-4√3 , √x +1/√x

√(7-4√3) +1/√7-4√3)=

8-4√x/√(7-4√3)= 4 ( use calculator)

Answer:

21

Step-by-step explanation:

4[tex]\frac{1}{5}[/tex] = [tex]\frac{21}{5}[/tex]

5 × [tex]\frac{21}{5}[/tex] = (5×21)/5

[tex]\frac{105}{5}[/tex] = 21

Answer:

a

Step-by-step explanation:

a because when you divide 80 by 12 you get 28, so then it is 12 x 28m. :/

Answer:

Width  W = 14 m

Length  L = 26 m

Step-by-step explanation:

Perimeter of a rectangle = 80 m = 2L + 2W

L = 12 + W

80 = 2L + 2W

80 = 2(12 + W) + 2W

80 = 24 + 2W + 2W

80 - 24 = 4W

56 = 4W

W = 56 / 4

W = 14 m

L = 12 + W

L = 12 + 14

L = 26 m

check:

80 = 2L + 2W

80 = 2(26) + 2(14)

80 = 52 + 28

80 = 80 ---- OK

Answer:

I am not good at word problems but I think I found some good examples

Step-by-step explanation:

Durain beans cost $9 per pound and they sold 11 pounds.

Multiply the cost by the amount sold: 9 x 11 = $99

Subtract that from the total sold:

196 - 99 = $97

Now divide the amount left by the cost per pound for Ice cream beans:

97 / 10 = 9.7 pounds.

Answer:

8

Step-by-step explanation:

total: 28 water attractions

pools: p

game areas: p + 2

water slides: 50% of 28 = 14

14 + p + p + 2 = 28

2p = 12

p = 6

game areas:

p + 2 = 6 + 2 = 8

Answer:

Step-by-step explanation:

a=3400t+600, we put in 21,000 for a. Because we have to find 't' when 'a' is 21,000.

which will give us  21,000 = 3400t+600.

Then,Subtract 600 to both sides to get 20,400 = 3400t

Divide both sides by 3,400 and you get 6 = t.

The ans is 6 minutes. The plane will take 6 min to reach the altitude 21,000 feet

Answer:

x = 2

Step-by-step explanation:

Probability that the marble comes to rest in the shaded region is equal to the ratio of the shaded area to the total area.

Probability 'P' = [tex]\frac{A'}{A}[/tex]

Area of the shaded region (A')= (x + 1)(x + 2)

Total area of the figure (A) = (2x + 1)(3x + 2)

P = [tex]\frac{(x+1)(x+2)}{(2x+1)(3x+2)}=\frac{3}{10}[/tex]

10(x + 1)(x + 2) = 3(2x + 1)(3x + 2)

10(x² + 3x + 2) = 3(6x² + 7x + 2)

10x² + 30x + 20 = 18x² + 21x + 6

(18x² - 10x²) + (21x - 30x) + (6 - 20) = 0

8x² - 9x - 14 = 0

x = [tex]\frac{9\pm\sqrt{(-9)^2-4(8)(-14)} }{2(8)}[/tex]

x = [tex]\frac{9\pm \sqrt{81+448}}{16}[/tex]

x = [tex]\frac{9\pm 23}{16}[/tex]

x = -[tex]\frac{7}{8}, 2[/tex]

Therefore, positive value of x = 2 will be the answer.

Answer:

C: Function 2 has the larger maximum at (2, 5).

Step-by-step explanation:

We are given two functions, with Function 1 being described by the graph and Function 2 given by the function:

[tex]f(x)=-x^2+4x+1[/tex]

Notice that the leading coefficient of Function 2 is negative. The graph of Function 1 is curving downwards. So, both functions will have maximum values.

Recall that for a parobala, the maximum (or minimum) values is the y-value of the vertex point. So, let's find the vertex for each function.

For Function 1, we can see that the vertex is at (4,1). Thus, its maximum value is y = 1.

For Function 2, we will need to work out the vertex. Recall that the vertex is given by:

[tex]\displaystyle \left(-\frac{b}{2a},f\left(-\frac{b}{2a}\right)\right)[/tex]

Function 2 is defined by:

[tex]f(x)=-x^2+4x+1[/tex]

Therefore, a = -1, b = 4, and c = 1.

Find the x-coorindate of the vertex:

[tex]\displaystyle x=-\frac{(4)}{2(-1)}=2[/tex]

Substitute this back into the function to find the y-coordinate.

[tex]f(2)=-(2)^2+4(2)+1=5[/tex]

So, the vertex of Function 2 is (2,5). Therefore, the maximum value of Function 2 is y = 5.

Since 5 is greater than 1, the maximum value of Function 2 is greater.

The answer is choice C.

Answer:

D. 9%, 440.36 million

Step-by-step explanation:

w = 221(1.09)t

9%, 440.36 million

Zoologists are studying two newly discovered species of insects in a previously unexplored section of rain forest. They estimate the current population of insect A to be 1.3 million and the current population of insect B to be 2.1 million. As development is encroaching on the section of rain forest where these insects live, the zoologists estimate the populations of insect A to be reducing at a rate of 3.8% and insect B to be reducing at a rate of 4.6%.

If P represents the population of each species of insect in millions, and t represents the elapsed time in years, then which of the following systems of equations can be used to determine how long it will be before the populations of the two species are equal?

Answer:

the  system of equation that  can be used to determine how long it will be before the populations of the two species are equal is :

[tex]\begin{cases} {\mathtt{P = 1.3 e^{-0.038 \ t}} & \\ \mathtt{P = 2.1 \ e^{-0.046 \ t}} & \end{cases}[/tex]

Step-by-step explanation:

Given that :

the current population of insect A to be 1.3 million

the current population of insect B to be 2.1 million.

As development is encroaching on the section of rain forest where these insects live, the zoologists estimate the populations of insect A to be reducing at a rate of 3.8% and insect B to be reducing at a rate of 4.6%.

The equation that can be used to determine how long it will be before the populations of the two species are equal is an equation for exponential decay, which can be represented as follows:

[tex]\mathtt{y = pe^{-rt}}[/tex]

where;

P represents the population of each species of insect in millions

t represents the elapsed time in years

r is the rate of decrease

So, we can have:

[tex]\mathtt{p_1 = 1.3 }[/tex] in million   and  [tex]\mathtt{p_2 = 2.1}[/tex] in million

Also for rate of decrease;

[tex]\mathtt{r_1 = 0.038}[/tex]     and [tex]\mathtt{r_2 = 0.046}[/tex]

Therefore;

the exponential decay for Population of insect A can now be:

[tex]\mathtt{P = 1.3 e^{-0.038 \ t}}[/tex]

the exponential decay for Population of insect B can now be:

[tex]\mathtt{P = 2.1 \ e^{-0.046 \ t}}[/tex]

Hence, the  system of equation that  can be used to determine how long it will be before the populations of the two species are equal is :

[tex]\begin{cases} {\mathtt{P = 1.3 e^{-0.038 \ t}} & \\ \mathtt{P = 2.1 \ e^{-0.046 \ t}} & \end{cases}[/tex]

Answer:

A!

Step-by-step explanation:

Plato

Answer:

1.015

Step-by-step explanation:

just find their average, which is adding them up and dividing by 2

(1.01 + 1.02)/2 = 1.015

The decimal number exactly halfway between 1.01 and 1.02 is 1.015.

A decimal numeral system is the standard system for denoting integer and non-integer numbers. The way of denoting numbers in the decimal system is often referred to as decimal notation.

The given numbers are,

1.01 and 1.02

Now to find the halfway between the number we need to find their sum first and then the half of the sum.

So, the sum of number,

1.01 + 1.02 = 1.03

Now for half way divide the sum by 2

1.03/2 = 1.015

Hence, The decimal number exactly halfway between 1.01 and 1.02 is 1.015.

More about decimal :

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Answer:

The probability that the sample proportion of households spending more than $125 a week is between 0.36 and 0.42 is 0.3115

Step-by-step explanation:

From the question, we can deduce the following;

n = 75

p = 0.35

where q = 1-p = 1-0.35 = 0.65

To compute the probability that the sample proportion of households spending more than $125 a week is between 0.36 and 0.42, we start by calculating the standard deviation of sample proportion.

Mathematically;

Standard deviation of sample proportion = √pq/n

SD = √(0.35)(0.65)/75 = 0.055 which is approximately 0.06

Let’s now compute the z-scores

For 0.36, we have ; (0.36-0.35)/0.06 = 0.01/0.06 = 0.17

For 0.42, we have; (0.42-0.35)/0.06 = 0.07/0.06 = 1.17

So the probability we want to calculate is :

P(0.17<z<1.17) = P(z<1.17) - P(z < 0.17) = 0.8790 - 0.5675 = 0.3115

Range: 71.9

Spread out above the median

The range is the biggest number minus the smallest number. This makes sense. The range here is 81.3 - 9.4 = 71.9.

Next, see the two middle groups? You can see the median, 45.5. Does the left or right side seem more spread out? It's the right side. 34.7 is closer to 45.5 than 63.6 is to 45.5.

Hope that helped,

-sirswagger21

Answer:

Around 18.18%

Step-by-step explanation:

We can use the percentage increase formula to find the gain here. The formula goes:

[tex]\frac{new-original}{original}\cdot100[/tex].

We know that the new value is 6500, and the old value is 5500, so we can substitute inside the equation.

[tex]\frac{6500-5500}{5500}\cdot100\\\\\frac{1000}{5500}\cdot100 \\\\0.\overline{18} \cdot100\\\\18.\overline{18}[/tex]

Which rounds to 18.18%.

Hope this helped!

Answer:

It should be 490000.0005

Step-by-step explanation:

4.9*10^5+.0005

10^5=100000

4.9*100000=490000

490000+.0005=490000.0005

Answer:

Step-by-step explanation:

[tex]10^{-5}=\frac{1}{10^{5}}=\frac{1}{100,000}=0.00001\\\\[/tex]

4.9* 10^-5 +0.0005 = 4.9 * 0.00001  + 0.0005

                               = 0.000049 + 0.0005

                              =  0.000549

Answer:

3 hours and 27 minutes

Step-by-step explanation:

2:05 pm = 14:05 hours

1 hour = 60 minutes

14:05 = 13 hours + 60 minutes + 5 minutes = 13 hours + 65 minutes

then:

 13h  65m

- 10h  38m

=  3h  27m

they drive:

3 hours and 27 minutes

Answer:

a) m∠BPD = 120°

b) m∠BC + m∠AD = 120°

Step-by-step explanation:

a) To solve for question a, we make use of a theorem called the intersecting chord theorem. This states that:

The measure of the angle formed by two chords that intersect inside a circle is the average of the measures of the intercepted arcs.

The Interior angle =( The larger exterior arc + The smaller exterior arcs) ÷ 2

The larger exterior arc (m∠BD) = 170°

The small exterior arc (m∠CA) = 70°

m∠BPD = m∠BD + m∠CA/2

m∠BPD = 170° + 70°/2

= 240°/2

= 120°

b) We are to find m∠BC + m∠AD

The sum of exterior angles in a circle = 360°

360° = m∠BD + m∠CA + m∠BC + m∠AD

360° = 170° + 70° + m∠BC + m∠AD

360° = 240 + m∠BC + m∠AD

360 - 240° = m∠BC + m∠AD

Thererefore,

m∠BC + m∠AD = 120°

Answer:

1. m∠BPD = 120°

2. m∠BC + m∠AD = 120°

Pregunta completa:

En una empresa trabajan 60 personas. Usan gafas el 16% de los hombres y el 20% de las mujeres. Si el numero total de personas que usan gafas es 11. ¿Cuantos hombres y mujeres hay en la empresa?

Responder:

Hombres = 25

Mujeres = 35

Explicación paso a paso:

Dado lo siguiente:

Número de personas que trabajan en la empresa = 60

Porcentaje de hombres que usan anteojos = 16%

Porcentaje de mujeres que usan anteojos = 20%

Número total de personas que usan anteojos = 11

Suponga, Número de hombres en la empresa = m

Número de mujeres = número total - número de hombres = 60 - m

Por lo tanto,

16% de los hombres = 0,16 m

20% de mujeres = 0,2 (60 - m) = 12 - 0,2 m

Por lo tanto,

0,16 m + 12 - 0,2 m = 11

- 0,04 m = 11 - 12

-0,04 m = - 1

m = 1 / 0.04 = 25

Por tanto, Número de hombres en la empresa = m = 25

Número de mujeres en la empresa = (60 - m) = (60 - 25) = 35 mujeres

Answer:

Step-by-step explanation:

The figure above is a rectangle

Area of a rectangle = length × width

From the question

The total length of the rectangle = 3x

The total width of the rectangle = 4x + 5

So the area of the figure is

A = 3x( 4x + 5)

Expand

We have the final answer as

Hope this helps you

Answer:

(6⁴ * 8⁻⁷) ⁻⁹

equivalent expressión is:

1 / (6⁴ * 8⁻⁷)⁹

Step-by-step explanation:

(6⁴ * 8⁻⁷) ⁻⁹

= 1 / (6⁴ * 8⁻⁷)⁹