A scale drawing of a lake has a scale of 1 cm to 80 m. If the actual width of the lake is 1,000 m, what is the width of the lake on the scale drawing? part 1,

. Write the equation for the line: (Hint: there are two points given to you!)

________________________

y= mx + b

the slope is m

or

(y - y1) = m (x - x1)

___________________

points (x,y)

point 1 (4, 4) x1 = 4; y1 = 4

point 2 (3 , -1) x2= 3; y2 = -1

The slope m = (y2- y1) / (x2 -x1)

m=(-1 - 4 )/( 3 - 4)

m= -5/-1 = 5

(In this case, you choose which point you want to put as point one and point two, you will always get the same answer)

____________________

(y - 4) = 5 (x - 4)

y= 5x -20 +4

y= 5x - 16

The equation for the line is y= 5x - 16

__________________

Do you have any questions regarding the solution?

The statement that the blue radius is perpendicular to the green cord is false

From the complete question,

The blue radius does not bisect the green chord

This means that the blue radius and the green chord do not meet at 90 degrees

Since both lines do not meet at 90 degrees, then they are not perpendicular

Hence, the statement that the blue radius is perpendicular to the green cord is false

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Answer:

720,000 is 719,618.4 larger than 3.6 x 106

Step-by-step explanation:

The critical value used to test if there is evidence of an effect due to blocks at the 5% level of significance is 10.76.

The critical value can be determined using a statistical table.

The degrees of freedom for the blocks is 4 (df_b = 5 - 1 = 4) and for the treatments is 2 (df_t = 3 - 1 = 2).

The critical value for a 5% level of significance is 10.76.

This value can be found in the statistical table given in the textbook.

The critical value used to test if there is evidence of an effect due to blocks at the 5% level of significance can be calculated by using the F-test statistic.

The F-test is used to compare the variance between the blocks (SSBL) and the variance between the groups (SSB).

The F statistic is calculated by dividing the variance between the blocks (SSBL) by the variance between the groups (SSB).

In this case,

The F statistic is 3738/1048.93 = 3.56.

The critical value for a 5% level of significance can be found using a statistical table.

According to the table,

The critical value for an F statistic of 3.56 with four degrees of freedom in the numerator and four degrees of freedom in the denominator is 10.76

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(x-2) is not a factor of f(\(x\)) = \(3x^{4}-3x^{3}-9x^{2} +5x-2\).

Remainder Theorem is an approach of Euclidean division of polynomials. According to this theorem, if we divide a polynomial P(x) by a factor ( x – a) that isn't essentially an element of the polynomial, you will find a smaller polynomial along with a remainder.

The Remainder Theorem: If (x-a) is a factor of the f(x) then f(a) = 0

Here,

f(\(x\)) = \(3x^{4}-3x^{3}-9x^{2} +5x-2\)

substitute a = 2

\(f(2)=3(2^{4}) -3(2) ^{3}-9(2)^{2}+5(2)-2\)

      = 48-24-36+10-2

      = 32-36

f(2)  = -4

f(2) \(\neq 0\)

Hence, (x-2) is not a factor of f(\(x\)) = \(3x^{4}-3x^{3}-9x^{2} +5x-2\).

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Answer:

b

Step-by-step explanation:

Answer:

#5- 7.8 hours  #6- $5.25

Step-by-step explanation

Question #5- 7.8 hours      

First we have to find the speed. If the speed was constant we should be able to divide the miles by the time to find the speed. So 239.82 divided by 4.2. This would leave us with a speed of 57.1 mph. So to finish the question, we have to take  what we know and divided it by the speed. If he drives 445.38 miles at the same speed of 57.1 mph it would take him 7.8 hours. I got this answer by dividing the miles by the speed. 445.38 divided by 57.1. Which got us our time, 7.8 hours.

Question #6- $5.25

Okay so we know that the chips cost .75 cents a bag, and he got two bags. So if we take .75 and multiply it by two we get 1.50. So the chips alone cost $1.50. We can take the price of the chips and subtract it from the total price. 22.50-1.50. 21. Now we have just the prices of the sandwiches. If we take the total price of the sandwiches and divide it by the number of sandwiches bought, we get $5.25. So each sandwich cost $5.25 each.

The sum of the two sides 13 inches and 6 inches is greater than the third side 18 inches. These are 18 in, 6 in, and 13 in the measurement of the triangle.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

Any two parts of a triangle can be added together to have a length larger than the third side.

If the side lengths could be from a triangle use an inequality to prove your answer 18 in, 6 in, 13 in.

Then the inequality is given as,

13 + 6 > 18

19 > 18

The sum of the two sides 13 inches and 6 inches is greater than the third side 18 inches. These are 18 in, 6 in, and 13 in the measurement of the triangle.

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Answer:

352 OZ

Step-by-step explanation:

One pound = 16 OZ

take 22 and multiply it by 16

22 x 16 = 352

Answer:

15 ounces per hour

Step-by-step explanation:

This is dimensional analysis, so we need to find conversion factors for ounces per pound and hours per day.  Once we have those we write the equation such that the units we need are left and the others cancel:

22lb/1 day  x  16 ounces/1 lb x 1 day/24hrs = 14.66666666666 ounces per hour

Since the problem was written with no decimals, our answer probably shouldn't either and in most cases like this we want to round to the nearest whole number, which is 15.

Given:

The expression is:

\(13-\dfrac{5}{y}\)

To find:

The description that matches the given expression.

Solution:

We have,

\(13-\dfrac{5}{y}\)

Here, \(\dfrac{5}{y}\) is describes as the quotient of five and a number and the minus sign describes the difference between 13 and the quotient.

So, the description that matches the given expression is "difference of thirteen and the quotient of five and a number".

Therefore, the correct option is C.

Answer:

the difference of thirteen and the quotient of five and a number

Step-by-step explanation:

The total price for an 8 pound package is B($17.20)

21.5 cents per pound for the unit price purchased an 8-pound package.

We should to convert cents into dollars .

How to convert pound into dollar?

You must multiply by 1.30 to convert pounds to dollars. Thus, you multiply £20 by 1.30 to get $26 in dollars to convert £20.  Divide the dollar amount you are exchanging by the current exchange rate for pounds using a calculator. For instance, if you want to convert 100 USD to pounds at the current exchange rate of 1.3845 GBP for every USD, divide 100 USD by 1.3845 to get 72.23 pounds.

21.5 cents x 1 dollar / 100 cents

= 21.5 dollar / 100

= 0.215 dollars

0.215 dollars x 8 pounds

= 1.72 dollars.

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Answer: 14,575

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

9 x 4 = 36

3 x 12 = 36

12 x 3 = 36

Answer:

the least or lowest common multiple is 36

Step-by-step explanation:

9x4=36

3x12=36

12x3=36

Answer:

c

Step-by-step explanation:

Answer:

guys its D

Step-by-step explanation:

A statistical test with a p-value (p) of 0.01 means that there is a 1% probability of obtaining the observed results, or more extreme results, purely by chance if the null hypothesis is true.

The null hypothesis typically states that there is no significant relationship or effect between the variables being studied. In other words, the p-value helps us determine the likelihood of observing the data we have if the null hypothesis holds true.

A p-value of 0.01 is considered statistically significant, as it is less than the commonly used threshold of 0.05. This means that there is strong evidence against the null hypothesis, and we might reject it in favor of the alternative hypothesis. The alternative hypothesis proposes that there is a significant relationship or effect between the variables. It's important to note that a low p-value doesn't prove causation, but it does suggest a significant association between the variables that warrants further investigation.

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Answer:

$6400

Step-by-step explanation:

If Mrs. Hill takes out a mortgage for $80,000 with a 4% interest rate, what will her interest be after 20 years?

First you want to find how much she will get each year.

Turn 4% into a decimal.

Which you have to move the decimal point over to spaces to the left.

4. ----- .4 ----- .04

Now that you have done that you need to multiply,

$80000 × .04

which is $3200.

Now you know she gets $3200 a year.

Now multiply $3200 by 20.

$3200 × 20

which is $6400.

She will get $6400 interest.

The value of the integral (9x + 9y) da over the region r is approximately 14.0625.

To evaluate the given integral using a transformation, we can use the concept of a double integral over a region in the xy-plane.

First, let's define the transformation T from the uv-plane to the xy-plane, where x = 9u and y = 9v. This transformation scales the coordinates by a factor of 9.

Next, let's find the Jacobian determinant of the transformation. The Jacobian determinant of T is given by the absolute value of the determinant of the matrix of partial derivatives of x and y with respect to u and v. In this case, the matrix is:

J(T) = |[∂x/∂u  ∂x/∂v]|
           |[∂y/∂u  ∂y/∂v]|

Taking the partial derivatives, we have:

∂x/∂u = 9   and   ∂x/∂v = 0
∂y/∂u = 0   and   ∂y/∂v = 9

Therefore, the Jacobian determinant is:

J(T) = |[9  0]|
           |[0  9]|

Taking the determinant, we have:

J(T) = (9)(9) - (0)(0) = 81

Now, we can evaluate the integral by transforming it into the uv-plane. The integral becomes:

∬(9x + 9y) dA = ∬(9(9u) + 9(9v))(J(T)) dA

Since x = 9u and y = 9v, we can substitute these expressions into the integral:

∬(9(9u) + 9(9v))(J(T)) dA = ∬(81u + 81v)(81) dA

Now, we need to find the limits of integration in the uv-plane. The region r in the xy-plane corresponds to a parallelogram in the uv-plane with vertices (-1/9, 2/9), (1/9, -2/9), (3/9, 0), and (1/9, 4/9).

Using these vertices, we can determine the limits of integration for u and v:

u ranges from -1/9 to 1/9
v ranges from 2/9 to 4/9

Therefore, the integral becomes:

∬(81u + 81v)(81) dA = ∫[u=-1/9 to 1/9] ∫[v=2/9 to 4/9] (81u + 81v)(81) dudv

Now, we can evaluate this double integral:

∫[u=-1/9 to 1/9] ∫[v=2/9 to 4/9] (81u + 81v)(81) dudv = (81)(81) ∫[u=-1/9 to 1/9] ∫[v=2/9 to 4/9] (u + v) dudv

Evaluating the inner integral with respect to u, we have:

(81)(81) ∫[u=-1/9 to 1/9] (1/2)u^2 + vu [v=2/9 to 4/9] dv

Simplifying further, we get:

(81)(81) ∫[u=-1/9 to 1/9] (1/2)u^2 + (vu)(4/9 - 2/9) dv

Now, we can evaluate the inner integral with respect to v:

(81)(81) ∫[u=-1/9 to 1/9] (1/2)u^2 + (vu)(4/9 - 2/9) dv = (81)(81) ∫[u=-1/9 to 1/9] (1/2)u^2 + (vu)(2/9) dv

Simplifying further, we have:

(81)(81) ∫[u=-1/9 to 1/9] (1/2)u^2 + (2/9)u(2/9) dv

Now, we can evaluate the inner integral with respect to v:

(81)(81) ∫[u=-1/9 to 1/9] (1/2)u^2 + (2/9)u(2/9) dv = (81)(81) ∫[u=-1/9 to 1/9] (1/2)u^2 + (4/81)u^2 du

Combining like terms, we get:

(81)(81) ∫[u=-1/9 to 1/9] (1/2 + 4/81)u^2 du

Simplifying further, we have:

(81)(81) ∫[u=-1/9 to 1/9] (85/162)u^2 du

Now, we can evaluate the integral:

(81)(81) ∫[u=-1/9 to 1/9] (85/162)u^2 du = (81)(81)(85/162) ∫[u=-1/9 to 1/9] u^2 du

Integrating u^2 with respect to u, we get:

(81)(81)(85/162) ∫[u=-1/9 to 1/9] u^2 du = (81)(81)(85/162) [u^3/3] from -1/9 to 1/9

Plugging in the limits of integration, we have:

(81)(81)(85/162) [(1/9)^3/3 - (-1/9)^3/3]

Simplifying further, we get:

(81)(81)(85/162) [(1/729)/3 - (-1/729)/3] = (81)(81)(85/162) [2/729]/3

Now, we can simplify this expression:

(81)(81)(85/162) [2/729]/3 = (81)(81)(85/162) (2/729)(1/3)

Finally, evaluating this expression, we get:

(81)(81)(85/162) (2/729)(1/3) ≈ 14.0625

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The instantaneous velocity of the rock at t = 0.6 is -19.2 ft/s. It's worth noting that you mentioned t ∈ [1, 2], but the calculation of the instantaneous velocity at t = 0.6 does not fall within this interval.

To find the instantaneous velocity of the rock at t = 0.6, we need to calculate the derivative of the position function S(t) with respect to time.

The position function is given by S(t) = -16t^2 + 64.

Step 1: Calculate the derivative of S(t) with respect to t.

Taking the derivative of S(t) with respect to t gives us the velocity function V(t):

V(t) = dS(t)/dt

Differentiating -16t^2 + 64 with respect to t, we get:

V(t) = -32t

Step 2: Evaluate the velocity at t = 0.6.

To find the instantaneous velocity at t = 0.6, we substitute t = 0.6 into the velocity function V(t):

V(0.6) = -32(0.6)

Calculating the expression:

V(0.6) = -19.2 ft/s

Since you specifically asked for the instantaneous velocity at t = 0.6, we evaluated it accordingly. If you need to find the velocity within the interval [1, 2], you can calculate V(t) = -32t within that range and evaluate it at the desired values of t.

Additionally, it's important to consider the context of the problem. The negative sign in the velocity indicates that the rock is falling downwards. The magnitude of the velocity, 19.2 ft/s, represents the speed at which the rock is falling.

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A rock is dropped from a height of 64ft. The position of the rock is given by ( S(t)=-16 t^{2}+64 \). What is the instantaneous velocity at t=0.6 where t∈[1,2]?

Answer:

x=3

Step-by-step explanation:

Therefore, the function y as a function of x is: y(x) = c1 e^(-x) - (1/2) e^x - (7/2) e^(3x) where c1 is a constant determined by the initial conditions.

We are given the differential equation:

y′′′ − 3y′′ − y′ + 3y = 0

To solve this equation, we can first find the characteristic equation by assuming that y = e^(rt), where r is a constant:

r^3 e^(rt) - 3r^2 e^(rt) - r e^(rt) + 3e^(rt) = 0

Simplifying and factoring out e^(rt), we get:

e^(rt) (r^3 - 3r^2 - r + 3) = 0

This equation has three roots, which we can find using numerical methods or by making educated guesses. We find that the roots are r = -1, r = 1, and r = 3.

Therefore, the general solution to the differential equation is:

y(t) = c1 e^(-t) + c2 e^t + c3 e^(3t)

where c1, c2, and c3 are constants that we need to determine.

Using the initial conditions, we can find these constants:

y(0) = c1 + c2 + c3 = -4

y′(0) = -c1 + c2 + 3c3 = -6

y′′(0) = c1 + c2 + 9c3 = -20

We can solve these equations simultaneously to find c1, c2, and c3. One way to do this is to subtract the first equation from the second and third equations, respectively:

c2 + 4c3 = -2

c2 + 8c3 = -16

Subtracting these two equations, we get:

4c3 = -14

Solving for c3, we get:

c3 = -14/4 = -7/2

Substituting this value of c3 into one of the earlier equations, we can solve for c2:

c2 + 8(-7/2) = -16

c2 = -1/2

Finally, we can use these values of c1, c2, and c3 to write the solution to the differential equation as:

y(t) = c1 e^(-t) - (1/2) e^t - (7/2) e^(3t)

Substituting x for t, we get:

y(x) = c1 e^(-x) - (1/2) e^x - (7/2) e^(3x)

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Answer:

f=1/18x+1/4 x=-9/2+18f

First, we convert 1/2% to a decimal.

Similarly:

The equation is | x - 4 | = 3

Here, we are given that x represents all numbers that are at a distance of 3 units from 4.

Now, the distance of x from 4 can be in the positive direction or in the negative direction.

This can be represented by an absolute value function as follows-

| x - 4 | = 3

we can check our result by solving the given equation

| x - 4 | = 3 can be written as-

x - 4 = 3  or  -x + 4 = 3

x = 7 or x = 1

Both, x = 1 and 7 are at a distance of 3 units from 4.

Thus, | x - 4 | = 3 is the absolute value function.

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Answer:

36

Step-by-step explanation:

FRIEND ME AM SMART

Answer:

Area = 35

Step-by-step explanation:

Area = base * height

A=b*h=7*5=35

Answer:

it would be 3rd one

Step-by-step explanation:

(2a)3 = (8a)3

(4b)3=64b3

simplify= (8ab)3

Jane should land 1.5 mi down the shoreline and walk the remaining 4.5 mi to the village to minimize her travel time.

Let x = distance travelled along the shore over water.

Then, 6 − x = distance travelled along the shore over land.

Let T = the total time taken to reach the destination.

T = distance/velocity = √(4 + x²)/3 + (6-x)/5 on [0, 6].

Note that T must be non negative and that x = 6 means the destination

is reached solely by rowing and without the benefit of faster land

travel. In actual fact, T is valid over [0, ∞) but [0, 6] is reasonable here.

T' = x/3√(4 + x²) - 1/5 = 5x - 3√(4 + x²) = 0

⇒5x = 3√(4 + x²)

⇒25x² = 9(4 + x²)

⇒16x² = 36

⇒x = ±6/4 = ±1.5

The negative x value is discarded since it does not belong to [0,6].

T(0) = 28/15 = 1.8667

T(1.5) = 1.733

T(6) = 2.1082

Therefore, Jane should land 1.5 mi down the shoreline and walk the

remaining 4.5 mi to the village to minimize her travel time.

Her minimum travel time will be T(1.5) = 1.733 hrs. or 1hr 44 min.

--The given question is incomplete, the correct question is

"Jane is 2 mi, offshore in a boat and wishes to reach a coastal village 6 mi, down a straight shoreline from the point nearest the boat. She can row at 3mph and can walk at 5 mph. Where should she land her boat to reach the village in the least amount of time?"--

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To calculate the value of the test statistic, we need to use the sample results provided: d-bar = 6.9, sD = 7.8, and n = 10. The value of the test statistic is approximately 1.983.

Given:

Sample mean difference (d-bar) = 6.9

Sample standard deviation of the differences (sD) = 7.8

Sample size (n) = 10

To calculate the test statistic, we can use the formula for the t-statistic:

t = (d-bar - μD) / (sD / sqrt(n))

where d-bar is the sample mean difference, μD is the hypothesized mean difference under the null hypothesis, sD is the sample standard deviation of the differences, and n is the sample size.

In this case, the null hypothesis (H0) states that μD is less than or equal to 2. Since the alternative hypothesis (HA) is μD > 2, this is a one-tailed test.

Plugging in the values into the formula:

t = (6.9 - 2) / (7.8 / sqrt(10))

t = 4.9 / (7.8 / 3.162)

t = 4.9 / 2.471

t ≈ 1.983

Therefore, the value of the test statistic is approximately 1.983.

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The probability that the first ruler he hands out will have centimeter markings and the second one does not have the markings is 9/40.

The probability of distributing the rulers is calculated as follows;

Total outcome = 15 rulers with centimeter markings + 10 rulers without centimeter markings

Total outcome = 25

The probability that the first ruler he hands out will have centimeter markings and the second one does not have the markings;

P = (R with M) and (R without M)

P = (15/25) x (9/24)

P = (3/5) x (3/8)

P = 9/40

Thus, the probability that the first ruler he hands out will have centimeter markings and the second one does not have the markings is 9/40.

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The height of the pyramid is 12 units.

The volume of the pyramid is 400 units cube.

The pyramid has a square base with side length of 10 units. Each segment that connect the apex to a midpoint of a side of the base has a length of 13 units.

Therefore, the height of the pyramid can be calculated as follows:

The height of the pyramid can be found using Pythagoras's theorem for right triangles.

Hence,

c² = a² + b²

where

Therefore,

h² = 13² - 5²

h = √169 - 25

h = √144

h = 12 units

Therefore,

height of the pyramid = 12 units

Volume of the square pyramid = 1 / 3 BH

where

Therefore,

B = 10² = 100 units²

Volume of the square pyramid = 1 / 3 × 100 × 12

Volume of the square pyramid = 1200 / 3

Volume of the square pyramid = 400 units³

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