Answer:
These kind of problem can be modeled by using the following equation
y = Po*e^(k*(t-to))
Where
Po = initial population
to = year of the initial population
y = Number of students at current year
k = constant rate of change
t = time in years
In 2012
695 = Po*e^(k*(2012 - 2012))
Po = 695
In 2016
825 = 695.e^(k*(2016-2012))
825/695 = e^(k*(4))
ln(825/695) = 4*k
k = ln(825/695) / 4
k = ln(825/695) / 4
k = 0.04287
in 2018
y = 695*e^(0.04287*(2018-2012))
y = 695*e^(0.04287*(6))
y = 695*e^(0.257)
y = 695*1.293
y = 898.85
approximately
899 students
Final answer:
The predicted school population in 2018, based on a constant rate of change, is 890 students. This is calculated by determining the annual rate of increase between 2012 and 2016 and applying it to the 2016 population.
Explanation:
To predict the population of the school in 2018, we need to calculate the constant rate of change between 2012 and 2016, and then apply that rate to extend the prediction to 2018. From 2012 to 2016, the school's population grew from 695 to 825 students. This is an increase of 825 - 695 = 130 students over 4 years.
The annual rate of change is thus 130 students
over 4 years = 32.5 students per year. To predict the population for 2018, we add twice the annual rate of change to the 2016 population (since 2018 is two years after 2016): 825 + (2 * 32.5) = 825 + 65 = 890 students.
Therefore, we can predict that the school population in 2018 will be 890 students.
What is the next term of the geometric sequence?
40/27,20/9,10/3
Answer:
5
Step-by-step explanation:
By trial and error, we see that we can multiply by 3/2 every time to continue the sequence! So multiplying 10/3 by 3/2, we get 5. So 5 is the next term of the geometric sequence.
Similiar triangles can have congruent angles and sides
Answer:
The statement is true.
Step-by-step explanation:
The statement is true.
This is true. Since they could be considered similar even when they are congruent, since in similar triangles, the measurements are proportional. In congruent triangles, this proportion is just one. or 1/1
Hope this helps!
6) A cereal box has the following dimensions:
height of 12 inches and width of 2 inches. If
the volume of the box is 192 cubic inches.
find the length of the box.
Hint: V = lwh
Answer:
8 inches
Step-by-step explanation:
The problem gives us a basic formula, the volume formula for a rectangular prism. All we have to do is use this formula, plug in all the values that are given, and solve for the unknown value.
[tex]V = lwh[/tex]
[tex]192 = l(12)(2)[/tex]
[tex]192 = 24l[/tex]
From here, all we need to do is divide 24 from both sides of the equation, since what you do to one side of the equation you must do to the other!
[tex]8 = l[/tex]
The length of the box will thus be 8 inches.
it is going to be 8 inches Hope it helps !!!!!
Use the number line to help you answer the question.
Which statements are true? Check all that apply.
–4 < –8
|–4| < |–8|
|–5| > 1
–5 > |1|
|–2| = |2|
Answer:
|–4| < |–8|, |–5| > 1, |–2| = |2|
Step-by-step explanation:
Answer:
B, C, and E.
Step-by-step explanation:
–4 < –8
|–4| < |–8|
|–5| > 1
–5 > |1|
|–2| = |2|
Absolute Value Assignment
Understanding Absolute Value and Magnitude
Explain why the solution to 3r=2 must be less than 1
Answer:
see below
Step-by-step explanation:
3r=2
We know that r must be less than 1 because we are multiplying 3 by a number and getting 2
Taking a larger number and multiplying by r and getting a smaller number means the number must be less than 1
Divide each side by 3
3r/3 = 2/3
r = 2/3
2/3 is less than 1
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21 POINTS!! What is the solution to the system of equations below?
y = -1/3x + 6 and x = –6
Answer:
y=8
Step-by-step explanation:
[tex]y = - \frac{1}{3} ( - 6) + 6 \\ y = 8[/tex]
i dont know how to divide
Answer:
Divide whole numbers
Divide the first digit of the dividend by the divisor. ...
Write the quotient above the dividend.
Multiply the quotient by the divisor and write the product under the dividend.
Subtract that product from the dividend.
Bring down the next digit of the dividend.
Step-by-step explanation:
brainliest please
What is the product of (3a + 2)(4a^2 – 2a + 9)
Answer:
[tex]\large\boxed{(3a+2)(4a^2-2a+9)=12a^3+2a^2+23a+18}[/tex]
Step-by-step explanation:
[tex](3a+2)(4a^2-2a+9)\qquad\text{use FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=(3a)(4a^2)+(3a)(-2a)+(3a)(9)+(2)(4a^2)+(2)(-2a)+(2)(9)\\\\=12a^3-6a^2+27a+8a^2-4a+18\qquad\text{combine like terms}\\\\=12a^3+(-6a^2+8a^2)+(27a-4a)+18\\\\=12a^3+2a^2+23a+18[/tex]
Evaluate |-10| - |-8|
Answer:2
Step-by-step explanation:
the bars make the integers absolute value so it would be 10-8 when you drop the bars making the answer 2
what is the average rate of change for this quadratic function for the interval from x=6 to x=8?
Find the output y, when input x is 6
Answer:
0
Step-by-step explanation:
Final answer:
To find the output y for an input x of 6, assuming a linear relationship based on a derivative example provided, we use the equation y = 3x + 6. Substituting x with 6 gives us y = 24.
Explanation:
The question requires us to find the output y when the input x is 6. The equation provided in the excerpts can be interpreted in many ways due to lack of clarity in the given information. However, a linear function example is given by dy/dx = 6+3x, where the derivative suggests an initial value of 6 increasing by 3 with each unit increase in x. If we assume a linear relationship y = mx + b, we can use the pattern in the derivative example and set the slope m as 3 and the y-intercept b as 6. This yields the equation y = 3x + 6. When x is 6, the output y is calculated as y = 3(6) + 6 = 18 + 6 = 24.
Remember, the equation provided in the tutorial only applies if we assume a linear relationship based on the derivative example mentioned. It is important to have the exact equation or context to provide the precise output y.
A number w increased by 7 is less than 25. Translate the sentence into an inequality
Answer:
w+7<26
Step-by-step explanation:
number w increased by 7 means w+7
ls less than 25 means <25
So we have w+7<26
If p(x)=2x^2-4x and q(x) = x-3, what is (p o q)(x)
Answer:
2x² - 16x + 30
Step-by-step explanation:
To evaluate (p ￮ q)(x)
Substitute x = q(x) into p(x)
2(x - 3)² - 4(x - 3)
= 2(x² - 6x + 9) - 4x + 12
= 2x² - 12x + 18 - 4x + 12
= 2x² - 16x + 30
The given graph represents the function f(x) = 2(5)x. How will the appearance of the graph change if the a value in the function is decreased, but remains greater than 0?
The graph will increase at a slower rate.
The graph will show a decreasing, rather than increasing, function.
The graph will show an initial value that is lower on the y-axis.
The graph will increase at a constant additive rate, rather than a multiplicative rate
Answer: its c.
Step-by-step explanation:
The graph will show an initial value that is lower on the y-axis.
aka c.
Answer:C
Step-by-step explanation:
3[–x + (2 x + 1)] = x – 1 solve for x
Hey there! :)
3[-x + (2x + 1)] = x - 1
Simplify the parenthesis!
3[-x + 2x + 1] =x - 1
Add like terms.
3[x + 1] = x - 1
Simplify!
3x + 3 = x - 1
Subtract 1x from both sides.
3x + 3 - 1x = x - 1 - 1x
Simplify.
2x + 3 = -1
Subtract 3 from both sides.
2x = -4
Divide both sides by 2.
2x ÷ 2 = -4 ÷ 2
Simplify.
x = -2
~Hope I helped! :)
The cost of performance tickets and beverages for a family of four can be modeled using the equation 4x + 12 = 48, where x
represents the cost of a ticket. How much is one ticket?
$3.00
$4.00
$9.00
$15.00
Answer:
C) $9.00
Step-by-step explanation:
You're trying to find the value of x. 4x + 12 = 48 Subtract 12 from both sides to get:4x = 36 Then, divide each side by 4 to get:x = 9For this case we have that the cost of a ticket is given by the variable "x". We have the following equation:
[tex]4x + 12 = 48[/tex]
By clearing "x" we have:
We subtract 12 on both sides of the equation:
[tex]4x = 48-12\\4x = 36[/tex]
Dividing between 4 on both sides of the equation:
[tex]x = \frac {36} {4}\\x = 9[/tex]
Then, a ticket costs $ 9.00
Answer:
Option C
Simplify 8x + 9x completely.
Answer:
[tex]17x[/tex]
Step-by-step explanation:
[tex]8x + 9x = 17x[/tex]
To simplify the expression 8x + 9x, you combine the like terms by adding the coefficients. The result is 17x.
Explanation:The process involved in simplifying an equation like this is known as combining like terms. In this example, the terms are 8x and 9x. Because they both contain the same variable, x, you can combine them.
To perform this operation, you add the coefficients (the numbers in front of the variable). In this case, the coefficients are 8 and 9. So, 8x + 9x simplifies to 17x.
Therefore, the simplified form of the equation 8x + 9x is 17x.
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Which expression is equivalent to..? Assume
Answer:
The equivalent ratio of (3m⁻²n)⁻³/6mn⁻² = m⁵/2n
Step-by-step explanation:
Points to remember
Identities
xᵃ * xᵇ = x⁽ᵃ ⁺ ᵇ⁾
xᵃ/xᵇ = x⁽ᵃ ⁻ ᵇ⁾
(xᵃ)ᵇ = xᵃᵇ
x⁻ᵃ = 1/xᵃ
To find the equivalent ratio of (3m⁻²n)⁻³/6mn⁻²
By using identities,
(3m⁻²n)⁻³ = 3m⁶n⁻³
(3m⁻²n)⁻³/6mn⁻² = 3m⁶n⁻³/6mn⁻²
= 3m⁽⁶⁻¹⁾n⁽⁻³ ⁻ ⁻²⁾/6
= m⁵n⁻¹/2
= m⁵/2n
Therefore the equivalent ratio of (3m⁻²n)⁻³/6mn⁻² = m⁵/2n
Find the value of x for which the lines are parallel.
Answer: 64 °
64-1=63.
The parallel lines make the angles equal so they have the same measurement.
What is the solution of the equation 92x = 6? Round your answer to the nearest ten-thousandth.
Answer:
The solution of the equation 92x = 6 is x= 0.065
Step-by-step explanation:
We need to solve the equation 92x = 6 and find the value of x.
Given: 92x = 6
Divide both sides of the equation with 92
92x/92 = 6/92
x = 3/46
x = 0.065
So, the solution of the equation 92x = 6 is x= 0.065
Triangle XYZ is shown, where n 25.
Which statements are true regarding the sides and angles
of the triangle? Check all that apply.
n +4
OXY is the longest side.
Angle X is the largest angle.
Angle Z is greater than angle Y.
XZ is opposite the largest angle.
XZ is the shortest side.
Save and Exit
Answer: 2nd, 3rd, and 5th are true
Step-by-step explanation:
The first statement cannot be true, if n ≥ 5, which is given, then ZY must be greater than XY
The second statement must be true, as long as n ≥ 5, ZY will always be greater than XZ and XY, and therefore, the angle opposite to ZY will always be the greatest angle, so X is the largest angle
The third statement must be true for the same reasoning as the second statement. The side opposite to angle Z will always be greater than the side opposite of angle Y, meaning that angle Z will always be greater than angle Y (assuming n ≥ 5).
The fourth statement is false, we already proved that X is the largest angle and XZ is not opposite of angle X.
The fifth statement is true, XZ will always have the lowest value as long as n ≥ 5.
All the correct statements regarding the sides and angles of the triangle are,
⇒ Angle X is the largest angle.
⇒ Angle Z is greater than angle Y.
⇒ XZ is the shortest side.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
Triangle XYZ is shown,
where n ≥ 5
Now, We get;
For n = 5;
XY = n + 4 = 5 + 4 = 9
YZ = 2n = 2 x 5 = 10
ZX = n - 2 = 5 - 2 = 3
Hence, We get;
⇒ ZX < XY < YZ
And, ∠X > ∠Z > ∠Y
Thus, All the correct statements regarding the sides and angles of the triangle are,
⇒ Angle X is the largest angle.
⇒ Angle Z is greater than angle Y.
⇒ XZ is the shortest side.
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Someone pleaseeee help!!!!
Which statements are true? Check all that apply.
Answer: A) arc CB = 120°
C) <COB = 2(m<CAB)
D) <COB = 120°
Step-by-step explanation:
The measure of an inscribed angle is half the measure of its intercepted arc
⇆ The measure of an arc is twice the measure of its inscribed angle.
Thus, since <CAB = 60°, then arc CB = 120° OPTION A
The measure of a central angle is congruent to its arc
⇆ The measure of an arc is congruent to the central angle.
Thus, since arc CB = 120°, then <COB = 120° OPTION D
Since <COB = 120°, and <CAB = 60°,
then <COB = 2(m<CAB) OPTION C
Answer: A. C. D.
Step-by-step explanation:
Got it right on edg
Find the distance between the given points.
E(-6, 4) and F(-12, 4)
Distance =
6
8
18
Answer:
d = 6
Step-by-step explanation:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2 )
Givens
x2 = -12
x1 = -6
y2 = 4
y1 = 4
Solution
d = sqrt (-12 - - 6)^2 + (4 - 4)^2 )
d = sqrt ( ( - 6)^2 + 0)
d = sqrt(36)
d = 6
Answer:
6
Step-by-step explanation:
Calculate the distance (d) using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 6, 4) and (x₂, y₂ ) = (- 12, 4)
d = [tex]\sqrt{(-12+6)^2+(4-4)^2}[/tex]
= [tex]\sqrt{(-6)^2+0^2}[/tex] = [tex]\sqrt{36}[/tex] = 6
Angela rode his bike around a bike trail that was 1/4 of a mile long he rode his bike around the trail eight times Angelo says he wrote a total of 8/4 miles Teresa says he is wrong and that he actually rode 2 miles who is correct use words and drawings to explain how you know
What is the general form of the equation of a circle with center at (a, b) and radius of length m?
Answer:
bru thats not the answer^
Step-by-step explanation:
The Door Company produces door seals. Its 9' by 10' seal costs $480 to produce. The markup rate is 75% of cost. What is the price tag the company will put on this seal?
A) $840
B)$600
C)$475
D)$120
The sum of two numbers is 90. The larger number is 14 more than 3 times the smaller number. Find the numbers
The larger number is 71 and the smaller number is 19.
Two equations can be derived from the question:
x + y = 90 equation 1
x = 14 + 3y equation 2
The larger number would be represented with x and the smaller number would be represented with y.
Substitute for x in equation 1
14 + 3y + y = 90
Add similar terms
14 + 4y = 90
Make y the subject of the formula
4y = 90 - 14
4y = 76
y = 76 / 4 = 19
Substitute for y in equation 1
x + 19 = 90
x = 90 - 19
x = 71
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The sum of numbers is the addition of the numbers.
The numbers are 19 and 71
Let the two numbers be x and y, where y is greater than x.
So, we have:
[tex]\mathbf{y = 3x + 14}[/tex]
The sum of the numbers is:
[tex]\mathbf{x +y = 90}[/tex]
Substitute [tex]\mathbf{y = 3x + 14}[/tex]
[tex]\mathbf{x +3x + 14 = 90}[/tex]
[tex]\mathbf{4x + 14 = 90}[/tex]
Subtract 14 from both sides
[tex]\mathbf{4x = 76}[/tex]
Divide both sides by 4
[tex]\mathbf{x = 19}[/tex]
Substitute [tex]\mathbf{x = 19}[/tex] in [tex]\mathbf{y = 3x + 14}[/tex]
[tex]\mathbf{y = 3(19) + 14}[/tex]
[tex]\mathbf{y = 71}[/tex]
Hence, the numbers are 19 and 71
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Evaluate u + xy , for u = 2, x = 9, and y = 6.
Answer:
56
Step-by-step explanation:
After inserting the given values, u + xy becomes (2) + (9)(6), or 2 + 54, or 56.
Answer:
56
Step-by-step explanation:
2 + 9(6) = 56
Find g(1) if g(x) = x 2 + 1.
Answer:
[tex]\large\boxed{g(1)=2}[/tex]
Step-by-step explanation:
[tex]g(x)=x^2+1\\\\g(1)-\text{put x = 1 to the equation of the function}\\\\g(1)=1^1+1=1+1=2[/tex]
Jane is cooking beans and rice for dinner
tonight. She has 4 cans of black beans,
6 cans of red beans, and 3 cans of
garbanzo beans in her cupboard. If she
grabs a can of beans without looking at the
label, what is the probability of her making
black beans and rice for dinner?
Answer:
4/13
Step-by-step explanation:
6+3+4 =13
4/13
Answer:
4/13
Step-by-step explanation:
P( blackbeans) = number of cans of black beans
----------------------------------------------
total cans
= 4
-------
( 4+6+3)
= 4
-----
13