AB and CD are tangent to circle F.
A
D
(5x+9) B
(7x-21)°
Solve for x and y.

Answer:

Store B

Step-by-step explanation:

Since the lowest common multiple of 2 and 3 is 6, so let's find the cost of 6 bags of chips from each store.

Store A

cost for 6 bags of chips

= 3(2.5)

= $7.50

Store B

cost for 6 bags of chips

= 2(3.25)

= $6.50

Since store B offers a cheaper price for 6 bags of chips, it offers a better deal.

Alternatively, you could work out the cost of each bag of chips for both stores.

Below is the answer

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Given:

In circle D, the measure of angle ADC is 108 degrees.

To find:

The measure of angle ABC.

Solution:

Central angle theorem: According to this theorem, the measure of central angle of an arc is twice of the measure of inscribed angle on that arc.

Using the Central angle theorem, we get

\(m\angle ADC=2\times m\angle ABC\)

\(108^\circ=2\times m\angle ABC\)

\(\dfrac{108^\circ}{2}= m\angle ABC\)

\(54^\circ= m\angle ABC\)

Therefore, the measure of angle ABC is 54 degrees.

y can be written as the sum of two orthogonal vectors, one in the span of {u} and one orthogonal to u: y = (-2.5, 2.5) + (3.5, 3.5)

To write y as the sum of two orthogonal vectors, we need to find the projection of y onto u (which will be in the span of {u}) and the difference between y and this projection (which will be orthogonal to u).

First, let's find the projection of y onto u:
proj_u(y) = (y·u / ||u||^2) * u

where "·" represents the dot product and "|| ||" represents the magnitude.

y·u = (1)(5) + (6) (-5) = 5 - 30 = -25
||u||^2 = (5) ^2 + (-5) ^2 = 25 + 25 = 50

proj_u(y) = (-25 / 50) * u = -0.5 * (5, -5) = (-2.5, 2.5)

Now, we find the difference between y and this projection:
y - proj_u(y) = (1 - -2.5, 6 - 2.5) = (3.5, 3.5)

Thus, y can be written as the sum of two orthogonal vectors, one in the span of {u} and one orthogonal to u:
y = (-2.5, 2.5) + (3.5, 3.5)

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Answer:

8/9

Step-by-step explanation:

The general form of linear functions are y = mx+b. Here, m is the slope and b is the y intercept. Therefore we can already see that m = 8/9 as the question is already in the general form y = mx+b.

The graph is misleading because the x-axis scale shows that the given data is more clustered than it actually is.

What is a misleading graph?

A misleading graph, sometimes referred to as a distorted graph, misrepresents data, amounts to statistical abuse, and may lead to the drawing of an inaccurate conclusion.

What is a data set?

A data set is a grouping of connected, discrete pieces of connected data that can be viewed separately, together, or handled as a single unit. A data structure of some kind is used to arrange a data set.

Here, we have

2 events with a cost of 1,000-1,499;

4 events with a cost of 1,500 to 1,999;

3 events with a cost of 2,000 to 2,499;

1 event with a cost of 3,000 to 3,499

We concluded from the given dataset that the cost of the event is plotted on the x-axis.

In a given dataset, the entry from 2500 to 2599 is missing.

The graph generates a point cluster that isn't actually displayed on the data components because of the missing item.

Hence, the graph is misleading because the x-axis scale shows that the given data is more clustered than it actually is.

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Step-by-step explanation:

x^2+6x+5=0

x^2+5x+1x+5=0

x(x+5)+1(x+5)

(x+5)(x+1)

x+5=0 x+1=0

x=-5 x=-1

There are 84 possible student body governments

The given parameters are:

Senior = 7

Junior = 3

Sophomore = 4

The number of student body governments is calculated as:

n = Senior * Junior * Sophomore

This gives

n = 7 * 3 * 4

Evaluate

n = 84

Hence, there are 84 possible student body governments

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Answer:

\(g(x)=2^{x-2}\)

Step-by-step explanation:

Translations

For \(a > 0\)

\(f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}\)

\(f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}\)

\(f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}\)

\(f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}\)

Parent function:  \(f(x)=2^x\)

Translated 2 units right:  \(g(x)=f(x-2)=2^{x-2}\)

We know the rule for shifting right(x is changed)

So

here

For a =2

A number c divided by 8 is greater than or equal to 26:

c/8 ≥ 26

Answer:

11

Step-by-step explanation:

You add the 2 ones side by side and you get 11

X can be expressed as a linear combination of v1 and v2 with the coordinates (a', b') in the basis B.  The coordinate vector [x]B:

[x]B = (a', b')

To determine whether the vector x is in the span V of vectors v1 and v2, we need to check if there exist scalar coefficients a and b such that:

x = a × v1 + b × v2

Given that x = [23 29], v1 = [46 58], and v2 = [61 67], the equation can be written as:

[23 29] = a × [46 58] + b × [61 67]

This equation can be represented in the form of a matrix:

| 46 61 | | a | = | 23 |
| 58 67 | | b | = | 29 |

We can now find the reduced row-echelon form of the augmented matrix to solve for a and b:

| 46 61 23 |
| 58 67 29 |

After row-reducing the matrix, we get:

| 1 0 a' |
| 0 1 b' |

Since the system has a unique solution, x is in the span V of vectors v1 and v2. We can now find the coordinates of x with respect to the basis B=(v1, v2) and write the coordinate vector [x]B:

[x]B = (a', b')

Therefore, x can be expressed as a linear combination of v1 and v2 with the coordinates (a', b') in the basis B.

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Line QT has a 5 unit length.

A line is a geometric object with an endless length and no breadth, depth, or curvature.

Lines are one-dimensional objects since they can exist in two, three, or higher-dimensional regions.

A line segment with two points indicating its endpoints is also referred to as a line in daily speech.

So, using the relationship between the sides of comparable triangles, we have the following.  ΔRST and  ΔRPQ:

   ST/RT = PQ/QR

   RQ = QT + RT

Then,

   ST/RT = PQ/QT + RT

Then, we obtain:

   QT + 5/RT = PQ/QT + RT

Given that QT is the natural number then, QT = 5 units.

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Moving Average and Exponential Smoothing is a method used in a forecasting model for a time series when a trend, seasonal, or cyclical effect is not significant.

When trend, seasonal, or cyclical effects are not significant in a time series, the most appropriate method for forecasting is typically the Moving Average or Exponential Smoothing method. The Moving Average method involves calculating the average of a set of previous observations to forecast the next data point.

The number of previous observations to include in the average is determined by the chosen window size, which can be adjusted based on the level of smoothing desired. On the other hand, the Exponential Smoothing method assigns more weight to recent observations and less weight to older observations. This method assumes that recent data points are more relevant for forecasting future values than older data points.

The level of smoothing can be controlled by adjusting the smoothing parameter. Linear regression and Holt-Winters methods are better suited for time series with significant trends, and seasonal, or cyclical effects. Holt-Winters is a more complex method that considers both trend and seasonal effects in addition to the level of smoothing.

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Answer:

44.8

Step-by-step explanation:

Given: Tyler's grandparents give him $3,000 in savings bonds at birth. Tyler cannot cash out the savings bond until he turns 21.To find: The amount Tyler will receive if he cashes it in on his 21st birthday.

Solution: As given, Tyler's b give him $3,000 in savings bonds at birth. This means the principal amount of the bond is $3,000. Also, the question does not specify the rate of interest or the compounding period for the bond. Since there is no given interest rate or compounding period, it is not possible to determine the exact amount that Tyler will receive on his 21st birthday. However, we do know that the amount he will receive will be more than the initial $3,000because of the accumulation of interest over time.

Based on the time period (birth to 21 years), the amount of interest accumulated on the bond will be more than 100. Therefore, we can estimate that the amount Tyler will receive when he cashes in the bond on his 21st birthday will be at least $6,000 (principal of $3,000 plus more than $3,000 in accumulated interest).The estimated amount is at least $6,000 as the compounding period and interest rate is not given in the question. Hence the estimated amount is $6,000 to the nearest hundredth.

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Savings bond is a security issued by the US Department of the Treasury to offer a higher rate of interest than a typical savings account, commonly used for education expenses.What are savings bondsSavings bonds are a debt security that the US Department of the Treasury issues, often used for education expenses.

Savings bonds offer a higher rate of interest than a regular savings account, though they have a lower interest rate than most bonds. Savings bonds are typically sold at a discount from their face value and do not pay interest unless they are held for at least five years.There are two types of savings bonds:Series EE savings bonds: Purchased at a discount of their face value and issued electronically.

You can buy electronic Series EE savings bonds online at TreasuryDirect.gov. These bonds earn interest until maturity, which is 30 years after they were issued. The interest rate is reset twice a year, on May 1 and November 1. For bonds purchased from May 1 through October 31, 2021, the interest rate is 0.10%.Series I savings bonds: These bonds earn interest based on a combination of a fixed rate and an inflation rate that is adjusted semiannually.

Like Series EE bonds, Series I bonds are sold at face value. You can buy I bonds at TreasuryDirect.gov in electronic form.What happens if you cash out a savings bond before maturity

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There are four levels of measurements in statistics, namely nominal, ordinal, interval, ratio. These levels are important when it comes to analyzing data, since it helps us determine the technique that we can use to support or refute our study.

In the nominal level, we can categorize data but they cannot be ranked. An example would be hair color. In an ordinal data, the data can be both categorize and ranked, but doing mathematical calculation may not make sense. Also, the intervals between rankings doesn't necessarily dictate how close or far apart the data are.

A good example is level of education. In an interval level, the data can be categorized, ranked, and measured but they do not have a true zero. An example could be a range of values that does not include zero. Lastly, in the Ratio level the data can be categorized, rank, and measured, and it has a true zero.

So ratio level is most appropriate for ages of children. Note that ages can be categorized, rank, and measured .Moreover, an age equal to zero means that there is no age or the absence of age.  

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Use the given functions to set up and simplify 1.

3.2x⋅10^5=320000x

m=320000x1=320000x

1.6x⋅(1064m)=1702.4xm

1=1702.4xm

HoPE ThuS HeLPs YOu :)

Answer:

5.12x10^9

Step-by-step explanation: the answers an equation in scientific notation well that's what i got and it was right in my forms. anyways

(3.2 x 10^5 m)x(1.6 x 10^4 m)= 3.2x1.6= 5.12 then you just add 5 plus 4 because that's how much times you had to multiply it by, you  get 10^9

if you still don't get how to do scientific notation jus search it up and look at a video. hope i helped out

Answer:

165 bike

110 bus

Step-by-step explanation:

Given:

The height of the slide from the ground = 12 feet

The angle of depression = 53 degrees

Required:

Find the length of the slide.

Explanation:

The given triangle is the right triangle.

adjacent = 12 ft

we have to find the hypotenuse side.

Let the length of the slide is h ft.

Use the following trigonometric ratio:

Final Answer:

The length of the slide is approximately 20 ft.

Answer:

-0.125

Hope this is right

Answer:- 1/8 as a fraction and - 0.125 as a decimal

Answer:

[B] x = 83, y = 60

Step-by-step explanation:

Find the value of x

we know that

\((x-3)=80\)  -------> by corresponding angles, because the given lines are parallel

Solve for x

\((x-3)=80\)

\(x=80+3\)

\(x=83\)

Find the value of y

we know that

\(x-3+42+(y-2)= 180\)

substitute the value of x and solve for y

\(83-3+42+(y-2)= 180\)

\(80+42-2+y=180\)

\(120+y=180\)

\(y=180-120\)

\(y=60\)

Therefore, the answer is [B] x = 83, y = 60

[RevyBreeze]

Answer:

AC=73

Step-by-step explanation:

Answer: N

Step-by-step explanation:

Answer:

each student gets 3 granola bars

The magnitude of the electric field E at the midpoint between two 10-cm-diameter charged rings, with charges of -21nC and +21nC and a separation of 30 cm, can be calculated using the electric field formula for a charged ring. The magnitude of the force F on a -1.0nC charge placed at the midpoint can be determined using the equation F = qE, where q is the charge and E is the electric field.

To find the magnitude of the electric field E at the midpoint between the two rings, we can use the formula for the electric field of a charged ring:

E = (k * Q) / (2 * π * r)

Where k is the electrostatic constant (approximately 9 * 10^9 Nm^2/C^2), Q is the charge on the ring, and r is the distance from the center of the ring to the point where the electric field is being measured.

Substituting the given values into the equation, we get:

E = (9 * 10^9 Nm^2/C^2 * 21nC) / (2 * π * 0.15m)

Calculating this expression, we find that the magnitude of the electric field at the midpoint is approximately 22,192 N/C.

To find the magnitude of the force F on a -1.0nC charge placed at the midpoint, we can use the equation F = qE, where q is the charge and E is the electric field. Substituting the values, we get:

F = (-1.0nC) * (22,192 N/C)

Calculating this expression, we find that the magnitude of the force on the charge is approximately 22,192 nN.

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Answer:

Approximate: C ≈ 50.27

Exact: C = 16π

Step-by-step explanation:

C = 2πr

We know that r is 8

C = 2π8

C = 16π

C ≈ 50.27

The circumference of a circle is 16π unit²

The circumference of a circle is defined as the linear distance around of circle.

Formula of circumference of a circle (C) = 2πr

Where r is radius of circle

Given radius of circle (r) = 8,

Substitute the value of r,

C = 2π(8)

C = 16π unit²

Substitute π = 3.14,

C ≈ 50.27 (approximate)

Thus, the circumference of a circle is 16π unit²

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Answer:

3 < square root of 12 < 4

Step-by-step explanation:

When estimating square roots find the closest perfect square.

So the previous root of 12 is √9 because it is 3, and the next root is √16 which is 4.

The best estimate for the number \(\sqrt{12}\) is;

⇒ \(3 < \sqrt{12} < 4\)

Here,

The number is \(\sqrt{12}\).

We have to find best estimate for the \(\sqrt{12}\).

What is Square root number?

A square root of a number is a value that, when multiplied by itself, gives the number.

Now,

The number is \(\sqrt{12}\).

Since, \(3 = \sqrt{9}\) and \(4 = \sqrt{16}\)

Hence, \(\sqrt{9} < \sqrt{12} < \sqrt{16}\)

        ⇒  \(3 < \sqrt{12} < 4\)

So, The best estimate for the number \(\sqrt{12}\) is;

⇒ \(3 < \sqrt{12} < 4\)

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Answer:

49

Step-by-step explanation:

Answer:

See below

Step-by-step explanation: