100 POINTS!!
A 28.5-Newton force is applied at a 30-degree angle to the horizontal to accelerate a 6.5-kg box across a rough surface (coefficient of friction = 0.22). Use g = 9.8 m/s/s to find frictional force (F(frict)) , normal force (F(norm)) , gravitational force (F(grav)) , and acceleration (a). Enter each answer accurate to the first decimal place.

The number combinations that fit the criteria will be 25 + 30 + 32 + 38.

It should be noted that the information illustrated that the sum of the four integers in that set must be no less than 118 and no greater than 144.

Therefore, the numbers that fit this will be:

= 25 + 30 + 32 + 38

= 125

Therefore, the number combinations that fit the criteria will be 25 + 30 + 32 + 38.

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Answer: x=-8   y=7

Step-by-step explanation:

[tex]\displaystyle\\\left \{ {{-2x-5y=-19\ \ \ \ (1)} \atop {3x+2y=-10\ \ \ \ \ (2)}} \right.[/tex]

Multiply both parts of the equation (1) by 3 and multiply both parts of the equation (2) by 2:

[tex]\displaystyle\\\left \{ {(-2x)(3)-(5y)(3)=(-19)(3)} \atop {(3x)(2)+(2y)(2)=(-10)(2)}} \right. \\\\\left \{ {{-6x-15y=-57\ \ \ \ (3)} \atop {6x+4y=-20\ \ \ \ (4)}} \right. \\[/tex]

Summarize equations(3) and (4):

[tex]-11y=-77[/tex]

Divide both parts of the equation by -11:

y=7

Hence,

[tex]3x+2*7=-10\\3x+14=-10\\3x+14-14=-10-14\\3x=-24[/tex]

Divide both parts of the equation by 3:

[tex]x=-8[/tex]

Step-by-step explanation:

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

[tex]3^{9} . 2^{12} .5^{11}[/tex]

Power :

An expression that represents repeated multiplication of the same factor is called a power.

Factor: The number 5 is called the base, and the number 2 is called the exponent. The exponent corresponds to the number of times the base is used as a factor.

the expression 5 x 5. This expression can be written in a shorter way using something called exponents.

5⋅5=5^2

An expression that represents repeated multiplication of the same factor is called a power.

The number 5 is called the base, and the number 2 is called the exponent. The exponent corresponds to the number of times the base is used as a factor.

3 to the first power 3

4^2 4 to the second power or 4 squared 4 ∙ 4

5^3 5 to the third power or 5 cubed 5 ∙ 5 ∙ 5

2^6 2 to the power of six

= [tex](3.5)^{4} (2.3)^{5} (2.5)^{7}[/tex]

= [tex]3^{4+5} .2^{5+7} .5^{4+7}[/tex]

=[tex]3^{9} . 2^{12} .5^{11}[/tex]

Ans : [tex]3^{9} . 2^{12} .5^{11}[/tex]

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4 significant digit the quotient have.

Significant digit are the important digit in a number which convey the accuracy. all non zero numbers are significant and zero between two non zero is a significant digit and all zeros at the right of decimal is significant digit in number.

Given numbers are 2.058 * 10^9 and 3.0571 * 10^-4

To calculate the division first we have to solve the exponent.

In divide we subtract the powers

10^(9-(-4)) = 10^13

Now do the division

(2.058 ÷ 3.0571)*10^13 = 0.67318*10^13 = 0.6732 *10^13

=6.732 * 10^12

Number of significant digit are 4.

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-33 is the value of f(-3) if the equation is If f(x)=x³- x²- x .

Explain what a linear equation is.

f(x)=x³- x²- x

f(-3) = ( - 3)³ - ( -3)² - ( -3)

      =  - 27 - 9 + 3

      =  - 36 + 3 = -33

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Answer:

Yes

Step-by-step explanation:

9.50=9.5+0.00 ==> The only difference between 9.50 and 9.5 is that it has an extra zero in the right hand side of .5. Hence, you add 0.00 to 9.5 to get 9.50. 0.00=0. Whenever you add 0 to a number, that number won't change. Hence, 9.5=9.50.

The difference between the absolute values of Kylie's and Bryan's depth is 2 feet.

Here, we are given that Kylie swam 6 feet below the sea level and Bryan swam 8 feet below sea level.

This implies,

Kylie's distance from the ground level = -6 feet

and Bryan's distance from the ground level = -8 feet

We need to find the difference between the absolute values of their depth.

Thus, we ignore the minus (-) sign and find the difference as follows-absolute difference = | 6 - 8 |

difference = 2 feet

Thus, the difference between the absolute values of their depth comes out to be 2 feet.

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  The binomial expansion of the given expression is:

p⁶ + q⁶ + 8p⁵q + 17p⁴q² + 20p³q³ + 11p²q⁴ + 4pq⁵

   A polynomial is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms.

 Depending on the number of terms it can be :

 We solve first by perfect square trinomial, then we apply the distributive property.

(p + q)⁶ = (p + q)²(p + q)²(p + q)²

(p + q)²= p² + 2pq + q²

p⁴ + 2p³q + p²q² + 2p³q + 4p²q² + 2pq³ + q²p² + 2pq³ + q⁴

p⁴ + 4p³q + 6p²q² + 2p³q + 2pq³ + q⁴

(p⁴ + 4p³q + 6p²q² + 2p³q + 2pq³ + q⁴)(p² + 2pq + q²)

    p⁶ + 4p⁵q + 6p⁴q² + 2p⁵q + 2p³q³ + p²q⁴

+( 2p⁵q + 8p⁴q² + 12p³q³ + 4p⁴q² + 4p²q⁴ + 2q⁵p)

+(p⁴q² + 4p³q³ + 6p²q⁴ + 2p³q³ + 2pq⁵ + q⁶)

p⁶ + q⁶ + 8p⁵q + 17p⁴q² + 20p³q³ + 11p²q⁴ + 4pq⁵

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Answer:

all integers are rational numbers

Answer:

Savannah will have 35 pennies after 10 days.

It will take her 49 days to have at least $1.50

Step-by-step explanation:

Start Value = .05

Linear Increase = .03

.05 + .03x = TV

TV = Total Value

10 days = .05 + .03(10)

10 days = $.35

.05 + .03x = 1.50

1.50 - .05 = 1.45

1.45/.03 = 48.33

48 days is not enough for her to have 1.50 as she is not gaining hourly but rather daily so it would take her 49 days to have at least 49

Answer:

use the math skills 9+9+9

Step-by-step explanation:

The lengthof the rectangle is 23 cm and width of the rectangle is 25cm.

Consecutive odd integers are odd integers that follow each other and they differ by 2.

Given that Length and width are consecutive odd integers then

Let length be x so width will be x+2.

The [tex]Perimeter \ of \ Rectangle = 2 (Length \ + \ Width)[/tex]

Perimeter of Rectangle= 96cm

[tex]96 = 2 (Length \ + \ Width)\\(Length \ + \ Width) = 48\\x + x + 2 = 48\\2x = 46\\x = 23[/tex]

So, length = x = 23cm

therefore, width = x+2 = 25cm

Therefore, Length of the rectangle is 23 cm and the Width of the rectangle is 25 cm.

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The height of the television is 13.268 inches.

The television is in the shape of a rectangle and when we draw an imaginary diagonal line it would become a right-angle triangle in which the diagonal line would become the hypotenuse and the length would become base.

We need to find out the tallness of the television which is the perpendicular of our imaginary right-angle triangle

By applying the Pythagoras theorem [tex]H^{2}[/tex]= [tex]P^{2} + B^{2}[/tex]

As we need perpendicular the formula would become P = [tex]\sqrt{H^{2} -B^{2} }[/tex]

After putting the values in the above equation,

         we get = [tex]\sqrt{(55) – (35.51)}[/tex]

        =[tex]\sqrt{3025-1260.96}[/tex]

                       =[tex]\sqrt{1764.04}[/tex]

            =13.268 inches

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For the equation 1 / 5 (2 x - 10) + 4 x = - 3 (1 / 5 x + 4), we get the value of x as - 2.

We are given the equation that:

1 / 5 (2 x - 10) + 4 x = - 3 (1 / 5 x + 4)

We need to solve the equation to find the value of x.

First, we will open the brackets in the equation:

2 / 5  x - 2 + 4 x = - 3 / 5 x - 12

Combining the like terms, we get that:

22 / 5 x - 2 = - 3 / 5 x - 12

Add 2 and 3 / 5 x to both the sides, we get that:

22 / 5 x - 2 + 2 + 3 / 5 x = - 3 / 5 x - 12 + 2 + 3 / 5 x

5 x = - 10

Divide both the sides by 5, we get that:

5 x / 5 = - 10 / 5

x = - 2

Therefore, for the equation 1 / 5 (2 x - 10) + 4 x = - 3 (1 / 5 x + 4), we get the value of x as - 2.

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The probability for the arrow that land in the odd number is 1/2.

Probability:

Basically, the word probability define the possible way of occurring the event.

Given,

The spinner is divided into 8 equal sections.

Here we need to find if the arrow lands on a number, what is the probability that it will land on an odd number.

Let us consider that the spinner has 8 equal-sized sections numbered 1 to 8.

Since the sections have equal size, each section is equally probable.

The probability of falling on each section is therefore 1/8.

We know that, in the 8 sections,

There are four odd numbered sections.

Hence, probability is

=> 4/8

When we simplify it,

=> 1/2

Therefore, the probability for the arrow that land in the odd number is 1/2.

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Using the formula for the distance between two points, the relationship between RA and R'A is given by:

RA = R'A.

Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

This formula is derived from the Pythagorean Theorem, as the points form a right triangle in the xy-plane, with the hypotenuse being the distance between them.

The coordinates of the points of interest to find the segments' lenghts are given as follows:

Applying the formula, the length of RA is given by:

[tex]RA = \sqrt{(1.5 - (-5))^2+(1.5 - (-5))^2} = 9.19[/tex]

Applying the formula, the length of R'A is given by:

[tex]R^{\prime}A = \sqrt{(1.5 - 8)^2+(1.5 - 8)^2} = 9.19[/tex]

Hence the relationship for the length of the segments is:

RA = R'A.

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The polynomial is quintic binomial.

The given polynomial is [tex]3r^5-7r[/tex]. The polynomial is given in standard form. i.e., terms are arranged in the decreasing order of its powers.

The degree of the polynomial is the highest power of 'r' in the polynomial.

So degree of the polynomial  [tex]3r^5-7r[/tex] is 5.

Polynomials of degree 5 are called quintic.

The polynomial has 2 terms:  [tex]3r^5, 7r[/tex]

Since the number of terms are two, we can call it binomial.

So the polynomial [tex]3r^5-7r[/tex] is quintic binomial.

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Geometric Progression is a type of recursive  mathematical sequence in which the next term is generated by multiplying the previous term with a fixed number that is called the Common Ratio represented by 'r'.It is calculated by the ratio of two consecutive terms.

The formula to calculate the 12th term of a Geometric Progression is :              

                                   =>       [tex]a_{12} = a.r^{(12-1)}[/tex]

Here a = first term, r = common ratio calculated by => r=(a2/a1), and n = [tex]n^{th}[/tex] term to find

In the given question, First term a = 10, n = 12, and calculating r,

                                   =>  r = (a2/a1) => r = (20/10) = 2

Calculating,

                         [tex]a_{12\\} = (10).(2^{(12-1)})[/tex] => [tex](10).(2048)[/tex]

                         [tex]a_{12} = 20480[/tex]

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Using the concepts of subsets and proper subsets, the statements are classified, respectively, as:

Suppose we have a set given by:

A = {a, b, c}.

The subsets will be all possible combinations involving at least one element of A, or the empty subset, hence:

S(A) = {∅, {a}, {b}, {c}, {a, b}, {a, c}, {b,c}, {a,b,c}}

In which S(A) is composed by the subsets of A.

The proper subsets are all the subsets, except the empty set, hence:

PS(A) = {{a}, {b}, {c}, {a, b}, {a, c}, {b,c}, {a,b,c}}

In which PS(A) is composed by the proper subsets of A.

Hence:

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The simplification by combining like terms of 2(h + 2g) - (g - h) is 3(h + g).

According to the given question.

We have an expression 2(h + 2g) - (g - h).

As we know that, like terms are terms whose variables (and their exponents such as the 2 in x2) are the same.  when we combine like terms, such as 2x and 3x, we add or subtract their coefficients.

Since, we have to combine the like terms of the given expression

2(h + 2g) - (g - h).

Here 2h, and h and 2g and -g are the like terms.

So, we add and subtract coeffcients of h and g to simplify the given expression.

Therefore, the simplification of 2(h + 2g) - (g - h) is given by

= 2(h + 2g) - (g - h)

= 2h + 4g - g + h

= 3h + 3g

= 3(h + g)

Hence, the simplification by combining like terms of 2(h + 2g) - (g - h) is

3( h + g).

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Answer:

[tex]\frac{2}{9}[/tex]

Step-by-step explanation:

Use slope formula.

y2-y1/x2-x1

Plug in the given info.

4-2/0+9

2/9

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When an angle exists encircled by a circle, its measure exists equivalent to the intercepted arc's measure divided by two.

The measure of m AC is 48.

The arc that is inside the inscribed angle and whose endpoints are on the angle is known as the intercepted arc. Anywhere on the circle that the sides of an inscribed angle intersect to produce an intercepted arc can serve as the angle's vertex.

Angles with vertices on a circle and that cross an arc on the circle are said to be inscribed angles. Half of the intercepted arc's length and half of the central angle's length intersecting that same arc make up the measure of an inscribed angle. Congruent inscribed angles are those that intersect the same arc.

According to the Inscribed Angle Theorem, an inscribed angle's measure is equal to half of its intercepted arc's measure. Congruent inscribed angles are those that intersect the same arc.

An angle's measure exists equivalent to the intercepted arc's measure divided by two when it is surrounded by a circle.

m AC = 2(m ∠B)

m AC = 2(m ∠B) = 48

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Answer: QT = 15

Step-by-step explanation:

RT=9, RS=7, and QS=13

Find QT=QR+RT

find QR=QS-RS

QR=13-7=6

therefore QT=QR+RT=6+9=15

Answer:

020

Step-by-step explanation:

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The percentage discount is 58%

The old price is $50

The new price is $21

The percentage discount can be calculated as follows

old price-new price/old price × 100

= 50-21/50 × 100

= 29/50 × 100

= 0.58 × 100

= 58

Hence the percentage discount is 58%

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Answer:

- 4 < n ≤ 4

Step-by-step explanation:

2 < n + 6 ≤ 10 ( subtract 6 from each interval )

- 4 < n ≤ 4

If angela uses this schedule for 4 weeks, the total number of hours she will many have practiced in total is 35.6 hours

Week 1:

Total = Monday + Tuesday + Saturday

= 1.4 + 2 1/2 + 5

= 1.4 + 2.5 + 5

= 8.9 hours

Total number of hours she practice for weeks = 8.9 hours × 4

= 35.6 hours

Therefore, if angela uses this schedule for 4 weeks, the total number of hours she will many have practiced in total is 35.6 hours.

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