Is the converse of the following conditional true?
If b≤2, then b≥2.
yes
or
no
The manager of a store that specializes in selling tea decides to experiment with a new blend. She will mix some Earl Grey tea that sells for $ 6$6 per pound with some Orange Pekoe tea that sells for $ 4$4 per pound to get 600600 pounds of the new blend. The selling price of the new blend is to be $ 4.50$4.50 per pound, and there is to be no difference in revenue from selling the new blend versus selling the other types. How many pounds of the Earl Grey tea and Orange Pekoe tea are required?
To find the quantities of Earl Grey and Orange Pekoe tea needed to make a 600-pound blend that sells for $4.50 per pound, we use the mixture price formula, leading to a linear equation representing the total cost of blending these teas.
Explanation:The manager wants to blend Earl Grey tea ($6 per pound) and Orange Pekoe tea ($4 per pound) to produce 600 pounds of a new blend selling for $4.50 per pound without affecting revenue. To determine the required pounds of each tea, we can use the mixture price formula: total cost = (quantity of Earl Grey × price of Earl Grey) + (quantity of Orange Pekoe × price of Orange Pekoe). Since the total pounds are given as 600, let the quantity of Earl Grey be x pounds and Orange Pekoe (600 - x) pounds. The equation becomes $4.50 × 600 = $6 × x + $4 × (600-x). Solving this equation gives us the quantities of Earl Grey and Orange Pekoe required.
The top of a 15-foot ladder leans against a wall, and the bottom of the ladder slides away from the wall at a rate of 4 ft/sec. find the velocity of the top of the ladder at time t = 1 sec if the bottom of the ladder is 5 feet away from the wall at time t = 0.
Final answer:
The velocity of the top of the ladder at time t = 1 sec is -4 ft/sec.
Explanation:
To find the velocity of the top of the ladder at time t = 1 sec, we can use the concept of similar triangles. Let x be the distance between the bottom of the ladder and the wall at time t = 1 sec. Since the bottom of the ladder slides away from the wall at a rate of 4 ft/sec, we have x = 5 + 4t.
The height of the ladder remains constant at 15 ft, so if we consider the triangle formed by the ladder, the wall, and the ground, we have the ratio of the height to the base is always 15 / x. Therefore, the velocity of the top of the ladder can be found by taking the derivative of the height with respect to time.
Let h be the height of the ladder at time t. Since h = 15, we have 15 / x = 15 / (5 + 4t). Taking the derivative of both sides, we get d/dt (15 / x) = d/dt (15 / (5 + 4t)). Using the quotient rule, we have d/dt (15 / x) = (0 - 15)(0 - (5 + 4t)-2)(4) = -60 / (5 + 4t)². This gives us the velocity of the top of the ladder at time t = 1 sec: v = -60 / (5 + 4(1))² = -4 ft/sec.
What is the trigonometric derivative of Y=2sinx-tanx
A model for my number has 2 hundreds blocks no tens blocks and 3 ones blocks
Find all local extrema and saddle points of the function ,
7,080,267 written in expanded form
The number 7,080,267 in expanded form is written as the sum of each digit multiplied by its place value: 7,000,000 + 80,000 + 800 + 200 + 60 + 7.
Explanation:To write the number 7,080,267 in expanded form, we break it down into each digit's place value and represent it as the sum of each digit multiplied by its place value.
The expanded form of 7,080,267 is:
7,000,000 + 80,000 + 800 + 200 + 60 + 7
This shows that there are seven millions, eighty thousands, eight hundreds, two hundreds, six tens, and seven ones.
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Need help with problem, been stuck on it for a while
a rectangle is 4 centimeters longer than it is wide. the area is 117 square centimeters. find the dimensions of the rectangle
Answer:
width: 9 cmlength: 13 cmStep-by-step explanation:
Integer factors of 117 include ...
... 117 = 1×117 = 3×39 ≈ 9×13
The last factor pair is two factors that differ by 4. We can take these to be the dimensions of the rectangle.
_____
If you want to write an equation for width (w), it might be ...
... w(w+4) = 117
... w² +4w -117 = 0
The factorization problem for this quadratic is the problem of finding two factors of 117 that differ by 4. That is what we have done, above.
If you want to solve this by completing the square, you can to this:
... w² +4w = 117
... w² +4w +4 = 121 . . . . . add 4 = (4/2)² to complete the square
... (w+2)² = 121
... w + 2 = ±√121 = ±11 . . . . take the square root
... w = -2 ± 11 . . . . . we're only interested in the positive solution
... w = 9, then w+4 = 13 and the dimensions are 9 cm by 13 cm.
Is 124 a prime number or not explain why (u can do division to)
Use the formula for interest. P= $250 r= 7.2% Y= 15 A= ?
Answer:
value of A is $520
Step-by-step explanation:
Calculate the amount 'A' by using formula:-
A = P ( 1 + r * Y )
Where A is amount, P is principle , r is rate of interest and Y is time in years
Now, put the given values in A = P ( 1 + r * Y ) to get the value of A.
Since, P= $250, r= 7.2% and Y= 15
r = 7.2% so r = 0.072
A = P ( 1 + r * Y )
A = $250 ( 1 +0.072 * 15 )
A = $250 ( 1 + 1.08 )
A = $250 ( 2.08 )
A = $520
Hence, value of A is $520
divide 28 cans of soda into two groups so the ratio is 3 to 4
Differentiate: x√(x+4)
Find the work done by the force field f(x, y, z) = x − y2, y − z2, z − x2 on a particle that moves along the line segment from (0, 0, 1) to (3, 1, 0).
The work done by force field on a particle moving from one point to another in space is calculated using the concept of dot-product. The force field is represented as a function and the movement of the particle is treated as a path. By integrating the dot product of the force field and the derivative of path over the interval, we get the work done.
Explanation:To calculate the work done by force field on a particle, you need to apply the concept of dot product in vector calculus. The force field is defined as f(x, y, z) = x − y², y - z², z - x² and the movement of the particle is from (0, 0, 1) to (3, 1, 0). We treat this movement as a line segment in the 3-dimensional space.
The work done by the force field on the particle is calculated as W = F . dr = ∫ F(r(t)) . r'(t) dt from t1 to t2. In this case, the force field F is f(x, y, z) and the line segment can be treated as a path r(t) = t * (3, 1, 0) + (1 - t) * (0, 0, 1) and t varies from 0 to 1. Hence, r'(t) = (3, 1, 0) - (0, 0, 1).
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An equation that represents the set of points that are 2 units from (-2,-6)
The equation representing the set of points that are 2 units from the point (-2,-6) is a circle with equation (x + 2)^2 + (y + 6)^2 = 4
The question asks for an equation that represents the set of points that are exactly 2 units from the point (-2,-6) in a coordinate system. This set of points forms a circle with a radius of 2 units centered at (-2,-6). The equation for a circle with radius r and center (h, k) is (x - h)² + (y - k)² = r². Thus, the equation of the circle is (x + 2)² + (y + 6)² = 2² or (x + 2)² + (y + 6)² = 4
Tabitha found the side length of a cube with a volume of 512 cubic centimeters using the following steps. Cube V = s3
Answer:
the answer is 3cm
HOPE THIS WORKED
Step-by-step explanation:
I JUST ANSWERED THIS ON EDG
The volume of a cube is given as 512 cubic cm then the side length of the cube is 8 mm.
What is the volume of a cube?The volume of a cube can be calculated as the cube of the sides of a given figure.
The volume of a cube = [tex]sides^3[/tex]
We have been given that the volume of a cube is 512 cubic cm. We need to find the side length of the cube.
The volume of a cube = [tex]sides^3[/tex]
64 = [tex]sides^3[/tex]
Now we will take cube-root on both sides of the equation;
∛ 512 = ∛ s^3
∛ 8^3 = ∛ s^3
8 = s
Therefore, the side length of the cube is 8 cm.
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Jose rented a truck for one day. There was a base fee of $14.99 , and there was an additional charge of 83 cents for each mile driven. Jose had to pay $238.26 when he returned the truck. For how many miles did he drive the truck?
Use the slope formula to find the slope of the line passing through the given points. (–4, 7) and (0, 8)
Hi there!
Step-by-step explanation:
[tex]Slope=\frac{Y_2-Y_1}{X_2-X_1}=\frac{RISE}{RUN}[/tex]
[tex]\frac{8-7}{0-(-4)}=\frac{1}{4}[/tex]
Final answer is 1/4.
Slope is 1/4.
Hope this helps!
Thanks!
-Charlie
Have a nice day! :)
:D
A person must score in the upper 2% of the population on an iq test to qualify for membership in mensa, the international high-iq society (us airways attache, september 2000). there are 110,000 mensa members in 100 countries throughout the world (mensa international website, january 8, 2013). if iq scores are normally distributed with a mean of 100 and a standard deviation of 15, what score must a person have to qualify for mensa (to the nearest whole number)?
To qualify for Mensa, a person must have an IQ score in the top 2% of the population. Using the normal distribution with a mean of 100 and standard deviation of 15, the minimum qualifying IQ score is approximately 131.
Explanation:To qualify for Mensa, an individual must have an IQ score within the top 2 percent of the population. Given that the IQ scores are normally distributed with a mean of 100 and a standard deviation of 15, we can use the Z-score formula to find the corresponding IQ score.
The Z-score that corresponds to the top 2 percent can be found using a standard normal distribution table or a calculator with inverse normal function. The Z-score for the 98th percentile is approximately 2.05. We can then use the Z-score formula:
Z = (X - Mean) / Standard Deviation
Substituting the values we have:
2.05 = (X - 100) / 15
Solving for X gives us:
X = 2.05 * 15 + 100
X = 130.75
Therefore, the minimum IQ score required to qualify for Mensa, to the nearest whole number, is 131.
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10x + 16 ≥ 6x + 20 what is the answer to this
Answer:
The solution of given inequality is x ≥1.
Step-by-step explanation:
The given inequality is
[tex]10x+16\geq 6x+20[/tex]
We need to separate the variable terms to solve the above inequality.
Subtract 6x and 16 from both sides to separate the variables on left side.
[tex]10x+16-6x-16\geq 6x+20-6x-16[/tex]
On combining like terms we get
[tex](10x-6x)+(16-16)\geq (6x-6x)+(20-16)[/tex]
[tex]4x\geq 4[/tex]
Divide both sides by 4.
[tex]x\geq \frac{4}{4}[/tex]
[tex]x\geq 1[/tex]
Therefore the solution of given inequality is x ≥1.
Josie has $47 left on her checking account. If she writes a check for $55, what ill josie's balance be?
Answer:
Step-by-step explanation:
Josie's balance would be -8 dollars.
47-55=-8
1 2 3 4 5 6 7 8 9 10
TIME REMAINING
48:54
What number should be added to both sides of the equation to complete the square?
x2 + 3x = 6
3
62
2.25
Explanation:Consider the square ...
... (x+a)² = x² +2ax +a²
The constant term (a²) is the square of half the x-coefficient: a² = (2a/2)².
The x-coefficient in your expression is 3. The square of half that is ...
... (3/2)² = 9/4 = 2.25
Adding 2.25 to both sides gives ...
... x² +3x + 2.25 = 6 + 2.25
... (x +1.5)² = 8.25 . . . . completed square
(3/2)^2
I believe it is (3/2)^2 because I tried working it out and got something like it. I did get an answer of x = ±[tex]\sqrt{33}[/tex] over 2.
Most sources appear to give 2.25, which is equal to 3/2 squared.
Attached some work.
Bertie is x years old now. Four years ago, Chloe was twice as old as Bertie. Write an expression for Chloe's age now.
The present Age of Chloe is 2x - 4 years old.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Bertie is x years old now.
Four years Ago,
Chloe was twice as old as Bertie.
Bertie Age four years ago = x - 4
So, Chloe Age four years ago = 2(x- 4) = 2x- 8
Now, Chloe is 4 years older than she was 4 years ago,
Then, Chloe present age is (2x - 8) + 4 = 2x - 4 years old.
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PLEASE HELP ASAP!!I WILL GIVE BRAINLIEST AND 5 STARS AND HEART AND PROFILE COMMENT (4 QUESTIONS)!!!!
Identify the corresponding word problem given the equation: x + 5 = 15
A) Billy is ten years older than his sister, Jenny. If Billy is 15 years old,
how old is Jenny?
B) Billy is five years older than his sister, Jenny. If Jenny is 15 years old,
how old is Jenny?
C) Billy is five years older than his sister, Jenny. If Billy is 15 years old,
how old is Jenny?
D) Billy is fifteen years older than his sister, Jenny. If Billy is 20 years old,
how old is Jenny?
Identify the corresponding word problem given the inequality: x ≤ 4.50
A) The price of diesel has been less than $4.50 for the last month.
B) The price of diesel has been more than $4.50 for the last month.
C) The price of diesel has been no more than $4.50 for the last month.
D) The price of diesel has been no less than $4.50 for the last month.
Identify the corresponding word problem given the equation: x - 9.2 = 12.8
A) Nick ran 9.2 miles less than Perry last week. If Nick ran 22 miles, how many miles did Perry run?
B) Nick ran 12.8 miles less than Perry last week. If Nick ran 9.2 miles, how many miles did Perry run?
C) Perry ran 9.2 miles less than Perry last week. If Nick ran 12.8 miles, how many miles did Perry run?
D) Nick ran 9.2 miles less than Perry last week. If Nick ran 12.8 miles, how many miles did Perry run?
Identify the corresponding word problem given the equation: x + 12.50 = 55.75
A) For mowing the neighbor's yard, Jessy was paid $12.50. If he now has $55.75, how much money did he have before?
B) For mowing the neighbor's yard, Jessy was paid $55.75. If he now has $12.50, how much money did he have before?
C) For mowing the neighbor's yard, Jessy was paid $43.25. If he now has $55.75, how much money did he have before?
D) For mowing the neighbor's yard, Jessy was paid $12.50. If he now has $68.25, how much money did he have before?
Whats between 0.4 and 0.5
The numbers between 0.4 and 0.5 are 0.41, 0.42, 0.43, 0.44, 0.45, 0.46, 0.47, 0.48, and 0.49.
Used the concept of the number system states that
A writing system used to express numbers is known as a number system. It is the mathematical notation used to consistently express the numbers in a particular set using digits or other symbols.
Here, the two numbers are 0.4 and 0.5
So, all the numbers that are between 0.4 and 0.5 are,
0.41, 0.42, 0.43, 0.44, 0.45, 0.46, 0.47, 0.48, 0.49
Therefore, the numbers are 0.41, 0.42, 0.43, 0.44, 0.45, 0.46, 0.47, 0.48, and 0.49.
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the perimeter of a rectangle is 24 centimeters. It's length is 9 centimeters. find the width
What is the equation of the horizontal line through (-7,-3)
A multivitamin tablet contains 0.16g of vitamin C. How much vitamin C does a bottle of 60 tablets contain?
What is 49.2532 to 1 decimal place
the second number to the right of the decimal point is 5 so you need to round the 2 up to 3
so the number becomes 49.3
help quick. first person with the right answer gets brainiest