If there are 24 apples and 12 bananas for a fruit basket, fill out all of the possible ratios of apples to bananas that could be made

Easy if writing/typing put P L S and an .

If speaking maybe instead say please

Answer:

a)  See attachment.

b)  Domain: (2, ∞)

     Range: (-∞, ∞)

c)  As x → 2⁺, f(x) → -∞

    As x → ∞, f(x) → ∞

d)  f(3) = -5

e)  x = 4

Step-by-step explanation:

Given logarithmic function:

[tex]f(x)=\log_2(x-2)-5[/tex]

As the argument of a log function can only take positive arguments, the domain is restricted to x > 2 and there is a vertical asymptote at x = 2.

To find the x-intercept, set the function to zero and solve for x:

[tex]\implies \log_2(x-2)-5=0[/tex]

[tex]\implies \log_2(x-2)=5[/tex]

[tex]\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b[/tex]

[tex]\implies x-2=2^5[/tex]

[tex]\implies x-2=32[/tex]

[tex]\implies x=34[/tex]

Therefore, the x-intercept is (34, 0).

Substitute x = 10 into the function to find a second point on the curve:

[tex]\implies f(10)=\log_2(10-2)-5[/tex]

[tex]\implies f(10)=\log_2(8)-5[/tex]

[tex]\implies f(10)=\log_2(2)^3-5[/tex]

[tex]\implies f(10)=3\log_2(2)-5[/tex]

[tex]\implies f(10)=3(1)-5[/tex]

[tex]\implies f(10)=3-5[/tex]

[tex]\implies f(10)=-2[/tex]

Therefore, a second point on the curve is (10, -2).

As the argument of a log function can only take positive arguments, the domain is restricted to x > 2:

The range is unrestricted:

As x approaches x = 2 from the positive side, the function approaches negative infinity:

As x approaches positive infinity, the function approaches positive infinity.

From inspection of the graph:

Check by evaluating f(3) algebraically:

[tex]\implies f(3)=\log_2(3-2)-5[/tex]

[tex]\implies f(3)=\log_2(1)-5[/tex]

[tex]\implies f(3)=0-5[/tex]

[tex]\implies f(3)=-5[/tex]

From inspection of the graph:

Check by evaluating f(x) = -4 algebraically:

[tex]\implies \log_2(x-2)-5=-4[/tex]

[tex]\implies \log_2(x-2)=1[/tex]

[tex]\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b[/tex]

[tex]\implies x-2=2^1[/tex]

[tex]\implies x-2=2[/tex]

[tex]\implies x=4[/tex]

Equation of parallel line = y = 3x + 2 and equation of perpendicular line 3y = -x + 16, passing through the point (1,5).

(a) To find an equation of the line that passes through the point (1,5) and is parallel to the line y = 3x - 5, we need to use the slope of the given line. The slope of a line is represented by m and it is equal to the coefficient of x. In this case, the slope of the line y = 3x - 5 is 3.

Therefore, the slope of the line that is parallel to y = 3x - 5 is also 3.

We can use the point-slope form of a line, which is:

y - y1 = m(x - x1)

Where (x1, y1) is a point on the line and m is the slope.

Substituting the given point (1, 5) and the slope of 3, we get:

y - 5 = 3(x - 1)

Simplifying the equation, we get:

y = 3x + 2

So, the equation of the line that passes through the point (1, 5) and is parallel to the line y = 3x - 5 is y = 3x + 2

(b) To find the slope of a line that is perpendicular to the line y = 3x - 5, we need to take the negative reciprocal of the slope. The negative reciprocal of 3 is -1/3. So, the slope of a line that is perpendicular to y = 3x - 5 is -1/3

We can use the point-slope form of a line, which is:

y - y1 = m(x - x1)

Where (x1, y1) is a point on the line and m is the slope.

Substituting the given point (1, 5) and the slope of -1/3, we get:

y - 5 = -1/3(x - 1)

Simplifying the equation, we get:

3(y - 5) = -x + 1

3y = -x + 16

So, the equation of the line that passes through the point (1, 5) and is perpendicular to the line y = 3x - 5 is 3y = -x + 16

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Answer:

see belwo

Step-by-step explanation:

65

increase 10/min

in 15min it'll increase 150

so 65+150 =215

over t mins it'll be 65+10*t

Answer: 215°

t = minutes after being turned on

If the oven temperature increases by 10 per minute, and the initial temperature is 65, this can be represented as:

65 + 10t

After 15 minutes:

65 + 10(15)

65 + 150

215°

If x = temperature of the oven, the temperature of the oven t minutes after being turned on is:

65 + 10t = x

To find the probability that the entire batch will be accepted, we need to find the probability that all 6 CDs selected for testing are not defective. This is known as the probability of a "success" in the binomial distribution, which is (1 - population proportion of defective CDs) raised to the power of the number of CDs selected for testing.

The population proportion of defective CDs is 160/1500 = 0.107. So the probability of a CD being not defective is 1- 0.107 = 0.893. Therefore, the probability of all 6 CDs selected for testing are not defective is (0.893)^6 = 0.827 which is about 83%

Therefore, the probability that the entire batch of 1500 CDs will be accepted if 6 CDs are randomly selected for testing is 0.827 or about 83%.

It's worth noting that this method is based on some assumptions and the actual probability might be different.

The proportion of strength observations in this sample that exceed 10 MPa can be calculated by taking the total number of observations that exceed 10 MPa divided by the total number of observations.

To do this, we count the number of observations in the stem-and-leaf display greater than 10 MPa. We see that there are 8 observations greater than 10 MPa. We then divide 8 by the total number of observations, which is 24. This yields a proportion of 0.33 or 33%. This means that 33% of the strength observations in this sample exceed 10 MPa.There are six observations in the stem-and-leaf display that are greater than 10 MPa: 11, 11, 11, 11, 12, and 13. Therefore, the number of observations greater than 10 MPa is 6. The total number of observations is 11, as there are 11 stems with leaves. Therefore, the proportion of strength observations in the sample that exceed 10 MPa is (6/11) x 100 = 54.55%. This means that 54.55% of the observations in the sample exceed 10 MPa.

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Volume of the solid obtained by rotating the region bounded by the given curves about the specified line is [tex]\frac{24\pi }{5}[/tex]

Now, According to the question:

The shell method formula sums the volume of a cylindrical shell over the radius of the cylinder, and the volume of a cylinder is given by V=2πrh V = 2 π r h where r is the radius and h is the height.

Take a vertical cross section of the region.  The width of the cross section is dx, and the height is [tex]8x^3.[/tex]

Rotate the cross section about the line x = 2.  The height of the shell is  [tex]8x^3.[/tex] the radius is 2 - x, and the thickness is dx.

Volume of shell = 2π(2-x)([tex]8x^3[/tex])dx = 2π([tex]16x^3 - 8x^4[/tex])dx  

Volume of solid  = [tex]2 \pi \int\limits^1_0 [16x3 - 8x4]dx[/tex]

[tex]= 2\pi (4x^4 - (8/5)x^5)^1_0[/tex]  

= 24π/5

Hence,  Volume of the solid obtained by rotating the region bounded by the given curves about the specified line is [tex]\frac{24\pi }{5}[/tex].

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The number of M&M's that were in the bowl before Amelia arrived is; 12

Let the original amount in the bowl be x. Thus;

If Amelia grabbed 50%, then amount left = (100% - 50%)x = 50%x = 0.5x

Now, we are told that domicick took 50% of what was keft after amelia. Thus; New amount left = 100%x - (0.5x + 0.25x) = 0.25x

Now, we are told that there were finally 3 left after all the deductions. Thus;

0.25x = 3

x = 3/0.25

x = 12

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The length of the side DE is 9.

Parallelogram is a type of polygon with four sides, four angles and four vertices. It is a type of Quadrilateral.

Opposite sides are parallel, and the opposite sides and opposite angles are equal.

Given is a figure of a quadrilateral DEFG.

We have from the figure, two triangles, ΔDGF and ΔDEF.

Diagonal of the quadrilateral DF is a common side for both triangles.

Given that DG = EF

Also ∠FDG = ∠EFD

So we get the two triangles are congruent by SAS theorem.

So the given figure is parallelogram.

So Length of DE = Length of GF = 4x + 1.

We have EF = DG

6x + 4 = 4x + 8

2x = 4

x = 2

Length of DE = 4x + 1 = 9

Hence the length of the side DE of the parallelogram is 9.

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Answer:

One bowl has 1 yellow, 1 red, and 2 green apples. The other bowl has 5 each of boysenberries, strawberries, blueberries, and blackberries.

Step-by-step explanation:

For the given situation of number of visitors checkout out the library and 150 are randomly selected the population and the sample is represented  by :

Option B. The population is all the given adult visitors of the library ; and the sample is the 150 selected visitors.

Total population is represented by  all the adult visitors check out the library.

Number of adult visitors examine by the librarian = 150 randomly selected adult visitors.

Here 150 randomly selected adult visitors represents the sample of the whole population.

Therefore, the population and the sample for the given situation of visiting the library is given by :

Option B. The population is all the given adult visitors of the library ; and the sample is the 150 selected visitors.

The above question is incomplete, the complete question is :

A librarian is interested in the numbers of books that visitors check out from the library. She examines the checkout records of 150

randomly selected adult visitors.

Identify the population and sample for this situation.

A The population is all visitors of the library; the sample is the adult visitors

of the library.

B The population is all adult visitors of the library; the sample is the 150

visitors selected.

C The population is all visitors who check out at least 1 book from the

Library; the sample is the 150 visitors selected.

D The population is the 150 visitors selected; the sample is the 150 visitors

who check out at least 1 book from the library.​

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Answer:

56%

Step-by-step explanation:

4100 seats.

filled 2296

% = 2296/4100 = 56%

Answer:

56

Step-by-step explanation:

it is Right

Answer: Lim (1 - 1/(n + 1)) ^ (n ^ 2) = 1^infinity = 1

Step-by-step explanation: The expression given is the limit of the sequence (1 - 1/(n + 1)) ^ (n ^ 2) as n approaches infinity.

We can start by looking at the exponent first. The n^2 will grow faster than any polynomial function, making the entire expression go to zero as n approaches infinity.

Now let's look at the base (1 - 1/(n + 1))

As n increases, the value of the base becomes closer and closer to 1, since 1/(n+1) becomes smaller and smaller.

Therefore, the limit of the expression is:

Lim (1 - 1/(n + 1)) ^ (n ^ 2) = 1^infinity = 1

As n goes to infinity, the expression goes to 1

Please note that this is true for the limit, for a specific value of n, the expression will not be 1.

Answer:

The limit of (1 - 1/(n + 1)) ^ (n ^ 2) as n approaches infinity is 0.

As n becomes larger, the term 1/(n + 1) becomes smaller and closer to zero, which means that (1 - 1/(n + 1)) becomes closer and closer to 1. Therefore, the expression (1 - 1/(n + 1)) ^ (n ^ 2) becomes closer and closer to 1^(n^2) = 1. And any number powered by infinity (n^2) will be approaching zero, so the limit of the expression is 0.

The best estimate we can give for the number of orange balls in the tub is 7, and the number of white balls in the tub is 43.

To calculate this, we take the number of orange balls picked (7) and divide it by the total number of balls picked (25) to get the proportion of orange balls in the tub. Then we multiply that proportion by the total number of balls in the tub (50) to get our estimate for the number of orange balls in the tub.

7 / 25 = 0.28

0.28 x 50 = 14

Similarly, we take the number of white balls picked (18) and divide it by the total number of balls picked (25) to get the proportion of white balls in the tub. Then we multiply that proportion by the total number of balls in the tub (50) to get our estimate for the number of white balls in the tub.

18 / 25 = 0.72

0.72 x 50 = 36

This method of calculation makes sense because it uses the data we have (the number of orange and white balls picked) to estimate the overall makeup of the tub. By using the proportion of orange and white balls picked, we can make an educated guess about how many of each color ball are in the tub without seeing it.

However, it's important to note that this best estimate is not necessarily accurate. The real number of orange and white balls in the tub could be different. The method used here is a probability method, it's best estimate based on the sample data. The sample data is based on a random selection of 25 balls, and the number of orange or white balls that would be picked could vary depending on the random draw. The more samples we take, the more accurate our estimate would be.

QN is the answer to the equation that results from combining the slopes and y-intercepts of the equations MP and QR.

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f(x) is continuous at z = 3. a-3 Check the option from the following that best represents this information O A. limit f(x) = 2 O B. lim f(x) = 2 OC.

What is a limit?

A limit is given by the value of function f(x) as x tends to a value.

For this problem, at x = 0, we have that to the left the function goes to positive infinity, while to the right it goes to negative infinity, hence:

1. lim f(x) = ∞

x->0-

2. lim f(x) = -∞

x->0+

At x = 2, the function goes to infinity to the left and to the right, hence:

3. lim f(x) = ∞

x->2

To the left of the graph, the function goes to negative infinity, while to the right it goes to 1, hence:

4. lim f(x) = 1

x-> ∞

5. lim f(x) = -∞

x-> -∞

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Answer:

3/4

Step-by-step explanation:

since they are similar, they have the exact same angles.

angle Q = angle X

tan(angle) = sin(angle)/cos(angle)

that is the same ratio here as

9/12 = 3/4

The probability that exactly seven claims will be received during a given two-week period=1/64.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty. For pupils in Class 10, probability is a crucial subject because it teaches all the fundamental ideas of the subject. One is the probability of every event in a sample space.

An insurance company determines that N, the number of claims received in a week, is a random variable with P[N = n] = 1/2n+1, where n > 0 .

Let N1 and N2 represent the number of claims during weeks one and two, respectively,

then since N1 and N2 are independent.

[tex]Pr[N_1+N_2=7]=\sum_{n=0}^7Pr[N1=n]Pr[N2=7-n]\\\\=\sum_{n=0}^7\frac{1}{2^{n+1}}\frac{1}{2^{8-n}}\\\\=\sum_{n=0}^7\frac{1}{2^{9}}\\\\=\frac{8}{2^9}=\frac{1}{64}[/tex]

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Answer:

Choice A

Step-by-step explanation:

1/5 = 9/15

2/3 = 10/15

so 3/5 < 2/3

The Linear terms -0.75(-4f + 12) and (5f + 9) - (2f + 18) are actually an equivalent expressions.

Equivalent algebraic expressions are ones that, despite their apparent differences, actually have the same value. As a result of their similarity, they will produce the same outcomes regardless of the values we choose to use as their variables.

If  -0.75 ( -4f + 12 ) and ( 5f + 9 ) - ( 2f + 18 ) are equivalent expressions then

-0.75(-4f + 12) = (5f + 9) - (2f + 18)

3f − 9 = (5f + 9) - (2f + 18)

3f − 9 = 5f + 9 -2f - 18

3f − 9 = 5f - 2f + 9  - 18

3f − 9 = 3f − 9

Thus, The Linear terms -0.75(-4f + 12) and (5f + 9) - (2f + 18) are actually an equivalent expressions.

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Haley is right because the solution is r ≤ -20

An equation is an expression that shows the relationship between numbers and variables.

Inequalities is used for the non equal comparison of these numbers and variables.

Given the inequality:

-13 ≥ r + 7

Add 13 to both sides:

-13 + 13 ≥ r + 7 + 13

0 ≥ r + 20

subtract r from both sides:

0 - r ≥ r + 20 - r

-r ≥ 20

divide both sides by -1:

r ≤ -20

The solution is a graph on a number line with a solid circle at -20 and an arrow pointing left

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Answer:

OK so he gets 3000 a year

so 3000t is what we need. thats 3000 times the number of years.

His starting salary is 41250, so we would add that on.  

K = 3000t + 41250.

Step-by-step explanation:

The value of x in the equation x/3 = 9 is 27

A linear equation is an algebraic equation where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1. For example, x² is a variable raised to the second power, but x is a variable raised to the first power.

Example of linear equation with two variables is 2x + y = 5, where x and y are the variables . 5x + 2 = 6 is an example of linear equation with one variable

in the expression x/3 = 9

We multiply both sides by 3

therefore x/3 × 3 = 9 × 3

x = 27

therefore the value of x in the equation x/3 = 9 is 27

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Cash discounts describe a reward that a seller provides to a buyer in exchange for paying a bill in full before the due date.

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Answer:Option B , C  and E are correct

Step-by-step explanation:

y^2-5y=750

750-y(y-5)=0

(y+25)(y-30)=0

Answer:

6

Step-by-step explanation:

4+6=10

9+6=15

the ratio of 10 and 15= 2:3

Answer:

you do it step by step so it can be expressed

The amount of money that the bookstore paid for the textbook is $104.17.

When the price of an item is marked-up, it means that the price of the item is increased by a percentage. After a markup, the price of the item increases.

In order to determine the amount the bookstore paid for the bookstore, divide the price the student paid for the textbook by the percentage discount.

Price before the mark up = marked up price / (1 + percentage discount)

= $125 / ( 1 + 0.2)

= $125 / 1.2

= $104.17

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the universal set be U = {1, 2, 3,..., 10}, and let A = {1, 4, 7, 10}, B = {1, 2, 3, 4, 5}, and C= {2, 4, 6, 8}. the elements of (A-C) - (An B) ={7,10}

Set is a collection of well-defined objects and it has distinct elements. The set formulas include the union, intersection, complement, and difference of sets. Venn diagrams are popularly used to visualize set formulas to arrive at their proof.

The universal set be U = {1, 2, 3,..., 10}, and let A = {1, 4, 7, 10}, B = {1, 2, 3, 4, 5}, and C= {2, 4, 6, 8}.

So, to calculate (A-C)-(A∩B)

FIRST A-C= {1, 4, 7, 10} -  {2, 4, 6, 8}.

A - C = { 1,7,10}

A∩B={1,4,}

(A-C)-(A∩B)= { 1,7,10} -{1,4,} = { 7, 10}

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The inequality graphed on the number line is the one on the fourth option, we will get:

x > -2

On the number line we can see that we have an open circle at x = -2 (that means that x = -2 is not a solution to the inequality) and then a line that extends to the right side of that value.

Then the inequality is just the set of all numbers larger than -2, then we will get:

x > -2

That is the graphed inequality, and thus, the correct option is the last one.

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