The value of f(13.8) = 636.8
What is a function?function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
For example f(y) = 5y+7
Similar the function given ;
f(x)=46x+2
when x = 13.8
f(13.8) = 46(13.8) + 2
= 636.8
therefore the value of the function f(x)=46x+2 at x = 13.8 is 636.8
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The value of the function f(x) = 46x + 2 at x = 13.8 is 636.8.
What is function?
Function is a rule that assigns a unique output value to each input value. A function is typically denoted by a letter such as f(x), where x is the input variable and f(x) is the output value.
To evaluate the function f(x) = 46x + 2 at x = 13.8, we simply substitute x = 13.8 into the expression for f(x):
f(13.8) = 46(13.8) + 2
Simplifying this expression, we get:
f(13.8) = 634.8 + 2
f(13.8) = 636.8
Therefore, the value of the function f(x) = 46x + 2 at x = 13.8 is 636.8.
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I'LL MARK THE BRAINLIEST!
Carlos uses a food delivery service to order lunch. He paid $13.75 for lunch, which included the cost of the food and a delivery fee, which is 10% of cost of the food.
What was the cost of Carlos' lunch before the delivery fee?
Answer: 3
Step-by-step exp lanation:
divided
Toby is buying milk. He needs 3 liters. A half-liter of costs $2.43. A 250 -milliliter container of costs $1.42. What should Toby buy so he gets 3 liters at the lowest price?
Answer:
6 half-liter
Step-by-step explanation:
To get 3 liters of milk, Toby has two options:
Option 1: Buy 6 half-liter containers
The cost of one half-liter container is $2.43, so the cost of six such containers is 6 x $2.43 = $14.58.
Option 2: Buy 12 250-milliliter containers
The cost of one 250-milliliter container is $1.42, which is equivalent to $5.68 per liter (since 1 liter is equal to 4 250-milliliter containers). Therefore, the cost of 3 liters (which is equivalent to 12 250-milliliter containers) is 12 x $1.42 = $17.04.
Therefore, Toby should buy 6 half-liter containers as it is the cheaper option.
In AOPQ, p = 6.3 cm, m/O=149° and m/P=29°. Find the length of q, to the nearest
10th of a centimeter.
The length of q is approximately is 0.4 cm.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
To solve for the length of q in triangle AOPQ, we can use the law of sines, which states:
a/sin A = b/sin B = c/sin C
where a, b, and c are the lengths of the sides opposite the angles A, B, and C, respectively.
In triangle AOPQ, we know that:
Side p = 6.3 cm (opposite angle P)
Angle O = 149° (opposite side q)
Angle P = 29° (opposite side p)
Let use angle sum property of triangles to find the measure of angle Q:
Angle Q = 180° - Angle O - Angle P
Angle Q = 180° - 149° - 29°
Angle Q = 2°
Now we can use the law of sines to solve for the length of q:
q/sin Q = p/sin P
q/sin(2°) = 6.3/sin(29°)
q = sin(2°) × (6.3/sin(29°))
q=0.034 × (6.3/0.484)
q = 0.442 cm
Therefore, the length of q is approximately is 0.4 cm.
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A triangle has two sides of length 7 and 10. What is the largest possible whole-number length for the third side?
Answer:
The largest possible whole-number length for the third side of a triangle with two sides of length 7 and 10 is 13. This is due to the fact that the two given lengths must be added together, and then subtracted from the third side in order to create a valid triangle. Therefore, the third side must be at least 13 in order to create a triangle.
Find the standard form of the eclipse with end points of Major Axis (2,2) & (8,2) and minor axis (5,3) & (5,1)
Answer:
Step-by-step explanation:
Pour trouver la forme standard de l'équation d'une ellipse à partir des extrémités des grands axes et des petits axes, nous pouvons utiliser les formules suivantes:
Le centre de l'ellipse est le point (h, k), où h est la moyenne des coordonnées x des extrémités des grands axes et k est la moyenne des coordonnées y des extrémités des petits axes. Donc,
h = (2 + 8) / 2 = 5
k = (3 + 1) / 2 = 2
Donc, le centre de l'ellipse est (5, 2).
La distance a est la moitié de la longueur du grand axe, donc
a = (8 - 2) / 2 = 3
La distance b est la moitié de la longueur du petit axe, donc
b = (3 - 1) / 2 = 1
Maintenant, nous pouvons utiliser ces valeurs pour écrire l'équation de l'ellipse en forme standard:
(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1
En substituant les valeurs trouvées précédemment, nous avons:
(x - 5)^2 / 3^2 + (y - 2)^2 / 1^2 = 1
Ce qui est la forme standard de l'équation de l'ellipse.
This is about Linear equations, please help.
Answer:
Step-by-step explanation:
line a is 5ft
Can someone check my wrong answers for another excercise?
The answers to the probability problem have been stated below
How to solve the probabilityThe mean of the distribution would be 29
The standard deviation would be 8.7/√40 = 1.38
If the sample was larger, the mean would stay the same, the standard error would decrease.
3. The corresponding z score with
43.8 - 29 / 8.7
= 1.70
b. z = (43.8-29)/(8.7/√40) = 8.94
14.8 /1.38
= 10.7
c) the fisherman is more likely to catch one fish
d) z = (30.8-29)/(8.7/√40) = 1.26
= 1.8 / 1.38
= 1.304
e) He is more likely to catch 40 fishes.
4.a) Proportion in the middle = 0.95
Proportion on left and right side of normal curve = (1-0.95)/2
= 0.025
Z score at p = 0.025 using excel = NORM.S.INV(0.025) = 1.96
X1 = µ - z*σ = 29 - (1.96)*8.7
= 11.948
X2 = µ + z*σ = 29 + (1.96)*8.7
= 46.052
between 11.948 and 46.052
b)
Proportion in the middle = 0.95
Proportion on left and right side of normal curve = (1-0.95)/2 = 0.025
NORM.S.INV(0.025) = 1.96
x1 = 29 - (1.96)*8.7/√40
= 29 - 2.698
= 26.30
x2 = 29 + 2.698
= 31.698
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Fill in the blanks:
1) if tan x=0, then tan(-x)= ___
2) If sin x= 0.3, then sin(-x)= ____
3) If cos x= 0.3, then cos(-x)= ____
4) If tan x= -2, the tan (pi+x)= ____
The values are :
tan(-x) = 0sin(-x) = -0.3cos(-x) =0.3tan(pie + x) = 2What is trigonometry ?
Trigonometry is a branch of mathematics that deals with the relationships and properties of angles and the trigonometric functions such as sine, cosine, and tangent. It is based on the study of the geometric properties of triangles and is used extensively in fields such as physics, engineering, architecture, and astronomy.
In trigonometry, the relationships between the sides and angles of a triangle are expressed using the six trigonometric functions: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). These functions describe the ratios between the sides of a right triangle, where one angle is 90 degrees. Trigonometric functions can also be defined for any angle, not just those in a right triangle, using the unit circle or other methods.
Trigonometry has many practical applications, such as in navigation, surveying, and the design of structures such as bridges and buildings. It is also used extensively in science and engineering, particularly in fields such as physics, mechanics, and electromagnetics.
If tan x = 0, then tan(-x) = 0.
The tangent function is an odd function, which means that tan(-x) = -tan(x). However, since tan x = 0, this means that -tan(x) = 0 as well. Therefore, tan(-x) = 0.
If sin x = 0.3, then sin(-x) = -0.3.
The sine function is an odd function, which means that sin(-x) = -sin(x). Since sin x = 0.3, this means that -sin(x) = -0.3. Therefore, sin(-x) = -0.3.
If cos x = 0.3, then cos(-x) = 0.3.
The cosine function is an even function, which means that cos(-x) = cos(x). Since cos x = 0.3, this means that cos(-x) = 0.3 as well.
If tan x = -2, then tan(pi+x) = tan(pi + atan(-2)) = tan(2.0344 + pi) = -2.
To find tan(pi + x), we need to use the identity tan(a + pi) = -tan(a). In this case, a = atan(-2), which is the inverse tangent of -2. Using a calculator or a table, we can find that a is approximately 2.0344 radians. Therefore, tan(pi + x) = -tan(2.0344) = -(-2) = 2.
Hence, values are
tan(-x) = 0sin(-x) = -0.3cos(-x) =0.3tan(pie + x) = 2To know more about trigonometry visit :
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Please Answer Quick!!
Therefore , the solution of the given problem of graph comes out to be
option c is correct it shows an association of the distribution of different mode of transportation among the same age of group.
What is graph ?Academics use graphs to visually represent or chart happenings or quantities in a logical manner. The interaction between a number of objects is frequently represented by a graph point. A graph is a non-linear storage structure made up of nodes, also known as vertices, and edges. The vertices, sometimes referred to as nodes, should be joined together with glue. Vertex numbers in this graph are 1, 2, 3, or 5, while edge numbers are 1, 2, 1, 3, 2, 4, etc. (2.5). (3.5). (4.5). (4.5). (4.5).
Here,
Given : A graph having choices of adult , child , teen and senior mode of transportation ,
In different age the mode of transportation preferred by among the same ages .
Thus ,
it shows an association of the distribution of different mode of transportation among the same age of group.
So , option c is the correct answer.
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Describe the type and degree of association in the scatter plot and what it means in terms of the time the player spent practicing and the number of points he scored in the game.
As the time a basketball player practices increases, the number of points scored in a game decreases with a weak linear association.
As the time a basketball player practices increases, the number of points scored in a game decreases with a weak nonlinear association.
As the time a basketball player practices increases, the number of points scored in a game increases with a strong linear association.
As the time a basketball player practices increases, the number of points scored in a game increases with a strong nonlinear association.
The correct statement regarding the association of the time the player spent practicing and the number of points he scored in the game is given as follows:
As the time a basketball player practices increases, the number of points scored in a game increases with a strong nonlinear association.
How to describe the association?The more the player practices, the better he/she performs, that is, the more points are scored, hence the number of points increases as the number of hours practiced increase.
However, there reaches a certain threshold where the player is as good as possible, hence the points tend to stabilize, meaning that there is a nonlinear association between the variables.
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Need help solving problem
The equations that determine the cost of each hamburger and each fries is 4x + 5y = 20 and 10x + 7y = 41.20
What is an equation?
An equation is an expression that shows the relationship between two numbers and variables using mathematical operations like addition, subtraction, multiplication, exponents
Let x represent the cost of each hamburger and y represent the cost of each fries.
She purchased 4 hamburgers and 5 fries for $20.00, hence:
4x + 5y = 20 (1)
She purchased 10 hamburgers and 7 fries for $41.20, hence:
10x + 7y = 41.20 (2)
From both equations, solving simultaneously:
x = 3; y = 1.6
The cost of each hamburger is $3 while the cost of each fries is $1.6
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the figure shows the graph of a function.
f(x)=
The domain are the possible input while the range are the possible output of a function.
(a) The domain = [-√2, √2], the range = [0, 2]
(b) The domain = [-1, 1], the range = [0, 1]
(c) The domain = [-1, 1], the range = [0, -1]
(d) The domain = [0, 2], the range = [0, 1]
(e) The domain = [-(2 + √2), (√2 - 2)], the range = [0, 2]
Reasons:
The given functions can be expressed by the equation; (-x + 1)·(x + 1) = -x² + 1
Therefore, we have;
(a) y = f(x) + 1 = -x² + 1 + 1 = -x² + 2
The x-intercept of the above function are, x = √2, and x = -√2
Which gives;
The domain = [-√2, √2]
The range = [0, 2]
(b) y = 3·f(x) = 3 × (-x² + 1) = -3·x² + 3
At the x–intercepts, we have;
-3·x² + 3 = 0
x = ±1
The domain = [-1, 1]
The maximum value of y is given at x = 0, therefore;
= -3 × 0² + 3 = 3
The range = [0, 1]
(c) y = -f(x) = -(-x² + 1) = x² - 1
At the x–intercepts, x² - 1 = 0
x = ± 1
The domain = [-1, 1]
The minimum value of y is given at x = 0, which is y = -1
The range = [0, -1]
(d) y = f(x - 1) = -(x - 1)² + 1 = -x² + 2·x
At the x–intercepts, we have; -x² + 2·x = 0, which gives;
(-x + 2)·x = 0
Which gives, x = 0, or x = 2
The domain = [0, 2]
The maximum value of y is given when x = -b/(2·a) = -2/(2×(-1)) = 1
y = f(1) = -1² + 2×1 = 1
Therefore;
The range = [0, 1]
(e) y = f(x + 2) + 1 = (-(x + 2)² + 1) + 1 = -x² - 4·x - 2
At the x–intercepts, we have; -x² - 4·x - 2 = 0, which gives;
x = -(2 + √2) or x = x = √2 - 2
The domain = [-(2 + √2), (√2 - 2)]
The maximum value of y is given when x = -4/(2)) = -2
Which gives;
-(-2)² - 4·(-2) - 2 = 2
The range = [0, 2]
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An open cardboard box is 20 cm long, 12 cm
wide and 8 cm deep (Fig. 14.9). Calculate
the total area of cardboard in the box.
The Total Surface area of cardboard in the box is 992 cm².
What is Total Surface Area?The region that includes the base(s) and the curved portion is referred to as the total surface area. It is the overall area that the object's surface occupies. The total area of a shape with a curved base and surface is equal to the sum of the two areas.
Given:
length= 20 cm
width = 12 cm
height= 8 cm
So, the TSA of Cuboid
= 2(lw + wh + lh)
=2( 20 x 12 + 12 x 8 + 8 x 20)
=2( 240 + 96 + 160)
= 2(496)
= 992 cm²
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The following sample observations were randomly selected. (Round intermediate calculations and final answers to 2 decimal places.) x: 4 5 6 6 9 y: 3 6 5 7 7 pictureClick here for the Excel Data File 1. The regression equation is y : ______ + _____ x 2. When x is 8 this gives y: _____
The regression equation is y = 1.56 + 0.69⋅x².
What is an Equations?Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.
x: 4 5 6 6 9
y: 3 6 5 7 7
Σx=28, ΣΥ=27, Σxy = 163, Σx' = 174
a = ΣΥ ΣΑΣΑ Σ ΑΥ = 27-174-28-163 = 1.558
b= 5.163 28 27 /5-174-(28)2 = 0.686
y = 1.558 + 0.686x²
Hence, The regression equation is y = 1.56 + 0.69⋅x².
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A certain market has both an express checkout line and a superexpress checkout line. Let X1 denote the number of customers in line at the express checkout at a particular time of day, and let X2 denote the number of customers in line at the superexpress checkout at the same time. Suppose the joint pmf of X1 and X2 is as given in the accompanying table. (a) What is P(X1 = 1, X2 = 1), that is, the probability that there is exactly one customer in each line? P(X1 = 1, X2 = 1) = (b) What is P(X1 = X2), that is, the probability that the numbers of customers in the two lines are identical? P(X1 = X2) = (c) Let A denote the event that there are at least two more customers In one line than in the other line. Express A in terms of X1 and X2. Calculate the probability of this event. P(A) = (d) What is the probability that the total number of customers in the two lines is exactly four? At least four? P(exactly four) = P(at least four) =
Required probability P(A)= 0.46. The problem here is a Joint Probability Distribution exercise. See the answers and explanation below.
What is Joint Probability Distribution?Joint Probability Distribution can be simply described as the likelihood of two events (variables) occurring at the same time. These two events are commonly referred to as event A and event B, and their formal names are: p (A and B).
here, we have,
What is the solution to the questions?
A - The likelihood that each line has exactly one customer: The probability relates to the associated row and column.
X₁ = 1 and X₂ = 1
P (X₁ = 1, X₂ =1) = 0.15
B - The sum of the diagonal elements of the joint pmf indicates the likelihood that the amount of clients in both lines is the same:
P(X₁ = X₂) =) p(0,0) + p (1,1) + p(2, 2) + p(3,3
= 0.08 + 0.15 + 0.10 + 0.07
= 0.4
Hence,
C - Let A represent the situation in which there are at least two more clients than the other line: The following are examples of variable combinations:
X₂ =0 ; X₁ = 2,3, 4
X₂ =1 ; X₁ = 3, 4
X₂ =2 ; X₁ = 0, 4
X₂ =3 ; X₁ = 0, 1
The probability is thus computed as follows:
P (A) = p(1, 3) + p (2,2) + p(2, 3) + p(3,1) + p(3,2) + p(3,3) + p(4,0) + p(4,1) + p(4,2) + p(4,3)
= 0.04 + 0.10 +0.06 + 0.03 + 0.04+ 0.07 + 0.00 + 0.01 + 0.05 + 0.06
= 0.46
Hence , P(A)= 0.46
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g five cards are dealt from a standard deck of playing cards.what is the probability that the you dealt 5 cards from same suit.
Answer:
the probability of being dealt 5 cards from the same suit is approximately 0.00198, or about 0.198%.
Step-by-step explanation:
The total number of ways to choose 5 cards from a deck of 52 cards is given by the combination formula:
C(52, 5) = 52! / (5! (52 - 5)!) = 2,598,960
Now, we need to count the number of ways of choosing 5 cards from the same suit. There are 4 suits in a deck of cards (hearts, diamonds, clubs, and spades), so we need to count the number of ways to choose 5 cards from each of these suits and add them up.
For each suit, the number of ways of choosing 5 cards from that suit is given by the combination formula:
C(13, 5) = 13! / (5! (13 - 5)!) = 1,287
So the total number of ways of choosing 5 cards from the same suit is:
4 * 1,287 = 5,148
Therefore, the probability of getting 5 cards from the same suit is:
5,148 / 2,598,960 ≈ 0.00198
So the probability of being dealt 5 cards from the same suit is approximately 0.00198, or about 0.198%.
What is the future value of $2,500 deposited for one year earning a 14 percent interest rate annually
Answer: $2,850
Step-by-step explanation:
Hope this helped you. Brainliest if possible! :D
I also answered first! (Please don't copy my answer for anyone that answer this question!) :D
Use equivalent ratios to find the unknown vaule step by step 7/11= 28/44
Answer:
7:11
28:44
Step-by-step explanation:
Multiply both sides by 4.
A study was conducted showing the relationship between the average maintenance cost and the age of a car in years.
Number of observations: 13
Least Squares | Standard | T
Parameter | Estimate | Error | Statistic| P-Value
Intercept | 54.7757 | 54.87 | 0.998282 | 0.3396
Slope | 120.689 | 11.8442 | 10.1898 | 0.0000
a) What is the formula for the regression function based on the output above (Write your equation in the context of question)?
b) Interpret the slope of the regression equation (In the context of question)?
c) Construct an 95% interval to predict the maintenance cost for a car that is 7 years old?
d) Based on this analysis, can we conclude that a relationship exists between the maintenance cost and the age of the car in years? What is the null and alternative hypothesis? Justify your answer using three steps process.
Step-by-step explanation:
classic Christian from x x + 4 + 8 is equal to 21 what is the answer
Write a polynomial f(x) that satisfies the given conditions. Polynomial of lowest degree with zeros of -1/4 (multiplicity 2) and 2/3 (multiplicity 1) and with f(0)=2.
f(x)=?
Answer:
Step-by-step explanation:
To obtain a polynomial of lowest degree with the given zeros and leading coefficient, we can use the fact that if a polynomial has a root of multiplicity m, then the factor (x - r)^m appears in the polynomial. Therefore, we can write:
f(x) = A(x + 1/4)^2(x - 2/3)
where A is a constant that we need to determine to satisfy the condition f(0) = 2.
To find A, we substitute x = 0 into f(x) and set the result equal to 2:
f(0) = A(0 + 1/4)^2(0 - 2/3) = -A/27 = 2
Solving for A, we find that A = -54.
Therefore, the polynomial f(x) is:
f(x) = -54(x + 1/4)^2(x - 2/3)
Raj encoded a secret phrase using matrix multiplication. Using A = 1, B = 2, C = 3, and so on, he multiplied the clear
25
c-1² ₂]
text code for each letter by the matrix C=
85
38 46
location of spaces after you decode the text.
representing the encoded text is
to get a matrix that represents the encoded text. The matrix
111 135 111 95
101 153
55 45 41 44 64
4
What is the secret phrase? Determine the
The solution is, the answer is: The color is blue (D).
What is matrix?In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.
here, we have,
Our matrix C is the encoder. Let X be our secret message and let B be our encoded message. Therefore the relationship between the 3 can be represented as:
CX = B
So we want to solve for X (our secret message). So using matrix algebra:
X = C^-1*B
where C^-1 is the inverse of C.
C^-1 = | 3 -2 |
|4 -3 |
So we take C^-1 and multiply it by matrix B to get X. Matrix B is already given to us. So just multiply those two. I used a calculator to get:
X = | 20 8 5 3 15 12 15 |
| 18 9 19 2 12 21 5 |
And since A = 1, B = 2, C = 3, etc....
We decode our message and it says:
X = | T H E C O L O |
| R I S B L U E |
So the answer is: The color is blue (D)
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Answer: D
Step-by-step explanation:
Solve for m.
Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
8m + 95 < -87m+5
The values of m for the given inequality should be in the interval
(-∞, -18/19).
What is meant by inequality?
In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using the inequality symbols. Typically, we use the "not equal" sign to indicate that two values are not equal. However several inequalities are utilised to compare the numbers, whether it is less than or higher than.
Given the inequality,
8m + 95 < -87m +5
We are asked to solve the inequality.
this means we have to find the value of m.
8m + 95 < -87m +5
8m + 87m < 5 - 95
95m < -90
m < -90/95
m< -18/19
Therefore the values of m for the given inequality should be in the interval (-∞, -18/19).
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An electrician purchases some outdoor lighting for a customer at a wholesale price of $950.40. The customer would
have paid the retail price of $1320. What was the wholesale discount?
(Type a whole number or an exact decimal of the decimal does not terminate round to one decimal place)
Answer:
the wholesale discount is 28%.
Step-by-step explanation:
To find the wholesale discount, we need to calculate the difference between the retail price and the wholesale price as a percentage of the retail price. We can use the following formula:
Wholesale discount = ((Retail price - Wholesale price) / Retail price) x 100%
Substituting the given values into the formula, we get:
Wholesale discount = ((1320 - 950.40) / 1320) x 100%
Wholesale discount = (369.60 / 1320) x 100%
Wholesale discount = 0.28 x 100%
Therefore, the wholesale discount is 28%.
To write the answer as a whole number or an exact decimal, we can multiply 0.28 by 100 to get:
Wholesale discount = 28%
So the wholesale discount is 28%.
Simply expression
Please show steps
The simplified expression for this problem is given as follows:
-3(x + y) = -3x - 3y.
What is the distributive property?With the application of the distributive property, the outer term multiplies each of the inner terms of the expression. If possible, these inner terms than can be added or subtracted combining the like terms.
For this problem, the outer term -3 multiplies both of the inner terms, x and y, hence:
-3x.-3y.Hence the simplified expression is defined as follows:
-3(x + y) = -3x - 3y.
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Can you help me find the point of intersection for the question in the picture attached?
Answer:
The ordered pair that is a solution is (2, 10)
Step-by-step explanation:
2x + 6 = 4x + 2 Subtract 2x from both sides
2x - 2x + 6 = 4x - 2x + 2
6 = 2x + 2 Subtract 2 from both sides
6 - 2 = 2x + 2 -2
4 = 2x Divide both sides by 2
2 = x
Substitute 2 for x in either of the two original equations.
y = 2x + 6
y = 2(2) + 6
y = 4 + 6
y = 10
The ordered pair that is a solution is (2, 10)
What is a placebo? Describe the placebo effect and how it can make experiments difficult to interpret. How can making an experiment single-blind or double-blind help?
What is a placebo?
A. A placebo refers to a specific member of a sample from which data are collected.
B. A placebo refers to any problem in the design or conduct of a statistical study that tends to favor certain results.
C. A placebo refers to a situation in which a patient improves simply because they believe they are receiving a useful treatment.
D. A placebo lacks the active ingredients of a treatment being tested in a study, but is identical in appearance to the treatment.
The placebo effect refers to an experiment where neither the participants nor the experimenters know who belongs to the treatment group and who belongs to the control group. As a result, it is impossible for the experiments to link certain effects to certain patients, which make the results difficult to interpret.
What is the placebo effect is an experimental study refers to the?
The placebo effect is a phenomenon where people report real improvement after taking a fake or nonexistent treatment, called a placebo. Because the placebo can't actually cure any condition, any beneficial effects reported are due to a person's belief or expectation that their condition is being treated.
Hence , The placebo effect refers to an experiment where neither the participants nor the experimenters know who belongs to the treatment group and who belongs to the control group. As a result, it is impossible for the experiments to link certain effects to certain patients, which make the results difficult to interpret.
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C. A placebo refers to a situation in which a patient improves simply because they believe they are receiving a useful treatment.
Ann had a total of 285 red and blue beads. She used 45 red beads and 40% of the blue bead. After that,the ratio of the number of red beads to blue beads Ann had was 1:3.
[a] what fraction of blue beads did Ann use
[b] How many beads did Ann have in the end
(a) Ann used 4/10 blue beads i.e. 80.
(b) Ann had 160 beads in the end.
The solution has been obtained by using arithmetic operations.
What are arithmetic operations?
According to mathematicians, any real number may be expressed using the four basic operations, also referred to as "arithmetic operations." The four mathematical operations that produce quotient, product, sum, and difference, respectively, are divide, multiply, add, and subtract.
(a) We are given that Ann had a total of 285 red and blue beads, and she used 45 red beads and 40% of the blue bead.
Let the red beads be x and blue beads be y
So, we get
x + y = 285
x = 285 - y
After using the beads, we get another equation as
⇒(x - 45) / (y - 0.4y) = 1/3
⇒(285 - y - 45) / (y - 0.4y) = 1/3
⇒(240 - y) / (0.6y) = 1/3
⇒720 - 3y = 0.6y
⇒720 = 3.6y
⇒y = 200
So, x = 85
Blue beads used = 40% of 200 = 80
(b) Since, Ann has used 80 blue beads and 45 red beads, so
Beads in the end = 285 - 45 - 80 = 160
Hence, Ann had 160 beads in the end.
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visitors to a park can take four different paths that lead to a lake. path w is 51 meters shorter than plath y. path y is 116 meters longer than path x. path z is 85 meters longer than path w. which path is the longest?
Path z is the longest path that leads to the lake.
Describe Algebraic Expression?An algebraic expression is a combination of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. It is a mathematical phrase that can contain one or more terms separated by mathematical operators.
For example, 3x + 4y - 2z is an algebraic expression that contains three terms: 3x, 4y, and -2z. Each term is made up of a coefficient and a variable, where the coefficient is the numerical value that multiplies the variable.
In algebraic expressions, variables are used to represent unknown values, and the expression can be evaluated by substituting known values for the variables. For instance, if x = 2, y = 3, and z = 1, then the expression 3x + 4y - 2z can be evaluated as 3(2) + 4(3) - 2(1) = 12.
Algebraic expressions can also include exponentiation, roots, and other advanced mathematical operations. They are widely used in mathematics and other fields, such as physics and engineering, to represent relationships between variables and to model real-world situations.
Let's start by assigning variables to each path:
Let x be the length of path x (in meters).
Then path y is 116 meters longer than path x, so its length is x + 116.
Path w is 51 meters shorter than path y, so its length is x + 116 - 51 = x + 65.
Path z is 85 meters longer than path w, so its length is x + 65 + 85 = x + 150.
To find the longest path, we need to compare the lengths of all four paths. We can do this by looking at the expressions we just derived:
Path x has length x.
Path y has length x + 116.
Path w has length x + 65.
Path z has length x + 150.
Since all four paths have a common component of x, the lengths of the paths can be compared by comparing the values of the expressions that add to x. We can see that x + 150 is the largest expression, which means that path z is the longest.
Therefore, path z is the longest path that leads to the lake.
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A 15-foot pole is leaning against a tree. The bottom of the pole is 8 feet away from the bottom of the tree. Approximately how high up the tree does the top of the pole reach? responses 1. 9 feet 1. 9 feet 7. 0 feet 7. 0 feet 12. 7 feet 12. 7 feet 17. 0 feet.
If A 15-foot pole is leaning against a tree and bottom of the pole is 8 feet away from the bottom of the tree. then the top of the pole reaches option (C) 12.7 feet
We can use the Pythagorean theorem to solve this problem. Let's call the height we're trying to find "x". Then, we have a right triangle where the pole is the hypotenuse, the distance from the bottom of the pole to the tree is one leg, and the height we're trying to find is the other leg. Using the Pythagorean theorem, we have:
15^2 = 8^2 + x^2
225 = 64 + x^2
Group the like terms
161 = x^2
x ≈ 12.7 feet
Therefore, the correct option is (c) 12.7 feet
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An ellipse has a vertex at (–5, 0), a co-vertex at (0, 4), and a center at the origin. Which is the equation of the ellipse in standard form?
The equation of the ellipse in standard form is 16x² + 25y² = 400.
What is the standard form of the equation of an ellipse?The standard form of the equation of an ellipse centered at the origin is:
x²/a² + y²/b² = 1
where a is the distance from the center to a vertex along the x-axis, and b is the distance from the center to a co-vertex along the y-axis.
In this case, we know that the center of the ellipse is at (0,0), a vertex is at (-5,0), and a co-vertex is at (0,4).
The distance from the center to a vertex along the x-axis is the absolute value of the x-coordinate of the vertex, which is 5. So, a = 5.
The distance from the center to a co-vertex along the y-axis is the absolute value of the y-coordinate of the co-vertex, which is also 4.
So, b = 4.
Substituting these values into the standard form equation, we get:
(x²/5²) + (y²/4²) = 1
Simplifying and multiplying by 5² and 4², we get the standard form equation of the ellipse:
16x² + 25y² = 400
Therefore, the equation of the ellipse in standard form is 16x² + 25y² = 400.
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