Pierre inherited 226,500 from his uncle and decided to invest the money. He put part of the

money in a money market account that earns 3.1% simple interest. The remaining money was

invested in a stock that returned 4% in the first year and a mutual fund that lost 2% in the first

year. He invested $10,000 more in the stock than in the mutual fund, and his net gain for 1 yr

was $3180. Determine the amount invested in each account.

Looking at these angles, we can see that they are alternate interior angles. Alternate interior angles are congruent. This means that to solve we will simply need to set the given expressions equal to each other and solve for x.

4x - 23 = 3x + 18

x - 23 = 18

x = 41

Answer: x = 41

Hope this helps!

Answer: If we multiply then I guess it’s 26*3=78 and 78*20=1,560

Step-by-step explanation:

Answer:

73.4 degrees

Step-by-step explanation:

1 cm = 10 mm. Length of book : 28 cm. Length of book = 280 mm. This shows that measurements in mm are the same but look to have a higher number .

The conversion factor provided states that 1 cm is equal to 10 mm, which means that 1 cm is made up of 10 individual millimeters.

The length of my book in when measured in millimeters is 280 mm.

In centimeters, this is therefore:

= 280 mm / 10 cm /mm

= 28 cm

Although the numerical value appears higher when expressed in millimeters, it is important to note that the actual length of the book remains the same.

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Answer:

b- they were on expeditions

Step-by-step explanation:

Answer:

They were on an expedition where they traveled in groups so they could support each other

Step-by-step explanation:

Answer: 0.04

Step-by-step explanation:

The area \(A_1\) of the square target with side length \(s_1=20 cm\) is:

\(A_1=s_1^{2}=20^{2}=400\)

The area \(A_2\) of the shaded square with side length \(s_2=4cm\) is:

\(A_2=s_2^{2}=4^{2}=16\)

So, the probability that the dart will land in the shaded square on the target is:

\(\frac{A_{2}}{A_{1}}=\frac{16}{400}=0.04\)

Answer:

$180

Step-by-step explanation:

(12*10)+(12*5)

12*5 = 120/2 = 60 (half of 12*10)

12*10= 120

120 + 60= $180

You don't even have to calculate (12*5) you can just do 12*10/2

Answer:

$56.70

Step-by-step explanation:

I used finace calculator : /

Okay, here are the steps to find the p-value:

1) The nationwide proportion of Americans who invest in the stock market is 55% (0.55)

2) The test statistic for Georgia is 1.75

3) To calculate the p-value, we need to know the degrees of freedom (df) and the critical value of the test statistic.

4) The df = 1, since we're comparing a single proportion (Georgia) to a fixed value (national average).

5) The critical value at df = 1 and 95% confidence is 3.84 (for a two-tailed test)

6) Since the test statistic of 1.75 is less than 3.84, we look up 1.75 in tables to find the p-value.

7) For a test statistic of 1.75 and df = 1, the p-value is 0.1860.

So the p-value to test if the proportion of Georgians who invest in the stock market is different than the nationwide average is 0.1860.

Let me know if you have any other questions!

Okay, here are the steps to find the p-value:

1) The nationwide proportion of Americans who invest in the stock market is 55% (0.55)

2) The test statistic for Georgia is 1.75

3) To calculate the p-value, we need to know the degrees of freedom (df) and the critical value of the test statistic.

4) The df = 1, since we're comparing a single proportion (Georgia) to a fixed value (national average).

5) The critical value at df = 1 and 95% confidence is 3.84 (for a two-tailed test)

6) Since the test statistic of 1.75 is less than 3.84, we look up 1.75 in tables to find the p-value.

7) For a test statistic of 1.75 and df = 1, the p-value is 0.1860.

So the p-value to test if the proportion of Georgians who invest in the stock market is different than the nationwide average is 0.1860.

Let me know if you have any other questions!

Answer:

C. All parallelograms are quadrilaterals.

Step-by-step explanation:

Quadrilateral are 2D shapes that are closed sides, with 4 sides.

Janet has 630 options to customize a car based on the given features.

How to solve the question?

To determine the number of ways Janet can customize a car, we need to multiply the number of choices she has for each feature. Therefore, the total number of ways Janet can customize a car can be calculated as:

10 car models x 7 exterior colors x 9 interior colors = 630

Thus, Janet has 630 options to customize a car based on the given features.

It's worth noting that this calculation assumes that each feature (car model, exterior color, and interior color) can be combined with any other feature, without any restrictions or dependencies. However, in reality, certain car models may not be available in certain exterior or interior colors, or there may be other restrictions on the customization options.

Additionally, there may be other features that Janet can customize, such as the type of engine, transmission, or other options. Therefore, the total number of customization options may be even greater than what we have calculated here.

In summary, based on the given information, Janet has 630 ways to customize a car, but in reality, the actual number of options may be more limited or varied depending on other factors.

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Answer:

12

Step-by-step explanation:

Answer:

the largest number that is less than (2+√3)^6 is 2701

Step-by-step explanation:

\(\bigstar \ (2+\sqrt{3})^6= \\\\C{}^{0}_{6}2^{6}+C{}^{1}_{6}2^{5}\sqrt{3}^1+C{}^{2}_{6}2^{4}\sqrt{3}^2+C{}^{3}_{6}2^{3}\sqrt{3}^3+C{}^{4}_{6}2^{2}\sqrt{3}^4+C{}^{5}_{6}2^{1}\sqrt{3}^5+C{}^{6}_{6}\sqrt{3}^6\)

\(=64+192\sqrt{3}+720 +480\sqrt{3} +540+108\sqrt{3} +27\\=1351+780\sqrt{3}\)

\(\bigstar\ (2-\sqrt{3} )^6 =\\\\1351-780\sqrt{3}\)

\(\bigstar\ \bigstar\ (2+\sqrt{3} )^6+(2-\sqrt{3} )^6 =\\\\1351+780\sqrt{3}+1351-780\sqrt{3}\)

\(\Longrightarrow(2+\sqrt{3} )^6+(2-\sqrt{3} )^6 =2702\)

\(\Longrightarrow(2+\sqrt{3} )^6 =2702-(2-\sqrt{3} )^6\)

\(0 < \left( 2-\sqrt{3} \right) < 1 \Longrightarrow 0 < \left( 2-\sqrt{3} \right)^{6} < 1 \Longrightarrow-1 < \left( 2-\sqrt{3} \right)^{6} < 0\)

\(\Longrightarrow2702-1 < 2702-\left( 2-\sqrt{3} \right)^{6} < 2702+0\)

\(\Longrightarrow 2701 < \left( 2+\sqrt{3} \right)^{6} < 2702\)

Therefore , the solution of the given problem of area comes out to be

r = 8.

The term "area" describes the amount of space occupied by a 2D form or surface. We use cm2 or m2 as our units for measuring area. A shape's area is determined by dividing its length by its breadth.

Here,

A 90 degree sector occupies 1/4 of a circle, which has 360 degrees. Consequently, the area of the whole circle can be written as

Sector Size/Sector Area = Circle Area/360

16 ft2/90 = n/360

(360) (16 ft2)/90 = n

(4)(16 ft2) = n

The total size of the circle is n = 64 ft2.

Since Area of a Circle equals r2,

∏r2 = 64

r2 = 64/∏

r = √(64/∏)

We multiply by / to get by rationalizing the denominator.

r = √(64∏)/√(∏2) Then using the denominator's square root, we can obtain the solution of

r = √(64∏)/∏

r = 8

Therefore , the solution of the given problem of area comes out to be

r = 8.

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Answer:

73°

Step-by-step explanation:

180°- 107° =73°

*one straight line equal to 180°

Answer:

you can do 107+x(suppose the angle 4 is X so)=180°(being sum of angle in a straight line)

so, X=180-107

x=73

Answer:

7/10 or 0.7

The probability of Sara NOT picking an orange is 7/10

Step-by-step explanation:

Given that the basket of fruit contains;

10 lemons,

1 pear,

6 oranges, and

3 apples

Total number of fruits N = 20

The probability of not picking orange P(O');

P(O') = 1 - P(O) ........1

P(O) = probability of picking orange

P(O) = number of orange/total number of fruits

P(O) = 6/20

Applying equation 1;

P(O') = 1 - 6/20

P(O') = 14/20 = 7/10

P(O') = 7/10 or 0.7

Answer:

Just some background:

Congruent means that a triangle has the same angle measures and side lengths of another triangle.

SAS congruence theorem: If two sides and the angle between these two sides are congruent to the corresponding sides and angle of another triangle, then the two triangles are congruent. Congruent triangles: When two triangles have the same shape and size, they are congruent.

Let's look at A first.

The triangle on left, we know 40 and 30 degree angles. So 3 all angles together = 180, so the 3rd angle = 180-30-40 = 110.

Now look at the triangle on the right. The angle shown is 110! This angle is between the sides marked with || and ||| marks, indicating that those two sides are the same length between both triangles.

Therefore both triangles are the same by Side-Angle-Side or SAS.

Now look at B.

It's a right triangle. We are missing 1 side of each triangle.

Let's solve for the missing "leg" of the triangle on the right. The pythagorean theorem says that a^2 + b^2 = c^2 where a and b are the 'legs' or sides of the triangle and c is the hypotenuse (always the longest length opposite the right angle).

so 2^2 + b^2 = 4^2

4 + b^2 = 16

b^2 = 16-4

b^2 = 12

That missing side is the \(\sqrt{12}\).

This does NOT match the triangle on the left.

Theses two triangles are NOT congruent.

Answer:

The missing side is 14.4

x=14.4

Answer:

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

it is not right triangle because when we use Pythagoras theorem by using these side

not satisfied

Answer:

It is not a right triangle.

Answer:

Choose

a

,

b

and

c

the make the equation true.

Step-by-step explanation:

A linear equation can be written in several forms. "Standard Form" is

a

x

+

b

y

=

c

where

a

,

b

and

c

are constants (numbers).

We want to make two equations that

(i) have this form,

(ii) do not have all the same solutions (the equations are not equivalent), and

(iii)

(

4

,

−

3

)

is a solution to both.

a

x

+

b

y

=

c

. We want

a

,

b

and

c

so that

a

(

4

)

+

b

(

−

3

)

=

c

\(\frac{7}{8} (-32-48x) + 36 = \frac{2}{3} (-33x-18) -10x\)

\(\frac{7}{8} (-32)+\frac{7}{8} (-48)+36=\frac{2}{3} (-33x)+\frac{2}{3} (-18)-10x\)

\(-28-42+36=-22x-12-10x\)

\(22x+10x=28+42-36-12\)

\(32x=22\)

\(x=\frac{22}{32} =\frac{11}{16} =0,6875\)

Answer: x = 0.6875

Ok done. Thank to me :>

Answer:

x = 2

Step-by-step explanation:

7/8 (-32-48x) + 36 = 2/3 (-33x-18) - 10x

Multiply,

7(-32-48x)/8 + 36 = 2(-33x-18)/3 -10x

Simpliy,

-336(3x+2) + 864 = -48(11x+6) - 240x

Expand,

-1008x + 192 = -768x - 288

Simplify,

-1008x = -768x -480

Simplify,

-240x = -480

Simplify,

x = -480/-240

Answer,

x = 2

The reminder of the equation using the long division method is 70X - 12.

long division method :

Four main steps to solving this problem:

\(x^2 - 3$\overline{)x^5 + 24x^3- 5x - 12}$( x^3 + 25x\\\\\)

           x₅ + 3 x³

          (-)    (-)                              

                 25x³ - 5x   -   12

                 25x³ - 75x

                 (-)      (+)                          

                            70x  - 12              

here

divisor - (x² - 3)

dividend - (x⁵ + 2x12x² - 5x - 12)

quotient - (x³ +25x)

the given question is incomplete the correct question is

Use long division to divide.

(x⁵ + 2x12x² - 5x - 12) / (x² - 3)

The reminder of the equation using the long division method is 70X - 12.

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Answer:

75200 x 1/100= 752

hope this helps!

The area of the shaded region is equal to 45 square units.

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

A = LW

Where:

By substituting the given side lengths into the formula for the area of a rectangle, we have the following;

Area of rectangle = 8 × 6

Area of rectangle = 48 square units.

Since the opposite sides of any rectangle are congruent (equal), the legs of the right triangle can be calculated as follows;

L₁ = 8 - 5 = 3 units.

L₂ = 6 - 4 = 2 units.

Area of right triangle = 1/2 × 3 × 2

Area of right triangle = 3 square units.

For the area of the shaded region, we have:

Area of the shaded region = 48 square units - 3 square units.

Area of the shaded region = 45 square units.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

48 miles

Step-by-step explanation:

i think thats it.

Answer: 4.

Step-by-step explanation: 8+8=16. count how many more until you get to 24, that is 8. Split 8 in half. We get 4.

                                Hope this helps!

Answer:

634

Step-by-step explanation:

it started 759 under went up 125 feet

use the equation 759-125=634

Answer:

Step-by-step explanation: 5.) Circular shape.

     6.) Feet.

     7.) Circle.

     8.) The circumference is 9 and the radius is 18.

     9.)  By the way we would need to use The Circumference as 2 and the radius to be 9 to equal 18 for the radius circle.

The lengths of the other two sides of the right triangle are 24m and 25m, respectively.

Let's assume the consecutive integers representing the lengths of the other two sides of the right triangle are x and x + 1, where x is the smaller integer. We are given that the shortest side measures 7m. Now, we can use the Pythagorean theorem to solve for the lengths of the other two sides.

According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Using this theorem, we have the equation:

\(7^2 + x^2 = (x + 1)^2\)

Expanding and simplifying this equation, we get:

\(49 + x^2 = x^2 + 2x + 1\)

Now, we can cancel out \(x^2\) from both sides of the equation:

49 = 2x + 1

Next, we can isolate 2x:

2x = 49 - 1

2x = 48

Dividing both sides by 2, we find:

x = 24

Therefore, the smaller integer representing the length of one side is 24, and the consecutive integer representing the length of the other side is 24 + 1 = 25.

Hence, the lengths of the other two sides of the right triangle are 24m and 25m, respectively.

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