A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a radioactive substance. After 20 hours, 55 mg of the substance remains. How many milligrams will remain after 26 hours

The relation between the variables in the equation x^4/y=7 is (b) x^4 varies directly as y

The complete question is added as an attachment

From the attached figure, we have the following equation

x^4/y = 7

Multiply both sides of the equation by y

x^4 = 7y

The above represents a direct variation from x^4 to y.

Where 7 represents the variation constant

Hence, the relation between the variables in the equation x^4/y=7 is (b) x^4 varies directly as y

Read more about direct variation at:

https://brainly.com/question/12179965

#SPJ1

Answer:

222

Step-by-step explanation:

Hey there!

250 - {(135 + 34) ÷ (46 - 33)} - 15 

= 250 - 169/(46 - 44) - 15

= 250 - 169/13 - 15

= 250 - 13 - 15

= 237 - 15

= 222

Therefore, your answer should be:

222

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

C)  x = 3

Step-by-step explanation:

Given equation:

[tex]5^x=125[/tex]

Rewrite 125 with base 5:  125 = 5³

[tex]\implies 5^x=5^3[/tex]

[tex]\textsf{Apply the one-to-one property of exponents}: \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x)[/tex]

[tex]\implies x=3[/tex]

Excel uses VAR function for determining the residual variance.

The variation of any error is known as residual variance, also known as unexplained variance or error variance.

Depending on the type of analysis you're doing, the precise definition will vary. For instance, random fluctuations in regression analysis produce volatility around the "actual" regression line.There are two components to a regression line's total variance: variation that can be explained and variance that cannot. Simply put, the residual variance after deducting the variation resulting from the regression from the total variance of the dependent variable is the residual variance.

Learn more about residual variance here:

https://brainly.com/question/27464491

#SPJ4

Answer:

h(x) = 6x² - 10x - 4

Step-by-step explanation:

h(x) = f(x) g(x)

       = (2x - 4)(3x + 1)

each term in the second factor is multiplied by each term in the first factor, that is

2x(3x + 1) - 4(3x + 1) ← distribute parenthesis

= 6x² + 2x - 12x - 4 ← collect like terms

= 6x² - 10x - 4

that is h(x) = 6x² - 10x - 4

Answer:

y = |x + 8|

Explanation:

Please see the table attached below.

Answer:y=|x+8|

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

The number of times that Derrick batted last season is 188 times.

Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred. Percentage is a measure of frequency. The sign used to denote percentage is %.

A percentage of 25% here means that twenty five times out of hundred times, Derrick hit the ball. In order to convert a percentage to a decimal, divide the percentage by 100.

Number of times Derrick bat last season = Number of hits last season / percentage of his batting average

47 / 25%

47 / 0.25 = 188

To learn more about percentages, please check: https://brainly.com/question/25764815

#SPJ1

Answer:

8(3j - 2).

Step-by-step explanation:

24j-16

GCF = 8

so the answer is

8(3j - 2).

1) Correct.

2) The y-intercept is when x=0, so it is (0,5).

Answer:

Quadrant II

Step-by-step explanation:

This is because the top right is I, the top left

is II, the bottom left is III, and the bottom right is IV.

Answer:

y=0.75x+3.75

Step-by-step explanation:

The slope is

[tex] \frac{6 - 4.5}{3 - 1} = \frac{3}{4} [/tex]

Substituting into point-slope form,

y - 6 = 0.75(x - 3)

y - 6 = 0.75x - 2.25

y = 0.75x + 3.75

Answer:

w = ±[tex]\sqrt{1/2}[/tex] or w= ±[tex]\sqrt{2}[/tex]

Step-by-step explanation:

if we say some variable y = w^2, we can rewrite the equation to:

2y^2 - 5y + 2 = 0

this can be factored into (2y-1)(y-2) = 0

putting w^2 back in the place of y, that's (2w^2 - 1)(w^2 - 2) = 0

The equation is a fourth degree polynomial, so there are four roots, or four values of w that will cause the equation to equal 0.

If 0 is multiplied by anything, the result is 0, so we set 2w^2 - 1 = 0 and solve for w, which is ±√1/2, then set w^2 - 2 = 0 to get w = ±√2 as our roots

the four solutions are ±√1/2 and ±√2

(because the positive counts as one solution and the negative another solution)

Answer: [tex]110^{\circ}[/tex]

Step-by-step explanation:

[tex]m\angle 20=62^{\circ}[/tex] (linear pair)

[tex]m\angle 11=70^{\circ}[/tex] (angle sum in a triangle)

[tex]m\angle 12=110^{\circ}[/tex] (linear pair)

On the number line the position of point F is at point 4.

According to the statement

We have a given that the on a number line , point D is at -3, and point E is at 6. The point F lies on the ratio of to is 2 : 3.

and we have to find the F point on the number line.

Firstly,

Number line is a line on which numbers are marked at intervals, used to illustrate simple numerical operations.

So, According to given information,

Point D is at -3, and point E is at 6.

Ratio of point E to F = 6*2/3

Then

Ratio of point E to F = 6*2/3

After solving it

The point F = 2*2

The point F = 4.

So, On the number line the position of point F is at point 4.

Learn more about number line here https://brainly.com/question/12399107

#SPJ4

1) [tex]\overline{JK} \perp \overline{MN}[/tex]

2) [tex]\angle JKM[/tex] is a right angle (perpendicular lines form right angles)

3) [tex]\triangle JKM[/tex] is a right triangle (definition of a right triangle)

4) [tex]\angle 1[/tex] and [tex]\angle 2[/tex] are complementary (the acute angles of a right triangle are complementary)

The lateral and total surface areas of the given cone are 753.98 cm² and 1206.31 cm² respectively.

A cone has a height 'h', radius 'r', and slant height 'l'.

The slant height of the cone is obtained by the Pythagorean theorem. I.e.,

l² = h² + r²

Then,

Its lateral surface area(LSA) = πr([tex]\sqrt{h^2+r^2}[/tex]) square units and

Its total surface area(TSA) = πr(r + l) square units

It is given that,

A cone has a height h = 16 cm and radius r = 12 cm

Then, the slant height is calculated by

l² = h² + r²

l  = [tex]\sqrt{h^2+r^2}[/tex]

On substituting,

l = [tex]\sqrt{16^2+12^2}[/tex]

 = [tex]\sqrt{400}[/tex]

 = 20 cm

So,

LSA = πr([tex]\sqrt{h^2+r^2}[/tex])

       = π × 12 × ([tex]\sqrt{16^2+12^2}[/tex])

       = π × 12 × 20

       = 753.98 cm²

and

TSA = πr(r + l)

       = π × 12 × (12 + 20)

       = π × 12 × 32

       = 1206.37 cm²

Therefore, the lateral and total surface areas of the cone with a height of 16 cm and a radius of 12 cm are 753.98 cm² and 1206.37 cm².

Learn more about a right cone and its surface areas here:

https://brainly.com/question/23340582

#SPJ4

Answer: The lateral area is 240π square centimeters. The total surface area is 384π square centimeters.

Step-by-step explanation:

Answer:

-500

Step-by-step explanation:

since 501 has a negative sign,add 1 to to the number,the next number will be -500

-501 +1 = -500

successor in this case means a number that succeeds another

Using a system of equations, the weight of 5 apples, 2 oranges are 4 bananas is given as follows:

B. 1147 gm.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

Considering the data given, the equations are:

From the first equation:

3x = 928 - 5y.

x = 309.33 - 1.667y.

From the second equation:

6z = 1088 - 4y

z = 181.33 - 0.667y

Replacing in the third equation:

5x + 3z = 799

5(309.33 - 1.667y) + 3(181.33 - 0.667y) = 799

10.336y = 12961.64

y = 1291.64/10.336

y = 125 gm.

The other weights are:

The weight of 5 apples, 2 oranges are 4 bananas is:

5x + 2y + 4z = 5 x 101 + 2 x 125 + 4 x 98 = 1147 gm, option B.

More can be learned about a system of equations at https://brainly.com/question/24342899

#SPJ1

Step-by-step explanation:

Use the slope-intercept form to find the slope and y-intercept.

Slope:

−

1

3

y-intercept:

(0 , 3)

Any line can be graphed using two points. Select two

x

values, and plug them into the equation to find the corresponding

y

values

Graph the line using the slope and the y-intercept, or the points.

Slope:

−

1

3

y-intercept:

(0 , 3)

8/9 = 0.888888....

7/18 = 0.388888888889

10/16 = 0.625

Ascending order - means going up, smallest to largest. (Imagine climbing a ladder, where you start of low, then, go higher up the ladder.)

Thus, answer is 7/18, 10/16, 8/9

Hope this helps!

The expressions for the length and the width of the rectangular garden are 3x + 2 feet, and x + 5 feet respectively where x is the length of the square patch for tomatoes.

A square is a quadrilateral with all four sides equal, and all four angles at 90°, whereas a rectangle is a quadrilateral with opposite pair of sides equal, and all four angles at 90°.

In the question, we are informed that Melissa is planning a rectangular vegetable garden with a square patch for tomatoes.

The side of the square is given to be x feet.

We are asked to write expressions for the length and width of the rectangular garden.

For the length of the rectangle:-

We are informed that she wants the length of the garden to exceed three times the length of the tomato patch by 2 feet.

Thus, the length of the garden can be shown as the expression 3x + 2 feet.

For the width of the rectangle:-

We are informed that she also wants the garden's width to exceed the width of the tomato patch by 5 feet.

Thus, the width of the garden can be shown as the expression x + 5 feet.

Thus, the expressions for the length and the width of the rectangular garden are 3x + 2 feet, and x + 5 feet respectively where x is the length of the square patch for tomatoes.

Learn more about writing expressions at

https://brainly.com/question/25956004

#SPJ4

The provided question is incomplete. The complete question is:

"Melissa is planning a rectangular vegetable garden with a square patch for tomatoes. She wants the length of the garden to exceed three times the length of the tomato patch by 2 feet. She also wants the garden's width to exceed the width of the tomato patch by 5 feet.

Let x represent the length, in feet, of the square tomato patch.

Write expressions to represent the length and width of Melissa's vegetable garden in terms of x.

Enter the correct answer in the box."

Answer:

1) [tex]x_1=-1-2\sqrt{2},\ x_2=-1+2\sqrt{2}[/tex]

2) [tex]x_1=\dfrac{-5 - \sqrt{13}}{6},\ x_2=\dfrac{-5 + \sqrt{13}}{6}[/tex]

Step-by-step explanation:

[tex]{\large \textsf{ Quadratic Formula: }}x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\ \Bigg{\|}\ \textsf{when }ax^2+bx+c=0[/tex]

Given quadratic equations:

1. [tex]x^2+2x-7=0[/tex]

2. [tex]4x^2-3=x^2-5x-4[/tex]

1. x² + 2x - 7 = 0

[tex]\implies a=\textsf{1},b=\textsf{2},c=\textsf{-7}[/tex]

Step 1: Substitute the given values into the formula and simplify.

[tex]\begin{aligned}\implies x&=\dfrac{-(\textsf{2})\pm \sqrt{(\textsf{2})^2-4(\textsf{1})(\textsf{-7})}}{2(\textsf{1})}\\\implies x&=\dfrac{-2\pm \sqrt{4-4(-7)}}{2}\\\implies x&=\dfrac{-2\pm \sqrt{4+28}}{2}\\\implies x&=\dfrac{-2\pm \sqrt{32}}{2}\end{aligned}[/tex]

Step 2: Simplify the radicand (under the square root).

[tex]\begin{aligned}x&=\dfrac{-2\pm \sqrt{16\times2}}{2}\\x&=\dfrac{-2\pm 4\times\sqrt{2}}{2}\\x&=\dfrac{-2\pm 4\sqrt{2}}{2}\end{aligned}[/tex]

Step 3: Separate into two solutions and simplify them.

[tex]\implies x_1&=\dfrac{-2 - 4\sqrt{2}}{2},\ x_2&=\dfrac{-2 + 4\sqrt{2}}{2}[/tex]

[tex]\begin{aligned}\implies x_1&=\dfrac{-2}{2}+\dfrac{- 4\sqrt{2}}{2},\ x_2=\dfrac{-2 + 4\sqrt{2}}{2}\\\implies {x_1&=\boxed{-1-2\sqrt{2}},\ x_2=\boxed{-1+2\sqrt{2}} \end{aligned}[/tex]

----------------------------------------------------------------------------------------------------------------

2. 4x² - 3 = x² - 5x - 4

Step 1: Set the equation to zero (by moving the "x² - 5x - 4" to the left).

4x² - 3 - x² + 5x + 4 = 0 [ Combine like terms. ]

3x² + 5x + 4 = 0

[tex]\implies a=\textsf{3},b=\textsf{5},c=\textsf{1}[/tex]

Step 2: Substitute the given values into the formula and simplify.

[tex]\begin{aligned}\implies x&=\dfrac{-(\textsf{5})\pm \sqrt{(\textsf{5})^2-4(\textsf{3})(\textsf{1})}}{2(\textsf{3})}\\\implies x&=\dfrac{-5\pm \sqrt{25-12}}{6}\\\implies x&=\dfrac{-5\pm \sqrt{13}}{6}\end{aligned}[/tex]

Step 3: Separate into two solutions.

[tex]\implies x_1=\dfrac{-5 - \sqrt{13}}{6},\ x_2=\dfrac{-5 + \sqrt{13}}{6}[/tex]

Learn more about quadratic equations here:

brainly.com/question/28123532

brainly.com/question/28063094

Answer:B & E

Step-by-step explanation:

We can first rearrange the function to isolate y. Then, we can find the slope as the function is in the form y=mx+b.

[tex]3x-4y=7\\-4y=-3x+7\\y=\frac{3}{4}x-\frac{7}{4}[/tex]

Since parallel lines have the same slope, we can put the slope of 3/4 into the point slope form to get the answer.

For reference, the point-slope form is [tex]y-y_1=m(x-x_1)[/tex]

[tex]y+2=\frac{3}{4}(x+4)\\y+2=\frac{3}{4}x+3\\y=\frac{3}{4}x+1[/tex]

The first line is found in option E, so option E is one of the correct options.

We can also move the x to the other side, as two of the 5 options have both variables on the left (B and C).

[tex]-\frac{3}{4}x+y=1[/tex]

If we multiply the whole equation by -4, we can get rid of the fraction.

[tex]-4(-\frac{3}{4}x+y)=-4(1)\\3x-4y=-4[/tex]

Hence, option B is also correct.

Answer:

  (c)  5y -17x +99 = 0

Step-by-step explanation:

The median of a triangle is the line through a vertex and the midpoint of the opposite side. The median of ΔXYZ from vertex Y will be the line through point Y and the midpoint of XZ.

The midpoint of XZ is the average of the coordinates of X and Z.

  M = (X +Z)/2

  M = ((1, -2) +(8, -7))/2 = (9, -9)/2 = (4.5, -4.5)

The slope of the median can be found using the slope formula:

  m = (y2 -y1)/(x2 -x1)

The slope of line YM is ...

  m = (-4.5 -4)/(4.5 -7) = -8.5/-2.5 = 17/5

The point-slope form of the equation of a line is ...

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

The line with slope 17/5 through point Y(7, 4) is ...

  y -4 = 17/5(x -7)

Subtracting the right side, and multiplying by 5 gives ...

  5(y -4) -17(x -7) = 0

  5y -17x +99 = 0 . . . . equation of the median through Y

Answer:

Step-by-step explanation:

      the answer is on the graph

Answer:  [tex]\frac{2}{9}[/tex]

Step-by-step explanation:

[tex]\frac{\sqrt{4} }{3^{3} }[/tex]
The square root of 4 can be written as 2
3 to the third power can be written as 9

So, the answer is [tex]\frac{2}{9}[/tex]

Answer:

3

Step-by-step explanation:

slope = (y_2 - y_1)/(x_2 - x_1)

slope = (1 - 7)/(3 - 5)

slope = -6/(-2)

slope = 3

Parallel lines have equal slopes.

Answer: 3

By applying the transformation rules for horizontal and vertical translation, we find that the resulting function is g(x) = cos (x - 7) + 4.

Transformation rules are rules that makes changes on charateristics and behavior of a function to create a new one. Rigid transformations like horizontal and vertical translations are examples of transformation rules. In this question we must apply the following transformation rules to the parent cosine function f(x) = cos x:

Now we proceed to derive the resulting function by applying the rules defined above:

Horizontal translation

f'(x) = cos (x - 7)      (3)

Vertical translation

g(x) = cos (x - 7) + 4     (4)

By applying the transformation rules for horizontal and vertical translation, we find that the resulting function is g(x) = cos (x - 7) + 4.

To learn more on transformation rules: https://brainly.com/question/9201867

#SPJ1