Answer: 16
Step-by-step explanation:
The geometric number between 7 and 28 is 16. Geometric numbers are the numbers you get by multiplying by a factor. If we multiply by 2 for this common geometric sequence, we get 16:
1 * 2 = 2, 2 * 2 = 4, 4 * 2 = 8, 8 * 2 = 16,16 * 2 = 32, etc.
7 < 16 < 28
2.discuss the differences between divergence and curl of function. can the divergence and curl be defined for a scalar function?
Divergence and curl are two important concepts in vector calculus. They are used to describe the behaviour of vector fields, which are functions that assign a vector to each point in space.
Divergence is a scalar function that describes the extent to which a vector field is spreading or contracting at a given point. If the vector field is spreading, the divergence at that point is positive; if it is contracting, the divergence is negative.
If the vector field is unchanged in size, the divergence is zero. The formula for the divergence of a vector field is given by the dot product of the gradient of the field with the unit normal vector at a point.
Curl, on the other hand, is a vector function that describes the rotational aspect of a vector field. It is defined as the cross-product of the del operator and the field. Curl measures the rate at which the vectors in a field are rotating about a point. If the curl is zero, the field is said to be irrotational. If the curl is non-zero, the field is said to be rotational.
Divergence and curl cannot be defined for a scalar function because a scalar function assigns a single scalar value to each point in space, while divergence and curl describe the behaviour of vector fields.
A scalar function has no direction or rotational component, so there is no way to describe the spreading or contracting behaviour or the rotational behaviour of the function.
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Please help I’m so bad at math I don’t understand
Answer:
f(-4) = -18
Step-by-step explanation:
So we have f(x) and we have f(-4). The X is where the -4 is so that means x = -4.
Since we know that, we plug it into the equation. Everywhere we see an X
So instead of 5(x) + 2, it will be 5(-4)+2.
5 times -4 is -20, which makes it -20 + 2
-20 + 2 = -18. Giving us our answer
Answer:
[tex]-18[/tex]
Step-by-step explanation:
f is a function of x. f depends on x. For every value of x, a certain value of f(x) is obtained.
This question requires us to determine the value of f(x) for x = [tex]-4[/tex]:
Substitute x = [tex]-4[/tex] into the provided function:
[tex]f(-4) = 5(-4) +2[/tex]
= [tex]-20 + 2[/tex]
= [tex]-18[/tex]
A type of Dark Chocolate is made by mixing cocoa and cocoa butter in the ratio 5 to 2. Let C be an unspecified number of grams of cocoa, which vary, and let B be the corresponding number of grams needed to make that type of dark chocolate. Reason about quantities and use math drawings to explain three different equations that relate C and B (and do not include any other variables)
Here are three different equations that relate C and B:
1. B = (2/7) * C
2. B/C = 2/5
3. 5C = 2B
Different Equation Divided1. B = (2/7) * C
Since the ratio of cocoa to cocoa butter is 5:2, we can write 5 + 2 = 7, which represents the total number of parts. Dividing 2 by 7, we get 2/7, which represents the fraction of cocoa butter in the mixture. To find the number of grams of cocoa butter needed for C grams of cocoa, we multiply C by 2/7.
2. B/C = 2/5
Dividing the number of grams of cocoa butter (B) by the number of grams of cocoa (C), we get the ratio of cocoa butter to cocoa, which is 2/5.
3. 5C = 2B
Since the ratio of cocoa to cocoa butter is 5:2, we can write the equation 5 * C = 2 * B, which represents the number of parts of cocoa to the number of parts of cocoa butter. Solving for B in terms of C, we get B = (2/5) * C.
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Amanda uses 1/3 of a cup of milk each time she makes a batch of pancakes. How many batches can she make if she only has 11/12 of a cup of milk left?
A circle is drawn. Two points are marked outside the circle such that only 3 tangents can be drawn to the circle using these two points.
Which of the following is true based on the above information?
A) All 3 tangents are equal in length.
B) Both the points lie on one of the tangents.
C) The tangents and the circle have two common points in total.
D) (such a situation is not possible as with 2 points, there will be 4 tangents to the circle)
Answer:
D) (such a situation is not possible as with 2 points, there will be 4 tangents to the circle)
Write a sentence to describe how you calculated the cost of Nadine's order
The cost of Nadine's order was found by multiplying the number of t - shirts she ordered, by their individual cost, and then deducting the value of the coupon.
How to find the cost of the order ?The order was that Nadine bough4 t - shirts for her class club from a website.
Each of these shirts cost $ 10. 95. But, Nadine gets a coupon of $ 12. 50 to be deducted from the total order.
To find the cost therefore, we can multiply the cost of the shirts and the number of shirt and then deduct the value of the coupon as shown in the formula :
= ( Cost of shirt x Number of shirts ) - coupon
= ( 10. 95 x 4 ) - 12. 50
= $ 31. 30
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The full question is:
Nadine ordered 4 t-shirts for her class club form a website. Each shirt is $10.95 and Nadine has a coupon for $12.50 off her total order. Write a sentence to describe how you calculated the cost of Nadine's order.
A. B. C. D. 1 2 Steps For Sally b = 11 For Sally m = 2(11) + 4 For Mike b = 22 4 For Mike m = 2(22+4) In which step did Mike make an error? 3 Mike's Work Step 1 Step 2 Step 3 Step 4
In Step 3, Mike made an error. He incorrectly calculated his value for m by multiplying 2 by 22 instead of 2 by (22 + 4). The correct equation should have been m = 2(22 + 4).
Which step did Mike make an error?Sally's formula for calculating b is correct:
b = 11
Sally's formula for calculating m is also correct:
m = 2(11) + 4 = 26
Mike's formula for calculating b is correct:
b = 22
However, Mike's formula for calculating m is incorrect. Instead of using the formula m = 2(b + 4), he used the formula m = 2(22 + 4), which gives him a value of 50 instead of the correct value of 50.
Therefore, Mike made a mistake in Step 3. He computed his answer for m erroneously by multiplying 2 by 22 rather than 2 by (22 + 4). The proper formula would have been m = 2(22 + 4).
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What are the leading coefficient and degree of the polynomial?
18 + 9w^2 - w^3 - w
Answer:
The leading coefficient is -1. The degree of the polynomial is cubic.
Step-by-step explanation:
The leading coefficient is the number in front of the variable showcasing the biggest exponent. The degree of the polynomial is considered by looking at the biggest exponent, and identifying which one it is. In this case, it's a cubic polynomial.
Given parallelogram A B C D below, DE = 31 If EB = x-7, solve for x.
The value of x of the parallelogram is x = 38
What is a Parallelogram?A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure
The four types are parallelograms, squares, rectangles, and rhombuses
Properties of Parallelogram
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent.
Same-Side interior angles (consecutive angles) are supplementary
Each diagonal of a parallelogram separates it into two congruent triangles
The diagonals of a parallelogram bisect each other
Given data ,
Let the parallelogram be represented as ABCD
Now , the diagonals of the parallelogram are AC and BD
The measure of DE = 31
The measure of EB = x - 7
Now , Each diagonal of a parallelogram separates it into two congruent triangles where the measure of AC = BD
So , substituting the values in the equation , we get
BD = BE + DE and BE = DE
On simplifying the equation , we get
31 = x - 7
Adding 7 on both sides of the equation , we get
x = 31 + 7
x = 38
Hence , the measure of x of parallelogram is 38
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Simplify 3sin²θ−3.
simplify
Answer:
- 3cos²Θ
Step-by-step explanation:
using the identity
sin²Θ + cos²Θ = 1 , then
sin²Θ = 1 - cos²Θ
given
3sin²Θ - 3
= 3(1 - cos²Θ) - 3
= 3 - 3cos²Θ - 3
= - 3cos²Θ
A temple has 14 cylindrical pillars made of concrete. If the radius of base of each pillar is 20 cm and height is 5 m,how much concrete is required to make the pillars?Find it
The volume of the 14 cylindrical pillars made of concrete is 8.8 m³
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.
The volume of a cylinder is:
Volume = π * radius² * height
A temple has 14 cylindrical pillars made of concrete. If the radius of base of each pillar is 20 cm and height is 5 m.
Radius = 20 cm = 0.2 m
Volume of each cylindrical pillar = π * 0.2² * 5 = 0.628 m³
Volume of 14 cylindrical pillar = 14 * 0.628 m³ = 8.8 m³
The volume of the pillars is 8.8 m³
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under ideal conditions a certain bacteria population is known to double every three hours. suppose that there are initially 200 bacteria. (a) what is the size of the population after 15 hours? bacteria
The size of the population after 15 hours is 6400 bacteria.
The size of the population after 15 hours can be found using the exponential growth formula. The formula for exponential growth is P = P₀ × 2^(t/k), where P₀ is the initial population, t is the time elapsed, k is the time it takes for the population to double, and 2^(t/k) is the exponential growth factor.
In this case, the initial population is 200, the time elapsed is 15 hours, and the time it takes for the population to double is 3 hours. Putting these values in the formula, we get:
P = 200 × 2^(15/3)
P = 200 × 2⁵
P = 200 × 32
P = 6400
So, the size of the population after 15 hours is 6400 bacteria.
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suppose 1/4 of your socks are blue. how many pairs of socks would you have to select randomly, on average, in order to get 4 pairs of blue socks?
To get 4 pairs of blue socks, on average, you would need to choose 16 pairs of socks at random.
The number of socks chosen at random will be denoted by the letter "n." Given by: The anticipated number of blue socks in "n" pairs
Expected number of blue socks = n * 1/4
In order for there to be four blue socks as expected, we need to determine the value of "n." Thus, we can construct the equation:
n * 1/4 = 4
And solving for n:
n = 4 / (1/4) = 4 * 4 = 16
So, To get 4 pairs of blue socks, on average, you would need to choose 16 pairs of socks at random.
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A farmer can buy two types of plant food, mix A and mix B. Each cubic yard of mix A contains 20 pounds of phosphoric acid, 30 pounds of nitrogen, and 5 pounds of potash. Each cubic yard of mix B contains 10 pounds of phosphoric acid,30 pounds of nitrogen, and 10 pounds of potash. The minimum monthly requirements are 400 pounds of phosphoric acid,960 pounds of nitrogen, and 210 pounds of potash. If mix A costs $25 per cubic yard and mix B costs $35 per cubic yard, how many cubic yards of each mix should the farmer blend to meet the minimum monthly requirements at a minimum cost? What is this cost? If mix A costs $25 per cubic yard and mix B costs $35 per cubic yard, the farmer should blend_____ yd3 of mix A and_____ yd3 of mix B to meet the minimum monthly requirements at a minimum cost. the cost is $_____
The segment [P3, P4] satisfies the minimum requirements, and the minimal price value is $840.
Let X be the amount of mix A (in pounds), and Y be the amount of mix B.
The constraints are
20X + 10Y >= 400
10X + 30Y >= 960
5X + 10Y >= 210
X >= 0, Y >= 10.
The objective function to minimize is F(X, Y) = 20X+40Y.
In the equivalent form, the constraints are
2X + 1Y >= 40
X+ Y >= 33
X+2Y >= 42
The feasibility area is the infinite area in the first quadrant which lies ABOVE each of the following straight lines :
A red (which represents the constraint (1'));
The green (which represents the constraint (2')),
A blue (which represents the constraint (3')).
Plot 2X + 1Y = 40 (const. (1'), red);
X+Y = 33 (const. (2'), green)
X+2Y = 42 (const. (3'), blue)
The four corner points of the area are:
P1 = (0,40), P2 = (7,26), P3 = (24,9), P4 = (42,0)
As per the Linear Programming method, we can calculate and compare the values at these 4 points.
These values of P1, P2, P3,P4 are:
P1: F(0,40) = 0 + 40*40 = 1600
P2: F(7,26) = 20*7+40*26 = 1180
P3: F(24,9) = 20*24+40*9 = 840
P4: F(42,0) = 20*42+0 = 840.
By comparing the numbers, any value of (X, Y) that lies on the segment [P3, P4] satisfies the minimum requirements.
The segment [P3, P4] satisfies the minimum requirements, and the minimal price value is $840.
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A rectangular dining room has an area of 42 square meters. Its perimeter is 26 meters. What
are the dimensions of the dining room?
The dimension of rectangular dining room measures length 24.3 and breadth 1.73 metres.
What does dimension explain?In mathematics, dimensions refer to the length or width of an area, region, or space in one direction. It is just the measurement of something's length, width, and height. Length, breadth, and height are common ways to describe dimensions.
What are the three dimensions of us?Our world has three dimensions.
Height, length, and width are the three dimensions that define everything around us, including the homes we live in and the everyday items we use.
Length, breadth, and height are the common three dimensions that can be described in three distinct ways.
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gianna has $760 to spend at a bicycle store for some new gear and biking outfits.assume all prices listed include tax she buys a new bicycle for $356.46 she buys 2 bicycle reflectors for $10.01 each and a pair of bike gloves for $20.72 she plans to spend some of all of the money she has left to buy new biking outfits for $45.35 each
Answer:
she can buy 2 outfits
Step-by-step explanation:
What does it mean when it says solve a system algebraically
Answer:
The system of equations are solved by eliminating a variable and solving for the remaining variable. Add the two equations together to eliminate the y, then solve for x.
Roving had to pack 720 packs of milk into boxes of 24. At the end of the day , he completed 18 boxes . What fraction of the packs does he have remaining the following day? Express the fraction in its lowest terms.
Answer:
288/720 or simplified to its lowest is 2/5
What is the measurement of
what is the measurement of
IMAGE BELOW PEASE HELP ASAP
The angles m∠w and m∠y are supplementary angles and their measures are 50° and 130° respectively.
How to evaluate for the unknown anglesIf two angles add up to 180°, they are considered supplementary angles, we can observe that the positions of the angles formed by the transversal cutting the parallel lines makes the two angles on a straight line which are supplementary so;
4x + 6 + 12x - 2 = 180
16x + 4 = 180°
16x = 180 - 4 {subtract 4 from both sides}
16x = 176
x = 176/16 {divide through by 16}
x = 11.
m∠w = 4(11) + 6 = 50°
m∠y = 12(11) - 2 = 130°
Therefore, the supplementary angles m∠w and m∠y have their measures as 50° and 130° respectively.
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Suppose that the distance a car travels varies directly with the amount of gasoline it uses. A certain car uses 23 gallons of gasoline to travel 713 miles. If the car travels 155 miles, how much gasoline does it need?
Answer:
Step-by-step explanation:
We can set up a proportion to solve for the unknown amount of gasoline needed:
distance traveled / amount of gasoline = constant
Let x be the amount of gasoline needed to travel 155 miles. Using the given information, we can set up the following proportion:
713 miles / 23 gallons = 155 miles / x
Simplifying, we get:
x = (155 miles * 23 gallons) / 713 miles
x = 5 gallons (rounded to the nearest gallon)
Therefore, the car needs 5 gallons of gasoline to travel 155 miles.
1 plus the product of 2 and m
Answer:
1+(2×m)
Step-by-step explanation:
We can break the problem down and find the keywords.
1 plus the product of 2 and m
plus=+
product=×
1+(2×m)
Part A
Create a random triangle, ΔABC. Measure and record its angles.
The triangle that's created has angles of 90°, 45° and 45°.
What is a triangle?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane.
A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.
The triangle is attached.
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What is the volume of the shape below?
Gabriel invested $23,000 in an account paying an interest rate of 11% compounded daily. Ava invested $23,000 in an account paying an interest rate of 0% compounded continuously. After 8 years, how much more money would Gabriel have in his account than Ava, to the nearest dollar?
Gabriel would have $45,985.67 more than Ava in his account. This is because Gabriel's account is compounded daily, meaning that his interest would be compounded 365 times a year, while Ava's account is compounded continuously,
What is compounded ?Compounding is the process of combining two or more elements to create a new, more complex product. In finance, compounding refers to the interest earned on an investment that is reinvested and earns additional interest. This cycle continues, allowing the principal to grow exponentially over time. The effective rate of return is greater than the stated interest rate.
The calculation for Gabriel's account is: 23,000 * (1.11^(365*8)) = $69,985.67. The calculation for Ava's account is: 23,000 * e^(0*8) = $24,000. The difference between the two is $45,985.67.
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Answer:997
Step-by-step explanation:
Find the difference of (-x^2 + 9xy) - (x^2 + 6xy - 8y^2)
Difference of (-x² + 9xy) and (x² + 6xy - 8y²) is - 2x² + 3xy + 8y².
What is subtraction?Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.
Given expression,
(-x² + 9xy) - (x² + 6xy - 8y²)
Distributing negative sign
-x² + 9xy - x² - 6xy + 8y²
Adding like terms
- 2x² + 3xy + 8y²
Hence, - 2x² + 3xy + 8y² is the difference of (-x² + 9xy) and (x² + 6xy - 8y²).
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1059 divided by 2.2, please show work
Use the equation to answer the question.
-(t+2) = -31 +23
What value of t makes the equation true? Enter the answer in the box.
Answer:
t = 6
Step-by-step explanation:
-(t+2) = -31 +23
Solve for t.
Combine like terms on the right.
-(t+2) = -8
Divide each side by -1.
t+2 = 8
Subtract 2 from each side.
t+2-2 = 8-2
t = 6
The tables show the number of necklaces made and the number of beads used. Which table shows a proportional relationship?
Select one:
Number of Necklaces 2 4 6 8
Number of Beads 20 40 60 80
Number of Necklaces 2 4 6 8
Number of Beads 10 15 20 25
Number of Necklaces 2 4 6 8
Number of Beads 14 21 28 35
Number of Necklaces 2 4 6 8
Number of Beads 15 20 25 30
HELP ME!!!!!!
The table shows a proportional relationship is:
Number of Necklaces 2 4 6 8
Number of Beads 20 40 60 80
As per the data given:
The tables show the number of necklaces made and the number of beads used.
Number of Necklaces 2 4 6 8
Number of Beads 20 40 60 80
From the table:
2 : 20 = 1 : 10
4 : 40 = 1 : 10
6 : 60 = 1 : 10
8 : 80 = 1 : 10
As there is a common ratio between each value there will be a proportional relationship
Number of Necklaces 2 4 6 8
Number of Beads 10 15 20 25
From the table:
2 : 10 = 1 : 5
4 : 15
6 : 20 = 3 : 10
8 : 25
As there is no common ratio between each value there will not be any proportional relationship
Number of Necklaces 2 4 6 8
Number of Beads 14 21 28 35
From the table:
2 : 14 = 1 : 7
4 : 21
6 : 28 = 3 : 14
8 : 35
As there is no common ratio between each value there will not be any proportional relationship
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Rocks are sometimes used along coasts
to prevent erosion. If a rock needs to
weigh 2,000 lb in order not to be shifted by
waves, how big (what volume) does it need
to be? You are using basalt, which has a
typical density of 3200 lb/in³.
Volume =
If a rock needs to weigh 2,000 lb in order not to be shifted by waves, the volume of this basalt rock is equal to 0.625 in³.
What is density?In Science, the density of a chemical substance such as lead can be calculated by using this formula:
Density = M/V
Where:
M represents the mass of a chemical substance or physical object.V represents the volume of a physical substance or object.Making volume the subject of formula, we have the following:
Volume = Mass/Density
Volume = 2,000/3,200
Volume = 0.625 in³.
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suppose a group completes a hike from the camp to the waterfall to the meadow and back to camp at n average rate 4.5 kilometers per hours
The distances of the following places are:
Camp → waterfall = 2.25 km
waterfall → meadow = 4.5 km
meadow → camp = 9 km
What is speed?Speed is the ratio of distance and time.
It shows how fast an object is moving at a given time.
We have,
Places traveled:
Camp → waterfall → meadow → camp.
We are assuming the time taken as follows:
Camp → waterfall = 30 minutes = 0.5 hour
waterfall → meadow = 1 hour
meadow → camp = 2 hours.
Now,
Speed = 4.5 km per hour.
Speed = Distance / Time
So,
The distance between camp → waterfall.
= 4.5 x 0.5
= 2.25 km
The distance between the waterfall → meadow.
= 4.5 x 1
= 4.5 km
The distance between the meadow → camp.
= 4.5 x 2
= 9 km.
Thus,
The distances are:
Camp → waterfall = 2.25 km
waterfall → meadow = 4.5 km
meadow → camp = 9 km
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