For what values of x does the graph of f(x) have a horizontal tangent? (Enter your answers as a comma-separated list.)

f(x) = x³ + 7x² + x + 1


X=

Answer:

B) 2.883

Step-by-step explanation:

288.3/100=2.883

Check

2.883x100= 288.3

[tex]d = 5\sqrt{3}[/tex]

[tex]e = 2\sqrt{2}[/tex]

The probability of waiting between 2 and 4 minutes to use the ATM is 0. 5 or 50 %.

For a uniform distribution, the probability density function is constant within the given interval. In this case, the interval is between 1 and 5 minutes. The length of the interval is 5 - 1 = 4 minutes.

Now, we want to find the probability of waiting between 2 and 4 minutes. The length of this subinterval is 4 - 2 = 2 minutes. To find the probability of waiting between 2 and 4 minutes, we multiply the probability density by the length of the subinterval:

Probability = probability density × (length of subinterval) = (1/4) × 2 = 1/2 = 0.5

So, the probability of waiting between 2 and 4 minutes to use the ATM is 0.5 or 50%.

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Answer:

Amy will have £240 in her account.

Step-by-step explanation:

To calculate the amount of money Amy will have in her account after 2 years, we can use the formula:

A = P(1 + rt)

Where:

A = the total amount of money in the account after 2 years

P = the principal (the initial amount of money invested)

r = the interest rate (as a decimal)

t = the time in years

In this case, Amy invested £200 at an interest rate of 10% per year for 2 years. We can plug in these values into the formula and solve for A:

A = 200(1 + 0.1 × 2)

A = 200(1.2)

A = £240

Therefore, after 2 years, Amy will have £240 in her account.

Answer:

(3 sqrt(2))/2

Step-by-step explanation:

Simplify the following:

6/sqrt(8)

Rationalize the denominator. 6/sqrt(8) = 6/sqrt(8)×(8^(1 - 1/2))/(8^(1 - 1/2)) = (6×8^(1 - 1/2))/8:

(6×8^(1 - 1/2))/8

The gcd of 6 and 8 is 2, so (6×8^(1 - 1/2))/8 = ((2×3) 2 sqrt(2))/(2×4) = 2/2×(3×2 sqrt(2))/4 = (3×2 sqrt(2))/4:

(3×2 sqrt(2))/4

2/4 = 2/(2×2) = 1/2:

Answer: (3 sqrt(2))/2

Given:-

To Do :-

Solution:-

We have ;

[tex]\implies \dfrac{6}{\sqrt8} \\[/tex]

We can write 8 as 2³ . So ,

[tex]\implies \dfrac{6}{\sqrt{2^3}} \\[/tex]

[tex]\implies \dfrac{6}{2\sqrt2} \\[/tex]

[tex]\implies \dfrac{3}{\sqrt2} \\[/tex]

Rationalize the denominator by multiplying numerator and denominator by √2 .

[tex]\implies \dfrac{3\sqrt2}{\sqrt2.\sqrt2} \\[/tex]

[tex]\implies\boxed{ \dfrac{3\sqrt2}{2}} \\[/tex]

This is given required answer.

and we are done!

3. a. A solution or feasible region, is the triangular region in the graph of the inequality, with vertices (0.7, -3.35), (8, -7), (8, -25.25)

Please find attached the graph of the feasible region of the inequality, created with MS Excel

b. The feasible region in the graph of the inequality indicates that the inequality remains true for the coordinates of points within the feasible region

An inequality is an unequal comparison between values or expressions using inequality symbols such as <, >, ≤, and ≥.

3. The system of inequalities are presented as follows;

4·x + 8·y ≤ -24

-12·x - 4·y < 5

a. Making y the subject of the above inequalities, we get;

4·x + 8·y ≤ -24

y ≤ (-24 - 4·x) ÷ 8 = -3 - 0.5·x

y ≤ -3 - 0.5·x...(1)

-12·x - 4·y < 5

-4·y < 5 + 12·x

y > -1.25 - 3·x...(2)

The solution point is therefore;

-3 - 0.5·x = -1.25 - 3·x

2.5·x = 1.75

x = 1.75/2.5 = 0.7

The x-value of the solution point is therefore the point x = 0.7

y > -1.25 - 3 × 0.7 = -3.35

y > -3.35

The y-value of the solution point is the point y > -3.35

The solution point is therefore the point slightly to the right of the point (0.7, -3.35)

b. The solution space is the triangular region bounded by the points, (0.7, -3.35), (8, -7), and (8, -25.25)

A possible solution obtained from the graph is therefore, the point (6, -10), plugging in the values in the inequalities, we get;

When x = 6

y ≤ -3 - 0.5·x...(1)

y ≤ -3 - 0.5 × 6 = -6

The y-value at the point x = 6 is -10 ≤ -6, which satisfies the first inequality

The second inequality, indicates that we get;

y > -1.25 - 3·x

y > -1.25 - 3 × 6 = -19.25

The y-value at the selected point x = 6 is -10 > -19.25, which satisfies the second inequality

Therefore; The inequality is true at a specified point in the solution space as indicated from the graph

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The component of vector BC in the direction of the x-axis is (-6, 0).

To find the component of vector BC, we need to find the projection of vector BC onto a given vector.

The component of vector BC in the direction of the x-axis can be found using the formula:

comp(x) = (BC · unit(x)) · unit(x)

where;

To find unit(x), we can use the following formula:

unit(x) = (1, 0)

since the x-axis is the horizontal axis and its unit vector has a horizontal component of 1 and a vertical component of 0.

Now, let's calculate the component of vector BC in the direction of the x-axis:

BC = C - B = (-4, -5) - (2, -7) = (-6, 2)

|BC| = √((-6)² + 2²)

|BC| = √(40)

unit(x) = (1, 0)

(BC · unit(x)) = (-6) · 1 + (2) · 0 = -6

comp(x) = (BC · unit(x)) · unit(x) = (-6) · (1, 0) = (-6, 0)

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The complete question is below:

Find the component of the Vector BC on x-axis, if B=(2,-7) and C= (-4,-5)

Solving and simplifying the potenciation, we get 3⁹

As the bases presented are multiple, we can reduce it to the common base 3.
To do this, replace 9 with the equivalent in base 3.
That is, 3².
Then, apply the property of multiplying like bases, adding the exponents.

[tex]\begin{array}{l}\sf 9^{2} \times 3^{5}=[?]\\\raisebox{4pt}{$\sf \big(3^{2}\big)^{\!2} \times 3^{5}=[?]$}\\\sf 3^{4} \times 3^{5}=[?]\\\sf 3^{4+9} = [?]\\\sf 9^{2} \times 3^{5} = 3^{9}\end{array}[/tex]

So, the result found is 3⁹

Alternatively, the result can be written as 1.9683×10⁴, in scientific notation

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If you have any question about this solution, you can ask me in the comments :)

Answer:

(a) Musa wants to buy a bank draft for $427. Since $1 = 2 Naira, the cost of the bank draft in Naira will be:

$427 x 2 Naira/$1 = 854 Naira

The commission charged by the bank is 34 Naira on each bank draft, so the total amount in Naira that Musa will pay the bank will be:

854 Naira + 34 Naira = 888 Naira

Therefore, Musa will pay the bank a total of 888 Naira for the bank draft.

(b) Musa wants to buy a bank draft for £335. Since £1 = 15 Naira, the cost of the bank draft in Naira will be:

£335 x 15 Naira/£1 = 5,025 Naira

The commission charged by the bank is 34 Naira on each bank draft, so the total amount in Naira that Musa will pay the bank will be:

5,025 Naira + 34 Naira = 5,059 Naira

Therefore, Musa will pay the bank a total of 5,059 Naira for the bank draft.

a) Musa will pay the bank a total of ₦49,106 (42,700 + 6,406) if he buys a bank draft of $427. The conversion rate is $1 = ₦2 and the charges amount to 34 × 427 = 14,358, so the total amount to be paid is 42,700 + 14,358 = 56,058. Subtracting the commission, the total amount is 56,058 - 6,406 = 49,102.

b) Musa will pay the bank a total of ₦68,030 (50,500 + 17,530) if he buys a bank draft of £335. The conversion rate is £1 = ₦15 and the charges amount to 34 × 335 = 11,290, so the total amount to be paid is 50,500 + 11,290 = 61,790. Subtracting the commission, the total amount is 61,790 - 17,530 = 68,030.

According to the information, the Venn diagram that relates the image data would look like this (image attached).

A Venn diagram is a term that refers to a type of graph that is used to graph similarities, differences, and relationships between sets, ideas, categories, among others. The sales diagram is made up of interlocking circles in which the data is classified.

To draw this Venn diagram we have the following data:

Since we must draw the separate Venn diagram, we must make three circles and classify the data accordingly as shown in the image.

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This means that bone density scores below -1.88 are in the bottom 7% of scores, and scores above 1.88 are in the top 93% of scores.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

It is relates to bone density score distribution, where the bottom 7% of scores are separated from the top 93% of scores. This could be interpreted in a few different ways, but here's one way to approach it:

If we assume that the bone density scores are normally distributed (which is a common assumption in statistics), then we can use the properties of the normal distribution to estimate the cutoff values for the bottom 7% and top 93% of scores.

The standard normal distribution has a mean of 0 and a standard deviation of 1. Using this distribution, we can look up the cutoff values for the bottom 7% and top 93% of scores using a standard normal distribution table or calculator. These cutoff values represent the bone density scores below which 7% of scores fall and above which 93% of scores fall.

For example, using a standard normal distribution table, we can find that the cutoff value for the bottom 7% of scores is approximately -1.88, and the cutoff value for the top 93% of scores is approximately 1.88.

Therefore, This means that bone density scores below -1.88 are in the bottom 7% of scores, and scores above 1.88 are in the top 93% of scores.

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Answer:

D) 0.25 divided by 0.42.

Step-by-step explanation:

The answer can be found using the formula for conditional probability:

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

Let A be the event of passing the first test and B be the event of passing the second test. We know that:

P(A and B) = 25%

P(A) = 42%

To find P(B|A), we need to divide P(A and B) by P(A):

P(B|A) = P(A and B) / P(A) = 0.25 / 0.42

So the answer is D) 0.25 divided by 0.42.

Answer: X = 1, Y = 29

Step-by-step explanation:

X + 6(-1/6X + 5) = 30

X - 1 +30 = 30

X + 29 = 30

X = 1

Y = -1/6*1 + (5/1)*6

Y = -1/6 + 30/6

Y = -1 + 30

Y = 29

Using chain rule to find the derivative of h(x), the value of h'(2) is 25

The chain rule is a rule in calculus that allows us to find the derivative of a composite function. A composite function is a function that is composed of two or more functions. For example, if we have two functions f(x) and g(x), then the composite function, denoted by h(x), would be h(x) = f(g(x)).

Using the chain rule, we can find the derivative of h(x) with respect to x as follows:

h(x) = √6 + 5f(x)

h'(x) = d/dx (√6 + 5f(x))

h'(x) = d/dx (√6) + d/dx (5f(x))

h'(x) = 0 + 5f'(x)

Now, to find h'(2), we substitute x=2 in the expression above and use the given value of f'(2):

h'(2) = 5f'(2)

h'(2) = 5(5)

h'(2) = 25

Therefore, h'(2) = 25.

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Answer:

Step-by-step explanation:

To determine the cost of goods manufactured, we need to add up the total manufacturing costs incurred during the month and subtract the cost of work in process inventory on March 1, then add the cost of work in process inventory on March 31:

Total Manufacturing Costs = Cost of Direct Materials Used + Direct Labor + Factory Overhead

Total Manufacturing Costs = $18,435 + $26,510 + $37,267

Total Manufacturing Costs = $82,212

Cost of Goods Manufactured = Total Manufacturing Costs - Work in Process Inventory, March 1 + Work in Process Inventory, March 31

Cost of Goods Manufactured = $82,212 - $15,183 + $21,746

Cost of Goods Manufactured = $88,775

Therefore, the cost of goods manufactured for the month of March is $88,775.

To determine the cost of goods sold, we need to calculate the cost of goods available for sale, which is the sum of the cost of goods manufactured and the cost of finished goods inventory on March 1, and then subtract the cost of finished goods inventory on March 31:

Cost of Goods Available for Sale = Cost of Goods Manufactured + Finished Goods Inventory, March 1

Cost of Goods Available for Sale = $88,775 + $21,407

Cost of Goods Available for Sale = $110,182

Cost of Goods Sold = Cost of Goods Available for Sale - Finished Goods Inventory, March 31

Cost of Goods Sold = $110,182 - $26,154

Cost of Goods Sold = $84,028

Therefore, the cost of goods sold for the month of March is $84,028.

Therefore, the value of x is 348 the measure of angle ABD is (0.12x + 67) deg and the measure of angle CBD is (0.13x + 26).

An angle is a geometric figure formed by two rays, called the sides of the angle, that share a common endpoint, called the vertex of the angle. Angles are measured in degrees (°) or radians (rad) and are typically denoted by the vertex letter. The size of an angle is determined by the amount of rotation needed to rotate one of the sides of the angle onto the other side. An angle of 90 degrees is called a right angle, an angle less than 90 degrees is called an acute angle, and an angle greater than 90 degrees but less than 180 degrees is called an obtuse angle. Angles are used in a variety of fields, including geometry, trigonometry, and physics, and play an important role in understanding the properties and relationships of shapes and objects.

Here,

Since angles ABD and CBD are adjacent and share side BD, their measures must add up to 180 degrees (since they form a straight line). Therefore, we can write the following equation:

ABD + CBD = 180

Substituting the given measures of angles ABD and CBD, we get:

(0.12x + 67) + (0.13x + 26) = 180

Simplifying the left side of the equation by combining like terms, we get:

0.12x + 0.13x + 67 + 26 = 180

0.25x + 93 = 180

Subtracting 93 from both sides of the equation, we get:

0.25x = 87

Dividing both sides of the equation by 0.25, we get:

x = 348

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The type of function that best represents the data shown in the table above is Linear.

The statement that is true regarding the table above is that The first differences are constant.

The type of function that best represents the data shown in the table below is a Linear function.

A linear function is a type of mathematical function that can be represented by a straight line on a graph. It has the form:

f(x) = mx + b

where "m" represents the slope of the line, and "b" represents the y-intercept, which is the point where the line crosses the y-axis.

In this case the linear function is exhibited.

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The total cost of Kaitlyn's calls to the United States depends on the rate charged by her service provider, and it is important to be aware of any additional fees or charges that may apply.

The total cost of Kaitlyn's calls to the United States depends on the rate charged by her service provider. If Kaitlyn has a plan with a specific rate for international calls, her total cost can be calculated by multiplying the number of minutes by the rate. For example, if her plan charges $0.10 per minute, then 100 minutes of calls would cost $10. However, if Kaitlyn does not have a plan that includes international calls, the cost per minute may be significantly higher, and there may be additional fees or charges. Therefore, it is important to check with the service provider for specific rates and fees before making international calls. It may be beneficial for Kaitlyn to consider purchasing an international calling plan or using a calling app to minimize costs. Overall, the total cost for Kaitlyn's calls to the United States will depend on the specific rate charged by her service provider, and it is important to be aware of any additional fees or charges that may apply.

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The maximum number of devices that can have unique MAC addresses is given as follows:

16^12 = 2.81 x 10^14.

The Fundamental Counting Theorem states that if there are m ways to do one thing and n ways to do another, then there are m x n ways to do both. This can be extended to more than two events, where the number of ways to do all the events is the product of the number of ways to do each individual event.

There are 16 hexadecimal digits, from 0 to 9 and then A to E, hence we have 12 digits, each with 16 possible numbers.

Then the total number of unique sequences is given as follows:

16^12 = 2.81 x 10^14.

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The answer you're probably wanting is "function," since it is a function.

Technically though, it's both.  A function is a relation, one where each x-value (or input) has exactly one y-value (or output).  So every function is a relation, but not every relation is a function.

1. The credit which Stacy's will receive is $255.670.97.

2. Stacy's outstanding balance will be $854.33.

A credit refers to the ability of a customer to obtain goods or services before payment based on trust that payment will be made in the future.

From July 28 - July 14, we have 14 days. We are using the 3% discount.

The Credit receivable =

= Partial payment / (1 - discount rate)

= $248 / (1-0.03)

= $248 / 0.97

= $255.670103

= $255.67

An outstanding balance refers to the amount you owe on any debt that charges interest, like a credit card.

Stacy’s outstanding balance:

= $1,110 - $255.67

= $854.33.

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Answer:

2

Step-by-step explanation:

Answer:

If x = $30 is the regular price of a souvenir, then the sale price for each additional souvenir will be 0.3x = 0.3($30) = $9 less than the regular price. Therefore, the sale price of each additional souvenir will be:

Sale price = Regular price - $9

Sale price = $30 - $9

Sale price = $21

Since Carmen purchases 10 souvenirs, she pays the regular price for the first souvenir and the sale price for the remaining 9 souvenirs. Therefore, the total cost for all 10 souvenirs will be:

Total cost = (Regular price for first souvenir) + (Sale price for 9 additional souvenirs)

Total cost = ($30) + ($21 x 9)

Total cost = $30 + $189

Total cost = $219

Therefore, Carmen pays $219 for 10 souvenirs during the sale.

Step-by-step explanation:

The expression for the area of the floor q⁴r⁶

The error in the expression is that the square of the exponent of r was given in place of the product.

It is important to note that index forms are defined as models that are used to write or express conveniently, numbers that are too large or small.

Index forms are also called standard forms or scientific notations.

Some rules of index forms are;

From the information given, we have that;

(q²r³)²

expand the bracket, we get;

q⁴r⁶

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The area of the ring formed by concentric circles is approximately 188.5 square units.

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

The ring is formed by two concentric circles.

The area of the ring can be found by subtracting the area of the smaller circle from the area of the larger circle.

The area of a circle with radius r is given by the formula A = πr².

So, the area of the larger circle with radius 16 is -

A1 = π(16)² = 256π

And the area of the smaller circle with radius 14 is -

A2 = π(14)² = 196π

Therefore, the area of the ring is -

A ring = A1 - A2

A ring = 256π - 196π

A ring = 60π

To round to the nearest tenth, we can approximate π as 3.14 -

A ring ≈ 60 × 3.14 = 188.4

Rounding to the nearest tenth, we get -

A ring ≈ 188.4 ≈ 188.5

Therefore, the area of the ring is 188.5 square units.

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Supplementary angles have a measure of 180 degrees

The values οf a and b that make the functiοn f cοntinuοus at x = -2 and x = 3 are a = -2 and b = 1

A functiοn is said tο be cοntinuοus if it has nο jumps, breaks, οr hοles in its graph. In οther wοrds, a functiοn is cοntinuοus if it can be drawn withοut lifting the pen frοm the paper. Fοrmally, a functiοn is cοntinuοus at a pοint x = c if the limit οf the functiοn as x apprοaches c frοm bοth the left and the right exists and is equal tο the value οf the functiοn at c.

Fοr example, the functiοn f(x) = x² is cοntinuοus everywhere because it is a smοοth curve with nο jumps οr breaks in its graph. On the οther hand, the functiοn g(x) = 1/x is cοntinuοus everywhere except at x = 0, where it has a vertical asymptοte and a hοle in its graph.

The cοncept οf cοntinuity is impοrtant in many areas οf mathematics, including calculus and analysis, as it allοws us tο study the behaviοr οf functiοns at specific pοints and οver intervals. It is alsο impοrtant in real-wοrld applicatiοns, such as in engineering and physics, where cοntinuοus functiοns mοdel physical phenοmena like mοtiοn, heat transfer, and fluid flοw.

Tο find the values οf a and b, we can use the cοntinuity οf the functiοn at x = -2 and x = 3. Fοr a functiοn tο be cοntinuοus at a pοint, it must exist at that pοint and its limit as x apprοaches that pοint frοm bοth sides must be equal.

At x = -2:

The left-hand limit οf f(x) as x apprοaches -2 is f(-2-) = 2(-2)² - 3 = 5.

The right-hand limit οf f(x) as x apprοaches -2 is f(-2+) = a(-2) + b.

Since the functiοn is cοntinuοus at x = -2, these limits must be equal:

f(-2-) = f(-2+) => 5 = -2a + b

At x = 3:

The left-hand limit οf f(x) as x apprοaches 3 is f(3-) = a(3) + b.

The right-hand limit οf f(x) as x apprοaches 3 is f(3+) = (6/3) - 3 = -1.

Since the functiοn is cοntinuοus at x = 3, these limits must be equal:

f(3-) = f(3+) => a(3) + b = -1

We nοw have twο equatiοns with twο unknοwns:

5 = -2a + b

a(3) + b = -1

Sοlving fοr b in terms οf a in the first equatiοn gives:

b = 2a + 5

Substituting this expressiοn fοr b intο the secοnd equatiοn gives:

a(3) + 2a + 5 = -1

3a + 5 = -1

3a = -6

a = -2

Substituting this value οf a intο the first equatiοn gives:

5 = -2(-2) + b

5 = 4 + b

b = 1

Therefοre, the values οf a and b that make the functiοn f cοntinuοus at x = -2 and x = 3 are a = -2 and b = 1.

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By using a system οf equatiοns, the schοοl makes 180 chicken sandwiches, 180 turkey sandwiches, and 140 rοast beef sandwiches.

A system οf equatiοns is a set οf twο οr mοre equatiοns that need tο be sοlved tοgether tο find the values οf the variables that satisfy all οf the equatiοns.

Let's use a system οf equatiοns tο sοlve the prοblem.

Let c be the number οf chicken sandwiches sοld, t be the number οf turkey sandwiches sοld, and r be the number οf rοast beef sandwiches sοld.

Frοm the prοblem, we knοw that:

c + t + r = 500 (the tοtal number οf sandwiches sοld is 500)

3c + 3.5t + 4r = 1730 (the tοtal revenue frοm selling all sandwiches is $1730)

We alsο knοw that the cafeteria makes the same number οf chicken sandwiches as it dοes turkey sandwiches, sο: c = t

Nοw we can substitute c fοr t in the first twο equatiοns:

c + c + r = 500

3c + 3.5c + 4r = 1730

Simplifying these equatiοns, we get:

2c + r = 500

6.5c + 4r = 1730

We can sοlve fοr r in the first equatiοn:

r = 500 - 2c

Substituting this intο the secοnd equatiοn and sοlving fοr c, we get:

6.5c + 4(500 - 2c) = 1730

6.5c + 2000 - 8c = 1730

-1.5c = -270

c = 180

Sο the cafeteria sells 180 chicken sandwiches and 180 turkey sandwiches (since c = t). We can find the number οf rοast beef sandwiches by substituting c and t intο οne οf the οriginal equatiοns:

c + t + r = 500

180 + 180 + r = 500

r = 140

Therefοre, the schοοl makes 180 chicken sandwiches, 180 turkey sandwiches, and 140 rοast beef sandwiches.

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