Determine the interval(s) on which the function Is constant.
Write your answer as an interval or list of intervals.
When writing a list of Intervals, make sure to separate each interval with a comma and to use as few intervals as possible.
Click on "None* if applicable.

Answer:

a) 5x/16

b) x = 32

Step-by-step explanation:

a) x/8 + 3x/16 can be simplified by getting a common denominator. x/8 can be changed like this:

x/8 × 2/2 is 2x/16

now we have:

2x/16 + 3x/16

= 5x/16

b) solve x/8+3x/16=10

change the left side of the equation as in part a.

5x/16 = 10

multiply both sides of the equation by 16

5x = 160

divide by 5

x = 32

Assuming the time begins after the car is fully accelerated to 64 mph, 4 hours 45 minutes

IG:whis.sama_ent

Answer:

below

Step-by-step explanation:

To find out how many bunches of each flower the shop should order, we need to calculate the percentage of customers who preferred each flower, and then use that percentage to estimate the number of bunches needed for each flower.

First, we need to calculate the total number of customers who were surveyed:

Total customers surveyed = 8 + 4 + 8 + 20 = 40

Next, we can calculate the percentage of customers who preferred each flower:

Percentage of customers who preferred daisy = (8/40) x 100% = 20%

Percentage of customers who preferred gardenia = (4/40) x 100% = 10%

Percentage of customers who preferred mum = (8/40) x 100% = 20%

Percentage of customers who preferred rose = (20/40) x 100% = 50%

Now, we can use these percentages to estimate how many bunches of each flower to order.

Let's assume that each bunch contains 10 flowers (this is just an example, the actual number may vary):

Number of bunches of daisy to order = 20% of 50 bunches = 10 bunches

Number of bunches of gardenia to order = 10% of 50 bunches = 5 bunches

Number of bunches of mum to order = 20% of 50 bunches = 10 bunches

Number of bunches of rose to order = 50% of 50 bunches = 25 bunches

So, the shop should order 10 bunches of daisy, 5 bunches of gardenia, 10 bunches of mum, and 25 bunches of rose to meet the expected demand on Sunday.

The weight of the diamonds in each lot is 4.9 pounds.

Here, the fractional idea can be used. A fraction represents a portion of a total. A fraction is a numerical figure that designates a portion of a whole. A fraction is a component or section taken from a whole, which can be any number, a certain value, or an object.

A cargo of half a pound's worth of diamonds was received by a diamond trader. He separated the stones into 4 equal lots and sold them to jewelers so they could be used to make necklaces and rings.

Total shipment = 7/10 pound

number of equal lots = 7

then,   7 x weight = 7/10

weight = 4.9

Therefore, the weight of each lot is 4.9 pounds.

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Answer:

it would be C

Step-by-step explanation:

The expression 8×2 can be used to find the total number of head wraps on the shelf when there are 8 head wraps per shelf and 2 shelves in total, resulting in a total of 16 head wraps.

Expression in mathematics is a combination of symbols and numbers, often using an operation, such as addition, subtraction, multiplication, or division. It can represent a number, a variable, a function, or a mathematical statement. It can also represent a combination of these things. Expressions are used to describe relationships between numbers, variables, and mathematical concepts.

The expression 8×2 can be used to find the total number of head wraps on the shelf when there are 8 head wraps per shelf and there are 2 shelves in total. This expression can be used to calculate the total number of head wraps on the shelves by multiplying 8 (the number of head wraps per shelf) by 2 (the number of shelves). As such, the expression 8×2 can be used to find the total number of head wraps on the shelf when there are 8 head wraps per shelf and 2 shelves in total, resulting in a total of 16 head wraps.

In conclusion, the expression 8x2 can be used to calculate the total number of head wraps on the shelf when there are 8 head wraps per shelf and 2 shelves in total. By multiplying 8 (the number of head wraps per shelf) by 2 (the number of shelves), the total number of head wraps on the shelf can be found, resulting in a total of 16 head wraps.

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Complete questions as follows-
In which situation can the Expression
on 8×2 be used to find the total number of head wraps on the shelf?

Standard deviation does not mean independent events.

No, the standard deviation is a measure of the spread or variability of a set of data. It measures how much the individual data points in a dataset deviate from the mean or average of the dataset.

Independence, on the other hand, refers to the relationship between two or more events, where the occurrence of one event does not affect the probability of the other event occurring.

Standard deviation is not directly related to the concept of independence. However, when calculating the standard deviation of a dataset, it assumes that each data point is independent and identically distributed. This means that the value of one data point does not affect the value of another data point, and that each data point is drawn from the same underlying distribution.

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The direction and angle of rotation include the following: B. 90° counterclockwise rotation.

In Mathematics and Geometry, a transformation is the movement of a point from its initial position to a new location. This ultimately implies that, when a geometric figure or object is transformed, all of its points would also be transformed;

In Mathematics, a rotation refers to a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

By critically observing the geometric figures, we can reasonably infer and logically deduce that the pre-image was rotated counterclockwise to produce the image.

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The probability of choosing 5 CDs in alphabetical order out of a collection of 23 CDs is approximately 0.00003 or 0.003%.

What is combination?

In mathematics, a combination is a way of selecting objects from a larger group of objects, where the order of selection is not important. A combination is a subset of objects that are chosen from a larger set without regard to the order in which they are selected.

The formula  is given by:

C(n, r) = [tex]\frac{n!}{r!* (n - r)!}[/tex]

The total number of ways to choose 5 CDs from a collection of 23 CDs is given by the combination formula:

C(23, 5) = [tex]\frac{23!}{5!* (23 - 5)!}[/tex]

             = 33649

This means there are 33649 different ways to arrange 5 CDs out of the 23 CDs.

Out of these 33649 ways, only one arrangement is alphabetical. For this to happen, the first CD chosen must be the first one alphabetically, the second CD chosen must be the second one alphabetically, and so on.

The first CD can be any of the 23 CDs. However, once the first CD is chosen, there is only one CD that can be the second one alphabetically, two CDs that can be the third one alphabetically, and so on. Therefore, the probability of choosing 5 CDs in alphabetical order is:

P = 1 / C(23, 5)

P = 1 / 33649

P ≈ 0.00003

So the probability of choosing 5 CDs in alphabetical order out of a collection of 23 CDs is approximately 0.00003 or 0.003%.

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a) The angular velocity of the wheel is approximately 1.0667 radians per second. b) The wheel will spin at approximately 10.16 revolutions per minute.

Angular velocity is a measure of how quickly an object rotates or revolves around a fixed point, such as an axis or a center of rotation. It is a vector quantity that describes the rate of change of an object's angular position with respect to time, and is usually expressed in units of radians per second (rad/s) or degrees per second (deg/s).

a) To find the angular velocity of the wheel, we can use the formula:

angular velocity = linear velocity / radius

In this case, the linear velocity of the hamster is 16 centimeters per second, and the radius of the wheel is 15 centimeters. So, we have:

angular velocity = 16 / 15

angular velocity = 1.0667 radians per second

Therefore, the angular velocity of the wheel is approximately 1.0667 radians per second.

b) To find the speed of the wheel in revolutions per minute, we need to convert the angular velocity from radians per second to revolutions per minute. There are 2π radians in one revolution, and 60 seconds in one minute. So, we can use the following formula:

angular velocity (in revolutions per minute) = angular velocity (in radians per second) * 60 / 2π

Plugging in the angular velocity we found in part (a), we get:

angular velocity (in revolutions per minute) = 1.0667 * 60 / 2π

angular velocity (in revolutions per minute) ≈ 10.16 revolutions per minute

Therefore, the wheel will spin at approximately 10.16 revolutions per minute.

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The height is 3 units.

We have,

l = 4 and b= 3

Using Pythagoras theorem

d² = l² + b²

d² = 4² + 3²

d² = 16 + 9

d² = 25

d= 5 unit

let h be the height.

Again, using Pythagoras theorem

34 = 25 + h²

h² = 9

h= 3 unit

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The function that models the relationship between the number of students enrolled, f(x) and the number of years after 2015, x,  is D. f(x) = 3000(0.98)*.

Mathematically, a function defines a mathematical relationship or an algebraic expression involving one variable (the independent variable) and another variable (the dependent variable).

There are four main types of mathematical functions, including:

The number of students enrolled in 2015 = 3,000

The annual decrease in students enrollment = 2%

Let f(x) the model modeling the relationship between the number of students enrolled and the number of years after 2015.

Let the number of years after 2015 = x.

Thus, the correction function is D. f(x) = 3000(0.98)*.

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Therefore, the graph of the given set is: closed circles on 1 and 4 with a line segment between.

A common form for an algebraic expression is one of the following: addition, subtraction, multiplication, or division. Simplify the values to determine the result.

The expression (x I x ≤ 1) U (x I x ≥ 24) represents the set of all values of x that are less than or equal to 1 or greater than or equal to 24.

the graph of this set will have a closed circle at x=1 and a closed circle at x=24

The arrows pointing outward indicate that the set continues indefinitely in both directions.

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Simplifying this fraction gives us 1/4. The answer is (D) 1/4.

What is arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.

Let's start by finding the fraction of Michelle's patients who are under 12 or over 65. We know that one-third of her patients are under 12, so two-thirds must be 12 or older. Similarly, five-twelfths of her patients are over 65, so seven-twelfths must be 65 or younger.

Now, we want to find the fraction of Michelle's patients who are between 12 and 65. To do this, we need to subtract the fraction of patients who are under 12 or over 65 from 1 (since these are the only two age groups we're considering).

Fraction of patients under 12: 1/3

Fraction of patients over 65: 5/12

Fraction of patients 12 to 65: 1 - 1/3 - 5/12

We can simplify this expression by finding a common denominator:

Fraction of patients 12 to 65: 12/12 - 4/12 - 5/12

Fraction of patients 12 to 65: 3/12

Simplifying this fraction gives us 1/4. Therefore, the answer is (D) 1/4.

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Answer:

hm

Step-by-step explanation:

The reason why it is possible to draw two different rectangles that have an area of 30 square inches is that there are multiple pairs of whole numbers that multiply to 30. For example, a rectangle with dimensions 5 inches by 6 inches has an area of 30 square inches, and so does a rectangle with dimensions 2 inches by 15 inches.

However, the number 7 is a prime number, which means it can only be divided evenly by 1 and itself. Therefore, the only way to get an area of 7 square inches for a rectangle is by multiplying 1 and 7, which means the dimensions of the rectangle would be 1 inch by 7 inches. Since there are no other pairs of whole numbers that multiply to 7, it is not possible to draw two different rectangles with an area of 7 square inches.

the total cost of the car rental for Nate if he rents a compact car with the optional insurance and fills up the gas tank before returning the car would be $[tex]570.[/tex]

To calculate the total cost of the car rental, we need to first determine the rental rate for a compact car for 8 days, including the optional insurance.

The daily rental rate for a compact car is $ [tex]56,[/tex] and the optional insurance costs $10 per day. Therefore, the total daily cost of renting a compact car with insurance is:

[tex]56 + 10 = 66[/tex]

To determine the total cost of renting the compact car for 8 days, we simply multiply the daily cost by the number of days:

[tex]66 \times 8 = $528[/tex]

Next, we need to determine the cost of gasoline if Nate returns the car without a full tank. The gasoline charge is $ [tex]3.50[/tex] per gallon, but we don't know how many gallons Nate will need to fill up the tank.

If we assume that a compact car has a gas tank capacity of around 12 gallons, and that Nate will need to refill the tank to its full capacity, then the gasoline charge would be:

$[tex]3.50 \times 12 = $42[/tex]

Finally, we can calculate the total cost of the rental, including the optional insurance and the gasoline charge if Nate returns the car without a full tank:

$[tex]528 + $42 = $570[/tex]

Therefore, the total cost of the car rental for Nate if he rents a compact car with the optional insurance and fills up the gas tank before returning the car would be $[tex]570[/tex].

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Answer:

Step-by-step explanation:

just add the two numbers up 576x1 1/2= 864

Answer:

C

Step-by-step explanation:

using the sine ratio and the exact value

sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{5}{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )

x = 5[tex]\sqrt{2}[/tex]

Answer:

7 batches

hope this helps

Step-by-step explanation:

1 n (batches of dumpling wrappers) = 3 cups flour

n = 21 / 3

n = 7

The chef can make 7 batches of dumpling wrappers :D.

The logarithmic form of the given exponential equation in the question,     4³ = (5x + 4) is Log₄ (5x + 4) = 3.

The exponential-to-logarithmic format is useful because it makes it easy to compute large numeric expressions. Expressions involving exponential multiplication and division can be converted to addition and subtraction by applying logarithms. Logarithmic exponential form is a common means of converting mathematical expressions in one form to another form.

The exponential form aˣ = N is transformed and written logarithmically as LogₐN = x.

The exponential form of a for the exponent of x equal to N is converted to the logarithm of the number N in base a, equal to x.

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To find the specified scalar, we need to first find the dot product of U and V, and then the dot product of U and W, and add these two dot products together:

U·V + U·W

where U·V denotes the dot product of U and V, and U·W denotes the dot product of U and W.

The dot product of two vectors a = (a1, a2) and b = (b1, b2) is given by:

a · b = a1b1 + a2b2

Using this formula, we can find the dot product of U and V:

U · V = (4i - j) · (5i + j) = 4i · 5i + 4i · j - j · 5i - j · j = 20i^2 + (4i · j - 5i · j) - j^2 = 20 + (-i · j) - 1 = 19 - i · j

Next, we can find the dot product of U and W:

U · W = (4i - j) · (i + 6j) = 4i · i + 4i · 6j - j · i - j · 6j = 4i^2 + (4i · 6j - j · i) - 6j^2 = 4 + (24i · j) - 6 = -2 + 24i · j

Now we can substitute these values into the original expression:

U·V + U·W = (19 - i·j) + (-2 + 24i·j) = 17 + 23i·j

Therefore, the specified scalar is 17 + 23i·j.

tan = 1/√3= perpendicular/ base

1/√3 = AB / AC

AB / 6 = 1/√3

AB = 6/√3

Answer:

Step-by-step explanation: $130-$70 lift = $60/$20 per hour= 3 hours ski time

Answer:

6xy^2 + 9(xy)^2.dy/dx

Step-by-step explanation:

d/dx(3x^2.y^3)=

3y^2.d/dx(x^2) + 3x^2.d/dx(y^3)      [Using uv rule, d/dx(uv)=u.dv/dx +v.du/dx]

= 3y^2.2x + 3x^2.3y^2.dy/dx

= 6xy^2 + 9(xy)^2.dy/dx

The correct answer is: A. Y intercept will be less and X will be less.

A linear function's slope is a gauge of how steep the line is. Between any two points on the line, it is the ratio of the change in the y-coordinate to the change in the x-coordinate. The formula is used to compute it:

slope equals (y2 - y1)/. (x2 - x1)

where any two points on the line (x1, y1) and (x2, y2) are.

The company's expenses will rise once it begins paying a driver at a rate of 0.25 cents per mile, which means its profit will decline. The profit curve on the y-axis will go vertically downward as a result of this. But, because the cost of paying the driver is fixed per mile and has no impact on the profit per mile, the slope of the line—which reflects the profit per mile—will stay the same.

Hence, A. Y intercept will be less and X will be less is correct.

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The value of

m∠GHJ = (3(20°)+50)° = 110°.

m∠GkJ = (4(20°)-10)° = 70°

m∠HJK = (4(20°))° = 80°

What is an angle?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

Here, we have

Given: Circle B is shown, with GHJK inscribed in the circle. The m∠GHJ = (3x+50)°, and m∠HJK = (4x)° and mLGK] = (4x-10)°.

we have to find the value of HJK and JHG.

We know that

m∠GHJ + m∠GkJ = 180°

(3x+50)° + (4x-10)° = 180°

7x + 40 = 180°

7x = 140°

x = 20°

Hence, the value of

m∠GHJ = (3(20°)+50)° = 110°.

m∠GkJ = (4(20°)-10)° = 70°

m∠HJK = (4(20°))° = 80°

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The ratio between yellow to red is 1 to 2 or 1:2. Answer: not listed.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

First, we can use the given information to find the ratio between green and yellow:

6 yellow = 5 green

=> green/yellow = 6/5

Next, we can use the given information to find the ratio between purple and green:

4 green = 3 purple

=> purple/green = 4/3

Finally, we can use the given information to find the ratio between red and purple:

5 purple = 2 red

=> red/purple = 5/2

To find the ratio between yellow and red, we can combine these ratios and simplify:

green/yellow = 6/5

=> yellow/green = 5/6

purple/green = 4/3

=> green/purple = 3/4

red/purple = 5/2

=> purple/red = 2/5

yellow/green * green/purple * purple/red = yellow/red

(5/6) * (3/4) * (2/5) = 1/2

Therefore, the ratio between yellow to red is 1 to 2 or 1:2. Answer: not listed.

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