The equation P = 0.00892t^2 + 1.1149t + 78.4491 models the
United States population, P, in millions since 1900. If t
represents the number of years after 1900, then what is
the estimated population in 2025 to the nearest tenth of a
million?
343.9
219.0
356.9
217.8

The magnitude of a vector can be calculated using the Pythagorean theorem, which states that the magnitude is equal to the square root of the sum of the squares of its components. In this case, the vector →/u is given as (-4, -5), representing the x and y components respectively. By applying the Pythagorean theorem, we can determine the magnitude of →/u.

The magnitude (|→/u|) of a vector →/u = (x, y) can be calculated using the formula:

|→/u| = sqrt(x^2 + y^2)

In this case, →/u is given as (-4, -5), so the magnitude is:

|→/u| = sqrt((-4)^2 + (-5)^2)

Simplifying the equation:

|→/u| = sqrt(16 + 25)

|→/u| = sqrt(41)

Calculating the square root of 41, we find that the magnitude of →/u is approximately 6.40 rounded to the nearest hundredth. Therefore, |→/u| ≈ 6.40.

To learn more about Equation - brainly.com/question/29538993

#SPJ11

The length of the ramp is solved to be 15.33 feet

The length of the ramp is worked using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The direction of movements describes a right triangle of

adjacent = 15 feet

hypotenuse = length of the ramp = ?

The length of the ramp is calculated using cos, CAH

let the angle be x

cos x = adjacent / hypotenuse

cos 12 =  15 / hypotenuse

hypotenuse = 15 / cos 12

hypotenuse = 15.334

length of ramp = 15.33 feet

Learn more about SOH CAH TOA here:

https://brainly.com/question/29402966

#SPJ1

The correct interpretation is that the total revenue generated at a production rate of 11 units is $368. The Correct option is:

d) None of the above.

The marginal revenue function R(x) represents the additional revenue generated by producing and selling one additional unit of a product. In this case, the marginal revenue function is given by R(x) = 500 - 12x.

The notation R(11) refers to evaluating the marginal revenue function at a production rate of 11 units, which means substituting x = 11 into the function. So, we have R(11) = 500 - 12(11) = 500 - 132 = 368.

The interpretation is that at a production rate of 11 units, the total revenue generated is $368.

This means that by producing and selling 11 units of the product, the company earns $368 in revenue.

Learn more about revenue

brainly.com/question/13383966

#SPJ11

Answer:

Step-by-step explanation:

\(V=\frac13\cdot A_b\cdot H\)

\(A_b\)  - Base Area

H - Height of the pyramid

Base is regular triangle:  \(A_b=\dfrac{8^2\sqrt3}4\)

The volume:

                    \(V=\dfrac13\times \dfrac{8^2\sqrt3}4\times 12=64\sqrt3\approx110.9\)

If your height is 5 feet 3 inches and your weight is 120 pounds, then the BMI is 21.23

To calculate your Body Mass Index (BMI), use the following formula:

BMI = weight in kilograms / (height in meters)²

First, convert your height to meters :

5 feet 3 inches = 63 inches

63 inches = 160.02 cm

160.02 cm = 1.6002 meters

Next, convert your weight to kilograms :

120 pounds = 54.43 kg

Now, plug in these values to calculate your BMI:

BMI = 54.43 kg / (1.6002 meters)²

Divide the terms

BMI = 21.23

Therefore, your BMI is approximately 21.23

Learn more about Body mass index here

brainly.com/question/29404782

#SPJ4

the criteria used when deciding upon the inclusion of a variable are A - Theory, B - t-statistic, C - Bias, and D - Adjusted R^2.

When deciding upon the inclusion of a variable, the following criteria are commonly used:

A - Theory: Theoretical justification is often considered to include a variable in a model. It involves assessing whether the variable is relevant and aligns with the underlying theory or conceptual framework.

B - t-statistic: The t-statistic is used to determine the statistical significance of a variable. A variable with a significant t-statistic suggests that it has a meaningful relationship with the dependent variable and may be included in the model.

C - Bias: Bias refers to the presence of systematic errors in the estimation of model parameters. It is important to consider the potential bias introduced by including or excluding a variable and assess whether it aligns with the research objectives.

D - Adjusted R^2: Adjusted R^2 is a measure of the goodness of fit of a regression model. It considers the trade-off between the number of variables included and the overall fit of the model. Adjusted R^2 helps in assessing whether the inclusion of a variable improves the model's explanatory power.

To know more about variable visit:

brainly.com/question/29583350

#SPJ11

Alex can find the product by shading 5 sections in each row. In this way, each shaded row represents 5/6.

Now, to find the product, Alex has to add the shaded values, that is,

Answer:

triangle E

Step-by-step explanation:

imagine the X-axis as a mirror, the mirror reflects the shape or the body, and you'll see that the same distance you're away from the mirror as your reflection distance

if you want to prove that the triangle E is the reflection of the triangle A, count from the nearest point from the X-axis, you'll count 3 to reach the X-axis ,and the difference will be also 3 from the X-axis to the nearest point to the triangle E

Answer:

The distance between 2 points is 16.1 units.

Step-by-step explanation:

You have to apply distance formula using coordinates,

\(distance = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } \)

Let (x1,y1) be (-6,2),

Let (x2,y2) be (8,10)

\(distance = \sqrt{ {(8 - ( - 6))}^{2} + {(10 - 2)}^{2} } \)

\(distance = \sqrt{196 + 64} \)

\(distance = \sqrt{260} \)

\(distance = 2 \sqrt{65} \)

\(distance = 16.1 \: units \: (3s.f)\)

Step-by-step explanation:

D= rt

Where D is distance r is rate and t is time

15 < r3

15/3 < r

5< r

The inequality is Rate > 15 / 3. And the swimming rate of a manatee swims for 15 miles in 3 hours will be 5 miles per hour.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The swimming rate of a manatee swims for 15 miles in 3 hours is given as,

Rate > 15 / 3

Rate > 5 miles per hour

The inequality is Rate > 15 / 3. And the swimming rate of a manatee swims for 15 miles in 3 hours will be 5 miles per hour.

More about the rate link is given below.

https://brainly.com/question/14731228

#SPJ2

The unit rate of the pound of rice is given by the equation A = $ 2

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the unit rate of the pound of rice be represented as A

Now , the equation will be

The cost of 2 pounds of rice = $ 4

So , the cost of 1 pound of rice = cost of 2 pounds of rice / 2

Substituting the values in the equation , we get

The cost of 1 pound of rice A = 4 / 2

The cost of 1 pound of rice A = $ 2

Therefore , the value of A is $ 2

Hence , the equation is A = $ 2

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ1

how many miles on 1 gallon?

Lauren: 320/10=32

Melissa:280/8=35

Who Drove farther?

32*40=1280

35*40=1400

Melissa can drive farther

Melissa drove farther of 1400 miles than Lauren.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Lauren can drive her car 320 miles on 10 gallons of gasoline. Melissa can drive her car 280 miles on 8 gallons of gasoline.

The distance for 40 gallons will be calculated as,

Lauren: 320/10=32

Melissa:280/8=35

Distance covered by Lauren,

32  x 40=1280 miles

Distance covered by Melissa,

35 x 40=1400 miles

To know more about an expression follow

https://brainly.com/question/1262967

#SPJ2

The exact value of the expression is -1.

The expression involves tan 25° and tan 110°. The expression you provided is:

tan 25° + tan 110° / (1 - tan 25° tan 110°)

First, we need to recognize that tan (180° - x) = -tan x. Since 110° = 180° - 70°, we have:

tan 110° = -tan 70°

Now, we can rewrite the expression as:

tan 25° - tan 70° / (1 + tan 25° tan 70°)

Next, we can apply the tangent addition formula, which is:

tan (a - b) = (tan a - tan b) / (1 + tan a tan b)

Comparing this formula with our expression, we see that a = 25° and b = 70°. So, the expression simplifies to:

tan (25° - 70°) = tan (-45°)

Since tan (-x) = -tan x, we have:

tan (-45°) = -tan 45°

Lastly, we know that tan 45° = 1, so:

-tan 45° = -1

Therefore, the exact value of the expression is -1.

Visit here to learn more about tangent:

brainly.com/question/19064965

#SPJ11

Answer:

8

Step-by-step explanation:

the numbers decrease by 1

Question:

QS and TV are parallel lines.



What angles are alternate exterior angles?



Options:

a) b) c) d)

Solution:

Remember that the alternate exterior angles are the exterior angles found on either side of the secant. Then, in our case we have that the alternate exterior angles are:

QRP and SRP



See below for the proof of the equation \(\frac{ax + by}{x + y} - \frac{ax - by}{x - y}= 2(a - b)\)

The equation is given as:

\(\frac{ax + by}{x + y} - \frac{ax - by}{x - y}= 2(a - b)\)

Take the LCM

\(\frac{(ax + by)(x - y) -(ax - by)(x + y)}{(x + y)(x - y)}= 2(a - b)\)

Expand

\(\frac{ax^2 - axy + bxy - by^2 -ax^2 - axy + bxy + by^2}{(x + y)(x - y)}= 2(a - b)\)

Evaluate the like terms

\(\frac{-2axy + 2bxy }{(x + y)(x - y)}= 2(a - b)\)

Rewrite as:

\(\frac{-2axy + 2bxy }{x^2 - y^2}= 2(a - b)\)

Factorize the numerator

\(\frac{2(a - b)(x^2 - y^2)}{x^2 - y^2}= 2(a - b)\)

Divide

2(a - b)= 2(a - b)

Both sides are equal

Hence, the equation \(\frac{ax + by}{x + y} - \frac{ax - by}{x - y}= 2(a - b)\) has been proved

Read more about equations at:

https://brainly.com/question/2972832

#SPJ1

The probability of selecting two red marbles and one blue marble is \(\frac{4}{15}\)

To calculate the probability, we first determine the total number of possible outcomes. Since three marbles are being selected simultaneously, there are C(6, 3) = 20 different ways to choose three marbles from the six available.

Next, we consider the number of favorable outcomes, which in this case is selecting two red marbles and one blue marble. We can choose two red marbles from the four available in C(4, 2) = 6 ways, and we have only one blue marble to select. Therefore, there are 6 × 1 = 6 favorable outcomes.

Finally, we calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes. Thus, the probability of selecting two red marbles and one blue marble is 6÷20, which simplifies to 3÷10 or approximately 0.4.

learn more about probability here:

https://brainly.com/question/32117953

#SPJ11

Answer: B

Step-by-step explanation:

We can see that the graph is being compressed, so f(x) is being transformed into f(ax), where 0<a<1.

The only option that satisfies this is y=f(x/2).

Answer:

1593 pandas 13 years ago.

Difference? ≈271 pandas

Keyword:

"Increase"

Step-by-step explanation:

Use the equation:

x + (x × P%) = y

x(1 + P%) = y

x = 1864/(1 + 17%)

x = 1864/(1 + 0.17(17%))

x = 1864/1.17

x = 1593.1624 ≈ 1593

Answer:

e, all of the above steps help establish good credit history

Step-by-step explanation:

Answer: E.

Hope this helps.

The probability that the system selected contains at least one Sony component is 0.875, and the probability that the system selected contains exactly one Sony component is 0.525.

There are eight possible configurations for the four switches, as each switch can either be "Sony" or "not Sony". Out of these eight configurations, there is only one where none of the switches are "Sony", which means there are seven configurations where at least one switch is "Sony". Therefore, the probability that the system selected contains at least one Sony component is 7/8 or 0.875.

To calculate the probability that the system selected contains exactly one Sony component, we need to count the number of configurations where exactly one switch is "Sony". There are four possible switches that could be "Sony", so we need to calculate the number of ways we can select one switch out of four. This is the combination formula: C(4,1) = 4. For each of these choices, there are three switches that are not "Sony", so we need to calculate the number of ways we can select three switches out of three. This is simply 1. Therefore, the total number of configurations with exactly one Sony component is 4*1 = 4. Dividing by the total number of configurations (8), we get the probability that the system selected contains exactly one Sony component as 4/8 or 0.525.

For more questions like Probability visit the link below:

https://brainly.com/question/5392252

#SPJ11

In triangle ΔDEF, we are given that ∠F = 90°, EF = 4.9 feet, and DE = 8.3 feet. We need to find the measure of ∠D to the nearest degree.Since ∠F is a right angle (∠F = 90°), triangle ΔDEF is a right triangle.

In a right triangle, the sum of the measures of the two acute angles is always 90°.

Therefore, ∠D + ∠E = 90°.

Since ∠F = 90° and the sum of the angles in a triangle is 180°, we can determine ∠E by subtracting the measures of ∠F and ∠D from 180°.

∠E = 180° - 90° - ∠D

∠E = 90° - ∠D

Now we can use the trigonometric ratio in a right triangle to find the measure of ∠D.

tan(∠D) = opposite/adjacent = EF/DE

tan(∠D) = 4.9/8.3

Using a calculator or trigonometric table, we can find the inverse tangent (arctan) of this ratio:

∠D ≈ arctan(4.9/8.3)

∠D ≈ 32.23°

Therefore, the measure of ∠D to the nearest degree is 32°.

Learn more about triangle here

https://brainly.com/question/17335144

#SPJ11

Answer: The total cost of the fences=$165.6

Step-by-step explanation:

Let a = the length of the side if the square.

The perimeter of the square is 60 ft

                                   4a = 60ft

divide both sides by

                                  4a = 60/4

                                    a = 15 ft

The garden is surrounded by two fences, one fence is around the perimeter of the garden, whereas the second fence is 3 feet from the first fence on the outside

Expand to get:

                               4*a + 4(a + 2*3)

Replace a with 15 to get:

                         =  4*15 + 4(15 + 6) 60 + 4(21) 60+84

                         = 144ft

The cost of the fence is $1.15 per foot

The cost of 144 ft fence will be:

                       = 144*1.15

                       = $165.6

Learn more about event correlation here: brainly.com/question/1333555

#21165

Answer: 4th option (the one already selected)

Step-by-step explanation: as the X variable changes by 7 the Y variable changes by 1

Using linear function concepts, the correct option is given by:

The slope is −0.3. Starting at 3.6, the GPA will decrease by 0.3 for every text sent in class.

A linear function is modeled by:

y = mx + b

In which:

For this problem, the function is:

y = 3.6 - 0.3x.

The function has a initial GPA of 3.6(student who sends 0 texts), then for each text the student sends, the GPA falls by 0.3(slope of -0.3), hence the correct option is:

The slope is −0.3. Starting at 3.6, the GPA will decrease by 0.3 for every text sent in class.

More can be learned about linear function concepts at https://brainly.com/question/24808124

#SPJ1

Step-by-step explanation:

Let's say that the you have to found the mean of 5, 2, and 8

first you would have to add up all of the number 5+2+8 which equals to 15

now you would have divide 15 by the amount of the data points which is 3, so your mean in this problem is 5.

here is an example by only using numbers:

(5+2+8) ÷ 3 = 5

Answer:

1.9 x 10 to the 7th power

Step-by-step explanation:

1.9 x 10 to the 7th power