The simplest form of log5+log6-log2​

Answer:

Ned has 20 white marbles.

Step-by-step explanation:

Let's call the number of red marbles "r".

We know that Ned has twice as many white marbles as red marbles, so the number of white marbles would be 2r.

We also know that he has five more blue marbles than white marbles, so the number of blue marbles would be 2r + 5.

The total number of marbles in Ned's collection is 55, so:

r + 2r + (2r + 5) = 55

Simplifying this equation, we get:

5r + 5 = 55

Subtracting 5 from both sides:

5r = 50

Dividing by 5:

r = 10

So Ned has 10 red marbles.

We can use this to find the number of white marbles:

2r = 2(10) = 20

So Ned has 20 white marbles.

The correct options are rectangular prism, square pyramid.

When a shape has a rectangular cross-section, it means that if the shape is cut perpendicular to its base, the resulting cut will be a rectangle. So, the only shapes that will have a rectangular cross section are those whose base is a rectangle or a shape that can be inscribed within a rectangle.

The shapes that have rectangular cross sections when they are cut perpendicular to the base are:

Rectangular prism

Square pyramid

Therefore, the correct options are rectangular prism, square pyramid.

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Complete question:

The length of wire used for the square is 0.25 meters and the length of wire used for the circle is 1 meter. To maximize the total area, the wire should be cut in half, with each piece having a length of 1 meter.

To minimize the total area of both figures and minimize the length of wire used, the wire should be cut in half, giving each piece a length of 1 meter.

For the square frame, we know that each side of the square is equal to the length of wire used to make it, so we can divide the 1 meter of wire in half to get 0.5 meters for each side of the square.

The perimeter of the circle is the length of wire used to make it, so we can use the remaining 1 meter of wire to find the radius of the circle:

2πr = 1

r = 1/(2π)

Using this radius, we can find the circumference of the circle and the length of wire used:

C = 2πr = 1 meter

Therefore, the length of wire used for the square is 0.5 meters and the length of wire used for the circle is 1 meter.

To maximize the total area, we need to cut the wire into two equal pieces, each with a length of 1 meter.

For the square frame, each side will have a length of 0.25 meters, which will give us a total area of 0.0625 square meters.

For the circle, the radius will be 1/(4π) meters, which will give us a circumference of 1/(2π) meters and a total area of π/(16) square meters.

Therefore, to maximize the total area, the wire should be cut in half, with each piece having a length of 1 meter.

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Answer:

Step-by-step explanation:

To write the standard equation of a circle with its center in the fourth quadrant tangent to x=7, y=-4 and x=17, we can first find the center of the circle.

Since the center is in the fourth quadrant and tangent to x=7, y=-4 and x=17, the center must lie on the line x=12 (the midpoint between 7 and 17) and y=-4 (the point of tangency).

So the center of the circle is (12, -4).

Next, we need to find the radius of the circle. Since the circle is tangent to x=7 and x=17, the radius is the distance from the center to either x=7 or x=17.

The radius is thus 12 (the difference between 12 and 7) or 5 (the difference between 12 and 17).

So the standard equation of the circle is:

(x - 12)^2 + (y + 4)^2 = 25

The correct sequence to model the given scenario is (b) f(n) = 1.12f(n-1)(1- f(n-1/6000)), and we can use this formula to calculate the oxygen released by the tree in each year, option (b) is correct.

The amount of oxygen released by the tree increases at a rate of 12% per year, which is represented by the factor 1.12f(n-1).

However, the tree cannot generate more than 6000 pounds of oxygen per year, which is represented by the limiting factor:

(1- f(n-1/6000)).

To understand this better, let's calculate the oxygen released by the tree in the second year using the formula

f(n) = 1.12f(n-1)(1- f(n-1/6000)).

f(2) = 1.12f(1)(1- f(1)/6000)

= 1.12(250)(1- 250/6000)

= 295.67 pounds of oxygen

Hence, option (b) is correct.

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The correct question is:

Which sequence below would best model the following description? A newly planted tree releases 250 pounds of oxygen over the period of its first year. The amount of oxygen released by the tree grows at a rate of 12% per year, but the tree cannot generate more than 6000 pounds of oxygen per year.

a. f(n) = 1.12f(n-1)(1+ f(n-1/6000)

b. f(n) = 1.12f(n-1)(1- f(n-1/6000)

c. f(n) = 1.12f(n-1) {6000/f(n-1)}

d. f(n) = 1.12f(n-1)(f(n-1) -6000)

The number of ways you can tile your walkway if you choose single tiles and double tiles is 3,992,781,803 ways.

To tile a 1x20 walkway using red, blue, and yellow single tiles (1x1) and green and white double tiles (1x2), we can consider the number of ways to combine the single and double tiles to fill the entire 1x20 space.

The exact number of ways to tile the 1x20 walkway using red, blue, and yellow single tiles and green and white double tiles:

= 3^20 + 3^18 x 2 + 3^16 x 4 + 3^14 x 8 + 3^12 x 16 + 3^10 x 32 + 3^8 x 64 + 3^6 x 128 + 3^4 x 256 + 3^2 x 512 + 1, 024

= 3486784401 + 258280326 + 172186884 + 38263752 + 8503056 + 1889568 + 419904 + 93456 + 20736 + 4608 + 1024

= 3,992,781,803 ways

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If lines m and n are parallel, then the value of x must be 4.

If lines m and n are parallel, then the measures of the angles in the correspondent quadrants must be the same ones.

Here we can see that the two angles are in the third quadrant, thus, these angles have the same measure. Then we can write this as:

6x² = 96

Now we can solve this for x, we will get:

x² = 96/6

x² = 16

x = √16

x = 4

That is the value of 4.

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The formula for the linear function is f(p) = -50p + 1750. So, correct option is E.

To find the formula for the linear function from the given table, we need to determine the equation of a straight line that passes through the three given points. We can use the point-slope form of the equation of a straight line to solve for the slope and y-intercept.

Let's choose two of the given points, say (15, 1000) and (25, 500), to calculate the slope:

slope = (change in y)/(change in x)

= (500 - 1000)/(25 - 15)

= -50

Now, we can use the slope and one of the given points, say (15, 1000), to solve for the y-intercept using the point-slope form:

y - y₁ = m(x - x₁)

y - 1000 = -50(x - 15)

y - 1000 = -50x + 750

y = -50x + 1750

Therefore, the formula for the linear function is f(p) = -50p + 1750, which means that for each additional dollar increase in price per shirt, the number of shirts sold decreases by 50. Option (e) is the correct answer.

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Answer:

198 ft^2

Step-by-step explanation:

l = 3

w = 3

h = 15

2(3*3) + 4(3*15) = 18 + 180

18 + 180 = 198 ft^2

The left-handed students in the music program are option A 15 students.

A table that shows the frequencies of two category variables is known as a two-way frequency table. It is a method for succinctly and clearly organising and displaying data for two variables. One variable is represented by the table's rows, while the other variable is represented by the table's columns. The frequency of each combination of categories is displayed in the table's cells. To examine the relationship between the two variables and to spot patterns and trends in the data, a two-way frequency table can be employed. To summarise and analyse data, it is frequently used in statistics, the social sciences, and other disciplines.

From the given table the number of students that are in music program and left handed is given by the intersection of the row and column of the two.

Thus, he left-handed students in the music program are 15.

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Answer: Since 1 and 2 have the same measure, angle CED is also equal to 1 and 2. Therefore, triangle CED and triangle CAB are similar by the Angle-Angle (AA) criterion.

Using the properties of similar triangles, we can set up the following proportion:

$\frac{CE}{CA}=\frac{CD}{CB}$

Substituting the given values:

$\frac{CE}{x+4}=\frac{x}{14}$

Cross-multiplying:

$14CE = x(x+4)$

$14CE=x^2+4x$

We also know that triangle ADE and triangle ABC are similar by the AA criterion. Therefore, we can set up the following proportion:

$\frac{DE}{AB}=\frac{AE}{AC}$

Substituting the given values:

$\frac{DE}{18}=\frac{AE}{x+4}$

Cross-multiplying:

$AE = 18\frac{DE}{x+4}$

Now, we can substitute the value of $AE$ in terms of $DE$ into the first equation:

$14CE=x^2+4x$

$14\frac{DE}{x+4}=x^2+4x$

$14DE=x^2+4x(x+4)$

$14DE=x^2+4x^2+16x$

$18x^2+16x-14DE=0$

We can now use the quadratic formula to solve for $x$:

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\frac{-16\pm\sqrt{(16)^2-4(18)(-14DE)}}{2(18)}$

$x=\frac{-16\pm\sqrt{256+1008DE}}{36}$

Since $DC=x$, we can now use this equation to find the value of $DC$ for a given value of $DE$. For example, if $DE=5$, we have:

$DC=\frac{-16\pm\sqrt{256+1008(5)}}{36}$

$DC\approx 2.3$ or $DC\approx -3.1$

Since distance cannot be negative, we choose the positive solution:

$DC\approx 2.3$ units.

To find $DE$, we can substitute the value of $DC$ back into one of the earlier equations:

$\frac{CE}{x+4}=\frac{x}{14}$

$\frac{CE}{2.3+4}=\frac{2.3}{14}$

$CE\approx 1.34$ units

Now we can use the second similarity proportion to find $DE$:

$\frac{DE}{18}=\frac{AE}{x+4}$

$\frac{DE}{18}=\frac{18-1.34}{2.3+4}$

$DE\approx 3.64$ units

Therefore, $DC\approx 2.3$ units and $DE\approx 3.64$ units.

Step-by-step explanation:

12 - 2^2 x 2

---Remember: PEMDAS

---In this case exponents are first, then multiplication, then subtraction

12 - 4 x 2

12 - 8

4

Answer: 4

Hope this helps!

The total power being emitted by the source, given the radiant flux density, is  28,274.3 watts of power.

The inverse square law can be used with the formula :

I = P / ( 4 π r ²)

We are given the radiant flux density I = 90 W/m² and the distance r = 5 m.

The power being emitted is therefore :

P = 90 W/ m ² x (4 π ( 5 m) ² )

P = 90 W / m ² x ( 4 π x 25 m ² )

P = 90 W / m² x 100 π m²

P = 28, 274.3 watts

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Full question is:

How much power is a source emitting with an amount of radiant flux density of 90w/m sq when the distance is 5 m

The raw x-value associated with a Z-score of 0.21 for the given distribution is 145.89.

To compute the raw x-value associated with a Z-score of 0.21 for a distribution with a population mean, μ, of 144 and a population standard deviation, σ, of 9, we can use the formula for standardizing a variable:

Z = (x - μ) / σ

Rearranging the formula to solve for x, we get:

x = Zσ + μ

Substituting the given values, we get:

x = 0.21(9) + 144

Simplifying the expression, we get:

x = 145.89

A Z-score represents the number of standard deviations a value is from the mean, and it can be used to standardize values from different distributions. By standardizing values, we can compare them on a common scale and make more meaningful statistical inferences.

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If the third term is 31, then let's get the second term. We have to use the rule we were given and work backwards. So, we will add three and then divide by 2.

31 + 3 = 34

34 / 2 = 17

17 is the second term. Let's do the same thing we just did to find the first term: add three, divide by 2.

17 + 3 = 20

20 / 2 = 10

Answer: the first term is 10

Hope this helps!

The result of the row 1 multiplication by 1/4 is determined as  [¹/₂  0 ].

The resultant of the row multiplication in the surd is calculated by applying the following method;

row 1 in the given surds = [2 0]

To multiply row by 1/4, we will multiply each entity by 1/4 as shown below;

[2 0] x 1/4 = 1/4(2 0)

= [¹/₂  0 ]

Thus, the result of the row multiplication is determined by multiplying each entry in row 1, that 2, and 0 by 1/4.

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If John pours the partially filled bucket into an empty one, he would still have 29 full buckets and a bucket with 2/3 of its capacity filled.

In order to arrive at a solution, it is necessary to commence by reducing the fraction 1/1.5 into a more basic form.

Thus, we do this below:

1 ÷ 1.5 = 1 ÷ (3/2) = 1 × (2/3) = 2/3

So, John has 29 full buckets and another bucket that is 2/3 full.

If he pours the partially filled bucket into an empty one, he would still have 29 full buckets and a bucket with 2/3 of its capacity filled.

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John has 29 full buckets of water and another bucket that is 1/1.5 full. How many full buckets of water would he have if he pours the partially filled bucket into an empty one?

For the drug used to treat asthma in a clinical trial:

Part 1:

The test is right-tailed because the alternative hypothesis is that less than 9% of treated subjects experienced headaches.

Part 2:

The test statistic is z = 0.64, rounded to two decimal places (given in the calculator display).

Part 3:

The P-value is 0.7401, rounded to four decimal places (also given in the calculator display).

Part 4:

The null hypothesis is Upper H₀: p ≥ 0.09. We conclude that there is not sufficient evidence to support the claim that less than 9% of treated subjects experienced headaches.

Part 5:

We fail to reject the null hypothesis because the P-value is greater than the significance level, α=0.01.

Part 6:

The final conclusion is: D, There is not sufficient evidence to support the claim that less than 9% of treated subjects experienced headaches.

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The value of x if the line BD is the perpendicular bisector of AC is 11.5

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

The figure where the line BD is the perpendicular bisector of AC.

To calculate the value of x, we use the following equation by setting the line segments equal to each other

3(2x - 8) = 45

Divide both sides of the above equation by 3

2x - 8 = 15

So, we have the following equation

2x = 23

Divide both sides of the above equation by 2

x = 11.5

Hence, the calculated value of x is 11.5

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Answer:

Let's use "K" to represent Kevin's current age, and "M" to represent his mother's current age.

According to the problem, if you triple Kevin's age, the result is 1 less than his mother's age:

3K = M - 1

We can simplify this equation by adding 1 to both sides:

3K + 1 = M

This equation tells us that if we add 1 to three times Kevin's age, we get his mother's age. We can use this equation to solve for Kevin's age if we know his mother's age, or we can use it to solve for his mother's age if we know Kevin's age.

The solution to the given inequality is: 10 > x ≤ 12

Inequalities are defined as mathematical expressions that involve the symbols >(greater than), <(less than), ≥(greater than or equal to) and ≤(less than or equal to).

In order for us to 'solve' an inequality, we have to find a range, or ranges, of values that an unknown x can take and still satisfy the inequality.

We are told that the angle (9x + 7)° is greater than 97° and at most 118°

Thus:

9x + 7 > 97

9x > 90

x > 10

Similarly:

9x + 7 ≤ 115

9x ≤ 108

x ≤ 12

Thus, the solution to the inequality is: 10 > x ≤ 12

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Step-by-step explanation:

V = 1/3 x π x r² x h

48 = 1/3 x π x r² x 9

48÷3π = r²

√48÷3π =r

so, r= 2.26 (3.s.f)

3.5= 35/10

35/10= 7/2

which is equal to 3 1/2

Therefore: 3 1/2 and 7/2

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.

The correct choice is: B. The statement is false because the reference values for the decrease and increase are not the same. The true improvement over the past two years is 8.56%.

In Mathematics, a percentage can be defined as any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.

Mathematically, percentage increase can be calculated by using this mathematical equation (formula):

Percentage increase = [Final value - Initial value]/Initial value × 100

Based on the information provided about the high school test scores, we have the following:

True improvement = (100% - 8%) × (100 + 18)

True improvement = (92%) × (100 + 18)

True improvement = (0.92) × (118)

True improvement = 108.56 ⇒ 8.56%.

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the approximate difference in the mean circumferences of the Earth and the Moon is about 29153.88 kilometers.

A circle is a particular type of ellipse in mathematics or geometry where the eccentricity is zero and the two foci are congruent.

A circle is also known as the location of points that are evenly spaced apart from the centre. The radius of a circle is measured from the centre to the edge. T

he line that splits a circle into two identical halves is its diameter, which is also twice as wide as its radius.

A circle is a fundamental 2D form whose radius is quantified. The interior and exterior parts of the aircraft are separated by the circles.

The formula for the circumference of a circle is:

C = 2πr

where C is the circumference, π (pi) is a constant approximately equal to 3.14, and r is the radius.

The difference in the mean circumferences of the Earth and the Moon can be found by subtracting the circumference of the Moon from the circumference of the Earth.

The circumference of the Earth is:

C earth = 2π * 6371.0 km = 40075.04 km (rounded to two decimal places)

The circumference of the Moon is:

C moon = 2π * 1737.5 km = 10921.16 km (rounded to two decimal places)

The difference in the mean circumferences of the Earth and the Moon is:

C earth - C moon = 40075.04 km - 10921.16 km ≈ 29153.88 km

Therefore, the approximate difference in the mean circumferences of the Earth and the Moon is about 29153.88 kilometers.

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The value of x in the circle is 4.2

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

The circle

Using the intersecting chords equation, we have

(5x - 8) * 4 = (x + 1) * 10

When solved for x, we have

x = 4.2

Hence. the value of x is 4.2

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