suppose the variable x, the modified dental anxiety scale scores, is normally distributed with a mean score of 11 and standard deviation of 4. (a) what is the probability that the modified dental anxiety scale scores is higher than 13? (b) what is the probability that the modified dental anxiety scale scores is lower than 10? (c) what is the probability that the modified dental anxiety scale scores is between 15 and 20? (d) find the modified dental anxiety scale score so that only 1% will exceed (higher than). (e) find the modified dental anxiety scale scores so that only 20% will be lower than.

Answers

Answer 1

(a) The probability that the modified dental anxiety scale score is higher than 13 is approximately 0.3085. (b) The probability that the score is lower than 10 is approximately 0.4013. (c) The probability that the score is between 15 and 20 is approximately 0.1465. (d) A score of approximately 20.32 will have only 1% exceeding it. (e) A score of approximately 7.64 will have only 20% lower than it.

To solve the given problems, we can utilize the properties of the normal distribution and standardize the scores using z-scores.

(a) Probability that the score is higher than 13:

First, we calculate the z-score:

z = (13 - 11) / 4 = 0.5

Using a standard normal distribution table or a calculator, we find the probability associated with the z-score of 0.5, which is approximately 0.3085. Therefore, the probability that the score is higher than 13 is 0.3085.

(b) Probability that the score is lower than 10:

Similarly, we calculate the z-score:

z = (10 - 11) / 4 = -0.25

Using the standard normal distribution table or a calculator, we find the probability associated with the z-score of -0.25, which is approximately 0.4013. Therefore, the probability that the score is lower than 10 is 0.4013.

(c) Probability that the score is between 15 and 20:

We calculate the z-scores for both values:

z1 = (15 - 11) / 4 = 1

z2 = (20 - 11) / 4 = 2.25

Using the standard normal distribution table or a calculator, we find the probabilities associated with the z-scores of 1 and 2.25. The probability associated with z = 1 is approximately 0.8413, and the probability associated with z = 2.25 is approximately 0.9878. Therefore, the probability that the score is between 15 and 20 is 0.9878 - 0.8413 = 0.1465.

(d) Modified dental anxiety scale score for which only 1% will exceed (higher than)

We need to find the z-score that corresponds to the cumulative probability of 0.99 (1% will exceed). Using the standard normal distribution table or a calculator, we find the z-score associated with a cumulative probability of 0.99, which is approximately 2.33. We can then use the z-score formula to find the corresponding score:

x = (z * standard deviation) + mean

x = (2.33 * 4) + 11

x ≈ 20.32

Therefore, a modified dental anxiety scale score of approximately 20.32 will have only 1% exceeding (higher than) it.

e) Modified dental anxiety scale score for which only 20% will be lower than, We need to find the z-score that corresponds to the cumulative probability of 0.20 (20% will be lower than).

Using the standard normal distribution table or a calculator, we find the z-score associated with a cumulative probability of 0.20, which is approximately -0.84. We can then use the z-score formula to find the corresponding score:

x = (z * standard deviation) + mean

x = (-0.84 * 4) + 11

x ≈ 7.64

Therefore, a modified dental anxiety scale score of approximately 7.64 will have only 20% lower than it.

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Related Questions

Please help!

This table shows the calories of several sandwiches at a restaurant. Find the mean and mean absolute deviation of this set of data, and then describe what the mean absolute deviation represents.


Sandwich Calories

242 290

290 280

390 350

Answers

The MAD of 42 calories indicates calorie values of the sandwiches deviate from the mean by 42 calories.

What is the mean and mean absolute deviation?

A mean means the average of a data set found by adding all numbers together and then dividing the sum of the numbers by the number of numbers.

Mean = Ef/n

Mean = (242 + 290 + 290 + 280 + 390 + 350) / 6

Mean = 1842 / 6

Mean = 307 calories

The mean absolute deviation represents the average amount of deviation or variation of the data points from the mean.

The absolute deviations from the mean:

|242 - 307| = 65

|290 - 307| = 17

|290 - 307| = 17

|280 - 307| = 27

|390 - 307| = 83

|350 - 307| = 43

The mean absolute deviation (MAD) is:

= (65 + 17 + 17 + 27 + 83 + 43) / 6

= 252 / 6

= 42 calories.

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for the following function, find the taylor series centered at =6 and give the first 5 nonzero terms of the taylor series. write the interval of convergence of the series. f(x) = ln(x)

Answers

The interval of convergence is (6-1/6, 6+1/6) = (35/6, 37/6).

To find the Taylor series of f(x) = ln(x) centered at c = 6, we first need to find the derivatives of f(x). We have:
f(x) = ln(x)
f'(x) = 1/x
f''(x) = -1/x^2
f'''(x) = 2/x^3
f''''(x) = -6/x^4
The Taylor series formula for a function centered at c is:
f(x) = f(c) + f'(c)(x-c)/1! + f''(c)(x-c)^2/2! + f'''(c)(x-c)^3/3! + ...
Plugging in the derivatives of f(x) and c = 6, we get:
f(x) = ln(6) + (1/6)(x-6) - (1/72)(x-6)^2 + (1/216)(x-6)^3 - (1/864)(x-6)^4 + ...
The first five nonzero terms are:
ln(6) + (1/6)(x-6) - (1/72)(x-6)^2 + (1/216)(x-6)^3 - (1/864)(x-6)^4
To find the interval of convergence of the series, we need to check the radius of convergence. The formula for the radius of convergence of a Taylor series centered at c is:
R = lim n->inf |(f^(n)(c))/n!|
Using the derivatives we calculated earlier, we have:
R = lim n->inf |(-1)^(n+1)/(n*6^(n-1))|
Using the ratio test, we can show that this limit is equal to 1/6, so the radius of convergence is R = 1/6. Therefore, the interval of convergence is (6-1/6, 6+1/6) = (35/6, 37/6).

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2x + 5 = 39 what is the answer ​

Answers

the answer is x = 17

"Another name for Phase 5: Systems Implementation is ________.
A) Feasibility
B) Conversion
C) Analysis
D) Development"

Answers

Phase 5: The system of implementation is conversion.

Option B is the correct answer.

We have,

Phase 5 of the system development life cycle is commonly referred to as "Conversion" or "Systems Implementation."

During this phase,

The focus shifts from planning and designing the system to actually implementing it.

This phase involves the conversion of the old system to the new system, which includes activities such as data conversion, software installation, hardware setup, user training, and system testing.

The term "Conversion" is used because it signifies the transition from the old system to the new system.

It involves migrating data, processes, and operations from the existing system to the new system.

This phase ensures that the newly developed system is successfully integrated into the organization and becomes fully operational.

Thus,

Phase 5: The system of implementation is conversion.

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You randomly choose a tile. Without replacing the first tile, you choose a second tile. Find the
probability of the compound event. Write your answer as a fraction or percent rounded to the
nearest tenth.


Need help asap

Answers

The calculated probability that both tiles are even is 2/7

Calculating the probability that both tiles are even?

from the question, we have the following parameters that can be used in our computation:

Tiles = 7

Even tiles = 4

So, we have

P(Even) = 4/7

Without replacement, we have

P(Even | Even) = 3/6

Simplify

P(Even | Even) = 1/2

Using the above as a guide, we have the following:

P(Even, Even) = 4/7 * 1/2

Evaluate the products

So, we have

P(Even, Even) = 2/7

Hence, the probability that both tiles are even is 2/7

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a company is marketing an investment opportunity to four potential customers. the company believes that its probability of making a sale is 0.5 for each of the first three customers but that it is only 0.1 for the fourth customer. the customers' purchases are independent of one another. calculate the probability that at most two customers purchase the investment

Answers

The probability that at most two customers purchase the investment is 0.1875 or 18.75%.

To calculate the probability that at most two customers purchase the investment,  to calculate the probabilities for each possible outcome: 0, 1, and 2 customers purchasing the investment, and then sum them up.

Let's consider the customers as A, B, C, and D, with D being the fourth customer.

Probability of 0 customers purchasing:

P(0 customers) = (1 - probability of sale)²number of customers

= (1 - 0.5)²4

= 0.0625

Probability of 1 customer purchasing:

P(1 customer) = (probability of sale)²1 ×(1 - probability of sale)²3 (since 3 customers won't purchase)

= 0.5²1 ×0.5²3

= 0.5 × 0.125

= 0.0625

Probability of 2 customers purchasing:

P(2 customers) = (probability of sale)²2 × (1 - probability of sale)²2 (since 2 customers will purchase)

= 0.5²2 ×0.5²2

= 0.25 × 0.25

= 0.0625

Now  sum up these probabilities to find the probability that at most two customers purchase the investment:

P(at most 2 customers) = P(0 customers) + P(1 customer) + P(2 customers)

= 0.0625 + 0.0625 + 0.0625

= 0.1875

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i need help with this ASAP

Answers

for a, draw a line around the middle of all the point like the average spot, and for b use that line to check where 6 hours meets the line and that’s the answer

ad←→ is tangent to circle b at point c. the measure of ∠abc is 40º. what is the measure of ∠bac?

Answers

the measure of ∠bac, which is formed by the radius of the circle and the tangent line, is also 90º. This is because ∠bac and ∠abc are complementary angles, meaning their measures add up to 90º.

When a tangent line is drawn to a circle at a specific point, it forms a right angle with the radius of the circle that passes through that point. In this case, the tangent line ad←→ is drawn to circle b at point c. The angle ∠abc is given as 40º.

Since ∠abc is formed between the tangent line ad←→ and the radius of the circle that passes through point c, it is a right angle. By definition, a right angle measures 90º.

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Identify the type of conic section whose equation is given and find the vertices and foci 4x2=y2+4

Answers

The given equation represents an ellipse.

What type of conic section does the equation represent?

To identify the type of conic section, we compare the given equation with the standard forms of conic sections.The equation [tex]4x^2 = y^2 + 4[/tex] can be rearranged as [tex](x^2)/1 + (y^2)/(4/4) = 1[/tex], which is in the form[tex](x^2)/(a^2) + (y^2)/(b^2) = 1.[/tex]Since the coefficients of [tex]x^2[/tex] and [tex]y^2[/tex] are positive and not equal, and the denominators of [tex]x^2[/tex] and [tex]y^2[/tex] are different, the equation represents an ellipse.

To find the vertices and foci of the ellipse:

The vertices of an ellipse are located on the major axis. In this case, the major axis is along the y-axis since[tex]b^2 (4/4)[/tex] is larger than[tex]a^2 (1)[/tex].

So, the vertices are at (0, ±a), where a is the square root of the denominator of [tex]y^2 (4/4)[/tex], which is 2.

Therefore, the vertices are (0, 2) and (0, -2).

To find the foci of the ellipse, we can use the relationship [tex]c^2 = a^2 - b^2[/tex], where c represents the distance from the center to each focus.

In this case, [tex]a^2[/tex]is 1 and [tex]b^2[/tex] is 4/4. Substituting the values, we get [tex]c^2 = 1 - 4/4[/tex]= 1 - 1 = 0.

Since [tex]c^2[/tex] is zero, it means that the foci coincide with the center of the ellipse.

Therefore, the foci are located at (0, 0).

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give an example of a linear transformation whose image is the line spanned by ⎡ ⎣ 7 6 5 ⎤ ⎦ in r3.

Answers

Suppose we have the vector ⎡ ⎣ 1 2 3 ⎤ ⎦ in R3. Then its projection onto L is:

   T ⎡ ⎣ 1 2 3 ⎤ ⎦ = P ⎡ ⎣ 1 2 3 ⎤ ⎦
                         = (⎡ ⎣ 1 2 3 ⎤ ⎦ · ⎡ ⎣ 7/9 6/9 5/9 ⎤ ⎦)⎡ ⎣ 7/9 6/9 5/9 ⎤ ⎦
                         = (1/3)⎡ ⎣ 7 6 5 ⎤ ⎦
                         = ⎡ ⎣ 7/3 2 5/3 ⎤ ⎦

And indeed, we see that this vector lies on L.

Let's call the line spanned by ⎡ ⎣ 7 6 5 ⎤ ⎦ in R3 "L". To create a linear transformation whose image is L, we need to map every vector in R3 to a vector on L. One way to do this is to project every vector onto L.
Here's how to do that:
- First, find a unit vector that lies on L. We can do this by normalizing the vector ⎡ ⎣ 7 6 5 ⎤ ⎦, which gives us:
   ⎡ ⎣ 7/9 6/9 5/9 ⎤ ⎦
- Next, let's call this unit vector "u". We can create a projection matrix P that projects any vector v in R3 onto L by the formula P(v) = (v · u)u. Here, · denotes the dot product.
So the linear transformation T(v) = P(v) is a linear transformation whose image is L. In other words, T(R3) = L.

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a scatter plot would be useful for question 17 options: showing the trend of sales, over time, of five different brands of blank dvds showing the relationship between the sales of blank cds and blank dvds showing the top selling brands of blank dvds showing the relative number of sales of four different brands of blank dvds

Answers

A scatter plot would be useful for showing the trend of sales, over time, of five different brands of blank DVDs. So, the correct answer is B).

A scatter plot is a type of graph that represents the relationship between two variables. It is particularly useful for showing the trend or pattern in data over time.

In this case, option B is the most appropriate because it involves plotting the sales data of different brands of blank DVDs over time. The scatter plot would allow for visualizing how the sales of each brand vary over different time periods, enabling the identification of any trends or patterns in the sales data.

So, the correct option is B).

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--The given question is incomplete, the complete question is given below " A scatter plot would be useful for

A. Showing the relative number of sales of four different brands of blank DVDs

B. Showing the trend of sales, over time, of five different brands of blank DVDs

C. Showing the relationship between the sales of blank CDs and blank DVDs

D. Showing the top selling brands of blank DVDs"--

a baker makes a layered cake with two layers that are rectangular prisms each layer is 2 inches tall what is the volumeof the cake

Answers

The volume of the layered cake is 16 cubic inches

How to calculate the volume of the layered cake

From the question, we have the following parameters that can be used in our computation:

Layers = 2

Length of each layer = 2 inches

Using the above as a guide, we have the following:

Dimension = 2 inches by 2 inches by 2 * 2 inches

The volume of the layered cake can be calculated as

Volume = Product of dimensions

substitute the known values in the above equation, so, we have the following representation

Volume = 2 * 2 * 2 * 2

Evaluate

Volume = 16 cubic inches

Hence, the volume of the layered cake is 16 cubic inches

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The table defines a discrete probability distribution. Find the expected value of the distribution.

x 0 1 2 3
Pr(x) 44930 44942 45062 44993

Answers

To find the expected value of a discrete probability distribution, we need to multiply each possible value by its probability and then add up the results.

We can set up a table to make the calculation easier:
x | Pr(x) | x * Pr(x)
--|------|---------
0 | 44930 | 0
1 | 44942 | 44942
2 | 45062 | 90124
3 | 44993 | 134979
To find the expected value, we add up the values in the last column: 0 + 44942 + 90124 + 134979 = 270045
So the expected value of this distribution is three hundred and seventy thousand forty-five (270,045).

In this case, the sum of probabilities is 44930 + 44942 + 45062 + 44993 = 179927. Now, let's convert the probabilities into decimal form: Pr(0) = 44930/179927, Pr(1) = 44942/179927, Pr(2) = 45062/179927, and Pr(3) = 44993/179927.
Now, you can calculate the expected value using the formula E(x) = Σ [x * Pr(x)]. E(x) = (0 * 44930/179927) + (1 * 44942/179927) + (2 * 45062/179927) + (3 * 44993/179927). By calculating the result, you get E(x) ≈ 1.499, which is the expected value of the distribution.

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the mast of a flag broke during a storm. The bottom of the mast, which height is 7m, is still planted verticlly in the ground, but the top fell over and its tip is now touching the ground, 24 metres from the base of the mast. What was the mast's height before it broke.

Answers

Based on the information, thee mast was 31 meters tall before it broke.

How to calculate the height

In order to solve this, we can use the Pythagorean Theorem.

We can set up the following equation:

(24 meters)² = (7 meters)² + (height of top of mast)²

Solve for the height of the top of the mast:

576 = 49 + (height of top of mast)²

527 = (height of top of mast)²

Take the square root of both sides:

23 = height of top of mast

Therefore, the mast was 31 meters tall before it broke.

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What is the chance of pulling a 4 and a club back to back from a deck of cards, if you do not replace the card?

Answers

The chance of pulling a 4 and a club is 0.0637

How to determine the chance of pulling a 4 and a club

From the question, we have the following parameters that can be used in our computation:

A standard deck of cards

In a standard deck of cards, we have

Cards = 52

Number of 4's = 13

Number of clubs = 13

Selecting 4 and c back to back from a deck of cards, if you do not replace the card, we have

P = 13/52 * 13/51

Evaluate

P = 0.0637

Hence, the probability is 0.0637

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One angle measures triangle that’s 84. the other two angles are in a ratio of 3:5, what are the measures of those two angles? No explanation just answer it’ll work out best!

Answers

The other two angles in a triangle are,

⇒ 36 degree

⇒ 60 degree

We have to given that;

One angle measures triangle that’s 84.

And, the other two angles are in a ratio of 3 : 5.

Since, the other two angles are in a ratio of 3 : 5.

Hence, the other two angles are,

⇒ 3x

⇒ 5x

Since, A triangle is a 3 - sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Hence, WE get;

⇒ 84 + 3x + 5x = 180

⇒ 8x = 180 - 84

⇒ 8x = 96

⇒ x = 96 / 8

⇒ x = 12

So, the other two angles are,

⇒ 3x = 3 × 12 = 36°

⇒ 5x = 5 × 12 = 60°

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given the function f(x)=-5|x+1|+3 for what values of c is f (x) =-12

Answers

Answer: x=2 and x=-4

Step-by-step explanation:

under what conditions is it permissible to proceed with a hypothesis test, even though the assumption that participants are randomly selected is violated?

Answers

it may be permissible to proceed with a hypothesis test even if the assumption of random participant selection is violated, under the conditions of known and accounted for non-random selection or random assignment to treatment groups

Random participant selection is an important assumption in hypothesis testing, as it helps ensure the generalizability of the results to the target population. However, in some situations, it may be impractical or impossible to achieve perfect random selection. In such cases, there are a few conditions under which it may still be permissible to proceed with a hypothesis test despite the violation of this assumption:

Non-random selection is known and accounted for: If the non-random selection process is well-documented and understood, researchers can adjust their analysis or statistical methods to account for potential biases introduced by the non-random selection.

Random assignment to treatment groups: Even if participants are not randomly selected, random assignment to different treatment groups can help mitigate the impact of non-random selection. By randomly assigning participants to treatment groups, the effects of non-random selection are distributed evenly across the groups, allowing for valid comparisons and hypothesis testing.

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two containers are used to hold liquid. these containers have exactly the same shape. the first container has a height of 20 cm, and it can hold 320 m3 of liquid. if the second container has a height of , how much liquid can it hold?

Answers

The second container can hold approximately 1715 m³ of liquid.

Two containers have exactly the same shape, we can use their height ratio to determine the liquid capacity ratio.

Let's denote the height of the first container as H1 = 20 m and its liquid capacity as C1 = 320 m³.

We want to find the liquid capacity of the second container, C2, given its height H2 = 35 m.

The ratio of the heights is H2 / H1 = 35 m / 20 m = 7/4.

The ratio of the liquid capacities is equal to the ratio of the volumes, since the containers have the same shape. Therefore, we have:

C2 / C1 = (H2 / H1)³

Substituting the given values:

C2 / 320 m³ = (7/4)³

Simplifying the exponent:

C2 / 320 m³ = 343 / 64

To find C2, we can cross-multiply:

C2 = (343 / 64) × 320 m³

Calculating the result:

C2 ≈ 1715 m³

Therefore, the second container can hold approximately 1715 m³ of liquid.

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The question is incomplete the complete question is :

two containers are used to hold liquid. these containers have exactly the same shape. the first container has a height of 20 m, and it can hold 320 m³ of liquid. if the second container has a height of 35 m, how much liquid can it hold?

Decide whether the triangles are similar. If they are, write a similarity statement and state the reason justifying the similarity.

Answers

The triangles are similar by SSS (side side side) similarity theorem

we have a segment that is also 4 units long in the other triangle; however, for the 2 unit segment. As it turns out, every side of the triangle on the right side is half that of the left side triangle.

Segment ED is 2 units long. thus AB and ED pair up

BC is 8 units long nd DF is 4 units long (half of BC). thus BC and DF pair up

We started at A, went to B, then to C in that exact order marking the side lengths of 4 and 8 respectively. At the same time for the other triangle, at E, moved to D, then to F recording the side lengths 2 and 4

So A pairs up with E, B pairs with D, and C pairs with F

hence, triangle ABC is similar to triangle EDF.

So, SSS (side side side) similarity theorem to prove the triangles similar.

Which says that if the sides are in proportion to one another, then the triangles are similar.

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Your Company's residual income was 58,250 . Net income was 5150,000 and average operating assets were 5675,000 , What was the expected return percentage?
$19 \%$
$18 \%$
214
$20 \%$
$22 \%$

Answers

the expected return percentage is approximately 8.04%. , which is not among the provided answer options.

To calculate the expected return percentage, Expected return percentage = (Residual Income / Average Operating Assets) × 100

Plugging in the given values:

Expected return percentage = (58,250 / 5,675,000) × 100 ≈ 1.026% The expected return percentage is typically calculated by dividing the residual income by the average operating assets and expressing it as a percentage.

Now, to calculate the expected return percentage, we divide the required return by the average operating assets:

Expected Return Percentage = (Required Return on Average Operating Assets) / Average Operating Assets

Expected Return Percentage = $456,750 / $5,675,000

Calculating this division, we get:

Expected Return Percentage ≈ 0.0804

Converting this to a percentage, we find that the expected return percentage is approximately 8.04%.

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2. Maria measured the height of a pea
plant to see how much it grew in a
month. The plant was 11 inches tall at
the beginning of the month and 3.5
feet tall at the end of the month. How
much did the plant grow?

Help plss

Answers

Over the course of the month, the pea plant expanded to a height of 31 inches.

It is necessary to calculate the measurements to a standard unit, such as inches or feet, in order to calculate the pea plant's growth.

For uniformity, let's convert both measurements to inches.

Given: 11 inches is the starting height.

Height at the end = 3.5 feet

3.5 feet to inches conversion:

12 inches = 1 foot.

42 inches = 3.5 feet (3.5 × 12).

Now that we have the starting height and the finishing height, we can compute the growth:

Growth = Ending height - Starting height

= 42 inches - 11 inches

= 31 inches

Therefore, the pea plant grew 31 inches in height over the course of the month.

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In​ March, a family starts saving for a vacation they are planning for the end of August. The family expects the vacation to cost ​$1428. They start with ​$130. At the beginning of each month they plan to deposit 20​% more than the previous month. Will they have enough money for their​ trip? If​ not, how much more do they​ need?

the answer is not 137 or 332

Answers

Answer:

The family still needs $1104.52 to reach their savings goal for the vacation.

Step-by-step explanation:

To determine whether the family will have enough money for their trip, we need to calculate the total savings at the end of August. Let's break down the savings for each month:

March: $130 (initial savings)

April: $130 + 20% = $156 (20% more than the previous month)

May: $156 + 20% = $187.20

June: $187.20 + 20% = $224.64

July: $224.64 + 20% = $269.57

August: $269.57 + 20% = $323.48

By the end of August, the family will have saved $323.48. However, their target amount for the vacation is $1428. Therefore, they do not have enough money for the trip.

To determine how much more they need, we subtract the total savings from the target cost:

$1428 - $323.48 = $1104.52

The family still needs $1104.52 to reach their savings goal for the vacation.

I NEED HELP QUICKLY for both X

Answers

The solution of the quadratic equation is x = 2. Therefore, [tex]\frac{4+\sqrt{-4^{2}-4(1)(4) } }{2(1)}[/tex]  or [tex]\frac{4-\sqrt{-4^{2}-4(1)(4) } }{2(1)}[/tex]

How to solve quadratic equation?

The quadratic formula can be use to solve the quadratic equation as follows:

x² - 4x + 4 = 0

Modelling it to quadratic equation, ax² + bx + c

Hence,

using quadratic formula,

[tex]\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex] or [tex]\frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex]

where

a, b and c are the coefficient in the equation

Hence,

a = 1

b = -4

c = 4

Therefore,

[tex]\frac{4+\sqrt{-4^{2}-4(1)(4) } }{2(1)}[/tex] or [tex]\frac{4-\sqrt{-4^{2}-4(1)(4) } }{2(1)}[/tex]

Finally

x = 2

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59:10
A coordinate grid with 2 lines. One line, labeled f(x) passing through (negative 2, 4), (0, 2), and the point (1, 1). The other line is labeled g(x) and passes through (negative 3, negative 3), (0, 0) and the point (1, 1).

Which input value produces the same output value for the two functions on the graph?

x = −1
x = 0
x = 1
x = 2

Answers

The input value that produces the same output value for the two functions on the graph is x = 1.

To find the input value that produces the same output value for the two functions, we need to evaluate the functions at different input values and compare their output values.

Let's start by evaluating the function f(x) at the given points:

f(-2) = 4

f(0) = 2

f(1) = 1

Now, let's evaluate the function g(x) at the given points:

g(-3) = -3

g(0) = 0

g(1) = 1

By comparing the output values of the two functions, we can see that f(1) = g(1) = 1.

Therefore, the input value that produces the same output value for both functions is x = 1.

In other words, if we substitute x = 1 into both functions, we will get the same result.

This can be seen on the coordinate grid as well.

The point (1, 1) lies on both the line labeled f(x) and the line labeled g(x), indicating that the functions have the same output value at x = 1.

So, the correct answer is x = 1.

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write a polar equation of the conic that has a focus at the origin, eccentricity 3 over 2, and directrix y

Answers

The polar equation of the conic with a focus at the origin, eccentricity of 3/2, and directrix y, is r = 0, which represents a single point at the origin.

To derive the polar equation, we start by considering the definition of an ellipse in polar coordinates.

For an ellipse with a focus at the origin and an eccentricity e, the polar equation is given by

[tex]r = \frac{d}{1 + e \cdot \cos(\theta)}[/tex]

where d is the distance from the origin to the directrix.

In this case, the directrix is the line y = 0, which means the distance from the origin to the directrix (d) is simply the distance from the origin to the x-axis, which is 0.

The eccentricity e is given as 3/2. Substituting the values into the polar equation, we have

[tex]r = \frac{0}{1 + \frac{3}{2} \cdot \cos(\theta)}[/tex]

Simplifying the equation, we get

[tex]r = \frac{0}{1 + \frac{3}{2} \cdot \cos(\theta)}=0[/tex]

Therefore, the polar equation of the conic is r = 0, which represents a single point at the origin.

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hydrostatic weighing uses which statistic to predict the percentage of body fat?

Answers

Hydrostatic weighing uses the statistic known as density to predict the percentage of body fat.

Hydrostatic weighing, also known as underwater weighing or densitometry, is a method used to estimate body composition by measuring the density of an individual's body.

The principle behind hydrostatic weighing is that fat tissue is less dense than lean tissue, such as muscle and bone.

During a hydrostatic weighing test, the individual is submerged in water while their body volume is measured. By comparing the weight on land with the weight in water, the density of the body can be calculated.

The measured density is then used in equations or regression models to estimate the percentage of body fat.

The statistic of density is crucial in this process because it represents the ratio of an individual's mass to their volume.

By accounting for the density of fat and lean tissue, hydrostatic weighing provides an estimate of body fat percentage based on the differences in density between these components.

It is worth noting that while hydrostatic weighing has been widely used as a reference method for body composition assessment, more modern techniques such as dual-energy X-ray absorptiometry (DXA) and bioelectrical impedance analysis (BIA) have gained popularity due to their convenience and accessibility.

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Simplify the question

Answers

Answer:

Here’s your answer!

Please help quick

Will give brainless to whoever helps first

Answers

Answer: 3 times as big

Step-by-step explanation:

200000

600000

What is the equation of the line that passes through the point (-4, 8) and has a slope of -1?

Answers

Step-by-step explanation:

Using point(-4,8) slope form of a line and then manipulating it :

y - 8 =  -1 (x - -4)

y - 8 = - (x+4 )

y-8  = - x -4

y = -x + 4        

The equation of the line in slope - intercept form will be y = (-1)x + 4.

What is the general equation of a Straight line?

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

Given is a line that passes through the point (-4, 8) and has a slope of -1.

The slope of the line will be m = -1

Assume the equation to be y = (-1)x + c.

We can write the equation for point (-4, 8) as →

8 = (-1) x (-4) + c

8 = 4 + c

c = 4

So, the equation of the line will be y = (-1)x + 4

Therefore, the equation of the line in slope - intercept form will be y = (-1)x + 4.

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