A passbook savings account has a rate of 10%. Find the effective annual yield, rounded to the nearest tenth of a percent, if the interest is compounded monthly.

The logarithmic expression is equal to:

Log₂(11)*log₆(2) = 1.34

Here we have the logarithmic expression:

Log₂(11)*log₆(2)

Now, remember that we can rewrite:

Logₐ(b) = Ln(b)/Ln(a)

Using that we can rewrite the expression:

Log₂(11)*log₆(2) = (Ln(11)/Ln(2))*(Ln(2)/Ln(6)) = Ln(11)/Ln(6)

Now using a calculator you can find these two natural logarithms:

Ln(11)/Ln(6) = 1.34

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Answer:

x = -2

Step-by-step explanation:

-12 = 1/2(6x - 12)  Multiply everything inside the parentheses by 1/2

-12 =1/2(6x) - (1/2)(12)

-12 = 3x - 6  Add 6 to both sides of the equation

-6 = 3x  Divide both sides by 3

-2 = x

Check:

Plug -2 in for x and see if statement is true

-12 = 1/2(6x - 12)

-12 = 1/2[(6)(-2) - 12]  Simplify inside the brackets

-12 = 1/2(-12 -12)

-12 = 1/2 (-24)

-12 = -12

Answer:

1)

D) -5<x≤-2

R) 0<y≤3

2)

D) 1≤x≤5

R)2≤y≤4

Step-by-step explanation:

(Only in 7th so might be wrong)

1)

D) -5<x≤-2

R) 0<y≤3

2)

D) 1≤x≤5

R)2≤y≤4

look at the range of where the x and y is at (1-2 included = 1<x≤2)

The total number of holes will be (a)15 and (b) 4 when the drilling machine is used whose standard deviation is 0.0028mm.

The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean.

The sum of all values divided by the total number of values constitutes a dataset's mean.

The mean of the holes are given as 4.05 mm([tex]\mu=4.08[/tex])

The standard deviation is given as 0.0028 mm([tex]\rho=0.0028[/tex])

Now we will use the z-score and probability distribution to calculate the frequency of the holes to have diameter between 4.048 and 4.0553.

Here [tex]Pr(4.048\leq X\leq 4.0053)[/tex] ,so we need to compute the z-values

[tex]Z_1=\frac{X_1-\mu}{\rho} \\Z_1=\frac{4.048-4.05}{0.0028} \\Z_1=-0.7143[/tex]

Similarly:

[tex]Z_2=1.8929[/tex]

Therefore from the above statements we can say that

[tex]Pr(-0.7143\leq X\leq 1.8929)[/tex]

Solving for probability distribution we get

[tex]Pr(4.048\leq X\leq 4.0053)=0.7333[/tex]

Total number of holes=0.7333 × 20= 14.666..

Therefore the number of holes is 15

Similarly

The z-value corresponding to 4.052 mm is given by 0.71

The z-value corresponding to 4.056 mm is given by:2.14

The probability of the diameter being between 4.052 mm and 4.056 mm is 0.4838 – 0.2611 =0.2227

The number likely to have a diameter between 4.052 mm and 4.056 mm = 0.2227 × 20

= 4.454

= 4, correct to nearest whole number

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we have found out the cumulative frequency (c f) and percentiles(c %) for the given data.

We are given the frequency distribution table as:

X                 f    

5                 2

4                 5

3                 6

2                 4

1                  3

We need to find cumulative frequency (c f) and percentiles(c %)

c % = 100 × ( c f / n )

c f means the frequency is calculated by adding each frequency from a frequency distribution table to the sum of its predecessors.

n = 20

X                 f             c f             c %

5                 2              2            10 %

4                 5              7            35 %

3                 6             13            65 %

2                 4             17            85 %

1                  3            20           100 %

Therefore, we have found out the cumulative frequency (c f) and percentiles(c %) for the given data.

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The inequality to represent the given condition is -3<x<7 .

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. [1] It is frequently used to compare two numbers on the number line based on their sizes. Different types of inequalities are represented by a variety of notations, including:

The given statement gives the solutions of all real numbers between 3 and 7.

Therefore if we consider a real number x then, x>-3 and x<7 .

Combining together for a compound inequality: -3<x<7.

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Answer:

Well the IMC 2014 is

IMC 2014 + hMc

The polynomial expression for the area of the room is f(x) = x^2 + 16x + 48.

Here, we are given that the side of the length of the rug = x

Now, the square rug is placed on the rectangular room such that on 2 sides the uncovered floor is 6 meters.

This means that the length of the 2 opposite sides of the rectangle will be (x + 6 + 6) = (x + 12)

Similarly, there is 2 feet of uncovered floor on the other 2 sides, which means that the length of other two opposite sides is- (x + 2 + 2) = (x + 4)

Kindly refer to the diagram below for a better clarity of how we found out the sides.

Now, the area of a rectangle = Length × Breadth

Thus, area of the room = (x + 12) (x + 4)

= x^2 + 4x + 12x + 48

= x^2 + 16x + 48

Thus, the polynomial expression for the area of the room is f(x) = x^2 + 16x + 48

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The values of all the required angles are; m∠5 = 42°; m∠8 = 138°; m∠10 = 138° and m∠11 = 42°

Corresponding angles are formed where a line known as an intersecting transversal, crosses through a pair of straight lines.

Now, we are given that; m∠1 = 42°

By corresponding angles, we can say that;

m∠1 = m∠5

Thus; m∠5 = 42°

Now, we know that sum of angles on a straight line is equal to 180° i.e. they are supplementary angles.

Now, from the diagram, we can see that m∠5 and m∠8 are supplementary angles and as such;

m∠5 + m∠8 = 180°

42 + m∠8 = 180

m∠8 = 180° - 42°

m∠8 = 138°

Now, m∠9 is a corresponding angle to both m∠1 and m∠5. Thus, we can say that; m∠9 = 42°. However, m∠9 is supplementary to m∠10. Thus;

m∠10 = 180 - 42

m∠10 = 138°

Lastly, m∠10 and m∠11 are supplementary angles and as such;

m∠10 + m∠11 = 180°

138 + m∠11 = 180

m∠11 = 180° - 38°

m∠11 = 42°

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Answer:

the action of inflating something or the condition of being inflated.

"the inflation of a balloon"

ASTRONOMY

(in some theories of cosmology) a very brief exponential expansion of the universe postulated to have interrupted the standard linear expansion shortly after the Big Bang.

2.

ECONOMICS

a general increase in prices and fall in the purchasing value of money.

"policies aimed at controlling inflation"

Answer:...

Step-by-step explanation:

Answer:

Step-by-step explanation:

444

Answer:

$42.00

Step-by-step explanation:

Let x  = the original cost of the sweatshirt

x - .15x = 35.70  We don't know the original cost so we will call it x.  I know that we are taking 15 off of this number to get the sale's price.  15% means per 100, so as a fraction this would be 15/100.  To make this a decimal, I would divide 15 by 100 to get .15

x - .15x = 35.70  Combine the like terms

.85x = 35.70  This is say that 85% if the original price is the sale price of 35.70

Divide both sides of the equation by .85 and we get x = 42.00

Check:

42 - .15(42) = 35.70

42 - 6.30 = 35.70

Answer:

36in

Step-by-step explanation:

A square has four sides. If the length of one is 9 inches, then we multiply it by four to get 9*4 = 36in as our perimeter.

FINAL ANSWER: 36in

Answer: I say 4/3 the fraction so your answer is D

Explanation: Because its white cars to blue cars the problem is whats equivalent to the ratio 40 to 30, 4:1 is not the same as 40 to 30 neither

is 1:4 or 3 to 4 So its D. :)

Answer: 0

Step-by-step explanation:

because -2+-1 is -3. then -3+0 is just -3. lastly -3+1 = -2 and -2 + 2 = 0

Answer:

3

Step-by-step explanation:

32 - 20 = 12

12/4 = 3

This assumes that by remainder they mean they twelve feet left over and not the twenty feet removed. This is likely what it means.

Answer:

Step-by-step explanation:

(2*9/5d*9)-(1*5/9d*5)

18/45d-5/45d

13/45d

Answer:





Find the multiplicative inverse of the following

(i) -13    (ii) -13/19    (iii) 1/5    (iv) -5/8 × -3/7    (v) -1 × -2/5

(vi) -1

Solution:

The reciprocal of a given rational number is known as its multiplicative inverse. The product of a rational number and its multiplicative inverse is 1.

(i) The Multiplicative inverse of -13 is -1/13

∵ -13 × (-1/13) = 1

(ii) The Multiplicative inverse of -13/19 is -19/13

∵ -13/19 × (-19/13) = 1

(iii) The Multiplicative inverse of 1/5 is 5

∵ 1/5 × 5 = 1

(iv) The Multiplicative inverse of -5/8 × -3/7 is 56/15

∵ -5/8 × (-3/7) = 15/56 and 15/56 × 56/15 = 1

(v) The Multiplicative inverse of -1 × -2/5 is 5/2

∵ -1 × (-2/5) = 2/5 and 2/5 × 5/2 = 1

(vi) The Multiplicative inverse of -1 is -1

∵ -1 × (-1) = 1

Using the Pythagorean Theorem, it is found that the length of AB is of 8.54 units, considering that BC = 3 and that AC = 8.

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:

[tex]h^2 = l_1^2 + l_2^2[/tex]

For this triangle, we have that:

Hence the length of AB is given as follows:

h² = 3² + 8²

h² = 73

h = sqrt(73)

h = 8.54 units.

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Answer:

x = 1

Step-by-step explanation:

2 x [tex]x[/tex] = 10

10 > -10

9 x [tex]x[/tex] = 9

9 < 18

Answer:

[tex]\frac{27}{20}[/tex]

Step-by-step explanation:

[tex]\frac{3}{5} + \frac{6}{8}[/tex]

adjust the denominators;

= [tex]\frac{3*8}{5*8} + \frac{6*5}{8*5}[/tex]

[tex]=\frac{24}{40} + \frac{30}{40} \\\\=\frac{24+30}{40} \\\\=\frac{54}{40} \\\\simplify\\\\=\frac{27}{20}[/tex]

The solution for the given system of equations is (3,5) and (-4,12).

Given two systems of equations i.e. x+y=8 and y=[tex]x^{2}[/tex]-4 and asked to solve them.

⇒x+y=8; let's assume this equation as A

⇒ y=[tex]x^{2}[/tex]-4; let's assume this equation as B

From equation A

⇒y=8-x

From equation B

⇒y=[tex]x^{2}[/tex]-4

Equating both the values of y

⇒8-x=[tex]x^{2}[/tex]-4

⇒[tex]x^{2}[/tex]-8-4+x=0

⇒[tex]x^{2}[/tex]-12+x=0

{solving quadratic equation}

⇒[tex]x^{2}[/tex]-12+4x-3x=0 { factorizing the quadratic equation}

⇒[tex]x^{2}[/tex]+4x-3x-12=0

⇒x(x+4)-3(x+4)=0

⇒(x-3)(x+4)=0

Therefore, the value's of x=3,-4

⇒if x=3

From  equation A

⇒y=8-3=5

For x=3 ; y=5

⇒if x=-4

From  equation A

⇒y=8-(-4)=12

For x=-4 ; y=12

Therefore,The solution for the given system of equations is (3,5) and (-4,12).

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Answer:

28

Step-by-step explanation:

-28 + 28 = 0

Answer:

No, 2 is not a solution

Step-by-step explanation:

x - 5>10  Add 5 to both sides of the equations

x > 10  The solutions are all numbers greater than 10.  Two is not greater than 10.

If a sophomore was chosen yesterday, the probability that a sophomore will be chosen again today is 3/10.

Given, number of students name put into the hat = 20

total number of freshmen in the class = 12

total number of sophomore in the class = 6

total number of juniors in the class = 2

we are asked to determine the probability that the sophomore will be selected the second day also = ?

Calculating a situation's probability allows us to determine its likelihood. Absolute certainty in forecasting is challenging in many situations. With its help, we are only able to anticipate the likelihood, or chance, that an event would occur.

from the given data,

n(s) = 20

n(A) = 6 ⇒ as the name selected in the first day is put back in the hat.

⇒ P(A) = n(A)/n(s)

P(A) = 6/20

P(A) = 3/10

hence the probability that the another day again a sophomore will be chosen is 3/10.

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Answer:

  a. (-12, 14), (6, 2), (-3, 8)

  b. yes; R(-12, 14)

Step-by-step explanation:

Points P(-6, 10), Q(0, -6), and R lie on a line, with one of them being the midpoint of the other two. You want to know the possible locations of R, and its location if RQ=√208.

Point M is the midpoint of AB when ...

  M = (A +B)/2

If M and A are given, then B is ...

  2M -A = B . . . . . . above equation solved for B

There are three choices for the location of R.

P is the midpoint

  R = 2P -Q = 2(-6, 10) -(0, 6) = (-12, 20-6)

  R = (-12, 14)

Q is the midpoint

  R = 2Q -P = 2(0, 6) -(-6, 10) = (6, 12 -10)

  R = (6, 2)

R is the midpoint

  R = (P +Q)/2 = ((-6, 10) +(0, 6))/2 = (-6, 16)/2

  R = (-3, 8)

The possible coordinates of R are (-12, 14), (6, 2), (-3, 8).

The length of the given segment PQ is ...

  d = √((x2 -x1)² +(y2 -y1)²) . . . . . distance formula

  d = √((0 -(-6))² +(6 -10)²) = √(6² +(-4)²) = √(36 +16) = √52

This is half the length of RQ, so we must have P as the midpoint of RQ.

This distance information chooses one of the three points found in part (a), R(-12, 14).

The solution to the inequality is x ≥ 3

Given the inequality;

– 7x + 3 ≥ – 18

To determine the solution , we take the following steps;

collect like terms

-7x ≥ - 18 - 3

Find the difference

- 7x ≥ - 21

Make 'x' the subject of the formula by dividing both sides by its coefficient, - 7

We have;

-7x / -7 ≥ - 21/ -7

x ≥ 3

Thus, the solution to the inequality is x ≥ 3

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