Mr. D'Alton made some radium in his lab. He used 2 kg of the radium every time he
ran his experiment. If he did the experiment four times and had 24 kg left, how much
radium did Mr. D'Alton make at first?​

The value of every variable in the parallelogram is: a = 9 HK = 27.0 GK = 46 G = 63.5°

A parallelogram is a special type of quadrilateral that has both pairs of opposite sides parallel and equal.These shapes include squares, rectangles, rhombuses, and rhomboids. All of these shapes have four sides, four corners, and four angles

We know that sides of a parallelogram are parallel and congruent, as opposite angle

According to question  that GA equals HK, as:

46 is equal to 3a plus 19 When we subtract 19 from both sides, we get:

27 x 3a is the result of dividing both sides by 3:

we know that opposite angles in a parallelogram are congruent, we can use a = 9. Since angle H is 56 degrees, angle K must also be 56 degrees. The length of side HK can be determined using the Law of Cosines:

HK2 = GA2 + GK2 - 2(GA)(GK)cos(H) When we substitute the values we are familiar with, we obtain:

After solving the equation we obtain: HK2 = 462 + (3a + 19)2 - 2(46)(3a + 19)cos(56°).

HK2 = 2112 + 9a2 + 342a - 2764cos(56°) HK2 = 2112 + 9(9)2 + 342(9) - 2764cos(56°) HK2  732.4 By taking the square root of both sides, we obtain the following results:

∵ GA = 46, we can use the parallelogram's opposite sides being congruent to determine the length of side GK: HK  27.0

Then, we can use the Law of Cosines to determine the angle G's measurement:

cos(G) = (HK2 + GA2 - GK2) / (2(HK)(GA)) Using the values we are familiar with, we get,

cos(G) = (27.02 + 462 - 462) / (2(27.0)(46)) cos(G)  0.465 Using the inverse cosine, we get the following:

G ≈ 63.5°

Hence, the worth of every variable in the parallelogram is:

a = 9 HK = 27.0 GK = 46 G = 63.5°

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Answer:

C, adding -1 1/5 to the coordinate of point J

Step-by-step explanation:

J= 1 1/5

1 1/5+(-1 1/5)

- use the distributive property

- positive x negative # = negative #

1 1/5 - 1 1/5

= 0

Answer:

\(v = 252mm ^{3} \)

Step-by-step explanation:

hope it helps you

have a great day

Answer:

hey! sis.

...............

The fixed cost per ball went to $4.5 when the company produce 22,500.

fixed cost per ball is three dollars when the company produces 15,000

fixed cost per ball went x to produce 22,500

So,

3 : 15000 = x : 22,500

3/15,000 = x/22,0/500

cross product

3 × 22,500 = 15,000 × x

67,500 = 15,000x

divide both sides by 15,000

x = 67,500 /15,000

x = 4.5

Therefore, the fixed cost per ball to produce 22,500 is $4.5

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Answer:

x = 148

Step-by-step explanation:

vertical angles are congruent

the angle with a measure of 148° and the angle labeled "x" are vertical angles.

Hence, x = 148

Answer:

x=148 because the opposite angles are equal

also, the rest of the smaller angles are both 32 degrees if you need them

you can check because 148+148+32+32=360

hope it helps:)

Answer:

8

Step-by-step explanation:

3/4 = 6/8

Answer:

8 cause common can be like

Answer:

tyyyyy for free points have a great day

3172.97 joules is the value of x when the Richter scale rating is 3.2

The equation that relates earthquake magnitude (M) and energy (E) is:

M = 2/3 × log(E) - 1.8

We have to find the value of X when the richer scale rating is 3.1

If an earthquake with a rating of 3.2 is not usually felt, then we can assume that x corresponds to the energy released by an earthquake that is just barely felt.

According to the United States Geological Survey, an earthquake with a magnitude of 2.5 corresponds to an energy release of about 1.3 × 10⁸ joules.

Using this as a reference point, we can set up the following equation:

3.2 = 2/3 × log(x) - 1.8

Solving for x, we get:

2.3 = 2/3 × log(x)

log(x) = 3.45

x = 3172.97

Therefore, the value of x when the Richter scale rating is 3.2 is approximately 3172.97 joules.

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Answer:

Part A: $3,415.50

B: 11.34%

Step-by-step explanation:

Part A: $31,000 is within the values 10,276≤x≤41,175, so use f(x)=0.12x-205.50

Part B: For the effective tax rate, divide the amount in part A by the taxable income

Part C: Compare both the taxable income and the effective tax rate to the income domains given and the % multiplier. This one is mostly about how you describe the situation, so I'll leave that up to you.

To calculate the taxes owed on a taxable income of $31,000, we use the appropriate equation for the tax bracket it falls into and substitute the value of x. The effective tax rate is calculated by dividing the amount of taxes owed by the taxable income and multiplying by 100. The piecewise function represents the marginal tax rate chart by using different equations for each tax bracket.

Part A:

To calculate the amount of taxes owed on a taxable income of $31,000, we need to determine which tax bracket it falls into. Since $31,000 is greater than $10,275 but less than $41,175, it falls into tax bracket 2. To find the amount of taxes owed, we use the equation for tax bracket 2: f(x) = 0.12x - 205.50. Plugging in $31,000 for x, we get:

f(x) = 0.12 * 31000 - 205.50 = $3,574.50

Therefore, the amount of taxes owed on a taxable income of $31,000 is $3,574.50.

Part B:

To determine the effective tax rate, we divide the amount of taxes owed by the taxable income. Using the result from Part A (taxes owed = $3,574.50) and the taxable income of $31,000, we have:

Effective tax rate = (taxes owed / taxable income) * 100 = (3,574.50 / 31,000) * 100 ≈ 11.52%

Therefore, the effective tax rate on a taxable income of $31,000 is approximately 11.52%.

Part C:

The piecewise function represents the amount of taxes owed as a function of the taxable income. Each part of the function corresponds to a different tax bracket, with the equation for that tax bracket. The marginal tax rate chart is represented in the piecewise function by the different equations for each tax bracket. For example, the equation in part 1 of the function (f(x) = 0.10x) corresponds to the 10% marginal tax rate for the tax bracket $0-$10,275.

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The fence in dead center is about 399 feet from the third base.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

For the triangle in this problem, we have that:

Hence the distance is obtained as follows:

d² + 90² = 409²

\(d = \sqrt{409^2 - 90^2}\)

d = 399 ft.

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The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Answer:

12.8 or option 3

Step-by-step explanation:

So this is actually a proportion:

The large triangle to the smaller one:

The angles of the triangles are the same so they are proportional

We know the larger one is 20/8 times the smaller one's sides because

YZ =  something times QR so:

20 = 8 times 20/8

In order to find PR, we have to divide ZX by the proportion rate thing so:

32 / (20/8)

= 32 * 8/20

= 64/5

= 12.8

Answer:

right

left

up

down

Step-by-step explanation:

Answer:

right

left

up

down

Step-by-step explanation:

Given:

Given that a diagram.

Required:

To name all the angles that equal to 90 degrees in the given diagram.

Explanation:

The 90 degree angles are,

Final Answer:

Answers:

8

6

1

3

Reason:

Add 5 to each value in the f(x) column.

Example: 3+5 = 8 for the first row.

This will shift each point 5 units up. This is because we're moving 5 units up the y axis.

Answer:

x = 3.25

Step-by-step explanation:

Use the Rule of 3 to solve this

Work in picture

Answer:

the comedy films, action and horror is 14, 49 and 7 respectively

Step-by-step explanation:

The computation of each one dvds is as follows;

Total dvds is 70

Now the ratio of comedy films to action to horror is 2:7:1

So the total of 10

Now the each one dvds is

For comedy flms

= 70 × 2 ÷ 10

= 14

For actions

= 70 × 7 ÷ 10

= 49

For horror

= 70 × 1 ÷ 10

= 7

Hence the comedy films, action and horror is 14, 49 and 7 respectively

The probability that a randomly selected point within the square falls in the red shaded square is 1/16

A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event to occur is 1 and it is 100% in percentage.

Probability = sample space /total outcome

sample space is the area of the red shaded square and the total outcome is the big square.

Area of red shaded square = 1 × 1 = 1unit²

area of the big square = 4 × 4 = 16 units²

Therefore the probability that a point selected falls on the red shaded square

= 1/16

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Hello there.

To answer this question, we'll use the information given by the question: the size of the cylinder given by the bore measure, the height given by the stroke size and the volume of the engine will be found multiplying that measure by the number of cylinders;

First, we'll find the size of a cylinder:

Given the bore size and the height, we can calculate the volume of just one cylinder, using the formula: pi * r^2 * h or pi * (d/2)^2 * h.

In this case, knowing that the bore size is equal to the diameter, we'll use the second formula:

pi * (4.25/2)^2 * 3.76

Using the approximation for pi, we get: 53,313275 in³

Now, multiplying by the number of cylinders, we get: 426,5062 in³.

Rounding up to the nearest hundreth, we may get 426.50 in³.

Answer:

??

Step-by-step explanation:

It is impossible

Answer: The dimensions of the gray rectangle is 1m by 12m.

Step-by-step explanation:

If you find out the perimeter of the pink square, you can use the same concept to find the dimensions of the gray rectangle:

Perimeter=(L+W)*2

Substitute it: (6+7)*2=13*2=26

Now basically do trial and error: 1*12=12m

Check it: (1+12)*2=13*2=26

In conclusion, the dimensions of the gray rectangle is 1m and 12m.

Answer:

37

Step-by-step explanation:

Before we find quartile, we have to arrange the data set in order first from least to greatest which this problem has already arranged the data for us.

Next, proceed with the calculation. The formula for finding position of quartile is:

\(\displaystyle{Q_r = \dfrac{r(N+1)}{4}}\)

Where \(\displaystyle{Q_r}\) means the rth quartile, N means number of data set. Since we want to find the third quartile, substitute r = 3 and there are 11 data so substitute N = 11:

\(\displaystyle{Q_3 = \dfrac{3(11+1)}{4}}\\\\\displaystyle{Q_3 = \dfrac{3(12)}{4}}\\\\\displaystyle{Q_3 = 3\cdot 3}\\\\\displaystyle{Q_3 = 9}\)

So the position of third quartile is at 9th position which is 37.

Henceforth, the third quartile is 37.

Answer:

37.

Step-by-step explanation:

The data is in ascending order, which is what we need to get the answer.

As there are 11 numbers the 9th number is the upper(third)  quartile.

The median ( middle) number is 29 and the upper quartile is the middle number of the 5 numbers to the right of the median.

It is 37.

Solving by substitution method.

If we clear y in equation 1, we get:

Now, if we substitute this result into equation 2, we have

By clearing parenthesis, we get 3x+3+x=-1.

Now, by combining similar terms, we obtain

If we move +3 to the right hand side as -3, we have

Finally, by substituting this result into out first equation, we get

Therefore, the solution of the system is x=-1 and y=2.

The answer of the question based on remainder and factor theorem is (1) The correct answer is (C) f(5) = -1. , (2)  The correct answer is (d) h(-3) = 10. , (3) (a) = True , (b) =False , (c) True , (d) = True.

The factor theorem is a theorem in algebra that states that if a polynomial f(x) has a factor (x - a), then f(a) = 0. In other words, if a is a root of the polynomial (i.e., if (x - a) is a factor), then substituting a for x in the polynomial will result in a value of 0.

(1) The correct answer is (C) f(5) = -1.

The remainder theorem states that when a polynomial f(x) is divided by (x-a), the remainder is equal to f(a). Therefore, in this case, when f(x) is divided by (x-5), the remainder is -1, which means that f(5) = -1.

(2) The correct answer is (d) h(-3) = 10.

When h(x) is divided by (x+3), the remainder theorem states that the remainder is equal to h(-3), which can be found by substituting -3 for x in the expression for h(x) and simplifying.

(3) Based on the completed synthetic division provided, we can check the following statements:

The quotient is equal to -2x²+2x-5. (True)

The quotient is equal to 2x² - 2x + 5. (False)

(x-1) must be a factor of the starting function. (True, since the final remainder is zero after synthetic division by (x-1))

If the starting function is f(x), then f(-1) = 0. (True, since (-1) is one of the divisors used in the synthetic division, and the final remainder is zero)

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According to the information, the perimeter of the triangle is ≈ 31.18

To find the distance between two points, we can use the distance formula:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Let's label the coordinates as follows:

Point 1: (-2, 3)

Point 2: (3, -2)

Now we can substitute these values into the distance formula:

distance = sqrt((3 - (-2))^2 + (-2 - 3)^2)

distance = sqrt((5)^2 + (-5)^2)

distance = sqrt(25 + 25)

distance = sqrt(50)

distance ≈ 7.07

Therefore, the distance from (-2, 3) to (3, -2) is approximately 7.07 units.

To find the perimeter of the triangle, we need to find the length of all three sides of the triangle and then add them up.

Using the distance formula, we can find the length of the sides:

Side 1: (-2,3) to (3,-2)

d = √[(3 - (-2))^2 + (-2 - 3)^2]

= √[5^2 + (-5)^2]

= √50

= 5√2

Side 2: (3,-2) to (-7,-2)

d = √[(-7 - 3)^2 + (-2 - (-2))^2]

= √[(-10)^2 + 0^2]

= 10

Side 3: (-7,-2) to (-2,3)

d = √[(-2 - (-7))^2 + (3 - (-2))^2]

= √[5^2 + 5^2]

= 5√2

Therefore, the perimeter of the triangle is:

5√2 + 10 + 5√2 = 15√2 + 10 ≈ 31.18 (rounded to two decimal places)

An two of the three sides are equal, so it is an isosceles triangle.

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Answer:

x = 3.75

y= 0.5

Step-by-step explanation:

2x and 3y and 6

2x and y and 7

the difference between those two is 2y and 1

because 3y-y = 2y and 7-6 = 1

2y=1    y = 0.5

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

2x - 3 = 6 is also 6 + 3y = 2x

3(0.5) = 1.5

6 + 1.5 = 75.5

2x = 7.5

x= 3.75

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

check:

2(3.75) = 7.5

3(0.5) = 1.5

7.5-1.5 = 6

2(3.75) = 7.5

y= (0.5)

7.5-0.5= 7

Answer:  You will have points plotted at +3 on the y axis, and +3 on the x axis.

The attachment shows what your graph should look like.

Step-by-step explanation:

The intercept is where the graphed line crosses an axis.

To find the y-intercept, substitute 0 for x and solve for y:

0 + y = 3.  Subtracting 0, you have y = 3

So you can plot a point at +3 on the y axis.

To find the x- intercept, substitute 0 for y, and solve for x

x + 0 = 3  Again, subtracting 0, x = 3

So plot a point on the x-axis at +3

Use the line tool to connect the two points.

Answer:

given,

selling price (sp)=rs 5 ×30

=rs 150

now, gain %=20%

cost price (cp)=

\( \frac{sp \times 100}{100 + gain\%} \)

\( = \frac{150 \times 100}{100 + 20} \)

therefore cp= rs125

now,

again in 2nd case

sp= rs 27×5

therefore sp=rs 135

and cp= rs125

now, sp>cp so,

\(gain\% = \frac{sp - cp}{cp} \times 100\%\)

or, gain=

\( = \frac{135 - 125}{125} \times 100\%\)

therefore gain %= 8%.... is answer

hope it helps..

Answer:

The warranty the company should use is of 57,520 mile.

Step-by-step explanation:

Let X denote the tread life of a particular brand of tire.

It is provided that,  \(X\sim N(60,000, 1600^{2})\).

Also provided that the company wants 94% of the tires to outlast the warranty.

Let x denote the warranty .

That is, P (X > x) = 0.94.

⇒ P (X < x) = 0.06

⇒ P (Z < z) = 0.06

The corresponding value of z is -1.55.

*Use a z-table.

Compute the value of x as follows:

\(z=\frac{X-\mu}{\sigma}\\\\-1.55=\frac{x-60000}{1600}\\\\x=60000-(1.55\times 1600)\\\\x=57520\)

Thus, the warranty the company should use is of 57,520 mile.

Answer:

\(\dashrightarrow \: { \tt{4 \frac{1}{3} - 8 }}\)

• first express the mixed fraction into an improper fraction:

\(\dashrightarrow \: { \tt{ \frac{(3 \times 4) + 1}{3} - 8}} \\ \\ \dashrightarrow \: { \tt{ \frac{13}{3} - \frac{8}{1} }}\)

• Find the L.C.M of 3 and 1, L.C.M is 3:

\(\dashrightarrow \: { \tt{ \frac{13 - (3 \times 8)}{3} }} \\ \\ \dashrightarrow \: { \tt{ \frac{13 - 24}{3} }} \\ \\ \dashrightarrow \: { \tt{ - \frac{11}{3} }} \\ \\ \dashrightarrow \: { \boxed{ \boxed{ \tt{ \: \: - 3 \frac{2}{3} }}}}\)

\(\\ \sf\longmapsto 4\dfrac{1}{3}-8\)

\(\\ \sf\longmapsto \dfrac{3(4)+1}{3}-8\)

\(\\ \sf\longmapsto \dfrac{12+1}{3}-8\)

\(\\ \sf\longmapsto \dfrac{13}{3}-8\)

\(\\ \sf\longmapsto \dfrac{13-24}{3}\)

\(\\ \sf\longmapsto \dfrac{-11}{3}\)

\(\\ \sf\longmapsto -3\dfrac{2}{3}\)