What inequality matches this graph?
A} x > -5

B} x ≥ -5

C} x < -5

D} x ≥-5

City Bank paid more interest than First National Bank over the 5-year period.

What is compound interest?

Compound interest is the interest earned on both the principal amount and the accumulated interest from previous periods.

We can use the formula for compound interest to calculate the amounts of interest earned by the two banks over 5 years:

Amount of interest with First National Bank = [tex]$P\left(1 + \frac{r}{n}\right)^{n\cdot t} - P$[/tex]

where P is the principal amount, r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the number of years.

Amount of interest with First National Bank

=[tex]$500\left(1 + \frac{0.085}{1}\right)^{1\times 5} - 500$[/tex]

= $235.15 (rounded to two decimal places)

Amount of interest with City Bank =[tex]$P\left(1 + \frac{r}{n}\right)^{n\cdot t} - P$[/tex]

where P is the principal amount, r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year (365 in this case, since interest is compounded daily), and t is the number of years.

Amount of interest with City Bank

=[tex]$500\left(1 + \frac{0.0825}{365}\right)^{365\times 5} - 500$[/tex]

= $240.45 (rounded to two decimal places)

The difference in the amounts of interest paid by the two banks is:

$240.45 - $235.15 = $5.30

Therefore, City Bank paid more interest than First National Bank over the 5-year period.

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It is true. The trigonometric identity  [tex]\frac{cscx+secx}{sinx + cosx}[/tex] = cotx + tanx

To verify that (cscx+secx)/(sinx + cosx) = cotx + tanx

csc = [tex]\frac{1}{sin}[/tex]  and Sec = [tex]\frac{1}{cos}[/tex]

If we insert the values, it would be

[tex]\frac{ 1/sinx + 1/cosx}{sinx + cosx}[/tex]

= [tex]\frac{cosx + sinx}{sinx * cosx}[/tex] ÷  ([tex]\frac{1}{sinx + cosx}[/tex])

= [tex]\frac{1}{sinx * cosx}[/tex]

[tex]\frac{Sin^2 x + Cos^2x}{Sin x Cos x}[/tex]  =  [tex]\frac{Sin^2x}{SinxCosx}[/tex]  +  [tex]\frac{Cos^2x}{SinxCosx}[/tex]

= cotx + Tanx

Mind you

cotx = [tex]\frac{1}{tanx}[/tex] = [tex]\frac{cosx}{sinx}[/tex]

tanx = [tex]\frac{sinx}{cosx}[/tex]

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The logarithmic form of the equation (1/7)³ = 1/343 is given as follows:

[tex]\log_3{\left(\frac{1}{343}\right)} = \frac{1}{7}[/tex]

A logarithm is a mathematical function that represents the power to which a given base must be raised in order to obtain a given number. Logarithms are often used to simplify calculations involving very large or very small numbers.

In this problem, we raise 1/7 to the third power to obtain the number 1/343, hence the logarithm of base 3 of the number 1/343 is of 1/7, and then the expression is given as follows:

[tex]\log_3{\left(\frac{1}{343}\right)} = \frac{1}{7}[/tex]

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The probability of selecting an elm or oak tree is 0.38.

The probability of selecting an elm or oak tree is the sum of the probabilities of selecting an elm and selecting an oak:

P(elm or oak) = P(elm) + P(oak)

P(elm) = 0.04

P(Oak) =0.34

Plug in these values

= 0.04 + 0.34

= 0.38

Therefore, the probability of selecting an elm or oak tree is 0.38.

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Answer:

30 minutes

Step-by-step explanation:

1/45 m + 1/90 m = 1

2/9 m + 1/90 m = 1

3/90 m = 1   Multiply both sides by 90/3

90/3 x 3/90 m = 1 x 90/3

m = 90/3

m = 30

Helping in the name of Jesus.

No, any court case should not be based solely on probabilities as probability does not imply certainty.

Compute the probability of another couple being in that area with the same characteristics

CHARACTERISTIC ASSUMED PROBABILITY

Drives a yellow car 1 out of 12

Man over 6 feet tall 1 /10

Man wearing tennis shoes 1/4

Man with beard 1/11

Woman with blond hair 1/3

Woman with hair in a ponytail 1 /13

Women over 6 feet tall 1/100

We will use the multiplication rule as all the characteristics should be present in the couple.

The probability of another couple being in that area with the same characteristics is given as

P(Drives a yellow car) x P(Man with beard) x P(Woman with blond hair) x P(Woman with hair in a ponytail) x P(Woman over 6 feet tall) = 1/12 x 1/11 x 1/3 x 1/13 x 1/100 = 1/514800

The characteristics dependent on the sum of the probabilities is not equal to 1.

The assumption of independence would lead to use of the addition rule instead of the multiplication rule, and hence the probability would change (the probability would increase).

No, any court case should not be based solely on probabilities as probability does not imply certainty.

No, the couple who was arrested should not be convicted if there were no eyewitnesses as probability does not imply certainty.

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The expression of 1 picoseconds as a decimal would be = 0.000000000001 picoseconds.

The scientific notation of representation of figures is a systematic way of representation of too large or too small figures encountered in everyday arithmetics.

From the table above, the larger figures are represented with 10 ^ X without a negative sign.

But the smallest figures are represented with 10 ^ -X with a negative sign.

The scientific notation for 1 picoseconds = 10^-12

When converted to decimal

= 0.000000000001 picoseconds.

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Answer: 13 units

Step-by-step explanation:

If you look at the corresponding side on the other triangle, it is also 13, and in the question it say the side on the other triangle has the same length as the one you are finding.

Answer:

D. 1,0 & -3,0

Step-by-step explanation:

because the two lines pass through points 1,0 and -3,0 at the x-axis

Answer:

your answer is D. 1,0 & -3,0

Step-by-step explanation:

The complete table is

Time (mins)              0     1      2     3     4      5     6     7     8     9     10  

Amount of air (ft³)   40   36   32   28   24    20   16   12    8      4     0

The rate of change refers to the speed at which a quantity is changing with respect to time or some other variable.

It is a measure of how quickly or slowly a quantity is increasing or decreasing, and it is often represented as the slope of a graph or function. To fill the table we need to know the rate of change per minute in the air. Using the rate of change we can fill the table as follows  

Here we have

A scuba tank started with 40 cubic feet of air and was empty after a 10-minute dive.

To complete the table, calculate the rate of change of the amount of air in the scuba tank.

We know that the scuba tank started with 40 cubic feet of air and was empty after a 10-minute dive, so we can use this information to find the rate of change:

Rate of change = (final amount - initial amount) / time

Rate of change = (0 - 40) / 10 = -4 ft³/min

The negative sign indicates that the amount of air in the scuba tank is decreasing over time, which makes sense since the diver is using up the air during the dive.

Using this rate of change, we can complete the table as follows:

For 1 min  = 40 ft³ - 4 ft³ = 36 ft³

For 2 min = 36 ft³ - 4 ft³ = 32 ft³

For 3 min = 32 ft³ - 4 ft³ = 28  ft³

Similarly, we can fill the table as given below

Therefore

The complete table is

Time (mins)              0     1      2     3     4      5     6     7     8     9     10  

Amount of air (ft³)   40   36   32   28   24    20   16   12    8      4     0

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The missing value in the table include the following: B. 4 1/2 in.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have;

50 5/8 = 5 × W × 2 1/4

Width, W = 4 1/2 inches.

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Complete Question:

The volume of a rectangular prism is 50 5/8 cubic inches.

The dimensions are given below.

What is the missing value in the table?

Length Width Height

5 in. 214 in.

A. 79in.

B. 412in.

C. 134in.

D. 1018in.

The inequality |x + 7| ≥ 2 has the solution set x ≤ –9 or x ≥ –5, as required.

We can write an absolute value inequality with the given solution set as follows:

|x + 7| ≥ 2

Here's how we arrived at this inequality:

First, we find the midpoint of the given solution set:

midpoint = (-9 + (-5)) / 2 = -7

Next, we find the distance from the midpoint to each endpoint of the solution set:

distance to -9 = |-7 - (-9)| = 2

distance to -5 = |-7 - (-5)| = 2

The maximum distance is 2, so we use c = 2 in the inequality.

Since the midpoint is to the left of both endpoints, we use the form |x - b| ≥ c.

Plugging in b = -7 and c = 2, we get:

|x + 7| ≥ 2

This inequality has the solution set x ≤ –9 or x ≥ –5, as required.

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Answer:

inflationary expenditure gap of $500

Step-by-step explanation:

At AE2 there is an inflationary expenditure gap of $500 (assuming full-employment output is $2000). The fiscal authority could increase taxes or decrease expenditures, which will shift the aggregate expenditures schedule down to AE0.

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The line of symmetry of the parabola is t = 1.875 and the vertex of the parabola is (1.875, 77).

A function is a mathematical concept that relates an input value (or values) to an output value (or values) according to a specific rule or set of rules. It can be thought of as a machine that takes in one or more inputs and produces a corresponding output. Functions are often represented using function notation, such as f(x) or g(t), where the variable in the parentheses (x or t) represents the input and the value of the function (f(x) or g(t)) represents the output.

To identify the line of symmetry and vertex of the parabola given by the function [tex]f(t) = -16t^2 + 60t + 16[/tex], we need to use the formula:

t = -b/2a

where "a" is the coefficient of the [tex]t^2[/tex] term (-16 in this case) and "b" is the coefficient of the t term (60 in this case).

Part A: Identify the line of symmetry of the parabola.

Using the formula above, we get:

t = -60 / 2(-16) = 1.875

So the line of symmetry of the parabola is t = 1.875.

Part B: Identify the vertex of the parabola.

To find the vertex, we need to substitute the value we found for t into the original function:

[tex]f(1.875) = -16(1.875)^2 + 60(1.875) + 16 = 77[/tex]

So the vertex of the parabola is (1.875, 77).

Therefore, the line of symmetry of the parabola is t = 1.875 and the vertex of the parabola is (1.875, 77).

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There are 1820 different orders possible for selecting any 4 toppings out of a list of 16 toppings.

To calculate the number of different orders possible for selecting any 4 toppings out of a list of 16 toppings,

we can use the combination formula:

nCr = n! / r!(n-r)!

where n is the total number of items, r is the number of items to be selected, and ! represents the factorial operation.

Substituting the given values, we get:

16C4 = 16! / 4!(16-4)!

16C4 = (16 × 15 × 14 × 13) / (4 × 3 × 2 × 1)

16C4 = 1820

Therefore, there are 1820 different orders possible.

Option D. 1,820 is the correct option.

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The solutions to the dividing fractions prompts are as follows:

6. 4/3

7. 2/13

8. 33/2

9. 24/35

10. 63/20

To solve the divisions, note that the second divisor is inversed and multiplied. For the following problems, the divisions can be gotten as follows:

6. 8/9 ÷ 2/3

= 8/9 × 3/2

=24/18

=4/3

7. 12/13 ÷ 6

= 12/13 × 1/6

= 12/78

=6/39

= 2/13

8.  11/5 ÷ 2/15

= 11/5 × 15/2

165/10

= 33/2

9. 6/7 ÷ 5/4

6/7 × 4/5

= 24/35

10. 7/2 ÷ 10/9

7/2 × 9/10

63/20

So, the above are ways to determine the step-by-step answers.

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For the pattern A, the terms are 6, 11, 16 and 21

For the pattern B, the terms are 24, 20, 16, 12

To determine the consecutive terms of the sequence, we need to take note of the rule of each.

From the information given, we have that;

For the Pattern A

Each term is the previous term plus 5

This is represented as;

Pattern A = a + 5,

The first term = 1

Second term = 1 + 5 = 6

Third term = 6 + 5 = 11

Fourth term = 11 + 5 = 16

Fifth term = 16 + 5 = 21

For Pattern B = a - 4

Second term = 28 - 4 = 24

Third term = 24 - 4 = 20

Fourth term = 20 -4 = 16

Fifth term = 16 - 4 = 12

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Based on the given data, the age of Mr. Wright currently is 30 years

If Micah is 3 years old, then Lilly is twice as old, which means that

Lilly is 2 * 3 = 6 years old.

Now we know that Mr. Wright is five times as old as his daughter, Lilly, so Mr. Wright's age is:

5 * 6 = 30 years old.

Therefore, Mr. Wright is 30 years old.

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(10) The value that will make the equation a perfect square is 25.

(11) The value that will make the equation a perfect square is 64.

(12) The value that will make the equation a perfect square is 400.

(13) The value that will make the equation a perfect square is 6.25.

To make a perfect square trinomial of the form x² + bx + c, we need to add (b/2)² to both sides.

the perfect square is calculated as;

x² + 10x + __

b = 10,

(b/2)² = 25

the perfect square is calculated as;

x² - 16x + __

b = -16

(b/2)² = 64

the perfect square is calculated as;

x² + 40x + __

b = 40

(b/2)² = 400

the perfect square is calculated as;

x² + 5x + __

b = 5

(b/2)² = 6.25

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The perimeter of the rhombus is approximately 7.6 units.

XZ is perpendicular to WY and XE is 4,

Since WXYZ is a rhombus because only the diagonal of the rhombus and square bisect each other at 90°

By the Pythagorean theorem, we have:

XE² = XY² + EY²

4² = XY² + (7/2)²

XY = 1.9

So the perimeter of WXYZ is 4(XY), rounded to the nearest tenth:

4(1.9) ≈ 7.6 units.

Therefore, the perimeter of the rhombus is approximately 7.6 units.

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As a result, angle B has a 24 degree measure as the total of the two angles, which are along a straight line, is 180 degrees.

Thus according their size or measurement, angles can be categorised. An oblique angle is larger than 90 degrees but far less than 180 degrees, a straight angle is exactly 90 degree, a right angle is turned 90 degrees, and an acute angle is less than 90 degrees. Reflex angles are angles that are higher than 180o but a little less than 360 degrees, and complete angles are angles that measure exactly 360 degrees. Geometry, trigonometry, physics, engineering, and many other branches of mathematics and science all make use of angles.

given

The total of the two angles, which are along a straight line, is 180 degrees. Let's refer to the angle B's measurement as x.

The information provided in the problem can then be used to create an equation as follows:

m∠A = 5(m∠B + 7.2°)

Due to the fact that the two angles are perpendicular to one another, we may replace mA with 180 - mB:

180 - m∠B = 5(m∠B + 7.2°)

The right side is being widened:

180 - m∠B = 5m∠B + 36

Simplifying and putting all the mB words to one side:

6m∠B = 144

m∠B = 24

As a result, angle B has a 24 degree measure as the total of the two angles, which are along a straight line, is 180 degrees.

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Answer: 5,8,6,1

Step-by-step explanation:

math

The given input-output relation is a nonlinear function of the input signal x(t), since it involves squaring the signal at every point in time. A linear system must satisfy the property of superposition, which states that the output to a linear combination of inputs must be the same as the linear combination of the outputs to each individual input.

To determine whether the system is time-invariant, we need to check if a time shift in the input signal produces the same time shift in the output signal. That is, if: [tex]y(t) = T{x(t)}[/tex] for all values of t. Then we want to check [tex]y(t - τ) = T{x(t - τ)}[/tex] for all values of [tex]τ[/tex] and [tex]t[/tex].

We shall the consider the case where [tex]τ > 0[/tex], then we have:

[tex]y(t - τ) = (x(t - τ))^2[/tex]

[tex]T{x(t - τ)} = (x(t - τ))^2[/tex]

Since [tex]y(t - τ) = T{x(t - τ)}[/tex], we can conclude that the given system is time-invariant.

Therefore, the given system is nonlinear but time-invariant.

Step-by-step explanation:

lets call the line (d)

amd the given eq of the line is (d')

so (d) is perpendicular to (d')

slope(d)×slope(d')=-1

-2(1/2)=-1

so (d): y=1/2x + b

point A (4, -3) belongs to (d) so,

Ya=1/2Xa+b

-3=1/2(4)+b

b=-5

(d):y=1/2x-5

Answer:

Step-by-step explanation:

To solve for f, we can cross-multiply the equation:

f/40 = 10/f

Multiplying both sides by 40f gives:

f^2 = 400

Taking the square root of both sides yields:

f = ±20

Therefore, the solutions for f are f = 20 and f = -20. However, since f represents a physical quantity (presumably a frequency), we take only the positive value:

f = 20