If the distance between A(0, 4) and B(3,a) is 5 units then find the value of a.​

Answer:

4/5

Step-by-step explanation:

All as percentages are:

0.6 = 60%

4/5 = 80% (largest)

0.75 = 75%

Therefore, Jake should select 4/5.

Answer:

c)  124.96

Step-by-step explanation:

Geometric series:  100 + 20 + ... + 0.16

First we need to find which term 0.16 is.

General form of a geometric sequence: \(a_n=ar^{n-1}\)

(where a is the first term and r is the common ratio)

To find the common ratio r, divide one term by the previous term:

\(\implies r=\dfrac{a_2}{a_1}=\dfrac{20}{100}=0.2\)

Therefore, \(a_n=100(0.2)^{n-1}\)

Substitute \(a_n=0.16\) into the equation and solve for n:

\(\implies 100(0.2)^{n-1}=0.16\)

\(\implies (0.2)^{n-1}=0.0016\)

\(\implies \ln(0.2)^{n-1}=\ln0.0016\)

\(\implies (n-1)\ln(0.2)=\ln0.0016\)

\(\implies n-1=\dfrac{\ln0.0016}{\ln(0.2)}\)

\(\implies n=\dfrac{\ln0.0016}{\ln(0.2)}+1\)

\(\implies n=5\)

Therefore, we need to find the sum of the first 5 terms.

Sum of the first n terms of a geometric series:

\(S_n=\dfrac{a(1-r^n)}{1-r}\)

Therefore, sum of the first 5 terms:

\(\implies S_5=\dfrac{100(1-0.2^5)}{1-0.2}\)

\(\implies S_5=124.96\)

AC = 18 + CB, AB = 18 + AD, BC = AB + AC - CB. The measures of the angles of the triangle are m∠BAC = 77°, ∠C = 18° and m∠A = 95°. The lengths of the sides of the triangle are AD = 18, AC = 18 + CB and AB = 18 + AD. The length of the side KL of the triangle KAL is KL = √(AK² + AL²).

AK = √(21² - (25)²) = 20

AL = √(21² - (20)²) = 25

KL = √(20² + 25²) = 29.7

AC = 18 + CB

AB = 18 + 18 = 36

BC = AB + AC - CB = 36 + 18 - CB = 54 - CB

The given information includes the measures of the angles of ΔABC, m∠BAC = 77°, ∠C = 18° and m∠A = 95°, and the length of the side AD = 18. We know that AD⊥CB, so we can use the Pythagorean Theorem to find the length of CB. We have CB = √(AD² - AC²) = √(18² - 18²) = 0. From this, we can calculate the lengths of the sides of the triangle. AC = 18 + CB = 18. AB = 18 + AD = 36. BC = AB + AC - CB = 54 - CB = 54.

The given information also includes the measure of m∠KAL = 100º and OA = 21. We can use the Pythagorean Theorem to find the lengths of the sides AK, AL, and KL of the triangle KAL. AK = √(OA² - AL²) = √(21² - (25)²) = 20. AL = √(OA² - AK²) = √(21² - (20)²) = 25. KL = √(AK² + AL²) = √(20² + 25²) = 29.7.

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Answer:

IT'S A. HEHEHEHEHEHEHE

Answer:

15, 21, 27

Step-by-step explanation:

\(a_n}\) = \(a_{1}\) + (n-1)d  

\(a_{n}\) is the number in the sequence we are looking for

\(a_{1}\)  This is the first term in the sequence that we do not know and we are looking for

n stands for the number of the term and d is the common difference.  We will put in all that we know and solve for the first term.

609 = \(a_{1}\) + (100-1)6  

609 =\(a_{1}\) + (99)6

609 = \(a_{1}\) + 594  Subtract 594 from both sides of the equation

15 = \(a_{1}\)

Now that we know that the first term is 15 we just add 6 to get the next term which is 21 and then add 6 again to get the last term 27.

48

Step-by-step explanation:

Answer:

2. -14 + 6

Step-by-step explanation:

-11 + 13 = 2

-14 + 6 = -8

23 + -10 = 13

19 + -17 = 2

Answer:

2.-14+6

if you struggle with adding or subtracting negatives and positives you can look at each number by itself. For example// the number 14 is greater than 6 so you know that because 14 is greater than 6 he product of -14 and positive 6 will be negative.

another example//-11+13, disregard the positive and negative and look at the number itself, 13 is greater than 11. Now look at the sign associated with the number, 13 is positive, because the greater number, 13, is positive the product will also be positive

Step-by-step explanation:

$20.70

Step-by-step explanation:

15% of 18 is 2.7 so 18 + 2.7 = 20.70

Answer:

It would be 14.2+-5a

Step-by-step explanation:

It would be that because first, u have to add all the numbers with the same variable ad 8 and 4a don't have the same variable, and as you can see the addition sign on 6.2 and they have the same variable so it would be 14.2. Then you would have to find the value of s so 4.2 u wouldn't add it with 9a even though it has the same variable  you have to subtract because it has a subtraction sign above it so since 4a came first u subtract 9a from 4a which would give u -5a.

Answer:

32 years

Step-by-step explanation:

32 years

Step-by-step explanation:

fist find how much of 6750 is 6.25%

6750 * .0625 = 421.875

then use trial and error until u get the number u want

421.875 * 10 = 4218.75 + 6750 = 1096875 NO

421.875 * 20 = 84375 + 6750 = 151875 NO

421.875 * 30 = 12656.25 + 6750 = 19406.25 NO

421.875 * 31 = 13078.125 + 6750 = 19828.125 NO

421.875 * 32 = 13500 + 6750 = 20250 YES

Step-by-step explanation:

-2/3x+ 3/7 = 1/2

-2/3x = 1/2 -3/7

-2/3x = 7-6 /14

-2/3x = 1/14

3x = 1/14×(-2)

3x = 1/ -28

x = 1/ -28×3

x = 1/-84

The vertices of the image of dilation are (4, 2), (-1, 2) and (3, 4)

The given parameters are:

Center, (a, b) = (-3, 0)

Scale factor, k = 1/2

The vertices of the figure are

(5,4), (-5, 4) and (3,8)

The rule of dilation is represented as:

(x, y) ⇒ (k(x -a), k(y -b))

So, we have:

Point (5,4)

(x, y) ⇒ (1/2(5 + 3), 1/2(4 -0))

(x, y) ⇒ (4, 2)

Point (-5,4)

(x, y) ⇒ (1/2(-5 + 3), 1/2(4 -0))

(x, y) ⇒ (-1, 2)

Point (3,8)

(x, y) ⇒ (1/2(3 + 3), 1/2(8 -0))

(x, y) ⇒ (3, 4)

So, the vertices of the image of dilation are (4, 2), (-1, 2) and (3, 4)

See attachment for the image

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Answer:

The point-slope form is  

y

+

6

=

1

5

(

x

−

4

)

or  

y

+

5

=

1

5

(

x

−

9

)

, depending on which point you use. If you solve for  

y

to get the slope-intercept form, both equations will convert to  

y

=

1

5

x

−

34

5

Step-by-step explanation:

Answer:

the slope is 1/3

Step-by-step explanation:

The new coordinates are : N'=(3,-7), O'=(-4,-5), W'=(-1,-1).

If a point \((x,y)\) is rotated \(90\) degrees counterclockwise about the origin, it becomes \((-y,x)\).

Here, \(N=(-7,-3)\). So, \(N'=(3,-7)\)

\(O=(-5,4)\). So, \(O'=(-4,-5)\)

\(W=(-2,1)\). So, \(W'=(-1,-1)\)

So, image after rotation is:  

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Answer:

The new coordinates are

Step-by-step explanation:

N'=(3,-7), O'=(-4,-5), W'=(-1,-2)

Answer:

x = -14

Step-by-step explanation:

The two marked angles are called vertical angles and they are EQUAL to each other. Write an equation:

9x + 184 = 7x + 156

subtract 7x from both sides.

2x + 184 = 156

subtract 184 from both sides.

2x = -28

divide by 2.

x = -14

to find the measure of the angles, substitute in -14 for x. They both come out to be 58°.

Answer:

10x larger

The is like 300 something and Canada is 30 something

The expressions aaaaaaa, aabbbb, aabbccc, and 3xxyyyz will be a⁷, a²b⁴,  a²b²c³, and 3x²y³z.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We know that if x is multiplied by n time of x, then we can be written as xⁿ.

1. aaaaaaa = a⁷

2. aabbbb = a²b⁴

3. aabbccc = a²b²c³

4. 3xxyyyz = 3x²y³z

The expressions aaaaaaa, aabbbb, aabbccc, and 3xxyyyz will be a⁷, a²b⁴,  a²b²c³, and 3x²y³z.

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This line integral represents the evaluation of the function xe^yz along the curve C from point (0, 0, 0) to point (4, 3, To (4, 3, 2).

evaluate the line integral of xe^yz ds along the line segment from (0, 0, 0) to (4, 3, 2), we first need to parameterize the curve.

Let's call the parameter t and define the position vector r(t) = . We can see that the line segment passes through the points (0, 0, 0) and (4, 3, 2), so we can set up the following equations:

x(t) = 4t
y(t) = 3t
z(t) = 2t

We also need to find the differential ds. Since we are dealing with a curve in three dimensions, ds is given by:

ds = sqrt(dx^2 + dy^2 + dz^2) dt

Plugging in our parameterizations, we get:

ds = sqrt((4dt)^2 + (3dt)^2 + (2dt)^2)
ds = sqrt(29) dt

Now we can set up the line integral:

integral_C xe^yz ds = integral_0^1 x(t) e^(y(t)z(t)) ds

Substituting in our parameterizations and ds, we get:

integral_0^1 (4t)(e^(3t*2t)) sqrt(29) dt

We can simplify the exponential term:

e^(3t*2t) = e^(6t^2)

And we can pull out the constant sqrt(29):

integral_0^1 4t e^(6t^2) sqrt(29) dt

This is now a standard integral that we can evaluate using u-substitution. Let u = 6t^2, du = 12t dt. The integral becomes:

(2/3) integral_0^6 e^u du

Evaluating the integral gives:

(2/3) (e^6 - 1)

Multiplying by sqrt(29/12) gives the final answer:

(2/3) sqrt(29/12) (e^6 - 1)
To evaluate the line integral of xe^yz ds along the curve C, which is the line segment from (0, 0, 0) to (4, 3, 2), we first need to parameterize the curve.

Let r(t) be the parameterization of C, where t ranges from 0 to 1:
r(t) = (4t, 3t, 2t)

Now, we can find the derivative of r(t) with respect to t:
r'(t) = (4, 3, 2)

Next, we find the magnitude of r'(t):
|r'(t)| = √(4^2 + 3^2 + 2^2) = √29

Now, we substitute the parameterization into the integral:
integral_C xe^yz ds = integral_0^1 (4t)e^(3t*2t) * |r'(t)| dt

We are given the value of the integral as (sqrt(29)/12)(e^6 - 1), so:
integral_0^1 (4t)e^(6t^2) * √29 dt = (sqrt(29)/12)(e^6 - 1)

This line integral represents the evaluation of the function xe^yz along the curve C from point (0, 0, 0) to point (4, 3, 2).

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In the graph of the simple linear regression equation, the parameter ß1 is the slope of the true regression line.

The simple linear regression equation represents a linear relationship between a dependent variable and an independent variable. It can be written as y = ß0 + ß1x, where ß0 is the intercept and ß1 is the slope of the regression line.

The slope (ß1) determines the rate of change in the dependent variable (y) for each unit change in the independent variable (x). It represents the steepness or inclination of the regression line. The sign of ß1 indicates whether the line has a positive or negative slope, indicating the direction of the relationship between the variables.

Thus, in the context of the simple linear regression equation, the parameter ß1 is the slope of the true regression line.

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Answer:

hope that helps

Step-by-step explanation:

- If graphed, Class B would look more like the red graph below and Class A would look more like the blue one.

- Based on the data, a score of 8 is more likely in Class B than Class A.

- Class A has a greater spread.

Answer: El número de grupos de Analistas que puede realizar la inducción es de 238 y el número de grupo Ingenieros en Mantenimiento  es de 227.

Explanations: Hacemos dos ecuaciones para resolver la incógnita. Siendo X el grupo de Técnicos y Y el grupo de Ingenieros Civiles.

17X + 18Y = 423 (1)

14X + 7Y = 231 (2)

Resolvemos el sistema de ecuaciones, multiplicamos por -14 a la primera ecuación y por 17 a la segunda ecuación:

(-14) (17X + 18Y = 423)

(17)  (14X + 7Y  = 231)

Sumamos y despejamos a Y:

-238X - 252Y = -59 976

238X + 119Y = 28.322

0 + 133Y = 31 654

Y = 31 654/133

Y = 238

Entonces el número de grupo de analistas que puede realizar la inducción es 238.

Ahora sustituimos el valor de Y en cualquiera de las ecuaciones y despejamos a X:

17X + 18*231 = 423

17X + 4284 = 423

17X = 4284-423

17X = 3861

X = 3861/17

X = 227

El número de grupo de Ingenieros en Mantenimiento que realizarán la inducción es 227.

The value of x in linear equation 3.8x-(-1-9.7x)=2.6+13.3x is 8

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

Given linear equation is 3.8x-(-1-9.7x)=2.6+13.3x

3.8x+1+9.7x=2.6+13.3x

Add the x variable terms on left

13.5x+1=2.6+13.3x

Subtract 13.3x and 1 on both sides

13.5x-13.3x=2.6-1

0.2x=1.6

Divide both sides by 0.2

x=8

Hence, the value of x in linear equation 3.8x-(-1-9.7x)=2.6+13.3x is 8

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There are 1,152 arrangements of "MATHEMATICS" in which each consonant is adjacent to a vowel.

To find the number of arrangements of the word "MATHEMATICS" in which each consonant is adjacent to a vowel, we can treat the consonants (M, T, H, M, T, C, and S) and vowels (A, E, A, I) as separate groups and arrange them in a way that each group of consonants is next to a group of vowels

We have two groups of vowels (A and E, and A and I) and three groups of consonants (MTHM, TC, and S). We can arrange the two vowel groups in 2! = 2 ways, and then arrange the three consonant groups in 3! = 6 ways. Within each group, the letters can be arranged in a total of 4! = 24 ways for the MTHM group, 2! = 2 ways for the TC group, and 1 way for the S group.

Therefore, the total number of arrangements in which each consonant is adjacent to a vowel is:

2! x 6 x 24 x 2 x 1 = 1,152

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A compound statement is a group of two or more statements connected using words such as 'or', 'and', 'if then', 'if and only if'.

Then, we have:

This is a compound statement of conditional type where the first simple statement is the condition for the second simple statement.

Then, we have:

p: The dog is hungry.

q: She is barking.

p→q: The dog is hungry if she is barking.

Thus, this statement is a compound statement of conditional type.

We can see this statement as a conjunction of two simple statements:

• p: Bill reads books.

• q: Bill reads magazines.

Then, we have:

p ∧ q: Bill reads books and magazines.

Thus, this statement is a compound statement of conjunction type.

We can see this statement as a conjunction of two simple statements:

• p: There are wild animals on G Ranch.

• q: There are wild animals on L Ranch.

Then, we have:

p ∧ q: There are wild animals on G and L Ranch.

Thus, this statement is a compound statement of conjunction type.

Part a) Compound statement of conditional type.

Part b) Compound statement of conjunction type.

Part c) Compound statement of conjunction type.

The probability that a designer does not prefer red is 0.77.

Probability (event) = favorable outcome / total outcome

Total primary color designers = 400.

The number of opinions for red = 92

The probability for designer prefer red = 92 /100

The probability for designer prefer red = 0.23

Then, the probability that a designer does not prefer red = 1 - 0.23

The probability that a designer does not prefer red = 0.77

Thus, the probability that a designer does not prefer red color = 0.77.

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The correct question along with table is attached-

Let the random variable p represent a randomly selected prize amount the expected value of p is $3.90  by using probability.

Prize                $1          $5            $10            $20              $50

Probability     0.60      0.30         0.05           0.04              0.01

It is based on the possible chances of something to happen. The theoretical probability is mainly based on the reasoning behind probability. For example, if a coin is tossed, the theoretical probability of getting a head will be ½.

The expected value is defined as the the sum of each outcome is multiplied by its probability.

p=x1p1+x2p2+x3p3+x4p4

p=1.0.60+5.0.30+10.0.05+20.0.04

p=3.90

Therefore, the correct option is A, i.e. $ 3.90 is the expected value of P.

Three Types of Probability

Classical: (equally probable outcomes) Let S=sample space (set of all possible distinct outcomes).

Relative Frequency Definition.

Subjective Probability.

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It will take approximately 4.4 years to earn enough money to go on the trip if we invest our 2200 in a savings account with a 1.55% interest rate compounded annually.

First, we need to calculate the amount of money that we need to save in order to cover the cost of the trip. This can be done by subtracting the amount we have already saved from the total cost of the trip:

Total cost of trip = 2500

Amount already saved = 2200

Amount to save = 2500 - 2200 = 300

Next, we can use the compound interest formula to calculate how long it will take to earn 300 with an interest rate of 1.55% compounded annually. We can set up the formula as follows:

A = P(1 + i)n

where:

A = accumulated amount = 300 + 2200 = 2500 (the total cost of the trip)

P = principal = 2200

i = interest rate per year = 1.55%

n = number of years we need to save for

We can now solve for n:

2500 = 2200(1 + 0.0155)n

Divide both sides by 2200:

1.13636 = 1.0155n

Take the natural logarithm of both sides:

ln(1.13636) = n ln(1.0155)

Divide both sides by ln(1.0155):

n = ln(1.13636)/ln(1.0155) ≈ 4.4 years

Therefore, it will take approximately 4.4 years to earn enough money to go on the trip if we invest our 2200 in a savings account with a 1.55% interest rate compounded annually.that we rounded our final answer to the nearest tenth as instructed.

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Answer:

The scale factor is 20.

Explanation:

The scale factor is the ratio of the corresponding side lengths (or areas or volumes) of the two similar figures. In this case, we are given the areas of the front sides of the toy building and the real building, and we want to find the scale factor between them.

Let x be the scale factor. Then, the area of the front side of the real building is x^2 times the area of the front side of the toy building. We can set up the equation:

x^2 * 1 square foot = 400 square feet

Solving for x, we get:

x^2 = 400

x = sqrt(400)

x = 20

Therefore, the scale factor between the toy building and the real building is 20.