The answer to your question would be 1530 because the whole number is 1800 and then the 85% would be 153.
The hiking club plans a 45-mile hike. They will hike 7. 5 miles each day. This equation represents the number of miles remaining to hike after each day of hiking. M=45−7. 5d
Yes, this equation M=45−7. 5d is useful to calculate the number of miles left after each day.
On the 6th day they cover 45 miles.
Plan to cover distance by hiking club to hike = 45 mile
Per day hiking = 7.5 miles
The equation M = 45 - 7.5d represents the number of miles remaining to hike after each day of hiking,
where M is the number of miles remaining and d is the number of days of hiking.
Let us use this equation to calculate the number of miles remaining after each day of hiking.
For Day 1,
d = 1
M = 45 - 7.5(1)
= 45 - 7.5
= 37.5 miles remaining
For Day 2,
d = 2
M = 45 - 7.5(2)
= 45 - 15
= 30 miles remaining
For Day 3,
d = 3
M = 45 - 7.5(3)
= 45 - 22.5
= 22.5 miles remaining
And so on...
For Day 4,
d = 4
M = 45 - 7.5(4)
= 45 - 30
= 15 miles remaining
For Day 5,
d = 5
M = 45 - 7.5(5)
= 45 - 37.5
= 7.5 miles remaining
For Day 6,
d = 6
M = 45 - 7.5(6)
= 45 - 45
= 0 miles remaining
By continuing the pattern it is easy to calculate the number of miles remaining .
After each day of hiking until the remaining miles reach 0, indicating the completion of the 45-mile hike.
Therefore, this equation help us to calculate the number of miles remaining.
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when testing the observed value of the z-score was found to be −2.15. then, the p-value for this test would be a. .0316 b. .9842 c. .0158 d. .9684
When the observed z-score is -2.15, we can find the p-value by looking up the value in a standard normal (z) table or using a calculator or software that provides p-values.
Step 1: Identify the z-score
The given z-score is -2.15.
Step 2: Find the p-value
To find the p-value, look up the z-score in a standard normal table or use a calculator. In this case, the p-value is approximately 0.0158.
So, the correct answer is:
c. 0.0158
This p-value represents the probability of observing a value as extreme or more extreme than the observed z-score in the standard normal distribution, assuming the null hypothesis is true.
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3) What is the distance between (-5, 2) and (-1, 6). Round to the nearest tenths if necessary. You can either graph it or use the distance formula below.
Step-by-step explanation:
Plug the values into the given distance formula
d = sqrt (( -5 - -1)^2 + ( 2-6)^2 )
d = sqrt ( 16 + 16 )
d = sqrt 32 = 5.7
Kariro had y cows. Ali had three times as much as kariro . Nabwiso had only half as kariro how many cows did nabwiso have if all had a total of 180 cows?
Okay, here are the steps to solve this problem:
* Kariro had y cows
* Ali had 3 times as much as Kariro, so Ali had 3y cows
* Nabwiso had half as much as Kariro, so Nabwiso had y/2 cows
* In total, they had:
** Kariro: y cows
** Ali: 3y cows
** Nabwiso: y/2 cows
* So in total: y + 3y + y/2 = 180
* 4.5y = 180
* y = 40
* So:
** Kariro had 40 cows
** Ali had 3 * 40 = 120 cows
** Nabwiso had 40/2 = 20 cows
Therefore, if the total cows was 180, then Nabwiso had 20 cows.
Let me know if you have any other questions!
A quadratic function f(x) is hidden from view. You must find all
intervals where f(x) is negative. Choose the form of the quadratic
function f(x) that you would like to see in order to answer the
question most efficiently.
Form: Standard Form
f(x)=2x²-16x - 30
Step-by-step explanation:
f'(x)=-4x-16
f'(x)=0 <=> x=-4
evaluating the derivative of fx on the numberline we get the negative interval is (-4;+infinity)
The function f(x) = 2x² - 16x - 30 is negative between the roots x = -3 and x = 5. This is found using the quadratic formula to identify the roots and observing that the function dips below the x-axis between these two points.
Explanation:To find the intervals where f(x) is negative, you would want to determine where the quadratic function is below the x-axis, which means finding the roots of the function first.
Given the quadratic function in standard form as: f(x) = 2x² - 16x - 30
To find the roots, you can use the quadratic formula: x = [-b ± sqrt(b² - 4ac)] / 2a
When you substitute a = 2, b = -16, and c = -30 into the formula, you get x = 5 and x = -3.
Therefore, the function f(x) is negative between these two roots (that is, -3 < x < 5).
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Let A be a set. Define a relation E on P(A), the power set of A (the collection of all subsets of A) as follows. For X,Y SA, XEYX SYi.e. if X is a subset of Y. Prove or give a counterexample for your answers to the following questions. a) E is a reflexive relation. b) E is a symmetric relation. c) E is an antisymmetric relation d) E is a transitive relation e) Eis an equivalence relation. 1) (PCA), E) is a partially ordered set?
E) is a partially ordered set. a) E is a reflexive relation: A relation is reflexive if for every element X in P(A), XEX holds true. Since every set is a subset of itself (X ⊆ X), the relation E is reflexive.
b) E is not a symmetric relation:
A relation is symmetric if for every pair of elements X, Y in P(A), whenever XEY, it's also true that YEX. To disprove symmetry, consider two distinct sets X and Y where X is a proper subset of Y (X ⊆ Y and X ≠ Y). In this case, XEY, but YEX does not hold, so E is not symmetric.
c) E is an antisymmetric relation:
A relation is antisymmetric if for every pair of elements X, Y in P(A), if XEY and YEX, then X = Y. Since X ⊆ Y and Y ⊆ X implies X = Y, the relation E is antisymmetric.
d) E is a transitive relation:
A relation is transitive if for every three elements X, Y, Z in P(A), if XEY and YEZ, then XEZ. If X ⊆ Y and Y ⊆ Z, then X ⊆ Z, which means XEZ holds true. Therefore, E is a transitive relation.
e) E is not an equivalence relation:
An equivalence relation must be reflexive, symmetric, and transitive. While E is reflexive and transitive, it is not symmetric, so E is not an equivalence relation.
1) (P(A), E) is a partially ordered set:
A partially ordered set is a set with a binary relation that is reflexive, antisymmetric, and transitive. Since E has these properties, (P(A), E) is a partially ordered set.
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Find the center of mass of cone of uniform density that has a radius R at the base, height h, and mass M. Let the origin be at the center of the base of the cone and have +z going through the cone vertex.
To find the center of mass of a cone of uniform density with radius R at the base, height h, and mass M, we need to use the formula:
x_cm = (1/M)∫∫∫xρdV
y_cm = (1/M)∫∫∫yρdV
z_cm = (1/M)∫∫∫zρdV
where x_cm, y_cm, and z_cm are the coordinates of the center of mass, ρ is the density, and V is the volume of the cone.
We can simplify the integral by using cylindrical coordinates, where the density is constant and equal to M/V, and the limits of integration are:
0 ≤ r ≤ R
0 ≤ θ ≤ 2π
0 ≤ z ≤ h(r/R)
Thus, the center of mass of the cone is:
x_cm = 0
y_cm = 0
z_cm = (3h/4)(r/R)^2
Therefore, the center of mass of the cone is located at (0, 0, (3h/4)(r/R)^2) with respect to the origin at the center of the base of the cone and +z going through the cone vertex.
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consider the poset (n, |). are there any minimal elements? are there any maximal elements? explain.
The poset (n, |) has a unique minimal element 1, but no maximal elements. The poset (n, |) is the set of natural numbers n with the relation "divides" denoted by |. In other words, a | b if and only if a divides b evenly with no remainder.
To determine if there are any minimal elements in this poset, we need to find the smallest element in the set that is related to all other elements. In this case, 1 is the smallest natural number and it is related to all other natural numbers since 1 | n for all n in the set. Therefore, 1 is a minimal element in this poset.
To determine if there are any maximal elements in this poset, we need to find the largest element in the set that is related to all other elements. However, there is no such element in this poset since for any natural number n, there is always another natural number greater than n that is related to it. For example, 2 | 4 and 4 | 8, so 8 is related to both 2 and 4 but it is greater than both of them. Therefore, there are no maximal elements in this poset.
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a die used in a certain board game has eight faces, of which 3 are red, 3 are yellow, and 2 are blue. each face is equally likely to land faceup when the die is tossed. in the game, a player tosses the die until blue lands faceup, and the number of tosses before blue lands faceup is counted. for example, a player who tosses the sequence shown in the following table has tossed the die 3 times before blue lands faceup. toss number 1 2 3 4 face color yellow yellow red blue what is the probability that a player will toss the die at least 2 times before blue lands faceup?
The probability that a player will toss the die at least 2 times before blue lands faceup is 15/28.
Geometric distribution:
The geometric distribution, which is a probability distribution that models the number of trials needed to achieve the first success in a sequence of Bernoulli trials, where each trial has a constant probability of success.
In this case, the Bernoulli trial is whether the die lands on blue, and the geometric distribution models the number of tosses needed to achieve the first blue face.
To find the probability that a player will toss the die at least 2 times before blue lands faceup, we need to find the probability of getting either a red or a yellow face on the first toss, and then either a blue face or another red/yellow face on the second toss.
The probability of getting a red or yellow face on the first toss is:
P(Red or Yellow) = 3/8 + 3/8 = 6/8 = 3/4
If the first toss is a red or yellow face,
then the probability of getting a blue face on the second toss is:
P(Blue on 2nd toss | Red or Yellow on 1st toss) = 2/7
So, the probability of getting blue on the second toss given the first toss is red or yellow is 2/7.
Therefore, the probability of not getting a blue face on the second toss given the first toss is red or yellow is 1-2/7=5/7.
Putting it all together, the probability of tossing the die at least 2 times before blue lands faceup is:
P(at least 2 tosses)
= P(Red or Yellow on 1st toss) × P(Not Blue on 2nd toss given Red or Yellow on 1st toss)
= (3/4) × (5/7)
= 15/28
Therefore,
The probability that a player will toss the die at least 2 times before blue lands faceup is 15/28.
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A claim has been made that men in the age group 20-30 average the same height in inches in the U.S. and the Netherland (the land of giants, by the way). I do not believe this claim. I want to be 99% confident and have 90% power. If I think both populations have a population standard deviation of 4, what sample size (total) would I need to reject the claim if the two populations different by 0.5 (inches)?
The required sample size (total) to reject the claim of men in the age group 20-30 averaging the same height in inches in the U.S. and the Netherlands, assuming both populations have a population standard deviation of 4, would be 1456.
To calculate the required sample size, we need to use the formula for sample size calculation in two-sample t-tests, which takes into account the desired level of significance, power, effect size, and population standard deviation. In this case, we want to be 99% confident (i.e., 1% level of significance) and have 90% power, which corresponds to a z-value of 2.33 and a t-value of 1.645. The effect size is 0.5/4 = 0.125, and plugging these values into the formula, we get a required sample size of 1456. This means that if we take a sample of 728 men from each population and find a difference of 0.5 inches or more between their means, we can reject the claim with 99% confidence and 90% power.
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You suspect minority students are not as supportive of the new principal of a large school because of a few recent conflicts on campus. You randomly choose students and ask them if they think the principal is doing a good job. You find that 45 out of 56 white students and 21 out of 33 minority students surveyed support the principal.
Show that the conditions and assumptions for inference are satisfied.
The conditions and assumptions for inference are reasonably satisfied, particularly with regard to random sampling, independence, and sample sizes.
To show that the conditions and assumptions for inference are satisfied, we need to assess whether the sample meets the necessary requirements. In this case, we are examining the support for the principal among white and minority students in a large school.
1. Random Sampling: The statement mentions that students were randomly chosen for the survey. Random sampling helps ensure that the sample is representative of the larger population. If the students were truly selected randomly, this condition is satisfied.
2. Independence: To conduct inference, it is essential to assume that the responses from different students are independent of each other. If students were selected randomly and surveyed independently without any influence from one another, this condition is likely to be satisfied.
3. Sample Size: The sample sizes for both white and minority students are given: 56 white students and 33 minority students. While sample size alone does not guarantee inference validity, larger samples tend to provide more reliable estimates.
4. Normality: For inference methods such as hypothesis testing or constructing confidence intervals, the sample data should follow an approximately normal distribution. Since we don't have information about the underlying population or the distribution of the responses, we cannot directly assess the normality assumption. However, if the sample sizes are sufficiently large (typically around 30 or more), the Central Limit Theorem suggests that the sampling distribution will tend to be approximately normal, even if the underlying population is not.
5. Random Assignment (for experiments): The statement doesn't mention whether this study is an experiment with a randomly assigned treatment. Since it only involves surveying students' opinions, this assumption is not applicable in this case.
Based on the information provided, it appears that the conditions and assumptions for inference are reasonably satisfied, particularly with regard to random sampling, independence, and sample sizes. However, without additional information or data, it cannot definitively confirm the exact nature of the population or distribution.
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Harper leans a 24-foot ladder against a wall so that it forms an angle of 69 degrees with the ground. What’s the horizontal distance between the bade of the ladder and the wall? Round your answer to the nearest tenth of a foot if necessary.
The horizontal distance between the base of the ladder and the wall is 8.6 feet.
What is distance?distance is the length between two points.
To calculate the horizontal distance between the ladder and the wall, we use the formula below.
Formula:
[tex]\sf cos \ \theta=\dfrac{adjacent(y)}{hypotenuse(h)}[/tex]
Make y the subject of the equation
[tex]\sf h = \dfrac{y}{ cos\ \theta}[/tex]........ Equation 2
Where:
[tex]\theta[/tex] = Angle between the wall and the laddery = horizontal distance between the base of the ladder and the wallh = Length of the ladder lean against the wallFrom the question,
Given:
y = 24 foot[tex]\theta[/tex] = 69°Substitute these values into equation 2
[tex]\sf y = \dfrac{24}{(cos \ 69^\circ)}[/tex]
[tex]\sf y = \dfrac{24}{0.358}[/tex]
[tex]\sf y =\bold{8.6 \ feet}[/tex]
Hence, The horizontal distance between the base of the ladder and the wall is 8.6 feet.
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A copy machine makes 44 copies per minute. How long does it take to make 209 copies.
Answer:4.75
Step-by-step explanation: 209 divided by 44
Help Please Thank you very much :)
Answer:
For n = 1, 2, 3,.....,
[tex] a(n) = \frac{10n(n + 1)}{2} + 1 = 5n(n + 1) + 1 [/tex]
[tex] = 5 {n}^{2} + 5n + 1[/tex]
what is the answer to: 15% x 1,200
100 points to anyone who answers
The answer will be 180 .
Given,
15% × 1200.
Firstly convert 15% to fraction form.
Percentage to fraction;
15% = 15/100
Now,
15/100 × 1200
15 × 12
180.
Thus the value of 15% of 1200 is 180.
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How many triangles exist with the given side lengths?
4m,4m,7m
How many triangles exist with the given side lengths: C) More than one triangle exists with the given side lengths.
What is the triangle inequality theorem?In Euclidean geometry, the Triangle Inequality Theorem states that the sum of any two side lengths of a triangle must be greater than or equal (≥) to the third side of the triangle.
Mathematically, the Triangle Inequality Theorem is represented by this mathematical expression:
b - c < n < b + c
Where:
n, b, and c represent the side lengths of this triangle.
4 + 4 > 7 (True).
4 + 7 > 4 (True).
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Complete Question:
How many triangles exist with the given side lengths?
4m, 4m, 7m
A) No triangle exists with the given side lengths.
B) Exactly one unique triangle exists with the given side lengths.
C) More than one triangle exists with the given side lengths.
use the table of values and produce a graph for the data. use the number of tables along the x-axis and the number of guests along the y-axis. plot each pair of values
By using the table of values, a graph of the number of tables along the x-axis and the number of guests along the y-axis is shown in the image below.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.Based on the sitting arrangement, we have:
x y_____
1 table 6 guests.
2 table 10 guests.
3 table 14 guests.
Next, we would determine the slope;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (10 - 6)/(2 - 1)
Slope (m) = 4/1
Slope (m) = 4
At data point (1, 6) and a slope of 4, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 6 = 4(x - 1)
y = 4x - 4 + 6
y = 4x + 2
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
find the distance between the given parallel planes. 2x − 5y z = 4, 4x − 10y 2z = 2
The distance between two parallel planes is given by the absolute value of the difference between the constant terms in their equations divided by the square root of the sum of the squares of the coefficients of x, y, and z.
In this case, the constant term in the equation 2x − 5y + z = 4 is 4, and the constant term in the equation 4x − 10y − 2z = 2 is 2. Therefore, the absolute value of their difference is |4 - 2| = 2. The coefficients of x, y, and z in the two equations are 2, -5, 1 and 4, -10, -2, respectively. The sum of the squares of these coefficients is 30 + 41 = 71. Therefore, the distance between the two planes is 2/√71.
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A teacher places a sketch of the original Ferris wheel on a coordinate plane.
The center of the Ferris wheel is at the origin, and one car lies on the x-axis g at (125, 0). The teacher wants to demonstrate the relationship between the number of seconds a car has been moving and the distance in feet between the car and the horizontal axis.
Construct a graph that relates the amount oftime the car is in motion (from time = 0 seconds to time = 40 seconds) to the position of the car with respect to the horizontal axis. Describe the steps you took to make your graph.
The function that represents the situation is y = 125 sin(πt/20).
To construct the graph, we need to first find the equation of the circle that represents the Ferris wheel.
We know that the center of the circle is at the origin and one point on the circle is (125, 0).
Since the radius of the Ferris wheel is not given, we can assume it to be 100 feet (a common value for Ferris wheels).
Using the standard form of the equation of a circle, we get:
x² + y² = r²
Substituting the coordinates of the point (125, 0), we get:
125² + 0² = r²
Simplifying, we get:
r = 125
So the equation of the circle is:
x² + y² = 125²
To find the distance between the car and the horizontal axis at any given time, we need to find the y-coordinate of the point on the circle that corresponds to the angle swept out by the car in that time.
We know that the car takes 40 seconds to make a complete revolution around the Ferris wheel, so the angle swept out in t seconds is:
θ = 2πt/40
Using this angle, we can find the y-coordinate of the point on the circle as:
y = r sin(θ) = 125 sin(πt/20)
We can now plot a graph of y versus t from t=0 to t=40 seconds using a graphing calculator or spreadsheet software.
The resulting graph will show the relationship between the amount of time the car is in motion and the distance in feet between the car and the horizontal axis.
The graph will be a sinusoidal wave with a period of 40 seconds, an amplitude of 125 feet, and a vertical shift of 125 feet (since the lowest point of the Ferris wheel is at y=-125).
The graph will start at y=0 feet when t=0 seconds and will complete one cycle (from y=0 feet to y=0 feet) when t=40 seconds.
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find the general solution near x = 0 of y'' - xy' 2y = 0
The general solution of the differential equation near x = 0 is: y(x) = c1 x + c1^3/3 x^3 + (c1^4/4 + c1^6/9) x^4 + ... where c1 is an arbitrary constant.
To find the general solution of the given differential equation near x = 0, we can use the power series method. We assume that the solution can be written as a power series in x, that is:
y(x) = ∑n=0∞ cn xn
Then, we can find the coefficients cn by substituting the power series into the differential equation and equating the coefficients of like powers of x. Let's begin by computing the first and second derivatives of y(x):
y'(x) = ∑n=1∞ n cn xn-1
y''(x) = ∑n=2∞ n(n-1) cn xn-2
Now, we substitute these expressions into the differential equation and simplify:
y''(x) - xy'(x)^2 y(x) = 0
∑n=2∞ n(n-1) cn xn-2 - x(∑n=1∞ n cn xn-1)^2 (∑n=0∞ cn xn) = 0
Expanding the squares and collecting like terms, we get:
∑n=2∞ n(n-1) cn xn-2 - x∑n=1∞∑m=1∞ mcmn xn+m-2 - ∑n=0∞ cn xn+2 = 0
We can simplify the double sum by changing the index of summation:
∑n=2∞ n(n-1) cn xn-2 - x∑k=2∞∑n+m=k+2∞ mn cm cn-m xn+k-2 - ∑n=2∞ cn-2 xn = 0
We observe that the coefficient of x^0 on the left-hand side is zero, so we can assume that c0 = c1 = 0. Also, the coefficient of x^1 is zero, so we get:
2c2 - 2c2c1 = 0
c2 = c1^2
For higher values of n, we can recursively compute the coefficients in terms of c1. For example, the coefficient of x^2 is:
6c3 - 6c1c2 - c1^4 = 0
c3 = c1c2/6 + c1^4/6
Substituting c2 = c1^2, we get:
c3 = c1^3/3
Similarly, we can find the coefficient of x^3:
24c4 - 24c1c3 - 6c2c2 - 6c1^2c2 - c1^6 = 0
c4 = c1^4/4 + c1^2c2/12 + c1^6/24
Substituting c2 = c1^2 and c3 = c1^3/3, we get:
c4 = c1^4/4 + c1^6/9 + c1^6/24
In general, we can express the coefficients cn in terms of c1 as follows:
cn = ∑k=0^n-2 pk,c1^k
where pk,k = 1 and pk,m = ∑j=1^m-1 (j+1) pj-1,k for m > k+1.
Therefore, the general solution of the differential equation near x = 0 is:
y(x) = c1 x + c1^3/3 x^3 + (c1^4/4 + c1^6/9) x^4 + ...
where c1 is an arbitrary constant.
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The circle below is centred at O.
What is the size of angle x?
Write a justification for your answer.
o =146°
Not drawn accurately
The value of angle x is 107°
What is circle geometry?A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.
There is a theorem in circle geometry that states that : The angle subtended at the centre of a circle is twice the angle at the circumference.
This means if the angle at the circumference is 50, the angle at the center is 100.
The angle at the center = 360 - 146( angle at a point)
= 214°
2x = 214
x = 214/2
x = 107°
therefore the value of x is 107°
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please help for grade 8 math's
Answer:
129*
Step-by-step explanation:
First notice the 2 parallel lines. Since the 2 parallel lines are intersecting the same line, the angle measures would be the same for both. Since the first angle is 51*, the corresponding angle for the next line is also 51*. Since it intersects a straight line, the angles need to add up to 180*. 51 + x = 180 so x = 129*
A researcher randomly selects and interviews fifty male and fifty female teachers.
a. systematic
b. convenience
c. random
d. stratified
e. cluster
The sampling method described in the scenario is d. stratified sampling.
In stratified sampling, the population is divided into distinct subgroups or strata based on certain characteristics or variables. The researcher then randomly selects samples from each stratum in proportion to their representation in the population. This approach ensures that the sample is representative of the population's diversity.
In this case, the researcher has divided the population of teachers into two strata: male teachers and female teachers. By randomly selecting 50 male teachers and 50 female teachers, the researcher is ensuring that both genders are represented in the sample.
The researcher's intention is to have a sample that reflects the gender distribution of teachers in the population accurately. Therefore, stratified sampling is the appropriate method in this scenario.
Other sampling methods, such as systematic sampling, convenience sampling, random sampling, and cluster sampling, are not applicable because they do not specifically address the need to ensure proportional representation of genders in the sample.
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27) A company promises to release a new
smartphone model every month. Each
model's battery life will be 4% longer than
the previous model's. If the current
model's battery life is 735.0 minutes, what
will the latest model's battery life be 7
months from now?
Write an exponential function, then answer the
question using that function. Show your
calculations.
Answer:
935.65 minutes.
Step-by-step explanation:
The battery life of the nth model can be represented by the exponential function:
f(n) = 735(1.04)^(n-1)
where n is the number of the model.
To find the battery life of the latest model 7 months from now, we need to find f(8):
f(8) = 735(1.04)^(8-1)
f(8) = 735(1.04)^7
f(8) = 935.65
Therefore, the battery life of the latest model 7 months from now will be approximately 935.65 minutes.
Note: The battery life is rounded to two decimal places.
Solve the simultaneous equation x-y=5 and 2x-y=13
if the poverty threshold is approximately $16,000 for a household of three, what would the census bureau consider the poverty status of a household of three that earns $12,000?
The census bureau would consider a household of three that earns $12,000 to be living below the poverty threshold. The poverty threshold is the minimum income required to meet basic needs such as food, shelter, and clothing. If a household earns less than the poverty threshold, it means they are unable to afford these basic necessities. In the case of a household of three, the poverty threshold is approximately $16,000. Therefore, a household earning $12,000 falls short of this minimum requirement and is considered to be living in poverty.
The poverty threshold is an important benchmark used by the census bureau to determine the poverty status of households. It is based on the income level required to meet basic needs such as food, shelter, and clothing. The poverty threshold varies based on the size of the household and is adjusted annually for inflation.
A household of three that earns $12,000 would be considered to be living below the poverty threshold by the census bureau. This means that they are unable to afford basic necessities and are experiencing financial hardship. It highlights the need for policies and programs that address poverty and support those who are struggling to make ends meet.
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The base of an isosceles triangle is x units. The sum of the lengths of the other two sides is one unit less than the length of the base. If the perimeter of the triangle is 67 units or less, which inequality describes all possible lengths of the
base?
A) x ≤ 34
B) x ≤ 16.5
C) x ≥ 34
D) x ≥ 16 5
The inequality that describes all possible lengths of the base is x ≤ 34 So, the correct option is (A).
Let the length of each of the other two sides be y. Since the triangle is isosceles, we have y = y. We also know that the sum of the lengths of the other two sides is one unit less than the length of the base, so:
2y = x - 1
Solving for y, we get:
y = (x - 1)/2
The perimeter of the triangle is:
P = x + y + y = x + 2y
Substituting the expression for y we obtained earlier, we get:
P = x + 2[(x - 1)/2] = 2x - 2
We are given that P ≤ 67, so:
2x - 2 ≤ 67
Solving for x, we get:
x ≤ 34.5
Therefore, the inequality that describes all possible lengths of the base is:
x ≤ 34
So, the correct option is (A).
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Data Completion. Determine a number that must be added to make each of the following a perfect square
trinomial.
26. x² + 3x +
27. t² + 10t +.
28. x² - 30x +
29. r²- 18r+.
30. x² - 10x +
31.
h²h+
2
32. 3x² + 3x +
33. 2x² -5x +_
34. s² + 6s+
35. x² - 12x +
_I
Giving out brainliest. please help ASAP
25$ will be the final cost.
The cost (y) depends on the number of items purchased (x). We know that there is a flat fee of $10, so we start with the equation
y = 10 + ...
Then we add the cost of each item, which is $5 per item:
y = 10 + 5x
This is the linear equation that represents the total cost as a function of the number of items purchased.
For example, if a customer purchases 3 items, the total cost would be:
y = 10 + 5(3) = 25
So the total cost would be $25.
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Complete question:
A store charges a flat fee of $10 for every purchase, plus an additional $5 for every item purchased. Write a linear equation that represents the total cost (y) as a function of the number of items purchased (x).
Convert the mixed numbers to improper fractions and solve
11) 9 1/2 + 1 1/2
12) 5 + 3 1/3
13) 2 4/5 + 16 2/5
14) 7 1/2 + 2 1/4
15) 8 5/6 + 3 2/3
16) 2 7/8 + 3 1/2 + 5 + 3 1/4
17) 5 1/2 + 2 1/3 + 9 1/6 + 2
18) 5 1/3 + 3 1/12 + 6 + 4 1/6
19) 2 1/15 + 7 2/5 + 5 + 3 1/3
Answer:
do you choose the best
Step-by-step explanation:
9 1/2 + 1 1/2
Converting to improper fractions: 9 1/2 = (9 * 2 + 1) / 2 = 19/2 and 1 1/2 = (1 * 2 + 1) / 2 = 3/2
Adding the fractions: 19/2 + 3/2 = (19 + 3) / 2 = 22/2 = 11/1 = 11
5 + 3 1/3
Converting to improper fractions: 5 = 5/1 and 3 1/3 = (3 * 3 + 1) / 3 = 10/3
Adding the fractions: 5/1 + 10/3 = (5 * 3 + 10) / 3 = 25/3
2 4/5 + 16 2/5
Converting to improper fractions: 2 4/5 = (2 * 5 + 4) / 5 = 14/5 and 16 2/5 = (16 * 5 + 2) / 5 = 82/5
Adding the fractions: 14/5 + 82/5 = (14 + 82) / 5 = 96/5
7 1/2 + 2 1/4
Converting to improper fractions: 7 1/2 = (7 * 2 + 1) / 2 = 15/2 and 2 1/4 = (2 * 4 + 1) / 4 = 9/4
Adding the fractions: 15/2 + 9/4 = (15 * 2 + 9) / 2 = 39/4
8 5/6 + 3 2/3
Converting to improper fractions: 8 5/6 = (8 * 6 + 5) / 6 = 53/6 and 3 2/3 = (3 * 3 + 2) / 3 = 11/3
Adding the fractions: 53/6 + 11/3 = (53 * 3 + 11 * 6) / 6 = 257/6
2 7/8 + 3 1/2 + 5 + 3 1/4
Converting to improper fractions: 2 7/8 = (2 * 8 + 7) / 8 = 23/8, 3 1/2 = (3 * 2 + 1) / 2 = 7/2, 3 1/4 = (3 * 4 + 1) / 4 = 13/4
Adding the fractions: 23/8 + 7/2 + 5 + 13/4 = (23 * 2 + 7 * 8 + 5 * 8 + 13 * 2) / 8 = 101/8
5 1/2 + 2 1/3 + 9 1/6 + 2
Converting to improper fractions: 5 1/2 = (5 * 2 + 1) / 2 = 11/2