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Answer:

1 + 17 = 18

2 + 16 = 18

3 + 15 = 18

4 + 14 = 18

5 + 13 = 18

6 + 12 = 18

7 + 11  =  18

8 + 10 = 18

9 + 9 = 18

Step-by-step explanation:

Answer:

0+18=18

1+17=18

2+16=18

3+15=18

4+14=18

5+13=18

6+12=18

7+11=18

8+10=18

9+9=18

10+8=18

11+7=18

12+6=18

13+5=18

14+4=18

15+3=18

16+2=18

17+1=18

18+0=18

Answer:900

Step-by-step explanation:

720=.80x

720/.80=900

to check it

900*.20=720

Based on the provided table and equation when the class size is 1, gymnastics is less expensive, and when the class size is 3 or 4, ice skating is less expensive.

Given that y denotes the price and x denotes the number of classes, the gymnastics programmed is completed by the table, whereas the ice skating program is concluded by the equation y = 18x + 20.

Find the cost of the ice skating programmed for classes 1, 2, 3, and 4 as the table already lists the price for each specified number of gymnastics courses.

For 1 class, substitute x = 1 into y = 18x + 20:

y = 18(1) + 20

y = $38

For 2 class, substitute x = 2 into y = 18x + 20:

y = 18(2) + 20

y = $56

For 3 class, substitute x = 3 into y = 18x + 20:

y = 18(3) + 20

y = $74

For 4 class, substitute x = 4 into the equation y = 18x + 20:

y = 18(4) + 20

y = $92

We may infer from the foregoing that gymnastics is less expensive when the number of lessons is 1. When there are three or four courses, ice skating is less expensive.

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Answer: 487.5

Step-by-step explanation:

Formula for Simple interest is

S.I = (P×R×T)/ 100

so, we are given with

P = 1500 ; R = 5% ;

T = 2 years 6 months    

*here we need to convert 6 months in to years

so,

6 months = 1/2 year

T = 6 year + 1/2 year = 13/2 years

Now putting these values in formula

We get;

S.I = (1500×5× 13/2) / 100

Ans : 487.5

Answer:

LOL

Step-by-step explanation:

Answer:

x=-9

y=-2

z=4

Step-by-step explanation:

5x+2y-2z=-57

3x-10y-z=-11

y=-2

5x+2(-2)-2z=-57

3x-10(-2)-z=-11

y = -2

5x-4-2z=-57

3x+20-z=-11

y = -2

5x-2z=-53

3x-z=-31

y = -2

5x-2z=-53

3x+31=z

y = -2

5x-2(3x+31)=-53

3x+31=z

y = -2

5x-6x-64=-53

3x+31=z

y = -2

-x=9

3x+31=z

y = -2

x=-9

3(-9)+31=z

y = -2

x=-9

-27+31=z

y = -2

x=-9

z=4

y = -2

Answer:

To represent the area of a stained-glass mosaic that sits under a parabolic arch, we can use the equation for a parabolic arch, which is of the form

y = a(x - h)^2 + k

where (h,k) is the vertex of the parabola. The width of the parabolic arch at the base is 8 feet, so the vertex of the parabola is located at (4,0). Therefore, the equation for the parabolic arch is

y = a(x - 4)^2

The height of the parabolic arch is 10 feet, so we can represent the area of the stained-glass mosaic as the region where y is between 0 and 10. This can be expressed as the inequality

0 ≤ a(x - 4)^2 ≤ 10

Solving this inequality for x gives us the solution

-2 ≤ x - 4 ≤ 2

which simplifies to

2 ≤ x ≤ 6

Therefore, the quadratic inequality that represents the area of the stained-glass mosaic is

2 ≤ x ≤ 6

Step-by-step explanation:

Answer:

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

According to given details we have:

The equation for the parabola is y = a(x - h)² + k, where (h, k) is vertex.

Substitute h = 4, k = 10:

We know y = 0 at x = 0, substitute to find the value of a:

So the parabola is:

We are looking for the area between the parabola and the x-axis, therefore we need two inequalities:

See attached for reference.

By using the given information we can prove that  m ∠ABC = m ∠EDC.

What are similar angles?

Polygons' corresponding sides and corresponding angles are compared as part of the geometric tests for congruence and similarity. With care taken to maintain the order of adjacency, each side and each angle in one polygon is paired with a side or angle in the other polygon in these tests.

Given:

m ∠1 = m ∠2

m ∠2 = m ∠4

We have to prove that m ∠ABC = m ∠EDC

Let, ∠ABC = ∠1 + ∠2

and  ∠EDC = ∠3 + ∠4

So, m ∠ABC = m ∠1 + m ∠2

and  m ∠EDC = m ∠3 + m ∠4

From the given information,

m ∠1 + m ∠2 = m ∠3 + m ∠4        (Since m ∠1 = m ∠3,  m ∠2 = m ∠4)

⇒ m ∠ABC = m ∠EDC

Hence, by using the given information we can prove that  

m ∠ABC = m ∠EDC.

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There are Three months in a quarter of a year.

To determine what is being asked, divide the total number by the denominator and get the portion using the numerator:

1 year = 4 quarters

1 quarter= [tex]\frac{1}{4}[/tex] year

1 year = 12 months

Thus,

1 quarter = (Total number of months in year) ÷ (Total number of quarters in a year)

1 quarter = [tex]\frac{12}{4}=3[/tex]

So, There are Three months in a quarter of a year.

One year typically refers to a period of 365 days or 12 months. It usually includes the entire calendar year from January 1st to December 31st. It can also refer to a fiscal year (a period of 12 consecutive months used for accounting purposes) or a school year (which may start in late summer).

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There are Three months in a quarter of a year.

To determine what is being asked, divide the total number by the denominator and get the portion using the numerator:

1 year = 4 quarters

1 quarter= [tex]\frac{1}{4}[/tex] year

1 year = 12 months

Thus,

1 quarter = (Total number of months in year) ÷ (Total number of quarters in a year)

1 quarter = [tex]\frac{12}{4} =3[/tex]

So, There are Three months in a quarter of a year.

One year typically refers to a period of 365 days or 12 months. It usually includes the entire calendar year from January 1st to December 31st. It can also refer to a fiscal year (a period of 12 consecutive months used for accounting purposes) or a school year (which may start in late summer).

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The probability that they have an average weight of greater than 10 pounds and less than 15 pounds is 0.84134

In this question we have been given there are 250 dogs at a dog show who weigh an average of 15 pounds, with a standard deviation of 6 pounds. of 10 dogs are chosen at random.

We need to find the probability that they have an average weight of greater than 10 pounds and less than 15 pounds.

Given, μ = 12, σ = 8, n = 4

P(X > 8)

= P(z > (8 - 12 / 8/√4))

= P(z > -1)

= 1 - P(z ≤ -1)

= 1 - [1 - P(z ≤ 1)]

=  P(z ≤ 1)

= 0.84134

Therefore, the required probability is 0.84134

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Answer:

Infinite

Step-by-step explanation:

2x + 12 = 2x + 12

they both are equal

Answer:

y = -3x + 1

Step-by-step explanation:

There are 18 million different choices for a player to pick six numbers from 1 to 51. By using the combinations formula, the required value is obtained.

The combinations formula is as follows:

ⁿCₓ = n!/(n - x)!x!

Where n is the total number of things and x is the required number of things.

It is given that,

In a 6/51 lottery game, a player picks six numbers from 1 to 51.

So, the number of different choices the player has if repetition is not allowed is

ⁿCₓ = n!/(n - x)!x!

Here, n = 51 and x = 6

On substituting the values, we get

⁵¹C₆ = 51!/(51 - 6)!6!

⇒ ⁵¹C₆ = 51!/45!6!

⇒ ⁵¹C₆ = (51 × 50 × 49 × 48 × 47 × 46 × 45!)/45! × 6!

⇒ ⁵¹C₆ = (51 × 50 × 49 × 48 × 47 × 46)/6 × 5 × 4 × 3 × 2 × 1

⇒ ⁵¹C₆ = 17 × 10 × 49 × 47 × 46 = 170 × 105938 = 18,009,460

Therefore, there are 18 million choices for the player to pick six numbers from a set of 51 numbers.

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Answer:

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

The equation should read:

Solve it in below steps:

Correct choice is A.

To find the derivative of f(x) at x = 1, we can use the formula for implicit differentiation:

d/dx[f(x) + x^2[f(x)]^5] = 0

d/dx[f(1) + 1^2[f(1)]^5] = 0

d/dx[2 + 1[2]^5] = 0

d/dx[2 + 1[2]^5] = 0

d/dx[2 + 32] = 0

0 + 32 = 0

Therefore, the derivative of f(x) at x = 1 is 32.

To find the equation of the tangent line to the curve at the given point (pi/2, pi/4), we can use the formula for the slope of a tangent line:

m = f'(x) = d/dx[y sin 12x] / d/dx[x cos 2y]

m = d/dx[pi/4 sin 12(pi/2)] / d/dx[pi/2 cos 2(pi/4)]

m = d/dx[pi/4 sin 6pi] / d/dx[pi/2 cos pi/2]

m = 0 / 0

Since the derivative of the numerator is 0 and the derivative of the denominator is 0, the slope of the tangent line is undefined. This means that the tangent line is vertical and parallel to the y-axis.

The equation of the tangent line at the given point is therefore of the form:

x = c

where c is the x-coordinate of the given point, which is pi/2. Therefore, the equation of the tangent line is:

x = pi/2

Note that this is just the equation of a vertical line with an x-intercept at pi/2.

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The given measurement in scientific notation as [tex]6\times10^9[/tex]. Therefore, option D is the correct answer.

Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as [tex]1.56\times10^7[/tex].

The given distance is 6,000,000,000 miles.

There are 9 zeros in the given number

So, scientific notation is [tex]6\times10^9[/tex]

Therefore, the number in scientific notation is [tex]6\times10^9[/tex].

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Answer:

Yes, there is. It's called a regular 52-gon.

Answer:

7/20 miles

Step-by-step explanation:

get a common denominator

subtract the numerators

then you have the fraction she biked

Therefore , the slope of the ski slope is 39.197°.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

Here ,

Given:

She begins her skiing at an elevation of 1.8 miles above sea level, 1.2 miles east of the ski lodge. At an altitude of 1.2 miles above sea level, she comes to an end 0.3 miles to the east of the ski lodge.

a = 1.2 miles

b =  1.8 miles

x = 1.2 miles

y= a-b = 1.8-1.2 = 0.6 miles

=>y tan A = A1

=> arctan(-) = arctan( 0.6 )

=> 0.68413 radian

A = A1 → degree= 0.68413 * 180 /π = 39.197°

Therefore, the slope of the ski slope is 39.197°.

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Answer:

all the above

Step-by-step explanation:

examples of undefined term are point line and plane

Therefore ,there are 158,184,000 ways to create a license plate in this system.

A selection from a group of separate items is called a combination in mathematics, and the order in which the elements are chosen is irrelevant (unlike permutations). An apple and a pear, an apple and an orange, or a pear and an orange are three combinations of two fruits that can be chosen from a set of three fruits, such as an apple, an orange, and a pear. Formally speaking, a set S's k-combination is a subset of S's k unique components. Two combinations are therefore equal if and only if they have the same elements in both combinations.

According to the counting principle, the total number of ways to obtain a license plate is calculated by multiplying the number of times each of these events might occur together.

The first number (the digits 1 through 9) can be obtained in nine different ways.

There are 26 methods to obtain the first letter. There are 26 ways to obtain the following letter (repetition is acceptable).

There are 26 methods to get the third letter, 10 ways to get the next number (zero is acceptable), and 10 ways to get the following number with repetitions.

How many ways are there to get the next number? 10 ways\s.

Thus ,total options for obtaining a license plate:

9 x 26 x 26 x 26 x 10 x 10=158184000

Therefore ,there are 158,184,000 ways to create a license plate in this system.

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Answer:

B. ​No, the congruent angles are not the included angles.

Step-by-step explanation:

The SAS (Side-Angle-Side) Postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

In the given figure, we can see that two sides of the two triangles are congruent: side AB is congruent to side DE, and side AC is congruent to side DF. However, the included angles, which are the angles formed by these sides, are not congruent. Angle BAC is not congruent to angle EDF.

Since the included angles are not congruent, we cannot use the SAS Postulate to conclude that the two triangles are congruent. Therefore, the correct answer is B: No, the congruent angles are not the included angles.

Answer:

  B.  ​No, the congruent angles are not the included angles.

Step-by-step explanation:

You want to know if the triangles shown are congruent by SAS.

The SAS congruence postulate tells you that two triangles are congruent if the angles between corresponding congruent sides are congruent. (The A=angle is between the S=side in SAS.)

In the diagrams, the marked angles are not between the marked sides. The SAS postulate cannot be used with these triangles.

In short, ...

  No, the congruent angles are not the included angles

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The missing statements and reasons in the proof are:

R3: Alternate Interior ∠s theorem

S4: Reflexive property

R5: ASA

A proof involves statements that are stated on one column, then followed by reasons that justify the statements stated, on another column.

The missing statements and reasons in the given proof above are explained below:

Statement                                                    Reason                                            

1. Parallelogram ABCD with diagonal AC  1. Given

2. AB║CD and AD║BC                               2. Def. of parallelogram

3. ∠1 ≅ ∠2 and ∠3 ≅ ∠4                             3. Alternate Interior ∠s theorem

4. AC ≅ AC                                                  4. Reflexive property

5. ΔABC ≅ ΔCDA                                       5. ASA

6. AB ≅ CD and AD ≅ BC                          6. CPCTC

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Using HCF to determine the integer with smallest number of factors, the value is 24

HCF stands for Highest Common Factor. It is the largest positive integer that divides two or more given numbers without leaving a remainder.

In this problem, we are asked to find number that will have the same number of factors as 2022, we can start by listing all factors of 2022.

The HCF of 2022 are

2022 : 1, 2, 3, 6, 337, 674, 1011, 2022

The factors of 24 are : 1, 2, 3, 4, 6, 8, 12, 24

24 has 8 factors, which is the same number of factors as 2022. 24 is the smallest positive integer with 8 factors.

From the explanation above, the smallest integer with same number of factors as 2022 is 24.

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Answer:

[tex]\boxed{0.49}[/tex]

Step-by-step explanation:

To find the price of one orange, we need to determine how much Gaya and Esteban paid for their oranges in total and then divide that amount by the number of oranges they bought.Gaya paid £1.25 for 1 orange and 1 cauliflower, so she paid £1.25 for her orange.Esteban paid £1.95 for 3 oranges and 1 cauliflower, so he paid £1.95 - £1.25 = £0.70 for his 3 oranges.In total, Gaya and Esteban paid £1.25 + £0.70 = £1.95 for 4 oranges.So, the price of one orange is £1.95 / 4 = £<<1.95/4=0.49>>0.49. Answer: \boxed{0.49}.

The exact length of the polar curve in this problem is given as follows:

320,597 units.

The definition of a polar curve is given as follows:

r(θ).

Then the length of the curve over an interval a ≤ θ ≤ b is given by the definite integral presented as follows:

[tex]L = \int_{a}^{b} \sqrt{r^2 + \left(\frac{dr}{d\theta}\right)^2} d\theta[/tex]

The curve in this problem is given as follows:

[tex]r = e^{2\theta}[/tex]

The derivative is given as follows:

[tex]\frac{dr}{d\theta} = 2e^{2\theta}[/tex]

Then the arc length is given by the integral presented as follows:

[tex]L = \int_{0}^{2\pi} \sqrt{e^{4\theta} + 4e^{4\theta}} d\theta[/tex]

[tex]L = \int_{0}^{2\pi} \sqrt{5e^{4\theta}} d\theta[/tex]

[tex]L = \sqrt{5}(\int_{0}^{2\pi} e^{2\theta} d\theta)[/tex]

[tex]L = \frac{\sqrt{5}}{2}(e^{2\theta})|_{\theta = 0}^{\theta = 2\pi}[/tex]

Applying the Fundamental Theorem of Calculus to solve the double integral, the length of the arc is givena s follows:

[tex]L = \frac{\sqrt{5}}{2}(e^{4\pi} - 1)[/tex]

L = 320,597 units.

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Answer: Yes

Step-by-step explanation:

Most of the time, if a graph passes through the origin it is a proportional relationship!

Answer:

To determine how much money Janet will save by purchasing round coins instead of rectangular bars, we need to find the difference in cost between the two options.

First, we can find the cost of the round coins by plugging 40 ounces into the equation p=27s:

p = 27 * 40 = 1080

Next, we can find the cost of the rectangular bars by plugging 40 ounces into the equation p = 27.5s + 50:

p = 27.5 * 40 + 50 = 1100

The difference in cost between the two options is 1100 - 1080 = $<<1100-1080=20>>20. Therefore, Janet will save $20 by purchasing round coins instead of rectangular bars.

Step-by-step explanation:

SELF EXPLANATORY

The required value of the coefficient of x is given as 12.

A simplified value of the coefficient of x is to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,

In order to simplify the given expression add the like terms first,
8x-3+4x + 3 = 180
x + 4x - 3 + 3 = 180
12x = 180

Thus, the needed coefficient of x value is provided as 12.

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