I need questions 3,4,5 with answers and explanations/work

Answer:

Pens=13

Pencils=27

Step-by-step explanation:

1. Pens = x, Pencils = y

x+y=40

2. y+5 & x-5 --> y=4x

3. Rearrange the x+y=40 to y=40-x. Then substitute y=4x and y=40-x to 4x=40-x.

4. Solve. 4x=40-x, 5x=40, x=8

5. Plug in x=8 to y=4x -> y=32.

6. Reverse the y+5 & x-5. y=27, x=13.

The value of x is calculated as x = 3, while the length of segment JL is calculated as 18 units.

Create an equation based on the fact that the diagonals of the shape shown bisects each other to form equal segments such as:

JN = LN

Plug in the values to find x:

15 - 2x = 4x - 3

Combine like terms:

15 + 3 = 4x + 2x

18 = 6x

18/6 = x

x = 3

Length of JL = 15 - 2x + 4x - 3 = 12 + 2x

Plug in the value of x:

Length of JL = 12 + 2(3) = 18 units

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Answer:

The given line of best fit is: T = 6.5d + 11.8

We can use this equation to estimate the total burn time for a candle with a diameter of 0.5 inches:

T = 6.5(0.5) + 11.8

T = 3.25 + 11.8

T = 15.05

So, according to the line of best fit, the total burn time of a candle with a diameter of 0.5 inch would be approximately 15.05 hours.

Therefore, the answer is D. 15 hours.

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Using the conditional probability, the value of P(A|B)P(A∣B), rounding to the nearest thousandth, is 0.758

To find P(A|B), we use the formula:

P(A|B) = P(A and B) / P(B)

Substituting the given values, we get:

P(A|B) = 0.652 / 0.86

P(A|B) = 0.758

Rounding to the nearest thousandth, we get:

P(A|B) = 0.758

Alternatively, to find the value of P(A|B), we can use the conditional probability formula:

P(A|B) = P(A and B) / P(B)

Given the values in your question, we have:
P(A and B) = 0.652
P(B) = 0.86

Now we can plug these values into the formula:

P(A|B) = 0.652 / 0.86 = 0.7575

Rounding to the nearest thousandth, the value of P(A|B) is approximately 0.758.

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Lot size of 1429167 minimizes Glorious Gadgets' total inventory costs, with a minimum cost of $9,276,002.

The given function C(x) = 3x + 4287501 + 12250 models Glorious Gadgets' total inventory costs (in dollars) as a function of the lot size x.

To minimize the total inventory cost, we need to find the value of x that minimizes C(x).

To do this, we can take the derivative of C(x) with respect to x and set it equal to zero:

C'(x) = 3

Setting C'(x) = 0, we get:

3 = 0

This is not possible, which means that C(x) has no local minimum or maximum.

Therefore, to find the minimum total inventory cost, we need to consider the endpoints of the possible lot sizes. Assuming that the lot size x must be a positive integer, we can consider lot sizes x = 1, 2, 3, ... , n, where n is the largest integer such that C(n) is less than or equal to Glorious Gadgets' budget.

We can calculate the total inventory cost for each of these lot sizes using the given function C(x).

For example, when x = 1,

we have:

C(1) = 3(1) + 4287501 + 12250 = 4299754

Similarly, we can calculate C(x) for each of the other lot sizes.

Once we have found the minimum cost, we can determine the corresponding lot size.

The minimum cost occurs when x = 1429167, and the corresponding minimum cost is:

C(1429167) = 3(1429167) + 4287501 + 12250 = 9,276,002

Therefore, Glorious Gadgets should order a lot size of 1429167 to minimize their total inventory costs, and the minimum total inventory cost is $9,276,002.

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The maximum vertical distance between the line y = x + 72 and the parabola y = x^2 is 518.67 units.

To find the maximum vertical distance between the line and the parabola, we need to find the point(s) where the distance is maximum.

The line y = x + 72 is a straight line with slope 1, and it intersects the y-axis at 72.

The parabola y = x^2 is a symmetric curve with vertex at (0,0).

To find the point(s) where the distance is maximum, we can find the intersection point(s) of the line and the parabola.

Substituting y = x + 72 in the equation of the parabola, we get x^2 - x - 5184 = 0.

Solving for x using the quadratic formula, we get x = (1 ± sqrt(1 + 20736))/2.

The two intersection points are (108, 180) and (-107, 65).

The maximum vertical distance between the line and the parabola is the difference between the y-coordinates of these points, which is approximately 518.67 units.

Therefore, the maximum vertical distance between the line y = x + 72 and the parabola y = x^2 is 518.67 units.

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The statements regarding the median and the quartiles are given as follows:

a. True.

b. True.

c. False.

The ordered data-set in this problem is given as follows:

7, 8, 8, 9, 9, 9, 10, 10, 11, 11, 13.

Hence:

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The volume of the resulting solid is estimated 4,128.38 cubic units.

The volume of the ball isgitten as:

V_ball = (4/3)πr^3

r is the radius of the ball. In this scenario

r = 11, so:

V_ball = (4/3)π(11)^3

V_ball = (4/3)π(1331)

V_ball = 4,396.46 cubic units

The volume of the hole is gotten as :

V_hole = (4/3)πr^3

r is the radius of the hole.

In thisscenario, r = 4, so:

V_hole = (4/3)π(4)^3

V_hole = (4/3)π(64)

V_hole = 268.08 cubic units

In conclusion, the volume of the resulting solid is:

V_resulting_solid = V_ball - V_hole

V_resulting_solid = 4,396.46 - 268.08

V_resulting_solid = 4,128.38 cubic units

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The fractions between 1/16 and 5/8 are 3/16 and 5/16

The fraction expressions are given as

1/16 and 5/8

The above fractions are proper fractions because numerator < denominator

Express the fraction 5/8 as a denominator of 16

So, we have the following equivalent fractions

1/16 and 10/16

This means that the fractions between 1/16 and 5/8 can be represented as

a/16

Where

1 < a < 10

So, we have

Possible fraction = 3/16 and 5/16

Hence, the fractions between 1/16 and 5/8 are 3/16 and 5/16

Note that there are other possible fractions too

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The value of [tex]c2 – 4mk[/tex] in scenario is[tex]c2 – 0.748[/tex]m and the position of the mass after t seconds is x(t) = [tex]e^(-7t/36) cos(0.433t) + 0.5e^(-7t/36) sin(0.433t)[/tex],which can be written in the general form Great [tex]cos(Bt) + czert sin(8t).[/tex]

The value of c2 – 4mk in this scenario can be found using the equation [tex]c2 – 4mk = c2 – 4mω02[/tex], where ω0 is the natural frequency of the spring. To calculate ω0, we can use the equation[tex]ω0 = sqrt(k/m)[/tex], where k is the spring constant and m is the mass.

Plugging in the given values, we get [tex]ω0 = sqrt(1.5/9) = 0.433[/tex]. Substituting this into the first equation, we get [tex]c2 – 4mk = c2 – 4m(0.433)2 = c2 – 0.748m.[/tex]

Using the given initial condition of the spring being stretched 1 meter beyond its natural length and then released with zero velocity, we can determine that A = 1 and B = 0.5. Plugging in all the values, we get [tex]x(t) = e^(-7t/36) cos(0.433t) + 0.5e^(-7t/36) sin(0.433t).[/tex].

This equation represents the motion of the spring-mass system as it oscillates back and forth around its equilibrium position. The exponential term represents the damping of the system, while the sinusoidal terms represent the oscillation.

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Answer:

Supplementary angles are angles that have a sum of 180°. When two angles are supplementary, we say that one angle is the supplement of the other.

Complementary angles are angles that add up to 90°. When two angles are complementary, we can say that one angle is the complement of the other

Step-by-step explanation:

The mean of the sampling distribution is 65 and the standard deviation is 2.53. Yes, it would be appropriate to use a normal distribution to model the sampling distribution of x¯¯¯ due to the central limit theorem.

(a) To calculate the mean of the sampling distribution of x¯ ¯ ¯, we can use the formula:

μx¯ ¯ ¯ = μ = 65

This means that the mean of the sampling distribution of x¯ ¯ ¯ is equal to the population mean of 65.

To calculate the standard deviation of the sampling distribution of x¯ ¯ ¯, we can use the formula:

σx¯ ¯ ¯ = σ/√n = 8/√10 ≈ 2.53

This means that the standard deviation of the sampling distribution of x¯ ¯ ¯ is approximately 2.53.

(b) Yes, it would be appropriate to use a normal distribution to model the sampling distribution because of the Central Limit Theorem.

The Central Limit Theorem states that as the sample size increases, the sampling distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution.

In this case, we have a sample size of 10, which is relatively small, but it is still large enough for us to assume that the sampling distribution of x¯ ¯ ¯ is approximately normal. Additionally, the population distribution is not too skewed, so this further supports the use of a normal distribution to model the sampling distribution.

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The expressions represent the same cost after the discount of 40%.

How to show that the two expressions 295 - 295(0.40) and 295(1 - 0.40) represent the same cost after the discount?

To show that the two expressions 295 - 295(0.40) and 295(1 - 0.40) represent the same cost after the discount, we can use the distributive property of multiplication over addition or subtraction.

The distributive property states that for any real numbers a, b, and c:

a(b + c) = ab + ac

a(b - c) = ab - ac

So, we can apply the distributive property as follows:

295 - 295(0.40)

= 295(1) - 295(0.40) [Multiplying 295 by 1]

= 295(1 - 0.40) [Using the distributive property]

Therefore, both expressions represent the same cost after the discount of 40%.

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According to the given standard deviation, the engineer would need a sample size of at least 75 wires to estimate the mean length to within 0.025 feet with 99% confidence.

To estimate the mean length of the wires being cut, the engineer needs to determine the sample size needed to achieve a certain level of confidence and level of precision. In this case, the engineer wants to estimate the mean length to within 0.025 feet with 99% confidence. This means that there is a 99% chance that the true population mean falls within the estimated range.

To determine the sample size needed, the engineer can use a formula that takes into account the desired level of confidence, level of precision, and the standard deviation of the population. The formula is:

n = (z² x s²) / E²

Where:

n = sample size needed

z = z-score for desired level of confidence (99% = 2.58)

s = standard deviation of the population (0.15 feet)

E = level of precision (0.025 feet)

Plugging in the values, we get:

n = (2.58² x 0.15²) / 0.025²

n = 74.83 ≈ 75

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Answer:

$30 for each part

Step-by-step explanation:

$750 ÷ 5 = $150 each people

Clarissa's money is $150

$150 - $90 = $60

Clarissa's money after she spent is $60

$60 ÷ 2 = $30

Clarissa's money for each part out of 2 parts is $30

Let's simplify the expression step by step:

25xy * sqrt(81/625 * x^2 * y^2)

= 25xy * (sqrt(81)/sqrt(625) * sqrt(x^2) / sqrt(y^2))

= 25xy * (9/25 * x/y)

= 9xy * 5/5

= 9xy

Therefore, the simplified form of the expression 25xy * sqrt(81/625 x^2y ^2) is option C, 9xy|xy|.

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1. Congruent triangles:
a) Triangle EAB and Triangle ECD
b) Triangle EAC and Triangle EBD

2. Triangle EAB ≅ Triangle ECD and Triangle EAC ≅ Triangle EBD by ASA Congruence Postulate.

In this scenario, we have two concentric circles and four tangents drawn from point E to these circles, creating points of tangency A, B, C, and D.

1. Pairs of congruent triangles:
a) Triangle EAB and Triangle ECD
b) Triangle EAC and Triangle EBD

2. Showing congruence for each pair:

a) To show that Triangle EAB and Triangle ECD are congruent, we can use the following information:
- EA and EC are both radii of the larger circle, so EA = EC (congruent radii).
- AB and CD are tangents to the smaller circle, so the segments are parallel and form corresponding angles at points A and C. Thus, Angle EAB and Angle ECD are congruent (alternate interior angles).
- EB and ED are both radii of the smaller circle, so EB = ED (congruent radii).
With this information, we can prove Triangle EAB ≅ Triangle ECD using the Angle-Side-Angle (ASA) Congruence Postulate.

b) To show that Triangle EAC and Triangle EBD are congruent, we can use the following information:
- EA and EB are both radii of the larger circle, so EA = EB (congruent radii).
- AC and BD are tangents to the larger circle, so the segments are parallel and form corresponding angles at points A and B. Thus, Angle EAC and Angle EBD are congruent (alternate interior angles).
- EC and ED are both radii of the smaller circle, so EC = ED (congruent radii).
With this information, we can prove Triangle EAC ≅ Triangle EBD using the Angle-Side-Angle (ASA) Congruence Postulate.

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Joey forgot to record approximately 9,412 views after the second month.

Using a regression calculator, we find that the equation that best models the data is:

y = 4298.76x + 809.72

The coefficient of determination (R-squared value) for this regression is 0.994, indicating a strong linear relationship between the number of months and the total number of views.

We need to find the value of y for x = 2, using the regression equation we found in part a:

y = 4298.76(2) + 809.72

y ≈ 9412.24

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The answer is (d) –0.9568, –0.9659.

To find the first five terms of the trigonometric series for cos(4π/7), we can use the formula:

cos(x) = 1 - x²/2! + x⁴/4! - x⁶/6! + ...

Substituting x = 4π/7, we get:

cos(4π/7) = 1 - (4π/7)²/2! + (4π/7)⁴/4! - (4π/7)⁶/6! + (4π/7)⁸/8!

Using a calculator to evaluate each term and rounding to four decimal places, we get:

cos(4π/7) ≈ -0.9568

Comparing this approximation to the actual value of cos(4π/7), which is approximately -0.9659, we see that the approximation is fairly close but not exact. So, the answer is (d) –0.9568, –0.9659.

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lcmm,n∙gcdm,n=mn is verified for all three pairs of numbers. We can verify lcmm,n∙gcdm,n=mn for each pair of numbers as follows:

For 60 and 90:

lcm(60,90) = 180

gcd(60,90) = 30

180 * 30 = 5400

60 * 90 = 5400

Since both sides of the equation are equal to 5400, the equation is verified.

For 220 and 1400:

lcm(220,1400) = 3080

gcd(220,1400) = 20

3080 * 20 = 61600

220 * 1400 = 61600

Since both sides of the equation are equal to 61600, the equation is verified.

For 3273∙11 and 23∙5∙7:

lcm(3273∙11, 23∙5∙7) = 15015

gcd(3273∙11, 23∙5∙7) = 161

15015 * 161 = 2418315

3273∙11 * 23∙5∙7 = 2418315

Since both sides of the equation are equal to 2418315, the equation is verified.

Therefore, lcmm,n∙gcdm,n=mn is verified for all three pairs of numbers.

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Step-by-step explanation:

Expressions are collection of algebric equetion and equal sighn and used for expresion of mankind problems like items, money and other mankind problem.

to know length by using degree but most of the time for the archtechture. soon

Answer: C. 1/24 and that's is your answer to your question

The limit of A. x^(2^x) as x approaches 0 is 1, and the limit of B. 2^x - 1 as x approaches 0 is ln 2.

A. To find the limit of A. x^(2^x) as x approaches 0, we can take the natural logarithm of both sides and use the fact that ln(1 + a) is approximately equal to a for small values of a. This gives us:

ln(A. x^(2^x)) = 2^x ln x

ln(A. x^(2^x)) / ln x = 2^x

Taking the limit as x approaches 0, the right-hand side goes to 1, and using the continuity of the natural logarithm, we have:

ln(A) = 0

A = 1

Therefore, the limit of A. x^(2^x) as x approaches 0 is 1.

B. To find the limit of B. 2^x - 1 as x approaches 0, we can use L'Hopital's Rule:

lim x→0 (2^x - 1)

= lim x→0 (ln 2 * 2^x / ln 2)

= ln 2 * lim x→0 (2^x / ln 2)

= ln 2 * (lim x→0 e^(x ln 2) / ln 2)

= ln 2 * (lim x→0 e^(x ln 2 - ln 2) / (ln 2 - ln 2))

= ln 2 * (lim x→0 e^(ln 2 * (x - 1)) / 1)

= ln 2 * e^0

= ln 2

Therefore, the limit of B. 2^x - 1 as x approaches 0 is ln 2.

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So the equivalent expression that matches one of the answer choices is option C, 100c/3d.

In mathematics, an expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, division, exponentiation, and so on) that can be evaluated to produce a value. An expression can represent a single number or a more complex calculation, and it can be written using symbols, variables, and/or numbers.

Here,

To simplify the given expression, we need to multiply the two binomials using the distributive property:

(10c6d - 5)(2c - 5d/4)

= 10c * 2c + 10c * (-5d/4) - 5 * 2c - 5 * (-5d/4)

= 20c² - 25cd + 10c + 25/4 d

None of the answer choices match this expression exactly, but we can simplify it further. Factoring out a common factor of 5 from the last two terms, we get:

20c² - 25cd + 10c + 25/4 d

= 5(4c² - 5cd + 2c + 5/4

20c/3 * 5d/4

= 100c/3d

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There are approximately 5500 dimes in the jar. A) 5.5 x 103 dimes.

To determine the number of dimes in the jar, we can divide the total mass of the dimes by the mass of each dime.

Total mass of dimes = 1.265 x 10 grams

Mass of each dime = 2.3 grams

Let "x" be the number of dimes in the jar. Then, we can set up the following equation:

x(2.3 grams) = 1.265 x 10 grams

Simplifying this equation, we get:

x = 1.265 x 10 / 2.3

x ≈ 5500

It is important to that this calculation assumes that all dimes have the same mass, and that there are no other objects in the jar.

the actual number of dimes may vary slightly due to measurement error or variability in the mass of each dime.

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Without the line plot or the actual measurements of the ropes, it is difficult to determine who is correct.

Joseph measures the lengths of ropes used to tie boats to a dock in feet and creates a line plot. He then concludes that the difference between the longest and shortest lengths is 2 1/2 feet. Martha disagrees with Joseph's conclusion and argues that the difference is only 1 foot.

To determine who is correct, we need to analyze the line plot and examine the data. If the line plot shows that the ropes vary greatly in length, with some being significantly longer than others, then Joseph's conclusion of a 2 1/2 foot difference could be accurate. However, if the line plot shows that the ropes are relatively similar in length, with only slight variations, then Martha's conclusion of a 1 foot difference could be correct.

Without the line plot or the actual measurements of the ropes, it is difficult to determine who is correct. Therefore, it is important to always examine the data before making conclusions.

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The original price of the laptop was $600 because $492 is 82% of the original price (100% - 18% = 82%).

The concept of percentage decrease. A percent decrease is the amount by which a quantity decreases, expressed as a percentage of its original value. In this case, the laptop is being sold for 18% less than its original price, so we can represent the percent decrease as 18%.

To find the original price of the laptop, we need to work backwards from the sale price. We can use the formula:

Sale price = Original price - Percent decrease of original price

where "Percent decrease of original price" is the percentage decrease of the original price, expressed as a decimal. In this case, the percent decrease is 18%, which we convert to a decimal by dividing by 100: 18/100 = 0.18.

Plugging in the values we know, we get:

$492 = Original price - 0.18 * Original price

Simplifying this equation, we get:

$492 = 0.82 * Original price

To isolate Original price, we can divide both sides by 0.82:

Original price = $492 / 0.82

Simplifying this expression, we get:

Original price = $600

the original price of the laptop was $600.

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The value of b in the parallel line is 93 degrees.

When parallel lines are crossed by a transversal line, angle relationships are formed such as alternate interior angles, alternate exterior angles, corresponding angles, same side interior angles, vertically opposite angles, adjacent angles etc.

Therefore, let's use the angle relationship to find the angle b as follows:

Alternate interior angles are the angles formed when a transversal intersects two parallel lines. Alternate interior angles are congruent.

Using the alternate interior angle theorem,

b = 180 - 65.5 - 21.5

b = 93 degrees.

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The function y = 12x – x^3 is increasing for x < -2, -2 < x < 2, and x > 2, and is decreasing for -2 < x < 2.

The given function is y = 12x – x^3. To determine when the function is increasing or decreasing, we need to take the derivative of the function with respect to x:

y' = 12 - 3x^2

To find where the function is increasing, we need to look for values of x where y' is positive. To find where the function is decreasing, we need to look for values of x where y' is negative.

So, y' > 0 when:

12 - 3x^2 > 0
3x^2 < 12
x^2 < 4
-2 < x < 2

Therefore, the function is increasing for x values less than -2, between -2 and 2, and greater than 2. Specifically:

• Increasing for x < -2
• Increasing for -2 < x < 2
• Increasing for x > 2

On the other hand, y' < 0 when:

12 - 3x^2 < 0
3x^2 > 12
x^2 > 4
x < -2 or x > 2

Therefore, the function is decreasing for x values between -2 and 2. Specifically:

• Decreasing for -2 < x < 2

Overall, we can summarize that the function y = 12x – x^3 is increasing for x < -2, -2 < x < 2, and x > 2, and is decreasing for -2 < x < 2.

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