After 1 year, $400 deposited in a savings account with simple interest had earned $16 in interest. What was the interest rate?

The both are correct because the same correct response was obtained in each case.

If we look at the both solutions, the basic rules for the operations on inequalities were obeyed. In this case, we are seeing that both Marta and Kareen followed through the correct procedure.

For the fact that correct sign was maintained in each of the cases implies that what we have now is the correct solution of the problem that we have in this case of the problem here stated in the question.

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Answer:

The graph that represents the solution to X > 1/2 is the graph where the line is vertical, passing through x = 1/2, and all the points to the right of this line are shaded. This is because the inequality X > 1/2 means that X can take any value greater than 1/2, but not including 1/2.

If a gasoline pump delivers 4 gallons of gas per minute, proportionately, it will take it 4 minutes to fill a gas tank that holds 16 gallons.

Proportion refers to the ratio of one unit or quantity compared to another unit or quantity.

Proportions are represented as fractional values using decimals, fractions, and percentages.

The time it takes the gasoline pump to deliver 4 gallons = 1 minute

Proportionately, to deliver 16 gallons, the time = 4 minutes (16 ÷ 4)

Thus, using proportional relationships, to deliver 16 gallons, the gasoline pump will take 4 minutes.

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An equation that represents the line: y = (7/5)x + 34/5

We know that the formula for the two point form of equation of line is:

(y - y₁)/(y₂ - y₁) = (x - x₁)(x₂ - x₁)

Here, the graph of a line goes through the points (-7, -3) and (-2, 4)

Let us assume that (x₁, y₁) = (-7, -3)

(x₂, y₂) = (-2, 4)

Using above formula the equation of the line would be,

(y - y₁)/(y₂ - y₁) = (x - x₁)(x₂ - x₁)

(y - (-3))/(4 - (-3)) = (x - (-7))(-2 - (-7))

(y + 3)/(4 + 3) = (x + 7)(-2 + 7)

(y + 3) / 7 = (x + 7) / 5

y + 3 = (7/5)x + (7/5)7

y + 3 = (7/5)x + (49/5)

y = (7/5)x + (49/5) - 3

y = (7/5)x + 34/5

This equation represents the line.

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The solution which one gets using the quadratic formula for; –4x² – 12x – 9 = 0 is; Choice A; -3/2.

The vertex of the graph is such that; Choice D; The vertex is on the x-axis.

Recall the formula method for solving a quadratic equation is such that;

x = ( -b ± √(b² - 4ac) ) / 2a

By observation; a = -4, b = -12 and c = -9;

Therefore, we have that;

x = {-(-12) ± √( (-12)² - (4 × -4 × -9))} / (2 × -4)

x = (12 ± √0) / -8

x = -3/2.

Ultimately, the value of x is; Choice A; -3 / 2.

Part B; Also, since the graph has one solution only, it can be inferred that the vertex of the graph of; f(x) = –4x2 – 12x – 9 is; Choice D; The vertex is on the x-axis.

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Using the concept of proportion, amount of gas needed to travel 250 miles is 9.5 gallons.

Given that,

Ms C's car uses 20 gallons of gas to travel 400 miles.

We have to first find the number of gallons of gas to be used to travel 250 miles.

Amount of gas used to travel 400 miles = 20 gallons

Using the concept of proportion,

Amount of gas used to travel 1 mile = 20 / 400

                                                           = 0.05 gallon

Amount of gas used to travel 250 miles = 0.05 × 250

                                                                  = 12.5 gallons

There is already 3 gallons of gas in her car.

Amount of gas needed = 12.5 - 3 = 9.5 gallons

Hence the amount of gas needed is 9.5 gallons.

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The angle between the beam and the 35 ft cable is 43 degrees

To determine the angle between the beam, we need to know all the trigonometric identities as well as their ratios.

We have the identities as;

Also, their ratios are represented as;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

From the information given, we have that;

sin θ = 65/95

divide the values

sin θ = 0. 6842

find the inverse

θ = 43 degrees

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The total value of the furniture sold by Joyce last week is A = $ 6,733.33

Given data ,

Let's call the value of the furniture Joyce sold "x".

She receives 10% commission on the first $1,200 of sales, which is $120:

Commission on first $1,200 = 0.1 * 1200 = 120

The remaining sales that she earns commission on is the difference between the total value of the furniture sold and the first $1,200:

Remaining sales = x - 1200

She earns 15% commission on the remaining sales, which is 0.15 times the remaining sales:

Commission on remaining sales = 0.15 * (x - 1200)

Her total earnings from commission last week was $950. So we can write an equation:

Commission on first $1,200 + Commission on remaining sales = $950

Substituting the expressions we found for the two commissions, we get:

120 + 0.15(x - 1200) = 950

120 + 0.15x - 180 = 950

On simplifying the equation , we get

0.15x - 60 = 950

0.15x = 1010

x = 6,733.33

Hence , the value of the furniture Joyce sold last week was $6,733.33

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A zero has the same meaning as the vertex.

The point where two lines meet forming an angle or set of angles is referred to as a vertex. This can also be called a point of origin especially when considering the axis of a Cartesian coordinate.

The vertex can be taken as zero since it is referred to as the point of origin. This is different to the axis of symmetry; as the axis of symmetry is one that splits a given plotted points i.e. a graph into two equal parts.

Thus, a zero has the same meaning as the vertex.

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The triangle that makes the statement true is Option A. ΔABC ≅ ΔRST

For two triangle to be similar, they must have share the same angle size and sides that are related with a common ratio.

All the angles in Option A Δ RST are similar to those ΔABC.

Also note that

ST = 1/2 AB
SR = 1/2 BC and
RT = 1/2 AC

hence, the correct statement is:

ΔABC ≅ ΔRST

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Full Question:

See attached image.

The equation is solved and the cost of one ticket is x = $ 8

Given data ,

Let the cost of each ticket be represented as x

Now , the purchasing fee for each ticket is $ 1.50

And , total cost of tickets is = $ 38

Let the number of tickets be represented as = 4 tickets

On simplifying the equation , we get

4x + 6 = 48

Subtracting 6 on both sides , we get

4x = 32

Divide by 4 on both sides , we get

x = $ 8

Hence , the cost of each ticket is $ 8

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The complete question is attached below :

A family purchased tickets to a museum and spent a total of $38.00. The family purchased 4 tickets. There was a $1.50 purchasing fee for each ticket. Write and solve an equation that can be used to solve for x, when x = the cost of one ticket to the museum. Show your work and explain your answer.

A cable network offers members a Basic plan for $7.88 per month. For $3.00 more per month, the cable network offers a Standard plan, which includes HD movies, there were 140 Basic plans purchased.

Let x be the number of Basic plans and y be the number of Standard plans.

From the problem, we know that:

- The cost of a Basic plan is $7.88 per month

- The cost of a Standard plan is $7.88 + $3.00 = $10.88 per month

- There were a total of 330 new subscribers

- The total amount paid for plans was $3110.40

We can set up a system of equations to represent the problem:

x + y = 330   (equation 1: the total number of plans is 330)

7.88x + 10.88y = 3110.40   (equation 2: the total amount paid for plans is $3110.40)

To solve for x and y, we can use elimination method. Multiplying equation 1 by 7.88 and subtracting it from equation 2, we get:

(7.88x + 10.88y) - (7.88x + 7.88y) = 3110.40 - (7.88 * 330)

3y = 570.48

y = 190

So there were 190 Standard plans purchased. To find the number of Basic plans, we can substitute y = 190 into equation 1:

x + 190 = 330

x = 140

Therefore, there were 140 Basic plans purchased.

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Answer:

ur image doesn't show the fractions they got cut off

dx/dt = -12, 12

The question asks us to find 'dx/dt' when y = 8, given that x² + y² = 100 and dy/dt = 9. The approach involves differentiating both sides of the equation x² + y² = 100 with respect to time 't' and then solving for 'dx/dt' using the given values.

[tex]\hrulefill[/tex]

We start with the equation:

[tex]\Longrightarrow x^2 + y^2 = 100[/tex]

Taking the derivative of both sides with respect to time 't' gives:

[tex]\Longrightarrow \displaystyle \frac{d}{dt}[x^2] + \frac{d}{dt}[y^2] = \frac{d}{dt}[100][/tex]

Using the chain rule, this simplifies to:

[tex]\Longrightarrow \displaystyle 2x\frac{dx}{dt} + 2y\frac{dy}{dt}= 0[/tex]

Further simplification leads to:

[tex]\Longrightarrow \displaystyle x\frac{dx}{dt} + y\frac{dy}{dt}= 0[/tex]

[tex]\hrulefill[/tex]

We are given that dy/dt = 9 and y = 8. To find 'x' when y = 8, we use the equation 'x² + y² = 100':

[tex]\Longrightarrow x^2 + (8)^2 = 100\\\\\\\\\Longrightarrow x^2 + 64 = 100\\\\\\\\\Longrightarrow x^2 = 36\\\\\\\\\thereforex = \pm 6[/tex]

Assuming x = 6 (the logic applies if x = -6 as well), we can now substitute these values into x dx/dt + y dy/dt = 0:

For x = 6:

[tex]\Longrightarrow \displaystyle (6)\frac{dx}{dt} + (8)(9)= 0\\\\\\\\\Longrightarrow \displaystyle 6\frac{dx}{dt} + 72= 0\\\\\\\\\Longrightarrow \displaystyle 6\frac{dx}{dt} = -72\\\\\\\\\therefore \boxed{\frac{dx}{dt}=-12}[/tex]

For x = -6:

[tex]\Longrightarrow \displaystyle (-6)\frac{dx}{dt} + (8)(9)= 0\\\\\\\\\Longrightarrow \displaystyle -6\frac{dx}{dt} + 72= 0\\\\\\\\\Longrightarrow \displaystyle -6\frac{dx}{dt} = -72\\\\\\\\\therefore \boxed{\frac{dx}{dt}=12}[/tex]

Thus, dx/dt = -12, 12.

Answer:

  -12, 12

Step-by-step explanation:

Given x² +y² = 100, dy/dt = 9, and y = 8, you want to find dx/dt.

Differentiating the given equation with respect to t, we have ...

  2x dx/dt +2y dy/dt = 0

Solving for dx/dt, we find ...

  dx/dt = -y/x·dy/dt

For the given values of y and dy/dt, this is ...

  dx/dt = -8/x·9 = -72/x

The value of x when y = 8 can be found from the original equation:

  x² +8² = 100

  x² = 36 . . . . . . . . subtract 64

  x = ±6 . . . . . . . . square root

Then the desired values of dx/dt are ...

  dx/dt = -72/6 = -12

  dx/dt = -72/(-6) = 12

The values of dx/dt are -12, 12.

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The null hypothesis in symbolic form is H0: p ≥ 0.0007

The alternative hypothesis in symbolic form is Ha: p < 0.0007

We have,

The null hypothesis in symbolic form is H0: p ≥ 0.0007

This means that the true proportion of male fireflies unable to produce light is greater than or equal to 7 in ten thousand.

The alternative hypothesis in symbolic form is Ha: p < 0.0007

This means that the true proportion of male fireflies unable to produce light is less than 7 in ten thousand.

Thus,

The null hypothesis in symbolic form is H0: p ≥ 0.0007

The alternative hypothesis in symbolic form is Ha: p < 0.0007

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Answer:

D)699

Step-by-step explanation:

Since Town A is 7 feet below sea level, you will need to add that to 692 instead of subtract.

692+7=699

Answer: D

Step-by-step explanation: 692+7=699

Answer: To simplify the expression 7a^⁻⁵b^3, we can use the negative exponent property, which states that a^⁻ⁿ = 1/aⁿ. Applying this property to the variable a gives us:

7a^⁻⁵b^3 = 7(1/a⁵)b^3

We can also simplify b^3 to get the final answer:

7a^⁻⁵b^3 = 7b^3/a⁵

Therefore, the simplified expression is 7b^3/a⁵.

The value of x in the equation 9x In x + x = 0 is x = 0.895

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

9x In x + x = 0

To calculate the value of x, we start by dividing through the equation by x

So, we have the following representation

9 In x + 1 = 0

Subtract 1 from both sides of the equation

This gives

9 ln x = -1

Divide both sides by 9

ln x = -1/9

So, we have

x = e^(-1/9)

Evaluate the exponent

x = 0.895

Hence, the solution to the equation is x = 0.895

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The tape diagram that represents 5÷2/3 is attached.

Start by drawing three unit tapes, and divide each one of them in 5 equal parts since we need to be dividing the quantity 3 by 3/5 (denominator 5)

In the second step, join the three tapes in one long one maintaining the original divisions.

In the third step, select groups of 3 divisions (recall you need to divide by 3/5) which will identify in your tape how many of these 3/5 groups you have

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Draw a tape diagram that represents 5÷2/3

The unit vector that has the same direction as v is given by u = (5/√(34)) i - (3/√(34)) j

A vector is defined as a quantity that has both magnitude (length) and direction. In this case, the vector v is defined as v = 5i - 3j, where i and j are the unit vectors in the x and y direction, respectively.

To find the unit vector that has the same direction as v, we need to normalize v by dividing it by its magnitude. The magnitude of v is given by the Pythagorean theorem as:

|v| = √((5² + (-3)²)) = √(34)

So, the unit vector that has the same direction as v is given by:

u = v / |v| = (5/√(34)) i - (3/√(34)) j

This unit vector represents the direction of v with a magnitude of 1. We can interpret this as a scaling factor that can be applied to u to obtain vectors of different lengths that have the same direction as v. For example, a vector of length 10 that has the same direction as v would be given by 10u.

In summary, to find the unit vector that has the same direction as a given vector, we normalize the vector by dividing it by its magnitude. This results in a vector of magnitude 1 that points in the same direction as the original vector.

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The "Ivan" section represents 45% of the whole circle, and the "Bernard" section (which is not relevant to this question) represents 55%.

Since a circle has 360 degrees, we can find the measure of the central angle in the "Ivan" section as follows:

- Calculate the fraction of the circle represented by the "Ivan" section: 45% = 0.45

- Multiply this fraction by the total number of degrees in a circle: 0.45 x 360 = 162

Therefore, the measure of the central angle in the "Ivan" section is 162 degrees.

Answer:

$42.00

Step-by-step explanation:

We can represent the given information as a ratio:

% of original price : price

                          5% : $2.00

Then, we can multiply both sides of this ratio by 20 (or 100% / 5%) to get 100% of the original price, which IS the original price.

5%      :  $2.00

↓ × 20   ↓ × 20

100%  :  $40.00

Now that we know the original price, we can add $2.00 to get the new price.

$40.00 + $2.00 = $42.00

The scale factor from shape A to shape B is 3/4. The value of side w is 5.25 cm

An exponential equation is an expression that shows how numbers and variables using mathematical operators.

Scale factor is the ratio of the corresponding sides of two similar figures. Two figures are similar if the ratio of their corresponding sides are congruent.

From the figure:

Scale factor = Ratio of corresponding shape B side / Ratio of corresponding shape A side

Scale factor = 9/12 = 3/4

The scale factor is 3/4

To find w:

scale factor = w/7

3/4 = w/7

w = 5.25 cm

The value of side w is 5.25 cm

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At the conclusion of the year, Alewuya's account had $19,570 in it.

To calculate the amount in Alewuya's account at the end of 1 year, we can use the formula for simple interest:

I = Prt

where I is the interest earned, P is the principal (the amount invested), r is the interest rate as a decimal, and t is the time in years.

In this case, P = $19,000, r = 0.03, and t = 1. Plugging these values into the formula, we get:

I = ($19,000)(0.03)(1) = $570

So Alewuya earned $570 in interest over the 1 year period. To find the total amount in the account at the end of the period, we add the interest to the principal:

$19,000 + $570 = $19,570

Therefore, there is $19,570 in Alewuya's account at the end of the 1 year period.

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The distance  between of the belt buckle from the ground is 2.40 feet.

The diameter of the head is 3 3/4 inches.

A scale drawing is either an enlarged or reduced image of another image or object. A scale drawing is enlarged or reduced using a scale. A scale is a used to determine the ratio between the scale drawing and the original diagram.

The distance between of the belt buckle from the ground in real life would be greater than that of the scale drawing. Also, the diameter of the head would be larger in real life.

Distance  between of the belt buckle from the ground = 12 / 5 = 2.40 feet

In order to determine the diameter of the scale head, first convert inches to feet.

1 inch = 1/12 feet

9/12   = 3/4 feet

Diameter of the scale head = 3/4  x 5 = 15/4 = 3 3/4 feet

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