Ray uses
of a gallon of gasoline to drive a distance of
miles. At this rate, how many miles can he drive on 1 gallon of gas?
Ray can drive
miles on 1 gallon of gas.

a. The null  hypotheses  H0: u = 150

The  alternative hypotheses for this situation : H1: u ≠ 150

b. We reject null hypothesis at 1% level of significance

c. We reject the null hypothesis at the 10% level  at X<= 146.03

X>=153.97

a.

H0: u = 150

H1: u ≠ 150

b.

Total sum = 15933.24

N = 100

Mean = 15933.24/100

= 159.3324

σ² = 25954.03 - (159.3324)²/100

σ² = 556.213

σ = √556.213

σ = 23.8162

Testing hypothesis

t = (bar x - u)/ σ/√n

= 159.3324-150/23.8162/√100

= 3.91

We will have a p value of 0.02

0.0002 < 0.01

Therefore, we reject null hypothesis at 1% level of significance

C.

Mean = 159.3324

Se= 2.3936

Df = 100-1 = 99

The Critical value at 0.01 = +-2.626

T = x-u/s.e

= -2.626 =( x -150)/2.3936

When we cross multiply and solve this

X = 143.714 for the lower tail

2.626 = (x-159)/2.3936

= 156.286 for upper tail.

We therefore reject H0 at

Bar X <= 143.71

Bar X >= 156.286

At 10%, Critical t = 1.660

-1.660 = (x - 150)/2.3936

X =146.02 at the lower tail

1.660 = (x-150)/2.3936

X = 153.97

We reject H0 at

X<= 146.03

X>=153.97

Learn more about null hypotheses at: https://brainly.com/question/4436370

#SPJ1

The expression for the variable b in terms of a, S, and n in the formula for the sum of an arithmetic sequence is; b = (2·S/n) - a

An arithmetic sequence is a sequence of numbers in which each subsequent term in the sequence increases from the value of the previous term by the same amount.

The formula for finding the finite sum of an arithmetic sequence can be presented as follows; S = (n/2)·(a + b), where;

n = The number of terms in the sequence

a = The first term in td sequence

b = The last term in the sequence

The steps that can be used to make the variable b the subject of the equation, are;

S = (n/2)·(a + b)

a + b = 2·S/n

b = 2·S/n - a

Learn more on the sum of an arithmetic sequence here: https://brainly.com/question/29140093

#SPJ1

The resulting vector matrix is [ -21 3 ]. Therefore, a = -21, and b = 3.

To find the resulting vector matrix of the given matrix multiplication, we need to multiply the first matrix, which is a 1x4 matrix, by the second matrix, which is a 4x1 matrix. The resulting matrix will be a 1x1 matrix (a scalar).

The calculation would be as follows:

[ 6 -5 -3 4 ] × [ -1 ] = [ (6 * -1) + (-5 * 3) + (-3 * 0) + (4 * 0) ]

[ 3 ]

Calculating the values:

[ (6 * -1) + (-5 * 3) + (-3 * 0) + (4 * 0) ]

[ 3 ]

= [ -6 - 15 + 0 + 0 ]

[ 3 ]

= [ -21 ]

[ 3 ]

So, the resulting vector matrix is [ -21 3 ]. Therefore, a = -21, and b = 3.

For such more questions on Vector Matrix Result

https://brainly.com/question/21752923

#SPJ8

We can show that ∆ABC is congruent to ∆A′B′C′ by a translation of 2 units left and a reflection across the x-axis.

In Mathematics and Geometry, the translation of a graph to the left means a digit would be subtracted from the numerical value on the x-coordinate of the pre-image:

g(x) = f(x + N)

In order to apply a translation of two (2) units to the left to triangle ABC, we would use this transformation rule;

(x, y)                               →                  (x - 2, y)

A (8, 8)                         →                    A (6, 8).

B (10, 4)                         →                   B (8, 4).

C (2, 6)                         →                    C (0, 6).

In Mathematics and Geometry, a reflection over or across the x-axis is represented by this transformation rule (x, y) → (x, -y).

Next, we would reflect triangle ABC across the x-axis as follows;

(x, y)                            →                      (x, -y)

A (6, 8)                         →                    A' (6, -8).

B (8, 4)                         →                    B' (8, -4).

C (0, 6)                         →                    C' (0, -6).

Read more on reflection here: brainly.com/question/20602330

#SPJ1

Missing information:

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

Answer: the second option.

Answer:

(4, 0 )

Step-by-step explanation:

2x + y = 8 → (1)

x + y = 4 ( subtract x from both sides )

y = 4 - x → (2)

substitute y = 4 - x into (1)

2x + 4 - x = 8

x + 4 = 8 ( subtract 4 from both sides )

x = 4

substitute x = 4 into (2)

y = x - 4 = 4 - 4 = 0

solution is (4, 0 )

First, we can set up a proportion to find the ratio of the width to length for the photograph:

We can then use this ratio to find the width of the photograph with a length of 24 inches:

To solve for the width, we can cross-multiply:

Then divide by 4:

[tex]\therefore[/tex] The width of the photograph is 18 inches.

[tex]\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}[/tex]

1. The area under the curve of f(x) = 2[tex]\sqrt{x}[/tex] from x = 1 to x = 9 is  16 square units.

2. Volume: 1936π/5 cubic units by sliding semi-circle and triangle.

3. Volume: -102π cubic units, Surface Area: (400π + 206)/3 square units.

1. To calculate the area of the region formed in the first quadrant under the function f(x) = 2 between x = 1 and x = 9, we can use integration. The integral of f(x) = 2 with respect to x from 1 to 9 is:

∫[1, 9] 2 dx = 2 * [x] evaluated from 1 to 9 = 2 * [(9) - (1)] = 2 * [8] = 16.

Therefore, the area of the region is 16 square units.

2. To calculate the volume created by sliding a semi-circle and an equilateral triangle along the x-axis, we can use the method of cylindrical shells. The volume of each shell is given by the formula:

V = 2πxf(x)dx.

We integrate the volume of each shell over the interval [1, 4] for the semi-circle and [4, 9] for the triangle:

V = ∫[1, 4] 2πx(2) dx + ∫[4, 9] 2πx(2) dx

 = 4π∫[1, 4[tex]] x^(^3^/^2^)[/tex]dx + 4π∫[4, 9] [tex]x^(^3^/^2^)[/tex]dx.

Using the power rule of integration, we have:

V = 4π * [(2/5)[tex](4^(^5^/^2^) - 1^(^5^/^2^))] + 4π * [(2/5)(9^(^5^/^2^) - 4^(^5^/^2^))][/tex]

 = 4π * [(2/5)(31)] + 4π * [(2/5)(211)]

 = 248π/5 + 1688π/5

 = 1936π/5.

Therefore, the volume created by sliding the semi-circle and equilateral triangle along the x-axis is 1936π/5 cubic units.

3. To calculate the resulting volume using two integrals, we can subtract the volume of the equilateral triangle from the volume of the semi-circle. The volume of the semi-circle is given by:

V(semi-circle) = ∫[1, 4] π[tex](2)^(2)[/tex]dx

             = π∫[1, 4] 4x dx

             = 4π∫[1, 4] x dx

             = 4π * [(1/2)x^2][tex][(1/2)x^2][/tex] evaluated from 1 to 4

             = 4π * [(1/2)(16) - (1/2)(1)]

             = 4π * [8 - 1]

             = 28π.

The volume of the equilateral triangle is given by:

V(triangle) = ∫[4, 9][tex](2)^(2)[/tex] dx

           = ∫[4, 9] 4x dx

           = 4∫[4, 9] x dx

           = 4 *[tex][(1/2)x^2][/tex]evaluated from 4 to 9

           = 4 * [(1/2)(81) - (1/2)(16)]

           = 4 * [(1/2)(65)]

           = 130.

The resulting volume is:

Volume = V(semi-circle) - V(triangle)

      = 28π - 130

      = -102π cubic units.

To calculate the surface area of the solid, we need to consider the surfaces of the semi-circle, triangle, and two quadrilaterals. The surface area of the semi-circle is given by:

Surface area(semi-circle) = ∫[1, 4] 2π(2) ds.

The differential arc length ds can be expressed as ds = [tex]\sqrt{(1 + (f'(x))^2)}[/tex] dx, where f(x) = 2. Since f(x) = 2, we have f'(x) = 0. Therefore, ds = [tex]\sqrt{(1 + 0^2) }[/tex]dx = dx.

Substituting this in the integral, we have:

Surface area(semi-circle) = ∫[1, 4] 2π(2) dx

                       = 4π∫[1, 4] 2 dx

                       = 8π * [tex][(2/3)x^3][/tex] evaluated from 1 to 4

                       = 8π * [(2/3)(64) - (2/3)(1)]

                       = 8π * [128/3 - 2/3]

                       = 8π * (126/3)

                       = 336π.

The surface area of the triangle is given by:

Surface area(triangle) = ∫[4, 9] (2) dx

                     = 2∫[4, 9] dx

                     = 2 * [x] evaluated from 4 to 9

                     = 2 * [(9) - (4)]

                     = 2 * [5]

                     = 10.

The surface area of the two quadrilaterals is equal to the sum of the areas of the semi-circle and triangle, which is:

Surface area(quadrilaterals) = 2 * (28π + 130)

                           = 2 * (28π + 130π/1)

                           = 316π.

Therefore, the total surface area of the solid is:

Surface area = Surface area(semi-circle) + Surface area(triangle) + Surface area(quadrilaterals) - Difference between the semi-circle and the triangle at x = 4

            = 336π + 10 + 316π - (28π - 130)

            = 400π + 206.

For more such information on: area

https://brainly.com/question/25292087

#SPJ8

Answer:

2

Step-by-step explanation:

1+1=2

Answer:

(a) therefore the equation is

a(t) = -1000t + 32800

Step-by-step explanation:

(a) a(t) = mt + b

(8, 24800). ( 20, 12800)

(t, a). ( t¹ , a¹)

slope or gradient, m = a¹ - t¹

a - t

m = 12800 - 24800

20 - 8

m = -12000

12

m = -1000

The slope is -1000

let's use (8, 24800) to find b.

24800 = -1000 (8) + b

24800 = -8000 + b

b= 24800 + 8000

b = 32800

therefore the equation is

a(t) = -1000t + 32800

(b) Since the slope is negative (-1000), it means that the altitude is decreasing at a constant rate of 1000 feet per minute. The negative sign indicates the descent, as the altitude is decreasing over time.

Therefore, the slope tells us that the plane is descending at a constant rate of 1000 feet per minute.

(c) The value 32800 tells us the initial altitude of the plane before descending. It indicates the starting point or the initial position of the aircraft above the ground level.

Therefore, the value 32800 represents the initial altitude of the plane before it began descending.

The statement "Each invitation costs $1.50 to print" is not true based on the given function. The cost depends on the number of invitations printed, as represented by c = 2.50(n – 2) + 1.50.

Among the given statements, the one that is not true is: "One can not print just one invitation."

The given function states that the cost of printing n invitations is represented by c = 2.50(n - 2) + 1.50. This function suggests that for each additional invitation beyond two, it costs an extra $2.50 to print. However, the function does not impose any restriction on the minimum number of invitations that can be printed.

Therefore, it is indeed possible to print just one invitation. The cost for one invitation would be c = 2.50(1 - 2) + 1.50 = 2.50(-1) + 1.50 = -2.50 + 1.50 = -1.00 dollars. Although printing a negative cost may not make practical sense, the statement that one cannot print just one invitation is not true based on the given function.

for such more question on function

https://brainly.com/question/11624077

#SPJ8

Question

The function c = 2.50(n – 2) + 1.50 represents the cost c in dollars of printing n invitations. Which of the following is not true? One can not print just one invitation. Each invitation costs $1.50 to print For each additional invitation, it costs an extra $2.50 to print. The cost depends on the number of invitations printed.

The height of the fish tank is 75 cm. The tank is filled to 60% of its capacity, so the total volume of water is 60% of the tank's.

To find the height of the fish tank, we can follow these steps:

Step 1: Calculate the volume of the tank before the water was poured.

The base of the tank has dimensions 80 cm by 40 cm, so the initial volume of the tank is given by:

Volume_before = length * width * height

             = 80 cm * 40 cm * h

             = 3200h cm³

Step 2: Calculate the volume of water that was poured into the tank.

The tank was initially filled with 33.6 liters of water, which is equivalent to 33,600 cm³.

Step 3: Calculate the additional volume of water poured into the tank.

The additional volume of water is 62.4 liters, which is equivalent to 62,400 cm³.

Step 4: Calculate the total volume of water after pouring.

The total volume of water in the tank after pouring is:

Total_volume = Volume_before + Volume_poured

            = 3200h cm³ + 33,600 cm³ + 62,400 cm³

            = 3200h cm³ + 96,000 cm³

Step 5: Calculate the height of the tank.

The tank is filled to 60% of its capacity, so the total volume of water is 60% of the tank's volume. We can set up the following equation:

Total_volume = 0.6 * Volume_before

3200h cm³ + 96,000 cm³ = 0.6 * 3200h cm³

Simplifying the equation:

3200h cm³ + 96,000 cm³ = 1920h cm³

1280h cm³ = 96,000 cm³

h = 96,000 cm³ / 1280 cm³

h = 75 cm

Therefore, the height of the fish tank is 75 cm.

for more such question on height visit

https://brainly.com/question/28990670

#SPJ8

Given sec 0= radical 10/2, cos(0) is equal to √10/5.

To find the value of cosine (cos) given the value of secant (sec), we can use the reciprocal identity between these two trigonometric functions.

The reciprocal identity states that:

sec(x) = 1/cos(x)

In this case, we are given sec(0) = √10/2.

We can rewrite this as:

1/cos(0) = √10/2

Multiplying both sides by cos(0), we get:

cos(0) * (1/cos(0)) = cos(0) * (√10/2)

The cos(0) terms cancel out on the left side, giving us:

1 = (√10/2) * cos(0)

Now, to isolate cos(0), we divide both sides by (√10/2):

1 / (√10/2) = cos(0)

To simplify the expression on the left side, we rationalize the denominator:

(1 * 2) / √10 = cos(0)

2/√10 = cos(0)

To express cos(0) in simplified radical form, we multiply the numerator and denominator by √10:

(2 * √10) / (√10 * √10) = cos(0)

(2√10) / 10 = cos(0)

Simplifying further, we get:

√10 / 5 = cos(0)

Therefore, cos(0) is equal to √10/5.

Learn more about reciprocal identity at https://brainly.com/question/33316863

#SPJ1

The estimated value of the car today would be around $1,987.50.

The value of a car purchased 5 years ago for $7,950.00 would depend on various factors, including the make, model, condition, mileage, market demand, and depreciation rates.

However, without specific details about the car, it is difficult to provide an accurate value. Generally, vehicles depreciate over time due to wear and tear, technological advancements, and changing market conditions.

On average, cars can depreciate between 15% and 25% annually. Considering this range, the car's value today could be estimated by applying an average annual depreciation rate.

Assuming a conservative depreciation rate of 15% per year, the value of the car after 5 years would be approximately:

[tex]\$7,950.00 - (5 years \times 15\% \$7,950.00) = \$7,950.00 - \$5,962.50 = \$1,987.50[/tex]

However, it's important to note that this is a rough estimate, and the actual value could vary based on the factors mentioned earlier. To get a more accurate value, it's recommended to consult sources like used car price guides, local market listings, or professional appraisers.

For more such questions on estimated value

https://brainly.com/question/29112017

#SPJ8

The resulting true inequality from -2 < 3 is 10 > -15

From the question, we have the following parameters that can be used in our computation:

Inequality

-2 < 3

Also, we have

Multiply each side by -5

Using the above as a guide, we have the following:

-5 * -2 < 3 * -5

Evaluate

10 > -15

Hence, the inequality is 10 > -15

Read more about inequality at

https://brainly.com/question/32124899

#SPJ1

Answer:

The **Gross Domestic Product (GDP)** is the total value of goods and services produced in a country in a year. According to the World Bank, the GDP of the United States was **$22.67 trillion** in 2020.

If the U.S. economy grows by 1%, the GDP would increase by **$226.7 billion** (1% of $22.67 trillion). If the U.S. economy contracts by 1%, the GDP would decrease by **$226.7 billion**.

The average American output is measured by Gross Domestic Product per capita (GDP per capita). According to the World Bank, the GDP per capita of the United States was **$68,309** in 2020.

If we assume that the population of the United States is 340 million people, then each person's share of GDP would be approximately **$201** ($68,309 divided by 340 million).

Therefore, if the U.S. economy grows by 1%, each person's share of GDP would increase by approximately **$0.67** ($201 times 1% growth rate). If the U.S. economy contracts by 1%, each person's share of GDP would decrease by approximately **$0.67** ($201 times 1% contraction rate).

(a) The range is 1.38.

(b) The standard deviation is 0.46.

In Mathematics and Statistics, the range of a data set can be calculated by using this mathematical expression;

Range of data set = Highest number - Lowest number

Range of data set = 85.63 - 84.25

Range of data set = 1.38.

In Mathematics and Statistics, the standard deviation of any data set can be calculated by using this formula:

Standard deviation, δx = √(1/n × ∑(x - [tex]\bar{x}[/tex])²)

Mean = (85.54+84.33+85.15+85.63+84.25+85.18+84.78+85.36+85.04)/9

Mean = 85.03

Standard deviation, δx = √[(85.54-85.03)² + (84.33-85.03)² + (85.15-85.03) + (85.63-85.03)² + (84.25-85.03)² + (85.18-85.03)² + (84.78-85.03)² + (85.36-85.03)² + (85.04-85.03)²

Standard deviation, δx = √0.21

Standard deviation, δx = 0.46.

Read more on standard deviation here: brainly.com/question/14467769

#SPJ1

Missing information:

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

The total cost for the business trip considering the given information would be $7750.

To calculate the total cost for a business trip, you need to consider various expenses such as labor hours, training costs, and travel expenses.

First, let's break down the given information:

Labor hours: 80 hours

Hourly rate: $75 per hour

Training cost: $1000

Travel cost: $750

To calculate the cost for the business trip, you need to consider the following components:

Labor Cost:

Multiply the number of labor hours (80) by the hourly rate ($75) to determine the labor cost:

Labor Cost = 80 hours * $75/hour

Training Cost:

The training cost is given as $1000 and is not dependent on labor hours or hourly rates. Therefore, you can add this directly to the total cost.

Travel Cost:

The travel cost is given as $750 and is also not dependent on labor hours or hourly rates. This can be added directly to the total cost.

Now, let's calculate the total cost for the business trip:

Labor Cost = 80 hours * $75/hour = $6000

Training Cost = $1000

Travel Cost = $750

Total Cost = Labor Cost + Training Cost + Travel Cost

Total Cost = $6000 + $1000 + $750

Therefore, the total cost for the business trip would be:

Total Cost = $7750

For more such questions on cost visit:

https://brainly.com/question/2292799

#SPJ8

Answer:

388 for the DVD

776 for the TV

Step-by-step explanation:

$1164= 2x + x

1164÷3

2[388] + 388 = 1164

Answer:

Step-by-step explanation:

To calculate the total balance on the next billing date, we need to consider the average daily balance and the unpaid balance from the previous month.

Given:

Average daily balance for November = $700

Unpaid balance at the end of November = $1,400

Annual percentage rate (APR) = 15.6%

Step 1: Calculate the interest charged for the month of November.

Interest = (Average daily balance * APR * Number of days in the month) / 365

Number of days in November = 30

Interest = (700 * 0.156 * 30) / 365 = $36.44 (rounded to the nearest cent)

Step 2: Add the interest to the unpaid balance to get the total balance on December 1.

Total balance = Unpaid balance + Interest

Total balance = $1,400 + $36.44 = $1,436.44

Therefore, the total balance on the next billing date, December 1, is $1,436.44 (rounded to the nearest cent).

The total balance on the next billing date December 1 is $1,509.20.

The annual interest produced by a sum that is paid to investors or charged to borrowers is referred to as the annual percentage rate (APR).

Given,

Then, the percentage rate for November = [tex]\sf\frac{15.6}{100}[/tex] × 700

[tex]\sf = \$109.20[/tex]

Balance on 1st December = unpaid balance at the end of November + percentage rate

[tex]\sf = $1400 +$109.20[/tex]

[tex]\sf =\$1509.20[/tex]

Therefore, the total balance on the next billing date December 1 is $1,509.20.

To learn more about percentage rate, visit:

https://brainly.com/question/30127793

Answer:

2 groups of 7 children and

1 group of 2

Step-by-step explanation:

if you want to find out how many times it would take? divide 16 by 7

= 2

and 2 left

because 7 * 2 = 14

16-14 = 2

Hope you understand

The domain and the range of the function are (-∝, ∝) and (-1, ∝), respectively

From the question, we have the following parameters that can be used in our computation:

The graph

The above graph is a polynomial function

The rule of this function is that

The domain is the set of all real values

In this case, the domain is (-∝, ∝)

For the range, we have

Range = (-1, ∝)

Read more about domain and range at

brainly.com/question/27910766

#SPJ1

The exponential equation to model this scenario is given  by y = 200(0.85)ˣ

An equation is an expression that shows the relationship between two or more numbers and variables.

A linear inequality has the form of a linear equation, showing the non equal comparison between numbers and variables.

The linear inequality y ≤ (1/3)x - 5 passes through the point (0, -5) and (15, 0)

Find out more on equation at: https://brainly.com/question/29797709

#SPJ1

If LJ is given as 46 units in parallelogram JKLM, we can conclude that LN is equal in length to JK

To find the length of LN in parallelogram JKLM, we can utilize the properties of parallelograms, particularly the diagonals.

In a parallelogram, the diagonals bisect each other. This means that the diagonal LN divides the parallelogram into two congruent triangles, JLN and KLN.

Given that LJ is 46 units, we know that LK, the other half of the diagonal, is also 46 units.

Now, we have a triangle JLN, in which we know LJ (46 units) and LK (46 units). Since JL and LK are congruent sides of a triangle, we can conclude that JLKN is an isosceles trapezoid.

In an isosceles trapezoid, the diagonals are also congruent. Therefore, LN is equal in length to JK.

Hence, LN = JK.

Since we don't have any specific information about the length of JK provided in the question, we cannot determine the exact length of LN without additional information. However, we can say that LN is equal in length to JK based on the properties of parallelograms and isosceles trapezoids.

In summary, if LJ is given as 46 units in parallelogram JKLM, we can conclude that LN is equal in length to JK. However, without knowing the length of JK specifically, we cannot determine the exact length of LN.

for more such question on parallelogram visit

https://brainly.com/question/970600

#SPJ8

The length of a side of the square-shaped table is 1.5 meters.

To find the length of a side of the square-shaped table, we need to calculate the square root of the given area.

The area of a square is given by the formula:

Area = side length * side length

In this case, we have:

Area = 144/64 square meters

To find the side length, we take the square root of the area:

√(144/64) square meters

To simplify the calculation, we can express 144 and 64 as the square of their factors:

√((12^2)/(8^2)) square meters

Taking the square root of the numerator and the denominator separately, we have:

(√12^2) / (√8^2) square meters

Simplifying further, we get:

12/8 square meters

The fraction 12/8 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 4:

(12 ÷ 4) / (8 ÷ 4) square meters

3/2 square meters

Therefore, the length of a side of the table is 3/2 square meters or 1.5 meters.

For more such question on length visit:

https://brainly.com/question/28322552

#SPJ8

The correct answer is a.) P(X=7) ≈ 0.1735b.) P(X<4) ≈ 0.0687c.) P(X>6) ≈ 0.6786

To determine the probabilities for the given binomial experiment, we can use the binomial probability formula:

[tex]P(X=k) = C(n, k) * p^k * (1-p)^(n-k)[/tex]

Where:

P(X=k) represents the probability of getting exactly k successes,

n represents the number of trials (10 in this case),

p represents the probability of success (0.43 in this case),

k represents the number of successes.

a.) P(X=7):

P(X=7) = C(10, 7) * 0.43^7 * (1-0.43)^(10-7)

P(X=7) = 120 * 0.43^7 * 0.57^3

b.) P(X<4):

P(X<4) = P(X=0) + P(X=1) + P(X=2) + P(X=3)

[tex]= C(10, 0) * 0.43^0 * (1-0.43)^10 + C(10, 1) * 0.43^1 * (1-0.43)^9 + C(10, 2) * 0.43^2 * (1-0.43)^8 + C(10, 3) * 0.43^3 * (1-0.43)^7c.) P(X > 6):[/tex]

P(X>6) = 1 - P(X<=6)

= 1 - (P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6))

By substituting the values and calculating the binomial probabilities using the formula, you can find the values for P(X=7), P(X<4), and P(X>6).Calculating this:

P(X < 4) ≈ 0.9619

Therefore, P(X < 4) is approximately 0.9619.

c.) P(X > 6)

To calculate P(X > 6), we need to sum the probabilities from X = 7 to X = 10.

P(X > 6) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

Using the binomial probability formula for each term:

P(X > 6) = (10 C 7) * 0.43^7 * 0.57^3 + (10 C 8) * 0.43^8 * 0.57^2 + (10 C 9) * 0.43^9 * 0.57^1 + (10 C 10) * 0.43^10 * 0.57^0

Calculating this:

P(X > 6) ≈ 0.3672

Therefore, P(X > 6) is approximately 0.3672.

Learn more about probability here:

https://brainly.com/question/23417919

#SPJ8

Given, the angle of elevation of the object from the observer's eye is 16° and the height of the object is 220 ft. So, the required answer is 697.44 ft (Approx).

What is the distance to the base of the object? Let AB be the height of the object, A be the position of the observer, and C be the position of the base of the object.

As per the diagram, we get; In right ΔABC, the Angle of elevation of the object = Angle BAC = 16°

We need to find the distance BC.So, we have; tan 16° = AB/BC  [∵ tan 16° = Perpendicular/Base = AB/BC]

tan 16° × BC = AB   [By cross-multiplication]

BC = AB/tan 16° [Dividing both sides by tan 16°]

BC = 220 ft/tan 16°

BC = 697.44 ft (Approx). Therefore, the distance to the base of the object is 697.44 ft (Approx). Hence, the required answer is 697.44 ft (Approx).

For more questions on: angle of elevation

https://brainly.com/question/30738434

#SPJ8    

The graph that correctly depicts Josiah's earnings, where the amount he earns and the number of chores completed is a proportional relationship, is the option;

On a coordinate plane, a graph titled Josiah's Earnings has chores completed on the x-axis and Money Earned on the y-axis. Points (4, 12), (5, 15), and (6, 18) are plotted.

A proportional relationship is one in which the ratio of the terms in the ordered pairs in the relation are the same.

The table in the question can be presented as follows;

[tex]\begin{tabular}{ | c | c | c | c | c | }\cline{1-5} & Week 1& Week 2 & Week 3 & Week 4 \\ \cline{1-5}Chores Completed & 4 & 6 & 4 & 5 \\\cline{1-5}Money Earned & \$12 & \$18 & \$12 & \multicolumn{1}{|c|}{} \\\cline{1-5}\cline{1-5}\end{tabular}[/tex]

The data in the above table indicates that when Josiah completes 4 chores, he earns $12, and when he completes 6 chres he earns $18

The amount Josiah earns and the number of chores Josiah completes is a proportional relationship, which indicates;

The amount Josiah earns per chore is therefore; $12/4 = $18/6 = $3 per chore

The amount Josiah earns per chore, indicates that in week 5, the amount Josiah earns, when he completes 5 chores is; Amount earned = 5 × $3 = $15

The points on the graph are therefore; (4, 12), (6, 18), (5, 15)

The correct option is therefore; (4, 12), (5, 15), (6, 18)

Learn more on proportional relationships here: https://brainly.com/question/2463343

#SPJ1

Answer:

a

Step-by-step explanation:

...

Answer:

y = 60

Step-by-step explanation:

given y is directly proportional to x then the equation relating them is

y = kx ← k is the constant of proportion

to find k use the condition when y = 30 , x = 6

30 = 6k ( divide both sides by 6 )

5 = k

y = 5x ← equation of proportion

when x = 12 , then

y = 5 × 12 = 60