-letter words (repeated letters not allowed) can be formed from the alphabet if we require;(a) the 2nd letter to be a vowel (a, e, i, o, u)?(b) exactly one vowel?

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:

[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:

1/20

Step-by-step explanation:

hope this helps

Answer:

49/20

Step-by-step explanation:

Bye! ~ SunnyBunny <3

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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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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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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Answer: Left 10 Units

Step-by-step explanation: hope this helps

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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i am 11th grade

but why?

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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Answer:

1805.38

Step-by-step explanation:

hope this helps

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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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

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:

Step-by-step explanation:

1) Find the LCD and multiply what is missing: LCD (x)(14)

-1x/14x + 33/14x

2) Get rid of the denominators

-1x+33

-x+33

That should be right! Sorry if it isn't!

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]

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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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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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:

None

Step-by-step explanation:

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

Answer:

16

Step-by-step explanation:

x=-3

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

g(x)=4(4)

g(x)=16

Apply the definition of linear pair, the measure of angle 1 is calculated as: 33°.

If two angles are a linear pair, then, the sum of their angle measures equal 180 degrees.

We are given that angle 1 and angle 2 are a linear pair. This means that:

Measure of angle 1 + measure of angle 2 = 180

Measure of angle 1 = x

Measure of angle 2 = 5x - 18

Substitute

x + 5x - 18 = 180

6x - 18 = 180

6x = 180 + 18

6x = 198

6x/6 = 198/6

x = 33

Measure of angle 1 = x = 33°.

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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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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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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

Probability that -2.51 < z < -1.53 = 0.057

Given that z is a standard normal random variable. Then the z - values are given by the area under standard normal curve. It can be found from the standard normal tables.

Now probability that  -2.51 < z < -1.53  = P( -2.51 < z < -1.53 )

                                                               = P( -2.51 < z < 0 ) - P( -1.53 < z < 0 )

                                                               = P( 0 < z < 2.51) - P( 0 < z < 1.53 ) [Since areas are equal for same positive and negative values]

P( 0 < z < 2.51) = 0.4940

P( 0 < z < 1.53) = 0.4370  

[From the normal tables]

Therefore, Probability that -2.51 < z < -1.53 = 0.4940 - 0.4370  = 0.057

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The simplest expression that represents the total number of beads in her bracelet design is 2b + 7.

Expression:

An expression is the  sentence with a minimum of two numbers or variables and at least one math operation.

This math operation can be addition, subtraction, multiplication, or division.

The structure of an expression is:

Expression = (Number/variable, Math Operator, Number/variable)

Given,

Jewelry Marena is using a certain number of blue beads in a bracelet

design. she will use 7 more red beads than blue beads.

Here we need to write an expression in simplest form that represents the total number of beads in her bracelet design.

Assign a variable for the unknown value.

Let b be the number of blue beads for the bracelet.

The number of red beads will be represented as b + 7.

Determine the expression for the total number of beads.

Then we can written it as,

=> b + (b +7)

=> 2b + 7.

Therefore, the total number of beads can be written as 2b + 7.

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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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