for a certain base, b, logb^8=3 and logb^0.5=-1 The value of logb^4b is 0, -3, 3

The volume of the cube will increase by 8 cubic centimeters per second.

Given,

The edge length of a cube is changing at a rate of 1/6 cm/sec.

We have to find the rate by which cube's volume changing when the edge length is 4 cm.

Here,

We have,

da/dt = 1/6 cm/sec

We know that, volume of cube is

V = a³

Differentiate with respect to t.

dV/dt = 3a² da/dt

Substituting da/dt = 1/6  and a = 4, we get;

dV/dt ₐ ₋ ₄ = 3 × 4² 1/6

dV/dt ₐ ₋ ₄ = 3 × 16 × 1/6

dV/dt ₐ ₋ ₄ = 16/2 = 8

Therefore,

The volume increased by 8 cubic centimeters per sec.

Learn more about volume of cube here;

https://brainly.com/question/19052845

#SPJ4

x²+ 12x + 1x + 12

x(x+12) + 1(x+12)

(X+1) (X+12)

The following equation could be used to represent a function w:

= w(x)=v(x-7)+7

According to the information provided,

The point of discontinuity of rational functions is at x=7.

When a rational function has a point of discontinuity, it generally occurs when,

q(x) = r(x-a), where x = a

In this case, we must pay attention to the following relationship, which is a combination of a parent rational function and a vertical translation:, (2)

If we know that a=7 and k=7.

The equation which can represent w is as follows,

w(x) = v ( x-7 ) + 7

A rational function can be represented as a polynomial split by another polynomial. Because polynomials are defined everywhere, the domain of a rational function is the set of all numbers except the zeros in the denominator.

Example: x = f(x) (x - 3). The denominator, x = 3, has only one zero. Rational functions are no longer defined when the denominator is zero.

To learn more about rational function

brainly.com/question/27914791

#SPJ4

The price of the stereo system after the markup was $691.20.

The original price of the stereo system was $720.

During the sale, the price was reduced by 20%, which is equivalent to multiplying by (1 - 0.2) = 0.8.

The discounted price was:

720 × 0.8 = $576

After the sale, the discounted price was marked up by 20%

It is equivalent to multiplying by (1 + 0.2) = 1.2.

So the final price was 576 × 1.2

= $691.20

Therefore, the price of the stereo system after the markup was $691.20.

To learn more on Percentage click:

https://brainly.com/question/24159063

#SPJ1

One possible set of points: (-9, 1), (-3, 5), (3, 9) which would have a positive linear association if they were graphed in a scatterplot.

A scatterplot is a graph that displays the relationship between two quantitative variables. It is a useful tool for exploring patterns and relationships in data, and can help identify trends, outliers, and potential correlations.

In the given question,

To create a set of 3 points with a positive linear association, we want to choose three points where the y-coordinate increases as the x-coordinate increases. Here's one possible set of points:

(-9, 1), (-3, 5), (3, 9)

If we graph these points on a scatterplot, we can see that there is a clear positive trend. As x increases, y also increases, suggesting a positive linear association between the two variables.

Note that there are many other sets of points we could choose that would also have a positive linear association. The key is to choose points where the y-coordinate tends to increase as the x-coordinate increases.

To know more about Scatterplot, visit:

https://brainly.com/question/30017616

#SPJ1

Answer:

B. 4.09 cm²

Step-by-step explanation:

Let point O be the center of the circle.

As the center of the circle is the midpoint of the diameter, place point O midway between P and R.

Therefore, line segments OP and OQ are the radii of the circle.

As the radius (r) of a circle is half its diameter, r = OP = OQ = 5 cm.

As OP = OQ, triangle POQ is an isosceles triangle, where its apex angle is the central angle θ.

To calculate the shaded area, we need to subtract the area of the isosceles triangle POQ from the area of the sector of the circle POQ.

To do this, we first need to find the measure of angle θ by using the chord length formula:

\(\boxed{\begin{minipage}{5.8 cm}\underline{Chord length formula}\\\\Chord length $=2r\sin\left(\dfrac{\theta}{2}\right)$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the central angle.\\\end{minipage}}\)

Given the radius is 5 cm and the chord length PQ is 6 cm.

\(\begin{aligned}\textsf{Chord length}&=2r\sin\left(\dfrac{\theta}{2}\right)\\\\\implies 6&=2(5)\sin \left(\dfrac{\theta}{2}\right)\\\\6&=10\sin \left(\dfrac{\theta}{2}\right)\\\\\dfrac{3}{5}&=\sin \left(\dfrac{\theta}{2}\right)\\\\\dfrac{\theta}{2}&=\sin^{-1} \left(\dfrac{3}{5}\right)\\\\\theta&=2\sin^{-1} \left(\dfrac{3}{5}\right)\\\\\theta&=73.73979529...^{\circ}\end{aligned}\)

Therefore, the measure of angle θ is 73.73979529...°.

Next, we need to find the area of the sector POQ.

To do this, use the formula for the area of a sector.

\(\boxed{\begin{minipage}{6.4 cm}\underline{Area of a sector}\\\\$A=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in degrees.\\\end{minipage}}\)

Substitute θ = 73.73979529...° and r = 5 into the formula:

\(\begin{aligned}\textsf{Area of section $POQ$}&=\left(\dfrac{73.73979529...^{\circ}}{360^{\circ}}\right) \pi (5)^2\\\\&=0.20483... \cdot 25\pi\\\\&=16.0875277...\; \sf cm^2\end{aligned}\)

Therefore, the area of sector POQ is 16.0875277... cm².

Now we need to find the area of the isosceles triangle POQ.

To do this, we can use the area of an isosceles triangle formula.

\(\boxed{\begin{minipage}{6.7 cm}\underline{Area of an isosceles triangle}\\\\$A=\dfrac{1}{2}b\sqrt{a^2-\dfrac{b^2}{4}}$\\\\where:\\ \phantom{ww}$\bullet$ $a$ is the leg (congruent sides). \\ \phantom{ww}$\bullet$ $b$ is the base (side opposite the apex).\\\end{minipage}}\)

The base of triangle POQ is the chord, so b = 6 cm.

The legs are the radii of the circle, so a = 5 cm.

Substitute these values into the formula:

\(\begin{aligned}\textsf{Area of $\triangle POQ$}&=\dfrac{1}{2}(6)\sqrt{5^2-\dfrac{6^2}{4}}\\\\ &=3\sqrt{25-9}\\\\&=3\sqrt{16}\\\\&=3\cdot 4\\\\&=12\; \sf cm^2\end{aligned}\)

So the area of the isosceles triangle POQ is 12 cm².

Finally, to calculate the shaded area, subtract the area of the isosceles triangle from the area of the sector:

\(\begin{aligned}\textsf{Shaded area}&=\textsf{Area of sector $POQ$}-\textsf{Area of $\triangle POQ$}\\\\&=16.0875277...-12\\\\&=4.0875277...\\\\&=4.09\; \sf cm^2\end{aligned}\)

Therefore, the area of the shaded region is 4.09 cm².

Answer:

15 mph

Step-by-step explanation:

30÷2=15

Answer:

I believe 15 mph

Step-by-step explanation:

He rides 30 miles in 2 hours and we need to find how much in ONE hour so just divide 30 by 2 which should give you 15 miles per hour.

30/2=15

15 (mph)!~

Answer:

x = 30

y = 5

Step-by-step explanation:

Because the top triangle shows 3 congruent angles, we know it's an equilateral.

Therefore 8y = 40

y = 5

______________

Now we have two sides of the triangle: 40 and 80.

The lower left angle of the whole triangle must be 90 degrees because if the hypotenuse is twice the adjacent side, it must be a 30-60-90 triangle.

So, the larger angle containing angle x must be 90 degrees. And because we know that the adjacent angle (equilateral triangle) is 60 degrees, angle x must be 30.

Value of sector m ∠AB=95 degree

An angle is a geometric figure formed by two rays or line segments that share a common endpoint, called the vertex. The rays or line segments are often referred to as the sides or arms of the angle. Angles are typically measured in degrees, with a full circle consisting of 360 degrees. Angles can also be measured in radians, which is another unit of angle measurement.

Value of sector m ∠AB=95°

Given ∠ADC=112°

m ∠BC=129°

m ∠DC=93°

Let AC and BD intersect at O

∠OBC=180-112/2=25.5°

∠ABO=∠BAO=68-25.5=42.5°

Applying triangle sum property

m ∠AB+∠OAB+∠OBA=180°

m ∠AB=180-42.5-42.5=95°

Hence, Value of sector m ∠AB=95°

To know more about line, visit:

https://brainly.com/question/30003330

#SPJ1

Answer:

√730

Step-by-step explanation:

The square root of 730 is already in the simplest radical form. This is because  730 has no square factors, so the square root cannot be simplified.

Answer:

55/7 in simplest form is 7 6/7

Answer:

3/5 or 0.6

Step-by-step explanation:

i dont really get the question, but 6+4= 10.

When comparing groups two at a time using the t-test for independent groups, a type I error can occur if the null hypothesis is rejected when it is actually true. This means that a researcher may conclude that there is a significant difference between the two groups when there really isn't.

This can happen when the sample size is too small, the variance within each group is too large, or when the alpha level (the level of significance chosen) is set too high.

When comparing multiple groups using the t-test, there is an increased chance of making a type I error due to the increased number of comparisons being made. This is known as the multiple comparisons problem, which increases the likelihood of obtaining a false positive result.

To avoid making type I errors when comparing groups two at a time using the t-test for independent groups, it is important to carefully choose the alpha level, increase the sample size, and reduce the variance within each group. Additionally, conducting post-hoc tests and adjusting for multiple comparisons can also help to minimize the risk of making a type I error.

To know more about Hypothesis  visit :

https://brainly.com/question/31319397

#SPJ11

Answer: OA) (4, -2), (-2, 2), (2, -2), (4, 2)

Step-by-step explanation:

Answer:

m = \(\frac{7}{4}\)

Step-by-step explanation:

We are given the points (2, -3), and (6,4), and we want to find the slope through these 2 points.

The formula for the slope (m) is \(\frac{y_2-y_1}{x_2-x_1}\), where \((x_1, y_1)\) and \((x_2, y_2)\) are points.

Even though we have 2 points (as stated in given), let's label their values to help avoid any confusion and mistakes.

\(x_1=2\\y_1=-3\\x_2=6\\y_2=4\)

We can substitute the values of \(x_1, y_1, x_2,\) and \(y_2\) into the formula to find the slope. Remember that the formula has subtraction.

m = \(\frac{y_2-y_1}{x_2-x_1}\)

m = \(\frac{4--3}{6-2}\)

Simplify.

m = \(\frac{4+3}{6-2}\)

Add/subtract.

m = \(\frac{7}{4}\)

The slope of the line is \(\frac{7}{4}\).

Topic: slope

See more: https://brainly.com/question/28143573

Answer:

B

Step-by-step explanation:

Answer:

b.) 350 = 0.25m + 300

Step-by-step explanation:

His earnings are a fixed amount, $300, and a variable amount that depends on the number of miles.

The variable amount depends on the number of miles he drives.

For 1 mile, he earns $0.25

For 2 miles, he earns $0.25 * 2

For m miles, he earns $0.25 * m

The total amount he earns is the fixed amount plus the variable amount

300 + 0.25m or 0.25m + 300

He earned $350, so we get the equation

350 = 0.25m + 300

Answer: b.) 350 = 0.25m + 300

Hi,

The correct answer should be "CE" and "CB" I just had the same question so my answer should be correct.

I hope that this helped you. :)

A $1,000 initial investment in Bank ABC's CD would be worth $1,628.89 at maturity.  A $1,000 initial investment in Bank XYZ's CD would be worth $1,622.82 at maturity.

The formula to calculate the value of a CD after a specific duration at a specific interest rate compounded annually is given by:

A = P(1 + r/n)^(nt)

where P is the principal,

r is the annual interest rate,

n is the number of times compounded per year,

t is the number of years, and

A is the value of the CD at maturity.

Here, we need to calculate the value of a $1,000 initial investment in each bank's CD at maturity.

Let's calculate the value of a $1,000 investment in Bank ABC's CD.

P = $1,000

r = 5.0% compounded annually

t = 10 years

n = 1

We have all the values; let's put them in the formula and solve:

A = $1,000(1 + 0.05/1)^(1x10)A = $1,628.89

Therefore, a $1,000 initial investment in Bank ABC's CD would be worth $1,628.89 at maturity.

Let's calculate the value of a $1,000 investment in Bank XYZ's CD.

P = $1,000

r = 4.95% compounded daily

t = 10 years

n = 365

We have all the values; let's put them in the formula and solve:

A = $1,000(1 + 0.0495/365)^(365x10)A = $1,622.82

Therefore, a $1,000 initial investment in Bank XYZ's CD would be worth $1,622.82 at maturity.

To know more about investments, visit:

https://brainly.com/question/31411302

#SPJ11

The slope of the line that divides the region bounded by the parabola \(y=5x-3x^2\)and the x-axis into two regions with equal area is 5.

To find the slope of the line that divides the region into two equal areas, we need to determine the point of intersection between the parabola and the x-axis. Since the line passes through the origin, its equation will be y = mx, where m represents the slope.

Setting the equation of the parabola equal to zero, we find the x-values where the parabola intersects the x-axis. By solving the equation\(5x - 3x^2 = 0\), we get x = 0 and x = 5/3.

To divide the region into two equal areas, the line must pass through the midpoint between these x-values, which is x = 5/6. Plugging this value into the equation of the line, we have y = (5/6)m.

Since the areas on both sides of the line need to be equal, we can set up an equation using definite integrals. By integrating the equation of the parabola from 0 to 5/6 and setting it equal to the integral of the line from 0 to 5/6, we can solve for m. After performing the integration, we find that m = 5.

Therefore, the slope of the line that divides the region into two equal areas is 5.

Learn more about: Parabola

brainly.com/question/11911877

#SPJ11

8(2y+y)

hope it helps!!!

The volume of a rectangular prism is 80 cm³.

The dimensions of a rectangular prism are length=8 cm, breadth=5 cm and height=2 cm.

The formula to find the volume of a rectangular prism is l×b×h.

Now, the volume of a rectangular prism=8×5×2=80 cm³.

Therefore, the volume of a rectangular prism is 80 cm³.

To learn more about a rectangular prism visit:

https://brainly.com/question/21308574.

#SPJ2

Answer:

$75 Have a nice day!   :)

here is how 50 x 10 = 500    500 x 30 = 15000    15000 divided by 2 = 7500 converted to dollars is $75

Answer:

$75.00

Step-by-step explanation:

50¢-25¢=25¢

30×10=300

300×25¢=7500¢

7500¢=$75$

Answer:

h = 9 yds,       assuming his treehouse is a rectangular shape. 9 yds seems pretty high.

Step-by-step explanation:

area = bh

108 yd³ = 12 yd² x h

h = 108/12 = 9 yds

 The prism is 9 yards tall

What is the Volume of Rectangular Prism?

The area occupied inside a rectangular prism is referred to as the volume of the prism. A polyhedron with two pairs of congruent and parallel bases is referred to as a rectangular prism. It has 12 sides, 6 faces (all of which are rectangles), and 8 vertices. Given that the rectangular prism is a three-dimensional (3D) shape, the units cm3, m3, and so forth are employed to express the volume of the rectangle prism. Any polyhedron that possesses all of these qualities is referred to as a cuboid in mathematics.

Given: base of the treehouse= 12 yards²

volume of the treehouse = 108 yards³

To find : how tall is the prism ( height of the treehouse) = ?

Formula Used : The volume of a rectangular prism is calculated using the formula volume of a rectangular prism (V) = l w h,

where "l" stands for base length

"w" for base width.

"h" refers to the prism's height.

Steps for calculating the height

Step 1: The foundation area of 12 square yards has previously been specified.

Step 2: The prism's volume is 108 cubic yards

Step 3: The given rectangular prism's volume = base area x height

=> 108 cubic yards = 12 x h

=> 108/ 12 = h

=> h = 9 yards

Since , the prism is 9 yards tall

To learn more about: volume of rectangular prism

Ref: https://brainly.com/question/28060173

#SPJ2

Answer:

I'm sorry I don't know

Step-by-step explanation

Pickles are pretty tasty, though!

Answer:

Q8. (D) 9x²

Q9. (A) \(\frac{5}{17}\)

Q10. (C) 10x²-9x+2

Step-by-step explanation:

Q8. Area of new canvas = (3x)(3x)

                                         = 9x²

Q9. Since F is the midpoint of line XY,

      6x = \(\frac{1}{3}\)(x+5)

     18x = x+5

     17x = 5

      ∴x = \(\frac{5}{17}\)

Q10. Area of rectangle = (2x-1)(5x-2)

                                      = 10x²-5x+2-4x

                                      = 10x²-9x+2

Answer:

The answer is below

Step-by-step explanation:

Since 1000ml Of Dextrose 25% is needed to be produced from Dextrose 70%. Let us assume that x ml of Dextrose 70% is mixed with a Dextrose 5% to get 1000 ml of Dextrose 25%. Hence:

The amount of Dextrose 5% = 1000 ml - x ml = 1000 - x

25% of 1000 ml = 70% of x + 5% of (1000 - x)

25000 = 70x + 5000 - 5x

Simplifying gives:

65x = 25000 - 5000

65x = 20000

x = 308 ml

Therefore 308 ml of Dextrose 70% was mixed with 692 ml of Dextrose 5% to produce 1000 ml of Dextrose 25%.

Answer:

b

Step-by-step explanation:

because X= the amount of time hes on each machine. so 8 times x

Answer: B

Step-by-step explanation:A P E X

Answer:

bjfdkkdkdkdieiekwkwkwkekkedlllldkd

Answer: Perimeter of given square:40,Area of given square:100

Perimeter of Dilated square:200

Area of Dilated square: 2500

Step-by-step explanation: