When a retired police officer passes away, he leaves $300,000 to be divided among his three children and six grandchildren. The will specifies that each child is to get twice as much as each grandchild. How much does each get?

Answer:

d = $350

Step-by-step explanation:

If we allow d to represent the cost of the dryer and w to represent the cost of the washer, we know that the total cost of the washer and dryer is

d + w = 770.

Since we're told that the washer costs $70 more than the dryer, we know that

w = d + 70

We can substitute equation for w in the original equation to find d:

d + d + 70 = 770

2d + 70 = 770

2d = 700

d = 350

If you went on to find w, you'd see that it'd be 420 since 770 - d = w and 770 - 350 = 420

We know that the dryer costs $350 and the washer costs $420.  420 is indeed $70 more than $350 so our answer for the cost of the dryer is correct.

The median weekly earnings of the data set of the workers in the occupations listed for 2010 is calculated as: $971.

To find the median weekly earnings for the occupations listed in 2010, we need to first arrange the earnings in order from least to greatest:

$501, $900, $971, $977, $1071

The median is the middle value in this ordered list. Since there are an odd number of values, the median is simply the middle value.

Therefore, the median weekly earnings of workers in the occupations listed for 2010 is $971.

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Spinner B is the spinner that has a probability of 1/3 of spinning orange.

a) For one of the spinners, the probability of spinning orange is 1/3. To identify which spinner this is, we need to find the spinner that has exactly one orange sector out of three total sectors.

From the given spinners, Spinner B is the only spinner that has one orange sector out of three, so Spinner B is the spinner that has a probability of 1/3 of spinning orange.

b) For two of the spinners, the probability of spinning orange is more than 40%. To find these spinners, we need to look for the spinners that have at least three orange sectors out of a total of eight sectors (since 3/8 is greater than 40%).

From the given spinners, Spinner A and Spinner C both have three orange sectors out of eight total sectors, so they are the two spinners for which the probability of spinning orange is more than 40%.

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The converse of the statement "A → B: If x = 3, then x + 8 = 11" is Option(c) which is "B → A: If x + 8 = 11, then x = 3."

The "Converse" of a "conditional-statement" can be expressed by interchanging the hypothesis and the conclusion of "original-statement".

In this case, The "conditional-statement" is given to be "A → B: If x = 3, then x+8=11", which is read-as that if "x" is equal to 3, then expression "x + 8" is equal to 11.

So, The converse statement would say that if "x + 8" is equal to 11, then x must be equal to 3.

Therefore, the correct option is (c).

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The total amount that the Bells will pay for their house would be $313, 680.

The cost that would be interest is $193, 680

The amount of the first payment going to mortgages is $165. 24

Find the down payment :

Down payment = House price - Mortgage amount = $120,000 - $90,000 = $30,000

Then the points paid at closing :

= $ 90,000 x 0. 02 = $1,800

Total amount paid = Total mortgage payments + Down payment + Points cost

= 281, 880 + 30, 000 + 1, 800

= $ 313, 680

The total that is interest is:

Total interest paid = Total interest paid through monthly payments + Points cost

Total interest paid = $ 191, 880 + $ 1, 800 = $193, 680

The amount of the first payment going to principal is:

Principal portion of first payment = 90, 000 - 89, 834.76 = $165. 24

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The sculpture's base length = 9 cm and the height of sculpture is found as 6 cm.

The base and apex are joined to form a pyramid. To identify them from the base, the triangular sides are also also referred to as lateral faces. In a pyramid, the apex, which creates the triangle face, is connected to each base edge.

Put the values and find the length.

162 = 1/3 (x)² (x-3)

162 * (3) =  (x)² (x-3)

486 = x²(x-3)

486 = x³ - 3x²

x³ - 3x² - 486 = 0

(use a graphing tool or calculator equation mode).

x = 9

Thus,

side length of sculpture = 9 cm

height of sculpture = 9 - 3   = 6cm

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Correct question:

Nathan has a sculpture in the shape of a pyramid. The height of the sculpture is 3 centimeters less than the side length,x,of its square base. Nathan uses the formula for the volume of a pyramid to determine the dimesnsioms of the sculpture.

V=1/3 a^2h

Here, a is the side length of the pyramids square base and h is it’s height.

If 162 cubic centimeters of clay were used to make the sculpture, the equation x^3 + _x^2+ _ =0 can be used to find that the length of the sculptures.  base is _ centimeters.

The sequence 1, 6, 30, 60, . . . is not a geometric sequence

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

1, 6, 30, 60, . . .

To check if the sequence is geometric, we calculae the common ratio of the sequence using

r = next term/previous term

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

r = 6/1 = 6

r = 30/6 = 5

r = 60/30 = 2

The common ratios of the sequence calculated above are different

This means that the sequence is not geometric

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The standard deviation for the given distribution is 8.739 using either the direct method or the shortcut method.

Standard deviation is defined as a measure of how spread out numbers are. It is also referred to as the square root of the Variance, and then the Variance is the average of the squared differences from the Mean.

To calculate the standard deviation for the given distribution, we will utilize either the direct method or the shortcut method.

Direct method:

Calculate the mean wage (F) for the distribution:

Mean = (20 + 22 + 27 + 30 + 31 + 32 + 35 + 45 + 40 + 48)/10

Mean = 34

Calculate the differences between each wage and the mean wage:

20 - 34 = -14

22 - 34 = -12

27 - 34 = -7

30 - 34 = -4

31 - 34 = -3

32 - 34 = -2

35 - 34 = 1

45 - 34 = 11

40 - 34 = 6

48 - 34 = 14

Square each of the differences:

(-14)² = 196

(-12)² = 144

(-7)² = 49

(-4)² = 16

(-3)² = 9

(-2)² = 4

1² = 1

11² = 121

6² = 36

14² = 196

Add up the squared differences: 196 + 144 + 49 + 16 + 9 + 4 + 1 + 121 + 36 + 196 = 756

Divide the sum of the squared differences by the number of workers: 756/10 = 75.6

Take the square root of the result to get the standard deviation:

√75.6 = 8.739

Shortcut method:

The mean wage (F) for the distribution:

(20 + 22 + 27 + 30 + 31 + 32 + 35 + 45 + 40 + 48)/10 = 34

The sum of the squares of the differences between each wage and the mean wage:

(20 - 34)² + (22 - 34)² + (27 - 34)² + (30 - 34)² + (31 - 34)² + (32 - 34)² + (35 - 34)² + (45 - 34)² + (40 - 34)² + (48 - 34)² = 756

Divide the sum by the number of workers: 756/10 = 75.6

Take the square root of the result to get the standard deviation:

Standard deviation = √75.6 = 8.739

Therefore,

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Complete question is:

Calculate standard deviation for the following

distribution by direct and shortcut method.

Assume mean as 32.

Serial No. of Workers

1

2

3

4

5

6

7

8

9

10

Wage (F)

20

22

27

30

31

32

35

45

40

48

The curved surface area of the cone is 148 cm².

Given that we need to find the curved surface area of the cone with height of 8 cm and radius of 5 cm,

The curved surface area gives the area of the face of an object.

The CSA of a cone = π × radius × slant height.

Slant height = √r²+h²

= √64+25

= 9.43 cm.

Now the csa = 3.14 × 5 × 9.43

= 148

Hence the curved surface area of the cone is 148 cm².

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Note that the limit of the expression as x approaches infinity is 1/2.

start by multiplying both the numerator and denominator by the conjugate  expression

√ (x ² - 9x + 1) + x,

this will eliminates the root in the numerator

lim x->∞ [(√(x ² - 9x + 1) - x)  * (√(x² - 9x + 1) + x)] / (√(x² - 9x + 1) + x)

Expanding the numerator

lim x- >∞ [(x² - 9x + 1) - x^2] / (√(x² - 9x + 1) + x)

Simplifying further:

lim x->∞ [(1 - 9/x + 1/ x²)] / (√(1 - 9/x + 1 /x²) + 1)

we can see that the 1/x ² term approaches zero, and the expression simplifies to

lim x->∞ [(1 - 0)]  / (√(1 - 0) + 1)

= 1/2

So it is correct to state that the limit of the expression as x approaches infinity is 1/2.

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Answer:

100

Step-by-step explanation:

The number has the same digit in its hundreds place and its hundredths place. The digit in the hundreds place is 100 times greater than the digit in the hundredths place (https://ccssmathanswers.com/hundredth-place-in-decimals). Therefore, the value of the digit in the hundreds place is 100 times greater than the value of the digit in the hundredths place.

Therefore, the answer is 100.

Answer:

x^2(x+5)-6(x+5)!!!!!!!!

Carson can line up his textbooks on his bookshelf in 24 different ways

What is Permutation?

Permutations are a way to count the number of ways that a set of objects can be arranged in a particular order. A permutation is an ordered arrangement of objects.

What is Combination?

The combination is a way to count the number of ways that a set of objects can be selected without regard to order. A combination is an unordered selection of objects.

According to the given information:

Carson has four textbooks that he wants to line up on his bookshelf. The number of different ways that he can do this is given by the permutation formula:

n! / (n - r)!

where n is the total number of objects (in this case, 4 textbooks), and r is the number of objects that he wants to arrange in a particular order (in this case, all 4 textbooks).

On substituting the values in the formula,

4! / (4 - 4)! = 4! / 0! = 4 x 3 x 2 x 1 / 1 = 24

Therefore, Carson can line up his textbooks on his bookshelf in 24 different ways.

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The inequality represented by the given graph as required to be determined in the task content is; y ≥ 0.5x.

It follows from the task content that the inequality which is represented by the given graph is required to be determined.

By observation; the slope of the border line is; 0.5 and the y-intercept is; 0.

Ultimately, the corresponding equation to the border line is; y = 0.5x.

Hence, since the region above the line is shaded and the line is a solid line; the required inequality is; y ≥ 0.5x.

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Some of the common order of operation mistakes that students make when evaluating expressions are the use of basic mathematical operations.

You should know that an error or fault results from defective judgment, deficient knowledge, or carelessness.

A combination of numbers, letters, and relational operators containing at least one operation is deemed a mathematical expression. Additionally, it must also include variables and/or numbers, excluding an equal sign.

Some prevalent errors include using both a positive and a negative sign, using two negative signs, and misusing brackets.

By being unable to comprehend the problems accurately, learners often commit significant errors while assessing formulations, which underscores the importance of employing fundamental mathematical operations.

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The dimensions of the sign are as follows, using an overall scale factor of 12 on the original graphic:

The scale factor refers to the ratio of an original scale, object, or drawing to its model or final version.

The scale factor may enlarge or reduce the original dimensions.

The dimensions of the street sign graphic on computer = 4 inches by 5 inches

Scale factor of the graphic on print = 3

The first smaller dimensions:

4 x 3 inches and 5 x 3 inches

= 12 inches by 15 inches

The second larger dimensions:

Scale factor = 4

12 x 4 inches by 15 x 4 inches60 i

= 48 inches by 60 inches

Overall scale factor of the original graphic to the last model = 12 (3 x 4)

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Answer:

We can use the given formula to calculate the decibel level D when the intensity level I is 63,096 times Io:

D = 10log(I/lo)

Where Io is the reference intensity level and is typically taken to be the threshold of hearing, which is 10^−12 watts/m^2.

So, substituting the values, we get:

D = 10log(63,096*Io/Io) = 10log(63,096)

Using a calculator, we find:

D ≈ 47.1 dB

Rounding this to the nearest whole number, we get:

The decibel level is 47 dB when I is 63,096 times Io.

I hope this helps mate.

The triangles represented in the picture attached are acute, obtuse, acute and right triangles respectively.

Acute Triangle is a triangle in which each of the three angles are less than 90°.

In fact all angles in an acute triangle are can be equal and sum to 180°.

Right Triangle is a triangle in which one of the angles is exactly 90°, often denoted as a "square corner".

The side opposite the right angle is called the hypotenuse and it is the longest side.

Obtuse Triangle is a triangle in which one of the angles is greater than 90°.

In other words, one of the angles in an obtuse triangle is "blunt" or greater than a right angle.

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Answer:

x=109 y=100

Step-by-step explanation:

Answer:

x=100

y=109

Step-by-step explanation:

For any quadrilateral (4-sided shape) inscribed in a circle (all 4 vertices of the quadrilateral are on the edge of the circle),  there is a special relationship between certain pairs of angles within the quadrilateral.

Specifically, opposite angles (angles across from each other) must sum (add) to 180 degrees.

The angle measuring 80 degrees is opposite the angle measuring x degrees, so x + 80 = 180, implying x = 100.

In this case, the angle measuring 71 degrees is opposite the angle measuring y degrees.  So, 71 + y = 180, which implies y = 109.

Answer: 8.7

Step-by-step explanation:

Given:

hypotenuse = 9

Angle x =75

opposite of angle = x

Solution:

From SOH CAH TOA, use SOH

sin x = [tex]\frac{opposite}{hypotenuse}[/tex]                  > substitute

sin 75  = [tex]\frac{x}{9}[/tex]                           > multiply both sides by 9

9*sin 75 =x

x=8.7

The measure of ∠ADC is equal to 180 degrees.

The measure of ∠ABC is equal to 90 degrees.

In Mathematics and Geometry, a circle simply refers to a closed, two-dimensional (2D) curved geometric shape with no edges or corners. Additionally, a circle refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).

Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can reasonably infer and logically deduce that the measure of angle ADC (∠ADC) is equal to 180 degrees.

In conclusion, the angle subtended by chord AB at point B has a measure of 90 degrees.

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18.2

Step-by-step explanation:

AB² =AC² + CB² -2(AC)(CB)CosA

X²=(17)² + (10)² - 2 (17)(10) Cos80

x² = 289 + 100- 340 cos 80

x= √289+100-340cos80

x= 18.2

The matrix after the row operation is given as follows:

[tex]\left[\begin{array}{ccc}1&-\frac{4}{7}&\frac{8}{7}\\-12&7&-13\end{array}\right][/tex]

The matrix in the context of this problem is defined as follows:

[tex]\left[\begin{array}{ccc}7&-4&8\\-12&7&-13\end{array}\right][/tex]

We want to have element 1 into row 1 and column 1, that is, the element of 7 must assume a value of -1.

A valid row operation is the multiplication of the row by a constant, and as the element has a value of 7, the constant to obtain a value of 1 is:

7/k = 1

k = 7.

Dividing every element of the first row by 7, the matrix is given as follows:

[tex]\left[\begin{array}{ccc}1&-\frac{4}{7}&\frac{8}{7}\\-12&7&-13\end{array}\right][/tex]

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Answer:

Correct ANSWER IS A

Step-by-step explanation:

For each coordinate pair (r,θ) listed in the table, first identify the ray on the graph created by the angle θ. On this ray, plot a point a distance of r from the pole.

Answer:

Let's start by using algebra to solve for the original amount that Alex paid for his shares.

Let X be the original amount that Alex paid for his shares.

We know that his shares dropped in value by 35%, so after the drop, he had 65% of his original investment left:

0.65X = $72,800

Solving for X:

X = $72,800 / 0.65

X = $112,000

Therefore, Alex paid $112,000 for his shares to begin with.

Answer:

50° F

Step-by-step explanation:

35 - -15= 50

Check
-15 + 50 = 35

And 35 - 50 = -15

The vertical shift and vertical shrink of the exponential function are 2 and 1/2 respectively and the graph of the function is attached below

An exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.

The vertical shift and vertical shrink of the function f(x) = 1/2(4 - eˣ) are 2 and 1/2

The vertical shift = 2

vertical shrink = 1/2

Kindly find the attached graph below

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Answer:

2:35

Step-by-step explanation:

it takes 2 hours to get to Muar so 9:45

he spends 1 hour 40 in muar so 11:35

he went at 60 Km/h before so he returns at 40Km/h so it takes 3 hours so 2:35

The unknown angles in the circle are as follows:

a. m∠AEB = 73°

b. arc angle VW = 155°

a.

If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.

Therefore,

m∠AEB = 1 / 2 (99 + 47)

m∠AEB = 146 / 2

m∠AEB = 73 degrees

b.

If two secants intersect outside a circle , then the measure of an angle formed by the two lines is one half the positive difference of the measures of the intercepted arcs .

Therefore,'

arc angle VW = x

55 = 1 / 2 (x - 45)

55 = 0.5x  - 22.5

0.5x = 55 + 22.5

0.5x = 77.5

divide both sides by 0.5

x = 77.5 / 0.5

x = 155 degrees

Therefore,

arc angle VW = 155 degrees

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Answer:

301.4 in^3

Step-by-step explanation:

Divide 12 by 2 to get the radius

12/2=6

Square 6 and multiply by 3.14 according to the area of a circle formula πr^2.

6^2=36 36*3.14=113.04

We now have the area of the base.

Multiply it by the height and divide by three to follow the formula for the volume of a cone, 1/3bh.

113.04*8=904.32. 904.32/3= 301.44, or 301.4 after rounding.