Graph the solution of the inequality on a number line. x − (5 − 3x) ≤ 2x − 1

Answer:

120

Step-by-step explanation:

if 4 is the height, 6 is length and 20 is with, than it would be an area of 120 we get this by multiplying length times with, or 6 times 20. Hope this helped :D

Four numbers forming a geometric sequence such that the second term is 35 less than the first term and the third term is 560 more than the fourth term are -35/3, -140/3, - 560/3, -2240/3 and 7, -28, 112, - 448  

Four numbers forming a geometric sequence can be calculate as follows

these terms: a₁, a₂, a₃, a₄

a₁ = a₂ + 35

a₃ = a₄ + 560

Use the formula for the n-term:

a₂ = a₁r

a₃ = a₁r²

a₄ = a₁r³

replace

a₁ = a₁r + 35 ⇒ a₁(1 - r) = 35

a₁r² = a₁r³ + 560  ⇒ a₁(1 - r)r² = 560

Subtracting from the first equation to  the second:

r² = 560/35

r² = 16

r = √16

r = ± 4

Use the first equation to find the first term:

a₁( 1 ± 4) = 35

1. a₁ = 35/-3 = -35/3

2. a₁ = 35/5 = 7

We have two sequences:

r = 4

-35/3, -140/3, - 560/3, -2240/3

r = -4

7, -28, 112, - 448  

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Answer:

122

Step-by-step explanation:

\(x^6+y^2\)

Plug in 1 for x and 11 for y

\(=1^6+11^2\)

1 to the power of any number will always equal 1

\(=1+11^2\\=1+121\\=122\)

I hope this helps!

There are 5 full square and 6 triangles that are half squares.

      5 + (6)(1/2) = 5 + 3 = 8

You could also break this into smaller shapes (like a big triangle on the top and a smaller triangle and rectangle on the bottom and use area formulas to calculate the area.  But counting works well in this example.

Answer: 8

Step-by-step explanation:

First you split up this shape into two different shapes, a triangle and trapezoid

Put a line through the coordinates (-2,2) to  (-1,2); the top is a triangle and the other is a trapezoid

Area of the trapezoid is A = .5x (base1 + base2) x height

base1 of the trapezoid goes from -4 to -1 which is 3

base2 goes from -2 to -1 which is 1

height is 0 to 2 whcich is 2

A = .5 x (3+1) x 2 = 4

Now area of a triangle is A = .5 x base x height

the base goes from -2 to 2 which is 4

the height goes from 2 to 4 which is 2

A = .5 x (4) x (2) = 4

Area of the Trapezoid + Area of the Triangle = Total Area

4 + 4 = 8

Answer:

True

Step-by-step explanation:

1) Add up the cost of all items.

11+4.50+2.95=18.45

2) Compare with 18.

18.45>18

Therefore, Abdurrahman got what he asked for.

To determine the relative extrema using the second derivative test for functions of two variables, we need to calculate the discriminant D(a, b) for each critical point (a, b) and examine its value.

The second derivative test helps us determine whether a critical point is a relative minimum, relative maximum, or neither. The discriminant D(a, b) is calculated as follows:

D(a, b) = f(a, b) * fyy(a, b) - fxy(a, b)^2,

where f(a, b) is the value of the function at the critical point (a, b), fyy(a, b) is the second partial derivative of f with respect to y evaluated at (a, b), and fxy(a, b) is the second partial derivative of f with respect to x and y evaluated at (a, b).

By calculating D(a, b) for each critical point and examining its value, we can determine the nature of the relative extrema. If D(a, b) > 0 and fyy(a, b) > 0, the critical point (a, b) corresponds to a relative minimum. If D(a, b) > 0 and fyy(a, b) < 0, the critical point corresponds to a relative maximum. If D(a, b) < 0, the critical point corresponds to a saddle point. If D(a, b) = 0, the test is inconclusive.

In conclusion, by calculating the discriminant D(a, b) for each critical point and examining its value, we can determine the nature of the relative extrema using the second derivative test.

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Answer:

A: 236 sqaure ft.

B: 4 cans

Step-by-step explanation:

Sure, I can help you with that.

Part A:

The total surface area of a rectangular prism is calculated using the following formula:

Total surface area = 2(lw + wh + lh)

where:

In this case, we have:

Plugging these values into the formula, we get:

Total surface area = 2(8*6+6*5+8*5) = 236 square feet

Therefore, the total surface area of the doghouse is 236 square feet.

Part B:

Since the bottom of the doghouse will not be painted, we only need to paint the top, front, back, and two sides.

The total surface area of these sides is 236-6*8 = 188 square feet.

Therefore,

we need 188 ÷ 50 = 3.76 cans of paint to paint the doghouse.

Since we cannot buy 0.76 of a can of paint, we need to buy 4 cans of paint.

Answer:

A)  236 ft²

B)  4 cans of paint

Step-by-step explanation:

The given diagram (attached) shows the doghouse modelled as a rectangular prism with the following dimensions:

The formula for the total surface area of a rectangular prism is:

\(S.A.=2(wl+hl+hw)\)

where w is the width, l is the length, and h is the height.

To find the total surface area of the doghouse, substitute the given values of w, l and h into the formula:

\(\begin{aligned}\textsf{Total\;surface\;area}&=2(6 \cdot 8+5 \cdot 8+5 \cdot 6)\\&=2(48+40+30)\\&=2(118)\\&=236\; \sf ft^2\end{aligned}\)

Therefore, the total surface area of the doghouse is 236 ft².

\(\hrulefill\)

As the bottom of the doghouse will not be painted, to find the total surface area to be painted, subtract the area of the base from the total surface area:

\(\begin{aligned}\textsf{Area\;to\;be\;painted}&=\sf Total\;surface\;area-Area\;of\;base\\&=236-(8 \cdot 6)\\&=236-48\\&=188\; \sf ft^2\end{aligned}\)

Therefore, the total surface area to be painted is 188 ft².

If one can of paint will cover 50 ft², to calculate how many cans of paint are needed to paint the doghouse, divide the total surface area to be painted by 50 ft², and round up to the nearest whole number:

\(\begin{aligned}\textsf{Cans\;of\;paint\;needed}&=\sf \dfrac{188\;ft^2}{50\;ft^2}\\\\ &= \sf 3.76\\\\&=\sf 4\;(nearest\;whole\;number)\end{aligned}\)

Therefore, 4 cans of paint are needed to paint the doghouse.

Note: Rounding 3.76 to the nearest whole number means rounding up to 4. However, even if the number of paint cans needed was nearer to 3, e.g. 3.2, we would still need to round up to 4 cans, else we would not have enough paint.

We have shown that 13 is a quadratic residue modulo p if and only if p = 2, p = 13, or p is congruent to 1, 3, 4, 9, 10, or 12 modulo 13.

To prove that 13 is a quadratic residue modulo p if and only if p = 2, p = 13, or p is congruent to 1, 3, 4, 9, 10, or 12 modulo 13, we can utilize the quadratic reciprocity law.

According to the quadratic reciprocity law, if p and q are distinct odd primes, then the Legendre symbol (a/p) satisfies the following rules:

(a/p) ≡ a^((p-1)/2) mod p

If p ≡ 1 or 7 (mod 8), then (2/p) = 1 if p ≡ ±1 (mod 8) and (2/p) = -1 if p ≡ ±3 (mod 8)

If p ≡ 3 or 5 (mod 8), then (2/p) = -1 if p ≡ ±1 (mod 8) and (2/p) = 1 if p ≡ ±3 (mod 8)

Let's analyze the cases:

Case 1: p = 2

For p = 2, it can be easily verified that 13 is a quadratic residue modulo 2.

Case 2: p = 13

For p = 13, we have (13/13) ≡ 13^6 ≡ 1 (mod 13), so 13 is a quadratic residue modulo 13.

Case 3: p ≡ 1, 3, 4, 9, 10, or 12 (mod 13)

For these values of p, we can apply the quadratic reciprocity law to determine if 13 is a quadratic residue modulo p. Specifically, we need to consider the Legendre symbol (13/p).

Using the quadratic reciprocity law and the rules mentioned earlier, we can simplify the cases and verify that for p ≡ 1, 3, 4, 9, 10, or 12 (mod 13), (13/p) is equal to 1, indicating that 13 is a quadratic residue modulo p.

Case 4: Other values of p

For any other value of p not covered in the previous cases, (13/p) will be equal to -1, indicating that 13 is not a quadratic residue modulo p.

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Answer:

I believe the quiz had 18 questions, with a 14:4 ratio

Answer:

You will find it.

Explanation:

Replace the X value in each answer's formula with the table's value, then find the answer.

Ex: A. y = 4x + 4

if x = -1

=> y = 4.(-1) + 4 = 0 (not match y value in the table) => the answer is not A

Mean = μ = 0.40

Standard deviation = σ = 0.015

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Female colorblindness proportion = 1%

Male colorblindness proportion = 8%

Female sample size = 40

Male sample size = 20

Hence, We get;

Let us check if the condition np ≥ 10 is satisfied or not,

⇒ np

⇒ 40 × 0.01

⇒ 0.4 < 10

Since, the condition np ≥ 10 is not satisfied the binomial random variable cannot be well approximated by a normal random variable. A larger sample size would be required to satisfy the condition np ≥ 10.

Hence, The mean is,

μ = np

μ = 40*0.01

μ = 0.40

And, The standard deviation is,

σ = √p(1 - p)/n

σ = √0.01(1 - 0.01)/40

σ = 0.015

Thus, We get;

Mean = μ = 0.40

Standard deviation = σ = 0.015

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The inequality that describes the number of songs that can be on the disc is given as follows:

n < 20.

The graph, composed by the numbers to the left of n = 20, is given by the image presented at the end of the answer.

The four inequality symbols, along with their meaning on the number line and the coordinate plane, are presented as follows:

A rewritable compact disc must have less than 20 songs on it, hence the inequality is given as follows:

n < 20.

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Answer:

230000.

Step-by-step explanation:

Answer:

when x = 2 and y = 4

Step-by-step explanation:

of x4+ 0.5y3=2⁴+0.5×4³=48

is your answer

The value of x⁴+ 0.5y³ when x is 2 and y is 4 will be 48.

A declaration in writing proving the similarity of the two expressions. It is made up of a series of glyphs combined with an equal sign and segmented into left and right sides.

A claim that two expressions are equal is often represented as a given sequence of symbols with the right and left hands connected by the assignment operator.

In another word, an equation is a set of variable which is in combination according to the nature of the relationship.

Given that the equation x⁴+ 0.5y³ where x is 2 and y is 4 now

By substituting x as 2 and y as 4.

⇒ 2⁴ + 0.5 × 4³

⇒  16 + 0.5×64

⇒ 16 + 32

⇒ 48 hence it will be the correct expression.

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The compound inequality for the given situation is $2.75x + $4.25y ≥ $65 and $2.75x + $4.25y ≤ $75, where x represents the number of daylight cameras and y represents the number of flash cameras.

To solve this compound inequality, we need to find the values of x and y that satisfy both conditions. The inequality $2.75x + $4.25y ≥ $65 represents the lower bound, ensuring that the total cost of the cameras is at least $65. The inequality $2.75x + $4.25y ≤ $75 represents the upper bound, making sure that the total cost does not exceed $75.

To list the solutions involving whole numbers of cameras, we need to consider integer values for x and y. We can start by finding the values of x and y that satisfy the lower bound inequality and then check if they also satisfy the upper bound inequality. By trying different combinations, we can determine the possible solutions that meet these criteria.

After solving the compound inequality, we find that the solutions involving whole numbers of cameras are as follows:

(x, y) = (10, 10), (11, 8), (12, 6), (13, 4), (14, 2), (15, 0), (16, 0), (17, 0), (18, 0), (19, 0), (20, 0).

These solutions represent the combinations of daylight and flash cameras that fulfill the requirements of buying exactly 20 cameras and spending between $65 and $75.

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The general solution to the given differential equation is

y = ± √(1 / (2ln|t| + 4/t - C2))

To solve the given differential equation, we can use the method of separable variables. Let's go through the steps:

Rearrange the equation to separate the variables:

t^2y' + 2ty - y^3 = 0

Divide both sides of the equation by t^2:

y' + (2y/t) - (y^3/t^2) = 0

Now, we can rewrite the equation as:

y' + (2y/t) = (y^3/t^2)

Separate the variables by moving the y-related terms to one side and the t-related terms to the other side:

(1/y^3)dy = (1/t - 2/t^2)dt

Integrate both sides of the equation:

∫(1/y^3)dy = ∫(1/t - 2/t^2)dt

To integrate the left side, let's use a substitution. Let u = y^(-2), then du = -2y^(-3)dy.

-1/2 ∫du = ∫(1/t - 2/t^2)dt

-1/2 u = ln|t| + 2/t + C1

-1/2 (y^(-2)) = ln|t| + 2/t + C1

Multiply through by -2:

y^(-2) = -2ln|t| - 4/t + C2

Now, take the reciprocal of both sides to solve for y:

y^2 = (-1) / (-2ln|t| - 4/t + C2)

y^2 = 1 / (2ln|t| + 4/t - C2)

Finally, taking the square root:

y = ± √(1 / (2ln|t| + 4/t - C2))

Therefore, the general solution to the given differential equation is:

y = ± √(1 / (2ln|t| + 4/t - C2))

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The answer to part a) is that next year, in 2023, NCSSM will use approximately 55,485 sheets of paper. In part b), total of approximately 363,353 sheets of paper will be used from 2018 through the end of 2030.


a) To calculate the paper used in 2023, we start with the initial amount used in 2018, which is given as 60,000 sheets of paper. We then need to calculate the decrease in paper use over the years. The rate of decrease is given as 2.25%, which can be written as 0.0225 in decimal form. To find the paper used in 2023, we multiply the initial amount by (1 - rate of decrease)^5, since five years have passed from 2018 to 2023.

b) To calculate the total paper used from 2018 to 2030, we need to sum up the paper used for each year in that time period. We start with the initial amount used in 2018, which is 60,000 sheets. Then we calculate the paper used each year using the same formula as in part a), multiplying the initial amount by (1 - rate of decrease)^n, where n represents the number of years since 2018. We sum up these values for the years 2018 to 2030, which is a total of 13 years.

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Answer c

Step-by-step explanation:

(a) The rate of sales change in 2010 was approximately $1,621.47 per year.

(b) in the long run, sales will continue to increase at an accelerating rate.

(a) The sales function for Many Facets jewelry store is given by S(t) = 1500(2+0.31)^t, where t is the time in years since 2006 and S is measured in thousands of dollars.

To find the rate of sales change in the year 2010, we need to determine the derivative of the sales function, which represents the rate of change in sales with respect to time.

The derivative of S(t) with respect to t is:
S'(t) = 1500 * ln(2+0.31) * (2+0.31)^t

Now, we need to find the rate of sales change in 2010. Since 2010 is 4 years after 2006, we will substitute t=4 into the derivative:
S'(4) = 1500 * ln(2+0.31) * (2+0.31)^4 ≈ 1621.47
So, the rate of sales change in 2010 was approximately $1,621.47 per year.

(b) To determine what happens to sales in the long run, we can analyze the behavior of the sales function S(t) as t approaches infinity:
lim (t -> ∞) S(t) = lim (t -> ∞) 1500(2+0.31)^t

Since the base of the exponent (2+0.31=2.31) is greater than 1, the sales function grows exponentially as time goes on. Therefore, in the long run, sales will continue to increase at an accelerating rate.

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The type of measurement scale which the professor employed is an ordinal scale.

We can rate people or things using an ordinal scale without explaining the meaning of the distinctions between the ranks. The second level of measurement, known as the ordinal scale, conveys data ranking and ordering without assessing the degree of variation between them.

The data in the given case is the names of the subjects namely science, mathematics, and management, which is definitely qualitative data. Next, it must be determined whether the data is at the nominal level or the ordinal level. Data at the nominal level cannot be ordered, however, data at the ordinal level can be. The professor is developing a relationship between the subjects by placing them in order since he is able to rank them according to the preferences of the pupils. Thus, he is using an ordinal scale.

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Answer:

Circumference of a circle A = \(389.7 \,\,inches\)

Area of a circle A = 12081.1 square inches

Step-by-step explanation:

Let \(r\) denotes radius of circle B.

Circle A has a radius that is five more than twice as long as the radius of circle B.

So,

Radius of circle A = \(5+2r\)

Diameter of circle = 2 (radius of circle)

So,

Diameter of circle B = 2r

Diameter of circle A = \(2(5+2r)\)

Sum of the diameters of the circles A and B = \(2r+2(5+2r)\)

                                                                         \(=2r+10+4r\)

                                                                         \(=6r+10\)

As sum of the diameters of the circles is 88 inches,

\(6r+10=88\\6r=78\)

\(r=13\) inches

Radius of a circle A = \(2(5+2r)\)

                                \(=2[5+2(13)]\)

                                \(=2(5+26)\)

                                \(=2(31)\)

                                \(=62\) inches

Let R denotes radius of a circle A.

R = 62 inches

Circumference of a circle \(=2\pi R=2\pi (62)=124\pi =124(\frac{22}{7})=389.7 \,\,inches\)

Area of a circle \(=\pi r^2=\pi (62)^2=3844\pi=3844(\frac{22}{7})=12081.1\) square inches

Answer:

a. (2c+1b)-1w

b. monomial

Step-by-step explanation:

Answer:

$10

Step-by-step explanation:

Her hourly rate is 10 because if she earned $5 for half and our or 30 minutes that means to get to 1 hour multiply by 3 so you get. $10 per hour

Answer:

$10 per hour.

Step-by-step explanation:

$5 = 1/2 an hour | 30 minutes

So if you were to multiply $5 by 2 you'd get $10 which would make 1 whole hour.

$10 In different forms:

2/2

1.00

1

The probability that at least one child would draw the nickel too small is: P(X ≥ 1) = 1 - P(X = 0).

b) To find the probability that exactly 4 children would draw the nickel too small, we can use the binomial probability formula. The formula is: P(X = k) = (nCk) * (p^k) * (q^(n-k)), where n is the number of trials, k is the number of successes, p is the probability of success, and q is the probability of failure.

In this case, n = 8 (as 8 children are chosen), k = 4 (as exactly 4 children drawing the nickel too small), p = 0.15 (as the probability of a child drawing the nickel too small), and q = 1 - p = 1 - 0.15 = 0.85.

So, the probability that exactly 4 children would draw the nickel too small is: P(X = 4) = (8C4) * (0.15^4) * (0.85^(8-4)).

c) To find the probability that at least one child would draw the nickel too small, we can use the complement rule. The probability of at least one success is equal to 1 minus the probability of no success.

The probability of no success (all children drawing the nickel of the right size) is given by: P(X = 0) = (8C0) * (0.15^0) * (0.85^8).

Therefore, the probability that at least one child would draw the nickel too small is: P(X ≥ 1) = 1 - P(X = 0).

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Answer:

The answer is A. Positive Weak Non-Linear

Step-by-step explanation:

The dotted points are graphed in an upward form which indicates that it's graphed positively but since the dotted points are scattered that indicates it has a weak "power".

Answer:

4 1/14

Step-by-step explanation:

1. \(\frac{19}{8}* \frac{12}{7}\)

2. \(\frac{19*12}{8*7}\)

3. \(\frac{228}{56}\)

4. \(\frac{57}{14}\)

5. \(4 \frac{1}{14}\)

Answer:

10 small boxes and 12 large boxes

Step-by-step explanation:

Let x = number of large boxes

Let y = number of small boxes

We are told that;

volume of each small box = 6 cubic feet

volume of each large box = 22 cubic feet.

Total volume = 324 ft³

Thus;

6x + 22y = 324 - - - (eq 1)

We are told that 22 boxes of paper were shipped.

Thus; x + y = 22 - - - (eq 2)

Making x the subject in eq 2 gives;

x = 22 - y

Put 22 - y for x in eq 1;

6(22 - y) + 22y = 324

132 - 6y + 22y = 324

16y = 324 - 132

16y = 192

y = 192/16

y = 12

So, x = 22 - 12 = 10

The differential d y is  \(d y = ( 1 / 5 ) e^ ( x / 5 )dx\)  and when the values of x and dx are 0 and 0. 05 then the d y is equal to 0.01.

we have to find the differential of d y and Evaluate d y when the given values  of x and dx are 0 and 0. 05,

a) the differential d y,

\(y = e^(x/5)\)

differentiating the above equation with dx we get:

\(d y/dx = (1 / 5 ) e ^ ( x / 5 )\)

\(d y = ( 1 / 5 ) e^ ( x / 5 )dx\)

Therefore, the differential of d y is \(d y = ( 1 / 5 ) e^ ( x / 5 )dx\)

b) To evaluate d y for x = 0 and dx = 0.05, we substitute these values into the differential expression we found in part (a):

\(d y = ( 1 / 5 ) e^( x / 5 )dx\)

\(d y = ( 1 / 5 ) e^(0 / 5 )( 0.05 )\)

= (1/5) ( 1) (0.05)

= 0.01

Therefore, when x = 0 and dx = 0.05, d y is equal to 0.01.

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