taotao wants to buy a bracelet. the bracelets have different beads on them, arranged in a circle. if she can choose the colors and placement of the beads, and the beads come in orange, white, and black, how many possible bracelets can she buy?

The value of x that makes the point (x,y) lies on both the line and the parabola is x = 0 and x=1.

The values of x for which the point (x,y) lies on both the line and the parabola, we set the equation of the line y = 4x equal to the equation of the parabola y^2 = 16x.

By substituting y = 4x into the equation of the parabola we get (4x)^2 = 16x and further simplifying it results in 16x^2 = 16x.

so x=1 and x=0

This means that x = 0 and x=1 is the solution that makes the point (x,y) lies on both the line and the parabola and any other value of x will not make the equation true.

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Complete question:

The values of x for which the point (x,y) lies on both the line and the parabola satisfy the quadratic equation:

The equation of line is y = 4x

equation of parabola is [tex]y^2[/tex] = 16x

the rate of change of height at h = 15cm, 0. 0159 cm/s

What is Rate?

A rate in arithmetic is a ratio that contrasts two separate values with various unit systems. For instance, if John types 50 words per minute, that means he types 50 words per minute. We are dealing with a rate because the word "per" is there. The symbol "/" can be used in place of the word "per" in issues.

When two or more similar amounts or numbers are being compared using the same units, a ratio is utilized. When referring to the ratio of one quantity "to" the second quantity in spoken language, it is frequently written with a colon.

Beads are dropped to create a conical pile such that the ratio of its radius to the height of the pile is constant at 2:3.

Volume is increasing at a rate of 5 cm3/s.

The volume of a Cone: 1/3 pi r^2 h

given r/h =2/3

V =0. 0159 cm/s

Hence the rate of change of height at h = 15cm, 0. 0159 cm/s

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Answer:

Step-by-step explanation:

The answer is C. 5x + 15 because the 5 outside the parentheses () is supposed to multiply by what's inside the parentheses. So multiply 5 and x and 5 and 3 (5 * X = 5x) (5 * 3 = 15).

The curvature of the curve is 55/9 in accordance with the provided declaration.

Curve, An abstract phrase used to express the trajectory of a steadily moving particle in mathematics (see continuity). Usually, an equation will create such a route. The term may also be used to describe a linear model or a collection of connected line segments. The IS curve displays variants of interest rates plus production levels where anticipated expenditure and income are equal. The many interest and income configurations along whom the merchandise is in homeostasis are represented by the IS Curve.

[tex]\mathbf{r}(t)=\left\langle 6 t, t^2, \frac{1}{9}\left(t^3\right)\right\rangle[/tex]

So,

[tex]x(t)=6 t, y(t)=t^2, z(t)=\frac{1}{9}\left(t^3\right)[/tex]

Then,

[tex]\begin{aligned}& x^{\prime}(t)=\frac{d}{d t}(6 t) \\& =6 \cdot \frac{d}{d t}(t)\end{aligned}[/tex]

= 6(1)

= 6

[tex]\begin{aligned}& y^{\prime}(t)=\frac{d}{d t}\left(t^2\right) \\& =2 t^{2-1}\end{aligned}[/tex]

= 2t

And,

[tex]\begin{aligned}& z^{\prime}(t)=\frac{d}{d t}\left(\frac{1}{9}\left(t^3\right)\right) \\& =\frac{1}{9}\left(3 t^{3-1}\right) \\& =\frac{1}{9}\left(3 t^2\right) \\& =\frac{1}{3}\left(t^2\right)\end{aligned}[/tex]

Now calculating length of the given curve from 0 to 1,

[tex]\begin{aligned}& L=\int_0^1 \sqrt{(6)^2+(2 t)^2+\left(\frac{1}{3}\left(t^2\right)\right)^2} d t \\& =\int_0^1 \sqrt{(6)^2+2 \cdot 6 \cdot \frac{1}{3}\left(t^2\right)+\left(\frac{1}{3}\left(t^2\right)\right)^2} d t \\& =\int_0^1 \sqrt{\left(6+\frac{1}{3}\left(t^2\right)\right)^2} d t\end{aligned}[/tex]

[tex]\begin{aligned}& =\int_0^1\left(6+\frac{1}{3}\left(t^2\right)\right) d t \\& =\int_0^1 6 d t+\int_0^1 \frac{1}{3}\left(t^2\right) d t \\& =6 \int_0^1 d t+\frac{1}{3} \int_0^1 t^2 d t \\& =6[t]_0^1+\frac{1}{3}\left[\frac{t^{2+1}}{2+1}\right]_0^1 \\& =6[1-0]+\frac{1}{3}\left[\frac{t^3}{3}\right]_0^1\end{aligned}[/tex]

[tex]\begin{aligned}& =6(1)+\frac{1}{3}\left[\frac{1^3}{3}-\frac{0^3}{3}\right] \\& =6+\frac{1}{3}\left[\frac{1}{3}-0\right] \\& =6+\frac{1}{9} \\& =\frac{54+1}{9}\end{aligned}[/tex]

= 55/9

Therefore, required arc length is 55/9

NOTE:

For a vector valued function,

[tex]\mathbf{r}(t)=\langle x(t), y(t), z(t)\rangle[/tex] arc length fro a to b

[tex]L=\int_a^b \sqrt{\left(x^{\prime}(t)\right)^2+\left(y^{\prime}(t)\right)^2+\left(z^{\prime}(t)\right)^2} d t[/tex]

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Answer:

I think there are 4 separate terms in that algerbric equation

Answer: To determine if there is evidence to suggest that the proportion of individuals who caught pertussis and were not up to date on their booster shot is higher than those that were, we can conduct a two-sample proportion test.

The null hypothesis is that the proportion of individuals who caught pertussis and were not up to date on their booster shot is the same as the proportion of individuals who caught pertussis and were up to date on their booster shot.

H0: p1 = p2

The alternative hypothesis is that the proportion of individuals who caught pertussis and were not up to date on their booster shot is higher than the proportion of individuals who caught pertussis and were up to date on their booster shot.

Ha: p1 > p2

Using a two-sample proportion test with a significance level of 0.05, we can calculate the test statistic and p-value.

p1 = 15/132 = 0.1136

p2 = 11/368 = 0.0301

p = (15 + 11)/(132 + 368) = 0.0564

SE = sqrt{p(1-p)((1/132)+(1/368))} = 0.0165

z = (p1 - p2) / SE = 4.0491

p-value = P(z > 4.0491) = 0.0000

Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is evidence to suggest that the proportion of individuals who caught pertussis and were not up to date on their booster shot is higher than those that were.

Step-by-step explanation:

Proven that expressions x = -1 in the quadratic function (2x + 1)(2x - 1) - 4(x + 2)² = -1.

Using coefficients, unknowable variables, algebraic operations, and constants, a mathematical expression is called an algebraic expression. A sign of equality, however, is not permitted in an expression.

Mathematical expressions and phrases can be of many different kinds. Let's look at the connections between algebraic expressions and numerical expressions and equation.

Given that

(2x + 1)(2x - 1) - 4(x + 2)² = -1

Apply a² - b² = (a + b)(a - b)

(2x)² - (1)² - 4(x + 2)² = -1

4x² - 1 - 4(x + 2)² = -1

Apply (a + b)² = a² +b² + 2ab

4x² - 1 - 4  (x² + 2² + 2x×2) = -1

4x² - 1 - 4x² -16 - 16x = -1

4x² - 4x² - 16x -16 - 1 = -1

-16x -16 - 1 = -1

-16x -16 = -1 + 1

-16x  =  16

x = 16/-16

x = -1

Hence, proven that expressions x = -1 in the quadratic function (2x + 1)(2x - 1) - 4(x + 2)² = -1.

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Step-by-step explanation:

Let x be the number of bricks Ram laid.

Shyam laid x/2 bricks.

Therefore, x + x/2 + 250 = x(3/2) + 250 = x(3/2) = 300

x = (2*300)/3 = 200

Ram laid 200 bricks.

Shyam laid 200/2 = 100 bricks.

The width of the last little parallelogram, 10/3, is determined by the provided statement.

Furthermore, despite the fact that this is never the case, every rhombus is considered to be a parallelogram. A quadrilateral is a form that is flat. They arrive in quartets. A parallelogram is formed by two opposing sides that are flat and proportional to one another. Parallelograms come in 4 distinct varieties, including 3 unique varieties. Rhombuses, triangular shapes, cubes, and squares are the four types.

The diagonal area products are equal.

Divide the two sides by 6 20/6 = x = 10/3 since 4*5 Equals 6 * x 20 Equals 6 * x

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The complete question is-

A large parallelogram is divided into four small parallelograms as shown. The areas of three of the four small parallelograms are labeled in the diagram. What is the area of the remaining small parallelogram?

Answer:

40 peaches.

Step-by-step explanation:

We can set up an equation using this information:

(x + 3) * 5 = x * 8

Expanding and simplifying the equation:

5x + 15 = 8x

Subtracting 5x from both sides:

15 = 3x

Dividing both sides by 3:

x = 5

So, if the peaches were shared among 8 people, each person would get 5 peaches. If each person got 3 more peaches if the peaches were shared among 5 people, each person would get 8 peaches.

So the box has 8 peaches per 5 people, 8*5 = 40 peaches

Answer:

There are 8 peaches in the box.

Step-by-step explanation:

It states that if the peaches were shared among 8 people, each person would get x/8 peaches, and if the peaches were shared among 5 people, each person would get x/5 + 3 peaches.

To find the total number of peaches in the box, we can use the equation to find the value of x.

We know that x/8 = x/5 + 3 , we can multiply both sides by 8*5 to get rid of the denominator

8(x/8) = 8(x/5 + 3)

x = 8(x/5 + 3)

5x = 8x + 24

Subtracting x from both sides

3x = 24

Dividing both sides by 4

x = 8

There are 8 peaches in the box.

Answer: [tex]4y=-3x+16[/tex]

Step-by-step explanation:

For there to be infinitely many solutions, the equations must represent the same graph.

The points [tex](0,4)[/tex] and [tex](4,1)[/tex] lie on the line. So, the slope is [tex]\frac{4-1}{0-4}=-\frac{3}{4}[/tex]. As the [tex]y[/tex]-intercept is [tex](0,4)[/tex], the equation is [tex]y=-\frac{3}{4}x+4[/tex].

Multiplying both sides by [tex]4[/tex] yields [tex]4y=-3x+16[/tex].

Answer:

Tn = 4 + (n – 1)3

is the arithmetic sequence for the nth term

Step-by-step explanation:

formula for an arithmetic sequence is

[tex]tn = a + ( n - 1)d[/tex]

where:-

Tn = nth term

a = first term

n = number of terms

d = common difference.

now back to the question

the 8th term of an arithmetic sequence is 25.

that will be written as

[tex]t8 = a \: + ( 8 - 1)d = 25[/tex]

[tex]a + (7 )d = 25 \: \: \: \: .....eqn1[/tex]

and the 14th term is 43

this will be written as

[tex]t14 = a + (14 - 1 )d = 43[/tex]

[tex]a + 13d = 43 \: \: \: \: .....eqn2[/tex]

subtract eqn 1 from 2

a – a, 13d – 7d, 43–25

[tex]6d = 18[/tex]

divide both sides by (6)

[tex] \frac{6d \\ }{6} = \frac{18}{6} [/tex]

d = 3

now that we know d = 3 let's substitute it in eqn 1 above.

a + 7d = 25

a + 7(3) = 25

a +21 = 25

a = 25 – 21

a = 4

now the normal arithmetic sequence given will be

[tex]tn = 4 + (n - 1 )3[/tex]

I hope this helps

Answer:

To solve this problem, we will use the following steps:

Step 1: Convert the minutes to hours by dividing the minutes by 60: 45 minutes / 60 = 0.75 hours

Step 2: Add the hours and minutes together to find the total time: 3 hours + 0.75 hours = 3.75 hours

Step 3: Multiply the total time by the average speed to find the distance: 3.75 hours * 80 km/hour = 300 km

Final Answer: Tim drives 300 km.

An absolute value graph has one axis of symmetry that passes through the vertex.

From the preceding graph, it can be seen that when the coefficient of x increases, the v form moves closer to the line of symmetry and vice versa.

However, it is not always the case that the symmetry line and the y-axis coincide.

For instance:

A line of symmetry for the equation -y=|3x-6|-5 runs parallel to the y-axis and through the x-axis.

You must be aware of the location of the graph's vertex and the line of symmetry.

To obtain the value of x, which will be the x coordinate for the vertex of the graph, take the equation inside the absolute value and equal it with 0. Then, replace the value of x with the main equation to obtain the y coordinate for the vertex of the graph.

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The probability that the person participates in at least one school-sponsored activity given that the student works part-time is 0.58.

The possibility of an event or outcome occurring based on the existence of a prior event or outcome is known as conditional probability.

Assume that events A and B are two independent occurrences with probabilities P(A) and P(B), respectively, such that the probability that event B will occur given that event A is given by: P(B|A) = P(A∩B)/P (A)

Given:

Percentage of the students who have part-time jobs, P(A) = 73%

Percentage of the students who participate in at least one school-sponsored activity, P(B)= 65%

Percentage of the students who work part-time and participate in at least one school-sponsored activity, P(A∩B) = 42%

The probability that the person participates in at least one school-sponsored activity given that the student works part-time is:

P(B|A) = P(A∩B)/P(A)

          = 42/73

          = 0.58

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Answer:

0.575

Step-by-step explanation:

nice job

Answer:

hope this helps you to understand.

If the value of 'a' changed from -a  to +a , the equation of the directrix of the parabola is x= a

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

If parabola is y² = 4ax and the equation of the directrix of the parabola is x= -a

when parabola becomes y² = - 4ax and the equation of the directrix of the parabola is x= a

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The length and breadth of a rectangle with an area of 2 square feet and a perimeter of 9 feet are 4 feet and 0.5 feet, respectively.

The size of a region on a surface is measured in area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina. The total space occupied by a flat (2-D) surface or the form of an item is defined as its area. Draw a square on a sheet of paper using a pencil. It is a two-dimensional figure. The area of the form on the paper is referred to as its Area. Consider your square to be made up of smaller unit squares.

Here,

area=2

perimeter=9

lw=2

w=2/l

2l+2w=9

2l+2*(2/l)=9

2l+4/l=9

2l²+4=9l

2l²-9l+4=0

2l²-8l-1l+4=0

2l(l-4)-1(l-4)=0

(2l-1)(l-4)=0

l=1/2, 4

l=4 feet

w=2/l

w=2/4

w=0.5 feet

l²+w²=4²+(0.5)²

=16.25

The length and width of rectangle whose area is 2 square feet and perimeter as 9 feet is 4 feet and 0.5 feet.

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Answer:

(0,-3)

Step-by-step explanation:

C( 5,1)

5 is the horizontal value.  It is the distance from zero.  If we go 5 units left we will be at 0

1 is the vertical value.  Is is the distance above the x axis.  If we go down 4 units, we will be at -3

(0,-3)

Answer:

Step-by-step explanation:

The equation given:

[tex]15 + \left(3x\right) = 24[/tex]

Our goal is to find x. To find x, what I like to do is add the given values together, then subtract them by 24 to find x's value.

[tex]15 + 3 = 18\\24 - 18 = x\\x = 6[/tex]

Hope this helps!

Answer:

1st number = 5.5

2nd number = -1.25

Step-by-step explanation:

1)  7x + 6y = 31     (multiply entire equation by 3) → 21x + 18y = 93

2)  3x - 10y + 29  (multiply entire equation by 7) →  21x - 70y = 203

3)    21x + 18y = 93

4)  -(21x - 70y = 203)    now subtract equation (4) from equation (3) to make the x terms drop out

0 + 88y = -110

y = -110/88 = -1.25   now plug this into equation (1) and solve for x

7x + 6(-1.25) = 31

7x = 38.5

x = 38.5/7 = 5.5

The measure of angle BAC from the given rectangle ABCD is 39°.

A rectangle is a closed two-dimensional figure with four sides. The opposite sides of a rectangle are equal and parallel to each other and all the angles of a rectangle are equal to 90°.

In the given rectangle ABCD, diagonals AC and BD bisect each other E.

27) m∠DAC=2x+4 and m∠BAC=3x+1,

Here, m∠DAC+m∠BAC=90°

2x+4+3x+1=90°

5x+5=90°

5x=85

x=17

So, m∠BAC=3x+1=52

28) m∠BDC=7x+1 and m∠ADB=9x-7,

Here, m∠BDC+m∠ADB=90°

7x+1+9x-7=90

16x-6=90

16x=96

x=6

So, m∠BDC=7x+1=43°

29) m∠ABD=7x-31 and m∠CDB=4x+5,

Here, 7x-31=4x+5

3x=36

x=12

m∠ABD=7x-31 =53°

30) m∠BAC=x+3 and m∠CAD=x+15

Here, m∠BAC+m∠CAD=90°

x+3+x+15=90

2x+18=90

2x=72

x=36

m∠BAC=x+3=39°

Therefore, the measure of angle BAC from the given rectangle ABCD is 39°.

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Answer:

1300.00%

Step-by-step explanation:

Answer:

B. Apples cost $2.50/pound

Step-by-step explanation:

B would be a multiplicative relationship because you would multiply the number of pounds by 2.50

Answer:

6x^2y

Solution

6x2 y

Step-by-step explanation:

hopefully this helped.bye:)

In order for the second plan to be preferable, a greater amount of 249.6 minutes would have to be used in one month.

Let

x -----> the number of minutes in a month

y ----> the charge  monthly

we know that

First Plan

y= 0.23 x ----> equation A

Second Plan

y= 0.12x+34.95 ----> equation B

Equate the equations A and B and solve for x

so x= 249.6

For x< 249.6  ----> is preferable the first plan

For  x> 249.6 ----> is preferable the second plan

therefore

In order for the second plan to be preferable, a greater amount of 249.6 minutes would have to be used in one month.

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Answer:

29/14

Explanataion:

Answer: its 1.6667.

Answer:

Step-by-step explanation

3*X=5

X=5/3

X=1.67