Suppose,
[tex]y=(x-3)^2-47 ----------------(1)\\y=17 -------------------------(2)[/tex]
Put [tex]y=17[/tex] in place of x in the first equation:
[tex]17=(x-3)^2-47[/tex]
To both sides, add [tex]47[/tex]:
[tex]64=(x-3)^2[/tex]
Add the square roots of both sides together:
[tex]8=x-3[/tex] or [tex]-8=x-3[/tex]
To each sides, add [tex]3[/tex]:
[tex]x=11 or -5[/tex]
As a result, the following are the equations' solutions:[tex]x=-5, y=17 or x=11, y=17[/tex].
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How many yards are equivalent to two miles
Answer:
2 miles = 3,520 yards
Step-by-step explanation:
You multiply the length value by 1,760.
3520 yards is equivalent to 2 miles.
Hope this helped! Have a nice day. :)−9, −4, 1, 6, .. aremetric or geometric
A 12-sided die is rolled. The set of equally likely outcomes is (1,2,3,4,5,6,7,8,9,10,11,12). Find the probability of rolling a 7.
←
The probability of rolling a 7 is
(Type an integer or a simplified fraction.)
Ans4863
Step-by-step explanation:
find the probability that a randomly selected Point within the circle falls in the red shaded triangle.
P = [?]
ENTER AS A DECIMAL ROUNDED TO THE NEAREST HUNDREDTH.
After considering all the given data we reach the conclusion that the probability of randomly selecting a point that falls in the red shaded triangle is 0.30.
To evaluate the probability that a randomly selected point within the circle falls in the red shaded triangle, we have to calculate the ratio of the area of the red shaded triangle to the area of the circle.
Let us consider that the radius of the circle is 4 cm. The area of the circle is
πr² = 3.14 × 5²
= 78.5 cm².
The concerned area of red shaded triangle is
(1/2) ×(3 + 3) × (8)
= 1/2 × 6 × 8
= 24 cm².
Therefore, the probability of randomly placing the point on the red part of the triangle is
P = Area of Triangle / Area of Circle = 24 / 78.5
≈ 0.30
So, P = 0.30 rounded to the nearest hundredth.
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A popular Dilbert cartoon strip (popular among statisticians, anyway) shows an allegedly “random” number generator produces the sequence 999999 with the accompanying comment, “That’s the problem with randomness: you can never be sure.” Most people would agree that 999999 seems less “random” than, say, 703928, but in what sense is that true? Imagine we randomly generate a six-digit number, i.e., we make six draws with replacement from the digits 0 through 9. (a) What is the probability of generating 999999?
(b) What is the probability of generating 703928?
(c) What is the probability of generating a sequence of six identical digits?
(d) What is the probability of generating a sequence with no identical digits? (Comparing the answers to (c) and (d) gives some sense of why some sequences feel intuitively more random than others
.)
(e) Here's a real challenge: what is the probability of generating a sequence with exactly one repeated digit?
(a) the probability of generating 999999 is [tex](1/10)^6[/tex]
(b) the probability of generating 703928 is [tex](1/10)^6[/tex]
(c) the probability of generating a sequence of six identical digits is [tex](1/10)^6[/tex]
(d) the probability of generating a sequence with no identical digits is 15,120/1,000,000.
(e) the probability of generating a sequence with exactly one repeated digit is[tex]10 * 6 * (9^4).[/tex]
What is probability?Probability is described as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
The probability of generating a sequence with no identical digits is calculated as (10/10) * (9/10) * (8/10) * (7/10) * (6/10) * (5/10) = 15,120/1,000,000.
We start by choosing the digit to be repeated, which can be done in 10 ways and the next thing is to choose the position of the repeated digit, and can be done in 6 ways.
We then see that remaining four positions can be filled out with any of the other 9 digits and this can also be done in [tex]9^4[/tex] ways.
So we can conclude that the number of possibilities in this case is [tex]10 * 6 * 9^4.[/tex]
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please solve to the nearest 10th
The value of the sides are;
c = 35. 5, y = 32. 2, <H = 65 degrees
Option D
How to determine the valueWe have that the ratios of the trigonometric identities are;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
From the information given, we have that;
Using sine identity
sin 25 = 15/c
cross multiply the values, we get;
c = 35. 5
Then, using tan identity;
tan 25 = 15/y
cross multiply
y = 32. 2
Sum of angles in a triangle is equal to 180 degrees.
Then, we have that;
90 + 25 + <H = 180
collect the terms
<H = 65 degrees
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Select the graph for the solution of the open sentence. Click until the correct graph appears. |x| + 3 > 3
The correct graph of the inequality ( |x| + 3 > 3) is attached accordingly.
Here is how the above was solvedRecall that the absolute value (or modulus) of a real number x is its non-negative value regardless of its sign. For example, 5 has an absolute value of 5, and 5 has an absolute value of 5.
A number's absolute value can be conceived of as its distance from zero along the real number line.
So, given |x| + 3 > 3
Add minus three to both sides
|x| + 3 + (-3) > 3 + (-3)
|x| > 0
Thus, the absolute value of x is
x > 0 or x < -0
put in the form of inequality, we have
x > 0 or x < 0
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Help pls! ( Don’t mind this text)
The value of the expression 10 ÷ 40 using the long division method will be 0.25.
The expression is given below.
10 ÷ 40
Division means the separation of something into different parts, sharing of something among different people, places, etc.
The division is given below by the long division method. Then
40 ) 100 ( 0.25
- 80
200
- 200
0
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An earthquake with a rating of 7.8 is
known to be a great earthquake that can
cause damage that extends several
hundred kilometers.
The value of x when the Richter scale rating is 7.9, rounded to the nearest whole number, is approximately 79,432,823.
The formula relating the Richter scale rating (r) and the intensity ratio (x) is r = log(x). To find the value of x when r is 7.9, we can rearrange the formula and solve for x,
x = 10ʳ
Substituting r=7.9 into the formula, we get,
[tex]x = log((10)^{7.9} )[/tex]
Using a calculator, we get,
x ≈ 79432823.09
Rounding this to the nearest whole number, we get,
x ≈ 79432823
Therefore, the value of x when the Richter scale rating is 7.9, rounded to the nearest whole number, is approximately 79,432,823.
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Complete question - What is the value of x when the Richter scale rating is 7.9 round your answer to the nearest
r=log x
r=rating of the earthquakes size on the Richter scale
x=ratio of earthquake intensity to a minimum level of intensity
It takes 14 hours for a tap with a flow of 18 litres per minute to fill a reservoir with water. How long will it take if the flow is reduced to 7 litres per minute? I need formulas
If the flow rate of the tap is reduced to 7 litres per minute, it would take 36 hours to fill the reservoir.
Let's use the formula:
time = volume/flow rate
where volume is the volume of the reservoir and flow rate is the flow rate of the tap.
Let V be the volume of the reservoir.
With a flow of 18 litres per minute, we have:
14 hours = V / 18 L/min
Solving for V, we get:
V = 14 hours x 18 L/min = 252 L
Now, let's find the time it takes to fill the same reservoir with a flow of 7 litres per minute:
time = V / 7 L/min
Substituting V with 252 L, we get:
time = 252 L / 7 L/min = 36 hours
Therefore, it will take 36 hours to fill the reservoir with a flow rate of 7 litres per minute.
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trig worksheet questions
The missing sides are;
1) √296 (2) √68 (3) 2√10 (4) 21 (5) 15√3 (6) 14√2
What is the right triangle?A right triangle is a triangle that has one angle equal to 90 degrees, which is also known as a right angle.
1) Using the Pythagoras theorem;
[tex]x^2 = 14^2 + 10^2[/tex]
x = √296
2) [tex]x^2 = 18^2 - 16^2[/tex]
x = √68
3) Tan 45 = x/2√10
x = 1 * 2√10
x = 2√10
4) Cos 30 = x/14√3
x = 14√3 * √3/2
x = 21
5) Sin 60 = x/30
x = 30 * √3/2
x = 15√3
6) Cos 45 = x/28
x = 28 * √2/2
x = 14√2
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The revenue R
from the sale of x
cameras is given by R=24x−x2.
The cost C
of producing x
cameras is given by C=30+13x.
How many cameras must be produced and sold in order to break even? If there is more than one break-even point, separate the answers with commas.
In order to break even, either 5 cameras or 6 cameras must be produced and sold.
Understanding Revenue and Break-even pointAt break-even point, revenue (R) equal is set to equal the cost (C)
Given that:
R = 24x - x².
C = 30 + 13x.
where
R is revenue and
C is the cost
Setting R equal to C:
24x - x² = 30 + 13x
Rearranging the equation:
x² - 11x + 30 = 0
Now, we can solve this quadratic equation to find the break-even point(s).
Factoring the quadratic equation:
(x - 6)(x - 5) = 0
Setting each factor equal to zero:
x - 6 = 0 ==> x = 6
x - 5 = 0 ==> x = 5
Therefore, the break-even point occurs when x = 6 or x = 5.
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Exponent
T-Table
Coincident (Consistent
Dependent)
Systems of Equations
Inconsistent
Consistent Independent
1.
2.
3.
4.
5.
6.
A set of two or more equations
with the same variables.
A system of linear equations with
EXACTLY ONE solution.
A system of linear equations with
INFINITELY MANY solutions.
A system of equations with NO
solution.
A number representing how many
times the Base number should be
multiplied by itself.
A chart of the different values for
an equation or graph.
A set of two or more equations with the same variables.
A system of linear equations with EXACTLY ONE solution.
A system of linear equations with INFINITELY MANY solutions.
A system of equations with NO solution.
A number representing how many times the Base number should be multiplied by itself.
A chart of the different values for an equation or graph.
Systems of Equations:
A set of two or more equations with the same variables.
These equations are solved simultaneously to find the values of the variables.
Consistent Independent:
A system of linear equations with EXACTLY ONE solution.
This means that the lines represented by the equations intersect at a single point.
Consistent Dependent (Coincident):
A system of linear equations with INFINITELY MANY solutions.
In this case, the equations represent the same line or overlapping lines, and every point on the line is a solution.
Inconsistent:
A system of equations with NO solution.
This occurs when the lines represented by the equations are parallel and never intersect.
Exponent:
A number representing how many times the base number should be multiplied by itself.
For example, in the expression[tex]2^3,[/tex] the exponent is 3, which means 2 should be multiplied by itself 3 times [tex](2 \times 2 \times 2 = 8).[/tex]
T-Table:
A chart of the different values for an equation or graph.
It typically includes two columns: one for the input values (usually x) and one for the corresponding output values (usually y).
T-tables are helpful for understanding the relationship between the variables in an equation and for plotting points on a graph.
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PLS HELP ASAP I WILL GIVE BRAINLIEST GEOMETRY
Answer: A. 32
Step-by-step explanation:
Rule: That if an angle is created on the end of circle The arc that it creates is 2 times the angle.
arc AX = 2 (<B)
arc AX = 2(56)
arc AX = 112
Rule: The angle of 2 secants = 1/2 (outer arc - inner arc)
<C = 1/2 (arc AB - arc AX)
<C = 1/2 ( 176 - 112)
<C = 1/2 (64)
<C = 32 >A
What do you know about the graphs of polynomials with positive end behavior compared to the graphs of polynomials with negative end behavior?
If "positive" end behavior:
1. The graph hits the x-axis
2. The arrows point in opposite directions
3. The arrows point in the same direction
4. The right arrow is up
5. The graph hits the y-axis
6. The right arrow is down
If "negative" end behavior:
1. The graph hits the x-axis
2. The right arrow is down
3. The graph hits the y-axis
4. The right arrow is up
5. The arrows point in the same direction
6. The arrows point in opposite directions
The correct statements are:
If "positive" end behaviour:
The arrows point in the same direction.
The right arrow is up.
The graph hits the y-axis.
If "negative" end behaviour:
The arrows point in opposite directions.
The right arrow is down.
The graph hits the X-axis.
In mathematics, a graph is a visual representation of a set of data, which consists of points, called vertices or nodes, and lines connecting them, called edges or arcs.
Graphs are often used to represent mathematical functions, data sets, or relationships between objects, and they can be used to model real-world phenomena.
Graphs can be drawn on a coordinate plane or in a more abstract form, and they can be used to analyze and understand complex systems and relationships.
The correct statements are:
If "positive" end behaviour:
The arrows point in the same direction.
The right arrow is up.
The graph hits the y-axis.
If "negative" end behaviour:
The arrows point in opposite directions.
The right arrow is down.
The graph hits the X-axis.
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Sam just bought a refrigerator for 1058. He paid 211.40 in a down payment and will pay the rest in 6 equal installments. How much does he need to pay for each installment?
The amount Sam needs to pay in each installment is $141.1
How much does he need to pay for each installment?From the question, we have the following parameters that can be used in our computation:
Cost of refrigerator = 1058
Down payment = 211.40
Number of equal installments = 6
Using the above as a guide, we have the following:
Each installment = (Cost of refrigerator - Down payment)/Number of equal installments
substitute the known values in the above equation, so, we have the following representation
Each installment = (1058 - 211.40)/6
Evaluate
Each installment = 141.1
Hence, the amount in each installment is $141.1
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Convert 1110100 base 2 to base 10
Step by step explanation
What is the length of C,D?
lengths:
a (-9,-12)
b (6,-12)
c (9,3)
d (-6,3)
Answer:
the length of C is 6, the length of D is 9,
Step-by-step explanation:
A cylinder has the height of 12 inches and radius of 7 inches what is the volume
Answer:
588π
Step-by-step explanation:
Volume of cylinder = π r ² h
= π (7)² (12)
= 588π
See photo how to use distributive property of multiplication to simplify the expression.
The simplest form of the expression by the use of the distributive property is;
[tex]12x^2 + 24x + 9[/tex]
What is the distributive property?In mathematics, the distributive property, which explains how multiplication interacts with addition or subtraction, is a fundamental concept. By allocating or multiplying a number or term to each term enclosed by a set of parenthesis, it enables you to simplify expressions.
The distributive property is frequently employed in algebraic expressions, equation simplification, and polynomial operations. By spreading out the multiplication over addition or subtraction, it aids in simplifying complex statements and makes calculations easier to understand.
We know that;
[tex]3(4x^2 + 8x + 3)\\12x^2 + 24x + 9[/tex]
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A box contains 12 transistors, 5 of which are defective. If 5 are selected at random, find the probability of the statements below.
a. All are defective
b. None are defective
Answer:
a. The probability that all 5 selected transistors are defective is 0.0024 or 0.24%.
To calculate this probability, we use the formula for the probability of the intersection of independent events:
P(all 5 defective) = P(defective) x P(defective) x P(defective) x P(defective) x P(defective)
where P(defective) = 5/12 for each transistor.
Plugging in the values, we get:
P(all 5 defective) = (5/12) x (5/12) x (5/12) x (5/12) x (5/12) = 0.0024
b. The probability that none of the selected transistors are defective is 0.163 or 16.3%.
To calculate this probability, we use the complement rule:
P(none defective) = 1 - P(at least one defective)
To calculate P(at least one defective), we can use the complement rule again:
P(at least one defective) = 1 - P(none defective)
So, we need to find P(none defective) first:
P(none defective) = P(not defective) x P(not defective) x P(not defective) x P(not defective) x P(not defective)
where P(not defective) = 7/12 for each transistor.
Plugging in the values, we get:
P(none defective) = (7/12) x (7/12) x (7/12) x (7/12) x (7/12) = 0.163
Then, we can find P(at least one defective):
P(at least one defective) = 1 - P(none defective) = 1 - 0.163 = 0.837
Finally, we can find P(none are defective) using the complement rule:
P(none defective) = 1 - P(at least one defective) = 1 - 0.837 = 0.163.
The following figure shows a cube. Which expression represents the surface area of the cube? Choose 1 answe B 6-10 5 5-5-5 25 + 25 + 25 + 25 + 25 + 25 5+5+5+5+5+5
The expression that represents the surface area of the cube is 25 + 25 + 25 + 25 + 25 + 25
Calculating the expression that represents the surface area of the cube?From the question, we have the following parameters that can be used in our computation:
The cube
The side length of the cube is
Side length = 5
The surface area of the cube is calculated as
SA = 6 * Side length²
So, we have
SA = 6 * 5²
Expand
SA = 6 * 25
Further expand
SA = 25 + 25 + 25 + 25 + 25 + 25
Hence, the expression that represents the surface area of the cube is 25 + 25 + 25 + 25 + 25 + 25
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Complete question
The following figure shows a cube. Which expression represents the surface area of the cube? Choose 1 answer
(a) 5 5 - 5 - 5
(b) 25 + 25 + 25 + 25 + 25 + 25
(c) 5 + 5 + 5 + 5 + 5 + 5
The figure is attached
What is the probability?
The true statements regarding the probability are:
It is likely that the bag has a black marbleIt is not unlikely that the bag has at least one pink marble (equivalently, it is likely that the bag has at least one pink marble)How to explain the probabilityBased on the given information, it is likely that the bag has at least one black marble (with a probability of 0.1). It is not certain or impossible, as the probability is not 0 or 1.
It is not certain or unlikely that the bag has at least one pink marble, as the probability is not 0 or 1. However, the probability of the bag having at least one pink marble is relatively high (0.79), so it is more likely than not that the bag has a pink marble.
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Which expression is equivalent to (2x – 5)(x + 9)?
Answer:
[tex]2x^{2} +13x-45[/tex]
Step-by-step explanation:
By using FOIL method.
you roll a aix sided die one time. what is the probability of not rolling a 1? write your answer as a percent rounded to the nearest whole number
The probability of not rolling a 1 when rolling a six-sided die is approximately 83%. This means that if you roll the die many times, you would expect to get a 1 about 1/6 of the time and not get a 1 about 5/6 of the time.
When you roll a six-sided die, there are six possible outcomes, each with equal probability. These outcomes are rolling a 1, 2, 3, 4, 5, or 6. If you want to find the probability of not rolling a 1, you can count the number of outcomes that are not 1 and divide by the total number of outcomes.
Since there are five outcomes that are not 1 (2, 3, 4, 5, and 6) and six total outcomes, the probability of not rolling a 1 is 5/6.
To write this as a percentage rounded to the nearest whole number, we can multiply by 100 and round to the nearest whole number:
5/6 × 100 ≈ 83%.
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In a recent poll, 130 people were asked if they liked dogs, and 65% said they did. Find the Margin of Error for this poll, at the 99% confidence level. Give your answer to four decimal places if possible.
We can say with 99% confidence that the true proportion of people who like dogs is within 8.44 percentage points of the sample proportion (65%).
To find the Margin of Error (MoE) for a poll, we need to use the formula:
MoE = [tex]z \times (\sqrt{(p \times q / n)} )[/tex]
where:
z is the z-score associated with the desired confidence level (99% confidence level corresponds to z = 2.576)
p is the proportion of people who said they liked dogs (0.65 in this case)
q is the complement of p (i.e., q = 1 - p)
n is the sample size (130 in this case)
Plugging in the values, we get:
MoE = [tex]2.576 \times (\sqrt{(0.65 \times 0.35 / 130)} )[/tex] ≈ 0.0844
Rounding to four decimal places, the Margin of Error is approximately 0.0844. Therefore, we can say with 99% confidence that the true proportion of people who like dogs is within 8.44 percentage points of the sample proportion (65%).
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Elia owns 2/5 of a cross fit training company. If the company is worth $157,000, what is the value of Elia's share of the
business. Round to the nearest dollar. Do not include a dollar sign in your answer.
Step-by-step explanation:
To calculate the value of Elia's share in the business, we need to multiply the company's worth by the fraction representing Elia's ownership.
Here's the calculation:
(2/5) * $157,000 = $62,800
So, the value of Elia's share in the business is approximately $62,800.
Answer:
His share is 62800 dollars
Step-by-step explanation:
You would divide 157000 by 5 and then multiply your answer by 2.
A bag of marbles has 12 green marbles, 5 red marbles, 8 blue marbles and 7 yellow marbles. What is the probability of randomly selecting a blue marble?
Probability = # of desired options / # of total options
Our desired option is blue and there are 9 blue marbles in the bag.
There are 32 total marbles (options) in the bag.
P(blue) = 9 / 32 = 0.28125 = 28.125%
Hope this helps!
Sm answer this asap 100 points.
At a recent football game of 8,450 in attendance, 150 people were asked what they prefer on a hot dog. The results are shown.
Ketchup Relish Chili
54 36 60
Based on the data in this sample, how many of the people in attendance would prefer ketchup on a hot dog?
4,225
3,380
3,127
3,042
An estimated 3,042 people in attendance would prefer relish on a hot dog.
Given that;
For a recent football game of 8,450 in attendance,
And, 150 people were asked for they prefer on a hot dog.
Now, For number of people in attendance would prefer relish on a hot dog, we can use the proportion of people in the sample who preferred relish:
By proportion we get;
x = (54/150) x 8450
x = 54 * 56 1/3
x = 3042
Therefore, An estimated 3,042 people in attendance would prefer relish on a hot dog.
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solve 6x²-42=0 with the exact values of x
Answer:
X=-√7 and √7
Step-by-step explanation:
To solve the equation 6x² - 42 = 0, we can begin by rearranging it to isolate the variable term:
6x² = 42
Then, we can divide both sides by 6:
x² = 7
To get the exact values of x, we need to take the square root of both sides:
x = ±√7
Therefore, the exact values of x are √7 and -√7.
