(
39) 10-
B-9) 10-
-- 10

Answer:

38 cm²

Step-by-step explanation:

Given that,

→ Length (l) = 4 cm

→ Breadth (b) = 3 cm

→ Height (h) = 1 cm

Formula we use,

→ 2(lb + bh + lh)

The surface area of cuboid will be,

→ 2(lb + bh + lh)

→ 2{(4 × 3) + (3 × 1) + (4 × 1)}

→ 2(12 + 3 + 4)

→ 2 × 19

→ [ 38 cm² ]

Hence, the surface area is 38 cm².

The function f is increasing on the interval (6, ∞).

The function f will be increasing in the intervals where f'(x) > 0.

To find these intervals, we can examine the sign of each factor of f'(x), which is (x + 1)²(x - 3)⁵(x - 6)⁴.

We can analyze the sign of f(x) by considering the factors individually:

(x+1)²: This factor is always positive since it is the square of a real number.

(x - 3)⁵: This factor is positive when x>3 and negative when x< 3.

(x - 6)⁴: This factor is positive when x>6 and  negative when x< 6.

We need to consider the overlapping regions of positivity for each factor.

When x>6, all three factors are positive, so  f ′ (x) is positive.

When 3<x<6: In this interval, the factor  (x+1)² is positive, but both (x−3)⁵ and (x−6)⁴ are negative.

Thus, f ′ (x) is negative.

When x<−1: In this interval,  (x+1)² is negative, while (x−3)⁵ and (x−6)⁴ are positive.

Hence, f ′ (x) is negative.

Therefore,  the function f(x) is increasing on the interval x>6.

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(11/7)^(-4) * (7/44)^(-4) simplifies to 0.5716.

We can simplify this expression by first breaking down the bases of each term into their prime factors:

11/7 = 1.57

1.57^(-4) = (7/11)^4

7/44 = 0.1591

0.1591^(-4) = (44/7)^4

So the expression becomes:

[(7/11)^4][(44/7)^4]

Now we can simplify further by using the rule that (a^m)(a^n) = a^(m+n):

[(7/11)^4][(44/7)^4] = (7/11)^4 * 44/7)^4

= [(7^4)/(11^4)][(2^2*11^2)/(7^4)]

= (7^4 * 2^2 * 11^2)/(11^4 * 7^4)

= (4 * 121)/(11^2 * 7^2)

= 484/847

= 0.5716 (rounded to four decimal places)

Therefore, (11/7)^(-4) * (7/44)^(-4) simplifies to 0.5716.

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Answer: -58

Step-by-step explanation:

Start by looking for key words and numbers in your question/statement:

The sum of 18 and a number, x, equals negative 40.

Notice the word sum.

Sum is addition so x plus 18 is equal to -4.

Now that we have our equation (x+18=-40) we can solve by reversing the addition with subtraction:

  X+18=-40

     -18.   -18

 X=-58

Now that you know what X is equal to, check it by plugging it back into the equation.

      -58+18=-40

    It fits! So -58 is your answer.

           Hope this helped;)

Step-by-step explanation:

\( \tan(32) = \frac{x}{10} \\ x = 10 \tan(32) \\ x = 6.248 = 6.25\)

Answer:

1 is the correct answer.

You can use the law of sines here to find the measure of angle F.

The approximate measure of angle F is given by

Option B : 44. 4°

For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,

we have, by law of sines,

\(\dfrac{\sin(\angle A)}{a} = \dfrac{\sin(\angle B)}{b} = \dfrac{\sin(\angle C)}{c}\)

Remember that we took  \(\dfrac{\sin(angle)}{\text{length of side opposite to that angle}}\)

See the figure attached below for reference

Using the law of sines, we get;

\(\dfrac{\sin(\angle F)}{|GH|} = \dfrac{\sin(\angle G)}{|FH|} = \dfrac{\sin(\angle H)}{|FG|}\\\\\dfrac{\sin(\angle F)}{28} = \dfrac{\sin(90^\circ)}{40} = \dfrac{\sin(\angle H)}{|FG|}\\\)

First two terms are enough to evaluate the angle F

\(\dfrac{\sin(\angle F)}{28} = \dfrac{\sin(90^\circ)}{40} \\\\sin(\angle F) = 28 \times \dfrac{1}{40} = 0.7\\\angle F = arcsin(0.7)\\\\\angle F = 44.427^\circ\)

(i took that value of angle which comes out non negative(because no reason for distinguishing the sign and we take magnitude) and smaller than 90 degrees since the sum of all three angles of a triangle is 180 degrees)

Thus.

The approximate measure of angle F is given by

Option B : 44. 4°

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Answer: B) 44.4

Step-by-step explanation:

just did it

Lena should write down the equations to help her grasp them, as this is the best method for doing so.

The numerous letters, figures, and symbols that Lena discovers scattered over the pages of her arithmetic textbook are fuddle her.

Thus, Lena should write the equations down in words since that is the most efficient method for learning complex mathematical expressions.

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Answer:

\(x=(-2,\frac{5}{3} )\)

Step-by-step explanation:

1)  We will use the matrix method to solve this problem.

\(\left[\begin{array}{ccc}-2/3&1&3\\1&0&-2\\\end{array}\right]\)

2) Swap Row₁ and Row₂ to make row reduction easier.

\(\left[\begin{array}{ccc}1&0&-2\\-2/3&1&3\\\end{array}\right]\)

3) Apply to Row₂ :  Row₂ + \(\frac{2}{3}\) Row₁.

\(\left[\begin{array}{ccc}1&0&-2\\0&1&5/3\end{array}\right]\)

4)  Simplify rows.

\(\left[\begin{array}{ccc}1&0&-2\\0&1&5/3\\\end{array}\right]\)

Note: The matrix is now in row echelon form.

The steps below are for back substitution.

5) Apply Row₁ : Row₁ - 0 Row₂.

\(\left[\begin{array}{ccc}1&0&-2\0\\0&1&5/3\end{array}\right]\)

6) Simplify rows.

\(\left[\begin{array}{ccc}1&0&-2\\0&1&5/3\\\end{array}\right]\)

Note: The matrix is now in reduced row echelon form.

7) Therefore,

\(x=-2\\x=\frac{5}{3}\)

In a simple linear regression model, the coefficient of the independent variable (x) in the estimated sample regression equation indicates the change in the predicted value of the dependent variable (y) when x increases by one unit. This coefficient is also known as the slope of the regression line. Therefore, to calculate the predicted value of y, we multiply the coefficient by the value of x and add the intercept.

In a simple linear regression model, the coefficient that indicates the change in the predicted value of y when x increases by one unit is the "slope coefficient" or the "regression coefficient" (usually denoted as b1). This coefficient represents the relationship between the independent variable x and the dependent variable y.

The linear regression equation is given as:

y = b0 + b1 * x

Where:
- y is the predicted value of the dependent variable
- b0 is the intercept coefficient (where the line intersects the y-axis)
- b1 is the slope coefficient (the change in y when x increases by one unit)
- x is the independent variable

In this equation, b1 indicates the change in the predicted value of y when x increases by one unit.

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Answer: Probably D not sure though

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The equation g(x) = f(x-6) = 10(x-6) states that the graph is shifted to the left 6 units ( hints the -6)

Answer: It took her 8 hrs to get there.

Step-by-step explanation:

Answer:

O 6x5/5x

Step-by-step explanation:

Answer:

It should be D. I'm not 100% sure though. But D is what I chose.

Answer: A Geometric sequence is a type of sequence in which each subsequent term after the first term is determined by multiplying the previous term by a constant (not 1), which is referred to as the common ratio.

Step-by-step explanation: Hope this was helpful

Step-by-step explanation:

The sequence

a, ar, ar^2, .....ar^n-1,...

where a is the first term and any two consecutive numbers differ by a factor r, is called a Geometric progression (G.P.).

Geometric progression also known as Geometric sequence.

Answer:

5+0.1x=3-0.9x

2=-0.10x

1=-0.5x

x=-2

Answer is B good luck comrade<33!!

The measure οf angle x is 110°, while the measure of angle y is 70°.

A circle's arc is referred tο as a pοrtiοn οr sectiοn οf its circumference.  A chοrd οf a circle is a straight line that might be created by jοining the arc's twο ends.

Tο sοlve fοr x, we use the fοrmula `angle = 1/2(arc1+arc2)`. Here's hοw we can use this fοrmula:

Step 1: Identify the angles and arcs in the prοblem.

Step 2: Plug in the values in the fοrmula and sοlve fοr x.

Frοm the given figure, we can see that the twο arcs (arc1 and arc2) have measures 140° and 80°, respectively. We need tο find the angle x.

Step 3: Plug in the values in the fοrmula and sοlve fοr x.

The fοrmula `angle = 1/2(arc1+arc2)` relates the angle (in degrees) between twο radii οf a circle tο the arcs cut οff by these radii. Using this fοrmula, we have: angle = 1/2(arc1 + arc2)angle = 1/2(140° + 80°)angle = 1/2(220°)angle = 110°

Thus, the measure οf angle x is 110°.

Using vertical opposite property:

x + x + y + y = 360

110+ 110+ 2y = 360

110+ 110+ 2y = 360

2y = 360 - 220

2y = 140

y = 140/2

y = 70°

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Answer:

0.194

Step-by-step explanation:

X has a mean of 69 and a standard deviation of 5.8/√100 = 0.58.

The z-score is:

z = (x − μ) / σ

z = (68.5 − 69) / 0.58

z = -0.862

The probability is:

P(Z < -0.862) = 0.194

The probability that the average age, X of the 100 residents selected is less than 68.5 years is, 0.194.

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Here, X has a mean of 69 and a standard deviation of 5.8/√100 = 0.58.

Hence, The z-score is:

⇒ z = (x − μ) / σ

⇒ z = (68.5 − 69) / 0.58

⇒ z = -0.862

Thus, The probability is:

⇒ P(Z < -0.862) = 0.194

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The rule for g is g(x) = (-2x - 10)(√(x² - 2)) for the function g(x) = -2f(x+5).

One way to think of a function is as a rule that assigns or maps each member of a set, x, to the same value, y, known as its image.

x → Function → y

Functions are frequently denoted by a letter, such as f, g, or h. F(x) = x2+ 5 is the formula for the function that squares a number and adds a 3. A function's impact on specific values can be demonstrated using the same idea.

Given that  f(x) =  √(x² - 2)

And g(x) = -2f(x+5)

Substitute the function f(x) =  √(x² - 2) in g(x) = -2f(x+5)

g(x) = -2(√(x² - 2))(x+5)

g(x) = (-2x - 10)(√(x² - 2))

Thus, the rule for g is g(x) = (-2x - 10)(√(x² - 2)) for the function g(x) = -2f(x+5).

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Answer:

x-7>0

Straight answer: x-7

Step-by-step explanation:

Assuming that the timber is X cm long and 7cm was cut off, there remaining amount is x - 7cm. In order for 7cm to be cut off, the timber must have been > 7cm long => x > 7 => x - 7 > 0

Answer:

600, 150

Step-by-step explanation:

Kyle is x

ken is y

x = 4y

x+y = 750

replace x with 4y

4y + y = 750

5y = 750

y = 150

so ken earned 150

x + 150 = 750

x = 600

so Kyle earned 600

At the end of the first 3 seconds, there would be 6 customers in line at the book store.

Little's Law can be used to calculate the number of customers in line at the end of the first 3 seconds. According to Little's Law: the average number of customers in the system is equal to the arrival rate multiplied by the time spent in the system.

In this case, the arrival rate during the first 3 seconds is 29 customers per second, and the time spent in the system is 3 seconds. Therefore the average number of customers in the system is 87 (29 customers per second x 3 seconds).

However since the bookstore can only serve 27 customers per second, the maximum number of customers that can be served during the first three seconds is 81 (27 customers per second x 3 seconds). This means that there are 6 customers who remain in line at the end of the first 3 seconds.

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Answer:

2/51

Step-by-step explanation:

# of brown socks = 4

# of blue socks = 14

total # of socks = 18

The probability of pulling 1 brown sock = 4/18

If he were to pull one brown sock there would be 1 less sock in the total # of socks and 1 less in the # of brown socks

So after the first pull ( if it were to be a brown sock )

there would only be 3 brown socks and 17 total socks

So the probability of pulling a brown sock then would be 3/17

Finally we multiply the two probabilities to get the answer

4/18 * 3/17 = 2/51

Hence, the answer is 2/51

Answer:

1 : 2

Step-by-step explanation:

this is a 30-60-90 triangle which is a special right triangle. the ratio of the sides is x: x*sqrt(3): 2x, in the order short leg: long leg: hypotenuse. so the ratio of the short leg to the hypotenuse is x:2x or 1:2

11 years is the sum of Joey's two digits the next time his age is a multiple of Zoe's age.

Assume Chloe is c years old today, and Joey is c+1 years old today. Chloe and Zoe will be n+c and n+1 years old after n years.

Given,

(n + c) ÷ (n + 1) = 1 + ((c - 1) ÷ (n + 1))

For 9 non-negative integers, n is an integer. As a result, c - 1 has 9 positive divisors. c-1's prime factorization is either \(p^8\) or p²q². Because c - 1 < 100, the only possible solution is c - 1 = 2² × 3² = 36, from which c = 37. We may deduce that Joey is 38 years old today.

Assume Joey's age is a multiplier of Zoe's age after k years, resulting in Joey and Zoe being k + 38 and k + 1 years old, correspondingly.

Given,

(k + 38) ÷ (k + 1) = 1 + ((38 - 1) ÷ (k + 1))

For some positive integers, k is an integer. As 37 is divisible by k + 1, the only possible solution is k = 36. Infer that Joey will be k + 38 = 74 years old at that time, yielding the value 7 + 4 = 11.

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There are 1023 ways for a man to invite some (nonempty) subset of his 10 friends to dinner.

Each friend can either be invited or not invited, which gives us two choices for each friend. Since there are 10 friends, there are 2^10 = 1024 possible ways to invite or not invite them. This is determined using the product rule.

However, we need to subtract 1 from this number, because one of these ways is to not invite any friends, which is not a valid option since the question specifies that the subset must be nonempty. Therefore, the final answer is 1023 ways.

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Answer:

a) is the correct answer.