We have the following:
we calculate the new values
[tex]\begin{gathered} 246-3=243 \\ 387-3=384 \\ 297-3=294 \\ 276-3=273 \\ 338-3=335 \\ 281-3=278 \\ 242-3=239 \end{gathered}[/tex]now, we calculate the mean
[tex]\frac{243+384+294+273+335+278+239}{7}=292.3[/tex]the standard deviation of the data set is:
[tex]\begin{gathered} s=\sqrt[]{\frac{\Sigma(x_i)^2}{n}-\bar{x}^2} \\ s=\sqrt[]{\frac{243^2+384^2+294^2+273^2+335^2+278^2+239^2}{7}-292.3^2} \\ s=\sqrt[]{\frac{614100}{7}-85439.3} \\ s=47.9 \end{gathered}[/tex]The answer is the option C. 47.9
kelly sold 35 books at £1.40 each. 28 bracelets at £1.50 each. some badges at 80p each. She got a total of £115. Work out how many badges Kelly sold
Answer:
the answer is 30 !! :)
Step-by-step explanation:
115-(35*1.40)-(28*1.50)= 24
24/.8 = 30
Identify the reason that would be used to justify step 2 in the proof below.
Converse of the Consecutive Interior Angle Theorem
Corresponding Angles Postulate
Alternate Exterior Angle Theorem
Vertical Angles Theorem
The reason that would be used to justify step 2 in the proof below is: Corresponding Angles Postulate (Option B).
What is A corresponding Angle Postulate?Congruence and likeness tests in geometry require comparing corresponding sides and angles of polygons. In these tests, each side and angle of one polygon are matched with a side or angle of the second polygon, with care taken to maintain the order of adjacency.
A mathematical proof is an inductive explanation for a mathematical assertion that demonstrates that the provided assumptions logically ensure the conclusion.
There are several methods for demonstrating anything. There are three of them:
direct proof, proof by contradiction, and proof by induction. We'll go through each of these proofs and when and how they're utilized.Learn more about Corresponding Angles:
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To solve 1-variable equations and inequalities, we use additive inverses and/or multiplicative inverses to isolate the variable.
Options:
True
False
The multiplicative inverse of 0.1
Options:
1/10
-10
10
-0.1
The multiplicative inverse of 2/6 is 3.
Options:
True
False
The additive inverse of 80.
Options:
80
1/80
-80
8
The multiplicative inverse of 13.
Options:
-13
0.13
1/13
13/1
1 of 5 questions saved
Answer:
false 1/10 false 80 13/1
33 percent of 300
And 24 percent of 300 PLSS
the first one is 99 and the second one is 72
Hope this helped
Answer:
33% of 300 is about 99, and 24% of 300 is about 72
Step-by-step explanation:
Hope this helps.
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Use the following variables for #'s
(3-5):
f= -6 g= 7 h=9
4) 5-f
The value of the expression 5 - f is 11.
An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.
A variable is a symbol and placeholder for any mathematical object. In particular, a variable may represent a vector, a number, a function, a matrix, the argument of a function, a set, or an element of a set.
We have the value of the following variables,
f = - 6,
g = 7 and,
h = 9
Now consider the expression 5 - f,
Substituting the value of f in the expression we get,
5 - f = 5 - ( - 6 )
5 - f = 5 + 6
5 - f = 11
Therefore, the value of 5 - f is 11.
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4 × logx -(2 × logv + 3 × logy)
Simplifying the given logarithmic equation, the expression is obtained as log([tex]\frac{x^{4} }{v^{2} y^{3} }[/tex]).
The objective is to find the resultant expression for 4 × logx -(2 × logv + 3 × logy)
According to logarithmic results,
The product of an integer constant and a logarithm term of a number is equivalent to the logarithm of the number raised to the power of the particular integer constant.
That is, b × log(a) = log([tex]a^{b}[/tex])
Hence, 4 × log(x) = log([tex]x^{4}[/tex]),
2 × log(v) = log([tex]v^{2}[/tex])
and, 3 × log(y) = log([tex]y^{3}[/tex])
So, the equation can be rewritten as log([tex]x^{4}[/tex]) - (log([tex]v^{2}[/tex]) + log([tex]y^{3}[/tex]))
The sum of the logarithms of two numbers is equivalent to the logarithm of their product.
That is, log(a) + log(b) = log(a×b)
Hence, log([tex]v^{2}[/tex]) + log([tex]y^{3}[/tex]) = log([tex]v^{2}[/tex][tex]y^{3}[/tex])
So, the equation can be rewritten as log([tex]x^{4}[/tex]) - log([tex]v^{2}[/tex][tex]y^{3}[/tex])
The difference in the logarithms of two numbers is equivalent to the logarithm of their fraction.
That is, log(a) - log(b) = log(a÷b)
Hence, log([tex]x^{4}[/tex]) - log([tex]v^{2}[/tex][tex]y^{3}[/tex]) = log([tex]\frac{x^{4} }{v^{2} y^{3} }[/tex])
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A 25-foot ladder is leaning against the side of a building and is positioned such that the base of the ladder is 15 feet from the base of the building. How far above the ground is the point where the ladder touches the building?
Let us use a diagram to demonstrate the event .
From the diagram we are asked to find the value h. The value h can be found using pythagora's theorem.
[tex]\begin{gathered} h^2=25^2-15^2 \\ h^2=625-225 \\ h^2=400 \\ \text{square root both sides} \\ h=\sqrt[]{400} \\ h=20\text{ ft} \end{gathered}[/tex]x>-4
except the greater than symbol has a line under. Graph each inequality and write the solution set using both set-builder notation and interval notation.
The solution set of the inequality x ≥ - 4 using set builder notation and interval notation is {x | x ∈ Z, - 4 ≤ x ≤ ∞ } and [ - 4, ∞ ) respectively.
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.
A set can be represented by its elements or the properties that each of its members must meet can be described using set-builder notation.
Interval Notation: A set of real numbers known as an interval contains all real numbers that fall inside any two of the set's numbers.
Consider the inequality,
x ≥ - 4
In the number line, the value of x is equal to and greater than - 4 increasing to infinity.
Therefore,
The solution set using the set builder notation is:
{x | x ∈ Z, - 4 ≤ x ≤ ∞ }
The solution set of the inequality using the interval notation is:
[ - 4, ∞ )
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Wendy has a negative balance in her checking account. Her balance is -$13.
If Wendy deposits $60, then buys 4 notebooks for 2 dollars each, how much money would Wendy have in her account after the purchases?
Quadrilateral PQRS is dilated by a scale factor of to
form quadrilateral P'Q'R'S'. What is the measure of side
QR?
Answer: 24 units
Step-by-step explanation:
If you are multiplying a shape by a scale factor, the dimensions are also multiplied by the scale factor.
QR= x
Q'R'= (1/2)(X)
12=(1/2)(X)
(2)12= 1/2x(2)
24=X
If you're multiplying QR by 1/2 you would get 12. 12 is a half of QR. Therefore, QR is 24.
He following cards are dealt to three people at random, so that everyone gets the same number of cards. what is the probability that everyone gets a red card?
The probability that everyone will get a red card is 0.5.
What probability exactly is?Probability is a branch of mathematics that deals with numerical representations of the probability that an event will happen or that a statement is true.The probability of an event is a number between 0 and 1, with 0 roughly denoting impossibility and 1 denoting certainty.The probability is the likelihood that something will happen, to put it simply.The likelihood or likelihood of various outcomes can be discussed when we don't know how an event will turn out.The study of events that fit into a probability distribution is known as statistics.So, the probability that everyone gets a red card:
Probability formula: P(E) = Favourable events/Total number of eventsAs cards are distributed to 3 people, divide both favorable events and total events by 3.Then,
P(E) = Favourable events/Total number of eventsP(E) = (26/3)/(52/3)P(E) = 26/3 × 3/52P(E) = 26/52P(E) = 0.5Therefore, the probability that everyone will get a red card is 0.5.
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The unit cost, in dollars, to produce bins of cat food is $18 and the fixed cost is $30000. The price-demandfunction, in dollars per bin, is p(x) = 568 - 2xFind the cost function.C(x) =Find the revenue function.R(x) = Find the profit function.P(x) = 568 – 2xAt what quantity is the smallest break-even point?
The smallest breakeven point attains at 75.
A formula or equation that describes the behavior of specific sources of income when it is plotted on a graph is called a revenue function.
The cost function calculates the lowest cost of producing a specific level of output at some fixed factor prices.
A relationship that demonstrates the difference that results from subtracting the cost function from the revenue function is called a profit function.
Here, the Price/Demand Function is presented as
P(x) = 568 - 2x
Which means that when there is a demand for x units of cat food, the price will be set at 568 - x for each unit.
Let's now consider the revenue resulting from this demand, or x units.
Revenue = Demand * Price per unit
R(x) = x * (568-2x)
= 568x – 〖2x〗^2
Now let us Evaluate the Cost Function
Cost = Variable cost + Fixed Cost
Variable cost = cost per unit * number of units
= 18*x
= 318
Fixed Cost = 30000 as given in the problem.
Hence
Cost Function C(x) = 18x + 30000
Now let’s find the Profit Function
Profit = Revenue - Cost
P(x) = R(x) - C(x)
568x - 〖2x〗^2 – (18x + 30000)
568x -〖 2x〗^2 – 18x + 30000
-〖 2x〗^2 + 550x - 30000
Finding the quantity at which we reach break-even point is the next step.
At break-even point, we understand this Profit = 0
Hence P(x) = 0
-〖 2x〗^2 - 550x + 30000 = 0
Dividing both sides by -2 we get
X2 – 275x + 15000 = 0
Now we have to find the factors of 15000 whose sum is 275.
Now we have to solve the above quadratic equation using splitting the middle term method.
X2 – 275x + 15000 = 0
X2 – 200x - 75x + 15000 =0
X(x-200) - 75 (x-200) = 0
(x-75) (x-200) = 0
Either (x - 75) = 0 or (x-200) = 0, therefore
(x-75) = 0 = x =75
(x-200) = 0 x =200
Smallest of which is 75.
As a result, 75 units are required to reach the break-even point.
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- 1/4 x (- 4/3) as a fracction
Answer: the answer is x/3
Step-by-step explanation:
I need some help... I am very confused.
The base of the triangle shown is 12 millimeters
What is an equation?An equation is an expression that can be used to show the relationship between numbers and variables.
Given that:
A is the area of the triangleb is the base of the triangleh is the heightb = 2A/h
For the triangle, A = 36 mm², h = 6 mm
Substituting:
b = 2(36)/6
Simplifying gives:
b = 12 mm
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Cheyenne is playing a board game. Her score was −175 at the start of her turn, and at the end of her turn her score was −325. What was the change in Cheyenne’s score from the start of her turn to the end of her turn? How did you determine your answer?
Enter the correct answers in the boxes.
points
I subtracted
from
.
Answer: -150
Step-by-step explanation:
To find the change in the score we need to find the difference between the two scores. To do this easily, we can add 175 to -325.
-325 + 175 = -150
By doing this we get the difference and the answer to the question.
Answer: -150
Step-by-step explanation: I subtracted from -325.
Samuel wants to save enough money to buy a new couch, but isn’t sure which bank’s savings account he should sign up for. Wells Fargo has a yearly interest rate of 6%. Chase has an interest rate of 0.5% compounded monthly. If Samuel deposits $3000 at the beginning of the year and makes no additional deposits or withdrawals, which bank would have the higher balance after one year?
wells Fargo would have a higher balance after one year
Step-by-step explanation:
wells Fargo would have a higher balance after one year
y = 2x - 3
I need to find the y-int and the slope for the graph
Answer:
y-int = (0,-3)
slope = 2
Step-by-step explanation:
The slope is found by the number before x. If its just x then the slope is 1. The y-int is found by the number all the way at the end. In this case its -3. So the y-int is (0,-3)
Answer:
Step-by-step explanation:
y
=
2
x
+
3
The slope-intercept form is
y
=
m
x
+
b
, where
m
is the slope and
b
is the y-intercept.
y
=
m
x
+
b
Find the values of
m
and
b
using the form
y
=
m
x
+
b
.
m
=
2
b
=
3
The slope of the line is the value of
m
, and the y-intercept is the value of
b
.
Slope:
2
y-intercept:
(
0
,
3
)
Please help me solve this algebra problem on my homework
We need to determine a few characteristics of the following linear equation:
[tex]y-5=-\frac{1}{2}(x-2)[/tex]The first step we need to take is to isolate the "y" variable on the left side.
[tex]\begin{gathered} y=\frac{-1}{2}(x-2)+5 \\ y=\frac{-1}{2}\cdot x+1+5 \\ y=\frac{-1}{2}\cdot x+6 \end{gathered}[/tex]Now we need to analyze this function and provide the necessary characteristics.
First is the Domain. The Domain of a function is the group of all numbers that can be used as an input (x), in this case the Domain is the whole Real group.
Second is the Range, which is the group of numbers that can be the output of the function (y), for this case we also have the whole Real group as Range.
Then we need to find the "Zero". Which is the value at which the function crosses the x-axis, to calculate it we must make "y=0" and solve for x.
[tex]\begin{gathered} 0=\frac{-x}{2}+6 \\ \frac{x}{2}=6 \\ x=12 \end{gathered}[/tex]The zero is equal to 12.
The slope of the function is the number multiplying "x", in this case it is -1/2.
The slope is negative, decrescent.
To find the value of f(8), we need to replace x by 8 and solve for y.
[tex]\begin{gathered} f(8)=\frac{-8}{2}+6 \\ f(8)=-4+6=2 \end{gathered}[/tex]The value of f(8) = 2.
To determine the value of x where f(x) is equal to 5, we need to replace f(x) by 5 and solve for x.
[tex]\begin{gathered} 5=\frac{-x}{2}+6 \\ \frac{-x}{2}=5-6 \\ \frac{-x}{2}=-1 \\ -x=-2 \\ x=2 \end{gathered}[/tex]The value of x for which f(x) is equal to 5, is 2.
Now we need to graph the equation, for that we have to use two of the points we found before, we will use (8, 2) and (2,5). We need to mark these points at the coordinate plane and draw a line between them:
When you write the equivalent algebraic expression f8 for f² f6, why do you add the exponents?
The equivalent algebraic expression f⁸ for f² f⁶ is because product of power law states to add the exponents.
What is algebraic expression?In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.).
Algebraic expression types:
Number ExpressionExpression of a BinomialExpression of a Polynomiallet,
RHS = f² f⁶
RHS = f²⁺⁶
RHS = f⁸ = LHS
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Classify the TriangleThe answer choices are : equilateral, scalene or isosceles
The three sides and three angles of the given triangle are given to be equal.
An equilateral triangle has three sides of equal length and three equal angles.
So, the given triangle is equilateral.
The prime factor tree for 6 is shown
below.
Complete the prime factor tree for 15 and
use it to help you find the lowest common
multiple (LCM) of 6 and 15.
2
6
3
15
Answer: 3
Step-by-step explanation:
6 - 2, 3
15- 3, 5
Select the correct answer.
Which expression is equivalent to 2x² . √16x, if x>0?
The expression is equivalent to option A, 8x[tex]\sqrt[6]{x}[/tex].
Option A is correct
How do expressions work?Variables, constants, and mathematical operators make up an expression, which is a mathematical statement.
How can one locate equivalent expressions?Add any like terms together, combining x-terms with x-terms and constants with constants, on either side of the equation. The x-term is typically put before constants when arranging the terms in the same sequence. It is said that two expressions are equivalent if every phrase in them is the same.
The expression is 2[tex]\sqrt[3]{x^2}[/tex]
The expression can be simplified as
= 2.4[tex]x^{2/3}[/tex][tex]x^{1/2}[/tex]
= 8[tex]x^{7/6}[/tex]
= 8x[tex]x^{1/6}[/tex]
= 8x[tex]\sqrt[6]{x}[/tex]
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Calculate rates (backwards)
If pipe costs $30, at $6 / m, how many metres would you get?
Answer:
5 m
Step-by-step explanation:
$30 divided by $6 a m
30/6=5 m
6.
Select all the conditions for which it is possible to construct a triangle.
A. A triangle with angle measures 60 degrees, 80 degrees, and 40 degrees
B. A triangle with side lengths 4 cm, 5 cm, and 9 cm
C. A triangle with side lengths 4 cm, 4 cm, and 7 cm
D. A triangle with side lengths 5 cm and 12 cm and a 90 degree angle.
E. A triangle with 2 right angles.
Help idmeadiitly
Carla has already written 10 pages of a novel. She plans to write 15 additional pages per month until she is finished. Write and solve a linear equation to find the total number of pages written at 5 months.
(show as much details upon answering)
Answer:
linear equations;15m+10=w
15 pages written for every month for 5 months plus the 10 pages she has already written is equal to the total number of pages written in 5 months m=number months written in this case it is 5 months.
w=number of pages written in 5 months 15(5)+10=w
75+10=w
85 Pages written=w
will have written 85 Pages in 5 months
i need help with the first question in this picture
Initial price of the TV = $899
discount in % = 25 % = 0.25
First, we will find the amount discounted:
[tex]\begin{gathered} Amount\text{ discounted = }25\text{ \% }\times\text{ 899} \\ Amount\text{ discounted = }0.25\text{ }\times\text{ 899} \\ Amount\text{ discounted = \$224.75} \end{gathered}[/tex]sales price after the discount was removed:
[tex]\begin{gathered} sales\text{ price = }initial\text{ price - amount discounted} \\ sales\text{ price = 899 - 224.75} \\ sales\text{ price before }Tax\text{ = \$674.25} \end{gathered}[/tex][tex]\begin{gathered} \text{Sales tax = 8.125 \% = 0.08125} \\ \text{Tax = sales price before tax }\times\text{ sales tax} \\ \text{Tax = 674.25 }\times\text{ 0.08125} \\ \text{Tax = \$}54.78 \end{gathered}[/tex][tex]\begin{gathered} \text{Sales price with tax = sales price before tax + Tax} \\ \text{Sales price with tax = 674.25 + 54.78} \\ \text{Sales price with tax = \$729.03} \end{gathered}[/tex]The scatter plot shows the number of roses (x) and daisies (y) a florist sold at a flower
show. How many roses did the florist who sold 125 daisies sell?
100
200
80
170
The number of roses that the florist sold who sold 125 daisies is; 200
How to Interpret Scatter Plots?Scatter plots are the graphs that present the relationship between two variables in a data-set.
From the given scatter plots, we see that the x and y axes are marked in intervals of 50 like 0, 50, 100, 150, 200,...e.t.c
Now, from the scatter plot, we see a couple of coordinates and we are told that the x-axis shows the number of roses sold at a flower show while the y-axis shows the number of daises sold at the flower show.
Now, from the scatter plot, we see that when the number of daises sold is 125, we can trace that the number of roses sold was 200 roses.
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Two angles form a linear pair. The measure of one angle is z and the measure of the other angle is 2.4 times z plus 10°. Find the measure of each angle.
Two angles form a linear pair.
so, the sum of the angles are 180
the measure of the angles are z and (2.4 * z + 10)
so,
z + (2.4 * z + 10) = 180
solve for z
so,
z + 2.4 * z + 10 = 180
3.4 z = 180 - 10
3.4 * z = 170
divide both sides by 3.4
so, z = 170/3.4 = 50
so, the angles are 50 and 130
Solve with substitution method: 3x+5y=10 and 9y+3x=15
The value of x and y using the substitution method are 5/4 and 5/4.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
Two equations:
3x + 5y = 10 _____(1)
9y + 3x = 15 ______(2)
From (1) we get,
3x = 10 - 5y
x = (10 - 5y) / 3 ______(3)
Putting (3) in (2) we get,
9y + 3 x [(10 - 5y) / 3] = 15
9y + 10 - 5y = 15
4y = 15 - 10
4y = 5
y = 5/4
Putting y = 5/4 in (3) we get,
x = (10 - 5 x 5/4) / 3
x = (10 - 25/4) / 3
x = (40 - 25) / (4 x 3)
x = 15 / 12
x = 3x5 / 3x4
x = 5/4
Thus,
The value of x and y using the substitution method are 5/4 and 5/4.
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