Answer:
Maria is able to spend less than $12.
C < 12
Step-by-step explanation:
If Maria has already spent 17 dollars, that means she has 12 dollars left. C cannot be greater than 12. It has to be less.
So think of this C < $12
So if we do the total on one side and the $17 and C on the other side of inequality we get
C + 17 < 29
It cannot be equal to 29 so that's why we don't use a less than or equal to symbol.
Simplify this to get C < 12
I hope this is able to help you :D
Expand a^2= (b-x)^2 +h^2
The expanded value of the given equation is a²+2bx = b² + x ²+ h² .
Expansion - what is it?Multiplication distributes over addition, so an expansion of a product of sums represents it as a sum of products.
Expansion is a scale-increasing affine transformation, sometimes known as enlargement or dilatation. It is also frequently referred to as an enlargement and is the polar opposite of a geometric contraction. An expansion and a translation are equivalent to a central dilation.
We must multiply out the brackets in order to expand and simplify an expression, and we must then collect like words in order to simplify the resulting expression.
Given : a^2= (b-x)^2 +h^2
a² = (b-x)² + h²
we know that (c-d)² = c²+d² + 2cd
So, a² = b² + x² -2bx + h²
a²+2bx = b² + x ²+ h²
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The initial bacterium count in a culture is 500. A biologist later makes a sample count ofbacteria in the culture and finds that the relative rate of growth is 40% per hour.(a)Find a function that models the number of bacteria after t hours.(b)What is the estimated count after 10 hours?(c)When will the bacteria count reach 80,000?(d)Sketch the graph of the function . n(t)
a) The function is P = 500e^0.4t
b) The count after 10 hours is 27299
c) it would reach 80000 in 13 hours
What is the function?We know that at this time we are dealing with the population of the bacteria and we have to invoke the exponential growth ideology and we would have;
P = Poe^rt
P = population at time t
Po = Initial population
r = Population growth rate
t = Time taken
Then we have;
P = 500e^0.4t
After ten hours;
P= 500e^0.4 * 10
P = 27299
The count would reach 80000 when;
80000 = 500e^0.4 t
80000/500 = e^0.4 t
160 = e^0.4 t
ln160 = e^0.4 t
ln160 = 0.4t
t = ln160/0.4
t = 13 hours
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The size of a pentagon are given as x, x+1,x+3,x-2 and 6.If the perimeter is less than 78cm and x is an interger.Find the largest value of x
The largest value of x is 13.
What is perimeter?A closed shape's perimeter is the sum of the lengths of its outside boundaries. The lengths of all the sides are added to determine the measurement.
Given:
The size of a pentagon are given as x, x+1,x+3,x-2 and 6.
The perimeter is less than 78 cm and x is an integer.
The perimeter of the pentagon = the sum of all the sides.
x + x+1 + x+3 + x-2 + 6 < 78
4x + 10 - 2 < 78
4x < 70
x < 14
The largest value of x is 13.
Therefore, the largest value of x is 13.
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in trigonometry it is important that the right triangles (reference triangles) have a consistent orientation. the reference triangles always have a leg perpendicular to the [ select ] , the value of the hypotenuse is [ select ] , and is the angle adjacent to the [ select ] .
In trigonometry it is important that the right triangles (reference triangles) have a consistent orientation. the reference triangles always have a leg perpendicular to the y-axis , the value of the hypotenuse is positive , and is the angle adjacent to the y-axis and hypotenuse.
A right angle triangle has six trigonometric ratios: Sin, Cos, Tan, Cosec, Sec, and Cot. They represent, successively, Sine, Cosine, Tangent, Cosecant, Secant, and Cotangent.
So, when we graph a right angle triangle, we draw a side of triangle perpendicular to y-axis and another side will be on y-axis. The remaining side left would be hypotenuse that will always be positive and is adjacent to the side perpendicular to y-axis and the side on the y-axis.
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an ordinary annuity pays 1000 quarterly for two years. how many payments are there?
The number of payments for the ordinary annuity that pays $1,000 quarterly for two years is 8.
What is an ordinary annuity?An ordinary annuity's cash flows or payments occur at the end of the period, unlike an annuity due.
For quarterly payments, in a year, payments are made 4 times, that is, every three months.
For two years, the payments will be made 8 times (4 x 2).
Thus, we expect the ordinary annuity to pay $8,000 ($1,000 x 2 x 4).
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If a particular sample has 36 participants and the other sample has 40 participants, the total degrees of freedom for the study is __________.
If a particular sample has 36 participants and the other sample has 40 participants, the total degrees of freedom for the study is
What is the degrees of freedom?In Mathematics, the degrees of freedom in a sample are typically used to correct a possible bias that exists between the alternative and null hypotheses.
Mathematically, total degrees of freedom for the study can be calculated by using this mathematical expression:
v = n - k
Where:
v represents the total degree of freedom.n represents the number of individuals in a samplek represents the number of parameters being estimated.Note: k is equal to 2 in this scenario.
Total degrees of freedom, v = n₁ + n₂ - k
Total degrees of freedom, v = 36 + 40 - 2
Total degrees of freedom, v = 74.
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Answer the questions in image!
(The answers are already there, just figure out which go where.)
50 points!
for 14-21 write two equivalent fractions for each
The fractions with different numerators and denominators but the same value are said to be equivalent fractions.
What is an equivalent fraction about?For instance, since 2/4 and 3/6 both equal the 1/2, they are equivalent fractions. An element of a whole is a fraction. The same amount of the whole is represented by equivalent fractions.
A rule that says the result of multiplying the numerator and denominator of a fraction by the same nonzero number is a fraction equal to the original fraction.
Equivalent fractions are those that, despite their visual differences, represent the same value. For instance, if you have a cake and cut it into two equal pieces, you will have consumed half of the cake.
In this case, it should be noted 1/2 is the same as 3/6.
Note that an overview was given as your information is incomplete.
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An experiment subject only to random fluctuation within a normal distribution collects the following set of unitless numerical values: 15.8, 17.8, 19.5, 20.0, 14.7, 16.6, 16.8, 19.4, 18.3
A number of hypotheses are put forward for the theoretical value of what is measured here. Select all of the theoretical values given below that can be ruled out by our usual 1-sigma uncertainty criterion. A. 15.6 B. 15.9 C. 19.5 D. 19.7 E. None of these theoretical values is confirmed by this data.
A one-sigma uncertainty criterion means that if a theoretical value falls within one standard deviation of the measured data, it is considered consistent with the data.
Using this criterion, we can rule out theoretical value D. 19.7, since it is outside the range of measured values.
The other theoretical values A. 15.6, B. 15.9, and C. 19.5 fall within one standard deviation of the measured data, so they cannot be ruled out by this criterion.
Therefore, the only theoretical value that can be ruled out by our usual 1-sigma uncertainty criterion is D. 19.7
It's worth noting that this method just gives a rough idea of the consistency of a theoretical value with the data.
Other methods, such as the chi-squared test, or Bayesian analysis could be used to find the best-fit theoretical value and its uncertainty, and confirm or rule out other theoretical values.
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Use the formula F =9 over 5 C + 32 to answer the following
Maha checked the outside temperature at noon one day and found it was 26° C. At 10 PM when she checked, the outside temperature was 18° C. How much, in degrees Fahrenheit, did the temperature drop between noon and 10 PM? Round your answer to the nearest tenth.
The temperature drop between noon and 10 PM is 14.4° F.
What is the conversion of Celsius to Fahrenheit?Celsius to Fahrenheit is the conversion of temperature from Celsius unit to Fahrenheit unit. Temperature scales provide a way of measuring how hot or cold a body is. Fahrenheit and Celsius are temperature scales.
The formula to convert Celsius to Fahrenheit is given by: °F = °C × (9/5) + 32.
Given that, Maha checked the outside temperature at noon one day and found it was 26° C.
So, the temperature in Fahrenheit is °F =26° ×(9/5)+32
= 46.8+32
= 78.8° F
At 10 PM when she checked, the outside temperature was 18° C.
So, the temperature in Fahrenheit is °F =18° ×(9/5)+32
= 32.4+32
= 64.4° F
Difference in temperature =78.8-64.4
= 14.4° F
Therefore, the temperature drop between noon and 10 PM is 14.4° F.
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Homework 3x-5; x-5; an al 2x-14;.:. arithmetic sequence. Calculate the Value of x Find the Which term the First three are in Determine the general term of the Sequence Soth term the sequence is equal to -62 terms of
The value of x is found to be 3 and the arithmetic sequence is found to be 4, -2, -8, ... .
What is arithmetic sequence?
The nth term of an arithmetic progression is determined using the arithmetic sequence formula. The series where the common difference between any two next words stays constant is known as an arithmetic sequence.
The arithmetic sequence is 3x - 5, x - 5, 2x - 14, ....
If the numbers are in an arithmetic sequence, then the difference between the first and second term must be the same as the difference between the second and third term.
(x - 5) - (3x - 5) = (2x - 14) - (x - 5)
x - 5 - 3x + 5 = 2x - 14 - x + 5
-2x = x - 9
-2x - x = -9
-3x = -9
x = 3
The first three terms can be obtained by substituting the value of x in the terms -
The first term - 3(3) - 5 = 4
The second term - 3 - 5 = -2
The third term = 2(3) - 14 = -8
Therefore, the arithmetic sequence is 4, -2, -8, .....
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A mathematics teacher wanted to see the correlation between test scores and homework. The homework grade (x) and test grade (y) are given in the accompanying table. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest tenth. Using this equation, find the projected test grade, to the nearest integer, for a student with a homework grade of 79.
The linear regression equation for this data is given as follows:
y = x - 6.
The projected grade for a student with homework grade of x = 79 is given as follows:
73.
How to obtain the equation for the regression line?The equation for the line of fit is obtained inserting the points of the data-set into a linear regression calculator.
The points from this data-set are given as follows:
(70, 55), (89, 92), (79, 81), (84, 74), (84, 77), (70, 65) and (64, 68).
Inserting these points into a calculator, the regression equation is given as follows:
y = x - 6.
The projected grade for a student with homework grade of x = 79 is obtained as follows:
y = 79 - 6
y = 73.
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The figure below is dilated by a factor of centered at the origin. Plot the resulting image.
A graph of the resulting image after a dilation by a factor of 1/4 centered at the origin is shown in the image attached below.
What is dilation?In Geometry, dilation simply refers to a type of transformation which typically changes the size of a geometric object, but not its shape.
Next, we would have to dilate the coordinates of the pre-image by using a scale factor of 1/4 centered at the origin as follows:
Ordered pair T (8, 8) → Ordered pair T' (8 × 1/4, 8 × 1/4) = Ordered pair T' (2, 2).
Ordered pair R (-8, -4) → Ordered pair R' (-8 × 1/4, -4 × 1/4) = Ordered pair R' (-2, -1).
Ordered pair S (4, -8) → Ordered pair S' (4 × 1/4, -8 × 1/4) = Ordered pair S' (1, -2).
Lastly, we would use an online graphing calculator to plot the resulting data points.
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show me prymind with base length: 8 feet side length: 6.56 feet (calculated using the pythagorean theorem) height: 12 feet rmid
A diagram of a pyramid with the given measurements is not possible to generate.
But we can calculate he base length, side length and height of a pyramid using the Pythagorean theorem.
In a pyramid, the slant height (rmid) can be found using the Pythagorean theorem. If the base length (b) and the height (h) of the pyramid are known, the slant height (rmid) can be calculated using the formula:
rmid = sqrt(b^2 + h^2)
In this case,
rmid = sqrt(8^2 + 12^2) = sqrt(64 + 144) = sqrt(208) = 14.4
You can also use this information to find the side length of the pyramid, which is the length of one of the triangular faces. Using the Pythagorean theorem again:
side length = sqrt(rmid^2 - (b/2)^2)
In this case,
side length = sqrt(14.4^2 - (8/2)^2) = sqrt(207.36 - 16) = sqrt(191.36) = 6.56
So, based on the information provided, the base length of the pyramid is 8 feet, the side length is 6.56 feet and the height is 12 feet and the slant height is 14.4 feet.
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Solve the equation on the
interval [0, 2π).
3 sin x = sin x + 1
The solution to the equation on the interval is x = π/6 + 2πn, where n is any non-negative integer less than 2.
How to determine the solutionFrom the question, we have the following parameters that can be used in our computation:
3 sin x = sin x + 1
Interval = [0, 2π).
To solve the equation 3sin(x) = sin(x) + 1, we first subtract sin(x) from both sides to get 2sin(x) = 1.
So, we have
2sin(x) = 1
Then, we divide both sides by 2
sin(x) = 1/2.
Therefore, x = arcsin(1/2) + 2πn, where n is any integer.
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A friend has a 81% average before the final exam for a course. That score includes everything but the final, which counts for 25%
The best grade that can be earned is given as 0.8575
How to solve for the gradeIf he is able to get the sum of 100 percent in the final exam, trhis would count as 25 percent of the total grade that he has
100 - 25 = 75%
Then we would have
0.75 * 81 + 25 / 100
= 85.75 / 100
= 0.8575
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Question
A friend has a 81% average before the final exam for a course. That score includes everything but the final, which counts for 15% of the course grade.
What is the best course grade your friend can earn?
As a town gets smaller the population of its high school decreases by 4% each year the senior class has 160 students now. In how many years will it have about 100 students? write an equation. then solve the equation without graphing.
The number of years that it will it have about 100 students is 11 years.
How to calculate the number of tears?Final population = Initial population * (1-0.04)^years
Where 0.04 is the percentage decrease (4%) converted to decimal form, and "years" is the number of years in the future.
We can use this formula to find the number of years it will take for the senior class to have about 100 students:
Final population = 100
Initial population = 160
100 = 160 * (1-0.04)^years
We can solve for "years" by taking the natural logarithm of both sides:
ln(100) = ln(160 * (1-0.04)^years)
ln(100) = ln(160) + ln((1-0.04)^years)
and then we can solve for the power of (1-0.04)
ln(100) - ln(160) = ln((1-0.04)^years)
now we can get the value of years
years = (ln(100) - ln(160)) / ln(1-0.04)
which is around 10.72 , so it would take about 11 years for the senior class to have about 100 students.
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The distribution of values taken by a statistic in all possible samples of the same size from the same population is None of the above The population parameter The sampling distribution of the statistic The probability that the statistic is obtained The variance of the values
The sampling distribution of a statistic is the distribution of values taken by the statistic in all possible samples of the same size from the same population.
The population parameter is the true value of the statistic for the entire population. The probability that the statistic is obtained is the probability that it will be obtained in a single sample from the population. The variance of the values is the amount of variation among the values of the statistic in the sample. The formula for calculating the variance is the sum of the squared deviations from the mean, divided by the number of values in the sample. This can be written mathematically as: Variance = Σ (x - X)2/ n, where x is each value in the sample, X is the mean value, and n is the number of values in the sample.
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Please help, I really need this.
Answer:
Step-by-step explanation:
The slope's simplest form is 1/2.
The t-test takes into account the _____ and _____ of the data, and the p-value tells us _____.
The p-value is the chance of finding a t-value with an absolute value at least as great as the one we actually observed in the sample data assuming the null hypothesis is actually true. The t-value is a way to measure the difference between the population means.
We reject the null hypothesis of the test if the p-value is less than a predetermined threshold (for example, 0.05). We are primarily concerned with the p-value for each form of t-test, and we merely employ the t-value as a first step in that process.
You'll see that we merely used the t-value as a first step before determining the p-value. The genuine value in which we were most interested was the p-value, but first, we had to determine the t-value.
Therefore the p-value is the likelihood that, if the null hypothesis is correct, each test will result in a t-value with an absolute value at least as great as the one we actually observed in the sample data. The t-value is a way to measure the difference between population means.
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A survey was done 1/4 voted for a restaurant 4/7 voted a library the rest voted for a gym what fraction voted for the gym
The fraction that voted for the gym is calculated as: 5/28.
How to Use Fractions to Solve Word Problems?To find out what fraction voted for the gym, you have to subtract the fractions that voted for the restaurant and the library from 1, which represents the total number of people surveyed.
You can do this by adding the fractions that voted for the restaurant and the library and then subtracting the sum from 1.
(1/4) + (4/7) = (7/28) + (16/28) = (23/28)
so 1 - (23/28) = (5/28)
Therefore, 5/28 of the people surveyed voted for the gym.
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In a right triangle, sin(7x+5)=cos(8x-5). Find the smaller of the triangles two acute angles
In a case whereby a right triangle, sin(7x+5)=cos(8x-5), the smaller of the triangles two acute angles is 43°.
How can the smaller of the triangles two acute angles be calculated?The concept that will be used is right triangle. An acute angle is one that is smaller than 90 degrees in length. The correct angle is larger than this angle (which is equal to 90 degrees).
We can see that sin(7x+5)=cos(8x-5)
An it implies that 7x+5 -8x-5 =90°
15x=90
x= 6
Then 7(6)+5= 47° 8(6)-5 = 43°
Hence the smaller of the triangles two acute angle is 43°
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division problem can be described using this model
The boxes are split in halves, and there is 4 boxes. The answer is 4 / 1/2.
What is division?
Division is a mathematical operation that involves dividing one number (the dividend) by another (the divisor). The result of this operation is called the quotient. Division is the inverse of multiplication, meaning that the product of a number divided by itself is equal to one. Division can also be used to find the number of times one number is contained in another. Division can be expressed in a variety of ways, such as by using fractions, decimals, or by using a long division algorithm.
When you look at the diagram, The boxes are split in halves, and there is 4 boxes. The answer is 4 / 1/2.
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In exercises 5–8 tell whether a correlation is likely in the situation. If so tell her there’s a casual relationship. Explain your reasoning. 6. favorite color and color of shoes 
ANSWER FAST PLEASE
WILL GIVE BRAINLIEST
There may be a correlation, but there is no direct link. This is because it is more likely that you will get shoes in the color you want.
It's likely that the preferred color and the color of the shoes are related. A person's favorite color may or may not match the color of their shoes, so there is no direct correlation. Particularly, the color of the shoes may have influenced the preferred color.
There may be a correlation, but there is no direct link.
How does correlation work?Correlation is a method for figuring out how two variables relate to each other. You learned that putting two variables on a "scatter plot" can help you figure out if they are usually connected. Despite the fact that there are other measures of association for variables measured at the ordinal or higher level of measurement, correlation is the strategy that is utilized the most frequently.
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Hassan's history class is taking a field trip to the state capitol building. The capitol building is
50 miles from Hassan's school. The class plans to stop after 45 minutes, or 0.75 hours, to
view a local monument. The bus driver plans to drive at an average speed of 40 miles per
hour.
Which equation can you use to find how many hours, x, the second part of the trip will take?
The equation that can be used to find how many hours, x, the second part of the trip will take is:
distance = rate x time
Which equation can you use to find how many hours?Where distance is the remaining distance from the capitol building to the school, rate is the average speed of the bus, and time is the time it takes to travel that distance.So, if we know that the distance is 50 miles and the rate is 40 miles/hour, we can find the time it takes to travel the remaining distance by plugging these values into the equation and solving for x:50 miles = 40 miles/hour x xthen by dividing both sides by 40 miles/hourx = 50/40 = 1.25 hours The equation to use to find how many hours, x, the second part of the trip will take is:distance = rate x timeIn this case, the distance is the remaining distance from the capitol building to the school, which is 50 miles - (40 miles/hour x 0.75 hours) = 35 miles. The rate is the average speed of the bus, which is 40 miles/hour. Therefore, the equation to find the time, x, of the second part of the trip is:35 miles = 40 miles/hour x xTo solve for x, divide both sides of the equation by 40 miles/hour:x = 35 miles / 40 miles/hour = 0.875 hours, or 52.5 minutes.To learn more about capitol building refer to;
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a manufacturer buys a new machine costing $180000 dollars. it is estimated that the machine has a useful lifetime of ten years and a salvage value of 6000 dollars at that time. assume the value of the machine varies linearly during this time. do not include dollar signs in your answers.
A manufacturer buys a new machine costing $180000 dollars. The value of the machine at the end of 10 years is $6000.
Calculate the annual depreciation of the machine.
Depreciation = (Purchase Price - Salvage Value) / Useful Life
Depreciation = (180000 - 6000) / 10
Depreciation = 174000 / 10
Depreciation = $17400 per year
Calculate the value of the machine at the end of each year.
Year 1: 180000 - 17400 = $162600
Year 2: 162600 - 17400 = $1452000
Year 3: 1452000 - 17400 = $1277600
Year 4: 1277600 - 17400 = $1103200
Year 5: 1103200 - 17400 = $928800
Year 6: 928800 - 17400 = $754400
Year 7: 754400 - 17400 = $580000
Year 8: 580000 - 17400 = $405600
Year 9: 405600 - 17400 = $231200
Year 10: 231200 - 17400 = $6000
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4. A distributor of fasteners is opening a new plant and considering whether to use a mechanized process or a manual process to package the product. The manual process will have a fixed cost of $36,234 and a variable cost of $2.14 per bag. The mechanized process would have a fixed cost of $84,420 and a variable cost of $1.85 per bag. The company expects to sell each bag of fasteners for $2.75. a) What is the break-even point for the manual process (in units)?
166158 is the break-even point for the manual process
What is Expression?An expression is combination of variables, numbers and operators.
Given that The manual process will have a fixed cost of $36,234 and a variable cost of $2.14 per bag.
Let the number of bags will be x
36234+2.14x..(1)
The mechanized process would have a fixed cost of $84,420 and a variable cost of $1.85 per bag.
84420+1.85x..(2)
From equation 1 and 2
36234+2.14x=84420+1.85x
2.14x-1.85x=84420-36234
0.29x=48186
Divide both sides by 0.29
x=166158
Hence, 166158 is the break-even point for the manual process
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Realiza el ejercicio utilizando las fórmulas para la curva normal.
Calcular la proporción de estudiantes que siguen una distribución normal, con media 78 y desviación estándar 36 y tienen puntuaciones que exceden por lo menos en cinco puntos de la puntuación que marca la frontera entre el Apto y No-Apto (es declarado No-Apto el 25 % de los estudiantes que obtuvieron las puntuaciones más bajas).
Datos:
Distribución normal
u = 78
O = 36
The proportion of students that had a grade at least 5 points greater than the 25th percentile is given as follows:
0.7054 = 70.54%.
How to obtain the z-scores?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 78, \sigma = 36[/tex]
The 25th percentile is X when Z = -0.675, hence:
-0.675 = (X - 78)/36
X - 78 = -0.675 x 36
X = 53.7
The proportion of students with a grade of at least 58.7 is one subtracted by the p-value of Z when X = 58.7, hence:
Z = (58.7 - 78)/36
Z = -0.54
Z = -0.54 has a p-value of 0.2946.
1 - 0.2946 = 0.7054 = 70.54%.
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In a garden 5/6 of the area is filled with native plants. The native plants take up to 107/4 m2 . Let g represent the total area of the garden. chooses 2 answers. pleas help me :(
The total area of the garden is given as follows:
32.1 m².
How to obtain the total area of the garden?The total area of the garden is obtained applying the proportions in the context of this problem.
The area of native plants is given as follows:
107/4 = 26.75 m².
This area of 26.75 m² represents a fraction of 5/6 of the total area g of the garden, hence the total area of the garden is obtained applying the proportion as follows:
5g/6 = 26.75.
g = 26.75 x 6/5
g = 32.1 m².
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What is the sum of the geometric sequence −2, −6, −18, … if there are seven terms?
Group of answer choices
−728
−128
−1,458
−2,186
The sum of the first seven terms is given by -2186
What is a geometric progression?Any progression in which the ratio of adjacent terms is fixed is a Geometric Progression. The general form of representation of a geometric sequence is a, ar, ar², ar³, ...
The geometric sequence is given here by -2,-6,-18...
We can observe that the common ratio is r=3
thus the sequence of upto 7 terms is given by
-2,-6,-18,-54,-162,-486.-1458
Thus the sum of all seven terms is given by
S=-2-6-18-54-162-486-1458
=-2186
Hence, The sum of the first seven terms is given by -2186
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