A circular rug has a radius of 4. 5 feet. What is the circumference of the rug? Use 3. 14 for Pi and round to the hundredths place. 14. 13 28. 26 44. 37 88. 74.
Answer:
28.26
Step-by-step explanation:
The circumference of a circle is equal to 2πr, where r is the radius. The radius is the distance from the center of the circle to a point on the outside of the circle.
To find the circumference you can plug in the known information and multiply. However, instead of using actual pi, we will use 3.14 because that is what the question says.
2 * 3.14 * 4.5 = 28.26This means that the distance around the rug is 28.26 feet.
If 35 gms of pure drug are contained in 150 mls, how many grams are contained in 75 mls?
Answer:
17.5
Step-by-step explanation:
The ratio of "pure drug" to liquid is 35:150
Therefore to evaluate for 75 mls we get the ratio 75/2150 or simply 1/2
we can then multiply 35 by the ratio 1/2
35/2=17.5
State the answer
In 75 mls there are 17.5 grams of pure drug
The amount of the pure drug in 75 ml will be 17.5 grams.
What are ratio and proportion?A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
The ratio of the two proportional items will remain the same.
The amount of the drug is directly proportional to the contained liquid.
If 35 gms of the pure drug are contained in 150 ml.
Then the amount of the pure drug in 1 ml will be
⇒ 35 / 150
⇒ 0.2333 grams per ml
Then the amount of the pure drug in 75 ml will be
⇒ 0.2333 x 75
⇒ 17.5 grams
The amount of the pure drug in 75 ml will be 17.5 grams.
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for travel purposes,a touring company places all 33 travelers into equal sized groups . how many groups are there and how many travelers are in each group
PLEASE HELP MEEE
There are 3 groups of 11 travellers each or 11 groups of 3 travellers each.
Since we have 33 travellers and we need to divide them into equal sized groups, we need to find the factors of 33.
Factors of 33So, 33 = 1 × 33 = 3 × 11
So, the two factors of 33 we require are 3 and 11.
The groups of travellersSince 11 × 3 = 3 × 11,
So, 3 × 11 implies that we can have 3 groups of 11 travellers each and,
11 × 3 implies that we can have 11 groups of 3 travellers each.
So, there are 3 groups of 11 travellers each or 11 groups of 3 travellers each.
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Could I please get assistance with this question. Create a mini cricket/rugby clinic explanation where you teach learners about cricket/rugby while incorporating Mathematics or English literacy. Your explanation should be informative and insightful.
As treasurer of her school's 4H club, Carol wants to buy gifts for all
11 members. She can buy t-shirts for $5 and sweatshirts for $12.
The club has $118 to spend and Carol wants to spend all of the
money. How many of each type of gift should she buy?
Using algebraic expressions and equations, Carol should buy 2 t-shirts and 9 sweatshirts.
We can set up an algebraic expressions and equations to determine how many of each type of gift should Carol buy.
An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".
1. Write an equation for the total number of members.
x + y = 11 (equation 1)
where x is the number of members who will get t-shirt
y is the number of members who will get sweatshirt
2. If each t-shirt costs $5 and each sweatshirt costs $12, write an equation for the total amount spent buying the gift.
$5(x) + $12(y) = $118 (equation 2)
where x is the number of members who will get t-shirt
y is the number of members who will get sweatshirt
3. Rewrite equation 1 as an equation of y in terms of x.
x + y = 11 (equation 1)
y = 11 - x
4 . Plug in the expression for y in equation 2 and solve for x.
$5(x) + $12(y) = $118 (equation 2)
5x + 12(11 - x) = 118
5x + 132 - 12x = 118
-7x = -14
x = 2
5. Substitute the value of x in either equation 1 or 2 and solve for x.
x + y = 11 (equation 1)
2 + y = 11
y = 11 - 2
y = 9
Hence, Carol should buy 2 t-shirts and 9 sweatshirts.
Checking,
2 + 9 = 11
Each member will receive a gift.
2($5) + 9($12) =$118
Carol will be spending $118 for the gifts.
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What is the maximum value of 5 - 4x - x2 and the value of x for which the maximum occurs? Explain your answer.
Answer:
Max value: 9
Max x value: -2
Step-by-step explanation:
We're trying to find the vertex of y = 5 - 4x - x²
We can try to convert this equation to vertex form
First, subtract 5 from both sides
y = 5 - 4x - x²
- 5 -5
y - 5 = -4x - x²
Then add -4 to both sides (this is because this the sqaure of half b -4)
y - 5 - 4 = -4x - x²+ 4
y - 9 = -4 - 4x - x²
Factor the right side of the equation
y - 9 = -(x + 2)(x + 2)
y - 9 = -(x + 2)²
Add 9 to both sides
y - 9 = -(x + 2)²
+ 9 + 9
y = -(x + 2)² + 9
To find the max values we have to make it to where x + 2 = 0
x + 2 = 0
- 2 - 2
x = - 2
When we make equation inside the parenthesis 0, we get y = 9
y = -(-2 + 2)² + 9
y = -(0)2 + 9
y = 9
Simplify the equation, 5a=2a+15
The expression of the simplified equation 5a = 2a + 15 is a = 3
How to simplify the equation?From the question, we have the following equation
5a = 2a + 15
To start with, we need to subtract 2a from both sides of the equation
This is represented as
5a - 2a = 2a - 2a + 15
Evaluate the like terms on both sides of the equation
This gives
3a = 15
Solving further, we divide both sides by 3
3a/3 = 15/3
Evaluate
a = 5
Hence, the solution is 5
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1/5(g - 10) I need a answer please help fast
Answer: \(\frac{1}{5}g - 2\)
Explanation:
Multiply the outer term \(\frac{1}{5}\) by each term inside the parenthesis. This is an example of the distributive property. Note that \(\frac{1}{5}\) times 10 is equal to 2, because \(\frac{1}{5}*10 = \frac{10}{5} = 2\).
Answer:
1/5g-2
Step-by-step explanation:
1/5(g-10)=1/5g-2
We have to distribute 1/5 (we multiply it by g and -10)
So, we get 1/5g-2.
I hope this helps!
\(*RosalindCordelia*\)
A survey is given to a random sample of some of the freshman students at a certain high school. Which statement about the results of the survey is true? O
O The responses can be used to make valid inferences about the entire freshman class at that school.
O The responses can be used to make valid inferences about the entire student body at that school.
O The responses can be used to represent freshman students at all high schools.
O The responses can be used to represent high school students at all high schools.
A survey is given to a random sample of some of the freshman students at a certain high school therefore the statement about the results of the survey which is true is that the responses can be used to make valid inferences about the entire freshman class at that school which is therefore denoted as option A.
What is a Survey?
This is referred to as a method of gathering information using relevant questions from a sample of people with the aim of understanding populations as a whole.
Since the survey was given to random freshman in that school, then it means that it is unbiased and will provide a valid information about them in that particular school.
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What is the eccentricity of the ellipse shown below?
(x + 7)² /16+ (y − 3)²/4 = 1
The eccentricity of the ellipse in discuss which is described by the given equation is; √3 / 2.
What is the eccentricity of an ellipse described by the given equation?It follows from the task content that the eccentricity of an ellipse described by the given equation is to be determined.
Recall that the standard form equation of an ellipse takes the form;
(x - h)² / a²+ (y − k)² / b² = 1
Hence, by comparison of the given equation; (x + 7)² /16+ (y − 3)²/4 = 1 to the standard equation; it can be inferred that;
a² = 16 and
b² = 4
Therefore; since the formula for calculating the eccentricity of an ellipse is;
e = √ (1 – ( b² /a² ) ).
Hence, upon substitution of a² = 16 and b² = 4; we have that;
e = √ ( 1 – ( 4 /16 ) ).
e = √ ( 1 - 0.25 )
e = √0.75
e = √3 / 2.
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please i beg of you please help me!
Answer:
Step-by-step explanation:
You need to convert all into decimals or all into fractions to compare
4 1/6= 4.166666
4.73
41/10= 4.1
4.168
Order:
41/10 4 1/6 4.168 4.73
Answer:
here's the list of numbers in order from least to greatest:
4 1/6, 4.160, 41/10, 4.73.
Why is (4x-2)(3x+5) not an intelligent
guess for factoring this trinomial even though
4.3=12 and -2.5=-10?
Trinomials are expressions with three terms
The factor is not an intelligent guess, because the expression can be further simplified
Why the factor is not intelligent?
The factor is given as:
(4x - 2)(3x + 5)
The above factor can further be factorized.
This is shown below
(4x - 2)(3x + 5) = 2(2x - 1)(3x + 5)
Hence, the factor is not an intelligent guess, because the factor can still be further simplified
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The total area of a cube is 1350 square inches. Find the dimensions of
this cube?
a line passing through the origin which is not contained in any of the three coordinate planes, include and label at least three labeled points on the line
Three labeled points on the line are (-2, -2m), (0, 0), and (2, 2m), where m is the slope of the line.
A line passing through the origin but not contained in any of the three coordinate planes can be represented by the equation y = mx, where m is the slope of the line. Since the line passes through the origin, the y-intercept is 0.
To find labeled points on the line, we can choose different values for x and calculate the corresponding y-values using the equation y = mx. Let's choose three values for x: -2, 0, and 2.
For x = -2:
y = m(-2) = -2m
So, one labeled point on the line is (-2, -2m).
For x = 0:
y = m(0) = 0
Another labeled point on the line is (0, 0).
For x = 2:
y = m(2) = 2m
So, the third labeled point on the line is (2, 2m).
These three labeled points (-2, -2m), (0, 0), and (2, 2m) lie on the line passing through the origin, and they are not contained in any of the coordinate planes.
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(2.3x−1.2y)+(1.4x+3.7y) add
\(\huge \bf༆ Answer ༄\)
Just add the like terms ~
\( \sf \: 2.3x - 1.2y + 1.4x + 3.7y\)\( \sf2.3x + 1.4x + 3.7y - 1.2y\)\( \sf3.7x + 2.5y\)I hope it helps ~
\( ꧁ \:\large \cal{kaul} \: ꧂\)
Answer:
3.7x + 2.5y
Hope you could get an idea from here.
Doubt clarification - use comment section.
a and b are two statements such that "if a, then b " is a compound statement which will always be true unless a is true and b is false. what is that mean ?
"if a, then b" means that a is a sufficient condition for b, and that b is a necessary condition for a to be true. The statement is true unless a is true and b is false.
The statement "if a, then b" is known as a conditional statement, which is a type of logical statement that is often used in mathematics and other fields. In this case, the statement means that if statement a is true, then statement b must also be true. If a is false, then the truth value of b is not relevant, as the statement is considered true regardless.
The statement "if a, then b" is often written as "a → b" using logical symbols. The symbol "→" is read as "implies" or "if-then".
For example, consider the statements "If it is raining, then the ground is wet" (a → b). This statement is considered true unless it is raining and the ground is not wet, which is a contradiction. If it is not raining, the truth value of "the ground is wet" is not relevant to the truth of the conditional statement.
In summary, "if a, then b" means that a is a sufficient condition for b, and that b is a necessary condition for a to be true. The statement is true unless a is true and b is false.
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What do you really know about the graphs of y = x and y = x^3 and y = x^5 despite the values you found in the 3 tables above ?
y = x is a linear function
y = x³ is a cubic function
y = x⁵ is a 5 power polynomial function.
What is graph of a function ?A relationship that has one output for each input value (x-value) is called a function (y-value). All functions are hence relations. However, not all relationships are functions since not every relationship will satisfy the condition that every distinct input generates just one output.
Check to see if there is a horizontal asymptote or an oblique asymptote by comparing the degrees of the numerator and denominator to the function's end behavior. Plot the asymptotes that are horizontal or oblique.
The Properties of the graph y = x are :
The graph passes through the originThe graph is a linear graph .The y-intercept is zero.The Properties of the graph y = x³ are :
The graph passes through the originThe function is a cubic function The graph is not linear.The Properties of the graph y = x⁵ are :
The graph passes through the originThe graph will folllow a similar path as y = x³ function The graph is not linear.To learn more about Graphs refer to :
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the girl to boy ratio is 3 to 7 if there are 50 students total how many boys
Answer:
15 girls, 35 boys
Step-by-step explanation:
Step 1:
3 : 7 Ratio
Step 2:
3x + 7x = 50 Substitute
Step 3:
10x = 50 Add
Step 4:
50 ÷ 10 Divide
Step 5:
x = 5
Answer:
15 girls, and 35 boys Multiply
Hope This Helps :)
-1/3(2p-9) what does p equal
Answer:
-2p/3+3
Step-by-step explanation:
Segments and Angles again.. this is a struggle for me
The calculated length of the segment AD is 14
How to determine the length of the segment ADFrom the question, we have the following parameters that can be used in our computation:
B is the midpoint of AC
BD = 9 and BC = 5
Using the above as a guide, we have the following:
AB = BC = 5
CD = BD - BC
So, we have
CD = 9 - 5
Evaluate
CD = 4
So, we have
AD = AB + BC + CD
substitute the known values in the above equation, so, we have the following representation
AD = 5 + 5 + 4
Evaluate
AD = 14
Hence, the length of the segment AD is 14
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Tell whether -3 is a solution to 3 -4x >= 15
Answer:
Yes, -3 is a solution to the inequality.
Step-by-step explanation:
Plug -3 into the inequality.
3 - 4x ≤ 15
3 - 4(-3) ≤ 15
3 + 12 ≤ 15
15 ≤ 15
The resulting inequality is true, so -3 is a solution.
Damien LOVES fruit. He has 22 oranges. If Damien, only eats .2 of a cupcake each day, how many days will it take him to eat all 22 cupcakes?
Answer:
c
Step-by-step explanation:
RIGHT ANSWER GETS BRAINLIST 100 POINTS
Samir is working on a project and has cut a number of wooden blocks of equal size that are represented by this right rectangular prism. He now needs to cover the wooden blocks on all sides with a blue fabric.
How much fabric does Samir need in order to cover 5 of these blocks?
12 cm²
34 cm²
60 cm²
170 cm²
Answer:
170 cm
Step-by-step explanation:
2 * 1 1/2 * 2 = 6
1 1/2 * 4 * 2 = 12
2 * 4 * 2 = 16
In total: 6 + 12 + 16 = 34.
Samir needs to cover 5 of these blocks so: 34 x 5 = 170
I also did the quiz.
Answer: 170cm
Step-by-step explanation: I did the test!! From k12
Which rectangle is similar to a rectangle with 1/2 yards and 2/3 yards?
Answer:
The answer is A=2/9 yards²
Step-by-step explanation:
The formula for a rectangle is A=B x H
So the equation is A= 1/3 yards x 2/3 yards
A 40 gram sample of a substance that’s used for drug research has a k-value of 0.1472.
Find the substance’s half-life, in days. Round your answer to the nearest tenth.
A 40 gram sample of a substance that’s used for drug research has a k-value of 0.1472. The substance's half-life, in days, is approximately 4.7 days.
The half-life of a substance is the time it takes for half of the substance to decay or undergo a transformation. The half-life can be determined using the formula:
t = (0.693 / k)
where t is the half-life and k is the decay constant.
In this case, we are given that the sample has a k-value of 0.1472. We can use this value to calculate the half-life.
t = (0.693 / 0.1472) ≈ 4.7 days
Therefore, the substance's half-life, rounded to the nearest tenth, is approximately 4.7 days.
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The picturegram shows information about CDs sold in a shop.
1 . How manny CDs were sold on Wednesday | Key = 3 |
2. How manny more CDs were sold on Thursday than Wednesday?
**If you know the answer let me know!**
Answer:
i believe number 1 is 18 and number 2 is 9.
Step-by-step explanation:
if one full circle represents 6 CDs then on wednesday 18 Cds were sold because 6+6+6=18 and on thursday they sold 9 more Cds than on wednesday because they sold 6+6+6+6+3 which equals 9.
Find a vector function, r (t), that represents the curve of intersection of the two surfaces. The cone z = squareroot x^2 + y^2 and the plane z = 3 + y r (t) =
The vector function that represents the curve of intersection of the cone and the plane is:
r(t) = [t, (t^2 - 9) / 6, √(t^2 + ((t^2 - 9)/6)^2)]
For a vector function that represents the curve of intersection between the cone and the plane, we need to set the equations of the cone and the plane equal to each other and solve for x, y, and z.
The cone equation is given as: z = √(x^2 + y^2)
The plane equation is given as: z = 3 + y
Setting these two equations equal to each other, we have:
√(x^2 + y^2) = 3 + y
To eliminate the square root, we can square both sides of the equation:
x^2 + y^2 = (3 + y)^2
x^2 + y^2 = 9 + 6y + y^2
Simplifying the equation, we have:
x^2 - 6y = 9
Now we can express x and y in terms of a parameter t to create the vector function r(t):
x = t
y = (t^2 - 9) / 6
Substituting these values back into the cone equation to find z:
z = √(x^2 + y^2) = √(t^2 + ((t^2 - 9)/6)^2)
Therefore, the vector function that represents the curve of intersection of the cone and the plane is:
r(t) = [t, (t^2 - 9) / 6, √(t^2 + ((t^2 - 9)/6)^2)]
Note that this is a parametric representation of the curve, where t is the parameter that determines points on the curve.
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Let f be a differentiable function such that f (2) = 4 and f (2) = − 1/2 . What is the approximation for f (2.1) found by using the line tangent to the graph of f at x = 2 ?
Using line tangent, the approximation for f(2.1) is 3.95
Given,
The point (a, f(a)) is on the line tangent to the graph of y = f(x) at x = a, which has a slope of f'(a).
The equation be like;
y - f(a) / (x - a) = f'(a)
y = f'(a) (x - a) + f(a)
Using the provided data and a = 2, we can determine that the tangent line to the graph of y = f(x) at x = 2 has equation
y = f'(2) (x - 2) + f(2)
y = -1/2 (x - 2) + 4
To compute a "approximation of f(2.1) using the line tangent to the graph of f at x = 2," one must substitute x = 2.1 for f in the equation for the tangent line (2.1). You get 2.1 when you plug this in.
y = -1/2 (x - 2) + 4
y = -1/2 (2.1 - 2) + 4
y = -1/2 x 0.1 + 4
y = 3.95
That is,
The approximation for f(2.1) using line tangent is 3.95
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he parcel of land you are viewing is 3 acres. the front of the lot is 450 feet wide. what is the depth?
The depth of the land parcel is 290.4 feet.
We have to give that,
The parcel of land you are viewing is 3 acres. the front of the lot is 450 feet wide.
Now, the formula for calculating area:
Area = length × width.
In this case, the area of the land parcel is given as 3 acres.
Since, 1 acre = 43,560 square feet,
Hence, the area can be converted as,
Area = 3 acres × 43,560 square feet/acre
= 130,680 square feet.
Since the front width of the lot is 450 feet.
Let's denote the depth as "d."
Using the formula for area,
Area = length × width
130,680 square feet = d × 450 feet.
Now, we can solve for the depth (d):
d = 130,680 square feet / 450 feet
d ≈ 290.4 feet.
Therefore, the approximate depth of the land parcel is 290.4 feet.
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The value of y is 4 when x is 16. Give the equation (in y=kx form) that describes the proportional relationship between these two variables.
The equation of the proportional relationship is \(y=\frac{1}{4}x\).
How to solve proportional relationships?Proportional relationships are relationships between two variables where their ratios are equivalent. A proportional relationship can be represented as follow:
y = kx
where
k = constant of proportionalityTherefore, the value of y is 4 when x is 16. Let's find the relationship in the form y = kx
4 = 16k
divide both sides by 16
4 / 16 = 16k / 16
k = 1 / 4
Therefore, the equation is \(y=\frac{1}{4}x\)
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