I only need help with part "b." I have provided the answer for "a" to help.

Using percentages, the answer to both the subparts are:

So, since the interest is annual 6.5%:

(A) Interest that will be owed after 178 days:

Now, 3.25% of 4200:

(B) Interest after 178 days if sop doesn't repay:

Now, 6.5% of 4200:

Therefore, using percentages, the answer to both the subparts are:

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Given data:

The given weight of 6 magazines is 5/8 pound.

The given expression is,

6M=5/8 pounds

6M=0.625 pounds

1M=0.1041667 pounds

The weight of one magzine is 0.104167 pounds.

The value of x⁻, is the mean of the x values of the table.

The mean of x is obtained by adding all values of x, and divided the result by the total number of data, which is 5.

Then, you have:

Hence, the mean of x, which is used in the formula to calculate the r-value, is 10

The area of the smaller rectangle is 108 inches².

The area of a rectangle is calculated to determine the area occupied by the rectangle within its boundary. A rectangle's area (A) is the product of its length 'a' and width or breadth 'b'. As a result, the Area of the Rectangle = (a × b) square units.

Given the dimensions of the smaller rectangle:

Length = 12 inches

Width = x inches

Given the dimensions of the larger rectangle:

Length = 20 inches

Width = 15 inches

To find the value of x we use proportion,

[tex]\frac{12}{x} = \frac{20}{15}[/tex]

Cross-multiplying, we get

12 × 15 = 20x

x = 180/20 = 9

Hence, the width of the smaller rectangle is 9 inches.

Area of the smaller rectangle = length × width

                                                = 12 × 9

                                                = 108 inches²

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Answer:

See below.

Step-by-step explanation:

Given multiplication:

[tex]3 \dfrac{1}{5} \times 2 \dfrac{5}{8}[/tex]

Convert the mixed numbers into improper fractions by multiplying the whole number by the denominator of the fraction, adding this to the numerator of the fraction, and placing the answer over the denominator:

[tex]\implies \dfrac{3 \times 5+1}{5} \times \dfrac{2 \times 8+5}{8}[/tex]

[tex]\implies \dfrac{15+1}{5} \times \dfrac{16+5}{8}[/tex]

[tex]\implies \dfrac{16}{5} \times \dfrac{21}{8}[/tex]

[tex]\textsf{Apply\;the\;fraction\;rule} \quad \dfrac{a}{b} \times \dfrac{c}{d}=\dfrac{ac}{bd}:[/tex]

[tex]\implies \dfrac{16 \times 21}{5 \times 8}[/tex]

[tex]\implies \dfrac{336}{40}[/tex]

Reduce the fraction by dividing the numerator and denominator by the common factor of 8:

[tex]\implies \dfrac{336 \div 8}{40 \div 8}[/tex]

[tex]\implies \dfrac{42}{5}[/tex]

Divide the numerator by the denominator:

[tex]\implies 42 \div 5=8\;\textsf{remainder}\;2[/tex]

The mixed number answer is the whole number and the remainder divided by the denominator:

[tex]\implies 8 \dfrac{2}{5}[/tex]

Step-by-step explanation:

when you want to start solving it you will do 16 over 5 * 21/8equals 8 whole number 2/5

it will give you 336 all over 40 if you divide by 8 you will get 42/5 which is 8 whole number 2/5

Answer:

  B, C

Step-by-step explanation:

You want to find the equivalent expressions among ...

The relevant rule of exponents is ...

  a^b = (1/a)^-b

Expressions with the same base and different exponents will not be equivalent. (A≠B).

Expressions with different bases and the same exponent will not be equivalent. (A≠C).

A variable in the base cannot replace a variable in the exponent. (A≠D).

The rule of exponents tells us replacing the base by its reciprocal and negating the exponent will result in an equivalent expression. (B=C).

The equivalent expressions are 4^(-3x^2) and (1/4)^(3x^2).

A percent discount of 30%

Explanation:

Since $129 represent 100% of the price, then the new price $90.30 represent 70 %

129 * 100 / 90.30 = 70 %

Since from the 100% of the price, it went to 70% of it, there was a discount of 30%

100 - 70 = 30%

The polynomial having the above quantities is expressed as x³ - 2x² - 5x + 10 = 0

The above situations will form a Cubic polynomial. A Cubic polynomial function may be defined as an expression which can be written in the form of ax³ + bx² + cx + d = 0 where a, b, c and d are coefficients and x is the independent variable. Since, the polynomial should have real coefficients so its multiplicity will be equal to 1. Now, the roots of the polynomial are given as 2 and √5. Since, square roots always occur in pair so the polynomial will have -√5 as its root. Now, the polynomial formed will be

(x - 2) (x - √5) (x + √5) = 0

(x - 2) (x² - 5) = 0

x³ - 5x - 2x² + 10 = 0

=> x³ - 2x² - 5x + 10 = 0 which is the required polynomial.

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The number of horses on the harm will be 24.

What is an expression?

Expression in math is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that;

A local farm raises horses and goats.

The total number of horses and goats on the farm is 96.

Let number of horses = x

Since, The number of goats is 3 times the number of horses.

Then, Number of goats = 3x

The total number of horses and goats on the farm is 96.

Hence, we can formulate;

x + 3x = 96

4x = 96

x = 24

Thus, The number of horses on the harm will be 24.

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Given: Given the function: f(x) = (x − 3)(x + 7)(x − 1)

Required: its f-intercept and its x-intercepts.

Explanation:

For f-intercept, put x = 0

So the f-intercept is (0,21).

For x-intercepts, put f(x) = 0

So x-intercepts are (3,0),(-7,0) and (1,0).

Final Answer:

f-intercept: (0,21)

x-intercept: (3,0),(-7,0),(1,0).

harry and marie despoit $800.00 into a savings account which earns 9% interest compounded monthly they want to use the money in the account to go on a trip in 2 years how much will they be able to spend​

we know that

The compound interest formula is equal to

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

P=$800

r=9%=9/100=0.09

n=12

t=2 years

substitute in the expression above

Answer: GAS

Step-by-step explanation:

The time taken by Town A to Town B will be 3 hours.

Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance traveled by time. The unit of speed in miles per hour.

Given that at 30 mph a trip from Town A to Town B takes 6 hours.

The time taken will be calculated as,

Total distance = 30 x 6 = 180 meters

Speed = 30 x 2 = 60 mph

The time,

T = 180 / 60= 3 hours

Therefore, the time taken by Town A to Town B will be 3 hours.

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We have to use the slope formula

Let's replace the points (9,-24) and (13,-21). Where

The different keypad patterns that are possible if the first three digits must be even and the last digit cannot be zero is 17500 ways.

It should be noted that the security keypad uses five digits (0 to 9) in a specific order. On this case, the numbers from 0 to 9 make up 10 numbers.

In this case, there are 5 even numbers.

The total number of possible codes will be:

= 5 × 5 × 10 × 10 × 7

= 17500

There are 17500 ways.

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Given the expression below:

To find the exact value of the expression, let us determine the quadrant of the expression. It should be noted that the value of angles compare with the quadrants is as shown below

It can be observed that the expression given in the question is a fraction of (pi), greater than half of (pi) but less than (pi). This means that it lies in the second quadrant.

It should be noted that sine is positive in the second quadrant

The equivalent of the expression in the first quadrant is as shown below:

Hence, the exact value of the expression is √3/2

We are given the following multiplication problem.

To perform the fractional multiplication, simply multiply the numerators and the denominators

Therefore, the result of the multiplication is 63/64

The equation of the circle that represents the dartboard is (x - 12)² + (y - 17/3)² = 9/16, where the origin is the lower left corner of the room and the unit of the radius is feet.  

The position of Brian's dart is represented by the coordinates (11.5, 5). Brian's dart does land on the dartboard.

Mathematically, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²

Where:

From the question, we have the following information:

The height of this standard dartboard, k = 5 feet, 8 inches.

The diameter of this standard dartboard = 18 inches.

The bull's eye, h = 12 feet.

Next, we would convert the all of the units in inches to feet as follows:

Height, k = 5 + 8/12

Height, k = 5 + 2/3

Height, k = 17/3 feet.

For the diameter, we have:

Diameter = 18/12

Diameter = 3/2 feet.

Also, we would determine the radius as follows:

Radius, r = diameter/2

Radius, r = (3/2)/2

Radius, r = 3/4 feet.

Substituting the parameters into the standard equation, we have;

(x - 12)² + (y - 17/3)² = (3/4)²

(x - 12)² + (y - 17/3)² = 9/16

Next, we would determine whether Brian's dart land on the dartboard:

(x - 12)² + (y - 17/3)² < 9/16

(x - 12)² + (y - 17/3)² < 9/16

(11.5 - 12)² + (5.5 - 5.67)² < 0.5625

0.25 + 0.0289 < 0.5625

0.2789 < 0.5625 (Yes, it does land because it's within the circumference of this standard dartboard).

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Given:

The leading coefficient of a polynomial is 3.

And the roots of the polynomial is -1, 1, and 2.

Required:

To write g(t) in factored form and standard form.

Explanation:

From the given data, the factored form is given by

The standard form is,

Final Answer:

The factored form:

The standard form:

Answer:

Step-by-step explanation:

Reduce the following expressions:

Operate like terms:

Answer:

Step-by-step explanation:

5.4*10*10*10*10*10+6.7* 10*10*10*10

540,000+6.7*10,000

540,000+60,000

114,000=1.14*10^5

The average rate of change of the function f(x) = -2x² - 2 from x = 2 to x = 6 is -16

An equation shows the relationship between two or more numbers and variables.

The average rate of change of a function f(x) over the interval x = a to x = b is given by:

A(x) = [f(b) - f(a)]/[b - a]

Given that function f(x) = -2x² - 2 from x = 2 to x = 6, hence:

f(2) = -2(2)² - 2 = -10

f(6) = -2(6)² - 2 = -74

The average rate of change is:

A = [f(b) - f(a)]/[b - a]

Substituting:

A = [-74 - (-10)] / [6 - 2] = -16

The average rate of change is -16

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Answer:

66

Explanation:

By the Thales theorem, if we have the following figure:

Then, the following equation applies:

So, in this case, we can formulate the following equation:

Then, solving for x, we get:

Therefore, the value of x is 66.

canThe first First step we need to do is to make the decomposition of the vectors W and P.

Both will have a component perpendicular and parallel to the plane. The perpendicular will be used to calculate the maximum static friction force, and the horizontal will be used to find the P required to prevent the block from sliding.

From the sketch, we are able to define both, parallel and perpendicular components of P, as it follows:

Now, we can do the same for W.

And for W we also can provide the two components as follows:

Now, we can elaborate on both equations: one for the perpendicular direction and the other for parallel. In the perpendicular direction, we have a component of W, one component of P, and the normal force N. Because the block is going to move, or change its movement along this direction, the sum of the forces pointing upwards must be equal to the sum of the forces pointing downwards. From this, we can write the following:

Now, for the horizontal, we have the P component to the right and the W component to the left. If we imagine the block is almost sliding. We can write the following equation, from the premise the forces will cancel each other just like the perpendicular case:

Here it is used the fact that the friction force is equal to the multiplication of the coefficient of static friction by the normal force. Here we assumed also that the friction is maximum because the block is on the verge of motion downwards, and for this reason, the Friction is upwards, with the P component.

Now, substituting N and the coefficient, we find:

From this, we can see that the force P made to the left with an intensity equal to -5.275 lbf will bring the block on the verge of motion downwards. If we consider that P is strong enough to make it almost move upwards, it is, the Normal Force will be downwards, we can remake the calculation as it follows:

And substituting values, we have:

From this, we know that the max value for P, where the block will not slide is going to be 196.46 lbf to the right.

We got the linear equation:

The slope of this line will be -8/5 and the y-intercept will be -4.

To graph it, first find the intercept with x - axis.

We can find it if we equal the equation to zero.

Now, we got two points:

To graph the function, we only join these points:

So that's the graph for the function.

Given the system:

First, we solve for 3x on both equations, as follows:

Equating both equations:

Substituting y on equation 2:

ANSWER

(1, -1)

The lines that are not intersecting and perpendicular to each other, are not parallel to each other, and are not coplanar are called skew lines.

The four lines that are skew to line EF are AB, GB, CH, and DC.

The lines that are not intersecting and perpendicular to each other, are not parallel to each other, and are not coplanar are called skew lines.

We have,

A line EF on the given square figure.

We have the following lines on the given figure.

DG, CB, HA, FA, FG, GB, AB, EH, ED, DC,CH,

We see that,

FG, FA, EH, and ED are perpendicular and intersecting to line EF.

DG, CB, and HA are parallel to line EF.

So the remaining lines will be skew to line EF

i.e AB, GB, CH, and DC

Thus,

The four lines that are skew to line EF are AB, GB, CH, and DC.

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After throughfall calculating the multiplication 4505 x 219 in standard algorithm, we have come to find that product is 986595

In elementary math, a standard algorithm or method is a particular computation technique that is typically taught for resolving particular mathematical issues. In general, these techniques include exchanging, regrouping, long division, long multiplication using a standard notation, and standard formulas for average, area, and volume.

These techniques can vary somewhat by country and time, but they typically include these techniques. Similar techniques are also available for more complex functions like square roots, but they are no longer taught in general mathematics classes because calculators are more convenient.

4505 x 219 in standard algorithm is as follows:

⇒        4 5 0 5

         ×    2 1 9              

        4 0 5 4 5    

    +  4 5 0 5        

  + 9 0 1 0        

     9 8 6 5 9 5

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2x² + 5x - 3 = 0

Multiply the coeeficient of x² and the constant (-3)

That is 2 ( - 3) = -6

Find the numbers whose sum is 5 and whose product is -6

The number is 6 and -1

Replace 5x by the numbers

2x² + 6x - x - 3 = 0

2x( x + 3) - 1 ( x + 3) = 0

(2x - 1 ) ( x + 3) = 0

Either 2x -1 = 0 or x + 3 = 0

2x = 1

x = 1/2 or x = -3

Answer:

maya is able to make 47 bracelets

Step-by-step explanation: