A bridge is supported by three arches. The function that describes the arches is
h(x) = -0.2x² + 3.0x, where h(x) is the height, in metres, of the arch above the ground at any distance, x, in metres,
from one end of the bridge. How tall is each arch?

This means that we can be 95% confident that the true mean score of all third-grade students in New Jersey falls between 60 (the sample average score) and 61.153.

To calculate the confidence interval, we use the formula: CI = Y ˉ ± t * (s/√n), where CI represents the confidence interval, Y ˉ is the sample average score, t is the critical value for the desired confidence level, s is the sample standard deviation, and n is the sample size.

In this case, the sample average score is 60 points, the sample standard deviation is 1 point, and the sample size is 81. The critical value for a 95% confidence level with 80 degrees of freedom is approximately 1.990.

Plugging these values into the formula, we have: CI = 60 ± 1.990 * (1/√81). Simplifying the equation gives us the confidence interval of (60, 61.153) for the mean score of New Jersey third-grade students. Therefore, the higher value of this interval is approximately 61.153 points.

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Answer:

D=12 cm

Step-by-step explanation:

please check the image for the answer. Thank you .

Doubling the mass of the block attached to the spring will result in a longer period of oscillation and halving the mass of the block attached to the spring will result in a shorter period of oscillation.

a. The period of oscillation for a mass-spring system is inversely proportional to the square root of the mass. Therefore, doubling the mass will result in a longer period of oscillation. The new period can be calculated using the formula T' = T * √(m'/m), where T is the original period, m is the original mass, and m' is the new mass.

b. Similarly, halving the mass of the block will result in a shorter period of oscillation. Using the same formula as above, the new period can be calculated by substituting m' as half of the original mass.

c. The amplitude of the oscillation, which represents the maximum displacement from the equilibrium position, does not affect the period of oscillation. Therefore, doubling the amplitude will not change the period.

d. The period of oscillation for a mass-spring system is directly proportional to the square root of the mass and inversely proportional to the square root of the spring constant. Doubling the spring constant will result in a shorter period of oscillation. The new period can be calculated using the formula T' = T * √(k/k'), where T is the original period, k is the original spring constant, and k' is the new spring constant.

By considering the relationships between mass, amplitude, spring constant, and period of oscillation, we can determine the effect of each change on the period of oscillation in a mass-spring system.

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To find the probability that more than 5 red blood cells are visible under a microscope, we can use the Poisson distribution with a mean of 4.

The Poisson distribution is used to model the number of events that occur in a fixed interval of time or space. In this case, we are interested in the number of red blood cells per square unit visible under the microscope.

The formula for the Poisson distribution is:

P(X = k) = (e^(-λ) * λ^k) / k!

Where:
- P(X = k) is the probability of observing k events
- e is Euler's number (approximately 2.71828)
- λ is the mean number of events in the interval
- k is the actual number of events observed

In this case, the mean (λ) is given as 4. We want to find the probability of observing more than 5 red blood cells.

To find this probability, we need to calculate the sum of the probabilities for observing 6, 7, 8, 9, and so on, up to infinity. Since calculating the infinite sum is not practical, we can use a scientific calculator or statistical software to find the cumulative probability.

For example, using a scientific calculator, you can calculate the cumulative probability as follows:

1 - P(X ≤ 5)

This will give you the probability of observing more than 5 red blood cells per square unit visible under the microscope.

Remember to substitute the values of λ and k in the Poisson distribution formula and perform the calculations accurately.

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Answer:

$2193.75

Step-by-step explanation:

9 times 13

times 18.75

Answer: 2019.08

Step-by-step explanation: To find the year when the car had the least value, we need to find the minimum value of the quadratic function V = 20x² - 363.2x + 2500, where x represents the number of years since 2010.

One way to find the minimum value is to use the formula for the vertex of a quadratic function, which is given by:

x = -b / (2a)

where a is the coefficient of the x² term, b is the coefficient of the x term, and x is the x-coordinate of the vertex.

In this case, a = 20 and b = -363.2, so we have:

x = -(-363.2) / (2 x 20)

x = 9.08

This means that the vertex of the parabola occurs at x = 9.08, which represents the year 2010 + 9.08 = 2019.08 (rounded to two decimal places).

Therefore, the car had the least value in the year 2019.

The probability that the įth cup you are given has really salty water is 1/100.

We are given that;

Number of cups = 100

Now,

The probability of an event is the ratio of the number of favorable outcomes to the total number of possible outcomes1. In this case, the event is that the įth cup has really salty water, and there is only one favorable outcome out of 100 possible outcomes. Therefore, the probability is:

P(įth cup has really salty water) = 1/100

This probability is the same for any value of į from 1 to 100.

b. we need to find the expected value of the number of cups you drink before you encounter the really salty water. The expected value is the weighted average of all possible outcomes, where the weights are the probabilities of each outcome2. In this case, the possible outcomes are that you drink 1 cup, 2 cups, …, or 100 cups before you stop. The probability of each outcome depends on where the really salty water is located among the 100 cups.

Therefore, by probability the answer will be 1/100.

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Answer:

$0.90

Step-by-step explanation:

0.0725(12.40) = 0.899
0.899 = 0.90
Hope this helps :)

A bell tower 24 meters tall casts a 45-meter-long shadow. If a neighboring observation tower is 16 meters tall, the shadow cast by the observation tower will be 30 meters long.

This can be solved by the application of trigonometry on the similar triangles formed by the bell tower, its shadow, and the observation tower and its shadow.

The ratio of the height of the bell tower to the length of its shadow is 24/45

This ratio must be the same as the ratio of the height of the observation tower to the length of its shadow because the triangles are similar.

Hence, assuming the observation tower's shadows length to be x, we can deduce,

\(\frac{24}{45} = \frac{16}{x}\)

To solve for x,

24x = 16*45    (by cross multiplying)

x = 16*45/24

x = 30

Therefore, the observation tower's shadow will be 30 meters long.

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When moving from a 95% confidence interval to a 90% confidence interval, the width of the interval will decrease. (option b).

To understand this, let's consider a simple example. Suppose we want to estimate the mean height of all high school students in a particular region. We take a sample of 100 students and calculate the mean height to be 65 inches, with a 95% confidence interval of (63, 67) inches. This means that if we were to repeat this process many times, we would expect the true population mean height to be within this interval 95% of the time.

Now, if we were to calculate a 90% confidence interval instead, we would obtain a narrower interval because we are now willing to accept a greater risk of being wrong.

It is important to note that the width of the confidence interval depends on the sample size and the variability of the data.

As the sample size increases or the variability decreases, the confidence interval will become narrower. Conversely, as the sample size decreases or the variability increases, the confidence interval will become wider.

Hence the correct option is (b)

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Answer:

C. 28.26

May I have brainliest please? :)

Answer:

The distance between E and F is 5 units

Step-by-step explanation:

E and F are share the same y-coordinates. So for this part it is okay to not use the distance formula.

So you will be having:

E (5,8) and F (5,3)

EF = 8-3=5

OR

YOU CAN USE THE DISTANCE FORMULA AS INDICAYED IN THE PICTURE.

Hopefully the picture is clear and understandable and younger the explanation.

Answer:

see explanation

Step-by-step explanation:

y₂ = - 3 × y₁

   = - 3(4x² - 5x + 1) ← distribute parenthesis by - 3

  = - 12x² + 15x - 3 → (a)

B

y₁ - y₂

= 4x² - 5x + 1 - (- 12x² + 15x - 3) ← distribute parenthesis by - 1

= 4x² - 5x + 1 + 12x² - 15x + 3 ← collect like terms

= 16x² - 20x + 4

The unit rate here is also 8 cups of water per day.

We need to remember that in the unit rate we have as the denominator one unit of any quantity.

In this case, we have a day as the denominator one day, since:

In summary, therefore, the unit rate, in this case, is 8 cups of water per day:

Corrected Question

Central High School plays Eastern High School in a basketball game. Eastern had double the score of Central before Central scored a three-pointer as the game ended.

The variable, c, represents Central's score before the three-pointer. Express the total points scored in the game as a variable expression. Check all that apply.

Answer:

(C)3c + 3

(F)2c + c + 3

Step-by-step explanation:

Therefore:

Total Points Scored in the game =c+2c+3 (This is option F)

Simplifying, we have:

c+2c+3=3c+3 (This is option C)

Therefore, C and F are the correct options.

These are just a few examples to help you understand each perception. It's important to remember that perception is subjective and can vary from person to person.

Attribution theory: Attribution theory refers to how individuals explain the causes of behavior. For example, if someone sees a classmate performing well on a test, they may attribute their success to their intelligence or hard work.

Selective perception: Selective perception is the tendency to filter and interpret information based on our own beliefs, attitudes, and expectations. For instance, if two people witness the same event, they may perceive it differently based on their preconceived notions or biases.

Halo effect: The halo effect occurs when an individual's overall impression of a person influences their perception of that person's specific traits. An example of the halo effect is when someone assumes that a person who is physically attractive is also intelligent and kind, without any concrete evidence.

Contrast effect: The contrast effect happens when the perception of something is influenced by comparing it to something else. For instance, if you try on an expensive dress after trying on a cheaper one, the expensive dress may seem even more extravagant and desirable due to the contrast effect.

Projection: Projection refers to the unconscious act of attributing one's own thoughts, feelings, or characteristics to others. For example, if someone is feeling guilty about something, they may project their guilt onto someone else and believe that the other person is feeling guilty.

Stereotyping: Stereotyping involves making generalizations about a group of people based on limited information or assumptions. For instance, assuming that all teenagers are rebellious or that all doctors are wealthy. Stereotypes can lead to unfair judgments and discrimination.

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Answer:

60 copies

Step-by-step explanation:

Answer: 60 copies

Step-by-step explanation:

The equation of the sphere passing through P(−6,3,8) and Q(2,−5,9) with its center at the midpoint of PQ is given as (x+2)²+(y+1)²+(z−217​)²=4129​.

The given points are P(−6,3,8) and Q(2,−5,9).

The midpoint of these points can be calculated as M, the center of the sphere.Midpoint of PQ, M = $[\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}, \frac{z_1 + z_2}{2}].

Here, x1=-6, y1=3, z1=8, x2=2, y2=-5, z2=9.

therefore M = [\frac{-6+2}{2}, \frac{3-5}{2}, \frac{8+9}{2}]$$⇒ M(−2,−1,17/2).

Now, the radius of the sphere is the distance between the midpoint and point P or Q.r=√[(-2 + 6)² + (-1 -3)² + (17/2-8)²]= √(28 + 16.25 + 0.25)= √44.5= 2√(11.125) = √(4 * 11.125) = √(44.5/4) = √11.125.

Now, the equation of the sphere is given as, $$(x-h)^2+(y-k)^2+(z-l)^2=r^2.

Substituting the values of h, k, l and r, we get;(x+2)²+(y+1)²+(z-17/2)²=11.125

Therefore, the main answer is;(x+2)²+(y+1)²+(z-17/2)²=11.125.

The main aim of the given question is to find out the equation of the sphere passing through P(-6, 3, 8) and Q(2, -5, 9) with its center at the midpoint of PQ.The midpoint of PQ is the center of the sphere.

Hence, using the midpoint formula, we can find the center of the sphere which is given as;M(−2,−1,17/2)Using the distance formula, we can find the radius of the sphere, which is given as;r = √(4 * 11.125)/4 = √(44.5/4) = √11.125The equation of a sphere with center (h,k,l) and radius r is given by;(x - h)² + (y - k)² + (z - l)² = r².

Substituting the values of h, k, l and r, we get the standard equation of the sphere as;(x+2)²+(y+1)²+(z-17/2)²=11.125.

Therefore, the conclusion is that the equation of the sphere passing through P(−6,3,8) and Q(2,−5,9) with its center at the midpoint of PQ is given as (x+2)²+(y+1)²+(z−217​)²=4129​.

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Answer:

28.27

Step-by-step explanation:

π x 6^2 x 90/360 = 28.27

Step-by-step explanation:

C. represent the number line for x

where x ix

Answer:

√3

Step-by-step explanation:

From the formula used in calculating Friction, we have:

Frictional Force = coefficient of Friction × Reaction

i.e Fr = μ × R

Resolving Frictional Force and Reaction of a body moving with on an Inclined plane,

Frictional Force = mass × g × sin a

where a = to the angle given

Reaction = mass × g × cos a

Therefore,

mass × g × sin a = μ × mass × g × cos a

mass and g cancels out on both sides.

Therefore,

sin a = μ × cos a

make "μ" subject.

μ = sin a/cos a

(recall: tan a = sin a /cos a)

μ = tan a

recall a = angle given = 60°

μ = tan 60°

μ = √3

or simply recall that

μ = tan a

μ = tan 60°

μ = √3

Step-by-step explanation:

Answer:

Hope this helps you look it once.

Answer:

(x-2)²+(y+1)²=16

Step-by-step explanation:

r = 4 units

center Point => (2,-1)

the equation :

(x-2)²+(y+1)²=4² or

(x-2)²+(y+1)²=16

Answer: 1.662E-7 square kilometers

Step-by-step explanation:

A circle of radius = 23 or diameter = 46 or circumference = 144.5 cm has an area of: 1.662E-7 square kilometers (km²) 0.1662 square meters (m²)

0.7n+0.8n=2.1

1.5n=2.1

n=1.4

Therefore, the answer is B.

Answer:

B). n = 1.40

Step-by-step explanation:

0.7n + 0.8n = 2.1

(0.7n + 0.8n) = 2.1

1.5n = 2.1

/1.5 /1.5

n = 1.40

hope this helped!

The radius of a circle circumscribed about a regular hexagon with a side length of 30 units is approximately 51.96 units.


To find the radius of a circle circumscribed about a regular hexagon, we can draw radii from the center of the circle to each vertex of the hexagon. This creates six congruent triangles, each with a central angle of 60 degrees.

Using trigonometry, we can calculate the length of the radius. The formula is r = a / (2 * sin(π/6)), where “r” is the radius and “a” is the side length of the hexagon. Plugging in the given side length of 30 units, we have r = 30 / (2 * sin(π/6)) ≈ 51.96 units. Therefore, the radius of the circle circumscribed about the regular hexagon is approximately 51.96 units.

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The quadratic equation 2a^2 = -6 + 8a has two solutions: a = 3 and a = 1.

To solve the quadratic equation 2a^2 = -6 + 8a, we need to rearrange it into standard quadratic form, which is ax^2 + bx + c = 0, where a, b, and c are coefficients.

Step 1: Move all the terms to one side of the equation to set it equal to zero:

2a^2 - 8a + 6 = 0

Step 2: The equation is now in standard quadratic form, so we can apply the quadratic formula to find the solutions for 'a':

a = (-b ± √(b^2 - 4ac))/(2a)

Comparing with our equation, we have:

a = (-(-8) ± √((-8)^2 - 4(2)(6)))/(2(2))

Simplifying further:

a = (8 ± √(64 - 48))/(4)

a = (8 ± √16)/(4)

a = (8 ± 4)/(4)

Now, we can calculate the two possible solutions:

a1 = (8 + 4)/(4) = 12/4 = 3

a2 = (8 - 4)/(4) = 4/4 = 1

Therefore, the quadratic equation 2a^2 = -6 + 8a has two solutions: a = 3 and a = 1.

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The required value of x is 22 degrees for the given figure.

Adjacent angles are a sort of additional angle. Adjacent angles share a common side and vertex, such as a corner point. Their points do not overlap in any manner.

As we know that supplementary angles are defined as when pairing of angles addition to 180° then they are called supplementary angles.:

According to the given figure, it can be written as follows:

2x + 24 + 6x - 20 = 180

8x + 4 = 180

8x = 180 - 4

8x = 176

x = 176/8

x = 22

Therefore, the required value of x is 22 degrees for the given figure.

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The complete question is as follows:

Find the value of x for the below figure.