z varies directly with x and inversely with y2.
When x = 2 and y = 5, z = 8.
What is the value of z when x = 4 and y = 9?

Steps to solve:

5a - 2(-3a + b)

~Distribute

5a + (-2 * -3a) + (-2 * b)

~Simplify

5a + 6a - 2b

~Simplify

11a - 2b

Best of Luck!

Answer:

2,674.14 g

Step-by-step explanation:

Recall that the formula for radioactive decay is

N = N₀ e^(-λt)

where,

N is the amount left at time t

N₀ is the initial amount when t=0, (given as 42,784 g)

λ = coefficient of radioactive decay

  = 0.693 ÷ Half Life

  = 0.693 ÷ 18

  = 0.0385

t = time elapsed (given as 72 years)

e = exponential constant ( approx 2.7183)

If we substitute these into our equation:

N = N₀ e^(-λt)

= (42,787) (2.7183)^[(-0.0385)(72)]

= (42,787) (2.7183)^(-2.7726)

=  (42,787) (0.0625)

= 2,674.14 g

Final answer:

After 72 years, which corresponds to 4 half-lives of the curium with a half-life of 18 years, the remaining amount of a 42,784 gram sample would be 2,674 grams, as it halves every 18 years.

Explanation:

The question asks how much of a radioactive sample of curium, with an initial mass of 42,784 grams and a half-life of 18 years, will remain after 72 years. To answer this, we apply the concept of radioactive decay, which follows a geometric sequence where the quantity of a radioactive substance halves every half-life period.

In this scenario, 72 years consist of 4 half-lives (since 72 ÷ 18 = 4). Therefore, after each half-life, the mass of the curium would be reduced by half. Following the sequence:

After 18 years, half of the 42,784 grams would remain, which is 21,392 grams.

After 36 years, half of that would remain, becoming 10,696 grams.

After 54 years, again half of that would remain, so 5,348 grams.

Finally, after 72 years, halving once more, we would be left with 2,674 grams.

The amount of curium remaining after 72 years is 2,674 grams.

Answer:

[tex]\frac{-19}{2}[/tex]

Step-by-step explanation:

[tex]\frac{5}{4}[/tex] + [tex]\frac{-43}{4}[/tex] = [tex]\frac{-19}{2}[/tex]

Answer:

C

Step-by-step explanation:

We can solve simultaneous equations using substitution method, elimination method or graphical method. But for this purpose, we will be using the elimination method.

3x+4y=8 Equation 1

2x+y=42 Equation 2

Multiply Equation 1 by 2 and equation 2 by 3, so as to get the same coefficient for x

2(3x+4y=8)= 6x+8y=16 Equation 3

3(2x+y=42)= 6x+3y=126 Equation 4

Subtract equation 4 from 3, to eliminate x

6x-6x=0

8y-3y= 5y

16-126= -110

We now have 5y=-110

Divide both sides by 5,

y= -110/5

= -22

Substituting for y in equation 2

2x+(-22)= 42

2x= 42+22

2x=64

x= 64/2

= 32

(x, y)

(32, -22)

Answer:

D

Step-by-step explanation:

To find two unknowns, you need atleast two different equations.

Answer:

9.57 inch

Step-by-step explanation:

(4/3)×pi×8³ = 14×16×h

h = (4/3)×pi×8³ ÷ (14×16)

h = 64pi/21 inch

Or, 9.57 inch (3 sf)

Answer:

47 degrees

Step-by-step explanation:

The interior angles of a triangle always equal 180 degrees, so add the other angles together and subtract that from 180

31+102= 133

180-133=47

Answer:

47

Step-by-step explanation:

Answer:

The Answer is A. 252π ft3

Step-by-step explanation:

Hence volume of shaded sphere is  [tex]113.09734ft^{2}[/tex]

What is Volume?

Volume refers to part inside 3 d figure which tell how much space it occupies.

How to solve?

Given two concentric spheres  one with D=12 ⇒ R= 6 feet other with r=3feet.

volume of shaded part[tex]=\frac{4}{3} \pi R^{3}-\frac{4}{3} \pi r^{3}[/tex]

[tex]=\frac{4}{3} \pi (R-r)^{3}[/tex]

[tex]=\frac{4}{3} \pi 3^{3}[/tex]=[tex]113.09734[/tex][tex]ft^{2}[/tex]

Hence volume of shaded sphere is  [tex]113.09734ft^{2}[/tex]

Learn more about volume

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Answer:

150000

Step-by-step explanation:

Answer:

150,000‬

Step-by-step explanation:

Answer:

See explanation

Step-by-step explanation:

Let the given equation be:

[tex]5 {x}^{2} - 400 = 0[/tex]

This implies that:

[tex]5 {x}^{2} = 400[/tex]

Divide through by 5 to get;

[tex] {x}^{2} = 80[/tex]

Take square root to obtain:

[tex]x = \pm \sqrt{80} [/tex]

This implies that

[tex]x = \pm4 \sqrt{5} [/tex]

[tex]x = - 4 \sqrt{5} \: or \: x = 4 \sqrt{5} [/tex]

Answer:15/8

Step-by-step explanation:

Answer:

15/8

Step-by-step explanation:

Cross multiply, 8x=15. Divide by 15 on both sides, 15/8 is your answer.

Answer:

3 3/7 hours

Step-by-step explanation:

(8×6)/(8+6) = 48/14 = 3 3/7 hours

In math, a loss of $20 is represented by the negative integer -20. The negative in front of the 20 represents the loss or decrement.

In mathematics, integers are whole numbers that can be either positive, negative, or zero. When we talk about a loss or decrement of something, it's universally symbolized with a negative integer.

In case of a loss of $20, it is represented as -20, where the negative sign indicates the loss or subtraction of money.

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Answer:

RS = 15 and RT = 18, then ST = 3!   :D

Step-by-step explanation:r = 1 --> s=15 & t=18 so st = 270

r = 3 --> s = 5 & t = 6 so st = 30

r = 5 --> s = 3 & t = 3.6 so st = 10.8

etc

==============

In literal terms:

s = 15/r

t = 18/r

Step-by-step explanation:

Answer:

[tex]2.25\ in^{2}[/tex]

Step-by-step explanation:

Area of a square is given by

[tex]A=b*b=b^{2}[/tex]

Where A is area and b is the length of any side. This question has only one thing that is square in shape, the mat hence the question directly requires its area.

Given that the mat has square shape and has dimensions of 1.5 in each then the area will be

A=1.5*1.5=2.25 square inches

Therefore, the area is 2.25 square inches.

Answer:

Step-by-step explanation:

Answer:

D(4) = -18

Step-by-step explanation:

D(n) = D(n – 1)(-6)

D(1) = 1/12

D(2) = D(2 – 1)(-6)

D(2) = D(1)(-6)

D(2) = 1/12 * (-6)

D(2) = -6/12

D(2) = -1/2

D(3) = D(3 – 1)(-6)

D(3) = D(2)(-6)

D(3) = -1/2 * (-6)

D(3) = 6/2

D(3) = 3

D(4) = D(4 – 1)(-6)

D(4) = D(3)(-6)

D(4) = 3 * (-6)

D(4) = -18

Answer:

D(4) = -18

Step-by-step explanation:

Answer:

1hr=60minutes

ATQ,20 minutes/60 minutes=1/n

1/3=1/n

so the value of n is 3...

Step-by-step explanation: Hope i helped please give brainliest!

Answer:

-2/3

[tex]\sqrt50[/tex]

-1

-2.3145

Step-by-step explanation:

Answer:

-2/3

\sqrt50

-1

-2.3145

Step-by-step explanation:

please brainlist!

Answer:

10 bows

Step-by-step explanation:

Each bow is 0.5 yards and you have 5 yards of ribbon. In equation form (where x = number of bows), that looks like: 0.5 * x = 5. Solve for x and you'll get x = 10.

This mathematics problem can be solved by multiplication. Since each bow requires half a yard of ribbon, each yard can produce two bows. Therefore, five yards of ribbon can produce 10 bows.

The question requires us to determine how many bows we can make with a given number of yards of ribbon. Since it takes half a yard of ribbon to make a bow, you can fit two bows in a single yard. To find how many bows can be made with 5 yards, you can perform multiplication.

To do this, you would multiply the number of yards by 2, since each yard can create two bows: 5 yards × 2 = 10 bows. So, you can make 10 bows out of 5 yards of ribbon.

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Well, there can be three different steps.

Rearrange the equation so "y" is on the left and everything else on the right.

Plot the "y=" line (make it a solid line for y≤ or y≥, and a dashed line for y< or y>)

Shade above the line for a "greater than" (y> or y≥) or below the line for a "less than" (y< or y≤).

The average value of f(x) = 3x sin(x) on the interval [tex]\( 1 \leq x \leq 7 \) is approximately \( -1.6204 \).[/tex]

To find the average value of a function f(x) on a closed interval [a, b], we use the formula:

[tex]\[ \text{Average value} = \frac{1}{b - a} \int_{a}^{b} f(x) \, dx \]In this case, the function \( f(x) = 3x \sin(x) \) and the closed interval is \( 1 \leq x \leq 7 \).So, the average value of \( f(x) \) on the interval \( 1 \leq x \leq 7 \) is:\[ \text{Average value} = \frac{1}{7 - 1} \int_{1}^{7} 3x \sin(x) \, dx \][/tex]

[tex]\[ \text{Average value} = \frac{1}{6} \int_{1}^{7} 3x \sin(x) \, dx \][/tex]

Now, we need to compute the integral. We can do this using integration by parts:

[tex]Let \( u = 3x \) and \( dv = \sin(x) \, dx \).Then, \( du = 3 \, dx \) and \( v = -\cos(x) \).Using the integration by parts formula:\[ \int u \, dv = uv - \int v \, du \]\[ \int_{1}^{7} 3x \sin(x) \, dx = \left[ -3x \cos(x) \right]_{1}^{7} - \int_{1}^{7} (-\cos(x)) \cdot 3 \, dx \][/tex]

[tex]\[ = \left[ -3x \cos(x) \right]_{1}^{7} + 3 \int_{1}^{7} \cos(x) \, dx \]\[ = \left[ -3x \cos(x) \right]_{1}^{7} + 3 \left[ \sin(x) \right]_{1}^{7} \]\[ = \left[ -21 \cos(7) + 3 \sin(7) \right] - \left[ -3 \cos(1) + 3 \sin(1) \right] \][/tex]

Now, let's compute these values:

[tex]\[ \text{Average value} = \frac{1}{6} \left[ \left( -21 \cos(7) + 3 \sin(7) \right) - \left( -3 \cos(1) + 3 \sin(1) \right) \right] \]\[ \text{Average value} = \frac{1}{6} \left[ (-21 \times 0.7539 + 3 \times 0.6560) - (-3 \times 0.5403 + 3 \times 0.8415) \right] \]\[ \text{Average value} = \frac{1}{6} \left[ (-15.8359 + 1.9680) - (-1.6209 + 2.5245) \right] \][/tex]

[tex]\[ \text{Average value} = \frac{1}{6} \left[ -13.8679 + 4.1454 \right] \]\[ \text{Average value} = \frac{1}{6} \times (-9.7225) \]\[ \text{Average value} \approx -1.6204 \][/tex]

So, the average value of f(x) = 3x sin(x) on the interval [tex]\( 1 \leq x \leq 7 \) is approximately \( -1.6204 \).[/tex]

The average value of [tex]\(f(x) = 3x \sin(x)\)[/tex] on the interval [tex]\(1 \leq x \leq 7\)[/tex] is approximately 1.879.

To find the average value of [tex]\( f(x) = 3x \sin(x) \)[/tex]on the closed interval [tex]\( 1 \leq x \leq 7 \)[/tex], we can use the formula for the average value of a function on a closed interval [a, b] :

[tex]\[ \text{Average value} = \frac{1}{b - a} \int_a^b f(x) \, dx \][/tex]

In this case, a = 1 and b = 7, so:

[tex]\[ \text{Average value} = \frac{1}{7 - 1} \int_1^7 3x \sin(x) \, dx \][/tex]

Now, we need to evaluate the integral:

[tex]\[ \int_1^7 3x \sin(x) \, dx \][/tex]

This integral can be evaluated using integration by parts or by using a software tool. After evaluation, we find that the average value is approximately 1.879.

So, the correct answer is 1.879.

Complete Question:

Let f be the function given by f(x)=3xsinx. What is the average value of f on the closed interval 1≤x≤7 ?

−14.764

−2.461

1.879

8.161

To determine the length of ZY for it to be a tangent to circle X at point Y, we must know additional measurements, such as the radius of the circle, because a tangent is perpendicular to the radius at the point of tangency.

To determine the length of ZY so that it is tangent to circle X at point Y, we need to apply properties of tangents to a circle. A tangent to a circle forms a right angle with the radius at the point of tangency. Therefore, in a right-angled triangle, with the radius XY being one side and ZY being the hypotenuse, we could use the Pythagorean theorem if we know the length of the radius and any other segment connected to the radius or tangent.

Without further information, such as the length of radius XY or any other segment, it's not possible to calculate the exact length of ZY. However, the essential condition is that radius XY must be perpendicular to the tangent ZY at point Y for ZY to be a proper tangent.

Answer:

60ft

Step-by-step explanation:

you havent multiplied it by [tex]\pi[/tex] yet do it would just be the radius multiplied by two so it would be 60, becuase the radius is 30.

C= 2[tex]\pi[/tex]r

By using the formula (Area = Length x Width) we can rearrange the equation to find the height of the rectangular poster. It comes out to be 4 feet.

To answer your question, we must use the formula for the area of a rectangle, which is Area = Length x Width. Here, the area of the poster is given as 38 square feet and the width is 9.5 feet. The length is what we're trying to find. We can set this up as an equation 38 = Length x 9.5. To find the Length, we divide both sides of the equation by 9.5 resulting in Length = 38 ÷ 9.5. Solving the equation gives us a length of approximately 4 feet. So, the 'height' of the poster would be 4 feet.

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Answer:

29.33π cm³  or 92.10 cm³

Step-by-step explanation:

To find the volume of a cone with height 5.5 and radius 4, we will simply use the formula;

volume of a cone = [tex]\frac{1}{3}[/tex] π r² h

h = 5.5  and r= 4, we will simply plug in these values into our formula

volume of a cone  =  [tex]\frac{1}{3}[/tex]   ×  π   × (4)² (5.5)

                               = [tex]\frac{1}{3}[/tex]  ×π × 16 × 5.5

                                =88π   /  3

                                 =29.33π

volume of cone = 29.33π

But π= 3.14

plugging in π=3.14, we have;

volume of cone = 29.33(3.14)=29.10

Answer:

88/3

Step-by-step explanation:

i just did the assignment

Answer:

D. 2 1/4

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

9 pies/4 friends =

9/4 = 2 1/4

D

Answer:

$36

Step-by-step explanation:

The amount spent on cloths is 1/3

The amount earned from washing the car is $5

Amount at the end of the week is $29

Let the amount earned that week be x

Then amount spent on cloths = 1/3x

so the equation is

x- 1/3 x+$5=$29

2/3 x=29-5

2/3 x= 24

x=(24*3)/2= $36

The volume of the given rectangular prism is option C. [tex]24 un^{3}[/tex].

Step-by-step explanation:

Step 1:

The dimensions of the given rectangular prism are 4 units × 3 units × 2 units.

So we take the length equals 4 units, the width is equal to 3 units and the height is 2 units.

Step 2:

The volume of this rectangular prism is calculated by multiplying the given prism's length, its width, and its height.

The Volume of the given rectangular prism = [tex]( Length) (Width) (Height) = (4units) (3units) (2 units) = 24 unit^{3} .[/tex]

So the given right rectangular prism's volume is [tex]24 unit^{3}[/tex] which is option C.