When comparing the data from the two locations, the measure of center that should be used to determine which location typically has the cooler temperature is the median.
In Sunny Town, the histogram shows that the shaded bars are skewed to the right, indicating that the distribution is positively skewed. This means that there are a few high temperatures that pull the mean towards the higher end.
However, the median, which represents the middle value when the data is arranged in ascending order, is less affected by extreme values and is a better measure of the center for skewed distributions.In Desert Landing, the histogram shows a symmetric distribution, with the shaded bars evenly distributed around the center.
In this case, both the mean and median can be considered reliable measures of the center.Therefore, to determine which location typically has the cooler temperature, we should use the median.
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an open box will be made by cutting a square from each corner of a 16-inches by 10-inches piece of cardboard and then folding up the sides. what size square should be cut from each corner in order to produce a box of maximum volume? what is that maximum volume?
The size of the square to cut is 5/3 inches and the maximum volume of the box is 266.67 cubic inches.
To find the size of the square to cut and the maximum volume, we can follow these steps:
Let's call the length of each side of the square to be cut x inches. So the dimensions of the base of the box would be (16-2x) inches by (10-2x) inches.
The height of the box would be x inches since we are folding up the sides.
The volume of the box can be found by multiplying the length, width, and height: V = (16-2x)(10-2x)x.
To find the maximum volume, we can take the derivative of V with respect to x and set it equal to zero, since the maximum volume occurs at a critical point.
After taking the derivative and simplifying it, we get the equation 24x^2 - 520x + 1600 = 0.
Solving this quadratic equation, we get x = 5/3 or x = 20/3. Since x must be less than 5 (the length of the shorter side), the only feasible solution is x = 5/3 inches.
Plugging this value of x back into the equation for the volume, we get V = (16-2(5/3))(10-2(5/3))(5/3) = 266.67 cubic inches.
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Let s be the set of all orderd pairs of real numbers. Define scalar multiplication and addition on s by
In the 8 Axioms, 4 and 6 axioms fails to holds and S is not a vector space. Rest of the axioms try to hold the vector space.
To demonstrate that S is not a vector space, we must demonstrate that at least one of the eight vector space axioms fails to hold. Let us examine each axiom in turn:
Closure under addition: For any (x₁, x₂) and (y₁, y₂) in S, their sum (x₁ + y₁, 0) is also in S. This axiom holds.Commutativity of addition: For any (x₁, x₂) and (y₁, y₂) in S, (x₁ + y₁, 0) = (y₁ + x₁, 0). This axiom holds.Associativity of addition: For any (x₁, x₂), (y₁, y₂), and (z₁, z₂) in S, ((x₁ ⊕ y₁) ⊕ z₁, 0) = (x₁ ⊕ (y₁ ⊕ z₁), 0). This axiom holds.The Identity element of addition: There exists an element (0, 0) in S such that for any (x₁, x₂) in S, (x₁, x₂) ⊕ (0, 0) = (x₁, x₂). This axiom fails because (x₁, x₂) ⊕ (0, 0) = (x₁, 0) ≠ (x₁, x₂) unless x₂ = 0.Closure under scalar multiplication: For any α in the field of real numbers and (x₁, x₂) in S, α(x₁, x₂) = (αx₁, αx₂) is also in S. This axiom holds.Inverse elements of addition: For any (x₁, x₂) in S, there exists an element (-x₁, 0) in S such that (x₁, x₂) ⊕ (-x₁, 0) = (0, 0). This axiom fails because (-x₁, 0) is not well-defined as the inverse of (x₁, x₂) because (x₁, x₂) ⊕ (-x₁, 0) = (0, 0) holds only if x₂=0.Distributivity of scalar multiplication over vector addition: For any α in the field of real numbers and (x₁, x₂), (y₁, y₂) in S, α ((x₁, x₂) ⊕ (y₁, y₂)) = α(x₁ + y₁, 0) = (αx₁ + αy₁, 0) = α(x₁, x₂) ⊕ α(y₁, y₂). This axiom holds.Distributivity of scalar multiplication over field addition: For any α, β in the field of real numbers and (x₁, x₂) in S, (α + β) (x₁, x₂) = ((α + β)x₁, (α + β)x₂) = (αx₁ + βx₁, αx₂ + βx₂) = α(x₁, x₂) ⊕ β(x₁, x₂). This axiom holds.Therefore, axioms 4 and 6 fail to hold, and S is not a vector space.
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The correct question:
Let S be the set of all ordered pairs of real numbers. Define scalar multiplication and addition on S by α(x₁, x₂) = (αx₁, αx₂); (x₁, x₂) ⊕ (y₁, y₂) = (x₁ + y₁, 0). We use the symbol ⊕ to denote the addition operation for this system in order to avoid confusion with the usual addition x + y of row vectors. Show that S, together with the ordinary scalar multiplication and the addition operation ⊕, is not a vector space. Which of the eight axioms fail to hold?
1. Find the square root of each of the following numbers: (i) 152.7696
Given C(2, −8), D(−6, 4), E(0, 4), U(1, −4), V(−3, 2), and W(0, 2), and that △CDE is the preimage of △UVW, represent the transformation algebraically.
Rotate triangle △C'D'E' counterclockwise by approximately -0.785 radians about the origin:
[tex]x1' = 1 \times cos(-0.785) - (-4) \times sin(-0.785) \approx 0.436[/tex]
[tex]y1' = 1 \times sin(-0.785) + (-4) \times cos(-0.785) \approx -3.678[/tex]
[tex]x2' = -7 \times cos(-0.785) - 8[/tex]
What is the coordinate of the point?The given point [tex]s C(2, -8), D(-6, 4),[/tex] and [tex]E(0, 4)[/tex] form the triangle △CDE, and the points U(1, -4), V(-3, 2), and W(0, 2) form the triangle △UVW, with △CDE being the preimage of △UVW.
To represent the transformation algebraically, we can use a combination of translations and rotations.
Translation:
To translate a point (x, y) by a vector (h, k), we add h to the x-coordinate and k to the y-coordinate of the point.
To transform triangle △CDE to triangle △UVW, we can first translate triangle △CDE by a vector (h, k) to obtain triangle △C'D'E', where C' = C + (h, k), D' = D + (h, k), and E' = E + (h, k).
Since the coordinates of C are (2, -8) and the coordinates of U are (1, -4), we can calculate the translation vector (h, k) as follows:
[tex]h = 1 - 2 = -1[/tex]
[tex]k = -4 - (-8) = 4[/tex]
So the translation vector is [tex](-1, 4).[/tex]
Rotation:
To rotate a point (x, y) by an angle θ counterclockwise about the origin, we use the following formulas:
[tex]x' = x \times \cos(\theta) - y times \sin(\theta)[/tex]
[tex]y' = x \times \sin(\theta) + y \times \cos(\theta)[/tex]
To transform triangle △C'D'E' to triangle △UVW, we can apply a rotation of angle θ counterclockwise about the origin to triangle △C'D'E', where C' = (x1', y1'), D' = (x2', y2'), and E' = (x3', y3'). Since the coordinates of C' are (2, -8) after translation, and the coordinates of U are (1, -4), we can calculate the rotation angle θ as follows:
[tex]\theta = atan2(y1' - y2', x1' - x2') - atan2(y1 - y2, x1 - x2)= atan2((-8 + 4) - (-4), (2 + 1) - (-6 + 3)) - atan2((-8) - (-4), 2 - (-6))[/tex]
Using a calculator, we can find θ to be approximately -0.785 radians.
So, the algebraic representation of the transformation that maps triangle [tex]\triangle CDE[/tex] to triangle [tex]\triangle UVW[/tex] is:
Translate triangle △CDE by the vector (-1, 4) to obtain triangle △C'D'E':
[tex]C' = (2, -8) + (-1, 4) = (1, -4)[/tex]
[tex]D' = (-6, 4) + (-1, 4) = (-7, 8)[/tex]
[tex]E' = (0, 4) + (-1, 4) = (-1, 8)[/tex]
Therefore, Rotate triangle △C'D'E' counterclockwise by approximately -0.785 radians about the origin:
[tex]x1' = 1 \times cos(-0.785) - (-4) \times sin(-0.785) \approx 0.436[/tex]
[tex]y1' = 1 \times sin(-0.785) + (-4) \times cos(-0.785) \approx -3.678[/tex]
[tex]x2' = -7 \times cos(-0.785) - 8[/tex]
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Identify the expression that is not equivalent to 6x + 3.
The resultant value of the given expression x² + 10x + 24 when x = 3 is (C) 63.
What are expressions?A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression.
Expressions in writing are made using mathematical operators such as addition, subtraction, multiplication, and division.
For instance, "4 added to 2" will have the mathematical formula 2+4.
So, we have the expression:
= x² + 10x + 24
Now, solve when x = 3 as follows:
= x² + 10x + 24
= 3² + 10(3) + 24
= 9 + 30 + 24
= 63
Therefore, the resultant value of the given expression x² + 10x + 24 when x = 3 is (C) 63.
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Correct question:
Evaluate the expression when x = 3.
x² + 10x + 24
a. 81
b. 86
c. 63
d. 60
a blanket measures 1 1/4 yards on each side. how many square yards does the blanket cover?
Answer:
Add 1 1/4 x 1 1/4
Step-by-step explanation:
if x is a matrix of centered data with a column for each field in the data and a row for each sample, how can we use matrix operations to compute the covariance matrix of the variables in the data, up to a scalar multiple?
To compute the covariance matrix of the variables in the data, the "matrix-operation" which should be used is ([tex]X^{t}[/tex] × X)/n.
The "Covariance" matrix is defined as a symmetric and positive semi-definite, with the entries representing the covariance between pairs of variables in the data.
The "diagonal-entries" represent the variances of individual variables, and the off-diagonal entries represent the covariances between pairs of variables.
Step(1) : Compute the transpose of the centered data matrix X, denoted as [tex]X^{t}[/tex]. The "transpose" of a matrix is found by inter-changing its rows and columns.
Step(2) : Compute the "dot-product" of [tex]X^{t}[/tex] with itself, denoted as [tex]X^{t}[/tex] × X.
The dot product of two matrices is computed by multiplying corresponding entries of the matrices and summing them up.
Step(3) : Divide the result obtained in step(2) by the number of samples in the data, denoted as "n", to get the covariance matrix.
This step scales the sum of the products by 1/n, which is equivalent to taking the average.
So, the covariance matrix "C" of variables in "centered-data" matrix X can be expressed as: C = ([tex]X^{t}[/tex] × X)/n.
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The given question is incomplete, the complete question is
Let X be a matrix of centered data with a column for each field in the data and a row for each sample. Then, not including a scalar multiple, how can we use matrix operations to compute the covariance matrix of the variables in the data?
Decide if the following situation is a permutation or combination and solve. A coach needs five starters from the team of 12 players. How many different choices are there?
Answer: This situation involves choosing a group of 5 players out of a total of 12 players, where the order in which the players are chosen does not matter. Therefore, this is an example of a combination problem.
The number of ways to choose a group of 5 players out of 12 is given by the formula for combinations:
n C r = n! / (r! * (n-r)!)
where n is the total number of players, r is the number of players being chosen, and "!" represents the factorial operation.
In this case, we have n = 12 and r = 5, so the number of different choices of starters is:
12 C 5 = 12! / (5! * (12-5)!)
= 792
Therefore, there are 792 different choices of starters that the coach can make from the team of 12 players.
Step-by-step explanation:
5(2x - 1) + 3(x - 3) = -(4x - 6) + 2(13 - 3x)
Answer:
The value of x is 2.
Step-by-step explanation:
5(2x -1) + 3(x -3) = -(4x - 6) + 2(13 -3x)
Expand both sides of the equation to remove parenthesis
10x - 5 + 3x - 9 = -4x + 6 + 26 - 6x
Transpose all terms with x as the coefficient on the left side of the equation and transpose the constants to the right.
10x + 3x + 4x + 6x = 6 + 26 + 5 + 9
Simplify
23x = 46
Divide both sides of the equation by 23
23x/23 = 46/23
x = 2
solve -3(x-3)≤ 5(1-x)
can someone give me the answers to these 5?? pleaseee!!
The MAD of the hourly wages given would be $ 0.48. The range would be $ 2.00. Q1 would be $8.25. Q3 would then be $9.25. The IQR would be $1.00
How to find the number summaries ?Calculate the MAD:
First, find the mean of the data set:
mean = (sum of all values) / (number of values)
mean = (8.25 + 8.50 + 9.25 + 8.00 + 10.00 + 8.75 + 8.25 + 9.50 + 8.50 + 9.00) / 10
mean = 88.00 / 10 = 8.80
Then, find the mean of these absolute deviations:
MAD = (sum of absolute deviations) / (number of values)
MAD = (0.55 + 0.30 + 0.45 + 0.80 + 1.20 + 0.05 + 0.55 + 0.70 + 0.30 + 0.20) / 10
MAD = 4.10 / 10 = 0.41
Calculate the range:
range = maximum value - minimum value
range = 10.00 - 8.00 = 2.00
Find Q1 and Q3:
{8.00, 8.25, 8.25, 8.50, 8.50, 8.75, 9.00, 9.25, 9.50, 10.00}
Q1 is the median of the lower half, and Q3 is the median of the upper half.
Lower half: {8.00, 8.25, 8.25, 8.50, 8.50}
Upper half: {8.75, 9.00, 9.25, 9.50, 10.00}
Q1 = median of lower half = 8.25
Q3 = median of upper half = 9.25
Calculate the IQR:
IQR = Q3 - Q1
IQR = 9.25 - 8.25 = 1.00
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-16x^2+160x+120 in vertex form
The vertex form of the quadratic expression -16x² +160x+120 is -16(x - 5)² + 520.
What is vertex form?
Vertex form is a way to write a quadratic function in the form:
f(x) = a(x - h)²+ k
where "a" is the vertical stretch or compression factor, "h" and "k" are the x-coordinate and y-coordinate of the vertex of the parabola respectively. The vertex form allows you to easily identify the vertex and the direction of the parabola's opening.
To write -16x²+160x+120 in vertex form, we need to complete the square.
First, let's factor out the coefficient of x²:
-16(x² - 10x) + 120
Next, we need to add and subtract (10/2)² = 25 to the expression inside the parentheses:
-16(x² - 10x + 25 - 25) + 120
Now we can group the first three terms and factor the perfect square trinomial:
-16((x - 5)² - 25) + 120
Simplifying:
-16(x - 5)² + 520
Therefore, the vertex form of the quadratic expression -16x² +160x+120 is -16(x - 5)² + 520.
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in general, if sample data are such that the null hypothesis is rejected at the a 5 1% level of significance based on a two-tailed test, is h0 also rejected at the a 5 1% level of significance for a corresponding onetailed test? explain.
The directionality of the alternative hypothesis and the support offered by the sample data determine whether the null hypothesis is likewise rejected at the 5% level of significance for a related one-tailed test.
When the two-tailed test rejects the null hypothesis, it means that the sample data, regardless of how we look at it, support the null hypothesis.. A one-tailed test, however, simply considers the evidence in one way. As a result, the null hypothesis should be used if the sample data only show evidence that the alternative hypothesis is true in one direction (for example, greater than).
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Select the correct answer. Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g. A. g(-13) = 20 B. g(7) = -1 C. g(0) = 2 D. g(-4) = -11
Therefore, the correct answer is A. We cannot determine whether g(-13) = 20 or not as -13 is outside the domain of g, but it is a possibility within the Domain range of g.
How are the domain and range determined?Determine the values of the independent variable x for which the function is specified in order to find the domain and range of the equation y = f(x). Simply write the equation as x = g(y), and then determine the domain of g(y) to determine the function's range.
Since g has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45, we can eliminate options B and D as they fall outside the range of g.
Since -13 is outside of the range of g, we are unable to verify whether g(-13) = 20 for option A.
For option C, we are given that g(0) = -2, so option C cannot be true.
Therefore, the correct answer is A. We cannot determine whether g(-13) = 20 or not as -13 is outside the domain of g, but it is a possibility within the range of g.
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Find all of the cube roots of 216i and write the answers in rectangular (standard) form.
The cube roots of 216 written in the rectangular (standard) form are 3 + 3√3, -3+3√3, and 6.
What is a cube root?In mathematics, the cube root formula is used to represent any number as its cube root, for example, any number x will have the cube root 3x = x1/3. For instance, 5 is the cube root of 125 as 5 5 5 equals 125.
3√216 = 3√(2x2x2)x(3x3x3)
= 2 x 3 = 6
the prime factors are represented as cubes by grouping them into pairs of three. As a result, the necessary number, which is 216's cube root, is 6.
Therefore, the cube roots of 216 are 3 + 3√3, -3+3√3, and 6.
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Help please, I'm so lost
I gotchu <3
Since the vertex is (0, -3), the quadratic function can be written in vertex form as:
f(x) = a(x - 0)^2 - 3
Where 'a' is a constant that determines the shape of the parabola. Since the end behavior of the function is y --> - Infinite as x --> - infinite and y --> - Infinite as x --> + infinite, the leading coefficient 'a' must be negative.
So, f(x) = -a(x^2 - 0x) - 3
Now, using the given point (1, -7) on the parabola, we can substitute the coordinates into the function and solve for 'a'.
-7 = -a(1^2 - 0(1)) - 3
-7 = -a - 3
a = 10
Therefore, the quadratic function that satisfies the given characteristics is:
f(x) = -10x^2 - 3
Hope this helps :)
what is the 4th term/number of (a+b)^9, pascal’s triangle?
Step-by-step explanation:
hope this will help you Thanks
Helppp on this problem
The missing angles of the diagram are:
∠1 = 118°
∠2 = 62°
∠3 = 118°
∠4 = 30°
∠5 = 32°
∠6 = 118°
∠7 = 30°
∠8 = 118°
How to find the missing angles?Supplementary angles are defined as two angles that sum up to 180 degrees. Thus:
∠1 + 62° = 180°
∠1 = 180 - 62
∠1 = 118°
Now, opposite angles are congruent and ∠2 is an opposite angle to 62°. Thus: ∠2 = 62°.
Similarly: ∠3 = 118° because it is congruent to ∠1
Alternate angles are congruent and ∠5 is an alternate angle to 32°. Thus:
∠5 = 32°
Sum of angle 4 and 5 is a corresponding angle to ∠2 . Thus:
∠4 + ∠5 = 62
∠4 + 32 = 62
∠4 = 30°
This is an alternate angle to ∠7 and as such ∠7 = 30°
Sum of angles on a straight line is 180 degrees and as such:
∠8 = 180 - (30 + 32)
∠8 = 118° = ∠6 because they are alternate angles
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SALES An automobile company sold 2.3 million new cars in a year. If the average price per car was $21,000, how
much money did the company make that year? Write your answer in scientific notation.
Therefore, the company made $48.3 million (written in scientific notation as 4.83 x 10⁷) that year from selling new cars.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The expressions on both sides of the equals sign must have the same value for the equation to be true. Equations can involve a wide range of mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots. They are used to solve problems in various fields such as physics, engineering, economics, and many others.
Here,
To find the total revenue generated by the company, we need to multiply the number of new cars sold by the average price per car. We can do this as follows:
Total revenue = number of new cars sold x average price per car
Total revenue = 2.3 million x $21,000
To multiply these two numbers, we can use the distributive property:
Total revenue = (2.3 x 10⁶) x ($21,000)
Total revenue = 2.3 x $21 x 10⁶
Multiplying 2.3 by 21 gives us 48.3, which we can write in scientific notation as 4.83 x 10¹. We can then add the exponents to get:
Total revenue = 4.83 x 10¹ x 10⁶
Total revenue = 4.83 x 10⁷
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Kelly went to a store to purchase a coffee pot. She will use a coupon for 20% off. She can calculate the cost before sales tax using the following expression, where c
represents the original cost of the coffee pot.
c−0.2c
Which other expression could Kelly use to calculate her cost before sales tax?
A. 0.8c
B. 1.2c
C.1.8c
D.80c
Find the length of the side labeled x. Explain.
The value of the length marked x is 61.5
What is trigonometrical ratio?Trigonometric ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle. The basic trigonometric ratios are sine, cosine, and tangent ratios. The other important trig ratios, cosec, sec, and cot can be derived using the sin, cos and tan respectively.
First using left hand side
Cos = Adj/Hypo
Cos22 = Adj/50
Adj = 50 * Cos 22
The adj = 50*0.9272
The adj = 46.4
The to find x, using
Cos 41 = 46.4/x
xCos41 =46.4
x = 46.4/Cos41
x = 46.4/.0755
Therefore the value of x = 61.5
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hat is the maximum speed of a point on the outside of the wheel, 15 cm from the axle?
It depends on the rotational speed of the wheel. To calculate this speed, we need to know the angular velocity of the wheel.
The maximum speed of a point on the outside of the wheel, 15 cm from the axle, if we assume that the wheel is rotating at a constant rate, we can use the formula v = rω, where v is the speed of the point on the outside of the wheel, r is the radius of the wheel (15 cm in this case), and ω is the angular velocity of the wheel. Therefore, the maximum speed of a point on the outside of the wheel would be directly proportional to the angular velocity of the wheel.
The formula to calculate the maximum linear speed (v) is:
v = ω × r
where v is the linear speed, ω is the angular velocity in radians per second, and r is the distance from the axle (15 cm, or 0.15 meters in this case).
Once you have the angular velocity (ω) of the wheel, you can plug it into the formula and find the maximum speed of a point on the outside of the wheel.
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when solving an oblique triangle given three sides, use the ---select--- form of the law of cosines to solve for an angle.
When solving an oblique triangle given three sides, use the inverse cosine form of the Law of cosines to solve for an angle.
When solving an "oblique-triangle" given three sides, we would use the inverse cosine, form of the Law of Cosines to solve for an angle.
The "Inverse-Cosine" function allows us to find the measure of an angle when given the ratio of the lengths of the triangle's sides.
The "Law-of-Cosines" relates the lengths of the sides of a triangle to the cosine of one of its angles.
The "Law-of-Cosines" states that for any triangle with sides of lengths a, b, and c, and opposite angles A, B, and C, respectively:
⇒ c² = a² + b² - 2ab × cos(C),
To solve for an angle, we would rearrange the equation to find the cosine of the angle,
⇒ Cos(C) = (a² + b² - c²)/(2ab),
Then, we will take the inverse cosine of both sides of the equation to find the value of the angle,
⇒ C = cos⁻¹((a² + b² - c²)/(2ab)),
This helps us to find the measure of angle C, depending on the units used in the original triangle sides.
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The given question is incomplete, the complete question is
When solving an oblique triangle given three sides, use the _____ form of the Law of cosines to solve for an angle.
hat kind of cups for measuring are sometimes made from glass or something transparent so the markings on the side with different measurements are visible? a tare measuring cups b maillard measuring cups c standard measuring cups d graduated measuring cups
The graduated measuring cups are made from something glass or something transparent to markings on the side with different measurements are visible. Option (d) is the correct answer.
The kind of cups for measuring that are sometimes made from glass or something transparent so the markings on the side with different measurements are visible are called graduated measuring cups. These cups are designed to make measuring precise amounts of liquid or dry ingredients easy, and the transparent material allows you to see the measurement markings clearly. Graduated measuring cups are commonly used in baking and cooking, as well as in scientific research and other applications where accurate measurements are essential.
Therefore, Graduated measuring cups is the answer.
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Solve for y in the two equations below using substitution.
3x - 9y = 9
-2x - 2y = 8
Answer:
C
Step-by-step explanation:
3x - 9y = 9 → (1)
- 2x +2y = 8 ( subtract 2y from both sides )
- 2x = - 2y + 8 ( divide through by - 2 )
x = y - 4
substitute x = y - 4 into (1)
3(y - 4) - 9y = 9
3y - 12 - 9y = 9
- 6y - 12 = 9 ( add 12 to both sides )
- 6y = 21 ( divide both sides by - 6 )
y = [tex]\frac{21}{-6}[/tex] = - [tex]\frac{7}{2}[/tex]
A frog catches insects for their lunch. The frog likes to eat flies and mosquitoes in a certain ratio, which the diagram shows.
A tape diagram with 2 tapes of unequal lengths. The first tape has 3 equal parts. A curved bracket above the first tape is labeled Flies. The second tape has 7 equal parts of the same size as in the first tape. A curved bracket below the second tape is labeled Mosquitoes.
A tape diagram with 2 tapes of unequal lengths. The first tape has 3 equal parts. A curved bracket above the first tape is labeled Flies. The second tape has 7 equal parts of the same size as in the first tape. A curved bracket below the second tape is labeled Mosquitoes.
The table shows the number of flies and the number of mosquitoes that the frog eats for two lunches.
Based on the ratio, complete the missing values in the table.
Day Flies Mosquitoes
Monday
15
1515
Tuesday
14
1414
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show all steps nd i will make u brainlist
Step-by-step explanation:
Again, using similar triangle ratios
7.2 m is to 2.4 m
as AB is to 12.0 m
7.2 / 2.4 = AB/12.0 Multiply both sides of the equation by 12
12 * 7.2 / 2.4 = AB = 36.0 meters
you are thinking of combining designer whey and muscle milk to obtain a 7-day supply that provides exactly 262 grams of protein and 54 grams of carbohydrates. how many servings of each supplement should you combine in order to meet your requirements?
We need approximately 12 servings of Designer Whey and 2 servings of Muscle Milk to obtain a 7-day supply that provides exactly 262 grams of protein and 54 grams of carbohydrates.
Let x be the number of servings of Designer Whey and y be the number of servings of Muscle Milk needed to obtain a 7-day supply that provides exactly 262 grams of protein and 54 grams of carbohydrates.
From the information given, we know that each serving of Designer Whey provides 20 grams of protein and 3 grams of carbohydrates, and each serving of Muscle Milk provides 16 grams of protein and 9 grams of carbohydrates.
Therefore, we can set up the following system of equations:
20x + 16y = 262
3x + 9y = 54
To solve for x and y, we can use any method of solving a system of equations. For example, we can use substitution:
From the second equation, we can solve for x in terms of y:
x = (54 - 9y)/3 = 18 - 3y
Substituting this into the first equation, we get:
20(18 - 3y) + 16y = 262
Simplifying, we get:
80y = 182
Solving for y, we get:
y = 2.275
Substituting this into the equation x = 18 - 3y, we get:
x = 12.175
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An investment of $600 is made into an account that earns 6. 5% annual simple interest for 15
years. Assuming no other deposits or withdrawals are made, what will be the balance in the
account?
According to the investment, after 15 years, the balance in the account would be $1185.
To calculate the final balance after 15 years, we can use the formula for simple interest:
Simple Interest = Principal x Interest Rate x Time
In this case, the principal is $600, the interest rate is 6.5%, and the time is 15 years.
Simple Interest = $600 x 0.065 x 15
Simple Interest = $585
So the investment of $600 earns $585 in simple interest over 15 years. To find the final balance, we add the interest earned to the initial investment:
Final Balance = Principal + Simple Interest
Final Balance = $600 + $585
Final Balance = $1185
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John buys new baseball equipment for $2000. The purchase made is with a credit card that has a 19% APR. John makes a $150 payment monthly. How many months will it take John to pay off the balance?
It will take John approximately 17 months to pay off the balance.
What is simple interest?
Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.
Assuming that John does not use the credit card for any other purchases and that the credit card company uses a simple interest calculation method, we can use the following steps to calculate the number of months it will take John to pay off the balance:
Calculate the monthly interest rate by dividing the annual percentage rate (APR) by 12:
Monthly interest rate = 19% / 12 = 0.01583
Calculate the monthly finance charge by multiplying the outstanding balance by the monthly interest rate:
Monthly finance charge = $2000 x 0.01583 = $31.66
Subtract the monthly payment from the monthly finance charge to get the amount that will be applied to the outstanding balance:
Payment applied to balance = $150 - $31.66 = $118.34
Divide the outstanding balance by the payment applied to balance to get the number of months it will take to pay off the balance:
Number of months to pay off balance = $2000 / $118.34 = 16.9
(rounded up to the nearest whole number)
Therefore, it will take John approximately 17 months to pay off the balance.
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