Solve for a.
5a + 2 - 7-8 = 0
What is the root? If there is no root, choose none.

The value of exponential expression ln e⁴ is 4

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given is an exponential expression ln e⁴ we need to simplify it,

So,

we know that,

ln aⁿ = n ln a

and =

ln e = 1

so,

ln e⁴ = 4 ln e

= 4 x 1

= 4

Hence, the value of exponential expression ln e⁴ is 4

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Step-by-step explanation:

How is the graph of y=(x-1)2-3 transformed to produce the graph of y-3(x+4)??

The graph is translated left 5 units, compressed vertically by a factor of 2, and translated up 3 units.

The graph is stretched vertically by a factor of Ź, translated left 5 units, and translated up 3 units.

O The graph is translated left 5 units, compressed horizontally by a factor of 3, and translated down 3 units.

O The graph is stretched horizontally by a factor of Ž, translated left 5 units, and translated down 3 units.

Answer:

B. The graph is stretched vertically by a factor of One-half, translated left 5 units, and translated up 3 units.

Step-by-step explanation:

just did the test

Answer:

(x+3) ( x^2 -6)

Step-by-step explanation:

x^3 + 3x^2 - 6x – 18

Factor by grouping

x^3 + 3x^2    - 6x – 18

Factor x^2 out of the first group and -6 out of the second group

x^2( x+3)  -6(x+3)

Factor out x+3

(x+3) ( x^2 -6)

Answer:

ascending order} an order of numbers from least to greatest like 1 2 3 4

descending order} an order of numbers from greatest to least like 4 3 2 1

Answer:

31/10,32/10,33/10,34/10,35/10

Step-by-step explanation:

a rational number is formed when any two integers p and q are expressed in the form of p/q

to find two two sets of rational numbers BETWEEN any two numbers

a and b we need to express a and b and rational numbers....let us express 3and4 as rational numbers 3=30/10 4=40/10

the list of rational numbers between 3and4,that is, 30/10,31/10,32/10,33/10,34/10,35/10,36/10,37/10,38/10,39/10,40/10.

therefore the five rational numbers between 3 and 4 are (31/10,32/10,33/10,34/10,35/10...

I hope that helps

Answer:

0.7 = 70% probability that the player will score 0 points.

Step-by-step explanation:

For each free throw, we have these following probabilities:

0.3 probability the player makes.

0.7 probability the player misses.

What is the probability that the player will score 0 points?

He is only allowed the second if he misses the first, thus, he ends with 0 points only if he misses the first.

For any free throw:

0.7 probability the player misses, so 0.7 = 70% probability that the player misses the first free throw, and 0.7 = 70% probability that the player will score 0 points.

Answer:

A. QT ≅ AZ

Step-by-step explanation:

When writing a congruence statement of two triangles, the order of arrangement of the letters used in naming the triangles are carefully considered. Corresponding sides and angles of both triangles are arranged accordingly in the order they appear.

Given that ∆QPT ≅ ∆ARZ, we have the following sides that correspond and are congruent to each other:

QP ≅ AR

PT ≅ RZ

QT ≅ AZ

The only correct one given in the options given above is QT ≅ AZ

Answer:

1. 1056.67

2. 29th percentile.

3. 79

4. 77

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean score of 1150, standard deviation of 90

This means that [tex]\mu = 1150, \sigma = 90[/tex]

1. What is the score for someone in the 15th percentile?

This is X when Z has a p-value of 0.15, so X when Z = -1.037.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.037 = \frac{X - 1150}{90}[/tex]

[tex]X - 1150 = -1.037*90[/tex]

[tex]X = 1056.67[/tex]

2. What is the percentile rank of someone with a score of 1100?

This is the p-value of Z when X = 1100. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1100 - 1150}{90}[/tex]

[tex]Z = -0.555[/tex]

[tex]Z = -0.555[/tex] has a p-value of 0.29, so 29th percentile.

3. How many students have scores of 1060 or greater?

The proportion is 1 subtracted by the p-value of Z when X = 1060. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1060 - 1150}{90}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a p-value of 0.1587.

Out of 500:

0.1587*500 = 79

79 is the answer.

4. How many students scored between 1200 and 1250?

The proportion is the p-value of Z when X = 1250 subtracted by the p-value of Z when X = 1200. So

X = 1250

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1250 - 1150}{90}[/tex]

[tex]Z = 1.1[/tex]

[tex]Z = 1.1[/tex] has a p-value of 0.8643.

X = 1200

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1200 - 1150}{90}[/tex]

[tex]Z = 0.555[/tex]

[tex]Z = 0.555[/tex] has a p-value of 0.7106

0.8643 - 0.7106 = 0.1537

Out of 500:

0.1537*500 = 77

77 is the answer.

You're looking for a solution in the form

[tex]y(x) = \displaystyle \sum_{n=0}^\infty a_nx^n[/tex]

Differentiating, we get

[tex]y'(x) = \displaystyle \sum_{n=0}^\infty na_nx^{n-1} = \sum_{n=1}^\infty na_nx^{n-1} = \sum_{n=0}^\infty (n+1)a_{n+1}x^n[/tex]

[tex]y''(x) = \displaystyle \sum_{n=0}^\infty (n+1)na_{n+1}x^{n-1} = \sum_{n=1}^\infty (n+1)na_{n+1}x^{n-1} = \sum_{n=0}^\infty (n+2)(n+1)a_{n+2}x^n[/tex]

Substitute these for y' and y'' in the differential equation:

[tex]\displaystyle \sum_{n=0}^\infty (n+2)(n+1)a_{n+2}x^n - \sum_{n=0}^\infty (n+1)a_{n+1}x^n = 0[/tex]

[tex]\displaystyle \sum_{n=0}^\infty \bigg((n+2)(n+1)a_{n+2}-(n+1)a_{n+1}\bigg)x^n = 0[/tex]

Then the coefficients of y are given by the recurrence

[tex]\begin{cases}a_0=y(0)\\a_1=y'(0)\\a_{n+2}=\frac{a_{n+1}}{n+2}&\text{for }n\ge0\end{cases}[/tex]

or

[tex]a_n = \dfrac{a_{n-1}}n[/tex]

But we cannot assume that [tex]a_0[/tex] and [tex]a_1[/tex] depend on each other; we can only guarantee that the recurrence holds for n ≥ 1, so that

[tex]a_2=\dfrac{a_1}2 \\\\ a_3=\dfrac{a_2}3=\dfrac{a_1}{3\times2} \\\\ a_4=\dfrac{a_3}4=\dfrac{a_1}{4\times3\times2} \\\\ \vdots \\\\ a_n=\dfrac{a_1}{n!}[/tex]

So in the power series solution, we split off the constant term and we're left with

[tex]y(x) = a_0 + a_1 \displaystyle \sum_{n=1}^\infty \frac{x^n}{n!}[/tex]

so that the fundamental solutions are

[tex]y_1=1[/tex]

and

[tex]y_2=x+\dfrac{x^2}{2!}+\dfrac{x^3}{3!}+\dfrac{x^4}{4!}+\cdots[/tex]

Answer:

GHC22.5

Step-by-step explanation:

90/3=30

30=0.75

30×0.75

=22.5

Answer:

4000

Step-by-step explanation:

from 1 - 1000 = 300

1's    = 100

10's  = 100

100's = 100

1000's = 0

300 * 10 = 3000

then add in all the 3000's (ie 3001,3002, etc ) that adds one more thousand

3000 + 1000 = 4000

Answer:

3000?

Step-by-step explanation:

Answer:

The best point estimate for the population's standard deviation is 37.3.

Step-by-step explanation:

Best point estimate:

The best point estimate for the population mean is the sample mean.

The best point estimate for the population standard deviation is the sample standard deviation.

In this question:

Sample standard deviation of 37.3, and thus, the best point estimate for the population's standard deviation is 37.3.

Base case (n = 1):

• On the left side: 1/(1×2) = 1/2

• On the right side: 1/(1 + 1) = 1/2

Induction hypothesis: Assume the statement is true for n = k ; that is,

1/(1×2) + 1/(2×3) + … + 1/(k × (k + 1))) = k/(k + 1)

Inductive step (n = k + 1):

1/(1×2) + 1/(2×3) + … + 1/(k × (k + 1))) + 1/((k + 1) × (k + 2)))

= k/(k + 1) + 1/((k + 1) × (k + 2))

= (k × (k + 2) + 1) / ((k + 1) × (k + 2))

= (k ² + 2k + 1) / ((k + 1) × (k + 2))

= (k + 1)² / ((k + 1) × (k + 2))

= (k + 1) / (k + 2)

and this is what we wanted to show.

9514 1404 393

Answer:

  $11,680.58

Step-by-step explanation:

Usually, I would say copy the example, using 70,000 instead of 55,000. However, the example you show has a couple of errors in it. You need to do what it says, not follow what it did.

__

The first 48,535 is taxed at 15%, so the tax is 0.15×48535 = 7280.25.

The next (70,000 -48,535) = 21,465 is taxed at 20.5%, so the tax is ...

  0.205×21,465 = 4400.325 ≈ 4400.33

The the total tax due on $70,000 is ...

  $7280.25 +4400.33 = $11,680.58 . . . . tax due on $70,000

_____

Additional comments

The example shown has a couple of errors. The tax on the excess amount is figured at 2.05%, not 20.5%, and the 132.53 value from that is shown as 132.23.

__

Any tax table like this one can be reduced to a set of simpler formulas. Here are the formulas for the brackets shown in your tax table.

  ≤ 48535 -- income × 0.15

  ≤ 97069 -- income × 0.205 -2669.425

  ≤ 150,473 -- income × 0.26 -8008.22

  ≤ 214,368 -- income × 0.29 -12,522.41

  > 214,368 -- income × 0.33 -21,097.13

In this case, the second row of this simpler table would give the tax on $70,000 as ...

  tax = 70,000 × 0.205 -2669.425

  tax = 14350 -2669.425 = 11680.575 ≈ 11,680.58 . . . same as above

Answer:

A and B must always be congruent

B and D

E and G

F and H

Step-by-step explanation:

I have to be honest. from the picture I cannot see the vertical angles. All I see is a straight blue line and red letters. But based on the vertical theorem

A and B must always be congruent

B and D

E and G

F and H

also if you want to make sure it's right try to include another picture.

Answer:

Step-by-step explanation:

edmentum :)

Answer:

The point slope form of the equation is,

[tex]y + 10 = - \frac{19(x + 6)}{5} [/tex]

m = (y2-y1)/(x2-x1) = (9-(-10))/((-6)-(-1)) = -19/5

b = y1-mx1 = -69/5

Answered by GAUTHMATH

Answer:

0.05x + 0.1(55 - x) = 3.9

Step-by-step explanation:

There are 55 coins.

Let x = number of nickels.

The number of dimes is 55 - x.

The value of a nickel is $0.05, and the value of a dime is $0.10.

The value of x nickels is 0.05x

The value of 55 - x dimes is 0.1(55 - x)

The total value of the coins is 0.05x + 0.1(55 - x)

The total value of the coins is $3.90

0.05x + 0.1(55 - x) = 3.9

y=x²-10x-7

a>0 so we will be looking for minimum

x=-b/2a=10/2=5

y=25-50-7=-32

Answer: (5;32)

Answer:

rhe

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Step-by-step explanation:

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Answer:

95% confidence level should be used for a confidence​ interval.

The given confidence interval contains the value of 85 ​sec, so there is not sufficient evidence to support the claim that the mean is greater than 85 sec.

Step-by-step explanation:

0.05 significance level

1 - 0.05 = 0.95

0.95*100% = 95%

This means that a 95% confidence level should be used for a confidence​ interval.

Confidence interval is found to be −1.8 sec<μ<213.5 ​sec, what should we conclude about the​ claim?

Contains the value of 85 sec, thus there is not sufficient evidence to support the claim that the mean is greater than 85 sec.

Answer:

D. Height

General Formulas and Concepts:

Geometry

Area of a Circle: A = πr²

Step-by-step explanation:

In order to find the area of a circle, we must follow the formula. Out of all the options given, height is not incorporated into the formula.

It wouldn't make sense to use height anyways since it would be 3-dimenional and we're talking 2-dimensional.

∴ our answer is D.

Answer:

I don't see the problem.

Step-by-step explanation:

Answer:

35

Step-by-step explanation:

35 because the two angles are added 22 and 123 = 145. 145-180=35

A factor is a natural number that can be multiplied by another natural number to get a value. The greatest common factor refers to when one compares the factors of two numbers, the largest natural number that both numbers have in common is the number's greatest common factor.

In the case of ([tex]m^2[/tex]) and ([tex]m^4[/tex]), the greatest common factor is ([tex]m^2[/tex]) because there are no factors of ([tex]m^2[/tex]) that are larger than it. No number can have a factor larger than itself. Since ([tex]m^2[/tex]) is also a factor of ([tex]m^4[/tex]) it is the greatest common factor of the two numbers.

Answer:

3/4

Step-by-step explanation:

There are 13 hearts in a 52 deck.

52-13=39

39/52=3/4

The probability that you are not dealt a heart from the deck of cards is 3/4.

Probability determines the chances that an event would occur. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that you are not dealth with a heart = 1 - (number of hearts / total number of cards)

1 - 13/52 = 39/52 =  3/4

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Answer:

πr

Step-by-step explanation:

radius = r/2

so circumference = 2π(r/2)

= 2πr/2

= πr

Answer:

The answer is B which is C=2πr

Step-by-step explanation:

i just did it

Answer:

x = 5

Step-by-step explanation:

I'm assuming that 3x +1 & 4x + 5 are all underneath the square root

2 √3x + 1  - √4x + 5 = 3

2 √3x + 1 = 3 + √4x + 5

4 (3x+1) = 9 + 6 √4x + 5 + 4x + 5

12x + 4 = 14 + 6√4x + 5 + 4x

-6 √4x + 5 = 14 + 4x - 12x - 4

-6 √4x + 5 = 10 - 8x

3 √4x + 5 = -5 + 4x  (divided both sides by - 2)

9 (4x +5) = 16x^2 - 40x + 25

36x + 45 = 16x^2 - 40x + 25

36x + 45 - 16x^2 + 40x - 25 = 0

76x + 20 - 16x^2 = 0

-16x^2 + 76x + 20 = 0

4x^2 - 19x -5 = 0  (dividied by -4)

4x^2 + x - 20x -5 = 0

x (4x + 1) -5 (4x +1) = 0

(4x +1) (x-5) = 0

Possible answers:

4x + 1 = 0

x - 5 = 0

x = -1/4

x =5

Now we will check which one satisfies the equation

2√3x+1 - √4x+5  

Substitue 5 for x and we get 3

Thus we know that 5 is the correct answer

Answered by Gauthmath