What is the position of C on the number line below?
Write your answer as a fraction or mixed number.

The function which is the vertex form of the equation whose first three steps shown in writing is  f(x)=5(x +4)²- 80.

Vertex form of parabola is the equation form of quadratic equation, which is used to find the coordinate of vertex points at which the parabola crosses its symmetry.

The standard equation of the vertex form of parabola is given as,

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

Here, (h, k) is the vertex point.

The first three steps in writing the function in vertex form are shown.

\(f(x) = 40x +5x^2\)

Write the function in standard form.

\(f(x) = 5x^2+ 40x\)

Factor out of the first two terms by taking out the common number 5 from the equation,

\(f(x) = 5(x^2 +8x)\)

Form a perfect square trinomial with (8/2)² = 16,

\(f(x) = 5(x^2 +8x+ 16) - 5(16)\\f(x) = 5(x+4)^2 - 80\)

Hence, the function which is the vertex form of the equation whose first three steps shown in writing is  f(x)=5(x +4)²- 80.

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Answer:

c

Step-by-step explanation:

The canonical expression equivalent to sinusoidal model y(t) = 2 · sin (4π · t) + 5 · cos (4π · t) is y(t) = (√ 29) · sin (4π · t + 0.379π) .

Herein we have a simple harmonic motion model represented by a sinusoidal expression of the form y(t) = A · sin (C · t) + B · cos (C · t), which must be transformed into its canonical form, that is, y(t) = A' · sin (C · t + D). We proceed to perform the procedure by algebraic and trigonometric handling.

The amplitude of the canonical function is determined by the Pythagorean theorem:

A' = √(2² + 5²)

A' = √ 29

The angular frequency C  is the constant within the trigonometric functions from the non-canonical formula:

C = 4π

Then, we find the initial position of the weight in time: (t = 0)

y(0) = 2 · sin (4π · 0) + 5 · cos (4π · 0)

y(0) = 5

And now we calculate the angular phase below: (A' = √ 29, C = 4π, y = 5)

5 = √ 29 · sin (4π · 0 + D)

5 / √ 29 = sin D

D ≈ 0.379π rad

The canonical expression equivalent to sinusoidal model y(t) = 2 · sin (4π · t) + 5 · cos (4π · t) is y(t) = (√ 29) · sin (4π · t + 0.379π) .

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Answer:

63°

Step-by-step explanation:

The line = 180

so 180-117

= 63°

Answer:

The value of a is 63°

Step-by-step explanation:

180-117=63°.

Yes, the data collected from interviewing customers at one ShopRite store in Jersey City from Monday to Friday, 9 am-3 pm, could have some issues and biases.

Potential issues include:

1. Limited sample: By conducting interviews only at one store, the percentage of  responses will not provide a comprehesive view of the customer base in Jersey City.

2. Time bias: Surveying customers only between 9 am and 3 pm may exclude individuals who shop outside these hours, leading to an incomplete picture of shopping habits.

3. Location bias: ShopRite customers may not accurately represent the diverse needs and preferences of all Jersey City residents.

4. Self-reported data: Customers may not accurately recall their shopping habits, leading to biased responses.

While the data collected can provide some insights, it may not be sufficient to open a grocery store. You should consider expanding your survey to multiple locations and times, including weekends, and collecting demographic information to better understand the diverse needs of Jersey City residents. Additionally, researching market trends, competitors, and successful grocery store models in similar areas can help inform your business plan.

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Given the problem, X represents the number of cities among the five neighboring cities (located within 10 miles of each other) in which it will rain tomorrow. X can be a value ranging from 0 (no rain in any city) to 5 (rain in all cities).

Based on the given information, X is the random variable representing the number of cities among the five neighboring cities that will experience rain tomorrow. Since the cities are located within 10 miles of each other, it can be assumed that they are geographically similar and therefore have similar weather patterns. However, the probability of rain occurring in each city may still vary due to microclimates or other factors.

In order to determine the probability distribution of X, more information is needed such as historical weather data, current weather conditions, and any forecasts or predictions. Without this additional information, it is not possible to provide a specific answer to the question.

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Answer:

10)

11x-1+20x-3=151 (the exterior angle of an triangle is equal to the sum of two opposite interior angles)

31x-4=151

31x=151+4

31x=155

x=155/31

x=5°

11)

14x-13=4x+13+6x+2

14x-4x-6x=13+13+2

4x=28

x=28÷4

x=7°

Answer:

Step-by-step explanation:

if x = y, and y = z, you can write that as x = y = z, which means that x = z

Answer:

Explanation:

a) To work out the average or mean age we must first calculate the total age.

19 x 2 = 38

20 x 3 = 60

21 x 1  = 21

22 x 4 = 88

23 x 1 = 23

Total = 230

Then... Divide the number of players with this figure

Number of players =  2 + 3 + 2 + 4 + 1 = 11

230/11 = 20.9 is the average age of the players

b) We know the average will now be 22 and we know the number of players is now 12.

So... 22 x 12 = 264 (This will be the new total age of all the players)

We know the previous total was 230

So 264-230 = 34 (years old)

I hope this helps you! :)

Step-by-step explanation:

Step 1:  Answer the first question

Area of a triangle → \(A = \frac{b*h}{2}\)

\(\frac{4*6}{2}\)

\(\frac{24}{2}\)

\(12\)

Total Area → \(12 * 2=24\)

Answer:  Option D, \(24\ square\ units\)

Step 2:  Answer the second question

We know that the total side length is 12 but we also know that the triangle base is 4 so we would subtract that from the total length and we get that the rectangle length is 8.  We also know that the width is 6 so we multiply 8 by 6 and we add 24.  This matches option B

Answer:  Option B, \((8 * 6 + 24)\ square\ units\)

Answer:

Its 24 for both combined (A)

Step-by-step explanation:

i would say for part B it would be B

There are 15 different possible outcomes when Hudson spins both spinners in his board game.

To determine the total number of possible outcomes when Hudson spins both spinners, you need to multiply the number of outcomes on the first spinner (Walk, Run, Stop) by the number of outcomes on the second spinner (Monday, Tuesday, Wednesday, Thursday, Friday).

Step 1: Determine the number of outcomes on the first spinner. There are 3 outcomes: Walk, Run, and Stop.

Step 2: Determine the number of outcomes on the second spinner. There are 5 outcomes: Monday, Tuesday, Wednesday, Thursday, and Friday.

Step 3: Multiply the number of outcomes from both spinners. 3 outcomes on the first spinner multiplied by 5 outcomes on the second spinner equals 15 total possible outcomes.

So, there are 15 different possible outcomes when Hudson spins both spinners in his board game.

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Answer:

1/4

Step-by-step explanation:

Multiply 75% and 1/3

Change 75% to a fraction

75/100 reduce the numerator and denominator by 25.

75/100 = 3/4

3/4 x 1/3

3/12

reduce

1/4

Answer:

Step-by-step explanation:

Given equation:

Answer:

Simplify:

Jeff Parent's data supports the presence of a hill on Mile 2, as there is a significant difference in the mean time it takes to ride each mile.

To test the claim that it takes the same time to ride each of the miles, we need to use a one-way ANOVA test.

Using the provided data, we calculate the mean time for each mile and find that Mile 2 has a significantly higher mean time than the other two miles. Therefore, it appears that Mile 2 has a hill.

Jeff Parent's data shows that there is a significant difference in the mean time it takes to ride each mile. Using a one-way ANOVA test with a 0.05 significance level, we found that Mile 2 has a significantly higher mean time than the other two miles. This indicates that there is a hill on Mile 2, which is causing the increased time.

Therefore, we reject the claim that it takes the same time to ride each of the miles and conclude that there is a hill on Mile 2.

Jeff Parent's data supports the presence of a hill on Mile 2, as there is a significant difference in the mean time it takes to ride each mile. This information can be useful for Jeff to adjust his training and race strategy accordingly.

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The 95% confidence interval estimate of the percentage of orders that are not accurate is approximately (17.37%, 27.83%)

Let's denote p as the proportion of orders that are not accurate.

The sample proportion of orders that are not accurate is given by:

p(bar) = 70 / (239 + 70)

= 70 / 309

≈ 0.226

The standard error of the proportion is calculated as:

SE = √[(p(bar)(1 - p(bar))) / n]

= √[(0.226(1 - 0.226)) / 309]

≈ √(0.1785 / 309)

≈ 0.0267

To find the margin of error, we need to multiply the standard error by the critical value corresponding to a 95% confidence level. For a 95% confidence level, the critical value is approximately 1.96.

Margin of error = 1.96 × SE

≈ 1.96 × 0.0267

≈ 0.0523

Now we can construct the confidence interval:

Lower limit = p(bar) - Margin of error

= 0.226 - 0.0523

≈ 0.1737

Upper limit = p(bar) + Margin of error

= 0.226 + 0.0523

≈ 0.2783

Therefore, the 95% confidence interval estimate of the percentage of orders that are not accurate is approximately (17.37%, 27.83%).

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x = 4.28

\(Given,\ To\ find\ for\ x,\)

\(Let\ c\ be\ the\ centre\ of\)

\(Circle,\ where\)\(AD=22.4\ (Diameter)\)

\(AC=\frac{22.4}{2}=11.2\ (radius)\)

\(AB=8.8\)

\(In\ \Delta\ ABC, Right\ angled\ at\)

\(B.\ USing Pythagoras\ theovem\)

\((AB)^2+(BC)^2=(AC)^2\)

\((8.8)^2+(BC)^2=(11,2)^2\)

\((BC)^2=125.44-77.44=48\)

\(BC=\sqrt{48}=6.92\)

\(E_c=x+y\ \ \ \ \(Where\ Fc\ is\ also\ radius\ of\ arcle\)

\(\therefore\ \ \ \ \11.2=x+6.92\)

\(x=11.2-6.92=4.28\)

\(Hence,\ x=4.28\ is\ the\ answer.\)

I hope this helps you

:)

The cheapest price for 100 square feet $527 is at the local hardware store.

The total price is equivalent to the price of tile per foot multiplied by 100.

The total price is equivalent to the price of tile per foot multiplied by 100.

Note: This question is incomplete because the graph is missing; here is the graph.

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(a) P(En(FUG)) = P(E)P(FUG) found by using the multiplication rule of probability.

Using the multiplication rule of probability, we have P(En(FUG)) = P(En∩F∩G) = P(E)P(F)P(G), since E, F, and G are independent events. Therefore, P(En(FUG)) = P(E)P(FUG).

(b) We want to show that P(A∩B) = P(A)P(B), given that A and B are independent events. Using the definition of independent events, we know that P(A∩B) = P(A)P(B|A) = P(A)P(B), since P(B|A) = P(B) by the independence of A and B. Therefore, A and B are independent events.

(c) To determine whether X and Y are independent, we need to check if P(X=x∩Y=y) = P(X=x)P(Y=y) for all x and y. We have P(X=0∩Y=0) = 1/2, P(X=0) = 1/2, and P(Y=0) = 1/2.

Therefore, P(X=0∩Y=0) ≠ P(X=0)P(Y=0), which implies that X and Y are not independent. In fact, we can compute all possible joint probabilities and see that none of them satisfy the condition for independence.

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Answer:

Well, since your question is asking how to simplify and not the actual answer itself, all we have to do is first simplify 7^6=117,649. Now we just take that number and make it 117,649^2. I hope im correct with the way i set up the equation even though the number is absurdly large

Step-by-step explanation:

Answer: (7⁶)² = 7¹²

Step-by-step explanation:

All you have to do is multiply the exponents here and keep the 7. So, your final answer is 7¹².

Hope this helps, and don't forget to mark me brainliest! Have a wonderful day!

The probability that a truck drives between 122 and 127 miles in a day is 0.0165, rounded to four decimal places.

To find the probability that a truck drives between 122 and 127 miles in a day, we'll use the z-score formula and standard normal distribution table. Follow these steps:

Step 1: Calculate the z-scores for 122 and 127 miles.
z = (X - μ) / σ

For 122 miles:
z1 = (122 - 90) / 18
z1 = 32 / 18
z1 ≈ 1.78

For 127 miles:
z2 = (127 - 90) / 18
z2 = 37 / 18
z2 ≈ 2.06

Step 2: Use the standard normal distribution table to find the probabilities for z1 and z2.
P(z1) ≈ 0.9625
P(z2) ≈ 0.9803

Step 3: Calculate the probability of a truck driving between 122 and 127 miles.
P(122 ≤ X ≤ 127) = P(z2) - P(z1)
P(122 ≤ X ≤ 127) = 0.9803 - 0.9625
P(122 ≤ X ≤ 127) ≈ 0.0178

So, the probability that a truck drives between 122 and 127 miles in a day is approximately 0.0178 or 1.78%.

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The inequality of the temperatures where yeast will NOT thrive is T < 90°F or T > 95°F

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

Yeast thrives between 90°F to 95°F

For the temperatures where yeast will not thrive, we have the temperatures to be out of the given range

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

T < 90°F or T > 95°F.

Where

T = Temperature

Hence, the inequality is T < 90°F or T > 95°F.

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Answer:

640cm³

Step-by-step explanation:

Length SF = ×2

Volume SF = ×2³ = ×8

Volume of B = 8 × 80 = 640cm³

The volume of the scale factor is 8. Then the volume of the solid B will be 640 cm³.

Volume is a measurement of three-dimensional space that is utilized. It is frequently mathematically quantified using SI-derived units or different imperial or US traditional units. The concept of length is linked to the notion of capacity.

The diagram shows two similar solids, A and B. Solid A has a volume of 80 cm³.

The scale factor is given as,

Scale factor = 8 / 4

Scale factor = 2

The scale factor of the volume is given as,

⇒ 2³

⇒ 8

Then the volume of the solid B will be given as,

Volume of B = 8 x 80

Volume of B = 640 cm³

The volume of the scale factor is 8. Then the volume of the solid B will be 640 cm³.

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Answer:

the circumference is 31.4

Step-by-step explanation:

The computation of the circumference is shown below:

As we know that

Circumference is

= 2πr

= 2π (10 ÷ 2)

= 2× 3.14 × 5

= 31.4

Hence, the circumference is 31.4

The pooled variance, s_p^2, is 368.6957.

To calculate s2, we first need to calculate the pooled variance using the given formula:

s_p^2 = ((n1 - 1)*s1^2 + (n2 - 1)*s2^2) / (df1 + df2)

We know the values of n1, n2, df1, df2, s1, and SS1. We can use SS1 to calculate the sample variance for the first sample, s1^2, as follows:

s1^2 = SS1 / (n1 - 1) = 291.6 / 10 = 29.16

Similarly, we can use SS2 to calculate the sample variance for the second sample, s2^2, as follows:

s2^2 = SS2 / (n2 - 1) = 12482 / 20 = 624.1

Now, substituting the values in the formula for pooled variance, we get:

s_p^2 = ((11 - 1)*29.16 + (21 - 1)*624.1) / (10 + 20) = 368.6957

Therefore, the pooled variance, s_p^2, is 368.6957.

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Answer:36

Step-by-step explanation:multiply divide and  subctract

Answer:

above sea level

Step-by-step explanation:

Answer:D).                  

Step-by-step explanation:ok

The experimental probability of landing on a number greater than 4 is 0.25 or 25%.

To find this probability, we need to determine the number of successful outcomes (landing on a number greater than 4) and divide that by the total number of trials (60).

The successful outcomes are 5 and 6, with a frequency of 10 and 8 respectively. To add these two frequencies together, we can use 10 + 8 = 18.

So, the experimental probability is 18/60 = 0.3 or 25%.

It's important to note that experimental probability is based on the outcomes of an experiment or a sample and it may not be the same as a theoretical probability which is based on the ratio of favorable outcomes to the total number of outcomes in a theoretical model.

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the answer in fraction form is 18/60

if thats what you are looking for.

Step-by-step explanation:

to select 3 out of 13.

no repetition, and the sequence of the selected items does not matter.

that means combinations :

C(13, 3) = 13! / (3! × (13 - 3)!) = 13! /(3! × 10!) =

= 13×12×11 / (3×2) = 13×2×11 = 286

there can be 286 different random samples of size 3.

The answer is 286.

The number of different simple random samples of size 3 that can be selected from a population consisting of 13 items is 286.Explanation:Simple random sampling is a statistical technique used in research. In this sampling method, a subset of a population is selected randomly, with each member of the population having an equal chance of being selected. There are different types of random sampling methods, such as systematic sampling, stratified sampling, cluster sampling, etc.The number of different simple random samples of size k that can be selected from a population of size N is given by the formula N!/k!(N-k)!, where ! denotes factorial. Here, the population consists of 13 items, and we need to find the number of different simple random samples of size 3 that can be selected from this population.So, the required number of different simple random samples of size 3 that can be selected from this population is 13!/3!(13-3)! = 286.

Therefore, the number of different simple random samples of size 3 that can be selected from a population consisting of 13 items is 286.

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