Step 2: Look at the second part of the word problem.

Cadence has 16 more blue-eyed dolls than green-eyed dolls.
Let b represent the dolls with blue eyes.

Let g represent the dolls with green eyes.

Write an equation for this part of the word problem.

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.

Answer:

all the above

Step-by-step explanation:

examples of undefined term are point line and plane

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: 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

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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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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Turn 33.3 into a fraction:

Write down 33.3 like this:

[tex]\dfrac{33.3}{1}[/tex]

Multiply the numerator and denominator by 10(since there is 1 digit after the decimal):

[tex]\dfrac{33.3\times10}{1\times10} \rightarrow\dfrac{333}{10}[/tex]

[tex]\dfrac{333}{10}[/tex] would be the fraction form of [tex]33.3[/tex].

To turn [tex]\dfrac{333}{10}[/tex] into a decimal, divide the numerator by the denominator:

[tex]333\div10=33.3[/tex]

Hope this helps!

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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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:

y = -3x + 1

Step-by-step explanation:

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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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

<95141404393>

Answer:

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

The equation should read:

Solve it in below steps:

Correct choice is A.

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

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:

[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}.

Answer:

Step-by-step explanation:

0 is the answer

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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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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The retail price of the driver of the clubs after will be $400.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

A golf store buys a driver at a discount cost of $200. Mr. Nganga discovered that the driver was increased by 100 percent.

The retail price of the clubs will be given as,

⇒ $200 x (1 + 100%)

⇒ $200 x (1 + 1)

⇒ $200 x 2

⇒ $400

The retail price of the driver of the clubs after will be $400.

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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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The lightbulb should be placed at the co-ordinate F(0,1)

The general equation of a parabola is as y²=4ax for a parabola opening towards the positive x-axis.

Here a represents the point on the x-axis where the focal point lies and through which the directrix passes.

For the given question,

Equation of Parabola: x²=4y

Comparing the given equation to standard parabolic equation for parabola on y-axis( x²= 4ay)

Then,  x²=4y: x²=4ay

thus value of a=1

Hence, the focal point of the parabola will be (0,1)

Since the lightbulb is to be placed on the focal point of the parabolic mirror, the lightbulb would be placed at a unit distance away from the vertex of the parabola

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A matched-subjects study and an independent-measures study both included 17 participants.

In statistics, the number of degrees of freedom is the number of values in the final computation of a statistic that are free to change. Estimates of statistical parameters might be based upon differing quantities of information or data. Degrees of freedom refer to the maximum number of logically independent values in a data sample, which are values with the freedom to vary. Degrees of freedom is calculated by subtracting one from the number of items within the data sample.

Here,

Sample size=degree of freedom(df)+1

=16+1

=17

17 individuals participated in each study of a matched-subjects study and an independent-measures study both.

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Answer:900

Step-by-step explanation:

720=.80x

720/.80=900

to check it

900*.20=720

Answer:

Infinite

Step-by-step explanation:

2x + 12 = 2x + 12

they both are equal

Answer: Yes

Step-by-step explanation:

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

Answer:

7/20 miles

Step-by-step explanation:

get a common denominator

subtract the numerators

then you have the fraction she biked

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:

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

Answer:

LOL

Step-by-step explanation: