If the school now has 1,378 students enrolled, last year, the number of students enrolled was B. 1,300.
How is the number of students determined?Using the mathematical operations of addition, subtraction, division, and multiplication, we can determine the number of students.
Mathematical operations help us to determine unknown values, given a known domain.
Data and Calculations:Increase in school enrollment over last year's = 6%
Enrollment for the current year = 1,378
Let last year's enrollment = 100%
And the current year's = 1.06 (100 + 6)
Therefore, the enrollment last year = 1,300 (1,378/1.06)
Thus, the enrollment (number) last school year was B. 1,300.
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A ship sails 300 km west and then 500 km south. How far, to the nearest km, is the ship now from its starting position?
Step-by-step explanation:
this creates a right-angled triangle, with the pure coordinate changes being the legs, and the actual distance being the Hypotenuse (the side opposite of the 90° angle).
and so, we can use Pythagoras :
distance² = leg1² + leg2² = 300² + 500² =
= 90000 + 250000 = 340000
distance = sqrt(340000) = sqrt(10000×34) = 100×sqrt(34) =
= 583.0951895... km ≈ 583 km
Evan needed to get his computer fixed. He took it to the repair store. The technician
at the store worked on the computer for 4.5 hours and charged him $97 for parts. The
total was $479.50. What was the cost of labor, per hour?
"a comparison of nine confidence intervals for a poisson parameter when the expected number of events is ≤ 5,
The exact interval for researchers who want real coverage that is at least nominal and a modified version of the variance stabilized interval for those who are OK with approximative coverage.
Let [tex]{ X_{i} }^{n} _{i = 1}[/tex] be a group of independent variables with Poisson distribution and the same distribution. Confidence intervals for can be created using a variety of methods, including the Wald method, precise inference, a variance stabilizing transformation, and many others. Actual and nominal coverage can differ significantly when n is small. For a Poisson mean, we compare nine confidence intervals in terms of coverage and expected width of the confidence bounds. We demonstrate that, for small n, only the exact interval maintains coverage probabilities; the scores interval maintains coverage probabilities roughly, but its expected width is greater than that of the exact interval.A modified confidence interval based on the variance stabilized confidence interval has coverage properties close to the nominal and an expected width that is not particularly large. Therefore, we advise using the exact interval for researchers who want real coverage that is at least nominal and a modified version of the variance stabilized interval for those who are OK with approximative coverage.
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find the HCF of: 6(p² +p-2), 15(p³ + 8) and 18(4p²-p-18)
Answer:
Hello,
[tex]answer=\boxed{HCF=3*(p+2)}[/tex]
Step-by-step explanation:
[tex]6(p^2+p-2)=6(p+2)(p-1)\\\\15(p^3+8)=15(p+2)(p^2-2p+4)\\\\18(4p^2-p-18)=18(p+2)(4p-9)\\\\\boxed{HCF=3*(p+2)}[/tex]
Complete each part.
(a) Write a function, (), that meets the following criteria: (3 points)
a. Non-linear
b. Does not go through the origin
c. At least 2 terms
(b) Write a function, (), that meets the following criteria: (3 points)
a. Non-linear
b. Contains an radical
(c) Find
(f g x )( )
(3 points)
(d) Find
(g f )(6)
(3 points
Using composite functions, we have that:
a) f(x) = x² + 3.
b) [tex]g(x) = \sqrt{x}[/tex]
c) f(g(x)) = x + 3.
d) [tex](g \circ f)(6) = \sqrt{39}[/tex]
What is the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is given by:
(f ∘ g)(x) = f(g(x)).
For item a, we want a non-linear function, which has a highest exponent different of 1, that does not go through the origin, hence the function can be:
f(x) = x² + 3.
For item b, we also want a non-linear function with a radical, hence the function can be:
[tex]g(x) = \sqrt{x}[/tex].
For item c, the composite function is:
[tex]f(g(x)) = f(\sqrt{x}) = (\sqrt{x})^2 + 3 = x + 3[/tex]
For item d, the composite function is:
[tex]g(f(x)) = g(x^2 + 3) = \sqrt{x^2 + 3}[/tex]
At x = 6, we have that:
[tex](g \circ f)(6) = \sqrt{6^2 + 3} = \sqrt{39}[/tex]
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PLEAS HELP ITS DUE TODAY
The slope for plane A is 375, this means its rate of speed is 375 ml/h.
The slope for plane B is 445, this means the rate of speed for Plane B is 445 ml/h.
What is the Slope of a Linear Equation?The slope of a linear equation = change in y / change in x.
A linear equation that is given as, y = mx + b or y = mx, has a slope that is represented as m.
Slope of Plane A:
Given the equation for Plane A as, y = 375x, the slope is, 375.
This means its rate of speed is: 375 ml/h.
Slope of Plane B:
Using two points, (1, 445) and (2, 890)
Slope for plane B = (890 - 445)/(2 - 1)
Slope for plane B = 445
This means the rate of speed for Plane B is: 445 ml/h.
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A sample of n = 5 scores has m = 20 and s2 = 4. what is the sample standard deviation?
The sample standard deviation is 0.89
In the given statement is:
A sample n = 5 scores which means that there are 5 sample having m = 20 which is the arithmetic mean (A.M.)of these samples, and [tex]s^{2}[/tex] = 4 is the variance of these samples.
Let us know the :
What is meant by Sample Standard deviation?
The sample standard deviation (s) is the square root of the sample variance and is also measure of the spread from the expected values.
Standard deviation is the square root of the variance.
Therefore, [tex]s^{2}[/tex] =4 => s = 2
(Where, s denotes sample standard deviation ,σ)
Also, Standard error of the sample S(E) = Sample standard variance / [tex]\sqrt{number of samples}[/tex]
= σ /[tex]\sqrt{n}[/tex] = 2/[tex]\sqrt{5}[/tex]
and, root 5 = 2.24
put the value of root 5
=2 / 2.24
= 0.89
Hence, The sample standard deviation is 0.89
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Heyy, If anyone can find the answer to this question, I’ll literally be in your DEBT
[tex]Answer: the\ number\ is\ \boxed{-26}[/tex]
Step-by-step explanation:
[tex]2(n-4)=3(n+6)\\2(n)-2(4)=3(n)+3(6)\\2n-8=3n+18\\2n-8-18=3n+18-18\\2n-26=3n\\2n-26-2n=3n-2n\\-26=n\\Thus,\\n=-26[/tex]
The function f(x)=80(1.5)x models a bacteria population after x hours. how does the average rate of change between hour 4 and hour 8 compare to the average rate of change between hour 0 and hour 4?
The average rate of change between hour 4 and hour 8 is equal to the average rate of change between hour 0 and hour 4.
Function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given,
The function f(x)=80(1.5)x
where x is the time in hours
Then,
f(4)=80(1.5)4=480
f(8)=80(1.5)8=960
f(0)=80(1.5)0=0
Then the average rate of change between 4 and 8 hours =[tex]\frac{960-480}{4}[/tex]
=120 units per hour
The average rate of change between 0 and 4 hours=[tex]\frac{480-0}{4}[/tex]
=120 units per hour
Hence, the average rate of change between hour 4 and hour 8 is equal to the average rate of change between hour 0 and hour 4.
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[tex]\sqrt{7} (2\sqrt{7}+4)[/tex]
Answer:
[tex] \sqrt{7 \times 2} \sqrt{7 + 4 \sqrt{7} } \\ 14 + 4 \sqrt{7} [/tex]
find the exact trigonometric ratios for the angle x whose radian measure is given. (if an answer is undefined, enter undefined.) −7????
1/[tex]\sqrt{3}[/tex] is the exact trigonometric ratios for the angle x whose radian measure is given.
What are trigonometric ratios?Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant are the six trigonometric ratios (sec). A branch of mathematics called trigonometry in geometry deals with the sides and angles of a right-angled triangle. Trig ratios are therefore assessed in relation to sides and angles.
Trigonometric ratios, which contain the values of all trigonometric functions, are based on the ratio of sides of a right-angled triangle. The ratios of a right-angled triangle's sides with regard to a certain acute angle are known as its trigonometric ratios.
The right triangle's three sides are as follows:
Hypotenuse (the longest side)Perpendicular (opposite side to the angle)Base (Adjacent side to the angle)sin(4π/3) = sin(π + π/3)
= - sin(π/3)
= - [tex]\sqrt{3}[/tex]/2
CSC(4π )/3) = csc(π + π /3)
= - csc(π /3)
= - 2/[tex]\sqrt{3\\[/tex]
cos(4π /3) = cos(π + π /3)
= - cos(π /3) = - 1/2
sec(4 π /3) = sec(π + π/3)
= - sec(π /3) = - 2
tan(4π )/3) = tan(π + π /3)
= tan(π/3) = [tex]\sqrt{3}[/tex]
Cot (4π/3 )= cot(π + π/3)
= Cot π/3 = 1/[tex]\sqrt{3}[/tex]
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A mountain climber camped at an elevation of 18,492 feet. The following day the climber descended 2,516 feet to another campsite. Write a numerical expression you can evaluate to find the elevation of the second campsite. Then find the elevation.
1. The elevation is -15,976 feet
2. The elevation is 15,976 feet
3. A good expression would be -18,492 + 2,516
4. The elevation is 21,008 feet
5. The elevation is -21,008 feet
6. A good expression would be 18,492 + 2,516
7. A good expression would be 18,492 + -2,516
8. A good expression would be -18,492 + -2,516
The correct options are:
The elevation is 15,976 feet
A good expression would be 18,492 + -2,516
What is the elevation?When a person goes up a mountain, the sign used to represent their height above sea level is a positive sign (+). When a person goes down a mountain, the sign used to represent their height above sea level is a negative sign (-). So, the sign in front of 18,492 would be positive and the sign in front of 2516 would be negative.
The expression that can be used to evaluate the elevation of the second campsite :
height of the first campsite - feet descended
18,492 - 2,516 = 15,976 feet
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It costs $5820 to get new windows for a certain house. Each of the 28 windows costs the same amount. Determine an estimate for the cost of each window. Justify your reasoning. What is the cost of each window, rounded to the nearest dollar? Show your work. Leave the remainder undivided.
Answer:
1. Determine the estimate.: Without solving I'd say 200, but you could try to think of your own estimate.
2. Justify.: 5820 rounds up to 6000, and 28 rounds up to 30. 6000/30 = 200
3. 207.85 (I don't know if your teacher makes you do the new way of rounding up, but if it says round to the nearest dollar I'd do $207.)
Step-by-step explanation:
Then you divide. Sorry I can't show you that!!! But I really hope this helped.
jayden's walkie-talkie has a range of 3 miles. jayden is traveling on a straight highway and is at mile marker 253. identify the absolute-value equation and solution to find the minimum and maximum mile marker from 253 that jayden's walkie-talkie will reach.
Jayden's maximum and minimum walkie-talkie will reach mile marker is:
|x + 253| = 3
x = 253
The range of Jayden's walkie-talkie is three miles.
At mile 253, Jayden is moving straight along a highway.
Find the least and maximum milepost that Jayden's walkie-talkie will reach from 253 by solving the absolute-value equation.
range of 3 miles.
mile marker 253.
Find maximum and minimum of walkie talkie will reach
|x + 3| - 253 = 3x
= 253 or x
= 250
|x + 3| = 253
x = 250 or x
= -256|x - 253|
= 3
x = 256 or x
= 250
|x + 253| = 3
x = 253
Therefore, Jayden's minimum and maximum mile marker from 253 that walkie-talkie will reach is
|x + 253| = 3
x = 253
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Which shows a way to factor the
expression 24 - 32x8
A -8(-3+4x)
B-4-6-8x)
C 41-6+8
D 81-3-4)
Answer:
Pretty sure A would be the answer
Step-by-step explanation:
Thirty-six friends are renting a party bus to the school prom. Rental of the
party bus will cost $300 up front plus $18 per hour. The friends have the
bus from 5:00 PM to 3:00 AM.
Each friend has agreed to chip in $12. One of the teachers at the high
school, Mr. Jones, has offered to chip in the rest. If he does, how much will
he pay
Answer:
$48
Step-by-step explanation:
The friends have the bus from 5:00 PM to 3:00 AM, so:
3 + 18 − 5 = 15 − 5 = 10 hours.
The cost of renting the bus will be:
$300 + $18 × 10 = $300 + $180 = $480.
The thirty-six students will contribute $12 each for a total of:
$12 × 36 = $432.
So Mr. Jones will pay:
$480 − $432 = $48.
Hope this helped :)
If a = 3, then 5a = 15. If a = 11⁄2, then a
3.
The value of the expression a^3 is 3 3/8
How to evaluate the expression?The given parameters can be represented as
If a = 3, then 5a = 15.
Also, we have the value of the variable a to be
a = 1 1/2
Express the value of the variable a as an improper fraction
So, we have
a = 3/2
When a = 1 1/2 or a = 3/2, the value of a³ is calculated using the following formula
a³ = (1 1/2)³ = (3/2)³
Rewrite the formula as
a³ = (3/2)³
Evaluate the exponent in the above equation
So, we have
a³ = (27/8)³
Evaluate the quotient in the above equation
So, we have
a³ = 3 3/8
Hence, the value of the expression a³ is 3 3/8
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pls helppppp fast needs to be submitted in a hour!!!Q
Answer: 2/9 of the book left
Step-by-step explanation: 5/9 + 2/9= 7/9
9/9- 7/9= 2/9
which term best describes the number of solutions that will maximize the function below given the constraints listed? (assume that and .) 3x 2y a. one optimal solution c. unbounded b. alternate optimal solutions d. infeasible please select the best answer from the choices provided a b c d
Final answer:
The best term that describes the number of solutions that will maximize the function is one optimal solution (a)
What exactly do you mean by a practical solution ?
A practicable solution is one that complies with all limitations and specifications. When all of the requirements and constraints cannot be satisfied by any combination of decision variable values, a solution is deemed to be infeasible. The parabola's highest or lowest point represents the ideal value. If only the parabola expands down words, the optimal value, also known as the vertex of the parabola, would be maximal. The minimal value is one opening upwards. The vertex's "Y" coordinate is it.
An option for making a judgment or a resolution that does not adhere to one or more constraints. The corners of the entire model's graph would contain the ideal answer.
Explanation:
(Assume that [tex]x > 0[/tex] and [tex]y > 0[/tex].)
[tex]x + 2 < 5x-y < 2[/tex]
[tex]F(x,y) = 2x+y[/tex]
So , the equation becomes a optimal solution.
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Find missing length.
A trapezoid has a height of 8 meters, a base length of 12 meters, and an area of 64 square meters. What is the length of the other base?
Answer:
good luckkkkkkkkkkkkkkk
A nursery is recording the heights of its available fruit trees. Which of the following displays could be used to represent the data, and why?
O Bar chart, because tree height is numerical
O Box plot, because tree height is numerical
O Histogram, because tree height is categorical
Stem-and-leaf-plot, because tree height is categorical
When the nursery is recording the heights of its available fruit trees. the display that can be used to represent the data, is A. Bar chart, because tree height is numerical.
What is a bar chart?Using rectangular bars with heights or lengths proportional to the values they represent, a bar chart or bar graph displays categorical data. Both a vertical and a horizontal bar plot are possible. A column chart is another name for a vertical bar graph.
When displaying the distribution of data points or comparing metric values across several subgroups of your data, a bar chart is employed. A bar graph allows us to determine which groupings are most numerous or prevalent as well as how different groups stack up against one another.
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Answer:
The answer would be B.
Step-by-step explanation:
Since we are doing heights, it would make since to have a box plot, since that includes minimum, maximum, median, Q1, & Q2. :)
that makes it easier to record height
prove that every positive integer can be written as a finite sum of distinct integral powers of the golden ratio.
z1 =........=zm = 0 and n=m because n0 cannot be expressed in the +ve Phi / golden ratio form.
What is golden ratio?important is that the ratio between each succeeding pair of Fibonacci numbers approaches 1.618, or its inverse, 0.618, as the numbers get bigger. The holy proportion, the golden ratio, and the golden mean are some additional names for this proportion. Then why is this number so important? The fact that so many items in nature have dimensions characteristics that conform to the 1.618 ratio suggests that it plays a fundamental role for the components of nature. Due to its visual appeal compared to other proportions, the golden ratio is frequently used in the arts. The Great Pyramid in Giza, the Mona Lisa by Da Vinci, and the Parthenon in Athens are all.
z1 =........=zm = 0 and n=m
z1 =........=zm = 0 and n=m because n0 cannot be expressed in the +ve Phi / golden ratio form.
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The table shows the proportional relationship between a hedgehog's
weight loss and the number of days of hibernation. How much weight does
the hedgehog lose during 120 days of hibernation?
Explain how you know that the relationship between the hedgehog's weight
loss and the number of days of hibernation is proportional.
The hedgehog’s total change in weight over 120 days is ____ ounces.
weight loss of hedgehog
days: change in weight:
12 -0.36
21 -0.63
71 -2.13
96 -2.88
for a field trip 19 students rode in cars and the rest filled the 10 buses how many students were in each bus if 519 students were on the trip
answer as an equation please help
Answer: 10x + 19 = 519 x = 50
Step-by-step explanation:
We are looking for the number of students that rode in each bus, so first lets subtract out those that drove in cars.
519-19=500
So 500 students rode on 10 buses. So now we divide the students onto the buses.
500/10 = 50
Each bus drove 50 students.
An equation to represent the total number of students as a function of those on the buses would be
10x + 19 = 519
x = 50 (the number of students on each bus)
9uv + 3s³t² + 5uv
Combine any like terms in the expression. if there are no like terms, rewrite the expression.
The expression after combining the like terms is 14uv+ 3s³t²
Expression:
Mathematical expression consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Variable:
A variable in algebra is an alphabet that is used to symbolise the unknowable integer. It stands in for the value. An amount that can fluctuate depending on the mathematical issue is referred to as a variable.
⇒9uv + 3s³t² + 5uv
⇒ 14uv+ 3s³t² { addition of like terms}
Therefore,The expression after combining the like terms is 14uv+ 3s³t²
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Express2a powered −5 with a positive exponent.
Answer:
To make a negative exponent positive you put it over 1
[tex]\frac{2}{a^{5} }[/tex]
Step-by-step explanation:
2[tex]a^{-5}[/tex] = [tex]\frac{2}{a^{5} }[/tex]
What is the mean of the following numbers?
11, 3, 5, 13
Answer:8
Step-by-step explanation:add them all together and divide by however many numbers you have
Answer:
the mean(average) is 5
Step-by-step explanation:
Find the sum of the values by adding them all up. Divide the sum by the number of values in the data set.
Multiply each side of the equation by a power of 10 to get the repeating digit(s) to the left of the decimal point. since you only need to move one place, multiply each side by 10.
To decide the power of 10 multiplies an equation with repeating digits; Round the equation to the required significant numbers.
when the numerator of an equation is divided by the denominator and the result is not a whole number ( i.e. number with some decimals)and sometimes the decimal places are unending. to present the result properly we have to round off the number to the nearest significant number, then you can multiply the equation with the power of 10, in relation to the number of significant places you rounded off.
Example :
5/200 = 0.025
To express this answer with the power of 10
0.025 = 2.5 * 10 ^-2
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For how many integers will 4x + 5 be greater than 4 and less than 175?
The linear equation 4 · x + 5 will be greater than 4 and less than 175 for 42 integers.
How many integers are within a linear inequality?
Herein we must find what integers are within the interval of a simultaneous linear inequality, whose definition is shown below:
4 < 4 · x + 5 < 175
Which is equivalent to the following two inequalities:
4 · x + 5 > 4 (2)
4 · x + 5 < 175 (3)
By (2):
4 · x + 5 > 4
4 · x > - 1
x > - 1 / 4
x > - 1
By (3):
4 · x + 5 < 175
4 · x < 170
x < 170 / 4
x < 85 / 2
x < 42.5
x < 43
Then, the number of integers within the simultaneous inequality is:
n = 1 + (42 - 1)
n = 42
The linear equation 4 · x + 5 will be greater than 4 and less than 175 for 42 integers.
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Write the linear equation in slope-intercept form passing through the given points. (-12, 14) and (6, -1) (Hint: Start by finding slope between the two points, then put in point-slope form and then convert to slope-intercept form.) y= type your answer... X+ type your answer...
The slope-intercept form of the equation of the line described is y = -6x/5 + 32/5.
Given the following data:
Points on x-axis = (-12, 6).
Points on y-axis = (14, -1).
What is a slope?A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.
How to calculate the slope of a line?Mathematically, the slope of any straight line can be calculated by using this formula;
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Substituting the given points into the formula, we have;
Slope = (6 + 12)/-1 - 14)
Slope = -18/15
Slope = -6/5
Mathematically, the standard form of the equation of a straight line is given by;
y = mx + c
Where:
x and y are the points.m represents the slope.c represents the intercept.At point (-12, 14), we have:
14 = -6/5(-12) + c
8 = 72/5 + c
40 = 72 + 5c
5c = 72 - 40
c = 32/5
In conclusion, we can reasonably and logically deduce that the slope-intercept form of the equation of the line described is y = -6x/5 + 32/5.
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