Erin wants to buy a new car. To do this, she takes out a loan of $24,000. The loan is to be repaired in seven years with an interest of 12% per annum. What is the total amount of interest she pays?

The surface area of the rectangular prism graphed is given as follows:

10.12 ft³.

The surface area of a rectangular prism of height h, width w and length l is given by:

S = 2(hw + lw + lh).

This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas.

Converting the mixed numbers to decimal, the dimensions of the rectangular prism are given as follows:

1.3 ft, 1.4 ft and 1.2 ft.

Hence the surface area of the prism is given as follows:

S = 2 x (1.3 x 1.4 + 1.3 x 1.2 + 1.4 x 1.2)

S = 10.12 ft³.

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The correct column is (A), which correctly represents the responses as probability.

Probability is a measure of the likelihood or chance that a particular event will occur. It is usually expressed as a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain.

The sum of all the responses is 558 + 79 + 20 + 7 = 664.

To represent the responses as a probability model, we need to divide each response by the total number of respondents, 664.  

The correct column is (A), which correctly represents the responses as probabilities:

(A)Very important 558/664 = 0.841

Somewhat important 79/664 = 0.119

Not too important 20/664 = 0.030

Not at all important 7/664 = 0.011

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Answer:

x =65°( being alternate angel)

Answer:

Step-by-step explanation:

Solution:

We can simplify the ratio 305 : 60 by dividing both terms by the greatest common factor (GCF).

The GCF of 305 and 60 is 5.

Divide both terms by 5.

305 ÷ 5 = 61

60 ÷ 5 = 12

Therefore:

305 : 60 = 61 : 12

The number of gold balls in the given bag is determined as 25 gold balls.

Let's use the formula for calculating probability:

Probability of an event = Number of favorable outcomes / Total number of outcomes

The total number of possible ways to choose 2 balls from a bag of 40 is:

40C2 = (40 x 39) / (2 x 1) = 780

Now we need to find the number of ways to choose 2 gold balls from the bag.

Let's say there are "g" gold balls in the bag. Then the number of ways to choose 2 gold balls is:

gC2 = (g x (g-1)) / (2 x 1)

We want to find the probability that 2 gold balls are removed, so we use the formula above to get:

Probability of choosing 2 gold balls = Number of ways to choose 2 gold balls / Total number of ways to choose 2 balls

Therefore, we have:

Probability of choosing 2 gold balls = gC2 / 40C2

We are given that this probability is 12/95, so we can set up an equation:

(g x (g-1)) / (2 x 1) / (40 x 39) / (2 x 1) = 12/95

Simplifying, we get:

g x (g-1) = (12/95) x (40 x 39)

g x (g-1) = 624

Expanding and rearranging, we get a quadratic equation:

g² - g - 624 = 0

Solving this quadratic equation, we get:

g = 25 or g = -24

We discard the negative solution, as the number of gold balls must be a positive integer. Therefore, there are 25 gold balls in the bag.

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Answer:

-4y2 +y - 12

Step-by-step explanation:

-3y2 - y2= -4y2

-y+2y= y

-8 - 4= -12

-4y2 + y - 12

Answer:

Step-by-step explanation:

the stabdard error is given with the se coefficient snf the y slope

1.  36x+8- 3rd column;

2. (9·4x)+(9·1)=36x+9 - 1st column;

3. (3·12x)-(3·3)=36x+9 - 2nd column;

4. 9(4x+1)=36x+9 - 1st column;

5.  36x-9- 2nd column;

6. 4(9x+2)=36x+8 - 3rd column

In mathematics, an equation is a statement that asserts the equality of two expressions, typically separated by an equals sign (=). Equations can contain one or more variables, which are quantities that can take on different values.

Start with expressions in blue boxes:

1st column) 36x+9;

2nd column) 9(4x-1)=36x-9;

3rd column) (4·9x)+(4·2)=36x+8.

You have 6 expressions. Consider all them:

1.  36x+8- 3rd column;

2. (9·4x)+(9·1)=36x+9 - 1st column;

3. (3·12x)-(3·3)=36x+9 - 2nd column;

4. 9(4x+1)=36x+9 - 1st column;

5.  36x-9- 2nd column;

6. 4(9x+2)=36x+8 - 3rd column

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The complete question is;

Drag each expression to show whether it is equivalent to 36x + 9, 9(4x – 1), or (4 • 9x) + (4 • 2).

Answer:

a) There are four prime numbers between 1 and 10: 2, 3, 5, and 7. So the probability of drawing a prime number is 4/10 or 2/5, which is 20% and not 10%. Therefore, option (a) is not correct.

b) As we saw in part (a), the probability of drawing a prime number is 2/5 or 40% (since 2/5 is equivalent to 0.4). Therefore, option (b) is correct.

c) The probability of drawing a prime number is 2/5 or 40%, which is not 25%. Therefore, option (c) is not correct.

d) As we saw in part (a) and (b), the probability of drawing a prime number is 2/5 or 40%, which is not 50%. Therefore, option (d) is not correct.

So, the correct answer is (b) 25%.

Hope This Helps!

The number of students who have both a cell phone and a tablet is 13. This corresponds to the intersection of the "Has Cell Phone" and "Has Tablet" sets.

What is meant by intersection?

In mathematics, the intersection of two sets A and B is a new set that contains all the elements that are common to both sets. In symbols, the intersection of A and B is denoted by A ∩ B, and it is defined as:

A ∩ B = {x : x ∈ A and x ∈ B}

Let A represent the set of students who have a cell phone, and B represent the set of students who have a tablet. The intersection of A and B, denoted by A ∩ B, represents the set of students who have both a cell phone and a tablet. Therefore, we want to find the cardinality (or size) of the set A ∩ B.

From the frequency table, we know that the total number of seventh graders surveyed is 100. We also know that there are 32 students who have a cell phone (i.e., |A| = 32) and 70 students who have a tablet (i.e., |B| = 70). We are given that 19 students who have a cell phone do not have a tablet, which means that there are 32 - 19 = 13 students who have both a cell phone and a tablet (i.e., |A ∩ B| = 13).

Therefore, the number of students who have both a cell phone and a tablet is 13. This corresponds to the intersection of the "Has Cell Phone" and "Has Tablet" sets.

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Answer:42

Step-by-step explanation:

The possible present ages of each cockatoo, given the sum of the cockatoos would be Galah cockatoo is currently 10 years old and the white cockatoo would be 34 years old

Let's use variables to represent the present ages of the two cockatoos. Let W be the present age of the white cockatoo and G be the present age of the Galah cockatoo. We're given that the sum of their ages is 44 years:

W + G = 44 (1)

In n years, the white cockatoo will be W + n years old, and the Galah cockatoo will be G + n years old:

W + n = 4(G + n) (2)

Since n > 0, 5G - 44 must be positive. We can try different values of G to find possible integer values for n.

For G = 8:

44 - 5(8) = 4

4 = -3n

n is not an integer.

For G = 10:

44 - 5(10) = -6

-6 = -3n

n = 2

So one possibility is that the Galah cockatoo is currently 10 years old. In this case, the white cockatoo would be 34 years old (since W + G = 44).

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Step-by-step explanation:

5(2 + 1) can be simplified using the distributive property of multiplication over addition, which states that a(b + c) = ab + ac. Using this property, we get:

5(2 + 1) = 5(2) + 5(1)

Simplifying the expression further, we get:

5(2) + 5(1) = 10 + 5 = 15

Therefore, 5(2 + 1) is equivalent to 15.

The graph is a parabola, with a vertex at (4,-4), an axis of symmetry at x = 4, x-intercepts at x = 10 and x = -2, and a y-intercept at (0,-20).

A quadratic function is a type of polynomial function of degree 2. It can be defined as a function in which the highest power of the independent variable x is 2.

The quadratic function f(x) = x² - 8x - 20 has a graph that is a parabola with a vertical axis of symmetry.

Vertex: The vertex of the parabola can be found using the formula x = -b/2a, where a and b are the coefficients of x² and x respectively.

In this case, a = 1 and b = -8, so the x-coordinate of the vertex is x = -(-8)/(2×1) = 4.

To find the y-coordinate of the vertex, substitute x = 4 into the equation: f(4) = 4² - 8(4) - 20 = -4. Therefore, the vertex is located at (4,-4).

Axis of symmetry: The axis of symmetry of the parabola is a vertical line passing through the vertex.

In this case, the axis of symmetry is the line x = 4.

Intercepts: To find the x-intercepts set y = 0 and solve for x: x² - 8x - 20 =0.

this quadratic equation can be factored as (x - 10)(x + 2) = 0

so the x-intercepts are x = 10 and x = -2.

To find the y-intercept, set x = 0 and evaluate f(0) = 0² - 8(0) - 20 = -20. Therefore, the y-intercept is (0,-20).

Image is attached below.

The graph is a upward-facing parabola, with a vertex at (4,-4), an axis of symmetry at x = 4, x-intercepts at x = 10 and x = -2, and a y-intercept at (0,-20).

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The measure of arc CD is equal to the measure of angle BCD, which is 240 degrees.

In the given diagram, we can see that angle ACD is a right angle, since it is formed by the radius AC and tangent CD at point C.

Therefore, angle BCD is equal to angle ACD, which is 90 degrees.

Since angle BCD is an exterior angle of triangle BCF, it is equal to the sum of the two remote interior angles, which are angles BFC and FCB.

Angle BFC is equal to angle ABC (since they are opposite angles), which is 60 degrees.

Similarly, angle FCB is equal to angle ACF, which is also 60 degrees.

Therefore, angle BCD is equal to angle BFC + angle FCB, which is 60 + 60 = 120 degrees.

Now, since arc CD is subtended by angle BCD, its measure is also equal to 120 degrees.

Hence, the measure of arc CD is 120 degrees.

Similarly, angles ACF and FCB are opposite angles in the cyclic quadrilateral AFCB, so they are supplementary. Therefore, angle FCB is equal to 180 - angle ACF,

Which is also 180 - 60 = 120 degrees.

Now we can apply the exterior angle theorem to find the measure of angle BCD. We have:

angle BCD = angle BFC + angle FCB

= 120 + 120

= 240 degrees

Finally, we can conclude that the measure of arc CD is equal to the measure of angle BCD, which is 240 degrees.

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There is a 15.74% chance that a randomly chosen employee will earn between $450 and $550.

The study of random occurrences or phenomena falls under the umbrella of the mathematic discipline known as probability. It is the measure of the likelihood or chance that an event will occur, expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

To find : the probability that a worker selected at random makes between $450 and $550

z = (x - μ) / б

where б is the standard deviation, μ is the mean, and x is the value we wish to normalize.

For $450, we have:

z₁ = (450 - 400) / 50 = 1

For $550, we have:

z₂ = (550 - 400) / 50 = 3

We can then use a standard normal distribution table or calculator to find the area under the standard normal curve between z₁and z₂:

P(z₁< z < z₂) = P(1 < z < 3) = 0.1574

This means that the probability that a worker selected at random makes between $450 and $550 is 15.74%.

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Store A would be the better choice as the final price is lower than Store B even though the original price was also lower at Store B.

What is discount?

Discount means the amount which is deducted by sellers from the amount to be payable by buyers.

Part A:

Store A is selling the laptop for $900 and has a discount coupon for 15% off. To calculate the amount of the discount, we can multiply the original price by the discount percentage:

Discount amount = $900 x 15% = $135

Therefore, the amount of the discount at Store A is $135.

Part B:

Store B is selling the laptop for $950 and has a discount coupon for 10% off. To calculate the amount of the discount, we can multiply the original price by the discount percentage:

Discount amount = $950 x 10% = $95

Therefore, the amount of the discount at Store B is $95.

Part C:

At Store A, the final price would be:

Final price at Store A = $900 - $135 = $765

At Store B, the final price would be:

Final price at Store B = $950 - $95 = $855

Therefore, Store A would be the better choice as the final price is lower than Store B even though the original price was also lower at Store B.

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The distance walked by Dario from to reach comic book store is 1.4 miles.

Displacement and distance are two terms that, while they appear to imply the same thing, have quite different definitions and meanings. Displacement is the measurement of "how much space an item has covered while it has been in motion," whereas distance is the indication of "how much ground an object has covered during its motion." Let's examine the distinction between displacement and distance in this essay.

For the given route we have:

House to jewelry store:

0.2 - (-0.5) = 0.2 + 0.5 = 0.7 miles.

Jewelry store to bank:

0.6 - 0.2 = 0.4 miles.

Bank to comic book store:

-0.5 -(-0.8) = -0.5 + 0.8 = 0.3 miles.

House to comic book store:

0.7 + 0.4 + 0.3 = 1.4 miles.

Hence, the distance walked by Dario from to reach comic book store is 1.4 miles.

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The complete question is:

The coordinates of the point on the directed line segment are (-6, 0)

Coordinates of a point refer to a set of numbers that represent the location of the point in a particular coordinate system.

To find the coordinates of the point that partitions the line segment from (-7,3) to (3,-9) into a ratio of 3 to 1, we can use the following formula:

P = [tex]( (3/4)*x_1 + (1/4)*x_2 , (3/4)*y_1 + (1/4)*y_2 )[/tex]

where P is the point that partitions the line segment, (x₁, y₁) and (x₂, y₂) are the coordinates of the endpoints of the segment, and the coefficients 3/4 and 1/4 correspond to the ratio in which the segment is divided.

Plugging in the values, we get:

P = ( (3/4)*(-7) + (1/4)*3 ,  (3/4)3 + (1/4)(-9) )

= (-21/4 - 3/4 ,   9/4 - 9/4)

= (-6, 0)

Therefore, the coordinates of the point that partitions the line segment from (-7,3) to (3,-9) into a ratio of 3 to 1 are (-6, 0).

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Answer:

8 sides

Step-by-step explanation:

Let n be the number of sides

Then sum of internal angles [tex]=(n-2)180[/tex]

——-(1)

It is given that one internal angle [tex]=135[/tex]

So sum of n equal internal angles [tex]=135n[/tex] ————(2)

From(1) and(2)

[tex](n-2)180=135n[/tex]

[tex]180n-360=135n[/tex]

[tex]180n-135n=360[/tex]

[tex]45n=360[/tex]

[tex]n=360\div45=8[/tex]

[tex]\bold{So \ the \ number \ of \ sides=8}[/tex]

Answer:

(7) AB is a tangent , (8) AB is not a tangent

Step-by-step explanation:

the angle between a tangent and the radius is 90°

if AB is a tangent then Δ ABC is right with hypotenuse AC

using Pythagoras' identity

the square on the hypotenuse of a right triangle is equal to the sum of the squares on the other 2 sides.

if AC² = AB² + BC² , then AB is a tangent to the circle

(7)

AC² = 34² = 1156

AB² + BC² = 30² + 16² = 900 + 256 = 1156

since AC² = AB² + BC² , then AB is a tangent to the circle

(8)

AC² = 28² = 784

AB² + BC² = 21² + 20² = 441 + 400 = 841

since AC² ≠ AB² + BC² , then AB is not a tangent to the circle

Answer:

The area of the shaded region equals 21.43 sq. units.

Step-by-step explanation:

When calculating how much material is needed to cover a wooden table, how many tiles are needed to tile the floor, how much space is needed for a parking lot, how much paint is needed for the walls, etc., we employ the notion of area.

Given, A circle is circumscribed in the square,

Area of shaded region = area of square - area of circle

Area of square = Side²

= 10 × 10 = 100 sq. units,

Area of circle = Πr²

Radius = Diameter / 2

radius = 10 / 2 = 5 unitsArea of circle = Πr²

Radius = Diameter / 2

radius = 10 / 2 = 5 units

Area of circle = 22/7 × 5 × 5

= 78.57 sq. units

Area of shaded region = 100 - 78.57,

Area of shaded region = 21.43 sq. units

Answer:

Step-by-step explanation:

explain you question more i cant understand if i could i would help

(a)The transformed vertices would be:

W' = (1, -3)

X' = (-3, 0)

Y' = (1, -2)

(b)The transformed vertices would be:

W' = (-0, 1)

X' = (4, 4)

Y' = (-0, 2)

a) Reflection: To reflect the triangle across the y-axis, we simply need to negate the x-coordinates of each vertex.

The transformed vertices would be:

W' = (-0, 1)

X' = (4, 4)

Y' = (-0, 2)

The reflected triangle would be W'X'Y'.

b) Translation: To translate the triangle by the vector (1, -4), we add (1, -4) to the coordinates of each vertex.

The transformed vertices would be:

W' = (1, -3)

X' = (-3, 0)

Y' = (1, -2)

The translated triangle would be W'X'Y'.

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Answer:249.98

Step-by-step explanation: i had a question like this before.

a) The total cost for renting a compact car for eight days is as follows for each plan:

b) It is more economical to take the weekly rental plan than the daily rental plan.

Each plan's total rental cost is determined using multiplication or addition.

For instance, the total cost for the daily plan is a product of the daily rental cost and the number of days the car is rented.

The total cost for the weekly plan is an addition operation since the car is rented for 7 days (weekly cost) and 1 day (daily cost).

                               Day                  Week

Rental cost per      $48                   $312

1 week = 7 days

Total rental cost for

8 days                $384 ($48 x 8)     $360 ($312 + $48)

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The probabilities of the events and their values are shown below

The total number of marbles in the bag is 13, with 6 blue, 2 green, and 5 red.

P(Blue or Green) represents the probability of selecting a blue or green marble on the first pick.

This is calculated as follows:

P(Blue or Green) = P(Blue) + P(Green)

= 6/13 + 2/13

= 61.5%

P(Blue and Green) represents the probability of selecting a blue marble and a green marble on two consecutive picks, with replacement.

Therefore:

P(Blue and Green) = P(Blue) * P(Green)

= (6/13) * (2/13)

= 7.1%

P(Blue and Green) represents the probability of selecting a blue marble and a green marble on two consecutive picks, without replacement.

Therefore:

P(Blue and Green) = P(Blue) * P(Green)

= (6/13) * (2/12)

= 7.7%

P(Blue) represents the probability of selecting a blue marble on the first pick.

This is simply the proportion of blue marbles in the bag:

P(Blue) = 46.2%

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The volume of the solid with a hole in the shape of a rectangular prism passing through the center of a cylinder with a radius of 10 yards is approximately 1410 cubic yards, rounded to the nearest ten.

The cylinder with the hole can be viewed as the difference of two solids: the cylinder and the rectangular prism. The volume of the cylinder is given by the formula V_cyl = π[tex]r^2h[/tex], where r is the radius and h is the height.

The height of the cylinder is equal to the height of the rectangular prism that passes through its center. The height of the rectangular prism is given as 12 yards, which is also the diameter of the cylinder. Therefore, the height of the cylinder is h = 12/2 = 6 yards.

The volume of the cylinder is therefore V_cyl = π[tex](10)^2(6)[/tex] = 600π cubic yards.

The rectangular prism has a length of 20 yards, a width of 10 yards, and a height of 12 yards. Therefore, its volume is V_prism = 20 × 10 × 12 = 2400 cubic yards.

The volume of the solid with the hole is then:

V = V_cyl - V_prism = 600π - 2400 = 600(π - 4) ≈ 1412.2 cubic yards.

Therefore, the volume of the solid is approximately 1410 cubic yards.

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Answer:

[tex]13 < \sqrt{181} < 14[/tex].

Step-by-step explanation:

We have been given an inequality ___[tex]< \sqrt{181} <[/tex]___. We are asked to fill in the blank with two consecutive integers to complete the given inequality.

We know that square root of 181 is not an integer. We can see that 181 is greater than square root 169 and and square root of 196.

[tex]\sqrt{169} < \sqrt{181} < \sqrt{196}[/tex]

We know that [tex]\sqrt{169}=13[/tex] and [tex]\sqrt{196}=14[/tex].

Therefore, our required inequality would be [tex]13 < \sqrt{181} < 14[/tex]