10 cards are numbered from 1 to 10 and placed in a box. One card is selected at random and is not replaced. Another card is then randomly selected. What is the probability of selecting two numbers that are less than 6?
A. 2/9
B. 5/18
C. 1/5
D. 1/4

Answer:

-∞<x<∞

Step-by-step explanation:

Answer:

First option

Step-by-step explanation:

There's no value of x which makes the function undefined .

So x can take any real value

i.e. -infinity < x < +infinity

Answer:

i) [tex]\frac{3}{5} + (- \frac{1}{2}) = \frac{6}{10} - \frac{5}{10} = \frac{1}{10}[/tex]    [tex]\Rightarrow[/tex] \frac{3}{5} + (- \frac{1}{2}) = \frac{6}{10} - \frac{5}{10} = \frac{1}{10}

ii)[tex]4^{3} + 8^{2} + \sqrt{9}[/tex]   [tex]\Rightarrow[/tex]  4^{3} + 8^{2} + \sqrt{9}

iii) [tex](\frac{4}{5})^{2}. \sqrt[3]{8} \leqx^{3} - 3x + 6 \leq \sqrt{\frac{1}{3}} \Rightarrow \hspace{0.2cm}[/tex]    (\frac{4}{5})^{2}. \sqrt[3]{8} \leqx^{3} - 3x + 6 \leq \sqrt{\frac{1}{3}}

Step-by-step explanation:

i) [tex]\frac{3}{5} + (- \frac{1}{2}) = \frac{6}{10} - \frac{5}{10} = \frac{1}{10}[/tex]    [tex]\Rightarrow[/tex] \frac{3}{5} + (- \frac{1}{2}) = \frac{6}{10} - \frac{5}{10} = \frac{1}{10}

ii)[tex]4^{3} + 8^{2} + \sqrt{9}[/tex]   [tex]\Rightarrow[/tex]  4^{3} + 8^{2} + \sqrt{9}

iii) [tex](\frac{4}{5})^{2}. \sqrt[3]{8} \leqx^{3} - 3x + 6 \leq \sqrt{\frac{1}{3}} \Rightarrow \hspace{0.2cm}[/tex]    (\frac{4}{5})^{2}. \sqrt[3]{8} \leqx^{3} - 3x + 6 \leq \sqrt{\frac{1}{3}}

Answer:

6 by 3

Step-by-step explanation:

a rectangle as 2 equal sides. so if we know that it is 6 by 3, then 6+6+3+3

=12+6=18

the area of a rectangle is base * height. so 6 * 3 = 18

Answer: the length is 6 inches and the width is 3 inches.

Step-by-step explanation:

Let L represent the length of the rectangular note card.

Let W represent the width of the rectangular note card.

The formula for determining the area of a rectangle is expressed as

Area = L × W

Area of the note card would be

LW = 18 - - - - - - - - - - - - 1

The formula for determining the perimeter of a rectangle is expressed as

Perimeter = 2(L + W)

Perimeter of the note card would be

2(L + W) = 18

(L + W) = 9 - - - - - - - - - - - - 2

Substituting L = 9 - W into equation 1, it becomes

W(9 - W) = 18

9W - W² = 18

W² - 9W + 18 = 0

W² - 6W - 3W + 18 = 0

W(W - 6) - 3(W - 6) = 0

W - 6 = 0 or W - 3 = 0

W = 6 or W = 3

Substituting W = 3 into equation 1, it becomes

3L = 18

L = 18/3 = 6

Answer:

1. 1.76x10^13,

2. 3.20x10^8,

3. 5.5x10^4

Step-by-step explanation:

Answer:

Step-by-step explanation:

GDP/POPULATION

1755x10^13/3.2x10^8 = .05484x10^5

=5.484x10^4

= 5.49x10^4

The money after 10 years is $ 13591.4091

Solution:

Given that,

If you have a bank account that is modeled by the following equation:

[tex]A = 5000e^{0.10t}[/tex]

To find: Money after 10 years

How much money would you have after 10 years

Substitute t = 10 in above given equation

[tex]A = 5000 \times e^{0.10 \times 10}\\\\A = 5000 \times e^{1}\\\\A = 5000 \times 2.71828\\\\A = 13591.4091[/tex]

Thus money after 10 years is $ 13591.4091

Answer:

a) Rate of brightness after t days = B(t) = 2.6 + 0.6sin(2×3.142 t /6.6)

b) 0.57

Step-by-step explanation:

Given

Number of days=6,6 days

Average brightness =2.6

B(t)= 2.6 + 0.6 sin (2× 3.142t/6.6)

b) B(1day) = 0.6 ×(2×3.142/6.6)cos (2×3.142/6.6)

B(1 day) = 0.6 × (6.248/6.6)cos 0.952

B(1 day) =0.6 × 0.952 ×0.9999

B(1day) = 0.5711

= 0.57

Answer:

x = 0 , y = 0 , z = -3

Step-by-step explanation:

Solve the following system:

{x - 6 y + 4 z = -12 | (equation 1)

x + y - 4 z = 12 | (equation 2)

2 x + 2 y + 5 z = -15 | (equation 3)

Swap equation 1 with equation 3:

{2 x + 2 y + 5 z = -15 | (equation 1)

x + y - 4 z = 12 | (equation 2)

x - 6 y + 4 z = -12 | (equation 3)

Subtract 1/2 × (equation 1) from equation 2:

{2 x + 2 y + 5 z = -15 | (equation 1)

0 x+0 y - (13 z)/2 = 39/2 | (equation 2)

x - 6 y + 4 z = -12 | (equation 3)

Multiply equation 2 by 2/13:

{2 x + 2 y + 5 z = -15 | (equation 1)

0 x+0 y - z = 3 | (equation 2)

x - 6 y + 4 z = -12 | (equation 3)

Subtract 1/2 × (equation 1) from equation 3:

{2 x + 2 y + 5 z = -15 | (equation 1)

0 x+0 y - z = 3 | (equation 2)

0 x - 7 y + (3 z)/2 = -9/2 | (equation 3)

Multiply equation 3 by 2:

{2 x + 2 y + 5 z = -15 | (equation 1)

0 x+0 y - z = 3 | (equation 2)

0 x - 14 y + 3 z = -9 | (equation 3)

Swap equation 2 with equation 3:

{2 x + 2 y + 5 z = -15 | (equation 1)

0 x - 14 y + 3 z = -9 | (equation 2)

0 x+0 y - z = 3 | (equation 3)

Multiply equation 3 by -1:

{2 x + 2 y + 5 z = -15 | (equation 1)

0 x - 14 y + 3 z = -9 | (equation 2)

0 x+0 y+z = -3 | (equation 3)

Subtract 3 × (equation 3) from equation 2:

{2 x + 2 y + 5 z = -15 | (equation 1)

0 x - 14 y+0 z = 0 | (equation 2)

0 x+0 y+z = -3 | (equation 3)

Divide equation 2 by -14:

{2 x + 2 y + 5 z = -15 | (equation 1)

0 x+y+0 z = 0 | (equation 2)

0 x+0 y+z = -3 | (equation 3)

Subtract 2 × (equation 2) from equation 1:

{2 x + 0 y+5 z = -15 | (equation 1)

0 x+y+0 z = 0 | (equation 2)

0 x+0 y+z = -3 | (equation 3)

Subtract 5 × (equation 3) from equation 1:

{2 x+0 y+0 z = 0 | (equation 1)

0 x+y+0 z = 0 | (equation 2)

0 x+0 y+z = -3 | (equation 3)

Divide equation 1 by 2:

{x+0 y+0 z = 0 | (equation 1)

0 x+y+0 z = 0 | (equation 2)

0 x+0 y+z = -3 | (equation 3)

Collect results:

Answer: {x = 0 , y = 0 , z = -3

To solve the given system of equations, use the method of elimination to eliminate one variable at a time and solve for the remaining variables.

To solve the system of equations:

x - 6y + 4z = -12

x + y - 4z = 12

2x + 2y + 5z = -15

We can use the method of substitution or elimination. Let's use the method of elimination:

Therefore, the solution is x = -5, y = 4, and z = 1.

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ANSWER:

1. How many possible combined page count and color choices are possible?

There are  3 choices for page size and 4 choices for color, and also, there are 3*4=12 possibilities to combine page size and color.

Number possibilities to combine and number of choices for size is: 12:3=4:1

Number of possibilities to combine and number of choices for color is 12:4=3:1

2. How does this number relate to the number of page size choices and to the number of color choices

There are 12 possibilities to combine size and color.

Number of possibilities to combine and number of choices for size is 4:1

Number of possibilities to combine and number of choices for color is 3:1

Answer:

We have 12 possibilities to combine page size and color.

Number of possibilities and number of choices is 12:4 that is 3:1

Step-by-step explanation:

have a nice day.

Answer:

  £100.32

Step-by-step explanation:

£88 + 14% × £88 = £88×(1 +0.14)

  = 1.14×£88

  = £100.32 . . . . using a calculator

£100.32 is £88 increased by 14%.

Final answer:

£100.32

Explanation:

To increase an amount by a certain percentage using the multiplier method, you can use the following steps:

Let's do the calculation:

Answer:

The required equation is [tex]4889=4850 +3n[/tex].

Step-by-step explanation:

Consider the provided information.

Melody has a new job recording for the All-Time Favorites record label.

She is paid a monthly base salary of $plus $3 for each CD sold.

Her pay stub for June indicates that she made $4,889 in that month.

Let n represents the number of CDs she sold.

Therefore, the required equation is [tex]4889=4850 +3n[/tex].

Answer:

0.0223

Step-by-step explanation:

Given the following data x(1) = 377, n(1) = 422, x(2) = 431, n(2) = 518

The sample proportion is the number of success divided by the sample.

P(1) = x(1)/n(1) = 377/422 = 0.8934

P(2) = x(2)/n(2) = 431/518 = 0.8320

Formular for the standard error of the difference in sample proportions

S.E = √p(1)q(1)/n(1)+P(2)q(2)/n(2)

S.E = √p1(1-P1)/n1+P2(1-P2)/n2

By substitution we have that,

S.E = √0.8934(1-0.8934)/422+0.8320(1-0.8320)/518

S.E = 0.0223

The domain for n is  [tex]-\infty<n<\infty[/tex]

Explanation:

The arithmetic sequence is    

To determine the domain of the sequence, let us consider  [tex]a_n[/tex] as  [tex]f(n)[/tex]  

Thus, the sequence becomes,  [tex]f(n)=4-4(n-1)[/tex]  

The domain of the function is the set of all x-values for which the function is real and well defined.

Since, the function has no domain constraints or undefined points. Therefore, the domain of the function is

Thus, the domain of the arithmetic sequence  [tex]a_n=4-4(n-1)[/tex] is  [tex]-\infty<n<\infty[/tex]

Answer:

$774

Step-by-step explanation:

We have been given that from January to June, a company spent $60 per month on office supplies. In July the price of office supplies increased by 15% and remained the same for the rest of the year.

Let us find increased cost of supplies as shown below:

[tex]\text{Increased cost of supplies}=60+\frac{15}{100}\times 60[/tex]

[tex]\text{Increased cost of supplies}=60+0.15\times 60[/tex]

[tex]\text{Increased cost of supplies}=60+9[/tex]

[tex]\text{Increased cost of supplies}=69[/tex]

There are 6 months from January to June, so cost of supplies on these 6 months would be 6 times $60.

There are 6 months from July to December, so cost of these months would be 6 times $69.

Total cost will be equal to sum of these two amounts.

[tex]\text{Amount spent on office supply in the year}=6\times \$60+6\times \$69[/tex]

[tex]\text{Amount spent on office supply in the year}=6( \$60+\$69)[/tex]

[tex]\text{Amount spent on office supply in the year}=6( \$129)[/tex]

[tex]\text{Amount spent on office supply in the year}=\$774[/tex]

Therefore, $774 were spent on office supplies.

The final velocity is 15.8 m/s in the forward direction

Step-by-step explanation:

An inelastic collision occurs when the two object after the collision stick together.

In any case, the total momentum of the system is conserved before and after the collision, in absence of external forces. Therefore, we can write:

[tex]p_i = p_f\\m u + MU = (m+M)v[/tex]

where in this problem:

m = 1300 kg is the mass of the small sedan

u = 20 m/s is the initial velocity of the small sedan

M = 7100 kg is the mass of the truck

U = 15 m/s is the initial velocity of the truck

v is the final combined velocity of the small sedan + truck

Here we have taken both the velocity of the sedan and the truck in the positive (forward) direction

Solving the equation for v, we find the final velocity:

[tex]v=\frac{mu+MU}{m+M}=\frac{(1300)(20)+(7100)(15)}{1300+7100}=15.8 m/s[/tex]

And since the sign is positive, this means that is direction is the same as the initial direction of the sedan and the truck, so forward.

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Answer:

The area of the rectangle TOUR is 80.00 unit².

Step-by-step explanation:

The area of a rectangle is computed using the formula:

[tex]Area\ of\ a\ Rectangle=length\times width[/tex]

Since the dimensions of the rectangle are not provided we can compute the dimensions using the distance formula for two points.

The distance formula using the two point is:

[tex]distance=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]

Considering the rectangle TOUR the area formula will be:

Area of Rectangle TOUR = TO × OU

The co-ordinates of the four vertices of a triangle are:

T = (-8, 0), O = (4, 4), U = (6, -2) and R = (-6, -6)

Compute the distance between the vertices T and O as:

[tex]TO=\sqrt{(4-(-8))^{2}+(4-0)^{2}}\\=\sqrt{12^{2}+4^{2}} \\=\sqrt{160} \\=4\sqrt{10}[/tex]

Compute the distance between the vertices O and U as:

[tex]OU=\sqrt{(6-4)^{2}+(-2-4)^{2}}\\=\sqrt{2^{2}+6^{2}} \\=\sqrt{40} \\=2\sqrt{10}[/tex]

Compute the area of rectangle TOUR as follows:

[tex]Area\ of\ TOUR=TO\times OU\\=4\sqrt{10}\times 2\sqrt{10}\\=80\\\approx80.00 unit^{2}[/tex]

Thus, the area of the rectangle TOUR is 80.00 unit².

Answer:

This answer is just here so you can give the other guy brainliest, as there can only be brainliest if there are two answers.

Step-by-step explanation:

Give that guy brainliest

Answer:

1st it: g(2)=1/3(2)+1=0.67+1=1.67

2nd it: g^2(2)=1/3(1.67)+1=0.56+1=1.56

3rd it: g^3(2)=1/3(1.56)+1=0.52+1=1.52

Answer:

The first three iterations are 1.67, 1.56 and 1.52

Step-by-step explanation:

Given the function g(x)=1/3x+1

To get the first threw iteration with initial value of x = 2

First iteration at x= 2:

g(2) = 2/3+1

g(2) = (2+3)/3

g(2) = 5/3 = 1.67

Second iteration will be when x = g(2) = 5/3

g²(2) = g(5/3) = 1/3(5/3) + 1

g²(2) = g(5/3) = 5/9 + 1

g²(2) = g(5/3) = 14/9 = 1.56

Third iteration will be at when

x = g²(2) = 14/9

g³(2) = g(14/9) = 1/3(14/9) + 1

g³(2) = g(14/9) = 14/27 + 1

g³(2) = g(14/9) = 41/27 = 1.52

The first three iterations are 1.67, 1.56 and 1.52

Answer:

e. Pie Chart

Step-by-step explanation:

In a student survey, students are asked about their favorite movie and so, the favorite movies can be divided into different categories but can't be meaningfully represented in numerical form. Thus, the favorite movie is a qualitative variable. For the qualitative type of variable pie chart is most suitable chart.

Histogram, IQR, box plot and steam plot are created for quantitative type of data.

Thus, the data would be best displayed by using Pie chart.

What is the question that is being asked?

Answer:

True, the scores are not valid.

Step-by-step explanation:

The test supposed to be measuring intelligence. We can assume that the intelligence of most people relatively stable (will not change too much over a short amount of time), and can expect it should go upward with brain growth and education. But the test seems to give a huge decrease from the first and second results. Then the third result is a huge increase that even higher than the first test.  

We don't know the true value of the subject, but seeing the huge gap for every repetition we can tell that the test result lacks precision.

Answer:

Therefore, 32  is he total number of vehicles sold at the dealership last month.

Step-by-step explanation:

We know that the ratio of the number of sedans to the number of trucks to the number of vans sold at the dealership last month was 4:5:7, respectively. We have :

[tex]4:5:7 \implies 4x+5x+7x=16x[/tex]

Therefore, 16x is he total number of vehicles sold at the dealership last month.

We know that:

1) The number of vans sold at the dealership last month was between 10 and 20.

2) The number of sedans sold at the dealership last month was less than 10

We get:

[tex]10\leq 7x \leq 20\\\implies x=2\\\\\\4x\leq 10\\x=1 \, \vee \, x=2[/tex]

We know that x is a positive integer. In order to satisfy both conditions, this is possible only if x = 2.

We get [tex]16x=16\cdot 2=32[/tex]

Therefore, 32  is he total number of vehicles sold at the dealership last month.

Answer: 20 feet

Step-by-step explanation:

in the attachment

The ladder reaches approximately 19.8 feet up the side of the house, as determined using the Pythagorean theorem.

The question is asking us to find the height the ladder reaches up the side of the house. This is a problem dealing with right triangles and can be solved using the Pythagorean theorem, which is a^2 + b^2 = c^2, where 'a' and 'b' are the shorter sides (base and height of the house) and 'c' is the hypotenuse (the ladder).

In this case, the ladder is 24 feet long (this is our c), and the base of the ladder is 13 feet from the house (this is our a). We are trying to find b (the height of the house the ladder reaches).

Substitute these values into the Pythagorean theorem and solve for 'b':

13^2 + b^2 = 24^2
b^2 = 24^2 - 13^2
b = sqrt(24^2 - 13^2)

So, the height that the ladder reaches up the side of the house is approximately 19.8 feet.

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Answer:

Step-by-step explanation:

The formula for determining the area of a sector is expressed as

Area = θ/360 × πr²

Where

θ represents the central angle formed by the radii.

r represents the radius of the circle.

π is a constant whose value is 3.14

From the information given,

θ = 167 degrees

r = 17.8 yards

Therefore,

Area of sector = 167/360 × 3.14 × 17.8² = 461.5 yards²

Answer:

263,606.9

Step-by-step explanation:

In 2004 the population in Morganton, Georgia, was 43,000.

(0, 43000)

The population in Morganton doubled by 2010

In 6 years the population is doubled (86000)

(6,86000)

[tex]A= a(b)^t[/tex]

Use (0,43000) in the above equation

[tex]A= a(b)^t\\43000= a(b)^0\\a=43000[/tex]

Now plug in (6,86000)

[tex]A= a(b)^t\\A= 43000(b)^t\\86000=43000(b)^6\\2=b^6\\b=\sqrt[6]{2} \\b=1.12[/tex]

[tex]A=43000(1.12)^t[/tex]

Now find out A when t=16 (2020)

[tex]A=43000(1.12)^t\\A=43000(1.12)^{16}\\A=263606.9[/tex]

If the growth rate from 2004 to 2010 continues, the expected population in Morganton, Georgia in 2020 would be around 172,000 as the population is doubling every 6 years.

The population of Morganton, Georgia in 2004 was 43,000 and it doubled by 2010 to 86,000. This shows a constant growth rate in which the population size doubles every 6 years. If this rate of growth remains consistent, the population of Morganton is expected to double again by 2020. Therefore, by 2020, the population of Morganton, Georgia could be around 172,000 people.

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Answer:

a.) 23

b.) y=14

c.) 23

d.) -23

e.) T=8

f.) f=1/8

Step-by-step explanation:

a.) general equation is Asin((2π/T))

A is the amplitude. It's A value is 23

b.)  Midline = vertical_shift = 14

c.) max = positive amplitude value = 23

d.) min = negative amplitude = -23

e.) Factor out 2π from your angular frequency to get the period.

ω = π/4 = (2π)/8 = (2π)/T

Period = 8

f.) Frequency is just the inverse of the period.

f = 1/T = 1/8

Answer:

x=42

Step-by-step explanation:

x-12=30

x=30+12

x=42

To solve for x in this equation, we want to get x by itself on the left side of the equation. Since 12 is being subtracted from x, to get x by itself, we need to add 12 to the left side of the equation. If we add 12 to the left side, we must also add 12 to the right side.

On the left side, -12 and +12 cancel each other out so we are simply left with x. On the right side, 30 + 12 is 42 so we have x = 42.

It's important to understand that we can check our answer by substituting 42 back into the original equation.

So we have (42) - 12 = 30.

42 - 12 is 30 so we have 30 = 30 which is a true statement so our answer, x = 42, is correct.

The location of the reflected post will be in the first quadrant at point (3, 2).

To reflect a point across the y-axis, we simply negate the x-coordinate while keeping the y-coordinate unchanged.

Given the point (-3, 2), when we reflect it across the y-axis, the x-coordinate becomes positive 3, while the y-coordinate remains 2. Therefore, the reflected point is (3, 2).

Since the original point (-3, 2) lies in the second quadrant (negative x, positive y), the reflected point (3, 2) will lie in the first quadrant (positive x, positive y).

Answer:

Maximum number of 3x3x2 bricks = 23.

Step-by-step explanation:

The volume of the box = 13 x 8 x 4 = 416 cubic unit

The volume of the brick with the dimensions = 18 cubic unit

Now as per the question, we want to fill an empty box with 416 cubic unit with the help of bricks which are 18 cubic unit each.

The maximum number of bricks required to fill the box = Volume of the box ÷ Volume of one brick.

→ The number of bricks required to fill the box = 416 ÷ 18 = 23.11

But, number of bricks can never be in fraction so it means a maximum of 23 bricks can accommodate in the given box. We will not choose 24 or more than 24 bricks because these much bricks will go out of the dimensions.

Note: Volume of a cuboid = length x breadth x height (l x b x h).

To solve the problem, you divide each dimension of the box by the corresponding dimension of the brick, rounding down to the nearest whole number to get the number of bricks that can fit in each direction. You then multiply these together to get the total. In this case, a maximum of 16 bricks can fit.

The problem at hand requires spatial reasoning and division. The challenge is to determine how many 'bricks' (which we'll engage as 3x3x2 units) can fit into a larger 'box' (which is 13x8x4 units). This can be determined by individually dividing the dimensions of the box by the dimensions of the brick.

For instance, considering the length, we divide 13 by 3 to get approximately 4.33. Considering that we can't fractionate a brick, we can place only 4 bricks along the length. Using the same approach, we divide 8 by 3 for the width to get approximately 2.67, and we can place 2 bricks here. It's the same for the height; 4 divided by 2 is 2. Therefore, we can place 2 bricks along the height.

To get the total number of bricks that can fit in the box, multiply the numbers together: 4 (length) x 2 (width) x 2 (height), giving a result of 16 bricks. Hence, a maximum of 16 bricks of size 3x3x2 can fit into a box of size 13x8x4 without going out of the box or overlapping.

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Answer:

17160

Step-by-step explanation:

1×2×3×4×5×6×7×8×9×10×11×12×13 / 1×2×3×4×5×6×7×8×9

10×11×12×13=17160

Answer: 6x^13-1.5w+156x+13 is the answer to the first equation and is that another equation?

The expression 13 - 0.5w + 6x evaluates to 11 when substituting w=10 and x=1/2.

The problem is to evaluate the expression 13 - 0.5w + 6x given the values w=10 and x=1/2. Following the order of operations, we first substitute the given values into the expression.

13 - 0.5(10) + 6(1/2) = 13 - 5 + 3 = 11.

The result of the evaluated expression is 11.

Answer: Segments AB / A"B" = √13 / 2 x √13

Step-by-step explanation:

The Triangle's vertices are at points A(-3,3), B(1,-3) and C(-3,-3).

• The reflection over x = 1 shows vertices A, B and C below:

A(-3,3)→A'(5,3);

B(1,-3)→B'(1,3);

C(-3,-3)→C'(5,-3).

• The Dilation by a scale factor of 2 from the origin is expressed as:

(x,y)→(2x,2y)

Therefore,

A'(5,3)→A''(10,6);

B'(1,3)→B''(2,6);

C'(5,-3)→C''(10,-6)

The attachment below completed the calculations and shows the segment in a simple graph.