why is root 3 not 1.5

like a square of 3m2

wouldn't both sides have 1.5

1.5x1.5 = 3 ?

So why is root 3 =1.73...​

Answer:

Because he thought it would make him stand out.

The requried coordinates of the image of the given triangle is A'(-2, 3), B'(-5, 6), and C' (-6, 0).

Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.

Here,
Coordinate of the given triangle before reflection across the y-axis,
A = (2, 3)
B = (5, 6)
C = (6, 0)

Since reflection is to be performed across the y-axis,
So the equation of the trasformation is given as,
Triangle A'B'C' ⇒ (-x,y)

So the coordinate of the image formed is given as,
A'(-2, 3), B'(-5, 6), and C' (-6, 0).

Thus, the requried coordinates of the image of the given triangle is A'(-2, 3), B'(-5, 6), and C' (-6, 0).

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AD-BD=22-15=7

AB is equal to 7.

AD-AC=22-10

AB is equal to 12.

AB+CD=7+12=19.

AD-(AB+CD)=22-19=3

Answer:

3

Step-by-step explanation:

As you can see from the image attached, the length of BC = 3 because:

AC= 10m, BD=15m and AD=22m

When we add up AC + BD = 25 but the length of AD is 22, the 3 extra from the sum of AC + BD is the length of BC.

Answer:20

Step-by-step explanation:

If 9 x 2=18 then 10 x 2=20 should be the answer.

Using a midpoint Riemann sum with 3 subintervals of equal length to approximate \(\int^{70}_{10}v(t)dt\) is 2020 and \(\int^{70}_{10}v(t)dt\) means the distance in feet, traveled by rocket A from t=0 seconds to t=70 seconds.

From the given question,

An initial height of 0 feet at time t=0 seconds.

The velocity of the rocket is recorded for selected values of over the interval 0 < t < 80 seconds.

(a) Using a midpoint Riemann sum with 3 subintervals of equal length to approximate \(\int^{70}_{10}v(t)dt\).

\(\int^{70}_{10}v(t)dt\)

A midpoint Riemann sum with 3 sub intervals so, n=3

∆t= (70-10)/3

∆t = 60/3

∆t = 20

Intervals: (10, 30), (30,50), (50,70)

Midpoint:      20        40         60

Midpoint Riemann Sum

\(\int^{70}_{10}v(t)dt\) = ∆t[v(20+v(40)+v(60)]

From the table

\(\int^{70}_{10}v(t)dt\) = 20[22+35+44]

\(\int^{70}_{10}v(t)dt\) = 20*101

\(\int^{70}_{10}v(t)dt\) = 2020

(b) Now we have to explain the meaning of v(t)dt in terms of the rocket's flight \(\int^{70}_{10}v(t)dt\).

It means the distance in feet, traveled by rocket A from t=0 seconds to t=70 seconds.

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Answer:

Below

Step-by-step explanation:

.014 g / .0022 cm^3   = 6.364  gm / cc   = 6364 kg/m^3

    density is too low to be pure gold  

Answer:

Step-by-step explanation:

Dr Davis says that ratios are everywhere like 4 legs on each dog, 2 arms on each person, etc. She also said that ratios can be 5 people per car, 2 people per elevator, etc.

Answer:C

Step-by-step explanation: (150,158,166,174,...)

Answer:

c

Step-by-step explanation:

it just is

The height of the gymnastic mats is \(\dfrac{5 \times \sqrt{3}}{3}\) feet.

The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,

\(\rm{Tangent(\theta) = \dfrac{Perpendicular}{Base}\)

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

Base is the adjacent smaller side of the angle θ.

As we can see in the below image the gymnastic mats are making the base of the right-angled triangle, therefore,

\(\rm{Tangent(\theta) = \dfrac{Perpendicular}{Base}\)

\(Tan (\angle ACB) = \dfrac{Height}{BC}\)

 \(Tan (30^o) = \dfrac{Height}{5\ feet}\)

\(\dfrac{1}{\sqrt{3}} = \dfrac{Height}{5\ feet}\\\\\dfrac{1 \times 5}{\sqrt{3}} = Height\\\\Height = \dfrac{5}{\sqrt{3}}\)

Multiplying √3 with both denominator and numerator,

\(Height = \dfrac{5 \times \sqrt{3}}{\sqrt{3}\times \sqrt{3}}\\\\Height = \dfrac{5 \times \sqrt{3}}{3}\)

Hence, the height of the gymnastic mats is \(\dfrac{5 \times \sqrt{3}}{3}\) feet.

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Answer: B

startFraction 5 StartRoot 3 EndRoot Over 3 EndFraction ft.

Step-by-step explanation:

answer:

x=74 y=27

steps:

triangle in the middle is

180-126 = 54

180-85 = 95

180-149 = 31

126=2x+1+31

126=2x+32

2x=94

x=74

126+2y=180

2y=54

y=27

Answer and Step-by-step explanation:

1a. The work is NOT correct.

1b. The mistake was keeping the 2 with the \(\frac{12}{15}\), in which this number was found by multiplying the denominator 5 by the whole number 2, then adding it to the numerator 2, resulting in \(\frac{12}{15}\).

1c. Multiply the denominator 5 by the whole number 2, then add it to the numerator 2, which results in \(\frac{12}{15}\). When you add \(\frac{1}{15}\), you get the answer to be \(\frac{13}{15}\).

Have a good day!

Answer:

0.000001019 in scientific notation

=

1.019 × 10-6  

Step-by-step explanation:

Answer:

\(1.019^{6}\)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Click this link to see the answer pls. I cannot explain it on this little square box.

i swear, just click it.

https://giphy.com/gifs/trolli-basketball-weirdly-awesome-sour-brite-slam-STcNf6rLHyMA8

k=7

given a quadratic polynomial

ax^2+bx+c

the sum of the roots is given by -(b/a)

and the product of the roots as (c/a)

hence we get sum of roots as -(-(k+6)/1) and product of roots as (2(2k-1))/1

since the sum is equal to half the Product then we get

k+6=2k-1 and solving for k we get 7

A large standard deviation means the view of the people is very dispersed and not near the mean or not similar.

Standard deviation is a very important terminology in Statistics which help to study dispersion of data from the mean

A lower value of standard deviation means the data is accumulated near the mean while a higher value means the data is dispersed in the entire range.

It is given in the question that

A researcher conducts a written survey to determine the opinion of subjects regarding their opinion of the favorability of a certain hospital.

The standard deviation value for the sample is large

A large standard deviation means the view of the people is very dispersed and not near the mean or not same.

There will be difference in the opinion as they deviate from the central value.

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First off, we factor out the expression:

\( \displaystyle \large{y = 2 {x}^{2} - 12x + 16} \\ \displaystyle \large{y = 2 ( {x}^{2} - 6x + 8) }\)

In the bracket, separate 8 out of the expression.

\( \displaystyle \large{y = 2[ ( {x}^{2} - 6x + 8)] }\\ \displaystyle \large{y = 2[ ( {x}^{2} - 6x) + 8]}\)

In x^2-6x, find the third term that can make up or convert it to a perfect square form. The third term is 9 because:

\( \displaystyle \large{ {(x - 3)}^{2} = {x}^{2} - 6x + 9}\)

So we add +9 in x^2-6x.

\( \displaystyle \large{y = 2[ ( {x}^{2} - 6x + 9) + 8]}\)

Convert the expression in the small bracket to perfect square.

\( \displaystyle \large{y = 2[ {(x - 3)}^{2} + 8]}\)

Since we add +9 in the small bracket, we have to subtract 8 with 9 as well.

\( \displaystyle \large{y = 2[ {(x - 3)}^{2} + 8 - 9]} \\ \displaystyle \large{y = 2[ {(x - 3)}^{2} - 1]}\)

Then we distribute 2 in.

\(\displaystyle \large{y = 2[ {(x - 3)}^{2} - 1]} \\ \)

\(\displaystyle \large{y = 2[ {(x - 3)}^{2} - 1]} \\ \displaystyle \large{y = [2 \times {(x - 3)}^{2} ]+[ 2 \times ( - 1)] } \\ \displaystyle \large{y = 2 {(x - 3)}^{2} - 2 }\)

Remember that negative multiply positive = negative.

Hence the vertex form is y = 2(x-3)^2-2 or first choice.

The sampling distribution of the sample mean will always have the same the mean of the original non-normal distribution, as the original distribution.

What is distribution?

Each of these samples contains a mean, and if we add up all of the means, we can construct a probability distribution that explains the distribution of the means. As long as we have sufficient samples, as will be discussed later, this distribution is always normal and is referred to as the sampling distribution of the sample mean.

Since the sample mean's sampling distribution is normal, we can naturally calculate the distribution's mean and standard deviation and utilise that information to analyse probability questions.

Here, The sample variance is equal to the population variance divided by the sample size if the population is infinite and the sampling is random, or if the population is finite but we are sampling with replacement.

So we need to use the mean of non-normal distribution.

Hence the answer will be the mean of the original non-normal distribution.

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Answer:

D) False, 7 isn't an element of the set.

Step-by-step explanation:

The set is written as { 14, 21, 28, 35, 42 }

And 7 isn't in there.

If, only if the set said { ... 14, 21, 28, 35, 42... }

7 would've been an element.

Have a wonderful day! :-)

Answer:

17 minutes    i had this same answer and question 2day, so ur lucky.

Step-by-step explanation:

The initial solution most people will think of is to use the fastest person as an usher to guide everyone across. How long would that take? 10 + 1 + 7 + 1 + 2 = 21 mins. Is that it? No. That would make this question too simple even as a warm up question.

To reduce the amount of time, we should find a way for 10 and 7 to go together. If they cross together, then we need one of them to come back to get the others. That would not be ideal. How do we get around that? Maybe we can have 1 waiting on the other side to bring the torch back. Ahaa, we are getting closer. The fastest way to get 1 across and be back is to use 2 to usher 1 across. So let's put all this together.

1 and 2 go cross

2 comes back

7 and 10 go across

1 comes back

1 and 2 go across (done)

Total time = 2 + 2 + 10 + 1 + 2 = 17 mins

Answer:

17 minutes

Step-by-step explanation:

Let A be the person who takes 1 min,

B who takes 2 mins, C who takes 7 mins and D who takes 10 mins

A and B cross the river in 2 mins, A comes back in 1 min

C and D cross the river in 10 mins, B comes back in 2 mins

A and B cross the river in 2 mins

Total time:

2 + 1 + 10 + 2 + 2 = 17 minutes

The probability that atleast one students is taking a language class is 0.7

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

Let :

Spanish = S ; French = F ; German = G

SnFnG = 3

(SnF) only = 9 - 3 = 6

(SnG) only = 5 - 3 = 2

(FnG) only = 5 - 3 = 2

S only = 28 - (6+3+2) = 17

F only = 21 - (2+3+2) = 14

G only = 12 - (6+3+2) = 1

Student not taking any of the classes are;

(100 - (17+14+1+2+2+6+3))

100 - 45 = 55

Atleast 1 is taking a language class out of 2 selected

The probability that atleast one students is taking a language class :

(45/100 * 55/99) + (55/100 * 45/99) + (45/100 * 44/99)

= 0.7

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The area of the trapezoid is equal to 122.5 square centimeters .

The Area of the Trapezoid can be calculated using the formula

Area = (1/2)*(a+b)h

where , a is the top base

b is the bottom base

h is the height .

in the question , it is given that

the top base of the trapezoid(a) = 14 cm

the bottom base of the trapezoid(b) = 21 cm

the height of the trapezoid(h) = 7 cm

So , the Area = (1/2)*(a+b)h

= (1/2)*(14+21)*7

= (1/2)*35*7

= 245/2

= 122.5

Therefore , the area of the trapezoid is equal to 122.5 square centimeters .

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The TI-84 Plus calculator can be used to find various percentiles and guarantee values for a certain type of automobile tire. The 19th percentile of tire lifetimes is approximately 35.38 thousand miles. The 71st percentile is approximately 42.85 thousand miles. The first quartile, which represents the 25th percentile, is approximately 37.07 thousand miles. To ensure that only 2% of the tires violate the guarantee, the tire company should guarantee a minimum of approximately 31.35 thousand miles.

To find the percentiles and guarantee values using the TI-84 Plus calculator, we can utilize the normal distribution function. Given that the lifetime of the automobile tires is normally distributed with a mean (μ) of 39 thousand miles and a standard deviation (σ) of 6 thousand miles, we can apply these values to the calculator.

(a) To find the 19th percentile, we input the following command: invNorm(0.19, 39, 6). The calculator will provide an output of approximately 35.38 thousand miles.

(b) For the 71st percentile, we use the command: invNorm(0.71, 39, 6). The calculator will yield an approximate value of 42.85 thousand miles.

(c) The first quartile, representing the 25th percentile, can be obtained by entering: invNorm(0.25, 39, 6). The calculator will give an output of approximately 37.07 thousand miles.

(d) To determine the guarantee value for which only 2% of the tires violate the guarantee, we use the command: invNorm(0.02, 39, 6). The calculator will provide an approximate value of 31.35 thousand miles.

These calculations give us the requested percentiles and guarantee value for the tire lifetimes, rounded to at least two decimal places.

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The width of the original piece of sheet metal is (w^2 - l^2)/(3w + 3l), and the length is (l^2 - w^2)/(3w + 3l).

To solve this problem, we can use the formula for the volume of a rectangular box, which is V = lwh, where l is the length, w is the width, and h is the height.

First, let's find the height of the box. Since we cut squares from each corner, the height of the box is the length of the square that was cut out. Let's call this length x.

The width of the box is the original width minus the lengths of the two squares that were cut out, which is w - 2x.

Similarly, the length of the box is the original length minus the lengths of the two squares that were cut out, which is l - 2x.

Now we can write the volume of the box in terms of x, w, and l:

V = (w - 2x)(l - 2x)(x)

Expanding this expression, we get:

V = x(4wl - 4wx - 4lx + 8x^2)

Simplifying further:

V = 4x^3 - 4wx^2 - 4lx^2 + 4wlx

To find the dimensions of the original piece of sheet metal, we need to maximize this volume. We can do this by taking the derivative of the volume with respect to x and setting it equal to zero:

dV/dx = 12x^2 - 8wx - 8lx + 4wl = 0

Solving for x, we get:

x = (2wl)/(3w + 3l)

Now we can use this value of x to find the width and length of the original piece of sheet metal:

w - 2x = w - 2(2wl)/(3w + 3l) = (w^2 - l^2)/(3w + 3l)

l - 2x = l - 2(2wl)/(3w + 3l) = (l^2 - w^2)/(3w + 3l)

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The force required to keep a hockey puck sliding at a constant velocity, neglecting ice friction and air resistance, is equal to its weight. The correct option is "equal to its weight."

When a hockey puck is set in motion across a frozen pond and there is no ice friction or air resistance, the only force acting on the puck is its weight, which is the force due to gravity pulling it downward. According to Newton's first law of motion (the law of inertia), an object at a constant velocity will continue to move at that velocity unless acted upon by an external force.

Since the puck is already in motion and we want to maintain its constant velocity, the force required to counteract its weight and keep it sliding is equal to its weight. This is because the weight of an object is the force exerted on it by gravity, and in the absence of other forces, an equal and opposite force is needed to maintain the object's motion without acceleration.

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With 95% confidence, there is a statistically significant difference in the proportion of patients who developed polyps. Taking an aspirin a day appears to be effective in reducing the chance of developing subsequent polyps.

According to the study done by the Ohio State University Medical Center, a 95% confidence interval on the difference in proportions of the two groups [aspirin group (p1) minus non-aspirin group (p2)] was found to be -0.164 < p1 - p2 < -0.036. This means that the probability of the difference in the proportions of polyp development in the aspirin group and the non-aspirin group is between -0.164 and -0.036 with 95% confidence level. Since the interval doesn't contain zero, it indicates that there is a statistically significant difference in the proportion of patients who developed polyps between the two groups. Therefore, taking an aspirin a day appears to be effective in reducing the chance of developing subsequent polyps.

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Answer:

40%

Step-by-step explanation:

percent change in Mike's long distance runs = (change in miles ran / initial longest mile ran) x 100

change in miles ran = new personal record - initial personal record

14 - 10 = 4

(4/10) x 100 = 40%

Answer:

The first one has a slope of 4

The second one has a slope of 0.3 repeating

Step-by-step explanation:

You pick two points on the graph.

You find the x and y coordinates of each point.

You find the difference between the two x coordinates.

You find the difference between the two y coordinates.

Divide the difference in the y coordinates by the x coordinates.

If im wrong sorry owo im only in elementary school... <3

Answer:

4/6

Step-by-step explanation: