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Suppose you find a rock and measure that 12.5% of the original uranium-235 still remains it, while the other 87.5% has decayed into lead-207. about how old is the rock?
The measure of Angle E, the angle of elevation from point A to point B, is ( 3 x plus 1 ). The measure of Angle D, the angle of depression from point B to point A, is 2 ( x plus 8 ) Find the measure of each angle.
A sandbox has a volume of 648 cubic feet. what is the volume, in cubic yards, of the sandbox?
What is the simplest form of (8x2)3?
About 65 out of 300 students prefer walking instead of riding the bus to school. About what percent of the students prefer walking?
To find the percentage of students who prefer walking, divide the number of students who prefer walking by the total number of students and multiply by 100. In this case, 65 students prefer walking out of a total of 300 students.
Explanation:To find the percentage of students who prefer walking, you divide the number of students who prefer walking by the total number of students and then multiply by 100. In this case, 65 students prefer walking out of a total of 300 students.
So, you divide 65 by 300 and multiply by 100 to get the percentage.
Percentage of students who prefer walking = (65/300) * 100 = 21.67%
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Calculate the principal amount which earns $500 simple interest over 3 Years at a rate of 8% p.a round to the nearest cent
Final answer:
To find the principal amount that would earn $500 in simple interest over 3 years at an 8% annual rate, divide the interest by the product of the rate and period. The principal amount is $2083.33.
Explanation:
Calculating the Principal Amount from Simple Interest
To calculate the principal amount that earns $500 in simple interest over 3 years at a rate of 8% per annum, we can utilize the simple interest formula:
Interest = Principal × rate × time. Plugging in the known values, we get $500 = Principal × 0.08 × 3. This yields the equation $500 = Principal × 0.24.
To find the Principal, we divide $500 by 0.24, which gives us approximately $2083.33. Therefore, the initial principal amount is $2083.33.
What must be the value of x so that lines c and d are parallel lines cut by transversal p?
12
18
81
99
The value of x so that lines c and d are parallel lines cut by transversal p is 18.
What is a Transversal line?Transversal lines are lines that passes intersects the two lines on a plane in two different points.
Given are two parallel lines c and d.
p is the transversal line passing through c and d.
The angle at the exterior side of angle 81° is 180° - 81° = 99°
When two parallel lines are intersected by a transversal line, then the angles formed at the corresponding corners of the transversal with each of the parallel line is called corresponding angles.
(3x + 45)° and 99° are corresponding angles.
Corresponding angles are always equal.
(3x + 45)° = 99°
3x = 99 - 45
3x = 54
x = 54 / 3
x = 18
Hence the value of x is 18.
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Find measure B ???????
find the arithmetic mean an of an-1 = 3.9 and an+1 = 7.1
a. 11
b. 5.5
c. 3.7
d. 1.6
Answer:
Step-by-step explanation:
Alright, lets get started.
We are asked to find arithmetic mean of two terms given.
For finding arithmetic mean, we add up the values and divide the sum by the number of values.
Here we have given two numbers , below
[tex]a_{n-1}=3.9[/tex]
[tex]a_{n+1}=7.1[/tex]
So, mean of these two numbers will be = [tex]\frac{3.9+7.1}{2}[/tex]
So, mean of these two numbers will be = [tex]\frac{11}{2}=5.5[/tex]
So, arithmetic mean for given two numbers are 5.5 : Answer (b)
Hope it will help :)
b. 5.5
Step-by-step explanation:FOR LEARNING ONLY.. not necessary to read, but I hope it helps!
you start with:
[tex]a_{n-1}=3.9\\a_{n-1}=7.1[/tex]
arithmetic questions like this are like finding an average.
so you add the values while dividing by the total of values there are.
in this case:
[tex]\frac{7.1+3.9}{2}[/tex]
which is simplified to:
[tex]\frac{11}{2}[/tex]
then decimal:
[tex]5.5[/tex]
2x + 3y = 18 3x -4y > 16. Give the Domain and Range, Slope, and Y-intercept for each line. Graph each equation above on the graph below and show all work. Give the Domain and Range, Slope, and Y-intercept for each line. Explain in detail how you got each answer. 2x + 3y = 18 3x -4y > 16 Slope-Intercept Form: Slope-Intercept Form: Domain: Domain: Range: Range: Slope: Slope: Y-intercept: Y-intercept:
Using the completing-the-square method, rewrite f(x) = x2 + 10x + 7 in vertex form.
Using the completing-the-square method the vertex form of the function
f(x) = x² + 10x + 7 is f(x) = (x + 5)² - 18
The given function is:
f(x) = x² + 10x + 7
Comparing f(x) = x² + 10x + 7 with f(x) = ax² + bx + c
a = 1, b = 10, c = 7
(b/2)² = (10/2)² = 5²
Add and subtract 5² to the right hand side of the equation
f(x) = x² + 10x + 5² + 7 - 5²
f(x) = x² + 10x + 5² + 7 - 25
f(x) = x² + 10x + 5² - 18
f(x) = (x + 5)² - 18
f(x) = (x + 5)² - 18 is of the form f(x) = a(x - h)² + k which is the vertex form of a quadratic equation
Therefore, the vertex form of the function f(x) = x² + 10x + 7 is
f(x) = (x + 5)² - 18
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The data set represents a bimonthly progression of gasoline prices over the course of several months in an unspecified city. Use a graphing calculator to determine the quadratic regression equation for this data set. x 0 2 4 6 8 y 2.86 2.89 2.93 3.04 3.11 a. c. b. d.
Answer:
y = 0.0027*x^2 + 0.0111*x + 2.8574
Step-by-step explanation:
Using Excel the procedure is:
First, insert x and y values in a table format, as can be seen in the figure
Then, select data
Next, go to insert tab and inside charts options select scatter plot without any lines
Finally, select a point in the plot, right-click, add trend line, polynomial order 2 and check display equation option
witch property is used to simplify 3 C + 9 + 4 C equals 3 C + 4 C + 9
Which statement about this product is true?
0.44 ×(−5 3/4)
It is equal to 0 because 0.44 rounded to the nearest whole number is 0, and 0 times any number is 0.
It is equal to −5 3/4 because 4/4 is equal to 1, and 1 times any number equals that number.
It is greater than −3 because 0.44 × 5 3/4 is less than 1/2 × 6
It is less than −5 3/4 because multiplying by a number less than 1 gives a smaller number.
Answer:
It is greater than −3 because 0.44 × 5 3/4 is less than 1/2 × 6
Step-by-step explanation:
i guessed it and it was right so ye.
Construction is under way at an airport. This map shows where the construction is taking place. If Road A and Road B are parallel, what is the distance from P to Q on Road C?
In this budget, how much money is going toward optional expenses?
Answer:
$70
Step-by-step explanation:
Let's define the expenses first
Fixed expenses are those expenses that remain constant in all months like mortage payments, rents etc
Flexible expenses also called variable expense are expenses that are used for comfortable living like car maintenance o groceries.
Discretionary expenses are the expenses spent on non essential items like movie tickets, outings etc.
Savings are the expenses that are stored for future plans.
Hence, from the given pie chart the money going for optional expenses is $70 ..
please help attachment on please don't skip any parts
will get brainliest
Which of these sequence is an arithmetic sequence??
Answer:
a and c
Step-by-step explanation:
A sine function has the following key features:
Period = 12
Amplitude = 4
Midline: y = 1
y-intercept: (0, 1)
The function is not a reflection of its parent function over the x-axis.
How would this graph look??
Final answer:
A sine function with an amplitude of 4, period of 12, midline of y = 1, and y-intercept of (0, 1) would oscillate between 5 and -3, with a wave repeating every 12 units along the x-axis and starting upward from the y-intercept.
Explanation:
The graph of the sine function with the given properties will have the following characteristics:
The amplitude is 4, which means the function will oscillate 4 units above and below the midline.
The period is 12, indicating that it takes 12 units along the x-axis for the function to repeat its pattern.
The midline is y = 1, so the center of oscillation is not at the x-axis but is shifted upwards by 1 unit.
The y-intercept is (0, 1), which means the function starts at the midline.
Since the function is not a reflection over the x-axis, it means that it starts off going upwards from the midline.
Mapping these points, we can sketch the sine graph starting from the point (0, 1), curving up to a maximum of 5 (midline + amplitude), then down through the midline, reaching a minimum of -3 (midline - amplitude), and back to the midline at (12, 1), completing one full cycle.
A pack of cinnamon-scented pencils sells for $5.00. What is the sales tax rate if the total cost of the pencils is $5.20?
Final answer:
The sales tax rate is 4%.
Explanation:
To calculate the sales tax rate for the cinnamon-scented pencils, you first need to determine the amount of sales tax paid and then relate that to the original price of the pencils.
The total cost is given as $5.20, and the original price is $5.00.
The difference between these two amounts is the sales tax paid.
Subtract the original price from the total cost to find the sales tax amount:
$5.20 - $5.00 = $0.20.
Next, to find the sales tax rate, divide the sales tax amount by the original price and multiply by 100 to get a percentage:
Sales Tax Rate = ($0.20 / $5.00) x 100 = 4%
Therefore, the sales tax rate is 4%.
Graph this function f(x)=x^2-4x-5
Answer:
Step 1: a = 1, b = -4
Step 2: x = 2, f(2) = -9
Step 4: (5,0) and (-1,0)
Step 6: f(0) = -5
On the graph the points plotted are (-1,0) , (0,-5) , (2,-9) , and (5,0)
Picture included!
What is the slope of the line shown in the graph?
A.) -1
B.) -2
C.) 1/2
D.) 2
What is the initial value of the function represented by this graph? A coordinate grid is shown with x and y axes labeled from 0 to 7 at increments of 1. A straight line joins the ordered pair 0, 2 with the ordered pair 7, 5. 0 1 2 5 Question 7(Multiple Choice Worth 5 points)
Answer:
The initial value of the graph is 2. Third option is correct.
Step-by-step explanation:
It is given that A coordinate grid is shown with x and y axes labeled from 0 to 7 at increments of 1.
The line is passing through the points (0,2) and (7,5).
The point (0,2) is the y-intercept and graph labeled from 0 to 7, therefore 2 is the initial value.
Slope of line is
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{5-2}{7-0}=\frac{3}{7}[/tex]
The equation of line is
[tex]y=mx+b[/tex]
Where, m is slope and b is y-intercept. So the equation of given line is
[tex]y=\frac{3}{7}x+2[/tex]
At initial condition the value of x is 0. So, put x=0.
[tex]y=\frac{3}{7}(0)+2=2[/tex]
Therefore the initial value of the graph is 2. Option 3 is correct.
Answer:
Option 3 rd is correct
Initial value = 2
Step-by-step explanation:
A equation of line is given by:
[tex]y =mx+b[/tex] ....[1]
where
m is the slope of the line and b is the y-intercept or the initial value
As per the statement:
A coordinate grid is shown with x and y axes labeled from 0 to 7 at increments of 1.
It is also given that:
A straight line joins the ordered pair (0, 2) with the ordered pair (7, 5)
Calculate slope:
using formula:
[tex]\text{Slope (m)} = \frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the given ordered pairs we have;
[tex]\text{Slope (m)} = \frac{5-2}{7-0}=\frac{3}{7}[/tex]
y-intercept states that the graph which cut y-axis.
Substitute x =0 and solve for x:
we have given with the ordered pair (0, 2)
⇒y-intercept(b) = 2
Substitute the given values of m and b in [1]
[tex]y = \frac{3}{7}x+2[/tex]
The equation of straight line joins the ordered pair (0, 2) with the ordered pair (7, 5) is:
[tex]y = \frac{3}{7}x+2[/tex]
The initial value of the function represented by the given graph as shown below is: 2
A jar contains 17 orange,7 pink, and 4 black marbles. A marble is drawn at random.What is the probability that the marble is pink or orange
You enter 5 tickets into a raffle, in which a total of 65 tickets are entered. the announcer chooses two tickets from the pool of raffle tickets. what is the probability that you win both prizes from the raffle? write your answer as a fraction in simplest form.
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Find the simplified form of the expression. Give your answer in scientific notation.
(9 x 10 5)(6 x 10 -7)
A. 5.4 x 10 -34
B. 1.5 x 10 -1
C. 5.4 x 10 -1
D. 1.5 x 10 -34
Which TWO transformations could show that triangle A and triangle B are similar triangles?
Give an indirect proof of the following statement
If x^2 + x = 4, then x ≠ 2.
Please help :)
By assuming that x = 2 and substituting this into the original equation x^2 + x = 4, we arrive at a contradiction because 4 + 2 ≠ 4. Thus, we conclude through indirect proof that x cannot equal 2.
To give an indirect proof of the statement If x2 + x = 4, then x ≠ 2, we start by assuming the opposite of what we want to prove, which is that x = 2. Our goal is to show that this assumption leads to a contradiction.
Assume that x = 2. Substituting 2 for x in the original equation gives us (2)2 + 2 = 4 + 2 = 6, which is clearly not equal to 4. This contradicts the original equation x2 + x = 4. Since our assumption that x = 2 leads to a false statement, it follows that x cannot be 2, thereby proving the original statement by contradiction.
The method of assuming the negation and arriving at a contradiction shows that the original statement must be true according to the logical principle of indirect proof. Hence, if x2 + x = 4, then indeed x ≠ 2.