how many four letter strings can be formed from the letters a,b,c,d,e if the first letter must be a vowel and the last letter must be a consonant?

Answer:

b₂ = [tex]\frac{2A}{h}[/tex] - b₁

Step-by-step explanation:

A = [tex]\frac{b_{1}+b_{2} }{2}[/tex] × h ( multiply both sides by 2 to clear the fraction )

2A = h(b₁ + b₂ ) ← divide both sides by h

[tex]\frac{2A}{h}[/tex] = b₁ + b₂ ( subtract b₁ from both sides )

[tex]\frac{2A}{h}[/tex] - b₁ = b₂

The solution is, the formula to find the base b₂ is : b₂ = 2A/h - b₁.

Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

here, we have,

given that,

The area of a trapezoid is calculated using the formula below, where A is the area of the trapezoid, b₁ and b₂ are the bases of the trapezoid, and h is the height of the trapezoid.

A = (b1+b2)/2 × h

( multiply both sides by 2 to clear the fraction )

2A = h(b₁ + b₂ )

← divide both sides by h

2A/h = b₁ + b₂

( subtract b₁ from both sides )

2A/h - b₁ = b₂

Hence, The solution is, the formula to find the base b₂ is : b₂ = 2A/h - b₁.

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Answer:

21

Step-by-step explanation:

rate of baskets *total shots = shots made

3/5*35=21

Answer:

Yes! The sides 5,3 and 7 can create a triangle!

Step-by-step explanation:

It follows the rule:

a + b > c

a + c > b

c + b > a

The height of the rocket at the end of the 25 seconds is 275 ft.

We have given that,

a rocket rises at 5 ft/s between 0 and 10 seconds,

therefore

V₁ = 5 ft/s

T₁ = 10 seconds

Height in first 10 seconds = ?

we know the formula to find the height,

i.e Height = velocity × time

⇒ H₁ = V₁ × T₁

        = 5 × 10

   H₁ = 50 ft

Therefore height of the rocket in the first 10 seconds is 50 ft.

Now it given that, rocket rises at 25 ft/s for another 15 seconds.

i.e V₂ = 15 ft/s

    T₂ = 15 seconds

    H₂ = ?

H₂ = V₂ × T₂

    = 15 × 15

H₂ = 225 ft

Therefore height of the rocket in next 15 seconds is 225 ft.

Now we will find the height of the rocket at the end of the 25 seconds.

i.e H = H₁ + H₂

       = 50 + 225

    H = 275 ft

Hence the height of the rocket at the end of 25 seconds is 275 ft.

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Answer: 110°

Step-by-step explanation: We know that a quadrilateral is always 360° in total, and two of the angles are right angles, which both equal 90°. We also know that one of the angles is 70° so, with this information, we can set up an equation. 90+90+70+x=360 To solve this, add 90, 90, and 70 together. This equals 250. Now we subtract 360 and 250, which equals 110°.

hope this helps!

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Two symbols are used in the expressions of three-part inequalities. Three-part inequality solutions are equivalent to two-part inequality equation solutions.

Solve the −4≤2x−1≤5-4≤2x-1≤5 equation.

Try to obtain x on your own then.

To the three sides, add one.

−4+1≤2x−1+1≤5+1-4+1≤2x-1+1≤5+1

−3≤2x≤6-3≤2x≤6

By dividing all three sides by 2, you get 1.5x3 (32 2 x 2 x 62).

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Number of degrees of freedom should we​ use for sample size of 15 at 95% confidence interval is 14.

Given:

Suppose we are making a​ 95% confidence interval for the population mean from a sample of size 15.

Degrees of freedom:

Degrees of freedom indicate the number of independent pieces of information used to calculate a statistic; in other words - they are the number of values that are able to be changed in a data set.

we know that,

Degrees of freedom df = n - 1.

where n = sample size

df = sample size - 1

= n - 1

= 15 - 1

= 14

Therefore number of degrees of freedom should we​ use for sample size of 15 at 95% confidence interval is 14.

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A provision that ensures performance fees are not earned until the value of a fund exceeds its previous highest level is referred to as High-water mark

A high-water mark is the highest peak in value that an investment fund or account has reached. This term is often used in the context of fund manager compensation, which is performance-based.

The high-water mark ensures the manager does not get paid large sums for poor performance. If the manager loses money over a period, he must get the fund above the high-water mark before receiving a performance bonus

With a high-water mark, the investor pays a fee that only covers the amount the fund earned between the point of entry and its highest level.

The high-water mark prevents this "double fee" from occurring.

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x-intercept and y-intercept of the line y = 4x+5 is -5/4 and 5 respectively.

What is the equation straight line?

The given equation Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.

The equation of the line is y = 4x+5

So the y-intercept is (x=0)

y = 5

And the x-intercept is (y=0)

4x +5 =0

x = -5/4

Hence, the x-intercept and y-intercept of the line y = 4x+5 is -5/4 and 5 respectively.

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The pair of triangles in the option B are congruent by AAS congruence theorem.

What is AAS congruence theorem ?

The Triangles Are Congruent Theorem (AAS) states that if two angles and a non-included side in one triangle are congruent to two angles and the matching non-included side in another triangle.

AAS congruence theorem full form is Angle Angle Side .

This means 2 angles 1 side have to be same for the two triangles to be congruent.

So, in the option B, the 2 angles and 1 side same for the two triangles .

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The angle of inclination of the ramp is approx. 4°.

Define the angle of inclination.

The angle formed between a line and the x-axis's positive direction is known as the inclination angle. This angle has a value between 0° and 180°. From the positive direction of the x-axis, it is measured counterclockwise.

Added definitions include The positive angle, measured counterclockwise from the x-axis to the line, with a value less than 180 degrees, which is the inclination of a non-horizontal line.

Solution Explained:
Given in question,

length (l) = 6.10m and height(h) = 0.45m

So the angle of inclination can be found using,

sin θ = h/l

sin θ = 0.45/6.10

θ = sin^-1(0.45/6.10)

θ ≈ 4°

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The cost for  [tex]1\frac{3}{4}[/tex] pounds of milk chocolate is $ 6.16 more than the cost for  [tex]1\frac{3}{4}[/tex] pounds of caramels.

Two or more expressions with an Equal sign is called as Equation.

The cost of each pounds of Caramels = $ 9.28,

So, the cost of [tex]1\frac{3}{4}[/tex]  pounds of caramels =  [tex]1\frac{3}{4}[/tex]×9.28

=7/4×9.28=$16.24

The cost of each pounds of milk chocolate = $ 12.80

So, the cost of [tex]1\frac{3}{4}[/tex]  pounds of milk chocolate = [tex]1\frac{3}{4}[/tex]  ×12.8

=$22.24

∵ 22.4 > 16.24,

the cost of  [tex]1\frac{3}{4}[/tex] pounds of milk chocolate  > The cost of   [tex]1\frac{3}{4}[/tex]pounds of caramels

22.4-16.24=6.16

Hence, the cost for  [tex]1\frac{3}{4}[/tex] pounds of milk chocolate is $ 6.16 more than the cost for  [tex]1\frac{3}{4}[/tex] pounds of caramels.

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In an experiment on a damped spring oscillator with spring constant n/m, student c obtains the displacement vs time curves as in fig. 2(a), and records the maximum displacement data points as below is y = - 3.7148.

Here we have to find the displacement for the graphs of y and t that is maximum and We can find that by y = mc where m, = slope, c= intercept.

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The critical value used is (10 – 2.5, 10 + 2.5) when, the mean is 10 and confidence level is 89%.

The confidence interval for a population with a known standard deviation is based on the fact that the sample means follow an approximately normal distribution. Suppose

mean = 10

as, we have 89% confidence interval (5, 15)

where EBM = 5.

To get 89% confidence interval,

mean = 10 of the normal distribution.

Then, the critical value we use is

(10 – 2.5, 10 + 2.5).

So, the critical value used is (10 – 2.5, 10 + 2.5) when, the mean is 10 and confidence level is 89%.

Hence, the critical value used is (10 – 2.5, 10 + 2.5) when, the mean is 10 and confidence level is 89%.

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Yes, leading coefficient and degree of the polynomial functions can affect the behavior of its graph. Because of the positive leading coefficient, the graph ascends to the right. To ascertain the behavior, consider the function's degree and the sign of the leading coefficient.

The term with the greatest x power is the leading term in a polynomial function. The leading coefficient is the coefficient of the leading phrase.

Given,

Yes, leading coefficient and degree of the polynomial functions can affect the behavior of its graph.

The graph's final behavior is determined by a polynomial function's degree and leading coefficient. For very big or very small values, the leading coefficient is more important than the other function coefficients. The coefficient of the leading term is the leading coefficient in a polynomial. Because of the positive leading coefficient, the graph ascends to the right. To ascertain the behavior, consider the function's degree and the sign of the leading coefficient.

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An integer's factors are other integers that, when multiplied, give the same result as the original integer. For instance, 33 and 55 are factors of 1515 since 35=1535=15. Knowing what a factor is, we frequently seek to identify an integer's "factorizations".

An integer is represented as the product of its factors in a factorization. The number 11 and the initial integer are always factors, as you can see. This is referred to as a "prime" or complete factorization of 88. The base number, in this case 22, is therefore prime. A prime integer is one with only itself and the number 11 as components. 11 is not a prime number by definition. Prime factors can be used to factor polynomials. Because the elements x+1x+1 and x+2x+2 are irreducible—they only have 11 and themselves as factors—the second factorization is known as the prime factorization. Similar to factoring integers into a product of integers, each smaller than the original, factoring polynomials aims to describe the original polynomial as a product of polynomials of lower degree.

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The probability the class average is less than 79 is 0.1587.

What is Normal Distribution ?

Given that,

Normally distributed with a mean μ = 80

sample standard deviation σ = 6

In a class, number of students n = 30   (This may be 36 in ques but we take 30 as mentioned in question )

Let, x = be the individual score

∑x = be the class average

It's given, class average is less than 79.

Now, the probability that the class average is less than 79.

P(∑x < 79) = P( (∑x - μ) / (σ/√n)  < (79 - 80) / (6 /√30) )

                = P( (∑x - μ) / (σ/√n)  < (-1) / 1.09 )

                = P( (∑x - μ) / (σ/√n)  < -1 )     [Round off the Denominator it gives 1]

we know, Standard normal distribution Z = (∑x - μ) / (σ/√n)

so,

P(∑x < 79) = P( Z < -1 )

By Standard normal distribution table,

P( Z < -1 ) = 0.1587

Hence, the probability the class average is less than 79 is 0.1587.

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In the given function f(x) = 3ˣ, a function table is created from -2 to 2 which is represented on a graph.

A function table is a visual table with columns and rows that displays the function with regards to the input and output. Younger students will also know function tables as function machines. Every function has a rule that applies and represents the relationships between the input and output.

In the function given;

f(x) = 3ˣ

The values of y from x = -2 to 2 are

f(-2) = 1/9

f(-1) = 1/3

f(0) = 1

f(1) = 3

f(2) = 9

Kindly find the attached graph below;

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The answer is 3/25

The calculation as follows.

First, convert to fraction version of the decimals.

0,12 means 12/100

Second, simplify both up and bottom value of the fraction by dividing it with 4

(12:4)/(100:4) = 3/25

So, the answer is 3/25

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As per the given simple interest, the amount invested in each account is 50000, 60000, and 10000 respectively.

Simple interest:

In math, the method of calculating the interest amount for a particular principal amount of money at some rate of interest is known as simple interest.

Given,

Pierre inherited $506,000 from his uncle and decided to invest the money. He put part of the money in a money market account that earns 4.5% simple Interest. The remaining money was invested in a stock that returned 5% in the first year and a mutual fund that lost 4% in the first year. He invested $10,000 more in the stock than in the mutual fund, and his net gain for 1 yr was $3060.

Here we need to determine the amount invested in each account.

Let us consider the total amount invested on is written as,

=> X+Y+Z = 120000

And according tot he given details we know that,

=> Y = Z + 10000

AS we apply the interest, then we get,

=> 0.022X + 0.06y - 0.02Z = 2820  

Apply the value of y as z + 10000, then  we get,

=> X+(Z+10000) + Z = 120000

=> 0.022X + 0.06(Z+10000) - 0.02Z = 2820

Then we simplify this one then we get,

=> X + 2Z = 110000

=> 0.022X + 0.06Z + 600 - 0.02Z = 2820

=> 0.022(110000 - 2Z) + 0.06Z + 600 - 0.02Z = 2820

=> 2420 - 0.044Z + 0.06Z + 600 - 0.02Z  = 2820

=>3020 - -0.004z = 2820

=> 0.004z = 200

Therefore, the amount invested on the funds are 50000, 60000, and 10000

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The same financial document number range can be assigned to several document types. Financial document number ranges defined at client level should NOT overlap. Financial document number ranges are defined at company code level.

Financial statements are official records of a person, business, or other entity's financial situation and actions. An easy-to-understand style is used to provide pertinent financial data in a systematic manner. Financial papers, usually referred to as financial statements, are used to present financial data about an organization in a consistent way. They come with a cash flow statement, an income statement, and a balance sheet. A balance sheet is a moment in time snapshot of your company's financial health.

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The interval of convergence of the given power series is I=[0, 2/9] and the radius of convergence of power series is R=1

The disk of convergence is the set of all places whose distance to an is strictly less than the radius of convergence.

Given, the power series is,

[tex]\sum_{k=1}^{\infty }[/tex] 1/(k²+k)[tex](9x-1)^{k}[/tex]

Let [tex]u_{k}[/tex]=1/(k²+k)

The radius of the convergence is,

R=[tex]\lim_{k \to \infty}[/tex]| [tex]u_{k}[/tex]/[tex]u_{k+1}[/tex]|

=[tex]\lim_{k \to \infty}[/tex] ((k+1)²+(k+1))/(k²+k)

=[tex]\lim_{k \to \infty}[/tex] (k²+3k+2)/(k²+k)

=[tex]\lim_{k \to \infty}[/tex] ((1+(3/k)+(2/k²))/(1+(1/k))=1

The interval of convergence is:

|9x-1|<1

Or, -1<9x-1<1

Or, 0<9x<2

Or, 0<x<2/9

Given the power series is converges in the interval (0, 2/9)

If x=0, then the power series becomes as shown,

[tex]\sum_{k=1}^{\infty }[/tex](1/(k²+k)([tex]-1^{k}[/tex])

Let [tex]a_{k}[/tex]=([tex]-1^{k}[/tex])(1/(k²+k)

[tex]\lim_{k \to \infty}[/tex]  [tex]a_{k}[/tex]=0 and { [tex]a_{k}[/tex]} sequence is monotone decreasing

Hence by Leibnitz's test,

[tex]\sum_{k=1}^{\infty }[/tex](1/(k²+k)([tex]-1^{k}[/tex]) is convergent

If x=2/9 then the power series becomes [tex]\sum_{k=1}^{\infty }[/tex](1/(k²+k)

Let  [tex]a_{k}[/tex]=(1/(k²+k)and let [tex]b_{k}[/tex]=1/k²

Then [tex]\sum_{k=1}^{\infty }[/tex]  [tex]a_{k}[/tex]/ [tex]b_{k}[/tex]

[tex]\sum_{k=1}^{\infty }[/tex] k²/(k²+k)=1 (≠0)

By comparison test, we know that ∑ [tex]a_{k}[/tex] and ∑ [tex]b_{k}[/tex] converge or diverge together.

As  ∑ [tex]b_{k}[/tex]= ∑1/k² converges this implies that  ∑ [tex]a_{k}[/tex]=(1/(k²+k) converges

Hence the interval of convergence of the given power series is,

I=[0, 2/9]

Therefore, the interval is I=[0, 2/9] and the radius of convergence in the power series is R=1.

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Interpreting the graph, it is found that the function has two real solutions

The number of different real solutions that a function has is given by the number of times it crosses the x-axis(also known as the horizontal axis) on the graph. If the graphs of the equations intersect, then there is one solution that is true for both equations.

In this problem, the function crosses the x-axis, at 0 and -4

Using the above we find that the given graph has solution at the x intercepts.

X intercepts are 0 and -4

Hence the solutions are two real and they are x=0 and x =-4

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After solving, the reaminder is 1 if x^3-2x^2+X+1 is divided by x-1.

In the given question we have to find the remainder if x^3-2x^2+X+1 is divided by x-1.

The given equation is x^3-2x^2+X+1.

We have to divide this equation by x-1 to find the remainder.

To find the remainder we firstly find the value of x from x-1. Then we put the value of x in the given equation then we can easily find the remainder.

Putting the x-1 equla to zero, so

x=1

Now putting the value of x in the given equation.

=x^3-2x^2+X+1

=(1)^3-2(1)^2+1+1

=1-2+1+1

=1

Hence, the remainder is 1 if x^3-2x^2+X+1 is divided by x-1.

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After 35 minutes there will be 40 bacteria remaining.

The process of a constant percentage rate decrease in an amount over time is referred to as "exponential decay." The formula to calculate exponential decay is given as, [tex]N_t=N_0\left(\frac{1}{2}\right)^{\frac{t}{t_{1/2}}}[/tex]. Here, Nt is the quantity after time t, N0 is the initial quantity, t1/2 is the half-life, and t is time.

For the first situation, Nt=360, N0=900, t=10 minutes. Therefore, substituting the given values get the value of t1/2. So,

[tex]\begin{aligned}360&=900\left(\frac{1}{2}\right)^{\frac{10}{t_{1/2}}} \\\frac{360}{900}&=\left(\frac{1}{2}\right)^{\frac{10}{t_{1/2}}}\\0.4&=\left(\frac{1}{2}\right)^{\frac{10}{t_{1/2}}}\\ \ln(0.4)&=\frac{10}{t_{1/2}}\ln(0.5)\\t_{1/2}&=10\times\frac{\ln(0.5)}{\ln(0.4)}\\&=7.6\end{aligned}[/tex]

Now, for the second situation,  Nt=40.  We have to find the time at which there will be 40 bacteria remaining. Then,

[tex]\begin{aligned}40&=900\left(\frac{1}{2}\right)^{t/7.6}\\0.04&=\left(\frac{1}{2}\right)^{t/7.6}\\\ln(0.04)&=\frac{t}{7.6}\ln(0.5)\\t&=7.6\times\frac{\ln(0.04)}{\ln(0.5)}\\&=7.6\times4.64\\&=35.26\\&\approx35\end{aligned}[/tex]

The answer is 35 minutes.

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The equation of a line given two points in point slope form is:

y - y1 = (y2-y1 / x2-x1)(x-x1).

Given:

Two points (x1,y1) and (x2,y2)

we know that,

slope m = y2-y1 / x2-x1

the equation passes through (x1,y1).

we know that:

Point slope form is y - y1 = m(x-x1)

substitute m value

y - y1 = (y2-y1 / x2-x1) (x-x1)

Therefore The equation of a line given two points in point slope form is:

y - y1 = (y2-y1 / x2-x1)(x-x1).

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An example of an obtuse angle is 135°.

When two straight lines or rays intersect at a shared terminal, an angle is generated.

An angle whose measure is more than 90° but less than 180° is said to be an obtuse angle.

Therefore, an example of an obtuse angle is 135°.

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There exists infinitely many solutions for the given equation 12x + 1 = 3(4x + 1) – 2  

Here, we are given an equation as follows-

12x + 1 = 3( 4x + 1 ) – 2

Let us solve the equation to get the value of the variable x.

12x + 1 = 12x + 3 – 2

12x + 1 = 12x + 1

Thus, here, we see that the Left hand side is exactly equal to the right hand side. This means that the given equation has infinitely many solutions.

Therefore, there exists infinitely many solutions for the given equation 12x + 1 = 3(4x + 1) – 2  

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There is a probability of 66.5 % chance of it landing on a 5 at least once in 6 dice.

Because there are six faces on a die, you have an even chance of the dice landing on one of these faces each time you roll:

This means that each time that you roll, there is a 5/6 chance that you will not roll a 5.

The probability of not rolling a 6 twice is 5/6 or 69.4%.

Roll the die six times, and the probability of not rolling a 5 is

(5/6) * (5/6) * (5/6) * (5/6) * (5/6) * (5/6) * (5/6)

= (5/6)⁶

= 33.5%

Therefore, the probability of rolling a 5 at least once in 6 dice

= 100%  - 33.5%

= 66.5%

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Answer:

6a= 400

6d=480

Step-by-step explanation: