The finding that average IQ has increased steadily over the 20th century is referred to as the ______________.

Answer:

Amount invested in account with 5% annual interest = $300

Amount invested in account with 7% annual interest = $400

Amount invested in account with 8% annual interest = $900

Step-by-step explanation:

Let the money invested in account with 5% annual interest = \(x\)

As per question statement,

Money invested in account with 8% annual interest = \(3x\)

Given that total amount invested in three accounts = $1600

So, Money invested in account with 7% annual interest = 1600- \(3x\) -\(x\) = 1600- \(4x\)

For one year, the compound interest is same as that of Simple Interest.

Formula for simple interest is given as:

\(SI =\dfrac{PRT}{100}\)

Where, P is the amount invested

R is the annual rate of interest

T is the time for which the amount is invested.

As per question statement:

\(\dfrac{x\times 5\times 1}{100}+\dfrac{(1600-4x)\times 7\times 1}{100}+\dfrac{3x\times 8\times 1}{100} =115\\\Rightarrow 5x\times +1600\times 7-28x+24x=11500\\\Rightarrow 29x-28x = 11500-11200\\\Rightarrow \bold{x =\$300}\)

Amount invested in account with 5% annual interest = $300

Amount invested in account with 7% annual interest = $1600-$1200 = $400

Amount invested in account with 8% annual interest = $900

The coefficient of variation (CV) is a measure of relative variability and is calculated by dividing the standard deviation by the mean, and then multiplying by 100 to express it as a percentage.

In this case, the mean weight is 340 grams, and the standard deviation is 5.2 grams.

CV = (Standard Deviation / Mean) * 100

CV = (5.2 / 340) * 100

CV ≈ 1.53%

Therefore, the correct answer is option B: 1.53%.

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Given that AC is a diameter of the circle, we can conclude that triangle ABC is a right triangle, with AC being the hypotenuse. The area of the circle is not directly related to finding the lengths of BC or AB, so we will focus on the given information: AB = 16 units.

Using the Pythagorean theorem, we can find BC. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (AC) is equal to the sum of the squares of the other two sides (AB and BC):

AC² = AB² + BC²

Substituting the given values, we have:

(AC)² = (AB)² + (BC)²

(AC)² = 16² + (BC)²

(AC)² = 256 + (BC)²

Now, we need to find the length of AC. Since AC is a diameter of the circle, the length of AC is equal to twice the radius of the circle.

AC = 2 * radius

To find the radius, we can use the formula for the area of a circle:

Area = π * radius²

Given that the area of the circle is 2897 units², we can solve for the radius:

2897 = π * radius²

radius² = 2897 / π

radius = √(2897 / π)

Now we have the length of AC, which is equal to twice the radius. We can substitute this value into the equation:

(2 * radius)² = 256 + (BC)²

4 * radius² = 256 + (BC)²

Substituting the value of radius, we have:

4 * (√(2897 / π))² = 256 + (BC)²

4 * (2897 / π) = 256 + (BC)²

Simplifying the equation gives:

(4 * 2897) / π = 256 + (BC)²

BC² = (4 * 2897) / π - 256

Now we can solve for BC by taking the square root of both sides:

BC = √((4 * 2897) / π - 256)

To find the measure of angle BC (mBC), we know that triangle ABC is a right triangle, so angle B will be 90 degrees.

In summary:

BC = √((4 * 2897) / π - 256)

mBC = 90 degrees

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The image doesn't load for me.

Answer:

im not sure if my answer is correct

Answer:

first one

Step-by-step explanation:

The graph intersects x-axis at (4,0)  and (-3,0)

If function f has zeros at -3 and 4 then the first graph represents the function f.

When a function has zeros at -3 and 4, it means that the function's value is equal to zero at those x-values.

In other words, when x = -3 and x = 4, the function f(x) becomes 0.

To represent this on a graph, you should look for two points where the graph intersects the x-axis at -3 and 4.

When the graph crosses the x-axis at these points, it indicates that the function has zeros at those x-values.

When we observe the graphs, the first graph has zeros at -3 and 4.

Hence, the first graph could represent the function f with zeros at -3 and 4.

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Answer:

495km

Step-by-step explanation:

180 km in 4 hours means x km in 11 hours.

Cross multiply and you'll find x as 495 km

The congruency statement that describes the figures is:
ΔDEF ≅ ΔRSU

To answer your question, let's first find the image of triangle DEF after reflecting over the y-axis and then translating down 4 units and right 3 units.

1. Reflect ΔDEF over the y-axis:
D'(−6, 4), E'(−5, 8), F'(−1, 2)

2. Translate ΔD'E'F' down 4 units and right 3 units:
D''(−3, 0), E''(−2, 4), F''(2, −2)

Now, we have ΔD''E''F'' with points (−3, 0), (−2, 4), and (2, −2). Comparing this to ΔRSU with points (−2, 4), (−3, 0), and (2, −2), we can see that:

ΔD''E''F'' ≅ ΔRSU
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Answer:

ΔDEF ≅ ΔRSU

Step-by-step explanation:

Therefore, The limit of the given function is evaluated using L'Hospital's Rule repeatedly. The final answer is 1.

Explanation:
The given problem involves finding the limit of a function as x approaches 0. To evaluate the limit, L'Hospital's Rule is applied repeatedly to simplify the function. The derivative of 1-cos(x) with respect to x is sin(x), and the derivative of 48x² with respect to x is 96x. Using these derivatives, the limit is reduced to an indeterminate form of 0/0, which is resolved by applying L'Hospital's Rule again. This process is repeated multiple times until a final expression for the limit is obtained. The final answer is that the limit is equal to 1.

Therefore, The limit of the given function is evaluated using L'Hospital's Rule repeatedly. The final answer is 1.

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In this scenario, Marcos is planning to travel from Phoenix to Flagstaff, and we are using variables to represent different aspects of his journey.

The variable t represents the number of hours since Marcos left Phoenix, which serves as a measure of time elapsed since the start of the journey. It allows us to track the progress of Marcos over time and analyze various time-related aspects such as the duration of the journey or the rate at which he is traveling. On the other hand, the variable d represents the number of miles Marcos has traveled from Phoenix. It serves as a measure of distance covered, indicating how far Marcos has progressed on his route. By monitoring the value of d, we can determine the distance remaining to reach Flagstaff or calculate other distance-related parameters such as average speed or total distance traveled.

By using these variables, we can establish a relationship between time and distance traveled by Marcos. This relationship can be represented by a function or equation that describes Marcos' progress over time, such as a velocity equation or a distance-time equation. These variables and their relationship allow us to analyze and make predictions about Marcos' journey. We can determine when he is expected to reach certain milestones, calculate his average speed or rate of travel, and estimate the time required to complete the journey. Additionally, these variables provide a framework for solving various problems or making decisions related to Marcos' travel, such as optimizing his route or estimating fuel consumption based on distance traveled.

In summary, by using the variables t and d to represent time and distance traveled, respectively, we can effectively describe and analyze Marcos' journey from Phoenix to Flagstaff, enabling us to make informed decisions and predictions about his travel experience.

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Answer:

\(\huge\boxed{\sf h \approx 7\ in}\)

Step-by-step explanation:

Volume = V = 2908.33 in³

Radius = r = 11.5 in.

π = 3.14

Height = h = ?

\(V= \pi r^2 h\)

Put the given data in the above formula.

2908.33 = (3.14)(11.5)²(h)

2908.33 = (3.14)(132.25)(h)

2908.33 = 415.265 (h)

2908.33/415.265 = h

\(\rule[225]{225}{2}\)

Answer:

-16

Step-by-step explanation:

-16+11=-5 that's it lol

Answer:

m= -16

Step-by-step explanation:

subtract 11 from both sides

-5 - 11 =m + 11 - 11

combine like terms (-5 - 11 and 11 - 11)

m= -16

14.

x is equal to y because they have the same angle 45 degrees.

a²+b²=c²

x²+x²=6²

a = 4.24

b = 4.24

16.

x = 27.71

y = 13.85

z = 24

14) The values of x and y for the right triangle are \(3\sqrt{2}\).

15) The values of x, y, and z for the right triangle are \(x=8\sqrt{3}\), \(y=16\sqrt{3}\), and \(z=24\).

Given are right triangles.

14) Here, the length of the hypotenuse is 6.

It is required to find the length of the two legs.

The angle opposite the hypotenuse is 90°.

Another angle = 45°.

So, by the angle sum property of triangles, the third angle is also 45°.

So, the sides opposite these angles will be equal.

So, x = y.

By the Pythagorean theorem:

\(\sqrt{x^2+y^2} =6\)

Since x = y,

\(\sqrt{2x^2} =6\)

Square both sides.

\(2x^2=36\)

Divide both sides by 2.

\(x^2=18\)

Take the square root on both sides.

\(x=3\sqrt{2}=y\)

15) There are two right triangles given.

Consider the right triangle on the left.

Hypotenuse = \(24\sqrt{2}\).

Let m denote the unnamed side of this triangle which is common to both right triangles.

Since one of the angles is 45°, the other is also 45°.

So, m = z.

So, using the Pythagorean theorem:

\(2z^2=(24\sqrt{2} )^2\)

\(2z^2=1152\)

Divide both sides by 2.

\(z^2=576\)

Take the square root on both sides.

\(z=24\)

From the other triangle, using the angle sum property, the third angle = 30°.

The side opposite 60° = z = 24.

The ratio of the sides for the 30°-60°-90° triangle is 1 : √3 : 2.

Here, \(\sqrt{3} x=24\).

So, \(x=8\sqrt{3}\).

And, \(y=2x\).

So, \(y=16\sqrt{3}\).

Hence the values of x and y are \(3\sqrt{2}\) for the first one, and the values of \(x=8\sqrt{3}\), \(y=16\sqrt{3}\), and \(z=24\).

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The partial fraction expansion will look like

(x - 2)/((x ² + 1) (x - 1)²) = (ax + b)/(x ² + 1) + c/(x - 1) + d/(x - 1)²

Get everything in terms of a common denominator, and compare the numerators on both sides:

x - 2 = (ax + b) (x - 1)² + c (x ² + 1) (x - 1) + d (x ² + 1)

Expand the right side:

x - 2 = (ax + b) (x - 1)² + c (x ² + 1) (x - 1) + d (x ² + 1)

x - 2 = (a + c) x ³ + (-2a + b - c + d) x ² + (a - 2b + c) x + b - c + d

Match up the coefficients and solve the resulting system of equations:

a + c = 0

-2a + b - c + d = 0

a - 2b + c = 1

b - c + d = -2

==>   a = -1, b = -1/2, c = 1, d = -1/2

So the expansion into partial fractions is

(x - 2)/((x ² + 1) (x - 1)²) = (-x - 1/2)/(x ² + 1) + 1/(x - 1) - 1/(2 (x - 1)²)

… = -(2x + 1)/(2 (x ² + 1)) + 1/(x - 1) - 1/(2 (x - 1)²)

There are 30 cubic feet of water in the pipe at time t = 0. 76.570 cubic feet of rainwater flow into the pipe during the 8-hour time interval 0 ≤ t ≤ 8.

\(\int\limits^8_0\)   [R(t) dt = \(\int\limits^8_0\) 20 sin \(\frac{t^2}{35}\) dt = 76.570

What Is Time Interval?

The amount of time between two given times is known as time interval. In other words, it is the amount of time that has passed between the beginning and end of the event. It is also known as elapsed time.

INTERVAL types are divided into two classes: year-month intervals and day-time intervals. A year-month interval can represent a span of years and months, and a day-time interval can represent a span of days, hours, minutes, seconds, and fractions of a second.

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The integer whose square root is close to 2.25 is 5, and the correct answer is √5 ≈ 9/4.

The given equation is 9/4 = 2.25, which is equivalent to saying that 2.25 is close to the fraction 9/4.

We can use this information to find an integer whose square root is close to 2.25.

Let's check the square root of some integers to see which one is closest to 2.25:

√1 ≈ 1.00

√2 ≈ 1.41

√3 ≈ 1.73

√4 ≈ 2.00

√5 ≈ 2.24

√6 ≈ 2.45

√7 ≈ 2.65

√8 ≈ 2.83

√9 ≈ 3.00

As we can see, the square root of 5, √5 ≈ 2.24, is the closest integer to 2.25.

So, the integer whose square root is close to 2.25 is 5, and the correct answer is √5 ≈ 2.24.

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The minimum possible number of handshakes would occur if each person only shakes hands with two other people. In this case, the first person would shake hands with the second and third person, the second person would shake hands with the first and fourth person, the third person would shake hands with the first and fifth person, and so on. This pattern would continue until the 22nd person shakes hands with the 21st and 23rd person, and the 23rd person shakes hands with the 22nd and 21st person. Therefore, the minimum possible number of handshakes would be (23-1) or 22 handshakes.
Hi! To find the minimum possible number of handshakes among the 23 people attending the party, we need to ensure that each person shakes hands with at least two other people. Here's a step-by-step explanation:

1. Have the first person shake hands with two other people. This results in 2 handshakes.
2. For each subsequent person, have them shake hands with the two people that the previous person shook hands with.

Following this pattern, the first person will have 2 handshakes, and the remaining 22 people will each contribute 1 additional handshake, making a total of 22 handshakes.

So, the minimum possible number of handshakes among the 23 people at the party is 22 handshakes.

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Answer:

Im pretty sure its f(0) = g(0)

Step-by-step explanation:

Answer:

yes you got it correct smart

Step-by-step explanation:

The measure of angle PZQ is equal to 70°.

In Mathematics, a circle can be defined as a closed, two-dimensional curved geometric shape with no edges or corners. Additionally, a circle refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis) with a measure of 360 degrees.

Generally speaking, the sum of all the angles around a point is equal to one full turn, which makes it equal to 360 degrees;

m∠PZR + m∠QZR + m∠PZQ = 360

120 + 170 + m∠PZQ = 360

290 + m∠PZQ = 360

m∠PZQ = 360 - 290

m∠PZQ = 70°.

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Therefore , the solution of the given problem of probability comes out to be -y^(β-1)/[(β-1)Β(1, β)] .

The primary goal of the structures in the style known as parameters is the determination of the likelihood that a claim is accurate or that a specific event will occur. Any number between 0 and 1, at which 1 typically denotes certainty but also 0 typically denotes potential, can be used to symbolise chance. A probability diagram shows the chance that a specific event will occur.

Here,

We are aware that X's PDF is provided by:

If x is between 0 and 1 and 0 otherwise, f(x) Equals 1/B

where represents the size factor.

The formula for Yn's cumulative distribution function (CDF) is

=> F(y) = P(Yn ≤ y) = [P(Xi > y)]ⁿ = [1 - P(Xi ≤ y)]ⁿ

Using the CDF of the beta distribution, we have:

=> F(y) = [1 - Β(1, β; y)]ⁿ

We can approximate Yn by a normal distribution with mean and variance given by the following formulas using the continuity adjustment and central limit theorem:

=> E(Yn) = Β(2, β; 1)/Β(1, β) and Var(Yn) = E(Yn) - [Β(1, β; 1)/Β(1, β)]²

Therefore, we have:

=> (Yn - E(Yn))/sqrt(Var(Yn)) → N(0,1)

With the formulas for E(Yn) and Var(Yn) substituted, we obtain:

=> (Yn - Β(2, β; 1)/Β(1, β))/sqrt[Β(2, β; 1)/Β(1, β) - [Β(1, β; 1)/Β(1, β)]²] → N(0,1)

We need to work out the solution to determine b:

where is the CDF's usual standard value.

After applying the limit and taking the logarithm of both sides, we obtain:

=> F(y) = lim n log[n] = lim n n log

=> [1 - B(1, β; y)] = lim n -n (y, n)/(1, n)

L'Hopital's law gives us:

=> lim n -d/dy [n -(1, y)/n -(1, y)] = lim nn y(-1), ((1, )) ^2Β(2, β; y)

=> -y^(β-1)/[(β-1)Β(1, β)]

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Answer:

The answer is 405

Step-by-step explanation:

FIrst you would do 27 times 30 which is 810 then you would divided by 2 which in turn gives you 405

Hope this helped!

p-value < 0.0001, reject null hypothesis. Proportion of supporters for issue 1 is significantly different from the majority.

To find the p-an incentive for this present circumstance, we really want to direct a speculation test. We should expect the invalid speculation is that the extent of allies for issue 1 is equivalent to the larger part, and the elective theory is that the extent of allies is not the same as the larger part.

Utilizing a two-followed z-test with an importance level of 0.05, we can work out the z-measurement as:

z = (210/400 - 0.5)/sqrt(0.5 * 0.5/400) = 4.14

The p-an incentive for this test is the likelihood of getting a z-score more noteworthy than 4.14 or not exactly - 4.14, which is tiny (under 0.0001). In this way, we can dismiss the invalid speculation and presume that there is sufficient proof to propose that the extent of allies for issue 1 is altogether not quite the same as the larger part.

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Answer:

Step-by-step explanation:

22.36067977

Answer:

-3 is what I got

Step-by-step explanation:

Answer: Your equation is y=85(1.18)^x and it will take a little under 12 years for the population to reach 600.

Step-by-step explanation:

The equation for an exponential equation is y=ab^x

Change 18% to a decimal and than add 1 to it because it has to be above 1 to increase.

This is your equation --->    y=85(1.18)^x

After 11 years, the population of the frogs would be 525 and for 12 years, the population will be 619. So for the population to reach 600, it will take a little under 12 years.

Answer:

B

Step-by-step explanation:

Total ounces of nuts is cashews (12.3 ounces) plus almonds (15.2 ounces) is 27.5 ounces. If you divide 27.5 ounces by 5 people, 27.5 / 5 = 5.5 ounces each.