what is the value of x?

Answer:

y=-3x+2

Step-by-step explanation:

Answer: 20 6-cents, 30 8-cents, 10 10-cents and 2 20- cents

Step-by-step explanation:

6 cent = x+10

10 cent= x

8 cent= 3x

20 cent=2

6x+60+10x+24x+40

400 divided by 40=X

x=10.

10+10=20/ 6 cents

3x10=30/ 8 cents

x=10/ 10 cents

20 cents= 2.

Answer:

Yes

Step-by-step explanation:

To prove that if O is an optimal solution to a linear program, then O is a vertex of the feasible region, we can use the following argument:

Assume that O is an optimal solution to a linear program.

By definition, an optimal solution maximizes or minimizes the objective function while satisfying all the constraints.

Suppose O is not a vertex of the feasible region.

If O is not a vertex, it must lie on an edge or in the interior of a line segment connecting two vertices.

Consider two neighboring feasible solutions, A and B, that define the line segment containing O.

Since O is not a vertex, there exists a feasible solution on the line segment between A and B that has a higher objective function value (if maximizing) or a lower objective function value (if minimizing) than O.

This contradicts our assumption that O is an optimal solution since there exists a feasible solution with a better objective function value.

Therefore, our initial assumption that O is not a vertex must be false.

Thus, O must be a vertex of the feasible region.

By contradiction, we have shown that if O is an optimal solution to a linear program, then O must be a vertex of the feasible region.

The final conclusion is that the data suggest the population mean retirement age for small business owners is not significantly younger than 64 at the α = 0.01 level.

For this study, we should use a t-test for a population mean. The null and alternative hypotheses would be: H0: μ ≥ 64 (The population mean retirement age for small business owners is greater than or equal to 64). H1: μ < 64 (The population mean retirement age for small business owners is less than 64). To calculate the test statistic, we need to find the sample mean and sample standard deviation: Sample mean (xbar) = (64 + 59 + 67 + 58 + 54 + 63 + 54 + 63 + 62 + 56 + 59 + 67) / 12 = 61.833. Sample standard deviation (s) = 4.751. The test statistic (t) can be calculated using the formula t = (xbar - μ) / (s / sqrt(n)), where n is the sample size.  t = (61.833 - 64) / (4.751 / sqrt(12)) ≈ -1.685 (rounded to 3 decimal places) .

To find the p-value, we would compare the test statistic to the t-distribution with (n-1) degrees of freedom. Since the sample size is small (n = 12), we should refer to the t-distribution. The p-value can be determined by looking up the t-value (-1.685) and degrees of freedom (n-1 = 11) in a t-table or using statistical software. Let's assume the p-value is approximately 0.0637 (rounded to 4 decimal places). Since the p-value (0.0637) is greater than the significance level (α = 0.01), we fail to reject the null hypothesis. Therefore, there is insufficient evidence to conclude that the population mean retirement age for small business owners is younger than 64 at the α = 0.01 level of significance. Thus, the final conclusion is that the data suggest the population mean retirement age for small business owners is not significantly younger than 64 at the α = 0.01 level.

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Answer: B

Step-by-step explanation:

Since they are all on one line, 27 + 90 + A = 180

Using this, we can get the value of A, which is 63 degrees.

Therefore, A is false.

C is equal to A since they are vertical angles.

Therefore, C is also false.

At this point, two statements are already wrong, so D is obviously false.

The correct statement is B, which we can test by subtracting 63 from 180. And sure enough, it's correct.

Answer:

ss

Step-by-step explanation:

sas

The radius of the circle who center is at ( 5 , 2 ) and the point on the circle is ( -3 , 4 ) is given by r = 2√17 units

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the radius of the circle be r

Let the center of the circle be A ( 5 , 2 )

Let the point on the circle be P ( -3 , 4 )

Now , standard form of a circle is

( x - h )² + ( y - k )² = r²

So , r² = ( 5 - ( -3 ) )² + ( 2 - 4 )²

On simplifying the equation , we get

r² = ( 8 )² + ( 2 )²

r² = 64 + 4

r² = 68

Taking square roots on both sides , we get

r = √68

r = 2√17

Hence , the radius of the circle is 2√17 units

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Answer:

$66

Step-by-step explanation:

→ Work out 45% as a multiplier

100 - 45 = 55 ⇒ 55 ÷ 100 = 0.55

→ Multiply the multiplier by the price

0.55 × 120 = $66

Answer:

54

Step-by-step explanation:

120 times 45 equals 5400 divided by 100 equals $54

The distance between the star and the sun is 4124966.128 AU and this can be determined by using the trigonometric function.

Stellar parallax is the apparent shift of position (parallax) of any nearby star (or other object) against the background of distant stars. By extension, it is a method for determining the distance to the star through trigonometry, the stellar parallax method.

Given :

i. Astronomers often measure large distances using astronomical units (AU) where 1 AU is the average distance from Earth to the Sun.

ii. The image, represents the distance from a star to the Sun.

iii.  Using a technique called “stellar parallax,” astronomers determined    θ is 0.00001389 degrees.

The following steps can be used in order to determine the distance between the star and the Sun in astronomical units:

Step 1 - The trigonometric function can be used in order to determine the distance between the star and the Sun in astronomical units.

Step 2 - The sine function can be used to determine the distance. \(sin\theta =\frac{P}{H}\) where P is the perpendicular and H is the Hypotenuse.

Step 3 - Substitute the known terms in the above expression.\(Sin( 0.00001389) =\frac{1}{d}\)

Step 4 - Simplify the above expression. d = 4124966.128

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Answer:

Step-by-step explanation:

m<5 and m<4 are  supplementary angles => m<5 + m< 4 = 180

                                                                         m<4 = 180 -77 = 103

m<4 and m<2 are corresponding angles => m<4 = m<2 = 103

The measure of the angle m∠2 is 103.

The supplementary angles are defined as the angles having a sum of 180 degrees. The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.

In the given image the given angle is m∠5=77°. The measure of the angle m∠2 will be calculated by using some of the angle properties.

m∠5 and m∠4 are supplementary angles:-

m∠5 + m∠4 = 180

m∠4 = 180 -77 = 103

m∠4 and m∠2 are corresponding angles => m∠4 = m∠2 = 103

Therefore, the measure of the angle m∠2 is 103.

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Answer:y=9x-7

Step-by-step explanation:

Answer:

y = 9x - 7

Step-by-step explanation:

Slope-intercept form is y =  mx + b

Y-intercept is where x = 0. In this instance, when x = 0, y = -7 (0, -7)

So at this point we know b = -7.

Then, take one of the values of x, such as 1, as well as the corresponding value of y and plug in. When x = 1, y = 2 (1, 2)

2 = m(1) - 7

Solve for m (slope)

2 = m - 7

Add 7 to both sides to get m alone.

9 = m

Now we know the slope, and the y-intercept, so we can fill in the equation for slope-intercept form for this linear function.

y =  mx + b

y = (9)x + (-7)

y = 9x - 7

Answer:

\(g(2)=11\)

Step-by-step explanation:

\(g(2)=5(2)+1=10+1=11\)

The amount of saving in pounds is £7.00 and in percentage is 29.167%

What is percentage ?

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

Cost of 500mm×500mm×0.7mm = £6.00

No. of sheets that can be cut will be = \(\frac{1000 * 1000 * 0.7}{500 *500 *0.7}\)

                                                             = 4 sheets

Cost of 1 sheet of 1000mm x 1,000 mm x 0.7 mm = £17.00

Cost of 4 sheets of 500 mm x 500 mm x 0.7 mm = £6.00 × £4.00

                                                                                 = £ 24.00

Hence saving = £ 24.00 - £17.00

                       = £ 7.00

Hence percentage of savings = 7/24 × 100

                                                  = 175/6

                                                  = 29.167%

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Given:

Aim:

We need to find the trigonometric function and the quadrant of the angle.

Explanation:

Take inverse trigonometry on both sides of the equation.

Final answer:

The fraction that he gave 5/42 of his paper to the classmate.

We know that Trevor cut off 1/7 of his paper. And we know that he gave 5/6 of that piece to a friend.

To find the of his paper did Trevor give to his classmate, we just need to take the product between the two fractions above.

Remember that to get the product, we take the products between the numerators and between the denominators.

(1/7)*(5/6) = 5/(7*6) = 5/42

Trevor gave 5/42 of his paper to the classmate.

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Answer:

A = 15 mm²

Step-by-step explanation:

the volume (V) of a prism is calculated as

V = Ah ( A is the cross section and h the depth )

here h = 12 and V = 180 , then

A × 12 = 180 ( divide both sides by 12 )

A = 15 mm²

The potential difference V(B) − V(A) is determined by subtracting the potential at A from the potential at B.

The potential difference V(B) − V(A) is -5V.

The potential difference between two points in an electric field is determined by subtracting the potential at one point from the potential at the other point.

The potential difference V(B) − V(A) in the given scenario can be determined as follows.

The electric field E due to the first charge Q1, which is +1×10^-8 C at the origin, at point A on the x-axis is given by,

E1 = kQ1/x

where k is the Coulomb constant k = 9 × 10^9 Nm^2/C^2 and x is the distance from the point to the charge.

According to the above equation,

E1 = (9 × 10^9)(1 × 10^-8)/4E1 = 2.25 V/m

The potential at point A due to the first charge Q1 is given by,V1 = E1 × xV1 = (2.25 V/m) × 4 mV1 = 9V

The electric field E due to the second charge Q2, which is -2×10^-8 C at a distance of 4m on the y-axis, at point B is given by,E2 = kQ2/d

where d is the distance from the point to the charge.

According to the above equation,E2 = (9 × 10^9)(-2 × 10^-8)/5E2 = -3.6 V/m

The potential at point B due to the second charge Q2 is given by,

V2 = E2 × dV2 = (-3.6 V/m) × 3 mV2 = -10.8 V

The potential difference V(B) − V(A) is determined by subtracting the potential at A from the potential at B.

V(B) − V(A) = V2 − V1V(B) − V(A)

= -10.8 V - 9 VV(B) − V(A)

= -19.8 VV(B) − V(A)

= -5 V

Therefore, the potential difference V(B) − V(A) is -5V.

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Answer:

1cesrutherford and Global business is the next 3.some 7th round and 50th 3 7th round ♥ in my car is a

Answer:

b = a + 2 or b = 2 - a

Step-by-step explanation:

Solve for b:

-4 + a^2 + 4 b - b^2 = 0

The left hand side factors into a product with two terms:

(2 + a - b) (-2 + a + b) = 0

Split into two equations:

2 + a - b = 0 or -2 + a + b = 0

Subtract a + 2 from both sides:

-b = -a - 2 or -2 + a + b = 0

Multiply both sides by -1:

b = a + 2 or -2 + a + b = 0

Subtract a - 2 from both sides:

Answer:

b = a + 2 or b = 2 - a

Answer:

2 and 3

Step-by-step explanation:

Let us start by representing the first consecutive number with x. In a similar sense, the next consecutive number would be x+1. According to the given question, we can write the following equation:

\(x+x+1=3x-1\)

Solving for the equation by isolating the term containing x, we have:

\(2x+1=3x-1\\2x+2=3x\\\fbox{x=2}\)

Since we have designated x as the first consecutive integer, the other integer we are looking for is x+1, or \(\fbox{3}\) .

I hope this helps! Let me know if you have any questionss :)

The Chang family has been traveling for 18 hours, thus, t-value is 18.

A significant t-score, also known as a t-value, implies that the groups are distinct, whereas a small t-score suggests that the groups are similar. Degrees of freedom are the values in a study that are open to change and are crucial for determining the significance and reliability of the null hypothesis.

D(t) = 2,280 - 60t

D(t) = 1,200; find t.

D(t) = 2,280 - 60t

1200 = 2280 - 60t

From both sides of the equation, deduct 2280.

1200 - 2,280 = 2280 - 60t - 2,280

- 1080 = - 60t

multiplied by -60 on both sides

- 1080 / -60 = - 60t / -60

18 = t

t = 18

The Chang family had travelled for 18 hours, according to this.

The Chang family has been traveling for 18 hours, t = 18.

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The complete question is,

Having just returned from a cross-country road vacation, the Chang family is traveling back home. They can visualize their distance from home in miles after t hours of travel by using the function D(t) = 2,280 - 60t during the journey. If D(t) = 1,200, what does t represent? That value stands for what?

A.t = 20; the Chang family has been traveling for 20 hours.

B. t = 20, meaning the Chang family will need to travel 20 more hours to reach home.

The Chang family has been traveling for 18 hours, thus c. t = 18.

The Chang family must go home for an additional 18 hours using the formula D. t = 18.

The measure of the inscribed angle is equal to 90 degrees

The inscribed angle theorem mentions that the angle inscribed inside a circle is always half the measure of the central angle or the intercepted arc that shares the endpoints of the inscribed angle's sides. In a circle, the angle formed by two chords with the common endpoints of a circle is called an inscribed angle and the common endpoint is considered as the vertex of the angle.

In this problem, the side length of the square is 5 which forms 90 degrees to all the other sides.

The measure of the circumscribed angle is 90 degree

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Answer:3x^2-9x/x^2-25

Step-by-step explanation:

To calculate the number of ways to arrange the books on a shelf, we can use the formula for permutations.

The formula for permutations is  \(\frac{n!}{(n-r)!}\)  

where:  n is the total number of items

              r is the number of items being selected.

a. In this case, there are 8 books total (3 blue + 3 green + 2 red), and we are arranging all of them.

so n= 8 and r = 8, the number of arrangements is

\(\frac{8!}{(8-8)!}\) = 8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 =  40320

So the answer to (a) is 40320.

b. To calculate the number of arrangements if the books of the same color are grouped, we can consider each group as one item.

There are 3 groups (blue, green, red), and we are arranging those

so n = 8 and r = 3.

Hence, the number of arrangements is

\(\frac{8!}{(8-3)!}\) = \(\frac{8!}{5!}\) = \(\frac{8x7x6x5x4x3x2x1}{5x4x3x2x1}\) = 336

So the answer to (b) is 336.

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Answer:

3/8 lb or 6 oz

Step-by-step explanation:

Answer:

ç

Step-by-step explanation:

The least number of socks you need to pick is 10 red socks, 10 blue socks, and 10 white socks to ensure you have a matching pair. The least number of socks that can be taken from the drawer is one.

Follow these steps:
1. Pick one sock from the drawer (it could be any color, let's say red).
2. Pick a second sock from the drawer (if it's red, you have a matching pair; if not, let's say it's blue).
3. If you don't have a matching pair yet, pick a third sock from the drawer (now, it's either red, blue, or white, and you'll have a matching pair for sure).
So, the least number of socks you need to pick to ensure a matching pair is 3.

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