Calcula la longitud del puente que se quiere construir entre los puntos A y B, para lo cual se sabe que los ángulos ABO Y OAB miden 32" y 48° respectivamente y que la


distancia entre Ay O medida en línea recta es 120 m. (sugerencia, trace una linea vertical desde o hasta el segemto AB).

The second partial sum for the given sequence is 2 + 2(0.4) = 2.8, under the condition that first term a1 = 2 and common ratio r = 0.4.

The given sequence follows geometric progression with first term a1 = 2 and common ratio r = 0.4. Then the formula for the sum of n terms of a geometric progression with first term a1 and common ratio r is
[tex]Sn = a1(1 - r^{n}) / (1 - r)[/tex]
The second partial sum of the given sequence can be evaluated
S2 = a1(1 - r²) / (1 - r)
Staging a1 = 2 and r = 0.4 in the above formula,
S2 = 2(1 - 0.4²) / (1 - 0.4)
= 2 + 2(0.4) = 2.8
Hence, the expression that presents the second partial sum for the given sequence is
2 + 2(0.4) = 2.8.

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Thus, equation that Tracy needs to use to obtain the number of tablespoons of flour to use in making 10 pancakes.

The unitary method is a method for determining the value of one unit from the values of several units or the other way around.

The unitary approach is a strategy for problem-solving that involves first determining the value of one unit, then multiplying that value to determine the required value.

Given data:

4 pancakes --->  6 teaspoon of flour.

For 1 pancake, divide above expression with 4 on both side.

1  pancakes --->  6/4 teaspoon of flour.

Now, for 10 pancake, multiply  above expression with 10 on both side.

10  pancakes --->  10* 6/4 teaspoon of flour.

Thus, equation that Tracy needs to use to obtain the number of tablespoons of flour to use in making 10 pancakes.

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The landscaper will need 10.99 feet of fencing to place around the circumference of the pond. Option B is the correct answer.

We need to find how many feet of the fence is needed to decorate the fence around the circumference of the pond. we can determine it by finding the circumference of a pound or circle. The circumference of a circle is calculated using the formula,

C = 2πr

Where:

C = the circumference

r = radius

Given data:

π = 3.14

r =  1. 75 feet.

Substuting the value of the radius in the formula we get

C = 2πr

C = 2π(1.75)

= 10.99

Therefore, the landscaper will need 10.99 feet of fencing to place around the circumference of the pond.

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(a) The 92% CI for overall proportion of pudding packs containing less than 3.25oz of pudding at α = 0.08 is (0.5806, 0.6994);

(b) The 99% CI for overall proportion of pudding packs containing more than 3.25oz of pudding at α = 0.01 is (0.2726, 0.4474).

Part (a) : To construct a confidence-interval for the overall proportion of pudding packs containing less than 3.25oz of pudding, we use the following formula : CI = p' ± [tex]z_{\frac{\alpha}{2} }[/tex] × √(p'(1-p')/n);

where p' is = sample proportion, [tex]z_{\frac{\alpha}{2} }[/tex]  is = critical z-value for the desired confidence level, and n is = sample size.

In this case, p' = (200-72)/200 = 128/200 = 0.64, the sample size is n = 200, and

We know that the critical z-value for a 92% confidence interval(α = 0.08) is approximately 1.75;

Substituting the values,

We get,

CI = 0.64 ± 1.75 × √(0.64(1 - 0.64)/200)

CI = 0.64 ± 0.059421;

CI = (0.5806, 0.6994);

Therefore, the required confidence interval is (0.5806, 0.6994).

Part (b) : In this case, p' = 72/200 = 0.36, the sample-size is n = 200, and

We know that the critical z-value for a 99% confidence interval (α = 0.01) is approximately 2.57;

Substituting the values,

We get,

CI = 0.36 ± 2..57 × √(0.36(1 - 0.36)/200)

CI = 0.36 ± 0.087426;

CI = (0.2726, 0.4474);

Therefore, the required confidence interval is (0.2726, 0.4474).

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To find -F+2G+H-R using the Graphical Tail-to-Tip method, measure the magnitude and direction of this resultant vector to find the sum F+2G+H-R.

To find the vector sum F+2G+H-R using the graphical tail-to-tip method, follow these steps:

Now, place the vectors tail-to-tip in the following order: F, 2G, H, and R (in opposite directions).

The sum of these vectors can be found by connecting the starting point (tail of F) to the endpoint (tip of R in the opposite direction).

Measure the magnitude and direction of this resultant vector to find the sum F+2G+H-R.

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An expression to represent the number of miles both boys ran this month is 3j + 4d + 10.

To begin solving this problem, we need to use the given information and create an expression to represent the number of miles both boys ran this month.
We know that James runs 3 miles per day, so in j days, he would have run 3j miles.

Similarly, Denis runs 4 miles per day and ran an additional 10 miles this month.

So in d days, he would have run 4d + 10 miles.
To find the total number of miles both boys ran this month, we need to add the number of miles James ran to the number of miles Denis ran.

Therefore, our expression is:
Total Miles = 3j + 4d + 10
This expression represents the total number of miles both boys ran this month.

To solve for j and d, we would need more information, such as the total number of miles the boys ran or the number of days they both ran.
In summary, we can use the given information about James and Denis's daily running habits to create an expression that represents the total number of miles both boys ran this month.

This expression is 3j + 4d + 10.

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The average change in temperature per hour during the temperature drop from 48°F to -16°F in Sioux Falls, South Dakota on February 6, 1995, was 8°F per hour.

On February 6, 1995, the temperature in Sioux Falls, South Dakota dropped dramatically from 48°F to -16°F in just eight hours. To calculate the average change in temperature per hour, we can use the formula:

Average Change in Temperature per Hour = (Change in Temperature) ÷ (Time)

Using this formula, we can calculate the average change in temperature per hour in Sioux Falls as follows:

Average Change in Temperature per Hour = (48°F - (-16°F)) ÷ 8 hours

Average Change in Temperature per Hour = 64°F ÷ 8 hours

Average Change in Temperature per Hour = 8°F per hour

Therefore, the average change in temperature per hour during that eight-hour period in Sioux Falls, South Dakota was 8°F. This rapid and significant change in temperature was likely due to a strong cold front moving through the area.

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The height of the replica souvenir is approximately 7.55 inches.

To find the height of the replica souvenir of the Statue of Liberty, we'll use the given scale factor of 1 inch = 20 feet. The original height of the statue is 151 feet. Divide the original height by the scale factor:

151 ft / 20 ft/in = 7.55 inches

The height of the replica souvenir is approximately 7.55 inches.

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68% of the stores will sell a gallon of milk for between $3.57 and $3.93 with one standard deviation of the mean.

Mean =  $3.75

Standard deviation = $0.09.

Selling variations = $3.57 to $3.93.

Chebyshev's theorem states that if k is a positive number, then, in any data at least [tex](1 - 1/k^2)[/tex] of the data will fall in K standard deviations from the mean data.

For normal distributions, 68% of the values will fall within one standard deviation of the mean.

For non-normal deviations, 75% of values will fall within 2 standard deviations of the mean.

Here we need to find the Upper limit and lower limit of the data.

$3.75 - $0.09 = $3.66

$3.75 + $0.09 = $3.84

The price range will be between $3.66 and $3.84.

To calculate the minimum percentage of stores using Chebyshev's theorem

minimum percentage = [tex]1 - 1/k^2[/tex]

minimum percentage = [tex]1 - 1/(1^2)[/tex]

minimum percentage = 0

Here, 0% of stores will fall with only one standard deviation from the Mean.

Therefore, we can conclude that 68% of the stores will sell a gallon of milk for between $3.57 and $3.93.

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Answer:

if the diagonal is 10 then the sides are 3*2 and 4*2 which is 6 and 8 respectively because the diagonal makes it a right angled triangle whereby the the 3,4,5 line steps in, so if the diagonal(hypotenuse) is 10 the 10/5 is 2 then you multiply both 3 and 4 by 2 and that gives you the length of two sides

Answer:

B) <FBG

Step-by-step explanation:

An adjacent angle is an angle that is right next to the given angle.

In this case, the given angle is <EBF.

We can see that the only 2 options here for an adjacent set of angles is either <FBG or <EBD.

Looking at the options, we can only see that <FBG is an option, making B the correct option.

Hope this helps :)

The value of x is 2.8 The scale factor of left polygon to the right polygon, GKNM to RPTV is 1.4.

Since the two polygons GKNM and RPTV are similar, their corresponding sides are proportional. Thus, we can set up the following proportion

(GK + KN + NM)/GK = (RP + PT + TV + VR)/RP

Plugging in the given values and simplifying, we get

(8.4 + 3x - 2 + 4)/8.4 = (x + 5 + 3 + 3 + 6.3)/(x + 5)

15.4/(3x + 2.4) = (x + 17.3)/(x + 5)

Cross-multiplying and solving for x, we get

x = 2.8

To find the scale factor of GKNM to RPTV, we can divide the corresponding side lengths

(GK + KN + NM)/(RP + PT + TV + VR) = (8.4 + 3(2.8) - 2 + 4)/(2.8 + 5 + 3 + 3 + 6.3) = 1.4

Therefore, the scale factor of GKNM to RPTV is 1.4.

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The height of the cone that the volume of a cylinder is twice the volume of a cone is 7.5 meters.

Let's first define some variables to represent the dimensions of the cone and cylinder. Let's use r for the radius of both shapes, h for the height of the cone, and 5 for the height of the cylinder.

The volume of a cone is given by V_cone = (1/3)πr^2h, and the volume of a cylinder is given by V_cylinder = πr^2h.

We are told that the volume of the cylinder is twice the volume of the cone:

V_cylinder = 2V_cone

Substituting the formulas for the volumes of the cone and cylinder, we get:

πr^2(5) = 2[(1/3)πr^2h]

Simplifying, we can cancel the π and the r^2 terms on both sides:

5 = (2/3)h

Multiplying both sides by 3/2, we get:

h = 7.5

Therefore, the height of the cone is 7.5 meters.

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if we need to purchase more than 10 gallons of gas, it is worth it to buy the car wash that costs $2.

With a car wash, the price per gallon is $3.19, which is $0.20 less than the price without a car wash ($3.39).

To determine whether it is worth it to buy the car wash, we need to calculate the cost savings per gallon by purchasing the car wash.

Cost savings per gallon = Price without car wash – Price with car wash

Cost savings per gallon = $3.39 – $3.19 = $0.20

So, if the car wash costs less than $0.20 per gallon, it is worth it to purchase it.

If the car wash costs $2, we need to determine how many gallons of gas we need to purchase in order for the cost savings to be greater than $2.

Let's assume we purchase x gallons of gas. The cost savings for purchasing the car wash will be:

Cost savings = x gallons × $0.20 per gallon = $0.20x

We want to find the value of x that makes the cost savings greater than $2:

$0.20x > $2

x > $2 ÷ $0.20

x > 10

Therefore, if we need to purchase more than 10 gallons of gas, it is worth it to buy the car wash that costs $2.

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The number of students who drive to school can be calculated as one-sixth of the total number of students.

Let's assume the total number of students in the Mupuvr CLC MLMMS4 group is represented by the variable 'x'. According to the given information, half of the students walk to school, which is equal to (1/2) * x. One-third of the students take a taxi, which is equal to (1/3) * x. The remaining students, who claim to drive, can be calculated as x - [(1/2) * x + (1/3) * x].

Simplifying this expression, we have x - (5/6) * x, which is equal to (1/6) * x. Therefore, the number of students who claim to drive to school is one-sixth of the total number of students.

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The couple needs to invest $9,060.52 per year to have enough money to send their daughter to university.  The couple needs to invest an additional $1,322.18 per year if they wait one year to start saving for their daughter's university education.

a. The amount of money the couple needs to invest each year can be calculated using the present value of annuity formula. The future value of the university cost after 10 years can be calculated by compounding the current cost for 10 years at an annual inflation rate of 5.6%.

Then, the present value of this future cost can be found by discounting it back to the present using the effective annual interest rate of 6.75%. Finally, this present value can be divided by the present value of an annuity factor for 9 years (one year before the university starts) at an effective annual interest rate of 6.75%.

Using these calculations, the couple needs to invest $9,060.52 per year to have enough money to send their daughter to university.

b. If the couple waits for one year, they will have nine years to save for their daughter's university education. This means they will have one less year to invest, so they will need to invest more each year to have enough money for their daughter's university education.

The additional amount they need to invest can be found by subtracting the present value of an annuity of $9,060.52 for 9 years from the present value of an annuity of $9,060.52 for 8 years.

Using these calculations, the couple needs to invest an additional $1,322.18 per year if they wait one year to start saving for their daughter's university education.

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The surface area of the pyramid is 72 + 486√3 metres.

The pyramid above is an hexagonal pyramid. The surface area of the hexagonal pyramid can be found as follows:

surface area of a hexagonal pyramid = ph / 2 + B

where

Therefore,

Base area = 1 / 2pa

where

Base area = 1 / 2 × (18 × 6) × 9√3

Base area = 1 / 2 × 108 × 9√3

Base area = 54 × 9√3

Base area = 486√3 metres

surface area of a hexagonal pyramid = 108 × 18 / 2 + 486√3

Therefore,

surface area of a hexagonal pyramid = 972 + 486√3 metres

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The equation in slope-intercept form for the line passing through each pair of points, (-4, 4) and (-5, -3) is expressed as: y = 7x + 32

Given the points, (-4, 4) and (-5, -3), first find the slope of the line.

Slope (m) = change in y / change in x = -3 - 4 / -5 -(-4)

m = -7/-1

m = 7

Substitute m = 7, a = -4, and b = 4 into y - b = m(x - a):

y - 4 = 7(x + 4)

Rewrite im slope-intercept form:

y - 4 = 7x + 28

y - 4 + 4 = 7x + 28 + 4

y = 7x + 32

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Answer:

V = 1,728 mi³

SA = 864 mi²

Step-by-step explanation:

We can find the volume of the triangular prism by multiplying the area of one of the triangle faces by the prism's depth.

First, we can solve for the area of one of the triangle sides:

A(triangle) = (1/2) · b · h

A(triangle) = (1/2) · 24 · 18

A(triangle) = 12 · 18

A(triangle) = 216 mi²

Next, we can get the volume of the prism by multiplying the area of the triangle face by the prism's depth.

V = A(triangle) · depth

V = 216 · 8

V = 1,728 mi³

__

We can find the surface area by finding the area of each side, then adding all of those areas together.

We already know that the area of each of the triangle sides is 216 mi².

Now, we can solve for the area of the base.

A(base) = length · width

A(base) = 24 · 8

A(base) = 192 cm²

Then, we can find the area of the top side.

A(top) = length · width

A(top) = 30 · 8

A(top) = 240 mi²

Finally, we can solve for the surface area of the prism by adding the areas of each of its sides.

SA = (2 · A(triangle)) + A(base) + A(top)

SA = 2(216) + 192 + 240

SA = 432 + 192 + 240

SA = 624 + 240

SA = 864 mi²

Part a. The magnitude of the angular acceleration of the salad spinner as it slows down is 4.00 radians/s².

Part b. It takes 1.00 seconds for the salad spinner to come to rest.

Part A:

The initial angular velocity of the spinner is given by:

ω1 = 20.0 rotations / 5.00 s = 4.00 rotations/s

The final angular velocity of the spinner is zero.

The number of rotations between the initial and final angular velocities is:

Δθ = 6.00 rotations

Using the equation of motion for rotational kinematics with constant angular acceleration:

Δθ = 1/2 α t^2 + ω1 t

where α is the angular acceleration, and t is the time it takes to stop spinning.

At the final angular velocity, ω2 = 0, so we can rearrange the equation to solve for t:

t = ω1 / α

Substituting the given values:

Δθ = 6.00 rotations

ω1 = 4.00 rotations/s

t = (4.00 rotations/s) / α

Solving for α:

Δθ = 1/2 α t^2 + ω1 t

6.00 rotations = 1/2 α (t^2) + (4.00 rotations/s) t

Substituting t = (4.00 rotations/s) / α:

6.00 rotations = 1/2 α [(4.00 rotations/s) / α]^2 + (4.00 rotations/s) [(4.00 rotations/s) / α]

6.00 rotations = 8.00 rotations + 16.00 rotations/s^2 / α

α = 16.00 rotations/s^2 / (6.00 rotations - 8.00 rotations)

α = 8.00 rotations/s^2 / 2.00 rotations

α = 4.00 radians/s^2

Therefore, the magnitude of the angular acceleration of the salad spinner as it slows down is 4.00 radians/s^2.

Part B:

Using the equation of motion for rotational kinematics with constant angular acceleration:

ω2 = ω1 + α t

At the final angular velocity, ω2 = 0, so we can rearrange the equation to solve for t:

t = -ω1 / α

Substituting the given values:

ω1 = 4.00 rotations/s

α = 4.00 radians/s^2

t = -(4.00 rotations/s) / (4.00 radians/s^2)

t = -1.00 s

Since the time cannot be negative, we take the absolute value of t:

t = 1.00 s

Therefore, it takes 1.00 seconds for the salad spinner to come to rest.

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The equations that will find the distance between the lions and giraffes include the following:

B. 11² + 16² = c².

D. 11(2) + 16(2) = 2.

In Mathematics and Science, distance can be defined as the amount of ground that is travelled by a physical object or body over a particular period of time and speed, irrespective of its direction, starting point or ending point.

Mathematically, the distance traveled by both the lions and giraffes when they are positioned one (1) unit apart can be calculated by using this equation:

11² + 16² = c²

Additionally, the distance traveled by both the lions and giraffes when they are positioned two (2) unit apart can be calculated by using this equation:

11(2) + 16(2) = c

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Answer: x^2 + 3x - 70 = 0

Step-by-step explanation:

Answer: 0= -5

Step-by-step explanation:

The work required to pump the liquid out of the bucket is approximately 2.482 x 10⁷ Joules.

To create a bucket by rotating around the y-axis, we will use the formula for volume of revolution:

V = π ∫[a,b] (f(y))² dy where f(y) is the function being rotated, and a and b are the limits of integration.

In this case, the limits of integration are y = 0 and y = 3, and the function being rotated is y = 4 ln(x - 4), or x = e⁽y/⁴⁾ + 4.

So, we have:

V = π ∫[0,3] ((e⁽y/⁴⁾ + 4))² dy

V = π ∫[0,3] (e⁽y/²⁾ + 8e⁽y/⁴⁾+ 16) dy

V = π (2e⁽³/²⁾ + 32e⁽³/⁴⁾ + 48)

Now, to find the work required to pump the liquid out of the bucket, we need to use the formula:

W = ∫[h1,h2] ρgV(y) dy

where h1 is the height of the liquid (2 meters in this case), h2 is the height of the top edge of the bucket, ρ is the density of the liquid (860 kg/m^3), g is the acceleration due to gravity (9.8 m/s²), and V(y) is the volume of the liquid at height y.

To find V(y), we need to first find the radius of the bucket at height y.

The radius is given by: r(y) = e⁽y/⁴⁾+ 4

So, the volume of the liquid at height y is:

V(y) = π(r(y))² (h2 - y)

Plugging in the values, we have:

W = ∫[0,2] 860×9.8×π((e⁽y/⁴ + 4)²)×(2-y) dy

W = 2.482 x 10⁷J

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The probability of a goal being scored in the first five minutes of the game, given that the team is team q is 1.24%. The correct option is a.

The probability of a goal being scored in the first five minutes of the game, given that the team is team q, is given by the conditional probability:

P(goal scored in first 5 min | team is q) = P(goal scored in first 5 min and team is q) / P(team is q)

From the table, we have:

P(goal scored in first 5 min and team is q) = 3.56%

P(team is q) = 3.56%

Therefore:

P(goal scored in first 5 min | team is q) = 3.56% / 3.56% = 1

This means that if we know the team is team q, the probability of a goal being scored in the first five minutes of the game is 100% (or certain). So the correct answer is (a) 1.24%.

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Answer:

Answer:17

Explanation: 5-0.75=4.25 4.25÷0.25=17

Hope this helps

Answer:

I think the answer might be -4 = 3x.

Step-by-step explanation:

-2 times x + 2 = -4 and 5 - 2x = 3x so i think the answer is -4 = 3x. Also, you're welcome if this helps.

The best interpretation of one of the values of the function is  The number of microorganisms increases by 16% each week.

The given function of the number of the microorganisms present in the water sample at the end of x weeks is

h(x) = 146(1.16)ˣ

To find the number of microorganisms present in the water sample after one week, we substitute x = 1 in the above equation

h(1) = 146(1.16)¹

h(1) = 169.36

Therefore, after one week, there will be approximately 169 microorganisms in the water sample.

Thus, the correct interpretation of one of the values of the function is F.

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