sixteen thousand, four hundred eighty-two. Write this number in standard
In a recent year, the population of Springfield, Illinois was one hundred
form. Show your work in the space below. Remember to check your solutic

The resultant of subtractions of u = <-8, 4> and v = <2, 7> are

-u-v = <6, -11>,

u-v = <-10, -3>,

and v-u= <10,3>.

What is a vector in simple definition?

The resultant of subtractions of u = <-8, 4> and v = <2, 7> are

-u-v = <6, -11>,

u-v = <-10, -3>,

and v-u= <10,3>.

Given that,

The results of the given vector subtractions for u = <-8, 4> and v = <2, 7>.

We have to determine,

The value of -u-v, u-v, and v-u.

According to the question,

The results of the given vector subtractions for u = <-8, 4> and v = <2, 7>.

The value of -u-v is,

-u -v = - < -8 ,4 > - <2,7>

-u -v = <8, -4> - < 2, 7 >

-u - v = < 8 - 2 , -4 - 7 >

-u -v =  < 6 , - 11 >

The value of u-v is,

u -v = < -8 ,4 > - < 2,7 >

u - v = < - 8  - 2, 4 - 7 >

u - v = < 10 ,3>

The value of v - u is,

v - u = < 2 , 7>  - < - 8,4 >

v - u = <  2 + 8 ,  7 - 4 >

v - 4 = <  10 , 3 >

Hence, The resultant of subtractions of u = <-8, 4> and v = <2, 7> are

-u-v = <6, -11>,

u-v = <-10, -3>,

and v-u= <10,3>.

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Answer:

Step-by-step explanation:

Quick Answer 1

Solution

x = 0.747 / 0.0747

When you do the division, you get 10. That means that you need to divide 0.747 by just 1 ten to get 0.0747

Answer:

Once

Step-by-step explanation:

You have to divide once because if you divide a decimal by 10, you add a zero before the decimal point

The system of equations is -x + y = 4 and -2x + y = 0

To do this, we make use of the following ordered pairs

(4, 8)

The above point represents April 2008.

Let the system of equations be

mx + ny = 4

2mx + ny = 0

Substitute (4, 8) for x and y in the above equations.

4m + 8n = 4

8m + 8n = 0

Subtract both equations

4m - 8m = 4

This gives

-4m = 4

Divide by 4

m = -1

Substitute m = -1 in 8m + 8n = 0

-8 + 8n = 0

This gives

8n = 8

Divide by 8

n = 1

So, the system of equations is -x + y = 4 and -2x + y = 0

The system of equations is -x + y = 4 and -2x + y = 0

See attachment for the graph of the system of equation

The above is represented in the (a) part of this solution

Verify that the solution is (4, 8)

We have:

-x + y = 4 and -2x + y = 0

Substitute (4, 8) for x and y in the above equations.

-4 + 8 = 4 --- true

-2*4 + 8 = 0 --- true

Both equations are true

Hence, the system of equations have been verified

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The value of each variable in the two-way table is:

a = 7

b = 31

c = 28

d = 13

e = 65

A Venn diagram uses circles that overlap each other to show the relationship between two or more sets of items. A two-way table represents the frequency of dataset by arranging the dataset into a table made up of rows and columns.

a = females that favor the left. Looking at the Venn diagram, this number is 7.

b = total number of females : 24 + 7 = 31

c = males that favor the right = total number of males - males that favor the left34 - 6 = 28

d = Total number of people who favor the left = 7 + 6 = 13

Total number of baseball players = 65

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The value of function f(x) over g(x) is [tex]2x^{2} +4x-1-\frac{9}{4x+1}[/tex]

Given functions are:

f(x)=8[tex]x^{3}[/tex]+18[tex]x^{2}[/tex]-10

g(x)=4x+1

In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). Functions exist everywhere, and they are crucial for constructing physical links in the sciences.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. A function is indicated by a mapping or transformation. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

[tex]\frac{f(x)}{g(x)}=\frac{8x^{3}+18x^{2} -10 }{4x+1}[/tex]

      = [tex]2x^{2} +4x-1-\frac{9}{4x+1}[/tex]

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Answer:

B 1233 ft^2

Step-by-step explanation:

I hope this is right

The Jacobian for this transformation is

[tex]J = \begin{bmatrix} x_u & x_v \\ y_u & y_v \end{bmatrix} = \begin{bmatrix} 4 & 0 \\ 0 & 3 \end{bmatrix}[/tex]

with determinant [tex]|J| = 12[/tex], hence the area element becomes

[tex]dA = dx\,dy = 12 \, du\,dv[/tex]

Then the integral becomes

[tex]\displaystyle \iint_{R'} 4x^2 \, dA = 768 \iint_R u^2 \, du \, dv[/tex]

where [tex]R'[/tex] is the unit circle,

[tex]\dfrac{x^2}{16} + \dfrac{y^2}9 = \dfrac{(4u^2)}{16} + \dfrac{(3v)^2}9 = u^2 + v^2 = 1[/tex]

so that

[tex]\displaystyle 768 \iint_R u^2 \, du \, dv = 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2 \, du \, dv[/tex]

Now you could evaluate the integral as-is, but it's really much easier to do if we convert to polar coordinates.

[tex]\begin{cases} u = r\cos(\theta) \\ v = r\sin(\theta) \\ u^2+v^2 = r^2\\ du\,dv = r\,dr\,d\theta\end{cases}[/tex]

Then

[tex]\displaystyle 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2\,du\,dv = 768 \int_0^{2\pi} \int_0^1 (r\cos(\theta))^2 r\,dr\,d\theta \\\\ ~~~~~~~~~~~~ = 768 \left(\int_0^{2\pi} \cos^2(\theta)\,d\theta\right) \left(\int_0^1 r^3\,dr\right) = \boxed{192\pi}[/tex]

Answer:

  5.09 years

Step-by-step explanation:

The formula for the future value of an investment can be filled with the given values and solved for time.

The future value of a one-time investment P earning interest at annual rate r compounded n times per year for t years is ...

  FV = P(1 +r/n)^(nt)

Using this formula with the given values, we have an expression for t:

  7300 = 5000(1 +0.075/4)^(4t)

Dividing by 5000, we have ...

  1.46 = 1.01875^(4t)

Taking logarithms gives the linear equation ...

  log(1.46) = 4t·log(1.01875)

Dividing by the coefficient of t, we find ...

  t = log(1.46)/(4·log(1.01875)) ≈ 5.0929

The time required for the value to reach $7300 is about 5.09 years.

__

Additional comment

The attachments show different calculator solutions. They give the same value for t.

The TVM Solver uses P/Y = 1 so the value of N is in years.

The graphical solution recasts the problem to f(x) = 0. It finds the value of t that makes the difference between the investment value and $7300 be zero.

The equation of the plane through the points p(0, 1, 1), q(1, 0, 1), and

r(1, 1, 0) is x + y + z = 2  .

According to the question

Let the points

p(0, 1, 1) = (x1,y1,z1)

q(1, 0, 1)= (x2,y2,z2)

r(1, 1, 0)= (x3,y3,z3)

now,

The equation of the plane through the points

i.e

The formula of equation of a plane passing through three non collinear points

[tex]\left[\begin{array}{ccc}x-x1&y-y1&z-z1\\x2-x1&y2-y1&z2-z1\\x3-x1&y3-y1&z3-z1\end{array}\right] = 0[/tex]

by substituting the values in the formula of equation of a plane

[tex]\left[\begin{array}{ccc}x-0&y-1&z-1\\1-0&0-1&1-1\\1-0&1-1&0-1\end{array}\right] = 0[/tex]

[tex]\left[\begin{array}{ccc}x&y-1&z-1\\1&-1&0\\1&0&-1\end{array}\right] = 0[/tex]  

x(1) - (y-1)(-1) + (z-1)(1) = 0

x + y - 1 + z - 1 = 0

x + y + z = 2

Hence, the equation of the plane through the points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0) is x + y + z = 2  .

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Answer:

29, 21, 84

Step-by-step explanation:

Let the first number be x.

The second number is x - 8.

The third number is 4(x - 8).

Their sum is 134.

x + (x - 8) + 4(x - 8) = 134

x + 5(x - 8) = 134

x + 5x - 40 = 134

6x = 174

x = 29

x - 8 = 29 - 8 = 21

4(x - 8) = 4(29 - 8) = 4(21) = 84

The above pattern follows an arithmetic sequence with a common difference of 14 and first term of 13

The pattern can be represented as follows:

13, 27, 41, 55

The first term of the sequence is 13 and the common difference is 14.

The above pattern is an arithmetic sequence.

Therefore, the following can be used to find the nth term.

nth term = a + (n - 1)d

where

Therefore,

a = 13

d = 27 - 13 = 14

Let's find the next term

5th term = 13 + (5 - 1)14

5th term = 13 +(4)14

5th term = 13 + 56

5th term = 69

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Haler ran farther than Tyler in 10 minutes. She covered an extra 0.05 miles compared to Tyler.

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

Tyler can run 1 mile in 8 minutes and 20 seconds.

Time taken = 8 mins + 20 sec (0.33 min) = 8.33 minutes

Speed = distance / time = 1 mile / 8.33 = 0.12 mile per min

In 10 minutes, distance = 0.12 mile per min * 10 min = 1.2 mile

Haler is given by:

y = 8x; where y is time and x is distance.

In 10 minutes, distance = y/8 = 10/8 = 1.25 miles

Haler ran farther than Tyler in 10 minutes. She covered an extra 0.05 miles compared to Tyler.

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The solution of the questions is given as

a)

The alternative hypothesis is that mu is equal to 3.0. ( the average GPA at KSU is not equal to 3.0)

b)

This is a case with two separate arguments. (This is a two-tailed case)

c)

Test Statistic is given by:

z= 2.00

d)

Critical values of Z come from the table and equal [tex]\pm[/tex]1.96.

e)

, p-value = 0.0455

f)

CI= (3.006, 3.594)

g)

Conclusion: The evidence does not back up the assertion that KSU students have a cumulative grade point average of 3.0.

h)

Conclusion: The evidence does not back up the assertion that KSU students have a cumulative grade point average of 3.0.

i) Conclusion: The evidence does not lend credence to the assertion that KSU's typical grade point average is equivalent to 3.0.

j)

The choices you choose in Questions 7, 8, and 9 are identical.

a)

The null hypothesis states that mu equals 3.0. ( the average GPA at KSU is equal to 3.0) (Claim)

The alternative hypothesis is that mu is equal to 3.0. ( the average GPA at KSU is not equal to 3.0)

b)

This is a case with two separate arguments.

c)

Test Statistic is given by:

[tex]z=\frac{\barx-u^0}{σ/Vn}\\\\z=33 - 3.0/1.5/V100[/tex]

z= 2.00

d)

[tex]\alpha = 0.05[/tex]

Critical values of Z come from the table and equal [tex]\pm[/tex]1.96.

e)

Z Score = 2.00

reading from table, p-value = 0.0455

f)

Confidence Interval:

[tex]CI= \barx \pm \frac{ZX\sigma }{\sqrt((n)}[/tex]

[tex]CI =3.3 \pm 1.96 x 1.5 / \sqrt{100}[/tex]

CI= (3.006, 3.594)

g)

The disparity is noteworthy given that the computed value of Z = 2.00 is higher than the crucial value of z = 1.96. Cast doubt on the null hypothesis.

Conclusion: The evidence does not back up the assertion that KSU students have a cumulative grade point average of 3.0.

h)

The difference may be considered statistically significant since the p-value of 0.0455 is lower than the alpha threshold of 0.05. Cast doubt on the null hypothesis.

Conclusion: The evidence does not back up the assertion that KSU students have a cumulative grade point average of 3.0.

i)

The difference is statistically significant since the value of 3.0 is not included in the confidence range (3.006 - 3.594). Cast doubt on the null hypothesis.

Conclusion: The evidence does not lend credence to the assertion that KSU's typical grade point average is equivalent to 3.0.

j)

The choices you choose in Questions 7, 8, and 9 are identical.

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Answer:

The actual prime factors of 60 are 2, 3, and 5.

Step-by-step explanation:

Greetings !

Use a factor tree to express 60 as a product of prime factors. So the prime factorization of 60 is 2 × 2 × 3 × 5, which can be written as 2² × 3 × 5.

The height of the basketball at 0.5 seconds will be = 26.5

A polynomial equation is an equation where a polynomial is set equal to zero. i.e., it is an equation formed with variables, non-negative integer exponents, and coefficients together with operations and an equal sign. It has different exponents. The highest one gives the degree of the equation.

Example of a polynomial equation is: 2x2 + 3x + 1 = 0, where 2x2 + 3x + 1 is basically a polynomial expression which has been set equal to zero, to form a polynomial equation.

According to the given equation if we put value in it we will follow the following steps -

[tex]h(t) = - 16t^{2} + 35t+ 5\\ h(0.5) = -16(0.5)^{2} + 35(0.5) + 5\\h(0.5) = -16(0.25) + 17.5 + 5\\h(0.5) = 4 + 17.5 + 5\\h(0.5) = 26.5\\[/tex]

Therefore, the height of the basketball at 0.5 s will be 26.5

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Answer:

Is the question supposed to be (1.5), if so then the answer would be 21.5

Step-by-step explanation:

ht=-16t^2+35t+5

h(1.5)=-16(1.5)^2+35(1.5)+5

=21.5

In regression, the difference between the confidence interval and the prediction interval formula is "The addition of 1 to the quantity under the radical sign i.e., standard error".

The formula for the confidence interval is

[tex]y_h[/tex] ± [tex]t_{(1-\alpha /2,n-2)[/tex] × √(MSE([tex]\frac{1}{n}[/tex] + ([tex]x_h[/tex] - μ)²/∑([tex]x_i[/tex] - μ)²))

The formula for prediction interval is

Prediction interval = Sample estimate ± (t multiplier × standard error)

[tex]y_{new}[/tex] = [tex]y_h[/tex] ± [tex]t_{(1-\alpha /2,n-2)[/tex] × √(MSE(1 + [tex]\frac{1}{n}[/tex] + ([tex]x_h[/tex] - μ)²/∑([tex]x_i[/tex] - μ)²))

Where μ = x bar.

From the above, the prediction interval has one additional MSE term in the standard error calculation. But in the confidence interval, only one term is used.

So, the difference between them occurs in the standard error value.

The formula shows it by adding 1 to the quantity under the radical sign.

Thus, the difference is in the standard error.

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Considering the equation of the parabola, the coefficients are given as follows: p = 5, q = -20, r = 19.

The graph is the one given at the side of the question.

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

In this problem, the turning point is (2,-1), hence h = 2, k = -1, and the equation has the following format:

y = a(x - 2)² - 1

The curve passes through (3,4), that is, when x = 3, y = 4, and we use it to find a.

y = a(x - 2)² - 1

4 = a(3 - 2)² - 1

a = 5.

Hence the equation is:

y = 5(x - 2)² - 1

Placing it into standard form, we have that:

y = 5(x² - 4x + 4) - 1

y = 5x² - 20x + 19

Hence the coefficients are:

p = 5, q = -20, r = 19.

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Answer:

Read Explanation

Step-by-step explanation:

The domain is a list of all possible x-values, this graph starts at 0 and proceeds to positive infinity, making the domain:

[0,∞)

The range is a list of all possible y-values, this graph starts at -1 and proceeds to positive infinity, making the range:

[-1,∞)

x-intercepts Are where the line crosses the x-axis, in this graph the line only crosses the x-axis at x of 2. Making its only x-intercept 2.

y-intercepts Are where the line crosses the y-axis, in this graph the line only crosses the y-axis at y of -1. Therefore its y-intercept is -1.

In function notation when a question asks for f(x) its asking for the y values at the given x-values. At x of 3 the y value equals 1.

The output, y, when the input, x, is -5 is -2

The input is given as:

-5

This means that

x = -5

This is so because x represents the input

From the graph, we have the following highlight

The line of the graph passes through the point x = -5

On the graph;

When x = -5, the value of y is -2

This means that the output, y, when the input, x, is -5 is -2

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There are 59 integer solutions

Such questions are best solved by writing cases and calculating the total number of cases. So beginning with

1)  x = -3. The possible combinations are as follows:-

-3 2 13

-3 3 12

-3 4 11

-3 5 10

-3 6 9

-3 7 8

-3 8 7

-3 9 6

-3 10 5

-3 11 4

10 combinations

2) x = -2

-2 2 12

through

-2 11 3

10 combinations

3) x = -1

-1 2 11

through

-1 10 3

9 combinations

4) x = 0

0 2 10

through

0 9 3

8 combinations

as we can see from the pattern at x =1  we get 7 combinations, at x =2  we get 6 combinations, at x=3 we get 5 combinations and at x =4  we get 5 combinations.

Thus total number of combinations 4+5+6+7+8+9+10+10 = 59 integer solution.

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One can prove congruence through transformation if they have the same shape and size.

The congruency postulates include:

In geometry, it should be noted that two figures are congruent if they have the same shape and size.

In this case, if two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the triangles are congruent.

One can prove triangle congruence using congruency postulates by using the SSS theorem( side side side theorem).

It should be noted that the congruence postulate is used to illustrate that the triangles are equal.

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Answer:

A. (3x + 4)(x-7)

Step-by-step explanation:

3x times x = 3x^2

3x times -7 = -21x

4 times x = 4x

4 times -7 = -28

-21x + 4x = -17x

3x^2 - 17x - 28

The option c is correct. The linear representation model is best for this situation out of the exponential, quadratic model.

According to the statement

we have given that:

Monthly Rate = $20, Number of customers = 5000

If there is a decrease of $1 in the monthly rate, the number of customers increase by 500.

And we have to find that The type of model that best fits the given situation.

So, according to the linear representation model

Monthly Rate = $20, Number of customers = 5000

Let us decrease the monthly rate by $1.

Monthly Rate = $20 - $1  = $19, Number of customers = 5000 + 500 = 5500

Let us decrease the monthly rate by $1 more.

Monthly Rate = $19 - $1  = $18, Number of customers = 5500 + 500 = 6000

Here, we can see that there is a linear change in the number of customers whenever there is decrease in the monthly rate.

We have 2 pair of values here,

x = 20, y = 5000

x = 19, y = 5500

Let us write the equation in slope intercept form:

y = mx + c

And Slope of a function is

m = y₂ - y₁ / x₂ - x₁

Then

m = 5500 - 5000 / 19 - 20

m = -500

So, the equation become

y = -500x +c

And find the value of by putting the values.

So, c = 15000

And the equation become

y = -500x + 15000.

According to this linear model is perfect for this situation.

So, The linear representation model is best for this situation.

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The addition equation to represent how their charges combine to make the overall charge of the atom is + 1 + - 1 = 0

A hydrogen atom has one positively charged proton and one negatively charged electron.

An atom of every elements has an electron(negatively charged) and positively charge(proton) part.

An atom as a whole is electrically neutral if the number of proton and electron are equal. They will cancel each other to make the atom neutral.

Therefore, the addition equation to represent how their charges combine to make the overall charge of the atom is as follows;

+ 1 + - 1 = 0

1 positively charged proton plus single negatively charged electron  = zero(neutral)

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The mean of the given data is 206.5.

To find the mean of the given data:

Sum of values = 211 + 226 + 186 + 221 + 181 + 228 + 207 + 215 + 203 + 203 + 204 + 196 + 226 + 212 + 212 + 201 + 219 + 191 + 191 + 185 + 193 + 231 = 4,542

Number of values = 22

Mean = 4,542 ÷ 22 = 206.5

Therefore, the mean of the given data is 206.5.

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Answer:

Step-by-step explanation:

The area of quadrilateral ABCD exists equivalent to the area of triangle ABD plus the area of triangle ADC

Heron's Formula exists a technique for estimating the area of a triangle when you know the lengths of all three sides.

Therefore, the total area of  quadrilateral abcd exists 28.53 [tex]$$units^2[/tex].

Let a, b, and c be the lengths of the sides of a triangle.

The area is given by:

[tex]$$A = \sqrt{p(p-a)(p-b)(p-c)}[/tex]

where p exists half the perimeter

[tex]$p = \frac{a+b+c}{2}[/tex]

To estimate the area of triangle ABD

we have

a = AB = 2.89 units

b = BD = 8.59 units

c = DA = 8.6 units

To estimate the perimeter

[tex]$p = \frac{2.89+8.59+8.6}{2}[/tex]

= 10.4 units

To estimate the area

[tex]$A = \sqrt{10.04(10.04-2.89)(10.04-8.59)(10.04-8.6)}[/tex]

[tex]$A = \sqrt{10.04(7.15)(1.45)(1.44)}[/tex]

[tex]$A = \sqrt{149.89}[/tex]

A = 12.24 [tex]$$units^2[/tex]

To estimate the area of the triangle ADC

we have

a = AC = 4.3 units

b = AD = 8.6 units

c = DC = 7.58 units

To estimate the half perimeter p

[tex]$p = \frac{4.3+8.6+7.58}{2}[/tex]

= 10.24 units

To estimate the area

[tex]$A = \sqrt{10.24(10.24-4.3)(10.24-8.6)(10.24-7.58)}[/tex]

[tex]$A = \sqrt{10.24(5.94)(1.64)(2.66)}[/tex]

[tex]$A = \sqrt{265.35}[/tex]

A = 16.29 [tex]$$units^2[/tex]

To estimate the total area

A = 12.24+16.29 = 28.53 [tex]$$units^2[/tex].

Therefore, the total area of  quadrilateral abcd exists 28.53 [tex]$$units^2[/tex].

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Into how many equal parts can the same cake be cut if the cuts can only be made along the gridlines, cake can be cut into 20 equal parts.

This is further explained below.

Generally, In spreadsheet software, gridlines are the light gray lines that divide the cells, rows, and columns. Gridlines are often used to maintain track of data. Gridlines are widely used in popular spreadsheet programs like Spreadsheet.

In conclusion, If the cuts can only be done along the gridlines, the cake may be divided into 20 equal pieces when cutting along the lines.

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Answer:

a) 18

b) 48

c) 192

a) 30

b) 150

Step-by-step explanation:

Answer:

1

a ) 18

b ) 48

c ) 144

2

a ) 30

b ) 150..

[tex]...[/tex]

The function [tex]H(t) = -16t^2 + 64t[/tex] exists in a parabola.

The axis of symmetry of a parabola exists at the midpoint between the two real roots.

The roots exist the solutions of H(t) = 0

To estimate the roots equation exists [tex]-16t^2 + 64t = 0[/tex]

Factor t(-16t + 64) = 0

t = 0 and -16t + 64 =0

-16t + 64 = 0

t = 64 / 16 = 4

t = 4

Then the two roots are t = 0 and t = 4, and the axis of symmetry exists

t = (0+4)/2 = 4/2 = 2

The axis of symmetry exists at t = 2.

It represents the time at which the ball is at the higher point, the maximum height.

You can find the maximum height replacing t = 2 in the function H(t)

[tex]H(t) = -16(2^2) + 64(2)[/tex]

= 64 feet.

And you can also deduce that the second part of the flight will take 2 seconds, for a total flight time of 4 seconds.

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Answer:

answer is a

Step-by-step explanation:

it takes 2 seconds for the ball to reach maximum height and 2 seconds to fall on the ground.

t = 2; it takes the ball 2 seconds to reach the maximum height and 2 more seconds to fall back to the ground

Took the FLVS test!

If a quadrilateral exists as a parallelogram, then opposite sides exist congruent and parallel.

If a quadrilateral exists as a parallelogram, then opposite sides exist congruent and parallel.

Given: AB = 6cm , BC = 5cm, AD = 4cm, CD = 7cm and BD = 6cm​

Draw a line AB with 6cm with A as the center draw an arc of radius 4 cm. And draw another arc of 6cm to cut the previous arc at D with B as the center draw an arc of radius 5cm. And with D draw another arc of 7cm to cut the previous arc at C. Join the lines of the quadrilateral.

Now ABCD exists as a required quadrilateral.

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