A line passes through (−1, 7) and (2, 10). Which answer is the equation of the line?

Answer:

The standard deviation σ = 0.6122

Step-by-step explanation:

Explanation:-

Given mean of the Population  = 5.5

we know that 95% of confidence interval of Z-score = 1.96

95% of confidence interval for mean in normal distribution

(μ±Z₀.₉₅σ)

(μ - 1.96σ , μ +1.96σ)

given that 95% of confidence interval between 4.3 and 6.7

μ - 1.96σ = 4.3

5.5 -1.96σ  = 4.3

5.5 - 4.3 = 1.96σ

1.2 = 1.96σ

σ = \(\frac{1.2}{1.96}\)

The standard deviation σ = 0.6122

Given the expression:

if x = 2, and y = -3, then we have the following:

therefore, the final result is 18

Answer:

Use the graph and table to answer the questions.

Which vehicle loses the most value each year?

Car

Which vehicle will lose all of its value first?

Car

If the truck’s rate of depreciation changes to a decrease of $1,650 each year, which vehicle will lose all of its value first?

Truck

Step-by-step explanation:

Answer:

car car truck

Step-by-step explanation:

Answer:

Step-by-step explanation:its ratxrat

...

The zeros of the divisor,

x-3=0,x=3

f(3)=4(3)²-3-3=30

The remainder is 30

The 99% confidence interval for mean temperature of human is :

( 98.04f, 98.40f )

A data set includes 108 body temperatures of healthy adult humans having a mean of 98.2 and a standard deviation of 0.64 .

Now, We have to construct  a 99% confidence interval estimate of the mean body temperature of all healthy humans.

We use these formula for upper limit and lower limit:

u = x + Zα/2 × (s/√n) (For the upper limit)

u = x - Zα/2 × (s/√n) (For the lower limit)

We have the information from question:

x = sample mean = 98.2

s = standard deviation = 0.64

n = sample size = 108.

\(Z_\frac{\alpha }{2}\) = critical value for a 2 tailed test performed at a 1% level of significance ( 100% - 99%) = 2.58

Now, Substitute the parameter,

For upper limit:

u = x + Zα/2 × (s/√n)

u = 98.2 + 2.58 ( 0.64/√108)

u = 98.2 + 2.58 ( 0.0616)

u = 98.2 + 0.1589

u = 98.4

For lower limit:

u = x - Zα/2 × (s/√n)

u = 98.2 - 2.58 ( 0.64/√108)

u = 98.2 - 2.58 ( 0.0616)

u = 98.2 - 0.1589

u = 98.04.

The 99% confidence interval for mean temperature of human is :

( 98.04f, 98.40f )

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Answer:

33 g

Step-by-step explanation:

the weight of the donut is a distractor number. if each donut has 11,000 mg of sugar, then 11,000 x 3 = 33,000 mg. In order to convert mg into g, we move the decimal over to the left 3 times.

33000. (0 times)

3300.0 (1 time)

330.00 (2 times)

33.000 (3 times)

By using a statistical calculator, the actual sample mean and sample standard deviation are:

Actual sample mean = 46.1500.

Actual ample standard deviation = 8.6256.

In Mathematics and Geometry, the sample mean for any set of data can be calculated by using the following formula:

Mean = ∑x/(n - 1)

In Mathematics and Geometry, the sample standard deviation for any set of data can be calculated by using the following formula:

Standard deviation, δx = √(1/N × ∑(x - \(\bar{x}\))²)

By using a statistical calculator, the actual sample mean and sample standard deviation are as follows;

Actual sample mean = 46.1500.

Actual ample standard deviation = 8.6256.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

10.50

Step-by-step explanation:

5+5.5=10.5............

Answer:

The answer is B $10.50 :)

Answer: (4,3) and (-1,8)

Step-by-step explanation:

Before I solve the system, I am going to rewrite it to make it easier for me to understand it.

\(y=x^2-4x+3\\y=-x+7\)

Notice that f(x) and g(x) have been changed into y. The reason is because f(x) and g(x) are the same and stand for y, but we only use f and g to distinguish between the 2 equations. We can use equal values to solve.

\(x^2-4x+3=-x+7\)          [add both sides by x]

\(x^2-3x+3=7\)                   [subtract both sides by 7]

\(x^2-3x-4=0\)                   [factor]

\((x-4)(x+1)=0\)

Notice that x-4=0 and x+1=0. This means the solutions are x=4 and x=-1.

To find the actual full solution, we have to plug those points back into the original equations.

\(-(4)+7=-4+7=3\\-(-1)+7=1+7=8\)

Therefore, the solutions to this system are (4,3) and (-1,8).

Answer:

-5 and +5

Step-by-step explanation:

add twelve to both sides

New equations: 2x= -+10

Divide by 2 on both sides

x=-5, +5

Answer:

x=11

Step-by-step explanation:

when we add 10 and 12 we get 22 and when we divide

22 by 2 we get 11

Answer:

No solution

Step-by-step explanation:

9(x-4)=9x-33

9x-36=9x-33

-9x       -9x

36=33

36 is not equal to 33 so therfore

there is no solution

Answer:the answer is 319.857 and round to 320

Step-by-step explanation:

The average rate of change for 1.8 < x < 2.5 is given as follows:

121.43.

The average rate of change of a function is given by the change in the output divided by the change in the input.

The change in the output for this problem is given as follows:

325 - 240 = 85.

The change in the input for this problem is given as follows:

2.5 - 1.8 = 0.7.

Hence the average rate of change is given as follows:

85/0.7 = 121.43.

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The probability that each bill is a $1 bill is given as follows:

1/16.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

The bills are replaced, hence we consider that for each trial, there is a 1/4 probability of selecting a $1 bill, as one out of the four bills are of $1.

Hence the probability that each bill is a $1 bill is obtained as follows:

p = 1/4 x 1/4

p = 1/16.

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Answer:

B.

True

Step-by-step explanation:

next time change it to is/are replace of is(are) (⁠~⁠_⁠~⁠;⁠)

Answer:

a ) dAt/dt  =  50,24 in/min

dh/dt  =  -  0,125 in/min

Step-by-step explanation:

The area of the top is At :

At = π*r²

a)  Tacking derivatives with respect to time:

dAt/dt  =  2* π*r * dr/dt

At   t  =  t₁      r  = 16 in     and  dr/dt =  0,5

Then

dAt/dt  =  2*3,14*16*0,5   in/min

a ) dAt/dt  =  50,24 in/min

b) The volume of the cylinder is:

Vc =  π*r²*h     ( where h is the heigh of the cylinder )

Tacking derivatives with respect to time

dVc/dt  =  2* π*r*h*dr/dt  +  π*r²*dh/dt

But  dVc/dt  = 0  since the volume remains constant, then:

π*r²*dh/dt  = -  2* π*r*h*dr/dt

r*dh/dt  =  -  2*h*dr/dt

dh/dt  = - 2*0,5*2/16  in/min

dh/dt  =  -  0,125 in/min

The height of the projectile after 4 seconds is 421.28 ft.

The projectile is in the air for 8.015 seconds.

The horizontal distance traveled by the projectile is 881.77 ft.

The maximum height of the projectile is 464.1 ft.

To solve this problem, we can use the kinematic equations of motion for a projectile.

Let's assume that the initial height of the projectile is zero.

What is the height of the projectile after 4 seconds:

We can use the equation:

\(y = yo + vot + 1/2at^2\)

where

y = height of the projectile

yo = initial height (zero in this case)

vo = initial vertical velocity = 220 sin(60°) = 190.53 ft/sec

a = acceleration due to gravity \(= -32.2 ft/sec^2\) ( negative since it acts downwards)

t = time = 4 sec

Plugging in the values, we get:

\(y = 0 + (190.53)(4) + 1/2(-32.2)(4)^2 = 421.28 ft\)

Therefore, the height of the projectile after 4 seconds is 421.28 ft.

Long is the projectile in the air:

The time of flight of a projectile can be calculated using the equation:

t = 2vo sinθ / g

where θ is the launch angle and g is the acceleration due to gravity.

Plugging in the values, we get:

t = 2(220 sin(60°)) / 32.2 = 8.015 sec

Therefore, the projectile is in the air for 8.015 seconds.

Horizontal distance traveled by the projectile:

The horizontal distance traveled by the projectile can be calculated using the equation:

\(x = xo + vot + 1/2at^2\)

where

x = horizontal distance traveled

xo = initial horizontal position (zero in this case)

vo = initial horizontal velocity = 220 cos(60°) = 110 ft/sec

a = acceleration due to gravity (zero in the horizontal direction)

t = time = 8.015 sec

Plugging in the values, we get:

\(x = 0 + (110)(8.015) + 1/2(0)(8.015)^2 = 881.77 ft\)

Therefore, the horizontal distance traveled by the projectile is 881.77 ft.

Maximum height of the projectile:

The maximum height of a projectile can be calculated using the equation:

\(ymax = yo + (vo^2 sin^2 \theta ) / 2g\)

Plugging in the values, we get:\(ymax = 0 + (190.53^2 sin^2(60\degree )) / (2)(32.2) = 464.1 ft\)

Therefore, the maximum height of the projectile is 464.1 ft.

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Given:

Required:

Simplify the expression.

Explanation:

The given expression is:

Simplify the expression as:

Apply the addition property.

Final answer:

The simplification of the expression is 3.7

The given statement defines a function F(x) that associates a unique ordinal number α to each initial segment of a well-ordered set W. The function F(x) assigns the ordinal α to the initial segment of W determined by x if and only if α is isomorphic (structurally equivalent) to that initial segment.

To prove the uniqueness of the ordinal number associated with each initial segment, we rely on Lemma 2.7 (presumably mentioned earlier). This lemma likely establishes some properties of isomorphic well-ordered sets, such as uniqueness of isomorphisms or a specific correspondence between ordinals and well-ordered sets.

Using the Replacement Axioms, we can show that the set F(W) exists, as it is obtained by applying the function F to each element of W and collecting the results as a set.

For each initial segment of W, there exists an ordinal α that is isomorphic to that segment; otherwise, we can consider the least element r for which no such ordinal exists. By definition, F(r) does not have a well-defined value, contradicting the construction of F.

Finally, if y is the least element in the set F(W), then F(W) = y, and we have established an isomorphism between W and the ordinal y.

In summary, the proof demonstrates that for any well-ordered set W, there exists a unique ordinal number (denoted by F(W)) that is isomorphic to W, confirming the statement that every well-ordered set is isomorphic to a unique ordinal number.

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The value of x, y and z in the diagram are:

1. The value of x in the diagram can be obtained as illustrated below:

x + 74 = 180° (angle on a straight line)

Collect like terms

x = 180 - 74

x = 106°

Thus, from the above calculation, we can conclude that the value of x is 106°

2. The value of y can be obtained as follow:

From the diagram,

m∠x = m∠y (Corresponding angles)

106° = m∠y

Value of y = 106°

3. The value of z can be obtained as follow:

From the diagram,

m∠y = m∠z (vertically opposite angles)

106° = m∠z

Value of z = 106°

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Answer:

.

Step-by-step explanation:

Answer: I believe it is 5

Step-by-step explanation: Because that's what the symbol is showing

All of the assertions are false. A statistically significant finding does not necessarily imply that the null hypothesis has been proven incorrect, nor does it indicate how likely it is to be true.

Generally speaking, the word "norm" describes something that is customary, typical, anticipated, or standard. Norms are established definitions of beneficial attitudes and actions that ought to be commonplace, or "the norm," whenever a group is working together. They apply to cooperation and collaboration.

When the variances are known and the sample size is large, a z-test is a statistical test that is used to assess whether two population means differ from one another.

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Answer:

(3+4)^2=9+24+16

7^2

=49

Answer:

8.25 minutes

Step-by-step explanation:

31 minutes-6.25 minutes=24.75 remaining miutes between the last 3 miles so then you take 24.75 minutes÷ 3 miles remaining= 8.25 minutes each last 3 miles

Answer:

D) h=2t+5

Step-by-step explanation:

Answer:

Height in w week = 12 + 2w

Step-by-step explanation:

Given:

Height of plant = 12 cm

Rate of plant growth = 2 cm per week

Find:

Equation

Computation:

Height in w week = Height of plant + (Rate of plant growth)(Number of week)

Height in w week = 12 + (2)(w)

Height in w week = 12 + 2w

The green family will double their investment in 34 years after the principal is subject to compound interest continuously.

The principal invested = $2500

Rate of interest annually = 2.75%

Time = t years

Amount  = double of principal = 2500 × 2 = $ 5000

Interest is compounded continuously

Formula to calculate the amount is given by:

\(A=Pe^{rt}\)

Now we will use the values to find the exact value of t

or, \(5000 = 2500 e^{0.0275t}\)

or, ln 2 = 0.0275t

or, t = 25.205 years

or, t ≈ 25 years

Compound interest allows interest to accumulate over time as opposed to simple interest, which does not compound because prior interest is simply not added to the principal for the current period.

The simple annual interest rate is obtained by multiplying the interest per period by the total number of periods in a year.

Hence the Green family will have doubled the investment in approximately 25 years.

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Answer:

5:3 = 10:6

10:6 = 20:12 or 5:3