If UW = 6x - 35, find UW.

Answer:

The 95 % confidence interval of the mean of the time playing video games. is

        \(15.67< \mu <17.52\)

Step-by-step explanation:

From the question we are told that

      The sample size is \(n = 35\)

        The sample mean is \(\= x = 16.6\)

       The standard deviation is  \(\sigma = 2.8\)

The confidence level is  95%  hence the level of significance is mathematically represented as

     \(\alpha = 100 - 95\)

     \(\alpha = 5\)%

      \(\alpha = 0.05\)

Now the critical value of half of this level of significance obtained from the normal distribution table is  

       \(Z_{\frac{\alpha }{2} } = 1.96\)

The  reason for the half is that we are considering the two tails of the normal distribution curve which we use to obtain the interval

Now the standard error of the mean is mathematically evaluated as

       \(\sigma _{\= x} = \frac{\sigma }{\sqrt{n} }\)

substituting values  

     \(\sigma _{\= x} = \frac{2.8 }{\sqrt{35} }\)

      \(\sigma _{\= x} = 0.473\)

the 95 % confidence interval of the mean of the time playing video games.

is mathematically evaluated as

    \(\= x - (Z_{\frac{\alpha }{2} } * \sigma_{\= x }) < \mu < \= x - (Z_{\frac{\alpha }{2} } * \sigma_{\= x })\)

substituting values

    \(16.6 - (1.96 * 0.473) < \mu < 16.6 + (1.96 * 0.473)\)

     \(15.67< \mu <17.52\)

\(x=\frac{1+4f-\sqrt{16f^{2}+8f+25 } }{2}\)

a) To re-express the given differential equation as a first-order differential equation using matrix and vector notation, we can rewrite it in the form:

\(x' = Ax\)

where x is a vector and A is a square matrix.

b) To determine the stability of the system obtained in part (a), we need to analyze the eigenvalues of matrix A.

If all eigenvalues have negative real parts, the system is stable.

If at least one eigenvalue has a zero real part, the system is neutrally stable.

If at least one eigenvalue has a positive real part, the system is unstable.

c) To compute the eigenvalues and eigenvectors of matrix A, we solve the characteristic equation

\(det(A - \lambda I) = 0\),

where λ is the eigenvalue and I is the identity matrix.

By solving this equation, we obtain the eigenvalues.

Substituting each eigenvalue into the equation

\((A - \lambda I)v = 0\),

where v is the eigenvector, we can solve for the eigenvectors.

d) Once we have computed the eigenvalues and eigenvectors of matrix A, we can construct the diagonalization relationship as follows:

\(A = PDP^{(-1)}\)

where P is a matrix whose columns are the eigenvectors of A, and D is a diagonal matrix whose diagonal elements are the eigenvalues of A.

To show that this relationship is valid, we can compute \(PDP^{(-1)}\) and verify that it equals A.

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The sequence is will always have even numbers, is hence proved.

Given, the quadratic sequence is: 44:52:64:80

Sequences with a term are known as quadratic sequences. They can be distinguished by the fact that the first differences between terms are not equal but the second differences between terms are. Utilizing the term sum in an arithmetic progression formula, the sum of even numbers formula is achieved. The equation is Sum of Even Numbers Formula = n(n+1), where n is the total number of terms in the series.

The formula is: Tₙ = 2n² ₊ 2n  ₊ 40

take 2 common

Tₙ = 2(n² ₊ n  ₊ 20)

in other words n² ₊ n  ₊ 20  = y

therefore , Tₙ = 2y

which by definition makes Tₙ an even number at all times.

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we have to do alot for this

so first we gotta change 12.3 into a mixed fraction

n = 5 so 5 ÷ 12.3

Answer:

The Burnets spent .22 × $5,825 = $1,281.50 on taxes and insurance.

Answer:

210 = 2 * 3 * 5 * 7

Step-by-step explanation:

210/2 = 105

105 / 3 = 35

35 / 5 = 7

7 / 7 = 0

210 = 2 * 3 * 5 * 7

Answer: D

Step-by-step explanation:

Fits the definition

Answer:

2mn

Step-by-step explanation:

To solve the expression 14m^2n^2/7mn, we need to simplify the fraction.

First, we can simplify the numerator by combining the 14 and m^2:

14m^2 * n^2 / 7mn = (14m^2) * (n^2) / (7mn) = 14mn * mn / 7mn = 14mn / 7

Next, we can simplify the denominator by  7

14mn / 7  = 14 / 7 = 2mn

Answer: C is the answer

The number of degrees below zero is given by A = 56° F

Regardless of the sign, a modulus function returns the magnitude of a number. The absolute value function is another name for it.

It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.

The value of the modulus function is always non-negative. If f(x) is a modulus function , then we have:

If x is positive, then f(x) = x

If x = 0, then f(x) = 0

If x < 0, then f(x) = -x

Given data ,

Let the initial temperature be represented as T

Let the number of degrees below zero be A

Now , the value of T is

T = -56° F

From the modulus function , we get

The value of the modulus function is always non-negative.

So , the measure of A = | T |

A = | -56 |

A = 56° F

Hence , the number of degrees below zero is 56° F

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The ball is in the air for approximately 2.8 + √7 seconds, which rounds to 5.2 seconds when rounded to one decimal place.To write the equation in vertex form, we need to complete the square.

The given equation is h = -4.9t² + 27.44t + 0.584. We can rewrite it as:

h = -4.9(t² - 5.6t) + 0.584

Now, we want to complete the square inside the parentheses. To do this, we need to add and subtract the square of half the coefficient of t. In this case, the coefficient is -5.6, so we have:

h = -4.9(t² - 5.6t + (5.6/2)² - (5.6/2)²) + 0.584

Simplifying, we get:

h = -4.9((t - 2.8)² - 2.8²) + 0.584

Expanding further:

h = -4.9(t - 2.8)² + 4.9(2.8)² + 0.584

Thus, the equation in vertex form is: h = -4.9(t - 2.8)² + 34.328

b) The ball's height when it was hit can be found by evaluating the equation at t = 0:

h = -4.9(0 - 2.8)² + 34.328

h = -4.9(-2.8)² + 4.328

h = -4.9(7.84) + 34.328

h ≈ 0.784 meters

To find the time at which the ball reaches its maximum height, we can use the fact that the maximum height occurs at the vertex of the parabolic equation. The vertex of a parabola in the form h = a(t - h₀)² + k is given by (h₀, k). Comparing this to our equation, we can see that the vertex occurs at t = 2.8 and h = 34.328. Therefore, the ball reaches its maximum height at 2.8 seconds, and the maximum height is 34.328 meters.

The total time the ball is in the air can be determined by finding the time it takes for the ball to reach the ground. When the ball hits the ground, its height is 0. To find this time, we can set the equation equal to 0 and solve for t:

0 = -4.9(t - 2.8)² + 34.328

4.9(t - 2.8)² = 34.328

(t - 2.8)² ≈ 7

t - 2.8 ≈ ±√7

t ≈ 2.8 ± √7

Since time cannot be negative in this context, we can ignore the negative value.

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Answer:

45/49

Step-by-step explanation:

The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. Finally, simplify the fractions if needed.

9/14 * 10/7 = 90/98

divide the numerator and the denominator by 2.

90 * 2 = 45

98 * 2 = 49

45/49

9514 1404 393

Answer:

  warmer by 30.2 degrees

Step-by-step explanation:

It might help to think of these values plotted on a number line. Both temperatures will be left of zero, with -63°C being farther to the left (colder).

The difference can be found by subtracting the colder temperature from the warmer one:

  -32.8 -(-63) = -32.8 +63 = 63 -32.8 = 30.2 . . . degrees

The South America temperature -32.8°C is 30.2° warmer than the North America temperature.

Answer:

y=1/2*x+1

explanation: The slope is 1/2 by picking any 2 points and doing rise/run. the y-intercept is 1 therefore +1 at the end.

the employer's total FUTA and SUTA tax is: $2,928

What is tax rate?

The percentage of income that a person or corporation must pay or withhold as taxes is known as the effective tax rate.

$7,000 (for Zachary Fox) + $7,000 (for Calvin Bell) + $7,000 (for David Alexander) + $7,000 (for Michael Sierra) = $28,000

The FUTA tax for this amount is:

$28,000 × 6.0% = $1,680

Therefore, the total taxable earnings subject to SUTA tax is:

$26,000 (for each employee) × 4 (number of employees) = $104,000

The SUTA tax for this amount is:

$104,000 × 1.2% = $1,248

The year-to-date FUTA and SUTA taxes are not given explicitly, so we cannot calculate the current period FUTA and SUTA taxes.

Therefore, the employer's total FUTA and SUTA tax is:

$1,680 (FUTA tax) + $1,248 (SUTA tax) = $2,928

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Check the picture below.

Answer:

Each base angle would be 70°.

Step-by-step explanation:

*Base angles means the two equal angles formed on the base are called base angles.

Base means the third unequal side of the triangle. *

Given triangle is isosceles triangle.

The angle of vertex which is given is 40°.

Let each base angle be x.

We know that,

There are two base angles in a isosceles triangle.

And, Sum of angles of triangle is 180° .

Therefore,

\( \tt \implies \: x + x + 40 {}^{ \circ} = 180 {}^\circ\)

Now Solve For x. That would be the solution.

Steps:

Combine like terms:

\(\tt \implies2x + 40{}^{ \circ} = 180{}^{ \circ} \)

Subtract 40 from both sides:

\(\tt \implies2x + 40{}^{ \circ} - 40 = 180{}^{ \circ} - 40{}^{ \circ} \)

Simplify the LHS and RHS:

\(\tt \implies2x + 0 = 140{}^{ \circ} \)

\(\tt \implies2x = 140 {}^{ \circ} \)

Divide both sides by 2:

\(\tt \implies \cfrac{2x}{2} = \cfrac{140{}^{ \circ} }{2{}^{ \circ} } \)

Use cancellation method and cancel LHS and RHS:

\(\tt \implies \cfrac{ \cancel2x}{ \cancel2} = \cfrac{ \cancel{140^{ \circ}} }{ \cancel{2{}^{ \circ} }} \)

\(\tt \implies \cfrac{1x}{1} = \cfrac{70{}^{ \circ} }{1{}^{ \circ} } \)

\(\tt \implies{1x} = {70}^{ \circ} \)

\(\tt \implies{x} = 70{}^{ \circ} \)

Hence, each base angle would be 70°.

Verification:

As we know that sum of angles of triangle is 180°.

So,

\(\tt \implies \: Base \: angle + other \: base \: angle + vertex \: angle= 180{}^{ \circ} \)

We got that one base angles of the given isosceles triangle is 70° and other is 70°, and the vertex angle is 40°[Given].

\(\tt \implies70{}^{ \circ} + 70{}^{ \circ} + 40{}^{ \circ} = 180{}^{ \circ} \)

Solve it.

\(\tt \implies140{}^{ \circ} + 40{}^{ \circ} = 180{}^{ \circ} \)

\(\tt \implies180{}^{ \circ} = 180{}^{ \circ} \)

\( \tt \: LHS = RHS\)

\( \star \sf \: Hence, Verified.\)

\( \rule{225pt}{2pt}\)

I hope this helps!

Let me know if you have any questions.

The measurements of Angle ABC = Angle ABC = 70°.

Step-by-step explanation:

Understanding concept:

Here, we are given with a triangle that has two sides equal. The triangle which has two sides as equal is said to be an isosceles triangle. The triangle which has two sides equal will also have two angles equal and the other different. In this question, we are given with the measurement of an angle of isosceles triangle. We are asked to find the other angle in this triangle. To find. the answer, we use the concept of angle sum property of the triangle. Thai concept says that all the angles in a triangle together adds up to 180°. If no, then it's not considered as a triangle.

Solution:

Angles sum property of a triangle (∆) = 180°

Angle BAC + Angle ABC + Angle ACB = 180°

Substitute all the given values then

→ 40° + x° + x° = 180°

Add the variables together .i.e., x° + x° is 2x.

→ 40° + 2x° = 180°

Shift, the number 40° from LHS to RHS, changing it's sign.

→ 2x° = 180° - 40°

Subtract the values on RHS.

→ 2x° = 140°

Shift the number 2° from LHS to RHS.

→ x° = 140°/2°

Simplify the fraction to get the value of x.

→ x° = 70°

Therefore, x = 70°

Answer: Hence, the measurement of both the base unknown angles x is 70°.

Explore More:

Let's check whether the values of x is true or false.

Verification:

If the values of x = 70° then the equation is

40° + x° + x° = 180°

Substitute the values of x = 70° then

→ 40° + 70° + 70° = 180°

Add the values on LHS.

→ 40° + 140° = 180°

→ 180° = 180°

LHS = RHS is true for x = 70°

Hence, verified.

Please let me know if you have any other questions.

Answer:

x < 5/4

Step-by-step explanation:

8x−2<8

Add 2 to each side

8x−2+2<8+1

8x<10

Divide each side by 8

8x/8 < 10/8

x < 10/8

Simplify

x < 5/4

Step-by-step explanation:

\( \tan( x ) = \frac{13}{18} \\ x = arctan (\frac{13}{18} ) \\ x = {79}^{o} \)

 y = 2/3x + 7  is slope-intercept form of the equation .

What exactly does slope intercept mean?

the equation of the parallel line in slope intercept form y=mx+b so that we can clearly see the slope and y intercept

      2x-3y = -9

      3y = 2x + 9

         y = 2/3x + 9/3

          y = 2/3x + 3

compare equation y = mx + c  

  slope = 2/3  

to find c put x = -3 and y = 5

     y = mx + c  

      5 = 2/3 * (-3) + c

      5 = -6/3  + c

        c = 5 + 2  = 7

put the final equation together

           y = 2/3x + 7

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The slοpes οf the οppοsite sides are negative reciprοcals and alsο, the rectangle is a square because the οppοsing angles are cοngruent.

A unique kind οf rectangle called a square is οne with fοur cοngruent sides and fοur cοngruent angles (90 degrees). A square alsο has the same characteristics as a rectangle (οppοsite sides are parallel and cοngruent, and οppοsing angles are cοngruent) plus the fοllοwing characteristics:

Cοngruence exists οn all fοur sides. Cοngruent angles exist fοr all fοur (90 degrees).

Right angles separate the diagοnals frοm οne anοther and they are cοngruent. The square is divided alοng the diagοnals intο fοur identical right triangles.

Tο determine if ABCD is a square, we need tο check if all fοur sides are cοngruent and if the οppοsite angles are cοngruent.

Using the distance fοrmula, we can find the lengths οf each side:

AB = √[(9-(-1))² + (4-9)²] = \(\sqrt{170}\)

BC = √[(4-9)² + (-6-4)²] = \(\sqrt{170}\)

CD = √[(-6-4)² + (-1-(-6))²] = \(\sqrt{170}\)

DA = √[(-1-(-6))² + (9-(-1))²] = \(\sqrt[]{170}\)

All fοur sides have the same length, thus the rectangle is a rhοmbus.

Tο determine if it is alsο a square, we need tο check the angles.

Using the slοpe fοrmula:

slοpe AB = (4-9)/(9-(-1)) = -5/10 = -1/2

slοpe BC = (-6-4)/(4-9) = -10/-5 = 2

slοpe CD = (-1-(-6))/(-6-4) = 5/10 = 1/2

slοpe DA = (9-(-1))/(-1-(-6)) = -10/-5 = 2

The slοpes οf the οppοsite sides are negative reciprοcals οf each οther, indicating that they are perpendicular tο οne anοther. The rectangle is a square because the οppοsing angles are cοngruent.

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Answer:

plz

Step-by-step explanation:

thx

Answer:

its 4 hours

Step-by-step explanation:

Answer:

blue 7.3

Step-by-step explanation:

Answer:

7.3

Step-by-step explanation:

There are 7 groups with 10 parts in each, 7 complete rows are filled in. 3 are left in the last row. This means that there are 7 wholes with 3 left over. 7.3

The result of 1/11 in the base 10 system is given as is 0.09.

To visualize the long division of 1 ÷ 11 in a base ten system:

Set up the long division: 11 outside and 1.00 inside the division bracket.

Place the decimal point in the quotient above the dividend's decimal point.

Bring down the first digit (0) and divide 11 into 10; it goes 0 times.

Subtract the product (0) from 10, leaving 10.

Bring down the next digit (0) and divide 11 into 100; it goes 9 times.

Subtract 99 from 100, leaving a remainder of 1.

The result is 0.09.

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Answer:

B. 11 1/4

Step-by-step explanation:

8 3/4 + 2 2/4 = 11 1/4

We want to sum two mixed numbers.

The correct option is D: 11 1/4

A mixed number is a number that is separated into a whole part and a rational part.

Here we want to sum:

(8 3/4) + (2 1/2)

This can be written as:

8 + 3/4 + 2 + 1/2

Now we group the whole numbers and we group the rational numbers:

8 + 3/4 + 2 + 1/2 = (8 + 2) + (3/4 + 1/2) = 10 + (3/4 + 1/2).

To perform the sum of the rational numbers, we can write:

1/2 = 2/4

Then we have:

10 + (3/4 + 1/2) = 10 + (3/4 + 2/4) = 10 + 5/4 = 10 + 4/4 + 1/4 = 11 + 1/4

Then we can see that the correct option is D.

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The solution of the inequality is 8 ≥  x  or x > 10. The graph of the solution is attached

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g. 5 < 6, x ≥ 2, etc.

Solving for x:

11≥ 2x - 5 or 2x - 5 > 15

Collect like terms:

11 + 5 ≥ 2x  or 2x > 15 + 5

16 ≥ 2x  or 2x > 20

8 ≥  x  or x > 10

Note:  8 ≥  x can also be written as x ≤ 8

We can combine the two as follow:

Inequality notation: 8 ≥  x > 10

The graph of the solution is attached

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Answer:

11/24

Step-by-step explanation:

change it to :

20/24-9/24

then solve

Answer:

11/24

Step-by-step explanation:

10/12 - 3/8

10/12 + -3/8

5/6 + -3/8

20/24 + -9/24

20 + -9 / 24

= 11/24

Answer:

D. its a two dimensional object

Answer:

A. It is a polygon

C. It is a one-dimensional object

The shape is a polygon in two dimensions since a polygon must have at least three straight sides.