Assume that a three-month CD purchased for $1900 pays simple interest at an annual rate of 7%. How much total interest does it earn? What is the balance at maturity?

Answer: hm

Step-by-step explanation: yes.

The cost for a child ticket was $4 less than the cost of an adult ticket.

Given that, 4 adults took their 5 children to a movie. The price for 9 people was $160.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the cost of adult tickets be x.

The 5 children received a 20% discount on their tickets.

Now, x-20% of x

= x-20/100 × x

= x-0.2x

= 0.8x

Here, 4x+5×0.8x=160

⇒ 4x+4x=160

⇒ 8x=160

⇒ x=20

So, the cost of children is 20-20% of 20

= 20-0.2×20

= 20-4

= 16

Therefore, the cost for a child ticket was $4 less than the cost of an adult ticket.

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The side length x of the following triangle is √40 or 2√10 when hypotenuse is 11 and one side is 9.

What is Pythagoras theorem?

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

a² + b² = c²

where a and b are sides of right angled triangle and c is the hypotenuse.

According to the given question:

Check the attachment below for figure

Hypotenuse = 11

Length of one side = 9

Length of other side = x

By Pythagoras theorem

9² + x² = 11²

81 + x² = 121

x² = 40

x = 2√10

Therefore side length x = 2√10

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Answer: 14h + 11d

That's it

It will take approximately 28 years to decay 15 gram sample to 12 gram.

Given,

The yearly decaying of Plutonium-238 = 7.9 × 10⁻³

The mass of original sample = 15 grams

We have to calculate the time taken to decay to 12 grams.

Here,

At = A0 × e^(-k × t)

At = 12 g

A0 = 15 g

k = 7.9 × 10⁻³ = 0.0079

We have to find t.

That is,

At = A0 × e^(-k × t)

12 = 15 × e^(-0.0079 × t)

12/15 = e^(-0.0079 × t)

0.8 = e^(-0.0079 × t)

Now,

Logarithm both sides (because ln(e) = 1:

ln(0.8) = ln(e^(-0.0079 × t))

ln(0.8) = (-0.0079 × t) × ln(e)

-0.223 = -0.0079 × t

t = -0.223 / -0.0079

t = 28.23

t ≈ 28 years

Therefore,

It will take approximately 28 years to decay 15 gram sample to 12 gram.

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Answer:

x=8

Step-by-step explanation:

2x+122=154-2x

4x+122=154

4x=32

X=8

hopes this helps

Answer:  The correct answer = 4

Step-by-step explanation:

(8^2)(4^−3)/(2^4)(8^−2)

=64(4^−3)/(2^4)(8^−2)

=1/(2^4)(8^−2)

=1/16(8−2)

=1/16(1/64)

=1/(1/4)

=4

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The Volume of the Ball Bearings is 1.76 cubic. inches

Given :

The diameter of the ball bearings = 3/2 inches

The radius of the ball bearings = 3/4 inches

Now, The Volume of the Sphere = [tex]\frac{4}{3} \pi r^{3}[/tex]

Putting the value of radius = 3/4 in the formula of the Volume,

We have :

The volume of the ball bearings =

[tex]V =\frac{4}{3} \pi (\frac{3}{4} )^{3} = \frac{4}{3} *\frac{22}{7}*\frac{3}{4} *\frac{3}{4} *\frac{3}{4}\\ \\V = 1.76[/tex]

Hence, The Volume of the Ball Bearings =  1.76 cubic. inches

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The quadratic functions x² = 16, (x - 4)² = 169 and 4x² - 225 = 0 have solutions 4, (17 or -9) and (7.5 or -7.5) respectively.

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term. The first condition for an equation to be a quadratic equation is the coefficient of x² is a non-zero term(a ≠ 0). For writing a quadratic equation in standard form, the x² term is written first, followed by the x term, and finally, the constant term is written. The numeric values of a, b, c are generally not written as fractions or decimals but are written as integral values.

In the first function;

1. x² = 16

take the square roots of both sides;

x = √16

x = 4

2. (x - 4)² = 169

Open the bracket

x² - 8x + 16 = 169

Solving for x

x = 17 or x = - 9

3. 4x² - 225 = 0

4x² = 225

x = 7.5 or x = -7.5

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The equation in slope - intercept form is y = x + 6

Given,

In the question:

A line has slope is 1 and passes through the point (-9, -3)

To find the equation in slope - intercept form.

Now, According to the question:

Based on the given conditions:

Slope (m) = 1

and, x = -9 , y = -3

Substitute the values into

y = mx + b

-3 = -9 +b

Calculate the sum or difference

-b = -6

Divide both sides of the equation by the coefficient of variable

b = 6

Substitute m = 1 and b = 6 into y = mx + b

y = x + 6

Rewrite y = x + 6 in slope intercept form.

Hence, The equation in slope - intercept form is y = x + 6.

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The radical expressed using the imaginary unit i  is ±(√77)*i  .

The iota(i) is an imaginary unit number that is denoted by i and the value of iota(i) is √-1  , that is √-1 = i .

In the question,

it is given that

the the radical expression is ±√-77 , we have to express it using the imaginary unit (i) .

So , ±√-77 can be written as

= ±√(-1 × 77)

= ±√-1 × √77

Substituting the value of i that is  √-1 = i ,

we get

= ± i * √77

= ±(√77)*i

Therefore ,The radical expressed using the imaginary number i  is ±(√77)*i .

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The graph best represents f^-1(x) is Option A so A is correct.

Given function:

f(x) = [tex]5\sqrt{x+3} -2[/tex]

Inverse of f(x) is:

[tex]= 5\sqrt{y+3}-2=x= 5\sqrt{y+3}=x+2= \sqrt{y+3}=(x+2)/5= y+3=((x+2)^2)/25= y=((x+2)^2)/25-3= y=(x^2)/25+(4x)/25+4/25-3= y=(x^2)/25+(4x)/25-71/25[/tex]

f^-1(x) = 1/25([tex]x^{2} +4x-71[/tex]).

Using graphing calculator:

The inverse of f(x) represents the graph Option A so A is correct.

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[tex]{ \green{ \boxed{ \purple{ \sf{(1 - {x}^{2}) \frac{ {d}^{2}y }{d {x}^{2} } - x \frac{dy}{dx} = 0}}}}}[/tex]

Step-by-step explanation:

Given,

[tex]{ \blue{ \sf{y = { \sin}^{ - 1}x}}}[/tex]

differentiate with respect to x

[tex]{ \purple{ \sf{ \frac{dy}{dx} = \frac{1}{ \sqrt{1 - {x}^{2} } } }}}[/tex]

[tex]{ \purple{ \sf{ \sqrt{1 - {x}^{2} } \frac{dy}{dx} = 1}}} \: { \to} \: { \tt{ {eq}^{n} (1)}}[/tex]

This is in the form of uv method

uv = uv' + vu' = 0

[tex]{ \tt{ \sqrt{1 - {x}^{2} } = u}}[/tex]

[tex]{ \tt{ \frac{dy}{dx} = v}}[/tex]

u' = differentiation of u

v' = differentiation of v

Apply uv method to Eqⁿ (1) then,

[tex]{ \purple{ \sf{ \sqrt{1 - {x}^{2} } = \frac{ {d}^{2} y}{d {x}^{2} } + \frac{dy}{dx} \frac{1}{ \cancel2 \sqrt{1 - {x}^{2} } } (0 { \cancel{- 2}}x) = 0}}}[/tex]

Multiply by [tex]{ \red{ \sf{ \sqrt{1 - {x}^{2}}}}} [/tex] then,

[tex]{ \boxed{ \purple{ \sf{(1 - {x}^{2}) \frac{ {d}^{2}y }{d {x}^{2} } - x \frac{dy}{dx} = 0}}}}[/tex]

Answer:

B. Rewarding yourself with a small treat every now and then is probably okay

Step-by-step explanation:

The lesson talks about shopping and how it’s not bad to go shopping.

The number of shares of $4.00's shares are125 and the number of shares of $5.00's shares are 375.

According to the question,

We have the following information:

An investor bought 500 shares of stock, some at $4.00 per share and some at $5.00 per share. And the total cost was $2375.00.

Let's take the cost of $4.00's share to be x and that of $5.00's share to be y.

x+y = 500

x = 500-y ...(1)

4x+5y = 2375

Putting the value of x from equation 1:

4(500-y) +5y = 2375

2000-4y+5y = 2375

2000+y = 2375

y = 2375-2000

y = 375

Putting the value of y in equation 1:

x = 500-375

x = 125

Hence, the number of shares of $4.00's shares are125 and the number of shares of $5.00's shares are 375.

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Answer:

69.06

Step-by-step:

1 ) Calculate the discount.

15% of 1250 is...

187.5

2 ) Subtract 187.5 from 1250...

1062.5

3 ) Calculate the sales tax.

6.5% of 1062.5 is...

69.06

4 ) Add 69.06 to 1062.5 to get the final answer...

$1131.56

Hope this helps! :)

Answer:

69.06

Step-by-step explanation:

15% of R1250

= R187, 5

R1250 - R187 ,5

= R1062,5

The logarithmic function f(x) = a·log₃(x - 4), passing through the points (13, 7), has the values;

5 a. The value of a is 3.5

b. Please find attached the graph of the function, f(x) = 3.5·log₃(x - 4), created with MS Excel

A logarithmic function is a function that contain and involves logarithm operation and it is the inverse of an exponential  function

The function is f(x) = a·log₃(x - 4),

x > 4 and a > 0

The coordinates of a point on the graph of the function, f is A(13, 7)

5 a. The value of a can be found by plugging in the value of (13, 7) = (x, f(x)), as follows

f(13) = 7 = a·log₃(13 - 4) = a·log₃9 = a·log₃3²

7 = a·log₃3²

7 = 2·a·log₃3 = 2·a·1 = 2·a

2·a = 7

a = 7 ÷ 2 = 3.5

a = 3.5

5 b. The coordinates of the x-intercept of the graph = (5, 0)

The equation of the function is;

f(x) = 3.5·log₃(x - 4)

A third point on the graph is given when f(x) = 14 as follows;

f(x) = 14 = 3.5·log₃(x - 4)

log₃(x - 4) = 14 ÷ 3.5 = 4

3⁴ = x - 4

x = 3⁴ + 4 = 85

Which gives the point, (85, 14)

Similarly, we have the point (31, 10.5), (7, 3.5)

Please find attached the graph of f(x) created with MS Excel

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Answer:

33.

Step-by-step explanation:

75%   x

100   44

x = (44 * 75 ) / 100 = 33.

The rise and the run of the line is shown in the diagram below.

The slope = rise/run = 1/4.

The rise of a line is the vertical distance along the line, which is equal to the number if units you move up or down from one point to another, while the run is the horizontal distance along the line, which is the number of units you move from left or right from a point to another.

The slope of any line (m) = rise of the line/run of the line.

Given the graph shown above:

Red line = rise of the line = 1 unit

Blue line = run of the line = 4 units

Slope of the line = 1/4

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Answer:

A

Step-by-step explanation:

Answer:

A)

Step-by-step explanation:

To find the percentage of the Pie-Chart , Divide each corresponding Number by the Total Frequency

Total Frequency = 9 + 20 + 25 + 39 = 93

% of Motorcycle = [tex]\frac{9}{93}* 100=9.7 %[/tex] %

% of Sedan  = [tex]\frac{20}{93}* 100=21.5 %[/tex] %

% of SUV  = [tex]\frac{25}{93}* 100=26.9 %[/tex] %

% of Truck  = [tex]\frac{39}{93}* 100=41.9 %[/tex] %

This is represented by Choice A)

Using the given graph, the function table that is completed would be:

Input       Output            

-9              1

-5              1

-2              1

A function is graphed by plotting the input values on the x-axis against the output values on the y-axis. This means all input values are on the x-axis, and their corresponding output values are on the y-axis.

To find the output value when an input value is given as 4, we need to trace the output value that corresponds to x = 4 on the graph.

Using the graph in the diagram, we know the following:

When the input value is x = -9, the output value is y = 1.

When the input value is x = -5, the output value is y = 1.

When the input value is x = -2, the output value is also y = 1.

The complete function table would be:

Input       Output            

-9              1

-5              1

-2              1

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Answer:

Hopefully this image helps, I am pretty sure you just have to rotate the shape by 270 degrees on the graph.

The slope of the line passing through (-4,5) and (-7,8) is -1.

Slope of line is the ratio of change in y-coordinate with the change in x-coordinate. It measures the steepness and direction of the line with x-axis (non vertical line.

Slope of line passing through two points (x₁,y₁) and (x₂,y₂) is given by

Slope of line = (y₂-y₁)/(x₂-x₁)

The given points are (-4,5) and (-7,8).

Here x₁ = -4, y₁ = 5

x₂ = -7, y₂ =8

Hence,

Slope of the line  = (8-5)/{-7-(-4)}

= (8-5)/(-7+4)

= 3/(-3)

= -3/3

= -1

The slope of line is given by -1.

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Answer:

5/6

Step-by-step explanation:

1/2 / 2/3 = 0.5/0.6

= 5/6

The missing lengths, using the Pythagorean Theorem, are given as follows:

The missing lengths are obtained using the Pythagorean Theorem, which states that:

The sum of the lengths of the sides between the right angle squared is equals to the length of the hypotenuse squared.

Hence, for the first triangle, the hypotenuse is given as follows:

h² = 2² + 3²

h = sqrt(13)

h = 3.6.

For the second triangle, the missing side is given as follows:

x² + 12² = 16²

x² = 16² - 12²

x = sqrt(16² - 12²)

x = 10.6.

For the third triangle, the missing side is given as follows:

x² + 2² = 5²

x² = 21

x = sqrt(21)

x = 4.6.

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The sets A and B are equivalent but they are not equal.

We know that a set is a collection of elements. The elements that we can find in a set are arranged in order such that we can easily see what is composed of the set.

Now two sets are said to be equivalent if they have the same cardinality. We can see that the set of the sets A and B are equal but not equivalent because they contain the same elements and also have the same cardinality since the cities must all have mayors.

Thus, the number of cities is equivalent to the number of mayors thus the two sets could have the same cardinality (equivalent) but not the same elements thus they are not equal.

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The answer is a because all the other ones are wrong

The compound inequality that represents this range is D) -19≤temp≤33.

What is inequality?

A mathematical statement known as an inequality in algebra uses the inequality symbol to show the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using the inequality symbols. When the symbols ">," <"  are used to connect two real numbers or algebraic expressions, the relationship is referred to as an inequality.

Here during the recent year the temperature in Chicago ranged from -19 degree celsius to 33 degree celsius.

Here from -19 degree increased to 33 degree. then the inequality is ,

=> -19 [tex]\leq temp\leq 33[/tex]

Hence the correct option is D)  -19 [tex]\leq temp\leq 33[/tex] .

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The 99% confidence interval for the difference between the average years of service between men and women would be = 3.43.

Confidence interval is defined as the statistical parameter that is used to know if a set of values would fall within a certain range of population or not.

Using the statistical table, the value of 99% or 0.99 confidence interval has a z-score = 2.576

The standard error that exists between the bothe value = SD/Ö

Where SD = difference between the standard deviations = 8.39 - 4.39 = 4

Where ñ = different between the average years of service = 9.62

Standard error= 4/√9.62 = 4/3.01 = 1.33

The confidence interval = 2.576 × 1.33 = 3.43.

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By using the fact that the angles are supplementary, we can write and solve a linear equation to find that x equal to 90

In the image, we can see two supplementary angles, where by definition, two angles are supplementary if their addition is equal to a plane angle (an angle of 180°).

With that in mind, we can write the linear equation:

x + 2x = 180

So we just need to isolate x in that simple linear equation.

If we subtract 2x in both sides, we will get:

x + 2x  = 180

x =180/2x

x= 180/2

90

So the unknown angle has a measure of 90°.

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