In investing $6,500 of a couple's money, a financial planner put some of it into a savings account paying 5% annual simple interest. The rest was invested in a riskier mini-mall development plan paying 13% annual simple interest. The combined interest earned for the first year was $637. How much money was invested at each rate?

The congruency rules which satisfy the given triangles are (B) AAS and (D) HA.

What is triangle congruency?

Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent.

Slide, twist, flip, and turn these triangles to create an identical appearance.

If two triangles meet all 5 requirements for congruence, then they are congruent.

They are right angle-hypotenuse-side (RAHS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and side-angle-side (SSS). (RHS).

So, according to the given, we can observe that:

2 pairs of angles are congruent one pair of which is 90°.

And 1 pair of sides are congruent.

Then, the rules that satisfy here will be:

AAS and HA

Therefore, the congruency rules which satisfy the given triangles are (B) AAS and (D) HA.

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Complete question:

Based only on the information given in the diagram, which congruence theorems or postulates could begin as reasons why HIJ = KLM?

So the area of the triangle is 216 square inches.

To find the area of a triangle, you can use the formula A = 1/2 * b * h, where A is the area, b is the length of the base, and h is the height of the triangle. In this case, we have a height of 12 inches and a base of 36 inches.

To find the length of the missing side of the triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. So, we have:

c² = a² + b²

c² = 12² + 34²

c² = 144 + 1156

c² = 1300

c = √(1300)

c = 36.06 (rounded to two decimal places)

Now that we know all three sides of the triangle, we can plug them into the formula for the area:

A = 1/2 * b * h

A = 1/2 * 36 * 12

A = 216

So the area of the triangle is 216 square inches.

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The functions which have a y-intercept which is greater than the y-intercept of the function g(x) = |x + 3| + 4 are :

h(x) = -5 |x| + 10

k(x) = 1/4 (x - 4)² + 4

m(x) = 1/4 |x - 8| + 6

Given function is,

g(x) = |x + 3| + 4

y intercept of a function is the value of the function when the input value is 0.

g(0) = |0 + 3| + 4 = 7

f(x) = -2 (x - 8)²

f(0) = -2 (0 - 8)² = -128

h(x) = -5 |x| + 10

h(0) = 10

j(x) = -4(x + 2)² + 8

j(0) = -4 (0 + 2)² + 8 = -8

k(x) = 1/4 (x - 4)² + 4

k(0) = 1/4 (0 - 4)² + 4 = 8

m(x) = 1/4 |x - 8| + 6

m(0) = 1/4 |0 - 8| + 6 = 8

Hence the functions h(x) = -5 |x| + 10, k(x) = 1/4 (x - 4)² + 4 and m(x) = 1/4 |x - 8| + 6 have the y intercept greater than that of g(x) = |x + 3| + 4.

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The total weight of the contents is 141.33 pounds.

What is a rectangular prism?

A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.

Here, we have

Given: A container built for transatlantic shipping is constructed in the shape of a right rectangular prism. Its dimensions are 5 ft by 14.5 ft by 6.5 ft. The container is entirely full and, on average, its contents weigh 0.3 pounds per cubic foot.

The volume of the container is calculated as:

5 ft× 14.5 ft× 6.5 ft= 471.125 ft³

Then, the total weight of the contents is calculated as:

471.125 ft³×  0.3 pounds per cubic foot= 141.3375 pounds≅ 141.33 pounds

Hence, the total weight of the contents is 141.33 pounds.

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The points that is in the solution set of y < x² - 2x - 8 is option A: (-2, -1)

When you Check the inequality by (-2,-1) then Put x=-2 and y=-1 in the given inequality.

1 < (-2)² - 2(-2) - 8

-1 < 4 + 4 - 8

-1 < 0

Hence:

(-2,-1) can be in the solution

( 0,-2) Cannot

(4,0) will not.

Therefore, The points that is in the solution set of y < x² - 2x - 8 is option A: (-2, -1)

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See full question below

Which of the following points is in the solution set of y < x2 - 2x - 8?

(-2, -1)(0, -2)(4, 0)

The maximum height attained by the arrow is 2128 feet

What is kinematic equation for vertical motion?

The kinematic equation for vertical motion is [tex]h = h_0 + v_0 \times (\frac{1}{2} )t - gt^2[/tex]

where:

h = height attained by the arrow (maximum height)

[tex]h_0 = [/tex]initial height (80 feet)

[tex]v_0 = [/tex]initial velocity (256 feet per second)

g = acceleration due to gravity (-32 feet per second squared)

t = time taken to reach maximum height

At the maximum height, the velocity of the arrow is zero. So we can use the fact that the final velocity is zero to find the time taken to reach the maximum height,

[tex]0 = v_0 - g \times t \\ t = \frac{ v_0}{g}[/tex]

Substituting this value of t into the first equation, we get:

[tex]h = h_0 + v_0 \times ( \frac{v_0}{g}) - ( \frac{1}{2} )g( \frac{v_0}{g})^2 \\ h = 80 + (256) \frac{256}{(-32)} - ( \frac{1}{2} )(-32)\frac{256^2}{(-32)^2} \\ h = 80 + 4096 - ( \frac{1}{2} ) \frac{(256)^2}{(32)} \\ h = 80 + 4096 - 2048 \\ h = 2128 \: feet[/tex]

Therefore, the maximum height attained by the arrow is 2128 feet.

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Answer:

Valid

Step-by-step explanation:

The volume of the batter in the pan can be found by multiplying the length, width, and height of the right rectangular prism-shaped pan. In this case, the length is 9 inches, the width is 5 inches, and the height is 3 inches.

Using the formula for the volume of a rectangular prism, V = lwh, we can substitute the given values to find:

V = (9 in.)(5 in.)(3 in.)

V = 135 cubic inches

Therefore, the volume of the batter in the pan is 135 cubic inches. This argument is valid because it follows the basic formula for calculating the volume of a rectangular prism and uses the specific measurements provided for the length, width, and height of the pan.

She can make 20 6-ounce servings to make fruit punch

How to determine this

Cassie uses 1 quart cranberry juice,

1/2 gallon ginger ale,

1 1/2 pint orange juice.

1 quart of cranberry juice when converted to ounce

1 quart = 32 ounces

1/2 gallon of ginger ale when converted to ounce

1 gallon = 128 ounces

1/2 gallon = 128/2

1/2 gallon = 64 ounces

1 1/2 pint orange juice to make fruit punch

1 pint = 16 ounces

1 1/2 pint = 16 + 16/2 ounces

= 16 + 8

= 24 ounces

How many 6-ounces servings can she make

32 + 64 + 24

= 120 ounces

6-ounces that can be made

= 120 ounces/6 ounces

= 20 servings

Therefore, 20 6-ounce servings can be make for fruit punch

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The length of a scaled drawing with a width of 9cm and the scale factor 3/4 s 6.75 cm

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

Width =  9cm

Scale factor = 3/4

Using the above as a guide, we have the following:

Length of a scaled drawing = Width * Scale factor

Substitute the known values in the above equation, so, we have the following representation

Length of a scaled drawing = 9 * 3/4

Evaluate

Length of a scaled drawing = 6.75

Hence, the length of a scaled drawing is 6.75 cm

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Check the picture below.

The slope of the line is -4, which means that the swimmer will complete 4 laps every minute.  For 5 weeks they have the same amount of money. The direction is 270° clockwise rotation. The pattern of scatter plot is that there is a weak, negative linear association. The measurement of FD = 1.52. The slope of the line is negative three halves. The probability of No Heads is 25%. The scale factor is one half. The correct answers are C), B), A), B), A), D), D) and B).

The slope of the line is the change in y divided by the change in x, which represents the rate of change of the line. In this case, the slope is negative 4, which means that for every minute that passes, the number of laps remaining decreases by 4. So, the swimmer completes 4 laps every minute.

To find the point at which the two savings accounts have the same amount of money, we need to set the two equations equal to each other and solve for x

10x + 25 = 5x + 50

5x = 25

x = 5

So, after 5 weeks, the two siblings will have the same amount of money saved.

The direction of rotation can be determined by looking at the relative positions of the vertices of the original polygon and its image. In this case, the vertices of the image are in quadrant 1, while the vertices of the original polygon are in quadrant 2. This means that the image has been rotated counterclockwise. Additionally, we can see that the image has been rotated by 90 degrees, so the angle of rotation is 90 degrees counterclockwise.

The scatter plot shows a general trend of decreasing cost per cupcake as the number of cupcakes in an order increases. However, there is a fair amount of variability in the data, so the association between the two variables is weak. Additionally, the association is negative, as the cost per cupcake decreases as the number of cupcakes in an order increases.

Similar triangles have proportional side lengths, so we can set up a proportion using corresponding side lengths of the two triangles

AB/DE = BC/EF = CA/FD

Plugging in the known values, we get

11/2.2 = 7.9/EF = 7.6/FD

Solving for FD, we get

FD = (7.6 * 2.2)/11 = 1.52

So, FD has a length of 1.52 units.

The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula

slope = (y2 - y1)/(x2 - x1)

Plugging in the given values, we get

slope = (-10 - (-1))/(3 - (-3)) = -9/6 = -3/2

So, the slope of the line is negative three halves.

The probability of getting no heads in two flips can be found by adding the frequencies of the outcomes where no heads occur (Tails, Tails) and (Tails, Heads) and dividing by the total number of trials

P(No Heads) = (50 + 35)/200 = 85/200 = 0.425 = 42.5%

So, the probability of getting no heads is 42.5%, which is equivalent to 0.425.

Dilations involve multiplying the coordinates of each vertex by a scale factor. To find the scale factor used in this dilation, we can compare the corresponding side lengths of the original triangle and its image. In this case, we can see that the sides of the image are half as long as the corresponding sides of the original triangle. So, the scale factor used to create the image is one half.

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The missing values are b = 4.37, C = 11° and A = 134°

Given is a triangle, we need to find the missing lengths and angles,

So,

Using the cosine rule,

b² = a²+c² - 2ac Cosb

b = √4²+7²-2(4)(7)cos35°

b = √16+49-45.87

b = √19.13

b = 4.37

Now, using the sine rule,

Sin C / 7 = Sin 35° / 4.37

C = 11°

Applying the angle sum property of triangles,

A = 180°-(11°+35°)

A = 134°

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The complete equation for the cosine rule is c² = 3² + 10² - 2(3)(10) × cos(34).

The cosine rule, also known as the law of cosines, is a formula used to find the lengths of sides or measures of angles in a triangle. It relates the lengths of the sides of a triangle to the cosine of one of its angles. The cosine rule is typically used when you have a triangle with at least one known side length and its opposite angle, and you want to find either another side length or another angle in the triangle.

The cosine rule is given by the following formula:

c² = a² + b² - 2ab × cos(C)

where:

For the given side c;

c² = 3² + 10² - 2(3)(10) × cos(34)

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Answer:

Class Rank | Frequency

--- | ---

Fr | 7

So | 3

Jr | 4

Se | 6

Answer:

Step-by-step explanation:

(a) Lena got 33 more

(b) Last one

Answer:

Yes, triangles ABC and DEC are similar by AA. Angles ABC and DEC are congruent, and angles ACB and DCE are congruent.

The slope of the line that is parallel to the line that contains side WV is 1.

What about slope of line?

The slope of a line is a measure of its steepness or inclination, defined as the ratio of the change in the vertical direction (y-axis) to the change in the horizontal direction (x-axis) between any two points on the line.

In other words, the slope of a line represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It is commonly denoted by the letter "m" and is calculated as:

m = (y₂ - y₁) / (x₂ - x₁) where (x₁, y₁) and (x₂, y₂) are any two points on the line.

The slope can be positive, negative, zero, or undefined. A positive slope indicates that the line rises as we move from left to right, while a negative slope indicates that the line falls as we move from left to right. A slope of zero indicates that the line is horizontal, and an undefined slope indicates that the line is vertical.

According to the given information:

W(a+3, b-3) and V(a+5, b-1)

So, the slope WV,

[tex]\frac{b-3-(b-1)}{a+3 - (a+5)} \\\\\frac{-2}{-2} = 1[/tex]

So, the slope of the given condition is 1.

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By subtraction between two points P₁(x, y) = (- 5, 3) and P₂(x, y) = (- 2, - 7), the vector V is 3 i - 10 j.

According to linear algebra, a vector can be formed by subtracting the initial point (P₁) from the final point (P₂). The equation is introduced below:

V = P₂(x, y) - P₁(x, y)

V = (- 2, - 7) - (- 5, 3)

V = (3, - 10)

V = 3 i - 10 j

The vector V = 3 i - 10 j is the result of subtracting the two points P₁(x, y) = (- 5, 3) and P₂(x, y) = (- 2, - 7).

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Answer:

55.5

Step-by-step explanation:

Using the Tangent and Intersected Chord Theorem we know that since the line is tangent to the circle, it will be half of the arc that surrounds the angle. Becuase the arc is 111, dividing it by 2 will give us 55.5

The current yield of a 4.95% coupon at a price of $102.53 is [tex]4.82%[/tex]%.

The current yield of bond means return on an investment based on its current market price.

To calculate the current yield, we will use (annual interest payment/current market price * 100).

Annual interest payment = $1,000 face value x 4.95% coupon

Annual interest payment = $49.50

Current market price = 102.53% of the face value

Current market price = $1,025.30

Current yield = $49.50 / $1,025.30 x 100

Current yield = 4.82%

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A recursive definition for the set S can be given as follows:

What is recursion?

Recursion is a programming technique where a function calls itself to solve a problem.

Base case: (1, n) is in S for all positive integers n, since 1 is a factor of all positive integers.

Recursive case: If (a, b) is in S, then (a', b) is in S for all positive integers a' that are factors of a, and (a, b') is in S for all positive integers b' that are multiples of b.

In other words, the set S contains all pairs (a,b) where a is a positive integer that divides b, and b can be obtained by multiplying any such a with another positive integer. The base case includes all pairs where a=1 and b is any positive integer.

The recursive case states that if (a,b) is in S, then all pairs where a' is a factor of a and b is a positive integer such that b=a'b are also in S, as well as all pairs where b' is a multiple of b and a is a positive integer that divides b'.

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Answer:

1.5=slope

Step-by-step explanation:

To do this, we need to solve the slope.

We will use rise/run

0-3=-3

0-2=-2

-3/-2=1.5

Check the picture below, so the angle looks more or less like so.

now, let's recall that the value pair in a terminal point is the adjacent and opposite sides

[tex]\cot(\theta )=\cfrac{\stackrel{adjacent}{0}}{\underset{opposite}{5}}\implies \cot(\theta )=0[/tex]

The mean and the median of the following gasoline prices that are listed above would be =3.29 and 4.85 respectively.

The formula that is used to calculate the mean of a data set is given as follows;

mean = sum of data set/number of data set

= 3.14+3.21+3.28+3.53/4

= 13.16/4 = 3.29

The median = 3.21+3.28/2 = 4.85

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The quadrant or axis for each of the given ordered pairs is:

a. (-x, y) - second quadrant

b. (-x, 0) - X-axis

c. (x, -y) - fourth quadrant

d. (0, y) - Y-axis

a. (-x, y):

As the x-coordinate is negative (-x), and the y-coordinate is positive (y), the ordered pair (-x, y) will lie in the second quadrant.

b. (-x, 0):

The x-coordinate being negative (-x), and the y-coordinate 0 renders that the ordered pair (-x, 0) lies on the x-axis. This horizontal axis records an unchanging value for y: zero.

c. (x, -y):

The x-coordinate here is a positive value (x), and the y coordinate a negative one (-y); it implies that the ordered pair (x, -y) lies within the fourth quadrant.  

d. (0, y):

In this case, the x-coordinate is 0 and the y-coordinate is positive (y); therefore, the ordered pair (0, y) has its place on the y-axis. The y-axis is the vertical line on which x retains a permanent numerical value of zero.

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Triangles RLG and PCN are similar. The similarity is by SSS criteria and the scale factor is 2/3.

Two triangles that are similar in shape but not necessarily in size are called similar triangles. To put it another way, the two triangles' angles are similar and their corresponding sides are proportional.

If two triangles are comparable, then all pairs of related sides have the same length-to-length ratio. The scale factor of similar triangles is the name given to this ratio. The scale factor between two triangles is 2:1, for instance, if one side of a triangle is twice as long as its counterpart side in another triangle.

In the given figure we have triangle RLG and triangle PCN.

Here, the ratio of the sides of the triangle are given as:

RG / PN = 32 / 48 = 2/3

Also we have:

LG / PC = 18/27 = 2/3

LR / CN = 30 / 45 = 2/3

RG / PN = LG / PC = LR / CN = 2/3

Hence, triangles RLG and PCN are similar. The similarity is by SSS criteria and the scale factor is 2/3.

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The complete question is:

The dimensions that can create more than one triangle are given as follows:

three angles measuring 25°, 65°, and 90°.

Suppose we have a triangle in which:

The lengths and the sine of the angles are related as follows:

[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]

The sum of the measures of the internal angles of a triangle is of:

180º.

Meaning that the first option is correct and the second is not.

Considering the law of sines, an infinite number of triangles can be formed, as long as:

sin(25º)/a = sin(65º)/b = sin(90º)/c.

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Answer:

∠ BAC = 66°

Step-by-step explanation:

the inscribed angle BAC is half the angle at the centre, subtended on the same arc BC , then

∠ BAC = [tex]\frac{1}{2}[/tex] × 132° = 66°

On the basis of this information, the ratio of married male non-members to the married female non-members is (b) 3 : 1

Total married male employees = 80% × 50% = 40%

Total male Trade Union members = 91.67%

Total male non-Trade Union members = 100% - 91.67% = 8.33%

Married male Trade Union members = 40% × 91.67% = 36.67%

Married male non-Trade Union members = 40% - 36.67% = 3.33%

Now, let's find the number of married female non-members:

The ratio based on the information is 3 to 1.

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