What is the solution set of 6x-15<3 ?
x>-1
x<-1
X<3
X> 3

Answer:

the answer is 5

Step-by-step explanation:

Answer:

So they just want you to solve the equation if x= -4

d(-4) = -(-4) + -4

y = 4 - 4

The solution would be 0.

The graph of the piece-wise function f(x) is given by the image presented at the end of the answer.

A piece-wise function is a function that has different definitions, depending on the input of the function.

The extreme points of the function in this problem are given as follows:

Hence the graph of the function in this problem is composed as follows:

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A Negative correlation coefficient means that as one variable increases, the other decreases (i.e., an inverse relationship).

Answer:

20.8333%

Step-by-step explanation:

It means There was shortage of food, so it ended up with 19 people.

Original Value = 24 people New Value = 19 people

There is a Percentage decrease

%decrease = Original Value - New Value / Original Value × 100%

%decrease = 5/24 × 100%

%decrease = 20.8333 %

So, more 20.8333% would be needed so that 24 people can get the food  .

Answer: 26

Step-by-step explanation:

(24-19)/19 * 100 = 26.3157894736842

But it said to round to the nearest percent I believe since I got the same question, so 31 isn't above 50 so 26 is just 26 since 31 not above 50, so the answer is just 26

Hope this helps, sorry if im wrong but for me it was right!

a) Recall the integration by parts formula:

\(\displaystyle \int u \, dw = uw - \int w \, du\)

Then with \(u = x\) and \(dw = e^x\,dx\) we have

\(\displaystyle v = \int e^x x \, dx = xe^x - \int e^x \, dx\)

\(\implies \boxed{v = xe^x - e^x + C}\)

since \(w=\int e^x\,dx=e^x\) and \(du=dx\). (C is of course an arbitrary constant that can be determined exactly if you know the velocity at some given value of x.)

b) No?

\(\displaystyle \int e^xx\,dx = \int xe^x\,dx\)

because multiplication is commutative. I get the feeling I'm missing something here...

The value of Double integral will be \(\mathrm{I}=4 \int_0^4 \ln |1+\mathrm{x}| \mathrm{dx}\)

A two-dimensional region can be integrated using double integrals. They enable us to, among other things, calculate the volume beneath a surface.

The integrals of a function in two variables over a region in R2, or the real number plane, are referred to as double integrals in mathematics. It is possible to write the double integral of a function of two variables, such as f(x, y), over a rectangular region as: R f (x, y) d A = R f (x, y) d x d y.

We know that by the property of integral \($\int u \mathrm{udv}=u v-v \int d u$\)

\($$\begin{aligned}& \mathrm{I}=4 \int_0^4 \ln |1+\mathrm{x}| \mathrm{dx}=\left[\mathrm{x} \ln (1+\mathrm{x})-\int \mathrm{x} \frac{.1}{1+\mathrm{x}} \mathrm{dx}\right]_0^4 \\& \mathrm{I}=4\left[\mathrm{x} \ln (1+\mathrm{x})-\int\left(1-\frac{1}{1+\mathrm{x}}\right) \mathrm{dx}\right]_0^4 \\& \mathrm{I}=4[\mathrm{x} \ln (1+\mathrm{x})-\mathrm{x}+\ln |1+\mathrm{x}|]_0^4 \\& \mathrm{I}=[4 \ln (5)-4+\ln (5)]-[0-0+0] \\& \mathrm{I}=4[5 \ln 5-4] \\& \mathrm{I}=20 \ln 5-16\end{aligned}$$\)

We have to evaluate the given double integral

\($$\iint_{\mathrm{R}} \frac{4 \mathrm{x}}{1+\mathrm{xy}} \mathrm{dA} \text { where } \mathrm{R}=[0,4] \times[0,1]$$\)

\($$\begin{aligned}& \mathrm{I}=\int_0^4 \int_0^1 \frac{4 \mathrm{x}}{1+\mathrm{xy}} \mathrm{dydx}=\int_0^4 4 \mathrm{x}\left[\frac{|1+\mathrm{xy}|}{\mathrm{x}}\right]_0^1 \mathrm{dx} \\& \mathrm{I}=\int_0^{44}[\ln |1+\mathrm{x}|-0] \mathrm{dx}=4 \int_0^4 \ln |1+\mathrm{x}| \mathrm{dx}\end{aligned}$$\)

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The formula for the volume of a cone is:

V = (1/3)πr²h

where r is the radius of the base, h is the height of the cone, and π is pi.

In this case, the slant height is given as 17 cm, which we can use with the radius to find the height of the cone using the Pythagorean theorem:

h² = s² - r²

h² = 17² - 8²

h² = 225

h = 15

Now that we have the height, we can plug in the values for r and h into the formula for the volume:

V = (1/3)π(8²)(15)

V = (1/3)π(64)(15)

V = (1/3)(960π)

V = 320π

Therefore, the volume of the cone is 320π cubic cm. Answer: 320π.

Answer:

Length: 14m

Breadth: 10m

Area: 140m^2

Step-by-step explanation:

Let length = l and breadth = b,

l = 4 + b

Perimeter = 2(l+b)

= 2(4 + b + b)

= 2(4 + 2b)

= 8 + 4b

Perimeter = 48

Hence,

4b + 8 = 48

4b = 40

b = 10m

l = 4 + b = 14m

A = lb = 10 * 14 = 140m^2

Feel free to mark this as brainliest! :)

Answer:

255 minutes

Step-by-step explanation:

The floor area of the engineer's model of the sugar factory is 10.825 square feet.

To determine the floor area of the engineer's model of a sugar factory in square feet, we need to convert the given measurements from inches to feet. Since there are 12 inches in a foot, we can divide both dimensions by 12 to convert them.

The length of the model in feet is 30 inches / 12 = 2.5 feet, and the width is 52 inches / 12 = 4.33 feet.

To find the floor area, we multiply the length by the width:

Area = Length × Width

= 2.5 feet × 4.33 feet

= 10.825 square feet

It's important to note that the given measurements are not a standard aspect ratio or scale for a sugar factory. The given dimensions may be scaled down for the model's convenience, so the calculated floor area is only applicable to the scale of the model.

In actuality, a sugar factory would have much larger dimensions.

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Answer:   C

Step-by-step explanation:

hope this helped

Answer:

A. 3x9x5

B. 2×3×7×10=420

C. 6×3×8×5=720

D.9×8×5=360

E. 3×10=30

F. 11×13=143

G. 41×7= 287

H. 67×73=4891

I. 89×97=8633

J. 53×1×61=3233

The factored forms of the equations and the intercepts would be:

g(x) = x² - 4x - 21:

h(x) = x² + 8x + 12:

For g(x) = x² - 4x - 21:

To find the factored form, we need to factor the quadratic expression:

g(x) = (x - 7)(x + 3)

To find the x-intercepts, we set g(x) = 0 and solve for x:

(x - 7)(x + 3) = 0

x = 7 or x = -3

To find the y-intercept, we set x = 0 and evaluate g(x):

g(0) = (0 - 7)(0 + 3) = -21

Therefore, the y-intercept of g(x) is (0,-21).

For h(x) = x² + 8x + 12:

h(x) = (x + 2)(x + 6)

To find the x-intercepts, we set h(x) = 0 and solve for x:

(x + 2)(x + 6) = 0

x = -2 or x = -6

To find the y-intercept, we set x = 0 and evaluate h(x):

h(0) = (0 + 2)(0 + 6) = 12

Therefore, the y-intercept of h(x) is (0,12).

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Answer:

I havent done this in a long time but I think it is 0x+4=y

Step-by-step explanation:

Answer:

y=2x+4

Step-by-step explanation:

The value of the vector VU is <44, 40>

Vector:

in math vector consist an object that has both a magnitude and a direction.

Given:-

Here we have the vector v and u with the value of v = <11, 5> and the value of u = <4, 8>.

Now, we have to find the value of VU.

In order to find the value of VU, we have to perform the multiplication operation on the given vector,

In order to perform the multiplication on it, we have to arrange them in the following order,

=> VU = <11, 5> x <4,8>

Now, we have to combine the values like the following,

=> <(11 x 4) , (5 x 8)>

Now, do the multiplication then we get,

=> <44, 40>

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Answer:

The probability of each is 1/33

Step-by-step explanation:

From the question, we are told that all has an equal chance of occurrence

Mathematically, to get the probability of one of the events, we need to divide the total probability of 1 by the number of values

Thus, we have this as;

1/33

The required sum of the positive integers x and y with the given condition of product of x and y as  square and cube is equal to 85.

Two positive integers are x and y.

Product of 360 and x is a square.

Product of 360 and y is a cube.

Prime factors of 360 equals to ,

360 = 2³ × 3² × 5

To make a product of 360 and x as square ,

Multiply by 2 and 5 and 3 is already a perfect square.

x = 2 × 5

 = 10

360 × 10 = 3600

Now , to make product of 360 and y as cube.

Multiply by 3  and 5² and 2 is already a perfect cube.

y = 3 × 5²

   = 75

360 × 75 = 27000

Sum of the values of x and y is equal to,

x + y

= 10 + 75

= 85

Therefore, the sum of the positive integers x and y are 85.

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The percentage of races in will his finishing time is between 64.5 and 65.5 seconds is 68%.

According to the empirical rule, also known as the 68-95-99.7 rule, the percentage of values that lie within an interval with 68%, 95%, and 99.7% the values lies within one, two, or three standard deviations of the mean of the distribution.

\(\rm P(\mu - \sigma \ \ < X < \mu + \sigma) \ \approx 68\%\\\\P(\mu - 2\sigma < X < \mu + 2\sigma) \approx 95\%\\\\P(\mu - 3\sigma < X < \mu + 3\sigma) \approx 99.7\%\)

where we had were mean of the distribution of X is μ and the standard deviation from the mean of the distribution of X is σ (assuming X is normally distributed).

When Kiran runs the 400 meters dash, his finishing times are normally distributed with a mean of 65 seconds and a standard deviation of 0.5 seconds.

Then by the formula, we have

\(\rm P (65-0.5 < X < 65+0.5) = P(64.5 < X < 65.5) \approx 68\%\)

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To determine how many years it will take for Tom's investment to double, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:

A is the final amount (double the initial investment)

P is the principal amount (initial investment)

r is the annual interest rate (9.24% or 0.0924)

n is the number of times the interest is compounded per year (monthly, so n = 12)

t is the time in years

In this case, Tom wants his investment to double, so the final amount (A) will be $8,000 * 2 = $16,000. We can plug in these values and solve for t:

$16,000 = $8,000(1 + 0.0924/12)^(12t)

Dividing both sides by $8,000:

2 = (1 + 0.0924/12)^(12t)

Taking the natural logarithm (ln) of both sides:

ln(2) = ln[(1 + 0.0924/12)^(12t)]

Using the logarithmic property ln(a^b) = b * ln(a):

ln(2) = 12t * ln(1 + 0.0924/12)

Dividing both sides by 12 * ln(1 + 0.0924/12):

t = ln(2) / (12 * ln(1 + 0.0924/12))

Using a calculator, we find:

t ≈ 9.81

Therefore, it will take approximately 9.81 years (rounding to hundredths) for Tom's investment to double.

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Answer:

114

Step-by-step explanation:

The question relates to the sum of an arithmetic progression, A. P.

The count of numbers added, n = 50

The sum of the numbers, Sₙ = 3,250

The formula for the sum of an A. P. is given as follows;

\(S_n = \dfrac{n}{2} \left[2 \cdot a + (n - 1)\cdot d\right]\)

\(S_n = \dfrac{n}{2} \left[a + a_n\right]\)

Where;

a = The first term of set of numbers

d = The common difference between consecutive numbers

n = The number of terms = 50

aₙ = The last term, the largest of the integers

Therefore, we get;

The common difference of consecutive even integers numbers, d = 2

Plugging in the values gives;

3,250 = (50/2) × (2·a + (50 - 1) × 2) = 25 × (2·a + 49 × 2)

2·a = (3,250/25) - 49 × 2 = 32

a = 32/2 = 16

From  \(S_n = \dfrac{n}{2} \left[a + a_n\right]\), we have;

3,250/25 = 16 + aₙ

aₙ = 3,250/25 - 16 = 114

The largest of the integers, aₙ = 114.

The angle θ between vectors a = ⟨3, -1⟩ and b = ⟨0, 15⟩ is approximately 2.944 radians.

To find the angle (θ) between two vectors, a = ⟨3, -1⟩ and b = ⟨0, 15⟩, we can use the dot product formula and the magnitudes of the vectors.

The dot product (or scalar product) of two vectors is given by the formula:

a · b = |a| |b| cos(θ)

where |a| and |b| are the magnitudes of vectors a and b, respectively.

First, let's calculate the magnitudes of vectors a and b:

|a| = √(3² + (-1)²) = √10

|b| = √(0² + 15²) = 15

Next, let's calculate the dot product of vectors a and b:

a · b = (3)(0) + (-1)(15) = -15

Now we can solve for cos(θ) by rearranging the dot product formula:

cos(θ) = (a · b) / (|a| |b|)

cos(θ) = -15 / (√10 * 15)

Finally, we can find the angle θ by taking the inverse cosine (arccos) of cos(θ):

θ = arccos(-15 / (√10 * 15))

Evaluating this expression gives θ ≈ 2.944 radians.

Therefore, the angle θ between vectors a = ⟨3, -1⟩ and b = ⟨0, 15⟩ is approximately 2.944 radians.

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The space C1(S1) is a Banach space, which means it is a complete normed vector space, equipped with the norm ||f|| = sup{|f(θ)| + |f'(θ)| : θ ∈ S1}.

The space C1(S1) is the space of continuously differentiable real-valued functions defined on the unit circle S1, which is a subset of the complex plane given by the equation |z| = 1, where z is a complex number.

Specifically, a function f: S1→R belongs to C1(S1) if it has a continuous first derivative f': S1→R that also belongs to C(S1), the space of continuous real-valued functions defined on S1.

Formally, we can define the space C1(S1) as follows:

C1(S1) = {f: S1→R | f is continuously differentiable on S1 and f' belongs to C(S1)}

Here, f' denotes the first derivative of f, which is defined as the limit:

f'(θ) = lim [f (θ + h) - f(θ)]/h

h→0

for all θ in S1

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The solution of the equation log(t - 3) = log(17 - 4t), is 4.

option A.

To find the solution for the equation log(t - 3) = log(17 - 4t), we can use the properties of logarithms.

Step 1: Remove the logarithms on both sides.

Applying the property of logarithms that states log(a) = log(b) if and only if a = b, we can remove the logarithms from both sides of the equation:

t - 3 = 17 - 4t

Step 2: Add 4t to both sides.

Adding 4t to both sides of the equation to isolate the t term on one side:

t + 4t - 3 = 17

Step 3: Combine like terms.

Combining like terms on the left-hand side:

5t - 3 = 17

Step 4: Add 3 to both sides.

Adding 3 to both sides of the equation to isolate the t term:

5t - 3 + 3 = 17 + 3

5t = 20

Step 5: Divide by 5.

Dividing both sides of the equation by 5 to solve for t:

5t/5 = 20/5

t = 4

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The statement which is true about the function of the temperature of the soup over time is D. As time increases, the temperature of the soup approaches 72 °F.

Given a table of values which shows the temperature of a bowl of soup left out on the kitchen counter with the time.

Here the time shown are ranged from 5, 10, 20, 30, 45, 60, 80.

Corresponding temperature of the soup left ranges from 139.503, 109.047, 83.158, 75.361, 72.556, 72.092, 72.008 respectively.

It is clear that as the time increases, the temperature of the soup is decreasing and at last approaches to 72 °F.

Hence the correct statement is D.

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After set s1.addAll(s2), s1 is [1, 2, 5, 2, 3, 6].

After performing the operation s1.addAll(s2) on sets s1 [1, 2, 5] and s2 [2, 3, 6], the set s1 would become[1, 2, 5, 2, 3, 6].

To determine the value of s1, the following steps has to be taken:

1. Start with sets s1 [1, 2, 5] and s2 [2, 3, 6].

2. Apply the addAll operation with set s2: [2, 3, 6]

3. Add each element from set s2 to set s1, while avoiding duplicates (since sets cannot have duplicate elements).

4. Therefore, suppose if set s1 is [1, 2, 5] and set s2 is [2, 3, 6] then, after s1.addAll(s2), the set s1 becomes [1, 2, 5, 2, 3, 6].

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The use of a "thumbs-up" gesture to symbolize the statement "good luck" is a common practice in many cultures. This gesture is typically used to express approval or agreement, but it can also be used to convey positive wishes, such as wishing someone good luck before an exam or a job interview.

It is believed that this gesture originated in ancient Rome, where it was used as a sign of approval in the gladiatorial arena. Today, the thumbs-up gesture has become a universal symbol of positivity and encouragement. So, if you want to wish someone good luck, a thumbs-up gesture is a great way to do it!

The use of a "thumbs-up" gesture to symbolize the statement "good luck" involves the following steps:

1. Extend your arm: To perform the thumbs-up gesture, first extend your arm in the direction of the person you want to wish good luck.
2. Make a fist: Close your fingers into a fist, with your thumb pointing upwards.
3. Show your thumb: Ensure that the thumb is clearly visible and pointing upwards. This represents the "thumbs-up" gesture.
4. Make eye contact: Look at the person you're wishing good luck to, so they know the gesture is directed at them.

By performing the thumbs-up gesture, you're using a universally recognized symbol to convey your positive sentiment and wish someone good luck in their endeavors.

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Answer:

36.

Step-by-step explanation:

Counting the squares, the length of the vertical side = 16.

The other 2 sides are of equal length and can be found by Pythagoras theorem:

The vertex of the triangle is 6 units from the longest side and the line of 6 units meets the longest side at its center ( 8 units from its ends),

so l^2 = 6^2 + 8^2

l^2 = 100

l = 10

So the perimeter is 16 + 10 + 10= 36.

A two-dimensional form that occupies an area is called a shape.

Shapes can be various types such as rectangles, circles, triangles, and many others, and they are defined by their properties such as sides, angles, and vertices. They are defined by their boundaries or edges and exist within a plane. These forms have dimensions of length and width, but not depth. Shapes play a fundamental role in geometry and are studied extensively in mathematics and art. They can be simple or complex, symmetrical or asymmetrical, and are used to represent objects, patterns, or designs. Whether in the natural world or man-made creations, shapes are integral to our understanding and appreciation of visual compositions.

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The correct formula that defines an arithmetic sequence is option d) tn = 5n + 14.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. In other words, each term can be obtained by adding a fixed value (the common difference) to the previous term.

In option a) tn = 5 + 14, the term does not depend on the value of n and does not exhibit a constant difference between terms. Therefore, it does not represent an arithmetic sequence.

Option b) tn = 5n² + 14 represents a quadratic sequence, where the difference between consecutive terms increases with each term. It does not represent an arithmetic sequence.

Option c) tn = 5n(n+14) represents a sequence with a varying difference, as it depends on the value of n. It does not represent an arithmetic sequence.

Option d) tn = 5n + 14 represents an arithmetic sequence, where each term is obtained by adding a constant value of 5 to the previous term. The common difference between consecutive terms is 5, making it the correct formula for an arithmetic sequence.

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