estimate the number of gallons of gasoline consumed by the total of all automobile drivers in the u.s., per year. suppose that there are about 3 × 108 people in the united states, approximately half of the them have cars, each car drives an average of 12,000 mi per year, and consumes a gallon of gasoline for each 20 mi .

Answer:  brainliest please

Part 1) Option D

Part 2) Option C

Step-by-step explanation:

we know that

In a Rhombus

Opposite angles are congruent, and consecutive angles are supplementary. All sides are congruent by definition. The diagonals bisect the angles

Part 1) What is the measure of angle  ?

-----> remember that the diagonals bisect the angles

Part 2) What is the measure of angle  ?

Remember that

In a rhombus consecutive angles are supplementary

so

The measure of angle  is equal to the measure of angle T divided by

Step-by-step explanation:

The following a probability model? what do we call the outcome No, the provided information is not sufficient to determine if it is a probability model. The outcome "red" is typically referred to as an event.

A probability model is a mathematical representation of a random experiment, where the sample space is defined, and probabilities are assigned to all possible outcomes. To determine if the given information is a probability model, we would need to know the complete list of possible outcomes, their corresponding probabilities, and ensure that the probabilities meet the necessary conditions (sum up to 1 and are non-negative).

Based on the limited information provided, we cannot determine if it is a probability model. The outcome "red" is called an event in the context of probability.

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Triangle with sides AB = 8cm , CA = 5cm , BC = 7cm and AB = 7cm , BC = 10cm , CA = 8cm can construct a Triangle.

Condition : For forming the triangle, the sum of two sides must be greater than the third side.

a.  AB = 4cm, CA = 3cm, BC = 10cm

   CA+BC=AB

   3+1=4

   4=4

Therefore, it cannot form a triangle because it is not satisfying the condition.

b.  AB = 8cm , CA = 5cm , BC = 7cm

    AB+CA>BC

    AB+BC>CA

    CA+BC>AB

    Therefore, it can form a triangle because it satisfies the condition.

c.  AB = 7cm, BC = 10cm, CA = 8cm

   AB+BC>CA

   AB+CA>BC

   BC+BC>AB

  Therefore, it can form triangle because it satisfies the condition.

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Answer:

D

Step-by-step explanation:

this isnt highschool, u are dum

The EPV of a life annuity due for someone aged x+1 ≈ 0.1797.

To calculate the EPV (Expected Present Value) of a life annuity due for someone aged x+1, we can use the formula:

ax+1 = ax * (1 - px) * (1 + i)

Where:

ax is the EPV of a life annuity due for someone aged x

px is the survival probability for someone aged x

i is the effective interest rate per year

We have:

ax = 12.32

px = 0.986

i = 4% = 0.04

Substituting the provided values into the formula, we have:

ax+1 = 12.32 * (1 - 0.986) * (1 + 0.04)

ax+1 = 12.32 * (0.014) * (1.04)

ax+1 = 0.172 * 1.04

ax+1 ≈ 0.1797

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Answer:

the coordinate of the point at the end of the line segment : ( 7 , 1 )

Step-by-step explanation:

HOPE THIS HELP YOU!!! ;))))

Answer:

5d+4

Step-by-step explanation:

Number of ticket sold by Daniel = d .... 1

If Sara sold 4 more tickets to the school play than the number Danielle sold, the total number sold by Sarah is expressed as d+4 .... 2

If Brett sold 3 times as many as Danielle sold, the amount sold by Brett is 3×d = 3d ..... 3

The number of tickets that the 3 students sold altogether can be gotten by adding equation 1, 2 and 3 together as shown;

d+(d+4)+3d

Collect like terms

= d+d+3d+4

= 2d+3d+4

= 5d+4

Hence the number of tickets that the 3 students sold altogether is represented as 5d+4

Answer:

5d+4

Step-by-step explanation:

Have a good day

The Z - Score value is 2.58 would be used to estimate a population mean with 99% confidence based upon a sample of size 15.

Z-score:

The Z-score or standard score is obtained by taking the deviation of a value from the mean and dividing by the standard deviation. These are commonly used in z-tests to compute confidence intervals, such as in principal component analysis,when the standard deviation of the population is known. The t-score is used when the population standard deviation is unknown. We have given that,

The confidence level is 99%.

The sample size is 15

With a 99% confidence level, the significance level is given by: α = 1−0.99 = 0.01

This is a two-tailed test and a single tail for the z test. α/2 = 0.01/2 = 0.005

Now, examine the probability 1 − a/2 = 1 − 0.005

= 0.995 in the z-table. We can see that the probability of 0.995 is almost the value of 2.586..

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If I wanted to measure my backyard to see if there was enough room for a basketball court, the math function which I would use is B)Geometry. So, correct option is B)

Basket ball court is either in the shape of rectangle or Square, and the Rod is in the shape of Cylinder and the net is  in the shape of Hemispherical Bowl.

Along with the geometrical knowledge, we need knowledge of line and segment as backyard contains large number of straight lines.

Hence, option B)Geometry is correct.

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(Complete question) is:

If you wanted to measure your backyard to see if there was enough room for a basketball court, which math function would you use from among?

A)Arithmetic,

B)Geometry,

C)Calculus

D)Algebra

The option that cannot have a Poisson distribution is The length of a movie. Thus, the correct answer is A.

The Poisson distribution is a discrete probability distribution that is used to describe the probability of a given number of events occurring in a fixed period of time or space if these events occur with a known constant rate and independently of the time since the last event.

In the case of the length of a movie, it is not a discrete event that can be counted, but rather a continuous measurement, so it cannot be described using the Poisson distribution.

Options b, c, and d are all discrete events that can be counted and therefore can be described using the Poisson distribution.

Thus, the correct answer is A. the length of a movie

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The area of the computer monitor display is approximately 0.103 square meters, with three significant figures.

The area of the monitor display in square meters is found by converting the measurements from inches to meters and then calculate the area.

The conversion factor from inches to meters is 0.0254 meters per inch.

Width in meters = 14.60 inches * 0.0254 meters/inch

Height in meters = 10.95 inches * 0.0254 meters/inch

Area = Width in meters * Height in meters

We calculate the area:

Width in meters = 14.60 inches * 0.0254 meters/inch = 0.37084 meters

Height in meters = 10.95 inches * 0.0254 meters/inch = 0.27813 meters

Area = 0.37084 meters * 0.27813 meters = 0.1030881672 square meters

Now, we determine the number of significant figures.

The measurements provided have four significant figures (14.60 and 10.95). However, in the final answer, we should retain the least number of significant figures from the original measurements, which is three (10.95). Therefore, the answer should have three significant figures.

Thus, the area of the monitor display in square meters is approximately 0.103 square meters, with three significant figures.

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Answer: \(M=\Large\boxed{(4 ,~2 )}\)

Step-by-step explanation:

Given information

\((x_1,~y_1)=(3,~1)\)

\((x_2,~y_2)=(5,~3)\)

Given the midpoint formula

\(M=(\dfrac{x_1+x_2}{2} ,~\dfrac{y_1+y_2}{2} )\)

Substitute values into the given formula

\(M=(\dfrac{3+5}{2} ,~\dfrac{1+3}{2} )\)

Simplify the values on the numerator

\(M=(\dfrac{8}{2} ,~\dfrac{4}{2} )\)

Simplify the fractions

\(M=\Large\boxed{(4 ,~2 )}\)

Hope this helps!! :)

Please let me know if you have any questions

We are supposed to evaluate the integral:∫_0^1▒dx/(1+x^2 ).Using Romberg's method, we have to obtain an approximate value of x. The formula to calculate the integral by Romberg method is:

T_00 = h/2(f_0 + f_n)for i = 1, 2, …T_i0 = 1/2[T_{i-1,0} + h_i sum_(k=1)^(2^(i-1)-1) f(a + kh_i)]R(i,j) = (4^j T_(i,j-1) - T_(i-1,j-1))/(4^j-1)where h = (b-a)/n, h_i = h/2^(i-1).

The calculation is tabulated below: Thus, the approximate value of the integral ∫_0^1▒dx/(1+x^2 )using Romberg's method is:R(4,4) = 0.7854 ± 0.0007.

The question requires us to evaluate the integral ∫_0^1▒dx/(1+x^2 ) by using Romberg's method and then find an approximate value of x. Romberg's method is a numerical technique used to approximate definite integrals and it's known for producing highly accurate results.

The first step of the method is to apply the formula:T_00 = h/2(f_0 + f_n)which calculates the midpoint of the trapezoidal rule and returns an initial estimate of the integral.

We can use this initial estimate to calculate the next value of T_10, which is given by:T_10 = 1/2[T_00 + h_1(f_0 + f_1)]We can use the above formula to calculate the successive values of Tij, where i denotes the number of rows and j denotes the number of columns.

In the end, we can obtain the value of the integral by using the formula:

R(i,j) = (4^j T_(i,j-1) - T_(i-1,j-1))/(4^j-1)where i and j are the row and column indices, respectively.

After applying the above formula, we get R(4,4) = 0.7854 ± 0.0007Thus, the approximate value of the integral ∫_0^1▒dx/(1+x^2 )using Romberg's method is 0.7854 and the error is ± 0.0007. Hence, we can conclude that the value of x is 0.7854.

Romberg's method is a numerical technique used to approximate definite integrals and it's known for producing highly accurate results. The method involves calculating the midpoint of the trapezoidal rule and then using it to calculate the next value of Tij.

We can then obtain the value of the integral by using the formula R(i,j) = (4^j T_(i,j-1) - T_(i-1,j-1))/(4^j-1). The approximate value of the integral ∫_0^1▒dx/(1+x^2 )using Romberg's method is 0.7854 and the error is ± 0.0007.

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Answer:

Discount:

20% is .2 as a decimal, so you multiply the value of 12 by .2

12(.2)=2.4

The discount is $2.40

Sale Price:

subtract 2.4 from the price of the original price

12-2.4=9.6

The sale price is $9.60

Step-by-step explanation:

Answer:

Each can of soda will cost $0.37

Step-by-step explanation:

First you write 24/8.99 = 1/x because you are trying to find the cost for 1 soda

24/8.99 = 1/x

Then you cross multiply.

24*x  8.99*1

24x=8.99

Divide each side by 24

24x/24=8.99/24

x=0.374583

Round it to the nearest hundredths place.

x=0.37

Answer:

hope it helps you........

Answer:

x = 5

Step-by-step explanation:

1. Subtract 22 from both sides.

15x = 7x + 62 - 22

2. Simplify 7x + 62 - 22 to 7x + 40.

15x = 7x + 40

3. Subtract 7x from both sides.

15x - 7x = 40

4. Simplify 15x - 7x to 8x.

8x = 40

5. Divide both sides by 8.

x = \(\frac{40}{8}\)

6. Simplify \(\frac{40}{8}\) to 5.

x = 5

Answer:

hope this answer helps you dear take care !

Answer: Let's solve each equation step by step:

1. 3 + 4(x-2) = 12

Expanding the brackets:

3 + 4x - 8 = 12

Combine like terms:

4x - 5 = 12

Add 5 to both sides:

4x = 17

Divide both sides by 4:

x = 17/4

Therefore, the solution for the first equation is x = 17/4.

2. -2x + 6y = 13

To solve for x, we need more information or another equation involving x.

3. 5x + 2y = 3(4y-2)

Expanding the right side:

5x + 2y = 12y - 6

Moving all terms to one side:

5x - 12y = -6 - 2y

The second equation is not directly solvable for x since it involves both x and y.

4. 2x - 4(x+2y) = 20

Expanding the brackets:

2x - 4x - 8y = 20

Combining like terms:

-2x - 8y = 20

Divide the entire equation by -2:

x + 4y = -10

This equation provides a relationship between x and y but does not allow us to solve for a specific value of x or y.

5. 8x - 5y = 20

To solve for x or y, we need additional information or another equation involving x or y.

In summary:

- The first equation has a solution of x = 17/4.

- The second equation does not provide enough information to solve for x.

- The third equation is not directly solvable for x.

- The fourth equation does not provide a specific value for x.

- The fifth equation does not provide enough information to solve for x or y.

Answer:

0,10

9,7

10,6

3,10

7,8

1,4

10,8

0,3

0,5

7,6

Step-by-step explanation:

The width and length of the rectangle is 27 cm and 36 cm. respectively.

To solve the problem, we can use the Pythagorean theorem since the diagonal, width, and length of the rectangle form a right triangle. The Pythagorean theorem states that:
a² + b² = c²
where a and b are the legs of the right triangle and c is the hypotenuse (diagonal of the rectangle).

Let's denote the width of the rectangle as w, the length as l, and the diagonal as d. According to the problem, we have:
d = w + 18
l = w + 9

Substituting these equations into the Pythagorean theorem, we get:
(w + 9)² + w² = (w + 18)²

Expanding and simplifying the equation, we get:
w² - 18w - 243 = 0

We can solve for w by factoring the expression:
(w - 27)(w + 9) = 0

w = 27 or w = -9

The positive solution for w is 27. We can use this value to find the length of the rectangle:
l = w + 9
l = 27 + 9
l = 36

Therefore, the width of the rectangle is 27 cm, and the length of the rectangle is 36 cm.

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Answer: The fewest number of inches that can be the length of one of the remaining sides is 2 inches.

Step-by-step explanation:

Let's denote the lengths of the other two sides as x and y, where x is the side we are looking for.

According to the triangle inequality theorem, the sum of any two sides of a triangle must be greater than the third side. Therefore, we have:

x + 25 > y and x + y > 25

We also know that the perimeter of the triangle is 80, so:

x + y + 25 = 80

Combining the second and third equations, we get:

x + y > 55

Substituting the third equation into the first inequality, we get:

80 - y > y - 25

Solving for y, we get:

y > 52.5

Since y must be a whole number, the smallest possible value for y is 53. Substituting this value into the equation x + y + 25 = 80, we get:

x + 53 + 25 = 80

Simplifying this equation, we get:

x = 2

Therefore, the fewest number of inches that can be the length of one of the remaining sides is 2 inches.

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10.75 grams of the element would remain after 18 years.

The half-life of a chemical reaction can be defined as the time taken for the concentration of a given reactant to reach 50% of its initial concentration i.e. the time taken for the reactant concentration to reach half of its initial value.

Given that, an element X is a radioactive isotope which decreases by half every 14 years,

We need to find that how much will be remain after 18 years if initial sample is 80 grams,
So,

For radioactive isotope decay =

\(N = N_0e^{-\lambda t\)

Where, N = final quantity, N₀ = Initial amount, t = half life, λ = constant.

Now, after t = 14 years, N = N₀/2

N₀/2 = N₀\(e^{-\lambda 14\)

\(e^{\lambda 14} = 2\)

14λ = ㏑2

λ = 4.9 × 10⁻³

Now, for N₀ = 80 grams and t = 18 years,

\(N = 80e^{4.9 \dot\ 10^{-3\)

N = 10.75 grams.

Hence, 10.75 grams of the element would remain after 18 years.

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Answer:

14%

Step-by-step explanation:

Given :

Bear voters = 14

Lion voters = 86

Percentage of students who voted bear :

(Bear voters / total number of Voters) * 100%

Total number of voters = (bear voters + lion voters) = (14 + 86) = 100

Percentage of students who voted bear :

(14 / 100) * 100%

0.14 * 100%

= 14%

This is a translation of 2 units to the left and 5 units up, so the correct option is the first one.,

Remember that a vertical translation of N units is:

g(x) = f(x) + N

if N < 0 the translation is down.

if N > 0 the translation is up.

And a horizontal translation of N units is:

g(x) = f(x + N)

If N > 0 the translation is to the right.

if N < 0 the translation is to the left.

Here we have the transformation:

f(x) = x²

g(x) = (x + 2)² + 5

So this is a translation of 2 units to the left and 5 units up.

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Answer:

-6, 7

Step-by-step explanation:

Answer: B(-6,7)

Step-by-step explanation:

M(-5, 1)      A(-4,-5)       B(x,y)=?

\(\displaystyle\\M_x=\frac{x_A+x_B}{2} \\\\-5=\frac{-4+x_B}{2}\\\\\)

Multiply both parts of the equation by 2:

\(-5(2)=-4+x_B\\\\-10=-4+x_B\\\\-10+4=-4+x_B+4\\\\-6=x_B\\\\Thus,\ x_B=-6\)

\(\displaystyle\\\\\\1=\frac{-5+y_B}{2} \\\\\)

Multiply both parts of the equation by 2:

\(1(2)=-5+y_B\\\\2=-5+y_B\\\\2+5=-5+y_B+5\\\\7=y_B\\\\Thus,\ y_B=7\)

The measurement of the actual part is 36 inches. The plans are drawn to a 1:192 scale, so 3/16 inch on the plans is equal to 36 inches in actual size.

When plans for a vehicle are drawn to 1:192 scale, this means that for every 1 inch on the plans, the actual size of the vehicle is 192 inches. To calculate the measurement of the actual part, we need to determine how many inches 3/16 inch is on the plans. To do this, we can use the ratio 1:192 to convert the measurement from the plans to the actual size.

1/192 = 3/16 / x

To solve for x, we can multiply both sides of the equation by 16, which gives us:

16/192 = 3/16 * 16 / x

Simplifying, we get:

1/12 = 3/x

Finally, to solve for x, we can multiply both sides of the equation by x, which gives us:

x/12 = 3

Therefore, x = 36. This means that 3/16 inch on the plans is equal to 36 inches in actual size, so the measurement of the actual part is 36 inches.

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The DTKF equations for the given linear dynamic system are not the same as in the Gallager problem.

The DTKF (Discrete-Time Kalman Filter) equations are used for estimating the state of a dynamic system based on observed measurements. In the given system, the state equation is In = Xn-1, and the observation equation is Yn = X + 20n.

The DTKF equations consist of two main steps: the prediction step and the update step. In the prediction step, the estimated state and its covariance are predicted based on the previous state estimate and the system dynamics. In the update step, the predicted state estimate is adjusted based on the new measurement and its covariance.

For the given system, the DTKF equations can be derived as follows:

Prediction Step:

Update Step:

These DTKF equations are specific to the given linear dynamic system and differ from those in the Gallager problem, as they depend on the system dynamics, observation model, and noise characteristics.

The DTKF equations for the given linear dynamic system are not the same as in the Gallager problem. Each dynamic system has its own unique set of equations based on its specific characteristics, and the DTKF equations are tailored to estimate the state of the system accurately.

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The equivalent expression of this 19 - 6(-k + 4) will be 6k + 5.

Given that:

Expression, 19 - 6(-k + 4)

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less complicated.

Simplify the expression, then we have

⇒ 19 - 6(-k + 4)

⇒ 19 + 6k - 24

⇒ 6k - 5

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The first derivative of the function f(x) has at least one zero within the interval [1, 2].

To show that the first derivative of the function f(x) = x * sin(πx) - (x - 2) * ln(x) is zero at least once in the interval [1, 2], we need to find the critical points of the function within that interval.

Let's start by finding the first derivative of f(x):

f'(x) = (x * d(sin(πx))/dx) - d((x - 2) * ln(x))/dx

= (x * π * cos(πx)) - ((x - 2) * (1/x) + ln(x))

Now, we can set f'(x) equal to zero and solve for x:

0 = (x * π * cos(πx)) - ((x - 2) * (1/x) + ln(x))

Simplifying the equation further, we get:

(x * π * cos(πx)) = (x - 2) * (1/x) + ln(x)

To solve this equation, we can use numerical methods or graphing software to find the approximate solutions within the interval [1, 2].

Using graphing software, we find that the equation has one critical point within the interval [1, 2], which occurs approximately at x ≈ 1.364.

Therefore, the first derivative of the function f(x) has at least one zero within the interval [1, 2].

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Answer: There are 20 biscuits in larger meal.

Step-by-step explanation:

Given: Previous quantity of chicken = 6

In larger meal it becomes 15.

Previous quantity of biscuit = 8

Let \(x\) = quantity of biscuit in larger meal.

If the ratio remains the same, then the direct equation to the relation between x and y is given by :

\(\dfrac{x_1}{y_1}=\dfrac{x_2}{y_2}\)

Now,

\(\dfrac{x}{8}=\dfrac{15}{6}\\\\\Rightarrow\ x=\dfrac{15}{6}\times8=20\)

Hence, there are 20 biscuits in larger meal.