The school finance committee has determined that a $28,000 facilities upgrade will be needed in 12 years. an alumnus has donated $20,000. if invested, will it grow to be enough?

The required GCF is 8.

The greatest common factor is that greatest number from the factors which divides the number completely.

For example take numbers 12 and 16.

The factors of 12 are 2×2×3.

And the factors of 16 are 2×2×2×2.

We can clearly see that the common factors are 2×2 which gives 4. So, 4 is the greatest common factor which divides both 12 and 16.

Here it is given to find the greatest common factor of 16 and 40.

Factors of 16 = 2×2×2×2

Factors of 40 = 2×2×2×5

We can see clearly the common factors are 2×2×2 which gives 8.

So, 8 is the greatest common factor.

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The average velocity in km/h is: 34.3km/hr

Average velocity refers to speed at which the time intervals (t) change in position or displacement happens, divided by the change in position or displacement (x).

=> Average velocity = [tex]\frac{displacement}{time}[/tex]

Now,

The time taken is missing in the question; the time taken = 18 mins = [tex]\frac{18}{60}[/tex] hours.

The distance of her home to the university = 10.3 km

As, average velocity = [tex]\frac{displacement}{time}[/tex]

=> Velocity = [tex]\frac{10.3\times60}{18}[/tex] = 34.3 km/hr

Hence, the average velocity = 34.3 km/hr

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Answer: -7/24

Step-by-step explanation:

move 2/3 to the opposite side of the equal sign which then changes the equation to...

3/8-2/3 = r

then change the denominators for both of them to 24.

so it would be 9/24 - 16/24

9-16 = -7

so it would be -7/24

Answer:

16

Step-by-step explanation:

x=-3

g(x)=4(-4(-3)-8)

g(x)=4(4)

g(x)=16

A scaled-down version of parallelogram is parallelogram be. What does w equal for U

X has a value of 4.

Line BC and line AD are parallel in the picture that was submitted, and segment 15 is the midpoint.

The Midsegment TrapezoidTheorem states that a line going through the midpoint of a trapezoid leg, parallel to both bases, will also go through the midpoint of the other leg

The formula for calculating a trapezoid's midsegment is as follows:

As a result, x has a value of 4.

A trapezoid is a quadrilateral with one pair of opposite sides parallel. It can have right angles (a right trapezoid), and it can have congruent sides (isosceles), but those are not required.

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Answer:

16cm

Step-by-step explanation:

The area of a 2d figure is w x h. We know the area, a, is 80cm^2, the height, h, is 5, and the width, w, is 2x + 8.

Since we are solving for x, we want to isolate the variable.

5 x 2x + 8 = 80
80/5 = 2x + 8

We can now solve for x.

80/5 = 2x + 8
16 = 2x + 8
16 - 8 = 2x + 8 - 8
8 = 2x
8/2 = 2x/2
4 = x

We aren't done, we still need to solve for w, where we now know x = 4

w = 2x + 8
w = 2(4) + 8
w = 8 + 8
w = 16

Answer:

x = 6

Explanation:

completing square:

[tex]y=x^2-12x+7[/tex]

[tex]y=(x^2-12x)+7[/tex]

[tex]y=(x-6)^2+7-(-6)^2[/tex]

[tex]y=(x-6)^2+7-36[/tex]

[tex]y=(x-6)^2-29[/tex]

Comparing with quadratic equation [tex]y=ax^2 + bx+c[/tex], in vertex form where [tex]y = a(x-h)^2+k[/tex]. In this x - h = 0, x = h defines the symmetry of equation.

So here the symmetry for parabola:

x - 6 = 0

x = 6

Answer:

x = 6

Step-by-step explanation:

The axis of symmetry of a parabola is the x-value of its vertex.

For a quadratic function in the form  [tex]y=ax^2+bx+c[/tex], the x-value of the vertex is:

[tex]x=-\dfrac{b}{2a}[/tex]

Given function:

[tex]y=x^2-12x+7[/tex]

Therefore:

[tex]a=1, \quad b=-12, \quad c=7[/tex]

So the axis of symmetry of the given quadratic function is:

[tex]\implies x=-\dfrac{b}{2a}=-\dfrac{-12}{2(1)}=\dfrac{12}{2}=6[/tex]

There is no real solution of given equation.

There is a special case that will tell us if a quadratic has no real solution: if b = 0 when a and c share the same sign (both positive or both negative), then there will be no real solution. The quadratic formula becomes much simpler when b = 0.

given equation [tex]x^{2} =-16[/tex]

         [tex]x=\sqrt{-16},\:x=-\sqrt{-16}[/tex]

          [tex]x=4i, x=-4i[/tex]

we get imaginary solutions of given equation

so, there is no real solution  equation is exist.

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The scores of two groups can be compared using coefficient of variation;

Coefficient of variation (C.V.) = (Standard Deviation/ Mean) × 100%;

For Data set 1;

Standard deviation = 3.6

Mean = 35.3

C.V. = (3.6/35.3) × 100%;

       = 10.19%

For Data set 2;

Standard deviation = 0.5

Mean = 34.1

C.V. = (0.5/34.1) × 100%;

       = 1.46%

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Approximately 99.7% of the data fall within three standard deviations of the mean.

In particular, the empirical rule predicts that 68% of observations falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ)

The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, almost all observed data will fall within three standard deviations (denoted by σ) of the mean or average (denoted by µ).

In particular, the empirical rule predicts that 68% of observations falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).

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The mass of water will change its temperature is 44.09 g.

Given that the temperature is change by 3.0°C when 635 J of heat is added to it.

Based on the given information, we know the following variables:

ΔT=3°C

Q=635J

C=(4.8 J)/(g×°C)

Here, we want to do is rearrange the equation to solve for m and this can be done by dividing both sides by C and ΔT to get m by itself like this:

m=Q/(ΔT×C)

Now, we want to substitute all the given values in the above formula, we get

m=635J/(3°C×(4.8J/(g×°C)))

m=635J/(14.4J/g)

m=44.09g.

Hence, the mass of water will change its temperature by 3.0 °C when 635 J of heat is added to it 44.09g.

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Answer:

None

Step-by-step explanation:

[tex]3b+4-3b=10+3b-3b\\4=10\\\sf Sides\:unbalanced.[/tex]

The function ƒ(x) = e^(2x + 1) when graphed could be described as; an increasing exponential graph.

The graphs of exponential functions are nonlinear—because their slopes are always changing, they look like curves, not straight lines.

Now, we are given the exponential function as;  ƒ(x) = e^(2x + 1)

Now, as the exponent increases, the curves get steeper and the rate of growth increases respectively. Thus, we can see that the exponent we are given increases as seen in the exponent attached to it.

Thus, we can conclude that The function ƒ(x) = e^(2x + 1) when graphed could be described as; an increasing exponential graph.

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[1/2, sqrt(3)/2] and [-1/2, -sqrt(3)/2] are  the unit vectors that are parallel to the tangent line to the curve.

Explain what a unit vector is?

y=2sin(x)

dy/dx equals 2 cos x at pi/6 for x.

pi/6 = 2 cos pi/6 = 2 sqrt(3)/2 = sqrt = dy/dx(pi/6) (3)

the line sqrt(3) (x-pi/6) is the tangent to y at pi/6.

Atan Theta = sqrt is the angle with the x axis (3)

θ = pi/3 radians at 60 degrees

the vectors of units at (pi/6,1) [cos(60), sin(60)] and [-cos(60), -sin(60)] are parallel to this line.

[1/2, sqrt(3)/2] as well as [-1/2, -sqrt(3)/2]

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When Milgram conducted his first series of experiments with a sample of 20- to 50-year-old men, he found that over 60 percent of them: went all the way to 450 volts.

Milgram's experiment examined if authority affected submission. Stanley Milgram, a Yale University psychologist, carried out several obedience tests in the 1960s that produced some providing more opportunities.

Milgram discovered that more than 60% of the men in his sample of 20 to 50-year-olds who participated in his initial series of trials reached 450 volts.

As a result, when Milgram conducted his first series of experiments with a sample of 20- to 50-year-old men, he found that over 60 percent of them: went all the way to 450 volts.

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Information security and ethics is defined as an all encompassing term that refers to all activities needed to secure information and systems that support it in order to facilitate its ethical use

ETHICS:

Derived from the Greek word “ethos”, which means “way of living”, ethics is a branch of philosophy that is concerned with human conduct, more specifically the behaviour of individuals in society. Ethics examines the rational justification for our moral judgments; it studies what is morally right or wrong, just or unjust.

In a broader sense, ethics reflects on human beings and their interaction with nature and with other humans, on freedom, on responsibility and on justice. It can be said that in general, ethics is concerned with human independence when it focuses on the relationship that exists between humans and the world

This independence is the primary condition in ethical decision-making and in any objective analysis of the facts. Individuals demonstrate independence when, in a decision-making process, they choose to free themselves as much as possible from their conditioning. Insofar as this operation assumes a degree of lucidity that allows us to judge objectively and to decide what direction to take, it will be understood that making ethical decisions is difficult.

SECURITY:

Security for information technology (IT) refers to the methods, tools and personnel used to defend an organization's digital assets. The goal of IT security is to protect these assets, devices and services from being disrupted, stolen or exploited by unauthorized users, otherwise known as threat actors. These threats can be external or internal and malicious or accidental in both origin and nature.

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Answer: Left 10 Units

Step-by-step explanation: hope this helps

Answer:The final balance is $28,043.4.

The total compound interest is $10,043.4.

Step-by-step explanation:

https://www.omnicalculator.com/finance/compound-interest?c=USD&v=var1:1,subject:1138535033,var2:1,subject2:1,FinalBal:20000,FinalBal_adj:20000,apy:1.95!perc,infl:0,PeriodicDep:50,q:1000!!l,type:1,DepositBal:0,PrincipalBal:0,g:0!perc,first_day:19255,select1:1,TableFreq:111,InitialDep:18000,r:3!perc,t:180!yrsmos,m:1,ct1:1,ct2:0,compound_frequency:21,ct3:3,represent:13

x-2y=8

Step-by-step explanation:

x=8+2y

The gradient is 2

Answer:

gradient = [tex]\frac{1}{2}[/tex] , y- intercept = - 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope (gradient) and c is the y- intercept )

given

x - 2y = 8 ( subtract x from both sides )

- 2y = - x + 8 ( divide through by - 2 )

y = [tex]\frac{1}{2}[/tex] x - 4 ← in slope- intercept form

with gradient m = [tex]\frac{1}{2}[/tex] and y- intercept c = - 4

The cost of a job that takes 6 hours is $280.

Discount:

Discount, the term referred as the amount or percentage deducted from the normal selling price of something. The discount means a reduction in the price of a good or service.

Given,

A repair shop charges $50 per hour. this week it is offering a $20 discount. And it represents the equation as,

c = 50h-20

Where

c represents the total cost, and

h represents the hours taken.

Here we need to find the total cost of a job that takes 6 hours.

According to the given details we know that the value of h = 6.

Then we need to find the value of c,

So,

=> c = 50(6) - 20

=> c = 300 - 20

=> c = 280

Therefore, the total cost of a job that takes 6 hours is $280.

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She ran 15 miles at a quicker speed based on the information supplied. See explanation below. This is a distance time problem.

The distances between the two "half" of the race are our unknowns here. We must assign them to variables - Alicia ran x miles in the first half of the race and y miles in the second.

Since the race is 21 miles in total, x and y together must add up to 21.

Hence,

x + y = 21

The speeds at which she raced and the total time involved are then given; we can link this to the distances using the speed and distance equation

d = st, or t = d/s.

Because she completed in two hours, the hours spent running the first and second parts must sum up to two hours, or:

x/8 + y/12 = 2

Two equations are sufficient to solve for two unknowns. We can approach this by multiplying the second equation by the LCM, 24

3x + 2y = 48

And rearrange the first to get y = 21 - x, which we can plug into the above. This gives us:

3x + 2(21 - x) = 48

3x + 42 - 2x = 48

x = 6

Use y = 21 - x again:

y = 21 - (6) = 15.

Recall that the question asks how long she ran at the faster speed - this would be the second half of the race, which we've labeled y, so 15 miles. But first, let's make sure our solution works.

Obviously, 15 + 6 = 21, thus the overall distance is correct.

In terms of time, 6 miles at 8 mph takes

6/8 =.75 hours = 45 minutes, whereas

15 miles at 12 mph takes 15/12 = 1.25 hours = 75 minutes.

As stated in the question, the total time to complete would be.

75 + 1.25 = 2 hours.

As a result, this solution is correct, as Alicia ran 15 miles at a quicker rate.

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The value of AB in the geometry is 24 units.

According to the diagram,

BD ≅ BC

BD = 5x - 26

BC = 2x + 1

AC = 43

Therefore, the value of AB can be found using the knowledge of geometry.

BD = BC

5x - 26 = 2x + 1

5x  - 2x = 1 + 26

3x = 27

divide both sides by 3

x = 27 / 3

x = 9

Therefore,

BC = 2x + 1 = 2(9) + 1 = 18 + 1 = 19

AC = BC + AB

AB = AC - BC

AB = 43 - 19

AB = 24 units

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We get the fractions in ascending order as -2350 / 1000, -1640 / 1000, 1225 / 1000 and 2050 / 1000.

We are given the daily changes in four stock prices as shown in the table.:

-2 35/100

-1.64

2.05

1 9/40

We have to arrange them from least to greatest in fraction form with a common denominator.

We can write -2 35/100 as:

-235 / 100 ( mixed fraction converted into the improper fraction)

= -2350 / 1000

We can write -1.64 as:

- 1.64 = -164 / 100 ( decimal into fraction)

= -1640 / 1000

We can write 2.05 as:

2.05 = 205 / 100 (decimal into fraction)

= 2050 / 1000

We can write 1  9/40 as:

1 9/40 = 49 / 40 ( mixed fraction converted into the improper fraction)

49 / 40 × 25 / 25

= 1225 / 1000

Arranging it from least to greatest, we get that:

-2350 / 1000, -1640 / 1000, 1225 / 1000 and 2050 / 1000

Therefore, we get the fractions in ascending order as -2350 / 1000, -1640 / 1000, 1225 / 1000 and 2050 / 1000.

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i am 11th grade

but why?

Answer:2

Step-by-step explanation:

Answer:

1805.38

Step-by-step explanation:

hope this helps

Answer:

[tex]\textsf{1.} \quad \dfrac{1}{5^5}[/tex]

[tex]\textsf{2.} \quad \dfrac{1}{5^7}[/tex]

[tex]\textsf{3.} \quad \dfrac{4^{21}}{5^{6}}[/tex]

[tex]\textsf{4.} \quad \left(2^6\right)^{-5}[/tex]

[tex]\textsf{5.} \quad \dfrac{1}{5^6}=\dfrac{1}{5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 }[/tex]

Step-by-step explanation:

Question 1

[tex]\textsf{Given}: \quad \dfrac{5^5}{5^8}[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies \dfrac{5^5}{5^8}=5^{(5-8)}=5^{-3}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]

[tex]\implies 5^{-3}=\dfrac{1}{5^3}[/tex]

--------------------------------------------------------------

Question 2

[tex]\textsf{Given}: \quad \dfrac{5^{-4}}{5^3}[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies \dfrac{5^{-4}}{5^3}=5^{(-4-3)}=5^{-7}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]

[tex]\implies 5^{-7}=\dfrac{1}{5^7}[/tex]

--------------------------------------------------------------

Question 3

[tex]\textsf{Given}: \quad \left(\dfrac{4^{7}}{5^2}\right)^3[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies \left(\dfrac{4^{7}}{5^2}\right)^3=\dfrac{4^{(7 \cdot 3)}}{5^{(2 \cdot 3)}}=\dfrac{4^{21}}{5^{6}}[/tex]

--------------------------------------------------------------

Question 4

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies \left(\dfrac{1}{5}\right)^2 \cdot\left(\dfrac{1}{5}\right)^6=\left(\dfrac{1}{5}\right)^{2+6}=\left(\dfrac{1}{5}\right)^8[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies \dfrac{9^3}{9^4}=9^{(3-4)}=9^{-1}=\dfrac{1}{9}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies 7^3 \cdot 7^8=7^{(3+8)}=7^{11}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies \left(2^6\right)^{-5}=2^{(6 \cdot -5)}=2^{-30}=\dfrac{1}{2^{30}}[/tex]

Therefore, the expression in which the exponents should be multiplied is (2⁶)⁻⁵.

--------------------------------------------------------------

Question 5

[tex]\textsf{Given}: \quad \left(5^3\right)^{-2}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies \left(5^3\right)^{-2}=5^{(3 \cdot -2)}=5^{-6}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]

[tex]\implies 5^{-6}=\dfrac{1}{5^6}=\dfrac{1}{5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 }[/tex]

Answer:

its the second option

Step-by-step explanation:

u can search for the formula for a right trapezoid and then solve it

Answer:

1/20

Step-by-step explanation:

hope this helps

Answer:

49/20

Step-by-step explanation:

Bye! ~ SunnyBunny <3