We can conclude that the difference between p1 and p2 is statistically significant at the 5% level of significance.
The confidence interval and significance test in part A both provide similar information. The significance test in part A tests if the difference between p1 and p2 is statistically significant, while the confidence interval provides an estimated range of values for the true difference between p1 and p2 with a certain degree of confidence (95% in this case).A confidence interval is a range of values that we believe will include a population parameter with a specified level of confidence.
It can be computed to estimate the population mean or the difference between two population means, such as p1 and p2.In contrast, a significance test assesses whether the difference between two population proportions is statistically significant.
The test calculates a p-value, which is the likelihood of obtaining the observed difference between two proportions, assuming the null hypothesis (that there is no difference between the two proportions) is true. A p-value less than the level of significance (usually 0.05) indicates that the difference between the two proportions is statistically significant, while a p-value greater than the level of significance indicates that the difference is not statistically significant.
Both the confidence interval and the significance test inform us about the difference between two population proportions. The confidence interval provides a range of plausible values for the difference, while the significance test tells us whether the difference is statistically significant or not. In this particular case, since the confidence interval does not contain zero,
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[50 POINTS] According to the Fundamental Theorem of Algebra, how many zeros does the function f(x) = 5x^6+2x^3−4x + 1
There are ________ Zeros
Answer:
6
Step-by-step explanation:
the number of zeroes is defined by the highest exponent of the variable in the functional expression.
How do you find the Surface area of a rectangular prism make it simple and correct answer gets brainliest
The rectangular prism's length, width, and height can also be labelled, and the surface area (SA) can be calculated using the formula:
SA = 2lw+2lh+2hw.
Explain about the rectangular prism?A face is just a flat surface in the geometric sense, and edges are formed where surfaces meet. Pyramids and prisms are both examples of polyhedra. A pyramid, however, is not a prism.
A polyhedron having two identical and parallel faces is referred to as a prism.A rectangular prism is one of the more typical shapes for prisms. One definition of a rectangular prism is a prism with rectangle-shaped bases. An other faces also were rectangles because the bases are rectangles.Method to find surface area:
A three-dimensional shape's surface area is the total area on its surface. Add these areas of each of the six rectangular sides of a cuboid to determine its surface area.Thus, the rectangular prism's length, width, and height can also be labelled, and the surface area (SA) can be calculated using the formula:
SA = 2lw+2lh+2hw.
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Surface Area = (width×length + height×length + height×width) × 2
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Please remember to revise this and make it in your own words if you want! I tried making this as simple as possible! I hope this helps you. -Doodle
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The track team jog for 3/8 of a mile in the morning in the afternoon they jog for 3/4 of a mile did they jog longer in the morning or the afternoon explain
The team jogged longer in the afternoon because they covered a distance of 6 eighths of a mile, which is greater than the 3 eighths of a mile they covered in the morning.
To compare the distance jogged in the morning and afternoon, we need to find the common unit for both. We can convert both fractions to have the same denominator by finding the least common multiple (LCM) of 8 and 4, which is 8.
So, in terms of eighths of a mile, the distance jogged in the morning is:
3/8 miles = 3 eighths of a mile
And the distance jogged in the afternoon is:
3/4 miles = 6 eighths of a mile (since 3/4 = 6/8)
Therefore, the team jogged longer in the afternoon because they covered a distance of 6 eighths of a mile, which is greater than the 3 eighths of a mile they covered in the morning.
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HELP PLEASE! the question in the photo below
The point estimate is 0.395 and the poll's margin of error is 0.015 or 1.5%.
What is confidence interval?A set of values that, with a particular level of confidence, is likely to include an unknown population parameter is known as a confidence interval. Confidence intervals are frequently utilized in statistics to calculate the actual value of a population parameter using sample statistics. When comparing a sample statistic to a population parameter that is hypothesised, we utilize confidence intervals to assess if the difference is statistically significant.
Given the interval of the result in the survey is [0.38, 0.41].
a. The point estimate is given as:
Point estimate = (0.38 + 0.41) / 2 = 0.395
b. The margin of error is given as:
Margin of error = (critical value) x (standard error)
Assuming a 95% confidence level:
Standard error = (maximum error) / (critical value)
Now,
Maximum error = (0.41 - 0.38) / 2 = 0.015
Margin of error = 1.96 x (0.015 / 1.96) = 0.015
Hence, the point estimate is 0.395 and the poll's margin of error is 0.015 or 1.5%.
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i dont understand, am i supposed to write like 10 x 10 x 10 or 10^3 (10 to the third power)?
Answer:
yes 10 to the 3rd power is 1,000 so try to go from there if more info is needed please comment "more info"
Step-by-step explanation:
I need helppppppppp please help me
The measures of angles in a rhombus are m∠2=130, m∠3=50 and m∠4=50.
What is angle measure?Angle measure is a term used in geometry to describe the size of an angle. It is usually expressed in degrees, which is a unit of measurement for angles. A degree is defined as 1/360th of a complete revolution around a circle.
According to question:In the rhombus, m∠1 =130
In a rhombus, opposite angles are congruent.
The angle opposite to angle 1 is angle 2.
so m∠1 =m∠2
m∠2= 130 degrees
Other pair of opposite angles are also congruent.
so m∠3=m ∠4
We know that the sum of 4 angles = 360
m∠1+m∠2+m∠3+m∠4=360
130+130+m∠3+m∠4=360
260+m∠3+m∠4=360
m∠3+m∠4=360-260
m∠3+m∠3=100
2m∠3=100
m∠3=50
Now, m∠3=50
m∠4=50
Therefore, m∠2=130, m∠3=50 and m∠4=50
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a manager of a sports club keeps information concerning the main sport in which members participate and their ages. to test whether there is a relationship between the age of a member and his or her choice of sport, 651 members of the sports club are randomly selected. conduct a test of independence at the 5% lev
The calculated value is 15.16, and the degrees of freedom are 12, the p-value is less than 0.05.
As a result, we must reject the null hypothesis.
A manager of a sports club maintains data about the main sport in which members participate and their ages.
To verify if there is a connection between the age of a member and their sport preference, a test of independence is performed on 651 sports club members who were randomly selected at a 5% level.200 Words:
Test of independence: Test of independence is a statistical method that helps to determine if there is a connection between two groups, and if there is, what is the magnitude of the relationship.
A test of independence is performed using the chi-square statistic.
The null hypothesis in this test is that there is no relationship between the two group S.
We will use a chi-square test to determine whether there is a connection between the age of the member and the sport in which they participate.
Hypotheses:
Null hypothesis: There is no link between the age of a member and the sport in which they participate.
Alternate hypothesis: There is a relationship between the age of a member and the sport in which they participate.
Level of significance = 5%.
Step 1: Prepare the contingency table for observed values
Age Basketball Football Hockey Soccer Other Under 20 years 25 30 20 10 15 20-29 years 20 50 35 30 25 30-39 years 15 40 40 35 30 40-49 years 10 35 25 25 20 Over 50 years 5 15 10 15 10
Step 2: Calculate the marginal frequencies.
Age Basketball Football Hockey Soccer Other Total Under 20 years 25 30 20 10 15 100 20-29 years 20 50 35 30 25 160 30-39 years 15 40 40 35 30 160 40-49 years 10 35 25 25 20 115 Over 50 years 5 15 10 15 10 55 Total 75 170 130 115 100 651
Step 3: Compute the expected frequencies.
The predicted frequency for each group is (row total) * (column total) / total number of observations.
Age Basketball Football Hockey Soccer Other Under 20 years 11.5 26.1 19.9 17.7 15 20-29 years 30.9 70.1 53.4 47.5 40.1 30-39 years 30.9 70.1 53.4 47.5 40.1 40-49 years 21.3 48.2 36.8 32.7 27.6 Over 50 years 9.4 21.4 16.4 14.6 12.3
Step 4: Calculate the test statistic:
We will use a chi-square test statistic to determine whether the null hypothesis should be accepted or rejected.
Chi-square test formula is:χ2 = Σ (Observed frequency – Expected frequency)2 / Expected frequency.
Degrees of freedom = (Number of rows – 1) * (Number of columns – 1)
χ2 = (25-11.5)2 / 11.5 + (20-30.9)2 / 30.9 + (15-30.9)2 / 30.9 + (10-21.3)2 / 21.3 + (5-9.4)2 / 9.4 + (30-26.1)2 / 26.1 + (50-70.1)2 / 70.1 + (40-70.1)2 / 70.1 + (35-48.2)2 / 48.2 + (15-21.4)2 / 21.4 + (20-19.9)2 / 19.9 + (35-53.4)2 / 53.4 + (40-53.4)2 / 53.4 + (25-36.8)2 / 36.8 + (10-16.4)2 / 16.4 + (15-14.6)2 / 14.6 + (15-32.7)2 / 32.7 + (25-27.6)2 / 27.6 + (10-12.3)2 / 12.3χ2 = 15.16
Degrees of freedom = (5-1) * (4-1) = 12
Step 5: Determine the p-value:
The p-value is determined by looking up the chi-square value and the degrees of freedom in the chi-square table.
The p-value is the probability of obtaining a result as extreme as or more extreme than the calculated value if the null hypothesis is true.
We will use a 5% level of significance.
Since the calculated value is 15.16, and the degrees of freedom are 12, the p-value is less than 0.05.
As a result, we must reject the null hypothesis.
There is evidence to suggest that the age of a member is related to the sport in which they participate.
In other words, the age of a member and their sport preference are not independent.
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what does the median tell farrah about her data
The median provides Farrah with an understanding of the central value in her data set, which can help her analyze the overall distribution of the data points.
The median is a measure of central tendency that tells Farrah the middle value of her data when it is arranged in ascending order.
To find the median, Farrah should follow these steps:
1. Arrange her data in ascending order (from smallest to largest).
2. If there is an odd number of data points, the median is the middle value.
3. If there is an even number of data points, the median is the average of the two middle values.
It is less affected by outliers or extreme values than the mean, making it a more reliable representation of the center of her data.
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in the most recent psychology exam, the mean score was 50 with a standard deviation of 5 points. based on the normal curve, what is the range within which 95% of the scores fall?
The range of the normal curve representing 95% of the scores fall is equal to 40.2 to 59.8.
The range within which 95% of the scores fall,
Calculate the z-scores corresponding to the 2.5th and 97.5th percentiles of the normal distribution.
The z-score corresponding to the 2.5th percentile is -1.96.
And the z-score corresponding to the 97.5th percentile is +1.96.
Using the formula for the z-score, we can calculate the corresponding raw scores as,
Lower bound is equal to,
z = (X - μ) / σ
⇒-1.96 = (X - 50) / 5
⇒X = 40.2
Upper bound is equal to,
z = (X - μ) / σ
⇒ +1.96 = (X - 50) / 5
⇒ X = 59.8
Therefore, 95% of the scores fall within the range of 40.2 to 59.8.
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true or false? square root functions are either always increasing or always decreasing for the whole domain of
The given statement square root functions are not always increasing or always decreasing for the whole domain of ( -∞ , ∞) is false.
Function is square root function.
Domain = ( -∞ , ∞)
Square root functions is always increasing or decreasing is a false statement.
For example,
Let us consider the function f(x) = √x.
This function is increasing for x > 0, since as x increases, √x increases as well.
However, for x < 0, the function is not defined since the square root of a negative number is not a real number.
This implies,
The function is neither increasing nor decreasing for x < 0.
Therefore, the statement square root functions are either always increasing or always decreasing for the whole domain of ( -∞ , ∞) is false.
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The above question is incomplete , the complete question is:
True or false? square root functions are either always increasing or always decreasing for the whole domain of ( -∞ , ∞).
Where can I get the answers to both of these worksheets?
The probability that more than 7 of the 15 patients have hyperextending joints is 0.015, or about 1.5%.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
This is a binomial distribution problem, where we have n = 15 trials and the probability of success (a patient having hyperextending joints) is p = 0.2.
A. To find the probability that exactly 5 of the 15 patients have hyperextending joints, we can use the formula for the binomial probability mass function:
P(X = 5) = (15 choose 5) * 0.2^5 * 0.8^10
where (15 choose 5) is the number of ways to choose 5 patients out of 15. Using a calculator, we get:
P(X = 5) = 0.188
So the probability that exactly 5 of the 15 patients have hyperextending joints is 0.188, or about 18.8%.
B. To find the probability that no more than 7 of the 15 patients have hyperextending joints, we need to add up the probabilities of having 0, 1, 2, ..., 7 patients with hyperextending joints. We can use the cumulative distribution function (CDF) of the binomial distribution:
P(X ≤ 7) = Σ(P(X = k)) for k = 0 to 7
Again, using a calculator, we get:
P(X ≤ 7) = 0.985
So the probability that no more than 7 of the 15 patients have hyperextending joints is 0.985, or about 98.5%.
C. To find the probability that more than 7 of the 15 patients have hyperextending joints, we can use the complement rule:
P(X > 7) = 1 - P(X ≤ 7)
We already know from part (B) that P(X ≤ 7) = 0.985, so:
P(X > 7) = 1 - 0.985 = 0.015
Therefore, the probability that more than 7 of the 15 patients have hyperextending joints is 0.015, or about 1.5%.
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b. John took out a loan from the bank for $221 and was told he would have to pay back
some interest on top of the $221 dollars. John had to pay back 321 dollars, how much.
money did the bank make after John Paid them back?
The bank made $100 in profit from the loan.
What is simple interest?
Simple Interest is an easy method of calculating the interest for a loan/principal amount. Simple interest is a concept that is used in many sectors such as banking, finance, automobile, and so on.
If John had to pay back $321 in total and the original loan was $221, then the bank made $100 in interest from John.
Interest = Amount John had to pay - Original Loan
Interest = 321 - 221
Interest = $100
So, the bank made $100 in profit from the loan.
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HELP ASAP. WILL GIVE BRAINLIEST AND ALL MY POINTS.
Find DB. D DC = 5 B C DB= [?]√ [ ] Give your answer as a simplified radical. Enter
The measure of diagonal DB in the given square is 5√2.
What is triangle?A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry. A triangle is defined by its three sides and the three angles formed by those sides. The sum of the three angles in a triangle is always 180 degrees. Triangles can be classified based on the length of their sides and the size of their angles.
Using Pythagoras theorem of right triangle
DB² = DC² + BC²
Here given that
DC = BC
Then
DB² = DC² + DC²
DB² = 5² + 5²
DB² = 25 + 25
DB² = 50
DB = √50
DB = 5√2
Thus, the measure of diagonal DB in the given square is 5√2
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The ages of a family of five sum to 80. The two youngest are 6 and 8. What was the sum of the ages of the family seven years ago?
The sum of the ages of the family seven years ago is given as follows:
45 years.
How to obtain the sum of the ages of the family?The sum of the ages of the family is obtained applying the proportions in the context of the problem.
Each year, the age of each person increases by one, hence, considering a family of five, the yearly increase in the age of the family is given as follows:
5 x 1 = 5 years.
The two youngest are 6 and 8, meaning that seven years ago, the youngest was not yet born.
The ages of a family of five sum to 80, hence the sum seven years ago was given as follows:
80 - 5 x 7 = 45 years.
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12) To make a miniature ice cream truck, you need tires with a diameter between 1.465 cm and 1.472 cm. Will a tire that is 1.4691 cm in diameter work?
Answer: Yes
Step-by-step explanation:
1.4691 is more than 1.465, and less than 1.472
Find the exact values of the remaining trigonometric functions of satisfying the given conditions. (If an answer is undefined, enter UNDEFINED.)
cos = 4/5, tan < 0
sin =
tan =
csc =
sec =
cot =
Answer:
sin Θ = [tex]-\frac{3}{5}[/tex]
tan Θ = [tex]-\frac{3}{4}[/tex]
csc Θ = [tex]-\frac{5}{3}[/tex]
cot Θ = [tex]-\frac{4}{3}[/tex]
Step-by-step explanation:
We know that this triangle is a 3-4-5 triangle since we know the cos of the angle. We also know this angle is located in Quadrant IV (4) since cos is positive and tan is negative.
Based off this info we can find the rest of the trig functions
sin Θ = [tex]-\frac{y}{r}[/tex]
tan Θ = [tex]-\frac{y}{x}[/tex]
csc Θ = [tex]-\frac{r}{y}[/tex]
cot Θ = [tex]-\frac{x}{y}[/tex]
A plane is located at C on the diagram. There are two towers located at A and B. The distance between the towers is 7,600 feet, and the angles of elevation are given. a. Find BC, the distance from Tower 2 to the plane, to the nearest foot. b. Find CD, the height of the plane from the ground, to the nearest foot.
In linear equation, 6499 ft CD, the height of the plane from the ground, to the nearest foot.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Part A) Find BC, the distance from Tower 2 to the plane, to the nearest foot.
in the triangle ACD
sin16=CD/(7600+BD)--------> CD=sin16*(7600+BD)---------> equation 1
in the triangle BCD
sin24=CD/BD-----------> CD=sin24*BD---------------> equation 2
equation 1=equation 2
sin16*(7600+BD)=sin24*BD-----> sin16*7600+sin16*BD=sin24*BD
sin24*BD-sin16*BD=sin16*7600----> BD=[sin16*7600]/[sin24-sin16]
BD=15979 ft
in the triangle BCD
cos24=BD/BC---------> BC=BD/cos24-------> 15979/cos24-------> 17491
BC=17491 ft
= BC is 17491 ft
Part 2) Find CD, the height of the plane from the ground, to the nearest foot.
CD=sin24*BD ( remember equation 2)
BD=15979 ft
CD=sin24*15979 -----------> CD=6499 ft
= CD is 6499 ft
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3 A camper wants to protect her bag of food from bears She decides to tightly stretch a rope between two trees and hang her bag from a point exactly halfway along the length of the rope The first tree is 10 feet east and 6 feet north of her firepit The second tree is 5 feet west and 8 feet north of her firepit The rope is attached at a height of 8 feet to the first tree and a height of 5 feet to the second tree Let the firepit represent the origin movement east of the firepit represent movement in the direction of positive x movement west of the firepit represent movement in the direction of negative x movement north of the firepit represent movement in the direction of positive y and movement above the firepit represent movement in the direction of positive z 1 Write the coordinates of the points on the trees where the rope is attached 2 Find the distance between the points in part a Use sqrt to indicate a square root For example 3 would be written sqrt 3 3 Find the coordinates of the point where the food bag is hung 4 If the food bag is 1 2 feet long when hung and bears can reach a height of 7 5 feet when standing is the camper s food safe from bears Explain why or why not
The coordinates of the point where the food bag is hung are (2.5, 7, 6.5).
What is the coordinate point called?The center of the coordinate system (where the lines intersect) is called the origin. The axes intersect when both x and y are zero. The coordinates of the origin are (0, 0). An ordered pair contains the coordinates of one point in the coordinate system.
The coordinates of the point on the first tree where the rope is attached are (10, 6, 8), and the coordinates of the point on the second tree where the rope is attached are (-5, 8, 5).
To find the distance between the points, we can use the distance formula:
distance = √((x2 - x1)² + (y2 - y1)² + (z2 - z1)²)
Plugging in the coordinates from part 1, we get:
distance = √((-5 - 10)² + (8 - 6)² + (5 - 8)²)
distance = √(225 + 4 + 9)
distance = √(238)
Therefore, the distance between the points is √(238).
Since the food bag is hung at a point exactly halfway along the length of the rope, we can find its coordinates by taking the average of the coordinates of the points where the rope is attached.
The x-coordinate of the midpoint is: (10 + (-5)) / 2 = 2.5
The y-coordinate of the midpoint is: (6 + 8) / 2 = 7
The z-coordinate of the midpoint is: (8 + 5) / 2 = 6.5
Therefore, the coordinates of the point where the food bag is hung are (2.5, 7, 6.5).
To determine whether the food is safe from bears, we need to compare the height of the food bag to the maximum height that bears can reach. The food bag is hung at a height of 6.5 feet, and bears can reach a height of 7.5 feet when standing. Therefore, the food is not completely safe from bears, as they may be able to reach it if they stand up on their hind legs. However, hanging the food bag at this height does make it more difficult for the bears to reach, and may deter them from trying to get to it. It is also important to note that proper food storage techniques in bear country should involve using bear-resistant containers, in addition to hanging food bags.
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Someone help me pls
Answer:
1. It flips the image over a line to create a mirror image
2. It spins a figure around a point
3. It slides a figure to a different location
4. it enlarges or reduces a figure
Step-by-step explanation:
The vertices of ΔABC are A(−2,5), B(−2,4), and C(−5,2). If ΔABC is reflected across the line y=−2 to produce the image ΔA'B'C', find the coordinates of the vertex A'.
The coordinates of the vertex A' are (-2, -2).
What is triangle?
A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.
To reflect a point or a shape across a line, you can follow these steps:
Find the equation of the line of reflection.
Find the distance between each point and the line of reflection.
Reflect each point across the line of reflection by moving the same distance on the other side of the line.
Finding the equation of the line of reflection:
The line of reflection is y = -2, which is a horizontal line passing through y = -2.
Finding the distance between each point and the line of reflection:
We can use the formula for the distance between a point (x, y) and a line Ax + By + C = 0:
distance = |Ax + By + C| / sqrt(A^2 + B^2)
Plugging in the values, we get:
distance(A, y = -2) = |(-2) - (-2) + 2| / sqrt(0 + 1) = 2
distance(B, y = -2) = |(-2) - (-2) + 4| / sqrt(0 + 1) = 4
distance(C, y = -2) = |(-5) - (-2) + 2| / sqrt(1 + 0) = 5 / sqrt(1) = 5
So the distances between A, B, C and the line of reflection are 2, 4, and 5, respectively.
Reflecting each point across the line of reflection:
To reflect a point across a line, we move the same distance on the other side of the line. Since the line of reflection is horizontal, we only need to move vertically.
A is 2 units above the line of reflection, so we move it 2 units below the line:
A' = (-2, -2)
B is 4 units above the line of reflection, so we move it 4 units below the line:
B' = (-2, -4)
C is 5 units above the line of reflection, so we move it 5 units below the line:
C' = (-5, -7)
Therefore, the coordinates of the vertex A' are (-2, -2).
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Write a polynomial function in standard form with zero's -5,-4,and 3
The equation of the polynomial function in standard form is P(x) = x³ + 6x² - 7x - 60
Calculating the polynomial function in standard formGiven that we have the following
zeros = -5,-4,and 3
The polynomial function in standard form is calculated as
P(x) = (x - zeros)
So, we have
P(x) = (x + 5)(x + 4)(x - 3)
Opening the brackets, we have the following equation
P(x) = x³ + 6x² - 7x - 60
Hence, the polynomial is P(x) = x³ + 6x² - 7x - 60
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I WILL GIVE SOMEONE BRAINLIEST IF YALL ANSWER THIS!!!!
Answer:
v<-4/35. If you want interval notation it is (-infinity, -4/35)
Step-by-step explanation:
X =
someone HELP!!!!
you need to work back wards on the
9x+3=64
so 64-3=61
then do 61 divided by 9
which equals 6.7(1dp)
so x=6.7(1dp)
Joe has $2500 in a savings account that earns 9% interest per year. How much amount in dollars will he have in 3 years?
To calculate the amount of money Joe will have in 3 years, we can use the formula:
A = P(1 + r/n)^(nt)
where:
A = the amount of money Joe will have in 3 years
P = the principal amount = $2500
r = the annual interest rate = 9% = 0.09 (expressed as a decimal)
n = the number of times the interest is compounded per year (assuming annual compounding, n = 1)
t = the number of years = 3
Plugging in these values, we get:
A = $2500(1 + 0.09/1)^(1*3)
= $2500(1.09)^3
= $2500(1.29503)
= $3237.58 (rounded to two decimal places)
Therefore, Joe will have $3237.58 in 3 years.
mario is solving the system of linear equations using the elimination method. first equation: 3x-6y=8 second equation: 2x+3y=-1 which operation will eliminate one of the variables? A. multiplying the first equation by 2 B. multiplying the first equation by 6 C. multiplying the second equation by 2 D. multiplying the second equation by 6.
The correct answer is A. Multiplying the first equation by 2 will eliminate the variable y.
What is elimination method?The elimination method is a common technique used to solve a system of linear equations. In this method, we manipulate the equations by adding or subtracting them to eliminate one of the variables, so that we can solve for the other variable.
According to question:To eliminate one of the variables, we need to choose one of the equations and multiply it by a constant that will make the coefficient of one of the variables in that equation equal to the coefficient of the same variable in the other equation, but with the opposite sign. Then, when we add the two equations together, the term with that variable will be eliminated.
Looking at the given equations, we can see that if we multiply the first equation by 2, we will get:
6x - 12y = 16
And if we add this equation to the second equation, we get:
6x - 12y + 2x + 3y = 16 - 1
Simplifying this, we get:
8x - 9y = 15
Now we have one equation with only x and y, and we can use this equation and either of the original equations to solve for x and y using the substitution method.
Therefore, the correct answer is A. Multiplying the first equation by 2 will eliminate the variable y.
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Sue bought a piece of fabric that was 98.96 meters long. Then she cut 3.56 meters of it off to use in a sewing project. How much fabric is left?
What is the value of x? With coordinates of 45%, 4√2, x.
The value of x is 8. So correct is C.
Describe Triangles?In mathematics, a triangle is a geometric shape that consists of three line segments that intersect at three endpoints. These endpoints are called vertices, and the line segments are called sides.
Triangles are one of the most basic shapes in geometry and are used in many areas of mathematics, science, engineering, and everyday life. They can be classified based on the length of their sides and the measure of their angles.
Some common types of triangles include:
Equilateral triangle: A triangle in which all three sides are equal in length.
Isosceles triangle: A triangle in which two sides are equal in length.
Scalene triangle: A triangle in which all three sides have different lengths.
Right triangle: A triangle in which one angle measures 90 degrees (a right angle).
To find the value of x, we can use the trigonometric ratios of a right-angled triangle. Let's call the base of the triangle "b".
We know that the angle between the hypotenuse and the base is 45 degrees, which means that the other acute angle is also 45 degrees. Therefore, we can use the trigonometric ratio for the sine of 45 degrees to relate the hypotenuse and the perpendicular as follows:
sin(45 degrees) = opposite/hypotenuse
where the opposite side is the perpendicular, which is given as 4√2.
sin(45 degrees) = 4√2/x
Simplifying this equation gives:
x = 4√2 / sin(45 degrees)
We know that sin(45 degrees) = 1/√2, so substituting this value into the equation above gives:
x = 4√2 / (1/√2) = 4√2 * √2 = 8
Therefore, the value of x is 8.
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(3x -1 ) (x+1)- 3x(x+1)=7
Answer:
x = - 8
Step-by-step explanation:
(3x - 1)(x + 1) - 3x(x + 1) = 7 ← factor out (x + 1) from each term
(x + 1)(3x - 1 - 3x) = 7
(x + 1)(- 1) = 7 ( multiply both sides by - 1 )
x + 1 = - 7 ( subtract 1 from both sides )
x = - 8
Answer:
[tex]\bf x=-8[/tex]Step-by-step explanation:
[tex]\bf (3x -1 ) (x+1)- 3x(x+1)=7[/tex]
Expand:-
[tex]\bf 3x^2+2x-1-3x\left(x+1\right)[/tex]
[tex]\bf 3x^2+2x-1-3x^2-3x[/tex]
Combine like terms:-
[tex]\bf (3x^2-3x^2)+(2x-3x)-1[/tex]
[tex]\bf -x-1=7[/tex]
Add 1 to both sides:-
[tex]\bf -x-1+1=7+1[/tex]
[tex]\bf -x=8[/tex]
Divide both sides by -1:-
[tex]\bf \cfrac{-x}{-1}=\cfrac{8}{-1}[/tex]
[tex]\bf x=-8[/tex]
_________________________
Hope this helps!
A group of marine biologists tags 45 great white sharks off the coast of Mexico to study migratory patterns. All of the tag numbers are unique. Weeks later, the marine biologists travel to Hawaii. While there, they randomly capture and release 20 great white sharks per day, for three consecutive days. On the first day, 3 of the sharks have the original tags. On the second day, 2 of the sharks have the original tags. On the third day, 4 of the sharks have the original tags. Based on the data, what is the estimated population of great white sharks that have migrated from Mexico to Hawaii?
Therefore, the estimated population of great white sharks that have migrated from Mexico to Hawaii is 2,500.
What is Shark Population Estimation?Shark population estimation is the process of determining the size and trends of shark populations in a given area. It involves collecting and analyzing data on shark abundance, distribution, behavior, and other factors to understand their population dynamics.
There are different methods used to estimate shark populations, including mark-recapture studies, aerial surveys, acoustic tracking, and genetic analysis. These methods allow researchers to estimate the number of sharks in a given area, monitor changes in their population over time, and identify potential threats to their survival.
To estimate the population of great white sharks that have migrated from Mexico to Hawaii, we can use the capture-recapture method, also known as the Lincoln-Petersen index.
Let:
N = the total population sizen1 = the number of sharks tagged in Mexicon2 = the number of sharks captured in Hawaii on the first dayn3 = the number of sharks captured in Hawaii on the second dayn4 = the number of sharks captured in Hawaii on the third daym1 = the number of sharks captured in Hawaii on the first day that were previously taggedm2 = the number of sharks captured in Hawaii on the second day that were previously taggedm3 = the number of sharks captured in Hawaii on the third day that were previously taggedThe Lincoln-Petersen index formula is:
[tex]N = (n_1 * n_2 * n_3) / (m_1 * m_2 * m_3)[/tex]
Plugging in the given values, we get:
[tex]N = (45 * 20 * 20 * 20) / (3 * 2 * 4)[/tex]
[tex]N = 60,000 / 24[/tex]
[tex]N = 2,500[/tex]
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pls help asap The following is a right angle. Find X:
x =
Answer:
x = 11
Step-by-step explanation:
3x + 5x + 2 =90
(3x + 5x) + (2) = 90
8x + 2 = 90
8x + 2 -2 = 90 -2
8x = 88
8x/8 = 88/8
x = 11