Answer:
Answer is 120
Step-by-step explanation:
180*(6-2)/6
120
Given: T = (2, -7) X = (–7, 5) Find: 3TX
Answer:
3TX = 45
Step-by-step explanation:
See attached graph.
Form a right triangle and use length of the the two sides to find the hypotenuse, XT, 15. 3XT = 45
Question: QUESTION 22 You would like to compare the mean birth weight in a sample with the mean birth weight in a population. What significance test should ...
To compare the mean birth weight in a sample with the mean birth weight in a population, a statistical test known as the one-sample t-test should be used.
The one-sample t-test is used when we have a single sample and want to determine if the mean of that sample significantly differs from a known or hypothesized population mean. In this case, the known or hypothesized population mean would be the mean birth weight in the population.
The t-test allows us to assess whether the difference between the sample mean and the population mean is statistically significant or simply due to random sampling variation. By calculating the t-statistic and comparing it to the critical values from the t-distribution, we can determine if the difference is statistically significant at a chosen significance level (typically 0.05 or 0.01).
In summary, to compare the mean birth weight in a sample with the mean birth weight in a population, the appropriate test is the one-sample t-test.
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Mr. Fredlin harvests oranges from his orange tree every year. The tree produced 75 pounds of oranges in its first crop. As the tree has matured since its first crop, the weight in pounds, , of the orange harvest has increased exponentially by 45% each year according to the function w (t)=75(1.45)^t , where is the number of years since the first crop. Based on this model, how many pounds of oranges is the tree expected to harvest in 4 years (rounded to the nearest whole pound)?
Answer:
Step-by-step explanation:
The weight of the orange harvest is given by the function:
w(t) = 75(1.45)^t
where t is the number of years since the first crop.
To find the expected weight of the orange harvest in 4 years, we need to evaluate w(4):
w(4) = 75(1.45)^4
w(4) ≈ 213.98
Rounding this to the nearest whole pound gives:
w(4) ≈ 214 pounds
Therefore, the tree is expected to harvest approximately 214 pounds of oranges in 4 years according to this model.
30 POINTS ANSWER ASAP!!!!
Determine the perimeter of the right triangle shown.
right triangle with vertices at negative 4 comma 4, 4 comma 4, and 4 comma negative 2
10 units
24 units
36 units
64 units
Answer: 24 units.
Step-by-step explanation: To find the perimeter of the right triangle, you need to add up the lengths of all three sides of the triangle.
The right triangle shown has a vertex at (-4, 4), another vertex at (4, 4), and a third vertex at (4, -2). The length of the side between the first two vertices can be calculated using the distance formula:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((4 - (-4))^2 + (4 - 4)^2)
= sqrt(8^2 + 0)
= sqrt(64)
= 8
The length of the side between the second and third vertices can be calculated using the distance formula:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((4 - 4)^2 + (-2 - 4)^2)
= sqrt(0 + (-6)^2)
= sqrt(36)
= 6
The length of the hypotenuse of the right triangle can be calculated using the Pythagorean theorem:
c^2 = a^2 + b^2
c = sqrt(a^2 + b^2)
= sqrt(8^2 + 6^2)
= sqrt(64 + 36)
= sqrt(100)
= 10
To find the perimeter of the triangle, add up the lengths of all three sides: 8 + 6 + 10 = 24 units.
Therefore, the perimeter of the right triangle is 24 units.
|y| x-3
what is the vertex
Answer:
(3,0)
Step-by-step explanation:
put x-3=0 and solve for it whic hwould be x=3
If the area of the triangle shown is 88 square inches, which equation could be used to find the value of x.
Answer:88= 6x+40
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
The formula for the area of a rectangle is L x W, so we just sub in the formula.
L × W = Area
8 × (¾x + 5) = 88
This is the same as 8¾x + 5 = 88.
If the pyramids below are similar, what is the
ratio of their surface area?
21 in
14 in
A. 3:2
B. 6:4
C. 9:4
D. 27:8
The required ratio of the surface area of the given pyramids is (A) 3:2.
What are ratios?A ratio can be used to show a relationship or to compare two numbers of the same type.
To compare things of the same type, ratios are utilized.
We might use a ratio, for example, to compare the proportion of boys to girls in your class.
If b is not equal to 0, an ordered pair of numbers a and b, denoted as a / b, is a ratio.
A proportion is an equation that equalizes two ratios.
For illustration, the ratio may be expressed as follows: 1: 3 in the case of 1 boy and 3 girls (for every one boy there are 3 girls)
So, the given surface area is:
- 21 in
- 14 in
Now, calculate the ratio as:
= 21/14
= 3/2
= 3:2
Therefore, the required ratio of the surface area of the given pyramids is (A) 3:2.
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Write a rule for the linear function shown in the graph.
y = 3x – 1
y = \(\frac{2}{y5}\)x +1
y = -\(\frac{5}{2}\)x -1
y = \(\frac{5}{3}\)x +1
Answer:
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Point Form:
( 1 , − 2 )
Equation Form:
x = 1 , y = − 2
Step-by-step explanation:
Graph.
y = 3 x − 1
y = x + 1
y = − x − 1
y = x + 1
Which relation in the below table(s) represents a function?
The relation 2 represents a function.
In order to determine which relation in the below table represents a function, we need to first understand what a function is.A function is a relationship in which each input value corresponds to exactly one output value.
To put it another way, each x-value has one and only one y-value. The most typical method to determine whether a relation is a function is to use the vertical line test.
The vertical line test is a way to determine if a relation is a function graphically. To test if a graph is a function, we draw a vertical line through each x-value on the graph. If a vertical line crosses the graph more than once, it is not a function.
If, on the other hand, the graph passes the vertical line test and no vertical line crosses the graph more than once, it is a function.Now let's look at the table below to determine which relation is a function.
We will first plot the x and y values of each relation on a coordinate system and then apply the vertical line test to each relation.
Relation 1: x | y0 | 10 | 11 | 22 | 23 | 34 | 35 | 4Relation 1 does not represent a function since we can draw a vertical line through x = 3 and the line will cross the graph more than once.
Relation 2: x | y2 | 33 | 34 | 45 | 46 | 57 | 5Relation 2 represents a function since we can draw a vertical line through each x-value on the graph and it will only cross the graph once.
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i need 2 more please help me
Select three expressions equivalent to 28xy + 16x.
Answer:
B,C,D
Step-by-step explanation:
Answer:
number 2
number 3
number 4
Step-by-step explanation:
B
A
8 cm
4cm
Two solid shapes, A and B, are mathematically similar.
The base of shape A is a circle with radius 4 cm
The base of shape B is a circle with radius 8 cm.
The surface area of shape A is 80 cm”,
(a)
Work out the surface area of shape B.
Answer:
(a) 320 cm²
(b) 75 cm³
Step-by-step explanation:
The scale factor from A to B is 8/4 = 2.
The scale factor of the areas is 2² = 4.
The scale factor of the volumes is 2³ = 8.
(a)
80 cm² * 4 = 320 cm²
(b)
600 cm / 8 = 75 cm³
The required surface area of shape B is 320 cm² and the volume of shape A is 75 cm³.
Given that,
The base of shape A is a circle with a radius of 4 cm
The base of shape B is a circle with a radius of 8 cm.
Surface area is defined as the area of the surface that is uncovered.
Here,
1)
The scale factor of area = 8²/4² = 4
The surface area of shape B = 4 surface area of shape A.
The surface area of shape B = 4 * 80
= 320 cm²
2)
The scale factor of volume = 8³ / 4³ = 8
The volume of shape B = 8 * the volume of shape A.
The volume of shape A = 600 / 8
The volume of shape A = 75 cm³
Thus, the required surface area of shape B is 320 cm² and the volume of shape A is 75 cm³.
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Write an expression for 267 multiplied by x
Answer:
267x
Step-by-step explanation:
Multiplication means times
267 * x
267x
Answer:
267x
when you multiply a number by a variable, you can combine the terms if there is no coefficient for the variable.
A distribution of exam scores has mean 60 and standard deviation 18. If each score is doubled, and then 5 is subtracted from that result, what will be the mean and standard deviation, respectively, of the new scores
If each score is doubled, and then 5 is subtracted from that result, then the mean and standard deviation will be 115 and 36 respectively.
What will be the mean and standard deviation?A huge group of test results has a mean of 60 and a standard deviation of 18. If each score is doubled and then 5 is deducted from the result, the mean and standard deviation are “ mean = 115; standard deviation = 36”. Mean = 2 x 60 -5 = 120 -5 = 115
2 x 18 = 36 standard deviation
The mean is the average and is calculated as the sum of all the results from the example divided by the total number of events.
The standard deviation (SD) is a statistic used to assess the degree of variation or dispersion in a set of data values.
A low standard deviation indicates that the information points slant toward being near the mean of the set, whereas an exclusive expectation deviation or a high standard deviation indicates that the information points tilt toward being near the mean of the set.
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use scenario 12-1. enough information is provided above to confirm that four conditions for slope inference have been satisfied, but we need a further analysis of the data to confirm that the fifth condition for inference has been satisfied. which condition requires further analysis of the data?
The condition that requires further analysis of the data for slope inference is the independence of errors.
In this scenario, we have to determine the condition that requires further analysis of the data. We know that there are five conditions that need to be satisfied to perform the linear regression.
The five conditions are: Linearity, Homoscedasticity, Normality of residuals, Independence of errors. And the last one is: Independence of errors is the fifth condition that requires further analysis of the data to confirm that it is satisfied or not. The independence of errors condition is that there should be no pattern in the residuals.
Residuals are the differences between the actual values and the predicted values. The independence of errors is important because it ensures that the errors are random and not influenced by any other variable.
The independence of errors condition can be checked by plotting the residuals against the predicted values. If there is a pattern in the residuals, then the independence of errors condition is not satisfied. So, in order to satisfy the fifth condition for slope inference, the independence of errors condition must be satisfied.
*Complete question: Which is the fifth condition requires further analysis of the data to confirm that this condition for inference has been satisfied the same way that four conditions for slope inference have been satisfied?
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One number is 8 less than twice a second number. Find a pair of such numbers so that their product is as small as possible. These two numbers are ____. (Use a comma to separate your numbers.)
The smallest possible product is ____.
These two numbers are -4, 2. The smallest possible product is -8.
To find a pair of numbers that satisfy the given conditions, we can use algebra. Let x be the first number and y be the second number. According to the problem, one number is 8 less than twice a second number. This can be written as:
x = 2y - 8
We need to find the product of these two numbers, which is x*y. Substituting the value of x from the equation above, we get:
x*y = (2y - 8)*y
= 2y^2 - 8y
To find the smallest possible product, we need to minimize this expression. We can do this by finding the vertex of the parabola represented by this equation. The vertex of a parabola in the form ax^2 + bx + c is given by (-b/2a, f(-b/2a)). In this case, a = 2, b = -8, and c = 0. So, the vertex is:
(-b/2a, f(-b/2a)) = (-(-8)/(2*2), f(-(-8)/(2*2)))
= (2, f(2))
Substituting y = 2 into the equation for the product, we get:
x*y = 2(2)^2 - 8(2)
= 8 - 16
= -8
So, the smallest possible product is -8. To find the pair of numbers that give this product, we can substitute y = 2 into the equation for x:
x = 2y - 8
= 2(2) - 8
= -4
Therefore, the pair of numbers are -4 and 2.
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help pls, i cant figure it out
Answer:
280 square units
Step-by-step explanation:
Area of the rectangle:
A = b* h = 16 * 15 = 240
Area of the triangle:
A = bh/2 = (16*5)/2 = 40
Total area = area of triangle + area of rectangle = 240 + 40 = 280 square untis.
Is the pair of equations y 0 and y =- 7 will have?
No Solution.
Since, the x-axis (equation y=0) does not intersect y=-7 at any point. The given pair of equations has no solution
Three Types of Solutions of a System of Linear EquationsConsider the pair of linear equations in two variables x and y.
a1x + b1y + c1 = 0
a2x + b2y + c2 = 0
Here a1, b1, c1, a2, b2, c2 are all real numbers.
Note that, a12 + b12 ≠ 0, a22 + b22 ≠ 0
1. If (a1/a2) ≠ (b1/b2), then there will be a unique solution. If we plot the graph, the lines will intersect. This type of equation is called a consistent pair of linear equations.
2. If (a1/a2) = (b1/b2) = (c1/c2), then there will be infinitely many solutions. The lines will coincide. This type of equation is called a dependent pair of linear equations in two variables
3. If (a1/a2) = (b1/b2) ≠ (c1/c2), then there will be no solution. If we plot the graph, the lines will be parallel. This type of equation is called an inconsistent pair of linear equations.
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Find the density of the object #3 if it has a mass of 100g
Answer:
Well i kinda think that this should also maybe be in science but here is the answer density = mass/volume = 100g/50mL = 2g/mL so its the density is 50,
Step-by-step explanation:
4. What are the Z-scores for the following Confidence Interval levels? Remember, you MUST account for both tails of the curve, positive and negative, when identifying each. That means you will need to do a little math to obtain the correct z-value. 3 Points 68%= 85% = 99% =
In order to calculate the z-scores for the given Confidence Interval (CI) levels, we need to use the Z-table. It is also known as the standard normal distribution table. Here are the z-scores for the given Confidence Interval levels:1. 68% CI: The confidence interval corresponds to 1 standard deviation on each side of the mean.
Thus, the z-score for the 68% \(CI is ±1.00.2. 85% CI\): The confidence interval corresponds to 1.44 standard deviations on each side of the mean.
We can calculate the z-score using the following formula:\(z = invNorm((1 + 0.85)/2)z = invNorm(0.925)z ≈ ±1.44\)Note that invNorm is the inverse normal cumulative distribution function (CDF) which tells us the z-score given a certain area under the curve.3. 99% CI: The confidence interval corresponds to 2.58 standard deviations on each side of the mean. We can calculate the z-score using the following formula:\(z = invNorm((1 + 0.99)/2)z = invNorm(0.995)z ≈ ±2.58\)
Note that in general, to calculate the z-score for a CI level of (100 - α)% where α is the level of significance, we can use the following formula:\(z = invNorm((1 + α/100)/2)\) Hope this helps!
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PLEASE HELP!!
The residuals for data set A and data set B were calculated and plotted on separate residual plots. If the residuals for data set A do not form a pattern, and the residuals for data set B form a pattern, what can be concluded?
A. Data set A is linear, and data set B is not linear.
B. Data set A is not linear, and data set B is not linear.
C. Data set A is linear, and data set B is linear.
D. Data set A is not linear, and data set B is linear.
Answer: A
Step-by-step explanation:
When the residuals are random, it implies that the linear fit is appropriate for the data set. When residuals form a pattern, it indicates that the linear fit for the data set is not appropriate since there is a systematic error instead of random error.
Afrah wants to buy a coat from Japan. It costs ¥7 320.50. She will have to pay shipping of £25.30. She has found a company that will charge her £80 for the coat and shipping combined. The exchange rate is currently £2 : ¥292.82. Should Afrah use the company or buy the coat and pay for shipping herself? Give a mathematical explanation.
Answer:
She should buy the coat and pay for shipping
Step-by-step explanation:
Set up a proportion to express the the 80 pounds to yen.
\(\frac{2}{292.82}\) = \(\frac{80}{x}\)
2 x 40 = 80
292.82 x 40 = 11,712.80
230.50 + 25.30 = 255.8
255.80 < 11,712.80
Helping in the name of Jesus.
Given this figure on a coordinate plane, determine which of the following statements
could prove ABCD is a parallelogram.
I need help plzzz
One of the lamp posts at a bank has a motion detector on it, and the equation (x 15)2 (y−12)2=25 describes the boundary within which motion can be sensed. what is the greatest distance, in feet, a person could be from the lamp and be detected? 5 ft 10 ft 50 ft 125 ft
5 feet is the greatest distance that a person could be from the lamp and be detected.
What is equation of circle?A circle is defined as round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center).
Since we have given that
The equation is :
\((x+15)^2+(y-12)^2=25\)
It is the equation of circle in which center is (h,k) i.e. ( 15,12)
The general equation of circle is given by
\((x-h)^2+(y-k)^2=r^2\)
Here, the radius 'r' is given by
\(r^2=25\)
\(r=\sqrt{25\)
\(r=5\)
Here, the greatest distance a person could be from the lamp and be detected is represented by radius i.e. r = 5 feet.
Hence, 5 feet is the greatest distance that a person could be from the lamp and be detected.
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Prove that there exist infinitely many primes p ≡ 3 mod 4 without using Dirichlet's theorem. (Hint: if n∈Z+ has a prime factorization consisting of only primes p≡ 1 mod 4, then what is n mod4?)
To prove that there exist infinitely many primes p ≡ 3 mod 4 without using Dirichlet's theorem, we can use a proof by contradiction. Assume that there are only finitely many primes p ≡ 3 mod 4, say p1, p2, ..., pk. Let N be the product of all these primes, i.e. N = p1p2...pk.
1. Let's denote these finitely many primes as {p_1, p_2, ..., p_k}, where each prime p_i ≡ 3 mod 4.
2. Now consider the number N = (4 * p_1 * p_2 * ... * p_k) - 1. Notice that N ≡ 3 mod 4.
3. N has a unique prime factorization, and since N ≡ 3 mod 4, at least one of its prime factors must be congruent to 3 mod 4.
4. Since we assumed there are only finitely many primes congruent to 3 mod 4, we can check if any prime in the set {p_1, p_2, ..., p_k} divides N. Notice that for every prime p_i in the set, N ≡ -1 mod p_i, which means that no prime p_i can divide N.
5. This leads to a contradiction since N must have a prime factor congruent to 3 mod 4, but none of the primes in our set can divide N. Therefore, our initial assumption is incorrect.
So, there must be infinitely many primes p ≡ 3 mod 4.
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Select the correct answer.
What is Vl92 in simplest form?
OA. 32V3
OB.
Oc. 8V3
OD.
3/8
2V48
The correct answer is option A, 32V3, in simplest form. In simpler terms, Vl92 is a simplified expression of a square root.
1. The expression consists of two parts, the radicand (92) and the radical symbol (√), which indicates that the number underneath it should be square rooted. The objective is to simplify the expression further by breaking down the radicand into its prime factors.
2. To simplify the square root of 92, we can find its prime factors: 92 = 2 x 2 x 23. We can then group the factors of 92 into two groups, where one group has a perfect square: √(2 x 2 x 23) = √(2 x 2) x √23 = 2√23. Therefore, the simplified form of Vl92 is 2√23.
3. In summary, Vl92 is equivalent to the square root of 92, and its simplest form is 2√23. The process to simplify a square root involves finding the prime factors of the radicand and grouping them into perfect squares and their corresponding radicals. By doing so, we can simplify square roots and make them more manageable.
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There are 600 seats in the Marshall Middles School Auditorium. Students are sitting in 4/5 of the seats in the auditorium. Teachers are sitting in 55 of the seats. How many seats are not being used?
A. 60
B. 65
C. 70
D. 75
Answer:
B. 65
Step-by-step explanation:
600 * 4/5 = 480 seats used by students
55 teachers + 480 students= 535 seats used
600-535 = 65 seats left over
video game:$49, tax:6.5%
Answer:
Tax will be 0.99$ ya yayayayaysy
calculate the area of a rectangle when b= a and h = a +2. Use A= bh
if p = 2^k + 1 is prime, show that every quadratic nonresidue of p is a primitive root of p.
Every quadratic nonresidue of p is a primitive root of p, when p = 2^k + 1 is primeIf p = 2^k + 1 is a prime number, we want to show that every quadratic nonresidue of p is a primitive root of p.
In other words, we aim to prove that if an element x is a quadratic nonresidue modulo p, then it is also a primitive root of p.
Let's assume p = 2^k + 1 is a prime number. To prove that every quadratic nonresidue of p is a primitive root of p, we can use the properties of quadratic residues and quadratic nonresidues.
A quadratic residue modulo p is an element y such that y^((p-1)/2) ≡ 1 (mod p), while a quadratic nonresidue is an element x such that x^((p-1)/2) ≡ -1 (mod p).
Now, let's consider an element x that is a quadratic nonresidue modulo p. We want to show that x is a primitive root of p.
Since x is a quadratic nonresidue, we know that x^((p-1)/2) ≡ -1 (mod p). By Euler's criterion, this implies that x^((p-1)/2) ≡ -1^((p-1)/2) ≡ -1^2 ≡ 1 (mod p).
Since x^((p-1)/2) ≡ 1 (mod p), we can conclude that the order of x modulo p is at least (p-1)/2. However, since p = 2^k + 1 is a prime, the order of x modulo p must be equal to (p-1)/2.
By definition, a primitive root of p has an order of (p-1). Since the order of x modulo p is (p-1)/2, it follows that x is a primitive root of p.
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