The total cost of a meal, including a 20% tip, can be calculated by the formulaT = C + 0.20C. where T is the total cost and O'is the price of the meal including the appropriate tax.
Complete the following statements.
To solve the equation for C, first factor out the common monomial C to rewrite the equation as [Drop Down 1]. Then, divide both sides by the factor [Drop Down 2] to isolate the variable.

Explanation:

A = set of odd numbers = {1,3,5}

B = set of factors of 12 = {1,2,3,4,6}

A U B = union of set A and set B

A U B = {1,3,5} union {1,2,3,4,6}

A U B = {1,3,5,       1,2,3,4,6}

A U B = {1,2,3,4,5,6}

The set union operation combines two sets into one bigger set. Duplicates are tossed out.

There are 6 elements in the set A U B = {1,2,3,4,5,6} out of 6 faces of the number cube.

Therefore, the probability event  A U B happens is 6/6 = 1 = 100%; i.e. it is guaranteed to happen. Each face of the number cube is either odd, a factor of 12, or both.

Side notes:

The 95 percent confidence interval is (0.20, 0.32).

a. We can construct a 95% confidence interval to estimate the percentage of yellow peas as follows:

Let p = proportion of yellow peas = 155/595 = 0.26

Sample size = n = 595

Standard error = SE = √(p × (1-p) / n) = √(0.26 × (1-0.26) / 595) = 0.03

95% confidence interval = p ± 1.96 × SE

= 0.26 ± 1.96 × 0.03

= 0.26 ± 0.06

So, the 95% confidence interval is (0.20, 0.32).

b. Yes, the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow, as the 95% confidence interval does not include the expected value of 0.25.

Therefore, the 95 percent confidence interval is (0.20, 0.32).

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Answer: 1226.72g

Step-by-step explanation:

If 460g of flour is needed to make enough dough balls for 6 people, we can find the amount of flour needed for each person by dividing 460 by 6:

460 g / 6 = 76.67 g/person

To find the amount of flour needed for 16 people, we can multiply the amount of flour needed per person by the number of people:

76.67 g/person * 16 people = 1226.72 g

Therefore, we need 1226.72 g of flour to serve 16 people.

Answer:

72

Step-by-step explanation:

no

The surface areas are 110 in², 87.6 mm² and 49 m².

Given that are solid figure, we need to find the surface area of them,

1) Triangular prism = perimeter × length + 2 × base area

= (5 + 5 + 6) × 5 + 2(3×5) = 110 in²

2) Triangular pyramid = base area + perimeter × slant height / 2

= 1/2 × 5.2 × 6 + 3 × 6 × 8/2

= 87.6 mm²

3) Cube = 4side²

= 4 × (3 1/2)²

= 4 × 3.5²

= 49 m²

Hence the surface areas are 110 in², 87.6 mm² and 49 m².

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The value of tan 2π/3 without calculator is -√3.

The value of tan 2π/3 without calculator is calculated by applying trig identities as follows;

the value of π = 180 degrees

So we can replace the value of π in the function with 180 degrees as follows;

tan ( 2π / 3) = tan (2 x 180 / 3)

tan (2 x 180 / 3) = tan (2 x 60)

tan (2 x 60) = tan (120)

tan (120) if found in the second quadrant, and the value will be negative since only sine is positive in the second quadrant.

tan (120) = - tan (180 - 120)

= - tan (60)

= -√3

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Answer:

----------------------------

Use of identities:

Simplify the given expression as below:

By comparing we see that:

The solution is::

a. 120 ways can they​ arrive.

b. 6 can Eduardo arrive first and Tyrone ​last

c. 0.05 is the probability that Eduardo will arrive first and Tyrone last.

Here, we have,

a) The ways Eduardo, Sarah, Maria, Jim, and Tyrone can arrive to the party is

5! = 5×4×3×2×1 = 120

The logic behind it is

5 different people can arrive first, after that

4 different people can arrive second, when first and second arrived is known,

3 different people can arrive third, then

2 different people can arrive fourth

only 1 person left to be fifth.

b) Using the same logic, when first and last arrived is known, there is

3!=3×2×1=6 ways they can arrive in this case.

c)  The probability that Eduardo will arrive first and Tyrone last is

the division of the ways Eduardo arrive first and Tyrone ​last by the ways 5 people can arrive = 6/120 = 0.05

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complete question:

Eduardo, Sarah, Maria, Jim, and Tyrone have all been invited to a dinner party. They arrive randomly and each person arrives at a different time.

a. In how many ways can they​ arrive?

b. In how many ways can Eduardo arrive first and Tyrone ​last?

c. Find the probability that Eduardo will arrive first and Tyrone last.

Answer:

use coordinate plane

Step-by-step explanation:

To find the inverse of an equation or graph, you can reflect the graph in the line y = x by switching the x and y coordinates of each point on the graph1. You can also find the equation for the inverse function by switching x and y in the original equation and solving for y12. To check if a graph has an inverse, you can use the horizontal line test: if any horizontal line intersects the graph only once, then the graph has an inverse1.

Answer:

  (c)  f(x) = x² +2x +3; g(x) = -x² +3

Step-by-step explanation:

You want the system of equations represented by the graph.

The parabola opening downward is one that has been reflected over the x-axis, then shifted upward by 3 units. Its equation will be ...

  y = -x² +3 . . . . . . . . the minus sign is the reflection, the +3 is the translation

Only one answer choice include this equation:

  Choice C

The system of equations is:

4x + 3y = 104

x = 4 + 2y

The correct options are C and D.

Let's describe the variables for our system:

x = cost of a can of paint.

y = cost of a brush.

We know that the total cost is $104, then one of the equations is:

4x + 3y = 104

And we know that the cost of a can is $4 more than the double of a brush, then the other equation is:

x = 4 + 2y

Then the correct options are C and D.

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The angles that are 118 degrees are ∠1 , ∠3, ∠5 and ∠7.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angles, alternate exterior angles, vertically opposite angles etc.

Therefore, let's find the angle relationship in the line and find the angles that are 118 degrees.

Hence,

∠3 = 180 - 62 = 118 degrees(angles on a straight line)

∠1 ≅ ∠3 (vertically opposite angles)

∠7 ≅ ∠3 (alternate interior angles)

∠5 ≅ ∠7 (vertically opposite angles)

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The least squares regression equation and the correlational figure collectively yield insightful details regarding the association among educational attainment and income in this region.

The least squares regression equation solely expresses the linear connection between two specific variables, y and x:

y = 726.4x + 14,063

A correlation coefficient of 0.7466 significantly suggests there is a moderate to strong positive association between the portion of inhabitants having at least an undergraduate degree and median returns in this area.

In conclusion, the least squares regression equation and the correlational figure collectively yield insightful details regarding the association among educational attainment and income in this region.

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Answer:

Step-by-step explanation:

8 is the whole number

11/100 = 0.11

ANSWER: 8.11

The measure of the angle ABC is 84 degrees and other measures are listed below

Here, we have

8n - 38 = 5n - 8

So, we have

3n = 30

n = 10

So, we have

ABC = 8n - 38 + 5n - 8

ABC = 8(10) - 38 + 5(10) - 8

ABC = 84

So, the measure of the angle ABC is 84 degrees

Here, we have

2k + 28 = 6k - 20

So, we have

4k = 8

k = 2

So, we have

CBW = 2k + 28

CBW = 2(2) + 28

CBW = 32

So, the measure of the angle CBW is 32 degrees

The interior angle is calculated as

Angle = 180 * (n - 2)/n

Regular 18-gon

Angle = 180 * (18 - 2)/18

Angle = 160

Regular 24-gon

Angle = 180 * (24 - 2)/24

Angle = 165

Here, we have

3x - 10 = x + 8

So, we have

2x = 18

x = 9

So, we have

YA = MA = 9 + 8

YA = MA = 17

Hence, the measures of YA and MA are 17

Here, we have

4x - 15 = 2x - 3

So, we have

2x = 12

x = 6

So, we have

NY = 2(6) - 3

NY = 9

NV = 2 * 9

NV = 18

Hence, the measures of NY and NV are 9 and 18, respectively

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Answer:2 hours, 15 minutes, and 0 second

2.25 hours

135 minutes

8,100 seconds

Option A. rubber, plastic and electrical insulation is the symbol of section lining.

Section lining (also referred to as cross-hatching or hatching) is an integral technique in technical drawing, engineering drafting, and architecture for representing the interior or cross-sectional view of an object. This form of sectioning uses parallel lines at 45 degree angles that fill an object's cut or sectioned areas - this helps visually differentiate solid material from empty space while emphasizing where cuts have occurred.

Complex drawings may include various methods for representing different materials, including using different thicknesses of line thicknesses or spacing or patterns in section linings to represent them

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The maximum number of visitors to the theme park p=14.

Given that few friends want to visit the amusement park.

They are limited to spending $325 for parking and admission.

Tickets are $39 per person, tax included, and parking is $13.

We have to find the maximum number of visitors to the amusement park p.

We can write as $13+$39p≤$325

$39p≤$325-$13

p≤14

Therefore, the maximum number of visitors to the amusement park p=14.

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Answer:

for times it would = 34600 but for adding it would be 3,470

then subtracting would be 3,450 then dividing would be 346

Step-by-step explanation:

HOPE THIS HELPSSS

The equivalent Expression of 8[tex]0^{1/2[/tex] is √80.

We have the expression as 8[tex]0^{1/2[/tex]

We know that

[tex]a^{1/2[/tex] = √a

So, 8[tex]0^{1/2[/tex]

= √80

= √ 2 x 2 x 2 x 2 x 5

= 2 x 2 √5

= 4√5

Thus, the equivalent expression is √80.

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Will ran longer.

Given that Will ran across the diagonal of a square field of the side 40 yd and the James ran across the diagonal of a rectangular field with a length of 25 yards and a width of 35 yards.

We need to find who ran longer,

So for the same we will simply apply Pythagoras theorem to find the length of the diagonal of the fields, whose diagonal will be longer he will run longer,

So, Will ran = √40²+40²

= √3200 = 56.56 yards

James = √25²+35²

= 43 yards

Since Will's diagonal is longer so he ran longer.

Hence, Will ran longer.

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The solutions for the given equation are x=−1,1,√2,−√2. Therefore, option B is the correct answer.

The given equation is x⁸-4x⁷+3x⁶+8x⁵-15x⁴+4x³+9x²-8x+2=0.

Move all terms to the left side and set equal to zero. Then set each factor equal to zero.

Here, (x⁸-4x⁷+8x⁵+4x³)+3x⁶-15x⁴+9x²+2=0

(x-1)⁵(x³+x²-2x-2)=0

(x-1)⁵(x²-2)(x-1)=0

(x-1)⁵=0, (x²-2)=0 and (x-1)=0

x=±1 x=±√2 and x-1

Exact Form: x=−1,1,√2,−√2

Therefore, option B is the correct answer.

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The values are a = 6, b = 7 and c = 3.

Given is a quadratic equation 6x² + 7x + 3 = 0, we need to compare this with the standard form of a quadratic equation.

We know that the standard form of a quadratic equation is given by =

ax² + bx + c = 0

So,

Comparing both the equations,

ax² + bx + c = 0

6x² + 7x + 3 = 0

We see, a = 6, b = 7 and c = 3.

Hence, the values are a = 6, b = 7 and c = 3.

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The translated figure will be entirely within the 3rd quadrant of the graph.

We have, translation (x, y)--> (x-7,y+1).

Here, the notation (x, y) ⇒ (x-7, y+1) means that each x-coordinate has 7 subtracted from it.

Additionally, each y-coordinate has a 1 added to it because of the notation. Point B's y-coordinate is -3. It becomes -2 by adding 1.

As a result, point B's image will be at (-7, -2), 7 units to the left and 1 unit to the upper right of B.

Thus, the translated figure will be entirely within the 3rd quadrant of the graph.

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The equation of the line in point-slope form is given as follows:

y - 60 = 0.5(x - 40).

The point-slope equation of a line is given as follows:

y - y* = m(x - x*).

In which:

The point in this problem is given as follows:

(40, 60).

The intercept is (0, 40), meaning that when x increases by 40, y increases by 20, hence the slope m is given as follows:

m = 20/40

m = 0.5.

Thus the equation is:

y - 60 = 0.5(x - 40).

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The results of the two-sample t-test, there does not appear to be enough evidence to support the claim that the mean FICO score of borrowers with high-interest mortgages is different than the mean FICO score of borrowers with low-interest mortgages.

To test the claim that the mean FICO score of borrowers with high-interest mortgages is different than the mean FICO score of borrowers with low-interest mortgages, we can perform a two-sample t-test.

Using the given data, we can calculate the test statistic as follows:

t = (492 - 508) / sqrt((49^2 / 19) + (38^2 / 26)) = -1.57

The degrees of freedom for this test are 19 + 26 - 2 = 43. Using a t-table or calculator and a significance level of 0.2, we can find the critical value to be approximately ±1.301.

Since the absolute value of the test statistic (1.57) is less than the critical value (1.301), we fail to reject the null hypothesis. This means that we do not have enough evidence to support the claim that the mean FICO score of high-interest mortgage borrowers is different than the mean FICO score of low-interest mortgage borrowers at the 0.2 significance level.

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The order of given numbers from least to greatest is -2.66<-2.43<2.045<2.55.

The given numbers are [tex]-2\frac{2}{3}, 2\frac{5}{9},[/tex] 2.045 and -2.43.

Ascending order means to arrange numbers in increasing order, that is, from smallest to largest.

Here, -2.66, 2.55, 2.045 and -2.43.

-2.66<-2.43<2.045<2.55

Therefore, the order of given numbers from least to greatest is -2.66<-2.43<2.045<2.55.

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The curved surface area of the frustum is approximately 1356.51m². The total surface area of the frustum is approximately 1915.09m². The volume of the frustum is approximately 12348.57m³.

To find the curved surface area of the frustum, we need to find the slant height of the frustum first. Using the Pythagorean theorem, we have

l = √(h² + (R-r)²)

where h = 28m, R = 14m, and r = 6m

l = √(28² + (14-6)²) = √(784 + 64) = √848 ≈ 29.12m

The curved surface area of the frustum can be calculated as

CSA = π(R+r)l

CSA = 22/7 × (14+6) × 29.12

CSA ≈ 1356.51m²

The total surface area of the frustum can be calculated as the sum of the curved surface area and the areas of the top and bottom circles. The area of a circle with radius r can be calculated as πr². Thus, we have

TSA = CSA + πR² + πr²

TSA ≈ 1356.51 + 22/7 × 14² + 22/7 × 6²

TSA ≈ 1915.09m²

The volume of the frustum can be calculated as

V = 1/3 × πh(R² + Rr + r²)

V = 1/3 × 22/7 × 28(14² + 14×6 + 6²)

V ≈ 12348.57m³

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A possible coordinate pair for vertex N is (2.42, 2.58).

We have,

The area of the square is 9 square units, and each side of the square must have a length of 3 units.

Let's start by finding the coordinates of vertex P.

Since the square is a square, we know that the x-coordinate of P is the same as the y-coordinate of M, and the y-coordinate of P is the same as the x-coordinate of M.

The coordinates of P are (3, 2).

To find the coordinates of N, we can use the fact that the diagonals of a square bisect each other and are perpendicular.

The midpoint of MP is the same as the midpoint of NQ, and the slope of MP is the negative reciprocal of the slope of NQ.

The midpoint of MP.

= [(2+3)/2, (3+2)/2]

= [2.5, 2.5]

Now,

The slope of MP is (2-3)/(3-2) = -1.

We now have the coordinates of one endpoint of NQ (the midpoint) and its slope.

We can use the point-slope form of the equation of a line to find the equation of NQ:

y - 2.5 = -1(x - 2.5)

y - 2.5 = -x + 2.5

y = -x + 5

We know that N is on the line NQ and that it is a distance of 3 units from the midpoint of NQ, which is (2.5, 2.5).

We can use the distance formula to find the coordinates of N:

d = √((x2 - x1)^2 + (y2 - y1)^2)

3 = √((x - 2.5)^2 + (y - 2.5)^2)

Squaring both sides:

9 = (x - 2.5)² + (y - 2.5)^2

We also know that N is on the line y = -x + 5.

We can substitute this into the equation above to get:

9 = (x - 2.5)^2 + (-x + 2.5 - 2.5)^2

9 = (x - 2.5)^2 + (x - 5)^2

9 = x^2 - 5x + 6.25 + x^2 - 10x + 25

0 = 2x^2 - 15x + 30.75

0 = x^2 - 7.5x + 15.375

We can use the quadratic formula to solve for x:

x = (7.5 ± √(7.5² - 4(1)(15.375))) / (2(1))

x = (7.5 ± √(13.875)) / 2

x ≈ 5.08 or x ≈ 2.42

Since vertex N is to the left of vertex M, we choose the smaller value of x: x ≈ 2.42.

Now we can substitute this value of x into the equation y = -x + 5 to find the corresponding value of y:

y ≈ 2.58

Therefore,

A possible coordinate pair for vertex N is (2.42, 2.58).

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